diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 00000000000..e69de29bb2d diff --git a/404.html b/404.html new file mode 100644 index 00000000000..0bfc3aad624 --- /dev/null +++ b/404.html @@ -0,0 +1 @@ + 404 · eQuantum
eQuantum
Mapping the quantum way
eQuantum

404

Not Found

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/CNAME b/CNAME new file mode 100644 index 00000000000..df3b2c517cb --- /dev/null +++ b/CNAME @@ -0,0 +1 @@ +www.eq19.com diff --git a/README.md b/README.md new file mode 100644 index 00000000000..c750ac37102 --- /dev/null +++ b/README.md @@ -0,0 +1,198 @@ +--- +sort: 0 +spin: +span: +suit: 0 +--- +# Prime Identity + +We are going to assign prime identity as a ***standard model*** that attempts to stimulate a quantum field model called ***[eQuantum](https://eq19.com/)*** for _[the four (4) known fundamental forces](https://en.wikipedia.org/wiki/Fundamental_interaction)_. + +{% include list.liquid all=true %} + +This presentation was inspired by [theoretical works](https://github.com/eq19/eq19.github.io/files/13468466/OU1938-Y1.1.pdf) from _[Hideki Yukawa](https://en.wikipedia.org/wiki/Hideki_Yukawa)_ who in 1935 had predicted the existence of _[mesons as the carrier particles](https://en.wikipedia.org/wiki/Meson)_ of strong nuclear force. + +## Addition Zones + +Here we would like to recompile the way we take on getting the arithmetic expresion of an ***individual unit expression (identity)*** such as a taxicab number below. + +```note +It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician _[GH Hardy](https://en.wikipedia.org/wiki/G._H._Hardy)_ when he visited Indian mathematician _[Srinivasa Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan)_ in hospital _([Wikipedia](https://en.wikipedia.org/wiki/1729_(number)))_. +``` + +[![Ramanujan-Hardy number](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)](https://en.wikipedia.org/wiki/1729_(number)) + +These three (3) number are [twin primes](https://en.wikipedia.org/wiki/Twin_prime). We called the pairs as _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. Our scenario is mapping the distribution out of these pairs by taking the symmetrical behaviour of 36 as the smallest power (greater than 1) which is not a prime power. + +```tip +The smallest square number expressible as the sum of **four (4) consecutive primes** in two ways (5 + 7 + 11 + 13 and 17 + 19) which are also **two (2) couples** of prime twins! _([Prime Curios!](https://en.wikipedia.org/wiki/1729_(number)](https://primes.utm.edu/curios/page.php?number_id=270)))_. +``` + +```scss +$True Prime Pairs: + (5,7), (11,13), (17,19) + + layer| i | f + -----+-----+--------- + | 1 | 5 + 1 +-----+ + | 2 | 7 + -----+-----+--- } 36 » 6® + | 3 | 11 + 2 +-----+ + | 4 | 13 + -----+-----+--------- + | 5 | 17 + 3 +-----+ } 36 » 6® + | 6 | 19 + -----+-----+--------- +``` + +Thus in short this is all about the method that we called as the ***[19 vs 18 Scenario](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-%CE%B419-vs-18-scenario)*** of mapping [the quantum way](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-utilization-md) within a huge of [primes objects](https://github.com/eq19) (5 to 19) by [lexering](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-lexer-md) (11) the un[grammar](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md)ed feed (7) and [parsering](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md) (13) across [syntax](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-syntax-md) (17). + +***Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)*** + +```scss +$True Prime Pairs: +(5,7), (11,13), (17,19) + +layer | node | sub | i | f +------+------+-----+---------- + | | | 1 | + | | 1 +-----+ + | 1 | | 2 | (5) + | |-----+-----+ + | | | 3 | + 1 +------+ 2 +-----+---- + | | | 4 | + | +-----+-----+ + | 2 | | 5 | (7) + | | 3 +-----+ + | | | 6 | +------+------+-----+-----+------ } (36) + | | | 7 | + | | 4 +-----+ + | 3 | | 8 | (11) + | +-----+-----+ + | | | 9 | + 2 +------| 5 +-----+----- + | | | 10 | + | |-----+-----+ + | 4 | | 11 | (13) + | | 6 +-----+ + | | | 12 | +------+------+-----+-----+------------------ + | | | 13 | + | | 7 +-----+ + | 5 | | 14 | (17) + | |-----+-----+ + | | | 15 | + 3 +------+ 8 +-----+----- } (36) + | | | 16 | + | |-----+-----+ + | 6 | | 17 | (19) + | | 9 +-----+ + | | | 18 | +------|------|-----+-----+------ +``` + +The main background is that, as you may aware, the prime number theorem describes the ***asymptotic distribution*** of prime numbers which is still a major problem in mathematic. + +## Multiplication Zones + +Instead of a proved formula we came to a unique expression called ***zeta function***. This expression first appeared in a paper in 1737 entitled _Variae observationes circa series infinitas_. + +```tip +This expression states that the sum of the zeta function is equal to the product of the reciprocal of one minus the reciprocal of primes to the powers. But what has this got to do with the primes? The answer is in the following product taken over the primes p (discovered by _[Leonhard Euler](https://en.wikipedia.org/wiki/Leonhard_Euler)_): +``` + +![zeta function](https://user-images.githubusercontent.com/8466209/219739322-ebdc1916-249a-49da-8ded-ce0fe1205550.png) + +This issue is actually come from ***[Riemann hypothesis](https://youtu.be/zlm1aajH6gY)***, a conjecture about the distribution of complex zeros of the Riemann zeta function that is considered to be ***the most important*** of _[unsolved problems](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics)_ in pure mathematics. + +```note +In addition to the trivial roots, there also exist ***complex roots*** for real t. We find that the he first ten (10) non-trivial roots of the Riemann zeta function is occured when the values of t below 50. A plot of the values of ζ(1/2 + it) for t ranging from –50 to +50 is shown below. The roots occur each time ***the locus passes through the origin***. _([mathpages](https://www.mathpages.com/home/kmath738/kmath738.htm))_. +``` + +[![trivial roots](https://user-images.githubusercontent.com/8466209/219828222-615a2037-dbcd-4412-95bf-740bb32094de.png)](https://www.mathpages.com/home/kmath738/kmath738.htm) + +Meanwhile obtaining the non complex numbers it is easier to look at a graph like the one below which shows Li(x) (blue), R(x) (black), π(x) (red) and x/ln x (green); and then proclaim "R(x) is the best estimate of π(x)." Indeed it is for that range, but as we mentioned above, Li(x)-π(x) changes sign infinitely often, and near where it does, Li(x) would be the best value. + +[![non complex numbers](https://user-images.githubusercontent.com/8466209/219214486-e6412fb0-d190-45ae-990f-524532661444.png)](https://primes.utm.edu/howmany.html#better) + +And we can see in the same way that the function Li(x)-(1/2)Li(x1/2) is 'on the average' a better approximation than Li(x) to π(x); but no importance can be attached to the latter terms in Riemann's formula even by repeated averaging. + +## Exponentiation Zones + +The problem is that the contributions from the non-trivial zeros at times swamps that of any but the main terms in these expansions. + +```warning +A. E. Ingham says it this way: Considerable importance was attached formerly to a function suggested by Riemann as an approximation to π(x)... This function represents π(x) with astonishing accuracy for all values of x for which π(x) has been calculated, but we now see that its superiority over Li(x) ***is illusory***... and for special values of x (as large as we please) the one approximation will deviate as widely as the other from the true value _([primes.utm.edu](https://primes.utm.edu/howmany.html#better))_. +``` + +[![howmany primes](https://user-images.githubusercontent.com/36441664/87958552-dea18f80-cadb-11ea-9499-6c2ee580a5ca.png)](https://primes.utm.edu/howmany.html#pnt) + +Moreover in it was verified numerically, in a rigorous way using interval arithmetic, that _[The Riemann hypothesis is true up to 3 · 10^12](https://arxiv.org/pdf/2004.09765.pdf)_. That is, all zeroes β+iγ of the Riemann zeta-function with 0<γ≤3⋅1012 have β=1/2. + +```danger +We have Λ ≤ 0.2. The next entry is conditional on taking H a little higher than 10*13, which of course, is not achieved by Theorem 1. This would enable one to prove Λ < 0.19. Given that our value of H falls between the entries in this table, it is possible that some extra decimals could be wrought out of the calculation. We have not pursued this _([arXiv:2004.09765](https://arxiv.org/abs/2004.09765))_. +``` + +[![functional equation](https://user-images.githubusercontent.com/8466209/219715694-751fe538-378d-4f58-ae82-ac9e6823ad65.png)](https://arxiv.org/pdf/2004.09765.pdf) + +This Euler formula represents the distribution of a group of numbers that are positioned at regular intervals on a straight line to each other. Riemann later extended the definition of zeta(s) to all complex numbers (***except the simple pole at s=1 with residue one***). Euler's product still holds if the real part of s is greater than one. Riemann derived the functional equation of zeta function. + +```danger +The Riemann zeta function has the trivial zeros at -2, -4, -6, ... (the poles of gamma(s/2)). Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 < Re(s) < 1, and that they are symmetric about the critical line Re(s)=1/2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line _([primes.utm.edu](https://primes.utm.edu/notes/rh.html))_. +``` + +[![zeta function](https://user-images.githubusercontent.com/8466209/219720444-e5ba30ac-e000-4c85-8678-186676b93d2b.png)](https://primes.utm.edu/notes/rh.html) + +If both of the above statements are true then mathematically this Riemann Hypothesis is proven to be incorrect because it only applies to certain cases or limitations. So first of all the basis of the Riemann Hypothesis has to be considered. + +```warning +The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the functional equations. _([Riemann Zeta - pdf](https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf))_ +``` + +[![Riemann hypothesis](https://user-images.githubusercontent.com/8466209/218374273-729fee09-5480-4fb3-a3a6-0dc050bdbe26.png)](https://en.wikipedia.org/wiki/Riemann_hypothesis) + +On the other hand, the possibility of obtaining the function of the distribution of prime numbers shall go backwards since it needs significant studies to be traced. + +Or may be ***start again from the Euleur Function***. + +## Identition Zones + +_[Freeman Dyson](https://en.wikipedia.org/wiki/Freeman_Dyson#Quantum_physics_and_prime_numbers)_ discovered an intriguing connection between quantum physics and [Montgomery's pair correlation conjecture](https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture) about the zeros of the [zeta function](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function) which dealts with the distribution of primes. + +```note +The Mathematical Elementary Cell 30 (***MEC30***) standard _[unites](https://www.eq19.com/multiplication/12.html#entrypoint-of-momentum-spin-3)_ the mathematical and physical results of 1972 by _the mathematician Hugh Montgomery and the physicist Freeman Dyson_ and thus reproduces energy distribution in systems as a path plan ***more accurately than a measurement***. _([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))_ +``` + +[![The Mathematical Elementary Cell 30](https://user-images.githubusercontent.com/36441664/74366957-992db780-4e03-11ea-8f26-cca32bd26003.png)](https://patentimages.storage.googleapis.com/6f/e3/f0/b8f7292f1f2749/DE102011101032A9.pdf) + +The path plan assume that a symmetric distribution of prime numbers with equal axial lengths from a ***middle zero axis = 15*** is able to determine the distribution of primes in a given number space. This assumption finally bring us to the equation of ***[Euler's identity](https://en.wikipedia.org/wiki/Euler%27s_identity)***. + +```note +Euler's identity is considered to be an exemplar of deep mathematical beauty as it shows a profound connection between the most fundamental numbers. Three (3) of the basic arithmetic operations occur exactly once each: ***addition***, ***multiplication***, and ***exponentiation*** _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_. +``` + +[![Euler's identity](https://user-images.githubusercontent.com/8466209/219584666-703f4584-db7c-4f2d-9714-f52067869ef3.png)](https://en.wikipedia.org/wiki/Euler%27s_identity) + +The finiteness position of Euler's identity by the said _MEC30_ opens up the possibility of accurately representing the self-similarity based on the distribution of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ so that all number would belongs together with [their own identitities](https://www.eq19.com/identition/). + +```tip +See that there are multiple repetition from addition to multiplication which may lead up to the concept of [11th-dimension](https://www.eq19.com/identition/#extra-dimensions). This path is being applied as you can find on the left sidebar. (Please change the view to desktop mode if you are on mobile browser). +``` + +[![DE102011101032A9.pdf](https://user-images.githubusercontent.com/36441664/74591731-f5cfe300-504c-11ea-9e04-d814c57aa969.png)](https://github.com/eq19/eq19.github.io/files/13814949/DE102011101032A9.pdf) + +Nothing is going to be easly about the nature of prime numbers but they demonstrably congruent to something organized. Let's discuss starting with the _[addition zones](https://www.eq19.com/addition/)_. + +**[eQuantum Project](https://github.com/eq19)** +Copyright © 2023-2024 + +Reference: +* [Riemann Zeta](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) +* [Mersenne Prime](https://en.wikipedia.org/wiki/Mersenne_prime) +* [The Prime Hexagon](https://www.hexspin.com/) +* [The Primes Demystified](https://www.primesdemystified.com/First1000Primes.html) diff --git a/addition/2.html b/addition/2.html new file mode 100644 index 00000000000..63a0f73a858 --- /dev/null +++ b/addition/2.html @@ -0,0 +1,293 @@ + True Prime Pairs · eQuantum
eQuantum
Mapping the quantum way
eQuantum

True Prime Pairs

This is the partial of the mapping scheme of our eQuantum Project. Our mapping is simulating a recombination of the three (3) layers of these prime pairs.

+
+ + Tip +
+
+

This section is referring to wiki page-2 of zone section-2 that is inherited from the zone section-2 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

An Independent claim is also included for the localization and determination, or their material structures, by graphical representation of base sequences on various media, based on the new assignments and the derived vibrations and amplitudes.

Prime Objects

In short this project is mapping the quantum way within a huge of prime objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

5, 2, 1, 0
+7, 3, 1, 0
+11, 4, 1, 0
+13, 5, 1, 0
+17, 0, 1, 1
+19, 1, 1, 1
+

default

+
+ + Note +
+
+

The 5+7+11+13 is the smallest square number expressible as the sum of four consecutive primes which are also two couples of prime twins!

  • Their sum is 36 which is the smallest square that is the sum of a twin prime pair {17, 19}.
  • This 36 is the smallest number expressible as the sum of consecutive prime in two (2) ways (5+7+11+13 and 17+19).
+
+ 
$True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | 
+      |      |  1  +-----+          
+      |  1   |     |  2  | (5)
+      |      |-----+-----+
+      |      |     |  3  |
+  1   +------+  2  +-----+----
+      |      |     |  4  |
+      |      +-----+-----+
+      |  2   |     |  5  | (7)
+      |      |  3  +-----+
+      |      |     |  6  |
+------+------+-----+-----+------      } (36)
+      |      |     |  7  |
+      |      |  4  +-----+
+      |  3   |     |  8  | (11)
+      |      +-----+-----+
+      |      |     |  9  |
+  2   +------|  5  +-----+-----
+      |      |     |  10 |
+      |      |-----+-----+
+      |  4   |     |  11 | (13)
+      |      |  6  +-----+
+      |      |     |  12 |
+------+------+-----+-----+------------------
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17)
+      |      |-----+-----+
+      |      |     |  15 |
+  3   +------+  8  +-----+-----       } (36)
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |
+------|------|-----+-----+------
+

Primes-vs-composites svg

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) ---------------------
+      |      |  6  +-----+        <-----------------  strip √
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s = f(1000)
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | --------------------------
+------|------|-----+-----+------# 
+
+
+ + Note +
+
+

We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius.

  • We show that the resulting 4D theory is (Riemannian) General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.
  • Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.

In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist. The metric, and in particular the 4D metric, is defined by the 3-form. (General relativity from three-forms in seven dimensions - pdf)

+
+

Symmetry State

+
+ + Note +
+
+

In this article we will support this conjecture and develop a new approach to quantum gravity called smooth quantum gravity by using smooth 4-manifolds with an exotic smoothness structure.

  • In particular we discuss the appearance of a wildly embedded 3-manifold which we identify with a quantum state.
  • Furthermore, we analyze this quantum state by using foliation theory and relate it to an element in an operator algebra.
  • Then we describe a set of geometric, non-commutative operators, the skein algebra, which can be used to determine the geometry of a 3-manifold.
  • This operator algebra can be understood as a deformation quantization of the classical Poisson algebra of observables given by holonomies.
  • The structure of this operator algebra induces an action by using the quantized calculus of Connes.

The scaling behavior of this action is analyzed to obtain the classical theory of General Relativity (GRT) for large scales. (Smooth quantum gravity - pdf)

+
+

addition zones

The holonomy tells you how to propagate MEC30. A spin network state assigns an amplitude to a set of spin half particles tracing out a path in space, merging and splitting.

This kind of approach has some obvious properties: there are non-linear gravitons, a connection to lattice gauge field theory and a dimensional reduction from 4D to 2D.

Construction of a State

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------    <----------------- Mobius strip √
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) ---------------------
+      |      |  6  +-----+        <----------------- Mobius strip
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s = f(1000)
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | --------------------------
+------|------|-----+-----+------  <----------------- Möbius strip √
+
+
+ + Note +
+
+

The funny looking Möbius strip, which was also independently discovered in 1858 by the unlucky Listing whose name left the history of mathematics untouched.

  • It is a surface with only one side and only one boundary, often used to puzzle young math students. You can easily create it by taking a strip of paper, twisting it and then joining the ends of the strip.

  • Being the first example of a surface without orientation it did not shake the grounds of mathematics as much as the other discoveries of this list did, yet it provided a lot of practical applications, such as a resistant belt, and inspired mathematicians to come up with unorientable surfaces, like the Klein bottle.

  • The name of this surface possibly comes from a double coincidence: Klein, its conceptor, originally named it Fläche, which means surface in German and sounds similar to Flasche, which means bottle. The fact that it also looked like a bottle seems to have sealed the renaming.

Mathematical fields were created, we got the Turing Machine, fancy looking surfaces and, most importantly, the ability to re-examine our perceptions and adapt our tools accordingly. (freeCodeCamp)

+
+

mobius strip

These items are elementary parts possessing familiar properties but they never exist as free particles. Instead they join together by the strong force into bound states.

f(18) = f(7) + f(11) = (1+7+29) + 11th prime = 37 + 31 = 36 + 32 = 68

Bilateral 9 Sums

+
+ + Note +
+
+

Eigennvalue curves (right) showing a triple eigenvalue at zero for τ = 1 and double eigenvalues at 1 ± √2i for τ = √43. On the left the graph of 1/|Q(λ)| with the same eigenvalue curves plotted in the ground plane. Green stars indicate the eigenvalues of A, blue stars the roots of puv(λ) and triangles the zeroes of Q0(λ)

+
+

10 + 10th prime + 10th prime = 10 + 29 + 29 = 68

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------    <----------------- Mobius strip
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- (71) √
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) ---------------------
+      |      |  6  +-----+        <----------------- Mobius strip
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- (43) √
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | --------------------------
+------|------|-----+-----+------  <----------------- Möbius strip
+

This pattern is raised up per six (6) cycles on the 19, 43 and 71. Since the members are limited to the sum of 43+71=114.

Polarity

So here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme.

+
+ + Note +
+
+

In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry). (PrimesDemystified)

+
+

7 x π(89) = 7 x 24 = 168 = π(1000)

collective bilateral 9 sum symmetry

Supersymmetric Multiplet

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                       MEC 30 / 2
+------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) √
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = (43-19) √
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}
+
+
+ + Note +
+
+

Given our domain is limited to numbers ≌ {1,7,11,13,17,19,23,29} modulo 30, only ϕ(m)/m = 8/30 or 26.66% of natural numbers N = {0, 1, 2, 3, …} need be sieved.

  • For example, to illustrate the proportionality of this ratio, we find that 25% of the first 100 natural numbers are prime, while 72% of numbers not divisible by 2, 3, or 5 are prime (and, curiously, if we count 2, 3, and 5 in after the fact, we get 75%, or exactly 3 x 25%).
  • Also note that if you plug the number 30 into Euler’s totient function, phi(n): phi(30)= 8, with the 8 integers (known as totatives) smaller than and having no factors in common with 30 being: 1, 7, 11, 13, 17, 19, 23 and 29, i.e., what are called “prime roots” above. Thirty is the largest integer with this property.]
  • The integer 30, product of the first three prime numbers (2, 3 and 5), and thus a primorial, plays a powerful role organizing the array’s perfect symmetry, viz., in the case of the 8 prime roots:

1+29=30; 7+23=30; 11+19=30; and 13+17=30.

  • In The Number Mysteries well-known mathematician Marcus Du Sautoy writes: “In the world of mathematics, the numbers 2, 3, and 5 are like hydrogen, helium, and lithium. That’s what makes them the most important numbers in mathematics.”
  • Although 2, 3 and 5 are the only prime numbers not included in the domain under discussion, they are nonetheless integral to it: First of all, they sieve out roughly 73% of all natural numbers, leaving only those nominally necessary to construct a geometry within which prime numbers can be optimally arrayed.
  • The remaining 26.66% (to be a bit more precise) constituting the array can be constructed with an elegantly simple interchangeable expression (or power series, if you prefer) that incorporates the first three primes. It’s conjectured that this manifold series ultimately consists of all (and only) the numbers not divisible by 2, 3, or 5 (and their negatives), which inclues all prime numbers >5 (more below under the heading “Conjectures and Facts Relating to the Prime Spiral Sieve”).

What is critical to understand, is that the invisible hand of 2, 3 and 5, and their factorial 30, create the structure within which the balance of the prime numbers, i.e., all those greater than 5, are arrayed algorithmically–as we shall demonstrate. Primes 2, 3 and 5 play out in modulo 30-60-90 cycles (decomposing to {3,6,9} sequencing at the digital root level). Once the role of 2, 3 and 5 is properly understood, all else falls beautifully into place. (PrimesDemystified)

+
+

One_Grand_Pyramid_Teaser

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/3.html b/addition/3.html new file mode 100644 index 00000000000..f8a43333ff7 --- /dev/null +++ b/addition/3.html @@ -0,0 +1,377 @@ + Primes Platform · eQuantum
eQuantum
Mapping the quantum way
eQuantum

Primes Platform

+
+ + Tip +
+
+

This section is referring to wiki page-3 of zone section-3 that is inherited from the zone section-3 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

Prime hexagon is a mathematical structure developed by mathematician T. Gallion that is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime is encountered.

+
+ + Note +
+
+

This is not easy as they are linked to the nature of prime numbers, and nothing is easy about the nature of prime numbers. But I begin with this assumption: if the hexagons participate in the Universe in any way other than haphazardly, they must be demonstrably congruent to something organized (T. Gallion).

+
+ 
s p i n
+0 0 0 0
+1 0 0 0
+2 0 1 0  ◄--- 1st prime
+3 1 1 0  ◄--- 2nd prime
+--------
+5 2 1 0  ◄--- 3rd prime
+7 3 1 0
+11 4 1 0
+13 5 1 0
+17 0 1 1 ◄--- 7th prime
+19 1 1 1 ◄--- 8th prime
+

17 = 7th prime = (18 - 11) th prime

p r i m e s
+1 0 0 0 0
+2 1 0 0 0
+3 2 0 1 0 2 ◄--- 1st prime
+4 3 1 1 0 3 ◄--- 2nd prime
+5 5 2 1 0 5 ◄--- 3rd prime
+6 7 3 1 0
+7 11 4 1 0
+8 13 5 1 0
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 19 ◄--- 8th prime
+-----
+11 23 2 1 1 23 ◄--- 9th prime √
+

Residual objects

You may learn that sets of algebraic objects has a multilinear relationship related to a vector space called tensor. Tensors may map between different objects such as vectors, scalars, and even other tensors.

300px-Components_stress_tensor svg

p r i m e s
+1 0 0 0 0
+2 1 0 0 0
+3 2 0 1 0 2 ◄--- 1st prime
+4 3 1 1 0 3 ◄--- 2nd prime
+5 5 2 1 0 5 ◄--- 3rd prime
+6 7 3 1 0
+7 11 4 1 0
+8 13 5 1 0
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 ∆1 ◄--- 8th prime ◄--- Terminating Digit
+-----
+11 23 2 1 1 √
+

(17+13) + (11+19) = (7+11) + (19+23) = 60

image

image

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 √
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 √
++29 rows √
+-----
+41 √
+

In order to maintain the 36 symmetry (whether it is an addition zone or not), with this prime number 19 was found at least seven (7) pairs of truncated patterns.

+
+ + Tip +
+
+

The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating 3 minor hexagons.

+
+

π(6+11) = π(17) = 7

Central Polarity

This polarity is happened per six (6) cycles by the polar of six (6) to one (1) and six (6) to seven (7) that leads to the prime number 61 and 67.

+
+ + Note +
+
+

The above characteristics of primes in the hexagon suggests 0 family numbers split more than twin primes. I speculate these numbers split all primes. That is, all primes have a partner (of the opposite family) equidistant from such a number. For instance, 0 family member 18 splits twin primes 17 and 19, but is also 5 more than 13 and 5 less than 23, and it is also 11 more the 7, and 11 less than 29, etc. (Hexspin)

+
+

By which we finally found if this behaviour is cascaded bilaterally within the correlation between 61 as the 18th prime and 67 as the 19th prime.

+
+ + Note +
+
+

The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the Functional equations of Riemann

+
+

18 + 19 = π(61) + π(67) = 37

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 (spin 18) √
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 (spin 19) √
++29 rows
+-----
+41
+
+
+ + Note +
+
+

The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period eight (8) difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2} (Primesdemystified).

+
+

image

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 (spin 18)
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 (spin 19)
++29 rows
+-----
+41
++59 rows √
+
+
+ + Note +
+
+

Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

+
+

11's additive sums

Fibonacci level-1 (29) x Fibonacci level-2 (59) = 10x10 = 💯

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 ◄- Fibonacci Index #18 √
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 ◄- Fibonacci Index #19 √
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄- Terminating Digit #11 ◄- Fibonacci Index #29 √
+-----
+41
++59 rows ◄--- total 41+59 = 💯 rows = 10x10 rows √
+

Numeric Symmetries

(59² − 31²) = 360 x 7

Squares_Distribution

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- 7th prime
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30 ✔️
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 ✔️
+-----
+

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s ✔️
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11s ✔️
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s ✔️
+-----
+
+
+ + Note +
+
+

These positions: 1 7 11 13 17 19 23 29. We refer to this basic system as MEC 30 - “Mathematical Elementary Cell 30”.

  • By repeating the positions we show the function of the basic system in the next step. If we extend the 30th order of the MEC, for example, to the number 120, the result is 4 times a 30th order and thus 4 × 8 = 32 prime positions.
  • Hypothetical assumption: If the product of the primes (except 2, 3, 5,) would not fall into the prime positions, thus be divided by 2, 3 or 5, the information would have 120 = 32 primes in 32 prime positions.
  • Prime positions (not the primes) 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17 , 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29,
  • The 30th order is repeated in the number space 120 = 4 times, 4 × 8 = 32 prime positions, thus 4 terms. From our considerations and also from the graphic see 2 However, we can conclude that the distribution of prime numbers must have a static base structure, which is also confirmed logically in the further course.

This static structure is altered by the products of the primes themselves, since these products must fall into the prime positions since they are not divisible by 2, 3 and 5.

+
+

+
+ + Note +
+
+

The numbers not divisible by 2, 3 or 5 are highlighted. We call them prime positions, hence 1, 7, 11, 13, 17, 19, 23, 29. Important for our work is that in the following the term prime refers only to prime numbers that are in the prime positions. So primes 2, 3 and 5 are always excluded.

+
+ 
p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ✔️
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7 ◄--- #23 ✔️
+7 11 4 1 0 11 ◄--- #19 ✔️
+8 13 5 1 0 13 ◄--- # 17 ✔️
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+
+
+ + Note +
+
+

In this one system, reproduced as an icon, we can show the distribution profile of the primes as well as their products over a checkerboard-like model in the 4.

  • We show this fundamental causal relationship in the MEC 30 mathematically accurate in the table 13 , The organization of this table is based on the well-known idea of Christian Goldbach. That every even number should consist of the sum of two primes.
  • All pairs of prime numbers without “1”, 2, 3, 5, we call henceforth Goldbach pairs. The MEC 30 transforms this idea of Christian Goldbach into the structure of a numerical double-strand, into an opposing member of the MEC 30 scale.
  • We call this double strand a convolution, which results in an opposite arrangement. It represents the natural vibration, thus also the redundant vibrations in the energy transfer. In the 6 For example, in the graph, the even number 60 is folded. At folding of the even number 60 6 result in 8 prime pairs.
  • In this case, among the 8 pairs of prime pairs there are only 6 Goldbach pairs. 2 prime positions in the prime position pairs carry products of the factors “1 × 1” and 7 × 7. Thus, 2 prime pairs do not fulfill the requirements of the Goldbach pairs. In general, any even number larger than 30 can be represented graphically within a cycle (MEC 30) as a specific cyclic convolution. This characteristic convolution of the even numbers is a fundamental test element in the numerical table. The result Even the even numbers to infinity occupy a fixed position within the 30s system MEC 30. The even numbers thus have 15 positions: 30/2 = 15 even positions of the MEC 30.
  • There are therefore only 15 even positions for all even numbers to infinity. Every even number has a specific convolution due to its position in the 30s system. First, we have to determine the positions of the even numbers in the 30s system to make them one in the following graph 7 attributable to the 15 specific folds.
+
+ 

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 ✔️
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49 ✔️
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43 ✔️
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

Palindromic Sequence

+
+ + Note +
+
+

In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry). (PrimesDemystified)

+
+

7 x π(89) = 7 x 24 = 168 = π(1000)

collective bilateral 9 sum symmetry

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2 ✔️
+4 3 1 1 0 3 👉 61 - 1 = 60 ✔️
+5 5 2 1 0 5
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+
+
+ + Note +
+
+

The color spin addresses for numbers are generally straightforward – a composite number takes the spin of the prior prime. 4 spins blue because 3 spins blue. 8 is red because 7 is red. However, twin primes, and the 0 type numbers between them, are open to some interpretation.

+
+

base

(43 - 19)the prime = 24th prime = 89

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                       MEC 30 / 2
+------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) √
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = (43-19) √
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}
+
+
+ + Note +
+
+

The number 120 has 32 prime positions minus 5 prime number products = 27 prime numbers. The information of the prime number products translates our theory into a checkerboard-like pattern using the finite 8 prime positions from the MEC 30, we call it Ikon. 8 × 8 primary positions = 64 primary positions of the checkerboard icon.

  • First, there are two main features that we use. To Ikon 1: The primes information and their products. In this left icon, the redundants (the doubles) are to be determined through the number information in the positions Impeccable.
  • Second: The product positions. In the icon, the cyclic behavior is shown in identical 8 horizontal and 8 vertical orders, we call these orders templates that would not be visible through the pure number information. The cyclical behavior of the 8 × 8 product positions continues indefinitely.
  • Since the prime positions are finite, a total of 8 positions in the 30th order, an already revolutionary system opens up, the entire infinite distribution of the prime number products in an icon as a “checkerboard pattern”. represent and thus obtain mathematically exact results.
  • The three and 4 , Square Graphics (Ikon) will now be in the following, larger graphic 5 transfer. As stated above, we use the properties of the numbers, they consist of one information and one position. Thus we are able to calculate the redundant product positions by means of identical information in different positions.
  • And subtracting them from the total prime positions gives us the number of prime numbers. This succeeds due to the self-similarity of the 30th order of the MEC 30, as shown in the graph 5 is articulated. At the top of the following larger graphic 5 the self-similarity of the 30th order (MEC 30) can be seen.
  • This results in a fundamental causal relation to the primes, systemically the products are entered into the position system. Therefore, the distribution of primes products also determines the distribution of primes themselves. The reason lies in the one-system, since the prime number as a number itself also consists of an information and a position.

We apply the same principle as above for the determination of the prime position. Only with the difference that we move in the even positions of the MEC 30.

+
+

7 x π(89) = 7 x 24 = 168 = π(1000)

Theory of Everything

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/4.html b/addition/4.html new file mode 100644 index 00000000000..b1434dbd581 --- /dev/null +++ b/addition/4.html @@ -0,0 +1,203 @@ + Pairwise Scenario · eQuantum
eQuantum
Mapping the quantum way
eQuantum

Pairwise Scenario

+
+ + Tip +
+
+

This section is referring to wiki page-4 of zone section-4 that is inherited from the zone section-5 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

image

(10 - 2) th prime = 8th prime = 19

default

The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.

Rank of a partition

tps://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#partition-function) represents the number of possible partitions of a non-negative integer n.

f(8 twins) = 60 - 23 = 37 inner partitions

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 -29 = 61 - 1 = 60 ✔️
+5 5 2 1 0 5 👉 f(37) = f(8 twins) ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

7 + 13 + 19 + 25 = 64 = 8 × 8 = 8²

Subclasses of Partitions

+
+ + Note +
+
+

Let weighted points be given in the plane . For each point a radius is given which is the expected ideal distance from this point to a new facility. We want to find the location of a new facility such that the sum of the weighted errors between the existing points and this new facility is minimized. This is in fact a nonconvex optimization problem. We show that the optimal solution lies in an extended rectangular hull of the existing points. Based on this finding then an efficient big square small square (BSSS) procedure is proposed.

+
+

A_BSSS_Algorithm_for_the_Location_Problem_with_Min.pdf

Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

+
+ + Note +
+
+

Young diagrams associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia).

+
+

f(8🪟8) = 1 + 7 + 29 = 37 inner partitions

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 -29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 f(37) = f(8🪟8) ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

When these subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent .

+
+ + Note +
+
+

It’s possible to build a Hessian matrix for a Newton’s method step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector (Tensorflow).

+
+

Partitioned-matrices-of-the-numbers-60-62-and-64-as-examples

+
+ + Note +
+
+

In summary, it has been shown that partitions into an even number of distinct parts and an odd number of distinct parts exactly cancel each other, producing null terms 0x^n, except if n is a generalized pentagonal number n=g_{k}=k(3k-1)/2}, in which case there is exactly one Ferrers diagram left over, producing a term (−1)kxn. But this is precisely what the right side of the identity says should happen, so we are finished. (Wikipedia)

+
+ 
p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 -29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 f(37) = f(29🪟23) ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

The code is interspersed with python, shell, perl, also demonstrates how multiple languages can be integrated seamlessly.

extended branes

These include generating variants of their abundance profile, assigning taxonomy and finally generating a rooted phylogenetic tree.

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 f(37) = ❓ 👈 Composite ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime 👉 7s 👈 Composite ✔️
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

This behaviour in a fundamental causal relation to the primes when the products are entered into the partitions system.

Composite behaviour

The subclasses of partitions systemically develops characters similar to the distribution of prime numbers. It would mean that there should be some undiscovered things hidden within the residual of the decimal values.

integer partition

168 + 2 = 170 = (10+30)+60+70 = 40+60+70 = 40 + 60 + ∆(2~71)

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 f(37) ✔️
+          6 👉 11s Composite Partition ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime
+           18 👉 7s Composite Partition ✔️
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+
+
+ + Note +
+
+

The initial concept of this work was the Partitioned Matrix of an even number w≥ 4:

  • It was shown that for every even number w≥ 4 it is possible to establish a corresponding Partitioned Matrix with a determined number of lines.
  • It was demonstrated that, fundamentally, the sum of the partitions is equal to the number of lines in the matrix: Lw = Cw + Gw + Mw.
  • It was also shown that for each and every Partitioned Matrix of an even number w ≥ 4 it is observed that Gw = π(w) − (Lw − Cw), which means that the number of Goldbach partitions or partitions of prime numbers of an even number w ≥ 4 is given by the number of prime numbers up to w minus the number of available lines (Lwd) calculated as follows: Lwd = Lw − Cw.

To analyze the adequacy of the proposed formulas, probabilistically calculated reference values were adopted. (Partitions of even numbers - pdf)

+
+

Batch Jacobian

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 ✔️
+          6 👉 11s Composite Partition ◄--- 2+60+40 = 102 ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime 
+           18 👉 7s Composite Partition 
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

(11x7) + (29+11) + (25+6) + (11+7) + 4 = 77+40+31+18+4 = 170

16S rRNA amplicons study

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/5.html b/addition/5.html new file mode 100644 index 00000000000..49efa863a17 --- /dev/null +++ b/addition/5.html @@ -0,0 +1,131 @@ + Power of Magnitude · eQuantum
eQuantum
Mapping the quantum way
eQuantum

Power of Magnitude

+
+ + Tip +
+
+

This section is referring to wiki page-5 of gist section-1 that is inherited from the gist section-7 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics
+
+ + Note +
+
+

The number 120 = MEC30 x 4 has 32 prime positions minus 5 prime number products = 27 prime numbers. The information of the prime number products translates our theory into a checkerboard-like pattern using the finite 8 prime positions from the MEC 30, we call it Ikon. 8 × 8 primary positions = 64 primary positions of the checkerboard icon.

+
+

Hebrew numerals

+
+ + Note +
+
+

Note that the hexagon in the middle has 37 circles and the total figure, a star of David has 73. For this one you go around one point of the pattern in a circle until you go past a letter that you have already covered. For instance in B-R-A-Sh you will have to switch the position for the Sh because it moves more than through the alphabet. S-I-T does the same with the T.

+
+

Torah geometri

Composite Contribution

The above seven (7) primes will act then as extended branes. This is what we mean by addition zones and it happens whenever a cycle is restarted.

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                       MEC 30 / 2
+------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2       |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7 x 24 = 168 ✔️
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}
+

This scheme goes to the unification of 11s with 7s to 18s meanwhile the 11th it self behave as residual by the 5th minor hexagon between the 30 to 36' cells.

74550123-6dd1d680-4f83-11ea-8810-3b8f4f50a9c0

 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18
+---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----+----
+ 19| 20| 21| 22| 23| 24| 25|
+---+---+---+---+---+---+---+
+ - | - | - | 28| 29|
+

By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

+
+ + Note +
+
+

You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why? Because they do not fit inside — they stick off the hexagon like a tail. Perhaps that’s where they belong. However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively. _(HexSpin)

+
+

0 + 30 + 36 + 102 = 168 = π(1000)

19 vs 18

 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 
+---+---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----
+ - | - | 20| 21| 22| 23| 24| 25|
+---+---+---+---+---+---+---+
+ - | - | - | - | 28| 29|
+---+---+---+---+---+---+
+ 30| 31|
+---+---+
+ 36|
+
+
+ + Tip +
+
+

This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with the prime distribution level as indicated by the self repetition on MEC30.

+
+

7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

IMG_20231221_074421

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin ✔️
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin ✔️
+6 7 3 1 0 7 ◄--- #23
+7 11 4 1 0 11 ◄--- #19
+8 13 5 1 0 13 ◄--- # 17 ◄--- #49
+9 17 0 1 1 17 ◄--- 7th prime
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin ✔️
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

It will be forced back to Δ19 making a cycle that bring back the 12 to → 13 of 9 collumns and replicate The Scheme 13:9 through (i=9,k=13)=9x3=27 with entry form of (100/50=2,60,40) as below:

default

The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

+
+ + Note +
+
+

I like that 0 can occupy a center point. Incidentally, this circular shape minus all my numbers and colors s has been called Seed of Life / Flower of Life by certain New Age groups who claim it has a sacred geometry. Please don’t see this as an endorsement of any spiritual group or religion. (Prime Hexagon - Circulat Form)

+
+

image

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/6.html b/addition/6.html new file mode 100644 index 00000000000..b11bf051abd --- /dev/null +++ b/addition/6.html @@ -0,0 +1,115 @@ + The Pairwise Disjoint · eQuantum
eQuantum
Mapping the quantum way
eQuantum

The Pairwise Disjoint

+
+ + Tip +
+
+

This section is referring to wiki page-6 of gist section-2 that is inherited from the gist section-11 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

Mobius Strip

There are some mathematical shape of this residual objects. Torus is basically a donut shape, which has the property of of having variable Gaussian curvature.

+
+ + Note +
+
+

The blue parts of the torus above have positive curvature, the red parts negative and the top grey band has zero curvature. If our 3 dimensional space was like the surface areas of a 4 dimensional torus, the parts would have different angle sums.

+
+

Torus

Some parts of the surface has positive curvature, others zero, others negative.

ring_tor1_anim

If you start anywhere on its surface and follow the curvature round you will eventually return to the same place having travelled on every part of the surface.

Mobius

Fiddler_crab_mobius_strip

Mobius strip only has one side, there are two more bizarre shapes with strange properties.

The Klein bottle

The Klein bottleis in someways a 3D version of the Mobius strip and even though it exists in 3 dimensions, to make a true one you need to "fold through" the 4th dimension.

+
+ + Note +
+
+

In mathematics, the Klein bottle (/ˈklaɪn/) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.

While a Möbius strip is a surface with a boundary, a Klein bottle has no boundary. For comparison, a sphere is an orientable surface with no boundary.

+
+

image

Klein bottle

A sign inversion visualized as a vector pointing along the Möbius band when the circle is continuously rotated through a full turn of 360°.

image

The Spinors

A spinor associated to the conformal group of the circle, exhibiting a sign inversion on a full rotation of the circle through an angle of 2π.

(17+13) + (11+19) = (7+11) + (19+23) = 60

Sipnors

3-Figure1-1

+
+ + Note +
+
+

Eigennvalue curves (right) showing a triple eigenvalue at zero for τ = 1 and double eigenvalues at 1 ± √2i for τ = √43. On the left the graph of 1/|Q(λ)| with the same eigenvalue curves plotted in the ground plane. Green stars indicate the eigenvalues of A, blue stars the roots of puv(λ) and triangles the zeroes of Q0(λ)

+
+

Global Properties

7 + 11 + 13 = 31 1 + (26+6) + (27+6) = 66

9 vs 18

 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 
+---+---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----
+ - | - | 20| 21| 22| 23| 24| 25|
+---+---+---+---+---+---+---+---+
+ - | - | - | - | 28| 29| ◄--- missing 26 & 27 ✔️
+---+---+---+---+---+---+
+ 30| 31| - | - | ◄--- missing 32 & 33 ✔️
+---+---+---+---+
+ 36|
+
+
+ + Tip +
+
+

This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with the prime distribution level as indicated by the self repetition on MEC30.

+
+

7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

IMG_20231221_074421

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                       MEC 30 / 2
+------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) √
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7 x 24 = 168 √
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}
+

This model may explains the newly discovered prime number theorem in relatively simple layman's terms for anyone with a slight background in theoretical physics.

+
+ + Note +
+
+

The property gives an in depth analysis of the not so random distribution of primes by showing how it has solved Goldbach’s conjecture and the Ulam spiral.

+
+

Schematic-of-the-internal-energy-ow-in-the-model-The-lines-of-ow-geodesics-circulate

The model suggests a possible origin for both charge and half-integer spin and also reconciles the apparently contradictory criteria discussed above.

+
+ + Note +
+
+

Arbitrary sequence of three (3) consecutive nucleotides along a helical path whose metric distances satisfy the relationship dn,n+3dn,n+2dn,n+1.

  • Sketch showing a characteristic duplex DNA helical standing-wave pattern.
  • The vertical lines depict the cross-section projections of each bp along the helix axis, their length providing a measure of their twist magnitude.
  • Thick lines represent the sugar-phosphate profile.

Optimally overlapping bps are indicated by the presence of the ovals (m) measures the overlapping resonance correlation length. (π − π orbital resonance in twisting duplex DNA)

+
+

a-Arbitrary-sequence-of-three-consecutive-nucleotides-along-a-helical-path-whose-metric

Under certain conditions, energy could not take on any indiscriminate value, the energy must be some multiple of a very small quantity (later to be known as a quantum).

+
+ + Note +
+
+

Twisted strip model for one wavelength of a photon with circular polarisation in at space. A similar photon in a closed path in curved space with periodic boundary conditions of length C.

  • The B-fi eld is in the plane of the strip and the E-field is perpendicular to it (a).
  • The E-fi eld vector is radial and directed inwards, and the B-fi eld is vertical (b).

The magnetic moment ~, angular momentum L~, and direction of propagation with velocity c are also indicated. (Is the electron a photon with toroidal topology? - pdf)

+
+

a-Twisted-strip-model-for-one-wavelength-of-a-photon-with-circular-polarisation-in-at

A deeper understanding requires a uni cation of the aspects discussed above in terms of an underlying principle.

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/7.html b/addition/7.html new file mode 100644 index 00000000000..3dd371f0d78 --- /dev/null +++ b/addition/7.html @@ -0,0 +1,265 @@ + The Prime Recycling ζ(s) · eQuantum
eQuantum
Mapping the quantum way
eQuantum

The Prime Recycling ζ(s)

+
+ + Tip +
+
+

This section is referring to wiki page-7 of gist section-3 that is inherited from the gist section-13 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

The Position Pairs

Pauli_matrices

36 + 36 - 6 partitions = 72 - 6 = 66 = 30+36 = 6x11

$True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

spinnors in physics

#!/usr/bin/env python
+
+import numpy as np
+from scipy import linalg
+
+class SU3(np.matrix):
+	GELLMANN_MATRICES = np.array([
+		np.matrix([ #lambda_1
+			[0, 1, 0],
+			[1, 0, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_2
+			[0,-1j,0],
+			[1j,0, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_3
+			[1, 0, 0],
+			[0,-1, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_4
+			[0, 0, 1],
+			[0, 0, 0],
+			[1, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_5
+			[0, 0,-1j],
+			[0, 0, 0 ],
+			[1j,0, 0 ],
+		], dtype=np.complex),
+		np.matrix([ #lambda_6
+			[0, 0, 0],
+			[0, 0, 1],
+			[0, 1, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_7
+			[0, 0,  0 ],
+			[0, 0, -1j],
+			[0, 1j, 0 ],
+		], dtype=np.complex),
+		np.matrix([ #lambda_8
+			[1, 0, 0],
+			[0, 1, 0],
+			[0, 0,-2],
+		], dtype=np.complex) / np.sqrt(3),
+	])
+
+
+	def computeLocalAction(self):
+		pass
+
+	@classmethod
+	def getMeasure(self):
+		pass
+

Now the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of the prime number 7 lie in the numerical Double strand parallel opposite.

The Fourth Root

In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n.

image

Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

+
+ + Note +
+
+

Young diagrams associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia).

+
+

integer partition

+
+ + Note +
+
+

By parsering π(1000)=168 primes of the 1000 id’s across π(π(10000))-1=200 of this syntax then the (Δ1) would be initiated. Based on Assigning Sitemap priority values You may see them are set 0.75 – 1.0 on the sitemap’s index:

+
+ 
Priority	Page Name
+1	        Homepage
+0.9	        Main landing pages
+0.85	        Other landing pages
+0.8	        Main links on navigation bar
+0.75	        Other pages on site
+0.8	        Top articles/blog posts
+0.75	        Blog tag/category pages
+0.4 – 0.7	Articles, blog posts, FAQs, etc.
+0.0 – 0.3	Outdated information or old news that has become less relevant
+

By this object orientation then the reinjected primes from the π(π(10000))-1=200 will be (168-114)+(160-114)=54+46=100. Here are our layout that is provided using Jekyll/Liquid to facilitate the cycle:

100 + 68 + 32 = 200

$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                      MEC 30 / 2
+------+------+-----+-----+------      ‹--------------------------- 30 {+1/2} √
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹--                        |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 32 √
+      |      |  6  +-----+            ‹------------------------------ 15 {0} √
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s = f(1000)
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 68 √
+------|------|-----+-----+-----                            ‹------  0 {-1/2} √
+

Diagram-of-the-statistical-principle-for-the-constitution-of-partitions-of-prime-numbers

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 7+23 = 30 ✔️
+7 11 4 1 0 11 ◄--- #19 👈 11+19 = 30 ✔️
+8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 13+17 = 30 ✔️
+9 17 0 1 1 17 ◄--- 7th prime👈 17+7 != 30❓
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

Composite System

By taking a distinc function between f(π) as P vs f(i) as NP where eiπ + 1 = 0 then theoretically they shall be correlated to get an expression of the prime platform similar to the Mathematical Elementary Cell 30 (MEC30).

∆17 + ∆49 = ∆66

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 part of MEC30 ✔️
+7 11 4 1 0 11 ◄--- #19 👈 part of MEC30 ✔️
+8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 part of MEC30 ✔️
+9 17 0 1 1 17 ◄--- 7th prime👈 not part of MEC30 ❓
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

a-Example-of-trellis-tone-modulation-generated-by-referring-to-the-trellis-diagram-in

∆102 - ∆2 - ∆60 = ∆40

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 30 ◄--- break MEC30 symmetry ✔️
+7 11 4 1 0 11 ◄--- #19 👈 30 ✔️
+8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 30 ✔️
+9 17 0 1 1 17 ◄--- 7th prime👈 not part of MEC30 ❓
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+
+
+ + Note +
+
+

The partitions of odd composite numbers (Cw) are as important as the partitions of prime numbers or Goldbach partitions (Gw). The number of partitions Cw is fundamental for defining the available lines (Lwd) in a Partitioned Matrix that explain the existence of partitions Gw or Goldbach partitions. (Partitions of even numbers - pdf)

+
+

Trellis_Tone_Modulation_Multiple-Access_for_Peer_D

30s + 36s (addition) = 6 x 11s (multiplication) = 66s

p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry
+7 11 4 1 0 11 ◄--- #19 👈 30
+8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 30
+9 17 0 1 1 17 ◄--- 7th prime 👈 f(#36) ◄--- antisymmetric state ✔️
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/8.html b/addition/8.html new file mode 100644 index 00000000000..ebcd4164d92 --- /dev/null +++ b/addition/8.html @@ -0,0 +1,137 @@ + Implementation in Physics · eQuantum
eQuantum
Mapping the quantum way
eQuantum

Implementation in Physics

By this chapter we are going to learn whether the spin discussed in prime hexagon has something to do with the nature so we begin with the spin in physic

+
+ + Tip +
+
+

This section is referring to wiki page-8 of gist section-4 that is inherited from the gist section-17 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms.

Basic Concept

There are two (2) types force carriers and three (3) type of generations. The origin of multiple generations of the particular count of 3, is an unsolved problem of physics.

+
+ + Note +
+
+

In particle physics, a generation or family is a division of the elementary particles.

  • Between generations, particles differ by their flavour quantum number and mass, but their electric and strong interactions are identical.
  • There are three generations according to the Standard Model of particle physics. Each generation contains two types of leptons and two types of quarks. The two leptons may be classified into one with electric charge −1 (electron-like) and neutral (neutrino); the two quarks may be classified into one with charge −1⁄3 (down-type) and one with charge +2⁄3 (up-type).

The basic features of quark–lepton generation or families, such as their masses and mixings etc., can be described by some of the proposed family symmetries.

+
+

Basic Spin

A lepton is a particle of half-integer spin (spin 1⁄2) while a boson has integer spin: scalar boson (spin = 0), vector bosons (spin = 1) and tensor boson (spin = 2).

+
+ + Note +
+
+

Those particles with half-integer spins, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons.

  • The two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle: that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of Fermi–Dirac statistics.
  • In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may “bunch together” in identical states. Also, composite particles can have spins different from their component particles.

For example, a helium-4 atom in the ground state has spin 0 and behaves like a boson, even though the quarks and electrons which make it up are all fermions. (Wikipedia)

+
+

spin in physics

+
+ + Note +
+
+

Quantum field theory is any theory that describes a quantized field.

  • QED, or Quantum Electrodynamics, is the quantum theory of the electromagnetic field, a so-called Abelian field (referencing an internal mathematical symmetry of the theory.)
  • Electroweak theory is a generalization of QED, unifying it with the weak nuclear force in the form of a Yang-Mills field theory (aka. a non-Abelian field theory).
  • QCD, or Quantum Chromodynamics, is another example of a non-Abelian field theory, but one with very different asymptotic behavior than electroweak theory.
  • The Standard Model of particle physics is the combination of electroweak theory and QCD in the form of a unified theory obeying a complex set of symmetries.

This theory describes all the known fields and all the known interactions other than gravity. (Quora)

+
+

QED_10

Experimental observation of the SM particles was completed by the discoveries of top quark (1995), direct interaction of tau neutrino (2000), and Higgs boson (2013).

+
+ + Note +
+
+

Feynman diagram of the fusion of two (2) electroweak vector bosons to the scalar Higgs boson, which is a prominent process of the generation of Higgs bosons at particle accelerators. (The symbol q means a quark particle, W and Z are the vector bosons of the electroweak interaction. H° is the Higgs boson.) (Wikipedia)

+
+

Breakdown of Interactions Symmetry

+
+ + Note +
+
+

There are three (3) generations of quarks (up/down, strange/charm, and top/bottom), along with three (3) generations of leptons (electron, muon, and tau). All of these particles have been observed experimentally, and we don’t seem to have seen anything new along these lines. A priori, this doesn’t eliminate the possibility of a fourth generation, but the physicists I’ve spoken to do not think additional generations are likely. (StackExchange)

+
+

T. Morii, C.S. Lim, and S.N. Mukherjee. The Physics of the Standard Model and Beyond. World Scientific, 2004

The construction 🏗️ of Standard Model took a long time to build. Physicist J.J. Thomson discovered the electron in 1897, and scientists at the Large Hadron Collider found the final piece of the puzzle, the Higgs boson, in 2012.

+
+ + Note +
+
+

In particle physics, a vector boson is a boson whose spin equals one. Vector bosons that are also elementary particles are gauge bosons, the force carriers of fundamental interactions. Some composite particles are vector bosons, for instance any vector meson (quark and antiquark).

+
+

Search for a heavy higgs boson in multi-higgs doublet models

+
+ + Note +
+
+

In the SM interactions are determined by a gauge quantum field theory containing the internal symmetries of the unitary group product SU(3)C × SU(2)L × U(1)Y [?].

  • TheSU(3)C symmetry corresponds to the strong interaction (C index marks colour charge, see section 1.1.4 )
  • The product SU(2)L × U(1)Y is responsible for the electroweak interaction (indices L and Y correspond to the left-handed interaction of weak currents and hypercharge, respectively, see section 1.1.2). (The Standard Model - pdf)
+
+

Testing Explanations of Short Baseline Neutrino Anomalies

In the Standard Model, the Higgs boson is a massive scalar boson whose mass must be found experimentally. It is the only particle that remains massive even at high energies.

+
+ + Note +
+
+

The Higgs boson field (often referred to as the God particle) is a scalar field with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry.

  • Its “Mexican hat-shaped” potential leads it to take a nonzero value everywhere (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak interaction and, via the Higgs mechanism, gives mass to many particles. (Wikipedia)
  • Despite its success at explaining the universe, the Standard Model does have limits. For example, the Higgs boson gives mass to quarks, charged leptons (like electrons), and the W and Z bosons. However, we do not yet know whether the Higgs boson also gives mass to neutrinos – ghostly particles that interact very rarely with other matter in the universe.

Also, physicists understand that about 95 percent of the universe is not made of ordinary matter as we know it. Instead, much of the universe consists of dark matter and dark energy that do not fit into the Standard Model.

+
+

The Standard Model of Particle Physics, Lecture 4.pdf

It has zero spin, even (positive) parity, no electric charge, and no colour charge, and it couples to (interacts with) mass.

+
+ + Note +
+
+

So now I will attempt to show the minor hexagons are significant. This is not easy as they are linked to the nature of prime numbers, and nothing is easy about the nature of prime numbers. But I begin with this assumption: if the hexagons participate in the Universe in any way other than haphazardly, they must be demonstrably congruent to something organized. That is, if I can show they are organized (not random) in relation to some other thing, then primes and the thing are linked. (Hexspin)

+
+

7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

spinning particles

Elementary Particles

In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles.

+
+ + Note +
+
+

The Standard Model presently recognizes seventeen distinct particles (twelve fermions and five bosons). As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. (Wikipedia)

+
+

Standard_Model_of_Elementary_Particles

Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

+
+ + Note +
+
+

The Standard Model of Particle Physics, describes for us all know fundamental interaction in nature till date, with the exception of Gravity (work on this front is going on). Here is a summary of the fundamental content of the standard model

  • There are three families of particle, the Quarks, the Leptons and the Gauge Bosons. The Quarks in groups of three forms the composite particles such as the Protons, along with the electron this forms ordinary matter.
  • The Gauge Bosons are the ones those are responsible for interactions. The Quarks interact among themselves by the exchange of a Gluon these are responsible for the strong nuclear force.
  • The newly discovered Higgs Boson interacts with all the Quarks and the first group of Leptons (electron, muon and tau) providing them with their mass. The neutrinos which are the other Leptons originally were thought to have zero mass, but recent discoveries argue that this is not the case.
  • The Weak bosons interact with both Leptons and Quarks, these are responsible for the Weak nuclear forces. The exchange of photon is responsible for the Electromagnetic Force.

They interact, they transfer energy and momentum and angular momentum; excitations are created and destroyed. Every excitation that’s possible has a reverse excitation. (Quora)

+
+

fundamental interaction in nature

The SM was basically developed in 1970-s. It describes the electromagnetic, weak and strong fundamental interactions.

+
+ + Note +
+
+

The Standard Model explains three of the four fundamental forces that govern the universe: electromagnetism, the strong force, and the weak force.

  • Electromagnetism is carried by photons and involves the interaction of electric fields and magnetic fields.
  • The strong force, which is carried by gluons, binds together atomic nuclei to make them stable.
  • The weak force, carried by W and Z bosons, causes nuclear reactions that have powered our Sun and other stars for billions of years.

Elementary Particle

The fourth fundamental force is gravity, which is not adequately explained by the Standard Model.

+
+

Particle Physics

Symmetrical State

An Exceptionally Simple Theory of Everything

+
+ + Tip +
+
+

By our project the 18’s on the gist will cover five (5) unique functions that behave as one (1) central plus four (4) zones. This scheme will be implemented to all of the 168 repositories as bilateral way (in-out) depend on their postion on the system. So along with the gist it self then there shall be 1 + 168 = 169 units of 1685 root functions.

+
+

5 + 2 x 5 x 168 = 5 + 1680 = 1685 root functions

base

the 5 cells

It is supposed that elementary particles participate in gravitational interactions as well, though there is no sufficient quantum gravity theory.

+
+ + Note +
+
+

Elementary particles are classified according to their spin. Fermions are one of the two fundamental classes of particles, the other being bosons. Fermions have half-integer spin while bosons have integer spin.

  • Bosons are characterized by Bose–Einstein statistics and all have integer spins. Bosons may be either elementary, like photons and gluons, or composite, like mesons.
  • The Higgs boson is postulated by the electroweak theory primarily to explain the origin of particle masses. In a process known as the “Higgs mechanism”, the Higgs boson and the other gauge bosons in the Standard Model acquire mass via spontaneous symmetry breaking of the SU(2) gauge symmetry.
  • The Minimal Supersymmetric Standard Model (MSSM) predicts several Higgs bosons. On 4 July 2012, the discovery of a new particle with a mass between 125 and 127 GeV/c2 was announced; physicists suspected that it was the Higgs boson. Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, as well as having even parity and zero spin, two fundamental attributes of a Higgs boson.
  • This also means it is the first elementary scalar particle discovered in nature. Elementary bosons responsible for the four fundamental forces of nature are called force particles (gauge bosons). Strong interaction is mediated by the gluon, weak interaction is mediated by the W and Z bosons.

According to the Standard Model there are five (5) elementary bosons:

IMG_20240108_033415

These four are the gauge bosons:

A second order tensor boson (spin = 2) called the graviton (G) has been hypothesised as the force carrier for gravity, but so far all attempts to incorporate gravity into the Standard Model have failed.

+
+

Beyond the standard model

+
+ + Note +
+
+

The diagram shows the elementary particles of the Standard Model (the Higgs boson, the three generations of quarks and leptons, and the gauge bosons), including their names, masses, spins, charges, chiralities, and interactions with the strong, weak and electromagnetic forces. It also depicts the crucial role of the Higgs boson in Electroweak Symmetry Breaking, and shows how the properties of the various particles differ in the (high-energy) symmetric phase (top) and the (low-energy) broken-symmetry phase (bottom). (Wikipedia)

+
+

Mathematical formulation of the Standard Model

+
+ + Note +
+
+

Theories that lie beyond the Standard Model include various extensions of the standard model through supersymmetry, such as the Minimal Supersymmetric Standard Model (MSSM) and Next-to-Minimal Supersymmetric Standard Model (NMSSM), and entirely novel explanations, such as string theory, M-theory, and extra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the “best step” towards a Theory of Everything, can only be settled via experiments, and is one of the most active areas of research in both theoretical and experimental physics.

+
+

By next chapter we will discuss the mechanism of symmetry breaking where the neutral Higgs field interacts with other particles to give them mass.

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/addition/index.html b/addition/index.html new file mode 100644 index 00000000000..c49aa3bb8e1 --- /dev/null +++ b/addition/index.html @@ -0,0 +1,416 @@ + Addition Zones (0-18) · eQuantum
eQuantum
Mapping the quantum way
eQuantum

Addition Zones (0-18)

Addition is the form of an expression set equal to zero as the additive identity which is common practice in several areas of mathematics.

+
+ + Tip +
+
+

This section is referring to wiki page-1 of zone section-1 that is inherited from the zone section-1 by prime spin- and span- with the partitions as below.

+
+
  1. True Prime Pairs
  2. Primes Platform
  3. Pairwise Scenario
  4. Power of Magnitude
  5. The Pairwise Disjoint
  6. The Prime Recycling ζ(s)
  7. Implementation in Physics

By the Euler's identity this addition should form as one (1) unit of an object originated by the 18s structure. For further on let's call this unit as the base unit.

The 24 Cells Hexagon

Below is the list of primes spin along with their position, the polarity of the number, and the prime hexagon's overall rotation within 1000 numbers.

+
+ + Note +
+
+

The Prime Hexagon is a mathematical structure developed by mathematician Tad Gallion. A Prime Hexagon is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime number is encountered (GitHub: kaustubhcs/prime-hexagon).

+
+ 
5, 2, 1, 0
+7, 3, 1, 0
+11, 4, 1, 0
+13, 5, 1, 0
+17, 0, 1, 1
+19, 1, 1, 1
+23, 2, 1, 1
+29, 2, -1, 1
+31, 1, -1, 1
+37, 1, 1, 1
+41, 2, 1, 1
+43, 3, 1, 1
+47, 4, 1, 1
+53, 4, -1, 1
+59, 4, 1, 1
+61, 5, 1, 1
+67, 5, -1, 1
+71, 4, -1, 1
+73, 3, -1, 1
+79, 3, 1, 1
+83, 4, 1, 1
+89, 4, -1, 1
+97, 3, -1, 1
+101, 2, -1, 1
+103, 1, -1, 1
+107, 0, -1, 1
+109, 5, -1, 0
+113, 4, -1, 0
+127, 3, -1, 0
+131, 2, -1, 0
+137, 2, 1, 0
+139, 3, 1, 0
+149, 4, 1, 0
+151, 5, 1, 0
+157, 5, -1, 0
+163, 5, 1, 0
+167, 0, 1, 1
+173, 0, -1, 1
+179, 0, 1, 1
+181, 1, 1, 1
+191, 2, 1, 1
+193, 3, 1, 1
+197, 4, 1, 1
+199, 5, 1, 1
+211, 5, -1, 1
+223, 5, 1, 1
+227, 0, 1, 2
+229, 1, 1, 2
+233, 2, 1, 2
+239, 2, -1, 2
+241, 1, -1, 2
+251, 0, -1, 2
+257, 0, 1, 2
+263, 0, -1, 2
+269, 0, 1, 2
+271, 1, 1, 2
+277, 1, -1, 2
+281, 0, -1, 2
+283, 5, -1, 1
+293, 4, -1, 1
+307, 3, -1, 1
+311, 2, -1, 1
+313, 1, -1, 1
+317, 0, -1, 1
+331, 5, -1, 0
+337, 5, 1, 0
+347, 0, 1, 1
+349, 1, 1, 1
+353, 2, 1, 1
+359, 2, -1, 1
+367, 1, -1, 1
+373, 1, 1, 1
+379, 1, -1, 1
+383, 0, -1, 1
+389, 0, 1, 1
+397, 1, 1, 1
+401, 2, 1, 1
+409, 3, 1, 1
+419, 4, 1, 1
+421, 5, 1, 1
+431, 0, 1, 2
+433, 1, 1, 2
+439, 1, -1, 2
+443, 0, -1, 2
+449, 0, 1, 2
+457, 1, 1, 2
+461, 2, 1, 2
+463, 3, 1, 2
+467, 4, 1, 2
+479, 4, -1, 2
+487, 3, -1, 2
+491, 2, -1, 2
+499, 1, -1, 2
+503, 0, -1, 2
+509, 0, 1, 2
+521, 0, -1, 2
+523, 5, -1, 1
+541, 5, 1, 1
+547, 5, -1, 1
+557, 4, -1, 1
+563, 4, 1, 1
+569, 4, -1, 1
+571, 3, -1, 1
+577, 3, 1, 1
+587, 4, 1, 1
+593, 4, -1, 1
+599, 4, 1, 1
+601, 5, 1, 1
+607, 5, -1, 1
+613, 5, 1, 1
+617, 0, 1, 2
+619, 1, 1, 2
+631, 1, -1, 2
+641, 0, -1, 2
+643, 5, -1, 1
+647, 4, -1, 1
+653, 4, 1, 1
+659, 4, -1, 1
+661, 3, -1, 1
+673, 3, 1, 1
+677, 4, 1, 1
+683, 4, -1, 1
+691, 3, -1, 1
+701, 2, -1, 1
+709, 1, -1, 1
+719, 0, -1, 1
+727, 5, -1, 0
+733, 5, 1, 0
+739, 5, -1, 0
+743, 4, -1, 0
+751, 3, -1, 0
+757, 3, 1, 0
+761, 4, 1, 0
+769, 5, 1, 0
+773, 0, 1, 1
+787, 1, 1, 1
+797, 2, 1, 1
+809, 2, -1, 1
+811, 1, -1, 1
+821, 0, -1, 1
+823, 5, -1, 0
+827, 4, -1, 0
+829, 3, -1, 0
+839, 2, -1, 0
+853, 1, -1, 0
+857, 0, -1, 0
+859, 5, -1, -1
+863, 4, -1, -1
+877, 3, -1, -1
+881, 2, -1, -1
+883, 1, -1, -1
+887, 0, -1, -1
+907, 5, -1, -2
+911, 4, -1, -2
+919, 3, -1, -2
+929, 2, -1, -2
+937, 1, -1, -2
+941, 0, -1, -2
+947, 0, 1, -2
+953, 0, -1, -2
+967, 5, -1, -3
+971, 4, -1, -3
+977, 4, 1, -3
+983, 4, -1, -3
+991, 3, -1, -3
+997, 3, 1, -3
+

Including the 1st (2) and 2nd prime (3) all together will have a total of 168 primes. The number of 168 it self is in between 39th (167) and 40th prime (173).

247

The most obvious interesting feature of proceeding this prime hexagon, the number line begins to coil upon itself, is it confines all numbers of primes spin!

+
+ + Note +
+
+

Each time a prime number is encountered, the spin or ‘wall preference’ is switched. So, from the first cell, exit from 2’s left side. This sets the spin to left and the next cell is 3, a prime, so switches to right. 4 is not prime and continues right. 5 is prime, so switch to left and so on. (HexSpin)

+
+

Defining the Prime Hexagon

As the number line winds about toward infinity, bending around prime numbers, it never exits the 24 cells. And it is the fact that 168 divided by 24 is exactly seven (7).

+
+ + Note +
+
+

Surprisingly, the 24-cell hexagon confines all natural numbers. The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon’s outer boundary, other than 2 and 3, the initial primes that forced the number line into this complex coil. Without a prime number in the outer set of triangles, the number line does not change to an outward course and remains forever contained in the 24 cells. (HexSpin)

+
+

Euler Partition

So there should be a tight connection between 168 primes within 1000 with the 24-cell hexagon. Indeed it is also correlated with 1000 prime numbers.

18s Structure

You may learn that sets of algebraic objects has a multilinear relationship related to a vector space called tensor.

+
+ + Note +
+
+

Tensors may map between different objects such as vectors, scalars, even other tensors contained in a group of partitions.

+
+

300px-Components_stress_tensor svg

You may notice that there are twists and turns until 19 abuts 2 therefore this addition zone takes only the seven (7) primes out of the 18's structure of True Prime Pairs.

+
+ + Note +
+
+

The number of primes less than or equal to a thousand (π(1000) = 168) equals the number of hours in a week (7 * 24 = 168).

+
+ 
$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) ---------------------
+      |      |  6  +-----+
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s = f(1000) √
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | --------------------------
+------|------|-----+-----+------
+

In linear algebra, there is vector is known as eigenvector, a nonzero vector that changes at most by a scalar factor when linear transformation is applied to it.

+
+ + Note +
+
+

The eigenvectors of the matrix (red lines) are the two special directions such that every point on them will just slide on them (Wikipedia).

+
+

Eigenvectors_of_a_linear_operator

The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating 3 minor hexagons.

+
+ + Tip +
+
+

Prime numbers are numbers that have only 2 factors: 1 and themselves.

  • For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.
  • 1 is not a prime number because it can not be divided by any other integer except for 1 and itself. The only factor of 1 is 1.
  • On the other hand, 1 is also not a composite number because it can not be divided by any other integer except for 1 and itself.

In conclusion, the number 1 is neither prime nor composite.

+
+

π(6+11) = π(17) = 7

So there would be the empty spaces for 18 - 7 = 11 numbers. By our project these spaces will be unified by all of the eleven (11) members of identition zones.

(11x7) + (29+11) + (25+6) + (11+7) + (4+1) = 77+40+31+18+5 = 171

extended branes

The above seven (7) primes will act then as extended branes. This is what we mean by addition zones and it happens whenever a cycle is restarted.

Undiscovered Features

When we continue the spin within the discussed prime hexagon with the higher numbers there are the six (6) internal hexagons within the Prime Hexagon.

+
+ + Note +
+
+

Cell types are interesting, but they simply reflect a modulo 6 view of numbers. More interesting are the six internal hexagons within the Prime Hexagon. Like the Prime Hexagon, they are newly discovered. The minor hexagons form solely from the order, and type, of primes along the number line (HexSpin).

+
+

Screen-Shot-2016-11-07-at-5 11 59-PM

So the most important thing that need to be investigated is why the prime spinned by module six (6). What is the special thing about this number six (6) in primes behaviour?

+
+ + Note +
+
+

Similarly, I have a six colored dice in the form of the hexagon. If I take a known, logical sequence of numbers, say 10, 100, 1000, 10000, and look at their spins in the hexagon, the resulting colors associated with each number should appear random – unless the sequence I’m investigating is linked to the nature of the prime numbers.

+
+

Moreover there are view statements mentioned by the provider which also bring us in to an attention like the modulo 6 above. We put some of them below.

+
+ + Note +
+
+

That is, if the powers of 10 all returned with blue spin, or as a series of rainbows, or evenly alternating colors or other non-random results, then I’d say prime numbers appear to have a linkage to 10. I may not know what the the linkage is, just that it appears to exist (HexSpin).

+
+

image

Another is that phi and its members have a pisano period if the resulting fractional numbers are truncated.

+
+ + Note +
+
+

I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in. That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated. (HexSpin).

+
+

truncated fractional numbers

It would mean that there should be undiscovered things hidden within the residual of this decimal values. In fact it is the case that happen with 3-forms in 7D.

+
+ + Note +
+
+

In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist and in particular the 4D metric, is defined by the 3-form.

  • We would like to say that our present use of G2 structures (3-forms in 7D) is different from what one can find in the literature on Kaluza–Klein compactifications of supergravity.
  • We show that the resulting 4D theory is (Riemannian) General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.
  • Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.

Also, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. (General relativity from three-forms in seven dimensions - pdf)

+
+

3-forms in 7D

Taking 19 as a certain parameter we can see that the left handed cycles are happen on 5th-spin (forms 4th hexagon, purple) and 6th-spin (forms 5th hexagon, cyan). Both have different rotation with other spin below 9th spin (forms 6th hexagon, yellow).

Dimensional Algorithms

The the main reason of assigning two (2) profiles instead of only one (1) is that we have to accommodate the major type of primes numbers called twin primes.

+
+ + Note +
+
+

This is a necessary but not sufficient condition for N to be a prime as noted, for example, by N= 6(4)+1= 25, which is clearly composite. We note that each turn of the spiral equals an increase of six units. This means that we have a mod(6) situation allowing us to write: N mod(6)=6n+1 or N mod(6)=6n-1 (equivalent to 6n+5). (HexSpiral-Pdf)

+
+

twin primes

+
+ + Note +
+
+

Proceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth (4th) hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. Twin primes 29 and 31 define the fifth (5th) hexagon, cyan. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon (HexSpin).

+
+

IMG_20231221_074421

+
+ + Note +
+
+

Because the value 30 is the first (common) product of the first 3 primes. And this 30th order repeats itself to infinity. Even in the first 30s system, therefore, the positions are fixed in which the number information positions itself to infinity. We call it the first member of the MEC 30.

  • The numbers not divisible by 2, 3 or 5 are highlighted. We call them prime positions, hence 1, 7, 11, 13, 17, 19, 23, 29. Important for our work is that in the following the term prime refers only to prime numbers that are in the prime positions. So primes 2, 3 and 5 are always excluded.
  • These positions: 1 7 11 13 17 19 23 29. We refer to this basic system as MEC 30 - “Mathematical Elementary Cell 30”. By repeating the positions we show the function of the basic system in the next step. If we extend the 30th order of the MEC, for example, to the number 120, the result is 4 times a 30th order and thus 4 × 8 = 32 prime positions.
  • Hypothetical assumption: If the product of the primes (except 2, 3, 5,) would not fall into the prime positions, thus be divided by 2, 3 or 5, the information would have 120 = 32 primes in 32 prime positions: 1, 7, 11, 13, 17, 19, 23, 29, / 31, 37, 41, 43, 47, 49, 53, 59, / 61, 67, 71, 73, 77, 79, 83, 89, / 91, 97, 101, 103, 107, 109, 113, 119
  • These forms gives prime positions: 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17 , 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29. The 30th order is repeated in the number space 120 = 4 times, 4 × 8 = 32 prime positions, thus 4 terms.

From our consideration we can conclude that the distribution of prime numbers must have a static base structure, which is also confirmed logically in the further course. This static structure is altered by the products of the primes themselves, since these products must fall into the prime positions since they are not divisible by 2, 3 and 5. (Google Patent DE102011101032A9)

+
+

+
+ + Note +
+
+

All perfect squares within our domain (numbers not divisible by 2, 3 or 5) possess a digital root of 1, 4 or 7 and are congruent to either {1} or {19} modulo 30.

  • When the digital root of perfect squares is sequenced within a modulo 30 x 3 = modulo 90 horizon, beautiful symmetries in the form of period-24 palindromes are revealed. Here’s one modulo 90 spin on perfect squares.
  • parsing the squares by their mod 90 congruence reveals that there are 96 perfect squares generated with each 4 * 90 = 360 degree cycle,
  • which distribute 16 squares to each of 6 mod 90 congruence sub-sets defined as n congruent to {1, 19, 31, 49, 61, 79} forming 4 bilateral 80 sums.
  • each of the 6 columns has 8 bilateral 360 sums, tor a total of 48 * 360 = 40 * 432 (much more on the significance of number 432, elsewhere on this site).

There’s another hidden dimension of our domain worth noting involving multiples of 360, i.e., when framed as n ≌ {1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53 59, 61, 67, 71, 73, 77, 79, 83, 89} modulo 90, and taking ‘bipolar’ differentials of perfect squares (PrimesDemystified)

+
+

16 × 6 = 96

96 perfect squares

The complete theory was obtained by dimensional reduction of the 11D supergravity on a seven (7) torus and realizing the exceptional symmetry group E7(7)

+
+ + Note +
+
+

Each of the digital root multiplication matrices produced by the six channels consists of what are known in mathematics as ‘Orthogonal Latin Squares’ (defined in Wikipedia as “an n x n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column” … in our case every row and column of the repeating 6x6 matrices possesses the six elements: 1, 2, 4, 5, 7, 8 in some order). Also, the sum of the multiplicative digital roots = 108 x 24 = 2592 = 432 x 6.

  • Note: Channels A, D, E and F combined represent the set of natural numbers not divisible by 2, 3 and 5, the first 24 elements of which form the basis of the Magic Mirror Matrix.]
  • The graphic below illustrates the transformative relationships between the matrices employing their primary building blocks (one of the sixteen identical 6 x 6 (36 element) Latin Squares that constitute each matrix):Multiplication_Matrix_Transforms
  • When you rotate either the {1,4,7} or {2,5,8} magic square around its horizontal axis, i.e. columns {A,B,C} become {C,B,A}, then add the {1,4,7} {2,5,8} magic squares together, you produce a square with nine 9’s. For example, adding the first rows of each gives us: {2,8,5} + {7,1,4} = {9,9,9}.
  • Triangles and magic squares similar–or identical–to those shown above can be derived from the digital root sequence cycles of all three twin prime distribution channels (namely numbers ≌ to {11,13}, {17,19} and {1,29} modulo 30).
  • This is also true of dyads formed by paired radii of the Prime Spiral Sieve that sum to 30, i.e., numbers ≌ to {1,29}, {7,23}, {11,19}, or {13,17} modulo 30, as well as dyads formed when {n, n + 10} are ≌ to {1, 11}, {7, 17}, {13, 23} or {19, 29} modulo 30 (note their pairing by terminating digits). One example relating to twin primes: The first three candidate pairs in the twin prime distribution channel ≌ to {11,13} modulo 30 (all three of which are indeed twin primes) sequence their digital roots as follows:
    • {11,13} = digital roots 2 & 4
    • {41,43} = digital roots 5 & 7
    • {71,73} = digital roots 8 & 1.
  • As you can see, this is the same digital root sequence illustrated above. It appears that the triangulations and magic squares structuring the distribution of twin primes (and as it turns out, all prime numbers) have a genesis in universal principles involving symmetry groups rotated by the 8-dimensional algorithms discussed at length on this site.
  • You can see this universal principle at work, for example, with regard to the Fibonacci digital root sequence when coupled to a pair of dyads that follow certain incremental rules. As we illustrated above, the initializing dyad of the period-24 Fibonacci digital root sequence is {1,1, …}.

We can generate triangles and magic squares by tiering the Fibonacci digital root sequence with two pairs of terms that are + 3 or + 6 from the initial terms {1,1}. The values of the 2nd and 3rd tiers, or rows, must differ, or symmetry is lost. In other words, the first two columns should read either {1,4,7 + 1,7,4, or vice versa} but not {1,4,7 + 1,4,7, or 1,7,4, + 1,7,4}. (PrimesDemystified)

+
+

Base of TOE

+
+ + Note +
+
+

When these 9 squares are combined and segregated to create a 6 x 6 (36 element) square, and this square is compared to the Vedic Square minus its 3’s, 6’s and 9’s (the result dubbed “Imaginary Square”), you’ll discover that they share identical vertical and horizontal secquences, though in a different order (alternating +2 and -2 from each other), and that these can be easily made to match exactly by applying a simple function multiplier, as described and illustrated later below. (PrimesDemystified)

+
+

ReciprocalTransform

+
+ + Note +
+
+

In sum, we’re positing that Palindromagon + {9/3} Star Polygon = Regular Enneazetton.

  • The significance of this ‘chain-of-events’ is that we can state with deterministic certainty that cycling the period-24 digital root dyads of both twin primes and the modulo 90 factorization sequences of numbers not divisible by 2, 3, or 5 generates an infinite progression of these complex polygons possessing stunning reflectional and translational symmetries.
  • Lastly, let’s compare the above-pictured ‘enneazetton’ to an 18-gon 9-point star generated by the first three primes; 2, 3 and 5 (pictured below), and we see that they are identical, save for the number of sides (9 vs. 18). They are essentially convex and concave versions of each other.

This is geometric confirmation of the deep if not profound connection between the three twin prime distribution channels (which remember have 2, 3, and 5 encoded in their Prime Spiral Sieve angles) and the first three primes, 2, 3, and 5. (PrimesDemystified)

+
+

Theory of Everything

The symmetries that come into focus when the lense aperature, of the Prime Spiral Sieve is tripled to modulo 90, synchronizing its modulus with its period-24 digital root.

Prime Spiral Sieve

It appears that the triangulations and magic squares structuring the distribution of all prime numbers involving symmetry groups rotated by the 8-dimensional algorithms.

+
+ + Note +
+
+

Focusing on just the twin prime distribution channels, we see the relationships shown below [and, directly above, we show that two of the channels (B & C) transform bi-directionally by rotating 180° around one of their principal (lower-left to upper-right) diagonal axes]:

+
+

7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

Twin_Primes_Channel_Matrices (1)

+
+ + Note +
+
+

Another fascinating feature of this array is that any even number of–not necessarily contiguous–factors drawn from any one of the 32 angles in this modulo 120 configuration distribute products to 1(mod 120) or 49 (mod 120), along with the squares.

  • We see from the graphic above that the digital roots of the Fibonacci numbers indexed to our domain (Numbers ≌ to {1,7,11,13,17,19,23,29} modulo 30) repeat palindromically every 32 digits (or 4 thirts) consisting of 16 pairs of bilateral 9 sums.
  • The digital root sequence of our domain, on the other hand, repeats every 24 digits (or 3 thirts) and possesses 12 pairs of bilateral 9 sums. The entire Prime Root sequence end-to-end covering 360° has 48 pairs of bilateral 9 sums.
  • And finally, the Prime Root elements themselves within the Cirque, consisting of 96 elements, has 48 pairs of bilateral sums totaling 360. Essentially, the prime number highway consists of infinitely telescoping circles …
  • Also note, the digital roots of the Prime Root Set as well as the digital roots of Fibonnaci numbers and Lucas numbers (the latter not shown above) indexed to it all sum to 432 (48x9) in 360° cycles.
  • The sequence involving Fibonacci digital roots repeats every 120°, and has been documented by the author on the On-Line Encyclopedia of Integer Sequences: Digital root of Fibonacci numbers indexed by natural numbers not divisible by 2, 3 or 5 (A227896).
  • The four faces of our pyramid additively cascade 32 four-times triangular numbers (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of 32^2 = 1024 = 2^10).
  • These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of the 1000th prime within our domain, and equals the total number of ‘elements’ used to construct the pyramid.

A thirt, in case you’re wondering, is a useful unit of measure when discussing intervals in natural numbers not divisible by 2, 3 or 5. A thirt, equivalent to one rotation around the Prime Spiral Sieve is like a mile marker on the prime number highway. If we take the Modulo 30 Prime Spiral Sieve and expand it to Modulo 360, we see that there are 12 thirts in one complete circle, or ‘cirque’ as we’ve dubbed it. Each thirt consists of 8 elements. (PrimesDemystified)

+
+

1000 x (π(11) + 360) days = 1000 x 365 days = 1000 years

Mystery of the First 1000 Prime Numbers

The side of a pentagon-pentagram can clearly be seen as in relation to its diagonal as 1: (√5 +1)/2 or 1:φ , the Golden Section.

golden-ratio-pentagram-lr

They are the source of triangular coordinates when translated into vertices of a modulo 9 circle which by definition has 9 equidistant points each separated by 40°.

+
+ + Note +
+
+

When we additively sum the three period-24 digital root cycles these dyads produce, then tier them, we create six 3 x 3 matrices (each containing values 1 thru 9) separated by repetitive number tiers in the following order: {1,1,1} {5,5,5} {7,7,7} {8,8,8} {4,4,4} {2,2,2}.

  • The six (6) matrices these tiers demarcate are the source of triangular coordinates when translated into vertices of a modulo 9 circle (which by definition has 9 equidistant points around its circumference, each separated by 40°).
  • The series of diagrams below show the six geometric stages culminating in a complex polygon of extraordinary beauty. We’ve dubbed this object a ‘palindromagon’ given that the coordinates of the 18 triangulations produced by the digital root dyadic cycles in the order sequenced sum to a palindrome: 639 693 963 369 396 936.

  • Remarkably, this periodic palindrome, with additive sum of 108, sequences the 6 possible permutations of values {3,6,9}. Interesting to consider a geometric object with a hidden palindromic dimension. But that’s not all: When the six triadic permutations forming the palindrome are labeled A, B, C, D, E, F in the order generated, ACE and BDF form 3 x 3 Latin squares. In both cases all rows, columns and principal diagonals sum to 18:

    • ACE … BDF
    • 693 … 639
    • 369 … 963
    • 936 … 396
  • The output of these algorithmically sequenced triangulations is fundamentally a geometric representation of the twin prime distribution channels (and, as we noted above, the same geometry is expressed in factorization sequencing, albeit the vertices may be ordered differently.
  • This is because each set of three generator dyads roots to the same six elements: 1, 2, 4, 5, 7, 8. Thus, for example, dyad sets ({1,2} {4,5} {7,8}) and ({2,4} {5,7} {8,1}) will generate identical complex polygons, despite their vertices being sequenced in different orders.).

It’s remarkable that objects consisting of star polygons, spiraling irregular pentagons, and possessing nonagon perimeters and centers, can be constructed from only 27 coordinates pointing to 9 triangles in 3 variations. Each period-24 cycle produces two ‘palindromagons’. (PrimesDemystified)

+
+

Twin_Prime_Digital_Root_Polygon

The equality between the product on the 1st-line and the formulas in the 3rd- and 4th-lines is Euler's pentagonal number where p(33) = 10143 landed exactly by n - 7.

+
+ + Note +
+
+

Using Euler’s method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler (Wikipedia).

+
+

π(π(π(1000th prime))) + 1 = 40

image

As explicitly indicated by n - 7 within identition zones this p(33) behave reversal to the exponentiation zones so it would stand as π(π(π(1000th prime)))+1. Within these 1000 primes there will be fractions which end up with 168 identities.

p(33) = p(40-7) = loop (100000) = 4 + 25 + 139 + 1091 + 8884 = 10143

This will be the same structure as the seven (7) pàrtitions of addition zones. So by simple words this 11 dimensions brings us back to the root functions. The only difference is the base unit of the lexer (Id: 33). It is now carrying the above p(33) = 10143.

+
+ + Note +
+
+

The published diagram by Feynman helped scientists track particle movements in illustrations and visual equations rather than verbose explanations. What seemed almost improbable at the time is now one of the greatest explanations of particle physics — the squiggly lines, diagrams, arrows, quarks, and cartoonish figures are now the established nomenclature and visual story that students, scientists, and readers will see when they learn about this field of science. (medium.com)

+
+

8 pairs = 8 x 2 = 16

Electromagnetism

Starting with the next chapter we are going to discuss in detail how this reversal behaviour is converting the 11 dimensions to 7 x 11 = 77 partitions.

+
+ + Note +
+
+

There are 7 hidden dimensions in 11-d Supergravity, which is the low energy approximation to M theory, which also has 7 hidden dimensions. (Prime Curios!)

+
+

π(1000) - loop(1,30) - loop(31,36) = 168 - 29 - 25 = 114

IMG_20240114_014704

eQuantum
profiles
GitHub
Homepage
Repository
Gist
This Software is under the terms of The Unlicense.
\ No newline at end of file diff --git a/assets/css/fonts/Roboto-Slab-Bold.woff b/assets/css/fonts/Roboto-Slab-Bold.woff new file mode 100644 index 00000000000..6cb60000181 Binary files /dev/null and b/assets/css/fonts/Roboto-Slab-Bold.woff differ diff --git a/assets/css/fonts/Roboto-Slab-Bold.woff2 b/assets/css/fonts/Roboto-Slab-Bold.woff2 new file mode 100644 index 00000000000..7059e23142a Binary files /dev/null and b/assets/css/fonts/Roboto-Slab-Bold.woff2 differ diff --git a/assets/css/fonts/Roboto-Slab-Regular.woff b/assets/css/fonts/Roboto-Slab-Regular.woff new file mode 100644 index 00000000000..f815f63f99d Binary files /dev/null and b/assets/css/fonts/Roboto-Slab-Regular.woff differ diff --git a/assets/css/fonts/Roboto-Slab-Regular.woff2 b/assets/css/fonts/Roboto-Slab-Regular.woff2 new file mode 100644 index 00000000000..f2c76e5bda1 Binary files /dev/null and b/assets/css/fonts/Roboto-Slab-Regular.woff2 differ diff --git a/assets/css/fonts/fontawesome-webfont.eot b/assets/css/fonts/fontawesome-webfont.eot new file mode 100644 index 00000000000..e9f60ca953f Binary files /dev/null and b/assets/css/fonts/fontawesome-webfont.eot differ diff --git a/assets/css/fonts/fontawesome-webfont.svg b/assets/css/fonts/fontawesome-webfont.svg new file mode 100644 index 00000000000..855c845e538 --- /dev/null +++ b/assets/css/fonts/fontawesome-webfont.svg @@ -0,0 +1,2671 @@ + + + + +Created by FontForge 20120731 at Mon Oct 24 17:37:40 2016 + By ,,, +Copyright Dave Gandy 2016. All rights reserved. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/assets/css/fonts/fontawesome-webfont.ttf b/assets/css/fonts/fontawesome-webfont.ttf new file mode 100644 index 00000000000..35acda2fa11 Binary files /dev/null and b/assets/css/fonts/fontawesome-webfont.ttf differ diff --git a/assets/css/fonts/fontawesome-webfont.woff b/assets/css/fonts/fontawesome-webfont.woff new file mode 100644 index 00000000000..400014a4b06 Binary files /dev/null and b/assets/css/fonts/fontawesome-webfont.woff differ diff --git a/assets/css/fonts/fontawesome-webfont.woff2 b/assets/css/fonts/fontawesome-webfont.woff2 new file mode 100644 index 00000000000..4d13fc60404 Binary files /dev/null and b/assets/css/fonts/fontawesome-webfont.woff2 differ diff --git a/assets/css/fonts/lato-bold-italic.woff b/assets/css/fonts/lato-bold-italic.woff new file mode 100644 index 00000000000..88ad05b9ff4 Binary files /dev/null and b/assets/css/fonts/lato-bold-italic.woff differ diff --git a/assets/css/fonts/lato-bold-italic.woff2 b/assets/css/fonts/lato-bold-italic.woff2 new file mode 100644 index 00000000000..c4e3d804b57 Binary files /dev/null and b/assets/css/fonts/lato-bold-italic.woff2 differ diff --git a/assets/css/fonts/lato-bold.woff b/assets/css/fonts/lato-bold.woff new file mode 100644 index 00000000000..c6dff51f063 Binary files /dev/null and b/assets/css/fonts/lato-bold.woff differ diff --git a/assets/css/fonts/lato-bold.woff2 b/assets/css/fonts/lato-bold.woff2 new file mode 100644 index 00000000000..bb195043cfc Binary files /dev/null and b/assets/css/fonts/lato-bold.woff2 differ diff --git a/assets/css/fonts/lato-normal-italic.woff b/assets/css/fonts/lato-normal-italic.woff new file mode 100644 index 00000000000..76114bc0336 Binary files /dev/null and b/assets/css/fonts/lato-normal-italic.woff differ diff --git a/assets/css/fonts/lato-normal-italic.woff2 b/assets/css/fonts/lato-normal-italic.woff2 new file mode 100644 index 00000000000..3404f37e2e3 Binary files /dev/null and b/assets/css/fonts/lato-normal-italic.woff2 differ diff --git a/assets/css/fonts/lato-normal.woff b/assets/css/fonts/lato-normal.woff new file mode 100644 index 00000000000..ae1307ff5f4 Binary files /dev/null and b/assets/css/fonts/lato-normal.woff differ diff --git a/assets/css/fonts/lato-normal.woff2 b/assets/css/fonts/lato-normal.woff2 new file mode 100644 index 00000000000..3bf9843328a Binary files /dev/null and b/assets/css/fonts/lato-normal.woff2 differ diff --git a/assets/css/theme.css b/assets/css/theme.css new file mode 100644 index 00000000000..e4f9eaffb41 --- /dev/null +++ b/assets/css/theme.css @@ -0,0 +1,10501 @@ +@charset "UTF-8"; +/** + * Copyright 2015 Google Inc. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +/*------------------------------------*\ + $CONTENTS +\*------------------------------------*/ +/** + * STYLE GUIDE VARIABLES------------------Declarations of Sass variables + * -----Typography + * -----Colors + * -----Textfield + * -----Switch + * -----Spinner + * -----Radio + * -----Menu + * -----List + * -----Layout + * -----Icon toggles + * -----Footer + * -----Column + * -----Checkbox + * -----Card + * -----Button + * -----Animation + * -----Progress + * -----Badge + * -----Shadows + * -----Grid + * -----Data table + * -----Dialog + * -----Snackbar + * -----Tooltip + * -----Chip + * + * Even though all variables have the `!default` directive, most of them + * should not be changed as they are dependent one another. This can cause + * visual distortions (like alignment issues) that are hard to track down + * and fix. + */ +/* ========== TYPOGRAPHY ========== */ +/* We're splitting fonts into "preferred" and "performance" in order to optimize + page loading. For important text, such as the body, we want it to load + immediately and not wait for the web font load, whereas for other sections, + such as headers and titles, we're OK with things taking a bit longer to load. + We do have some optional classes and parameters in the mixins, in case you + definitely want to make sure you're using the preferred font and don't mind + the performance hit. + We should be able to improve on this once CSS Font Loading L3 becomes more + widely available. +*/ +/* ========== COLORS ========== */ +/** +* +* Material design color palettes. +* @see http://www.google.com/design/spec/style/color.html +* +**/ +/** + * Copyright 2015 Google Inc. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +/* ========== Color Palettes ========== */ +/* colors.scss */ +/** + * Copyright 2015 Google Inc. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +/* ========== IMAGES ========== */ +/* ========== Color & Themes ========== */ +/* ========== Typography ========== */ +/* ========== Components ========== */ +/* ========== Standard Buttons ========== */ +/* ========== Icon Toggles ========== */ +/* ========== Radio Buttons ========== */ +/* ========== Ripple effect ========== */ +/* ========== Layout ========== */ +/* ========== Content Tabs ========== */ +/* ========== Checkboxes ========== */ +/* ========== Switches ========== */ +/* ========== Spinner ========== */ +/* ========== Text fields ========== */ +/* ========== Card ========== */ +/* ========== Sliders ========== */ +/* ========== Progress ========== */ +/* ========== List ========== */ +/* ========== Item ========== */ +/* ========== Dropdown menu ========== */ +/* ========== Tooltips ========== */ +/* ========== Footer ========== */ +/* TEXTFIELD */ +/* SWITCH */ +/* SPINNER */ +/* RADIO */ +/* MENU */ +/* LIST */ +/* LAYOUT */ +/* ICON TOGGLE */ +/* FOOTER */ +/*mega-footer*/ +/*mini-footer*/ +/* CHECKBOX */ +/* CARD */ +/* Card dimensions */ +/* Cover image */ +/* BUTTON */ +/** + * + * Dimensions + * + */ +/* ANIMATION */ +/* PROGRESS */ +/* BADGE */ +/* SHADOWS */ +/* GRID */ +/* DATA TABLE */ +/* DIALOG */ +/* SNACKBAR */ +/* TOOLTIP */ +/* CHIP */ +/** + * Copyright 2015 Google Inc. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +/* Typography */ +/* Shadows */ +/* Animations */ +/* Dialog */ +:root { + --toc-1: #e6e9eb; + --toc-2: #ccd2d8; + --toc-3: #b3bcc4; + --toc-4: #9aa5b1; + --toc-5: #e6e9eb; + --toc-6: #ccd2d8; + --toc-7: #b3bcc4; + --toc-8: #9aa5b1; + --toc-9: #e6e9eb; + --toc-10: #ccd2d8; + --toc-11: #b3bcc4; + --toc-12: #9aa5b1; } + +/*! normalize.css v4.1.1 | MIT License | github.com/necolas/normalize.css */ +/** + * 1. Change the default font family in all browsers (opinionated). + * 2. Prevent adjustments of font size after orientation changes in IE and iOS. + */ +html { + font-family: sans-serif; + /* 1 */ + -ms-text-size-adjust: 100%; + /* 2 */ + -webkit-text-size-adjust: 100%; + /* 2 */ } + +/** + * Remove the margin in all browsers (opinionated). + */ +body { + margin: 0; } + +/* HTML5 display definitions + ========================================================================== */ +/** + * Add the correct display in IE 9-. + * 1. Add the correct display in Edge, IE, and Firefox. + * 2. Add the correct display in IE. + */ +article, +aside, +details, +figcaption, +figure, +footer, +header, +main, +menu, +nav, +section { + /* 1 */ + display: block; } + +summary { + display: list-item; } + +/** + * Add the correct display in IE 9-. + */ +audio, +canvas, +progress, +video { + display: inline-block; } + +/** + * Add the correct display in iOS 4-7. + */ +audio:not([controls]) { + display: none; + height: 0; } + +/** + * Add the correct vertical alignment in Chrome, Firefox, and Opera. + */ +progress { + vertical-align: baseline; } + +/** + * Add the correct display in IE 10-. + * 1. Add the correct display in IE. + */ +template, +[hidden] { + display: none !important; } + +/* Links + ========================================================================== */ +/** + * Remove the gray background on active links in IE 10. + */ +a { + background-color: transparent; + /* 1 */ } + +/** + * Remove the outline on focused links when they are also active or hovered + * in all browsers (opinionated). + */ +a:active, +a:hover { + outline-width: 0; } + +/* Text-level semantics + ========================================================================== */ +/** + * 1. Remove the bottom border in Firefox 39-. + * 2. Add the correct text decoration in Chrome, Edge, IE, Opera, and Safari. + */ +abbr[title] { + border-bottom: none; + /* 1 */ + text-decoration: underline; + /* 2 */ + text-decoration: underline dotted; + /* 2 */ } + +/** + * Prevent the duplicate application of `bolder` by the next rule in Safari 6. + */ +b, +strong { + font-weight: inherit; } + +/** + * Add the correct font weight in Chrome, Edge, and Safari. + */ +b, +strong { + font-weight: bolder; } + +/** + * Add the correct font style in Android 4.3-. + */ +dfn { + font-style: italic; } + +/** + * Correct the font size and margin on `h1` elements within `section` and + * `article` contexts in Chrome, Firefox, and Safari. + */ +h1 { + font-size: 2em; + margin: 0.67em 0; } + +/** + * Add the correct background and color in IE 9-. + */ +mark { + background-color: #ff0; + color: #1b1f23; } + +/** + * Add the correct font size in all browsers. + */ +small { + font-size: 80%; } + +/** + * Prevent `sub` and `sup` elements from affecting the line height in + * all browsers. + */ +sub, +sup { + font-size: 75%; + line-height: 0; + position: relative; + vertical-align: baseline; } + +sub { + bottom: -0.25em; } + +sup { + top: -0.5em; } + +/* Embedded content + ========================================================================== */ +/** + * Remove the border on images inside links in IE 10-. + */ +img { + border-style: none; } + +/** + * Hide the overflow in IE. + */ +svg:not(:root) { + overflow: hidden; } + +/* Grouping content + ========================================================================== */ +/** + * 1. Correct the inheritance and scaling of font size in all browsers. + * 2. Correct the odd `em` font sizing in all browsers. + */ +code, +kbd, +pre, +samp { + font-family: monospace, monospace; + /* 1 */ + font-size: 1em; + /* 2 */ } + +/** + * Add the correct margin in IE 8. + */ +figure { + margin: 1em 40px; } + +/** + * 1. Add the correct box sizing in Firefox. + * 2. Show the overflow in Edge and IE. + */ +hr { + box-sizing: content-box; + /* 1 */ + height: 0; + /* 1 */ + overflow: visible; + /* 2 */ } + +/* Forms + ========================================================================== */ +/** + * 1. Change font properties to `inherit` in all browsers (opinionated). + * 2. Remove the margin in Firefox and Safari. + */ +button, +input, +select, +textarea { + font: inherit; + /* 1 */ + margin: 0; + /* 2 */ } + +/** + * Restore the font weight unset by the previous rule. + */ +optgroup { + font-weight: 600; } + +/** + * Show the overflow in IE. + * 1. Show the overflow in Edge. + */ +button, +input { + /* 1 */ + overflow: visible; } + +/** + * Remove the inheritance of text transform in Edge, Firefox, and IE. + * 1. Remove the inheritance of text transform in Firefox. + */ +button, +select { + /* 1 */ + text-transform: none; } + +/** + * 1. Prevent a WebKit bug where (2) destroys native `audio` and `video` + * controls in Android 4. + * 2. Correct the inability to style clickable types in iOS and Safari. + */ +button, +html [type="button"], +[type="reset"], +[type="submit"] { + -webkit-appearance: button; + /* 2 */ } + +/** + * Remove the inner border and padding in Firefox. + */ +button::-moz-focus-inner, +[type="button"]::-moz-focus-inner, +[type="reset"]::-moz-focus-inner, +[type="submit"]::-moz-focus-inner { + border-style: none; + padding: 0; } + +/** + * Restore the focus styles unset by the previous rule. + */ +button:-moz-focusring, +[type="button"]:-moz-focusring, +[type="reset"]:-moz-focusring, +[type="submit"]:-moz-focusring { + outline: 1px dotted ButtonText; } + +/** + * Change the border, margin, and padding in all browsers (opinionated). + */ +fieldset { + border: 1px solid #c0c0c0; + margin: 0 2px; + padding: 0.35em 0.625em 0.75em; } + +/** + * 1. Correct the text wrapping in Edge and IE. + * 2. Correct the color inheritance from `fieldset` elements in IE. + * 3. Remove the padding so developers are not caught out when they zero out + * `fieldset` elements in all browsers. + */ +legend { + box-sizing: border-box; + /* 1 */ + color: inherit; + /* 2 */ + display: table; + /* 1 */ + max-width: 100%; + /* 1 */ + padding: 0; + /* 3 */ + white-space: normal; + /* 1 */ } + +/** + * Remove the default vertical scrollbar in IE. + */ +textarea { + overflow: auto; } + +/** + * 1. Add the correct box sizing in IE 10-. + * 2. Remove the padding in IE 10-. + */ +[type="checkbox"], +[type="radio"] { + box-sizing: border-box; + /* 1 */ + padding: 0; + /* 2 */ } + +/** + * Correct the cursor style of increment and decrement buttons in Chrome. + */ +[type="number"]::-webkit-inner-spin-button, +[type="number"]::-webkit-outer-spin-button { + height: auto; } + +/** + * 1. Correct the odd appearance in Chrome and Safari. + * 2. Correct the outline style in Safari. + */ +[type="search"] { + -webkit-appearance: textfield; + /* 1 */ + outline-offset: -2px; + /* 2 */ } + +/** + * Remove the inner padding and cancel buttons in Chrome and Safari on OS X. + */ +[type="search"]::-webkit-search-cancel-button, +[type="search"]::-webkit-search-decoration { + -webkit-appearance: none; } + +/** + * Correct the text style of placeholders in Chrome, Edge, and Safari. + */ +::-webkit-input-placeholder { + color: inherit; + opacity: 0.54; } + +/** + * 1. Correct the inability to style clickable types in iOS and Safari. + * 2. Change font properties to `inherit` in Safari. + */ +::-webkit-file-upload-button { + -webkit-appearance: button; + /* 1 */ + font: inherit; + /* 2 */ } + +* { + box-sizing: border-box; } + +input, +select, +textarea, +button { + font-family: inherit; + font-size: inherit; + line-height: inherit; } + +body { + font-family: "Lato", BlinkMacSystemFont, "Segoe UI", Helvetica, sans-serif; + font-size: 14px; + line-height: 1.5; + color: #24292e; + background-color: #fff; } + +a { + color: #0366d6; + text-decoration: none; } + a:hover { + text-decoration: underline; } + +b, +strong { + font-weight: 600; } + +hr, +.rule { + height: 0; + margin: 15px 0; + overflow: hidden; + background: transparent; + border: 0; + border-bottom: 1px solid #dfe2e5; } + hr::before, + .rule::before { + display: table; + content: ""; } + hr::after, + .rule::after { + display: table; + clear: both; + content: ""; } + +table { + border-spacing: 0; + border-collapse: collapse; } + +td, +th { + padding: 0; } + +button { + cursor: pointer; + border-radius: 0; } + +[hidden][hidden] { + display: none !important; } + +details summary { + cursor: pointer; } +details:not([open]) > *:not(summary) { + display: none !important; } + +kbd { + display: inline-block; + padding: 3px 5px; + font: 11px "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; + line-height: 10px; + color: #444d56; + vertical-align: middle; + background-color: #fafbfc; + border: solid 1px #d1d5da; + border-bottom-color: #d1d5da; + border-radius: 6px; + box-shadow: inset 0 -1px 0 #d1d5da; } + +h1, +h2, +h3, +h4, +h5, +h6 { + margin-top: 0; + margin-bottom: 0; } + +h1 { + font-size: 32px; + font-weight: 600; } + +h2 { + font-size: 24px; + font-weight: 600; } + +h3 { + font-size: 20px; + font-weight: 600; } + +h4 { + font-size: 16px; + font-weight: 600; } + +h5 { + font-size: 14px; + font-weight: 600; } + +h6 { + font-size: 12px; + font-weight: 600; } + +p { + margin-top: 0; + margin-bottom: 10px; } + +small { + font-size: 90%; } + +blockquote { + margin: 0; } + +ul, +ol { + padding-left: 0; + margin-top: 0; + margin-bottom: 0; } + +ol ol, +ul ol { + list-style-type: lower-roman; } + +ul ul ol, +ul ol ol, +ol ul ol, +ol ol ol { + list-style-type: lower-alpha; } + +dd { + margin-left: 0; } + +tt, +code { + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; + font-size: 12px; } + +pre { + margin-top: 0; + margin-bottom: 0; + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; + font-size: 12px; } + +.octicon { + vertical-align: text-bottom; } + +.breadcrumb-item { + display: inline-block; + margin-left: -0.35em; + white-space: nowrap; + list-style: none; } + .breadcrumb-item::after { + padding-right: 0.5em; + padding-left: 0.5em; + color: #e1e4e8; + content: "/"; } + .breadcrumb-item:first-child { + margin-left: 0; } + +.breadcrumb-item-selected, +.breadcrumb-item[aria-current]:not([aria-current="false"]) { + color: #586069; } + .breadcrumb-item-selected::after, + .breadcrumb-item[aria-current]:not([aria-current="false"])::after { + content: none; } + +.btn { + position: relative; + display: inline-block; + padding: 5px 16px; + font-size: 14px; + font-weight: 500; + line-height: 20px; + white-space: nowrap; + vertical-align: middle; + cursor: pointer; + user-select: none; + border: 1px solid; + border-radius: 6px; + appearance: none; } + .btn:hover { + text-decoration: none; } + .btn:disabled, .btn.disabled, .btn[aria-disabled="true"] { + cursor: default; } + .btn:disabled .octicon, .btn.disabled .octicon, .btn[aria-disabled="true"] .octicon { + color: inherit; } + .btn i { + font-style: normal; + font-weight: 500; + opacity: 0.75; } + .btn .octicon { + margin-right: 4px; + color: #6a737d; + vertical-align: text-bottom; } + .btn .octicon:only-child { + margin-right: 0; } + .btn .Counter { + margin-left: 2px; + color: inherit; + text-shadow: none; + vertical-align: top; + background-color: rgba(27, 31, 35, 0.08); } + .btn .dropdown-caret { + margin-left: 4px; + opacity: 0.8; } + +.btn { + color: #24292e; + background-color: #fafbfc; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.04), inset 0 1px 0 rgba(255, 255, 255, 0.25); + transition: background-color 0.2s cubic-bezier(0.3, 0, 0.5, 1); } + .btn:hover, .btn.hover, [open] > .btn { + background-color: #f3f4f6; + transition-duration: 0.1s; } + .btn:active, .btn.selected, .btn[aria-selected="true"] { + background-color: #edeff2; + box-shadow: inset 0 1px 0 rgba(225, 228, 232, 0.2); + transition: none; } + .btn:disabled, .btn.disabled, .btn[aria-disabled="true"] { + color: #959da5; + background-color: #fafbfc; + border-color: rgba(27, 31, 35, 0.15); } + .btn:focus, .btn.focus { + outline: 1px dotted transparent; + outline-offset: 2px; + box-shadow: 0 0 0 3px rgba(3, 102, 214, 0.3); } + +.btn-primary { + color: #fff; + background-color: #2ea44f; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.1), inset 0 1px 0 rgba(255, 255, 255, 0.03); } + .btn-primary:hover, .btn-primary.hover, [open] > .btn-primary { + background-color: #2c974b; } + .btn-primary:active, .btn-primary.selected, .btn-primary[aria-selected="true"] { + background-color: #2a8f47; + box-shadow: inset 0 1px 0 rgba(20, 70, 32, 0.2); } + .btn-primary:disabled, .btn-primary.disabled, .btn-primary[aria-disabled="true"] { + color: rgba(255, 255, 255, 0.8); + background-color: #94d3a2; + border-color: rgba(27, 31, 35, 0.1); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.1), inset 0 1px 0 rgba(255, 255, 255, 0.03); } + .btn-primary:focus, .btn-primary.focus { + box-shadow: 0 0 0 3px rgba(46, 164, 79, 0.4); } + .btn-primary .Counter { + color: inherit; + background-color: rgba(255, 255, 255, 0.2); } + .btn-primary .octicon { + color: rgba(255, 255, 255, 0.8); } + +.btn-danger { + color: #cb2431; + transition: none; } + .btn-danger:hover, [open] > .btn-danger { + color: #fff; + background-color: #cb2431; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.1), inset 0 1px 0 rgba(255, 255, 255, 0.03); } + .btn-danger:hover .Counter, [open] > .btn-danger .Counter { + background-color: rgba(255, 255, 255, 0.2); } + .btn-danger:hover .octicon, [open] > .btn-danger .octicon { + color: inherit; } + .btn-danger:active, .btn-danger.selected, .btn-danger[aria-selected="true"] { + color: #fff; + background-color: #be222e; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: inset 0 1px 0 rgba(134, 24, 29, 0.2); } + .btn-danger:disabled, .btn-danger.disabled, .btn-danger[aria-disabled="true"] { + color: rgba(203, 36, 49, 0.5); + background-color: #fafbfc; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.04), inset 0 1px 0 rgba(255, 255, 255, 0.25); } + .btn-danger:disabled .Counter, .btn-danger.disabled .Counter, .btn-danger[aria-disabled="true"] .Counter { + background-color: rgba(203, 36, 49, 0.05); } + .btn-danger:focus { + box-shadow: 0 0 0 3px rgba(203, 36, 49, 0.4); } + .btn-danger .Counter { + color: inherit; + background-color: rgba(203, 36, 49, 0.1); } + +.btn-outline { + color: #0366d6; + transition: none; } + .btn-outline:hover, [open] > .btn-outline { + color: #fff; + background-color: #0366d6; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.1), inset 0 1px 0 rgba(255, 255, 255, 0.03); } + .btn-outline:hover .Counter, [open] > .btn-outline .Counter { + background-color: rgba(255, 255, 255, 0.2); } + .btn-outline:hover .octicon, [open] > .btn-outline .octicon { + color: inherit; } + .btn-outline:active, .btn-outline.selected, .btn-outline[aria-selected="true"] { + color: #fff; + background-color: #035fc7; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: inset 0 1px 0 rgba(5, 38, 76, 0.2); } + .btn-outline:disabled, .btn-outline.disabled, .btn-outline[aria-disabled="true"] { + color: rgba(3, 102, 214, 0.5); + background-color: #fafbfc; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.04), inset 0 1px 0 rgba(255, 255, 255, 0.25); } + .btn-outline:disabled .Counter, .btn-outline.disabled .Counter, .btn-outline[aria-disabled="true"] .Counter { + background-color: rgba(3, 102, 214, 0.05); } + .btn-outline:focus { + box-shadow: 0 0 0 3px rgba(3, 102, 214, 0.4); } + .btn-outline .Counter { + color: inherit; + background-color: rgba(3, 102, 214, 0.1); } + +.btn-blue { + color: #fff; + background-color: #0361cc; + background-image: linear-gradient(-180deg, #0679fc 0%, #0361cc 90%); } + .btn-blue:focus, .btn-blue.focus { + box-shadow: 0 0 0 0.2em rgba(6, 121, 252, 0.4); } + .btn-blue:hover, .btn-blue.hover { + background-color: #035cc2; + background-image: linear-gradient(-180deg, #0374f4 0%, #035cc2 90%); + background-position: -0.5em; + border-color: rgba(27, 31, 35, 0.5); } + .btn-blue:active, .btn-blue.selected, .btn-blue[aria-selected="true"], [open] > .btn-blue { + background-color: #045cc1; + background-image: none; + border-color: rgba(27, 31, 35, 0.5); + box-shadow: inset 0 0.15em 0.3em rgba(27, 31, 35, 0.15); } + .btn-blue:disabled, .btn-blue.disabled, .btn-blue[aria-disabled="true"] { + color: rgba(255, 255, 255, 0.75); + background-color: #81b0e6; + background-image: none; + border-color: rgba(27, 31, 35, 0.15); + box-shadow: none; } + .btn-blue .Counter { + color: #0366d6; + background-color: #fff; } + +.btn-sm { + padding: 3px 12px; + font-size: 12px; + line-height: 20px; } + .btn-sm .octicon { + vertical-align: text-top; } + +.btn-large { + padding: 0.75em 1.5em; + font-size: inherit; + line-height: 1.5; + border-radius: 0.5em; } + +.btn-block { + display: block; + width: 100%; + text-align: center; } + +.BtnGroup { + display: inline-block; + vertical-align: middle; } + .BtnGroup::before { + display: table; + content: ""; } + .BtnGroup::after { + display: table; + clear: both; + content: ""; } + .BtnGroup + .BtnGroup, + .BtnGroup + .btn { + margin-left: 4px; } + +.BtnGroup-item { + position: relative; + float: left; + border-right-width: 0; + border-radius: 0; } + .BtnGroup-item:first-child { + border-top-left-radius: 6px; + border-bottom-left-radius: 6px; } + .BtnGroup-item:last-child { + border-right-width: 1px; + border-top-right-radius: 6px; + border-bottom-right-radius: 6px; } + .BtnGroup-item.selected, .BtnGroup-item[aria-selected="true"], .BtnGroup-item:focus, .BtnGroup-item:active, .BtnGroup-item:hover { + border-right-width: 1px; } + .BtnGroup-item.selected + .BtnGroup-item, + .BtnGroup-item.selected + .BtnGroup-parent .BtnGroup-item, .BtnGroup-item[aria-selected="true"] + .BtnGroup-item, + .BtnGroup-item[aria-selected="true"] + .BtnGroup-parent .BtnGroup-item, .BtnGroup-item:focus + .BtnGroup-item, + .BtnGroup-item:focus + .BtnGroup-parent .BtnGroup-item, .BtnGroup-item:active + .BtnGroup-item, + .BtnGroup-item:active + .BtnGroup-parent .BtnGroup-item, .BtnGroup-item:hover + .BtnGroup-item, + .BtnGroup-item:hover + .BtnGroup-parent .BtnGroup-item { + border-left-width: 0; } + +.BtnGroup-parent { + float: left; } + .BtnGroup-parent:first-child .BtnGroup-item { + border-top-left-radius: 6px; + border-bottom-left-radius: 6px; } + .BtnGroup-parent:last-child .BtnGroup-item { + border-right-width: 1px; + border-top-right-radius: 6px; + border-bottom-right-radius: 6px; } + .BtnGroup-parent .BtnGroup-item { + border-right-width: 0; + border-radius: 0; } + .BtnGroup-parent.selected .BtnGroup-item, .BtnGroup-parent[aria-selected="true"] .BtnGroup-item, .BtnGroup-parent:focus .BtnGroup-item, .BtnGroup-parent:active .BtnGroup-item, .BtnGroup-parent:hover .BtnGroup-item { + border-right-width: 1px; } + .BtnGroup-parent.selected + .BtnGroup-item, + .BtnGroup-parent.selected + .BtnGroup-parent .BtnGroup-item, .BtnGroup-parent[aria-selected="true"] + .BtnGroup-item, + .BtnGroup-parent[aria-selected="true"] + .BtnGroup-parent .BtnGroup-item, .BtnGroup-parent:focus + .BtnGroup-item, + .BtnGroup-parent:focus + .BtnGroup-parent .BtnGroup-item, .BtnGroup-parent:active + .BtnGroup-item, + .BtnGroup-parent:active + .BtnGroup-parent .BtnGroup-item, .BtnGroup-parent:hover + .BtnGroup-item, + .BtnGroup-parent:hover + .BtnGroup-parent .BtnGroup-item { + border-left-width: 0; } + +.BtnGroup-item:focus, .BtnGroup-item:active, +.BtnGroup-parent:focus, +.BtnGroup-parent:active { + z-index: 1; } + +.btn-link { + display: inline-block; + padding: 0; + font-size: inherit; + color: #0366d6; + text-decoration: none; + white-space: nowrap; + cursor: pointer; + user-select: none; + background-color: transparent; + border: 0; + appearance: none; } + .btn-link:hover { + text-decoration: underline; } + .btn-link:disabled, .btn-link:disabled:hover, .btn-link[aria-disabled="true"], .btn-link[aria-disabled="true"]:hover { + color: rgba(88, 96, 105, 0.5); + cursor: default; } + +.btn-invisible { + color: #0366d6; + background-color: transparent; + border: 0; + border-radius: 0; + box-shadow: none; } + .btn-invisible:hover, .btn-invisible:active, .btn-invisible:focus, .btn-invisible.selected, .btn-invisible[aria-selected="true"], .btn-invisible.zeroclipboard-is-hover, .btn-invisible.zeroclipboard-is-active { + color: #0366d6; + background: none; + outline: none; + box-shadow: none; } + +.btn-octicon { + display: inline-block; + padding: 5px; + margin-left: 5px; + line-height: 1; + color: #586069; + vertical-align: middle; + background: transparent; + border: 0; } + .btn-octicon:hover { + color: #0366d6; } + .btn-octicon.disabled, .btn-octicon[aria-disabled="true"] { + color: #959da5; + cursor: default; } + .btn-octicon.disabled:hover, .btn-octicon[aria-disabled="true"]:hover { + color: #959da5; } + +.btn-octicon-danger:hover { + color: #cb2431; } + +.close-button { + padding: 0; + background: transparent; + border: 0; + outline: none; } + +.hidden-text-expander { + display: block; } + .hidden-text-expander.inline { + position: relative; + top: -1px; + display: inline-block; + margin-left: 5px; + line-height: 0; } + +.hidden-text-expander a, +.ellipsis-expander { + display: inline-block; + height: 12px; + padding: 0 5px 5px; + font-size: 12px; + font-weight: 600; + line-height: 6px; + color: #444d56; + text-decoration: none; + vertical-align: middle; + background: #dfe2e5; + border: 0; + border-radius: 1px; } + .hidden-text-expander a:hover, + .ellipsis-expander:hover { + text-decoration: none; + background-color: #c6cbd1; } + .hidden-text-expander a:active, + .ellipsis-expander:active { + color: #fff; + background-color: #2188ff; } + +.btn-with-count { + float: left; + border-top-right-radius: 0; + border-bottom-right-radius: 0; } + .btn-with-count:focus { + z-index: 1; } + +.social-count { + position: relative; + float: left; + padding: 3px 12px; + font-size: 12px; + font-weight: 600; + line-height: 20px; + color: #24292e; + vertical-align: middle; + background-color: #fff; + border: 1px solid rgba(27, 31, 35, 0.15); + border-left: 0; + border-top-right-radius: 6px; + border-bottom-right-radius: 6px; + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.04), inset 0 1px 0 rgba(255, 255, 255, 0.25); } + .social-count:hover, .social-count:active { + text-decoration: none; } + .social-count:hover { + color: #0366d6; + cursor: pointer; } + .social-count:focus { + z-index: 1; + outline: 0; + box-shadow: 0 0 0 3px rgba(3, 102, 214, 0.3); } + +fieldset { + padding: 0; + margin: 0; + border: 0; } + +label { + font-weight: 600; } + +.form-control, +.form-select { + padding: 5px 12px; + font-size: 14px; + line-height: 20px; + color: #24292e; + vertical-align: middle; + background-color: #fff; + background-repeat: no-repeat; + background-position: right 8px center; + border: 1px solid #e1e4e8; + border-radius: 6px; + outline: none; + box-shadow: inset 0 1px 0 rgba(225, 228, 232, 0.2); } + .form-control.focus, .form-control:focus, + .form-select.focus, + .form-select:focus { + border-color: #0366d6; + outline: none; + box-shadow: 0 0 0 3px rgba(3, 102, 214, 0.3); } + .form-control[disabled], + .form-select[disabled] { + color: #959da5; + background-color: #f3f4f6; } + @supports (-webkit-touch-callout: none) { + .form-control, + .form-select { + font-size: 16px; } + @media (min-width: 768px) { + .form-control, + .form-select { + font-size: 14px; } } } + +textarea.form-control { + padding-top: 8px; + padding-bottom: 8px; + line-height: 1.5; } + +.input-contrast { + background-color: #fafbfc; } + .input-contrast:focus { + background-color: #fff; } + +.input-dark { + color: #fff; + background-color: rgba(255, 255, 255, 0.15); + border-color: transparent; + box-shadow: none; } + .input-dark::placeholder { + color: inherit; + opacity: 0.6; } + .input-dark.focus, .input-dark:focus { + border-color: rgba(27, 31, 35, 0.3); + box-shadow: 0 0 0 0.2em rgba(121, 184, 255, 0.4); } + +::placeholder { + color: #6a737d; + opacity: 1; } + +.input-sm { + padding-top: 3px; + padding-bottom: 3px; + font-size: 12px; + line-height: 20px; } + +.input-lg { + font-size: 16px; } + +.input-block { + display: block; + width: 100%; } + +.input-monospace { + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; } + +.input-hide-webkit-autofill::-webkit-contacts-auto-fill-button { + position: absolute; + right: 0; + display: none !important; + pointer-events: none; + visibility: hidden; } + +.form-checkbox { + padding-left: 20px; + margin: 15px 0; + vertical-align: middle; } + .form-checkbox label em.highlight { + position: relative; + left: -4px; + padding: 2px 4px; + font-style: normal; + background: #fffbdd; + border-radius: 6px; } + .form-checkbox input[type="checkbox"], + .form-checkbox input[type="radio"] { + float: left; + margin: 5px 0 0 -20px; + vertical-align: middle; } + .form-checkbox .note { + display: block; + margin: 0; + font-size: 12px; + font-weight: 400; + color: #586069; } + +.form-checkbox-details { + display: none; } + +.form-checkbox-details-trigger:checked ~ * .form-checkbox-details, +.form-checkbox-details-trigger:checked ~ .form-checkbox-details { + display: block; } + +.hfields { + margin: 15px 0; } + .hfields::before { + display: table; + content: ""; } + .hfields::after { + display: table; + clear: both; + content: ""; } + .hfields .form-group { + float: left; + margin: 0 30px 0 0; } + .hfields .form-group dt label, + .hfields .form-group .form-group-header label { + display: inline-block; + margin: 5px 0 0; + color: #586069; } + .hfields .form-group dt img, + .hfields .form-group .form-group-header img { + position: relative; + top: -2px; } + .hfields .btn { + float: left; + margin: 28px 25px 0 -20px; } + .hfields .form-select { + margin-top: 5px; } + +input::-webkit-outer-spin-button, +input::-webkit-inner-spin-button { + margin: 0; + appearance: none; } + +.form-actions::before { + display: table; + content: ""; } +.form-actions::after { + display: table; + clear: both; + content: ""; } +.form-actions .btn { + float: right; } + .form-actions .btn + .btn { + margin-right: 5px; } + +.form-warning { + padding: 8px 10px; + margin: 10px 0; + font-size: 14px; + color: #735c0f; + background: #fffbdd; + border: 1px solid #f9c513; + border-radius: 6px; } + .form-warning p { + margin: 0; + line-height: 1.5; } + .form-warning a { + font-weight: 600; } + +.form-select { + display: inline-block; + max-width: 100%; + height: 32px; + padding-right: 24px; + background-color: #fff; + background-image: url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAUCAMAAACzvE1FAAAADFBMVEUzMzMzMzMzMzMzMzMKAG/3AAAAA3RSTlMAf4C/aSLHAAAAPElEQVR42q3NMQ4AIAgEQTn//2cLdRKppSGzBYwzVXvznNWs8C58CiussPJj8h6NwgorrKRdTvuV9v16Afn0AYFOB7aYAAAAAElFTkSuQmCC"); + background-repeat: no-repeat; + background-position: right 8px center; + background-size: 8px 10px; + appearance: none; } + .form-select::-ms-expand { + opacity: 0; } + .form-select[multiple] { + height: auto; } + +.select-sm { + height: 28px; + padding-top: 3px; + padding-bottom: 3px; + font-size: 12px; } + .select-sm[multiple] { + height: auto; + min-height: 0; } + +.form-group { + margin: 15px 0; } + .form-group .form-control { + width: 440px; + max-width: 100%; + margin-right: 5px; + background-color: #fafbfc; } + .form-group .form-control:focus { + background-color: #fff; } + .form-group .form-control.shorter { + width: 130px; } + .form-group .form-control.short { + width: 250px; } + .form-group .form-control.long { + width: 100%; } + .form-group textarea.form-control { + width: 100%; + height: 200px; + min-height: 200px; } + .form-group textarea.form-control.short { + height: 50px; + min-height: 50px; } + .form-group dt, + .form-group .form-group-header { + margin: 0 0 6px; } + .form-group label { + position: relative; } + .form-group.flattened dt, .form-group.flattened .form-group-header { + float: left; + margin: 0; + line-height: 32px; } + .form-group.flattened dd, .form-group.flattened .form-group-body { + line-height: 32px; } + .form-group dd h4, + .form-group .form-group-body h4 { + margin: 4px 0 0; } + .form-group dd h4.is-error, + .form-group .form-group-body h4.is-error { + color: #cb2431; } + .form-group dd h4.is-success, + .form-group .form-group-body h4.is-success { + color: #22863a; } + .form-group dd h4 + .note, + .form-group .form-group-body h4 + .note { + margin-top: 0; } + .form-group.required dt label::after, + .form-group.required .form-group-header label::after { + padding-left: 5px; + color: #cb2431; + content: "*"; } + .form-group .success, + .form-group .error, + .form-group .indicator { + display: none; + font-size: 12px; + font-weight: 600; } + .form-group.loading { + opacity: 0.5; } + .form-group.loading .indicator { + display: inline; } + .form-group.loading .spinner { + display: inline-block; + vertical-align: middle; } + .form-group.successful .success { + display: inline; + color: #22863a; } + .form-group.successed .success, + .form-group.successed .warning, + .form-group.successed .error, .form-group.warn .success, + .form-group.warn .warning, + .form-group.warn .error, .form-group.errored .success, + .form-group.errored .warning, + .form-group.errored .error { + position: absolute; + z-index: 10; + display: block; + max-width: 450px; + padding: 4px 8px; + margin: 8px 0 0; + font-size: 12px; + font-weight: 400; + border-style: solid; + border-width: 1px; + border-radius: 6px; } + .form-group.successed .success::after, .form-group.successed .success::before, + .form-group.successed .warning::after, + .form-group.successed .warning::before, + .form-group.successed .error::after, + .form-group.successed .error::before, .form-group.warn .success::after, .form-group.warn .success::before, + .form-group.warn .warning::after, + .form-group.warn .warning::before, + .form-group.warn .error::after, + .form-group.warn .error::before, .form-group.errored .success::after, .form-group.errored .success::before, + .form-group.errored .warning::after, + .form-group.errored .warning::before, + .form-group.errored .error::after, + .form-group.errored .error::before { + position: absolute; + bottom: 100%; + left: 10px; + z-index: 15; + width: 0; + height: 0; + pointer-events: none; + content: " "; + border: solid transparent; } + .form-group.successed .success::after, + .form-group.successed .warning::after, + .form-group.successed .error::after, .form-group.warn .success::after, + .form-group.warn .warning::after, + .form-group.warn .error::after, .form-group.errored .success::after, + .form-group.errored .warning::after, + .form-group.errored .error::after { + border-width: 5px; } + .form-group.successed .success::before, + .form-group.successed .warning::before, + .form-group.successed .error::before, .form-group.warn .success::before, + .form-group.warn .warning::before, + .form-group.warn .error::before, .form-group.errored .success::before, + .form-group.errored .warning::before, + .form-group.errored .error::before { + margin-left: -1px; + border-width: 6px; } + .form-group.successed .success { + color: #144620; + background-color: #dcffe4; + border-color: #34d058; } + .form-group.successed .success::after { + border-bottom-color: #dcffe4; } + .form-group.successed .success::before { + border-bottom-color: #34d058; } + .form-group.warn .form-control { + border-color: #f9c513; } + .form-group.warn .warning { + background-color: #fff5b1; + border-color: #f9c513; } + .form-group.warn .warning::after { + border-bottom-color: #fff5b1; } + .form-group.warn .warning::before { + border-bottom-color: #f9c513; } + .form-group.errored .form-control { + border-color: #cb2431; } + .form-group.errored label { + color: #cb2431; } + .form-group.errored .error { + background-color: #ffeef0; + border-color: #f97583; } + .form-group.errored .error::after { + border-bottom-color: #ffeef0; } + .form-group.errored .error::before { + border-bottom-color: #f97583; } + +.note { + min-height: 17px; + margin: 4px 0 2px; + font-size: 12px; + color: #586069; } + .note .spinner { + margin-right: 3px; + vertical-align: middle; } + +dl.form-group > dd .form-control.is-autocheck-loading, dl.form-group > dd .form-control.is-autocheck-successful, dl.form-group > dd .form-control.is-autocheck-errored, +.form-group > .form-group-body .form-control.is-autocheck-loading, +.form-group > .form-group-body .form-control.is-autocheck-successful, +.form-group > .form-group-body .form-control.is-autocheck-errored { + padding-right: 30px; } +dl.form-group > dd .form-control.is-autocheck-loading, +.form-group > .form-group-body .form-control.is-autocheck-loading { + background-image: url("/images/spinners/octocat-spinner-16px.gif"); } +dl.form-group > dd .form-control.is-autocheck-successful, +.form-group > .form-group-body .form-control.is-autocheck-successful { + background-image: url("/images/modules/ajax/success.png"); } +dl.form-group > dd .form-control.is-autocheck-errored, +.form-group > .form-group-body .form-control.is-autocheck-errored { + background-image: url("/images/modules/ajax/error.png"); } + +@media only screen and (-webkit-min-device-pixel-ratio: 2), only screen and (min--moz-device-pixel-ratio: 2), only screen and (-moz-min-device-pixel-ratio: 2), only screen and (-o-min-device-pixel-ratio: 2 / 1), only screen and (min-device-pixel-ratio: 2), only screen and (min-resolution: 192dpi), only screen and (min-resolution: 2dppx) { + dl.form-group > dd .form-control.is-autocheck-loading, dl.form-group > dd .form-control.is-autocheck-successful, dl.form-group > dd .form-control.is-autocheck-errored, + .form-group > .form-group-body .form-control.is-autocheck-loading, + .form-group > .form-group-body .form-control.is-autocheck-successful, + .form-group > .form-group-body .form-control.is-autocheck-errored { + background-size: 16px 16px; } + dl.form-group > dd .form-control.is-autocheck-loading, + .form-group > .form-group-body .form-control.is-autocheck-loading { + background-image: url("/images/spinners/octocat-spinner-32.gif"); } + dl.form-group > dd .form-control.is-autocheck-successful, + .form-group > .form-group-body .form-control.is-autocheck-successful { + background-image: url("/images/modules/ajax/success@2x.png"); } + dl.form-group > dd .form-control.is-autocheck-errored, + .form-group > .form-group-body .form-control.is-autocheck-errored { + background-image: url("/images/modules/ajax/error@2x.png"); } } +.status-indicator { + display: inline-block; + width: 16px; + height: 16px; + margin-left: 5px; } + .status-indicator .octicon { + display: none; } + +.status-indicator-success::before { + content: ""; } +.status-indicator-success .octicon-check { + display: inline-block; + color: #28a745; + fill: #28a745; } +.status-indicator-success .octicon-x { + display: none; } + +.status-indicator-failed::before { + content: ""; } +.status-indicator-failed .octicon-check { + display: none; } +.status-indicator-failed .octicon-x { + display: inline-block; + color: #cb2431; + fill: #d73a49; } + +.status-indicator-loading { + width: 16px; + background-image: url("/images/spinners/octocat-spinner-32-EAF2F5.gif"); + background-repeat: no-repeat; + background-position: 0 0; + background-size: 16px; } + +.inline-form { + display: inline-block; } + .inline-form .btn-plain { + background-color: transparent; + border: 0; } + +.drag-and-drop { + padding: 7px 10px; + margin: 0; + font-size: 13px; + line-height: 16px; + color: #586069; + background-color: #fafbfc; + border: 1px solid #c3c8cf; + border-top: 0; + border-bottom-right-radius: 6px; + border-bottom-left-radius: 6px; } + .drag-and-drop .default, + .drag-and-drop .loading, + .drag-and-drop .error { + display: none; } + .drag-and-drop .error { + color: #cb2431; } + .drag-and-drop img { + vertical-align: top; } + +.is-default .drag-and-drop .default { + display: inline-block; } + +.is-uploading .drag-and-drop .loading { + display: inline-block; } + +.is-bad-file .drag-and-drop .bad-file { + display: inline-block; } + +.is-duplicate-filename .drag-and-drop .duplicate-filename { + display: inline-block; } + +.is-too-big .drag-and-drop .too-big { + display: inline-block; } + +.is-hidden-file .drag-and-drop .hidden-file { + display: inline-block; } + +.is-empty .drag-and-drop .empty { + display: inline-block; } + +.is-bad-permissions .drag-and-drop .bad-permissions { + display: inline-block; } + +.is-repository-required .drag-and-drop .repository-required { + display: inline-block; } + +.drag-and-drop-error-info { + font-weight: 400; + color: #586069; } + .drag-and-drop-error-info a { + color: #0366d6; } + +.is-failed .drag-and-drop .failed-request { + display: inline-block; } + +.manual-file-chooser { + position: absolute; + width: 240px; + padding: 5px; + margin-left: -80px; + cursor: pointer; + opacity: 0.0001; } + +.manual-file-chooser:hover + .manual-file-chooser-text { + text-decoration: underline; } + +.btn .manual-file-chooser { + top: 0; + padding: 0; + line-height: 34px; } + +.upload-enabled textarea { + display: block; + border-bottom: 1px dashed #dfe2e5; + border-bottom-right-radius: 0; + border-bottom-left-radius: 0; } +.upload-enabled.focused { + border-radius: 6px; + box-shadow: inset 0 1px 2px rgba(27, 31, 35, 0.075), 0 0 0 0.2em rgba(3, 102, 214, 0.3); } + .upload-enabled.focused .form-control { + box-shadow: none; } + .upload-enabled.focused .drag-and-drop { + border-color: #4a9eff; } + +.dragover textarea, +.dragover .drag-and-drop { + box-shadow: #c9ff00 0 0 3px; } + +.write-content { + position: relative; } + +.previewable-comment-form { + position: relative; } + .previewable-comment-form .tabnav { + position: relative; + padding: 8px 8px 0; } + .previewable-comment-form .comment { + border: 1px solid #c3c8cf; } + .previewable-comment-form .comment-form-error { + margin-bottom: 8px; } + .previewable-comment-form .write-content, + .previewable-comment-form .preview-content { + display: none; + margin: 0 8px 8px; } + .previewable-comment-form.write-selected .write-content, .previewable-comment-form.preview-selected .preview-content { + display: block; } + .previewable-comment-form textarea { + display: block; + width: 100%; + min-height: 100px; + max-height: 500px; + padding: 8px; + resize: vertical; } + +.form-action-spacious { + margin-top: 10px; } + +div.composer { + margin-top: 0; + border: 0; } + +.composer .comment-form-textarea { + height: 200px; + min-height: 200px; } + +.composer .tabnav { + margin: 0 0 10px; } + +h2.account { + margin: 15px 0 0; + font-size: 18px; + font-weight: 400; + color: #586069; } + +p.explain { + position: relative; + font-size: 12px; + color: #586069; } + p.explain strong { + color: #24292e; } + p.explain .octicon { + margin-right: 5px; + color: #959da5; } + p.explain .minibutton { + top: -4px; + float: right; } + +.form-group label { + position: static; } + +.input-group { + display: table; } + .input-group .form-control { + position: relative; + width: 100%; } + .input-group .form-control:focus { + z-index: 2; } + .input-group .form-control + .btn { + margin-left: 0; } + .input-group.inline { + display: inline-table; } + +.input-group .form-control, +.input-group-button { + display: table-cell; } + +.input-group-button { + width: 1%; + vertical-align: middle; } + +.input-group .form-control:first-child, +.input-group-button:first-child .btn { + border-top-right-radius: 0; + border-bottom-right-radius: 0; } + +.input-group-button:first-child .btn { + margin-right: -1px; } + +.input-group .form-control:last-child, +.input-group-button:last-child .btn { + border-top-left-radius: 0; + border-bottom-left-radius: 0; } + +.input-group-button:last-child .btn { + margin-left: -1px; } + +.radio-group::before { + display: table; + content: ""; } +.radio-group::after { + display: table; + clear: both; + content: ""; } + +.radio-label { + float: left; + padding: 6px 16px 6px 36px; + margin-left: -1px; + font-size: 14px; + line-height: 20px; + color: #24292e; + cursor: pointer; + border: 1px solid #e1e4e8; } + :checked + .radio-label { + position: relative; + z-index: 1; + border-color: #0366d6; } + .radio-label:first-of-type { + margin-left: 0; + border-top-left-radius: 6px; + border-bottom-left-radius: 6px; } + .radio-label:last-of-type { + border-top-right-radius: 6px; + border-bottom-right-radius: 6px; } + +.radio-input { + z-index: 3; + float: left; + margin: 10px -32px 0 16px; } + +.AnimatedEllipsis { + display: inline-block; + overflow: hidden; + vertical-align: bottom; } + .AnimatedEllipsis::after { + display: inline-block; + content: "..."; + animation: AnimatedEllipsis-keyframes 1.2s steps(4, jump-none) infinite; } +@keyframes AnimatedEllipsis-keyframes { + 0% { + transform: translateX(-100%); } } +.markdown-body { + font-family: "Lato", BlinkMacSystemFont, "Segoe UI", Helvetica, sans-serif; + font-size: 16px; + line-height: 1.5; + word-wrap: break-word; } + .markdown-body kbd { + display: inline-block; + padding: 3px 5px; + font: 11px "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; + line-height: 10px; + color: #444d56; + vertical-align: middle; + background-color: #fafbfc; + border: solid 1px #d1d5da; + border-bottom-color: #d1d5da; + border-radius: 6px; + box-shadow: inset 0 -1px 0 #d1d5da; } + .markdown-body::before { + display: table; + content: ""; } + .markdown-body::after { + display: table; + clear: both; + content: ""; } + .markdown-body > *:first-child { + margin-top: 0 !important; } + .markdown-body > *:last-child { + margin-bottom: 0 !important; } + .markdown-body a:not([href]) { + color: inherit; + text-decoration: none; } + .markdown-body .absent { + color: #cb2431; } + .markdown-body .anchor { + float: left; + padding-right: 4px; + margin-left: -20px; + line-height: 1; } + .markdown-body .anchor:focus { + outline: none; } + .markdown-body p, + .markdown-body blockquote, + .markdown-body ul, + .markdown-body ol, + .markdown-body dl, + .markdown-body table, + .markdown-body pre, + .markdown-body details { + margin-top: 0; + margin-bottom: 16px; } + .markdown-body hr { + height: 0.25em; + padding: 0; + margin: 24px 0; + background-color: #e1e4e8; + border: 0; } + .markdown-body blockquote { + padding: 0 1em; + color: #6a737d; + border-left: 0.25em solid #dfe2e5; } + .markdown-body blockquote > :first-child { + margin-top: 0; } + .markdown-body blockquote > :last-child { + margin-bottom: 0; } + +.markdown-body h1, +.markdown-body h2, +.markdown-body h3, +.markdown-body h4, +.markdown-body h5, +.markdown-body h6 { + margin-top: 24px; + margin-bottom: 16px; + font-weight: 600; + line-height: 1.25; } + .markdown-body h1 .octicon-link, + .markdown-body h2 .octicon-link, + .markdown-body h3 .octicon-link, + .markdown-body h4 .octicon-link, + .markdown-body h5 .octicon-link, + .markdown-body h6 .octicon-link { + color: #1b1f23; + vertical-align: middle; + visibility: hidden; } + .markdown-body h1:hover .anchor, + .markdown-body h2:hover .anchor, + .markdown-body h3:hover .anchor, + .markdown-body h4:hover .anchor, + .markdown-body h5:hover .anchor, + .markdown-body h6:hover .anchor { + text-decoration: none; } + .markdown-body h1:hover .anchor .octicon-link, + .markdown-body h2:hover .anchor .octicon-link, + .markdown-body h3:hover .anchor .octicon-link, + .markdown-body h4:hover .anchor .octicon-link, + .markdown-body h5:hover .anchor .octicon-link, + .markdown-body h6:hover .anchor .octicon-link { + visibility: visible; } + .markdown-body h1 tt, + .markdown-body h1 code, + .markdown-body h2 tt, + .markdown-body h2 code, + .markdown-body h3 tt, + .markdown-body h3 code, + .markdown-body h4 tt, + .markdown-body h4 code, + .markdown-body h5 tt, + .markdown-body h5 code, + .markdown-body h6 tt, + .markdown-body h6 code { + font-size: inherit; } +.markdown-body h1 { + padding-bottom: 0.3em; + font-size: 2em; + border-bottom: 1px solid #eaecef; } +.markdown-body h2 { + padding-bottom: 0.3em; + font-size: 1.5em; + border-bottom: 1px solid #eaecef; } +.markdown-body h3 { + font-size: 1.25em; } +.markdown-body h4 { + font-size: 1em; } +.markdown-body h5 { + font-size: 0.875em; } +.markdown-body h6 { + font-size: 0.85em; + color: #6a737d; } + +.markdown-body ul, +.markdown-body ol { + padding-left: 2em; } + .markdown-body ul.no-list, + .markdown-body ol.no-list { + padding: 0; + list-style-type: none; } +.markdown-body ul ul, +.markdown-body ul ol, +.markdown-body ol ol, +.markdown-body ol ul { + margin-top: 0; + margin-bottom: 0; } +.markdown-body li { + word-wrap: break-all; } +.markdown-body li > p { + margin-top: 16px; } +.markdown-body li + li { + margin-top: 0.25em; } +.markdown-body dl { + padding: 0; } + .markdown-body dl dt { + padding: 0; + margin-top: 16px; + font-size: 1em; + font-style: italic; + font-weight: 600; } + .markdown-body dl dd { + padding: 0 16px; + margin-bottom: 16px; } + +.markdown-body table { + display: block; + width: 100%; + width: max-content; + max-width: 100%; + overflow: auto; } + .markdown-body table th { + font-weight: 600; } + .markdown-body table th, + .markdown-body table td { + padding: 6px 13px; + border: 1px solid #dfe2e5; } + .markdown-body table tr { + background-color: #fff; + border-top: 1px solid #c6cbd1; } + .markdown-body table tr:nth-child(2n) { + background-color: #f6f8fa; } + .markdown-body table img { + background-color: transparent; } + +.markdown-body img { + max-width: 100%; + box-sizing: content-box; + background-color: #fff; } + .markdown-body img[align="right"] { + padding-left: 20px; } + .markdown-body img[align="left"] { + padding-right: 20px; } +.markdown-body .emoji { + max-width: none; + vertical-align: text-top; + background-color: transparent; } +.markdown-body span.frame { + display: block; + overflow: hidden; } + .markdown-body span.frame > span { + display: block; + float: left; + width: auto; + padding: 7px; + margin: 13px 0 0; + overflow: hidden; + border: 1px solid #dfe2e5; } + .markdown-body span.frame span img { + display: block; + float: left; } + .markdown-body span.frame span span { + display: block; + padding: 5px 0 0; + clear: both; + color: #24292e; } +.markdown-body span.align-center { + display: block; + overflow: hidden; + clear: both; } + .markdown-body span.align-center > span { + display: block; + margin: 13px auto 0; + overflow: hidden; + text-align: center; } + .markdown-body span.align-center span img { + margin: 0 auto; + text-align: center; } +.markdown-body span.align-right { + display: block; + overflow: hidden; + clear: both; } + .markdown-body span.align-right > span { + display: block; + margin: 13px 0 0; + overflow: hidden; + text-align: right; } + .markdown-body span.align-right span img { + margin: 0; + text-align: right; } +.markdown-body span.float-left { + display: block; + float: left; + margin-right: 13px; + overflow: hidden; } + .markdown-body span.float-left span { + margin: 13px 0 0; } +.markdown-body span.float-right { + display: block; + float: right; + margin-left: 13px; + overflow: hidden; } + .markdown-body span.float-right > span { + display: block; + margin: 13px auto 0; + overflow: hidden; + text-align: right; } + +.markdown-body code, +.markdown-body tt { + padding: 0.2em 0.4em; + margin: 0; + font-size: 85%; + background-color: rgba(27, 31, 35, 0.05); + border-radius: 6px; } + .markdown-body code br, + .markdown-body tt br { + display: none; } +.markdown-body del code { + text-decoration: inherit; } +.markdown-body pre { + word-wrap: normal; } + .markdown-body pre > code { + padding: 0; + margin: 0; + font-size: 100%; + word-break: normal; + white-space: pre; + background: transparent; + border: 0; } +.markdown-body .highlight { + margin-bottom: 16px; } + .markdown-body .highlight pre { + margin-bottom: 0; + word-break: normal; } +.markdown-body .highlight pre, +.markdown-body pre { + padding: 16px; + overflow: auto; + font-size: 85%; + line-height: 1.45; + background-color: #f6f8fa; + border-radius: 6px; } +.markdown-body pre code, +.markdown-body pre tt { + display: inline; + max-width: auto; + padding: 0; + margin: 0; + overflow: visible; + line-height: inherit; + word-wrap: normal; + background-color: transparent; + border: 0; } + +.markdown-body .csv-data td, +.markdown-body .csv-data th { + padding: 5px; + overflow: hidden; + font-size: 12px; + line-height: 1; + text-align: left; + white-space: nowrap; } +.markdown-body .csv-data .blob-num { + padding: 10px 8px 9px; + text-align: right; + background: #fff; + border: 0; } +.markdown-body .csv-data tr { + border-top: 0; } +.markdown-body .csv-data th { + font-weight: 600; + background: #f6f8fa; + border-top: 0; } + +.highlight { + background-color: #f8f8f8; } + .highlight table td { + padding: 5px; } + .highlight table pre { + margin: 0; } + .highlight .cm { + color: #999988; + font-style: italic; } + .highlight .cp { + color: #999999; + font-weight: bold; } + .highlight .c1 { + color: #999988; + font-style: italic; } + .highlight .cs { + color: #999999; + font-weight: bold; + font-style: italic; } + .highlight .c, + .highlight .ch, + .highlight .cd, + .highlight .cpf { + color: #999988; + font-style: italic; } + .highlight .err { + color: #a61717; + background-color: #e3d2d2; } + .highlight .gd { + color: #000000; + background-color: #ffdddd; } + .highlight .ge { + color: #000000; + font-style: italic; } + .highlight .gr { + color: #aa0000; } + .highlight .gh { + color: #999999; } + .highlight .gi { + color: #000000; + background-color: #ddffdd; } + .highlight .go { + color: #888888; } + .highlight .gp { + color: #555555; } + .highlight .gs { + font-weight: bold; } + .highlight .gu { + color: #aaaaaa; } + .highlight .gt { + color: #aa0000; } + .highlight .kc, + .highlight .kd, + .highlight .kn, + .highlight .kp, + .highlight .kr { + color: #000000; + font-weight: bold; } + .highlight .kt { + color: #445588; + font-weight: bold; } + .highlight .k, + .highlight .kv { + color: #000000; + font-weight: bold; } + .highlight .mf, + .highlight .mh, + .highlight .il, + .highlight .mi, + .highlight .mo, + .highlight .m, + .highlight .mb, + .highlight .mx { + color: #009999; } + .highlight .sb, + .highlight .sc, + .highlight .sd, + .highlight .s2, + .highlight .se, + .highlight .sh, + .highlight .si, + .highlight .sx { + color: #d14; } + .highlight .sr { + color: #009926; } + .highlight .s1 { + color: #d14; } + .highlight .ss { + color: #990073; } + .highlight .s, + .highlight .sa, + .highlight .dl { + color: #d14; } + .highlight .na { + color: #008080; } + .highlight .bp { + color: #999999; } + .highlight .nb { + color: #0086b3; } + .highlight .nc { + color: #445588; + font-weight: bold; } + .highlight .no { + color: #008080; } + .highlight .nd { + color: #3c5d5d; + font-weight: bold; } + .highlight .ni { + color: #800080; } + .highlight .ne, + .highlight .nf, + .highlight .fm, + .highlight .nl { + color: #990000; + font-weight: bold; } + .highlight .nn { + color: #555555; } + .highlight .nt { + color: #000080; } + .highlight .vc, + .highlight .vg, + .highlight .vi, + .highlight .nv, + .highlight .vm { + color: #008080; } + .highlight .ow, + .highlight .o { + color: #000000; + font-weight: bold; } + .highlight .w { + color: #bbbbbb; } + +@font-face { + font-family: "Lato"; + font-weight: 400; + font-style: normal; + font-display: block; + src: url("fonts/lato-normal.woff2") format("woff2"), url("fonts/lato-normal.woff") format("woff"); } +@font-face { + font-family: "Lato"; + font-weight: 400; + font-style: italic; + font-display: block; + src: url("fonts/lato-normal-italic.woff2") format("woff2"), url("fonts/lato-normal-italic.woff") format("woff"); } +@font-face { + font-family: "Lato"; + font-weight: 600; + font-style: normal; + font-display: block; + src: url("fonts/lato-bold.woff2") format("woff2"), url("fonts/lato-bold.woff") format("woff"); } +@font-face { + font-family: "Lato"; + font-weight: 600; + font-style: italic; + font-display: block; + src: url("fonts/lato-bold-italic.woff2") format("woff2"), url("fonts/lato-bold-italic.woff") format("woff"); } +@font-face { + font-family: "Roboto-Slab"; + font-weight: 400; + font-style: normal; + font-display: block; + src: url("fonts/Roboto-Slab-Regular.woff2") format("woff2"), url("fonts/Roboto-Slab-Regular.woff") format("woff"); } +@font-face { + font-family: "Roboto-Slab"; + font-weight: 600; + font-style: normal; + font-display: block; + src: url("fonts/Roboto-Slab-Bold.woff2") format("woff2"), url("fonts/Roboto-Slab-Bold.woff") format("woff"); } +@font-face { + font-family: "FontAwesome"; + font-weight: normal; + font-style: normal; + font-display: block; + src: url("fonts/fontawesome-webfont.eot"); + src: url("fonts/fontawesome-webfont.eot?#iefix") format("embedded-opentype"), url("fonts/fontawesome-webfont.woff2") format("woff2"), url("fonts/fontawesome-webfont.woff") format("woff"), url("fonts/fontawesome-webfont.ttf") format("truetype"), url("fonts/fontawesome-webfont.svg#fontawesomeregular") format("svg"); } +/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen + readers do not read off random characters that represent icons */ +.fa-glass:before { + content: ""; } + +.fa-music:before { + content: ""; } + +.fa-search:before { + content: ""; } + +.fa-envelope-o:before { + content: ""; } + +.fa-heart:before { + content: ""; } + +.fa-star:before { + content: ""; } + +.fa-star-o:before { + content: ""; } + +.fa-user:before { + content: ""; } + +.fa-film:before { + content: ""; } + +.fa-th-large:before { + content: ""; } + +.fa-th:before { + content: ""; } + +.fa-th-list:before { + content: ""; } + +.fa-check:before { + content: ""; } + +.fa-remove:before, +.fa-close:before, +.fa-times:before { + content: ""; } + +.fa-search-plus:before { + content: ""; } + +.fa-search-minus:before { + content: ""; } + +.fa-power-off:before { + content: ""; } + +.fa-signal:before { + content: ""; } + +.fa-gear:before, +.fa-cog:before { + content: ""; } + +.fa-trash-o:before { + content: ""; } + +.fa-home:before { + content: ""; } + +.fa-file-o:before { + content: ""; } + +.fa-clock-o:before { + content: ""; } + +.fa-road:before { + content: ""; } + +.fa-download:before { + content: ""; } + +.fa-arrow-circle-o-down:before { + content: ""; } + +.fa-arrow-circle-o-up:before { + content: ""; } + +.fa-inbox:before { + content: ""; } + +.fa-play-circle-o:before { + content: ""; } + +.fa-rotate-right:before, +.fa-repeat:before { + content: ""; } + +.fa-refresh:before { + content: ""; } + +.fa-list-alt:before { + content: ""; } + +.fa-lock:before { + content: ""; } + +.fa-flag:before { + content: ""; } + +.fa-headphones:before { + content: ""; } + +.fa-volume-off:before { + content: ""; } + +.fa-volume-down:before { + content: ""; } + +.fa-volume-up:before { + content: ""; } + +.fa-qrcode:before { + content: ""; } + +.fa-barcode:before { + content: ""; } + +.fa-tag:before { + content: ""; } + +.fa-tags:before { + content: ""; } + +.fa-book:before { + content: ""; } + +.fa-bookmark:before { + content: ""; } + +.fa-print:before { + content: ""; } + +.fa-camera:before { + content: ""; } + +.fa-font:before { + content: ""; } + +.fa-bold:before { + content: ""; } + +.fa-italic:before { + content: ""; } + +.fa-text-height:before { + content: ""; } + +.fa-text-width:before { + content: ""; } + +.fa-align-left:before { + content: ""; } + +.fa-align-center:before { + content: ""; } + +.fa-align-right:before { + content: ""; } + +.fa-align-justify:before { + content: ""; } + +.fa-list:before { + content: ""; } + +.fa-dedent:before, +.fa-outdent:before { + content: ""; } + +.fa-indent:before { + content: ""; } + +.fa-video-camera:before { + content: ""; } + +.fa-photo:before, +.fa-image:before, +.fa-picture-o:before { + content: ""; } + +.fa-pencil:before { + content: ""; } + +.fa-map-marker:before { + content: ""; } + +.fa-adjust:before { + content: ""; } + +.fa-tint:before { + content: ""; } + +.fa-edit:before, +.fa-pencil-square-o:before { + content: ""; } + +.fa-share-square-o:before { + content: ""; } + +.fa-check-square-o:before { + content: ""; } + +.fa-arrows:before { + content: ""; } + +.fa-step-backward:before { + content: ""; } + +.fa-fast-backward:before { + content: ""; } + +.fa-backward:before { + content: ""; } + +.fa-play:before { + content: ""; } + +.fa-pause:before { + content: ""; } + +.fa-stop:before { + content: ""; } + +.fa-forward:before { + content: ""; } + +.fa-fast-forward:before { + content: ""; } + +.fa-step-forward:before { + content: ""; } + +.fa-eject:before { + content: ""; } + +.fa-chevron-left:before { + content: ""; } + +.fa-chevron-right:before { + content: ""; } + +.fa-plus-circle:before { + content: ""; } + +.fa-minus-circle:before { + content: ""; } + +.fa-times-circle:before { + content: ""; } + +.fa-check-circle:before { + content: ""; } + +.fa-question-circle:before { + content: ""; } + +.fa-info-circle:before { + content: ""; } + +.fa-crosshairs:before { + content: ""; } + +.fa-times-circle-o:before { + content: ""; } + +.fa-check-circle-o:before { + content: ""; } + +.fa-ban:before { + content: ""; } + +.fa-arrow-left:before { + content: ""; } + +.fa-arrow-right:before { + content: ""; } + +.fa-arrow-up:before { + content: ""; } + +.fa-arrow-down:before { + content: ""; } + +.fa-mail-forward:before, +.fa-share:before { + content: ""; } + +.fa-expand:before { + content: ""; } + +.fa-compress:before { + content: ""; } + +.fa-plus:before { + content: ""; } + +.fa-minus:before { + content: ""; } + +.fa-asterisk:before { + content: ""; } + +.fa-exclamation-circle:before { + content: ""; } + +.fa-gift:before { + content: ""; } + +.fa-leaf:before { + content: ""; } + +.fa-fire:before { + content: ""; } + +.fa-eye:before { + content: ""; } + +.fa-eye-slash:before { + content: ""; } + +.fa-warning:before, +.fa-exclamation-triangle:before { + content: ""; } + +.fa-plane:before { + content: ""; } + +.fa-calendar:before { + content: ""; } + +.fa-random:before { + content: ""; } + +.fa-comment:before { + content: ""; } + +.fa-magnet:before { + content: ""; } + +.fa-chevron-up:before { + content: ""; } + +.fa-chevron-down:before { + content: ""; } + +.fa-retweet:before { + content: ""; } + +.fa-shopping-cart:before { + content: ""; } + +.fa-folder:before { + content: ""; } + +.fa-folder-open:before { + content: ""; } + +.fa-arrows-v:before { + content: ""; } + +.fa-arrows-h:before { + content: ""; } + +.fa-bar-chart-o:before, +.fa-bar-chart:before { + content: ""; } + +.fa-twitter-square:before { + content: ""; } + +.fa-facebook-square:before { + content: ""; } + +.fa-camera-retro:before { + content: ""; } + +.fa-key:before { + content: ""; } + +.fa-gears:before, +.fa-cogs:before { + content: ""; } + +.fa-comments:before { + content: ""; } + +.fa-thumbs-o-up:before { + content: ""; } + +.fa-thumbs-o-down:before { + content: ""; } + +.fa-star-half:before { + content: ""; } + +.fa-heart-o:before { + content: ""; } + +.fa-sign-out:before { + content: ""; } + +.fa-linkedin-square:before { + content: ""; } + +.fa-thumb-tack:before { + content: ""; } + +.fa-external-link:before { + content: ""; } + +.fa-sign-in:before { + content: ""; } + +.fa-trophy:before { + content: ""; } + +.fa-github-square:before { + content: ""; } + +.fa-upload:before { + content: ""; } + +.fa-lemon-o:before { + content: ""; } + +.fa-phone:before { + content: ""; } + +.fa-square-o:before { + content: ""; } + +.fa-bookmark-o:before { + content: ""; } + +.fa-phone-square:before { + content: ""; } + +.fa-twitter:before { + content: ""; } + +.fa-facebook-f:before, +.fa-facebook:before { + content: ""; } + +.fa-github:before { + content: ""; } + +.fa-unlock:before { + content: ""; } + +.fa-credit-card:before { + content: ""; } + +.fa-feed:before, +.fa-rss:before { + content: ""; } + +.fa-hdd-o:before { + content: ""; } + +.fa-bullhorn:before { + content: ""; } + +.fa-bell:before { + content: ""; } + +.fa-certificate:before { + content: ""; } + +.fa-hand-o-right:before { + content: ""; } + +.fa-hand-o-left:before { + content: ""; } + +.fa-hand-o-up:before { + content: ""; } + +.fa-hand-o-down:before { + content: ""; } + +.fa-arrow-circle-left:before { + content: ""; } + +.fa-arrow-circle-right:before { + content: ""; } + +.fa-arrow-circle-up:before { + content: ""; } + +.fa-arrow-circle-down:before { + content: ""; } + +.fa-globe:before { + content: ""; } + +.fa-wrench:before { + content: ""; } + +.fa-tasks:before { + content: ""; } + +.fa-filter:before { + content: ""; } + +.fa-briefcase:before { + content: ""; } + +.fa-arrows-alt:before { + content: ""; } + +.fa-group:before, +.fa-users:before { + content: ""; } + +.fa-chain:before, +.fa-link:before { + content: ""; } + +.fa-cloud:before { + content: ""; } + +.fa-flask:before { + content: ""; } + +.fa-cut:before, +.fa-scissors:before { + content: ""; } + +.fa-copy:before, +.fa-files-o:before { + content: ""; } + +.fa-paperclip:before { + content: ""; } + +.fa-save:before, +.fa-floppy-o:before { + content: ""; } + +.fa-square:before { + content: ""; } + +.fa-navicon:before, +.fa-reorder:before, +.fa-bars:before { + content: ""; } + +.fa-list-ul:before { + content: ""; } + +.fa-list-ol:before { + content: ""; } + +.fa-strikethrough:before { + content: ""; } + +.fa-underline:before { + content: ""; } + +.fa-table:before { + content: ""; } + +.fa-magic:before { + content: ""; } + +.fa-truck:before { + content: ""; } + +.fa-pinterest:before { + content: ""; } + +.fa-pinterest-square:before { + content: ""; } + +.fa-google-plus-square:before { + content: ""; } + +.fa-google-plus:before { + content: ""; } + +.fa-money:before { + content: ""; } + +.fa-caret-down:before { + content: ""; } + +.fa-caret-up:before { + content: ""; } + +.fa-caret-left:before { + content: ""; } + +.fa-caret-right:before { + content: ""; } + +.fa-columns:before { + content: ""; } + +.fa-unsorted:before, +.fa-sort:before { + content: ""; } + +.fa-sort-down:before, +.fa-sort-desc:before { + content: ""; } + +.fa-sort-up:before, +.fa-sort-asc:before { + content: ""; } + +.fa-envelope:before { + content: ""; } + +.fa-linkedin:before { + content: ""; } + +.fa-rotate-left:before, +.fa-undo:before { + content: ""; } + +.fa-legal:before, +.fa-gavel:before { + content: ""; } + +.fa-dashboard:before, +.fa-tachometer:before { + content: ""; } + +.fa-comment-o:before { + content: ""; } + +.fa-comments-o:before { + content: ""; } + +.fa-flash:before, +.fa-bolt:before { + content: ""; } + +.fa-sitemap:before { + content: ""; } + +.fa-umbrella:before { + content: ""; } + +.fa-paste:before, +.fa-clipboard:before { + content: ""; } + +.fa-lightbulb-o:before { + content: ""; } + +.fa-exchange:before { + content: ""; } + +.fa-cloud-download:before { + content: ""; } + +.fa-cloud-upload:before { + content: ""; } + +.fa-user-md:before { + content: ""; } + +.fa-stethoscope:before { + content: ""; } + +.fa-suitcase:before { + content: ""; } + +.fa-bell-o:before { + content: ""; } + +.fa-coffee:before { + content: ""; } + +.fa-cutlery:before { + content: ""; } + +.fa-file-text-o:before { + content: ""; } + +.fa-building-o:before { + content: ""; } + +.fa-hospital-o:before { + content: ""; } + +.fa-ambulance:before { + content: ""; } + +.fa-medkit:before { + content: ""; } + +.fa-fighter-jet:before { + content: ""; } + +.fa-beer:before { + content: ""; } + +.fa-h-square:before { + content: ""; } + +.fa-plus-square:before { + content: ""; } + +.fa-angle-double-left:before { + content: ""; } + +.fa-angle-double-right:before { + content: ""; } + +.fa-angle-double-up:before { + content: ""; } + +.fa-angle-double-down:before { + content: ""; } + +.fa-angle-left:before { + content: ""; } + +.fa-angle-right:before { + content: ""; } + +.fa-angle-up:before { + content: ""; } + +.fa-angle-down:before { + content: ""; } + +.fa-desktop:before { + content: ""; } + +.fa-laptop:before { + content: ""; } + +.fa-tablet:before { + content: ""; } + +.fa-mobile-phone:before, +.fa-mobile:before { + content: ""; } + +.fa-circle-o:before { + content: ""; } + +.fa-quote-left:before { + content: ""; } + +.fa-quote-right:before { + content: ""; } + +.fa-spinner:before { + content: ""; } + +.fa-circle:before { + content: ""; } + +.fa-mail-reply:before, +.fa-reply:before { + content: ""; } + +.fa-github-alt:before { + content: ""; } + +.fa-folder-o:before { + content: ""; } + +.fa-folder-open-o:before { + content: ""; } + +.fa-smile-o:before { + content: ""; } + +.fa-frown-o:before { + content: ""; } + +.fa-meh-o:before { + content: ""; } + +.fa-gamepad:before { + content: ""; } + +.fa-keyboard-o:before { + content: ""; } + +.fa-flag-o:before { + content: ""; } + +.fa-flag-checkered:before { + content: ""; } + +.fa-terminal:before { + content: ""; } + +.fa-code:before { + content: ""; } + +.fa-mail-reply-all:before, +.fa-reply-all:before { + content: ""; } + +.fa-star-half-empty:before, +.fa-star-half-full:before, +.fa-star-half-o:before { + content: ""; } + +.fa-location-arrow:before { + content: ""; } + +.fa-crop:before { + content: ""; } + +.fa-code-fork:before { + content: ""; } + +.fa-unlink:before, +.fa-chain-broken:before { + content: ""; } + +.fa-question:before { + content: ""; } + +.fa-info:before { + content: ""; } + +.fa-exclamation:before { + content: ""; } + +.fa-superscript:before { + content: ""; } + +.fa-subscript:before { + content: ""; } + +.fa-eraser:before { + content: ""; } + +.fa-puzzle-piece:before { + content: ""; } + +.fa-microphone:before { + content: ""; } + +.fa-microphone-slash:before { + content: ""; } + +.fa-shield:before { + content: ""; } + +.fa-calendar-o:before { + content: ""; } + +.fa-fire-extinguisher:before { + content: ""; } + +.fa-rocket:before { + content: ""; } + +.fa-maxcdn:before { + content: ""; } + +.fa-chevron-circle-left:before { + content: ""; } + +.fa-chevron-circle-right:before { + content: ""; } + +.fa-chevron-circle-up:before { + content: ""; } + +.fa-chevron-circle-down:before { + content: ""; } + +.fa-html5:before { + content: ""; } + +.fa-css3:before { + content: ""; } + +.fa-anchor:before { + content: ""; } + +.fa-unlock-alt:before { + content: ""; } + +.fa-bullseye:before { + content: ""; } + +.fa-ellipsis-h:before { + content: ""; } + +.fa-ellipsis-v:before { + content: ""; } + +.fa-rss-square:before { + content: ""; } + +.fa-play-circle:before { + content: ""; } + +.fa-ticket:before { + content: ""; } + +.fa-minus-square:before { + content: ""; } + +.fa-minus-square-o:before, .toctree > ul .toc.current > a .fa-plus-square-o:before { + content: ""; } + +.fa-level-up:before { + content: ""; } + +.fa-level-down:before { + content: ""; } + +.fa-check-square:before { + content: ""; } + +.fa-pencil-square:before { + content: ""; } + +.fa-external-link-square:before { + content: ""; } + +.fa-share-square:before { + content: ""; } + +.fa-compass:before { + content: ""; } + +.fa-toggle-down:before, +.fa-caret-square-o-down:before { + content: ""; } + +.fa-toggle-up:before, +.fa-caret-square-o-up:before { + content: ""; } + +.fa-toggle-right:before, +.fa-caret-square-o-right:before { + content: ""; } + +.fa-euro:before, +.fa-eur:before { + content: ""; } + +.fa-gbp:before { + content: ""; } + +.fa-dollar:before, +.fa-usd:before { + content: ""; } + +.fa-rupee:before, +.fa-inr:before { + content: ""; } + +.fa-cny:before, +.fa-rmb:before, +.fa-yen:before, +.fa-jpy:before { + content: ""; } + +.fa-ruble:before, +.fa-rouble:before, +.fa-rub:before { + content: ""; } + +.fa-won:before, +.fa-krw:before { + content: ""; } + +.fa-bitcoin:before, +.fa-btc:before { + content: ""; } + +.fa-file:before { + content: ""; } + +.fa-file-text:before { + content: ""; } + +.fa-sort-alpha-asc:before { + content: ""; } + +.fa-sort-alpha-desc:before { + content: ""; } + +.fa-sort-amount-asc:before { + content: ""; } + +.fa-sort-amount-desc:before { + content: ""; } + +.fa-sort-numeric-asc:before { + content: ""; } + +.fa-sort-numeric-desc:before { + content: ""; } + +.fa-thumbs-up:before { + content: ""; } + +.fa-thumbs-down:before { + content: ""; } + +.fa-youtube-square:before { + content: ""; } + +.fa-youtube:before { + content: ""; } + +.fa-xing:before { + content: ""; } + +.fa-xing-square:before { + content: ""; } + +.fa-youtube-play:before { + content: ""; } + +.fa-dropbox:before { + content: ""; } + +.fa-stack-overflow:before { + content: ""; } + +.fa-instagram:before { + content: ""; } + +.fa-flickr:before { + content: ""; } + +.fa-adn:before { + content: ""; } + +.fa-bitbucket:before { + content: ""; } + +.fa-bitbucket-square:before { + content: ""; } + +.fa-tumblr:before { + content: ""; } + +.fa-tumblr-square:before { + content: ""; } + +.fa-long-arrow-down:before { + content: ""; } + +.fa-long-arrow-up:before { + content: ""; } + +.fa-long-arrow-left:before { + content: ""; } + +.fa-long-arrow-right:before { + content: ""; } + +.fa-apple:before { + content: ""; } + +.fa-windows:before { + content: ""; } + +.fa-android:before { + content: ""; } + +.fa-linux:before { + content: ""; } + +.fa-dribbble:before { + content: ""; } + +.fa-skype:before { + content: ""; } + +.fa-foursquare:before { + content: ""; } + +.fa-trello:before { + content: ""; } + +.fa-female:before { + content: ""; } + +.fa-male:before { + content: ""; } + +.fa-gittip:before, +.fa-gratipay:before { + content: ""; } + +.fa-sun-o:before { + content: ""; } + +.fa-moon-o:before { + content: ""; } + +.fa-archive:before { + content: ""; } + +.fa-bug:before { + content: ""; } + +.fa-vk:before { + content: ""; } + +.fa-weibo:before { + content: ""; } + +.fa-renren:before { + content: ""; } + +.fa-pagelines:before { + content: ""; } + +.fa-stack-exchange:before { + content: ""; } + +.fa-arrow-circle-o-right:before { + content: ""; } + +.fa-arrow-circle-o-left:before { + content: ""; } + +.fa-toggle-left:before, +.fa-caret-square-o-left:before { + content: ""; } + +.fa-dot-circle-o:before { + content: ""; } + +.fa-wheelchair:before { + content: ""; } + +.fa-vimeo-square:before { + content: ""; } + +.fa-turkish-lira:before, +.fa-try:before { + content: ""; } + +.fa-plus-square-o:before { + content: ""; } + +.fa-space-shuttle:before { + content: ""; } + +.fa-slack:before { + content: ""; } + +.fa-envelope-square:before { + content: ""; } + +.fa-wordpress:before { + content: ""; } + +.fa-openid:before { + content: ""; } + +.fa-institution:before, +.fa-bank:before, +.fa-university:before { + content: ""; } + +.fa-mortar-board:before, +.fa-graduation-cap:before { + content: ""; } + +.fa-yahoo:before { + content: ""; } + +.fa-google:before { + content: ""; } + +.fa-reddit:before { + content: ""; } + +.fa-reddit-square:before { + content: ""; } + +.fa-stumbleupon-circle:before { + content: ""; } + +.fa-stumbleupon:before { + content: ""; } + +.fa-delicious:before { + content: ""; } + +.fa-digg:before { + content: ""; } + +.fa-pied-piper-pp:before { + content: ""; } + +.fa-pied-piper-alt:before { + content: ""; } + +.fa-drupal:before { + content: ""; } + +.fa-joomla:before { + content: ""; } + +.fa-language:before { + content: ""; } + +.fa-fax:before { + content: ""; } + +.fa-building:before { + content: ""; } + +.fa-child:before { + content: ""; } + +.fa-paw:before { + content: ""; } + +.fa-spoon:before { + content: ""; } + +.fa-cube:before { + content: ""; } + +.fa-cubes:before { + content: ""; } + +.fa-behance:before { + content: ""; } + +.fa-behance-square:before { + content: ""; } + +.fa-steam:before { + content: ""; } + +.fa-steam-square:before { + content: ""; } + +.fa-recycle:before { + content: ""; } + +.fa-automobile:before, +.fa-car:before { + content: ""; } + +.fa-cab:before, +.fa-taxi:before { + content: ""; } + +.fa-tree:before { + content: ""; } + +.fa-spotify:before { + content: ""; } + +.fa-deviantart:before { + content: ""; } + +.fa-soundcloud:before { + content: ""; } + +.fa-database:before { + content: ""; } + +.fa-file-pdf-o:before { + content: ""; } + +.fa-file-word-o:before { + content: ""; } + +.fa-file-excel-o:before { + content: ""; } + +.fa-file-powerpoint-o:before { + content: ""; } + +.fa-file-photo-o:before, +.fa-file-picture-o:before, +.fa-file-image-o:before { + content: ""; } + +.fa-file-zip-o:before, +.fa-file-archive-o:before { + content: ""; } + +.fa-file-sound-o:before, +.fa-file-audio-o:before { + content: ""; } + +.fa-file-movie-o:before, +.fa-file-video-o:before { + content: ""; } + +.fa-file-code-o:before { + content: ""; } + +.fa-vine:before { + content: ""; } + +.fa-codepen:before { + content: ""; } + +.fa-jsfiddle:before { + content: ""; } + +.fa-life-bouy:before, +.fa-life-buoy:before, +.fa-life-saver:before, +.fa-support:before, +.fa-life-ring:before { + content: ""; } + +.fa-circle-o-notch:before { + content: ""; } + +.fa-ra:before, +.fa-resistance:before, +.fa-rebel:before { + content: ""; } + +.fa-ge:before, +.fa-empire:before { + content: ""; } + +.fa-git-square:before { + content: ""; } + +.fa-git:before { + content: ""; } + +.fa-y-combinator-square:before, +.fa-yc-square:before, +.fa-hacker-news:before { + content: ""; } + +.fa-tencent-weibo:before { + content: ""; } + +.fa-qq:before { + content: ""; } + +.fa-wechat:before, +.fa-weixin:before { + content: ""; } + +.fa-send:before, +.fa-paper-plane:before { + content: ""; } + +.fa-send-o:before, +.fa-paper-plane-o:before { + content: ""; } + +.fa-history:before { + content: ""; } + +.fa-circle-thin:before { + content: ""; } + +.fa-header:before { + content: ""; } + +.fa-paragraph:before { + content: ""; } + +.fa-sliders:before { + content: ""; } + +.fa-share-alt:before { + content: ""; } + +.fa-share-alt-square:before { + content: ""; } + +.fa-bomb:before { + content: ""; } + +.fa-soccer-ball-o:before, +.fa-futbol-o:before { + content: ""; } + +.fa-tty:before { + content: ""; } + +.fa-binoculars:before { + content: ""; } + +.fa-plug:before { + content: ""; } + +.fa-slideshare:before { + content: ""; } + +.fa-twitch:before { + content: ""; } + +.fa-yelp:before { + content: ""; } + +.fa-newspaper-o:before { + content: ""; } + +.fa-wifi:before { + content: ""; } + +.fa-calculator:before { + content: ""; } + +.fa-paypal:before { + content: ""; } + +.fa-google-wallet:before { + content: ""; } + +.fa-cc-visa:before { + content: ""; } + +.fa-cc-mastercard:before { + content: ""; } + +.fa-cc-discover:before { + content: ""; } + +.fa-cc-amex:before { + content: ""; } + +.fa-cc-paypal:before { + content: ""; } + +.fa-cc-stripe:before { + content: ""; } + +.fa-bell-slash:before { + content: ""; } + +.fa-bell-slash-o:before { + content: ""; } + +.fa-trash:before { + content: ""; } + +.fa-copyright:before { + content: ""; } + +.fa-at:before { + content: ""; } + +.fa-eyedropper:before { + content: ""; } + +.fa-paint-brush:before { + content: ""; } + +.fa-birthday-cake:before { + content: ""; } + +.fa-area-chart:before { + content: ""; } + +.fa-pie-chart:before { + content: ""; } + +.fa-line-chart:before { + content: ""; } + +.fa-lastfm:before { + content: ""; } + +.fa-lastfm-square:before { + content: ""; } + +.fa-toggle-off:before { + content: ""; } + +.fa-toggle-on:before { + content: ""; } + +.fa-bicycle:before { + content: ""; } + +.fa-bus:before { + content: ""; } + +.fa-ioxhost:before { + content: ""; } + +.fa-angellist:before { + content: ""; } + +.fa-cc:before { + content: ""; } + +.fa-shekel:before, +.fa-sheqel:before, +.fa-ils:before { + content: ""; } + +.fa-meanpath:before { + content: ""; } + +.fa-buysellads:before { + content: ""; } + +.fa-connectdevelop:before { + content: ""; } + +.fa-dashcube:before { + content: ""; } + +.fa-forumbee:before { + content: ""; } + +.fa-leanpub:before { + content: ""; } + +.fa-sellsy:before { + content: ""; } + +.fa-shirtsinbulk:before { + content: ""; } + +.fa-simplybuilt:before { + content: ""; } + +.fa-skyatlas:before { + content: ""; } + +.fa-cart-plus:before { + content: ""; } + +.fa-cart-arrow-down:before { + content: ""; } + +.fa-diamond:before { + content: ""; } + +.fa-ship:before { + content: ""; } + +.fa-user-secret:before { + content: ""; } + +.fa-motorcycle:before { + content: ""; } + +.fa-street-view:before { + content: ""; } + +.fa-heartbeat:before { + content: ""; } + +.fa-venus:before { + content: ""; } + +.fa-mars:before { + content: ""; } + +.fa-mercury:before { + content: ""; } + +.fa-intersex:before, +.fa-transgender:before { + content: ""; } + +.fa-transgender-alt:before { + content: ""; } + +.fa-venus-double:before { + content: ""; } + +.fa-mars-double:before { + content: ""; } + +.fa-venus-mars:before { + content: ""; } + +.fa-mars-stroke:before { + content: ""; } + +.fa-mars-stroke-v:before { + content: ""; } + +.fa-mars-stroke-h:before { + content: ""; } + +.fa-neuter:before { + content: ""; } + +.fa-genderless:before { + content: ""; } + +.fa-facebook-official:before { + content: ""; } + +.fa-pinterest-p:before { + content: ""; } + +.fa-whatsapp:before { + content: ""; } + +.fa-server:before { + content: ""; } + +.fa-user-plus:before { + content: ""; } + +.fa-user-times:before { + content: ""; } + +.fa-hotel:before, +.fa-bed:before { + content: ""; } + +.fa-viacoin:before { + content: ""; } + +.fa-train:before { + content: ""; } + +.fa-subway:before { + content: ""; } + +.fa-medium:before { + content: ""; } + +.fa-yc:before, +.fa-y-combinator:before { + content: ""; } + +.fa-optin-monster:before { + content: ""; } + +.fa-opencart:before { + content: ""; } + +.fa-expeditedssl:before { + content: ""; } + +.fa-battery-4:before, +.fa-battery:before, +.fa-battery-full:before { + content: ""; } + +.fa-battery-3:before, +.fa-battery-three-quarters:before { + content: ""; } + +.fa-battery-2:before, +.fa-battery-half:before { + content: ""; } + +.fa-battery-1:before, +.fa-battery-quarter:before { + content: ""; } + +.fa-battery-0:before, +.fa-battery-empty:before { + content: ""; } + +.fa-mouse-pointer:before { + content: ""; } + +.fa-i-cursor:before { + content: ""; } + +.fa-object-group:before { + content: ""; } + +.fa-object-ungroup:before { + content: ""; } + +.fa-sticky-note:before { + content: ""; } + +.fa-sticky-note-o:before { + content: ""; } + +.fa-cc-jcb:before { + content: ""; } + +.fa-cc-diners-club:before { + content: ""; } + +.fa-clone:before { + content: ""; } + +.fa-balance-scale:before { + content: ""; } + +.fa-hourglass-o:before { + content: ""; } + +.fa-hourglass-1:before, +.fa-hourglass-start:before { + content: ""; } + +.fa-hourglass-2:before, +.fa-hourglass-half:before { + content: ""; } + +.fa-hourglass-3:before, +.fa-hourglass-end:before { + content: ""; } + +.fa-hourglass:before { + content: ""; } + +.fa-hand-grab-o:before, +.fa-hand-rock-o:before { + content: ""; } + +.fa-hand-stop-o:before, +.fa-hand-paper-o:before { + content: ""; } + +.fa-hand-scissors-o:before { + content: ""; } + +.fa-hand-lizard-o:before { + content: ""; } + +.fa-hand-spock-o:before { + content: ""; } + +.fa-hand-pointer-o:before { + content: ""; } + +.fa-hand-peace-o:before { + content: ""; } + +.fa-trademark:before { + content: ""; } + +.fa-registered:before { + content: ""; } + +.fa-creative-commons:before { + content: ""; } + +.fa-gg:before { + content: ""; } + +.fa-gg-circle:before { + content: ""; } + +.fa-tripadvisor:before { + content: ""; } + +.fa-odnoklassniki:before { + content: ""; } + +.fa-odnoklassniki-square:before { + content: ""; } + +.fa-get-pocket:before { + content: ""; } + +.fa-wikipedia-w:before { + content: ""; } + +.fa-safari:before { + content: ""; } + +.fa-chrome:before { + content: ""; } + +.fa-firefox:before { + content: ""; } + +.fa-opera:before { + content: ""; } + +.fa-internet-explorer:before { + content: ""; } + +.fa-tv:before, +.fa-television:before { + content: ""; } + +.fa-contao:before { + content: ""; } + +.fa-500px:before { + content: ""; } + +.fa-amazon:before { + content: ""; } + +.fa-calendar-plus-o:before { + content: ""; } + +.fa-calendar-minus-o:before { + content: ""; } + +.fa-calendar-times-o:before { + content: ""; } + +.fa-calendar-check-o:before { + content: ""; } + +.fa-industry:before { + content: ""; } + +.fa-map-pin:before { + content: ""; } + +.fa-map-signs:before { + content: ""; } + +.fa-map-o:before { + content: ""; } + +.fa-map:before { + content: ""; } + +.fa-commenting:before { + content: ""; } + +.fa-commenting-o:before { + content: ""; } + +.fa-houzz:before { + content: ""; } + +.fa-vimeo:before { + content: ""; } + +.fa-black-tie:before { + content: ""; } + +.fa-fonticons:before { + content: ""; } + +.fa-reddit-alien:before { + content: ""; } + +.fa-edge:before { + content: ""; } + +.fa-credit-card-alt:before { + content: ""; } + +.fa-codiepie:before { + content: ""; } + +.fa-modx:before { + content: ""; } + +.fa-fort-awesome:before { + content: ""; } + +.fa-usb:before { + content: ""; } + +.fa-product-hunt:before { + content: ""; } + +.fa-mixcloud:before { + content: ""; } + +.fa-scribd:before { + content: ""; } + +.fa-pause-circle:before { + content: ""; } + +.fa-pause-circle-o:before { + content: ""; } + +.fa-stop-circle:before { + content: ""; } + +.fa-stop-circle-o:before { + content: ""; } + +.fa-shopping-bag:before { + content: ""; } + +.fa-shopping-basket:before { + content: ""; } + +.fa-hashtag:before { + content: ""; } + +.fa-bluetooth:before { + content: ""; } + +.fa-bluetooth-b:before { + content: ""; } + +.fa-percent:before { + content: ""; } + +.fa-gitlab:before { + content: ""; } + +.fa-wpbeginner:before { + content: ""; } + +.fa-wpforms:before { + content: ""; } + +.fa-envira:before { + content: ""; } + +.fa-universal-access:before { + content: ""; } + +.fa-wheelchair-alt:before { + content: ""; } + +.fa-question-circle-o:before { + content: ""; } + +.fa-blind:before { + content: ""; } + +.fa-audio-description:before { + content: ""; } + +.fa-volume-control-phone:before { + content: ""; } + +.fa-braille:before { + content: ""; } + +.fa-assistive-listening-systems:before { + content: ""; } + +.fa-asl-interpreting:before, +.fa-american-sign-language-interpreting:before { + content: ""; } + +.fa-deafness:before, +.fa-hard-of-hearing:before, +.fa-deaf:before { + content: ""; } + +.fa-glide:before { + content: ""; } + +.fa-glide-g:before { + content: ""; } + +.fa-signing:before, +.fa-sign-language:before { + content: ""; } + +.fa-low-vision:before { + content: ""; } + +.fa-viadeo:before { + content: ""; } + +.fa-viadeo-square:before { + content: ""; } + +.fa-snapchat:before { + content: ""; } + +.fa-snapchat-ghost:before { + content: ""; } + +.fa-snapchat-square:before { + content: ""; } + +.fa-pied-piper:before { + content: ""; } + +.fa-first-order:before { + content: ""; } + +.fa-yoast:before { + content: ""; } + +.fa-themeisle:before { + content: ""; } + +.fa-google-plus-circle:before, +.fa-google-plus-official:before { + content: ""; } + +.fa-fa:before, +.fa-font-awesome:before { + content: ""; } + +.fa-handshake-o:before { + content: ""; } + +.fa-envelope-open:before { + content: ""; } + +.fa-envelope-open-o:before { + content: ""; } + +.fa-linode:before { + content: ""; } + +.fa-address-book:before { + content: ""; } + +.fa-address-book-o:before { + content: ""; } + +.fa-vcard:before, +.fa-address-card:before { + content: ""; } + +.fa-vcard-o:before, +.fa-address-card-o:before { + content: ""; } + +.fa-user-circle:before { + content: ""; } + +.fa-user-circle-o:before { + content: ""; } + +.fa-user-o:before { + content: ""; } + +.fa-id-badge:before { + content: ""; } + +.fa-drivers-license:before, +.fa-id-card:before { + content: ""; } + +.fa-drivers-license-o:before, +.fa-id-card-o:before { + content: ""; } + +.fa-quora:before { + content: ""; } + +.fa-free-code-camp:before { + content: ""; } + +.fa-telegram:before { + content: ""; } + +.fa-thermometer-4:before, +.fa-thermometer:before, +.fa-thermometer-full:before { + content: ""; } + +.fa-thermometer-3:before, +.fa-thermometer-three-quarters:before { + content: ""; } + +.fa-thermometer-2:before, +.fa-thermometer-half:before { + content: ""; } + +.fa-thermometer-1:before, +.fa-thermometer-quarter:before { + content: ""; } + +.fa-thermometer-0:before, +.fa-thermometer-empty:before { + content: ""; } + +.fa-shower:before { + content: ""; } + +.fa-bathtub:before, +.fa-s15:before, +.fa-bath:before { + content: ""; } + +.fa-podcast:before { + content: ""; } + +.fa-window-maximize:before { + content: ""; } + +.fa-window-minimize:before { + content: ""; } + +.fa-window-restore:before { + content: ""; } + +.fa-times-rectangle:before, +.fa-window-close:before { + content: ""; } + +.fa-times-rectangle-o:before, +.fa-window-close-o:before { + content: ""; } + +.fa-bandcamp:before { + content: ""; } + +.fa-grav:before { + content: ""; } + +.fa-etsy:before { + content: ""; } + +.fa-imdb:before { + content: ""; } + +.fa-ravelry:before { + content: ""; } + +.fa-eercast:before { + content: ""; } + +.fa-microchip:before { + content: ""; } + +.fa-snowflake-o:before { + content: ""; } + +.fa-superpowers:before { + content: ""; } + +.fa-wpexplorer:before { + content: ""; } + +.fa-meetup:before { + content: ""; } + +.menu-sm, .sidebar-wrap, .addons-wrap { + position: fixed; + bottom: 0; + left: -85%; + width: 85%; + max-height: 100%; } + .menu-sm.shift, .shift.sidebar-wrap, .shift.addons-wrap { + left: 0; } + +.sidebar-wrap { + top: 0; } + .sidebar-wrap .sidebar > :last-child { + margin-bottom: 5em; } + +.content-wrap.shift { + position: fixed; + top: 0; + bottom: 0; + left: 85%; + min-width: 100%; } + +@media (min-width: 768px) { + .menu-md, .sidebar-wrap, .addons-wrap { + left: 0; + width: 300px; } + + .sidebar-wrap .sidebar { + width: 320px; } + .sidebar-wrap .sidebar .header, + .sidebar-wrap .sidebar .toctree { + width: 300px; } + + .content-wrap { + margin-left: 300px; } + .content-wrap.shift { + position: relative; + left: 0; + min-width: 0; } } +@media (min-width: 1280px) { + .content-wrap { + max-width: 980px; } } +.font-body { + font-family: "Lato", BlinkMacSystemFont, "Segoe UI", Helvetica, sans-serif; + font-weight: 400; } + +.font-head { + font-family: "Roboto-Slab", sans-serif; + font-weight: 600; } + +.font-mono { + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; } + +.fa { + display: inline-block; + font: normal normal normal 14px/1 "FontAwesome"; } + +.breadcrumb-item { + margin: 0; } + .breadcrumb-item::after { + padding-right: 3px; + padding-left: 3px; } + +.container { + font-weight: 400; + color: #3c454e; + background: white; } + +@media (min-width: 1280px) { + .container { + background: rgba(60, 69, 78, 0.1); } } +.sidebar { + color: white; + background: #262c31; } + .sidebar a { + text-decoration: none; } + .sidebar li { + list-style: none; } + .sidebar .version { + color: rgba(255, 255, 255, 0.3); } + +.toctree a { + color: white; + padding: 0.5em; } +.toctree .caption { + color: #55a5d9; + font-weight: 600; + line-height: 32px; } +.toctree .fa { + margin-right: 2px; } +.toctree > ul > .toc > a { + padding-left: 12px; } +.toctree > ul > .toc:not(.current) > a:hover { + background: rgba(255, 255, 255, 0.1); } +.toctree > ul > .toc:not(.current) > a:active { + background: #1b557a; } +.toctree > ul .toc.current a { + color: #404040; } + .toctree > ul .toc.current a:hover { + background: rgba(255, 255, 255, 0.1); } + .toctree > ul .toc.current a.current { + font-weight: bold; + background: white; + border-top: 1px solid var(--toc-2); + border-bottom: 1px solid var(--toc-2); } +.toctree > ul > .toc.current { + background: var(--toc-1); } + +.toc.level-1.current > a { + padding-left: 12px; + background: var(--toc-1); } +.toc.level-1.current > ul { + background: var(--toc-2); } +.toc.level-1.current .level-2 > a { + padding-left: 36px; } +.toc.level-2.current > a { + padding-left: 36px; + background: var(--toc-2); } +.toc.level-2.current > ul { + background: var(--toc-3); } +.toc.level-2.current .level-3 > a { + padding-left: 60px; } +.toc.level-3.current > a { + padding-left: 60px; + background: var(--toc-3); } +.toc.level-3.current > ul { + background: var(--toc-4); } +.toc.level-3.current .level-4 > a { + padding-left: 84px; } +.toc.level-4.current > a { + padding-left: 84px; + background: var(--toc-4); } +.toc.level-4.current > ul { + background: var(--toc-5); } +.toc.level-4.current .level-5 > a { + padding-left: 108px; } +.toc.level-5.current > a { + padding-left: 108px; + background: var(--toc-5); } +.toc.level-5.current > ul { + background: var(--toc-6); } +.toc.level-5.current .level-6 > a { + padding-left: 132px; } +.toc.level-6.current > a { + padding-left: 132px; + background: var(--toc-6); } +.toc.level-6.current > ul { + background: var(--toc-7); } +.toc.level-6.current .level-7 > a { + padding-left: 156px; } +.toc.level-7.current > a { + padding-left: 156px; + background: var(--toc-7); } +.toc.level-7.current > ul { + background: var(--toc-8); } +.toc.level-7.current .level-8 > a { + padding-left: 180px; } +.toc.level-8.current > a { + padding-left: 180px; + background: var(--toc-8); } +.toc.level-8.current > ul { + background: var(--toc-9); } +.toc.level-8.current .level-9 > a { + padding-left: 204px; } +.toc.level-9.current > a { + padding-left: 204px; + background: var(--toc-9); } +.toc.level-9.current > ul { + background: var(--toc-10); } +.toc.level-9.current .level-10 > a { + padding-left: 228px; } +.toc.level-10.current > a { + padding-left: 228px; + background: var(--toc-10); } +.toc.level-10.current > ul { + background: var(--toc-11); } +.toc.level-10.current .level-11 > a { + padding-left: 252px; } +.toc.level-11.current > a { + padding-left: 252px; + background: var(--toc-11); } +.toc.level-11.current > ul { + background: var(--toc-12); } +.toc.level-11.current .level-12 > a { + padding-left: 276px; } + +.addons-wrap { + background-color: #14171a; } + .addons-wrap .status { + cursor: pointer; + background-color: #1b1f23; } + .addons-wrap .status .branch .fa { + color: white; } + .addons-wrap .status .branch .name { + color: #28a745; } + .addons-wrap .status:active { + background: #1b557a; } + .addons-wrap .addons { + color: grey; } + .addons-wrap .addons dl { + margin: 0; } + .addons-wrap .addons dd { + display: inline-block; } + .addons-wrap .addons dd a { + display: inline-block; + padding: 6px; + color: white; } + +.content-wrap { + font-size: 16px; + background: white; } + +.header { + color: white; + background: #2980b9; } + .header input { + border-radius: 50px; + border: 1px solid #2472a4; + font-size: 80%; } + +.title { + font-weight: 600; + color: white; } + .title a { + color: white; } + .title a:hover { + background: rgba(255, 255, 255, 0.1); } + +.markdown-body { + font-weight: 400; } + .markdown-body .d-lang, .markdown-body div.highlighter-rouge, .markdown-body .mermaid-wrap { + position: relative; } + .markdown-body .d-lang:after, .markdown-body div.highlighter-rouge:after, .markdown-body .mermaid-wrap:after { + position: absolute; + right: 0px; + top: 0px; + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; + font-size: 12px; + content: attr(data-lang); + padding: 0 5px; + color: #bbc0c5; } + .markdown-body a { + color: #0366d6; } + .markdown-body a:hover { + color: #107ffc; } + .markdown-body a code, + .markdown-body a tt { + color: #0366d6; } + .markdown-body h1, + .markdown-body h2, + .markdown-body h3, + .markdown-body h4, + .markdown-body h5, + .markdown-body h6, + .markdown-body dt { + font-family: "Roboto-Slab", sans-serif; } + .markdown-body table { + font-size: 14px; } + .markdown-body figure { + margin: 0; } + .markdown-body .anchor { + float: none; + padding-right: 0; + margin-left: 3px; + margin-right: 3px; } + .markdown-body code, + .markdown-body tt { + font-size: 12px; + border: 1px #e1e4e8 solid; + color: #e74c3c; + background-color: #f9fafb; } + .markdown-body pre > code { + color: #3c454e; } + .markdown-body .highlight pre, + .markdown-body pre { + font-size: 12px; + border: 1px #e1e4e8 solid; + background-color: #f6f8fa; } + .markdown-body .search-results li { + list-style: none; } + .markdown-body .task-list-item-checkbox { + margin-right: 3px; } + .markdown-body .mermaid-wrap { + box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.14), 0 3px 1px -2px rgba(0, 0, 0, 0.2), 0 1px 5px 0 rgba(0, 0, 0, 0.12); } + .markdown-body .mermaid-wrap .mermaid { + font-size: 12px; + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace; + white-space: pre; } + +.toasts { + font-size: 16px; + box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.14), 0 3px 1px -2px rgba(0, 0, 0, 0.2), 0 1px 5px 0 rgba(0, 0, 0, 0.12); } + .toasts .title { + box-shadow: 0 0 1px 1px rgba(0, 0, 0, 0.14); } + .toasts .content :first-child { + margin-top: 0; } + .toasts .content :last-child { + margin-bottom: 0; } + .toasts.note { + background-color: #e7f2fa; } + .toasts.note .title { + background: #6ab0de; } + .toasts.tip { + background-color: #dbfaf4; } + .toasts.tip .title { + background: #1abc9c; } + .toasts.warning { + background-color: #fbe9d9; } + .toasts.warning .title { + background: #f0b37e; } + .toasts.danger { + background-color: #fdf3f2; } + .toasts.danger .title { + background: #f29f97; } + +html[dir="rtl"] ul, +html[dir="rtl"] ol { + padding-right: 0; } +html[dir="rtl"] dd { + margin-right: 0; } +html[dir="rtl"] .menu-sm, html[dir="rtl"] .sidebar-wrap, html[dir="rtl"] .addons-wrap { + left: unset; + right: -85%; } + html[dir="rtl"] .menu-sm.shift, html[dir="rtl"] .shift.sidebar-wrap, html[dir="rtl"] .shift.addons-wrap { + left: unset; + right: 0; } +html[dir="rtl"] .content-wrap.shift { + left: unset; + right: 85%; } +@media (min-width: 768px) { + html[dir="rtl"] .menu-md, html[dir="rtl"] .sidebar-wrap, html[dir="rtl"] .addons-wrap { + left: unset; + right: 0; } + html[dir="rtl"] .content-wrap { + margin-left: unset; + margin-right: 300px; } + html[dir="rtl"] .content-wrap.shift { + left: unset; + right: 0; } } +html[dir="rtl"] .toctree .fa { + margin-right: unset; + margin-left: 2px; } +html[dir="rtl"] .toctree > ul > .toc > a { + padding-left: unset; + padding-right: 12px; } +html[dir="rtl"] .toc.level-1.current > a { + padding-left: unset; + padding-right: 12px; } +html[dir="rtl"] .toc.level-1.current .level-2 > a { + padding-left: unset; + padding-right: 36px; } +html[dir="rtl"] .toc.level-2.current > a { + padding-left: unset; + padding-right: 36px; } +html[dir="rtl"] .toc.level-2.current .level-3 > a { + padding-left: unset; + padding-right: 60px; } +html[dir="rtl"] .toc.level-3.current > a { + padding-left: unset; + padding-right: 60px; } +html[dir="rtl"] .toc.level-3.current .level-4 > a { + padding-left: unset; + padding-right: 84px; } +html[dir="rtl"] .toc.level-4.current > a { + padding-left: unset; + padding-right: 84px; } +html[dir="rtl"] .toc.level-4.current .level-5 > a { + padding-left: unset; + padding-right: 108px; } +html[dir="rtl"] .toc.level-5.current > a { + padding-left: unset; + padding-right: 108px; } +html[dir="rtl"] .toc.level-5.current .level-6 > a { + padding-left: unset; + padding-right: 132px; } +html[dir="rtl"] .toc.level-6.current > a { + padding-left: unset; + padding-right: 132px; } +html[dir="rtl"] .toc.level-6.current .level-7 > a { + padding-left: unset; + padding-right: 156px; } +html[dir="rtl"] .toc.level-7.current > a { + padding-left: unset; + padding-right: 156px; } +html[dir="rtl"] .toc.level-7.current .level-8 > a { + padding-left: unset; + padding-right: 180px; } +html[dir="rtl"] .toc.level-8.current > a { + padding-left: unset; + padding-right: 180px; } +html[dir="rtl"] .toc.level-8.current .level-9 > a { + padding-left: unset; + padding-right: 204px; } +html[dir="rtl"] .toc.level-9.current > a { + padding-left: unset; + padding-right: 204px; } +html[dir="rtl"] .toc.level-9.current .level-10 > a { + padding-left: unset; + padding-right: 228px; } +html[dir="rtl"] .toc.level-10.current > a { + padding-left: unset; + padding-right: 228px; } +html[dir="rtl"] .toc.level-10.current .level-11 > a { + padding-left: unset; + padding-right: 252px; } +html[dir="rtl"] .toc.level-11.current > a { + padding-left: unset; + padding-right: 252px; } +html[dir="rtl"] .toc.level-11.current .level-12 > a { + padding-left: unset; + padding-right: 276px; } +html[dir="rtl"] .markdown-body .highlight { + direction: ltr; } +html[dir="rtl"] .markdown-body blockquote { + border-left: none; + border-right: 0.25em solid #dfe2e5; } +html[dir="rtl"] .markdown-body ul, +html[dir="rtl"] .markdown-body ol { + padding-left: 0; + padding-right: 2em; } +html[dir="rtl"] .markdown-body .task-list-item-checkbox { + margin-right: unset; + margin-left: 3px; } +html[dir="rtl"] .fa-arrow-circle-left:before { + content: ""; } +html[dir="rtl"] .fa-arrow-circle-right:before { + content: ""; } + +/* Fade in an element */ +.anim-fade-in { + animation-name: fade-in; + animation-duration: 1s; + animation-timing-function: ease-in-out; } + .anim-fade-in.fast { + animation-duration: 300ms; } + +@keyframes fade-in { + 0% { + opacity: 0; } + 100% { + opacity: 1; } } +/* Fade out an element */ +.anim-fade-out { + animation-name: fade-out; + animation-duration: 1s; + animation-timing-function: ease-out; } + .anim-fade-out.fast { + animation-duration: 0.3s; } + +@keyframes fade-out { + 0% { + opacity: 1; } + 100% { + opacity: 0; } } +/* Fade in and slide up an element */ +.anim-fade-up { + opacity: 0; + animation-name: fade-up; + animation-duration: 0.3s; + animation-fill-mode: forwards; + animation-timing-function: ease-out; + animation-delay: 1s; } + +@keyframes fade-up { + 0% { + opacity: 0.8; + transform: translateY(100%); } + 100% { + opacity: 1; + transform: translateY(0); } } +/* Fade an element out and slide down */ +.anim-fade-down { + animation-name: fade-down; + animation-duration: 0.3s; + animation-fill-mode: forwards; + animation-timing-function: ease-in; } + +@keyframes fade-down { + 0% { + opacity: 1; + transform: translateY(0); } + 100% { + opacity: 0.5; + transform: translateY(100%); } } +/* Grow an element width from 0 to 100% */ +.anim-grow-x { + width: 0%; + animation-name: grow-x; + animation-duration: 0.3s; + animation-fill-mode: forwards; + animation-timing-function: ease; + animation-delay: 0.5s; } + +@keyframes grow-x { + to { + width: 100%; } } +/* Shrink an element from 100% to 0% */ +.anim-shrink-x { + animation-name: shrink-x; + animation-duration: 0.3s; + animation-fill-mode: forwards; + animation-timing-function: ease-in-out; + animation-delay: 0.5s; } + +@keyframes shrink-x { + to { + width: 0%; } } +/* Fade in an element and scale it fast */ +.anim-scale-in { + animation-name: scale-in; + animation-duration: 0.15s; + animation-timing-function: cubic-bezier(0.2, 0, 0.13, 1.5); } + +@keyframes scale-in { + 0% { + opacity: 0; + transform: scale(0.5); } + 100% { + opacity: 1; + transform: scale(1); } } +/* Pulse an element's opacity */ +.anim-pulse { + animation-name: pulse; + animation-duration: 2s; + animation-timing-function: linear; + animation-iteration-count: infinite; } + +@keyframes pulse { + 0% { + opacity: 0.3; } + 10% { + opacity: 1; } + 100% { + opacity: 0.3; } } +/* Pulse in an element */ +.anim-pulse-in { + animation-name: pulse-in; + animation-duration: 0.5s; } + +@keyframes pulse-in { + 0% { + transform: scale3d(1, 1, 1); } + 50% { + transform: scale3d(1.1, 1.1, 1.1); } + 100% { + transform: scale3d(1, 1, 1); } } +/* Increase scale of an element on hover */ +.hover-grow { + transition: transform 0.3s; + backface-visibility: hidden; } + .hover-grow:hover { + transform: scale(1.025); } + +/* Add a gray border to the left and right */ +.border-x { + border-right: 1px #e1e4e8 solid !important; + border-left: 1px #e1e4e8 solid !important; } + +/* Add a gray border to the top and bottom */ +.border-y { + border-top: 1px #e1e4e8 solid !important; + border-bottom: 1px #e1e4e8 solid !important; } + +/* Responsive gray borders */ +/* Add a gray border on all sides at/above this breakpoint */ +.border { + border: 1px #e1e4e8 solid !important; } + +/* Set the border width to 0 on all sides at/above this breakpoint */ +.border-0 { + border: 0 !important; } + +/* Add a gray border to the top */ +.border-top { + border-top: 1px #e1e4e8 solid !important; } + +/* Add a gray border to the right */ +.border-right { + border-right: 1px #e1e4e8 solid !important; } + +/* Add a gray border to the bottom */ +.border-bottom { + border-bottom: 1px #e1e4e8 solid !important; } + +/* Add a gray border to the left */ +.border-left { + border-left: 1px #e1e4e8 solid !important; } + +/* Remove the top border */ +.border-top-0 { + border-top: 0 !important; } + +/* Remove the right border */ +.border-right-0 { + border-right: 0 !important; } + +/* Remove the bottom border */ +.border-bottom-0 { + border-bottom: 0 !important; } + +/* Remove the left border */ +.border-left-0 { + border-left: 0 !important; } + +.rounded { + border-radius: 6px !important; } + +.rounded-0 { + border-radius: 0 !important; } + +.rounded-1 { + border-radius: 4px !important; } + +.rounded-2 { + border-radius: 6px !important; } + +.rounded-3 { + border-radius: 8px !important; } + +.rounded-top-0 { + border-top-left-radius: 0 !important; + border-top-right-radius: 0 !important; } + +.rounded-top-1 { + border-top-left-radius: 4px !important; + border-top-right-radius: 4px !important; } + +.rounded-top-2 { + border-top-left-radius: 6px !important; + border-top-right-radius: 6px !important; } + +.rounded-top-3 { + border-top-left-radius: 8px !important; + border-top-right-radius: 8px !important; } + +.rounded-right-0 { + border-top-right-radius: 0 !important; + border-bottom-right-radius: 0 !important; } + +.rounded-right-1 { + border-top-right-radius: 4px !important; + border-bottom-right-radius: 4px !important; } + +.rounded-right-2 { + border-top-right-radius: 6px !important; + border-bottom-right-radius: 6px !important; } + +.rounded-right-3 { + border-top-right-radius: 8px !important; + border-bottom-right-radius: 8px !important; } + +.rounded-bottom-0 { + border-bottom-right-radius: 0 !important; + border-bottom-left-radius: 0 !important; } + +.rounded-bottom-1 { + border-bottom-right-radius: 4px !important; + border-bottom-left-radius: 4px !important; } + +.rounded-bottom-2 { + border-bottom-right-radius: 6px !important; + border-bottom-left-radius: 6px !important; } + +.rounded-bottom-3 { + border-bottom-right-radius: 8px !important; + border-bottom-left-radius: 8px !important; } + +.rounded-left-0 { + border-bottom-left-radius: 0 !important; + border-top-left-radius: 0 !important; } + +.rounded-left-1 { + border-bottom-left-radius: 4px !important; + border-top-left-radius: 4px !important; } + +.rounded-left-2 { + border-bottom-left-radius: 6px !important; + border-top-left-radius: 6px !important; } + +.rounded-left-3 { + border-bottom-left-radius: 8px !important; + border-top-left-radius: 8px !important; } + +@media (min-width: 544px) { + /* Add a gray border on all sides at/above this breakpoint */ + .border-sm { + border: 1px #e1e4e8 solid !important; } + + /* Set the border width to 0 on all sides at/above this breakpoint */ + .border-sm-0 { + border: 0 !important; } + + /* Add a gray border to the top */ + .border-sm-top { + border-top: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the right */ + .border-sm-right { + border-right: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the bottom */ + .border-sm-bottom { + border-bottom: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the left */ + .border-sm-left { + border-left: 1px #e1e4e8 solid !important; } + + /* Remove the top border */ + .border-sm-top-0 { + border-top: 0 !important; } + + /* Remove the right border */ + .border-sm-right-0 { + border-right: 0 !important; } + + /* Remove the bottom border */ + .border-sm-bottom-0 { + border-bottom: 0 !important; } + + /* Remove the left border */ + .border-sm-left-0 { + border-left: 0 !important; } + + .rounded-sm { + border-radius: 6px !important; } + + .rounded-sm-0 { + border-radius: 0 !important; } + + .rounded-sm-1 { + border-radius: 4px !important; } + + .rounded-sm-2 { + border-radius: 6px !important; } + + .rounded-sm-3 { + border-radius: 8px !important; } + + .rounded-sm-top-0 { + border-top-left-radius: 0 !important; + border-top-right-radius: 0 !important; } + + .rounded-sm-top-1 { + border-top-left-radius: 4px !important; + border-top-right-radius: 4px !important; } + + .rounded-sm-top-2 { + border-top-left-radius: 6px !important; + border-top-right-radius: 6px !important; } + + .rounded-sm-top-3 { + border-top-left-radius: 8px !important; + border-top-right-radius: 8px !important; } + + .rounded-sm-right-0 { + border-top-right-radius: 0 !important; + border-bottom-right-radius: 0 !important; } + + .rounded-sm-right-1 { + border-top-right-radius: 4px !important; + border-bottom-right-radius: 4px !important; } + + .rounded-sm-right-2 { + border-top-right-radius: 6px !important; + border-bottom-right-radius: 6px !important; } + + .rounded-sm-right-3 { + border-top-right-radius: 8px !important; + border-bottom-right-radius: 8px !important; } + + .rounded-sm-bottom-0 { + border-bottom-right-radius: 0 !important; + border-bottom-left-radius: 0 !important; } + + .rounded-sm-bottom-1 { + border-bottom-right-radius: 4px !important; + border-bottom-left-radius: 4px !important; } + + .rounded-sm-bottom-2 { + border-bottom-right-radius: 6px !important; + border-bottom-left-radius: 6px !important; } + + .rounded-sm-bottom-3 { + border-bottom-right-radius: 8px !important; + border-bottom-left-radius: 8px !important; } + + .rounded-sm-left-0 { + border-bottom-left-radius: 0 !important; + border-top-left-radius: 0 !important; } + + .rounded-sm-left-1 { + border-bottom-left-radius: 4px !important; + border-top-left-radius: 4px !important; } + + .rounded-sm-left-2 { + border-bottom-left-radius: 6px !important; + border-top-left-radius: 6px !important; } + + .rounded-sm-left-3 { + border-bottom-left-radius: 8px !important; + border-top-left-radius: 8px !important; } } +@media (min-width: 768px) { + /* Add a gray border on all sides at/above this breakpoint */ + .border-md { + border: 1px #e1e4e8 solid !important; } + + /* Set the border width to 0 on all sides at/above this breakpoint */ + .border-md-0 { + border: 0 !important; } + + /* Add a gray border to the top */ + .border-md-top { + border-top: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the right */ + .border-md-right { + border-right: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the bottom */ + .border-md-bottom { + border-bottom: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the left */ + .border-md-left { + border-left: 1px #e1e4e8 solid !important; } + + /* Remove the top border */ + .border-md-top-0 { + border-top: 0 !important; } + + /* Remove the right border */ + .border-md-right-0 { + border-right: 0 !important; } + + /* Remove the bottom border */ + .border-md-bottom-0 { + border-bottom: 0 !important; } + + /* Remove the left border */ + .border-md-left-0 { + border-left: 0 !important; } + + .rounded-md { + border-radius: 6px !important; } + + .rounded-md-0 { + border-radius: 0 !important; } + + .rounded-md-1 { + border-radius: 4px !important; } + + .rounded-md-2 { + border-radius: 6px !important; } + + .rounded-md-3 { + border-radius: 8px !important; } + + .rounded-md-top-0 { + border-top-left-radius: 0 !important; + border-top-right-radius: 0 !important; } + + .rounded-md-top-1 { + border-top-left-radius: 4px !important; + border-top-right-radius: 4px !important; } + + .rounded-md-top-2 { + border-top-left-radius: 6px !important; + border-top-right-radius: 6px !important; } + + .rounded-md-top-3 { + border-top-left-radius: 8px !important; + border-top-right-radius: 8px !important; } + + .rounded-md-right-0 { + border-top-right-radius: 0 !important; + border-bottom-right-radius: 0 !important; } + + .rounded-md-right-1 { + border-top-right-radius: 4px !important; + border-bottom-right-radius: 4px !important; } + + .rounded-md-right-2 { + border-top-right-radius: 6px !important; + border-bottom-right-radius: 6px !important; } + + .rounded-md-right-3 { + border-top-right-radius: 8px !important; + border-bottom-right-radius: 8px !important; } + + .rounded-md-bottom-0 { + border-bottom-right-radius: 0 !important; + border-bottom-left-radius: 0 !important; } + + .rounded-md-bottom-1 { + border-bottom-right-radius: 4px !important; + border-bottom-left-radius: 4px !important; } + + .rounded-md-bottom-2 { + border-bottom-right-radius: 6px !important; + border-bottom-left-radius: 6px !important; } + + .rounded-md-bottom-3 { + border-bottom-right-radius: 8px !important; + border-bottom-left-radius: 8px !important; } + + .rounded-md-left-0 { + border-bottom-left-radius: 0 !important; + border-top-left-radius: 0 !important; } + + .rounded-md-left-1 { + border-bottom-left-radius: 4px !important; + border-top-left-radius: 4px !important; } + + .rounded-md-left-2 { + border-bottom-left-radius: 6px !important; + border-top-left-radius: 6px !important; } + + .rounded-md-left-3 { + border-bottom-left-radius: 8px !important; + border-top-left-radius: 8px !important; } } +@media (min-width: 1012px) { + /* Add a gray border on all sides at/above this breakpoint */ + .border-lg { + border: 1px #e1e4e8 solid !important; } + + /* Set the border width to 0 on all sides at/above this breakpoint */ + .border-lg-0 { + border: 0 !important; } + + /* Add a gray border to the top */ + .border-lg-top { + border-top: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the right */ + .border-lg-right { + border-right: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the bottom */ + .border-lg-bottom { + border-bottom: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the left */ + .border-lg-left { + border-left: 1px #e1e4e8 solid !important; } + + /* Remove the top border */ + .border-lg-top-0 { + border-top: 0 !important; } + + /* Remove the right border */ + .border-lg-right-0 { + border-right: 0 !important; } + + /* Remove the bottom border */ + .border-lg-bottom-0 { + border-bottom: 0 !important; } + + /* Remove the left border */ + .border-lg-left-0 { + border-left: 0 !important; } + + .rounded-lg { + border-radius: 6px !important; } + + .rounded-lg-0 { + border-radius: 0 !important; } + + .rounded-lg-1 { + border-radius: 4px !important; } + + .rounded-lg-2 { + border-radius: 6px !important; } + + .rounded-lg-3 { + border-radius: 8px !important; } + + .rounded-lg-top-0 { + border-top-left-radius: 0 !important; + border-top-right-radius: 0 !important; } + + .rounded-lg-top-1 { + border-top-left-radius: 4px !important; + border-top-right-radius: 4px !important; } + + .rounded-lg-top-2 { + border-top-left-radius: 6px !important; + border-top-right-radius: 6px !important; } + + .rounded-lg-top-3 { + border-top-left-radius: 8px !important; + border-top-right-radius: 8px !important; } + + .rounded-lg-right-0 { + border-top-right-radius: 0 !important; + border-bottom-right-radius: 0 !important; } + + .rounded-lg-right-1 { + border-top-right-radius: 4px !important; + border-bottom-right-radius: 4px !important; } + + .rounded-lg-right-2 { + border-top-right-radius: 6px !important; + border-bottom-right-radius: 6px !important; } + + .rounded-lg-right-3 { + border-top-right-radius: 8px !important; + border-bottom-right-radius: 8px !important; } + + .rounded-lg-bottom-0 { + border-bottom-right-radius: 0 !important; + border-bottom-left-radius: 0 !important; } + + .rounded-lg-bottom-1 { + border-bottom-right-radius: 4px !important; + border-bottom-left-radius: 4px !important; } + + .rounded-lg-bottom-2 { + border-bottom-right-radius: 6px !important; + border-bottom-left-radius: 6px !important; } + + .rounded-lg-bottom-3 { + border-bottom-right-radius: 8px !important; + border-bottom-left-radius: 8px !important; } + + .rounded-lg-left-0 { + border-bottom-left-radius: 0 !important; + border-top-left-radius: 0 !important; } + + .rounded-lg-left-1 { + border-bottom-left-radius: 4px !important; + border-top-left-radius: 4px !important; } + + .rounded-lg-left-2 { + border-bottom-left-radius: 6px !important; + border-top-left-radius: 6px !important; } + + .rounded-lg-left-3 { + border-bottom-left-radius: 8px !important; + border-top-left-radius: 8px !important; } } +@media (min-width: 1280px) { + /* Add a gray border on all sides at/above this breakpoint */ + .border-xl { + border: 1px #e1e4e8 solid !important; } + + /* Set the border width to 0 on all sides at/above this breakpoint */ + .border-xl-0 { + border: 0 !important; } + + /* Add a gray border to the top */ + .border-xl-top { + border-top: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the right */ + .border-xl-right { + border-right: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the bottom */ + .border-xl-bottom { + border-bottom: 1px #e1e4e8 solid !important; } + + /* Add a gray border to the left */ + .border-xl-left { + border-left: 1px #e1e4e8 solid !important; } + + /* Remove the top border */ + .border-xl-top-0 { + border-top: 0 !important; } + + /* Remove the right border */ + .border-xl-right-0 { + border-right: 0 !important; } + + /* Remove the bottom border */ + .border-xl-bottom-0 { + border-bottom: 0 !important; } + + /* Remove the left border */ + .border-xl-left-0 { + border-left: 0 !important; } + + .rounded-xl { + border-radius: 6px !important; } + + .rounded-xl-0 { + border-radius: 0 !important; } + + .rounded-xl-1 { + border-radius: 4px !important; } + + .rounded-xl-2 { + border-radius: 6px !important; } + + .rounded-xl-3 { + border-radius: 8px !important; } + + .rounded-xl-top-0 { + border-top-left-radius: 0 !important; + border-top-right-radius: 0 !important; } + + .rounded-xl-top-1 { + border-top-left-radius: 4px !important; + border-top-right-radius: 4px !important; } + + .rounded-xl-top-2 { + border-top-left-radius: 6px !important; + border-top-right-radius: 6px !important; } + + .rounded-xl-top-3 { + border-top-left-radius: 8px !important; + border-top-right-radius: 8px !important; } + + .rounded-xl-right-0 { + border-top-right-radius: 0 !important; + border-bottom-right-radius: 0 !important; } + + .rounded-xl-right-1 { + border-top-right-radius: 4px !important; + border-bottom-right-radius: 4px !important; } + + .rounded-xl-right-2 { + border-top-right-radius: 6px !important; + border-bottom-right-radius: 6px !important; } + + .rounded-xl-right-3 { + border-top-right-radius: 8px !important; + border-bottom-right-radius: 8px !important; } + + .rounded-xl-bottom-0 { + border-bottom-right-radius: 0 !important; + border-bottom-left-radius: 0 !important; } + + .rounded-xl-bottom-1 { + border-bottom-right-radius: 4px !important; + border-bottom-left-radius: 4px !important; } + + .rounded-xl-bottom-2 { + border-bottom-right-radius: 6px !important; + border-bottom-left-radius: 6px !important; } + + .rounded-xl-bottom-3 { + border-bottom-right-radius: 8px !important; + border-bottom-left-radius: 8px !important; } + + .rounded-xl-left-0 { + border-bottom-left-radius: 0 !important; + border-top-left-radius: 0 !important; } + + .rounded-xl-left-1 { + border-bottom-left-radius: 4px !important; + border-top-left-radius: 4px !important; } + + .rounded-xl-left-2 { + border-bottom-left-radius: 6px !important; + border-top-left-radius: 6px !important; } + + .rounded-xl-left-3 { + border-bottom-left-radius: 8px !important; + border-top-left-radius: 8px !important; } } +/* Add a 50% border-radius to make something into a circle */ +.circle { + border-radius: 50% !important; } + +/* Change the border style to dashed, in conjunction with another utility */ +.border-dashed { + border-style: dashed !important; } + +/* Use with .border to turn the border blue */ +.border-blue { + border-color: #0366d6 !important; } + +/* Use with .border to turn the border blue-light */ +.border-blue-light { + border-color: #c8e1ff !important; } + +/* Use with .border to turn the border green */ +.border-green { + border-color: #34d058 !important; } + +/* Use with .border to turn the border green light */ +.border-green-light { + border-color: #a2cbac !important; } + +/* Use with .border to turn the border red */ +.border-red { + border-color: #d73a49 !important; } + +/* Use with .border to turn the border red-light */ +.border-red-light { + border-color: #f97583 !important; } + +/* Use with .border to turn the border purple */ +.border-purple { + border-color: #6f42c1 !important; } + +/* Use with .border to turn the border yellow */ +.border-yellow { + border-color: #f9c513 !important; } + +/* Use with .border to turn the border gray-light */ +.border-gray-light { + border-color: #eaecef !important; } + +/* Use with .border to turn the border gray-dark */ +.border-gray-dark { + border-color: #d1d5da !important; } + +/* Use with .border to turn the border rgba black 0.15 */ +.border-black-fade { + border-color: rgba(27, 31, 35, 0.15) !important; } + +/* Use with .border to turn the border rgba white 0.15 */ +.border-white-fade { + border-color: rgba(255, 255, 255, 0.15) !important; } + +/* Use with .border to turn the border white w/varying transparency */ +.border-white-fade-15 { + border-color: rgba(255, 255, 255, 0.15) !important; } + +.border-white-fade-30 { + border-color: rgba(255, 255, 255, 0.3) !important; } + +.border-white-fade-50 { + border-color: rgba(255, 255, 255, 0.5) !important; } + +.border-white-fade-70 { + border-color: rgba(255, 255, 255, 0.7) !important; } + +.border-white-fade-85 { + border-color: rgba(255, 255, 255, 0.85) !important; } + +.box-shadow { + box-shadow: 0 1px 0 rgba(27, 31, 35, 0.04) !important; } + +.box-shadow-medium { + box-shadow: 0 3px 6px rgba(149, 157, 165, 0.15) !important; } + +.box-shadow-large { + box-shadow: 0 8px 24px rgba(149, 157, 165, 0.2) !important; } + +.box-shadow-extra-large { + box-shadow: 0 12px 48px rgba(149, 157, 165, 0.3) !important; } + +.box-shadow-none { + box-shadow: none !important; } + +/* Set the background to $bg-white */ +.bg-white { + background-color: #fff !important; } + +/* Set the background to $bg-blue */ +.bg-blue { + background-color: #0366d6 !important; } + +/* Set the background to $bg-blue-light */ +.bg-blue-light { + background-color: #f1f8ff !important; } + +/* Set the background to $bg-gray-dark */ +.bg-gray-dark { + background-color: #24292e !important; } + +/* Set the background to $bg-gray */ +.bg-gray { + background-color: #f6f8fa !important; } + +/* Set the background to $bg-gray-light */ +.bg-gray-light { + background-color: #fafbfc !important; } + +/* Set the background to $bg-green */ +.bg-green { + background-color: #28a745 !important; } + +/* Set the background to $bg-green-light */ +.bg-green-light { + background-color: #dcffe4 !important; } + +/* Set the background to $bg-red */ +.bg-red { + background-color: #d73a49 !important; } + +/* Set the background to $bg-red-light */ +.bg-red-light { + background-color: #ffeef0 !important; } + +/* Set the background to $bg-yellow */ +.bg-yellow { + background-color: #ffd33d !important; } + +/* Set the background to $bg-yellow-light */ +.bg-yellow-light { + background-color: #fff5b1 !important; } + +/* Set the background to $bg-yellow-dark */ +.bg-yellow-dark { + background-color: #dbab09 !important; } + +/* Set the background to $bg-purple */ +.bg-purple { + background-color: #6f42c1 !important; } + +/* Set the background to $bg-pink */ +.bg-pink { + background-color: #ea4aaa !important; } + +/* Set the background to $bg-purple-light */ +.bg-purple-light { + background-color: #f5f0ff !important; } + +/* Set the background to $bg-orange */ +.bg-orange { + background-color: #d15704 !important; } + +.color-gray-0 { + color: #fafbfc !important; } + +.bg-gray-0 { + background-color: #fafbfc !important; } + +.color-gray-1 { + color: #f6f8fa !important; } + +.bg-gray-1 { + background-color: #f6f8fa !important; } + +.color-gray-2 { + color: #e1e4e8 !important; } + +.bg-gray-2 { + background-color: #e1e4e8 !important; } + +.color-gray-3 { + color: #d1d5da !important; } + +.bg-gray-3 { + background-color: #d1d5da !important; } + +.color-gray-4 { + color: #959da5 !important; } + +.bg-gray-4 { + background-color: #959da5 !important; } + +.color-gray-5 { + color: #6a737d !important; } + +.bg-gray-5 { + background-color: #6a737d !important; } + +.color-gray-6 { + color: #586069 !important; } + +.bg-gray-6 { + background-color: #586069 !important; } + +.color-gray-7 { + color: #444d56 !important; } + +.bg-gray-7 { + background-color: #444d56 !important; } + +.color-gray-8 { + color: #2f363d !important; } + +.bg-gray-8 { + background-color: #2f363d !important; } + +.color-gray-9 { + color: #24292e !important; } + +.bg-gray-9 { + background-color: #24292e !important; } + +.color-blue-0 { + color: #f1f8ff !important; } + +.bg-blue-0 { + background-color: #f1f8ff !important; } + +.color-blue-1 { + color: #dbedff !important; } + +.bg-blue-1 { + background-color: #dbedff !important; } + +.color-blue-2 { + color: #c8e1ff !important; } + +.bg-blue-2 { + background-color: #c8e1ff !important; } + +.color-blue-3 { + color: #79b8ff !important; } + +.bg-blue-3 { + background-color: #79b8ff !important; } + +.color-blue-4 { + color: #2188ff !important; } + +.bg-blue-4 { + background-color: #2188ff !important; } + +.color-blue-5 { + color: #0366d6 !important; } + +.bg-blue-5 { + background-color: #0366d6 !important; } + +.color-blue-6 { + color: #005cc5 !important; } + +.bg-blue-6 { + background-color: #005cc5 !important; } + +.color-blue-7 { + color: #044289 !important; } + +.bg-blue-7 { + background-color: #044289 !important; } + +.color-blue-8 { + color: #032f62 !important; } + +.bg-blue-8 { + background-color: #032f62 !important; } + +.color-blue-9 { + color: #05264c !important; } + +.bg-blue-9 { + background-color: #05264c !important; } + +.color-green-0 { + color: #f0fff4 !important; } + +.bg-green-0 { + background-color: #f0fff4 !important; } + +.color-green-1 { + color: #dcffe4 !important; } + +.bg-green-1 { + background-color: #dcffe4 !important; } + +.color-green-2 { + color: #bef5cb !important; } + +.bg-green-2 { + background-color: #bef5cb !important; } + +.color-green-3 { + color: #85e89d !important; } + +.bg-green-3 { + background-color: #85e89d !important; } + +.color-green-4 { + color: #34d058 !important; } + +.bg-green-4 { + background-color: #34d058 !important; } + +.color-green-5 { + color: #28a745 !important; } + +.bg-green-5 { + background-color: #28a745 !important; } + +.color-green-6 { + color: #22863a !important; } + +.bg-green-6 { + background-color: #22863a !important; } + +.color-green-7 { + color: #176f2c !important; } + +.bg-green-7 { + background-color: #176f2c !important; } + +.color-green-8 { + color: #165c26 !important; } + +.bg-green-8 { + background-color: #165c26 !important; } + +.color-green-9 { + color: #144620 !important; } + +.bg-green-9 { + background-color: #144620 !important; } + +.color-yellow-0 { + color: #fffdef !important; } + +.bg-yellow-0 { + background-color: #fffdef !important; } + +.color-yellow-1 { + color: #fffbdd !important; } + +.bg-yellow-1 { + background-color: #fffbdd !important; } + +.color-yellow-2 { + color: #fff5b1 !important; } + +.bg-yellow-2 { + background-color: #fff5b1 !important; } + +.color-yellow-3 { + color: #ffea7f !important; } + +.bg-yellow-3 { + background-color: #ffea7f !important; } + +.color-yellow-4 { + color: #ffdf5d !important; } + +.bg-yellow-4 { + background-color: #ffdf5d !important; } + +.color-yellow-5 { + color: #ffd33d !important; } + +.bg-yellow-5 { + background-color: #ffd33d !important; } + +.color-yellow-6 { + color: #f9c513 !important; } + +.bg-yellow-6 { + background-color: #f9c513 !important; } + +.color-yellow-7 { + color: #dbab09 !important; } + +.bg-yellow-7 { + background-color: #dbab09 !important; } + +.color-yellow-8 { + color: #b08800 !important; } + +.bg-yellow-8 { + background-color: #b08800 !important; } + +.color-yellow-9 { + color: #735c0f !important; } + +.bg-yellow-9 { + background-color: #735c0f !important; } + +.color-orange-0 { + color: #fff8f2 !important; } + +.bg-orange-0 { + background-color: #fff8f2 !important; } + +.color-orange-1 { + color: #ffebda !important; } + +.bg-orange-1 { + background-color: #ffebda !important; } + +.color-orange-2 { + color: #ffd1ac !important; } + +.bg-orange-2 { + background-color: #ffd1ac !important; } + +.color-orange-3 { + color: #ffab70 !important; } + +.bg-orange-3 { + background-color: #ffab70 !important; } + +.color-orange-4 { + color: #fb8532 !important; } + +.bg-orange-4 { + background-color: #fb8532 !important; } + +.color-orange-5 { + color: #f66a0a !important; } + +.bg-orange-5 { + background-color: #f66a0a !important; } + +.color-orange-6 { + color: #e36209 !important; } + +.bg-orange-6 { + background-color: #e36209 !important; } + +.color-orange-7 { + color: #d15704 !important; } + +.bg-orange-7 { + background-color: #d15704 !important; } + +.color-orange-8 { + color: #c24e00 !important; } + +.bg-orange-8 { + background-color: #c24e00 !important; } + +.color-orange-9 { + color: #a04100 !important; } + +.bg-orange-9 { + background-color: #a04100 !important; } + +.color-red-0 { + color: #ffeef0 !important; } + +.bg-red-0 { + background-color: #ffeef0 !important; } + +.color-red-1 { + color: #ffdce0 !important; } + +.bg-red-1 { + background-color: #ffdce0 !important; } + +.color-red-2 { + color: #fdaeb7 !important; } + +.bg-red-2 { + background-color: #fdaeb7 !important; } + +.color-red-3 { + color: #f97583 !important; } + +.bg-red-3 { + background-color: #f97583 !important; } + +.color-red-4 { + color: #ea4a5a !important; } + +.bg-red-4 { + background-color: #ea4a5a !important; } + +.color-red-5 { + color: #d73a49 !important; } + +.bg-red-5 { + background-color: #d73a49 !important; } + +.color-red-6 { + color: #cb2431 !important; } + +.bg-red-6 { + background-color: #cb2431 !important; } + +.color-red-7 { + color: #b31d28 !important; } + +.bg-red-7 { + background-color: #b31d28 !important; } + +.color-red-8 { + color: #9e1c23 !important; } + +.bg-red-8 { + background-color: #9e1c23 !important; } + +.color-red-9 { + color: #86181d !important; } + +.bg-red-9 { + background-color: #86181d !important; } + +.color-purple-0 { + color: #f5f0ff !important; } + +.bg-purple-0 { + background-color: #f5f0ff !important; } + +.color-purple-1 { + color: #e6dcfd !important; } + +.bg-purple-1 { + background-color: #e6dcfd !important; } + +.color-purple-2 { + color: #d1bcf9 !important; } + +.bg-purple-2 { + background-color: #d1bcf9 !important; } + +.color-purple-3 { + color: #b392f0 !important; } + +.bg-purple-3 { + background-color: #b392f0 !important; } + +.color-purple-4 { + color: #8a63d2 !important; } + +.bg-purple-4 { + background-color: #8a63d2 !important; } + +.color-purple-5 { + color: #6f42c1 !important; } + +.bg-purple-5 { + background-color: #6f42c1 !important; } + +.color-purple-6 { + color: #5a32a3 !important; } + +.bg-purple-6 { + background-color: #5a32a3 !important; } + +.color-purple-7 { + color: #4c2889 !important; } + +.bg-purple-7 { + background-color: #4c2889 !important; } + +.color-purple-8 { + color: #3a1d6e !important; } + +.bg-purple-8 { + background-color: #3a1d6e !important; } + +.color-purple-9 { + color: #29134e !important; } + +.bg-purple-9 { + background-color: #29134e !important; } + +.color-pink-0 { + color: #ffeef8 !important; } + +.bg-pink-0 { + background-color: #ffeef8 !important; } + +.color-pink-1 { + color: #fedbf0 !important; } + +.bg-pink-1 { + background-color: #fedbf0 !important; } + +.color-pink-2 { + color: #f9b3dd !important; } + +.bg-pink-2 { + background-color: #f9b3dd !important; } + +.color-pink-3 { + color: #f692ce !important; } + +.bg-pink-3 { + background-color: #f692ce !important; } + +.color-pink-4 { + color: #ec6cb9 !important; } + +.bg-pink-4 { + background-color: #ec6cb9 !important; } + +.color-pink-5 { + color: #ea4aaa !important; } + +.bg-pink-5 { + background-color: #ea4aaa !important; } + +.color-pink-6 { + color: #d03592 !important; } + +.bg-pink-6 { + background-color: #d03592 !important; } + +.color-pink-7 { + color: #b93a86 !important; } + +.bg-pink-7 { + background-color: #b93a86 !important; } + +.color-pink-8 { + color: #99306f !important; } + +.bg-pink-8 { + background-color: #99306f !important; } + +.color-pink-9 { + color: #6d224f !important; } + +.bg-pink-9 { + background-color: #6d224f !important; } + +.bg-shade-gradient { + background-image: linear-gradient(180deg, rgba(27, 31, 35, 0.065), rgba(27, 31, 35, 0)) !important; + background-repeat: no-repeat !important; + background-size: 100% 200px !important; } + +/* Set the text color to $text-blue */ +.text-blue { + color: #0366d6 !important; } + +/* Set the text color to $text-red */ +.text-red { + color: #cb2431 !important; } + +/* Set the text color to $text-gray-light */ +.text-gray-light { + color: #6a737d !important; } + +/* Set the text color to $text-gray */ +.text-gray { + color: #586069 !important; } + +/* Set the text color to $text-gray-dark */ +.text-gray-dark { + color: #24292e !important; } + +/* Set the text color to $text-green */ +.text-green { + color: #22863a !important; } + +/* Set the text color to $text-yellow */ +.text-yellow { + color: #b08800 !important; } + +/* Set the text color to $text-orange */ +.text-orange { + color: #a04100 !important; } + +/* Set the text color to $text-orange-light */ +.text-orange-light { + color: #e36209 !important; } + +/* Set the text color to $text-purple */ +.text-purple { + color: #6f42c1 !important; } + +/* Set the text color to $text-pink */ +.text-pink { + color: #ea4aaa !important; } + +/* Set the text color to $text-white */ +.text-white { + color: #fff !important; } + +/* Set the text color to inherit */ +.text-inherit { + color: inherit !important; } + +.link-gray { + color: #586069 !important; } + .link-gray:hover { + color: #0366d6 !important; } + +.link-gray-dark { + color: #24292e !important; } + .link-gray-dark:hover { + color: #0366d6 !important; } + +/* Set the link color to $text-blue on hover + Useful when you want only part of a link to turn blue on hover */ +.link-hover-blue:hover { + color: #0366d6 !important; } + +/* Make a link $text-gray, then $text-blue on hover and removes the underline */ +.muted-link { + color: #586069 !important; } + .muted-link:hover { + color: #0366d6 !important; + text-decoration: none; } + +.details-overlay[open] > summary::before { + position: fixed; + top: 0; + right: 0; + bottom: 0; + left: 0; + z-index: 80; + display: block; + cursor: default; + content: " "; + background: transparent; } + +.details-overlay-dark[open] > summary::before { + z-index: 99; + background: rgba(27, 31, 35, 0.5); } + +.details-reset > summary { + list-style: none; } +.details-reset > summary::before { + display: none; } +.details-reset > summary::-webkit-details-marker { + display: none; } + +.flex-row { + flex-direction: row !important; } + +.flex-row-reverse { + flex-direction: row-reverse !important; } + +.flex-column { + flex-direction: column !important; } + +.flex-column-reverse { + flex-direction: column-reverse !important; } + +.flex-wrap { + flex-wrap: wrap !important; } + +.flex-nowrap { + flex-wrap: nowrap !important; } + +.flex-wrap-reverse { + flex-wrap: wrap-reverse !important; } + +.flex-justify-start { + justify-content: flex-start !important; } + +.flex-justify-end { + justify-content: flex-end !important; } + +.flex-justify-center { + justify-content: center !important; } + +.flex-justify-between { + justify-content: space-between !important; } + +.flex-justify-around { + justify-content: space-around !important; } + +.flex-items-start { + align-items: flex-start !important; } + +.flex-items-end { + align-items: flex-end !important; } + +.flex-items-center { + align-items: center !important; } + +.flex-items-baseline { + align-items: baseline !important; } + +.flex-items-stretch { + align-items: stretch !important; } + +.flex-content-start { + align-content: flex-start !important; } + +.flex-content-end { + align-content: flex-end !important; } + +.flex-content-center { + align-content: center !important; } + +.flex-content-between { + align-content: space-between !important; } + +.flex-content-around { + align-content: space-around !important; } + +.flex-content-stretch { + align-content: stretch !important; } + +.flex-1 { + flex: 1 !important; } + +.flex-auto { + flex: auto !important; } + +.flex-grow-0 { + flex-grow: 0 !important; } + +.flex-shrink-0 { + flex-shrink: 0 !important; } + +.flex-self-auto { + align-self: auto !important; } + +.flex-self-start { + align-self: flex-start !important; } + +.flex-self-end { + align-self: flex-end !important; } + +.flex-self-center { + align-self: center !important; } + +.flex-self-baseline { + align-self: baseline !important; } + +.flex-self-stretch { + align-self: stretch !important; } + +.flex-order-1 { + order: 1 !important; } + +.flex-order-2 { + order: 2 !important; } + +.flex-order-none { + order: inherit !important; } + +@media (min-width: 544px) { + .flex-sm-row { + flex-direction: row !important; } + + .flex-sm-row-reverse { + flex-direction: row-reverse !important; } + + .flex-sm-column { + flex-direction: column !important; } + + .flex-sm-column-reverse { + flex-direction: column-reverse !important; } + + .flex-sm-wrap { + flex-wrap: wrap !important; } + + .flex-sm-nowrap { + flex-wrap: nowrap !important; } + + .flex-sm-wrap-reverse { + flex-wrap: wrap-reverse !important; } + + .flex-sm-justify-start { + justify-content: flex-start !important; } + + .flex-sm-justify-end { + justify-content: flex-end !important; } + + .flex-sm-justify-center { + justify-content: center !important; } + + .flex-sm-justify-between { + justify-content: space-between !important; } + + .flex-sm-justify-around { + justify-content: space-around !important; } + + .flex-sm-items-start { + align-items: flex-start !important; } + + .flex-sm-items-end { + align-items: flex-end !important; } + + .flex-sm-items-center { + align-items: center !important; } + + .flex-sm-items-baseline { + align-items: baseline !important; } + + .flex-sm-items-stretch { + align-items: stretch !important; } + + .flex-sm-content-start { + align-content: flex-start !important; } + + .flex-sm-content-end { + align-content: flex-end !important; } + + .flex-sm-content-center { + align-content: center !important; } + + .flex-sm-content-between { + align-content: space-between !important; } + + .flex-sm-content-around { + align-content: space-around !important; } + + .flex-sm-content-stretch { + align-content: stretch !important; } + + .flex-sm-1 { + flex: 1 !important; } + + .flex-sm-auto { + flex: auto !important; } + + .flex-sm-grow-0 { + flex-grow: 0 !important; } + + .flex-sm-shrink-0 { + flex-shrink: 0 !important; } + + .flex-sm-self-auto { + align-self: auto !important; } + + .flex-sm-self-start { + align-self: flex-start !important; } + + .flex-sm-self-end { + align-self: flex-end !important; } + + .flex-sm-self-center { + align-self: center !important; } + + .flex-sm-self-baseline { + align-self: baseline !important; } + + .flex-sm-self-stretch { + align-self: stretch !important; } + + .flex-sm-order-1 { + order: 1 !important; } + + .flex-sm-order-2 { + order: 2 !important; } + + .flex-sm-order-none { + order: inherit !important; } } +@media (min-width: 768px) { + .flex-md-row { + flex-direction: row !important; } + + .flex-md-row-reverse { + flex-direction: row-reverse !important; } + + .flex-md-column { + flex-direction: column !important; } + + .flex-md-column-reverse { + flex-direction: column-reverse !important; } + + .flex-md-wrap { + flex-wrap: wrap !important; } + + .flex-md-nowrap { + flex-wrap: nowrap !important; } + + .flex-md-wrap-reverse { + flex-wrap: wrap-reverse !important; } + + .flex-md-justify-start { + justify-content: flex-start !important; } + + .flex-md-justify-end { + justify-content: flex-end !important; } + + .flex-md-justify-center { + justify-content: center !important; } + + .flex-md-justify-between { + justify-content: space-between !important; } + + .flex-md-justify-around { + justify-content: space-around !important; } + + .flex-md-items-start { + align-items: flex-start !important; } + + .flex-md-items-end { + align-items: flex-end !important; } + + .flex-md-items-center { + align-items: center !important; } + + .flex-md-items-baseline { + align-items: baseline !important; } + + .flex-md-items-stretch { + align-items: stretch !important; } + + .flex-md-content-start { + align-content: flex-start !important; } + + .flex-md-content-end { + align-content: flex-end !important; } + + .flex-md-content-center { + align-content: center !important; } + + .flex-md-content-between { + align-content: space-between !important; } + + .flex-md-content-around { + align-content: space-around !important; } + + .flex-md-content-stretch { + align-content: stretch !important; } + + .flex-md-1 { + flex: 1 !important; } + + .flex-md-auto { + flex: auto !important; } + + .flex-md-grow-0 { + flex-grow: 0 !important; } + + .flex-md-shrink-0 { + flex-shrink: 0 !important; } + + .flex-md-self-auto { + align-self: auto !important; } + + .flex-md-self-start { + align-self: flex-start !important; } + + .flex-md-self-end { + align-self: flex-end !important; } + + .flex-md-self-center { + align-self: center !important; } + + .flex-md-self-baseline { + align-self: baseline !important; } + + .flex-md-self-stretch { + align-self: stretch !important; } + + .flex-md-order-1 { + order: 1 !important; } + + .flex-md-order-2 { + order: 2 !important; } + + .flex-md-order-none { + order: inherit !important; } } +@media (min-width: 1012px) { + .flex-lg-row { + flex-direction: row !important; } + + .flex-lg-row-reverse { + flex-direction: row-reverse !important; } + + .flex-lg-column { + flex-direction: column !important; } + + .flex-lg-column-reverse { + flex-direction: column-reverse !important; } + + .flex-lg-wrap { + flex-wrap: wrap !important; } + + .flex-lg-nowrap { + flex-wrap: nowrap !important; } + + .flex-lg-wrap-reverse { + flex-wrap: wrap-reverse !important; } + + .flex-lg-justify-start { + justify-content: flex-start !important; } + + .flex-lg-justify-end { + justify-content: flex-end !important; } + + .flex-lg-justify-center { + justify-content: center !important; } + + .flex-lg-justify-between { + justify-content: space-between !important; } + + .flex-lg-justify-around { + justify-content: space-around !important; } + + .flex-lg-items-start { + align-items: flex-start !important; } + + .flex-lg-items-end { + align-items: flex-end !important; } + + .flex-lg-items-center { + align-items: center !important; } + + .flex-lg-items-baseline { + align-items: baseline !important; } + + .flex-lg-items-stretch { + align-items: stretch !important; } + + .flex-lg-content-start { + align-content: flex-start !important; } + + .flex-lg-content-end { + align-content: flex-end !important; } + + .flex-lg-content-center { + align-content: center !important; } + + .flex-lg-content-between { + align-content: space-between !important; } + + .flex-lg-content-around { + align-content: space-around !important; } + + .flex-lg-content-stretch { + align-content: stretch !important; } + + .flex-lg-1 { + flex: 1 !important; } + + .flex-lg-auto { + flex: auto !important; } + + .flex-lg-grow-0 { + flex-grow: 0 !important; } + + .flex-lg-shrink-0 { + flex-shrink: 0 !important; } + + .flex-lg-self-auto { + align-self: auto !important; } + + .flex-lg-self-start { + align-self: flex-start !important; } + + .flex-lg-self-end { + align-self: flex-end !important; } + + .flex-lg-self-center { + align-self: center !important; } + + .flex-lg-self-baseline { + align-self: baseline !important; } + + .flex-lg-self-stretch { + align-self: stretch !important; } + + .flex-lg-order-1 { + order: 1 !important; } + + .flex-lg-order-2 { + order: 2 !important; } + + .flex-lg-order-none { + order: inherit !important; } } +@media (min-width: 1280px) { + .flex-xl-row { + flex-direction: row !important; } + + .flex-xl-row-reverse { + flex-direction: row-reverse !important; } + + .flex-xl-column { + flex-direction: column !important; } + + .flex-xl-column-reverse { + flex-direction: column-reverse !important; } + + .flex-xl-wrap { + flex-wrap: wrap !important; } + + .flex-xl-nowrap { + flex-wrap: nowrap !important; } + + .flex-xl-wrap-reverse { + flex-wrap: wrap-reverse !important; } + + .flex-xl-justify-start { + justify-content: flex-start !important; } + + .flex-xl-justify-end { + justify-content: flex-end !important; } + + .flex-xl-justify-center { + justify-content: center !important; } + + .flex-xl-justify-between { + justify-content: space-between !important; } + + .flex-xl-justify-around { + justify-content: space-around !important; } + + .flex-xl-items-start { + align-items: flex-start !important; } + + .flex-xl-items-end { + align-items: flex-end !important; } + + .flex-xl-items-center { + align-items: center !important; } + + .flex-xl-items-baseline { + align-items: baseline !important; } + + .flex-xl-items-stretch { + align-items: stretch !important; } + + .flex-xl-content-start { + align-content: flex-start !important; } + + .flex-xl-content-end { + align-content: flex-end !important; } + + .flex-xl-content-center { + align-content: center !important; } + + .flex-xl-content-between { + align-content: space-between !important; } + + .flex-xl-content-around { + align-content: space-around !important; } + + .flex-xl-content-stretch { + align-content: stretch !important; } + + .flex-xl-1 { + flex: 1 !important; } + + .flex-xl-auto { + flex: auto !important; } + + .flex-xl-grow-0 { + flex-grow: 0 !important; } + + .flex-xl-shrink-0 { + flex-shrink: 0 !important; } + + .flex-xl-self-auto { + align-self: auto !important; } + + .flex-xl-self-start { + align-self: flex-start !important; } + + .flex-xl-self-end { + align-self: flex-end !important; } + + .flex-xl-self-center { + align-self: center !important; } + + .flex-xl-self-baseline { + align-self: baseline !important; } + + .flex-xl-self-stretch { + align-self: stretch !important; } + + .flex-xl-order-1 { + order: 1 !important; } + + .flex-xl-order-2 { + order: 2 !important; } + + .flex-xl-order-none { + order: inherit !important; } } +/* Position */ +.position-static { + position: static !important; } + +.position-relative { + position: relative !important; } + +.position-absolute { + position: absolute !important; } + +.position-fixed { + position: fixed !important; } + +.position-sticky { + position: sticky !important; } + +@media (min-width: 544px) { + .position-sm-static { + position: static !important; } + + .position-sm-relative { + position: relative !important; } + + .position-sm-absolute { + position: absolute !important; } + + .position-sm-fixed { + position: fixed !important; } + + .position-sm-sticky { + position: sticky !important; } } +@media (min-width: 768px) { + .position-md-static { + position: static !important; } + + .position-md-relative { + position: relative !important; } + + .position-md-absolute { + position: absolute !important; } + + .position-md-fixed { + position: fixed !important; } + + .position-md-sticky { + position: sticky !important; } } +@media (min-width: 1012px) { + .position-lg-static { + position: static !important; } + + .position-lg-relative { + position: relative !important; } + + .position-lg-absolute { + position: absolute !important; } + + .position-lg-fixed { + position: fixed !important; } + + .position-lg-sticky { + position: sticky !important; } } +@media (min-width: 1280px) { + .position-xl-static { + position: static !important; } + + .position-xl-relative { + position: relative !important; } + + .position-xl-absolute { + position: absolute !important; } + + .position-xl-fixed { + position: fixed !important; } + + .position-xl-sticky { + position: sticky !important; } } +/* Final position */ +.top-0 { + top: 0 !important; } + +.right-0 { + right: 0 !important; } + +.bottom-0 { + bottom: 0 !important; } + +.left-0 { + left: 0 !important; } + +.top-auto { + top: auto !important; } + +.right-auto { + right: auto !important; } + +.bottom-auto { + bottom: auto !important; } + +.left-auto { + left: auto !important; } + +@media (min-width: 544px) { + .top-sm-0 { + top: 0 !important; } + + .right-sm-0 { + right: 0 !important; } + + .bottom-sm-0 { + bottom: 0 !important; } + + .left-sm-0 { + left: 0 !important; } + + .top-sm-auto { + top: auto !important; } + + .right-sm-auto { + right: auto !important; } + + .bottom-sm-auto { + bottom: auto !important; } + + .left-sm-auto { + left: auto !important; } } +@media (min-width: 768px) { + .top-md-0 { + top: 0 !important; } + + .right-md-0 { + right: 0 !important; } + + .bottom-md-0 { + bottom: 0 !important; } + + .left-md-0 { + left: 0 !important; } + + .top-md-auto { + top: auto !important; } + + .right-md-auto { + right: auto !important; } + + .bottom-md-auto { + bottom: auto !important; } + + .left-md-auto { + left: auto !important; } } +@media (min-width: 1012px) { + .top-lg-0 { + top: 0 !important; } + + .right-lg-0 { + right: 0 !important; } + + .bottom-lg-0 { + bottom: 0 !important; } + + .left-lg-0 { + left: 0 !important; } + + .top-lg-auto { + top: auto !important; } + + .right-lg-auto { + right: auto !important; } + + .bottom-lg-auto { + bottom: auto !important; } + + .left-lg-auto { + left: auto !important; } } +@media (min-width: 1280px) { + .top-xl-0 { + top: 0 !important; } + + .right-xl-0 { + right: 0 !important; } + + .bottom-xl-0 { + bottom: 0 !important; } + + .left-xl-0 { + left: 0 !important; } + + .top-xl-auto { + top: auto !important; } + + .right-xl-auto { + right: auto !important; } + + .bottom-xl-auto { + bottom: auto !important; } + + .left-xl-auto { + left: auto !important; } } +/* Vertical align middle */ +.v-align-middle { + vertical-align: middle !important; } + +/* Vertical align top */ +.v-align-top { + vertical-align: top !important; } + +/* Vertical align bottom */ +.v-align-bottom { + vertical-align: bottom !important; } + +/* Vertical align to the top of the text */ +.v-align-text-top { + vertical-align: text-top !important; } + +/* Vertical align to the bottom of the text */ +.v-align-text-bottom { + vertical-align: text-bottom !important; } + +/* Vertical align to the parent's baseline */ +.v-align-baseline { + vertical-align: baseline !important; } + +.overflow-visible { + overflow: visible !important; } + +.overflow-x-visible { + overflow-x: visible !important; } + +.overflow-y-visible { + overflow-y: visible !important; } + +.overflow-hidden { + overflow: hidden !important; } + +.overflow-x-hidden { + overflow-x: hidden !important; } + +.overflow-y-hidden { + overflow-y: hidden !important; } + +.overflow-auto { + overflow: auto !important; } + +.overflow-x-auto { + overflow-x: auto !important; } + +.overflow-y-auto { + overflow-y: auto !important; } + +.overflow-scroll { + overflow: scroll !important; } + +.overflow-x-scroll { + overflow-x: scroll !important; } + +.overflow-y-scroll { + overflow-y: scroll !important; } + +@media (min-width: 544px) { + .overflow-sm-visible { + overflow: visible !important; } + + .overflow-sm-x-visible { + overflow-x: visible !important; } + + .overflow-sm-y-visible { + overflow-y: visible !important; } + + .overflow-sm-hidden { + overflow: hidden !important; } + + .overflow-sm-x-hidden { + overflow-x: hidden !important; } + + .overflow-sm-y-hidden { + overflow-y: hidden !important; } + + .overflow-sm-auto { + overflow: auto !important; } + + .overflow-sm-x-auto { + overflow-x: auto !important; } + + .overflow-sm-y-auto { + overflow-y: auto !important; } + + .overflow-sm-scroll { + overflow: scroll !important; } + + .overflow-sm-x-scroll { + overflow-x: scroll !important; } + + .overflow-sm-y-scroll { + overflow-y: scroll !important; } } +@media (min-width: 768px) { + .overflow-md-visible { + overflow: visible !important; } + + .overflow-md-x-visible { + overflow-x: visible !important; } + + .overflow-md-y-visible { + overflow-y: visible !important; } + + .overflow-md-hidden { + overflow: hidden !important; } + + .overflow-md-x-hidden { + overflow-x: hidden !important; } + + .overflow-md-y-hidden { + overflow-y: hidden !important; } + + .overflow-md-auto { + overflow: auto !important; } + + .overflow-md-x-auto { + overflow-x: auto !important; } + + .overflow-md-y-auto { + overflow-y: auto !important; } + + .overflow-md-scroll { + overflow: scroll !important; } + + .overflow-md-x-scroll { + overflow-x: scroll !important; } + + .overflow-md-y-scroll { + overflow-y: scroll !important; } } +@media (min-width: 1012px) { + .overflow-lg-visible { + overflow: visible !important; } + + .overflow-lg-x-visible { + overflow-x: visible !important; } + + .overflow-lg-y-visible { + overflow-y: visible !important; } + + .overflow-lg-hidden { + overflow: hidden !important; } + + .overflow-lg-x-hidden { + overflow-x: hidden !important; } + + .overflow-lg-y-hidden { + overflow-y: hidden !important; } + + .overflow-lg-auto { + overflow: auto !important; } + + .overflow-lg-x-auto { + overflow-x: auto !important; } + + .overflow-lg-y-auto { + overflow-y: auto !important; } + + .overflow-lg-scroll { + overflow: scroll !important; } + + .overflow-lg-x-scroll { + overflow-x: scroll !important; } + + .overflow-lg-y-scroll { + overflow-y: scroll !important; } } +@media (min-width: 1280px) { + .overflow-xl-visible { + overflow: visible !important; } + + .overflow-xl-x-visible { + overflow-x: visible !important; } + + .overflow-xl-y-visible { + overflow-y: visible !important; } + + .overflow-xl-hidden { + overflow: hidden !important; } + + .overflow-xl-x-hidden { + overflow-x: hidden !important; } + + .overflow-xl-y-hidden { + overflow-y: hidden !important; } + + .overflow-xl-auto { + overflow: auto !important; } + + .overflow-xl-x-auto { + overflow-x: auto !important; } + + .overflow-xl-y-auto { + overflow-y: auto !important; } + + .overflow-xl-scroll { + overflow: scroll !important; } + + .overflow-xl-x-scroll { + overflow-x: scroll !important; } + + .overflow-xl-y-scroll { + overflow-y: scroll !important; } } +/* Clear floats around the element */ +.clearfix::before { + display: table; + content: ""; } +.clearfix::after { + display: table; + clear: both; + content: ""; } + +/* Float to the left */ +.float-left { + float: left !important; } + +/* Float to the right */ +.float-right { + float: right !important; } + +/* No float */ +.float-none { + float: none !important; } + +@media (min-width: 544px) { + /* Float to the left */ + .float-sm-left { + float: left !important; } + + /* Float to the right */ + .float-sm-right { + float: right !important; } + + /* No float */ + .float-sm-none { + float: none !important; } } +@media (min-width: 768px) { + /* Float to the left */ + .float-md-left { + float: left !important; } + + /* Float to the right */ + .float-md-right { + float: right !important; } + + /* No float */ + .float-md-none { + float: none !important; } } +@media (min-width: 1012px) { + /* Float to the left */ + .float-lg-left { + float: left !important; } + + /* Float to the right */ + .float-lg-right { + float: right !important; } + + /* No float */ + .float-lg-none { + float: none !important; } } +@media (min-width: 1280px) { + /* Float to the left */ + .float-xl-left { + float: left !important; } + + /* Float to the right */ + .float-xl-right { + float: right !important; } + + /* No float */ + .float-xl-none { + float: none !important; } } +/* Max width 100% */ +.width-fit { + max-width: 100% !important; } + +/* Set the width to 100% */ +.width-full { + width: 100% !important; } + +/* Max height 100% */ +.height-fit { + max-height: 100% !important; } + +/* Set the height to 100% */ +.height-full { + height: 100% !important; } + +/* Remove min-width from element */ +.min-width-0 { + min-width: 0 !important; } + +.width-auto { + width: auto !important; } + +/* Set the direction to rtl */ +.direction-rtl { + direction: rtl !important; } + +/* Set the direction to ltr */ +.direction-ltr { + direction: ltr !important; } + +@media (min-width: 544px) { + .width-sm-auto { + width: auto !important; } + + /* Set the direction to rtl */ + .direction-sm-rtl { + direction: rtl !important; } + + /* Set the direction to ltr */ + .direction-sm-ltr { + direction: ltr !important; } } +@media (min-width: 768px) { + .width-md-auto { + width: auto !important; } + + /* Set the direction to rtl */ + .direction-md-rtl { + direction: rtl !important; } + + /* Set the direction to ltr */ + .direction-md-ltr { + direction: ltr !important; } } +@media (min-width: 1012px) { + .width-lg-auto { + width: auto !important; } + + /* Set the direction to rtl */ + .direction-lg-rtl { + direction: rtl !important; } + + /* Set the direction to ltr */ + .direction-lg-ltr { + direction: ltr !important; } } +@media (min-width: 1280px) { + .width-xl-auto { + width: auto !important; } + + /* Set the direction to rtl */ + .direction-xl-rtl { + direction: rtl !important; } + + /* Set the direction to ltr */ + .direction-xl-ltr { + direction: ltr !important; } } +/* Set a $size margin to all sides at $breakpoint */ +.m-0 { + margin: 0 !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-0 { + margin-top: 0 !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-0 { + margin-right: 0 !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-0 { + margin-bottom: 0 !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-0 { + margin-left: 0 !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-0 { + margin-right: 0 !important; + margin-left: 0 !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-0 { + margin-top: 0 !important; + margin-bottom: 0 !important; } + +/* Set a $size margin to all sides at $breakpoint */ +.m-1 { + margin: 4px !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-1 { + margin-top: 4px !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-1 { + margin-right: 4px !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-1 { + margin-bottom: 4px !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-1 { + margin-left: 4px !important; } + +/* Set a negative $size margin on top at $breakpoint */ +.mt-n1 { + margin-top: -4px !important; } + +/* Set a negative $size margin on the right at $breakpoint */ +.mr-n1 { + margin-right: -4px !important; } + +/* Set a negative $size margin on the bottom at $breakpoint */ +.mb-n1 { + margin-bottom: -4px !important; } + +/* Set a negative $size margin on the left at $breakpoint */ +.ml-n1 { + margin-left: -4px !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-1 { + margin-right: 4px !important; + margin-left: 4px !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-1 { + margin-top: 4px !important; + margin-bottom: 4px !important; } + +/* Set a $size margin to all sides at $breakpoint */ +.m-2 { + margin: 8px !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-2 { + margin-top: 8px !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-2 { + margin-right: 8px !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-2 { + margin-bottom: 8px !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-2 { + margin-left: 8px !important; } + +/* Set a negative $size margin on top at $breakpoint */ +.mt-n2 { + margin-top: -8px !important; } + +/* Set a negative $size margin on the right at $breakpoint */ +.mr-n2 { + margin-right: -8px !important; } + +/* Set a negative $size margin on the bottom at $breakpoint */ +.mb-n2 { + margin-bottom: -8px !important; } + +/* Set a negative $size margin on the left at $breakpoint */ +.ml-n2 { + margin-left: -8px !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-2 { + margin-right: 8px !important; + margin-left: 8px !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-2 { + margin-top: 8px !important; + margin-bottom: 8px !important; } + +/* Set a $size margin to all sides at $breakpoint */ +.m-3 { + margin: 16px !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-3 { + margin-top: 16px !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-3 { + margin-right: 16px !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-3 { + margin-bottom: 16px !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-3 { + margin-left: 16px !important; } + +/* Set a negative $size margin on top at $breakpoint */ +.mt-n3 { + margin-top: -16px !important; } + +/* Set a negative $size margin on the right at $breakpoint */ +.mr-n3 { + margin-right: -16px !important; } + +/* Set a negative $size margin on the bottom at $breakpoint */ +.mb-n3 { + margin-bottom: -16px !important; } + +/* Set a negative $size margin on the left at $breakpoint */ +.ml-n3 { + margin-left: -16px !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-3 { + margin-right: 16px !important; + margin-left: 16px !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-3 { + margin-top: 16px !important; + margin-bottom: 16px !important; } + +/* Set a $size margin to all sides at $breakpoint */ +.m-4 { + margin: 24px !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-4 { + margin-top: 24px !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-4 { + margin-right: 24px !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-4 { + margin-bottom: 24px !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-4 { + margin-left: 24px !important; } + +/* Set a negative $size margin on top at $breakpoint */ +.mt-n4 { + margin-top: -24px !important; } + +/* Set a negative $size margin on the right at $breakpoint */ +.mr-n4 { + margin-right: -24px !important; } + +/* Set a negative $size margin on the bottom at $breakpoint */ +.mb-n4 { + margin-bottom: -24px !important; } + +/* Set a negative $size margin on the left at $breakpoint */ +.ml-n4 { + margin-left: -24px !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-4 { + margin-right: 24px !important; + margin-left: 24px !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-4 { + margin-top: 24px !important; + margin-bottom: 24px !important; } + +/* Set a $size margin to all sides at $breakpoint */ +.m-5 { + margin: 32px !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-5 { + margin-top: 32px !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-5 { + margin-right: 32px !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-5 { + margin-bottom: 32px !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-5 { + margin-left: 32px !important; } + +/* Set a negative $size margin on top at $breakpoint */ +.mt-n5 { + margin-top: -32px !important; } + +/* Set a negative $size margin on the right at $breakpoint */ +.mr-n5 { + margin-right: -32px !important; } + +/* Set a negative $size margin on the bottom at $breakpoint */ +.mb-n5 { + margin-bottom: -32px !important; } + +/* Set a negative $size margin on the left at $breakpoint */ +.ml-n5 { + margin-left: -32px !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-5 { + margin-right: 32px !important; + margin-left: 32px !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-5 { + margin-top: 32px !important; + margin-bottom: 32px !important; } + +/* Set a $size margin to all sides at $breakpoint */ +.m-6 { + margin: 40px !important; } + +/* Set a $size margin on the top at $breakpoint */ +.mt-6 { + margin-top: 40px !important; } + +/* Set a $size margin on the right at $breakpoint */ +.mr-6 { + margin-right: 40px !important; } + +/* Set a $size margin on the bottom at $breakpoint */ +.mb-6 { + margin-bottom: 40px !important; } + +/* Set a $size margin on the left at $breakpoint */ +.ml-6 { + margin-left: 40px !important; } + +/* Set a negative $size margin on top at $breakpoint */ +.mt-n6 { + margin-top: -40px !important; } + +/* Set a negative $size margin on the right at $breakpoint */ +.mr-n6 { + margin-right: -40px !important; } + +/* Set a negative $size margin on the bottom at $breakpoint */ +.mb-n6 { + margin-bottom: -40px !important; } + +/* Set a negative $size margin on the left at $breakpoint */ +.ml-n6 { + margin-left: -40px !important; } + +/* Set a $size margin on the left & right at $breakpoint */ +.mx-6 { + margin-right: 40px !important; + margin-left: 40px !important; } + +/* Set a $size margin on the top & bottom at $breakpoint */ +.my-6 { + margin-top: 40px !important; + margin-bottom: 40px !important; } + +/* responsive horizontal auto margins */ +.mx-auto { + margin-right: auto !important; + margin-left: auto !important; } + +@media (min-width: 544px) { + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-0 { + margin: 0 !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-0 { + margin-top: 0 !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-0 { + margin-right: 0 !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-0 { + margin-bottom: 0 !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-0 { + margin-left: 0 !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-0 { + margin-right: 0 !important; + margin-left: 0 !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-0 { + margin-top: 0 !important; + margin-bottom: 0 !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-1 { + margin: 4px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-1 { + margin-top: 4px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-1 { + margin-right: 4px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-1 { + margin-bottom: 4px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-1 { + margin-left: 4px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-sm-n1 { + margin-top: -4px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-sm-n1 { + margin-right: -4px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-sm-n1 { + margin-bottom: -4px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-sm-n1 { + margin-left: -4px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-1 { + margin-right: 4px !important; + margin-left: 4px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-1 { + margin-top: 4px !important; + margin-bottom: 4px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-2 { + margin: 8px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-2 { + margin-top: 8px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-2 { + margin-right: 8px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-2 { + margin-bottom: 8px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-2 { + margin-left: 8px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-sm-n2 { + margin-top: -8px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-sm-n2 { + margin-right: -8px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-sm-n2 { + margin-bottom: -8px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-sm-n2 { + margin-left: -8px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-2 { + margin-right: 8px !important; + margin-left: 8px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-2 { + margin-top: 8px !important; + margin-bottom: 8px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-3 { + margin: 16px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-3 { + margin-top: 16px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-3 { + margin-right: 16px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-3 { + margin-bottom: 16px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-3 { + margin-left: 16px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-sm-n3 { + margin-top: -16px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-sm-n3 { + margin-right: -16px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-sm-n3 { + margin-bottom: -16px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-sm-n3 { + margin-left: -16px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-3 { + margin-right: 16px !important; + margin-left: 16px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-3 { + margin-top: 16px !important; + margin-bottom: 16px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-4 { + margin: 24px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-4 { + margin-top: 24px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-4 { + margin-right: 24px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-4 { + margin-bottom: 24px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-4 { + margin-left: 24px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-sm-n4 { + margin-top: -24px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-sm-n4 { + margin-right: -24px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-sm-n4 { + margin-bottom: -24px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-sm-n4 { + margin-left: -24px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-4 { + margin-right: 24px !important; + margin-left: 24px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-4 { + margin-top: 24px !important; + margin-bottom: 24px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-5 { + margin: 32px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-5 { + margin-top: 32px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-5 { + margin-right: 32px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-5 { + margin-bottom: 32px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-5 { + margin-left: 32px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-sm-n5 { + margin-top: -32px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-sm-n5 { + margin-right: -32px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-sm-n5 { + margin-bottom: -32px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-sm-n5 { + margin-left: -32px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-5 { + margin-right: 32px !important; + margin-left: 32px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-5 { + margin-top: 32px !important; + margin-bottom: 32px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-sm-6 { + margin: 40px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-sm-6 { + margin-top: 40px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-sm-6 { + margin-right: 40px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-sm-6 { + margin-bottom: 40px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-sm-6 { + margin-left: 40px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-sm-n6 { + margin-top: -40px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-sm-n6 { + margin-right: -40px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-sm-n6 { + margin-bottom: -40px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-sm-n6 { + margin-left: -40px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-sm-6 { + margin-right: 40px !important; + margin-left: 40px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-sm-6 { + margin-top: 40px !important; + margin-bottom: 40px !important; } + + /* responsive horizontal auto margins */ + .mx-sm-auto { + margin-right: auto !important; + margin-left: auto !important; } } +@media (min-width: 768px) { + /* Set a $size margin to all sides at $breakpoint */ + .m-md-0 { + margin: 0 !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-0 { + margin-top: 0 !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-0 { + margin-right: 0 !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-0 { + margin-bottom: 0 !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-0 { + margin-left: 0 !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-0 { + margin-right: 0 !important; + margin-left: 0 !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-0 { + margin-top: 0 !important; + margin-bottom: 0 !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-md-1 { + margin: 4px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-1 { + margin-top: 4px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-1 { + margin-right: 4px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-1 { + margin-bottom: 4px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-1 { + margin-left: 4px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-md-n1 { + margin-top: -4px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-md-n1 { + margin-right: -4px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-md-n1 { + margin-bottom: -4px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-md-n1 { + margin-left: -4px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-1 { + margin-right: 4px !important; + margin-left: 4px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-1 { + margin-top: 4px !important; + margin-bottom: 4px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-md-2 { + margin: 8px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-2 { + margin-top: 8px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-2 { + margin-right: 8px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-2 { + margin-bottom: 8px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-2 { + margin-left: 8px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-md-n2 { + margin-top: -8px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-md-n2 { + margin-right: -8px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-md-n2 { + margin-bottom: -8px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-md-n2 { + margin-left: -8px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-2 { + margin-right: 8px !important; + margin-left: 8px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-2 { + margin-top: 8px !important; + margin-bottom: 8px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-md-3 { + margin: 16px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-3 { + margin-top: 16px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-3 { + margin-right: 16px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-3 { + margin-bottom: 16px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-3 { + margin-left: 16px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-md-n3 { + margin-top: -16px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-md-n3 { + margin-right: -16px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-md-n3 { + margin-bottom: -16px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-md-n3 { + margin-left: -16px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-3 { + margin-right: 16px !important; + margin-left: 16px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-3 { + margin-top: 16px !important; + margin-bottom: 16px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-md-4 { + margin: 24px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-4 { + margin-top: 24px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-4 { + margin-right: 24px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-4 { + margin-bottom: 24px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-4 { + margin-left: 24px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-md-n4 { + margin-top: -24px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-md-n4 { + margin-right: -24px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-md-n4 { + margin-bottom: -24px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-md-n4 { + margin-left: -24px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-4 { + margin-right: 24px !important; + margin-left: 24px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-4 { + margin-top: 24px !important; + margin-bottom: 24px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-md-5 { + margin: 32px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-5 { + margin-top: 32px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-5 { + margin-right: 32px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-5 { + margin-bottom: 32px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-5 { + margin-left: 32px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-md-n5 { + margin-top: -32px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-md-n5 { + margin-right: -32px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-md-n5 { + margin-bottom: -32px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-md-n5 { + margin-left: -32px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-5 { + margin-right: 32px !important; + margin-left: 32px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-5 { + margin-top: 32px !important; + margin-bottom: 32px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-md-6 { + margin: 40px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-md-6 { + margin-top: 40px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-md-6 { + margin-right: 40px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-md-6 { + margin-bottom: 40px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-md-6 { + margin-left: 40px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-md-n6 { + margin-top: -40px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-md-n6 { + margin-right: -40px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-md-n6 { + margin-bottom: -40px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-md-n6 { + margin-left: -40px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-md-6 { + margin-right: 40px !important; + margin-left: 40px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-md-6 { + margin-top: 40px !important; + margin-bottom: 40px !important; } + + /* responsive horizontal auto margins */ + .mx-md-auto { + margin-right: auto !important; + margin-left: auto !important; } } +@media (min-width: 1012px) { + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-0 { + margin: 0 !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-0 { + margin-top: 0 !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-0 { + margin-right: 0 !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-0 { + margin-bottom: 0 !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-0 { + margin-left: 0 !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-0 { + margin-right: 0 !important; + margin-left: 0 !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-0 { + margin-top: 0 !important; + margin-bottom: 0 !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-1 { + margin: 4px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-1 { + margin-top: 4px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-1 { + margin-right: 4px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-1 { + margin-bottom: 4px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-1 { + margin-left: 4px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-lg-n1 { + margin-top: -4px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-lg-n1 { + margin-right: -4px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-lg-n1 { + margin-bottom: -4px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-lg-n1 { + margin-left: -4px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-1 { + margin-right: 4px !important; + margin-left: 4px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-1 { + margin-top: 4px !important; + margin-bottom: 4px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-2 { + margin: 8px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-2 { + margin-top: 8px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-2 { + margin-right: 8px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-2 { + margin-bottom: 8px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-2 { + margin-left: 8px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-lg-n2 { + margin-top: -8px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-lg-n2 { + margin-right: -8px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-lg-n2 { + margin-bottom: -8px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-lg-n2 { + margin-left: -8px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-2 { + margin-right: 8px !important; + margin-left: 8px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-2 { + margin-top: 8px !important; + margin-bottom: 8px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-3 { + margin: 16px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-3 { + margin-top: 16px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-3 { + margin-right: 16px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-3 { + margin-bottom: 16px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-3 { + margin-left: 16px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-lg-n3 { + margin-top: -16px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-lg-n3 { + margin-right: -16px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-lg-n3 { + margin-bottom: -16px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-lg-n3 { + margin-left: -16px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-3 { + margin-right: 16px !important; + margin-left: 16px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-3 { + margin-top: 16px !important; + margin-bottom: 16px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-4 { + margin: 24px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-4 { + margin-top: 24px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-4 { + margin-right: 24px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-4 { + margin-bottom: 24px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-4 { + margin-left: 24px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-lg-n4 { + margin-top: -24px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-lg-n4 { + margin-right: -24px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-lg-n4 { + margin-bottom: -24px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-lg-n4 { + margin-left: -24px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-4 { + margin-right: 24px !important; + margin-left: 24px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-4 { + margin-top: 24px !important; + margin-bottom: 24px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-5 { + margin: 32px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-5 { + margin-top: 32px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-5 { + margin-right: 32px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-5 { + margin-bottom: 32px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-5 { + margin-left: 32px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-lg-n5 { + margin-top: -32px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-lg-n5 { + margin-right: -32px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-lg-n5 { + margin-bottom: -32px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-lg-n5 { + margin-left: -32px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-5 { + margin-right: 32px !important; + margin-left: 32px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-5 { + margin-top: 32px !important; + margin-bottom: 32px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-lg-6 { + margin: 40px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-lg-6 { + margin-top: 40px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-lg-6 { + margin-right: 40px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-lg-6 { + margin-bottom: 40px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-lg-6 { + margin-left: 40px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-lg-n6 { + margin-top: -40px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-lg-n6 { + margin-right: -40px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-lg-n6 { + margin-bottom: -40px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-lg-n6 { + margin-left: -40px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-lg-6 { + margin-right: 40px !important; + margin-left: 40px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-lg-6 { + margin-top: 40px !important; + margin-bottom: 40px !important; } + + /* responsive horizontal auto margins */ + .mx-lg-auto { + margin-right: auto !important; + margin-left: auto !important; } } +@media (min-width: 1280px) { + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-0 { + margin: 0 !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-0 { + margin-top: 0 !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-0 { + margin-right: 0 !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-0 { + margin-bottom: 0 !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-0 { + margin-left: 0 !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-0 { + margin-right: 0 !important; + margin-left: 0 !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-0 { + margin-top: 0 !important; + margin-bottom: 0 !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-1 { + margin: 4px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-1 { + margin-top: 4px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-1 { + margin-right: 4px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-1 { + margin-bottom: 4px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-1 { + margin-left: 4px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-xl-n1 { + margin-top: -4px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-xl-n1 { + margin-right: -4px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-xl-n1 { + margin-bottom: -4px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-xl-n1 { + margin-left: -4px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-1 { + margin-right: 4px !important; + margin-left: 4px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-1 { + margin-top: 4px !important; + margin-bottom: 4px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-2 { + margin: 8px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-2 { + margin-top: 8px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-2 { + margin-right: 8px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-2 { + margin-bottom: 8px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-2 { + margin-left: 8px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-xl-n2 { + margin-top: -8px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-xl-n2 { + margin-right: -8px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-xl-n2 { + margin-bottom: -8px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-xl-n2 { + margin-left: -8px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-2 { + margin-right: 8px !important; + margin-left: 8px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-2 { + margin-top: 8px !important; + margin-bottom: 8px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-3 { + margin: 16px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-3 { + margin-top: 16px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-3 { + margin-right: 16px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-3 { + margin-bottom: 16px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-3 { + margin-left: 16px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-xl-n3 { + margin-top: -16px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-xl-n3 { + margin-right: -16px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-xl-n3 { + margin-bottom: -16px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-xl-n3 { + margin-left: -16px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-3 { + margin-right: 16px !important; + margin-left: 16px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-3 { + margin-top: 16px !important; + margin-bottom: 16px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-4 { + margin: 24px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-4 { + margin-top: 24px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-4 { + margin-right: 24px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-4 { + margin-bottom: 24px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-4 { + margin-left: 24px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-xl-n4 { + margin-top: -24px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-xl-n4 { + margin-right: -24px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-xl-n4 { + margin-bottom: -24px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-xl-n4 { + margin-left: -24px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-4 { + margin-right: 24px !important; + margin-left: 24px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-4 { + margin-top: 24px !important; + margin-bottom: 24px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-5 { + margin: 32px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-5 { + margin-top: 32px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-5 { + margin-right: 32px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-5 { + margin-bottom: 32px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-5 { + margin-left: 32px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-xl-n5 { + margin-top: -32px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-xl-n5 { + margin-right: -32px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-xl-n5 { + margin-bottom: -32px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-xl-n5 { + margin-left: -32px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-5 { + margin-right: 32px !important; + margin-left: 32px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-5 { + margin-top: 32px !important; + margin-bottom: 32px !important; } + + /* Set a $size margin to all sides at $breakpoint */ + .m-xl-6 { + margin: 40px !important; } + + /* Set a $size margin on the top at $breakpoint */ + .mt-xl-6 { + margin-top: 40px !important; } + + /* Set a $size margin on the right at $breakpoint */ + .mr-xl-6 { + margin-right: 40px !important; } + + /* Set a $size margin on the bottom at $breakpoint */ + .mb-xl-6 { + margin-bottom: 40px !important; } + + /* Set a $size margin on the left at $breakpoint */ + .ml-xl-6 { + margin-left: 40px !important; } + + /* Set a negative $size margin on top at $breakpoint */ + .mt-xl-n6 { + margin-top: -40px !important; } + + /* Set a negative $size margin on the right at $breakpoint */ + .mr-xl-n6 { + margin-right: -40px !important; } + + /* Set a negative $size margin on the bottom at $breakpoint */ + .mb-xl-n6 { + margin-bottom: -40px !important; } + + /* Set a negative $size margin on the left at $breakpoint */ + .ml-xl-n6 { + margin-left: -40px !important; } + + /* Set a $size margin on the left & right at $breakpoint */ + .mx-xl-6 { + margin-right: 40px !important; + margin-left: 40px !important; } + + /* Set a $size margin on the top & bottom at $breakpoint */ + .my-xl-6 { + margin-top: 40px !important; + margin-bottom: 40px !important; } + + /* responsive horizontal auto margins */ + .mx-xl-auto { + margin-right: auto !important; + margin-left: auto !important; } } +/* Set a $size padding to all sides at $breakpoint */ +.p-0 { + padding: 0 !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-0 { + padding-top: 0 !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-0 { + padding-right: 0 !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-0 { + padding-bottom: 0 !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-0 { + padding-left: 0 !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-0 { + padding-right: 0 !important; + padding-left: 0 !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-0 { + padding-top: 0 !important; + padding-bottom: 0 !important; } + +/* Set a $size padding to all sides at $breakpoint */ +.p-1 { + padding: 4px !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-1 { + padding-top: 4px !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-1 { + padding-right: 4px !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-1 { + padding-bottom: 4px !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-1 { + padding-left: 4px !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-1 { + padding-right: 4px !important; + padding-left: 4px !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-1 { + padding-top: 4px !important; + padding-bottom: 4px !important; } + +/* Set a $size padding to all sides at $breakpoint */ +.p-2 { + padding: 8px !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-2 { + padding-top: 8px !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-2 { + padding-right: 8px !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-2 { + padding-bottom: 8px !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-2 { + padding-left: 8px !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-2 { + padding-right: 8px !important; + padding-left: 8px !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-2 { + padding-top: 8px !important; + padding-bottom: 8px !important; } + +/* Set a $size padding to all sides at $breakpoint */ +.p-3 { + padding: 16px !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-3 { + padding-top: 16px !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-3 { + padding-right: 16px !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-3 { + padding-bottom: 16px !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-3 { + padding-left: 16px !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-3 { + padding-right: 16px !important; + padding-left: 16px !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-3 { + padding-top: 16px !important; + padding-bottom: 16px !important; } + +/* Set a $size padding to all sides at $breakpoint */ +.p-4 { + padding: 24px !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-4 { + padding-top: 24px !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-4 { + padding-right: 24px !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-4 { + padding-bottom: 24px !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-4 { + padding-left: 24px !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-4 { + padding-right: 24px !important; + padding-left: 24px !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-4 { + padding-top: 24px !important; + padding-bottom: 24px !important; } + +/* Set a $size padding to all sides at $breakpoint */ +.p-5 { + padding: 32px !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-5 { + padding-top: 32px !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-5 { + padding-right: 32px !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-5 { + padding-bottom: 32px !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-5 { + padding-left: 32px !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-5 { + padding-right: 32px !important; + padding-left: 32px !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-5 { + padding-top: 32px !important; + padding-bottom: 32px !important; } + +/* Set a $size padding to all sides at $breakpoint */ +.p-6 { + padding: 40px !important; } + +/* Set a $size padding to the top at $breakpoint */ +.pt-6 { + padding-top: 40px !important; } + +/* Set a $size padding to the right at $breakpoint */ +.pr-6 { + padding-right: 40px !important; } + +/* Set a $size padding to the bottom at $breakpoint */ +.pb-6 { + padding-bottom: 40px !important; } + +/* Set a $size padding to the left at $breakpoint */ +.pl-6 { + padding-left: 40px !important; } + +/* Set a $size padding to the left & right at $breakpoint */ +.px-6 { + padding-right: 40px !important; + padding-left: 40px !important; } + +/* Set a $size padding to the top & bottom at $breakpoint */ +.py-6 { + padding-top: 40px !important; + padding-bottom: 40px !important; } + +@media (min-width: 544px) { + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-0 { + padding: 0 !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-0 { + padding-top: 0 !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-0 { + padding-right: 0 !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-0 { + padding-bottom: 0 !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-0 { + padding-left: 0 !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-0 { + padding-right: 0 !important; + padding-left: 0 !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-0 { + padding-top: 0 !important; + padding-bottom: 0 !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-1 { + padding: 4px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-1 { + padding-top: 4px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-1 { + padding-right: 4px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-1 { + padding-bottom: 4px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-1 { + padding-left: 4px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-1 { + padding-right: 4px !important; + padding-left: 4px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-1 { + padding-top: 4px !important; + padding-bottom: 4px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-2 { + padding: 8px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-2 { + padding-top: 8px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-2 { + padding-right: 8px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-2 { + padding-bottom: 8px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-2 { + padding-left: 8px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-2 { + padding-right: 8px !important; + padding-left: 8px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-2 { + padding-top: 8px !important; + padding-bottom: 8px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-3 { + padding: 16px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-3 { + padding-top: 16px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-3 { + padding-right: 16px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-3 { + padding-bottom: 16px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-3 { + padding-left: 16px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-3 { + padding-right: 16px !important; + padding-left: 16px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-3 { + padding-top: 16px !important; + padding-bottom: 16px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-4 { + padding: 24px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-4 { + padding-top: 24px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-4 { + padding-right: 24px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-4 { + padding-bottom: 24px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-4 { + padding-left: 24px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-4 { + padding-right: 24px !important; + padding-left: 24px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-4 { + padding-top: 24px !important; + padding-bottom: 24px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-5 { + padding: 32px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-5 { + padding-top: 32px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-5 { + padding-right: 32px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-5 { + padding-bottom: 32px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-5 { + padding-left: 32px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-5 { + padding-right: 32px !important; + padding-left: 32px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-5 { + padding-top: 32px !important; + padding-bottom: 32px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-sm-6 { + padding: 40px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-sm-6 { + padding-top: 40px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-sm-6 { + padding-right: 40px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-sm-6 { + padding-bottom: 40px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-sm-6 { + padding-left: 40px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-sm-6 { + padding-right: 40px !important; + padding-left: 40px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-sm-6 { + padding-top: 40px !important; + padding-bottom: 40px !important; } } +@media (min-width: 768px) { + /* Set a $size padding to all sides at $breakpoint */ + .p-md-0 { + padding: 0 !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-0 { + padding-top: 0 !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-0 { + padding-right: 0 !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-0 { + padding-bottom: 0 !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-0 { + padding-left: 0 !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-0 { + padding-right: 0 !important; + padding-left: 0 !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-0 { + padding-top: 0 !important; + padding-bottom: 0 !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-md-1 { + padding: 4px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-1 { + padding-top: 4px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-1 { + padding-right: 4px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-1 { + padding-bottom: 4px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-1 { + padding-left: 4px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-1 { + padding-right: 4px !important; + padding-left: 4px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-1 { + padding-top: 4px !important; + padding-bottom: 4px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-md-2 { + padding: 8px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-2 { + padding-top: 8px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-2 { + padding-right: 8px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-2 { + padding-bottom: 8px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-2 { + padding-left: 8px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-2 { + padding-right: 8px !important; + padding-left: 8px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-2 { + padding-top: 8px !important; + padding-bottom: 8px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-md-3 { + padding: 16px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-3 { + padding-top: 16px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-3 { + padding-right: 16px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-3 { + padding-bottom: 16px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-3 { + padding-left: 16px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-3 { + padding-right: 16px !important; + padding-left: 16px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-3 { + padding-top: 16px !important; + padding-bottom: 16px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-md-4 { + padding: 24px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-4 { + padding-top: 24px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-4 { + padding-right: 24px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-4 { + padding-bottom: 24px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-4 { + padding-left: 24px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-4 { + padding-right: 24px !important; + padding-left: 24px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-4 { + padding-top: 24px !important; + padding-bottom: 24px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-md-5 { + padding: 32px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-5 { + padding-top: 32px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-5 { + padding-right: 32px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-5 { + padding-bottom: 32px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-5 { + padding-left: 32px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-5 { + padding-right: 32px !important; + padding-left: 32px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-5 { + padding-top: 32px !important; + padding-bottom: 32px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-md-6 { + padding: 40px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-md-6 { + padding-top: 40px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-md-6 { + padding-right: 40px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-md-6 { + padding-bottom: 40px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-md-6 { + padding-left: 40px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-md-6 { + padding-right: 40px !important; + padding-left: 40px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-md-6 { + padding-top: 40px !important; + padding-bottom: 40px !important; } } +@media (min-width: 1012px) { + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-0 { + padding: 0 !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-0 { + padding-top: 0 !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-0 { + padding-right: 0 !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-0 { + padding-bottom: 0 !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-0 { + padding-left: 0 !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-0 { + padding-right: 0 !important; + padding-left: 0 !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-0 { + padding-top: 0 !important; + padding-bottom: 0 !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-1 { + padding: 4px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-1 { + padding-top: 4px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-1 { + padding-right: 4px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-1 { + padding-bottom: 4px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-1 { + padding-left: 4px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-1 { + padding-right: 4px !important; + padding-left: 4px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-1 { + padding-top: 4px !important; + padding-bottom: 4px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-2 { + padding: 8px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-2 { + padding-top: 8px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-2 { + padding-right: 8px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-2 { + padding-bottom: 8px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-2 { + padding-left: 8px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-2 { + padding-right: 8px !important; + padding-left: 8px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-2 { + padding-top: 8px !important; + padding-bottom: 8px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-3 { + padding: 16px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-3 { + padding-top: 16px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-3 { + padding-right: 16px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-3 { + padding-bottom: 16px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-3 { + padding-left: 16px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-3 { + padding-right: 16px !important; + padding-left: 16px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-3 { + padding-top: 16px !important; + padding-bottom: 16px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-4 { + padding: 24px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-4 { + padding-top: 24px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-4 { + padding-right: 24px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-4 { + padding-bottom: 24px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-4 { + padding-left: 24px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-4 { + padding-right: 24px !important; + padding-left: 24px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-4 { + padding-top: 24px !important; + padding-bottom: 24px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-5 { + padding: 32px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-5 { + padding-top: 32px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-5 { + padding-right: 32px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-5 { + padding-bottom: 32px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-5 { + padding-left: 32px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-5 { + padding-right: 32px !important; + padding-left: 32px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-5 { + padding-top: 32px !important; + padding-bottom: 32px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-lg-6 { + padding: 40px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-lg-6 { + padding-top: 40px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-lg-6 { + padding-right: 40px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-lg-6 { + padding-bottom: 40px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-lg-6 { + padding-left: 40px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-lg-6 { + padding-right: 40px !important; + padding-left: 40px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-lg-6 { + padding-top: 40px !important; + padding-bottom: 40px !important; } } +@media (min-width: 1280px) { + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-0 { + padding: 0 !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-0 { + padding-top: 0 !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-0 { + padding-right: 0 !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-0 { + padding-bottom: 0 !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-0 { + padding-left: 0 !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-0 { + padding-right: 0 !important; + padding-left: 0 !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-0 { + padding-top: 0 !important; + padding-bottom: 0 !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-1 { + padding: 4px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-1 { + padding-top: 4px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-1 { + padding-right: 4px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-1 { + padding-bottom: 4px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-1 { + padding-left: 4px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-1 { + padding-right: 4px !important; + padding-left: 4px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-1 { + padding-top: 4px !important; + padding-bottom: 4px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-2 { + padding: 8px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-2 { + padding-top: 8px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-2 { + padding-right: 8px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-2 { + padding-bottom: 8px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-2 { + padding-left: 8px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-2 { + padding-right: 8px !important; + padding-left: 8px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-2 { + padding-top: 8px !important; + padding-bottom: 8px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-3 { + padding: 16px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-3 { + padding-top: 16px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-3 { + padding-right: 16px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-3 { + padding-bottom: 16px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-3 { + padding-left: 16px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-3 { + padding-right: 16px !important; + padding-left: 16px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-3 { + padding-top: 16px !important; + padding-bottom: 16px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-4 { + padding: 24px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-4 { + padding-top: 24px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-4 { + padding-right: 24px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-4 { + padding-bottom: 24px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-4 { + padding-left: 24px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-4 { + padding-right: 24px !important; + padding-left: 24px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-4 { + padding-top: 24px !important; + padding-bottom: 24px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-5 { + padding: 32px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-5 { + padding-top: 32px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-5 { + padding-right: 32px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-5 { + padding-bottom: 32px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-5 { + padding-left: 32px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-5 { + padding-right: 32px !important; + padding-left: 32px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-5 { + padding-top: 32px !important; + padding-bottom: 32px !important; } + + /* Set a $size padding to all sides at $breakpoint */ + .p-xl-6 { + padding: 40px !important; } + + /* Set a $size padding to the top at $breakpoint */ + .pt-xl-6 { + padding-top: 40px !important; } + + /* Set a $size padding to the right at $breakpoint */ + .pr-xl-6 { + padding-right: 40px !important; } + + /* Set a $size padding to the bottom at $breakpoint */ + .pb-xl-6 { + padding-bottom: 40px !important; } + + /* Set a $size padding to the left at $breakpoint */ + .pl-xl-6 { + padding-left: 40px !important; } + + /* Set a $size padding to the left & right at $breakpoint */ + .px-xl-6 { + padding-right: 40px !important; + padding-left: 40px !important; } + + /* Set a $size padding to the top & bottom at $breakpoint */ + .py-xl-6 { + padding-top: 40px !important; + padding-bottom: 40px !important; } } +.p-responsive { + padding-right: 16px !important; + padding-left: 16px !important; } + @media (min-width: 544px) { + .p-responsive { + padding-right: 40px !important; + padding-left: 40px !important; } } + @media (min-width: 1012px) { + .p-responsive { + padding-right: 16px !important; + padding-left: 16px !important; } } + +/* Set the font size to 26px */ +.h1 { + font-size: 26px !important; } + @media (min-width: 768px) { + .h1 { + font-size: 32px !important; } } + +/* Set the font size to 22px */ +.h2 { + font-size: 22px !important; } + @media (min-width: 768px) { + .h2 { + font-size: 24px !important; } } + +/* Set the font size to 18px */ +.h3 { + font-size: 18px !important; } + @media (min-width: 768px) { + .h3 { + font-size: 20px !important; } } + +/* Set the font size to 16px */ +.h4 { + font-size: 16px !important; } + +/* Set the font size to 14px */ +.h5 { + font-size: 14px !important; } + +/* Set the font size to 12px */ +.h6 { + font-size: 12px !important; } + +.h1, +.h2, +.h3, +.h4, +.h5, +.h6 { + font-weight: 600 !important; } + +/* Set the font size to 26px */ +.f1 { + font-size: 26px !important; } + @media (min-width: 768px) { + .f1 { + font-size: 32px !important; } } + +/* Set the font size to 22px */ +.f2 { + font-size: 22px !important; } + @media (min-width: 768px) { + .f2 { + font-size: 24px !important; } } + +/* Set the font size to 18px */ +.f3 { + font-size: 18px !important; } + @media (min-width: 768px) { + .f3 { + font-size: 20px !important; } } + +/* Set the font size to 16px */ +.f4 { + font-size: 16px !important; } + @media (min-width: 768px) { + .f4 { + font-size: 16px !important; } } + +/* Set the font size to 14px */ +.f5 { + font-size: 14px !important; } + +/* Set the font size to 12px */ +.f6 { + font-size: 12px !important; } + +/* Set the font size to 40px and weight to light */ +.f00-light { + font-size: 40px !important; + font-weight: 300 !important; } + @media (min-width: 768px) { + .f00-light { + font-size: 48px !important; } } + +/* Set the font size to 32px and weight to light */ +.f0-light { + font-size: 32px !important; + font-weight: 300 !important; } + @media (min-width: 768px) { + .f0-light { + font-size: 40px !important; } } + +/* Set the font size to 26px and weight to light */ +.f1-light { + font-size: 26px !important; + font-weight: 300 !important; } + @media (min-width: 768px) { + .f1-light { + font-size: 32px !important; } } + +/* Set the font size to 22px and weight to light */ +.f2-light { + font-size: 22px !important; + font-weight: 300 !important; } + @media (min-width: 768px) { + .f2-light { + font-size: 24px !important; } } + +/* Set the font size to 18px and weight to light */ +.f3-light { + font-size: 18px !important; + font-weight: 300 !important; } + @media (min-width: 768px) { + .f3-light { + font-size: 20px !important; } } + +/* Set the font size to ${#h6-size} */ +.text-small { + font-size: 12px !important; } + +/* Large leading paragraphs */ +.lead { + margin-bottom: 30px; + font-size: 20px; + font-weight: 300; + color: #586069; } + +/* Set the line height to ultra condensed */ +.lh-condensed-ultra { + line-height: 1 !important; } + +/* Set the line height to condensed */ +.lh-condensed { + line-height: 1.25 !important; } + +/* Set the line height to default */ +.lh-default { + line-height: 1.5 !important; } + +/* Set the line height to zero */ +.lh-0 { + line-height: 0 !important; } + +@media (min-width: 544px) { + /* Set the line height to ultra condensed */ + .lh-sm-condensed-ultra { + line-height: 1 !important; } + + /* Set the line height to condensed */ + .lh-sm-condensed { + line-height: 1.25 !important; } + + /* Set the line height to default */ + .lh-sm-default { + line-height: 1.5 !important; } + + /* Set the line height to zero */ + .lh-sm-0 { + line-height: 0 !important; } } +@media (min-width: 768px) { + /* Set the line height to ultra condensed */ + .lh-md-condensed-ultra { + line-height: 1 !important; } + + /* Set the line height to condensed */ + .lh-md-condensed { + line-height: 1.25 !important; } + + /* Set the line height to default */ + .lh-md-default { + line-height: 1.5 !important; } + + /* Set the line height to zero */ + .lh-md-0 { + line-height: 0 !important; } } +@media (min-width: 1012px) { + /* Set the line height to ultra condensed */ + .lh-lg-condensed-ultra { + line-height: 1 !important; } + + /* Set the line height to condensed */ + .lh-lg-condensed { + line-height: 1.25 !important; } + + /* Set the line height to default */ + .lh-lg-default { + line-height: 1.5 !important; } + + /* Set the line height to zero */ + .lh-lg-0 { + line-height: 0 !important; } } +@media (min-width: 1280px) { + /* Set the line height to ultra condensed */ + .lh-xl-condensed-ultra { + line-height: 1 !important; } + + /* Set the line height to condensed */ + .lh-xl-condensed { + line-height: 1.25 !important; } + + /* Set the line height to default */ + .lh-xl-default { + line-height: 1.5 !important; } + + /* Set the line height to zero */ + .lh-xl-0 { + line-height: 0 !important; } } +/* Text align to the right */ +.text-right { + text-align: right !important; } + +/* Text align to the left */ +.text-left { + text-align: left !important; } + +/* Text align to the center */ +.text-center { + text-align: center !important; } + +@media (min-width: 544px) { + /* Text align to the right */ + .text-sm-right { + text-align: right !important; } + + /* Text align to the left */ + .text-sm-left { + text-align: left !important; } + + /* Text align to the center */ + .text-sm-center { + text-align: center !important; } } +@media (min-width: 768px) { + /* Text align to the right */ + .text-md-right { + text-align: right !important; } + + /* Text align to the left */ + .text-md-left { + text-align: left !important; } + + /* Text align to the center */ + .text-md-center { + text-align: center !important; } } +@media (min-width: 1012px) { + /* Text align to the right */ + .text-lg-right { + text-align: right !important; } + + /* Text align to the left */ + .text-lg-left { + text-align: left !important; } + + /* Text align to the center */ + .text-lg-center { + text-align: center !important; } } +@media (min-width: 1280px) { + /* Text align to the right */ + .text-xl-right { + text-align: right !important; } + + /* Text align to the left */ + .text-xl-left { + text-align: left !important; } + + /* Text align to the center */ + .text-xl-center { + text-align: center !important; } } +/* Set the font weight to normal */ +.text-normal { + font-weight: 400 !important; } + +/* Set the font weight to bold */ +.text-bold { + font-weight: 600 !important; } + +/* Set the font to italic */ +.text-italic { + font-style: italic !important; } + +/* Make text uppercase */ +.text-uppercase { + text-transform: uppercase !important; } + +/* Underline text */ +.text-underline { + text-decoration: underline !important; } + +/* Don't underline text */ +.no-underline { + text-decoration: none !important; } + +/* Don't wrap white space */ +.no-wrap { + white-space: nowrap !important; } + +/* Normal white space */ +.ws-normal { + white-space: normal !important; } + +/* Force long "words" to wrap if they exceed the width of the container */ +.break-word { + word-break: break-word !important; + word-wrap: break-word !important; + overflow-wrap: break-word !important; } + +/* + * Specifically apply word-break: break-all; per MDN: + * + * > Note: In contrast to `word-break: break-word` and `overflow-wrap: break-word`, + * > `word-break: break-all` will create a break at the exact place where text would + * > otherwise overflow its container (even if putting an entire word on its own line + * > would negate the need for a break). + * + * see: https://developer.mozilla.org/en-US/docs/Web/CSS/word-break#Values + */ +.wb-break-all { + word-break: break-all !important; } + +.text-emphasized { + font-weight: 600; + color: #24292e; } + +.list-style-none { + list-style: none !important; } + +/* Add a dark text shadow */ +.text-shadow-dark { + text-shadow: 0 1px 1px rgba(27, 31, 35, 0.25), 0 1px 25px rgba(27, 31, 35, 0.75); } + +/* Add a light text shadow */ +.text-shadow-light { + text-shadow: 0 1px 0 rgba(255, 255, 255, 0.5); } + +/* Set to monospace font */ +.text-mono { + font-family: "SFMono-Regular", Consolas, "Liberation Mono", Menlo, monospace !important; } + +/* Disallow user from selecting text */ +.user-select-none { + user-select: none !important; } + +.d-block, .toc.level-1.current > ul, .toc.level-2.current > ul, .toc.level-3.current > ul, .toc.level-4.current > ul, .toc.level-5.current > ul, .toc.level-6.current > ul, .toc.level-7.current > ul, .toc.level-8.current > ul, .toc.level-9.current > ul, .toc.level-10.current > ul, .toc.level-11.current > ul { + display: block !important; } + +.d-flex { + display: flex !important; } + +.d-inline { + display: inline !important; } + +.d-inline-block { + display: inline-block !important; } + +.d-inline-flex { + display: inline-flex !important; } + +.d-none, .toc > ul { + display: none !important; } + +.d-table { + display: table !important; } + +.d-table-cell { + display: table-cell !important; } + +@media (min-width: 544px) { + .d-sm-block { + display: block !important; } + + .d-sm-flex { + display: flex !important; } + + .d-sm-inline { + display: inline !important; } + + .d-sm-inline-block { + display: inline-block !important; } + + .d-sm-inline-flex { + display: inline-flex !important; } + + .d-sm-none { + display: none !important; } + + .d-sm-table { + display: table !important; } + + .d-sm-table-cell { + display: table-cell !important; } } +@media (min-width: 768px) { + .d-md-block { + display: block !important; } + + .d-md-flex { + display: flex !important; } + + .d-md-inline { + display: inline !important; } + + .d-md-inline-block { + display: inline-block !important; } + + .d-md-inline-flex { + display: inline-flex !important; } + + .d-md-none { + display: none !important; } + + .d-md-table { + display: table !important; } + + .d-md-table-cell { + display: table-cell !important; } } +@media (min-width: 1012px) { + .d-lg-block { + display: block !important; } + + .d-lg-flex { + display: flex !important; } + + .d-lg-inline { + display: inline !important; } + + .d-lg-inline-block { + display: inline-block !important; } + + .d-lg-inline-flex { + display: inline-flex !important; } + + .d-lg-none { + display: none !important; } + + .d-lg-table { + display: table !important; } + + .d-lg-table-cell { + display: table-cell !important; } } +@media (min-width: 1280px) { + .d-xl-block { + display: block !important; } + + .d-xl-flex { + display: flex !important; } + + .d-xl-inline { + display: inline !important; } + + .d-xl-inline-block { + display: inline-block !important; } + + .d-xl-inline-flex { + display: inline-flex !important; } + + .d-xl-none { + display: none !important; } + + .d-xl-table { + display: table !important; } + + .d-xl-table-cell { + display: table-cell !important; } } +.v-hidden { + visibility: hidden !important; } + +.v-visible { + visibility: visible !important; } + +@media (max-width: 543px) { + .hide-sm { + display: none !important; } } +@media (min-width: 544px) and (max-width: 767px) { + .hide-md { + display: none !important; } } +@media (min-width: 768px) and (max-width: 1011px) { + .hide-lg { + display: none !important; } } +@media (min-width: 1012px) { + .hide-xl { + display: none !important; } } +/* Set the table-layout to fixed */ +.table-fixed { + table-layout: fixed !important; } + +.sr-only { + position: absolute; + width: 1px; + height: 1px; + padding: 0; + overflow: hidden; + clip: rect(0, 0, 0, 0); + word-wrap: normal; + border: 0; } + +.show-on-focus { + position: absolute; + width: 1px; + height: 1px; + margin: 0; + overflow: hidden; + clip: rect(1px, 1px, 1px, 1px); } + .show-on-focus:focus { + z-index: 20; + width: auto; + height: auto; + clip: auto; } diff --git a/assets/css/theme.min.css b/assets/css/theme.min.css new file mode 100644 index 00000000000..dbfb91c892c --- /dev/null +++ b/assets/css/theme.min.css @@ -0,0 +1 @@ +:root{--toc-1: #e6e9eb;--toc-2: #ccd2d8;--toc-3: #b3bcc4;--toc-4: #9aa5b1;--toc-5: #e6e9eb;--toc-6: #ccd2d8;--toc-7: #b3bcc4;--toc-8: #9aa5b1;--toc-9: #e6e9eb;--toc-10: #ccd2d8;--toc-11: #b3bcc4;--toc-12: #9aa5b1}/*! normalize.css v4.1.1 | MIT License | github.com/necolas/normalize.css */html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}body{margin:0}article,aside,details,figcaption,figure,footer,header,main,menu,nav,section{display:block}summary{display:list-item}audio,canvas,progress,video{display:inline-block}audio:not([controls]){display:none;height:0}progress{vertical-align:baseline}template,[hidden]{display:none !important}a{background-color:transparent}a:active,a:hover{outline-width:0}abbr[title]{border-bottom:none;text-decoration:underline;text-decoration:underline dotted}b,strong{font-weight:inherit}b,strong{font-weight:bolder}dfn{font-style:italic}h1{font-size:2em;margin:.67em 0}mark{background-color:#ff0;color:#1b1f23}small{font-size:80%}sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}sub{bottom:-0.25em}sup{top:-0.5em}img{border-style:none}svg:not(:root){overflow:hidden}code,kbd,pre,samp{font-family:monospace,monospace;font-size:1em}figure{margin:1em 40px}hr{box-sizing:content-box;height:0;overflow:visible}button,input,select,textarea{font:inherit;margin:0}optgroup{font-weight:600}button,input{overflow:visible}button,select{text-transform:none}button,html [type=button],[type=reset],[type=submit]{-webkit-appearance:button}button::-moz-focus-inner,[type=button]::-moz-focus-inner,[type=reset]::-moz-focus-inner,[type=submit]::-moz-focus-inner{border-style:none;padding:0}button:-moz-focusring,[type=button]:-moz-focusring,[type=reset]:-moz-focusring,[type=submit]:-moz-focusring{outline:1px dotted ButtonText}fieldset{border:1px solid silver;margin:0 2px;padding:.35em .625em .75em}legend{box-sizing:border-box;color:inherit;display:table;max-width:100%;padding:0;white-space:normal}textarea{overflow:auto}[type=checkbox],[type=radio]{box-sizing:border-box;padding:0}[type=number]::-webkit-inner-spin-button,[type=number]::-webkit-outer-spin-button{height:auto}[type=search]{-webkit-appearance:textfield;outline-offset:-2px}[type=search]::-webkit-search-cancel-button,[type=search]::-webkit-search-decoration{-webkit-appearance:none}::-webkit-input-placeholder{color:inherit;opacity:.54}::-webkit-file-upload-button{-webkit-appearance:button;font:inherit}*{box-sizing:border-box}input,select,textarea,button{font-family:inherit;font-size:inherit;line-height:inherit}body{font-family:"Lato",BlinkMacSystemFont,"Segoe UI",Helvetica,sans-serif;font-size:14px;line-height:1.5;color:#24292e;background-color:#fff}a{color:#0366d6;text-decoration:none}a:hover{text-decoration:underline}b,strong{font-weight:600}hr,.rule{height:0;margin:15px 0;overflow:hidden;background:transparent;border:0;border-bottom:1px solid #dfe2e5}hr::before,.rule::before{display:table;content:""}hr::after,.rule::after{display:table;clear:both;content:""}table{border-spacing:0;border-collapse:collapse}td,th{padding:0}button{cursor:pointer;border-radius:0}[hidden][hidden]{display:none !important}details summary{cursor:pointer}details:not([open])>*:not(summary){display:none !important}kbd{display:inline-block;padding:3px 5px;font:11px "SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace;line-height:10px;color:#444d56;vertical-align:middle;background-color:#fafbfc;border:solid 1px #d1d5da;border-bottom-color:#d1d5da;border-radius:6px;box-shadow:inset 0 -1px 0 #d1d5da}h1,h2,h3,h4,h5,h6{margin-top:0;margin-bottom:0}h1{font-size:32px;font-weight:600}h2{font-size:24px;font-weight:600}h3{font-size:20px;font-weight:600}h4{font-size:16px;font-weight:600}h5{font-size:14px;font-weight:600}h6{font-size:12px;font-weight:600}p{margin-top:0;margin-bottom:10px}small{font-size:90%}blockquote{margin:0}ul,ol{padding-left:0;margin-top:0;margin-bottom:0}ol ol,ul ol{list-style-type:lower-roman}ul ul ol,ul ol ol,ol ul ol,ol ol ol{list-style-type:lower-alpha}dd{margin-left:0}tt,code{font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace;font-size:12px}pre{margin-top:0;margin-bottom:0;font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace;font-size:12px}.octicon{vertical-align:text-bottom}.breadcrumb-item{display:inline-block;margin-left:-0.35em;white-space:nowrap;list-style:none}.breadcrumb-item::after{padding-right:.5em;padding-left:.5em;color:#e1e4e8;content:"/"}.breadcrumb-item:first-child{margin-left:0}.breadcrumb-item-selected,.breadcrumb-item[aria-current]:not([aria-current=false]){color:#586069}.breadcrumb-item-selected::after,.breadcrumb-item[aria-current]:not([aria-current=false])::after{content:none}.btn{position:relative;display:inline-block;padding:5px 16px;font-size:14px;font-weight:500;line-height:20px;white-space:nowrap;vertical-align:middle;cursor:pointer;user-select:none;border:1px solid;border-radius:6px;appearance:none}.btn:hover{text-decoration:none}.btn:disabled,.btn.disabled,.btn[aria-disabled=true]{cursor:default}.btn:disabled .octicon,.btn.disabled .octicon,.btn[aria-disabled=true] .octicon{color:inherit}.btn i{font-style:normal;font-weight:500;opacity:.75}.btn .octicon{margin-right:4px;color:#6a737d;vertical-align:text-bottom}.btn .octicon:only-child{margin-right:0}.btn .Counter{margin-left:2px;color:inherit;text-shadow:none;vertical-align:top;background-color:rgba(27,31,35,.08)}.btn .dropdown-caret{margin-left:4px;opacity:.8}.btn{color:#24292e;background-color:#fafbfc;border-color:rgba(27,31,35,.15);box-shadow:0 1px 0 rgba(27,31,35,.04),inset 0 1px 0 rgba(255,255,255,.25);transition:background-color .2s cubic-bezier(0.3, 0, 0.5, 1)}.btn:hover,.btn.hover,[open]>.btn{background-color:#f3f4f6;transition-duration:.1s}.btn:active,.btn.selected,.btn[aria-selected=true]{background-color:#edeff2;box-shadow:inset 0 1px 0 rgba(225,228,232,.2);transition:none}.btn:disabled,.btn.disabled,.btn[aria-disabled=true]{color:#959da5;background-color:#fafbfc;border-color:rgba(27,31,35,.15)}.btn:focus,.btn.focus{outline:1px dotted transparent;outline-offset:2px;box-shadow:0 0 0 3px rgba(3,102,214,.3)}.btn-primary{color:#fff;background-color:#2ea44f;border-color:rgba(27,31,35,.15);box-shadow:0 1px 0 rgba(27,31,35,.1),inset 0 1px 0 rgba(255,255,255,.03)}.btn-primary:hover,.btn-primary.hover,[open]>.btn-primary{background-color:#2c974b}.btn-primary:active,.btn-primary.selected,.btn-primary[aria-selected=true]{background-color:#2a8f47;box-shadow:inset 0 1px 0 rgba(20,70,32,.2)}.btn-primary:disabled,.btn-primary.disabled,.btn-primary[aria-disabled=true]{color:rgba(255,255,255,.8);background-color:#94d3a2;border-color:rgba(27,31,35,.1);box-shadow:0 1px 0 rgba(27,31,35,.1),inset 0 1px 0 rgba(255,255,255,.03)}.btn-primary:focus,.btn-primary.focus{box-shadow:0 0 0 3px rgba(46,164,79,.4)}.btn-primary .Counter{color:inherit;background-color:rgba(255,255,255,.2)}.btn-primary .octicon{color:rgba(255,255,255,.8)}.btn-danger{color:#cb2431;transition:none}.btn-danger:hover,[open]>.btn-danger{color:#fff;background-color:#cb2431;border-color:rgba(27,31,35,.15);box-shadow:0 1px 0 rgba(27,31,35,.1),inset 0 1px 0 rgba(255,255,255,.03)}.btn-danger:hover .Counter,[open]>.btn-danger .Counter{background-color:rgba(255,255,255,.2)}.btn-danger:hover .octicon,[open]>.btn-danger .octicon{color:inherit}.btn-danger:active,.btn-danger.selected,.btn-danger[aria-selected=true]{color:#fff;background-color:#be222e;border-color:rgba(27,31,35,.15);box-shadow:inset 0 1px 0 rgba(134,24,29,.2)}.btn-danger:disabled,.btn-danger.disabled,.btn-danger[aria-disabled=true]{color:rgba(203,36,49,.5);background-color:#fafbfc;border-color:rgba(27,31,35,.15);box-shadow:0 1px 0 rgba(27,31,35,.04),inset 0 1px 0 rgba(255,255,255,.25)}.btn-danger:disabled .Counter,.btn-danger.disabled .Counter,.btn-danger[aria-disabled=true] .Counter{background-color:rgba(203,36,49,.05)}.btn-danger:focus{box-shadow:0 0 0 3px rgba(203,36,49,.4)}.btn-danger .Counter{color:inherit;background-color:rgba(203,36,49,.1)}.btn-outline{color:#0366d6;transition:none}.btn-outline:hover,[open]>.btn-outline{color:#fff;background-color:#0366d6;border-color:rgba(27,31,35,.15);box-shadow:0 1px 0 rgba(27,31,35,.1),inset 0 1px 0 rgba(255,255,255,.03)}.btn-outline:hover .Counter,[open]>.btn-outline .Counter{background-color:rgba(255,255,255,.2)}.btn-outline:hover .octicon,[open]>.btn-outline .octicon{color:inherit}.btn-outline:active,.btn-outline.selected,.btn-outline[aria-selected=true]{color:#fff;background-color:#035fc7;border-color:rgba(27,31,35,.15);box-shadow:inset 0 1px 0 rgba(5,38,76,.2)}.btn-outline:disabled,.btn-outline.disabled,.btn-outline[aria-disabled=true]{color:rgba(3,102,214,.5);background-color:#fafbfc;border-color:rgba(27,31,35,.15);box-shadow:0 1px 0 rgba(27,31,35,.04),inset 0 1px 0 rgba(255,255,255,.25)}.btn-outline:disabled .Counter,.btn-outline.disabled .Counter,.btn-outline[aria-disabled=true] .Counter{background-color:rgba(3,102,214,.05)}.btn-outline:focus{box-shadow:0 0 0 3px rgba(3,102,214,.4)}.btn-outline .Counter{color:inherit;background-color:rgba(3,102,214,.1)}.btn-blue{color:#fff;background-color:#0361cc;background-image:linear-gradient(-180deg, #0679fc 0%, #0361cc 90%)}.btn-blue:focus,.btn-blue.focus{box-shadow:0 0 0 .2em rgba(6,121,252,.4)}.btn-blue:hover,.btn-blue.hover{background-color:#035cc2;background-image:linear-gradient(-180deg, #0374f4 0%, #035cc2 90%);background-position:-0.5em;border-color:rgba(27,31,35,.5)}.btn-blue:active,.btn-blue.selected,.btn-blue[aria-selected=true],[open]>.btn-blue{background-color:#045cc1;background-image:none;border-color:rgba(27,31,35,.5);box-shadow:inset 0 .15em .3em rgba(27,31,35,.15)}.btn-blue:disabled,.btn-blue.disabled,.btn-blue[aria-disabled=true]{color:rgba(255,255,255,.75);background-color:#81b0e6;background-image:none;border-color:rgba(27,31,35,.15);box-shadow:none}.btn-blue .Counter{color:#0366d6;background-color:#fff}.btn-sm{padding:3px 12px;font-size:12px;line-height:20px}.btn-sm .octicon{vertical-align:text-top}.btn-large{padding:.75em 1.5em;font-size:inherit;line-height:1.5;border-radius:.5em}.btn-block{display:block;width:100%;text-align:center}.BtnGroup{display:inline-block;vertical-align:middle}.BtnGroup::before{display:table;content:""}.BtnGroup::after{display:table;clear:both;content:""}.BtnGroup+.BtnGroup,.BtnGroup+.btn{margin-left:4px}.BtnGroup-item{position:relative;float:left;border-right-width:0;border-radius:0}.BtnGroup-item:first-child{border-top-left-radius:6px;border-bottom-left-radius:6px}.BtnGroup-item:last-child{border-right-width:1px;border-top-right-radius:6px;border-bottom-right-radius:6px}.BtnGroup-item.selected,.BtnGroup-item[aria-selected=true],.BtnGroup-item:focus,.BtnGroup-item:active,.BtnGroup-item:hover{border-right-width:1px}.BtnGroup-item.selected+.BtnGroup-item,.BtnGroup-item.selected+.BtnGroup-parent .BtnGroup-item,.BtnGroup-item[aria-selected=true]+.BtnGroup-item,.BtnGroup-item[aria-selected=true]+.BtnGroup-parent .BtnGroup-item,.BtnGroup-item:focus+.BtnGroup-item,.BtnGroup-item:focus+.BtnGroup-parent .BtnGroup-item,.BtnGroup-item:active+.BtnGroup-item,.BtnGroup-item:active+.BtnGroup-parent .BtnGroup-item,.BtnGroup-item:hover+.BtnGroup-item,.BtnGroup-item:hover+.BtnGroup-parent .BtnGroup-item{border-left-width:0}.BtnGroup-parent{float:left}.BtnGroup-parent:first-child .BtnGroup-item{border-top-left-radius:6px;border-bottom-left-radius:6px}.BtnGroup-parent:last-child .BtnGroup-item{border-right-width:1px;border-top-right-radius:6px;border-bottom-right-radius:6px}.BtnGroup-parent .BtnGroup-item{border-right-width:0;border-radius:0}.BtnGroup-parent.selected .BtnGroup-item,.BtnGroup-parent[aria-selected=true] .BtnGroup-item,.BtnGroup-parent:focus .BtnGroup-item,.BtnGroup-parent:active .BtnGroup-item,.BtnGroup-parent:hover .BtnGroup-item{border-right-width:1px}.BtnGroup-parent.selected+.BtnGroup-item,.BtnGroup-parent.selected+.BtnGroup-parent .BtnGroup-item,.BtnGroup-parent[aria-selected=true]+.BtnGroup-item,.BtnGroup-parent[aria-selected=true]+.BtnGroup-parent .BtnGroup-item,.BtnGroup-parent:focus+.BtnGroup-item,.BtnGroup-parent:focus+.BtnGroup-parent .BtnGroup-item,.BtnGroup-parent:active+.BtnGroup-item,.BtnGroup-parent:active+.BtnGroup-parent .BtnGroup-item,.BtnGroup-parent:hover+.BtnGroup-item,.BtnGroup-parent:hover+.BtnGroup-parent .BtnGroup-item{border-left-width:0}.BtnGroup-item:focus,.BtnGroup-item:active,.BtnGroup-parent:focus,.BtnGroup-parent:active{z-index:1}.btn-link{display:inline-block;padding:0;font-size:inherit;color:#0366d6;text-decoration:none;white-space:nowrap;cursor:pointer;user-select:none;background-color:transparent;border:0;appearance:none}.btn-link:hover{text-decoration:underline}.btn-link:disabled,.btn-link:disabled:hover,.btn-link[aria-disabled=true],.btn-link[aria-disabled=true]:hover{color:rgba(88,96,105,.5);cursor:default}.btn-invisible{color:#0366d6;background-color:transparent;border:0;border-radius:0;box-shadow:none}.btn-invisible:hover,.btn-invisible:active,.btn-invisible:focus,.btn-invisible.selected,.btn-invisible[aria-selected=true],.btn-invisible.zeroclipboard-is-hover,.btn-invisible.zeroclipboard-is-active{color:#0366d6;background:none;outline:none;box-shadow:none}.btn-octicon{display:inline-block;padding:5px;margin-left:5px;line-height:1;color:#586069;vertical-align:middle;background:transparent;border:0}.btn-octicon:hover{color:#0366d6}.btn-octicon.disabled,.btn-octicon[aria-disabled=true]{color:#959da5;cursor:default}.btn-octicon.disabled:hover,.btn-octicon[aria-disabled=true]:hover{color:#959da5}.btn-octicon-danger:hover{color:#cb2431}.close-button{padding:0;background:transparent;border:0;outline:none}.hidden-text-expander{display:block}.hidden-text-expander.inline{position:relative;top:-1px;display:inline-block;margin-left:5px;line-height:0}.hidden-text-expander a,.ellipsis-expander{display:inline-block;height:12px;padding:0 5px 5px;font-size:12px;font-weight:600;line-height:6px;color:#444d56;text-decoration:none;vertical-align:middle;background:#dfe2e5;border:0;border-radius:1px}.hidden-text-expander a:hover,.ellipsis-expander:hover{text-decoration:none;background-color:#c6cbd1}.hidden-text-expander a:active,.ellipsis-expander:active{color:#fff;background-color:#2188ff}.btn-with-count{float:left;border-top-right-radius:0;border-bottom-right-radius:0}.btn-with-count:focus{z-index:1}.social-count{position:relative;float:left;padding:3px 12px;font-size:12px;font-weight:600;line-height:20px;color:#24292e;vertical-align:middle;background-color:#fff;border:1px solid rgba(27,31,35,.15);border-left:0;border-top-right-radius:6px;border-bottom-right-radius:6px;box-shadow:0 1px 0 rgba(27,31,35,.04),inset 0 1px 0 rgba(255,255,255,.25)}.social-count:hover,.social-count:active{text-decoration:none}.social-count:hover{color:#0366d6;cursor:pointer}.social-count:focus{z-index:1;outline:0;box-shadow:0 0 0 3px rgba(3,102,214,.3)}fieldset{padding:0;margin:0;border:0}label{font-weight:600}.form-control,.form-select{padding:5px 12px;font-size:14px;line-height:20px;color:#24292e;vertical-align:middle;background-color:#fff;background-repeat:no-repeat;background-position:right 8px center;border:1px solid #e1e4e8;border-radius:6px;outline:none;box-shadow:inset 0 1px 0 rgba(225,228,232,.2)}.form-control.focus,.form-control:focus,.form-select.focus,.form-select:focus{border-color:#0366d6;outline:none;box-shadow:0 0 0 3px rgba(3,102,214,.3)}.form-control[disabled],.form-select[disabled]{color:#959da5;background-color:#f3f4f6}@supports(-webkit-touch-callout: none){.form-control,.form-select{font-size:16px}@media(min-width: 768px){.form-control,.form-select{font-size:14px}}}textarea.form-control{padding-top:8px;padding-bottom:8px;line-height:1.5}.input-contrast{background-color:#fafbfc}.input-contrast:focus{background-color:#fff}.input-dark{color:#fff;background-color:rgba(255,255,255,.15);border-color:transparent;box-shadow:none}.input-dark::placeholder{color:inherit;opacity:.6}.input-dark.focus,.input-dark:focus{border-color:rgba(27,31,35,.3);box-shadow:0 0 0 .2em rgba(121,184,255,.4)}::placeholder{color:#6a737d;opacity:1}.input-sm{padding-top:3px;padding-bottom:3px;font-size:12px;line-height:20px}.input-lg{font-size:16px}.input-block{display:block;width:100%}.input-monospace{font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace}.input-hide-webkit-autofill::-webkit-contacts-auto-fill-button{position:absolute;right:0;display:none !important;pointer-events:none;visibility:hidden}.form-checkbox{padding-left:20px;margin:15px 0;vertical-align:middle}.form-checkbox label em.highlight{position:relative;left:-4px;padding:2px 4px;font-style:normal;background:#fffbdd;border-radius:6px}.form-checkbox input[type=checkbox],.form-checkbox input[type=radio]{float:left;margin:5px 0 0 -20px;vertical-align:middle}.form-checkbox .note{display:block;margin:0;font-size:12px;font-weight:400;color:#586069}.form-checkbox-details{display:none}.form-checkbox-details-trigger:checked~* .form-checkbox-details,.form-checkbox-details-trigger:checked~.form-checkbox-details{display:block}.hfields{margin:15px 0}.hfields::before{display:table;content:""}.hfields::after{display:table;clear:both;content:""}.hfields .form-group{float:left;margin:0 30px 0 0}.hfields .form-group dt label,.hfields .form-group .form-group-header label{display:inline-block;margin:5px 0 0;color:#586069}.hfields .form-group dt img,.hfields .form-group .form-group-header img{position:relative;top:-2px}.hfields .btn{float:left;margin:28px 25px 0 -20px}.hfields .form-select{margin-top:5px}input::-webkit-outer-spin-button,input::-webkit-inner-spin-button{margin:0;appearance:none}.form-actions::before{display:table;content:""}.form-actions::after{display:table;clear:both;content:""}.form-actions .btn{float:right}.form-actions .btn+.btn{margin-right:5px}.form-warning{padding:8px 10px;margin:10px 0;font-size:14px;color:#735c0f;background:#fffbdd;border:1px solid #f9c513;border-radius:6px}.form-warning p{margin:0;line-height:1.5}.form-warning a{font-weight:600}.form-select{display:inline-block;max-width:100%;height:32px;padding-right:24px;background-color:#fff;background-image:url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAUCAMAAACzvE1FAAAADFBMVEUzMzMzMzMzMzMzMzMKAG/3AAAAA3RSTlMAf4C/aSLHAAAAPElEQVR42q3NMQ4AIAgEQTn//2cLdRKppSGzBYwzVXvznNWs8C58CiussPJj8h6NwgorrKRdTvuV9v16Afn0AYFOB7aYAAAAAElFTkSuQmCC");background-repeat:no-repeat;background-position:right 8px center;background-size:8px 10px;appearance:none}.form-select::-ms-expand{opacity:0}.form-select[multiple]{height:auto}.select-sm{height:28px;padding-top:3px;padding-bottom:3px;font-size:12px}.select-sm[multiple]{height:auto;min-height:0}.form-group{margin:15px 0}.form-group .form-control{width:440px;max-width:100%;margin-right:5px;background-color:#fafbfc}.form-group .form-control:focus{background-color:#fff}.form-group .form-control.shorter{width:130px}.form-group .form-control.short{width:250px}.form-group .form-control.long{width:100%}.form-group textarea.form-control{width:100%;height:200px;min-height:200px}.form-group textarea.form-control.short{height:50px;min-height:50px}.form-group dt,.form-group .form-group-header{margin:0 0 6px}.form-group label{position:relative}.form-group.flattened dt,.form-group.flattened .form-group-header{float:left;margin:0;line-height:32px}.form-group.flattened dd,.form-group.flattened .form-group-body{line-height:32px}.form-group dd h4,.form-group .form-group-body h4{margin:4px 0 0}.form-group dd h4.is-error,.form-group .form-group-body h4.is-error{color:#cb2431}.form-group dd h4.is-success,.form-group .form-group-body h4.is-success{color:#22863a}.form-group dd h4+.note,.form-group .form-group-body h4+.note{margin-top:0}.form-group.required dt label::after,.form-group.required .form-group-header label::after{padding-left:5px;color:#cb2431;content:"*"}.form-group .success,.form-group .error,.form-group .indicator{display:none;font-size:12px;font-weight:600}.form-group.loading{opacity:.5}.form-group.loading .indicator{display:inline}.form-group.loading .spinner{display:inline-block;vertical-align:middle}.form-group.successful .success{display:inline;color:#22863a}.form-group.successed .success,.form-group.successed .warning,.form-group.successed .error,.form-group.warn .success,.form-group.warn .warning,.form-group.warn .error,.form-group.errored .success,.form-group.errored .warning,.form-group.errored .error{position:absolute;z-index:10;display:block;max-width:450px;padding:4px 8px;margin:8px 0 0;font-size:12px;font-weight:400;border-style:solid;border-width:1px;border-radius:6px}.form-group.successed .success::after,.form-group.successed .success::before,.form-group.successed .warning::after,.form-group.successed .warning::before,.form-group.successed .error::after,.form-group.successed .error::before,.form-group.warn .success::after,.form-group.warn .success::before,.form-group.warn .warning::after,.form-group.warn .warning::before,.form-group.warn .error::after,.form-group.warn .error::before,.form-group.errored .success::after,.form-group.errored .success::before,.form-group.errored .warning::after,.form-group.errored .warning::before,.form-group.errored .error::after,.form-group.errored .error::before{position:absolute;bottom:100%;left:10px;z-index:15;width:0;height:0;pointer-events:none;content:" ";border:solid transparent}.form-group.successed .success::after,.form-group.successed .warning::after,.form-group.successed .error::after,.form-group.warn .success::after,.form-group.warn .warning::after,.form-group.warn .error::after,.form-group.errored .success::after,.form-group.errored .warning::after,.form-group.errored .error::after{border-width:5px}.form-group.successed .success::before,.form-group.successed .warning::before,.form-group.successed .error::before,.form-group.warn .success::before,.form-group.warn .warning::before,.form-group.warn .error::before,.form-group.errored .success::before,.form-group.errored .warning::before,.form-group.errored .error::before{margin-left:-1px;border-width:6px}.form-group.successed .success{color:#144620;background-color:#dcffe4;border-color:#34d058}.form-group.successed .success::after{border-bottom-color:#dcffe4}.form-group.successed .success::before{border-bottom-color:#34d058}.form-group.warn .form-control{border-color:#f9c513}.form-group.warn .warning{background-color:#fff5b1;border-color:#f9c513}.form-group.warn .warning::after{border-bottom-color:#fff5b1}.form-group.warn .warning::before{border-bottom-color:#f9c513}.form-group.errored .form-control{border-color:#cb2431}.form-group.errored label{color:#cb2431}.form-group.errored .error{background-color:#ffeef0;border-color:#f97583}.form-group.errored .error::after{border-bottom-color:#ffeef0}.form-group.errored .error::before{border-bottom-color:#f97583}.note{min-height:17px;margin:4px 0 2px;font-size:12px;color:#586069}.note .spinner{margin-right:3px;vertical-align:middle}dl.form-group>dd .form-control.is-autocheck-loading,dl.form-group>dd .form-control.is-autocheck-successful,dl.form-group>dd .form-control.is-autocheck-errored,.form-group>.form-group-body .form-control.is-autocheck-loading,.form-group>.form-group-body .form-control.is-autocheck-successful,.form-group>.form-group-body .form-control.is-autocheck-errored{padding-right:30px}dl.form-group>dd .form-control.is-autocheck-loading,.form-group>.form-group-body .form-control.is-autocheck-loading{background-image:url("/images/spinners/octocat-spinner-16px.gif")}dl.form-group>dd .form-control.is-autocheck-successful,.form-group>.form-group-body .form-control.is-autocheck-successful{background-image:url("/images/modules/ajax/success.png")}dl.form-group>dd .form-control.is-autocheck-errored,.form-group>.form-group-body .form-control.is-autocheck-errored{background-image:url("/images/modules/ajax/error.png")}@media only screen and (-webkit-min-device-pixel-ratio: 2),only screen and (min--moz-device-pixel-ratio: 2),only screen and (-moz-min-device-pixel-ratio: 2),only screen and (-o-min-device-pixel-ratio: 2/1),only screen and (min-device-pixel-ratio: 2),only screen and (min-resolution: 192dpi),only screen and (min-resolution: 2dppx){dl.form-group>dd .form-control.is-autocheck-loading,dl.form-group>dd .form-control.is-autocheck-successful,dl.form-group>dd .form-control.is-autocheck-errored,.form-group>.form-group-body .form-control.is-autocheck-loading,.form-group>.form-group-body .form-control.is-autocheck-successful,.form-group>.form-group-body .form-control.is-autocheck-errored{background-size:16px 16px}dl.form-group>dd .form-control.is-autocheck-loading,.form-group>.form-group-body .form-control.is-autocheck-loading{background-image:url("/images/spinners/octocat-spinner-32.gif")}dl.form-group>dd .form-control.is-autocheck-successful,.form-group>.form-group-body .form-control.is-autocheck-successful{background-image:url("/images/modules/ajax/success@2x.png")}dl.form-group>dd .form-control.is-autocheck-errored,.form-group>.form-group-body .form-control.is-autocheck-errored{background-image:url("/images/modules/ajax/error@2x.png")}}.status-indicator{display:inline-block;width:16px;height:16px;margin-left:5px}.status-indicator .octicon{display:none}.status-indicator-success::before{content:""}.status-indicator-success .octicon-check{display:inline-block;color:#28a745;fill:#28a745}.status-indicator-success .octicon-x{display:none}.status-indicator-failed::before{content:""}.status-indicator-failed .octicon-check{display:none}.status-indicator-failed .octicon-x{display:inline-block;color:#cb2431;fill:#d73a49}.status-indicator-loading{width:16px;background-image:url("/images/spinners/octocat-spinner-32-EAF2F5.gif");background-repeat:no-repeat;background-position:0 0;background-size:16px}.inline-form{display:inline-block}.inline-form .btn-plain{background-color:transparent;border:0}.drag-and-drop{padding:7px 10px;margin:0;font-size:13px;line-height:16px;color:#586069;background-color:#fafbfc;border:1px solid #c3c8cf;border-top:0;border-bottom-right-radius:6px;border-bottom-left-radius:6px}.drag-and-drop .default,.drag-and-drop .loading,.drag-and-drop .error{display:none}.drag-and-drop .error{color:#cb2431}.drag-and-drop img{vertical-align:top}.is-default .drag-and-drop .default{display:inline-block}.is-uploading .drag-and-drop .loading{display:inline-block}.is-bad-file .drag-and-drop .bad-file{display:inline-block}.is-duplicate-filename .drag-and-drop .duplicate-filename{display:inline-block}.is-too-big .drag-and-drop .too-big{display:inline-block}.is-hidden-file .drag-and-drop .hidden-file{display:inline-block}.is-empty .drag-and-drop .empty{display:inline-block}.is-bad-permissions .drag-and-drop .bad-permissions{display:inline-block}.is-repository-required .drag-and-drop .repository-required{display:inline-block}.drag-and-drop-error-info{font-weight:400;color:#586069}.drag-and-drop-error-info a{color:#0366d6}.is-failed .drag-and-drop .failed-request{display:inline-block}.manual-file-chooser{position:absolute;width:240px;padding:5px;margin-left:-80px;cursor:pointer;opacity:.0001}.manual-file-chooser:hover+.manual-file-chooser-text{text-decoration:underline}.btn .manual-file-chooser{top:0;padding:0;line-height:34px}.upload-enabled textarea{display:block;border-bottom:1px dashed #dfe2e5;border-bottom-right-radius:0;border-bottom-left-radius:0}.upload-enabled.focused{border-radius:6px;box-shadow:inset 0 1px 2px rgba(27,31,35,.075),0 0 0 .2em rgba(3,102,214,.3)}.upload-enabled.focused .form-control{box-shadow:none}.upload-enabled.focused .drag-and-drop{border-color:#4a9eff}.dragover textarea,.dragover .drag-and-drop{box-shadow:#c9ff00 0 0 3px}.write-content{position:relative}.previewable-comment-form{position:relative}.previewable-comment-form .tabnav{position:relative;padding:8px 8px 0}.previewable-comment-form .comment{border:1px solid #c3c8cf}.previewable-comment-form .comment-form-error{margin-bottom:8px}.previewable-comment-form .write-content,.previewable-comment-form .preview-content{display:none;margin:0 8px 8px}.previewable-comment-form.write-selected .write-content,.previewable-comment-form.preview-selected .preview-content{display:block}.previewable-comment-form textarea{display:block;width:100%;min-height:100px;max-height:500px;padding:8px;resize:vertical}.form-action-spacious{margin-top:10px}div.composer{margin-top:0;border:0}.composer .comment-form-textarea{height:200px;min-height:200px}.composer .tabnav{margin:0 0 10px}h2.account{margin:15px 0 0;font-size:18px;font-weight:400;color:#586069}p.explain{position:relative;font-size:12px;color:#586069}p.explain strong{color:#24292e}p.explain .octicon{margin-right:5px;color:#959da5}p.explain .minibutton{top:-4px;float:right}.form-group label{position:static}.input-group{display:table}.input-group .form-control{position:relative;width:100%}.input-group .form-control:focus{z-index:2}.input-group .form-control+.btn{margin-left:0}.input-group.inline{display:inline-table}.input-group .form-control,.input-group-button{display:table-cell}.input-group-button{width:1%;vertical-align:middle}.input-group .form-control:first-child,.input-group-button:first-child .btn{border-top-right-radius:0;border-bottom-right-radius:0}.input-group-button:first-child .btn{margin-right:-1px}.input-group .form-control:last-child,.input-group-button:last-child .btn{border-top-left-radius:0;border-bottom-left-radius:0}.input-group-button:last-child .btn{margin-left:-1px}.radio-group::before{display:table;content:""}.radio-group::after{display:table;clear:both;content:""}.radio-label{float:left;padding:6px 16px 6px 36px;margin-left:-1px;font-size:14px;line-height:20px;color:#24292e;cursor:pointer;border:1px solid #e1e4e8}:checked+.radio-label{position:relative;z-index:1;border-color:#0366d6}.radio-label:first-of-type{margin-left:0;border-top-left-radius:6px;border-bottom-left-radius:6px}.radio-label:last-of-type{border-top-right-radius:6px;border-bottom-right-radius:6px}.radio-input{z-index:3;float:left;margin:10px -32px 0 16px}.AnimatedEllipsis{display:inline-block;overflow:hidden;vertical-align:bottom}.AnimatedEllipsis::after{display:inline-block;content:"...";animation:AnimatedEllipsis-keyframes 1.2s steps(4, jump-none) infinite}@keyframes AnimatedEllipsis-keyframes{0%{transform:translateX(-100%)}}.markdown-body{font-family:"Lato",BlinkMacSystemFont,"Segoe UI",Helvetica,sans-serif;font-size:16px;line-height:1.5;word-wrap:break-word}.markdown-body kbd{display:inline-block;padding:3px 5px;font:11px "SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace;line-height:10px;color:#444d56;vertical-align:middle;background-color:#fafbfc;border:solid 1px #d1d5da;border-bottom-color:#d1d5da;border-radius:6px;box-shadow:inset 0 -1px 0 #d1d5da}.markdown-body::before{display:table;content:""}.markdown-body::after{display:table;clear:both;content:""}.markdown-body>*:first-child{margin-top:0 !important}.markdown-body>*:last-child{margin-bottom:0 !important}.markdown-body a:not([href]){color:inherit;text-decoration:none}.markdown-body .absent{color:#cb2431}.markdown-body .anchor{float:left;padding-right:4px;margin-left:-20px;line-height:1}.markdown-body .anchor:focus{outline:none}.markdown-body p,.markdown-body blockquote,.markdown-body ul,.markdown-body ol,.markdown-body dl,.markdown-body table,.markdown-body pre,.markdown-body details{margin-top:0;margin-bottom:16px}.markdown-body hr{height:.25em;padding:0;margin:24px 0;background-color:#e1e4e8;border:0}.markdown-body blockquote{padding:0 1em;color:#6a737d;border-left:.25em solid #dfe2e5}.markdown-body blockquote>:first-child{margin-top:0}.markdown-body blockquote>:last-child{margin-bottom:0}.markdown-body h1,.markdown-body h2,.markdown-body h3,.markdown-body h4,.markdown-body h5,.markdown-body h6{margin-top:24px;margin-bottom:16px;font-weight:600;line-height:1.25}.markdown-body h1 .octicon-link,.markdown-body h2 .octicon-link,.markdown-body h3 .octicon-link,.markdown-body h4 .octicon-link,.markdown-body h5 .octicon-link,.markdown-body h6 .octicon-link{color:#1b1f23;vertical-align:middle;visibility:hidden}.markdown-body h1:hover .anchor,.markdown-body h2:hover .anchor,.markdown-body h3:hover .anchor,.markdown-body h4:hover .anchor,.markdown-body h5:hover .anchor,.markdown-body h6:hover .anchor{text-decoration:none}.markdown-body h1:hover .anchor .octicon-link,.markdown-body h2:hover .anchor .octicon-link,.markdown-body h3:hover .anchor .octicon-link,.markdown-body h4:hover .anchor .octicon-link,.markdown-body h5:hover .anchor .octicon-link,.markdown-body h6:hover .anchor .octicon-link{visibility:visible}.markdown-body h1 tt,.markdown-body h1 code,.markdown-body h2 tt,.markdown-body h2 code,.markdown-body h3 tt,.markdown-body h3 code,.markdown-body h4 tt,.markdown-body h4 code,.markdown-body h5 tt,.markdown-body h5 code,.markdown-body h6 tt,.markdown-body h6 code{font-size:inherit}.markdown-body h1{padding-bottom:.3em;font-size:2em;border-bottom:1px solid #eaecef}.markdown-body h2{padding-bottom:.3em;font-size:1.5em;border-bottom:1px solid #eaecef}.markdown-body h3{font-size:1.25em}.markdown-body h4{font-size:1em}.markdown-body h5{font-size:.875em}.markdown-body h6{font-size:.85em;color:#6a737d}.markdown-body ul,.markdown-body ol{padding-left:2em}.markdown-body ul.no-list,.markdown-body ol.no-list{padding:0;list-style-type:none}.markdown-body ul ul,.markdown-body ul ol,.markdown-body ol ol,.markdown-body ol ul{margin-top:0;margin-bottom:0}.markdown-body li{word-wrap:break-all}.markdown-body li>p{margin-top:16px}.markdown-body li+li{margin-top:.25em}.markdown-body dl{padding:0}.markdown-body dl dt{padding:0;margin-top:16px;font-size:1em;font-style:italic;font-weight:600}.markdown-body dl dd{padding:0 16px;margin-bottom:16px}.markdown-body table{display:block;width:100%;width:max-content;max-width:100%;overflow:auto}.markdown-body table th{font-weight:600}.markdown-body table th,.markdown-body table td{padding:6px 13px;border:1px solid #dfe2e5}.markdown-body table tr{background-color:#fff;border-top:1px solid #c6cbd1}.markdown-body table tr:nth-child(2n){background-color:#f6f8fa}.markdown-body table img{background-color:transparent}.markdown-body img{max-width:100%;box-sizing:content-box;background-color:#fff}.markdown-body img[align=right]{padding-left:20px}.markdown-body img[align=left]{padding-right:20px}.markdown-body .emoji{max-width:none;vertical-align:text-top;background-color:transparent}.markdown-body span.frame{display:block;overflow:hidden}.markdown-body span.frame>span{display:block;float:left;width:auto;padding:7px;margin:13px 0 0;overflow:hidden;border:1px solid #dfe2e5}.markdown-body span.frame span img{display:block;float:left}.markdown-body span.frame span span{display:block;padding:5px 0 0;clear:both;color:#24292e}.markdown-body span.align-center{display:block;overflow:hidden;clear:both}.markdown-body span.align-center>span{display:block;margin:13px auto 0;overflow:hidden;text-align:center}.markdown-body span.align-center span img{margin:0 auto;text-align:center}.markdown-body span.align-right{display:block;overflow:hidden;clear:both}.markdown-body span.align-right>span{display:block;margin:13px 0 0;overflow:hidden;text-align:right}.markdown-body span.align-right span img{margin:0;text-align:right}.markdown-body span.float-left{display:block;float:left;margin-right:13px;overflow:hidden}.markdown-body span.float-left span{margin:13px 0 0}.markdown-body span.float-right{display:block;float:right;margin-left:13px;overflow:hidden}.markdown-body span.float-right>span{display:block;margin:13px auto 0;overflow:hidden;text-align:right}.markdown-body code,.markdown-body tt{padding:.2em .4em;margin:0;font-size:85%;background-color:rgba(27,31,35,.05);border-radius:6px}.markdown-body code br,.markdown-body tt br{display:none}.markdown-body del code{text-decoration:inherit}.markdown-body pre{word-wrap:normal}.markdown-body pre>code{padding:0;margin:0;font-size:100%;word-break:normal;white-space:pre;background:transparent;border:0}.markdown-body .highlight{margin-bottom:16px}.markdown-body .highlight pre{margin-bottom:0;word-break:normal}.markdown-body .highlight pre,.markdown-body pre{padding:16px;overflow:auto;font-size:85%;line-height:1.45;background-color:#f6f8fa;border-radius:6px}.markdown-body pre code,.markdown-body pre tt{display:inline;max-width:auto;padding:0;margin:0;overflow:visible;line-height:inherit;word-wrap:normal;background-color:transparent;border:0}.markdown-body .csv-data td,.markdown-body .csv-data th{padding:5px;overflow:hidden;font-size:12px;line-height:1;text-align:left;white-space:nowrap}.markdown-body .csv-data .blob-num{padding:10px 8px 9px;text-align:right;background:#fff;border:0}.markdown-body .csv-data tr{border-top:0}.markdown-body .csv-data th{font-weight:600;background:#f6f8fa;border-top:0}.highlight{background-color:#f8f8f8}.highlight table td{padding:5px}.highlight table pre{margin:0}.highlight .cm{color:#998;font-style:italic}.highlight .cp{color:#999;font-weight:bold}.highlight .c1{color:#998;font-style:italic}.highlight .cs{color:#999;font-weight:bold;font-style:italic}.highlight .c,.highlight .ch,.highlight .cd,.highlight .cpf{color:#998;font-style:italic}.highlight .err{color:#a61717;background-color:#e3d2d2}.highlight .gd{color:#000;background-color:#fdd}.highlight .ge{color:#000;font-style:italic}.highlight .gr{color:#a00}.highlight .gh{color:#999}.highlight .gi{color:#000;background-color:#dfd}.highlight .go{color:#888}.highlight .gp{color:#555}.highlight .gs{font-weight:bold}.highlight .gu{color:#aaa}.highlight .gt{color:#a00}.highlight .kc,.highlight .kd,.highlight .kn,.highlight .kp,.highlight .kr{color:#000;font-weight:bold}.highlight .kt{color:#458;font-weight:bold}.highlight .k,.highlight .kv{color:#000;font-weight:bold}.highlight .mf,.highlight .mh,.highlight .il,.highlight .mi,.highlight .mo,.highlight .m,.highlight .mb,.highlight .mx{color:#099}.highlight .sb,.highlight .sc,.highlight .sd,.highlight .s2,.highlight .se,.highlight .sh,.highlight .si,.highlight .sx{color:#d14}.highlight .sr{color:#009926}.highlight .s1{color:#d14}.highlight .ss{color:#990073}.highlight .s,.highlight .sa,.highlight .dl{color:#d14}.highlight .na{color:teal}.highlight .bp{color:#999}.highlight .nb{color:#0086b3}.highlight .nc{color:#458;font-weight:bold}.highlight .no{color:teal}.highlight .nd{color:#3c5d5d;font-weight:bold}.highlight .ni{color:purple}.highlight .ne,.highlight .nf,.highlight .fm,.highlight .nl{color:#900;font-weight:bold}.highlight .nn{color:#555}.highlight .nt{color:navy}.highlight .vc,.highlight .vg,.highlight .vi,.highlight .nv,.highlight .vm{color:teal}.highlight .ow,.highlight .o{color:#000;font-weight:bold}.highlight .w{color:#bbb}@font-face{font-family:"Lato";font-weight:400;font-style:normal;font-display:block;src:url("fonts/lato-normal.woff2") format("woff2"),url("fonts/lato-normal.woff") format("woff")}@font-face{font-family:"Lato";font-weight:400;font-style:italic;font-display:block;src:url("fonts/lato-normal-italic.woff2") format("woff2"),url("fonts/lato-normal-italic.woff") format("woff")}@font-face{font-family:"Lato";font-weight:600;font-style:normal;font-display:block;src:url("fonts/lato-bold.woff2") format("woff2"),url("fonts/lato-bold.woff") format("woff")}@font-face{font-family:"Lato";font-weight:600;font-style:italic;font-display:block;src:url("fonts/lato-bold-italic.woff2") format("woff2"),url("fonts/lato-bold-italic.woff") format("woff")}@font-face{font-family:"Roboto-Slab";font-weight:400;font-style:normal;font-display:block;src:url("fonts/Roboto-Slab-Regular.woff2") format("woff2"),url("fonts/Roboto-Slab-Regular.woff") format("woff")}@font-face{font-family:"Roboto-Slab";font-weight:600;font-style:normal;font-display:block;src:url("fonts/Roboto-Slab-Bold.woff2") format("woff2"),url("fonts/Roboto-Slab-Bold.woff") format("woff")}@font-face{font-family:"FontAwesome";font-weight:normal;font-style:normal;font-display:block;src:url("fonts/fontawesome-webfont.eot");src:url("fonts/fontawesome-webfont.eot?#iefix") format("embedded-opentype"),url("fonts/fontawesome-webfont.woff2") format("woff2"),url("fonts/fontawesome-webfont.woff") format("woff"),url("fonts/fontawesome-webfont.ttf") format("truetype"),url("fonts/fontawesome-webfont.svg#fontawesomeregular") format("svg")}.fa-glass:before{content:""}.fa-music:before{content:""}.fa-search:before{content:""}.fa-envelope-o:before{content:""}.fa-heart:before{content:""}.fa-star:before{content:""}.fa-star-o:before{content:""}.fa-user:before{content:""}.fa-film:before{content:""}.fa-th-large:before{content:""}.fa-th:before{content:""}.fa-th-list:before{content:""}.fa-check:before{content:""}.fa-remove:before,.fa-close:before,.fa-times:before{content:""}.fa-search-plus:before{content:""}.fa-search-minus:before{content:""}.fa-power-off:before{content:""}.fa-signal:before{content:""}.fa-gear:before,.fa-cog:before{content:""}.fa-trash-o:before{content:""}.fa-home:before{content:""}.fa-file-o:before{content:""}.fa-clock-o:before{content:""}.fa-road:before{content:""}.fa-download:before{content:""}.fa-arrow-circle-o-down:before{content:""}.fa-arrow-circle-o-up:before{content:""}.fa-inbox:before{content:""}.fa-play-circle-o:before{content:""}.fa-rotate-right:before,.fa-repeat:before{content:""}.fa-refresh:before{content:""}.fa-list-alt:before{content:""}.fa-lock:before{content:""}.fa-flag:before{content:""}.fa-headphones:before{content:""}.fa-volume-off:before{content:""}.fa-volume-down:before{content:""}.fa-volume-up:before{content:""}.fa-qrcode:before{content:""}.fa-barcode:before{content:""}.fa-tag:before{content:""}.fa-tags:before{content:""}.fa-book:before{content:""}.fa-bookmark:before{content:""}.fa-print:before{content:""}.fa-camera:before{content:""}.fa-font:before{content:""}.fa-bold:before{content:""}.fa-italic:before{content:""}.fa-text-height:before{content:""}.fa-text-width:before{content:""}.fa-align-left:before{content:""}.fa-align-center:before{content:""}.fa-align-right:before{content:""}.fa-align-justify:before{content:""}.fa-list:before{content:""}.fa-dedent:before,.fa-outdent:before{content:""}.fa-indent:before{content:""}.fa-video-camera:before{content:""}.fa-photo:before,.fa-image:before,.fa-picture-o:before{content:""}.fa-pencil:before{content:""}.fa-map-marker:before{content:""}.fa-adjust:before{content:""}.fa-tint:before{content:""}.fa-edit:before,.fa-pencil-square-o:before{content:""}.fa-share-square-o:before{content:""}.fa-check-square-o:before{content:""}.fa-arrows:before{content:""}.fa-step-backward:before{content:""}.fa-fast-backward:before{content:""}.fa-backward:before{content:""}.fa-play:before{content:""}.fa-pause:before{content:""}.fa-stop:before{content:""}.fa-forward:before{content:""}.fa-fast-forward:before{content:""}.fa-step-forward:before{content:""}.fa-eject:before{content:""}.fa-chevron-left:before{content:""}.fa-chevron-right:before{content:""}.fa-plus-circle:before{content:""}.fa-minus-circle:before{content:""}.fa-times-circle:before{content:""}.fa-check-circle:before{content:""}.fa-question-circle:before{content:""}.fa-info-circle:before{content:""}.fa-crosshairs:before{content:""}.fa-times-circle-o:before{content:""}.fa-check-circle-o:before{content:""}.fa-ban:before{content:""}.fa-arrow-left:before{content:""}.fa-arrow-right:before{content:""}.fa-arrow-up:before{content:""}.fa-arrow-down:before{content:""}.fa-mail-forward:before,.fa-share:before{content:""}.fa-expand:before{content:""}.fa-compress:before{content:""}.fa-plus:before{content:""}.fa-minus:before{content:""}.fa-asterisk:before{content:""}.fa-exclamation-circle:before{content:""}.fa-gift:before{content:""}.fa-leaf:before{content:""}.fa-fire:before{content:""}.fa-eye:before{content:""}.fa-eye-slash:before{content:""}.fa-warning:before,.fa-exclamation-triangle:before{content:""}.fa-plane:before{content:""}.fa-calendar:before{content:""}.fa-random:before{content:""}.fa-comment:before{content:""}.fa-magnet:before{content:""}.fa-chevron-up:before{content:""}.fa-chevron-down:before{content:""}.fa-retweet:before{content:""}.fa-shopping-cart:before{content:""}.fa-folder:before{content:""}.fa-folder-open:before{content:""}.fa-arrows-v:before{content:""}.fa-arrows-h:before{content:""}.fa-bar-chart-o:before,.fa-bar-chart:before{content:""}.fa-twitter-square:before{content:""}.fa-facebook-square:before{content:""}.fa-camera-retro:before{content:""}.fa-key:before{content:""}.fa-gears:before,.fa-cogs:before{content:""}.fa-comments:before{content:""}.fa-thumbs-o-up:before{content:""}.fa-thumbs-o-down:before{content:""}.fa-star-half:before{content:""}.fa-heart-o:before{content:""}.fa-sign-out:before{content:""}.fa-linkedin-square:before{content:""}.fa-thumb-tack:before{content:""}.fa-external-link:before{content:""}.fa-sign-in:before{content:""}.fa-trophy:before{content:""}.fa-github-square:before{content:""}.fa-upload:before{content:""}.fa-lemon-o:before{content:""}.fa-phone:before{content:""}.fa-square-o:before{content:""}.fa-bookmark-o:before{content:""}.fa-phone-square:before{content:""}.fa-twitter:before{content:""}.fa-facebook-f:before,.fa-facebook:before{content:""}.fa-github:before{content:""}.fa-unlock:before{content:""}.fa-credit-card:before{content:""}.fa-feed:before,.fa-rss:before{content:""}.fa-hdd-o:before{content:""}.fa-bullhorn:before{content:""}.fa-bell:before{content:""}.fa-certificate:before{content:""}.fa-hand-o-right:before{content:""}.fa-hand-o-left:before{content:""}.fa-hand-o-up:before{content:""}.fa-hand-o-down:before{content:""}.fa-arrow-circle-left:before{content:""}.fa-arrow-circle-right:before{content:""}.fa-arrow-circle-up:before{content:""}.fa-arrow-circle-down:before{content:""}.fa-globe:before{content:""}.fa-wrench:before{content:""}.fa-tasks:before{content:""}.fa-filter:before{content:""}.fa-briefcase:before{content:""}.fa-arrows-alt:before{content:""}.fa-group:before,.fa-users:before{content:""}.fa-chain:before,.fa-link:before{content:""}.fa-cloud:before{content:""}.fa-flask:before{content:""}.fa-cut:before,.fa-scissors:before{content:""}.fa-copy:before,.fa-files-o:before{content:""}.fa-paperclip:before{content:""}.fa-save:before,.fa-floppy-o:before{content:""}.fa-square:before{content:""}.fa-navicon:before,.fa-reorder:before,.fa-bars:before{content:""}.fa-list-ul:before{content:""}.fa-list-ol:before{content:""}.fa-strikethrough:before{content:""}.fa-underline:before{content:""}.fa-table:before{content:""}.fa-magic:before{content:""}.fa-truck:before{content:""}.fa-pinterest:before{content:""}.fa-pinterest-square:before{content:""}.fa-google-plus-square:before{content:""}.fa-google-plus:before{content:""}.fa-money:before{content:""}.fa-caret-down:before{content:""}.fa-caret-up:before{content:""}.fa-caret-left:before{content:""}.fa-caret-right:before{content:""}.fa-columns:before{content:""}.fa-unsorted:before,.fa-sort:before{content:""}.fa-sort-down:before,.fa-sort-desc:before{content:""}.fa-sort-up:before,.fa-sort-asc:before{content:""}.fa-envelope:before{content:""}.fa-linkedin:before{content:""}.fa-rotate-left:before,.fa-undo:before{content:""}.fa-legal:before,.fa-gavel:before{content:""}.fa-dashboard:before,.fa-tachometer:before{content:""}.fa-comment-o:before{content:""}.fa-comments-o:before{content:""}.fa-flash:before,.fa-bolt:before{content:""}.fa-sitemap:before{content:""}.fa-umbrella:before{content:""}.fa-paste:before,.fa-clipboard:before{content:""}.fa-lightbulb-o:before{content:""}.fa-exchange:before{content:""}.fa-cloud-download:before{content:""}.fa-cloud-upload:before{content:""}.fa-user-md:before{content:""}.fa-stethoscope:before{content:""}.fa-suitcase:before{content:""}.fa-bell-o:before{content:""}.fa-coffee:before{content:""}.fa-cutlery:before{content:""}.fa-file-text-o:before{content:""}.fa-building-o:before{content:""}.fa-hospital-o:before{content:""}.fa-ambulance:before{content:""}.fa-medkit:before{content:""}.fa-fighter-jet:before{content:""}.fa-beer:before{content:""}.fa-h-square:before{content:""}.fa-plus-square:before{content:""}.fa-angle-double-left:before{content:""}.fa-angle-double-right:before{content:""}.fa-angle-double-up:before{content:""}.fa-angle-double-down:before{content:""}.fa-angle-left:before{content:""}.fa-angle-right:before{content:""}.fa-angle-up:before{content:""}.fa-angle-down:before{content:""}.fa-desktop:before{content:""}.fa-laptop:before{content:""}.fa-tablet:before{content:""}.fa-mobile-phone:before,.fa-mobile:before{content:""}.fa-circle-o:before{content:""}.fa-quote-left:before{content:""}.fa-quote-right:before{content:""}.fa-spinner:before{content:""}.fa-circle:before{content:""}.fa-mail-reply:before,.fa-reply:before{content:""}.fa-github-alt:before{content:""}.fa-folder-o:before{content:""}.fa-folder-open-o:before{content:""}.fa-smile-o:before{content:""}.fa-frown-o:before{content:""}.fa-meh-o:before{content:""}.fa-gamepad:before{content:""}.fa-keyboard-o:before{content:""}.fa-flag-o:before{content:""}.fa-flag-checkered:before{content:""}.fa-terminal:before{content:""}.fa-code:before{content:""}.fa-mail-reply-all:before,.fa-reply-all:before{content:""}.fa-star-half-empty:before,.fa-star-half-full:before,.fa-star-half-o:before{content:""}.fa-location-arrow:before{content:""}.fa-crop:before{content:""}.fa-code-fork:before{content:""}.fa-unlink:before,.fa-chain-broken:before{content:""}.fa-question:before{content:""}.fa-info:before{content:""}.fa-exclamation:before{content:""}.fa-superscript:before{content:""}.fa-subscript:before{content:""}.fa-eraser:before{content:""}.fa-puzzle-piece:before{content:""}.fa-microphone:before{content:""}.fa-microphone-slash:before{content:""}.fa-shield:before{content:""}.fa-calendar-o:before{content:""}.fa-fire-extinguisher:before{content:""}.fa-rocket:before{content:""}.fa-maxcdn:before{content:""}.fa-chevron-circle-left:before{content:""}.fa-chevron-circle-right:before{content:""}.fa-chevron-circle-up:before{content:""}.fa-chevron-circle-down:before{content:""}.fa-html5:before{content:""}.fa-css3:before{content:""}.fa-anchor:before{content:""}.fa-unlock-alt:before{content:""}.fa-bullseye:before{content:""}.fa-ellipsis-h:before{content:""}.fa-ellipsis-v:before{content:""}.fa-rss-square:before{content:""}.fa-play-circle:before{content:""}.fa-ticket:before{content:""}.fa-minus-square:before{content:""}.fa-minus-square-o:before,.toctree>ul .toc.current>a .fa-plus-square-o:before{content:""}.fa-level-up:before{content:""}.fa-level-down:before{content:""}.fa-check-square:before{content:""}.fa-pencil-square:before{content:""}.fa-external-link-square:before{content:""}.fa-share-square:before{content:""}.fa-compass:before{content:""}.fa-toggle-down:before,.fa-caret-square-o-down:before{content:""}.fa-toggle-up:before,.fa-caret-square-o-up:before{content:""}.fa-toggle-right:before,.fa-caret-square-o-right:before{content:""}.fa-euro:before,.fa-eur:before{content:""}.fa-gbp:before{content:""}.fa-dollar:before,.fa-usd:before{content:""}.fa-rupee:before,.fa-inr:before{content:""}.fa-cny:before,.fa-rmb:before,.fa-yen:before,.fa-jpy:before{content:""}.fa-ruble:before,.fa-rouble:before,.fa-rub:before{content:""}.fa-won:before,.fa-krw:before{content:""}.fa-bitcoin:before,.fa-btc:before{content:""}.fa-file:before{content:""}.fa-file-text:before{content:""}.fa-sort-alpha-asc:before{content:""}.fa-sort-alpha-desc:before{content:""}.fa-sort-amount-asc:before{content:""}.fa-sort-amount-desc:before{content:""}.fa-sort-numeric-asc:before{content:""}.fa-sort-numeric-desc:before{content:""}.fa-thumbs-up:before{content:""}.fa-thumbs-down:before{content:""}.fa-youtube-square:before{content:""}.fa-youtube:before{content:""}.fa-xing:before{content:""}.fa-xing-square:before{content:""}.fa-youtube-play:before{content:""}.fa-dropbox:before{content:""}.fa-stack-overflow:before{content:""}.fa-instagram:before{content:""}.fa-flickr:before{content:""}.fa-adn:before{content:""}.fa-bitbucket:before{content:""}.fa-bitbucket-square:before{content:""}.fa-tumblr:before{content:""}.fa-tumblr-square:before{content:""}.fa-long-arrow-down:before{content:""}.fa-long-arrow-up:before{content:""}.fa-long-arrow-left:before{content:""}.fa-long-arrow-right:before{content:""}.fa-apple:before{content:""}.fa-windows:before{content:""}.fa-android:before{content:""}.fa-linux:before{content:""}.fa-dribbble:before{content:""}.fa-skype:before{content:""}.fa-foursquare:before{content:""}.fa-trello:before{content:""}.fa-female:before{content:""}.fa-male:before{content:""}.fa-gittip:before,.fa-gratipay:before{content:""}.fa-sun-o:before{content:""}.fa-moon-o:before{content:""}.fa-archive:before{content:""}.fa-bug:before{content:""}.fa-vk:before{content:""}.fa-weibo:before{content:""}.fa-renren:before{content:""}.fa-pagelines:before{content:""}.fa-stack-exchange:before{content:""}.fa-arrow-circle-o-right:before{content:""}.fa-arrow-circle-o-left:before{content:""}.fa-toggle-left:before,.fa-caret-square-o-left:before{content:""}.fa-dot-circle-o:before{content:""}.fa-wheelchair:before{content:""}.fa-vimeo-square:before{content:""}.fa-turkish-lira:before,.fa-try:before{content:""}.fa-plus-square-o:before{content:""}.fa-space-shuttle:before{content:""}.fa-slack:before{content:""}.fa-envelope-square:before{content:""}.fa-wordpress:before{content:""}.fa-openid:before{content:""}.fa-institution:before,.fa-bank:before,.fa-university:before{content:""}.fa-mortar-board:before,.fa-graduation-cap:before{content:""}.fa-yahoo:before{content:""}.fa-google:before{content:""}.fa-reddit:before{content:""}.fa-reddit-square:before{content:""}.fa-stumbleupon-circle:before{content:""}.fa-stumbleupon:before{content:""}.fa-delicious:before{content:""}.fa-digg:before{content:""}.fa-pied-piper-pp:before{content:""}.fa-pied-piper-alt:before{content:""}.fa-drupal:before{content:""}.fa-joomla:before{content:""}.fa-language:before{content:""}.fa-fax:before{content:""}.fa-building:before{content:""}.fa-child:before{content:""}.fa-paw:before{content:""}.fa-spoon:before{content:""}.fa-cube:before{content:""}.fa-cubes:before{content:""}.fa-behance:before{content:""}.fa-behance-square:before{content:""}.fa-steam:before{content:""}.fa-steam-square:before{content:""}.fa-recycle:before{content:""}.fa-automobile:before,.fa-car:before{content:""}.fa-cab:before,.fa-taxi:before{content:""}.fa-tree:before{content:""}.fa-spotify:before{content:""}.fa-deviantart:before{content:""}.fa-soundcloud:before{content:""}.fa-database:before{content:""}.fa-file-pdf-o:before{content:""}.fa-file-word-o:before{content:""}.fa-file-excel-o:before{content:""}.fa-file-powerpoint-o:before{content:""}.fa-file-photo-o:before,.fa-file-picture-o:before,.fa-file-image-o:before{content:""}.fa-file-zip-o:before,.fa-file-archive-o:before{content:""}.fa-file-sound-o:before,.fa-file-audio-o:before{content:""}.fa-file-movie-o:before,.fa-file-video-o:before{content:""}.fa-file-code-o:before{content:""}.fa-vine:before{content:""}.fa-codepen:before{content:""}.fa-jsfiddle:before{content:""}.fa-life-bouy:before,.fa-life-buoy:before,.fa-life-saver:before,.fa-support:before,.fa-life-ring:before{content:""}.fa-circle-o-notch:before{content:""}.fa-ra:before,.fa-resistance:before,.fa-rebel:before{content:""}.fa-ge:before,.fa-empire:before{content:""}.fa-git-square:before{content:""}.fa-git:before{content:""}.fa-y-combinator-square:before,.fa-yc-square:before,.fa-hacker-news:before{content:""}.fa-tencent-weibo:before{content:""}.fa-qq:before{content:""}.fa-wechat:before,.fa-weixin:before{content:""}.fa-send:before,.fa-paper-plane:before{content:""}.fa-send-o:before,.fa-paper-plane-o:before{content:""}.fa-history:before{content:""}.fa-circle-thin:before{content:""}.fa-header:before{content:""}.fa-paragraph:before{content:""}.fa-sliders:before{content:""}.fa-share-alt:before{content:""}.fa-share-alt-square:before{content:""}.fa-bomb:before{content:""}.fa-soccer-ball-o:before,.fa-futbol-o:before{content:""}.fa-tty:before{content:""}.fa-binoculars:before{content:""}.fa-plug:before{content:""}.fa-slideshare:before{content:""}.fa-twitch:before{content:""}.fa-yelp:before{content:""}.fa-newspaper-o:before{content:""}.fa-wifi:before{content:""}.fa-calculator:before{content:""}.fa-paypal:before{content:""}.fa-google-wallet:before{content:""}.fa-cc-visa:before{content:""}.fa-cc-mastercard:before{content:""}.fa-cc-discover:before{content:""}.fa-cc-amex:before{content:""}.fa-cc-paypal:before{content:""}.fa-cc-stripe:before{content:""}.fa-bell-slash:before{content:""}.fa-bell-slash-o:before{content:""}.fa-trash:before{content:""}.fa-copyright:before{content:""}.fa-at:before{content:""}.fa-eyedropper:before{content:""}.fa-paint-brush:before{content:""}.fa-birthday-cake:before{content:""}.fa-area-chart:before{content:""}.fa-pie-chart:before{content:""}.fa-line-chart:before{content:""}.fa-lastfm:before{content:""}.fa-lastfm-square:before{content:""}.fa-toggle-off:before{content:""}.fa-toggle-on:before{content:""}.fa-bicycle:before{content:""}.fa-bus:before{content:""}.fa-ioxhost:before{content:""}.fa-angellist:before{content:""}.fa-cc:before{content:""}.fa-shekel:before,.fa-sheqel:before,.fa-ils:before{content:""}.fa-meanpath:before{content:""}.fa-buysellads:before{content:""}.fa-connectdevelop:before{content:""}.fa-dashcube:before{content:""}.fa-forumbee:before{content:""}.fa-leanpub:before{content:""}.fa-sellsy:before{content:""}.fa-shirtsinbulk:before{content:""}.fa-simplybuilt:before{content:""}.fa-skyatlas:before{content:""}.fa-cart-plus:before{content:""}.fa-cart-arrow-down:before{content:""}.fa-diamond:before{content:""}.fa-ship:before{content:""}.fa-user-secret:before{content:""}.fa-motorcycle:before{content:""}.fa-street-view:before{content:""}.fa-heartbeat:before{content:""}.fa-venus:before{content:""}.fa-mars:before{content:""}.fa-mercury:before{content:""}.fa-intersex:before,.fa-transgender:before{content:""}.fa-transgender-alt:before{content:""}.fa-venus-double:before{content:""}.fa-mars-double:before{content:""}.fa-venus-mars:before{content:""}.fa-mars-stroke:before{content:""}.fa-mars-stroke-v:before{content:""}.fa-mars-stroke-h:before{content:""}.fa-neuter:before{content:""}.fa-genderless:before{content:""}.fa-facebook-official:before{content:""}.fa-pinterest-p:before{content:""}.fa-whatsapp:before{content:""}.fa-server:before{content:""}.fa-user-plus:before{content:""}.fa-user-times:before{content:""}.fa-hotel:before,.fa-bed:before{content:""}.fa-viacoin:before{content:""}.fa-train:before{content:""}.fa-subway:before{content:""}.fa-medium:before{content:""}.fa-yc:before,.fa-y-combinator:before{content:""}.fa-optin-monster:before{content:""}.fa-opencart:before{content:""}.fa-expeditedssl:before{content:""}.fa-battery-4:before,.fa-battery:before,.fa-battery-full:before{content:""}.fa-battery-3:before,.fa-battery-three-quarters:before{content:""}.fa-battery-2:before,.fa-battery-half:before{content:""}.fa-battery-1:before,.fa-battery-quarter:before{content:""}.fa-battery-0:before,.fa-battery-empty:before{content:""}.fa-mouse-pointer:before{content:""}.fa-i-cursor:before{content:""}.fa-object-group:before{content:""}.fa-object-ungroup:before{content:""}.fa-sticky-note:before{content:""}.fa-sticky-note-o:before{content:""}.fa-cc-jcb:before{content:""}.fa-cc-diners-club:before{content:""}.fa-clone:before{content:""}.fa-balance-scale:before{content:""}.fa-hourglass-o:before{content:""}.fa-hourglass-1:before,.fa-hourglass-start:before{content:""}.fa-hourglass-2:before,.fa-hourglass-half:before{content:""}.fa-hourglass-3:before,.fa-hourglass-end:before{content:""}.fa-hourglass:before{content:""}.fa-hand-grab-o:before,.fa-hand-rock-o:before{content:""}.fa-hand-stop-o:before,.fa-hand-paper-o:before{content:""}.fa-hand-scissors-o:before{content:""}.fa-hand-lizard-o:before{content:""}.fa-hand-spock-o:before{content:""}.fa-hand-pointer-o:before{content:""}.fa-hand-peace-o:before{content:""}.fa-trademark:before{content:""}.fa-registered:before{content:""}.fa-creative-commons:before{content:""}.fa-gg:before{content:""}.fa-gg-circle:before{content:""}.fa-tripadvisor:before{content:""}.fa-odnoklassniki:before{content:""}.fa-odnoklassniki-square:before{content:""}.fa-get-pocket:before{content:""}.fa-wikipedia-w:before{content:""}.fa-safari:before{content:""}.fa-chrome:before{content:""}.fa-firefox:before{content:""}.fa-opera:before{content:""}.fa-internet-explorer:before{content:""}.fa-tv:before,.fa-television:before{content:""}.fa-contao:before{content:""}.fa-500px:before{content:""}.fa-amazon:before{content:""}.fa-calendar-plus-o:before{content:""}.fa-calendar-minus-o:before{content:""}.fa-calendar-times-o:before{content:""}.fa-calendar-check-o:before{content:""}.fa-industry:before{content:""}.fa-map-pin:before{content:""}.fa-map-signs:before{content:""}.fa-map-o:before{content:""}.fa-map:before{content:""}.fa-commenting:before{content:""}.fa-commenting-o:before{content:""}.fa-houzz:before{content:""}.fa-vimeo:before{content:""}.fa-black-tie:before{content:""}.fa-fonticons:before{content:""}.fa-reddit-alien:before{content:""}.fa-edge:before{content:""}.fa-credit-card-alt:before{content:""}.fa-codiepie:before{content:""}.fa-modx:before{content:""}.fa-fort-awesome:before{content:""}.fa-usb:before{content:""}.fa-product-hunt:before{content:""}.fa-mixcloud:before{content:""}.fa-scribd:before{content:""}.fa-pause-circle:before{content:""}.fa-pause-circle-o:before{content:""}.fa-stop-circle:before{content:""}.fa-stop-circle-o:before{content:""}.fa-shopping-bag:before{content:""}.fa-shopping-basket:before{content:""}.fa-hashtag:before{content:""}.fa-bluetooth:before{content:""}.fa-bluetooth-b:before{content:""}.fa-percent:before{content:""}.fa-gitlab:before{content:""}.fa-wpbeginner:before{content:""}.fa-wpforms:before{content:""}.fa-envira:before{content:""}.fa-universal-access:before{content:""}.fa-wheelchair-alt:before{content:""}.fa-question-circle-o:before{content:""}.fa-blind:before{content:""}.fa-audio-description:before{content:""}.fa-volume-control-phone:before{content:""}.fa-braille:before{content:""}.fa-assistive-listening-systems:before{content:""}.fa-asl-interpreting:before,.fa-american-sign-language-interpreting:before{content:""}.fa-deafness:before,.fa-hard-of-hearing:before,.fa-deaf:before{content:""}.fa-glide:before{content:""}.fa-glide-g:before{content:""}.fa-signing:before,.fa-sign-language:before{content:""}.fa-low-vision:before{content:""}.fa-viadeo:before{content:""}.fa-viadeo-square:before{content:""}.fa-snapchat:before{content:""}.fa-snapchat-ghost:before{content:""}.fa-snapchat-square:before{content:""}.fa-pied-piper:before{content:""}.fa-first-order:before{content:""}.fa-yoast:before{content:""}.fa-themeisle:before{content:""}.fa-google-plus-circle:before,.fa-google-plus-official:before{content:""}.fa-fa:before,.fa-font-awesome:before{content:""}.fa-handshake-o:before{content:""}.fa-envelope-open:before{content:""}.fa-envelope-open-o:before{content:""}.fa-linode:before{content:""}.fa-address-book:before{content:""}.fa-address-book-o:before{content:""}.fa-vcard:before,.fa-address-card:before{content:""}.fa-vcard-o:before,.fa-address-card-o:before{content:""}.fa-user-circle:before{content:""}.fa-user-circle-o:before{content:""}.fa-user-o:before{content:""}.fa-id-badge:before{content:""}.fa-drivers-license:before,.fa-id-card:before{content:""}.fa-drivers-license-o:before,.fa-id-card-o:before{content:""}.fa-quora:before{content:""}.fa-free-code-camp:before{content:""}.fa-telegram:before{content:""}.fa-thermometer-4:before,.fa-thermometer:before,.fa-thermometer-full:before{content:""}.fa-thermometer-3:before,.fa-thermometer-three-quarters:before{content:""}.fa-thermometer-2:before,.fa-thermometer-half:before{content:""}.fa-thermometer-1:before,.fa-thermometer-quarter:before{content:""}.fa-thermometer-0:before,.fa-thermometer-empty:before{content:""}.fa-shower:before{content:""}.fa-bathtub:before,.fa-s15:before,.fa-bath:before{content:""}.fa-podcast:before{content:""}.fa-window-maximize:before{content:""}.fa-window-minimize:before{content:""}.fa-window-restore:before{content:""}.fa-times-rectangle:before,.fa-window-close:before{content:""}.fa-times-rectangle-o:before,.fa-window-close-o:before{content:""}.fa-bandcamp:before{content:""}.fa-grav:before{content:""}.fa-etsy:before{content:""}.fa-imdb:before{content:""}.fa-ravelry:before{content:""}.fa-eercast:before{content:""}.fa-microchip:before{content:""}.fa-snowflake-o:before{content:""}.fa-superpowers:before{content:""}.fa-wpexplorer:before{content:""}.fa-meetup:before{content:""}.menu-sm,.addons-wrap,.sidebar-wrap{position:fixed;bottom:0;left:-85%;width:85%;max-height:100%}.menu-sm.shift,.shift.addons-wrap,.shift.sidebar-wrap{left:0}.sidebar-wrap{top:0}.sidebar-wrap .sidebar>:last-child{margin-bottom:5em}.content-wrap.shift{position:fixed;top:0;bottom:0;left:85%;min-width:100%}@media(min-width: 768px){.menu-md,.addons-wrap,.sidebar-wrap{left:0;width:300px}.sidebar-wrap .sidebar{width:320px}.sidebar-wrap .sidebar .header,.sidebar-wrap .sidebar .toctree{width:300px}.content-wrap{margin-left:300px}.content-wrap.shift{position:relative;left:0;min-width:0}}@media(min-width: 1280px){.content-wrap{max-width:980px}}.font-body{font-family:"Lato",BlinkMacSystemFont,"Segoe UI",Helvetica,sans-serif;font-weight:400}.font-head{font-family:"Roboto-Slab",sans-serif;font-weight:600}.font-mono{font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace}.fa{display:inline-block;font:normal normal normal 14px/1 "FontAwesome"}.breadcrumb-item{margin:0}.breadcrumb-item::after{padding-right:3px;padding-left:3px}.container{font-weight:400;color:#3c454e;background:#fff}@media(min-width: 1280px){.container{background:rgba(60,69,78,.1)}}.sidebar{color:#fff;background:#262c31}.sidebar a{text-decoration:none}.sidebar li{list-style:none}.sidebar .version{color:rgba(255,255,255,.3)}.toctree a{color:#fff;padding:.5em}.toctree .caption{color:#55a5d9;font-weight:600;line-height:32px}.toctree .fa{margin-right:2px}.toctree>ul>.toc>a{padding-left:12px}.toctree>ul>.toc:not(.current)>a:hover{background:rgba(255,255,255,.1)}.toctree>ul>.toc:not(.current)>a:active{background:#1b557a}.toctree>ul .toc.current a{color:#404040}.toctree>ul .toc.current a:hover{background:rgba(255,255,255,.1)}.toctree>ul .toc.current a.current{font-weight:bold;background:#fff;border-top:1px solid var(--toc-2);border-bottom:1px solid var(--toc-2)}.toctree>ul>.toc.current{background:var(--toc-1)}.toc.level-1.current>a{padding-left:12px;background:var(--toc-1)}.toc.level-1.current>ul{background:var(--toc-2)}.toc.level-1.current .level-2>a{padding-left:36px}.toc.level-2.current>a{padding-left:36px;background:var(--toc-2)}.toc.level-2.current>ul{background:var(--toc-3)}.toc.level-2.current .level-3>a{padding-left:60px}.toc.level-3.current>a{padding-left:60px;background:var(--toc-3)}.toc.level-3.current>ul{background:var(--toc-4)}.toc.level-3.current .level-4>a{padding-left:84px}.toc.level-4.current>a{padding-left:84px;background:var(--toc-4)}.toc.level-4.current>ul{background:var(--toc-5)}.toc.level-4.current .level-5>a{padding-left:108px}.toc.level-5.current>a{padding-left:108px;background:var(--toc-5)}.toc.level-5.current>ul{background:var(--toc-6)}.toc.level-5.current .level-6>a{padding-left:132px}.toc.level-6.current>a{padding-left:132px;background:var(--toc-6)}.toc.level-6.current>ul{background:var(--toc-7)}.toc.level-6.current .level-7>a{padding-left:156px}.toc.level-7.current>a{padding-left:156px;background:var(--toc-7)}.toc.level-7.current>ul{background:var(--toc-8)}.toc.level-7.current .level-8>a{padding-left:180px}.toc.level-8.current>a{padding-left:180px;background:var(--toc-8)}.toc.level-8.current>ul{background:var(--toc-9)}.toc.level-8.current .level-9>a{padding-left:204px}.toc.level-9.current>a{padding-left:204px;background:var(--toc-9)}.toc.level-9.current>ul{background:var(--toc-10)}.toc.level-9.current .level-10>a{padding-left:228px}.toc.level-10.current>a{padding-left:228px;background:var(--toc-10)}.toc.level-10.current>ul{background:var(--toc-11)}.toc.level-10.current .level-11>a{padding-left:252px}.toc.level-11.current>a{padding-left:252px;background:var(--toc-11)}.toc.level-11.current>ul{background:var(--toc-12)}.toc.level-11.current .level-12>a{padding-left:276px}.addons-wrap{background-color:#14171a}.addons-wrap .status{cursor:pointer;background-color:#1b1f23}.addons-wrap .status .branch .fa{color:#fff}.addons-wrap .status .branch .name{color:#28a745}.addons-wrap .status:active{background:#1b557a}.addons-wrap .addons{color:gray}.addons-wrap .addons dl{margin:0}.addons-wrap .addons dd{display:inline-block}.addons-wrap .addons dd a{display:inline-block;padding:6px;color:#fff}.content-wrap{font-size:16px;background:#fff}.header{color:#fff;background:#2980b9}.header input{border-radius:50px;border:1px solid #2472a4;font-size:80%}.title{font-weight:600;color:#fff}.title a{color:#fff}.title a:hover{background:rgba(255,255,255,.1)}.markdown-body{font-weight:400}.markdown-body .d-lang,.markdown-body .mermaid-wrap,.markdown-body div.highlighter-rouge{position:relative}.markdown-body .d-lang:after,.markdown-body .mermaid-wrap:after,.markdown-body div.highlighter-rouge:after{position:absolute;right:0px;top:0px;font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace;font-size:12px;content:attr(data-lang);padding:0 5px;color:#bbc0c5}.markdown-body a{color:#0366d6}.markdown-body a:hover{color:#107ffc}.markdown-body a code,.markdown-body a tt{color:#0366d6}.markdown-body h1,.markdown-body h2,.markdown-body h3,.markdown-body h4,.markdown-body h5,.markdown-body h6,.markdown-body dt{font-family:"Roboto-Slab",sans-serif}.markdown-body table{font-size:14px}.markdown-body figure{margin:0}.markdown-body .anchor{float:none;padding-right:0;margin-left:3px;margin-right:3px}.markdown-body code,.markdown-body tt{font-size:12px;border:1px #e1e4e8 solid;color:#e74c3c;background-color:#f9fafb}.markdown-body pre>code{color:#3c454e}.markdown-body .highlight pre,.markdown-body pre{font-size:12px;border:1px #e1e4e8 solid;background-color:#f6f8fa}.markdown-body .search-results li{list-style:none}.markdown-body .task-list-item-checkbox{margin-right:3px}.markdown-body .mermaid-wrap{box-shadow:0 2px 2px 0 rgba(0,0,0,.14),0 3px 1px -2px rgba(0,0,0,.2),0 1px 5px 0 rgba(0,0,0,.12)}.markdown-body .mermaid-wrap .mermaid{font-size:12px;font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace;white-space:pre}.toasts{font-size:16px;box-shadow:0 2px 2px 0 rgba(0,0,0,.14),0 3px 1px -2px rgba(0,0,0,.2),0 1px 5px 0 rgba(0,0,0,.12)}.toasts .title{box-shadow:0 0 1px 1px rgba(0,0,0,.14)}.toasts .content :first-child{margin-top:0}.toasts .content :last-child{margin-bottom:0}.toasts.note{background-color:#e7f2fa}.toasts.note .title{background:#6ab0de}.toasts.tip{background-color:#dbfaf4}.toasts.tip .title{background:#1abc9c}.toasts.warning{background-color:#fbe9d9}.toasts.warning .title{background:#f0b37e}.toasts.danger{background-color:#fdf3f2}.toasts.danger .title{background:#f29f97}html[dir=rtl] ul,html[dir=rtl] ol{padding-right:0}html[dir=rtl] dd{margin-right:0}html[dir=rtl] .menu-sm,html[dir=rtl] .sidebar-wrap,html[dir=rtl] .addons-wrap{left:unset;right:-85%}html[dir=rtl] .menu-sm.shift,html[dir=rtl] .shift.sidebar-wrap,html[dir=rtl] .shift.addons-wrap{left:unset;right:0}html[dir=rtl] .content-wrap.shift{left:unset;right:85%}@media(min-width: 768px){html[dir=rtl] .menu-md,html[dir=rtl] .sidebar-wrap,html[dir=rtl] .addons-wrap{left:unset;right:0}html[dir=rtl] .content-wrap{margin-left:unset;margin-right:300px}html[dir=rtl] .content-wrap.shift{left:unset;right:0}}html[dir=rtl] .toctree .fa{margin-right:unset;margin-left:2px}html[dir=rtl] .toctree>ul>.toc>a{padding-left:unset;padding-right:12px}html[dir=rtl] .toc.level-1.current>a{padding-left:unset;padding-right:12px}html[dir=rtl] .toc.level-1.current .level-2>a{padding-left:unset;padding-right:36px}html[dir=rtl] .toc.level-2.current>a{padding-left:unset;padding-right:36px}html[dir=rtl] .toc.level-2.current .level-3>a{padding-left:unset;padding-right:60px}html[dir=rtl] .toc.level-3.current>a{padding-left:unset;padding-right:60px}html[dir=rtl] .toc.level-3.current .level-4>a{padding-left:unset;padding-right:84px}html[dir=rtl] .toc.level-4.current>a{padding-left:unset;padding-right:84px}html[dir=rtl] .toc.level-4.current .level-5>a{padding-left:unset;padding-right:108px}html[dir=rtl] .toc.level-5.current>a{padding-left:unset;padding-right:108px}html[dir=rtl] .toc.level-5.current .level-6>a{padding-left:unset;padding-right:132px}html[dir=rtl] .toc.level-6.current>a{padding-left:unset;padding-right:132px}html[dir=rtl] .toc.level-6.current .level-7>a{padding-left:unset;padding-right:156px}html[dir=rtl] .toc.level-7.current>a{padding-left:unset;padding-right:156px}html[dir=rtl] .toc.level-7.current .level-8>a{padding-left:unset;padding-right:180px}html[dir=rtl] .toc.level-8.current>a{padding-left:unset;padding-right:180px}html[dir=rtl] .toc.level-8.current .level-9>a{padding-left:unset;padding-right:204px}html[dir=rtl] .toc.level-9.current>a{padding-left:unset;padding-right:204px}html[dir=rtl] .toc.level-9.current .level-10>a{padding-left:unset;padding-right:228px}html[dir=rtl] .toc.level-10.current>a{padding-left:unset;padding-right:228px}html[dir=rtl] .toc.level-10.current .level-11>a{padding-left:unset;padding-right:252px}html[dir=rtl] .toc.level-11.current>a{padding-left:unset;padding-right:252px}html[dir=rtl] .toc.level-11.current .level-12>a{padding-left:unset;padding-right:276px}html[dir=rtl] .markdown-body .highlight{direction:ltr}html[dir=rtl] .markdown-body blockquote{border-left:none;border-right:.25em solid #dfe2e5}html[dir=rtl] .markdown-body ul,html[dir=rtl] .markdown-body ol{padding-left:0;padding-right:2em}html[dir=rtl] .markdown-body .task-list-item-checkbox{margin-right:unset;margin-left:3px}html[dir=rtl] .fa-arrow-circle-left:before{content:""}html[dir=rtl] .fa-arrow-circle-right:before{content:""}.anim-fade-in{animation-name:fade-in;animation-duration:1s;animation-timing-function:ease-in-out}.anim-fade-in.fast{animation-duration:300ms}@keyframes fade-in{0%{opacity:0}100%{opacity:1}}.anim-fade-out{animation-name:fade-out;animation-duration:1s;animation-timing-function:ease-out}.anim-fade-out.fast{animation-duration:.3s}@keyframes fade-out{0%{opacity:1}100%{opacity:0}}.anim-fade-up{opacity:0;animation-name:fade-up;animation-duration:.3s;animation-fill-mode:forwards;animation-timing-function:ease-out;animation-delay:1s}@keyframes fade-up{0%{opacity:.8;transform:translateY(100%)}100%{opacity:1;transform:translateY(0)}}.anim-fade-down{animation-name:fade-down;animation-duration:.3s;animation-fill-mode:forwards;animation-timing-function:ease-in}@keyframes fade-down{0%{opacity:1;transform:translateY(0)}100%{opacity:.5;transform:translateY(100%)}}.anim-grow-x{width:0%;animation-name:grow-x;animation-duration:.3s;animation-fill-mode:forwards;animation-timing-function:ease;animation-delay:.5s}@keyframes grow-x{to{width:100%}}.anim-shrink-x{animation-name:shrink-x;animation-duration:.3s;animation-fill-mode:forwards;animation-timing-function:ease-in-out;animation-delay:.5s}@keyframes shrink-x{to{width:0%}}.anim-scale-in{animation-name:scale-in;animation-duration:.15s;animation-timing-function:cubic-bezier(0.2, 0, 0.13, 1.5)}@keyframes scale-in{0%{opacity:0;transform:scale(0.5)}100%{opacity:1;transform:scale(1)}}.anim-pulse{animation-name:pulse;animation-duration:2s;animation-timing-function:linear;animation-iteration-count:infinite}@keyframes pulse{0%{opacity:.3}10%{opacity:1}100%{opacity:.3}}.anim-pulse-in{animation-name:pulse-in;animation-duration:.5s}@keyframes pulse-in{0%{transform:scale3d(1, 1, 1)}50%{transform:scale3d(1.1, 1.1, 1.1)}100%{transform:scale3d(1, 1, 1)}}.hover-grow{transition:transform .3s;backface-visibility:hidden}.hover-grow:hover{transform:scale(1.025)}.border-x{border-right:1px #e1e4e8 solid !important;border-left:1px #e1e4e8 solid !important}.border-y{border-top:1px #e1e4e8 solid !important;border-bottom:1px #e1e4e8 solid !important}.border{border:1px #e1e4e8 solid !important}.border-0{border:0 !important}.border-top{border-top:1px #e1e4e8 solid !important}.border-right{border-right:1px #e1e4e8 solid !important}.border-bottom{border-bottom:1px #e1e4e8 solid !important}.border-left{border-left:1px #e1e4e8 solid !important}.border-top-0{border-top:0 !important}.border-right-0{border-right:0 !important}.border-bottom-0{border-bottom:0 !important}.border-left-0{border-left:0 !important}.rounded{border-radius:6px !important}.rounded-0{border-radius:0 !important}.rounded-1{border-radius:4px !important}.rounded-2{border-radius:6px !important}.rounded-3{border-radius:8px !important}.rounded-top-0{border-top-left-radius:0 !important;border-top-right-radius:0 !important}.rounded-top-1{border-top-left-radius:4px !important;border-top-right-radius:4px !important}.rounded-top-2{border-top-left-radius:6px !important;border-top-right-radius:6px !important}.rounded-top-3{border-top-left-radius:8px !important;border-top-right-radius:8px !important}.rounded-right-0{border-top-right-radius:0 !important;border-bottom-right-radius:0 !important}.rounded-right-1{border-top-right-radius:4px !important;border-bottom-right-radius:4px !important}.rounded-right-2{border-top-right-radius:6px !important;border-bottom-right-radius:6px !important}.rounded-right-3{border-top-right-radius:8px !important;border-bottom-right-radius:8px !important}.rounded-bottom-0{border-bottom-right-radius:0 !important;border-bottom-left-radius:0 !important}.rounded-bottom-1{border-bottom-right-radius:4px !important;border-bottom-left-radius:4px !important}.rounded-bottom-2{border-bottom-right-radius:6px !important;border-bottom-left-radius:6px !important}.rounded-bottom-3{border-bottom-right-radius:8px !important;border-bottom-left-radius:8px !important}.rounded-left-0{border-bottom-left-radius:0 !important;border-top-left-radius:0 !important}.rounded-left-1{border-bottom-left-radius:4px !important;border-top-left-radius:4px !important}.rounded-left-2{border-bottom-left-radius:6px !important;border-top-left-radius:6px !important}.rounded-left-3{border-bottom-left-radius:8px !important;border-top-left-radius:8px !important}@media(min-width: 544px){.border-sm{border:1px #e1e4e8 solid !important}.border-sm-0{border:0 !important}.border-sm-top{border-top:1px #e1e4e8 solid !important}.border-sm-right{border-right:1px #e1e4e8 solid !important}.border-sm-bottom{border-bottom:1px #e1e4e8 solid !important}.border-sm-left{border-left:1px #e1e4e8 solid !important}.border-sm-top-0{border-top:0 !important}.border-sm-right-0{border-right:0 !important}.border-sm-bottom-0{border-bottom:0 !important}.border-sm-left-0{border-left:0 !important}.rounded-sm{border-radius:6px !important}.rounded-sm-0{border-radius:0 !important}.rounded-sm-1{border-radius:4px !important}.rounded-sm-2{border-radius:6px !important}.rounded-sm-3{border-radius:8px !important}.rounded-sm-top-0{border-top-left-radius:0 !important;border-top-right-radius:0 !important}.rounded-sm-top-1{border-top-left-radius:4px !important;border-top-right-radius:4px !important}.rounded-sm-top-2{border-top-left-radius:6px !important;border-top-right-radius:6px !important}.rounded-sm-top-3{border-top-left-radius:8px !important;border-top-right-radius:8px !important}.rounded-sm-right-0{border-top-right-radius:0 !important;border-bottom-right-radius:0 !important}.rounded-sm-right-1{border-top-right-radius:4px !important;border-bottom-right-radius:4px !important}.rounded-sm-right-2{border-top-right-radius:6px !important;border-bottom-right-radius:6px !important}.rounded-sm-right-3{border-top-right-radius:8px !important;border-bottom-right-radius:8px !important}.rounded-sm-bottom-0{border-bottom-right-radius:0 !important;border-bottom-left-radius:0 !important}.rounded-sm-bottom-1{border-bottom-right-radius:4px !important;border-bottom-left-radius:4px !important}.rounded-sm-bottom-2{border-bottom-right-radius:6px !important;border-bottom-left-radius:6px !important}.rounded-sm-bottom-3{border-bottom-right-radius:8px !important;border-bottom-left-radius:8px !important}.rounded-sm-left-0{border-bottom-left-radius:0 !important;border-top-left-radius:0 !important}.rounded-sm-left-1{border-bottom-left-radius:4px !important;border-top-left-radius:4px !important}.rounded-sm-left-2{border-bottom-left-radius:6px !important;border-top-left-radius:6px !important}.rounded-sm-left-3{border-bottom-left-radius:8px !important;border-top-left-radius:8px !important}}@media(min-width: 768px){.border-md{border:1px #e1e4e8 solid !important}.border-md-0{border:0 !important}.border-md-top{border-top:1px #e1e4e8 solid !important}.border-md-right{border-right:1px #e1e4e8 solid !important}.border-md-bottom{border-bottom:1px #e1e4e8 solid !important}.border-md-left{border-left:1px #e1e4e8 solid !important}.border-md-top-0{border-top:0 !important}.border-md-right-0{border-right:0 !important}.border-md-bottom-0{border-bottom:0 !important}.border-md-left-0{border-left:0 !important}.rounded-md{border-radius:6px !important}.rounded-md-0{border-radius:0 !important}.rounded-md-1{border-radius:4px !important}.rounded-md-2{border-radius:6px !important}.rounded-md-3{border-radius:8px !important}.rounded-md-top-0{border-top-left-radius:0 !important;border-top-right-radius:0 !important}.rounded-md-top-1{border-top-left-radius:4px !important;border-top-right-radius:4px !important}.rounded-md-top-2{border-top-left-radius:6px !important;border-top-right-radius:6px !important}.rounded-md-top-3{border-top-left-radius:8px !important;border-top-right-radius:8px !important}.rounded-md-right-0{border-top-right-radius:0 !important;border-bottom-right-radius:0 !important}.rounded-md-right-1{border-top-right-radius:4px !important;border-bottom-right-radius:4px !important}.rounded-md-right-2{border-top-right-radius:6px !important;border-bottom-right-radius:6px !important}.rounded-md-right-3{border-top-right-radius:8px !important;border-bottom-right-radius:8px !important}.rounded-md-bottom-0{border-bottom-right-radius:0 !important;border-bottom-left-radius:0 !important}.rounded-md-bottom-1{border-bottom-right-radius:4px !important;border-bottom-left-radius:4px !important}.rounded-md-bottom-2{border-bottom-right-radius:6px !important;border-bottom-left-radius:6px !important}.rounded-md-bottom-3{border-bottom-right-radius:8px !important;border-bottom-left-radius:8px !important}.rounded-md-left-0{border-bottom-left-radius:0 !important;border-top-left-radius:0 !important}.rounded-md-left-1{border-bottom-left-radius:4px !important;border-top-left-radius:4px !important}.rounded-md-left-2{border-bottom-left-radius:6px !important;border-top-left-radius:6px !important}.rounded-md-left-3{border-bottom-left-radius:8px !important;border-top-left-radius:8px !important}}@media(min-width: 1012px){.border-lg{border:1px #e1e4e8 solid !important}.border-lg-0{border:0 !important}.border-lg-top{border-top:1px #e1e4e8 solid !important}.border-lg-right{border-right:1px #e1e4e8 solid !important}.border-lg-bottom{border-bottom:1px #e1e4e8 solid !important}.border-lg-left{border-left:1px #e1e4e8 solid !important}.border-lg-top-0{border-top:0 !important}.border-lg-right-0{border-right:0 !important}.border-lg-bottom-0{border-bottom:0 !important}.border-lg-left-0{border-left:0 !important}.rounded-lg{border-radius:6px !important}.rounded-lg-0{border-radius:0 !important}.rounded-lg-1{border-radius:4px !important}.rounded-lg-2{border-radius:6px !important}.rounded-lg-3{border-radius:8px !important}.rounded-lg-top-0{border-top-left-radius:0 !important;border-top-right-radius:0 !important}.rounded-lg-top-1{border-top-left-radius:4px !important;border-top-right-radius:4px !important}.rounded-lg-top-2{border-top-left-radius:6px !important;border-top-right-radius:6px !important}.rounded-lg-top-3{border-top-left-radius:8px !important;border-top-right-radius:8px !important}.rounded-lg-right-0{border-top-right-radius:0 !important;border-bottom-right-radius:0 !important}.rounded-lg-right-1{border-top-right-radius:4px !important;border-bottom-right-radius:4px !important}.rounded-lg-right-2{border-top-right-radius:6px !important;border-bottom-right-radius:6px !important}.rounded-lg-right-3{border-top-right-radius:8px !important;border-bottom-right-radius:8px !important}.rounded-lg-bottom-0{border-bottom-right-radius:0 !important;border-bottom-left-radius:0 !important}.rounded-lg-bottom-1{border-bottom-right-radius:4px !important;border-bottom-left-radius:4px !important}.rounded-lg-bottom-2{border-bottom-right-radius:6px !important;border-bottom-left-radius:6px !important}.rounded-lg-bottom-3{border-bottom-right-radius:8px !important;border-bottom-left-radius:8px !important}.rounded-lg-left-0{border-bottom-left-radius:0 !important;border-top-left-radius:0 !important}.rounded-lg-left-1{border-bottom-left-radius:4px !important;border-top-left-radius:4px !important}.rounded-lg-left-2{border-bottom-left-radius:6px !important;border-top-left-radius:6px !important}.rounded-lg-left-3{border-bottom-left-radius:8px !important;border-top-left-radius:8px !important}}@media(min-width: 1280px){.border-xl{border:1px #e1e4e8 solid !important}.border-xl-0{border:0 !important}.border-xl-top{border-top:1px #e1e4e8 solid !important}.border-xl-right{border-right:1px #e1e4e8 solid !important}.border-xl-bottom{border-bottom:1px #e1e4e8 solid !important}.border-xl-left{border-left:1px #e1e4e8 solid !important}.border-xl-top-0{border-top:0 !important}.border-xl-right-0{border-right:0 !important}.border-xl-bottom-0{border-bottom:0 !important}.border-xl-left-0{border-left:0 !important}.rounded-xl{border-radius:6px !important}.rounded-xl-0{border-radius:0 !important}.rounded-xl-1{border-radius:4px !important}.rounded-xl-2{border-radius:6px !important}.rounded-xl-3{border-radius:8px !important}.rounded-xl-top-0{border-top-left-radius:0 !important;border-top-right-radius:0 !important}.rounded-xl-top-1{border-top-left-radius:4px !important;border-top-right-radius:4px !important}.rounded-xl-top-2{border-top-left-radius:6px !important;border-top-right-radius:6px !important}.rounded-xl-top-3{border-top-left-radius:8px !important;border-top-right-radius:8px !important}.rounded-xl-right-0{border-top-right-radius:0 !important;border-bottom-right-radius:0 !important}.rounded-xl-right-1{border-top-right-radius:4px !important;border-bottom-right-radius:4px !important}.rounded-xl-right-2{border-top-right-radius:6px !important;border-bottom-right-radius:6px !important}.rounded-xl-right-3{border-top-right-radius:8px !important;border-bottom-right-radius:8px !important}.rounded-xl-bottom-0{border-bottom-right-radius:0 !important;border-bottom-left-radius:0 !important}.rounded-xl-bottom-1{border-bottom-right-radius:4px !important;border-bottom-left-radius:4px !important}.rounded-xl-bottom-2{border-bottom-right-radius:6px !important;border-bottom-left-radius:6px !important}.rounded-xl-bottom-3{border-bottom-right-radius:8px !important;border-bottom-left-radius:8px !important}.rounded-xl-left-0{border-bottom-left-radius:0 !important;border-top-left-radius:0 !important}.rounded-xl-left-1{border-bottom-left-radius:4px !important;border-top-left-radius:4px !important}.rounded-xl-left-2{border-bottom-left-radius:6px !important;border-top-left-radius:6px !important}.rounded-xl-left-3{border-bottom-left-radius:8px !important;border-top-left-radius:8px !important}}.circle{border-radius:50% !important}.border-dashed{border-style:dashed !important}.border-blue{border-color:#0366d6 !important}.border-blue-light{border-color:#c8e1ff !important}.border-green{border-color:#34d058 !important}.border-green-light{border-color:#a2cbac !important}.border-red{border-color:#d73a49 !important}.border-red-light{border-color:#f97583 !important}.border-purple{border-color:#6f42c1 !important}.border-yellow{border-color:#f9c513 !important}.border-gray-light{border-color:#eaecef !important}.border-gray-dark{border-color:#d1d5da !important}.border-black-fade{border-color:rgba(27,31,35,.15) !important}.border-white-fade{border-color:rgba(255,255,255,.15) !important}.border-white-fade-15{border-color:rgba(255,255,255,.15) !important}.border-white-fade-30{border-color:rgba(255,255,255,.3) !important}.border-white-fade-50{border-color:rgba(255,255,255,.5) !important}.border-white-fade-70{border-color:rgba(255,255,255,.7) !important}.border-white-fade-85{border-color:rgba(255,255,255,.85) !important}.box-shadow{box-shadow:0 1px 0 rgba(27,31,35,.04) !important}.box-shadow-medium{box-shadow:0 3px 6px rgba(149,157,165,.15) !important}.box-shadow-large{box-shadow:0 8px 24px rgba(149,157,165,.2) !important}.box-shadow-extra-large{box-shadow:0 12px 48px rgba(149,157,165,.3) !important}.box-shadow-none{box-shadow:none !important}.bg-white{background-color:#fff !important}.bg-blue{background-color:#0366d6 !important}.bg-blue-light{background-color:#f1f8ff !important}.bg-gray-dark{background-color:#24292e !important}.bg-gray{background-color:#f6f8fa !important}.bg-gray-light{background-color:#fafbfc !important}.bg-green{background-color:#28a745 !important}.bg-green-light{background-color:#dcffe4 !important}.bg-red{background-color:#d73a49 !important}.bg-red-light{background-color:#ffeef0 !important}.bg-yellow{background-color:#ffd33d !important}.bg-yellow-light{background-color:#fff5b1 !important}.bg-yellow-dark{background-color:#dbab09 !important}.bg-purple{background-color:#6f42c1 !important}.bg-pink{background-color:#ea4aaa !important}.bg-purple-light{background-color:#f5f0ff !important}.bg-orange{background-color:#d15704 !important}.color-gray-0{color:#fafbfc !important}.bg-gray-0{background-color:#fafbfc !important}.color-gray-1{color:#f6f8fa !important}.bg-gray-1{background-color:#f6f8fa !important}.color-gray-2{color:#e1e4e8 !important}.bg-gray-2{background-color:#e1e4e8 !important}.color-gray-3{color:#d1d5da !important}.bg-gray-3{background-color:#d1d5da !important}.color-gray-4{color:#959da5 !important}.bg-gray-4{background-color:#959da5 !important}.color-gray-5{color:#6a737d !important}.bg-gray-5{background-color:#6a737d !important}.color-gray-6{color:#586069 !important}.bg-gray-6{background-color:#586069 !important}.color-gray-7{color:#444d56 !important}.bg-gray-7{background-color:#444d56 !important}.color-gray-8{color:#2f363d !important}.bg-gray-8{background-color:#2f363d !important}.color-gray-9{color:#24292e !important}.bg-gray-9{background-color:#24292e !important}.color-blue-0{color:#f1f8ff !important}.bg-blue-0{background-color:#f1f8ff !important}.color-blue-1{color:#dbedff !important}.bg-blue-1{background-color:#dbedff !important}.color-blue-2{color:#c8e1ff !important}.bg-blue-2{background-color:#c8e1ff !important}.color-blue-3{color:#79b8ff !important}.bg-blue-3{background-color:#79b8ff !important}.color-blue-4{color:#2188ff !important}.bg-blue-4{background-color:#2188ff !important}.color-blue-5{color:#0366d6 !important}.bg-blue-5{background-color:#0366d6 !important}.color-blue-6{color:#005cc5 !important}.bg-blue-6{background-color:#005cc5 !important}.color-blue-7{color:#044289 !important}.bg-blue-7{background-color:#044289 !important}.color-blue-8{color:#032f62 !important}.bg-blue-8{background-color:#032f62 !important}.color-blue-9{color:#05264c !important}.bg-blue-9{background-color:#05264c !important}.color-green-0{color:#f0fff4 !important}.bg-green-0{background-color:#f0fff4 !important}.color-green-1{color:#dcffe4 !important}.bg-green-1{background-color:#dcffe4 !important}.color-green-2{color:#bef5cb !important}.bg-green-2{background-color:#bef5cb !important}.color-green-3{color:#85e89d !important}.bg-green-3{background-color:#85e89d !important}.color-green-4{color:#34d058 !important}.bg-green-4{background-color:#34d058 !important}.color-green-5{color:#28a745 !important}.bg-green-5{background-color:#28a745 !important}.color-green-6{color:#22863a !important}.bg-green-6{background-color:#22863a !important}.color-green-7{color:#176f2c !important}.bg-green-7{background-color:#176f2c !important}.color-green-8{color:#165c26 !important}.bg-green-8{background-color:#165c26 !important}.color-green-9{color:#144620 !important}.bg-green-9{background-color:#144620 !important}.color-yellow-0{color:#fffdef !important}.bg-yellow-0{background-color:#fffdef !important}.color-yellow-1{color:#fffbdd !important}.bg-yellow-1{background-color:#fffbdd !important}.color-yellow-2{color:#fff5b1 !important}.bg-yellow-2{background-color:#fff5b1 !important}.color-yellow-3{color:#ffea7f !important}.bg-yellow-3{background-color:#ffea7f !important}.color-yellow-4{color:#ffdf5d !important}.bg-yellow-4{background-color:#ffdf5d !important}.color-yellow-5{color:#ffd33d !important}.bg-yellow-5{background-color:#ffd33d !important}.color-yellow-6{color:#f9c513 !important}.bg-yellow-6{background-color:#f9c513 !important}.color-yellow-7{color:#dbab09 !important}.bg-yellow-7{background-color:#dbab09 !important}.color-yellow-8{color:#b08800 !important}.bg-yellow-8{background-color:#b08800 !important}.color-yellow-9{color:#735c0f !important}.bg-yellow-9{background-color:#735c0f !important}.color-orange-0{color:#fff8f2 !important}.bg-orange-0{background-color:#fff8f2 !important}.color-orange-1{color:#ffebda !important}.bg-orange-1{background-color:#ffebda !important}.color-orange-2{color:#ffd1ac !important}.bg-orange-2{background-color:#ffd1ac !important}.color-orange-3{color:#ffab70 !important}.bg-orange-3{background-color:#ffab70 !important}.color-orange-4{color:#fb8532 !important}.bg-orange-4{background-color:#fb8532 !important}.color-orange-5{color:#f66a0a !important}.bg-orange-5{background-color:#f66a0a !important}.color-orange-6{color:#e36209 !important}.bg-orange-6{background-color:#e36209 !important}.color-orange-7{color:#d15704 !important}.bg-orange-7{background-color:#d15704 !important}.color-orange-8{color:#c24e00 !important}.bg-orange-8{background-color:#c24e00 !important}.color-orange-9{color:#a04100 !important}.bg-orange-9{background-color:#a04100 !important}.color-red-0{color:#ffeef0 !important}.bg-red-0{background-color:#ffeef0 !important}.color-red-1{color:#ffdce0 !important}.bg-red-1{background-color:#ffdce0 !important}.color-red-2{color:#fdaeb7 !important}.bg-red-2{background-color:#fdaeb7 !important}.color-red-3{color:#f97583 !important}.bg-red-3{background-color:#f97583 !important}.color-red-4{color:#ea4a5a !important}.bg-red-4{background-color:#ea4a5a !important}.color-red-5{color:#d73a49 !important}.bg-red-5{background-color:#d73a49 !important}.color-red-6{color:#cb2431 !important}.bg-red-6{background-color:#cb2431 !important}.color-red-7{color:#b31d28 !important}.bg-red-7{background-color:#b31d28 !important}.color-red-8{color:#9e1c23 !important}.bg-red-8{background-color:#9e1c23 !important}.color-red-9{color:#86181d !important}.bg-red-9{background-color:#86181d !important}.color-purple-0{color:#f5f0ff !important}.bg-purple-0{background-color:#f5f0ff !important}.color-purple-1{color:#e6dcfd !important}.bg-purple-1{background-color:#e6dcfd !important}.color-purple-2{color:#d1bcf9 !important}.bg-purple-2{background-color:#d1bcf9 !important}.color-purple-3{color:#b392f0 !important}.bg-purple-3{background-color:#b392f0 !important}.color-purple-4{color:#8a63d2 !important}.bg-purple-4{background-color:#8a63d2 !important}.color-purple-5{color:#6f42c1 !important}.bg-purple-5{background-color:#6f42c1 !important}.color-purple-6{color:#5a32a3 !important}.bg-purple-6{background-color:#5a32a3 !important}.color-purple-7{color:#4c2889 !important}.bg-purple-7{background-color:#4c2889 !important}.color-purple-8{color:#3a1d6e !important}.bg-purple-8{background-color:#3a1d6e !important}.color-purple-9{color:#29134e !important}.bg-purple-9{background-color:#29134e !important}.color-pink-0{color:#ffeef8 !important}.bg-pink-0{background-color:#ffeef8 !important}.color-pink-1{color:#fedbf0 !important}.bg-pink-1{background-color:#fedbf0 !important}.color-pink-2{color:#f9b3dd !important}.bg-pink-2{background-color:#f9b3dd !important}.color-pink-3{color:#f692ce !important}.bg-pink-3{background-color:#f692ce !important}.color-pink-4{color:#ec6cb9 !important}.bg-pink-4{background-color:#ec6cb9 !important}.color-pink-5{color:#ea4aaa !important}.bg-pink-5{background-color:#ea4aaa !important}.color-pink-6{color:#d03592 !important}.bg-pink-6{background-color:#d03592 !important}.color-pink-7{color:#b93a86 !important}.bg-pink-7{background-color:#b93a86 !important}.color-pink-8{color:#99306f !important}.bg-pink-8{background-color:#99306f !important}.color-pink-9{color:#6d224f !important}.bg-pink-9{background-color:#6d224f !important}.bg-shade-gradient{background-image:linear-gradient(180deg, rgba(27, 31, 35, 0.065), rgba(27, 31, 35, 0)) !important;background-repeat:no-repeat !important;background-size:100% 200px !important}.text-blue{color:#0366d6 !important}.text-red{color:#cb2431 !important}.text-gray-light{color:#6a737d !important}.text-gray{color:#586069 !important}.text-gray-dark{color:#24292e !important}.text-green{color:#22863a !important}.text-yellow{color:#b08800 !important}.text-orange{color:#a04100 !important}.text-orange-light{color:#e36209 !important}.text-purple{color:#6f42c1 !important}.text-pink{color:#ea4aaa !important}.text-white{color:#fff !important}.text-inherit{color:inherit !important}.link-gray{color:#586069 !important}.link-gray:hover{color:#0366d6 !important}.link-gray-dark{color:#24292e !important}.link-gray-dark:hover{color:#0366d6 !important}.link-hover-blue:hover{color:#0366d6 !important}.muted-link{color:#586069 !important}.muted-link:hover{color:#0366d6 !important;text-decoration:none}.details-overlay[open]>summary::before{position:fixed;top:0;right:0;bottom:0;left:0;z-index:80;display:block;cursor:default;content:" ";background:transparent}.details-overlay-dark[open]>summary::before{z-index:99;background:rgba(27,31,35,.5)}.details-reset>summary{list-style:none}.details-reset>summary::before{display:none}.details-reset>summary::-webkit-details-marker{display:none}.flex-row{flex-direction:row !important}.flex-row-reverse{flex-direction:row-reverse !important}.flex-column{flex-direction:column !important}.flex-column-reverse{flex-direction:column-reverse !important}.flex-wrap{flex-wrap:wrap !important}.flex-nowrap{flex-wrap:nowrap !important}.flex-wrap-reverse{flex-wrap:wrap-reverse !important}.flex-justify-start{justify-content:flex-start !important}.flex-justify-end{justify-content:flex-end !important}.flex-justify-center{justify-content:center !important}.flex-justify-between{justify-content:space-between !important}.flex-justify-around{justify-content:space-around !important}.flex-items-start{align-items:flex-start !important}.flex-items-end{align-items:flex-end !important}.flex-items-center{align-items:center !important}.flex-items-baseline{align-items:baseline !important}.flex-items-stretch{align-items:stretch !important}.flex-content-start{align-content:flex-start !important}.flex-content-end{align-content:flex-end !important}.flex-content-center{align-content:center !important}.flex-content-between{align-content:space-between !important}.flex-content-around{align-content:space-around !important}.flex-content-stretch{align-content:stretch !important}.flex-1{flex:1 !important}.flex-auto{flex:auto !important}.flex-grow-0{flex-grow:0 !important}.flex-shrink-0{flex-shrink:0 !important}.flex-self-auto{align-self:auto !important}.flex-self-start{align-self:flex-start !important}.flex-self-end{align-self:flex-end !important}.flex-self-center{align-self:center !important}.flex-self-baseline{align-self:baseline !important}.flex-self-stretch{align-self:stretch !important}.flex-order-1{order:1 !important}.flex-order-2{order:2 !important}.flex-order-none{order:inherit !important}@media(min-width: 544px){.flex-sm-row{flex-direction:row !important}.flex-sm-row-reverse{flex-direction:row-reverse !important}.flex-sm-column{flex-direction:column !important}.flex-sm-column-reverse{flex-direction:column-reverse !important}.flex-sm-wrap{flex-wrap:wrap !important}.flex-sm-nowrap{flex-wrap:nowrap !important}.flex-sm-wrap-reverse{flex-wrap:wrap-reverse !important}.flex-sm-justify-start{justify-content:flex-start !important}.flex-sm-justify-end{justify-content:flex-end !important}.flex-sm-justify-center{justify-content:center !important}.flex-sm-justify-between{justify-content:space-between !important}.flex-sm-justify-around{justify-content:space-around !important}.flex-sm-items-start{align-items:flex-start !important}.flex-sm-items-end{align-items:flex-end !important}.flex-sm-items-center{align-items:center !important}.flex-sm-items-baseline{align-items:baseline !important}.flex-sm-items-stretch{align-items:stretch !important}.flex-sm-content-start{align-content:flex-start !important}.flex-sm-content-end{align-content:flex-end !important}.flex-sm-content-center{align-content:center !important}.flex-sm-content-between{align-content:space-between !important}.flex-sm-content-around{align-content:space-around !important}.flex-sm-content-stretch{align-content:stretch !important}.flex-sm-1{flex:1 !important}.flex-sm-auto{flex:auto !important}.flex-sm-grow-0{flex-grow:0 !important}.flex-sm-shrink-0{flex-shrink:0 !important}.flex-sm-self-auto{align-self:auto !important}.flex-sm-self-start{align-self:flex-start !important}.flex-sm-self-end{align-self:flex-end !important}.flex-sm-self-center{align-self:center !important}.flex-sm-self-baseline{align-self:baseline !important}.flex-sm-self-stretch{align-self:stretch !important}.flex-sm-order-1{order:1 !important}.flex-sm-order-2{order:2 !important}.flex-sm-order-none{order:inherit !important}}@media(min-width: 768px){.flex-md-row{flex-direction:row !important}.flex-md-row-reverse{flex-direction:row-reverse !important}.flex-md-column{flex-direction:column !important}.flex-md-column-reverse{flex-direction:column-reverse !important}.flex-md-wrap{flex-wrap:wrap !important}.flex-md-nowrap{flex-wrap:nowrap !important}.flex-md-wrap-reverse{flex-wrap:wrap-reverse !important}.flex-md-justify-start{justify-content:flex-start !important}.flex-md-justify-end{justify-content:flex-end !important}.flex-md-justify-center{justify-content:center !important}.flex-md-justify-between{justify-content:space-between !important}.flex-md-justify-around{justify-content:space-around !important}.flex-md-items-start{align-items:flex-start !important}.flex-md-items-end{align-items:flex-end !important}.flex-md-items-center{align-items:center !important}.flex-md-items-baseline{align-items:baseline !important}.flex-md-items-stretch{align-items:stretch !important}.flex-md-content-start{align-content:flex-start !important}.flex-md-content-end{align-content:flex-end !important}.flex-md-content-center{align-content:center !important}.flex-md-content-between{align-content:space-between !important}.flex-md-content-around{align-content:space-around !important}.flex-md-content-stretch{align-content:stretch !important}.flex-md-1{flex:1 !important}.flex-md-auto{flex:auto !important}.flex-md-grow-0{flex-grow:0 !important}.flex-md-shrink-0{flex-shrink:0 !important}.flex-md-self-auto{align-self:auto !important}.flex-md-self-start{align-self:flex-start !important}.flex-md-self-end{align-self:flex-end !important}.flex-md-self-center{align-self:center !important}.flex-md-self-baseline{align-self:baseline !important}.flex-md-self-stretch{align-self:stretch !important}.flex-md-order-1{order:1 !important}.flex-md-order-2{order:2 !important}.flex-md-order-none{order:inherit !important}}@media(min-width: 1012px){.flex-lg-row{flex-direction:row !important}.flex-lg-row-reverse{flex-direction:row-reverse !important}.flex-lg-column{flex-direction:column !important}.flex-lg-column-reverse{flex-direction:column-reverse !important}.flex-lg-wrap{flex-wrap:wrap !important}.flex-lg-nowrap{flex-wrap:nowrap !important}.flex-lg-wrap-reverse{flex-wrap:wrap-reverse !important}.flex-lg-justify-start{justify-content:flex-start !important}.flex-lg-justify-end{justify-content:flex-end !important}.flex-lg-justify-center{justify-content:center !important}.flex-lg-justify-between{justify-content:space-between !important}.flex-lg-justify-around{justify-content:space-around !important}.flex-lg-items-start{align-items:flex-start !important}.flex-lg-items-end{align-items:flex-end !important}.flex-lg-items-center{align-items:center !important}.flex-lg-items-baseline{align-items:baseline !important}.flex-lg-items-stretch{align-items:stretch !important}.flex-lg-content-start{align-content:flex-start !important}.flex-lg-content-end{align-content:flex-end !important}.flex-lg-content-center{align-content:center !important}.flex-lg-content-between{align-content:space-between !important}.flex-lg-content-around{align-content:space-around !important}.flex-lg-content-stretch{align-content:stretch !important}.flex-lg-1{flex:1 !important}.flex-lg-auto{flex:auto !important}.flex-lg-grow-0{flex-grow:0 !important}.flex-lg-shrink-0{flex-shrink:0 !important}.flex-lg-self-auto{align-self:auto !important}.flex-lg-self-start{align-self:flex-start !important}.flex-lg-self-end{align-self:flex-end !important}.flex-lg-self-center{align-self:center !important}.flex-lg-self-baseline{align-self:baseline !important}.flex-lg-self-stretch{align-self:stretch !important}.flex-lg-order-1{order:1 !important}.flex-lg-order-2{order:2 !important}.flex-lg-order-none{order:inherit !important}}@media(min-width: 1280px){.flex-xl-row{flex-direction:row !important}.flex-xl-row-reverse{flex-direction:row-reverse !important}.flex-xl-column{flex-direction:column !important}.flex-xl-column-reverse{flex-direction:column-reverse !important}.flex-xl-wrap{flex-wrap:wrap !important}.flex-xl-nowrap{flex-wrap:nowrap !important}.flex-xl-wrap-reverse{flex-wrap:wrap-reverse !important}.flex-xl-justify-start{justify-content:flex-start !important}.flex-xl-justify-end{justify-content:flex-end !important}.flex-xl-justify-center{justify-content:center !important}.flex-xl-justify-between{justify-content:space-between !important}.flex-xl-justify-around{justify-content:space-around !important}.flex-xl-items-start{align-items:flex-start !important}.flex-xl-items-end{align-items:flex-end !important}.flex-xl-items-center{align-items:center !important}.flex-xl-items-baseline{align-items:baseline !important}.flex-xl-items-stretch{align-items:stretch !important}.flex-xl-content-start{align-content:flex-start !important}.flex-xl-content-end{align-content:flex-end !important}.flex-xl-content-center{align-content:center !important}.flex-xl-content-between{align-content:space-between !important}.flex-xl-content-around{align-content:space-around !important}.flex-xl-content-stretch{align-content:stretch !important}.flex-xl-1{flex:1 !important}.flex-xl-auto{flex:auto !important}.flex-xl-grow-0{flex-grow:0 !important}.flex-xl-shrink-0{flex-shrink:0 !important}.flex-xl-self-auto{align-self:auto !important}.flex-xl-self-start{align-self:flex-start !important}.flex-xl-self-end{align-self:flex-end !important}.flex-xl-self-center{align-self:center !important}.flex-xl-self-baseline{align-self:baseline !important}.flex-xl-self-stretch{align-self:stretch !important}.flex-xl-order-1{order:1 !important}.flex-xl-order-2{order:2 !important}.flex-xl-order-none{order:inherit !important}}.position-static{position:static !important}.position-relative{position:relative !important}.position-absolute{position:absolute !important}.position-fixed{position:fixed !important}.position-sticky{position:sticky !important}@media(min-width: 544px){.position-sm-static{position:static !important}.position-sm-relative{position:relative !important}.position-sm-absolute{position:absolute !important}.position-sm-fixed{position:fixed !important}.position-sm-sticky{position:sticky !important}}@media(min-width: 768px){.position-md-static{position:static !important}.position-md-relative{position:relative !important}.position-md-absolute{position:absolute !important}.position-md-fixed{position:fixed !important}.position-md-sticky{position:sticky !important}}@media(min-width: 1012px){.position-lg-static{position:static !important}.position-lg-relative{position:relative !important}.position-lg-absolute{position:absolute !important}.position-lg-fixed{position:fixed !important}.position-lg-sticky{position:sticky !important}}@media(min-width: 1280px){.position-xl-static{position:static !important}.position-xl-relative{position:relative !important}.position-xl-absolute{position:absolute !important}.position-xl-fixed{position:fixed !important}.position-xl-sticky{position:sticky !important}}.top-0{top:0 !important}.right-0{right:0 !important}.bottom-0{bottom:0 !important}.left-0{left:0 !important}.top-auto{top:auto !important}.right-auto{right:auto !important}.bottom-auto{bottom:auto !important}.left-auto{left:auto !important}@media(min-width: 544px){.top-sm-0{top:0 !important}.right-sm-0{right:0 !important}.bottom-sm-0{bottom:0 !important}.left-sm-0{left:0 !important}.top-sm-auto{top:auto !important}.right-sm-auto{right:auto !important}.bottom-sm-auto{bottom:auto !important}.left-sm-auto{left:auto !important}}@media(min-width: 768px){.top-md-0{top:0 !important}.right-md-0{right:0 !important}.bottom-md-0{bottom:0 !important}.left-md-0{left:0 !important}.top-md-auto{top:auto !important}.right-md-auto{right:auto !important}.bottom-md-auto{bottom:auto !important}.left-md-auto{left:auto !important}}@media(min-width: 1012px){.top-lg-0{top:0 !important}.right-lg-0{right:0 !important}.bottom-lg-0{bottom:0 !important}.left-lg-0{left:0 !important}.top-lg-auto{top:auto !important}.right-lg-auto{right:auto !important}.bottom-lg-auto{bottom:auto !important}.left-lg-auto{left:auto !important}}@media(min-width: 1280px){.top-xl-0{top:0 !important}.right-xl-0{right:0 !important}.bottom-xl-0{bottom:0 !important}.left-xl-0{left:0 !important}.top-xl-auto{top:auto !important}.right-xl-auto{right:auto !important}.bottom-xl-auto{bottom:auto !important}.left-xl-auto{left:auto !important}}.v-align-middle{vertical-align:middle !important}.v-align-top{vertical-align:top !important}.v-align-bottom{vertical-align:bottom !important}.v-align-text-top{vertical-align:text-top !important}.v-align-text-bottom{vertical-align:text-bottom !important}.v-align-baseline{vertical-align:baseline !important}.overflow-visible{overflow:visible !important}.overflow-x-visible{overflow-x:visible !important}.overflow-y-visible{overflow-y:visible !important}.overflow-hidden{overflow:hidden !important}.overflow-x-hidden{overflow-x:hidden !important}.overflow-y-hidden{overflow-y:hidden !important}.overflow-auto{overflow:auto !important}.overflow-x-auto{overflow-x:auto !important}.overflow-y-auto{overflow-y:auto !important}.overflow-scroll{overflow:scroll !important}.overflow-x-scroll{overflow-x:scroll !important}.overflow-y-scroll{overflow-y:scroll !important}@media(min-width: 544px){.overflow-sm-visible{overflow:visible !important}.overflow-sm-x-visible{overflow-x:visible !important}.overflow-sm-y-visible{overflow-y:visible !important}.overflow-sm-hidden{overflow:hidden !important}.overflow-sm-x-hidden{overflow-x:hidden !important}.overflow-sm-y-hidden{overflow-y:hidden !important}.overflow-sm-auto{overflow:auto !important}.overflow-sm-x-auto{overflow-x:auto !important}.overflow-sm-y-auto{overflow-y:auto !important}.overflow-sm-scroll{overflow:scroll !important}.overflow-sm-x-scroll{overflow-x:scroll !important}.overflow-sm-y-scroll{overflow-y:scroll !important}}@media(min-width: 768px){.overflow-md-visible{overflow:visible !important}.overflow-md-x-visible{overflow-x:visible !important}.overflow-md-y-visible{overflow-y:visible !important}.overflow-md-hidden{overflow:hidden !important}.overflow-md-x-hidden{overflow-x:hidden !important}.overflow-md-y-hidden{overflow-y:hidden !important}.overflow-md-auto{overflow:auto !important}.overflow-md-x-auto{overflow-x:auto !important}.overflow-md-y-auto{overflow-y:auto !important}.overflow-md-scroll{overflow:scroll !important}.overflow-md-x-scroll{overflow-x:scroll !important}.overflow-md-y-scroll{overflow-y:scroll !important}}@media(min-width: 1012px){.overflow-lg-visible{overflow:visible !important}.overflow-lg-x-visible{overflow-x:visible !important}.overflow-lg-y-visible{overflow-y:visible !important}.overflow-lg-hidden{overflow:hidden !important}.overflow-lg-x-hidden{overflow-x:hidden !important}.overflow-lg-y-hidden{overflow-y:hidden !important}.overflow-lg-auto{overflow:auto !important}.overflow-lg-x-auto{overflow-x:auto !important}.overflow-lg-y-auto{overflow-y:auto !important}.overflow-lg-scroll{overflow:scroll !important}.overflow-lg-x-scroll{overflow-x:scroll !important}.overflow-lg-y-scroll{overflow-y:scroll !important}}@media(min-width: 1280px){.overflow-xl-visible{overflow:visible !important}.overflow-xl-x-visible{overflow-x:visible !important}.overflow-xl-y-visible{overflow-y:visible !important}.overflow-xl-hidden{overflow:hidden !important}.overflow-xl-x-hidden{overflow-x:hidden !important}.overflow-xl-y-hidden{overflow-y:hidden !important}.overflow-xl-auto{overflow:auto !important}.overflow-xl-x-auto{overflow-x:auto !important}.overflow-xl-y-auto{overflow-y:auto !important}.overflow-xl-scroll{overflow:scroll !important}.overflow-xl-x-scroll{overflow-x:scroll !important}.overflow-xl-y-scroll{overflow-y:scroll !important}}.clearfix::before{display:table;content:""}.clearfix::after{display:table;clear:both;content:""}.float-left{float:left !important}.float-right{float:right !important}.float-none{float:none !important}@media(min-width: 544px){.float-sm-left{float:left !important}.float-sm-right{float:right !important}.float-sm-none{float:none !important}}@media(min-width: 768px){.float-md-left{float:left !important}.float-md-right{float:right !important}.float-md-none{float:none !important}}@media(min-width: 1012px){.float-lg-left{float:left !important}.float-lg-right{float:right !important}.float-lg-none{float:none !important}}@media(min-width: 1280px){.float-xl-left{float:left !important}.float-xl-right{float:right !important}.float-xl-none{float:none !important}}.width-fit{max-width:100% !important}.width-full{width:100% !important}.height-fit{max-height:100% !important}.height-full{height:100% !important}.min-width-0{min-width:0 !important}.width-auto{width:auto !important}.direction-rtl{direction:rtl !important}.direction-ltr{direction:ltr !important}@media(min-width: 544px){.width-sm-auto{width:auto !important}.direction-sm-rtl{direction:rtl !important}.direction-sm-ltr{direction:ltr !important}}@media(min-width: 768px){.width-md-auto{width:auto !important}.direction-md-rtl{direction:rtl !important}.direction-md-ltr{direction:ltr !important}}@media(min-width: 1012px){.width-lg-auto{width:auto !important}.direction-lg-rtl{direction:rtl !important}.direction-lg-ltr{direction:ltr !important}}@media(min-width: 1280px){.width-xl-auto{width:auto !important}.direction-xl-rtl{direction:rtl !important}.direction-xl-ltr{direction:ltr !important}}.m-0{margin:0 !important}.mt-0{margin-top:0 !important}.mr-0{margin-right:0 !important}.mb-0{margin-bottom:0 !important}.ml-0{margin-left:0 !important}.mx-0{margin-right:0 !important;margin-left:0 !important}.my-0{margin-top:0 !important;margin-bottom:0 !important}.m-1{margin:4px !important}.mt-1{margin-top:4px !important}.mr-1{margin-right:4px !important}.mb-1{margin-bottom:4px !important}.ml-1{margin-left:4px !important}.mt-n1{margin-top:-4px !important}.mr-n1{margin-right:-4px !important}.mb-n1{margin-bottom:-4px !important}.ml-n1{margin-left:-4px !important}.mx-1{margin-right:4px !important;margin-left:4px !important}.my-1{margin-top:4px !important;margin-bottom:4px !important}.m-2{margin:8px !important}.mt-2{margin-top:8px !important}.mr-2{margin-right:8px !important}.mb-2{margin-bottom:8px !important}.ml-2{margin-left:8px !important}.mt-n2{margin-top:-8px !important}.mr-n2{margin-right:-8px !important}.mb-n2{margin-bottom:-8px !important}.ml-n2{margin-left:-8px !important}.mx-2{margin-right:8px !important;margin-left:8px !important}.my-2{margin-top:8px !important;margin-bottom:8px !important}.m-3{margin:16px !important}.mt-3{margin-top:16px !important}.mr-3{margin-right:16px !important}.mb-3{margin-bottom:16px !important}.ml-3{margin-left:16px !important}.mt-n3{margin-top:-16px !important}.mr-n3{margin-right:-16px !important}.mb-n3{margin-bottom:-16px !important}.ml-n3{margin-left:-16px !important}.mx-3{margin-right:16px !important;margin-left:16px !important}.my-3{margin-top:16px !important;margin-bottom:16px !important}.m-4{margin:24px !important}.mt-4{margin-top:24px !important}.mr-4{margin-right:24px !important}.mb-4{margin-bottom:24px !important}.ml-4{margin-left:24px !important}.mt-n4{margin-top:-24px !important}.mr-n4{margin-right:-24px !important}.mb-n4{margin-bottom:-24px !important}.ml-n4{margin-left:-24px !important}.mx-4{margin-right:24px !important;margin-left:24px !important}.my-4{margin-top:24px !important;margin-bottom:24px !important}.m-5{margin:32px !important}.mt-5{margin-top:32px !important}.mr-5{margin-right:32px !important}.mb-5{margin-bottom:32px !important}.ml-5{margin-left:32px !important}.mt-n5{margin-top:-32px !important}.mr-n5{margin-right:-32px !important}.mb-n5{margin-bottom:-32px !important}.ml-n5{margin-left:-32px !important}.mx-5{margin-right:32px !important;margin-left:32px !important}.my-5{margin-top:32px !important;margin-bottom:32px !important}.m-6{margin:40px !important}.mt-6{margin-top:40px !important}.mr-6{margin-right:40px !important}.mb-6{margin-bottom:40px !important}.ml-6{margin-left:40px !important}.mt-n6{margin-top:-40px !important}.mr-n6{margin-right:-40px !important}.mb-n6{margin-bottom:-40px !important}.ml-n6{margin-left:-40px !important}.mx-6{margin-right:40px !important;margin-left:40px !important}.my-6{margin-top:40px !important;margin-bottom:40px !important}.mx-auto{margin-right:auto !important;margin-left:auto !important}@media(min-width: 544px){.m-sm-0{margin:0 !important}.mt-sm-0{margin-top:0 !important}.mr-sm-0{margin-right:0 !important}.mb-sm-0{margin-bottom:0 !important}.ml-sm-0{margin-left:0 !important}.mx-sm-0{margin-right:0 !important;margin-left:0 !important}.my-sm-0{margin-top:0 !important;margin-bottom:0 !important}.m-sm-1{margin:4px !important}.mt-sm-1{margin-top:4px !important}.mr-sm-1{margin-right:4px !important}.mb-sm-1{margin-bottom:4px !important}.ml-sm-1{margin-left:4px !important}.mt-sm-n1{margin-top:-4px !important}.mr-sm-n1{margin-right:-4px !important}.mb-sm-n1{margin-bottom:-4px !important}.ml-sm-n1{margin-left:-4px !important}.mx-sm-1{margin-right:4px !important;margin-left:4px !important}.my-sm-1{margin-top:4px !important;margin-bottom:4px !important}.m-sm-2{margin:8px !important}.mt-sm-2{margin-top:8px !important}.mr-sm-2{margin-right:8px !important}.mb-sm-2{margin-bottom:8px !important}.ml-sm-2{margin-left:8px !important}.mt-sm-n2{margin-top:-8px !important}.mr-sm-n2{margin-right:-8px !important}.mb-sm-n2{margin-bottom:-8px !important}.ml-sm-n2{margin-left:-8px !important}.mx-sm-2{margin-right:8px !important;margin-left:8px !important}.my-sm-2{margin-top:8px !important;margin-bottom:8px !important}.m-sm-3{margin:16px !important}.mt-sm-3{margin-top:16px !important}.mr-sm-3{margin-right:16px !important}.mb-sm-3{margin-bottom:16px !important}.ml-sm-3{margin-left:16px !important}.mt-sm-n3{margin-top:-16px !important}.mr-sm-n3{margin-right:-16px !important}.mb-sm-n3{margin-bottom:-16px !important}.ml-sm-n3{margin-left:-16px !important}.mx-sm-3{margin-right:16px !important;margin-left:16px !important}.my-sm-3{margin-top:16px !important;margin-bottom:16px !important}.m-sm-4{margin:24px !important}.mt-sm-4{margin-top:24px !important}.mr-sm-4{margin-right:24px !important}.mb-sm-4{margin-bottom:24px !important}.ml-sm-4{margin-left:24px !important}.mt-sm-n4{margin-top:-24px !important}.mr-sm-n4{margin-right:-24px !important}.mb-sm-n4{margin-bottom:-24px !important}.ml-sm-n4{margin-left:-24px !important}.mx-sm-4{margin-right:24px !important;margin-left:24px !important}.my-sm-4{margin-top:24px !important;margin-bottom:24px !important}.m-sm-5{margin:32px !important}.mt-sm-5{margin-top:32px !important}.mr-sm-5{margin-right:32px !important}.mb-sm-5{margin-bottom:32px !important}.ml-sm-5{margin-left:32px !important}.mt-sm-n5{margin-top:-32px !important}.mr-sm-n5{margin-right:-32px !important}.mb-sm-n5{margin-bottom:-32px !important}.ml-sm-n5{margin-left:-32px !important}.mx-sm-5{margin-right:32px !important;margin-left:32px !important}.my-sm-5{margin-top:32px !important;margin-bottom:32px !important}.m-sm-6{margin:40px !important}.mt-sm-6{margin-top:40px !important}.mr-sm-6{margin-right:40px !important}.mb-sm-6{margin-bottom:40px !important}.ml-sm-6{margin-left:40px !important}.mt-sm-n6{margin-top:-40px !important}.mr-sm-n6{margin-right:-40px !important}.mb-sm-n6{margin-bottom:-40px !important}.ml-sm-n6{margin-left:-40px !important}.mx-sm-6{margin-right:40px !important;margin-left:40px !important}.my-sm-6{margin-top:40px !important;margin-bottom:40px !important}.mx-sm-auto{margin-right:auto !important;margin-left:auto !important}}@media(min-width: 768px){.m-md-0{margin:0 !important}.mt-md-0{margin-top:0 !important}.mr-md-0{margin-right:0 !important}.mb-md-0{margin-bottom:0 !important}.ml-md-0{margin-left:0 !important}.mx-md-0{margin-right:0 !important;margin-left:0 !important}.my-md-0{margin-top:0 !important;margin-bottom:0 !important}.m-md-1{margin:4px !important}.mt-md-1{margin-top:4px !important}.mr-md-1{margin-right:4px !important}.mb-md-1{margin-bottom:4px !important}.ml-md-1{margin-left:4px !important}.mt-md-n1{margin-top:-4px !important}.mr-md-n1{margin-right:-4px !important}.mb-md-n1{margin-bottom:-4px !important}.ml-md-n1{margin-left:-4px !important}.mx-md-1{margin-right:4px !important;margin-left:4px !important}.my-md-1{margin-top:4px !important;margin-bottom:4px !important}.m-md-2{margin:8px !important}.mt-md-2{margin-top:8px !important}.mr-md-2{margin-right:8px !important}.mb-md-2{margin-bottom:8px !important}.ml-md-2{margin-left:8px !important}.mt-md-n2{margin-top:-8px !important}.mr-md-n2{margin-right:-8px !important}.mb-md-n2{margin-bottom:-8px !important}.ml-md-n2{margin-left:-8px !important}.mx-md-2{margin-right:8px !important;margin-left:8px !important}.my-md-2{margin-top:8px !important;margin-bottom:8px !important}.m-md-3{margin:16px !important}.mt-md-3{margin-top:16px !important}.mr-md-3{margin-right:16px !important}.mb-md-3{margin-bottom:16px !important}.ml-md-3{margin-left:16px !important}.mt-md-n3{margin-top:-16px !important}.mr-md-n3{margin-right:-16px !important}.mb-md-n3{margin-bottom:-16px !important}.ml-md-n3{margin-left:-16px !important}.mx-md-3{margin-right:16px !important;margin-left:16px !important}.my-md-3{margin-top:16px !important;margin-bottom:16px !important}.m-md-4{margin:24px !important}.mt-md-4{margin-top:24px !important}.mr-md-4{margin-right:24px !important}.mb-md-4{margin-bottom:24px !important}.ml-md-4{margin-left:24px !important}.mt-md-n4{margin-top:-24px !important}.mr-md-n4{margin-right:-24px !important}.mb-md-n4{margin-bottom:-24px !important}.ml-md-n4{margin-left:-24px !important}.mx-md-4{margin-right:24px !important;margin-left:24px !important}.my-md-4{margin-top:24px !important;margin-bottom:24px !important}.m-md-5{margin:32px !important}.mt-md-5{margin-top:32px !important}.mr-md-5{margin-right:32px !important}.mb-md-5{margin-bottom:32px !important}.ml-md-5{margin-left:32px !important}.mt-md-n5{margin-top:-32px !important}.mr-md-n5{margin-right:-32px !important}.mb-md-n5{margin-bottom:-32px !important}.ml-md-n5{margin-left:-32px !important}.mx-md-5{margin-right:32px !important;margin-left:32px !important}.my-md-5{margin-top:32px !important;margin-bottom:32px !important}.m-md-6{margin:40px !important}.mt-md-6{margin-top:40px !important}.mr-md-6{margin-right:40px !important}.mb-md-6{margin-bottom:40px !important}.ml-md-6{margin-left:40px !important}.mt-md-n6{margin-top:-40px !important}.mr-md-n6{margin-right:-40px !important}.mb-md-n6{margin-bottom:-40px !important}.ml-md-n6{margin-left:-40px !important}.mx-md-6{margin-right:40px !important;margin-left:40px !important}.my-md-6{margin-top:40px !important;margin-bottom:40px !important}.mx-md-auto{margin-right:auto !important;margin-left:auto !important}}@media(min-width: 1012px){.m-lg-0{margin:0 !important}.mt-lg-0{margin-top:0 !important}.mr-lg-0{margin-right:0 !important}.mb-lg-0{margin-bottom:0 !important}.ml-lg-0{margin-left:0 !important}.mx-lg-0{margin-right:0 !important;margin-left:0 !important}.my-lg-0{margin-top:0 !important;margin-bottom:0 !important}.m-lg-1{margin:4px !important}.mt-lg-1{margin-top:4px !important}.mr-lg-1{margin-right:4px !important}.mb-lg-1{margin-bottom:4px !important}.ml-lg-1{margin-left:4px !important}.mt-lg-n1{margin-top:-4px !important}.mr-lg-n1{margin-right:-4px !important}.mb-lg-n1{margin-bottom:-4px !important}.ml-lg-n1{margin-left:-4px !important}.mx-lg-1{margin-right:4px !important;margin-left:4px !important}.my-lg-1{margin-top:4px !important;margin-bottom:4px !important}.m-lg-2{margin:8px !important}.mt-lg-2{margin-top:8px !important}.mr-lg-2{margin-right:8px !important}.mb-lg-2{margin-bottom:8px !important}.ml-lg-2{margin-left:8px !important}.mt-lg-n2{margin-top:-8px !important}.mr-lg-n2{margin-right:-8px !important}.mb-lg-n2{margin-bottom:-8px !important}.ml-lg-n2{margin-left:-8px !important}.mx-lg-2{margin-right:8px !important;margin-left:8px !important}.my-lg-2{margin-top:8px !important;margin-bottom:8px !important}.m-lg-3{margin:16px !important}.mt-lg-3{margin-top:16px !important}.mr-lg-3{margin-right:16px !important}.mb-lg-3{margin-bottom:16px !important}.ml-lg-3{margin-left:16px !important}.mt-lg-n3{margin-top:-16px !important}.mr-lg-n3{margin-right:-16px !important}.mb-lg-n3{margin-bottom:-16px !important}.ml-lg-n3{margin-left:-16px !important}.mx-lg-3{margin-right:16px !important;margin-left:16px !important}.my-lg-3{margin-top:16px !important;margin-bottom:16px !important}.m-lg-4{margin:24px !important}.mt-lg-4{margin-top:24px !important}.mr-lg-4{margin-right:24px !important}.mb-lg-4{margin-bottom:24px !important}.ml-lg-4{margin-left:24px !important}.mt-lg-n4{margin-top:-24px !important}.mr-lg-n4{margin-right:-24px !important}.mb-lg-n4{margin-bottom:-24px !important}.ml-lg-n4{margin-left:-24px !important}.mx-lg-4{margin-right:24px !important;margin-left:24px !important}.my-lg-4{margin-top:24px !important;margin-bottom:24px !important}.m-lg-5{margin:32px !important}.mt-lg-5{margin-top:32px !important}.mr-lg-5{margin-right:32px !important}.mb-lg-5{margin-bottom:32px !important}.ml-lg-5{margin-left:32px !important}.mt-lg-n5{margin-top:-32px !important}.mr-lg-n5{margin-right:-32px !important}.mb-lg-n5{margin-bottom:-32px !important}.ml-lg-n5{margin-left:-32px !important}.mx-lg-5{margin-right:32px !important;margin-left:32px !important}.my-lg-5{margin-top:32px !important;margin-bottom:32px !important}.m-lg-6{margin:40px !important}.mt-lg-6{margin-top:40px !important}.mr-lg-6{margin-right:40px !important}.mb-lg-6{margin-bottom:40px !important}.ml-lg-6{margin-left:40px !important}.mt-lg-n6{margin-top:-40px !important}.mr-lg-n6{margin-right:-40px !important}.mb-lg-n6{margin-bottom:-40px !important}.ml-lg-n6{margin-left:-40px !important}.mx-lg-6{margin-right:40px !important;margin-left:40px !important}.my-lg-6{margin-top:40px !important;margin-bottom:40px !important}.mx-lg-auto{margin-right:auto !important;margin-left:auto !important}}@media(min-width: 1280px){.m-xl-0{margin:0 !important}.mt-xl-0{margin-top:0 !important}.mr-xl-0{margin-right:0 !important}.mb-xl-0{margin-bottom:0 !important}.ml-xl-0{margin-left:0 !important}.mx-xl-0{margin-right:0 !important;margin-left:0 !important}.my-xl-0{margin-top:0 !important;margin-bottom:0 !important}.m-xl-1{margin:4px !important}.mt-xl-1{margin-top:4px !important}.mr-xl-1{margin-right:4px !important}.mb-xl-1{margin-bottom:4px !important}.ml-xl-1{margin-left:4px !important}.mt-xl-n1{margin-top:-4px !important}.mr-xl-n1{margin-right:-4px !important}.mb-xl-n1{margin-bottom:-4px !important}.ml-xl-n1{margin-left:-4px !important}.mx-xl-1{margin-right:4px !important;margin-left:4px !important}.my-xl-1{margin-top:4px !important;margin-bottom:4px !important}.m-xl-2{margin:8px !important}.mt-xl-2{margin-top:8px !important}.mr-xl-2{margin-right:8px !important}.mb-xl-2{margin-bottom:8px !important}.ml-xl-2{margin-left:8px !important}.mt-xl-n2{margin-top:-8px !important}.mr-xl-n2{margin-right:-8px !important}.mb-xl-n2{margin-bottom:-8px !important}.ml-xl-n2{margin-left:-8px !important}.mx-xl-2{margin-right:8px !important;margin-left:8px !important}.my-xl-2{margin-top:8px !important;margin-bottom:8px !important}.m-xl-3{margin:16px !important}.mt-xl-3{margin-top:16px !important}.mr-xl-3{margin-right:16px !important}.mb-xl-3{margin-bottom:16px !important}.ml-xl-3{margin-left:16px !important}.mt-xl-n3{margin-top:-16px !important}.mr-xl-n3{margin-right:-16px !important}.mb-xl-n3{margin-bottom:-16px !important}.ml-xl-n3{margin-left:-16px !important}.mx-xl-3{margin-right:16px !important;margin-left:16px !important}.my-xl-3{margin-top:16px !important;margin-bottom:16px !important}.m-xl-4{margin:24px !important}.mt-xl-4{margin-top:24px !important}.mr-xl-4{margin-right:24px !important}.mb-xl-4{margin-bottom:24px !important}.ml-xl-4{margin-left:24px !important}.mt-xl-n4{margin-top:-24px !important}.mr-xl-n4{margin-right:-24px !important}.mb-xl-n4{margin-bottom:-24px !important}.ml-xl-n4{margin-left:-24px !important}.mx-xl-4{margin-right:24px !important;margin-left:24px !important}.my-xl-4{margin-top:24px !important;margin-bottom:24px !important}.m-xl-5{margin:32px !important}.mt-xl-5{margin-top:32px !important}.mr-xl-5{margin-right:32px !important}.mb-xl-5{margin-bottom:32px !important}.ml-xl-5{margin-left:32px !important}.mt-xl-n5{margin-top:-32px !important}.mr-xl-n5{margin-right:-32px !important}.mb-xl-n5{margin-bottom:-32px !important}.ml-xl-n5{margin-left:-32px !important}.mx-xl-5{margin-right:32px !important;margin-left:32px !important}.my-xl-5{margin-top:32px !important;margin-bottom:32px !important}.m-xl-6{margin:40px !important}.mt-xl-6{margin-top:40px !important}.mr-xl-6{margin-right:40px !important}.mb-xl-6{margin-bottom:40px !important}.ml-xl-6{margin-left:40px !important}.mt-xl-n6{margin-top:-40px !important}.mr-xl-n6{margin-right:-40px !important}.mb-xl-n6{margin-bottom:-40px !important}.ml-xl-n6{margin-left:-40px !important}.mx-xl-6{margin-right:40px !important;margin-left:40px !important}.my-xl-6{margin-top:40px !important;margin-bottom:40px !important}.mx-xl-auto{margin-right:auto !important;margin-left:auto !important}}.p-0{padding:0 !important}.pt-0{padding-top:0 !important}.pr-0{padding-right:0 !important}.pb-0{padding-bottom:0 !important}.pl-0{padding-left:0 !important}.px-0{padding-right:0 !important;padding-left:0 !important}.py-0{padding-top:0 !important;padding-bottom:0 !important}.p-1{padding:4px !important}.pt-1{padding-top:4px !important}.pr-1{padding-right:4px !important}.pb-1{padding-bottom:4px !important}.pl-1{padding-left:4px !important}.px-1{padding-right:4px !important;padding-left:4px !important}.py-1{padding-top:4px !important;padding-bottom:4px !important}.p-2{padding:8px !important}.pt-2{padding-top:8px !important}.pr-2{padding-right:8px !important}.pb-2{padding-bottom:8px !important}.pl-2{padding-left:8px !important}.px-2{padding-right:8px !important;padding-left:8px !important}.py-2{padding-top:8px !important;padding-bottom:8px !important}.p-3{padding:16px !important}.pt-3{padding-top:16px !important}.pr-3{padding-right:16px !important}.pb-3{padding-bottom:16px !important}.pl-3{padding-left:16px !important}.px-3{padding-right:16px !important;padding-left:16px !important}.py-3{padding-top:16px !important;padding-bottom:16px !important}.p-4{padding:24px !important}.pt-4{padding-top:24px !important}.pr-4{padding-right:24px !important}.pb-4{padding-bottom:24px !important}.pl-4{padding-left:24px !important}.px-4{padding-right:24px !important;padding-left:24px !important}.py-4{padding-top:24px !important;padding-bottom:24px !important}.p-5{padding:32px !important}.pt-5{padding-top:32px !important}.pr-5{padding-right:32px !important}.pb-5{padding-bottom:32px !important}.pl-5{padding-left:32px !important}.px-5{padding-right:32px !important;padding-left:32px !important}.py-5{padding-top:32px !important;padding-bottom:32px !important}.p-6{padding:40px !important}.pt-6{padding-top:40px !important}.pr-6{padding-right:40px !important}.pb-6{padding-bottom:40px !important}.pl-6{padding-left:40px !important}.px-6{padding-right:40px !important;padding-left:40px !important}.py-6{padding-top:40px !important;padding-bottom:40px !important}@media(min-width: 544px){.p-sm-0{padding:0 !important}.pt-sm-0{padding-top:0 !important}.pr-sm-0{padding-right:0 !important}.pb-sm-0{padding-bottom:0 !important}.pl-sm-0{padding-left:0 !important}.px-sm-0{padding-right:0 !important;padding-left:0 !important}.py-sm-0{padding-top:0 !important;padding-bottom:0 !important}.p-sm-1{padding:4px !important}.pt-sm-1{padding-top:4px !important}.pr-sm-1{padding-right:4px !important}.pb-sm-1{padding-bottom:4px !important}.pl-sm-1{padding-left:4px !important}.px-sm-1{padding-right:4px !important;padding-left:4px !important}.py-sm-1{padding-top:4px !important;padding-bottom:4px !important}.p-sm-2{padding:8px !important}.pt-sm-2{padding-top:8px !important}.pr-sm-2{padding-right:8px !important}.pb-sm-2{padding-bottom:8px !important}.pl-sm-2{padding-left:8px !important}.px-sm-2{padding-right:8px !important;padding-left:8px !important}.py-sm-2{padding-top:8px !important;padding-bottom:8px !important}.p-sm-3{padding:16px !important}.pt-sm-3{padding-top:16px !important}.pr-sm-3{padding-right:16px !important}.pb-sm-3{padding-bottom:16px !important}.pl-sm-3{padding-left:16px !important}.px-sm-3{padding-right:16px !important;padding-left:16px !important}.py-sm-3{padding-top:16px !important;padding-bottom:16px !important}.p-sm-4{padding:24px !important}.pt-sm-4{padding-top:24px !important}.pr-sm-4{padding-right:24px !important}.pb-sm-4{padding-bottom:24px !important}.pl-sm-4{padding-left:24px !important}.px-sm-4{padding-right:24px !important;padding-left:24px !important}.py-sm-4{padding-top:24px !important;padding-bottom:24px !important}.p-sm-5{padding:32px !important}.pt-sm-5{padding-top:32px !important}.pr-sm-5{padding-right:32px !important}.pb-sm-5{padding-bottom:32px !important}.pl-sm-5{padding-left:32px !important}.px-sm-5{padding-right:32px !important;padding-left:32px !important}.py-sm-5{padding-top:32px !important;padding-bottom:32px !important}.p-sm-6{padding:40px !important}.pt-sm-6{padding-top:40px !important}.pr-sm-6{padding-right:40px !important}.pb-sm-6{padding-bottom:40px !important}.pl-sm-6{padding-left:40px !important}.px-sm-6{padding-right:40px !important;padding-left:40px !important}.py-sm-6{padding-top:40px !important;padding-bottom:40px !important}}@media(min-width: 768px){.p-md-0{padding:0 !important}.pt-md-0{padding-top:0 !important}.pr-md-0{padding-right:0 !important}.pb-md-0{padding-bottom:0 !important}.pl-md-0{padding-left:0 !important}.px-md-0{padding-right:0 !important;padding-left:0 !important}.py-md-0{padding-top:0 !important;padding-bottom:0 !important}.p-md-1{padding:4px !important}.pt-md-1{padding-top:4px !important}.pr-md-1{padding-right:4px !important}.pb-md-1{padding-bottom:4px !important}.pl-md-1{padding-left:4px !important}.px-md-1{padding-right:4px !important;padding-left:4px !important}.py-md-1{padding-top:4px !important;padding-bottom:4px !important}.p-md-2{padding:8px !important}.pt-md-2{padding-top:8px !important}.pr-md-2{padding-right:8px !important}.pb-md-2{padding-bottom:8px !important}.pl-md-2{padding-left:8px !important}.px-md-2{padding-right:8px !important;padding-left:8px !important}.py-md-2{padding-top:8px !important;padding-bottom:8px !important}.p-md-3{padding:16px !important}.pt-md-3{padding-top:16px !important}.pr-md-3{padding-right:16px !important}.pb-md-3{padding-bottom:16px !important}.pl-md-3{padding-left:16px !important}.px-md-3{padding-right:16px !important;padding-left:16px !important}.py-md-3{padding-top:16px !important;padding-bottom:16px !important}.p-md-4{padding:24px !important}.pt-md-4{padding-top:24px !important}.pr-md-4{padding-right:24px !important}.pb-md-4{padding-bottom:24px !important}.pl-md-4{padding-left:24px !important}.px-md-4{padding-right:24px !important;padding-left:24px !important}.py-md-4{padding-top:24px !important;padding-bottom:24px !important}.p-md-5{padding:32px !important}.pt-md-5{padding-top:32px !important}.pr-md-5{padding-right:32px !important}.pb-md-5{padding-bottom:32px !important}.pl-md-5{padding-left:32px !important}.px-md-5{padding-right:32px !important;padding-left:32px !important}.py-md-5{padding-top:32px !important;padding-bottom:32px !important}.p-md-6{padding:40px !important}.pt-md-6{padding-top:40px !important}.pr-md-6{padding-right:40px !important}.pb-md-6{padding-bottom:40px !important}.pl-md-6{padding-left:40px !important}.px-md-6{padding-right:40px !important;padding-left:40px !important}.py-md-6{padding-top:40px !important;padding-bottom:40px !important}}@media(min-width: 1012px){.p-lg-0{padding:0 !important}.pt-lg-0{padding-top:0 !important}.pr-lg-0{padding-right:0 !important}.pb-lg-0{padding-bottom:0 !important}.pl-lg-0{padding-left:0 !important}.px-lg-0{padding-right:0 !important;padding-left:0 !important}.py-lg-0{padding-top:0 !important;padding-bottom:0 !important}.p-lg-1{padding:4px !important}.pt-lg-1{padding-top:4px !important}.pr-lg-1{padding-right:4px !important}.pb-lg-1{padding-bottom:4px !important}.pl-lg-1{padding-left:4px !important}.px-lg-1{padding-right:4px !important;padding-left:4px !important}.py-lg-1{padding-top:4px !important;padding-bottom:4px !important}.p-lg-2{padding:8px !important}.pt-lg-2{padding-top:8px !important}.pr-lg-2{padding-right:8px !important}.pb-lg-2{padding-bottom:8px !important}.pl-lg-2{padding-left:8px !important}.px-lg-2{padding-right:8px !important;padding-left:8px !important}.py-lg-2{padding-top:8px !important;padding-bottom:8px !important}.p-lg-3{padding:16px !important}.pt-lg-3{padding-top:16px !important}.pr-lg-3{padding-right:16px !important}.pb-lg-3{padding-bottom:16px !important}.pl-lg-3{padding-left:16px !important}.px-lg-3{padding-right:16px !important;padding-left:16px !important}.py-lg-3{padding-top:16px !important;padding-bottom:16px !important}.p-lg-4{padding:24px !important}.pt-lg-4{padding-top:24px !important}.pr-lg-4{padding-right:24px !important}.pb-lg-4{padding-bottom:24px !important}.pl-lg-4{padding-left:24px !important}.px-lg-4{padding-right:24px !important;padding-left:24px !important}.py-lg-4{padding-top:24px !important;padding-bottom:24px !important}.p-lg-5{padding:32px !important}.pt-lg-5{padding-top:32px !important}.pr-lg-5{padding-right:32px !important}.pb-lg-5{padding-bottom:32px !important}.pl-lg-5{padding-left:32px !important}.px-lg-5{padding-right:32px !important;padding-left:32px !important}.py-lg-5{padding-top:32px !important;padding-bottom:32px !important}.p-lg-6{padding:40px !important}.pt-lg-6{padding-top:40px !important}.pr-lg-6{padding-right:40px !important}.pb-lg-6{padding-bottom:40px !important}.pl-lg-6{padding-left:40px !important}.px-lg-6{padding-right:40px !important;padding-left:40px !important}.py-lg-6{padding-top:40px !important;padding-bottom:40px !important}}@media(min-width: 1280px){.p-xl-0{padding:0 !important}.pt-xl-0{padding-top:0 !important}.pr-xl-0{padding-right:0 !important}.pb-xl-0{padding-bottom:0 !important}.pl-xl-0{padding-left:0 !important}.px-xl-0{padding-right:0 !important;padding-left:0 !important}.py-xl-0{padding-top:0 !important;padding-bottom:0 !important}.p-xl-1{padding:4px !important}.pt-xl-1{padding-top:4px !important}.pr-xl-1{padding-right:4px !important}.pb-xl-1{padding-bottom:4px !important}.pl-xl-1{padding-left:4px !important}.px-xl-1{padding-right:4px !important;padding-left:4px !important}.py-xl-1{padding-top:4px !important;padding-bottom:4px !important}.p-xl-2{padding:8px !important}.pt-xl-2{padding-top:8px !important}.pr-xl-2{padding-right:8px !important}.pb-xl-2{padding-bottom:8px !important}.pl-xl-2{padding-left:8px !important}.px-xl-2{padding-right:8px !important;padding-left:8px !important}.py-xl-2{padding-top:8px !important;padding-bottom:8px !important}.p-xl-3{padding:16px !important}.pt-xl-3{padding-top:16px !important}.pr-xl-3{padding-right:16px !important}.pb-xl-3{padding-bottom:16px !important}.pl-xl-3{padding-left:16px !important}.px-xl-3{padding-right:16px !important;padding-left:16px !important}.py-xl-3{padding-top:16px !important;padding-bottom:16px !important}.p-xl-4{padding:24px !important}.pt-xl-4{padding-top:24px !important}.pr-xl-4{padding-right:24px !important}.pb-xl-4{padding-bottom:24px !important}.pl-xl-4{padding-left:24px !important}.px-xl-4{padding-right:24px !important;padding-left:24px !important}.py-xl-4{padding-top:24px !important;padding-bottom:24px !important}.p-xl-5{padding:32px !important}.pt-xl-5{padding-top:32px !important}.pr-xl-5{padding-right:32px !important}.pb-xl-5{padding-bottom:32px !important}.pl-xl-5{padding-left:32px !important}.px-xl-5{padding-right:32px !important;padding-left:32px !important}.py-xl-5{padding-top:32px !important;padding-bottom:32px !important}.p-xl-6{padding:40px !important}.pt-xl-6{padding-top:40px !important}.pr-xl-6{padding-right:40px !important}.pb-xl-6{padding-bottom:40px !important}.pl-xl-6{padding-left:40px !important}.px-xl-6{padding-right:40px !important;padding-left:40px !important}.py-xl-6{padding-top:40px !important;padding-bottom:40px !important}}.p-responsive{padding-right:16px !important;padding-left:16px !important}@media(min-width: 544px){.p-responsive{padding-right:40px !important;padding-left:40px !important}}@media(min-width: 1012px){.p-responsive{padding-right:16px !important;padding-left:16px !important}}.h1{font-size:26px !important}@media(min-width: 768px){.h1{font-size:32px !important}}.h2{font-size:22px !important}@media(min-width: 768px){.h2{font-size:24px !important}}.h3{font-size:18px !important}@media(min-width: 768px){.h3{font-size:20px !important}}.h4{font-size:16px !important}.h5{font-size:14px !important}.h6{font-size:12px !important}.h1,.h2,.h3,.h4,.h5,.h6{font-weight:600 !important}.f1{font-size:26px !important}@media(min-width: 768px){.f1{font-size:32px !important}}.f2{font-size:22px !important}@media(min-width: 768px){.f2{font-size:24px !important}}.f3{font-size:18px !important}@media(min-width: 768px){.f3{font-size:20px !important}}.f4{font-size:16px !important}@media(min-width: 768px){.f4{font-size:16px !important}}.f5{font-size:14px !important}.f6{font-size:12px !important}.f00-light{font-size:40px !important;font-weight:300 !important}@media(min-width: 768px){.f00-light{font-size:48px !important}}.f0-light{font-size:32px !important;font-weight:300 !important}@media(min-width: 768px){.f0-light{font-size:40px !important}}.f1-light{font-size:26px !important;font-weight:300 !important}@media(min-width: 768px){.f1-light{font-size:32px !important}}.f2-light{font-size:22px !important;font-weight:300 !important}@media(min-width: 768px){.f2-light{font-size:24px !important}}.f3-light{font-size:18px !important;font-weight:300 !important}@media(min-width: 768px){.f3-light{font-size:20px !important}}.text-small{font-size:12px !important}.lead{margin-bottom:30px;font-size:20px;font-weight:300;color:#586069}.lh-condensed-ultra{line-height:1 !important}.lh-condensed{line-height:1.25 !important}.lh-default{line-height:1.5 !important}.lh-0{line-height:0 !important}@media(min-width: 544px){.lh-sm-condensed-ultra{line-height:1 !important}.lh-sm-condensed{line-height:1.25 !important}.lh-sm-default{line-height:1.5 !important}.lh-sm-0{line-height:0 !important}}@media(min-width: 768px){.lh-md-condensed-ultra{line-height:1 !important}.lh-md-condensed{line-height:1.25 !important}.lh-md-default{line-height:1.5 !important}.lh-md-0{line-height:0 !important}}@media(min-width: 1012px){.lh-lg-condensed-ultra{line-height:1 !important}.lh-lg-condensed{line-height:1.25 !important}.lh-lg-default{line-height:1.5 !important}.lh-lg-0{line-height:0 !important}}@media(min-width: 1280px){.lh-xl-condensed-ultra{line-height:1 !important}.lh-xl-condensed{line-height:1.25 !important}.lh-xl-default{line-height:1.5 !important}.lh-xl-0{line-height:0 !important}}.text-right{text-align:right !important}.text-left{text-align:left !important}.text-center{text-align:center !important}@media(min-width: 544px){.text-sm-right{text-align:right !important}.text-sm-left{text-align:left !important}.text-sm-center{text-align:center !important}}@media(min-width: 768px){.text-md-right{text-align:right !important}.text-md-left{text-align:left !important}.text-md-center{text-align:center !important}}@media(min-width: 1012px){.text-lg-right{text-align:right !important}.text-lg-left{text-align:left !important}.text-lg-center{text-align:center !important}}@media(min-width: 1280px){.text-xl-right{text-align:right !important}.text-xl-left{text-align:left !important}.text-xl-center{text-align:center !important}}.text-normal{font-weight:400 !important}.text-bold{font-weight:600 !important}.text-italic{font-style:italic !important}.text-uppercase{text-transform:uppercase !important}.text-underline{text-decoration:underline !important}.no-underline{text-decoration:none !important}.no-wrap{white-space:nowrap !important}.ws-normal{white-space:normal !important}.break-word{word-break:break-word !important;word-wrap:break-word !important;overflow-wrap:break-word !important}.wb-break-all{word-break:break-all !important}.text-emphasized{font-weight:600;color:#24292e}.list-style-none{list-style:none !important}.text-shadow-dark{text-shadow:0 1px 1px rgba(27,31,35,.25),0 1px 25px rgba(27,31,35,.75)}.text-shadow-light{text-shadow:0 1px 0 rgba(255,255,255,.5)}.text-mono{font-family:"SFMono-Regular",Consolas,"Liberation Mono",Menlo,monospace !important}.user-select-none{user-select:none !important}.d-block,.toc.level-1.current>ul,.toc.level-2.current>ul,.toc.level-3.current>ul,.toc.level-4.current>ul,.toc.level-5.current>ul,.toc.level-6.current>ul,.toc.level-7.current>ul,.toc.level-8.current>ul,.toc.level-9.current>ul,.toc.level-10.current>ul,.toc.level-11.current>ul{display:block !important}.d-flex{display:flex !important}.d-inline{display:inline !important}.d-inline-block{display:inline-block !important}.d-inline-flex{display:inline-flex !important}.d-none,.toc>ul{display:none !important}.d-table{display:table !important}.d-table-cell{display:table-cell !important}@media(min-width: 544px){.d-sm-block{display:block !important}.d-sm-flex{display:flex !important}.d-sm-inline{display:inline !important}.d-sm-inline-block{display:inline-block !important}.d-sm-inline-flex{display:inline-flex !important}.d-sm-none{display:none !important}.d-sm-table{display:table !important}.d-sm-table-cell{display:table-cell !important}}@media(min-width: 768px){.d-md-block{display:block !important}.d-md-flex{display:flex !important}.d-md-inline{display:inline !important}.d-md-inline-block{display:inline-block !important}.d-md-inline-flex{display:inline-flex !important}.d-md-none{display:none !important}.d-md-table{display:table !important}.d-md-table-cell{display:table-cell !important}}@media(min-width: 1012px){.d-lg-block{display:block !important}.d-lg-flex{display:flex !important}.d-lg-inline{display:inline !important}.d-lg-inline-block{display:inline-block !important}.d-lg-inline-flex{display:inline-flex !important}.d-lg-none{display:none !important}.d-lg-table{display:table !important}.d-lg-table-cell{display:table-cell !important}}@media(min-width: 1280px){.d-xl-block{display:block !important}.d-xl-flex{display:flex !important}.d-xl-inline{display:inline !important}.d-xl-inline-block{display:inline-block !important}.d-xl-inline-flex{display:inline-flex !important}.d-xl-none{display:none !important}.d-xl-table{display:table !important}.d-xl-table-cell{display:table-cell !important}}.v-hidden{visibility:hidden !important}.v-visible{visibility:visible !important}@media(max-width: 543px){.hide-sm{display:none !important}}@media(min-width: 544px)and (max-width: 767px){.hide-md{display:none !important}}@media(min-width: 768px)and (max-width: 1011px){.hide-lg{display:none !important}}@media(min-width: 1012px){.hide-xl{display:none !important}}.table-fixed{table-layout:fixed !important}.sr-only{position:absolute;width:1px;height:1px;padding:0;overflow:hidden;clip:rect(0, 0, 0, 0);word-wrap:normal;border:0}.show-on-focus{position:absolute;width:1px;height:1px;margin:0;overflow:hidden;clip:rect(1px, 1px, 1px, 1px)}.show-on-focus:focus{z-index:20;width:auto;height:auto;clip:auto} diff --git a/assets/images/Bootable/AutoUnattend.xml b/assets/images/Bootable/AutoUnattend.xml new file mode 100644 index 00000000000..9a343fc91c4 --- /dev/null +++ b/assets/images/Bootable/AutoUnattend.xml @@ -0,0 +1,133 @@ + + + + + + + + +1 +cmd /q /c "FOR %i IN (C D E F G H I J K L N M O P Q R S T U V W X Y Z) DO IF EXIST %i:\FIRADISK\LOADISO.CMD cmd /k %i:\FIRADISK\LOADISO.cmd" +Detecting usb drive + + + + +true + +H3N87-KPGJ8-6H6DT-H6FCH-3JXT7 + + + + + + + + +1 +cmd /q /c "FOR %i IN (C D E F G H I J K L N M O P Q R S T U V W X Y Z) DO IF EXIST %i:\FIRADISK\LOADISO.CMD cmd /k %i:\FIRADISK\LOADISO.cmd" +Detecting usb drive + + + + +true + +H3N87-KPGJ8-6H6DT-H6FCH-3JXT7 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/assets/images/Bootable/BackUpRestoreMenu.lst b/assets/images/Bootable/BackUpRestoreMenu.lst new file mode 100644 index 00000000000..cbc865126fd --- /dev/null +++ b/assets/images/Bootable/BackUpRestoreMenu.lst @@ -0,0 +1,84 @@ +#version 4 2012.02.19 + +#check version of grub4dos +checkrange 20120201:-1 read 0x8278 || pause --wait=3 Please use grub4dos-0.4.5c-2012-02-01 or later! && exit 1 + +write (md)0x220+1 !BAT\necho -n -P:0000 $[0133] --- Abhijeet's Multiboot USB Drive--- \0 +initscript (md)0x220+1 + +write 0x8274 0x2001 + +color black/cyan yellow/cyan +#timeout 5 +default 1 +debug 1 + +#uncomment this for a hi-res background - but changes menu behaviour +gfxmenu /message + +#comment this next line out if you don't want a background image at all +#splashimage /back.xpm.gz +#foreground 555599 +#background 661100 + +clear + +title ----------- Partition Backup and Restore ------------- +root + +iftitle [if exist /_iso/Tools/acronis-trueimage-14.iso] Acronis True Image 2014 Premium +find --set-root /_iso/Tools/acronis-trueimage-14.iso +map /_iso/Tools/acronis-trueimage-14.iso (hd32) +map --hook +root (hd32) +chainloader (hd32) + +iftitle [if exist /_iso/Tools/acronis-trueimage-12.iso] Acronis True Image 2012 Home +find --set-root /_iso/Tools/acronis-trueimage-12.iso +map /_iso/Tools/acronis-trueimage-12.iso (hd32) +map --hook +root (hd32) +chainloader (hd32) + +iftitle [if exist /_iso/Tools/ParagonBackupRestore2012Free.iso] Paragon Backup & Restore 2012 Free +find --set-root /_iso/Tools/ParagonBackupRestore2012Free.iso +map /_iso/Tools/ParagonBackupRestore2012Free.iso (hd32) +map --hook +root (hd32) +chainloader (hd32) + +title Parted Magic 2012-04 +find --set-root /_iso/Tools/pmagic_2012_04_21.iso +map /_iso/Tools/pmagic_2012_04_21.iso (hd32) || map --mem /_iso/Tools/pmagic_2012_04_21.iso (hd32) +map --hook +root (hd32) +kernel /pmagic/bzImage iso_filename=/_iso/Tools/pmagic_2012_04_21.iso noapic load_ramdisk=1 prompt_ramdisk=0 rw vga=normal loglevel=9 max_loop=256 vmalloc=256MiB +initrd /pmagic/initrd.img + + +title Back to Main Menu +configfile /Menu.lst + +title +root + +title ----------- System Option ------------- +root + +title Boot from 1st Hard Disk +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +chainloader (hd0)+1 +rootnoverify (hd0) + +title Reboot \nReboot system +savedefault --wait=2 +reboot + +title Switch Off system +savedefault --wait=2 +halt + +title Reload menu\nReload the menu.lst file +configfile /menu.lst \ No newline at end of file diff --git a/assets/images/Bootable/DiskManagemenMenu.lst b/assets/images/Bootable/DiskManagemenMenu.lst new file mode 100644 index 00000000000..360740cc0e6 --- /dev/null +++ b/assets/images/Bootable/DiskManagemenMenu.lst @@ -0,0 +1,77 @@ +#version 4 2012.02.19 + +#check version of grub4dos +checkrange 20120201:-1 read 0x8278 || pause --wait=3 Please use grub4dos-0.4.5c-2012-02-01 or later! && exit 1 + +write (md)0x220+1 !BAT\necho -n -P:0000 $[0133] --- Abhijeet's Multiboot USB Drive--- \0 +initscript (md)0x220+1 + +write 0x8274 0x2001 + +color black/cyan yellow/cyan +#timeout 5 +default 1 +debug 1 + +#uncomment this for a hi-res background - but changes menu behaviour +gfxmenu /message + +#comment this next line out if you don't want a background image at all +#splashimage /back.xpm.gz +#foreground 555599 +#background 661100 + +clear + +title ----------- Disk Management ------------- +root + +iftitle [if exist /_iso/Tools/DiskDirectorSuite11.iso] Acronis Disk Director Suite 11 +find --set-root /_iso/Tools/DiskDirectorSuite11.iso +map /_iso/Tools/DiskDirectorSuite11.iso (hd32) +map --hook +root (hd32) +chainloader (hd32) + +iftitle [if exist /_iso/Tools/ParagonPatitionMgrPersonal11.iso] Paragon Partition MGR Personal 11 +find --set-root /_iso/Tools/ParagonPatitionMgrPersonal11.iso +map /_iso/Tools/ParagonPatitionMgrPersonal11.iso (hd32) +map --hook +root (hd32) +chainloader (hd32) + +title Parted Magic 2012-04 +find --set-root /_iso/Tools/pmagic_2012_04_21.iso +map /_iso/Tools/pmagic_2012_04_21.iso (hd32) || map --mem /_iso/Tools/pmagic_2012_04_21.iso (hd32) +map --hook +root (hd32) +kernel /pmagic/bzImage iso_filename=/_iso/Tools/pmagic_2012_04_21.iso noapic load_ramdisk=1 prompt_ramdisk=0 rw vga=normal loglevel=9 max_loop=256 vmalloc=256MiB +initrd /pmagic/initrd.img + + +title Back to Main Menu +configfile /Menu.lst + +title +root + +title ----------- System Option ------------- +root + +title Boot from 1st Hard Disk +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +chainloader (hd0)+1 +rootnoverify (hd0) + +title Reboot \nReboot system +savedefault --wait=2 +reboot + +title Switch Off system +savedefault --wait=2 +halt + +title Reload menu\nReload the menu.lst file +configfile /menu.lst \ No newline at end of file diff --git a/assets/images/Bootable/Menu.lst b/assets/images/Bootable/Menu.lst new file mode 100644 index 00000000000..d52c8b81d35 --- /dev/null +++ b/assets/images/Bootable/Menu.lst @@ -0,0 +1,148 @@ +#Author: Abhijeet Nayak +#Date 2013.11.1 + +#check version of grub4dos +checkrange 20120201:-1 read 0x8278 || pause --wait=3 Please use grub4dos-0.4.5c-2012-02-01 or later! && exit 1 + +write (md)0x220+1 !BAT\necho -n -P:0000 $[0133] --- Abhijeet's Multiboot USB Drive--- \0 +initscript (md)0x220+1 + +write 0x8274 0x2001 + +color black/cyan yellow/cyan +#timeout 5 +default 1 +debug 1 + +#uncomment this for a hi-res background - but changes menu behaviour +gfxmenu /message + +#comment this next line out if you don't want a background image at all +#splashimage /back.xpm.gz +#foreground 555599 +#background 661100 + +clear + +title --- Abhijeet's Multi Boot USB Drive --- +root +title ----------- System Tools ------------- +root + +title Partition Backup & Restore +configfile /BackUpRestoreMenu.lst + +title Disk Management Tools +configfile /DiskManagemenMenu.lst + +title Other Tools +configfile /OtherToolsMenu.lst + + +title ---------- Operating Systems ---------- +root + +title Windows 8 Professional 64Bit +debug off +set MYISO=Win8.iso +dd if=()/firadisk/auwin8.xml of=()/AutoUnattend.xml +dd if=()/firadisk/spaces.txt of=()/firadisk/ISONAME.CMD +write ()/firadisk/ISONAME.CMD SET MYISO=\\_iso\\Windows\\%MYISO%\r\n +map --mem (md)0x800+4 (99) +map /_iso/Windows/%MYISO% (0xff) +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +write (99) [FiraDisk]\nStartOptions=cdrom,vmem=find:/_iso/Windows/%MYISO%;\n\0 +chainloader (0xff)/BOOTMGR || chainloader (0xff) + +iftitle [if exist /_iso/Windows/Win7.iso] WINDOWS 7 SP1 32Bit & 64Bit +debug off +set MYISO=Win7.iso +dd if=()/firadisk/au.xml of=()/AutoUnattend.xml +dd if=()/firadisk/spaces.txt of=()/firadisk/ISONAME.CMD +write ()/firadisk/ISONAME.CMD SET MYISO=\\_iso\\Windows\\%MYISO%\r\n +map --mem (md)0x800+4 (99) +echo Mapping /_iso/Windows/%MYISO% as an optical drive... +map /_iso/Windows/%MYISO% (0xff) +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +write (99) [FiraDisk]\nStartOptions=cdrom,vmem=find:/_iso/Windows/%MYISO%;\n\0 +chainloader (0xff)/BOOTMGR || chainloader (0xff) + +# note: --mem is not needed to load XP.ISO in this step +iftitle [if exist /_iso/Windows/XPPROSP3.iso]Windows XP (Remember to select both AHCI driver AND winvbloc/FiraDisk driver ) +find --set-root --ignore-floppies --ignore-cd /winvblock.ima.gz +map --mem /winvblock.ima.gz (fd0) +map --mem /winvblock.ima.gz (fd1) +# if this loads the ISO into memory slowly - then you need to run WinContig on the ISO file on your USB drive to speed it up! +map /_iso/Windows/XPPROSP3.iso (0xff) || map --mem /_iso/Windows/XPPROSP3.iso (0xff) +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +root (0xff) +chainloader (0xff)/i386/setupldr.bin || chainloader (0xff)/I386/SETUPLDR.BIN || chainloader (0xff) +pause If you have an AHCI HDD you MUST press F6 when prompted, then hit S to select WinVBlock or FiraDisk (recommended) driver, then hit S again to select your AHCI driver (e.g. Atom Netbook=WinVBlock+ICH7R/DH, DQ67 series 6=FiraDisk+Desktop,Workstation,Server Express) +pause Now quickly hit [Enter] twice (and then F6 if you need to install an AHCI driver) ... + +title Linux Mint 16 64Bit +find --set-root /_iso/Linux/linuxmint16.iso +map /_iso/Linux/linuxmint16.iso (0xff) || map --mem /_iso/Linux/linuxmint16.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/linuxmint16.iso splash +initrd /casper/initrd.lz + +title Ubuntu 13.10 Desktop +find --set-root /_iso/Linux/ubuntu1310.iso +map /_iso/Linux/ubuntu1310.iso (0xff) || map --mem /_iso/Linux/ubuntu1310.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz.efi cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/ubuntu1310.iso splash +initrd /casper/initrd.lz + +title Ubuntu 13.04 Desktop +find --set-root /_iso/Linux/ubuntu1304.iso +map /_iso/Linux/ubuntu1304.iso (0xff) || map --mem /_iso/Linux/ubuntu1304.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz.efi cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/ubuntu1304.iso splash +initrd /casper/initrd.lz + +title Xubuntu 13.04 Desktop +find --set-root /_iso/Linux/xubuntu1304.iso +map /_iso/Linux/xubuntu1304.iso (0xff) || map --mem /_iso/Linux/xubuntu1304.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/xubuntu1304.iso splash +initrd /casper/initrd.lz + +title Ubuntu 12.04 Desktop +find --set-root /_iso/Linux/ubuntu1204.iso +map /_iso/Linux/ubuntu1204.iso (0xff) || map --mem /_iso/Linux/ubuntu1204.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/ubuntu1204.iso splash +initrd /casper/initrd.lz + +#title +#root + +title ----------- System Option ------------- +root + +title Boot from 1st Hard Disk +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +chainloader (hd0)+1 +rootnoverify (hd0) + +title Reboot \nReboot system +savedefault --wait=2 +reboot + +title Switch Off system +savedefault --wait=2 +halt diff --git a/assets/images/Bootable/Menu_backup.lst b/assets/images/Bootable/Menu_backup.lst new file mode 100644 index 00000000000..219e052268f --- /dev/null +++ b/assets/images/Bootable/Menu_backup.lst @@ -0,0 +1,139 @@ +#version 4 2012.02.19 + +#check version of grub4dos +checkrange 20120201:-1 read 0x8278 || pause --wait=3 Please use grub4dos-0.4.5c-2012-02-01 or later! && exit 1 + +write (md)0x220+1 !BAT\necho -n -P:0000 $[0133] --- Abhijeet's Multiboot USB Drive--- \0 +initscript (md)0x220+1 + +write 0x8274 0x2001 + +color black/cyan yellow/cyan +#timeout 5 +default 1 +debug 1 + +#uncomment this for a hi-res background - but changes menu behaviour +gfxmenu /message + +#comment this next line out if you don't want a background image at all +#splashimage /back.xpm.gz +#foreground 555599 +#background 661100 + +clear + +title --- Abhijeet's Multi Boot USB Drive --- +root +title ----------- System Tools ------------- +root + +title Partition Backup & Restore +configfile /BackUpRestoreMenu.lst + +title Disk Management Tools +configfile /DiskManagemenMenu.lst + +title Other Tools +configfile /OtherToolsMenu.lst + + +title ---------- Operating Systems ---------- +root + +iftitle [if exist /_iso/Windows/Win7.iso] WINDOWS 7 SP1 32Bit & 64Bit +debug off +set MYISO=Win7.iso +dd if=()/firadisk/au.xml of=()/AutoUnattend.xml +dd if=()/firadisk/spaces.txt of=()/firadisk/ISONAME.CMD +write ()/firadisk/ISONAME.CMD SET MYISO=\\_iso\\Windows\\%MYISO%\r\n +map --mem (md)0x800+4 (99) +echo Mapping /_iso/Windows/%MYISO% as an optical drive... +map /_iso/Windows/%MYISO% (0xff) +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +write (99) [FiraDisk]\nStartOptions=cdrom,vmem=find:/_iso/Windows/%MYISO%;\n\0 +chainloader (0xff)/BOOTMGR || chainloader (0xff) + +title Windows 8 Professional 64Bit +debug off +set MYISO=Win8.iso +dd if=()/firadisk/auwin8.xml of=()/AutoUnattend.xml +dd if=()/firadisk/spaces.txt of=()/firadisk/ISONAME.CMD +write ()/firadisk/ISONAME.CMD SET MYISO=\\_iso\\Windows\\%MYISO%\r\n +map --mem (md)0x800+4 (99) +map /_iso/Windows/%MYISO% (0xff) +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +write (99) [FiraDisk]\nStartOptions=cdrom,vmem=find:/_iso/Windows/%MYISO%;\n\0 +chainloader (0xff)/BOOTMGR || chainloader (0xff) + +# note: --mem is not needed to load XP.ISO in this step +iftitle [if exist /_iso/Windows/XPPROSP3.iso]Windows XP (Remember to select both AHCI driver AND winvbloc/FiraDisk driver ) +find --set-root --ignore-floppies --ignore-cd /winvblock.ima.gz +map --mem /winvblock.ima.gz (fd0) +map --mem /winvblock.ima.gz (fd1) +# if this loads the ISO into memory slowly - then you need to run WinContig on the ISO file on your USB drive to speed it up! +map /_iso/Windows/XPPROSP3.iso (0xff) || map --mem /_iso/Windows/XPPROSP3.iso (0xff) +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +root (0xff) +chainloader (0xff)/i386/setupldr.bin || chainloader (0xff)/I386/SETUPLDR.BIN || chainloader (0xff) +pause If you have an AHCI HDD you MUST press F6 when prompted, then hit S to select WinVBlock or FiraDisk (recommended) driver, then hit S again to select your AHCI driver (e.g. Atom Netbook=WinVBlock+ICH7R/DH, DQ67 series 6=FiraDisk+Desktop,Workstation,Server Express) +pause Now quickly hit [Enter] twice (and then F6 if you need to install an AHCI driver) ... + +title Xubuntu 13.04 Desktop +find --set-root /_iso/Linux/xubuntu1304.iso +map /_iso/Linux/xubuntu1304.iso (0xff) || map --mem /_iso/Linux/xubuntu1304.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/xubuntu1304.iso splash +initrd /casper/initrd.lz + +title Ubuntu 13.04 Desktop +find --set-root /_iso/Linux/ubuntu1304.iso +map /_iso/Linux/ubuntu1304.iso (0xff) || map --mem /_iso/Linux/ubuntu1304.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz.efi cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/ubuntu1304.iso splash +initrd /casper/initrd.lz + +title Zorin OS 7 Core 64Bit +find --set-root /_iso/Linux/zorin-os-7-core-64.iso +map /_iso/Linux/zorin-os-7-core-64.iso (0xff) || map --mem /_iso/Linux/zorin-os-7-core-64.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz.efi cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/zorin-os-7-core-64.iso splash +initrd /casper/initrd.lz + +title Ubuntu 12.04 Desktop +find --set-root /_iso/Linux/ubuntu1204.iso +map /_iso/Linux/ubuntu1204.iso (0xff) || map --mem /_iso/Linux/ubuntu1204.iso (0xff) +map --hook +root (0xff) +kernel /casper/vmlinuz cdrom-detect/try-usb=true file=/cdrom/preseed/ubuntu.seed noprompt boot=casper only-ubiquity iso-scan/filename=/_iso/Linux/ubuntu1204.iso splash +initrd /casper/initrd.lz + +#title +#root + +title ----------- System Option ------------- +root + +title Boot from 1st Hard Disk +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +chainloader (hd0)+1 +rootnoverify (hd0) + +title Reboot \nReboot system +savedefault --wait=2 +reboot + +title Switch Off system +savedefault --wait=2 +halt diff --git a/assets/images/Bootable/OtherToolsMenu.lst b/assets/images/Bootable/OtherToolsMenu.lst new file mode 100644 index 00000000000..84e7ebe23cd --- /dev/null +++ b/assets/images/Bootable/OtherToolsMenu.lst @@ -0,0 +1,64 @@ +#version 4 2012.02.19 + +#check version of grub4dos +checkrange 20120201:-1 read 0x8278 || pause --wait=3 Please use grub4dos-0.4.5c-2012-02-01 or later! && exit 1 + +write (md)0x220+1 !BAT\necho -n -P:0000 $[0133] --- Abhijeet's Multiboot USB Drive--- \0 +initscript (md)0x220+1 + +write 0x8274 0x2001 + +color black/cyan yellow/cyan +#timeout 5 +default 1 +debug 1 + +#uncomment this for a hi-res background - but changes menu behaviour +gfxmenu /message + +#comment this next line out if you don't want a background image at all +#splashimage /back.xpm.gz +#foreground 555599 +#background 661100 + +clear + +title ----------- Disk Management ------------- +root + +title Hirens Boot CD 15.1 +configfile /HBCD/menu.lst + +iftitle [if exist /_iso/Tools/ParagonRescueKit2012Free.iso] Paragon Rescue Kit 2012 Free +find --set-root /_iso/Tools/ParagonRescueKit2012Free.iso +map /_iso/Tools/ParagonRescueKit2012Free.iso (hd32) +map --hook +root (hd32) +chainloader (hd32) + +title Back to Main Menu +configfile /Menu.lst + +title +root + +title ----------- System Option ------------- +root + +title Boot from 1st Hard Disk +map (hd0) (hd1) +map (hd1) (hd0) +map --hook +chainloader (hd0)+1 +rootnoverify (hd0) + +title Reboot \nReboot system +savedefault --wait=2 +reboot + +title Switch Off system +savedefault --wait=2 +halt + +title Reload menu\nReload the menu.lst file +configfile /menu.lst \ No newline at end of file diff --git a/assets/images/Bootable/back.xpm.gz b/assets/images/Bootable/back.xpm.gz new file mode 100644 index 00000000000..ea6d65a3946 Binary files /dev/null and b/assets/images/Bootable/back.xpm.gz differ diff --git a/assets/images/Bootable/grldr b/assets/images/Bootable/grldr new file mode 100644 index 00000000000..afcb62cfeb8 Binary files /dev/null and b/assets/images/Bootable/grldr differ diff --git a/assets/images/Bootable/link b/assets/images/Bootable/link new file mode 100644 index 00000000000..5c26eaf5d77 --- /dev/null +++ b/assets/images/Bootable/link @@ -0,0 +1,7 @@ +http://xubuntugeek.blogspot.com/2012/10/solved-amd-catalyst-and-ubuntu-1210.html + +xfce4-appfinder + +http://www.techlw.com/2013/01/install-amd-ati-drivers-in-ubuntu.html + +qweZXC123ASD \ No newline at end of file diff --git a/assets/images/Bootable/message b/assets/images/Bootable/message new file mode 100644 index 00000000000..70dcd9f2c15 Binary files /dev/null and b/assets/images/Bootable/message differ diff --git a/assets/images/Bootable/winvblock.ima.gz b/assets/images/Bootable/winvblock.ima.gz new file mode 100644 index 00000000000..d38387a1a2a Binary files /dev/null and b/assets/images/Bootable/winvblock.ima.gz differ diff --git a/assets/images/apple-touch-icon-300x300.jpg b/assets/images/apple-touch-icon-300x300.jpg new file mode 100644 index 00000000000..a34cbb01754 Binary files /dev/null and b/assets/images/apple-touch-icon-300x300.jpg differ diff --git a/assets/images/favicon-16x16.png b/assets/images/favicon-16x16.png new file mode 100644 index 00000000000..a829e875278 Binary files /dev/null and b/assets/images/favicon-16x16.png differ diff --git a/assets/images/favicon-32x32.png b/assets/images/favicon-32x32.png new file mode 100644 index 00000000000..42e8a6de70c Binary files /dev/null and b/assets/images/favicon-32x32.png differ diff --git a/assets/images/favicon-96x96.png b/assets/images/favicon-96x96.png new file mode 100644 index 00000000000..4725c950461 Binary files /dev/null and b/assets/images/favicon-96x96.png differ diff --git a/assets/images/favicon.svg b/assets/images/favicon.svg new file mode 100644 index 00000000000..47b1d23b161 --- /dev/null +++ b/assets/images/favicon.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/assets/js/jquery.min.js b/assets/js/jquery.min.js new file mode 100644 index 00000000000..b0614034ad3 --- /dev/null +++ b/assets/js/jquery.min.js @@ -0,0 +1,2 @@ +/*! jQuery v3.5.1 | (c) JS Foundation and other contributors | jquery.org/license */ +!function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],r=Object.getPrototypeOf,s=t.slice,g=t.flat?function(e){return t.flat.call(e)}:function(e){return t.concat.apply([],e)},u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType},x=function(e){return null!=e&&e===e.window},E=C.document,c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof e?n[o.call(e)]||"object":typeof e}var f="3.5.1",S=function(e,t){return new S.fn.init(e,t)};function p(e){var t=!!e&&"length"in e&&e.length,n=w(e);return!m(e)&&!x(e)&&("array"===n||0===t||"number"==typeof t&&0+~]|"+M+")"+M+"*"),U=new RegExp(M+"|>"),X=new RegExp(F),V=new RegExp("^"+I+"$"),G={ID:new RegExp("^#("+I+")"),CLASS:new RegExp("^\\.("+I+")"),TAG:new RegExp("^("+I+"|[*])"),ATTR:new RegExp("^"+W),PSEUDO:new RegExp("^"+F),CHILD:new RegExp("^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\("+M+"*(even|odd|(([+-]|)(\\d*)n|)"+M+"*(?:([+-]|)"+M+"*(\\d+)|))"+M+"*\\)|)","i"),bool:new RegExp("^(?:"+R+")$","i"),needsContext:new RegExp("^"+M+"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\("+M+"*((?:-\\d)?\\d*)"+M+"*\\)|)(?=[^-]|$)","i")},Y=/HTML$/i,Q=/^(?:input|select|textarea|button)$/i,J=/^h\d$/i,K=/^[^{]+\{\s*\[native \w/,Z=/^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,ee=/[+~]/,te=new RegExp("\\\\[\\da-fA-F]{1,6}"+M+"?|\\\\([^\\r\\n\\f])","g"),ne=function(e,t){var n="0x"+e.slice(1)-65536;return t||(n<0?String.fromCharCode(n+65536):String.fromCharCode(n>>10|55296,1023&n|56320))},re=/([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,ie=function(e,t){return t?"\0"===e?"\ufffd":e.slice(0,-1)+"\\"+e.charCodeAt(e.length-1).toString(16)+" ":"\\"+e},oe=function(){T()},ae=be(function(e){return!0===e.disabled&&"fieldset"===e.nodeName.toLowerCase()},{dir:"parentNode",next:"legend"});try{H.apply(t=O.call(p.childNodes),p.childNodes),t[p.childNodes.length].nodeType}catch(e){H={apply:t.length?function(e,t){L.apply(e,O.call(t))}:function(e,t){var n=e.length,r=0;while(e[n++]=t[r++]);e.length=n-1}}}function se(t,e,n,r){var i,o,a,s,u,l,c,f=e&&e.ownerDocument,p=e?e.nodeType:9;if(n=n||[],"string"!=typeof t||!t||1!==p&&9!==p&&11!==p)return n;if(!r&&(T(e),e=e||C,E)){if(11!==p&&(u=Z.exec(t)))if(i=u[1]){if(9===p){if(!(a=e.getElementById(i)))return n;if(a.id===i)return n.push(a),n}else if(f&&(a=f.getElementById(i))&&y(e,a)&&a.id===i)return n.push(a),n}else{if(u[2])return H.apply(n,e.getElementsByTagName(t)),n;if((i=u[3])&&d.getElementsByClassName&&e.getElementsByClassName)return H.apply(n,e.getElementsByClassName(i)),n}if(d.qsa&&!N[t+" "]&&(!v||!v.test(t))&&(1!==p||"object"!==e.nodeName.toLowerCase())){if(c=t,f=e,1===p&&(U.test(t)||z.test(t))){(f=ee.test(t)&&ye(e.parentNode)||e)===e&&d.scope||((s=e.getAttribute("id"))?s=s.replace(re,ie):e.setAttribute("id",s=S)),o=(l=h(t)).length;while(o--)l[o]=(s?"#"+s:":scope")+" "+xe(l[o]);c=l.join(",")}try{return H.apply(n,f.querySelectorAll(c)),n}catch(e){N(t,!0)}finally{s===S&&e.removeAttribute("id")}}}return g(t.replace($,"$1"),e,n,r)}function ue(){var r=[];return function e(t,n){return r.push(t+" ")>b.cacheLength&&delete e[r.shift()],e[t+" "]=n}}function le(e){return e[S]=!0,e}function ce(e){var t=C.createElement("fieldset");try{return!!e(t)}catch(e){return!1}finally{t.parentNode&&t.parentNode.removeChild(t),t=null}}function fe(e,t){var n=e.split("|"),r=n.length;while(r--)b.attrHandle[n[r]]=t}function pe(e,t){var n=t&&e,r=n&&1===e.nodeType&&1===t.nodeType&&e.sourceIndex-t.sourceIndex;if(r)return r;if(n)while(n=n.nextSibling)if(n===t)return-1;return e?1:-1}function de(t){return function(e){return"input"===e.nodeName.toLowerCase()&&e.type===t}}function he(n){return function(e){var t=e.nodeName.toLowerCase();return("input"===t||"button"===t)&&e.type===n}}function ge(t){return function(e){return"form"in e?e.parentNode&&!1===e.disabled?"label"in e?"label"in e.parentNode?e.parentNode.disabled===t:e.disabled===t:e.isDisabled===t||e.isDisabled!==!t&&ae(e)===t:e.disabled===t:"label"in e&&e.disabled===t}}function ve(a){return le(function(o){return o=+o,le(function(e,t){var n,r=a([],e.length,o),i=r.length;while(i--)e[n=r[i]]&&(e[n]=!(t[n]=e[n]))})})}function ye(e){return e&&"undefined"!=typeof e.getElementsByTagName&&e}for(e in d=se.support={},i=se.isXML=function(e){var t=e.namespaceURI,n=(e.ownerDocument||e).documentElement;return!Y.test(t||n&&n.nodeName||"HTML")},T=se.setDocument=function(e){var t,n,r=e?e.ownerDocument||e:p;return r!=C&&9===r.nodeType&&r.documentElement&&(a=(C=r).documentElement,E=!i(C),p!=C&&(n=C.defaultView)&&n.top!==n&&(n.addEventListener?n.addEventListener("unload",oe,!1):n.attachEvent&&n.attachEvent("onunload",oe)),d.scope=ce(function(e){return a.appendChild(e).appendChild(C.createElement("div")),"undefined"!=typeof e.querySelectorAll&&!e.querySelectorAll(":scope fieldset div").length}),d.attributes=ce(function(e){return e.className="i",!e.getAttribute("className")}),d.getElementsByTagName=ce(function(e){return e.appendChild(C.createComment("")),!e.getElementsByTagName("*").length}),d.getElementsByClassName=K.test(C.getElementsByClassName),d.getById=ce(function(e){return a.appendChild(e).id=S,!C.getElementsByName||!C.getElementsByName(S).length}),d.getById?(b.filter.ID=function(e){var t=e.replace(te,ne);return function(e){return e.getAttribute("id")===t}},b.find.ID=function(e,t){if("undefined"!=typeof t.getElementById&&E){var n=t.getElementById(e);return n?[n]:[]}}):(b.filter.ID=function(e){var n=e.replace(te,ne);return function(e){var t="undefined"!=typeof e.getAttributeNode&&e.getAttributeNode("id");return t&&t.value===n}},b.find.ID=function(e,t){if("undefined"!=typeof t.getElementById&&E){var n,r,i,o=t.getElementById(e);if(o){if((n=o.getAttributeNode("id"))&&n.value===e)return[o];i=t.getElementsByName(e),r=0;while(o=i[r++])if((n=o.getAttributeNode("id"))&&n.value===e)return[o]}return[]}}),b.find.TAG=d.getElementsByTagName?function(e,t){return"undefined"!=typeof t.getElementsByTagName?t.getElementsByTagName(e):d.qsa?t.querySelectorAll(e):void 0}:function(e,t){var n,r=[],i=0,o=t.getElementsByTagName(e);if("*"===e){while(n=o[i++])1===n.nodeType&&r.push(n);return r}return o},b.find.CLASS=d.getElementsByClassName&&function(e,t){if("undefined"!=typeof t.getElementsByClassName&&E)return t.getElementsByClassName(e)},s=[],v=[],(d.qsa=K.test(C.querySelectorAll))&&(ce(function(e){var t;a.appendChild(e).innerHTML="",e.querySelectorAll("[msallowcapture^='']").length&&v.push("[*^$]="+M+"*(?:''|\"\")"),e.querySelectorAll("[selected]").length||v.push("\\["+M+"*(?:value|"+R+")"),e.querySelectorAll("[id~="+S+"-]").length||v.push("~="),(t=C.createElement("input")).setAttribute("name",""),e.appendChild(t),e.querySelectorAll("[name='']").length||v.push("\\["+M+"*name"+M+"*="+M+"*(?:''|\"\")"),e.querySelectorAll(":checked").length||v.push(":checked"),e.querySelectorAll("a#"+S+"+*").length||v.push(".#.+[+~]"),e.querySelectorAll("\\\f"),v.push("[\\r\\n\\f]")}),ce(function(e){e.innerHTML="";var t=C.createElement("input");t.setAttribute("type","hidden"),e.appendChild(t).setAttribute("name","D"),e.querySelectorAll("[name=d]").length&&v.push("name"+M+"*[*^$|!~]?="),2!==e.querySelectorAll(":enabled").length&&v.push(":enabled",":disabled"),a.appendChild(e).disabled=!0,2!==e.querySelectorAll(":disabled").length&&v.push(":enabled",":disabled"),e.querySelectorAll("*,:x"),v.push(",.*:")})),(d.matchesSelector=K.test(c=a.matches||a.webkitMatchesSelector||a.mozMatchesSelector||a.oMatchesSelector||a.msMatchesSelector))&&ce(function(e){d.disconnectedMatch=c.call(e,"*"),c.call(e,"[s!='']:x"),s.push("!=",F)}),v=v.length&&new RegExp(v.join("|")),s=s.length&&new RegExp(s.join("|")),t=K.test(a.compareDocumentPosition),y=t||K.test(a.contains)?function(e,t){var n=9===e.nodeType?e.documentElement:e,r=t&&t.parentNode;return e===r||!(!r||1!==r.nodeType||!(n.contains?n.contains(r):e.compareDocumentPosition&&16&e.compareDocumentPosition(r)))}:function(e,t){if(t)while(t=t.parentNode)if(t===e)return!0;return!1},D=t?function(e,t){if(e===t)return l=!0,0;var n=!e.compareDocumentPosition-!t.compareDocumentPosition;return n||(1&(n=(e.ownerDocument||e)==(t.ownerDocument||t)?e.compareDocumentPosition(t):1)||!d.sortDetached&&t.compareDocumentPosition(e)===n?e==C||e.ownerDocument==p&&y(p,e)?-1:t==C||t.ownerDocument==p&&y(p,t)?1:u?P(u,e)-P(u,t):0:4&n?-1:1)}:function(e,t){if(e===t)return l=!0,0;var n,r=0,i=e.parentNode,o=t.parentNode,a=[e],s=[t];if(!i||!o)return e==C?-1:t==C?1:i?-1:o?1:u?P(u,e)-P(u,t):0;if(i===o)return pe(e,t);n=e;while(n=n.parentNode)a.unshift(n);n=t;while(n=n.parentNode)s.unshift(n);while(a[r]===s[r])r++;return r?pe(a[r],s[r]):a[r]==p?-1:s[r]==p?1:0}),C},se.matches=function(e,t){return se(e,null,null,t)},se.matchesSelector=function(e,t){if(T(e),d.matchesSelector&&E&&!N[t+" "]&&(!s||!s.test(t))&&(!v||!v.test(t)))try{var n=c.call(e,t);if(n||d.disconnectedMatch||e.document&&11!==e.document.nodeType)return n}catch(e){N(t,!0)}return 0":{dir:"parentNode",first:!0}," ":{dir:"parentNode"},"+":{dir:"previousSibling",first:!0},"~":{dir:"previousSibling"}},preFilter:{ATTR:function(e){return e[1]=e[1].replace(te,ne),e[3]=(e[3]||e[4]||e[5]||"").replace(te,ne),"~="===e[2]&&(e[3]=" "+e[3]+" "),e.slice(0,4)},CHILD:function(e){return e[1]=e[1].toLowerCase(),"nth"===e[1].slice(0,3)?(e[3]||se.error(e[0]),e[4]=+(e[4]?e[5]+(e[6]||1):2*("even"===e[3]||"odd"===e[3])),e[5]=+(e[7]+e[8]||"odd"===e[3])):e[3]&&se.error(e[0]),e},PSEUDO:function(e){var t,n=!e[6]&&e[2];return G.CHILD.test(e[0])?null:(e[3]?e[2]=e[4]||e[5]||"":n&&X.test(n)&&(t=h(n,!0))&&(t=n.indexOf(")",n.length-t)-n.length)&&(e[0]=e[0].slice(0,t),e[2]=n.slice(0,t)),e.slice(0,3))}},filter:{TAG:function(e){var t=e.replace(te,ne).toLowerCase();return"*"===e?function(){return!0}:function(e){return e.nodeName&&e.nodeName.toLowerCase()===t}},CLASS:function(e){var t=m[e+" "];return t||(t=new RegExp("(^|"+M+")"+e+"("+M+"|$)"))&&m(e,function(e){return t.test("string"==typeof e.className&&e.className||"undefined"!=typeof e.getAttribute&&e.getAttribute("class")||"")})},ATTR:function(n,r,i){return function(e){var t=se.attr(e,n);return null==t?"!="===r:!r||(t+="","="===r?t===i:"!="===r?t!==i:"^="===r?i&&0===t.indexOf(i):"*="===r?i&&-1:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i;function D(e,n,r){return m(n)?S.grep(e,function(e,t){return!!n.call(e,t,e)!==r}):n.nodeType?S.grep(e,function(e){return e===n!==r}):"string"!=typeof n?S.grep(e,function(e){return-1)[^>]*|#([\w-]+))$/;(S.fn.init=function(e,t,n){var r,i;if(!e)return this;if(n=n||j,"string"==typeof e){if(!(r="<"===e[0]&&">"===e[e.length-1]&&3<=e.length?[null,e,null]:q.exec(e))||!r[1]&&t)return!t||t.jquery?(t||n).find(e):this.constructor(t).find(e);if(r[1]){if(t=t instanceof S?t[0]:t,S.merge(this,S.parseHTML(r[1],t&&t.nodeType?t.ownerDocument||t:E,!0)),N.test(r[1])&&S.isPlainObject(t))for(r in t)m(this[r])?this[r](t[r]):this.attr(r,t[r]);return this}return(i=E.getElementById(r[2]))&&(this[0]=i,this.length=1),this}return e.nodeType?(this[0]=e,this.length=1,this):m(e)?void 0!==n.ready?n.ready(e):e(S):S.makeArray(e,this)}).prototype=S.fn,j=S(E);var L=/^(?:parents|prev(?:Until|All))/,H={children:!0,contents:!0,next:!0,prev:!0};function O(e,t){while((e=e[t])&&1!==e.nodeType);return e}S.fn.extend({has:function(e){var t=S(e,this),n=t.length;return this.filter(function(){for(var e=0;e\x20\t\r\n\f]*)/i,he=/^$|^module$|\/(?:java|ecma)script/i;ce=E.createDocumentFragment().appendChild(E.createElement("div")),(fe=E.createElement("input")).setAttribute("type","radio"),fe.setAttribute("checked","checked"),fe.setAttribute("name","t"),ce.appendChild(fe),y.checkClone=ce.cloneNode(!0).cloneNode(!0).lastChild.checked,ce.innerHTML="",y.noCloneChecked=!!ce.cloneNode(!0).lastChild.defaultValue,ce.innerHTML="",y.option=!!ce.lastChild;var ge={thead:[1,"","
"],col:[2,"","
"],tr:[2,"","
"],td:[3,"","
"],_default:[0,"",""]};function ve(e,t){var n;return n="undefined"!=typeof e.getElementsByTagName?e.getElementsByTagName(t||"*"):"undefined"!=typeof e.querySelectorAll?e.querySelectorAll(t||"*"):[],void 0===t||t&&A(e,t)?S.merge([e],n):n}function ye(e,t){for(var n=0,r=e.length;n",""]);var me=/<|&#?\w+;/;function xe(e,t,n,r,i){for(var o,a,s,u,l,c,f=t.createDocumentFragment(),p=[],d=0,h=e.length;d\s*$/g;function qe(e,t){return A(e,"table")&&A(11!==t.nodeType?t:t.firstChild,"tr")&&S(e).children("tbody")[0]||e}function Le(e){return e.type=(null!==e.getAttribute("type"))+"/"+e.type,e}function He(e){return"true/"===(e.type||"").slice(0,5)?e.type=e.type.slice(5):e.removeAttribute("type"),e}function Oe(e,t){var n,r,i,o,a,s;if(1===t.nodeType){if(Y.hasData(e)&&(s=Y.get(e).events))for(i in Y.remove(t,"handle events"),s)for(n=0,r=s[i].length;n").attr(n.scriptAttrs||{}).prop({charset:n.scriptCharset,src:n.url}).on("load error",i=function(e){r.remove(),i=null,e&&t("error"===e.type?404:200,e.type)}),E.head.appendChild(r[0])},abort:function(){i&&i()}}});var Ut,Xt=[],Vt=/(=)\?(?=&|$)|\?\?/;S.ajaxSetup({jsonp:"callback",jsonpCallback:function(){var e=Xt.pop()||S.expando+"_"+Ct.guid++;return this[e]=!0,e}}),S.ajaxPrefilter("json jsonp",function(e,t,n){var r,i,o,a=!1!==e.jsonp&&(Vt.test(e.url)?"url":"string"==typeof e.data&&0===(e.contentType||"").indexOf("application/x-www-form-urlencoded")&&Vt.test(e.data)&&"data");if(a||"jsonp"===e.dataTypes[0])return r=e.jsonpCallback=m(e.jsonpCallback)?e.jsonpCallback():e.jsonpCallback,a?e[a]=e[a].replace(Vt,"$1"+r):!1!==e.jsonp&&(e.url+=(Et.test(e.url)?"&":"?")+e.jsonp+"="+r),e.converters["script json"]=function(){return o||S.error(r+" was not called"),o[0]},e.dataTypes[0]="json",i=C[r],C[r]=function(){o=arguments},n.always(function(){void 0===i?S(C).removeProp(r):C[r]=i,e[r]&&(e.jsonpCallback=t.jsonpCallback,Xt.push(r)),o&&m(i)&&i(o[0]),o=i=void 0}),"script"}),y.createHTMLDocument=((Ut=E.implementation.createHTMLDocument("").body).innerHTML="
",2===Ut.childNodes.length),S.parseHTML=function(e,t,n){return"string"!=typeof e?[]:("boolean"==typeof t&&(n=t,t=!1),t||(y.createHTMLDocument?((r=(t=E.implementation.createHTMLDocument("")).createElement("base")).href=E.location.href,t.head.appendChild(r)):t=E),o=!n&&[],(i=N.exec(e))?[t.createElement(i[1])]:(i=xe([e],t,o),o&&o.length&&S(o).remove(),S.merge([],i.childNodes)));var r,i,o},S.fn.load=function(e,t,n){var r,i,o,a=this,s=e.indexOf(" ");return-1").append(S.parseHTML(e)).find(r):e)}).always(n&&function(e,t){a.each(function(){n.apply(this,o||[e.responseText,t,e])})}),this},S.expr.pseudos.animated=function(t){return S.grep(S.timers,function(e){return t===e.elem}).length},S.offset={setOffset:function(e,t,n){var r,i,o,a,s,u,l=S.css(e,"position"),c=S(e),f={};"static"===l&&(e.style.position="relative"),s=c.offset(),o=S.css(e,"top"),u=S.css(e,"left"),("absolute"===l||"fixed"===l)&&-1<(o+u).indexOf("auto")?(a=(r=c.position()).top,i=r.left):(a=parseFloat(o)||0,i=parseFloat(u)||0),m(t)&&(t=t.call(e,n,S.extend({},s))),null!=t.top&&(f.top=t.top-s.top+a),null!=t.left&&(f.left=t.left-s.left+i),"using"in t?t.using.call(e,f):("number"==typeof f.top&&(f.top+="px"),"number"==typeof f.left&&(f.left+="px"),c.css(f))}},S.fn.extend({offset:function(t){if(arguments.length)return void 0===t?this:this.each(function(e){S.offset.setOffset(this,t,e)});var e,n,r=this[0];return r?r.getClientRects().length?(e=r.getBoundingClientRect(),n=r.ownerDocument.defaultView,{top:e.top+n.pageYOffset,left:e.left+n.pageXOffset}):{top:0,left:0}:void 0},position:function(){if(this[0]){var e,t,n,r=this[0],i={top:0,left:0};if("fixed"===S.css(r,"position"))t=r.getBoundingClientRect();else{t=this.offset(),n=r.ownerDocument,e=r.offsetParent||n.documentElement;while(e&&(e===n.body||e===n.documentElement)&&"static"===S.css(e,"position"))e=e.parentNode;e&&e!==r&&1===e.nodeType&&((i=S(e).offset()).top+=S.css(e,"borderTopWidth",!0),i.left+=S.css(e,"borderLeftWidth",!0))}return{top:t.top-i.top-S.css(r,"marginTop",!0),left:t.left-i.left-S.css(r,"marginLeft",!0)}}},offsetParent:function(){return this.map(function(){var e=this.offsetParent;while(e&&"static"===S.css(e,"position"))e=e.offsetParent;return e||re})}}),S.each({scrollLeft:"pageXOffset",scrollTop:"pageYOffset"},function(t,i){var o="pageYOffset"===i;S.fn[t]=function(e){return $(this,function(e,t,n){var r;if(x(e)?r=e:9===e.nodeType&&(r=e.defaultView),void 0===n)return r?r[i]:e[t];r?r.scrollTo(o?r.pageXOffset:n,o?n:r.pageYOffset):e[t]=n},t,e,arguments.length)}}),S.each(["top","left"],function(e,n){S.cssHooks[n]=$e(y.pixelPosition,function(e,t){if(t)return t=Be(e,n),Me.test(t)?S(e).position()[n]+"px":t})}),S.each({Height:"height",Width:"width"},function(a,s){S.each({padding:"inner"+a,content:s,"":"outer"+a},function(r,o){S.fn[o]=function(e,t){var n=arguments.length&&(r||"boolean"!=typeof e),i=r||(!0===e||!0===t?"margin":"border");return $(this,function(e,t,n){var r;return x(e)?0===o.indexOf("outer")?e["inner"+a]:e.document.documentElement["client"+a]:9===e.nodeType?(r=e.documentElement,Math.max(e.body["scroll"+a],r["scroll"+a],e.body["offset"+a],r["offset"+a],r["client"+a])):void 0===n?S.css(e,t,i):S.style(e,t,n,i)},s,n?e:void 0,n)}})}),S.each(["ajaxStart","ajaxStop","ajaxComplete","ajaxError","ajaxSuccess","ajaxSend"],function(e,t){S.fn[t]=function(e){return this.on(t,e)}}),S.fn.extend({bind:function(e,t,n){return this.on(e,null,t,n)},unbind:function(e,t){return this.off(e,null,t)},delegate:function(e,t,n,r){return this.on(t,e,n,r)},undelegate:function(e,t,n){return 1===arguments.length?this.off(e,"**"):this.off(t,e||"**",n)},hover:function(e,t){return this.mouseenter(e).mouseleave(t||e)}}),S.each("blur focus focusin focusout resize scroll click dblclick mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave change select submit keydown keypress keyup contextmenu".split(" "),function(e,n){S.fn[n]=function(e,t){return 0e?1:t>=e?0:NaN},i=function(t){var e;return 1===t.length&&(e=t,t=function(t,n){return r(e(t),n)}),{left:function(e,n,r,i){for(null==r&&(r=0),null==i&&(i=e.length);r>>1;t(e[a],n)<0?r=a+1:i=a}return r},right:function(e,n,r,i){for(null==r&&(r=0),null==i&&(i=e.length);r>>1;t(e[a],n)>0?i=a:r=a+1}return r}}};var a=i(r),o=a.right,s=a.left,c=o,u=function(t,e){null==e&&(e=l);for(var n=0,r=t.length-1,i=t[0],a=new Array(r<0?0:r);nt?1:e>=t?0:NaN},d=function(t){return null===t?NaN:+t},p=function(t,e){var n,r,i=t.length,a=0,o=-1,s=0,c=0;if(null==e)for(;++o1)return c/(a-1)},g=function(t,e){var n=p(t,e);return n?Math.sqrt(n):n},y=function(t,e){var n,r,i,a=t.length,o=-1;if(null==e){for(;++o=n)for(r=i=n;++on&&(r=n),i=n)for(r=i=n;++on&&(r=n),i0)return[t];if((r=e0)for(t=Math.ceil(t/o),e=Math.floor(e/o),a=new Array(i=Math.ceil(e-t+1));++s=0?(a>=w?10:a>=E?5:a>=T?2:1)*Math.pow(10,i):-Math.pow(10,-i)/(a>=w?10:a>=E?5:a>=T?2:1)}function A(t,e,n){var r=Math.abs(e-t)/Math.max(0,n),i=Math.pow(10,Math.floor(Math.log(r)/Math.LN10)),a=r/i;return a>=w?i*=10:a>=E?i*=5:a>=T&&(i*=2),eh;)f.pop(),--d;var p,g=new Array(d+1);for(i=0;i<=d;++i)(p=g[i]=[]).x0=i>0?f[i-1]:l,p.x1=i=1)return+n(t[r-1],r-1,t);var r,i=(r-1)*e,a=Math.floor(i),o=+n(t[a],a,t);return o+(+n(t[a+1],a+1,t)-o)*(i-a)}},N=function(t,e,n){return t=b.call(t,d).sort(r),Math.ceil((n-e)/(2*(D(t,.75)-D(t,.25))*Math.pow(t.length,-1/3)))},B=function(t,e,n){return Math.ceil((n-e)/(3.5*g(t)*Math.pow(t.length,-1/3)))},L=function(t,e){var n,r,i=t.length,a=-1;if(null==e){for(;++a=n)for(r=n;++ar&&(r=n)}else for(;++a=n)for(r=n;++ar&&(r=n);return r},F=function(t,e){var n,r=t.length,i=r,a=-1,o=0;if(null==e)for(;++a=0;)for(e=(r=t[i]).length;--e>=0;)n[--o]=r[e];return n},j=function(t,e){var n,r,i=t.length,a=-1;if(null==e){for(;++a=n)for(r=n;++an&&(r=n)}else for(;++a=n)for(r=n;++an&&(r=n);return r},R=function(t,e){for(var n=e.length,r=new Array(n);n--;)r[n]=t[e[n]];return r},Y=function(t,e){if(n=t.length){var n,i,a=0,o=0,s=t[o];for(null==e&&(e=r);++a=0&&(n=t.slice(r+1),t=t.slice(0,r)),t&&!e.hasOwnProperty(t))throw new Error("unknown type: "+t);return{type:t,name:n}}))}function ct(t,e){for(var n,r=0,i=t.length;r0)for(var n,r,i=new Array(n),a=0;ae?1:t>=e?0:NaN}var _t="http://www.w3.org/1999/xhtml",kt={svg:"http://www.w3.org/2000/svg",xhtml:_t,xlink:"http://www.w3.org/1999/xlink",xml:"http://www.w3.org/XML/1998/namespace",xmlns:"http://www.w3.org/2000/xmlns/"},wt=function(t){var e=t+="",n=e.indexOf(":");return n>=0&&"xmlns"!==(e=t.slice(0,n))&&(t=t.slice(n+1)),kt.hasOwnProperty(e)?{space:kt[e],local:t}:t};function Et(t){return function(){this.removeAttribute(t)}}function Tt(t){return function(){this.removeAttributeNS(t.space,t.local)}}function Ct(t,e){return function(){this.setAttribute(t,e)}}function St(t,e){return function(){this.setAttributeNS(t.space,t.local,e)}}function At(t,e){return function(){var n=e.apply(this,arguments);null==n?this.removeAttribute(t):this.setAttribute(t,n)}}function Mt(t,e){return function(){var n=e.apply(this,arguments);null==n?this.removeAttributeNS(t.space,t.local):this.setAttributeNS(t.space,t.local,n)}}var Ot=function(t){return t.ownerDocument&&t.ownerDocument.defaultView||t.document&&t||t.defaultView};function Dt(t){return function(){this.style.removeProperty(t)}}function Nt(t,e,n){return function(){this.style.setProperty(t,e,n)}}function Bt(t,e,n){return function(){var r=e.apply(this,arguments);null==r?this.style.removeProperty(t):this.style.setProperty(t,r,n)}}function Lt(t,e){return t.style.getPropertyValue(e)||Ot(t).getComputedStyle(t,null).getPropertyValue(e)}function Ft(t){return function(){delete this[t]}}function Pt(t,e){return function(){this[t]=e}}function It(t,e){return function(){var n=e.apply(this,arguments);null==n?delete this[t]:this[t]=n}}function jt(t){return t.trim().split(/^|\s+/)}function Rt(t){return t.classList||new Yt(t)}function Yt(t){this._node=t,this._names=jt(t.getAttribute("class")||"")}function zt(t,e){for(var n=Rt(t),r=-1,i=e.length;++r=0&&(this._names.splice(e,1),this._node.setAttribute("class",this._names.join(" ")))},contains:function(t){return this._names.indexOf(t)>=0}};function Ht(){this.textContent=""}function Gt(t){return function(){this.textContent=t}}function qt(t){return function(){var e=t.apply(this,arguments);this.textContent=null==e?"":e}}function Xt(){this.innerHTML=""}function Zt(t){return function(){this.innerHTML=t}}function Jt(t){return function(){var e=t.apply(this,arguments);this.innerHTML=null==e?"":e}}function Qt(){this.nextSibling&&this.parentNode.appendChild(this)}function Kt(){this.previousSibling&&this.parentNode.insertBefore(this,this.parentNode.firstChild)}function te(t){return function(){var e=this.ownerDocument,n=this.namespaceURI;return n===_t&&e.documentElement.namespaceURI===_t?e.createElement(t):e.createElementNS(n,t)}}function ee(t){return function(){return this.ownerDocument.createElementNS(t.space,t.local)}}var ne=function(t){var e=wt(t);return(e.local?ee:te)(e)};function re(){return null}function ie(){var t=this.parentNode;t&&t.removeChild(this)}function ae(){var t=this.cloneNode(!1),e=this.parentNode;return e?e.insertBefore(t,this.nextSibling):t}function oe(){var t=this.cloneNode(!0),e=this.parentNode;return e?e.insertBefore(t,this.nextSibling):t}var se={},ce=null;"undefined"!=typeof document&&("onmouseenter"in document.documentElement||(se={mouseenter:"mouseover",mouseleave:"mouseout"}));function ue(t,e,n){return t=le(t,e,n),function(e){var n=e.relatedTarget;n&&(n===this||8&n.compareDocumentPosition(this))||t.call(this,e)}}function le(t,e,n){return function(r){var i=ce;ce=r;try{t.call(this,this.__data__,e,n)}finally{ce=i}}}function he(t){return t.trim().split(/^|\s+/).map((function(t){var e="",n=t.indexOf(".");return n>=0&&(e=t.slice(n+1),t=t.slice(0,n)),{type:t,name:e}}))}function fe(t){return function(){var e=this.__on;if(e){for(var n,r=0,i=-1,a=e.length;r=_&&(_=x+1);!(b=v[_])&&++_=0;)(r=i[a])&&(o&&4^r.compareDocumentPosition(o)&&o.parentNode.insertBefore(r,o),o=r);return this},sort:function(t){function e(e,n){return e&&n?t(e.__data__,n.__data__):!e-!n}t||(t=xt);for(var n=this._groups,r=n.length,i=new Array(r),a=0;a1?this.each((null==e?Dt:"function"==typeof e?Bt:Nt)(t,e,null==n?"":n)):Lt(this.node(),t)},property:function(t,e){return arguments.length>1?this.each((null==e?Ft:"function"==typeof e?It:Pt)(t,e)):this.node()[t]},classed:function(t,e){var n=jt(t+"");if(arguments.length<2){for(var r=Rt(this.node()),i=-1,a=n.length;++i>8&15|e>>4&240,e>>4&15|240&e,(15&e)<<4|15&e,1):8===n?new qe(e>>24&255,e>>16&255,e>>8&255,(255&e)/255):4===n?new qe(e>>12&15|e>>8&240,e>>8&15|e>>4&240,e>>4&15|240&e,((15&e)<<4|15&e)/255):null):(e=Le.exec(t))?new qe(e[1],e[2],e[3],1):(e=Fe.exec(t))?new qe(255*e[1]/100,255*e[2]/100,255*e[3]/100,1):(e=Pe.exec(t))?Ve(e[1],e[2],e[3],e[4]):(e=Ie.exec(t))?Ve(255*e[1]/100,255*e[2]/100,255*e[3]/100,e[4]):(e=je.exec(t))?Qe(e[1],e[2]/100,e[3]/100,1):(e=Re.exec(t))?Qe(e[1],e[2]/100,e[3]/100,e[4]):Ye.hasOwnProperty(t)?We(Ye[t]):"transparent"===t?new qe(NaN,NaN,NaN,0):null}function We(t){return new qe(t>>16&255,t>>8&255,255&t,1)}function Ve(t,e,n,r){return r<=0&&(t=e=n=NaN),new qe(t,e,n,r)}function He(t){return t instanceof Me||(t=$e(t)),t?new qe((t=t.rgb()).r,t.g,t.b,t.opacity):new qe}function Ge(t,e,n,r){return 1===arguments.length?He(t):new qe(t,e,n,null==r?1:r)}function qe(t,e,n,r){this.r=+t,this.g=+e,this.b=+n,this.opacity=+r}function Xe(){return"#"+Je(this.r)+Je(this.g)+Je(this.b)}function Ze(){var t=this.opacity;return(1===(t=isNaN(t)?1:Math.max(0,Math.min(1,t)))?"rgb(":"rgba(")+Math.max(0,Math.min(255,Math.round(this.r)||0))+", "+Math.max(0,Math.min(255,Math.round(this.g)||0))+", "+Math.max(0,Math.min(255,Math.round(this.b)||0))+(1===t?")":", "+t+")")}function Je(t){return((t=Math.max(0,Math.min(255,Math.round(t)||0)))<16?"0":"")+t.toString(16)}function Qe(t,e,n,r){return r<=0?t=e=n=NaN:n<=0||n>=1?t=e=NaN:e<=0&&(t=NaN),new en(t,e,n,r)}function Ke(t){if(t instanceof en)return new en(t.h,t.s,t.l,t.opacity);if(t instanceof Me||(t=$e(t)),!t)return new en;if(t instanceof en)return t;var e=(t=t.rgb()).r/255,n=t.g/255,r=t.b/255,i=Math.min(e,n,r),a=Math.max(e,n,r),o=NaN,s=a-i,c=(a+i)/2;return s?(o=e===a?(n-r)/s+6*(n0&&c<1?0:o,new en(o,s,c,t.opacity)}function tn(t,e,n,r){return 1===arguments.length?Ke(t):new en(t,e,n,null==r?1:r)}function en(t,e,n,r){this.h=+t,this.s=+e,this.l=+n,this.opacity=+r}function nn(t,e,n){return 255*(t<60?e+(n-e)*t/60:t<180?n:t<240?e+(n-e)*(240-t)/60:e)}function rn(t,e,n,r,i){var a=t*t,o=a*t;return((1-3*t+3*a-o)*e+(4-6*a+3*o)*n+(1+3*t+3*a-3*o)*r+o*i)/6}Se(Me,$e,{copy:function(t){return Object.assign(new this.constructor,this,t)},displayable:function(){return this.rgb().displayable()},hex:ze,formatHex:ze,formatHsl:function(){return Ke(this).formatHsl()},formatRgb:Ue,toString:Ue}),Se(qe,Ge,Ae(Me,{brighter:function(t){return t=null==t?1/.7:Math.pow(1/.7,t),new qe(this.r*t,this.g*t,this.b*t,this.opacity)},darker:function(t){return t=null==t?.7:Math.pow(.7,t),new qe(this.r*t,this.g*t,this.b*t,this.opacity)},rgb:function(){return this},displayable:function(){return-.5<=this.r&&this.r<255.5&&-.5<=this.g&&this.g<255.5&&-.5<=this.b&&this.b<255.5&&0<=this.opacity&&this.opacity<=1},hex:Xe,formatHex:Xe,formatRgb:Ze,toString:Ze})),Se(en,tn,Ae(Me,{brighter:function(t){return t=null==t?1/.7:Math.pow(1/.7,t),new en(this.h,this.s,this.l*t,this.opacity)},darker:function(t){return t=null==t?.7:Math.pow(.7,t),new en(this.h,this.s,this.l*t,this.opacity)},rgb:function(){var t=this.h%360+360*(this.h<0),e=isNaN(t)||isNaN(this.s)?0:this.s,n=this.l,r=n+(n<.5?n:1-n)*e,i=2*n-r;return new qe(nn(t>=240?t-240:t+120,i,r),nn(t,i,r),nn(t<120?t+240:t-120,i,r),this.opacity)},displayable:function(){return(0<=this.s&&this.s<=1||isNaN(this.s))&&0<=this.l&&this.l<=1&&0<=this.opacity&&this.opacity<=1},formatHsl:function(){var t=this.opacity;return(1===(t=isNaN(t)?1:Math.max(0,Math.min(1,t)))?"hsl(":"hsla(")+(this.h||0)+", "+100*(this.s||0)+"%, "+100*(this.l||0)+"%"+(1===t?")":", "+t+")")}}));var an=function(t){var e=t.length-1;return function(n){var r=n<=0?n=0:n>=1?(n=1,e-1):Math.floor(n*e),i=t[r],a=t[r+1],o=r>0?t[r-1]:2*i-a,s=r180||n<-180?n-360*Math.round(n/360):n):sn(isNaN(t)?e:t)}function ln(t){return 1==(t=+t)?hn:function(e,n){return n-e?function(t,e,n){return t=Math.pow(t,n),e=Math.pow(e,n)-t,n=1/n,function(r){return Math.pow(t+r*e,n)}}(e,n,t):sn(isNaN(e)?n:e)}}function hn(t,e){var n=e-t;return n?cn(t,n):sn(isNaN(t)?e:t)}var fn=function t(e){var n=ln(e);function r(t,e){var r=n((t=Ge(t)).r,(e=Ge(e)).r),i=n(t.g,e.g),a=n(t.b,e.b),o=hn(t.opacity,e.opacity);return function(e){return t.r=r(e),t.g=i(e),t.b=a(e),t.opacity=o(e),t+""}}return r.gamma=t,r}(1);function dn(t){return function(e){var n,r,i=e.length,a=new Array(i),o=new Array(i),s=new Array(i);for(n=0;na&&(i=e.slice(a,i),s[o]?s[o]+=i:s[++o]=i),(n=n[0])===(r=r[0])?s[o]?s[o]+=r:s[++o]=r:(s[++o]=null,c.push({i:o,x:_n(n,r)})),a=En.lastIndex;return a=0&&e._call.call(null,t),e=e._next;--Bn}function Hn(){In=(Pn=Rn.now())+jn,Bn=Ln=0;try{Vn()}finally{Bn=0,function(){var t,e,n=Tn,r=1/0;for(;n;)n._call?(r>n._time&&(r=n._time),t=n,n=n._next):(e=n._next,n._next=null,n=t?t._next=e:Tn=e);Cn=t,qn(r)}(),In=0}}function Gn(){var t=Rn.now(),e=t-Pn;e>1e3&&(jn-=e,Pn=t)}function qn(t){Bn||(Ln&&(Ln=clearTimeout(Ln)),t-In>24?(t<1/0&&(Ln=setTimeout(Hn,t-Rn.now()-jn)),Fn&&(Fn=clearInterval(Fn))):(Fn||(Pn=Rn.now(),Fn=setInterval(Gn,1e3)),Bn=1,Yn(Hn)))}$n.prototype=Wn.prototype={constructor:$n,restart:function(t,e,n){if("function"!=typeof t)throw new TypeError("callback is not a function");n=(null==n?zn():+n)+(null==e?0:+e),this._next||Cn===this||(Cn?Cn._next=this:Tn=this,Cn=this),this._call=t,this._time=n,qn()},stop:function(){this._call&&(this._call=null,this._time=1/0,qn())}};var Xn=function(t,e,n){var r=new $n;return e=null==e?0:+e,r.restart((function(n){r.stop(),t(n+e)}),e,n),r},Zn=lt("start","end","cancel","interrupt"),Jn=[],Qn=function(t,e,n,r,i,a){var o=t.__transition;if(o){if(n in o)return}else t.__transition={};!function(t,e,n){var r,i=t.__transition;function a(c){var u,l,h,f;if(1!==n.state)return s();for(u in i)if((f=i[u]).name===n.name){if(3===f.state)return Xn(a);4===f.state?(f.state=6,f.timer.stop(),f.on.call("interrupt",t,t.__data__,f.index,f.group),delete i[u]):+u0)throw new Error("too late; already scheduled");return n}function tr(t,e){var n=er(t,e);if(n.state>3)throw new Error("too late; already running");return n}function er(t,e){var n=t.__transition;if(!n||!(n=n[e]))throw new Error("transition not found");return n}var nr,rr,ir,ar,or=function(t,e){var n,r,i,a=t.__transition,o=!0;if(a){for(i in e=null==e?null:e+"",a)(n=a[i]).name===e?(r=n.state>2&&n.state<5,n.state=6,n.timer.stop(),n.on.call(r?"interrupt":"cancel",t,t.__data__,n.index,n.group),delete a[i]):o=!1;o&&delete t.__transition}},sr=180/Math.PI,cr={translateX:0,translateY:0,rotate:0,skewX:0,scaleX:1,scaleY:1},ur=function(t,e,n,r,i,a){var o,s,c;return(o=Math.sqrt(t*t+e*e))&&(t/=o,e/=o),(c=t*n+e*r)&&(n-=t*c,r-=e*c),(s=Math.sqrt(n*n+r*r))&&(n/=s,r/=s,c/=s),t*r180?e+=360:e-t>180&&(t+=360),a.push({i:n.push(i(n)+"rotate(",null,r)-2,x:_n(t,e)})):e&&n.push(i(n)+"rotate("+e+r)}(a.rotate,o.rotate,s,c),function(t,e,n,a){t!==e?a.push({i:n.push(i(n)+"skewX(",null,r)-2,x:_n(t,e)}):e&&n.push(i(n)+"skewX("+e+r)}(a.skewX,o.skewX,s,c),function(t,e,n,r,a,o){if(t!==n||e!==r){var s=a.push(i(a)+"scale(",null,",",null,")");o.push({i:s-4,x:_n(t,n)},{i:s-2,x:_n(e,r)})}else 1===n&&1===r||a.push(i(a)+"scale("+n+","+r+")")}(a.scaleX,a.scaleY,o.scaleX,o.scaleY,s,c),a=o=null,function(t){for(var e,n=-1,r=c.length;++n=0&&(t=t.slice(0,e)),!t||"start"===t}))}(e)?Kn:tr;return function(){var o=a(this,t),s=o.on;s!==r&&(i=(r=s).copy()).on(e,n),o.on=i}}var Br=_e.prototype.constructor;function Lr(t){return function(){this.style.removeProperty(t)}}function Fr(t,e,n){return function(r){this.style.setProperty(t,e.call(this,r),n)}}function Pr(t,e,n){var r,i;function a(){var a=e.apply(this,arguments);return a!==i&&(r=(i=a)&&Fr(t,a,n)),r}return a._value=e,a}function Ir(t){return function(e){this.textContent=t.call(this,e)}}function jr(t){var e,n;function r(){var r=t.apply(this,arguments);return r!==n&&(e=(n=r)&&Ir(r)),e}return r._value=t,r}var Rr=0;function Yr(t,e,n,r){this._groups=t,this._parents=e,this._name=n,this._id=r}function zr(t){return _e().transition(t)}function Ur(){return++Rr}var $r=_e.prototype;function Wr(t){return t*t*t}function Vr(t){return--t*t*t+1}function Hr(t){return((t*=2)<=1?t*t*t:(t-=2)*t*t+2)/2}Yr.prototype=zr.prototype={constructor:Yr,select:function(t){var e=this._name,n=this._id;"function"!=typeof t&&(t=ft(t));for(var r=this._groups,i=r.length,a=new Array(i),o=0;o1&&n.name===e)return new Yr([[t]],Xr,e,+r);return null},Jr=function(t){return function(){return t}},Qr=function(t,e,n){this.target=t,this.type=e,this.selection=n};function Kr(){ce.stopImmediatePropagation()}var ti=function(){ce.preventDefault(),ce.stopImmediatePropagation()},ei={name:"drag"},ni={name:"space"},ri={name:"handle"},ii={name:"center"};function ai(t){return[+t[0],+t[1]]}function oi(t){return[ai(t[0]),ai(t[1])]}function si(t){return function(e){return Dn(e,ce.touches,t)}}var ci={name:"x",handles:["w","e"].map(yi),input:function(t,e){return null==t?null:[[+t[0],e[0][1]],[+t[1],e[1][1]]]},output:function(t){return t&&[t[0][0],t[1][0]]}},ui={name:"y",handles:["n","s"].map(yi),input:function(t,e){return null==t?null:[[e[0][0],+t[0]],[e[1][0],+t[1]]]},output:function(t){return t&&[t[0][1],t[1][1]]}},li={name:"xy",handles:["n","w","e","s","nw","ne","sw","se"].map(yi),input:function(t){return null==t?null:oi(t)},output:function(t){return t}},hi={overlay:"crosshair",selection:"move",n:"ns-resize",e:"ew-resize",s:"ns-resize",w:"ew-resize",nw:"nwse-resize",ne:"nesw-resize",se:"nwse-resize",sw:"nesw-resize"},fi={e:"w",w:"e",nw:"ne",ne:"nw",se:"sw",sw:"se"},di={n:"s",s:"n",nw:"sw",ne:"se",se:"ne",sw:"nw"},pi={overlay:1,selection:1,n:null,e:1,s:null,w:-1,nw:-1,ne:1,se:1,sw:-1},gi={overlay:1,selection:1,n:-1,e:null,s:1,w:null,nw:-1,ne:-1,se:1,sw:1};function yi(t){return{type:t}}function vi(){return!ce.ctrlKey&&!ce.button}function mi(){var t=this.ownerSVGElement||this;return t.hasAttribute("viewBox")?[[(t=t.viewBox.baseVal).x,t.y],[t.x+t.width,t.y+t.height]]:[[0,0],[t.width.baseVal.value,t.height.baseVal.value]]}function bi(){return navigator.maxTouchPoints||"ontouchstart"in this}function xi(t){for(;!t.__brush;)if(!(t=t.parentNode))return;return t.__brush}function _i(t){return t[0][0]===t[1][0]||t[0][1]===t[1][1]}function ki(t){var e=t.__brush;return e?e.dim.output(e.selection):null}function wi(){return Ci(ci)}function Ei(){return Ci(ui)}var Ti=function(){return Ci(li)};function Ci(t){var e,n=mi,r=vi,i=bi,a=!0,o=lt("start","brush","end"),s=6;function c(e){var n=e.property("__brush",g).selectAll(".overlay").data([yi("overlay")]);n.enter().append("rect").attr("class","overlay").attr("pointer-events","all").attr("cursor",hi.overlay).merge(n).each((function(){var t=xi(this).extent;ke(this).attr("x",t[0][0]).attr("y",t[0][1]).attr("width",t[1][0]-t[0][0]).attr("height",t[1][1]-t[0][1])})),e.selectAll(".selection").data([yi("selection")]).enter().append("rect").attr("class","selection").attr("cursor",hi.selection).attr("fill","#777").attr("fill-opacity",.3).attr("stroke","#fff").attr("shape-rendering","crispEdges");var r=e.selectAll(".handle").data(t.handles,(function(t){return t.type}));r.exit().remove(),r.enter().append("rect").attr("class",(function(t){return"handle handle--"+t.type})).attr("cursor",(function(t){return hi[t.type]})),e.each(u).attr("fill","none").attr("pointer-events","all").on("mousedown.brush",f).filter(i).on("touchstart.brush",f).on("touchmove.brush",d).on("touchend.brush touchcancel.brush",p).style("touch-action","none").style("-webkit-tap-highlight-color","rgba(0,0,0,0)")}function u(){var t=ke(this),e=xi(this).selection;e?(t.selectAll(".selection").style("display",null).attr("x",e[0][0]).attr("y",e[0][1]).attr("width",e[1][0]-e[0][0]).attr("height",e[1][1]-e[0][1]),t.selectAll(".handle").style("display",null).attr("x",(function(t){return"e"===t.type[t.type.length-1]?e[1][0]-s/2:e[0][0]-s/2})).attr("y",(function(t){return"s"===t.type[0]?e[1][1]-s/2:e[0][1]-s/2})).attr("width",(function(t){return"n"===t.type||"s"===t.type?e[1][0]-e[0][0]+s:s})).attr("height",(function(t){return"e"===t.type||"w"===t.type?e[1][1]-e[0][1]+s:s}))):t.selectAll(".selection,.handle").style("display","none").attr("x",null).attr("y",null).attr("width",null).attr("height",null)}function l(t,e,n){return!n&&t.__brush.emitter||new h(t,e)}function h(t,e){this.that=t,this.args=e,this.state=t.__brush,this.active=0}function f(){if((!e||ce.touches)&&r.apply(this,arguments)){var n,i,o,s,c,h,f,d,p,g,y,v=this,m=ce.target.__data__.type,b="selection"===(a&&ce.metaKey?m="overlay":m)?ei:a&&ce.altKey?ii:ri,x=t===ui?null:pi[m],_=t===ci?null:gi[m],k=xi(v),w=k.extent,E=k.selection,T=w[0][0],C=w[0][1],S=w[1][0],A=w[1][1],M=0,O=0,D=x&&_&&a&&ce.shiftKey,N=ce.touches?si(ce.changedTouches[0].identifier):Nn,B=N(v),L=B,F=l(v,arguments,!0).beforestart();"overlay"===m?(E&&(p=!0),k.selection=E=[[n=t===ui?T:B[0],o=t===ci?C:B[1]],[c=t===ui?S:n,f=t===ci?A:o]]):(n=E[0][0],o=E[0][1],c=E[1][0],f=E[1][1]),i=n,s=o,h=c,d=f;var P=ke(v).attr("pointer-events","none"),I=P.selectAll(".overlay").attr("cursor",hi[m]);if(ce.touches)F.moved=R,F.ended=z;else{var j=ke(ce.view).on("mousemove.brush",R,!0).on("mouseup.brush",z,!0);a&&j.on("keydown.brush",U,!0).on("keyup.brush",$,!0),Te(ce.view)}Kr(),or(v),u.call(v),F.start()}function R(){var t=N(v);!D||g||y||(Math.abs(t[0]-L[0])>Math.abs(t[1]-L[1])?y=!0:g=!0),L=t,p=!0,ti(),Y()}function Y(){var t;switch(M=L[0]-B[0],O=L[1]-B[1],b){case ni:case ei:x&&(M=Math.max(T-n,Math.min(S-c,M)),i=n+M,h=c+M),_&&(O=Math.max(C-o,Math.min(A-f,O)),s=o+O,d=f+O);break;case ri:x<0?(M=Math.max(T-n,Math.min(S-n,M)),i=n+M,h=c):x>0&&(M=Math.max(T-c,Math.min(S-c,M)),i=n,h=c+M),_<0?(O=Math.max(C-o,Math.min(A-o,O)),s=o+O,d=f):_>0&&(O=Math.max(C-f,Math.min(A-f,O)),s=o,d=f+O);break;case ii:x&&(i=Math.max(T,Math.min(S,n-M*x)),h=Math.max(T,Math.min(S,c+M*x))),_&&(s=Math.max(C,Math.min(A,o-O*_)),d=Math.max(C,Math.min(A,f+O*_)))}h0&&(n=i-M),_<0?f=d-O:_>0&&(o=s-O),b=ni,I.attr("cursor",hi.selection),Y());break;default:return}ti()}function $(){switch(ce.keyCode){case 16:D&&(g=y=D=!1,Y());break;case 18:b===ii&&(x<0?c=h:x>0&&(n=i),_<0?f=d:_>0&&(o=s),b=ri,Y());break;case 32:b===ni&&(ce.altKey?(x&&(c=h-M*x,n=i+M*x),_&&(f=d-O*_,o=s+O*_),b=ii):(x<0?c=h:x>0&&(n=i),_<0?f=d:_>0&&(o=s),b=ri),I.attr("cursor",hi[m]),Y());break;default:return}ti()}}function d(){l(this,arguments).moved()}function p(){l(this,arguments).ended()}function g(){var e=this.__brush||{selection:null};return e.extent=oi(n.apply(this,arguments)),e.dim=t,e}return c.move=function(e,n){e.selection?e.on("start.brush",(function(){l(this,arguments).beforestart().start()})).on("interrupt.brush end.brush",(function(){l(this,arguments).end()})).tween("brush",(function(){var e=this,r=e.__brush,i=l(e,arguments),a=r.selection,o=t.input("function"==typeof n?n.apply(this,arguments):n,r.extent),s=An(a,o);function c(t){r.selection=1===t&&null===o?null:s(t),u.call(e),i.brush()}return null!==a&&null!==o?c:c(1)})):e.each((function(){var e=this,r=arguments,i=e.__brush,a=t.input("function"==typeof n?n.apply(e,r):n,i.extent),o=l(e,r).beforestart();or(e),i.selection=null===a?null:a,u.call(e),o.start().brush().end()}))},c.clear=function(t){c.move(t,null)},h.prototype={beforestart:function(){return 1==++this.active&&(this.state.emitter=this,this.starting=!0),this},start:function(){return this.starting?(this.starting=!1,this.emit("start")):this.emit("brush"),this},brush:function(){return this.emit("brush"),this},end:function(){return 0==--this.active&&(delete this.state.emitter,this.emit("end")),this},emit:function(e){pe(new Qr(c,e,t.output(this.state.selection)),o.apply,o,[e,this.that,this.args])}},c.extent=function(t){return arguments.length?(n="function"==typeof t?t:Jr(oi(t)),c):n},c.filter=function(t){return arguments.length?(r="function"==typeof t?t:Jr(!!t),c):r},c.touchable=function(t){return arguments.length?(i="function"==typeof t?t:Jr(!!t),c):i},c.handleSize=function(t){return arguments.length?(s=+t,c):s},c.keyModifiers=function(t){return arguments.length?(a=!!t,c):a},c.on=function(){var t=o.on.apply(o,arguments);return t===o?c:t},c}var Si=Math.cos,Ai=Math.sin,Mi=Math.PI,Oi=Mi/2,Di=2*Mi,Ni=Math.max;function Bi(t){return function(e,n){return t(e.source.value+e.target.value,n.source.value+n.target.value)}}var Li=function(){var t=0,e=null,n=null,r=null;function i(i){var a,o,s,c,u,l,h=i.length,f=[],d=k(h),p=[],g=[],y=g.groups=new Array(h),v=new Array(h*h);for(a=0,u=-1;++u1e-6)if(Math.abs(l*s-c*u)>1e-6&&i){var f=n-a,d=r-o,p=s*s+c*c,g=f*f+d*d,y=Math.sqrt(p),v=Math.sqrt(h),m=i*Math.tan((Ii-Math.acos((p+h-g)/(2*y*v)))/2),b=m/v,x=m/y;Math.abs(b-1)>1e-6&&(this._+="L"+(t+b*u)+","+(e+b*l)),this._+="A"+i+","+i+",0,0,"+ +(l*f>u*d)+","+(this._x1=t+x*s)+","+(this._y1=e+x*c)}else this._+="L"+(this._x1=t)+","+(this._y1=e);else;},arc:function(t,e,n,r,i,a){t=+t,e=+e,a=!!a;var o=(n=+n)*Math.cos(r),s=n*Math.sin(r),c=t+o,u=e+s,l=1^a,h=a?r-i:i-r;if(n<0)throw new Error("negative radius: "+n);null===this._x1?this._+="M"+c+","+u:(Math.abs(this._x1-c)>1e-6||Math.abs(this._y1-u)>1e-6)&&(this._+="L"+c+","+u),n&&(h<0&&(h=h%ji+ji),h>Ri?this._+="A"+n+","+n+",0,1,"+l+","+(t-o)+","+(e-s)+"A"+n+","+n+",0,1,"+l+","+(this._x1=c)+","+(this._y1=u):h>1e-6&&(this._+="A"+n+","+n+",0,"+ +(h>=Ii)+","+l+","+(this._x1=t+n*Math.cos(i))+","+(this._y1=e+n*Math.sin(i))))},rect:function(t,e,n,r){this._+="M"+(this._x0=this._x1=+t)+","+(this._y0=this._y1=+e)+"h"+ +n+"v"+ +r+"h"+-n+"Z"},toString:function(){return this._}};var Ui=zi;function $i(t){return t.source}function Wi(t){return t.target}function Vi(t){return t.radius}function Hi(t){return t.startAngle}function Gi(t){return t.endAngle}var qi=function(){var t=$i,e=Wi,n=Vi,r=Hi,i=Gi,a=null;function o(){var o,s=Fi.call(arguments),c=t.apply(this,s),u=e.apply(this,s),l=+n.apply(this,(s[0]=c,s)),h=r.apply(this,s)-Oi,f=i.apply(this,s)-Oi,d=l*Si(h),p=l*Ai(h),g=+n.apply(this,(s[0]=u,s)),y=r.apply(this,s)-Oi,v=i.apply(this,s)-Oi;if(a||(a=o=Ui()),a.moveTo(d,p),a.arc(0,0,l,h,f),h===y&&f===v||(a.quadraticCurveTo(0,0,g*Si(y),g*Ai(y)),a.arc(0,0,g,y,v)),a.quadraticCurveTo(0,0,d,p),a.closePath(),o)return a=null,o+""||null}return o.radius=function(t){return arguments.length?(n="function"==typeof t?t:Pi(+t),o):n},o.startAngle=function(t){return arguments.length?(r="function"==typeof t?t:Pi(+t),o):r},o.endAngle=function(t){return arguments.length?(i="function"==typeof t?t:Pi(+t),o):i},o.source=function(e){return arguments.length?(t=e,o):t},o.target=function(t){return arguments.length?(e=t,o):e},o.context=function(t){return arguments.length?(a=null==t?null:t,o):a},o};function Xi(){}function Zi(t,e){var n=new Xi;if(t instanceof Xi)t.each((function(t,e){n.set(e,t)}));else if(Array.isArray(t)){var r,i=-1,a=t.length;if(null==e)for(;++i=r.length)return null!=t&&n.sort(t),null!=e?e(n):n;for(var c,u,l,h=-1,f=n.length,d=r[i++],p=Ji(),g=o();++hr.length)return n;var o,s=i[a-1];return null!=e&&a>=r.length?o=n.entries():(o=[],n.each((function(e,n){o.push({key:n,values:t(e,a)})}))),null!=s?o.sort((function(t,e){return s(t.key,e.key)})):o}(a(t,0,ea,na),0)},key:function(t){return r.push(t),n},sortKeys:function(t){return i[r.length-1]=t,n},sortValues:function(e){return t=e,n},rollup:function(t){return e=t,n}}};function Ki(){return{}}function ta(t,e,n){t[e]=n}function ea(){return Ji()}function na(t,e,n){t.set(e,n)}function ra(){}var ia=Ji.prototype;function aa(t,e){var n=new ra;if(t instanceof ra)t.each((function(t){n.add(t)}));else if(t){var r=-1,i=t.length;if(null==e)for(;++r6/29*(6/29)*(6/29)?Math.pow(t,1/3):t/(6/29*3*(6/29))+4/29}function va(t){return t>6/29?t*t*t:6/29*3*(6/29)*(t-4/29)}function ma(t){return 255*(t<=.0031308?12.92*t:1.055*Math.pow(t,1/2.4)-.055)}function ba(t){return(t/=255)<=.04045?t/12.92:Math.pow((t+.055)/1.055,2.4)}function xa(t){if(t instanceof wa)return new wa(t.h,t.c,t.l,t.opacity);if(t instanceof ga||(t=fa(t)),0===t.a&&0===t.b)return new wa(NaN,0r!=d>r&&n<(f-u)*(r-l)/(d-l)+u&&(i=-i)}return i}function Ia(t,e,n){var r,i,a,o;return function(t,e,n){return(e[0]-t[0])*(n[1]-t[1])==(n[0]-t[0])*(e[1]-t[1])}(t,e,n)&&(i=t[r=+(t[0]===e[0])],a=n[r],o=e[r],i<=a&&a<=o||o<=a&&a<=i)}var ja=function(){},Ra=[[],[[[1,1.5],[.5,1]]],[[[1.5,1],[1,1.5]]],[[[1.5,1],[.5,1]]],[[[1,.5],[1.5,1]]],[[[1,1.5],[.5,1]],[[1,.5],[1.5,1]]],[[[1,.5],[1,1.5]]],[[[1,.5],[.5,1]]],[[[.5,1],[1,.5]]],[[[1,1.5],[1,.5]]],[[[.5,1],[1,.5]],[[1.5,1],[1,1.5]]],[[[1.5,1],[1,.5]]],[[[.5,1],[1.5,1]]],[[[1,1.5],[1.5,1]]],[[[.5,1],[1,1.5]]],[]],Ya=function(){var t=1,e=1,n=M,r=s;function i(t){var e=n(t);if(Array.isArray(e))e=e.slice().sort(Ba);else{var r=y(t),i=r[0],o=r[1];e=A(i,o,e),e=k(Math.floor(i/e)*e,Math.floor(o/e)*e,e)}return e.map((function(e){return a(t,e)}))}function a(n,i){var a=[],s=[];return function(n,r,i){var a,s,c,u,l,h,f=new Array,d=new Array;a=s=-1,u=n[0]>=r,Ra[u<<1].forEach(p);for(;++a=r,Ra[c|u<<1].forEach(p);Ra[u<<0].forEach(p);for(;++s=r,l=n[s*t]>=r,Ra[u<<1|l<<2].forEach(p);++a=r,h=l,l=n[s*t+a+1]>=r,Ra[c|u<<1|l<<2|h<<3].forEach(p);Ra[u|l<<3].forEach(p)}a=-1,l=n[s*t]>=r,Ra[l<<2].forEach(p);for(;++a=r,Ra[l<<2|h<<3].forEach(p);function p(t){var e,n,r=[t[0][0]+a,t[0][1]+s],c=[t[1][0]+a,t[1][1]+s],u=o(r),l=o(c);(e=d[u])?(n=f[l])?(delete d[e.end],delete f[n.start],e===n?(e.ring.push(c),i(e.ring)):f[e.start]=d[n.end]={start:e.start,end:n.end,ring:e.ring.concat(n.ring)}):(delete d[e.end],e.ring.push(c),d[e.end=l]=e):(e=f[l])?(n=d[u])?(delete f[e.start],delete d[n.end],e===n?(e.ring.push(c),i(e.ring)):f[n.start]=d[e.end]={start:n.start,end:e.end,ring:n.ring.concat(e.ring)}):(delete f[e.start],e.ring.unshift(r),f[e.start=u]=e):f[u]=d[l]={start:u,end:l,ring:[r,c]}}Ra[l<<3].forEach(p)}(n,i,(function(t){r(t,n,i),function(t){for(var e=0,n=t.length,r=t[n-1][1]*t[0][0]-t[n-1][0]*t[0][1];++e0?a.push([t]):s.push(t)})),s.forEach((function(t){for(var e,n=0,r=a.length;n0&&o0&&s0&&a>0))throw new Error("invalid size");return t=r,e=a,i},i.thresholds=function(t){return arguments.length?(n="function"==typeof t?t:Array.isArray(t)?La(Na.call(t)):La(t),i):n},i.smooth=function(t){return arguments.length?(r=t?s:ja,i):r===s},i};function za(t,e,n){for(var r=t.width,i=t.height,a=1+(n<<1),o=0;o=n&&(s>=a&&(c-=t.data[s-a+o*r]),e.data[s-n+o*r]=c/Math.min(s+1,r-1+a-s,a))}function Ua(t,e,n){for(var r=t.width,i=t.height,a=1+(n<<1),o=0;o=n&&(s>=a&&(c-=t.data[o+(s-a)*r]),e.data[o+(s-n)*r]=c/Math.min(s+1,i-1+a-s,a))}function $a(t){return t[0]}function Wa(t){return t[1]}function Va(){return 1}var Ha=function(){var t=$a,e=Wa,n=Va,r=960,i=500,a=20,o=2,s=3*a,c=r+2*s>>o,u=i+2*s>>o,l=La(20);function h(r){var i=new Float32Array(c*u),h=new Float32Array(c*u);r.forEach((function(r,a,l){var h=+t(r,a,l)+s>>o,f=+e(r,a,l)+s>>o,d=+n(r,a,l);h>=0&&h=0&&f>o),Ua({width:c,height:u,data:h},{width:c,height:u,data:i},a>>o),za({width:c,height:u,data:i},{width:c,height:u,data:h},a>>o),Ua({width:c,height:u,data:h},{width:c,height:u,data:i},a>>o),za({width:c,height:u,data:i},{width:c,height:u,data:h},a>>o),Ua({width:c,height:u,data:h},{width:c,height:u,data:i},a>>o);var d=l(i);if(!Array.isArray(d)){var p=L(i);d=A(0,p,d),(d=k(0,Math.floor(p/d)*d,d)).shift()}return Ya().thresholds(d).size([c,u])(i).map(f)}function f(t){return t.value*=Math.pow(2,-2*o),t.coordinates.forEach(d),t}function d(t){t.forEach(p)}function p(t){t.forEach(g)}function g(t){t[0]=t[0]*Math.pow(2,o)-s,t[1]=t[1]*Math.pow(2,o)-s}function y(){return c=r+2*(s=3*a)>>o,u=i+2*s>>o,h}return h.x=function(e){return arguments.length?(t="function"==typeof e?e:La(+e),h):t},h.y=function(t){return arguments.length?(e="function"==typeof t?t:La(+t),h):e},h.weight=function(t){return arguments.length?(n="function"==typeof t?t:La(+t),h):n},h.size=function(t){if(!arguments.length)return[r,i];var e=Math.ceil(t[0]),n=Math.ceil(t[1]);if(!(e>=0||e>=0))throw new Error("invalid size");return r=e,i=n,y()},h.cellSize=function(t){if(!arguments.length)return 1<=1))throw new Error("invalid cell size");return o=Math.floor(Math.log(t)/Math.LN2),y()},h.thresholds=function(t){return arguments.length?(l="function"==typeof t?t:Array.isArray(t)?La(Na.call(t)):La(t),h):l},h.bandwidth=function(t){if(!arguments.length)return Math.sqrt(a*(a+1));if(!((t=+t)>=0))throw new Error("invalid bandwidth");return a=Math.round((Math.sqrt(4*t*t+1)-1)/2),y()},h},Ga=function(t){return function(){return t}};function qa(t,e,n,r,i,a,o,s,c,u){this.target=t,this.type=e,this.subject=n,this.identifier=r,this.active=i,this.x=a,this.y=o,this.dx=s,this.dy=c,this._=u}function Xa(){return!ce.ctrlKey&&!ce.button}function Za(){return this.parentNode}function Ja(t){return null==t?{x:ce.x,y:ce.y}:t}function Qa(){return navigator.maxTouchPoints||"ontouchstart"in this}qa.prototype.on=function(){var t=this._.on.apply(this._,arguments);return t===this._?this:t};var Ka=function(){var t,e,n,r,i=Xa,a=Za,o=Ja,s=Qa,c={},u=lt("start","drag","end"),l=0,h=0;function f(t){t.on("mousedown.drag",d).filter(s).on("touchstart.drag",y).on("touchmove.drag",v).on("touchend.drag touchcancel.drag",m).style("touch-action","none").style("-webkit-tap-highlight-color","rgba(0,0,0,0)")}function d(){if(!r&&i.apply(this,arguments)){var o=b("mouse",a.apply(this,arguments),Nn,this,arguments);o&&(ke(ce.view).on("mousemove.drag",p,!0).on("mouseup.drag",g,!0),Te(ce.view),we(),n=!1,t=ce.clientX,e=ce.clientY,o("start"))}}function p(){if(Ee(),!n){var r=ce.clientX-t,i=ce.clientY-e;n=r*r+i*i>h}c.mouse("drag")}function g(){ke(ce.view).on("mousemove.drag mouseup.drag",null),Ce(ce.view,n),Ee(),c.mouse("end")}function y(){if(i.apply(this,arguments)){var t,e,n=ce.changedTouches,r=a.apply(this,arguments),o=n.length;for(t=0;t9999?"+"+io(e,6):io(e,4))+"-"+io(t.getUTCMonth()+1,2)+"-"+io(t.getUTCDate(),2)+(a?"T"+io(n,2)+":"+io(r,2)+":"+io(i,2)+"."+io(a,3)+"Z":i?"T"+io(n,2)+":"+io(r,2)+":"+io(i,2)+"Z":r||n?"T"+io(n,2)+":"+io(r,2)+"Z":"")}var oo=function(t){var e=new RegExp('["'+t+"\n\r]"),n=t.charCodeAt(0);function r(t,e){var r,i=[],a=t.length,o=0,s=0,c=a<=0,u=!1;function l(){if(c)return eo;if(u)return u=!1,to;var e,r,i=o;if(34===t.charCodeAt(i)){for(;o++=a?c=!0:10===(r=t.charCodeAt(o++))?u=!0:13===r&&(u=!0,10===t.charCodeAt(o)&&++o),t.slice(i+1,e-1).replace(/""/g,'"')}for(;o=(a=(g+v)/2))?g=a:v=a,(l=n>=(o=(y+m)/2))?y=o:m=o,i=d,!(d=d[h=l<<1|u]))return i[h]=p,t;if(s=+t._x.call(null,d.data),c=+t._y.call(null,d.data),e===s&&n===c)return p.next=d,i?i[h]=p:t._root=p,t;do{i=i?i[h]=new Array(4):t._root=new Array(4),(u=e>=(a=(g+v)/2))?g=a:v=a,(l=n>=(o=(y+m)/2))?y=o:m=o}while((h=l<<1|u)==(f=(c>=o)<<1|s>=a));return i[f]=d,i[h]=p,t}var _s=function(t,e,n,r,i){this.node=t,this.x0=e,this.y0=n,this.x1=r,this.y1=i};function ks(t){return t[0]}function ws(t){return t[1]}function Es(t,e,n){var r=new Ts(null==e?ks:e,null==n?ws:n,NaN,NaN,NaN,NaN);return null==t?r:r.addAll(t)}function Ts(t,e,n,r,i,a){this._x=t,this._y=e,this._x0=n,this._y0=r,this._x1=i,this._y1=a,this._root=void 0}function Cs(t){for(var e={data:t.data},n=e;t=t.next;)n=n.next={data:t.data};return e}var Ss=Es.prototype=Ts.prototype;function As(t){return t.x+t.vx}function Ms(t){return t.y+t.vy}Ss.copy=function(){var t,e,n=new Ts(this._x,this._y,this._x0,this._y0,this._x1,this._y1),r=this._root;if(!r)return n;if(!r.length)return n._root=Cs(r),n;for(t=[{source:r,target:n._root=new Array(4)}];r=t.pop();)for(var i=0;i<4;++i)(e=r.source[i])&&(e.length?t.push({source:e,target:r.target[i]=new Array(4)}):r.target[i]=Cs(e));return n},Ss.add=function(t){var e=+this._x.call(null,t),n=+this._y.call(null,t);return xs(this.cover(e,n),e,n,t)},Ss.addAll=function(t){var e,n,r,i,a=t.length,o=new Array(a),s=new Array(a),c=1/0,u=1/0,l=-1/0,h=-1/0;for(n=0;nl&&(l=r),ih&&(h=i));if(c>l||u>h)return this;for(this.cover(c,u).cover(l,h),n=0;nt||t>=i||r>e||e>=a;)switch(s=(ef||(a=c.y0)>d||(o=c.x1)=v)<<1|t>=y)&&(c=p[p.length-1],p[p.length-1]=p[p.length-1-u],p[p.length-1-u]=c)}else{var m=t-+this._x.call(null,g.data),b=e-+this._y.call(null,g.data),x=m*m+b*b;if(x=(s=(p+y)/2))?p=s:y=s,(l=o>=(c=(g+v)/2))?g=c:v=c,e=d,!(d=d[h=l<<1|u]))return this;if(!d.length)break;(e[h+1&3]||e[h+2&3]||e[h+3&3])&&(n=e,f=h)}for(;d.data!==t;)if(r=d,!(d=d.next))return this;return(i=d.next)&&delete d.next,r?(i?r.next=i:delete r.next,this):e?(i?e[h]=i:delete e[h],(d=e[0]||e[1]||e[2]||e[3])&&d===(e[3]||e[2]||e[1]||e[0])&&!d.length&&(n?n[f]=d:this._root=d),this):(this._root=i,this)},Ss.removeAll=function(t){for(var e=0,n=t.length;ec+d||iu+d||as.index){var p=c-o.x-o.vx,g=u-o.y-o.vy,y=p*p+g*g;yt.r&&(t.r=t[e].r)}function s(){if(e){var r,i,a=e.length;for(n=new Array(a),r=0;r1?(null==n?s.remove(t):s.set(t,d(n)),e):s.get(t)},find:function(e,n,r){var i,a,o,s,c,u=0,l=t.length;for(null==r?r=1/0:r*=r,u=0;u1?(u.on(t,n),e):u.on(t)}}},js=function(){var t,e,n,r,i=ms(-30),a=1,o=1/0,s=.81;function c(r){var i,a=t.length,o=Es(t,Ls,Fs).visitAfter(l);for(n=r,i=0;i=o)){(t.data!==e||t.next)&&(0===l&&(d+=(l=bs())*l),0===h&&(d+=(h=bs())*h),d1?r[0]+r.slice(2):r,+t.slice(n+1)]},$s=function(t){return(t=Us(Math.abs(t)))?t[1]:NaN},Ws=/^(?:(.)?([<>=^]))?([+\-( ])?([$#])?(0)?(\d+)?(,)?(\.\d+)?(~)?([a-z%])?$/i;function Vs(t){if(!(e=Ws.exec(t)))throw new Error("invalid format: "+t);var e;return new Hs({fill:e[1],align:e[2],sign:e[3],symbol:e[4],zero:e[5],width:e[6],comma:e[7],precision:e[8]&&e[8].slice(1),trim:e[9],type:e[10]})}function Hs(t){this.fill=void 0===t.fill?" ":t.fill+"",this.align=void 0===t.align?">":t.align+"",this.sign=void 0===t.sign?"-":t.sign+"",this.symbol=void 0===t.symbol?"":t.symbol+"",this.zero=!!t.zero,this.width=void 0===t.width?void 0:+t.width,this.comma=!!t.comma,this.precision=void 0===t.precision?void 0:+t.precision,this.trim=!!t.trim,this.type=void 0===t.type?"":t.type+""}Vs.prototype=Hs.prototype,Hs.prototype.toString=function(){return this.fill+this.align+this.sign+this.symbol+(this.zero?"0":"")+(void 0===this.width?"":Math.max(1,0|this.width))+(this.comma?",":"")+(void 0===this.precision?"":"."+Math.max(0,0|this.precision))+(this.trim?"~":"")+this.type};var Gs,qs,Xs,Zs,Js=function(t,e){var n=Us(t,e);if(!n)return t+"";var r=n[0],i=n[1];return i<0?"0."+new Array(-i).join("0")+r:r.length>i+1?r.slice(0,i+1)+"."+r.slice(i+1):r+new Array(i-r.length+2).join("0")},Qs={"%":function(t,e){return(100*t).toFixed(e)},b:function(t){return Math.round(t).toString(2)},c:function(t){return t+""},d:function(t){return Math.round(t).toString(10)},e:function(t,e){return t.toExponential(e)},f:function(t,e){return t.toFixed(e)},g:function(t,e){return t.toPrecision(e)},o:function(t){return Math.round(t).toString(8)},p:function(t,e){return Js(100*t,e)},r:Js,s:function(t,e){var n=Us(t,e);if(!n)return t+"";var r=n[0],i=n[1],a=i-(Gs=3*Math.max(-8,Math.min(8,Math.floor(i/3))))+1,o=r.length;return a===o?r:a>o?r+new Array(a-o+1).join("0"):a>0?r.slice(0,a)+"."+r.slice(a):"0."+new Array(1-a).join("0")+Us(t,Math.max(0,e+a-1))[0]},X:function(t){return Math.round(t).toString(16).toUpperCase()},x:function(t){return Math.round(t).toString(16)}},Ks=function(t){return t},tc=Array.prototype.map,ec=["y","z","a","f","p","n","µ","m","","k","M","G","T","P","E","Z","Y"],nc=function(t){var e,n,r=void 0===t.grouping||void 0===t.thousands?Ks:(e=tc.call(t.grouping,Number),n=t.thousands+"",function(t,r){for(var i=t.length,a=[],o=0,s=e[0],c=0;i>0&&s>0&&(c+s+1>r&&(s=Math.max(1,r-c)),a.push(t.substring(i-=s,i+s)),!((c+=s+1)>r));)s=e[o=(o+1)%e.length];return a.reverse().join(n)}),i=void 0===t.currency?"":t.currency[0]+"",a=void 0===t.currency?"":t.currency[1]+"",o=void 0===t.decimal?".":t.decimal+"",s=void 0===t.numerals?Ks:function(t){return function(e){return e.replace(/[0-9]/g,(function(e){return t[+e]}))}}(tc.call(t.numerals,String)),c=void 0===t.percent?"%":t.percent+"",u=void 0===t.minus?"-":t.minus+"",l=void 0===t.nan?"NaN":t.nan+"";function h(t){var e=(t=Vs(t)).fill,n=t.align,h=t.sign,f=t.symbol,d=t.zero,p=t.width,g=t.comma,y=t.precision,v=t.trim,m=t.type;"n"===m?(g=!0,m="g"):Qs[m]||(void 0===y&&(y=12),v=!0,m="g"),(d||"0"===e&&"="===n)&&(d=!0,e="0",n="=");var b="$"===f?i:"#"===f&&/[boxX]/.test(m)?"0"+m.toLowerCase():"",x="$"===f?a:/[%p]/.test(m)?c:"",_=Qs[m],k=/[defgprs%]/.test(m);function w(t){var i,a,c,f=b,w=x;if("c"===m)w=_(t)+w,t="";else{var E=(t=+t)<0;if(t=isNaN(t)?l:_(Math.abs(t),y),v&&(t=function(t){t:for(var e,n=t.length,r=1,i=-1;r0&&(i=0)}return i>0?t.slice(0,i)+t.slice(e+1):t}(t)),E&&0==+t&&(E=!1),f=(E?"("===h?h:u:"-"===h||"("===h?"":h)+f,w=("s"===m?ec[8+Gs/3]:"")+w+(E&&"("===h?")":""),k)for(i=-1,a=t.length;++i(c=t.charCodeAt(i))||c>57){w=(46===c?o+t.slice(i+1):t.slice(i))+w,t=t.slice(0,i);break}}g&&!d&&(t=r(t,1/0));var T=f.length+t.length+w.length,C=T>1)+f+t+w+C.slice(T);break;default:t=C+f+t+w}return s(t)}return y=void 0===y?6:/[gprs]/.test(m)?Math.max(1,Math.min(21,y)):Math.max(0,Math.min(20,y)),w.toString=function(){return t+""},w}return{format:h,formatPrefix:function(t,e){var n=h(((t=Vs(t)).type="f",t)),r=3*Math.max(-8,Math.min(8,Math.floor($s(e)/3))),i=Math.pow(10,-r),a=ec[8+r/3];return function(t){return n(i*t)+a}}}};function rc(t){return qs=nc(t),Xs=qs.format,Zs=qs.formatPrefix,qs}rc({decimal:".",thousands:",",grouping:[3],currency:["$",""],minus:"-"});var ic=function(t){return Math.max(0,-$s(Math.abs(t)))},ac=function(t,e){return Math.max(0,3*Math.max(-8,Math.min(8,Math.floor($s(e)/3)))-$s(Math.abs(t)))},oc=function(t,e){return t=Math.abs(t),e=Math.abs(e)-t,Math.max(0,$s(e)-$s(t))+1},sc=function(){return new cc};function cc(){this.reset()}cc.prototype={constructor:cc,reset:function(){this.s=this.t=0},add:function(t){lc(uc,t,this.t),lc(this,uc.s,this.s),this.s?this.t+=uc.t:this.s=uc.t},valueOf:function(){return this.s}};var uc=new cc;function lc(t,e,n){var r=t.s=e+n,i=r-e,a=r-i;t.t=e-a+(n-i)}var hc=Math.PI,fc=hc/2,dc=hc/4,pc=2*hc,gc=180/hc,yc=hc/180,vc=Math.abs,mc=Math.atan,bc=Math.atan2,xc=Math.cos,_c=Math.ceil,kc=Math.exp,wc=(Math.floor,Math.log),Ec=Math.pow,Tc=Math.sin,Cc=Math.sign||function(t){return t>0?1:t<0?-1:0},Sc=Math.sqrt,Ac=Math.tan;function Mc(t){return t>1?0:t<-1?hc:Math.acos(t)}function Oc(t){return t>1?fc:t<-1?-fc:Math.asin(t)}function Dc(t){return(t=Tc(t/2))*t}function Nc(){}function Bc(t,e){t&&Fc.hasOwnProperty(t.type)&&Fc[t.type](t,e)}var Lc={Feature:function(t,e){Bc(t.geometry,e)},FeatureCollection:function(t,e){for(var n=t.features,r=-1,i=n.length;++r=0?1:-1,i=r*n,a=xc(e=(e*=yc)/2+dc),o=Tc(e),s=Uc*o,c=zc*a+s*xc(i),u=s*r*Tc(i);Wc.add(bc(u,c)),Yc=t,zc=a,Uc=o}var Jc=function(t){return Vc.reset(),$c(t,Hc),2*Vc};function Qc(t){return[bc(t[1],t[0]),Oc(t[2])]}function Kc(t){var e=t[0],n=t[1],r=xc(n);return[r*xc(e),r*Tc(e),Tc(n)]}function tu(t,e){return t[0]*e[0]+t[1]*e[1]+t[2]*e[2]}function eu(t,e){return[t[1]*e[2]-t[2]*e[1],t[2]*e[0]-t[0]*e[2],t[0]*e[1]-t[1]*e[0]]}function nu(t,e){t[0]+=e[0],t[1]+=e[1],t[2]+=e[2]}function ru(t,e){return[t[0]*e,t[1]*e,t[2]*e]}function iu(t){var e=Sc(t[0]*t[0]+t[1]*t[1]+t[2]*t[2]);t[0]/=e,t[1]/=e,t[2]/=e}var au,ou,su,cu,uu,lu,hu,fu,du,pu,gu=sc(),yu={point:vu,lineStart:bu,lineEnd:xu,polygonStart:function(){yu.point=_u,yu.lineStart=ku,yu.lineEnd=wu,gu.reset(),Hc.polygonStart()},polygonEnd:function(){Hc.polygonEnd(),yu.point=vu,yu.lineStart=bu,yu.lineEnd=xu,Wc<0?(au=-(su=180),ou=-(cu=90)):gu>1e-6?cu=90:gu<-1e-6&&(ou=-90),pu[0]=au,pu[1]=su},sphere:function(){au=-(su=180),ou=-(cu=90)}};function vu(t,e){du.push(pu=[au=t,su=t]),ecu&&(cu=e)}function mu(t,e){var n=Kc([t*yc,e*yc]);if(fu){var r=eu(fu,n),i=eu([r[1],-r[0],0],r);iu(i),i=Qc(i);var a,o=t-uu,s=o>0?1:-1,c=i[0]*gc*s,u=vc(o)>180;u^(s*uucu&&(cu=a):u^(s*uu<(c=(c+360)%360-180)&&ccu&&(cu=e)),u?tEu(au,su)&&(su=t):Eu(t,su)>Eu(au,su)&&(au=t):su>=au?(tsu&&(su=t)):t>uu?Eu(au,t)>Eu(au,su)&&(su=t):Eu(t,su)>Eu(au,su)&&(au=t)}else du.push(pu=[au=t,su=t]);ecu&&(cu=e),fu=n,uu=t}function bu(){yu.point=mu}function xu(){pu[0]=au,pu[1]=su,yu.point=vu,fu=null}function _u(t,e){if(fu){var n=t-uu;gu.add(vc(n)>180?n+(n>0?360:-360):n)}else lu=t,hu=e;Hc.point(t,e),mu(t,e)}function ku(){Hc.lineStart()}function wu(){_u(lu,hu),Hc.lineEnd(),vc(gu)>1e-6&&(au=-(su=180)),pu[0]=au,pu[1]=su,fu=null}function Eu(t,e){return(e-=t)<0?e+360:e}function Tu(t,e){return t[0]-e[0]}function Cu(t,e){return t[0]<=t[1]?t[0]<=e&&e<=t[1]:eEu(r[0],r[1])&&(r[1]=i[1]),Eu(i[0],r[1])>Eu(r[0],r[1])&&(r[0]=i[0])):a.push(r=i);for(o=-1/0,e=0,r=a[n=a.length-1];e<=n;r=i,++e)i=a[e],(s=Eu(r[1],i[0]))>o&&(o=s,au=i[0],su=r[1])}return du=pu=null,au===1/0||ou===1/0?[[NaN,NaN],[NaN,NaN]]:[[au,ou],[su,cu]]},Wu={sphere:Nc,point:Vu,lineStart:Gu,lineEnd:Zu,polygonStart:function(){Wu.lineStart=Ju,Wu.lineEnd=Qu},polygonEnd:function(){Wu.lineStart=Gu,Wu.lineEnd=Zu}};function Vu(t,e){t*=yc;var n=xc(e*=yc);Hu(n*xc(t),n*Tc(t),Tc(e))}function Hu(t,e,n){++Su,Mu+=(t-Mu)/Su,Ou+=(e-Ou)/Su,Du+=(n-Du)/Su}function Gu(){Wu.point=qu}function qu(t,e){t*=yc;var n=xc(e*=yc);Yu=n*xc(t),zu=n*Tc(t),Uu=Tc(e),Wu.point=Xu,Hu(Yu,zu,Uu)}function Xu(t,e){t*=yc;var n=xc(e*=yc),r=n*xc(t),i=n*Tc(t),a=Tc(e),o=bc(Sc((o=zu*a-Uu*i)*o+(o=Uu*r-Yu*a)*o+(o=Yu*i-zu*r)*o),Yu*r+zu*i+Uu*a);Au+=o,Nu+=o*(Yu+(Yu=r)),Bu+=o*(zu+(zu=i)),Lu+=o*(Uu+(Uu=a)),Hu(Yu,zu,Uu)}function Zu(){Wu.point=Vu}function Ju(){Wu.point=Ku}function Qu(){tl(ju,Ru),Wu.point=Vu}function Ku(t,e){ju=t,Ru=e,t*=yc,e*=yc,Wu.point=tl;var n=xc(e);Yu=n*xc(t),zu=n*Tc(t),Uu=Tc(e),Hu(Yu,zu,Uu)}function tl(t,e){t*=yc;var n=xc(e*=yc),r=n*xc(t),i=n*Tc(t),a=Tc(e),o=zu*a-Uu*i,s=Uu*r-Yu*a,c=Yu*i-zu*r,u=Sc(o*o+s*s+c*c),l=Oc(u),h=u&&-l/u;Fu+=h*o,Pu+=h*s,Iu+=h*c,Au+=l,Nu+=l*(Yu+(Yu=r)),Bu+=l*(zu+(zu=i)),Lu+=l*(Uu+(Uu=a)),Hu(Yu,zu,Uu)}var el=function(t){Su=Au=Mu=Ou=Du=Nu=Bu=Lu=Fu=Pu=Iu=0,$c(t,Wu);var e=Fu,n=Pu,r=Iu,i=e*e+n*n+r*r;return i<1e-12&&(e=Nu,n=Bu,r=Lu,Au<1e-6&&(e=Mu,n=Ou,r=Du),(i=e*e+n*n+r*r)<1e-12)?[NaN,NaN]:[bc(n,e)*gc,Oc(r/Sc(i))*gc]},nl=function(t){return function(){return t}},rl=function(t,e){function n(n,r){return n=t(n,r),e(n[0],n[1])}return t.invert&&e.invert&&(n.invert=function(n,r){return(n=e.invert(n,r))&&t.invert(n[0],n[1])}),n};function il(t,e){return[vc(t)>hc?t+Math.round(-t/pc)*pc:t,e]}function al(t,e,n){return(t%=pc)?e||n?rl(sl(t),cl(e,n)):sl(t):e||n?cl(e,n):il}function ol(t){return function(e,n){return[(e+=t)>hc?e-pc:e<-hc?e+pc:e,n]}}function sl(t){var e=ol(t);return e.invert=ol(-t),e}function cl(t,e){var n=xc(t),r=Tc(t),i=xc(e),a=Tc(e);function o(t,e){var o=xc(e),s=xc(t)*o,c=Tc(t)*o,u=Tc(e),l=u*n+s*r;return[bc(c*i-l*a,s*n-u*r),Oc(l*i+c*a)]}return o.invert=function(t,e){var o=xc(e),s=xc(t)*o,c=Tc(t)*o,u=Tc(e),l=u*i-c*a;return[bc(c*i+u*a,s*n+l*r),Oc(l*n-s*r)]},o}il.invert=il;var ul=function(t){function e(e){return(e=t(e[0]*yc,e[1]*yc))[0]*=gc,e[1]*=gc,e}return t=al(t[0]*yc,t[1]*yc,t.length>2?t[2]*yc:0),e.invert=function(e){return(e=t.invert(e[0]*yc,e[1]*yc))[0]*=gc,e[1]*=gc,e},e};function ll(t,e,n,r,i,a){if(n){var o=xc(e),s=Tc(e),c=r*n;null==i?(i=e+r*pc,a=e-c/2):(i=hl(o,i),a=hl(o,a),(r>0?ia)&&(i+=r*pc));for(var u,l=i;r>0?l>a:l1&&e.push(e.pop().concat(e.shift()))},result:function(){var n=e;return e=[],t=null,n}}},pl=function(t,e){return vc(t[0]-e[0])<1e-6&&vc(t[1]-e[1])<1e-6};function gl(t,e,n,r){this.x=t,this.z=e,this.o=n,this.e=r,this.v=!1,this.n=this.p=null}var yl=function(t,e,n,r,i){var a,o,s=[],c=[];if(t.forEach((function(t){if(!((e=t.length-1)<=0)){var e,n,r=t[0],o=t[e];if(pl(r,o)){for(i.lineStart(),a=0;a=0;--a)i.point((l=u[a])[0],l[1]);else r(f.x,f.p.x,-1,i);f=f.p}u=(f=f.o).z,d=!d}while(!f.v);i.lineEnd()}}};function vl(t){if(e=t.length){for(var e,n,r=0,i=t[0];++r=0?1:-1,T=E*w,C=T>hc,S=g*_;if(ml.add(bc(S*E*Tc(T),y*k+S*xc(T))),o+=C?w+E*pc:w,C^d>=n^b>=n){var A=eu(Kc(f),Kc(m));iu(A);var M=eu(a,A);iu(M);var O=(C^w>=0?-1:1)*Oc(M[2]);(r>O||r===O&&(A[0]||A[1]))&&(s+=C^w>=0?1:-1)}}return(o<-1e-6||o<1e-6&&ml<-1e-6)^1&s},_l=function(t,e,n,r){return function(i){var a,o,s,c=e(i),u=dl(),l=e(u),h=!1,f={point:d,lineStart:g,lineEnd:y,polygonStart:function(){f.point=v,f.lineStart=m,f.lineEnd=b,o=[],a=[]},polygonEnd:function(){f.point=d,f.lineStart=g,f.lineEnd=y,o=I(o);var t=xl(a,r);o.length?(h||(i.polygonStart(),h=!0),yl(o,wl,t,n,i)):t&&(h||(i.polygonStart(),h=!0),i.lineStart(),n(null,null,1,i),i.lineEnd()),h&&(i.polygonEnd(),h=!1),o=a=null},sphere:function(){i.polygonStart(),i.lineStart(),n(null,null,1,i),i.lineEnd(),i.polygonEnd()}};function d(e,n){t(e,n)&&i.point(e,n)}function p(t,e){c.point(t,e)}function g(){f.point=p,c.lineStart()}function y(){f.point=d,c.lineEnd()}function v(t,e){s.push([t,e]),l.point(t,e)}function m(){l.lineStart(),s=[]}function b(){v(s[0][0],s[0][1]),l.lineEnd();var t,e,n,r,c=l.clean(),f=u.result(),d=f.length;if(s.pop(),a.push(s),s=null,d)if(1&c){if((e=(n=f[0]).length-1)>0){for(h||(i.polygonStart(),h=!0),i.lineStart(),t=0;t1&&2&c&&f.push(f.pop().concat(f.shift())),o.push(f.filter(kl))}return f}};function kl(t){return t.length>1}function wl(t,e){return((t=t.x)[0]<0?t[1]-fc-1e-6:fc-t[1])-((e=e.x)[0]<0?e[1]-fc-1e-6:fc-e[1])}var El=_l((function(){return!0}),(function(t){var e,n=NaN,r=NaN,i=NaN;return{lineStart:function(){t.lineStart(),e=1},point:function(a,o){var s=a>0?hc:-hc,c=vc(a-n);vc(c-hc)<1e-6?(t.point(n,r=(r+o)/2>0?fc:-fc),t.point(i,r),t.lineEnd(),t.lineStart(),t.point(s,r),t.point(a,r),e=0):i!==s&&c>=hc&&(vc(n-i)<1e-6&&(n-=1e-6*i),vc(a-s)<1e-6&&(a-=1e-6*s),r=function(t,e,n,r){var i,a,o=Tc(t-n);return vc(o)>1e-6?mc((Tc(e)*(a=xc(r))*Tc(n)-Tc(r)*(i=xc(e))*Tc(t))/(i*a*o)):(e+r)/2}(n,r,a,o),t.point(i,r),t.lineEnd(),t.lineStart(),t.point(s,r),e=0),t.point(n=a,r=o),i=s},lineEnd:function(){t.lineEnd(),n=r=NaN},clean:function(){return 2-e}}}),(function(t,e,n,r){var i;if(null==t)i=n*fc,r.point(-hc,i),r.point(0,i),r.point(hc,i),r.point(hc,0),r.point(hc,-i),r.point(0,-i),r.point(-hc,-i),r.point(-hc,0),r.point(-hc,i);else if(vc(t[0]-e[0])>1e-6){var a=t[0]0,i=vc(e)>1e-6;function a(t,n){return xc(t)*xc(n)>e}function o(t,n,r){var i=[1,0,0],a=eu(Kc(t),Kc(n)),o=tu(a,a),s=a[0],c=o-s*s;if(!c)return!r&&t;var u=e*o/c,l=-e*s/c,h=eu(i,a),f=ru(i,u);nu(f,ru(a,l));var d=h,p=tu(f,d),g=tu(d,d),y=p*p-g*(tu(f,f)-1);if(!(y<0)){var v=Sc(y),m=ru(d,(-p-v)/g);if(nu(m,f),m=Qc(m),!r)return m;var b,x=t[0],_=n[0],k=t[1],w=n[1];_0^m[1]<(vc(m[0]-x)<1e-6?k:w):k<=m[1]&&m[1]<=w:E>hc^(x<=m[0]&&m[0]<=_)){var C=ru(d,(-p+v)/g);return nu(C,f),[m,Qc(C)]}}}function s(e,n){var i=r?t:hc-t,a=0;return e<-i?a|=1:e>i&&(a|=2),n<-i?a|=4:n>i&&(a|=8),a}return _l(a,(function(t){var e,n,c,u,l;return{lineStart:function(){u=c=!1,l=1},point:function(h,f){var d,p=[h,f],g=a(h,f),y=r?g?0:s(h,f):g?s(h+(h<0?hc:-hc),f):0;if(!e&&(u=c=g)&&t.lineStart(),g!==c&&(!(d=o(e,p))||pl(e,d)||pl(p,d))&&(p[0]+=1e-6,p[1]+=1e-6,g=a(p[0],p[1])),g!==c)l=0,g?(t.lineStart(),d=o(p,e),t.point(d[0],d[1])):(d=o(e,p),t.point(d[0],d[1]),t.lineEnd()),e=d;else if(i&&e&&r^g){var v;y&n||!(v=o(p,e,!0))||(l=0,r?(t.lineStart(),t.point(v[0][0],v[0][1]),t.point(v[1][0],v[1][1]),t.lineEnd()):(t.point(v[1][0],v[1][1]),t.lineEnd(),t.lineStart(),t.point(v[0][0],v[0][1])))}!g||e&&pl(e,p)||t.point(p[0],p[1]),e=p,c=g,n=y},lineEnd:function(){c&&t.lineEnd(),e=null},clean:function(){return l|(u&&c)<<1}}}),(function(e,r,i,a){ll(a,t,n,i,e,r)}),r?[0,-t]:[-hc,t-hc])};function Cl(t,e,n,r){function i(i,a){return t<=i&&i<=n&&e<=a&&a<=r}function a(i,a,s,u){var l=0,h=0;if(null==i||(l=o(i,s))!==(h=o(a,s))||c(i,a)<0^s>0)do{u.point(0===l||3===l?t:n,l>1?r:e)}while((l=(l+s+4)%4)!==h);else u.point(a[0],a[1])}function o(r,i){return vc(r[0]-t)<1e-6?i>0?0:3:vc(r[0]-n)<1e-6?i>0?2:1:vc(r[1]-e)<1e-6?i>0?1:0:i>0?3:2}function s(t,e){return c(t.x,e.x)}function c(t,e){var n=o(t,1),r=o(e,1);return n!==r?n-r:0===n?e[1]-t[1]:1===n?t[0]-e[0]:2===n?t[1]-e[1]:e[0]-t[0]}return function(o){var c,u,l,h,f,d,p,g,y,v,m,b=o,x=dl(),_={point:k,lineStart:function(){_.point=w,u&&u.push(l=[]);v=!0,y=!1,p=g=NaN},lineEnd:function(){c&&(w(h,f),d&&y&&x.rejoin(),c.push(x.result()));_.point=k,y&&b.lineEnd()},polygonStart:function(){b=x,c=[],u=[],m=!0},polygonEnd:function(){var e=function(){for(var e=0,n=0,i=u.length;nr&&(f-a)*(r-o)>(d-o)*(t-a)&&++e:d<=r&&(f-a)*(r-o)<(d-o)*(t-a)&&--e;return e}(),n=m&&e,i=(c=I(c)).length;(n||i)&&(o.polygonStart(),n&&(o.lineStart(),a(null,null,1,o),o.lineEnd()),i&&yl(c,s,e,a,o),o.polygonEnd());b=o,c=u=l=null}};function k(t,e){i(t,e)&&b.point(t,e)}function w(a,o){var s=i(a,o);if(u&&l.push([a,o]),v)h=a,f=o,d=s,v=!1,s&&(b.lineStart(),b.point(a,o));else if(s&&y)b.point(a,o);else{var c=[p=Math.max(-1e9,Math.min(1e9,p)),g=Math.max(-1e9,Math.min(1e9,g))],x=[a=Math.max(-1e9,Math.min(1e9,a)),o=Math.max(-1e9,Math.min(1e9,o))];!function(t,e,n,r,i,a){var o,s=t[0],c=t[1],u=0,l=1,h=e[0]-s,f=e[1]-c;if(o=n-s,h||!(o>0)){if(o/=h,h<0){if(o0){if(o>l)return;o>u&&(u=o)}if(o=i-s,h||!(o<0)){if(o/=h,h<0){if(o>l)return;o>u&&(u=o)}else if(h>0){if(o0)){if(o/=f,f<0){if(o0){if(o>l)return;o>u&&(u=o)}if(o=a-c,f||!(o<0)){if(o/=f,f<0){if(o>l)return;o>u&&(u=o)}else if(f>0){if(o0&&(t[0]=s+u*h,t[1]=c+u*f),l<1&&(e[0]=s+l*h,e[1]=c+l*f),!0}}}}}(c,x,t,e,n,r)?s&&(b.lineStart(),b.point(a,o),m=!1):(y||(b.lineStart(),b.point(c[0],c[1])),b.point(x[0],x[1]),s||b.lineEnd(),m=!1)}p=a,g=o,y=s}return _}}var Sl,Al,Ml,Ol=function(){var t,e,n,r=0,i=0,a=960,o=500;return n={stream:function(n){return t&&e===n?t:t=Cl(r,i,a,o)(e=n)},extent:function(s){return arguments.length?(r=+s[0][0],i=+s[0][1],a=+s[1][0],o=+s[1][1],t=e=null,n):[[r,i],[a,o]]}}},Dl=sc(),Nl={sphere:Nc,point:Nc,lineStart:function(){Nl.point=Ll,Nl.lineEnd=Bl},lineEnd:Nc,polygonStart:Nc,polygonEnd:Nc};function Bl(){Nl.point=Nl.lineEnd=Nc}function Ll(t,e){Sl=t*=yc,Al=Tc(e*=yc),Ml=xc(e),Nl.point=Fl}function Fl(t,e){t*=yc;var n=Tc(e*=yc),r=xc(e),i=vc(t-Sl),a=xc(i),o=r*Tc(i),s=Ml*n-Al*r*a,c=Al*n+Ml*r*a;Dl.add(bc(Sc(o*o+s*s),c)),Sl=t,Al=n,Ml=r}var Pl=function(t){return Dl.reset(),$c(t,Nl),+Dl},Il=[null,null],jl={type:"LineString",coordinates:Il},Rl=function(t,e){return Il[0]=t,Il[1]=e,Pl(jl)},Yl={Feature:function(t,e){return Ul(t.geometry,e)},FeatureCollection:function(t,e){for(var n=t.features,r=-1,i=n.length;++r0&&(i=Rl(t[a],t[a-1]))>0&&n<=i&&r<=i&&(n+r-i)*(1-Math.pow((n-r)/i,2))<1e-12*i)return!0;n=r}return!1}function Vl(t,e){return!!xl(t.map(Hl),Gl(e))}function Hl(t){return(t=t.map(Gl)).pop(),t}function Gl(t){return[t[0]*yc,t[1]*yc]}var ql=function(t,e){return(t&&Yl.hasOwnProperty(t.type)?Yl[t.type]:Ul)(t,e)};function Xl(t,e,n){var r=k(t,e-1e-6,n).concat(e);return function(t){return r.map((function(e){return[t,e]}))}}function Zl(t,e,n){var r=k(t,e-1e-6,n).concat(e);return function(t){return r.map((function(e){return[e,t]}))}}function Jl(){var t,e,n,r,i,a,o,s,c,u,l,h,f=10,d=f,p=90,g=360,y=2.5;function v(){return{type:"MultiLineString",coordinates:m()}}function m(){return k(_c(r/p)*p,n,p).map(l).concat(k(_c(s/g)*g,o,g).map(h)).concat(k(_c(e/f)*f,t,f).filter((function(t){return vc(t%p)>1e-6})).map(c)).concat(k(_c(a/d)*d,i,d).filter((function(t){return vc(t%g)>1e-6})).map(u))}return v.lines=function(){return m().map((function(t){return{type:"LineString",coordinates:t}}))},v.outline=function(){return{type:"Polygon",coordinates:[l(r).concat(h(o).slice(1),l(n).reverse().slice(1),h(s).reverse().slice(1))]}},v.extent=function(t){return arguments.length?v.extentMajor(t).extentMinor(t):v.extentMinor()},v.extentMajor=function(t){return arguments.length?(r=+t[0][0],n=+t[1][0],s=+t[0][1],o=+t[1][1],r>n&&(t=r,r=n,n=t),s>o&&(t=s,s=o,o=t),v.precision(y)):[[r,s],[n,o]]},v.extentMinor=function(n){return arguments.length?(e=+n[0][0],t=+n[1][0],a=+n[0][1],i=+n[1][1],e>t&&(n=e,e=t,t=n),a>i&&(n=a,a=i,i=n),v.precision(y)):[[e,a],[t,i]]},v.step=function(t){return arguments.length?v.stepMajor(t).stepMinor(t):v.stepMinor()},v.stepMajor=function(t){return arguments.length?(p=+t[0],g=+t[1],v):[p,g]},v.stepMinor=function(t){return arguments.length?(f=+t[0],d=+t[1],v):[f,d]},v.precision=function(f){return arguments.length?(y=+f,c=Xl(a,i,90),u=Zl(e,t,y),l=Xl(s,o,90),h=Zl(r,n,y),v):y},v.extentMajor([[-180,1e-6-90],[180,90-1e-6]]).extentMinor([[-180,-80-1e-6],[180,80+1e-6]])}function Ql(){return Jl()()}var Kl,th,eh,nh,rh=function(t,e){var n=t[0]*yc,r=t[1]*yc,i=e[0]*yc,a=e[1]*yc,o=xc(r),s=Tc(r),c=xc(a),u=Tc(a),l=o*xc(n),h=o*Tc(n),f=c*xc(i),d=c*Tc(i),p=2*Oc(Sc(Dc(a-r)+o*c*Dc(i-n))),g=Tc(p),y=p?function(t){var e=Tc(t*=p)/g,n=Tc(p-t)/g,r=n*l+e*f,i=n*h+e*d,a=n*s+e*u;return[bc(i,r)*gc,bc(a,Sc(r*r+i*i))*gc]}:function(){return[n*gc,r*gc]};return y.distance=p,y},ih=function(t){return t},ah=sc(),oh=sc(),sh={point:Nc,lineStart:Nc,lineEnd:Nc,polygonStart:function(){sh.lineStart=ch,sh.lineEnd=hh},polygonEnd:function(){sh.lineStart=sh.lineEnd=sh.point=Nc,ah.add(vc(oh)),oh.reset()},result:function(){var t=ah/2;return ah.reset(),t}};function ch(){sh.point=uh}function uh(t,e){sh.point=lh,Kl=eh=t,th=nh=e}function lh(t,e){oh.add(nh*t-eh*e),eh=t,nh=e}function hh(){lh(Kl,th)}var fh=sh,dh=1/0,ph=dh,gh=-dh,yh=gh;var vh,mh,bh,xh,_h={point:function(t,e){tgh&&(gh=t);eyh&&(yh=e)},lineStart:Nc,lineEnd:Nc,polygonStart:Nc,polygonEnd:Nc,result:function(){var t=[[dh,ph],[gh,yh]];return gh=yh=-(ph=dh=1/0),t}},kh=0,wh=0,Eh=0,Th=0,Ch=0,Sh=0,Ah=0,Mh=0,Oh=0,Dh={point:Nh,lineStart:Bh,lineEnd:Ph,polygonStart:function(){Dh.lineStart=Ih,Dh.lineEnd=jh},polygonEnd:function(){Dh.point=Nh,Dh.lineStart=Bh,Dh.lineEnd=Ph},result:function(){var t=Oh?[Ah/Oh,Mh/Oh]:Sh?[Th/Sh,Ch/Sh]:Eh?[kh/Eh,wh/Eh]:[NaN,NaN];return kh=wh=Eh=Th=Ch=Sh=Ah=Mh=Oh=0,t}};function Nh(t,e){kh+=t,wh+=e,++Eh}function Bh(){Dh.point=Lh}function Lh(t,e){Dh.point=Fh,Nh(bh=t,xh=e)}function Fh(t,e){var n=t-bh,r=e-xh,i=Sc(n*n+r*r);Th+=i*(bh+t)/2,Ch+=i*(xh+e)/2,Sh+=i,Nh(bh=t,xh=e)}function Ph(){Dh.point=Nh}function Ih(){Dh.point=Rh}function jh(){Yh(vh,mh)}function Rh(t,e){Dh.point=Yh,Nh(vh=bh=t,mh=xh=e)}function Yh(t,e){var n=t-bh,r=e-xh,i=Sc(n*n+r*r);Th+=i*(bh+t)/2,Ch+=i*(xh+e)/2,Sh+=i,Ah+=(i=xh*t-bh*e)*(bh+t),Mh+=i*(xh+e),Oh+=3*i,Nh(bh=t,xh=e)}var zh=Dh;function Uh(t){this._context=t}Uh.prototype={_radius:4.5,pointRadius:function(t){return this._radius=t,this},polygonStart:function(){this._line=0},polygonEnd:function(){this._line=NaN},lineStart:function(){this._point=0},lineEnd:function(){0===this._line&&this._context.closePath(),this._point=NaN},point:function(t,e){switch(this._point){case 0:this._context.moveTo(t,e),this._point=1;break;case 1:this._context.lineTo(t,e);break;default:this._context.moveTo(t+this._radius,e),this._context.arc(t,e,this._radius,0,pc)}},result:Nc};var $h,Wh,Vh,Hh,Gh,qh=sc(),Xh={point:Nc,lineStart:function(){Xh.point=Zh},lineEnd:function(){$h&&Jh(Wh,Vh),Xh.point=Nc},polygonStart:function(){$h=!0},polygonEnd:function(){$h=null},result:function(){var t=+qh;return qh.reset(),t}};function Zh(t,e){Xh.point=Jh,Wh=Hh=t,Vh=Gh=e}function Jh(t,e){Hh-=t,Gh-=e,qh.add(Sc(Hh*Hh+Gh*Gh)),Hh=t,Gh=e}var Qh=Xh;function Kh(){this._string=[]}function tf(t){return"m0,"+t+"a"+t+","+t+" 0 1,1 0,"+-2*t+"a"+t+","+t+" 0 1,1 0,"+2*t+"z"}Kh.prototype={_radius:4.5,_circle:tf(4.5),pointRadius:function(t){return(t=+t)!==this._radius&&(this._radius=t,this._circle=null),this},polygonStart:function(){this._line=0},polygonEnd:function(){this._line=NaN},lineStart:function(){this._point=0},lineEnd:function(){0===this._line&&this._string.push("Z"),this._point=NaN},point:function(t,e){switch(this._point){case 0:this._string.push("M",t,",",e),this._point=1;break;case 1:this._string.push("L",t,",",e);break;default:null==this._circle&&(this._circle=tf(this._radius)),this._string.push("M",t,",",e,this._circle)}},result:function(){if(this._string.length){var t=this._string.join("");return this._string=[],t}return null}};var ef=function(t,e){var n,r,i=4.5;function a(t){return t&&("function"==typeof i&&r.pointRadius(+i.apply(this,arguments)),$c(t,n(r))),r.result()}return a.area=function(t){return $c(t,n(fh)),fh.result()},a.measure=function(t){return $c(t,n(Qh)),Qh.result()},a.bounds=function(t){return $c(t,n(_h)),_h.result()},a.centroid=function(t){return $c(t,n(zh)),zh.result()},a.projection=function(e){return arguments.length?(n=null==e?(t=null,ih):(t=e).stream,a):t},a.context=function(t){return arguments.length?(r=null==t?(e=null,new Kh):new Uh(e=t),"function"!=typeof i&&r.pointRadius(i),a):e},a.pointRadius=function(t){return arguments.length?(i="function"==typeof t?t:(r.pointRadius(+t),+t),a):i},a.projection(t).context(e)},nf=function(t){return{stream:rf(t)}};function rf(t){return function(e){var n=new af;for(var r in t)n[r]=t[r];return n.stream=e,n}}function af(){}function of(t,e,n){var r=t.clipExtent&&t.clipExtent();return t.scale(150).translate([0,0]),null!=r&&t.clipExtent(null),$c(n,t.stream(_h)),e(_h.result()),null!=r&&t.clipExtent(r),t}function sf(t,e,n){return of(t,(function(n){var r=e[1][0]-e[0][0],i=e[1][1]-e[0][1],a=Math.min(r/(n[1][0]-n[0][0]),i/(n[1][1]-n[0][1])),o=+e[0][0]+(r-a*(n[1][0]+n[0][0]))/2,s=+e[0][1]+(i-a*(n[1][1]+n[0][1]))/2;t.scale(150*a).translate([o,s])}),n)}function cf(t,e,n){return sf(t,[[0,0],e],n)}function uf(t,e,n){return of(t,(function(n){var r=+e,i=r/(n[1][0]-n[0][0]),a=(r-i*(n[1][0]+n[0][0]))/2,o=-i*n[0][1];t.scale(150*i).translate([a,o])}),n)}function lf(t,e,n){return of(t,(function(n){var r=+e,i=r/(n[1][1]-n[0][1]),a=-i*n[0][0],o=(r-i*(n[1][1]+n[0][1]))/2;t.scale(150*i).translate([a,o])}),n)}af.prototype={constructor:af,point:function(t,e){this.stream.point(t,e)},sphere:function(){this.stream.sphere()},lineStart:function(){this.stream.lineStart()},lineEnd:function(){this.stream.lineEnd()},polygonStart:function(){this.stream.polygonStart()},polygonEnd:function(){this.stream.polygonEnd()}};var hf=xc(30*yc),ff=function(t,e){return+e?function(t,e){function n(r,i,a,o,s,c,u,l,h,f,d,p,g,y){var v=u-r,m=l-i,b=v*v+m*m;if(b>4*e&&g--){var x=o+f,_=s+d,k=c+p,w=Sc(x*x+_*_+k*k),E=Oc(k/=w),T=vc(vc(k)-1)<1e-6||vc(a-h)<1e-6?(a+h)/2:bc(_,x),C=t(T,E),S=C[0],A=C[1],M=S-r,O=A-i,D=m*M-v*O;(D*D/b>e||vc((v*M+m*O)/b-.5)>.3||o*f+s*d+c*p2?t[2]%360*yc:0,S()):[y*gc,v*gc,m*gc]},T.angle=function(t){return arguments.length?(b=t%360*yc,S()):b*gc},T.precision=function(t){return arguments.length?(o=ff(s,E=t*t),A()):Sc(E)},T.fitExtent=function(t,e){return sf(T,t,e)},T.fitSize=function(t,e){return cf(T,t,e)},T.fitWidth=function(t,e){return uf(T,t,e)},T.fitHeight=function(t,e){return lf(T,t,e)},function(){return e=t.apply(this,arguments),T.invert=e.invert&&C,S()}}function mf(t){var e=0,n=hc/3,r=vf(t),i=r(e,n);return i.parallels=function(t){return arguments.length?r(e=t[0]*yc,n=t[1]*yc):[e*gc,n*gc]},i}function bf(t,e){var n=Tc(t),r=(n+Tc(e))/2;if(vc(r)<1e-6)return function(t){var e=xc(t);function n(t,n){return[t*e,Tc(n)/e]}return n.invert=function(t,n){return[t/e,Oc(n*e)]},n}(t);var i=1+n*(2*r-n),a=Sc(i)/r;function o(t,e){var n=Sc(i-2*r*Tc(e))/r;return[n*Tc(t*=r),a-n*xc(t)]}return o.invert=function(t,e){var n=a-e;return[bc(t,vc(n))/r*Cc(n),Oc((i-(t*t+n*n)*r*r)/(2*r))]},o}var xf=function(){return mf(bf).scale(155.424).center([0,33.6442])},_f=function(){return xf().parallels([29.5,45.5]).scale(1070).translate([480,250]).rotate([96,0]).center([-.6,38.7])};var kf=function(){var t,e,n,r,i,a,o=_f(),s=xf().rotate([154,0]).center([-2,58.5]).parallels([55,65]),c=xf().rotate([157,0]).center([-3,19.9]).parallels([8,18]),u={point:function(t,e){a=[t,e]}};function l(t){var e=t[0],o=t[1];return a=null,n.point(e,o),a||(r.point(e,o),a)||(i.point(e,o),a)}function h(){return t=e=null,l}return l.invert=function(t){var e=o.scale(),n=o.translate(),r=(t[0]-n[0])/e,i=(t[1]-n[1])/e;return(i>=.12&&i<.234&&r>=-.425&&r<-.214?s:i>=.166&&i<.234&&r>=-.214&&r<-.115?c:o).invert(t)},l.stream=function(n){return t&&e===n?t:(r=[o.stream(e=n),s.stream(n),c.stream(n)],i=r.length,t={point:function(t,e){for(var n=-1;++n0?e<1e-6-fc&&(e=1e-6-fc):e>fc-1e-6&&(e=fc-1e-6);var n=i/Ec(Nf(e),r);return[n*Tc(r*t),i-n*xc(r*t)]}return a.invert=function(t,e){var n=i-e,a=Cc(r)*Sc(t*t+n*n);return[bc(t,vc(n))/r*Cc(n),2*mc(Ec(i/a,1/r))-fc]},a}var Lf=function(){return mf(Bf).scale(109.5).parallels([30,30])};function Ff(t,e){return[t,e]}Ff.invert=Ff;var Pf=function(){return yf(Ff).scale(152.63)};function If(t,e){var n=xc(t),r=t===e?Tc(t):(n-xc(e))/(e-t),i=n/r+t;if(vc(r)<1e-6)return Ff;function a(t,e){var n=i-e,a=r*t;return[n*Tc(a),i-n*xc(a)]}return a.invert=function(t,e){var n=i-e;return[bc(t,vc(n))/r*Cc(n),i-Cc(r)*Sc(t*t+n*n)]},a}var jf=function(){return mf(If).scale(131.154).center([0,13.9389])},Rf=1.340264,Yf=-.081106,zf=893e-6,Uf=.003796,$f=Sc(3)/2;function Wf(t,e){var n=Oc($f*Tc(e)),r=n*n,i=r*r*r;return[t*xc(n)/($f*(Rf+3*Yf*r+i*(7*zf+9*Uf*r))),n*(Rf+Yf*r+i*(zf+Uf*r))]}Wf.invert=function(t,e){for(var n,r=e,i=r*r,a=i*i*i,o=0;o<12&&(a=(i=(r-=n=(r*(Rf+Yf*i+a*(zf+Uf*i))-e)/(Rf+3*Yf*i+a*(7*zf+9*Uf*i)))*r)*i*i,!(vc(n)<1e-12));++o);return[$f*t*(Rf+3*Yf*i+a*(7*zf+9*Uf*i))/xc(r),Oc(Tc(r)/$f)]};var Vf=function(){return yf(Wf).scale(177.158)};function Hf(t,e){var n=xc(e),r=xc(t)*n;return[n*Tc(t)/r,Tc(e)/r]}Hf.invert=Ef(mc);var Gf=function(){return yf(Hf).scale(144.049).clipAngle(60)};function qf(t,e,n,r){return 1===t&&1===e&&0===n&&0===r?ih:rf({point:function(i,a){this.stream.point(i*t+n,a*e+r)}})}var Xf=function(){var t,e,n,r,i,a,o=1,s=0,c=0,u=1,l=1,h=ih,f=null,d=ih;function p(){return r=i=null,a}return a={stream:function(t){return r&&i===t?r:r=h(d(i=t))},postclip:function(r){return arguments.length?(d=r,f=t=e=n=null,p()):d},clipExtent:function(r){return arguments.length?(d=null==r?(f=t=e=n=null,ih):Cl(f=+r[0][0],t=+r[0][1],e=+r[1][0],n=+r[1][1]),p()):null==f?null:[[f,t],[e,n]]},scale:function(t){return arguments.length?(h=qf((o=+t)*u,o*l,s,c),p()):o},translate:function(t){return arguments.length?(h=qf(o*u,o*l,s=+t[0],c=+t[1]),p()):[s,c]},reflectX:function(t){return arguments.length?(h=qf(o*(u=t?-1:1),o*l,s,c),p()):u<0},reflectY:function(t){return arguments.length?(h=qf(o*u,o*(l=t?-1:1),s,c),p()):l<0},fitExtent:function(t,e){return sf(a,t,e)},fitSize:function(t,e){return cf(a,t,e)},fitWidth:function(t,e){return uf(a,t,e)},fitHeight:function(t,e){return lf(a,t,e)}}};function Zf(t,e){var n=e*e,r=n*n;return[t*(.8707-.131979*n+r*(r*(.003971*n-.001529*r)-.013791)),e*(1.007226+n*(.015085+r*(.028874*n-.044475-.005916*r)))]}Zf.invert=function(t,e){var n,r=e,i=25;do{var a=r*r,o=a*a;r-=n=(r*(1.007226+a*(.015085+o*(.028874*a-.044475-.005916*o)))-e)/(1.007226+a*(.045255+o*(.259866*a-.311325-.005916*11*o)))}while(vc(n)>1e-6&&--i>0);return[t/(.8707+(a=r*r)*(a*(a*a*a*(.003971-.001529*a)-.013791)-.131979)),r]};var Jf=function(){return yf(Zf).scale(175.295)};function Qf(t,e){return[xc(e)*Tc(t),Tc(e)]}Qf.invert=Ef(Oc);var Kf=function(){return yf(Qf).scale(249.5).clipAngle(90+1e-6)};function td(t,e){var n=xc(e),r=1+xc(t)*n;return[n*Tc(t)/r,Tc(e)/r]}td.invert=Ef((function(t){return 2*mc(t)}));var ed=function(){return yf(td).scale(250).clipAngle(142)};function nd(t,e){return[wc(Ac((fc+e)/2)),-t]}nd.invert=function(t,e){return[-e,2*mc(kc(t))-fc]};var rd=function(){var t=Df(nd),e=t.center,n=t.rotate;return t.center=function(t){return arguments.length?e([-t[1],t[0]]):[(t=e())[1],-t[0]]},t.rotate=function(t){return arguments.length?n([t[0],t[1],t.length>2?t[2]+90:90]):[(t=n())[0],t[1],t[2]-90]},n([0,0,90]).scale(159.155)};function id(t,e){return t.parent===e.parent?1:2}function ad(t,e){return t+e.x}function od(t,e){return Math.max(t,e.y)}var sd=function(){var t=id,e=1,n=1,r=!1;function i(i){var a,o=0;i.eachAfter((function(e){var n=e.children;n?(e.x=function(t){return t.reduce(ad,0)/t.length}(n),e.y=function(t){return 1+t.reduce(od,0)}(n)):(e.x=a?o+=t(e,a):0,e.y=0,a=e)}));var s=function(t){for(var e;e=t.children;)t=e[0];return t}(i),c=function(t){for(var e;e=t.children;)t=e[e.length-1];return t}(i),u=s.x-t(s,c)/2,l=c.x+t(c,s)/2;return i.eachAfter(r?function(t){t.x=(t.x-i.x)*e,t.y=(i.y-t.y)*n}:function(t){t.x=(t.x-u)/(l-u)*e,t.y=(1-(i.y?t.y/i.y:1))*n})}return i.separation=function(e){return arguments.length?(t=e,i):t},i.size=function(t){return arguments.length?(r=!1,e=+t[0],n=+t[1],i):r?null:[e,n]},i.nodeSize=function(t){return arguments.length?(r=!0,e=+t[0],n=+t[1],i):r?[e,n]:null},i};function cd(t){var e=0,n=t.children,r=n&&n.length;if(r)for(;--r>=0;)e+=n[r].value;else e=1;t.value=e}function ud(t,e){var n,r,i,a,o,s=new dd(t),c=+t.value&&(s.value=t.value),u=[s];for(null==e&&(e=ld);n=u.pop();)if(c&&(n.value=+n.data.value),(i=e(n.data))&&(o=i.length))for(n.children=new Array(o),a=o-1;a>=0;--a)u.push(r=n.children[a]=new dd(i[a])),r.parent=n,r.depth=n.depth+1;return s.eachBefore(fd)}function ld(t){return t.children}function hd(t){t.data=t.data.data}function fd(t){var e=0;do{t.height=e}while((t=t.parent)&&t.height<++e)}function dd(t){this.data=t,this.depth=this.height=0,this.parent=null}dd.prototype=ud.prototype={constructor:dd,count:function(){return this.eachAfter(cd)},each:function(t){var e,n,r,i,a=this,o=[a];do{for(e=o.reverse(),o=[];a=e.pop();)if(t(a),n=a.children)for(r=0,i=n.length;r=0;--n)i.push(e[n]);return this},sum:function(t){return this.eachAfter((function(e){for(var n=+t(e.data)||0,r=e.children,i=r&&r.length;--i>=0;)n+=r[i].value;e.value=n}))},sort:function(t){return this.eachBefore((function(e){e.children&&e.children.sort(t)}))},path:function(t){for(var e=this,n=function(t,e){if(t===e)return t;var n=t.ancestors(),r=e.ancestors(),i=null;t=n.pop(),e=r.pop();for(;t===e;)i=t,t=n.pop(),e=r.pop();return i}(e,t),r=[e];e!==n;)e=e.parent,r.push(e);for(var i=r.length;t!==n;)r.splice(i,0,t),t=t.parent;return r},ancestors:function(){for(var t=this,e=[t];t=t.parent;)e.push(t);return e},descendants:function(){var t=[];return this.each((function(e){t.push(e)})),t},leaves:function(){var t=[];return this.eachBefore((function(e){e.children||t.push(e)})),t},links:function(){var t=this,e=[];return t.each((function(n){n!==t&&e.push({source:n.parent,target:n})})),e},copy:function(){return ud(this).eachBefore(hd)}};var pd=Array.prototype.slice;var gd=function(t){for(var e,n,r=0,i=(t=function(t){for(var e,n,r=t.length;r;)n=Math.random()*r--|0,e=t[r],t[r]=t[n],t[n]=e;return t}(pd.call(t))).length,a=[];r0&&n*n>r*r+i*i}function bd(t,e){for(var n=0;n(o*=o)?(r=(u+o-i)/(2*u),a=Math.sqrt(Math.max(0,o/u-r*r)),n.x=t.x-r*s-a*c,n.y=t.y-r*c+a*s):(r=(u+i-o)/(2*u),a=Math.sqrt(Math.max(0,i/u-r*r)),n.x=e.x+r*s-a*c,n.y=e.y+r*c+a*s)):(n.x=e.x+n.r,n.y=e.y)}function Ed(t,e){var n=t.r+e.r-1e-6,r=e.x-t.x,i=e.y-t.y;return n>0&&n*n>r*r+i*i}function Td(t){var e=t._,n=t.next._,r=e.r+n.r,i=(e.x*n.r+n.x*e.r)/r,a=(e.y*n.r+n.y*e.r)/r;return i*i+a*a}function Cd(t){this._=t,this.next=null,this.previous=null}function Sd(t){if(!(i=t.length))return 0;var e,n,r,i,a,o,s,c,u,l,h;if((e=t[0]).x=0,e.y=0,!(i>1))return e.r;if(n=t[1],e.x=-n.r,n.x=e.r,n.y=0,!(i>2))return e.r+n.r;wd(n,e,r=t[2]),e=new Cd(e),n=new Cd(n),r=new Cd(r),e.next=r.previous=n,n.next=e.previous=r,r.next=n.previous=e;t:for(s=3;s0)throw new Error("cycle");return a}return n.id=function(e){return arguments.length?(t=Od(e),n):t},n.parentId=function(t){return arguments.length?(e=Od(t),n):e},n};function Hd(t,e){return t.parent===e.parent?1:2}function Gd(t){var e=t.children;return e?e[0]:t.t}function qd(t){var e=t.children;return e?e[e.length-1]:t.t}function Xd(t,e,n){var r=n/(e.i-t.i);e.c-=r,e.s+=n,t.c+=r,e.z+=n,e.m+=n}function Zd(t,e,n){return t.a.parent===e.parent?t.a:n}function Jd(t,e){this._=t,this.parent=null,this.children=null,this.A=null,this.a=this,this.z=0,this.m=0,this.c=0,this.s=0,this.t=null,this.i=e}Jd.prototype=Object.create(dd.prototype);var Qd=function(){var t=Hd,e=1,n=1,r=null;function i(i){var c=function(t){for(var e,n,r,i,a,o=new Jd(t,0),s=[o];e=s.pop();)if(r=e._.children)for(e.children=new Array(a=r.length),i=a-1;i>=0;--i)s.push(n=e.children[i]=new Jd(r[i],i)),n.parent=e;return(o.parent=new Jd(null,0)).children=[o],o}(i);if(c.eachAfter(a),c.parent.m=-c.z,c.eachBefore(o),r)i.eachBefore(s);else{var u=i,l=i,h=i;i.eachBefore((function(t){t.xl.x&&(l=t),t.depth>h.depth&&(h=t)}));var f=u===l?1:t(u,l)/2,d=f-u.x,p=e/(l.x+f+d),g=n/(h.depth||1);i.eachBefore((function(t){t.x=(t.x+d)*p,t.y=t.depth*g}))}return i}function a(e){var n=e.children,r=e.parent.children,i=e.i?r[e.i-1]:null;if(n){!function(t){for(var e,n=0,r=0,i=t.children,a=i.length;--a>=0;)(e=i[a]).z+=n,e.m+=n,n+=e.s+(r+=e.c)}(e);var a=(n[0].z+n[n.length-1].z)/2;i?(e.z=i.z+t(e._,i._),e.m=e.z-a):e.z=a}else i&&(e.z=i.z+t(e._,i._));e.parent.A=function(e,n,r){if(n){for(var i,a=e,o=e,s=n,c=a.parent.children[0],u=a.m,l=o.m,h=s.m,f=c.m;s=qd(s),a=Gd(a),s&&a;)c=Gd(c),(o=qd(o)).a=e,(i=s.z+h-a.z-u+t(s._,a._))>0&&(Xd(Zd(s,e,r),e,i),u+=i,l+=i),h+=s.m,u+=a.m,f+=c.m,l+=o.m;s&&!qd(o)&&(o.t=s,o.m+=h-l),a&&!Gd(c)&&(c.t=a,c.m+=u-f,r=e)}return r}(e,i,e.parent.A||r[0])}function o(t){t._.x=t.z+t.parent.m,t.m+=t.parent.m}function s(t){t.x*=e,t.y=t.depth*n}return i.separation=function(e){return arguments.length?(t=e,i):t},i.size=function(t){return arguments.length?(r=!1,e=+t[0],n=+t[1],i):r?null:[e,n]},i.nodeSize=function(t){return arguments.length?(r=!0,e=+t[0],n=+t[1],i):r?[e,n]:null},i},Kd=function(t,e,n,r,i){for(var a,o=t.children,s=-1,c=o.length,u=t.value&&(i-n)/t.value;++sf&&(f=s),y=l*l*g,(d=Math.max(f/y,y/h))>p){l-=s;break}p=d}v.push(o={value:l,dice:c1?e:1)},n}(tp),rp=function(){var t=np,e=!1,n=1,r=1,i=[0],a=Dd,o=Dd,s=Dd,c=Dd,u=Dd;function l(t){return t.x0=t.y0=0,t.x1=n,t.y1=r,t.eachBefore(h),i=[0],e&&t.eachBefore(jd),t}function h(e){var n=i[e.depth],r=e.x0+n,l=e.y0+n,h=e.x1-n,f=e.y1-n;h=n-1){var l=s[e];return l.x0=i,l.y0=a,l.x1=o,void(l.y1=c)}var h=u[e],f=r/2+h,d=e+1,p=n-1;for(;d>>1;u[g]c-a){var m=(i*v+o*y)/r;t(e,d,y,i,a,m,c),t(d,n,v,m,a,o,c)}else{var b=(a*v+c*y)/r;t(e,d,y,i,a,o,b),t(d,n,v,i,b,o,c)}}(0,c,t.value,e,n,r,i)},ap=function(t,e,n,r,i){(1&t.depth?Kd:Rd)(t,e,n,r,i)},op=function t(e){function n(t,n,r,i,a){if((o=t._squarify)&&o.ratio===e)for(var o,s,c,u,l,h=-1,f=o.length,d=t.value;++h1?e:1)},n}(tp),sp=function(t){var e=t.length;return function(n){return t[Math.max(0,Math.min(e-1,Math.floor(n*e)))]}},cp=function(t,e){var n=un(+t,+e);return function(t){var e=n(t);return e-360*Math.floor(e/360)}},up=function(t,e){return t=+t,e=+e,function(n){return Math.round(t*(1-n)+e*n)}},lp=Math.SQRT2;function hp(t){return((t=Math.exp(t))+1/t)/2}var fp=function(t,e){var n,r,i=t[0],a=t[1],o=t[2],s=e[0],c=e[1],u=e[2],l=s-i,h=c-a,f=l*l+h*h;if(f<1e-12)r=Math.log(u/o)/lp,n=function(t){return[i+t*l,a+t*h,o*Math.exp(lp*t*r)]};else{var d=Math.sqrt(f),p=(u*u-o*o+4*f)/(2*o*2*d),g=(u*u-o*o-4*f)/(2*u*2*d),y=Math.log(Math.sqrt(p*p+1)-p),v=Math.log(Math.sqrt(g*g+1)-g);r=(v-y)/lp,n=function(t){var e,n=t*r,s=hp(y),c=o/(2*d)*(s*(e=lp*n+y,((e=Math.exp(2*e))-1)/(e+1))-function(t){return((t=Math.exp(t))-1/t)/2}(y));return[i+c*l,a+c*h,o*s/hp(lp*n+y)]}}return n.duration=1e3*r,n};function dp(t){return function(e,n){var r=t((e=tn(e)).h,(n=tn(n)).h),i=hn(e.s,n.s),a=hn(e.l,n.l),o=hn(e.opacity,n.opacity);return function(t){return e.h=r(t),e.s=i(t),e.l=a(t),e.opacity=o(t),e+""}}}var pp=dp(un),gp=dp(hn);function yp(t,e){var n=hn((t=pa(t)).l,(e=pa(e)).l),r=hn(t.a,e.a),i=hn(t.b,e.b),a=hn(t.opacity,e.opacity);return function(e){return t.l=n(e),t.a=r(e),t.b=i(e),t.opacity=a(e),t+""}}function vp(t){return function(e,n){var r=t((e=ka(e)).h,(n=ka(n)).h),i=hn(e.c,n.c),a=hn(e.l,n.l),o=hn(e.opacity,n.opacity);return function(t){return e.h=r(t),e.c=i(t),e.l=a(t),e.opacity=o(t),e+""}}}var mp=vp(un),bp=vp(hn);function xp(t){return function e(n){function r(e,r){var i=t((e=Oa(e)).h,(r=Oa(r)).h),a=hn(e.s,r.s),o=hn(e.l,r.l),s=hn(e.opacity,r.opacity);return function(t){return e.h=i(t),e.s=a(t),e.l=o(Math.pow(t,n)),e.opacity=s(t),e+""}}return n=+n,r.gamma=e,r}(1)}var _p=xp(un),kp=xp(hn);function wp(t,e){for(var n=0,r=e.length-1,i=e[0],a=new Array(r<0?0:r);n1&&(e=t[a[o-2]],n=t[a[o-1]],r=t[s],(n[0]-e[0])*(r[1]-e[1])-(n[1]-e[1])*(r[0]-e[0])<=0);)--o;a[o++]=s}return a.slice(0,o)}var Mp=function(t){if((n=t.length)<3)return null;var e,n,r=new Array(n),i=new Array(n);for(e=0;e=0;--e)u.push(t[r[a[e]][2]]);for(e=+s;es!=u>s&&o<(c-n)*(s-r)/(u-r)+n&&(l=!l),c=n,u=r;return l},Dp=function(t){for(var e,n,r=-1,i=t.length,a=t[i-1],o=a[0],s=a[1],c=0;++r1);return t+n*a*Math.sqrt(-2*Math.log(i)/i)}}return n.source=t,n}(Np),Fp=function t(e){function n(){var t=Lp.source(e).apply(this,arguments);return function(){return Math.exp(t())}}return n.source=t,n}(Np),Pp=function t(e){function n(t){return function(){for(var n=0,r=0;rr&&(e=n,n=r,r=e),function(t){return Math.max(n,Math.min(r,t))}}function tg(t,e,n){var r=t[0],i=t[1],a=e[0],o=e[1];return i2?eg:tg,i=a=null,h}function h(e){return isNaN(e=+e)?n:(i||(i=r(o.map(t),s,c)))(t(u(e)))}return h.invert=function(n){return u(e((a||(a=r(s,o.map(t),_n)))(n)))},h.domain=function(t){return arguments.length?(o=Up.call(t,Xp),u===Jp||(u=Kp(o)),l()):o.slice()},h.range=function(t){return arguments.length?(s=$p.call(t),l()):s.slice()},h.rangeRound=function(t){return s=$p.call(t),c=up,l()},h.clamp=function(t){return arguments.length?(u=t?Kp(o):Jp,h):u!==Jp},h.interpolate=function(t){return arguments.length?(c=t,l()):c},h.unknown=function(t){return arguments.length?(n=t,h):n},function(n,r){return t=n,e=r,l()}}function ig(t,e){return rg()(t,e)}var ag=function(t,e,n,r){var i,a=A(t,e,n);switch((r=Vs(null==r?",f":r)).type){case"s":var o=Math.max(Math.abs(t),Math.abs(e));return null!=r.precision||isNaN(i=ac(a,o))||(r.precision=i),Zs(r,o);case"":case"e":case"g":case"p":case"r":null!=r.precision||isNaN(i=oc(a,Math.max(Math.abs(t),Math.abs(e))))||(r.precision=i-("e"===r.type));break;case"f":case"%":null!=r.precision||isNaN(i=ic(a))||(r.precision=i-2*("%"===r.type))}return Xs(r)};function og(t){var e=t.domain;return t.ticks=function(t){var n=e();return C(n[0],n[n.length-1],null==t?10:t)},t.tickFormat=function(t,n){var r=e();return ag(r[0],r[r.length-1],null==t?10:t,n)},t.nice=function(n){null==n&&(n=10);var r,i=e(),a=0,o=i.length-1,s=i[a],c=i[o];return c0?r=S(s=Math.floor(s/r)*r,c=Math.ceil(c/r)*r,n):r<0&&(r=S(s=Math.ceil(s*r)/r,c=Math.floor(c*r)/r,n)),r>0?(i[a]=Math.floor(s/r)*r,i[o]=Math.ceil(c/r)*r,e(i)):r<0&&(i[a]=Math.ceil(s*r)/r,i[o]=Math.floor(c*r)/r,e(i)),t},t}function sg(){var t=ig(Jp,Jp);return t.copy=function(){return ng(t,sg())},Rp.apply(t,arguments),og(t)}function cg(t){var e;function n(t){return isNaN(t=+t)?e:t}return n.invert=n,n.domain=n.range=function(e){return arguments.length?(t=Up.call(e,Xp),n):t.slice()},n.unknown=function(t){return arguments.length?(e=t,n):e},n.copy=function(){return cg(t).unknown(e)},t=arguments.length?Up.call(t,Xp):[0,1],og(n)}var ug=function(t,e){var n,r=0,i=(t=t.slice()).length-1,a=t[r],o=t[i];return o0){for(;fc)break;g.push(h)}}else for(;f=1;--l)if(!((h=u*l)c)break;g.push(h)}}else g=C(f,d,Math.min(d-f,p)).map(n);return r?g.reverse():g},r.tickFormat=function(t,i){if(null==i&&(i=10===a?".0e":","),"function"!=typeof i&&(i=Xs(i)),t===1/0)return i;null==t&&(t=10);var o=Math.max(1,a*t/r.ticks().length);return function(t){var r=t/n(Math.round(e(t)));return r*a0?i[r-1]:e[0],r=r?[i[r-1],n]:[i[o-1],i[o]]},o.unknown=function(e){return arguments.length?(t=e,o):o},o.thresholds=function(){return i.slice()},o.copy=function(){return Mg().domain([e,n]).range(a).unknown(t)},Rp.apply(og(o),arguments)}function Og(){var t,e=[.5],n=[0,1],r=1;function i(i){return i<=i?n[c(e,i,0,r)]:t}return i.domain=function(t){return arguments.length?(e=$p.call(t),r=Math.min(e.length,n.length-1),i):e.slice()},i.range=function(t){return arguments.length?(n=$p.call(t),r=Math.min(e.length,n.length-1),i):n.slice()},i.invertExtent=function(t){var r=n.indexOf(t);return[e[r-1],e[r]]},i.unknown=function(e){return arguments.length?(t=e,i):t},i.copy=function(){return Og().domain(e).range(n).unknown(t)},Rp.apply(i,arguments)}var Dg=new Date,Ng=new Date;function Bg(t,e,n,r){function i(e){return t(e=0===arguments.length?new Date:new Date(+e)),e}return i.floor=function(e){return t(e=new Date(+e)),e},i.ceil=function(n){return t(n=new Date(n-1)),e(n,1),t(n),n},i.round=function(t){var e=i(t),n=i.ceil(t);return t-e0))return s;do{s.push(o=new Date(+n)),e(n,a),t(n)}while(o=e)for(;t(e),!n(e);)e.setTime(e-1)}),(function(t,r){if(t>=t)if(r<0)for(;++r<=0;)for(;e(t,-1),!n(t););else for(;--r>=0;)for(;e(t,1),!n(t););}))},n&&(i.count=function(e,r){return Dg.setTime(+e),Ng.setTime(+r),t(Dg),t(Ng),Math.floor(n(Dg,Ng))},i.every=function(t){return t=Math.floor(t),isFinite(t)&&t>0?t>1?i.filter(r?function(e){return r(e)%t==0}:function(e){return i.count(0,e)%t==0}):i:null}),i}var Lg=Bg((function(t){t.setMonth(0,1),t.setHours(0,0,0,0)}),(function(t,e){t.setFullYear(t.getFullYear()+e)}),(function(t,e){return e.getFullYear()-t.getFullYear()}),(function(t){return t.getFullYear()}));Lg.every=function(t){return isFinite(t=Math.floor(t))&&t>0?Bg((function(e){e.setFullYear(Math.floor(e.getFullYear()/t)*t),e.setMonth(0,1),e.setHours(0,0,0,0)}),(function(e,n){e.setFullYear(e.getFullYear()+n*t)})):null};var Fg=Lg,Pg=Lg.range,Ig=Bg((function(t){t.setDate(1),t.setHours(0,0,0,0)}),(function(t,e){t.setMonth(t.getMonth()+e)}),(function(t,e){return e.getMonth()-t.getMonth()+12*(e.getFullYear()-t.getFullYear())}),(function(t){return t.getMonth()})),jg=Ig,Rg=Ig.range;function Yg(t){return Bg((function(e){e.setDate(e.getDate()-(e.getDay()+7-t)%7),e.setHours(0,0,0,0)}),(function(t,e){t.setDate(t.getDate()+7*e)}),(function(t,e){return(e-t-6e4*(e.getTimezoneOffset()-t.getTimezoneOffset()))/6048e5}))}var zg=Yg(0),Ug=Yg(1),$g=Yg(2),Wg=Yg(3),Vg=Yg(4),Hg=Yg(5),Gg=Yg(6),qg=zg.range,Xg=Ug.range,Zg=$g.range,Jg=Wg.range,Qg=Vg.range,Kg=Hg.range,ty=Gg.range,ey=Bg((function(t){t.setHours(0,0,0,0)}),(function(t,e){t.setDate(t.getDate()+e)}),(function(t,e){return(e-t-6e4*(e.getTimezoneOffset()-t.getTimezoneOffset()))/864e5}),(function(t){return t.getDate()-1})),ny=ey,ry=ey.range,iy=Bg((function(t){t.setTime(t-t.getMilliseconds()-1e3*t.getSeconds()-6e4*t.getMinutes())}),(function(t,e){t.setTime(+t+36e5*e)}),(function(t,e){return(e-t)/36e5}),(function(t){return t.getHours()})),ay=iy,oy=iy.range,sy=Bg((function(t){t.setTime(t-t.getMilliseconds()-1e3*t.getSeconds())}),(function(t,e){t.setTime(+t+6e4*e)}),(function(t,e){return(e-t)/6e4}),(function(t){return t.getMinutes()})),cy=sy,uy=sy.range,ly=Bg((function(t){t.setTime(t-t.getMilliseconds())}),(function(t,e){t.setTime(+t+1e3*e)}),(function(t,e){return(e-t)/1e3}),(function(t){return t.getUTCSeconds()})),hy=ly,fy=ly.range,dy=Bg((function(){}),(function(t,e){t.setTime(+t+e)}),(function(t,e){return e-t}));dy.every=function(t){return t=Math.floor(t),isFinite(t)&&t>0?t>1?Bg((function(e){e.setTime(Math.floor(e/t)*t)}),(function(e,n){e.setTime(+e+n*t)}),(function(e,n){return(n-e)/t})):dy:null};var py=dy,gy=dy.range;function yy(t){return Bg((function(e){e.setUTCDate(e.getUTCDate()-(e.getUTCDay()+7-t)%7),e.setUTCHours(0,0,0,0)}),(function(t,e){t.setUTCDate(t.getUTCDate()+7*e)}),(function(t,e){return(e-t)/6048e5}))}var vy=yy(0),my=yy(1),by=yy(2),xy=yy(3),_y=yy(4),ky=yy(5),wy=yy(6),Ey=vy.range,Ty=my.range,Cy=by.range,Sy=xy.range,Ay=_y.range,My=ky.range,Oy=wy.range,Dy=Bg((function(t){t.setUTCHours(0,0,0,0)}),(function(t,e){t.setUTCDate(t.getUTCDate()+e)}),(function(t,e){return(e-t)/864e5}),(function(t){return t.getUTCDate()-1})),Ny=Dy,By=Dy.range,Ly=Bg((function(t){t.setUTCMonth(0,1),t.setUTCHours(0,0,0,0)}),(function(t,e){t.setUTCFullYear(t.getUTCFullYear()+e)}),(function(t,e){return e.getUTCFullYear()-t.getUTCFullYear()}),(function(t){return t.getUTCFullYear()}));Ly.every=function(t){return isFinite(t=Math.floor(t))&&t>0?Bg((function(e){e.setUTCFullYear(Math.floor(e.getUTCFullYear()/t)*t),e.setUTCMonth(0,1),e.setUTCHours(0,0,0,0)}),(function(e,n){e.setUTCFullYear(e.getUTCFullYear()+n*t)})):null};var Fy=Ly,Py=Ly.range;function Iy(t){if(0<=t.y&&t.y<100){var e=new Date(-1,t.m,t.d,t.H,t.M,t.S,t.L);return e.setFullYear(t.y),e}return new Date(t.y,t.m,t.d,t.H,t.M,t.S,t.L)}function jy(t){if(0<=t.y&&t.y<100){var e=new Date(Date.UTC(-1,t.m,t.d,t.H,t.M,t.S,t.L));return e.setUTCFullYear(t.y),e}return new Date(Date.UTC(t.y,t.m,t.d,t.H,t.M,t.S,t.L))}function Ry(t,e,n){return{y:t,m:e,d:n,H:0,M:0,S:0,L:0}}function Yy(t){var e=t.dateTime,n=t.date,r=t.time,i=t.periods,a=t.days,o=t.shortDays,s=t.months,c=t.shortMonths,u=Qy(i),l=Ky(i),h=Qy(a),f=Ky(a),d=Qy(o),p=Ky(o),g=Qy(s),y=Ky(s),v=Qy(c),m=Ky(c),b={a:function(t){return o[t.getDay()]},A:function(t){return a[t.getDay()]},b:function(t){return c[t.getMonth()]},B:function(t){return s[t.getMonth()]},c:null,d:xv,e:xv,f:Tv,H:_v,I:kv,j:wv,L:Ev,m:Cv,M:Sv,p:function(t){return i[+(t.getHours()>=12)]},q:function(t){return 1+~~(t.getMonth()/3)},Q:em,s:nm,S:Av,u:Mv,U:Ov,V:Dv,w:Nv,W:Bv,x:null,X:null,y:Lv,Y:Fv,Z:Pv,"%":tm},x={a:function(t){return o[t.getUTCDay()]},A:function(t){return a[t.getUTCDay()]},b:function(t){return c[t.getUTCMonth()]},B:function(t){return s[t.getUTCMonth()]},c:null,d:Iv,e:Iv,f:Uv,H:jv,I:Rv,j:Yv,L:zv,m:$v,M:Wv,p:function(t){return i[+(t.getUTCHours()>=12)]},q:function(t){return 1+~~(t.getUTCMonth()/3)},Q:em,s:nm,S:Vv,u:Hv,U:Gv,V:qv,w:Xv,W:Zv,x:null,X:null,y:Jv,Y:Qv,Z:Kv,"%":tm},_={a:function(t,e,n){var r=d.exec(e.slice(n));return r?(t.w=p[r[0].toLowerCase()],n+r[0].length):-1},A:function(t,e,n){var r=h.exec(e.slice(n));return r?(t.w=f[r[0].toLowerCase()],n+r[0].length):-1},b:function(t,e,n){var r=v.exec(e.slice(n));return r?(t.m=m[r[0].toLowerCase()],n+r[0].length):-1},B:function(t,e,n){var r=g.exec(e.slice(n));return r?(t.m=y[r[0].toLowerCase()],n+r[0].length):-1},c:function(t,n,r){return E(t,e,n,r)},d:lv,e:lv,f:yv,H:fv,I:fv,j:hv,L:gv,m:uv,M:dv,p:function(t,e,n){var r=u.exec(e.slice(n));return r?(t.p=l[r[0].toLowerCase()],n+r[0].length):-1},q:cv,Q:mv,s:bv,S:pv,u:ev,U:nv,V:rv,w:tv,W:iv,x:function(t,e,r){return E(t,n,e,r)},X:function(t,e,n){return E(t,r,e,n)},y:ov,Y:av,Z:sv,"%":vv};function k(t,e){return function(n){var r,i,a,o=[],s=-1,c=0,u=t.length;for(n instanceof Date||(n=new Date(+n));++s53)return null;"w"in a||(a.w=1),"Z"in a?(i=(r=jy(Ry(a.y,0,1))).getUTCDay(),r=i>4||0===i?my.ceil(r):my(r),r=Ny.offset(r,7*(a.V-1)),a.y=r.getUTCFullYear(),a.m=r.getUTCMonth(),a.d=r.getUTCDate()+(a.w+6)%7):(i=(r=Iy(Ry(a.y,0,1))).getDay(),r=i>4||0===i?Ug.ceil(r):Ug(r),r=ny.offset(r,7*(a.V-1)),a.y=r.getFullYear(),a.m=r.getMonth(),a.d=r.getDate()+(a.w+6)%7)}else("W"in a||"U"in a)&&("w"in a||(a.w="u"in a?a.u%7:"W"in a?1:0),i="Z"in a?jy(Ry(a.y,0,1)).getUTCDay():Iy(Ry(a.y,0,1)).getDay(),a.m=0,a.d="W"in a?(a.w+6)%7+7*a.W-(i+5)%7:a.w+7*a.U-(i+6)%7);return"Z"in a?(a.H+=a.Z/100|0,a.M+=a.Z%100,jy(a)):Iy(a)}}function E(t,e,n,r){for(var i,a,o=0,s=e.length,c=n.length;o=c)return-1;if(37===(i=e.charCodeAt(o++))){if(i=e.charAt(o++),!(a=_[i in Hy?e.charAt(o++):i])||(r=a(t,n,r))<0)return-1}else if(i!=n.charCodeAt(r++))return-1}return r}return(b.x=k(n,b),b.X=k(r,b),b.c=k(e,b),x.x=k(n,x),x.X=k(r,x),x.c=k(e,x),{format:function(t){var e=k(t+="",b);return e.toString=function(){return t},e},parse:function(t){var e=w(t+="",!1);return e.toString=function(){return t},e},utcFormat:function(t){var e=k(t+="",x);return e.toString=function(){return t},e},utcParse:function(t){var e=w(t+="",!0);return e.toString=function(){return t},e}})}var zy,Uy,$y,Wy,Vy,Hy={"-":"",_:" ",0:"0"},Gy=/^\s*\d+/,qy=/^%/,Xy=/[\\^$*+?|[\]().{}]/g;function Zy(t,e,n){var r=t<0?"-":"",i=(r?-t:t)+"",a=i.length;return r+(a68?1900:2e3),n+r[0].length):-1}function sv(t,e,n){var r=/^(Z)|([+-]\d\d)(?::?(\d\d))?/.exec(e.slice(n,n+6));return r?(t.Z=r[1]?0:-(r[2]+(r[3]||"00")),n+r[0].length):-1}function cv(t,e,n){var r=Gy.exec(e.slice(n,n+1));return r?(t.q=3*r[0]-3,n+r[0].length):-1}function uv(t,e,n){var r=Gy.exec(e.slice(n,n+2));return r?(t.m=r[0]-1,n+r[0].length):-1}function lv(t,e,n){var r=Gy.exec(e.slice(n,n+2));return r?(t.d=+r[0],n+r[0].length):-1}function hv(t,e,n){var r=Gy.exec(e.slice(n,n+3));return r?(t.m=0,t.d=+r[0],n+r[0].length):-1}function fv(t,e,n){var r=Gy.exec(e.slice(n,n+2));return r?(t.H=+r[0],n+r[0].length):-1}function dv(t,e,n){var r=Gy.exec(e.slice(n,n+2));return r?(t.M=+r[0],n+r[0].length):-1}function pv(t,e,n){var r=Gy.exec(e.slice(n,n+2));return r?(t.S=+r[0],n+r[0].length):-1}function gv(t,e,n){var r=Gy.exec(e.slice(n,n+3));return r?(t.L=+r[0],n+r[0].length):-1}function yv(t,e,n){var r=Gy.exec(e.slice(n,n+6));return r?(t.L=Math.floor(r[0]/1e3),n+r[0].length):-1}function vv(t,e,n){var r=qy.exec(e.slice(n,n+1));return r?n+r[0].length:-1}function mv(t,e,n){var r=Gy.exec(e.slice(n));return r?(t.Q=+r[0],n+r[0].length):-1}function bv(t,e,n){var r=Gy.exec(e.slice(n));return r?(t.s=+r[0],n+r[0].length):-1}function xv(t,e){return Zy(t.getDate(),e,2)}function _v(t,e){return Zy(t.getHours(),e,2)}function kv(t,e){return Zy(t.getHours()%12||12,e,2)}function wv(t,e){return Zy(1+ny.count(Fg(t),t),e,3)}function Ev(t,e){return Zy(t.getMilliseconds(),e,3)}function Tv(t,e){return Ev(t,e)+"000"}function Cv(t,e){return Zy(t.getMonth()+1,e,2)}function Sv(t,e){return Zy(t.getMinutes(),e,2)}function Av(t,e){return Zy(t.getSeconds(),e,2)}function Mv(t){var e=t.getDay();return 0===e?7:e}function Ov(t,e){return Zy(zg.count(Fg(t)-1,t),e,2)}function Dv(t,e){var n=t.getDay();return t=n>=4||0===n?Vg(t):Vg.ceil(t),Zy(Vg.count(Fg(t),t)+(4===Fg(t).getDay()),e,2)}function Nv(t){return t.getDay()}function Bv(t,e){return Zy(Ug.count(Fg(t)-1,t),e,2)}function Lv(t,e){return Zy(t.getFullYear()%100,e,2)}function Fv(t,e){return Zy(t.getFullYear()%1e4,e,4)}function Pv(t){var e=t.getTimezoneOffset();return(e>0?"-":(e*=-1,"+"))+Zy(e/60|0,"0",2)+Zy(e%60,"0",2)}function Iv(t,e){return Zy(t.getUTCDate(),e,2)}function jv(t,e){return Zy(t.getUTCHours(),e,2)}function Rv(t,e){return Zy(t.getUTCHours()%12||12,e,2)}function Yv(t,e){return Zy(1+Ny.count(Fy(t),t),e,3)}function zv(t,e){return Zy(t.getUTCMilliseconds(),e,3)}function Uv(t,e){return zv(t,e)+"000"}function $v(t,e){return Zy(t.getUTCMonth()+1,e,2)}function Wv(t,e){return Zy(t.getUTCMinutes(),e,2)}function Vv(t,e){return Zy(t.getUTCSeconds(),e,2)}function Hv(t){var e=t.getUTCDay();return 0===e?7:e}function Gv(t,e){return Zy(vy.count(Fy(t)-1,t),e,2)}function qv(t,e){var n=t.getUTCDay();return t=n>=4||0===n?_y(t):_y.ceil(t),Zy(_y.count(Fy(t),t)+(4===Fy(t).getUTCDay()),e,2)}function Xv(t){return t.getUTCDay()}function Zv(t,e){return Zy(my.count(Fy(t)-1,t),e,2)}function Jv(t,e){return Zy(t.getUTCFullYear()%100,e,2)}function Qv(t,e){return Zy(t.getUTCFullYear()%1e4,e,4)}function Kv(){return"+0000"}function tm(){return"%"}function em(t){return+t}function nm(t){return Math.floor(+t/1e3)}function rm(t){return zy=Yy(t),Uy=zy.format,$y=zy.parse,Wy=zy.utcFormat,Vy=zy.utcParse,zy}rm({dateTime:"%x, %X",date:"%-m/%-d/%Y",time:"%-I:%M:%S %p",periods:["AM","PM"],days:["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"],shortDays:["Sun","Mon","Tue","Wed","Thu","Fri","Sat"],months:["January","February","March","April","May","June","July","August","September","October","November","December"],shortMonths:["Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"]});function im(t){return new Date(t)}function am(t){return t instanceof Date?+t:+new Date(+t)}function om(t,e,n,r,a,o,s,c,u){var l=ig(Jp,Jp),h=l.invert,f=l.domain,d=u(".%L"),p=u(":%S"),g=u("%I:%M"),y=u("%I %p"),v=u("%a %d"),m=u("%b %d"),b=u("%B"),x=u("%Y"),_=[[s,1,1e3],[s,5,5e3],[s,15,15e3],[s,30,3e4],[o,1,6e4],[o,5,3e5],[o,15,9e5],[o,30,18e5],[a,1,36e5],[a,3,108e5],[a,6,216e5],[a,12,432e5],[r,1,864e5],[r,2,1728e5],[n,1,6048e5],[e,1,2592e6],[e,3,7776e6],[t,1,31536e6]];function k(i){return(s(i)1)&&(t-=Math.floor(t));var e=Math.abs(t-.5);return qb.h=360*t-100,qb.s=1.5-1.5*e,qb.l=.8-.9*e,qb+""},Zb=Ge(),Jb=Math.PI/3,Qb=2*Math.PI/3,Kb=function(t){var e;return t=(.5-t)*Math.PI,Zb.r=255*(e=Math.sin(t))*e,Zb.g=255*(e=Math.sin(t+Jb))*e,Zb.b=255*(e=Math.sin(t+Qb))*e,Zb+""},tx=function(t){return t=Math.max(0,Math.min(1,t)),"rgb("+Math.max(0,Math.min(255,Math.round(34.61+t*(1172.33-t*(10793.56-t*(33300.12-t*(38394.49-14825.05*t)))))))+", "+Math.max(0,Math.min(255,Math.round(23.31+t*(557.33+t*(1225.33-t*(3574.96-t*(1073.77+707.56*t)))))))+", "+Math.max(0,Math.min(255,Math.round(27.2+t*(3211.1-t*(15327.97-t*(27814-t*(22569.18-6838.66*t)))))))+")"};function ex(t){var e=t.length;return function(n){return t[Math.max(0,Math.min(e-1,Math.floor(n*e)))]}}var nx=ex(Nm("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")),rx=ex(Nm("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")),ix=ex(Nm("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")),ax=ex(Nm("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")),ox=function(t){return ke(ne(t).call(document.documentElement))},sx=0;function cx(){return new ux}function ux(){this._="@"+(++sx).toString(36)}ux.prototype=cx.prototype={constructor:ux,get:function(t){for(var e=this._;!(e in t);)if(!(t=t.parentNode))return;return t[e]},set:function(t,e){return t[this._]=e},remove:function(t){return this._ in t&&delete t[this._]},toString:function(){return this._}};var lx=function(t){return"string"==typeof t?new be([document.querySelectorAll(t)],[document.documentElement]):new be([null==t?[]:t],me)},hx=function(t,e){null==e&&(e=Mn().touches);for(var n=0,r=e?e.length:0,i=new Array(r);n1?0:t<-1?xx:Math.acos(t)}function Ex(t){return t>=1?_x:t<=-1?-_x:Math.asin(t)}function Tx(t){return t.innerRadius}function Cx(t){return t.outerRadius}function Sx(t){return t.startAngle}function Ax(t){return t.endAngle}function Mx(t){return t&&t.padAngle}function Ox(t,e,n,r,i,a,o,s){var c=n-t,u=r-e,l=o-i,h=s-a,f=h*c-l*u;if(!(f*f<1e-12))return[t+(f=(l*(e-a)-h*(t-i))/f)*c,e+f*u]}function Dx(t,e,n,r,i,a,o){var s=t-n,c=e-r,u=(o?a:-a)/bx(s*s+c*c),l=u*c,h=-u*s,f=t+l,d=e+h,p=n+l,g=r+h,y=(f+p)/2,v=(d+g)/2,m=p-f,b=g-d,x=m*m+b*b,_=i-a,k=f*g-p*d,w=(b<0?-1:1)*bx(yx(0,_*_*x-k*k)),E=(k*b-m*w)/x,T=(-k*m-b*w)/x,C=(k*b+m*w)/x,S=(-k*m+b*w)/x,A=E-y,M=T-v,O=C-y,D=S-v;return A*A+M*M>O*O+D*D&&(E=C,T=S),{cx:E,cy:T,x01:-l,y01:-h,x11:E*(i/_-1),y11:T*(i/_-1)}}var Nx=function(){var t=Tx,e=Cx,n=fx(0),r=null,i=Sx,a=Ax,o=Mx,s=null;function c(){var c,u,l=+t.apply(this,arguments),h=+e.apply(this,arguments),f=i.apply(this,arguments)-_x,d=a.apply(this,arguments)-_x,p=dx(d-f),g=d>f;if(s||(s=c=Ui()),h1e-12)if(p>kx-1e-12)s.moveTo(h*gx(f),h*mx(f)),s.arc(0,0,h,f,d,!g),l>1e-12&&(s.moveTo(l*gx(d),l*mx(d)),s.arc(0,0,l,d,f,g));else{var y,v,m=f,b=d,x=f,_=d,k=p,w=p,E=o.apply(this,arguments)/2,T=E>1e-12&&(r?+r.apply(this,arguments):bx(l*l+h*h)),C=vx(dx(h-l)/2,+n.apply(this,arguments)),S=C,A=C;if(T>1e-12){var M=Ex(T/l*mx(E)),O=Ex(T/h*mx(E));(k-=2*M)>1e-12?(x+=M*=g?1:-1,_-=M):(k=0,x=_=(f+d)/2),(w-=2*O)>1e-12?(m+=O*=g?1:-1,b-=O):(w=0,m=b=(f+d)/2)}var D=h*gx(m),N=h*mx(m),B=l*gx(_),L=l*mx(_);if(C>1e-12){var F,P=h*gx(b),I=h*mx(b),j=l*gx(x),R=l*mx(x);if(p1e-12?A>1e-12?(y=Dx(j,R,D,N,h,A,g),v=Dx(P,I,B,L,h,A,g),s.moveTo(y.cx+y.x01,y.cy+y.y01),A1e-12&&k>1e-12?S>1e-12?(y=Dx(B,L,P,I,l,-S,g),v=Dx(D,N,j,R,l,-S,g),s.lineTo(y.cx+y.x01,y.cy+y.y01),S=l;--h)s.point(y[h],v[h]);s.lineEnd(),s.areaEnd()}g&&(y[u]=+t(f,u,c),v[u]=+n(f,u,c),s.point(e?+e(f,u,c):y[u],r?+r(f,u,c):v[u]))}if(d)return s=null,d+""||null}function u(){return Ix().defined(i).curve(o).context(a)}return c.x=function(n){return arguments.length?(t="function"==typeof n?n:fx(+n),e=null,c):t},c.x0=function(e){return arguments.length?(t="function"==typeof e?e:fx(+e),c):t},c.x1=function(t){return arguments.length?(e=null==t?null:"function"==typeof t?t:fx(+t),c):e},c.y=function(t){return arguments.length?(n="function"==typeof t?t:fx(+t),r=null,c):n},c.y0=function(t){return arguments.length?(n="function"==typeof t?t:fx(+t),c):n},c.y1=function(t){return arguments.length?(r=null==t?null:"function"==typeof t?t:fx(+t),c):r},c.lineX0=c.lineY0=function(){return u().x(t).y(n)},c.lineY1=function(){return u().x(t).y(r)},c.lineX1=function(){return u().x(e).y(n)},c.defined=function(t){return arguments.length?(i="function"==typeof t?t:fx(!!t),c):i},c.curve=function(t){return arguments.length?(o=t,null!=a&&(s=o(a)),c):o},c.context=function(t){return arguments.length?(null==t?a=s=null:s=o(a=t),c):a},c},Rx=function(t,e){return et?1:e>=t?0:NaN},Yx=function(t){return t},zx=function(){var t=Yx,e=Rx,n=null,r=fx(0),i=fx(kx),a=fx(0);function o(o){var s,c,u,l,h,f=o.length,d=0,p=new Array(f),g=new Array(f),y=+r.apply(this,arguments),v=Math.min(kx,Math.max(-kx,i.apply(this,arguments)-y)),m=Math.min(Math.abs(v)/f,a.apply(this,arguments)),b=m*(v<0?-1:1);for(s=0;s0&&(d+=h);for(null!=e?p.sort((function(t,n){return e(g[t],g[n])})):null!=n&&p.sort((function(t,e){return n(o[t],o[e])})),s=0,u=d?(v-f*b)/d:0;s0?h*u:0)+b,g[c]={data:o[c],index:s,value:h,startAngle:y,endAngle:l,padAngle:m};return g}return o.value=function(e){return arguments.length?(t="function"==typeof e?e:fx(+e),o):t},o.sortValues=function(t){return arguments.length?(e=t,n=null,o):e},o.sort=function(t){return arguments.length?(n=t,e=null,o):n},o.startAngle=function(t){return arguments.length?(r="function"==typeof t?t:fx(+t),o):r},o.endAngle=function(t){return arguments.length?(i="function"==typeof t?t:fx(+t),o):i},o.padAngle=function(t){return arguments.length?(a="function"==typeof t?t:fx(+t),o):a},o},Ux=Wx(Lx);function $x(t){this._curve=t}function Wx(t){function e(e){return new $x(t(e))}return e._curve=t,e}function Vx(t){var e=t.curve;return t.angle=t.x,delete t.x,t.radius=t.y,delete t.y,t.curve=function(t){return arguments.length?e(Wx(t)):e()._curve},t}$x.prototype={areaStart:function(){this._curve.areaStart()},areaEnd:function(){this._curve.areaEnd()},lineStart:function(){this._curve.lineStart()},lineEnd:function(){this._curve.lineEnd()},point:function(t,e){this._curve.point(e*Math.sin(t),e*-Math.cos(t))}};var Hx=function(){return Vx(Ix().curve(Ux))},Gx=function(){var t=jx().curve(Ux),e=t.curve,n=t.lineX0,r=t.lineX1,i=t.lineY0,a=t.lineY1;return t.angle=t.x,delete t.x,t.startAngle=t.x0,delete t.x0,t.endAngle=t.x1,delete t.x1,t.radius=t.y,delete t.y,t.innerRadius=t.y0,delete t.y0,t.outerRadius=t.y1,delete t.y1,t.lineStartAngle=function(){return Vx(n())},delete t.lineX0,t.lineEndAngle=function(){return Vx(r())},delete t.lineX1,t.lineInnerRadius=function(){return Vx(i())},delete t.lineY0,t.lineOuterRadius=function(){return Vx(a())},delete t.lineY1,t.curve=function(t){return arguments.length?e(Wx(t)):e()._curve},t},qx=function(t,e){return[(e=+e)*Math.cos(t-=Math.PI/2),e*Math.sin(t)]},Xx=Array.prototype.slice;function Zx(t){return t.source}function Jx(t){return t.target}function Qx(t){var e=Zx,n=Jx,r=Fx,i=Px,a=null;function o(){var o,s=Xx.call(arguments),c=e.apply(this,s),u=n.apply(this,s);if(a||(a=o=Ui()),t(a,+r.apply(this,(s[0]=c,s)),+i.apply(this,s),+r.apply(this,(s[0]=u,s)),+i.apply(this,s)),o)return a=null,o+""||null}return o.source=function(t){return arguments.length?(e=t,o):e},o.target=function(t){return arguments.length?(n=t,o):n},o.x=function(t){return arguments.length?(r="function"==typeof t?t:fx(+t),o):r},o.y=function(t){return arguments.length?(i="function"==typeof t?t:fx(+t),o):i},o.context=function(t){return arguments.length?(a=null==t?null:t,o):a},o}function Kx(t,e,n,r,i){t.moveTo(e,n),t.bezierCurveTo(e=(e+r)/2,n,e,i,r,i)}function t_(t,e,n,r,i){t.moveTo(e,n),t.bezierCurveTo(e,n=(n+i)/2,r,n,r,i)}function e_(t,e,n,r,i){var a=qx(e,n),o=qx(e,n=(n+i)/2),s=qx(r,n),c=qx(r,i);t.moveTo(a[0],a[1]),t.bezierCurveTo(o[0],o[1],s[0],s[1],c[0],c[1])}function n_(){return Qx(Kx)}function r_(){return Qx(t_)}function i_(){var t=Qx(e_);return t.angle=t.x,delete t.x,t.radius=t.y,delete t.y,t}var a_={draw:function(t,e){var n=Math.sqrt(e/xx);t.moveTo(n,0),t.arc(0,0,n,0,kx)}},o_={draw:function(t,e){var n=Math.sqrt(e/5)/2;t.moveTo(-3*n,-n),t.lineTo(-n,-n),t.lineTo(-n,-3*n),t.lineTo(n,-3*n),t.lineTo(n,-n),t.lineTo(3*n,-n),t.lineTo(3*n,n),t.lineTo(n,n),t.lineTo(n,3*n),t.lineTo(-n,3*n),t.lineTo(-n,n),t.lineTo(-3*n,n),t.closePath()}},s_=Math.sqrt(1/3),c_=2*s_,u_={draw:function(t,e){var n=Math.sqrt(e/c_),r=n*s_;t.moveTo(0,-n),t.lineTo(r,0),t.lineTo(0,n),t.lineTo(-r,0),t.closePath()}},l_=Math.sin(xx/10)/Math.sin(7*xx/10),h_=Math.sin(kx/10)*l_,f_=-Math.cos(kx/10)*l_,d_={draw:function(t,e){var n=Math.sqrt(.8908130915292852*e),r=h_*n,i=f_*n;t.moveTo(0,-n),t.lineTo(r,i);for(var a=1;a<5;++a){var o=kx*a/5,s=Math.cos(o),c=Math.sin(o);t.lineTo(c*n,-s*n),t.lineTo(s*r-c*i,c*r+s*i)}t.closePath()}},p_={draw:function(t,e){var n=Math.sqrt(e),r=-n/2;t.rect(r,r,n,n)}},g_=Math.sqrt(3),y_={draw:function(t,e){var n=-Math.sqrt(e/(3*g_));t.moveTo(0,2*n),t.lineTo(-g_*n,-n),t.lineTo(g_*n,-n),t.closePath()}},v_=Math.sqrt(3)/2,m_=1/Math.sqrt(12),b_=3*(m_/2+1),x_={draw:function(t,e){var n=Math.sqrt(e/b_),r=n/2,i=n*m_,a=r,o=n*m_+n,s=-a,c=o;t.moveTo(r,i),t.lineTo(a,o),t.lineTo(s,c),t.lineTo(-.5*r-v_*i,v_*r+-.5*i),t.lineTo(-.5*a-v_*o,v_*a+-.5*o),t.lineTo(-.5*s-v_*c,v_*s+-.5*c),t.lineTo(-.5*r+v_*i,-.5*i-v_*r),t.lineTo(-.5*a+v_*o,-.5*o-v_*a),t.lineTo(-.5*s+v_*c,-.5*c-v_*s),t.closePath()}},__=[a_,o_,u_,p_,d_,y_,x_],k_=function(){var t=fx(a_),e=fx(64),n=null;function r(){var r;if(n||(n=r=Ui()),t.apply(this,arguments).draw(n,+e.apply(this,arguments)),r)return n=null,r+""||null}return r.type=function(e){return arguments.length?(t="function"==typeof e?e:fx(e),r):t},r.size=function(t){return arguments.length?(e="function"==typeof t?t:fx(+t),r):e},r.context=function(t){return arguments.length?(n=null==t?null:t,r):n},r},w_=function(){};function E_(t,e,n){t._context.bezierCurveTo((2*t._x0+t._x1)/3,(2*t._y0+t._y1)/3,(t._x0+2*t._x1)/3,(t._y0+2*t._y1)/3,(t._x0+4*t._x1+e)/6,(t._y0+4*t._y1+n)/6)}function T_(t){this._context=t}T_.prototype={areaStart:function(){this._line=0},areaEnd:function(){this._line=NaN},lineStart:function(){this._x0=this._x1=this._y0=this._y1=NaN,this._point=0},lineEnd:function(){switch(this._point){case 3:E_(this,this._x1,this._y1);case 2:this._context.lineTo(this._x1,this._y1)}(this._line||0!==this._line&&1===this._point)&&this._context.closePath(),this._line=1-this._line},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1,this._line?this._context.lineTo(t,e):this._context.moveTo(t,e);break;case 1:this._point=2;break;case 2:this._point=3,this._context.lineTo((5*this._x0+this._x1)/6,(5*this._y0+this._y1)/6);default:E_(this,t,e)}this._x0=this._x1,this._x1=t,this._y0=this._y1,this._y1=e}};var C_=function(t){return new T_(t)};function S_(t){this._context=t}S_.prototype={areaStart:w_,areaEnd:w_,lineStart:function(){this._x0=this._x1=this._x2=this._x3=this._x4=this._y0=this._y1=this._y2=this._y3=this._y4=NaN,this._point=0},lineEnd:function(){switch(this._point){case 1:this._context.moveTo(this._x2,this._y2),this._context.closePath();break;case 2:this._context.moveTo((this._x2+2*this._x3)/3,(this._y2+2*this._y3)/3),this._context.lineTo((this._x3+2*this._x2)/3,(this._y3+2*this._y2)/3),this._context.closePath();break;case 3:this.point(this._x2,this._y2),this.point(this._x3,this._y3),this.point(this._x4,this._y4)}},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1,this._x2=t,this._y2=e;break;case 1:this._point=2,this._x3=t,this._y3=e;break;case 2:this._point=3,this._x4=t,this._y4=e,this._context.moveTo((this._x0+4*this._x1+t)/6,(this._y0+4*this._y1+e)/6);break;default:E_(this,t,e)}this._x0=this._x1,this._x1=t,this._y0=this._y1,this._y1=e}};var A_=function(t){return new S_(t)};function M_(t){this._context=t}M_.prototype={areaStart:function(){this._line=0},areaEnd:function(){this._line=NaN},lineStart:function(){this._x0=this._x1=this._y0=this._y1=NaN,this._point=0},lineEnd:function(){(this._line||0!==this._line&&3===this._point)&&this._context.closePath(),this._line=1-this._line},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1;break;case 1:this._point=2;break;case 2:this._point=3;var n=(this._x0+4*this._x1+t)/6,r=(this._y0+4*this._y1+e)/6;this._line?this._context.lineTo(n,r):this._context.moveTo(n,r);break;case 3:this._point=4;default:E_(this,t,e)}this._x0=this._x1,this._x1=t,this._y0=this._y1,this._y1=e}};var O_=function(t){return new M_(t)};function D_(t,e){this._basis=new T_(t),this._beta=e}D_.prototype={lineStart:function(){this._x=[],this._y=[],this._basis.lineStart()},lineEnd:function(){var t=this._x,e=this._y,n=t.length-1;if(n>0)for(var r,i=t[0],a=e[0],o=t[n]-i,s=e[n]-a,c=-1;++c<=n;)r=c/n,this._basis.point(this._beta*t[c]+(1-this._beta)*(i+r*o),this._beta*e[c]+(1-this._beta)*(a+r*s));this._x=this._y=null,this._basis.lineEnd()},point:function(t,e){this._x.push(+t),this._y.push(+e)}};var N_=function t(e){function n(t){return 1===e?new T_(t):new D_(t,e)}return n.beta=function(e){return t(+e)},n}(.85);function B_(t,e,n){t._context.bezierCurveTo(t._x1+t._k*(t._x2-t._x0),t._y1+t._k*(t._y2-t._y0),t._x2+t._k*(t._x1-e),t._y2+t._k*(t._y1-n),t._x2,t._y2)}function L_(t,e){this._context=t,this._k=(1-e)/6}L_.prototype={areaStart:function(){this._line=0},areaEnd:function(){this._line=NaN},lineStart:function(){this._x0=this._x1=this._x2=this._y0=this._y1=this._y2=NaN,this._point=0},lineEnd:function(){switch(this._point){case 2:this._context.lineTo(this._x2,this._y2);break;case 3:B_(this,this._x1,this._y1)}(this._line||0!==this._line&&1===this._point)&&this._context.closePath(),this._line=1-this._line},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1,this._line?this._context.lineTo(t,e):this._context.moveTo(t,e);break;case 1:this._point=2,this._x1=t,this._y1=e;break;case 2:this._point=3;default:B_(this,t,e)}this._x0=this._x1,this._x1=this._x2,this._x2=t,this._y0=this._y1,this._y1=this._y2,this._y2=e}};var F_=function t(e){function n(t){return new L_(t,e)}return n.tension=function(e){return t(+e)},n}(0);function P_(t,e){this._context=t,this._k=(1-e)/6}P_.prototype={areaStart:w_,areaEnd:w_,lineStart:function(){this._x0=this._x1=this._x2=this._x3=this._x4=this._x5=this._y0=this._y1=this._y2=this._y3=this._y4=this._y5=NaN,this._point=0},lineEnd:function(){switch(this._point){case 1:this._context.moveTo(this._x3,this._y3),this._context.closePath();break;case 2:this._context.lineTo(this._x3,this._y3),this._context.closePath();break;case 3:this.point(this._x3,this._y3),this.point(this._x4,this._y4),this.point(this._x5,this._y5)}},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1,this._x3=t,this._y3=e;break;case 1:this._point=2,this._context.moveTo(this._x4=t,this._y4=e);break;case 2:this._point=3,this._x5=t,this._y5=e;break;default:B_(this,t,e)}this._x0=this._x1,this._x1=this._x2,this._x2=t,this._y0=this._y1,this._y1=this._y2,this._y2=e}};var I_=function t(e){function n(t){return new P_(t,e)}return n.tension=function(e){return t(+e)},n}(0);function j_(t,e){this._context=t,this._k=(1-e)/6}j_.prototype={areaStart:function(){this._line=0},areaEnd:function(){this._line=NaN},lineStart:function(){this._x0=this._x1=this._x2=this._y0=this._y1=this._y2=NaN,this._point=0},lineEnd:function(){(this._line||0!==this._line&&3===this._point)&&this._context.closePath(),this._line=1-this._line},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1;break;case 1:this._point=2;break;case 2:this._point=3,this._line?this._context.lineTo(this._x2,this._y2):this._context.moveTo(this._x2,this._y2);break;case 3:this._point=4;default:B_(this,t,e)}this._x0=this._x1,this._x1=this._x2,this._x2=t,this._y0=this._y1,this._y1=this._y2,this._y2=e}};var R_=function t(e){function n(t){return new j_(t,e)}return n.tension=function(e){return t(+e)},n}(0);function Y_(t,e,n){var r=t._x1,i=t._y1,a=t._x2,o=t._y2;if(t._l01_a>1e-12){var s=2*t._l01_2a+3*t._l01_a*t._l12_a+t._l12_2a,c=3*t._l01_a*(t._l01_a+t._l12_a);r=(r*s-t._x0*t._l12_2a+t._x2*t._l01_2a)/c,i=(i*s-t._y0*t._l12_2a+t._y2*t._l01_2a)/c}if(t._l23_a>1e-12){var u=2*t._l23_2a+3*t._l23_a*t._l12_a+t._l12_2a,l=3*t._l23_a*(t._l23_a+t._l12_a);a=(a*u+t._x1*t._l23_2a-e*t._l12_2a)/l,o=(o*u+t._y1*t._l23_2a-n*t._l12_2a)/l}t._context.bezierCurveTo(r,i,a,o,t._x2,t._y2)}function z_(t,e){this._context=t,this._alpha=e}z_.prototype={areaStart:function(){this._line=0},areaEnd:function(){this._line=NaN},lineStart:function(){this._x0=this._x1=this._x2=this._y0=this._y1=this._y2=NaN,this._l01_a=this._l12_a=this._l23_a=this._l01_2a=this._l12_2a=this._l23_2a=this._point=0},lineEnd:function(){switch(this._point){case 2:this._context.lineTo(this._x2,this._y2);break;case 3:this.point(this._x2,this._y2)}(this._line||0!==this._line&&1===this._point)&&this._context.closePath(),this._line=1-this._line},point:function(t,e){if(t=+t,e=+e,this._point){var n=this._x2-t,r=this._y2-e;this._l23_a=Math.sqrt(this._l23_2a=Math.pow(n*n+r*r,this._alpha))}switch(this._point){case 0:this._point=1,this._line?this._context.lineTo(t,e):this._context.moveTo(t,e);break;case 1:this._point=2;break;case 2:this._point=3;default:Y_(this,t,e)}this._l01_a=this._l12_a,this._l12_a=this._l23_a,this._l01_2a=this._l12_2a,this._l12_2a=this._l23_2a,this._x0=this._x1,this._x1=this._x2,this._x2=t,this._y0=this._y1,this._y1=this._y2,this._y2=e}};var U_=function t(e){function n(t){return e?new z_(t,e):new L_(t,0)}return n.alpha=function(e){return t(+e)},n}(.5);function $_(t,e){this._context=t,this._alpha=e}$_.prototype={areaStart:w_,areaEnd:w_,lineStart:function(){this._x0=this._x1=this._x2=this._x3=this._x4=this._x5=this._y0=this._y1=this._y2=this._y3=this._y4=this._y5=NaN,this._l01_a=this._l12_a=this._l23_a=this._l01_2a=this._l12_2a=this._l23_2a=this._point=0},lineEnd:function(){switch(this._point){case 1:this._context.moveTo(this._x3,this._y3),this._context.closePath();break;case 2:this._context.lineTo(this._x3,this._y3),this._context.closePath();break;case 3:this.point(this._x3,this._y3),this.point(this._x4,this._y4),this.point(this._x5,this._y5)}},point:function(t,e){if(t=+t,e=+e,this._point){var n=this._x2-t,r=this._y2-e;this._l23_a=Math.sqrt(this._l23_2a=Math.pow(n*n+r*r,this._alpha))}switch(this._point){case 0:this._point=1,this._x3=t,this._y3=e;break;case 1:this._point=2,this._context.moveTo(this._x4=t,this._y4=e);break;case 2:this._point=3,this._x5=t,this._y5=e;break;default:Y_(this,t,e)}this._l01_a=this._l12_a,this._l12_a=this._l23_a,this._l01_2a=this._l12_2a,this._l12_2a=this._l23_2a,this._x0=this._x1,this._x1=this._x2,this._x2=t,this._y0=this._y1,this._y1=this._y2,this._y2=e}};var W_=function t(e){function n(t){return e?new $_(t,e):new P_(t,0)}return n.alpha=function(e){return t(+e)},n}(.5);function V_(t,e){this._context=t,this._alpha=e}V_.prototype={areaStart:function(){this._line=0},areaEnd:function(){this._line=NaN},lineStart:function(){this._x0=this._x1=this._x2=this._y0=this._y1=this._y2=NaN,this._l01_a=this._l12_a=this._l23_a=this._l01_2a=this._l12_2a=this._l23_2a=this._point=0},lineEnd:function(){(this._line||0!==this._line&&3===this._point)&&this._context.closePath(),this._line=1-this._line},point:function(t,e){if(t=+t,e=+e,this._point){var n=this._x2-t,r=this._y2-e;this._l23_a=Math.sqrt(this._l23_2a=Math.pow(n*n+r*r,this._alpha))}switch(this._point){case 0:this._point=1;break;case 1:this._point=2;break;case 2:this._point=3,this._line?this._context.lineTo(this._x2,this._y2):this._context.moveTo(this._x2,this._y2);break;case 3:this._point=4;default:Y_(this,t,e)}this._l01_a=this._l12_a,this._l12_a=this._l23_a,this._l01_2a=this._l12_2a,this._l12_2a=this._l23_2a,this._x0=this._x1,this._x1=this._x2,this._x2=t,this._y0=this._y1,this._y1=this._y2,this._y2=e}};var H_=function t(e){function n(t){return e?new V_(t,e):new j_(t,0)}return n.alpha=function(e){return t(+e)},n}(.5);function G_(t){this._context=t}G_.prototype={areaStart:w_,areaEnd:w_,lineStart:function(){this._point=0},lineEnd:function(){this._point&&this._context.closePath()},point:function(t,e){t=+t,e=+e,this._point?this._context.lineTo(t,e):(this._point=1,this._context.moveTo(t,e))}};var q_=function(t){return new G_(t)};function X_(t){return t<0?-1:1}function Z_(t,e,n){var r=t._x1-t._x0,i=e-t._x1,a=(t._y1-t._y0)/(r||i<0&&-0),o=(n-t._y1)/(i||r<0&&-0),s=(a*i+o*r)/(r+i);return(X_(a)+X_(o))*Math.min(Math.abs(a),Math.abs(o),.5*Math.abs(s))||0}function J_(t,e){var n=t._x1-t._x0;return n?(3*(t._y1-t._y0)/n-e)/2:e}function Q_(t,e,n){var r=t._x0,i=t._y0,a=t._x1,o=t._y1,s=(a-r)/3;t._context.bezierCurveTo(r+s,i+s*e,a-s,o-s*n,a,o)}function K_(t){this._context=t}function tk(t){this._context=new ek(t)}function ek(t){this._context=t}function nk(t){return new K_(t)}function rk(t){return new tk(t)}function ik(t){this._context=t}function ak(t){var e,n,r=t.length-1,i=new Array(r),a=new Array(r),o=new Array(r);for(i[0]=0,a[0]=2,o[0]=t[0]+2*t[1],e=1;e=0;--e)i[e]=(o[e]-i[e+1])/a[e];for(a[r-1]=(t[r]+i[r-1])/2,e=0;e=0&&(this._t=1-this._t,this._line=1-this._line)},point:function(t,e){switch(t=+t,e=+e,this._point){case 0:this._point=1,this._line?this._context.lineTo(t,e):this._context.moveTo(t,e);break;case 1:this._point=2;default:if(this._t<=0)this._context.lineTo(this._x,e),this._context.lineTo(t,e);else{var n=this._x*(1-this._t)+t*this._t;this._context.lineTo(n,this._y),this._context.lineTo(n,e)}}this._x=t,this._y=e}};var ck=function(t){return new sk(t,.5)};function uk(t){return new sk(t,0)}function lk(t){return new sk(t,1)}var hk=function(t,e){if((i=t.length)>1)for(var n,r,i,a=1,o=t[e[0]],s=o.length;a=0;)n[e]=e;return n};function dk(t,e){return t[e]}var pk=function(){var t=fx([]),e=fk,n=hk,r=dk;function i(i){var a,o,s=t.apply(this,arguments),c=i.length,u=s.length,l=new Array(u);for(a=0;a0){for(var n,r,i,a=0,o=t[0].length;a0)for(var n,r,i,a,o,s,c=0,u=t[e[0]].length;c0?(r[0]=a,r[1]=a+=i):i<0?(r[1]=o,r[0]=o+=i):(r[0]=0,r[1]=i)},vk=function(t,e){if((n=t.length)>0){for(var n,r=0,i=t[e[0]],a=i.length;r0&&(r=(n=t[e[0]]).length)>0){for(var n,r,i,a=0,o=1;oa&&(a=e,r=n);return r}var _k=function(t){var e=t.map(kk);return fk(t).sort((function(t,n){return e[t]-e[n]}))};function kk(t){for(var e,n=0,r=-1,i=t.length;++r0)){if(a/=f,f<0){if(a0){if(a>h)return;a>l&&(l=a)}if(a=r-c,f||!(a<0)){if(a/=f,f<0){if(a>h)return;a>l&&(l=a)}else if(f>0){if(a0)){if(a/=d,d<0){if(a0){if(a>h)return;a>l&&(l=a)}if(a=i-u,d||!(a<0)){if(a/=d,d<0){if(a>h)return;a>l&&(l=a)}else if(d>0){if(a0||h<1)||(l>0&&(t[0]=[c+l*f,u+l*d]),h<1&&(t[1]=[c+h*f,u+h*d]),!0)}}}}}function Uk(t,e,n,r,i){var a=t[1];if(a)return!0;var o,s,c=t[0],u=t.left,l=t.right,h=u[0],f=u[1],d=l[0],p=l[1],g=(h+d)/2,y=(f+p)/2;if(p===f){if(g=r)return;if(h>d){if(c){if(c[1]>=i)return}else c=[g,n];a=[g,i]}else{if(c){if(c[1]1)if(h>d){if(c){if(c[1]>=i)return}else c=[(n-s)/o,n];a=[(i-s)/o,i]}else{if(c){if(c[1]=r)return}else c=[e,o*e+s];a=[r,o*r+s]}else{if(c){if(c[0]=-lw)){var d=c*c+u*u,p=l*l+h*h,g=(h*d-u*p)/f,y=(c*p-l*d)/f,v=Gk.pop()||new qk;v.arc=t,v.site=i,v.x=g+o,v.y=(v.cy=y+s)+Math.sqrt(g*g+y*y),t.circle=v;for(var m=null,b=sw._;b;)if(v.yuw)s=s.L;else{if(!((i=a-iw(s,o))>uw)){r>-uw?(e=s.P,n=s):i>-uw?(e=s,n=s.N):e=n=s;break}if(!s.R){e=s;break}s=s.R}!function(t){ow[t.index]={site:t,halfedges:[]}}(t);var c=Kk(t);if(aw.insert(e,c),e||n){if(e===n)return Zk(e),n=Kk(e.site),aw.insert(c,n),c.edge=n.edge=jk(e.site,c.site),Xk(e),void Xk(n);if(n){Zk(e),Zk(n);var u=e.site,l=u[0],h=u[1],f=t[0]-l,d=t[1]-h,p=n.site,g=p[0]-l,y=p[1]-h,v=2*(f*y-d*g),m=f*f+d*d,b=g*g+y*y,x=[(y*m-d*b)/v+l,(f*b-g*m)/v+h];Yk(n.edge,u,p,x),c.edge=jk(u,t,null,x),n.edge=jk(t,p,null,x),Xk(e),Xk(n)}else c.edge=jk(e.site,c.site)}}function rw(t,e){var n=t.site,r=n[0],i=n[1],a=i-e;if(!a)return r;var o=t.P;if(!o)return-1/0;var s=(n=o.site)[0],c=n[1],u=c-e;if(!u)return s;var l=s-r,h=1/a-1/u,f=l/u;return h?(-f+Math.sqrt(f*f-2*h*(l*l/(-2*u)-c+u/2+i-a/2)))/h+r:(r+s)/2}function iw(t,e){var n=t.N;if(n)return rw(n,e);var r=t.site;return r[1]===e?r[0]:1/0}var aw,ow,sw,cw,uw=1e-6,lw=1e-12;function hw(t,e){return e[1]-t[1]||e[0]-t[0]}function fw(t,e){var n,r,i,a=t.sort(hw).pop();for(cw=[],ow=new Array(t.length),aw=new Ik,sw=new Ik;;)if(i=Hk,a&&(!i||a[1]uw||Math.abs(i[0][1]-i[1][1])>uw)||delete cw[a]}(o,s,c,u),function(t,e,n,r){var i,a,o,s,c,u,l,h,f,d,p,g,y=ow.length,v=!0;for(i=0;iuw||Math.abs(g-f)>uw)&&(c.splice(s,0,cw.push(Rk(o,d,Math.abs(p-t)uw?[t,Math.abs(h-t)uw?[Math.abs(f-r)uw?[n,Math.abs(h-n)uw?[Math.abs(f-e)=s)return null;var c=t-i.site[0],u=e-i.site[1],l=c*c+u*u;do{i=a.cells[r=o],o=null,i.halfedges.forEach((function(n){var r=a.edges[n],s=r.left;if(s!==i.site&&s||(s=r.right)){var c=t-s[0],u=e-s[1],h=c*c+u*u;hr?(r+i)/2:Math.min(0,r)||Math.max(0,i),o>a?(a+o)/2:Math.min(0,a)||Math.max(0,o))}var Sw=function(){var t,e,n=_w,r=kw,i=Cw,a=Ew,o=Tw,s=[0,1/0],c=[[-1/0,-1/0],[1/0,1/0]],u=250,l=fp,h=lt("start","zoom","end"),f=0;function d(t){t.property("__zoom",ww).on("wheel.zoom",x).on("mousedown.zoom",_).on("dblclick.zoom",k).filter(o).on("touchstart.zoom",w).on("touchmove.zoom",E).on("touchend.zoom touchcancel.zoom",T).style("touch-action","none").style("-webkit-tap-highlight-color","rgba(0,0,0,0)")}function p(t,e){return(e=Math.max(s[0],Math.min(s[1],e)))===t.k?t:new yw(e,t.x,t.y)}function g(t,e,n){var r=e[0]-n[0]*t.k,i=e[1]-n[1]*t.k;return r===t.x&&i===t.y?t:new yw(t.k,r,i)}function y(t){return[(+t[0][0]+ +t[1][0])/2,(+t[0][1]+ +t[1][1])/2]}function v(t,e,n){t.on("start.zoom",(function(){m(this,arguments).start()})).on("interrupt.zoom end.zoom",(function(){m(this,arguments).end()})).tween("zoom",(function(){var t=this,i=arguments,a=m(t,i),o=r.apply(t,i),s=null==n?y(o):"function"==typeof n?n.apply(t,i):n,c=Math.max(o[1][0]-o[0][0],o[1][1]-o[0][1]),u=t.__zoom,h="function"==typeof e?e.apply(t,i):e,f=l(u.invert(s).concat(c/u.k),h.invert(s).concat(c/h.k));return function(t){if(1===t)t=h;else{var e=f(t),n=c/e[2];t=new yw(n,s[0]-e[0]*n,s[1]-e[1]*n)}a.zoom(null,t)}}))}function m(t,e,n){return!n&&t.__zooming||new b(t,e)}function b(t,e){this.that=t,this.args=e,this.active=0,this.extent=r.apply(t,e),this.taps=0}function x(){if(n.apply(this,arguments)){var t=m(this,arguments),e=this.__zoom,r=Math.max(s[0],Math.min(s[1],e.k*Math.pow(2,a.apply(this,arguments)))),o=Nn(this);if(t.wheel)t.mouse[0][0]===o[0]&&t.mouse[0][1]===o[1]||(t.mouse[1]=e.invert(t.mouse[0]=o)),clearTimeout(t.wheel);else{if(e.k===r)return;t.mouse=[o,e.invert(o)],or(this),t.start()}xw(),t.wheel=setTimeout(u,150),t.zoom("mouse",i(g(p(e,r),t.mouse[0],t.mouse[1]),t.extent,c))}function u(){t.wheel=null,t.end()}}function _(){if(!e&&n.apply(this,arguments)){var t=m(this,arguments,!0),r=ke(ce.view).on("mousemove.zoom",u,!0).on("mouseup.zoom",l,!0),a=Nn(this),o=ce.clientX,s=ce.clientY;Te(ce.view),bw(),t.mouse=[a,this.__zoom.invert(a)],or(this),t.start()}function u(){if(xw(),!t.moved){var e=ce.clientX-o,n=ce.clientY-s;t.moved=e*e+n*n>f}t.zoom("mouse",i(g(t.that.__zoom,t.mouse[0]=Nn(t.that),t.mouse[1]),t.extent,c))}function l(){r.on("mousemove.zoom mouseup.zoom",null),Ce(ce.view,t.moved),xw(),t.end()}}function k(){if(n.apply(this,arguments)){var t=this.__zoom,e=Nn(this),a=t.invert(e),o=t.k*(ce.shiftKey?.5:2),s=i(g(p(t,o),e,a),r.apply(this,arguments),c);xw(),u>0?ke(this).transition().duration(u).call(v,s,e):ke(this).call(d.transform,s)}}function w(){if(n.apply(this,arguments)){var e,r,i,a,o=ce.touches,s=o.length,c=m(this,arguments,ce.changedTouches.length===s);for(bw(),r=0;rh&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},M={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),56;case 1:return this.begin("type_directive"),57;case 2:return this.popState(),this.begin("arg_directive"),14;case 3:return this.popState(),this.popState(),59;case 4:return 58;case 5:return 5;case 6:case 7:case 8:case 9:case 10:break;case 11:return this.begin("ID"),16;case 12:return e.yytext=e.yytext.trim(),this.begin("ALIAS"),48;case 13:return this.popState(),this.popState(),this.begin("LINE"),18;case 14:return this.popState(),this.popState(),5;case 15:return this.begin("LINE"),27;case 16:return this.begin("LINE"),29;case 17:return this.begin("LINE"),30;case 18:return this.begin("LINE"),31;case 19:return this.begin("LINE"),36;case 20:return this.begin("LINE"),33;case 21:return this.begin("LINE"),35;case 22:return this.popState(),19;case 23:return 28;case 24:return 43;case 25:return 44;case 26:return 39;case 27:return 37;case 28:return this.begin("ID"),22;case 29:return this.begin("ID"),23;case 30:return 25;case 31:return 7;case 32:return 21;case 33:return 42;case 34:return 5;case 35:return e.yytext=e.yytext.trim(),48;case 36:return 51;case 37:return 52;case 38:return 49;case 39:return 50;case 40:return 53;case 41:return 54;case 42:return 55;case 43:return 46;case 44:return 47;case 45:return 5;case 46:return"INVALID"}},rules:[/^(?:%%\{)/i,/^(?:((?:(?!\}%%)[^:.])*))/i,/^(?::)/i,/^(?:\}%%)/i,/^(?:((?:(?!\}%%).|\n)*))/i,/^(?:[\n]+)/i,/^(?:\s+)/i,/^(?:((?!\n)\s)+)/i,/^(?:#[^\n]*)/i,/^(?:%(?!\{)[^\n]*)/i,/^(?:[^\}]%%[^\n]*)/i,/^(?:participant\b)/i,/^(?:[^\->:\n,;]+?(?=((?!\n)\s)+as(?!\n)\s|[#\n;]|$))/i,/^(?:as\b)/i,/^(?:(?:))/i,/^(?:loop\b)/i,/^(?:rect\b)/i,/^(?:opt\b)/i,/^(?:alt\b)/i,/^(?:else\b)/i,/^(?:par\b)/i,/^(?:and\b)/i,/^(?:(?:[:]?(?:no)?wrap)?[^#\n;]*)/i,/^(?:end\b)/i,/^(?:left of\b)/i,/^(?:right of\b)/i,/^(?:over\b)/i,/^(?:note\b)/i,/^(?:activate\b)/i,/^(?:deactivate\b)/i,/^(?:title\b)/i,/^(?:sequenceDiagram\b)/i,/^(?:autonumber\b)/i,/^(?:,)/i,/^(?:;)/i,/^(?:[^\+\->:\n,;]+((?!(-x|--x))[\-]*[^\+\->:\n,;]+)*)/i,/^(?:->>)/i,/^(?:-->>)/i,/^(?:->)/i,/^(?:-->)/i,/^(?:-[x])/i,/^(?:--[x])/i,/^(?::(?:(?:no)?wrap)?[^#\n;]+)/i,/^(?:\+)/i,/^(?:-)/i,/^(?:$)/i,/^(?:.)/i],conditions:{open_directive:{rules:[1,8],inclusive:!1},type_directive:{rules:[2,3,8],inclusive:!1},arg_directive:{rules:[3,4,8],inclusive:!1},ID:{rules:[7,8,12],inclusive:!1},ALIAS:{rules:[7,8,13,14],inclusive:!1},LINE:{rules:[7,8,22],inclusive:!1},INITIAL:{rules:[0,5,6,8,9,10,11,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],inclusive:!0}}};function O(){this.yy={}}return A.lexer=M,O.prototype=A,A.Parser=O,new O}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){var r=n(198);t.exports={Graph:r.Graph,json:n(301),alg:n(302),version:r.version}},function(t,e,n){var r;try{r={cloneDeep:n(313),constant:n(86),defaults:n(154),each:n(87),filter:n(128),find:n(314),flatten:n(156),forEach:n(126),forIn:n(319),has:n(93),isUndefined:n(139),last:n(320),map:n(140),mapValues:n(321),max:n(322),merge:n(324),min:n(329),minBy:n(330),now:n(331),pick:n(161),range:n(162),reduce:n(142),sortBy:n(338),uniqueId:n(163),values:n(147),zipObject:n(343)}}catch(t){}r||(r=window._),t.exports=r},function(t,e){var n=Array.isArray;t.exports=n},function(t,e,n){ +/** + * @license + * Copyright (c) 2012-2013 Chris Pettitt + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + * THE SOFTWARE. + */ +t.exports={graphlib:n(311),dagre:n(153),intersect:n(368),render:n(370),util:n(12),version:n(382)}},function(t,e){t.exports=function(t){return t.webpackPolyfill||(t.deprecate=function(){},t.paths=[],t.children||(t.children=[]),Object.defineProperty(t,"loaded",{enumerable:!0,get:function(){return t.l}}),Object.defineProperty(t,"id",{enumerable:!0,get:function(){return t.i}}),t.webpackPolyfill=1),t}},function(t,e,n){"use strict";var r=n(4),i=n(17).Graph;function a(t,e,n,i){var a;do{a=r.uniqueId(i)}while(t.hasNode(a));return n.dummy=e,t.setNode(a,n),a}function o(t){return r.max(r.map(t.nodes(),(function(e){var n=t.node(e).rank;if(!r.isUndefined(n))return n})))}t.exports={addDummyNode:a,simplify:function(t){var e=(new i).setGraph(t.graph());return r.forEach(t.nodes(),(function(n){e.setNode(n,t.node(n))})),r.forEach(t.edges(),(function(n){var r=e.edge(n.v,n.w)||{weight:0,minlen:1},i=t.edge(n);e.setEdge(n.v,n.w,{weight:r.weight+i.weight,minlen:Math.max(r.minlen,i.minlen)})})),e},asNonCompoundGraph:function(t){var e=new i({multigraph:t.isMultigraph()}).setGraph(t.graph());return r.forEach(t.nodes(),(function(n){t.children(n).length||e.setNode(n,t.node(n))})),r.forEach(t.edges(),(function(n){e.setEdge(n,t.edge(n))})),e},successorWeights:function(t){var e=r.map(t.nodes(),(function(e){var n={};return r.forEach(t.outEdges(e),(function(e){n[e.w]=(n[e.w]||0)+t.edge(e).weight})),n}));return r.zipObject(t.nodes(),e)},predecessorWeights:function(t){var e=r.map(t.nodes(),(function(e){var n={};return r.forEach(t.inEdges(e),(function(e){n[e.v]=(n[e.v]||0)+t.edge(e).weight})),n}));return r.zipObject(t.nodes(),e)},intersectRect:function(t,e){var n,r,i=t.x,a=t.y,o=e.x-i,s=e.y-a,c=t.width/2,u=t.height/2;if(!o&&!s)throw new Error("Not possible to find intersection inside of the rectangle");Math.abs(s)*c>Math.abs(o)*u?(s<0&&(u=-u),n=u*o/s,r=u):(o<0&&(c=-c),n=c,r=c*s/o);return{x:i+n,y:a+r}},buildLayerMatrix:function(t){var e=r.map(r.range(o(t)+1),(function(){return[]}));return r.forEach(t.nodes(),(function(n){var i=t.node(n),a=i.rank;r.isUndefined(a)||(e[a][i.order]=n)})),e},normalizeRanks:function(t){var e=r.min(r.map(t.nodes(),(function(e){return t.node(e).rank})));r.forEach(t.nodes(),(function(n){var i=t.node(n);r.has(i,"rank")&&(i.rank-=e)}))},removeEmptyRanks:function(t){var e=r.min(r.map(t.nodes(),(function(e){return t.node(e).rank}))),n=[];r.forEach(t.nodes(),(function(r){var i=t.node(r).rank-e;n[i]||(n[i]=[]),n[i].push(r)}));var i=0,a=t.graph().nodeRankFactor;r.forEach(n,(function(e,n){r.isUndefined(e)&&n%a!=0?--i:i&&r.forEach(e,(function(e){t.node(e).rank+=i}))}))},addBorderNode:function(t,e,n,r){var i={width:0,height:0};arguments.length>=4&&(i.rank=n,i.order=r);return a(t,"border",i,e)},maxRank:o,partition:function(t,e){var n={lhs:[],rhs:[]};return r.forEach(t,(function(t){e(t)?n.lhs.push(t):n.rhs.push(t)})),n},time:function(t,e){var n=r.now();try{return e()}finally{console.log(t+" time: "+(r.now()-n)+"ms")}},notime:function(t,e){return e()}}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(173),i=n(174),a=n(175),o={channel:r.default,lang:i.default,unit:a.default};e.default=o},function(t,e,n){var r;try{r={clone:n(199),constant:n(86),each:n(87),filter:n(128),has:n(93),isArray:n(5),isEmpty:n(276),isFunction:n(37),isUndefined:n(139),keys:n(30),map:n(140),reduce:n(142),size:n(279),transform:n(285),union:n(286),values:n(147)}}catch(t){}r||(r=window._),t.exports=r},function(t,e){t.exports=function(t){var e=typeof t;return null!=t&&("object"==e||"function"==e)}},function(t,e,n){var r=n(43);t.exports={isSubgraph:function(t,e){return!!t.children(e).length},edgeToId:function(t){return a(t.v)+":"+a(t.w)+":"+a(t.name)},applyStyle:function(t,e){e&&t.attr("style",e)},applyClass:function(t,e,n){e&&t.attr("class",e).attr("class",n+" "+t.attr("class"))},applyTransition:function(t,e){var n=e.graph();if(r.isPlainObject(n)){var i=n.transition;if(r.isFunction(i))return i(t)}return t}};var i=/:/g;function a(t){return t?String(t).replace(i,"\\:"):""}},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[1,7],n=[1,6],r=[1,14],i=[1,25],a=[1,28],o=[1,26],s=[1,27],c=[1,29],u=[1,30],l=[1,31],h=[1,33],f=[1,34],d=[1,35],p=[10,19],g=[1,47],y=[1,48],v=[1,49],m=[1,50],b=[1,51],x=[1,52],_=[10,19,25,32,33,41,44,45,46,47,48,49],k=[10,19,23,25,32,33,37,41,44,45,46,47,48,49,66,67,68],w=[10,13,17,19],E=[41,66,67,68],T=[41,48,49,66,67,68],C=[41,44,45,46,47,66,67,68],S=[10,19,25],A=[1,81],M={trace:function(){},yy:{},symbols_:{error:2,start:3,mermaidDoc:4,directive:5,graphConfig:6,openDirective:7,typeDirective:8,closeDirective:9,NEWLINE:10,":":11,argDirective:12,open_directive:13,type_directive:14,arg_directive:15,close_directive:16,CLASS_DIAGRAM:17,statements:18,EOF:19,statement:20,className:21,alphaNumToken:22,GENERICTYPE:23,relationStatement:24,LABEL:25,classStatement:26,methodStatement:27,annotationStatement:28,clickStatement:29,cssClassStatement:30,CLASS:31,STYLE_SEPARATOR:32,STRUCT_START:33,members:34,STRUCT_STOP:35,ANNOTATION_START:36,ANNOTATION_END:37,MEMBER:38,SEPARATOR:39,relation:40,STR:41,relationType:42,lineType:43,AGGREGATION:44,EXTENSION:45,COMPOSITION:46,DEPENDENCY:47,LINE:48,DOTTED_LINE:49,CALLBACK:50,LINK:51,CSSCLASS:52,commentToken:53,textToken:54,graphCodeTokens:55,textNoTagsToken:56,TAGSTART:57,TAGEND:58,"==":59,"--":60,PCT:61,DEFAULT:62,SPACE:63,MINUS:64,keywords:65,UNICODE_TEXT:66,NUM:67,ALPHA:68,$accept:0,$end:1},terminals_:{2:"error",10:"NEWLINE",11:":",13:"open_directive",14:"type_directive",15:"arg_directive",16:"close_directive",17:"CLASS_DIAGRAM",19:"EOF",23:"GENERICTYPE",25:"LABEL",31:"CLASS",32:"STYLE_SEPARATOR",33:"STRUCT_START",35:"STRUCT_STOP",36:"ANNOTATION_START",37:"ANNOTATION_END",38:"MEMBER",39:"SEPARATOR",41:"STR",44:"AGGREGATION",45:"EXTENSION",46:"COMPOSITION",47:"DEPENDENCY",48:"LINE",49:"DOTTED_LINE",50:"CALLBACK",51:"LINK",52:"CSSCLASS",55:"graphCodeTokens",57:"TAGSTART",58:"TAGEND",59:"==",60:"--",61:"PCT",62:"DEFAULT",63:"SPACE",64:"MINUS",65:"keywords",66:"UNICODE_TEXT",67:"NUM",68:"ALPHA"},productions_:[0,[3,1],[3,2],[4,1],[5,4],[5,6],[7,1],[8,1],[12,1],[9,1],[6,4],[18,1],[18,2],[18,3],[21,1],[21,2],[21,3],[21,2],[20,1],[20,2],[20,1],[20,1],[20,1],[20,1],[20,1],[20,1],[26,2],[26,4],[26,5],[26,7],[28,4],[34,1],[34,2],[27,1],[27,2],[27,1],[27,1],[24,3],[24,4],[24,4],[24,5],[40,3],[40,2],[40,2],[40,1],[42,1],[42,1],[42,1],[42,1],[43,1],[43,1],[29,3],[29,4],[29,3],[29,4],[30,3],[53,1],[53,1],[54,1],[54,1],[54,1],[54,1],[54,1],[54,1],[54,1],[56,1],[56,1],[56,1],[56,1],[22,1],[22,1],[22,1]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 6:r.parseDirective("%%{","open_directive");break;case 7:r.parseDirective(a[s],"type_directive");break;case 8:a[s]=a[s].trim().replace(/'/g,'"'),r.parseDirective(a[s],"arg_directive");break;case 9:r.parseDirective("}%%","close_directive","class");break;case 14:this.$=a[s];break;case 15:this.$=a[s-1]+a[s];break;case 16:this.$=a[s-2]+"~"+a[s-1]+a[s];break;case 17:this.$=a[s-1]+"~"+a[s];break;case 18:r.addRelation(a[s]);break;case 19:a[s-1].title=r.cleanupLabel(a[s]),r.addRelation(a[s-1]);break;case 26:r.addClass(a[s]);break;case 27:r.addClass(a[s-2]),r.setCssClass(a[s-2],a[s]);break;case 28:r.addClass(a[s-3]),r.addMembers(a[s-3],a[s-1]);break;case 29:r.addClass(a[s-5]),r.setCssClass(a[s-5],a[s-3]),r.addMembers(a[s-5],a[s-1]);break;case 30:r.addAnnotation(a[s],a[s-2]);break;case 31:this.$=[a[s]];break;case 32:a[s].push(a[s-1]),this.$=a[s];break;case 33:break;case 34:r.addMember(a[s-1],r.cleanupLabel(a[s]));break;case 35:case 36:break;case 37:this.$={id1:a[s-2],id2:a[s],relation:a[s-1],relationTitle1:"none",relationTitle2:"none"};break;case 38:this.$={id1:a[s-3],id2:a[s],relation:a[s-1],relationTitle1:a[s-2],relationTitle2:"none"};break;case 39:this.$={id1:a[s-3],id2:a[s],relation:a[s-2],relationTitle1:"none",relationTitle2:a[s-1]};break;case 40:this.$={id1:a[s-4],id2:a[s],relation:a[s-2],relationTitle1:a[s-3],relationTitle2:a[s-1]};break;case 41:this.$={type1:a[s-2],type2:a[s],lineType:a[s-1]};break;case 42:this.$={type1:"none",type2:a[s],lineType:a[s-1]};break;case 43:this.$={type1:a[s-1],type2:"none",lineType:a[s]};break;case 44:this.$={type1:"none",type2:"none",lineType:a[s]};break;case 45:this.$=r.relationType.AGGREGATION;break;case 46:this.$=r.relationType.EXTENSION;break;case 47:this.$=r.relationType.COMPOSITION;break;case 48:this.$=r.relationType.DEPENDENCY;break;case 49:this.$=r.lineType.LINE;break;case 50:this.$=r.lineType.DOTTED_LINE;break;case 51:this.$=a[s-2],r.setClickEvent(a[s-1],a[s],void 0);break;case 52:this.$=a[s-3],r.setClickEvent(a[s-2],a[s-1],a[s]);break;case 53:this.$=a[s-2],r.setLink(a[s-1],a[s],void 0);break;case 54:this.$=a[s-3],r.setLink(a[s-2],a[s-1],a[s]);break;case 55:r.setCssClass(a[s-1],a[s])}},table:[{3:1,4:2,5:3,6:4,7:5,13:e,17:n},{1:[3]},{1:[2,1]},{3:8,4:2,5:3,6:4,7:5,13:e,17:n},{1:[2,3]},{8:9,14:[1,10]},{10:[1,11]},{14:[2,6]},{1:[2,2]},{9:12,11:[1,13],16:r},t([11,16],[2,7]),{5:23,7:5,13:e,18:15,20:16,21:24,22:32,24:17,26:18,27:19,28:20,29:21,30:22,31:i,36:a,38:o,39:s,50:c,51:u,52:l,66:h,67:f,68:d},{10:[1,36]},{12:37,15:[1,38]},{10:[2,9]},{19:[1,39]},{10:[1,40],19:[2,11]},t(p,[2,18],{25:[1,41]}),t(p,[2,20]),t(p,[2,21]),t(p,[2,22]),t(p,[2,23]),t(p,[2,24]),t(p,[2,25]),t(p,[2,33],{40:42,42:45,43:46,25:[1,44],41:[1,43],44:g,45:y,46:v,47:m,48:b,49:x}),{21:53,22:32,66:h,67:f,68:d},t(p,[2,35]),t(p,[2,36]),{22:54,66:h,67:f,68:d},{21:55,22:32,66:h,67:f,68:d},{21:56,22:32,66:h,67:f,68:d},{41:[1,57]},t(_,[2,14],{22:32,21:58,23:[1,59],66:h,67:f,68:d}),t(k,[2,69]),t(k,[2,70]),t(k,[2,71]),t(w,[2,4]),{9:60,16:r},{16:[2,8]},{1:[2,10]},{5:23,7:5,13:e,18:61,19:[2,12],20:16,21:24,22:32,24:17,26:18,27:19,28:20,29:21,30:22,31:i,36:a,38:o,39:s,50:c,51:u,52:l,66:h,67:f,68:d},t(p,[2,19]),{21:62,22:32,41:[1,63],66:h,67:f,68:d},{40:64,42:45,43:46,44:g,45:y,46:v,47:m,48:b,49:x},t(p,[2,34]),{43:65,48:b,49:x},t(E,[2,44],{42:66,44:g,45:y,46:v,47:m}),t(T,[2,45]),t(T,[2,46]),t(T,[2,47]),t(T,[2,48]),t(C,[2,49]),t(C,[2,50]),t(p,[2,26],{32:[1,67],33:[1,68]}),{37:[1,69]},{41:[1,70]},{41:[1,71]},{22:72,66:h,67:f,68:d},t(_,[2,15]),t(_,[2,17],{22:32,21:73,66:h,67:f,68:d}),{10:[1,74]},{19:[2,13]},t(S,[2,37]),{21:75,22:32,66:h,67:f,68:d},{21:76,22:32,41:[1,77],66:h,67:f,68:d},t(E,[2,43],{42:78,44:g,45:y,46:v,47:m}),t(E,[2,42]),{22:79,66:h,67:f,68:d},{34:80,38:A},{21:82,22:32,66:h,67:f,68:d},t(p,[2,51],{41:[1,83]}),t(p,[2,53],{41:[1,84]}),t(p,[2,55]),t(_,[2,16]),t(w,[2,5]),t(S,[2,39]),t(S,[2,38]),{21:85,22:32,66:h,67:f,68:d},t(E,[2,41]),t(p,[2,27],{33:[1,86]}),{35:[1,87]},{34:88,35:[2,31],38:A},t(p,[2,30]),t(p,[2,52]),t(p,[2,54]),t(S,[2,40]),{34:89,38:A},t(p,[2,28]),{35:[2,32]},{35:[1,90]},t(p,[2,29])],defaultActions:{2:[2,1],4:[2,3],7:[2,6],8:[2,2],14:[2,9],38:[2,8],39:[2,10],61:[2,13],88:[2,32]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},O={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),13;case 1:return this.begin("type_directive"),14;case 2:return this.popState(),this.begin("arg_directive"),11;case 3:return this.popState(),this.popState(),16;case 4:return 15;case 5:case 6:break;case 7:return 10;case 8:break;case 9:case 10:return 17;case 11:return this.begin("struct"),33;case 12:return"EOF_IN_STRUCT";case 13:return"OPEN_IN_STRUCT";case 14:return this.popState(),35;case 15:break;case 16:return"MEMBER";case 17:return 31;case 18:return 52;case 19:return 50;case 20:return 51;case 21:return 36;case 22:return 37;case 23:this.begin("generic");break;case 24:this.popState();break;case 25:return"GENERICTYPE";case 26:this.begin("string");break;case 27:this.popState();break;case 28:return"STR";case 29:case 30:return 45;case 31:case 32:return 47;case 33:return 46;case 34:return 44;case 35:return 48;case 36:return 49;case 37:return 25;case 38:return 32;case 39:return 64;case 40:return"DOT";case 41:return"PLUS";case 42:return 61;case 43:case 44:return"EQUALS";case 45:return 68;case 46:return"PUNCTUATION";case 47:return 67;case 48:return 66;case 49:return 63;case 50:return 19}},rules:[/^(?:%%\{)/,/^(?:((?:(?!\}%%)[^:.])*))/,/^(?::)/,/^(?:\}%%)/,/^(?:((?:(?!\}%%).|\n)*))/,/^(?:%%(?!\{)*[^\n]*(\r?\n?)+)/,/^(?:%%[^\n]*(\r?\n)*)/,/^(?:(\r?\n)+)/,/^(?:\s+)/,/^(?:classDiagram-v2\b)/,/^(?:classDiagram\b)/,/^(?:[{])/,/^(?:$)/,/^(?:[{])/,/^(?:[}])/,/^(?:[\n])/,/^(?:[^{}\n]*)/,/^(?:class\b)/,/^(?:cssClass\b)/,/^(?:callback\b)/,/^(?:link\b)/,/^(?:<<)/,/^(?:>>)/,/^(?:[~])/,/^(?:[~])/,/^(?:[^~]*)/,/^(?:["])/,/^(?:["])/,/^(?:[^"]*)/,/^(?:\s*<\|)/,/^(?:\s*\|>)/,/^(?:\s*>)/,/^(?:\s*<)/,/^(?:\s*\*)/,/^(?:\s*o\b)/,/^(?:--)/,/^(?:\.\.)/,/^(?::{1}[^:\n;]+)/,/^(?::{3})/,/^(?:-)/,/^(?:\.)/,/^(?:\+)/,/^(?:%)/,/^(?:=)/,/^(?:=)/,/^(?:\w+)/,/^(?:[!"#$%&'*+,-.`?\\/])/,/^(?:[0-9]+)/,/^(?:[\u00AA\u00B5\u00BA\u00C0-\u00D6\u00D8-\u00F6]|[\u00F8-\u02C1\u02C6-\u02D1\u02E0-\u02E4\u02EC\u02EE\u0370-\u0374\u0376\u0377]|[\u037A-\u037D\u0386\u0388-\u038A\u038C\u038E-\u03A1\u03A3-\u03F5]|[\u03F7-\u0481\u048A-\u0527\u0531-\u0556\u0559\u0561-\u0587\u05D0-\u05EA]|[\u05F0-\u05F2\u0620-\u064A\u066E\u066F\u0671-\u06D3\u06D5\u06E5\u06E6\u06EE]|[\u06EF\u06FA-\u06FC\u06FF\u0710\u0712-\u072F\u074D-\u07A5\u07B1\u07CA-\u07EA]|[\u07F4\u07F5\u07FA\u0800-\u0815\u081A\u0824\u0828\u0840-\u0858\u08A0]|[\u08A2-\u08AC\u0904-\u0939\u093D\u0950\u0958-\u0961\u0971-\u0977]|[\u0979-\u097F\u0985-\u098C\u098F\u0990\u0993-\u09A8\u09AA-\u09B0\u09B2]|[\u09B6-\u09B9\u09BD\u09CE\u09DC\u09DD\u09DF-\u09E1\u09F0\u09F1\u0A05-\u0A0A]|[\u0A0F\u0A10\u0A13-\u0A28\u0A2A-\u0A30\u0A32\u0A33\u0A35\u0A36\u0A38\u0A39]|[\u0A59-\u0A5C\u0A5E\u0A72-\u0A74\u0A85-\u0A8D\u0A8F-\u0A91\u0A93-\u0AA8]|[\u0AAA-\u0AB0\u0AB2\u0AB3\u0AB5-\u0AB9\u0ABD\u0AD0\u0AE0\u0AE1\u0B05-\u0B0C]|[\u0B0F\u0B10\u0B13-\u0B28\u0B2A-\u0B30\u0B32\u0B33\u0B35-\u0B39\u0B3D\u0B5C]|[\u0B5D\u0B5F-\u0B61\u0B71\u0B83\u0B85-\u0B8A\u0B8E-\u0B90\u0B92-\u0B95\u0B99]|[\u0B9A\u0B9C\u0B9E\u0B9F\u0BA3\u0BA4\u0BA8-\u0BAA\u0BAE-\u0BB9\u0BD0]|[\u0C05-\u0C0C\u0C0E-\u0C10\u0C12-\u0C28\u0C2A-\u0C33\u0C35-\u0C39\u0C3D]|[\u0C58\u0C59\u0C60\u0C61\u0C85-\u0C8C\u0C8E-\u0C90\u0C92-\u0CA8\u0CAA-\u0CB3]|[\u0CB5-\u0CB9\u0CBD\u0CDE\u0CE0\u0CE1\u0CF1\u0CF2\u0D05-\u0D0C\u0D0E-\u0D10]|[\u0D12-\u0D3A\u0D3D\u0D4E\u0D60\u0D61\u0D7A-\u0D7F\u0D85-\u0D96\u0D9A-\u0DB1]|[\u0DB3-\u0DBB\u0DBD\u0DC0-\u0DC6\u0E01-\u0E30\u0E32\u0E33\u0E40-\u0E46\u0E81]|[\u0E82\u0E84\u0E87\u0E88\u0E8A\u0E8D\u0E94-\u0E97\u0E99-\u0E9F\u0EA1-\u0EA3]|[\u0EA5\u0EA7\u0EAA\u0EAB\u0EAD-\u0EB0\u0EB2\u0EB3\u0EBD\u0EC0-\u0EC4\u0EC6]|[\u0EDC-\u0EDF\u0F00\u0F40-\u0F47\u0F49-\u0F6C\u0F88-\u0F8C\u1000-\u102A]|[\u103F\u1050-\u1055\u105A-\u105D\u1061\u1065\u1066\u106E-\u1070\u1075-\u1081]|[\u108E\u10A0-\u10C5\u10C7\u10CD\u10D0-\u10FA\u10FC-\u1248\u124A-\u124D]|[\u1250-\u1256\u1258\u125A-\u125D\u1260-\u1288\u128A-\u128D\u1290-\u12B0]|[\u12B2-\u12B5\u12B8-\u12BE\u12C0\u12C2-\u12C5\u12C8-\u12D6\u12D8-\u1310]|[\u1312-\u1315\u1318-\u135A\u1380-\u138F\u13A0-\u13F4\u1401-\u166C]|[\u166F-\u167F\u1681-\u169A\u16A0-\u16EA\u1700-\u170C\u170E-\u1711]|[\u1720-\u1731\u1740-\u1751\u1760-\u176C\u176E-\u1770\u1780-\u17B3\u17D7]|[\u17DC\u1820-\u1877\u1880-\u18A8\u18AA\u18B0-\u18F5\u1900-\u191C]|[\u1950-\u196D\u1970-\u1974\u1980-\u19AB\u19C1-\u19C7\u1A00-\u1A16]|[\u1A20-\u1A54\u1AA7\u1B05-\u1B33\u1B45-\u1B4B\u1B83-\u1BA0\u1BAE\u1BAF]|[\u1BBA-\u1BE5\u1C00-\u1C23\u1C4D-\u1C4F\u1C5A-\u1C7D\u1CE9-\u1CEC]|[\u1CEE-\u1CF1\u1CF5\u1CF6\u1D00-\u1DBF\u1E00-\u1F15\u1F18-\u1F1D]|[\u1F20-\u1F45\u1F48-\u1F4D\u1F50-\u1F57\u1F59\u1F5B\u1F5D\u1F5F-\u1F7D]|[\u1F80-\u1FB4\u1FB6-\u1FBC\u1FBE\u1FC2-\u1FC4\u1FC6-\u1FCC\u1FD0-\u1FD3]|[\u1FD6-\u1FDB\u1FE0-\u1FEC\u1FF2-\u1FF4\u1FF6-\u1FFC\u2071\u207F]|[\u2090-\u209C\u2102\u2107\u210A-\u2113\u2115\u2119-\u211D\u2124\u2126\u2128]|[\u212A-\u212D\u212F-\u2139\u213C-\u213F\u2145-\u2149\u214E\u2183\u2184]|[\u2C00-\u2C2E\u2C30-\u2C5E\u2C60-\u2CE4\u2CEB-\u2CEE\u2CF2\u2CF3]|[\u2D00-\u2D25\u2D27\u2D2D\u2D30-\u2D67\u2D6F\u2D80-\u2D96\u2DA0-\u2DA6]|[\u2DA8-\u2DAE\u2DB0-\u2DB6\u2DB8-\u2DBE\u2DC0-\u2DC6\u2DC8-\u2DCE]|[\u2DD0-\u2DD6\u2DD8-\u2DDE\u2E2F\u3005\u3006\u3031-\u3035\u303B\u303C]|[\u3041-\u3096\u309D-\u309F\u30A1-\u30FA\u30FC-\u30FF\u3105-\u312D]|[\u3131-\u318E\u31A0-\u31BA\u31F0-\u31FF\u3400-\u4DB5\u4E00-\u9FCC]|[\uA000-\uA48C\uA4D0-\uA4FD\uA500-\uA60C\uA610-\uA61F\uA62A\uA62B]|[\uA640-\uA66E\uA67F-\uA697\uA6A0-\uA6E5\uA717-\uA71F\uA722-\uA788]|[\uA78B-\uA78E\uA790-\uA793\uA7A0-\uA7AA\uA7F8-\uA801\uA803-\uA805]|[\uA807-\uA80A\uA80C-\uA822\uA840-\uA873\uA882-\uA8B3\uA8F2-\uA8F7\uA8FB]|[\uA90A-\uA925\uA930-\uA946\uA960-\uA97C\uA984-\uA9B2\uA9CF\uAA00-\uAA28]|[\uAA40-\uAA42\uAA44-\uAA4B\uAA60-\uAA76\uAA7A\uAA80-\uAAAF\uAAB1\uAAB5]|[\uAAB6\uAAB9-\uAABD\uAAC0\uAAC2\uAADB-\uAADD\uAAE0-\uAAEA\uAAF2-\uAAF4]|[\uAB01-\uAB06\uAB09-\uAB0E\uAB11-\uAB16\uAB20-\uAB26\uAB28-\uAB2E]|[\uABC0-\uABE2\uAC00-\uD7A3\uD7B0-\uD7C6\uD7CB-\uD7FB\uF900-\uFA6D]|[\uFA70-\uFAD9\uFB00-\uFB06\uFB13-\uFB17\uFB1D\uFB1F-\uFB28\uFB2A-\uFB36]|[\uFB38-\uFB3C\uFB3E\uFB40\uFB41\uFB43\uFB44\uFB46-\uFBB1\uFBD3-\uFD3D]|[\uFD50-\uFD8F\uFD92-\uFDC7\uFDF0-\uFDFB\uFE70-\uFE74\uFE76-\uFEFC]|[\uFF21-\uFF3A\uFF41-\uFF5A\uFF66-\uFFBE\uFFC2-\uFFC7\uFFCA-\uFFCF]|[\uFFD2-\uFFD7\uFFDA-\uFFDC])/,/^(?:\s)/,/^(?:$)/],conditions:{string:{rules:[27,28],inclusive:!1},generic:{rules:[24,25],inclusive:!1},struct:{rules:[12,13,14,15,16],inclusive:!1},open_directive:{rules:[1],inclusive:!1},type_directive:{rules:[2,3],inclusive:!1},arg_directive:{rules:[3,4],inclusive:!1},INITIAL:{rules:[0,5,6,7,8,9,10,11,17,18,19,20,21,22,23,26,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],inclusive:!0}}};function D(){this.yy={}}return M.lexer=O,D.prototype=M,M.Parser=D,new D}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e){var n,r,i=t.exports={};function a(){throw new Error("setTimeout has not been defined")}function o(){throw new Error("clearTimeout has not been defined")}function s(t){if(n===setTimeout)return setTimeout(t,0);if((n===a||!n)&&setTimeout)return n=setTimeout,setTimeout(t,0);try{return n(t,0)}catch(e){try{return n.call(null,t,0)}catch(e){return n.call(this,t,0)}}}!function(){try{n="function"==typeof setTimeout?setTimeout:a}catch(t){n=a}try{r="function"==typeof clearTimeout?clearTimeout:o}catch(t){r=o}}();var c,u=[],l=!1,h=-1;function f(){l&&c&&(l=!1,c.length?u=c.concat(u):h=-1,u.length&&d())}function d(){if(!l){var t=s(f);l=!0;for(var e=u.length;e;){for(c=u,u=[];++h1)for(var n=1;n=0;r--){var i=t[r];"."===i?t.splice(r,1):".."===i?(t.splice(r,1),n++):n&&(t.splice(r,1),n--)}if(e)for(;n--;n)t.unshift("..");return t}function r(t,e){if(t.filter)return t.filter(e);for(var n=[],r=0;r=-1&&!i;a--){var o=a>=0?arguments[a]:t.cwd();if("string"!=typeof o)throw new TypeError("Arguments to path.resolve must be strings");o&&(e=o+"/"+e,i="/"===o.charAt(0))}return(i?"/":"")+(e=n(r(e.split("/"),(function(t){return!!t})),!i).join("/"))||"."},e.normalize=function(t){var a=e.isAbsolute(t),o="/"===i(t,-1);return(t=n(r(t.split("/"),(function(t){return!!t})),!a).join("/"))||a||(t="."),t&&o&&(t+="/"),(a?"/":"")+t},e.isAbsolute=function(t){return"/"===t.charAt(0)},e.join=function(){var t=Array.prototype.slice.call(arguments,0);return e.normalize(r(t,(function(t,e){if("string"!=typeof t)throw new TypeError("Arguments to path.join must be strings");return t})).join("/"))},e.relative=function(t,n){function r(t){for(var e=0;e=0&&""===t[n];n--);return e>n?[]:t.slice(e,n-e+1)}t=e.resolve(t).substr(1),n=e.resolve(n).substr(1);for(var i=r(t.split("/")),a=r(n.split("/")),o=Math.min(i.length,a.length),s=o,c=0;c=1;--a)if(47===(e=t.charCodeAt(a))){if(!i){r=a;break}}else i=!1;return-1===r?n?"/":".":n&&1===r?"/":t.slice(0,r)},e.basename=function(t,e){var n=function(t){"string"!=typeof t&&(t+="");var e,n=0,r=-1,i=!0;for(e=t.length-1;e>=0;--e)if(47===t.charCodeAt(e)){if(!i){n=e+1;break}}else-1===r&&(i=!1,r=e+1);return-1===r?"":t.slice(n,r)}(t);return e&&n.substr(-1*e.length)===e&&(n=n.substr(0,n.length-e.length)),n},e.extname=function(t){"string"!=typeof t&&(t+="");for(var e=-1,n=0,r=-1,i=!0,a=0,o=t.length-1;o>=0;--o){var s=t.charCodeAt(o);if(47!==s)-1===r&&(i=!1,r=o+1),46===s?-1===e?e=o:1!==a&&(a=1):-1!==e&&(a=-1);else if(!i){n=o+1;break}}return-1===e||-1===r||0===a||1===a&&e===r-1&&e===n+1?"":t.slice(e,r)};var i="b"==="ab".substr(-1)?function(t,e,n){return t.substr(e,n)}:function(t,e,n){return e<0&&(e=t.length+e),t.substr(e,n)}}).call(this,n(14))},function(t,e){t.exports=function(t){return null!=t&&"object"==typeof t}},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[1,2],n=[1,3],r=[1,5],i=[1,7],a=[2,5],o=[1,15],s=[1,17],c=[1,19],u=[1,20],l=[1,21],h=[1,22],f=[1,28],d=[1,23],p=[1,24],g=[1,25],y=[1,26],v=[1,29],m=[1,32],b=[1,4,5,14,15,17,19,20,22,23,24,25,26,36,39],x=[1,4,5,12,13,14,15,17,19,20,22,23,24,25,26,36,39],_=[1,4,5,7,14,15,17,19,20,22,23,24,25,26,36,39],k=[4,5,14,15,17,19,20,22,23,24,25,26,36,39],w={trace:function(){},yy:{},symbols_:{error:2,start:3,SPACE:4,NL:5,directive:6,SD:7,document:8,line:9,statement:10,idStatement:11,DESCR:12,"--\x3e":13,HIDE_EMPTY:14,scale:15,WIDTH:16,COMPOSIT_STATE:17,STRUCT_START:18,STRUCT_STOP:19,STATE_DESCR:20,AS:21,ID:22,FORK:23,JOIN:24,CONCURRENT:25,note:26,notePosition:27,NOTE_TEXT:28,openDirective:29,typeDirective:30,closeDirective:31,":":32,argDirective:33,eol:34,";":35,EDGE_STATE:36,left_of:37,right_of:38,open_directive:39,type_directive:40,arg_directive:41,close_directive:42,$accept:0,$end:1},terminals_:{2:"error",4:"SPACE",5:"NL",7:"SD",12:"DESCR",13:"--\x3e",14:"HIDE_EMPTY",15:"scale",16:"WIDTH",17:"COMPOSIT_STATE",18:"STRUCT_START",19:"STRUCT_STOP",20:"STATE_DESCR",21:"AS",22:"ID",23:"FORK",24:"JOIN",25:"CONCURRENT",26:"note",28:"NOTE_TEXT",32:":",35:";",36:"EDGE_STATE",37:"left_of",38:"right_of",39:"open_directive",40:"type_directive",41:"arg_directive",42:"close_directive"},productions_:[0,[3,2],[3,2],[3,2],[3,2],[8,0],[8,2],[9,2],[9,1],[9,1],[10,1],[10,2],[10,3],[10,4],[10,1],[10,2],[10,1],[10,4],[10,3],[10,6],[10,1],[10,1],[10,1],[10,4],[10,4],[10,1],[6,3],[6,5],[34,1],[34,1],[11,1],[11,1],[27,1],[27,1],[29,1],[30,1],[33,1],[31,1]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 4:return r.setRootDoc(a[s]),a[s];case 5:this.$=[];break;case 6:"nl"!=a[s]&&(a[s-1].push(a[s]),this.$=a[s-1]);break;case 7:case 8:this.$=a[s];break;case 9:this.$="nl";break;case 10:this.$={stmt:"state",id:a[s],type:"default",description:""};break;case 11:this.$={stmt:"state",id:a[s-1],type:"default",description:r.trimColon(a[s])};break;case 12:this.$={stmt:"relation",state1:{stmt:"state",id:a[s-2],type:"default",description:""},state2:{stmt:"state",id:a[s],type:"default",description:""}};break;case 13:this.$={stmt:"relation",state1:{stmt:"state",id:a[s-3],type:"default",description:""},state2:{stmt:"state",id:a[s-1],type:"default",description:""},description:a[s].substr(1).trim()};break;case 17:this.$={stmt:"state",id:a[s-3],type:"default",description:"",doc:a[s-1]};break;case 18:var c=a[s],u=a[s-2].trim();if(a[s].match(":")){var l=a[s].split(":");c=l[0],u=[u,l[1]]}this.$={stmt:"state",id:c,type:"default",description:u};break;case 19:this.$={stmt:"state",id:a[s-3],type:"default",description:a[s-5],doc:a[s-1]};break;case 20:this.$={stmt:"state",id:a[s],type:"fork"};break;case 21:this.$={stmt:"state",id:a[s],type:"join"};break;case 22:this.$={stmt:"state",id:r.getDividerId(),type:"divider"};break;case 23:this.$={stmt:"state",id:a[s-1].trim(),note:{position:a[s-2].trim(),text:a[s].trim()}};break;case 30:case 31:this.$=a[s];break;case 34:r.parseDirective("%%{","open_directive");break;case 35:r.parseDirective(a[s],"type_directive");break;case 36:a[s]=a[s].trim().replace(/'/g,'"'),r.parseDirective(a[s],"arg_directive");break;case 37:r.parseDirective("}%%","close_directive","state")}},table:[{3:1,4:e,5:n,6:4,7:r,29:6,39:i},{1:[3]},{3:8,4:e,5:n,6:4,7:r,29:6,39:i},{3:9,4:e,5:n,6:4,7:r,29:6,39:i},{3:10,4:e,5:n,6:4,7:r,29:6,39:i},t([1,4,5,14,15,17,20,22,23,24,25,26,36,39],a,{8:11}),{30:12,40:[1,13]},{40:[2,34]},{1:[2,1]},{1:[2,2]},{1:[2,3]},{1:[2,4],4:o,5:s,6:27,9:14,10:16,11:18,14:c,15:u,17:l,20:h,22:f,23:d,24:p,25:g,26:y,29:6,36:v,39:i},{31:30,32:[1,31],42:m},t([32,42],[2,35]),t(b,[2,6]),{6:27,10:33,11:18,14:c,15:u,17:l,20:h,22:f,23:d,24:p,25:g,26:y,29:6,36:v,39:i},t(b,[2,8]),t(b,[2,9]),t(b,[2,10],{12:[1,34],13:[1,35]}),t(b,[2,14]),{16:[1,36]},t(b,[2,16],{18:[1,37]}),{21:[1,38]},t(b,[2,20]),t(b,[2,21]),t(b,[2,22]),{27:39,28:[1,40],37:[1,41],38:[1,42]},t(b,[2,25]),t(x,[2,30]),t(x,[2,31]),t(_,[2,26]),{33:43,41:[1,44]},t(_,[2,37]),t(b,[2,7]),t(b,[2,11]),{11:45,22:f,36:v},t(b,[2,15]),t(k,a,{8:46}),{22:[1,47]},{22:[1,48]},{21:[1,49]},{22:[2,32]},{22:[2,33]},{31:50,42:m},{42:[2,36]},t(b,[2,12],{12:[1,51]}),{4:o,5:s,6:27,9:14,10:16,11:18,14:c,15:u,17:l,19:[1,52],20:h,22:f,23:d,24:p,25:g,26:y,29:6,36:v,39:i},t(b,[2,18],{18:[1,53]}),{28:[1,54]},{22:[1,55]},t(_,[2,27]),t(b,[2,13]),t(b,[2,17]),t(k,a,{8:56}),t(b,[2,23]),t(b,[2,24]),{4:o,5:s,6:27,9:14,10:16,11:18,14:c,15:u,17:l,19:[1,57],20:h,22:f,23:d,24:p,25:g,26:y,29:6,36:v,39:i},t(b,[2,19])],defaultActions:{7:[2,34],8:[2,1],9:[2,2],10:[2,3],41:[2,32],42:[2,33],44:[2,36]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},E={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),39;case 1:return this.begin("type_directive"),40;case 2:return this.popState(),this.begin("arg_directive"),32;case 3:return this.popState(),this.popState(),42;case 4:return 41;case 5:break;case 6:console.log("Crap after close");break;case 7:return 5;case 8:case 9:case 10:case 11:break;case 12:return this.pushState("SCALE"),15;case 13:return 16;case 14:this.popState();break;case 15:this.pushState("STATE");break;case 16:return this.popState(),e.yytext=e.yytext.slice(0,-8).trim(),23;case 17:return this.popState(),e.yytext=e.yytext.slice(0,-8).trim(),24;case 18:return this.popState(),e.yytext=e.yytext.slice(0,-8).trim(),23;case 19:return this.popState(),e.yytext=e.yytext.slice(0,-8).trim(),24;case 20:this.begin("STATE_STRING");break;case 21:return this.popState(),this.pushState("STATE_ID"),"AS";case 22:return this.popState(),"ID";case 23:this.popState();break;case 24:return"STATE_DESCR";case 25:return 17;case 26:this.popState();break;case 27:return this.popState(),this.pushState("struct"),18;case 28:return this.popState(),19;case 29:break;case 30:return this.begin("NOTE"),26;case 31:return this.popState(),this.pushState("NOTE_ID"),37;case 32:return this.popState(),this.pushState("NOTE_ID"),38;case 33:this.popState(),this.pushState("FLOATING_NOTE");break;case 34:return this.popState(),this.pushState("FLOATING_NOTE_ID"),"AS";case 35:break;case 36:return"NOTE_TEXT";case 37:return this.popState(),"ID";case 38:return this.popState(),this.pushState("NOTE_TEXT"),22;case 39:return this.popState(),e.yytext=e.yytext.substr(2).trim(),28;case 40:return this.popState(),e.yytext=e.yytext.slice(0,-8).trim(),28;case 41:case 42:return 7;case 43:return 14;case 44:return 36;case 45:return 22;case 46:return e.yytext=e.yytext.trim(),12;case 47:return 13;case 48:return 25;case 49:return 5;case 50:return"INVALID"}},rules:[/^(?:%%\{)/i,/^(?:((?:(?!\}%%)[^:.])*))/i,/^(?::)/i,/^(?:\}%%)/i,/^(?:((?:(?!\}%%).|\n)*))/i,/^(?:%%(?!\{)[^\n]*)/i,/^(?:[^\}]%%[^\n]*)/i,/^(?:[\n]+)/i,/^(?:[\s]+)/i,/^(?:((?!\n)\s)+)/i,/^(?:#[^\n]*)/i,/^(?:%[^\n]*)/i,/^(?:scale\s+)/i,/^(?:\d+)/i,/^(?:\s+width\b)/i,/^(?:state\s+)/i,/^(?:.*<>)/i,/^(?:.*<>)/i,/^(?:.*\[\[fork\]\])/i,/^(?:.*\[\[join\]\])/i,/^(?:["])/i,/^(?:\s*as\s+)/i,/^(?:[^\n\{]*)/i,/^(?:["])/i,/^(?:[^"]*)/i,/^(?:[^\n\s\{]+)/i,/^(?:\n)/i,/^(?:\{)/i,/^(?:\})/i,/^(?:[\n])/i,/^(?:note\s+)/i,/^(?:left of\b)/i,/^(?:right of\b)/i,/^(?:")/i,/^(?:\s*as\s*)/i,/^(?:["])/i,/^(?:[^"]*)/i,/^(?:[^\n]*)/i,/^(?:\s*[^:\n\s\-]+)/i,/^(?:\s*:[^:\n;]+)/i,/^(?:\s*[^:;]+end note\b)/i,/^(?:stateDiagram\s+)/i,/^(?:stateDiagram-v2\s+)/i,/^(?:hide empty description\b)/i,/^(?:\[\*\])/i,/^(?:[^:\n\s\-\{]+)/i,/^(?:\s*:[^:\n;]+)/i,/^(?:-->)/i,/^(?:--)/i,/^(?:$)/i,/^(?:.)/i],conditions:{LINE:{rules:[9,10],inclusive:!1},close_directive:{rules:[9,10],inclusive:!1},arg_directive:{rules:[3,4,9,10],inclusive:!1},type_directive:{rules:[2,3,9,10],inclusive:!1},open_directive:{rules:[1,9,10],inclusive:!1},struct:{rules:[9,10,15,28,29,30,44,45,46,47,48],inclusive:!1},FLOATING_NOTE_ID:{rules:[37],inclusive:!1},FLOATING_NOTE:{rules:[34,35,36],inclusive:!1},NOTE_TEXT:{rules:[39,40],inclusive:!1},NOTE_ID:{rules:[38],inclusive:!1},NOTE:{rules:[31,32,33],inclusive:!1},SCALE:{rules:[13,14],inclusive:!1},ALIAS:{rules:[],inclusive:!1},STATE_ID:{rules:[22],inclusive:!1},STATE_STRING:{rules:[23,24],inclusive:!1},FORK_STATE:{rules:[],inclusive:!1},STATE:{rules:[9,10,16,17,18,19,20,21,25,26,27],inclusive:!1},ID:{rules:[9,10],inclusive:!1},INITIAL:{rules:[0,5,6,7,8,10,11,12,15,27,30,41,42,43,44,45,46,47,49,50],inclusive:!0}}};function T(){this.yy={}}return w.lexer=E,T.prototype=w,w.Parser=T,new T}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){(function(t){t.exports=function(){"use strict";var e,r;function i(){return e.apply(null,arguments)}function a(t){return t instanceof Array||"[object Array]"===Object.prototype.toString.call(t)}function o(t){return null!=t&&"[object Object]"===Object.prototype.toString.call(t)}function s(t){return void 0===t}function c(t){return"number"==typeof t||"[object Number]"===Object.prototype.toString.call(t)}function u(t){return t instanceof Date||"[object Date]"===Object.prototype.toString.call(t)}function l(t,e){var n,r=[];for(n=0;n>>0,r=0;ryt(t)?(a=t+1,s-yt(t)):(a=t,s),{year:a,dayOfYear:o}}function Ft(t,e,n){var r,i,a=Bt(t.year(),e,n),o=Math.floor((t.dayOfYear()-a-1)/7)+1;return o<1?r=o+Pt(i=t.year()-1,e,n):o>Pt(t.year(),e,n)?(r=o-Pt(t.year(),e,n),i=t.year()+1):(i=t.year(),r=o),{week:r,year:i}}function Pt(t,e,n){var r=Bt(t,e,n),i=Bt(t+1,e,n);return(yt(t)-r+i)/7}function It(t,e){return t.slice(e,7).concat(t.slice(0,e))}W("w",["ww",2],"wo","week"),W("W",["WW",2],"Wo","isoWeek"),L("week","w"),L("isoWeek","W"),j("week",5),j("isoWeek",5),lt("w",Q),lt("ww",Q,q),lt("W",Q),lt("WW",Q,q),gt(["w","ww","W","WW"],(function(t,e,n,r){e[r.substr(0,1)]=w(t)})),W("d",0,"do","day"),W("dd",0,0,(function(t){return this.localeData().weekdaysMin(this,t)})),W("ddd",0,0,(function(t){return this.localeData().weekdaysShort(this,t)})),W("dddd",0,0,(function(t){return this.localeData().weekdays(this,t)})),W("e",0,0,"weekday"),W("E",0,0,"isoWeekday"),L("day","d"),L("weekday","e"),L("isoWeekday","E"),j("day",11),j("weekday",11),j("isoWeekday",11),lt("d",Q),lt("e",Q),lt("E",Q),lt("dd",(function(t,e){return e.weekdaysMinRegex(t)})),lt("ddd",(function(t,e){return e.weekdaysShortRegex(t)})),lt("dddd",(function(t,e){return e.weekdaysRegex(t)})),gt(["dd","ddd","dddd"],(function(t,e,n,r){var i=n._locale.weekdaysParse(t,r,n._strict);null!=i?e.d=i:p(n).invalidWeekday=t})),gt(["d","e","E"],(function(t,e,n,r){e[r]=w(t)}));var jt="Sunday_Monday_Tuesday_Wednesday_Thursday_Friday_Saturday".split("_"),Rt="Sun_Mon_Tue_Wed_Thu_Fri_Sat".split("_"),Yt="Su_Mo_Tu_We_Th_Fr_Sa".split("_"),zt=ct,Ut=ct,$t=ct;function Wt(){function t(t,e){return e.length-t.length}var e,n,r,i,a,o=[],s=[],c=[],u=[];for(e=0;e<7;e++)n=d([2e3,1]).day(e),r=this.weekdaysMin(n,""),i=this.weekdaysShort(n,""),a=this.weekdays(n,""),o.push(r),s.push(i),c.push(a),u.push(r),u.push(i),u.push(a);for(o.sort(t),s.sort(t),c.sort(t),u.sort(t),e=0;e<7;e++)s[e]=ft(s[e]),c[e]=ft(c[e]),u[e]=ft(u[e]);this._weekdaysRegex=new RegExp("^("+u.join("|")+")","i"),this._weekdaysShortRegex=this._weekdaysRegex,this._weekdaysMinRegex=this._weekdaysRegex,this._weekdaysStrictRegex=new RegExp("^("+c.join("|")+")","i"),this._weekdaysShortStrictRegex=new RegExp("^("+s.join("|")+")","i"),this._weekdaysMinStrictRegex=new RegExp("^("+o.join("|")+")","i")}function Vt(){return this.hours()%12||12}function Ht(t,e){W(t,0,0,(function(){return this.localeData().meridiem(this.hours(),this.minutes(),e)}))}function Gt(t,e){return e._meridiemParse}W("H",["HH",2],0,"hour"),W("h",["hh",2],0,Vt),W("k",["kk",2],0,(function(){return this.hours()||24})),W("hmm",0,0,(function(){return""+Vt.apply(this)+R(this.minutes(),2)})),W("hmmss",0,0,(function(){return""+Vt.apply(this)+R(this.minutes(),2)+R(this.seconds(),2)})),W("Hmm",0,0,(function(){return""+this.hours()+R(this.minutes(),2)})),W("Hmmss",0,0,(function(){return""+this.hours()+R(this.minutes(),2)+R(this.seconds(),2)})),Ht("a",!0),Ht("A",!1),L("hour","h"),j("hour",13),lt("a",Gt),lt("A",Gt),lt("H",Q),lt("h",Q),lt("k",Q),lt("HH",Q,q),lt("hh",Q,q),lt("kk",Q,q),lt("hmm",K),lt("hmmss",tt),lt("Hmm",K),lt("Hmmss",tt),pt(["H","HH"],3),pt(["k","kk"],(function(t,e,n){var r=w(t);e[3]=24===r?0:r})),pt(["a","A"],(function(t,e,n){n._isPm=n._locale.isPM(t),n._meridiem=t})),pt(["h","hh"],(function(t,e,n){e[3]=w(t),p(n).bigHour=!0})),pt("hmm",(function(t,e,n){var r=t.length-2;e[3]=w(t.substr(0,r)),e[4]=w(t.substr(r)),p(n).bigHour=!0})),pt("hmmss",(function(t,e,n){var r=t.length-4,i=t.length-2;e[3]=w(t.substr(0,r)),e[4]=w(t.substr(r,2)),e[5]=w(t.substr(i)),p(n).bigHour=!0})),pt("Hmm",(function(t,e,n){var r=t.length-2;e[3]=w(t.substr(0,r)),e[4]=w(t.substr(r))})),pt("Hmmss",(function(t,e,n){var r=t.length-4,i=t.length-2;e[3]=w(t.substr(0,r)),e[4]=w(t.substr(r,2)),e[5]=w(t.substr(i))}));var qt,Xt=xt("Hours",!0),Zt={calendar:{sameDay:"[Today at] LT",nextDay:"[Tomorrow at] LT",nextWeek:"dddd [at] LT",lastDay:"[Yesterday at] LT",lastWeek:"[Last] dddd [at] LT",sameElse:"L"},longDateFormat:{LTS:"h:mm:ss A",LT:"h:mm A",L:"MM/DD/YYYY",LL:"MMMM D, YYYY",LLL:"MMMM D, YYYY h:mm A",LLLL:"dddd, MMMM D, YYYY h:mm A"},invalidDate:"Invalid date",ordinal:"%d",dayOfMonthOrdinalParse:/\d{1,2}/,relativeTime:{future:"in %s",past:"%s ago",s:"a few seconds",ss:"%d seconds",m:"a minute",mm:"%d minutes",h:"an hour",hh:"%d hours",d:"a day",dd:"%d days",M:"a month",MM:"%d months",y:"a year",yy:"%d years"},months:Tt,monthsShort:Ct,week:{dow:0,doy:6},weekdays:jt,weekdaysMin:Yt,weekdaysShort:Rt,meridiemParse:/[ap]\.?m?\.?/i},Jt={},Qt={};function Kt(t){return t?t.toLowerCase().replace("_","-"):t}function te(e){var r=null;if(!Jt[e]&&void 0!==t&&t&&t.exports)try{r=qt._abbr,n(171)("./"+e),ee(r)}catch(e){}return Jt[e]}function ee(t,e){var n;return t&&((n=s(e)?re(t):ne(t,e))?qt=n:"undefined"!=typeof console&&console.warn&&console.warn("Locale "+t+" not found. Did you forget to load it?")),qt._abbr}function ne(t,e){if(null===e)return delete Jt[t],null;var n,r=Zt;if(e.abbr=t,null!=Jt[t])M("defineLocaleOverride","use moment.updateLocale(localeName, config) to change an existing locale. moment.defineLocale(localeName, config) should only be used for creating a new locale See http://momentjs.com/guides/#/warnings/define-locale/ for more info."),r=Jt[t]._config;else if(null!=e.parentLocale)if(null!=Jt[e.parentLocale])r=Jt[e.parentLocale]._config;else{if(null==(n=te(e.parentLocale)))return Qt[e.parentLocale]||(Qt[e.parentLocale]=[]),Qt[e.parentLocale].push({name:t,config:e}),null;r=n._config}return Jt[t]=new N(D(r,e)),Qt[t]&&Qt[t].forEach((function(t){ne(t.name,t.config)})),ee(t),Jt[t]}function re(t){var e;if(t&&t._locale&&t._locale._abbr&&(t=t._locale._abbr),!t)return qt;if(!a(t)){if(e=te(t))return e;t=[t]}return function(t){for(var e,n,r,i,a=0;a=e&&E(i,n,!0)>=e-1)break;e--}a++}return qt}(t)}function ie(t){var e,n=t._a;return n&&-2===p(t).overflow&&(e=n[1]<0||11wt(n[0],n[1])?2:n[3]<0||24Pt(n,a,o)?p(t)._overflowWeeks=!0:null!=c?p(t)._overflowWeekday=!0:(s=Lt(n,r,i,a,o),t._a[0]=s.year,t._dayOfYear=s.dayOfYear)}(t),null!=t._dayOfYear&&(o=ae(t._a[0],r[0]),(t._dayOfYear>yt(o)||0===t._dayOfYear)&&(p(t)._overflowDayOfYear=!0),n=Nt(o,0,t._dayOfYear),t._a[1]=n.getUTCMonth(),t._a[2]=n.getUTCDate()),e=0;e<3&&null==t._a[e];++e)t._a[e]=s[e]=r[e];for(;e<7;e++)t._a[e]=s[e]=null==t._a[e]?2===e?1:0:t._a[e];24===t._a[3]&&0===t._a[4]&&0===t._a[5]&&0===t._a[6]&&(t._nextDay=!0,t._a[3]=0),t._d=(t._useUTC?Nt:function(t,e,n,r,i,a,o){var s;return t<100&&0<=t?(s=new Date(t+400,e,n,r,i,a,o),isFinite(s.getFullYear())&&s.setFullYear(t)):s=new Date(t,e,n,r,i,a,o),s}).apply(null,s),a=t._useUTC?t._d.getUTCDay():t._d.getDay(),null!=t._tzm&&t._d.setUTCMinutes(t._d.getUTCMinutes()-t._tzm),t._nextDay&&(t._a[3]=24),t._w&&void 0!==t._w.d&&t._w.d!==a&&(p(t).weekdayMismatch=!0)}}var se=/^\s*((?:[+-]\d{6}|\d{4})-(?:\d\d-\d\d|W\d\d-\d|W\d\d|\d\d\d|\d\d))(?:(T| )(\d\d(?::\d\d(?::\d\d(?:[.,]\d+)?)?)?)([\+\-]\d\d(?::?\d\d)?|\s*Z)?)?$/,ce=/^\s*((?:[+-]\d{6}|\d{4})(?:\d\d\d\d|W\d\d\d|W\d\d|\d\d\d|\d\d))(?:(T| )(\d\d(?:\d\d(?:\d\d(?:[.,]\d+)?)?)?)([\+\-]\d\d(?::?\d\d)?|\s*Z)?)?$/,ue=/Z|[+-]\d\d(?::?\d\d)?/,le=[["YYYYYY-MM-DD",/[+-]\d{6}-\d\d-\d\d/],["YYYY-MM-DD",/\d{4}-\d\d-\d\d/],["GGGG-[W]WW-E",/\d{4}-W\d\d-\d/],["GGGG-[W]WW",/\d{4}-W\d\d/,!1],["YYYY-DDD",/\d{4}-\d{3}/],["YYYY-MM",/\d{4}-\d\d/,!1],["YYYYYYMMDD",/[+-]\d{10}/],["YYYYMMDD",/\d{8}/],["GGGG[W]WWE",/\d{4}W\d{3}/],["GGGG[W]WW",/\d{4}W\d{2}/,!1],["YYYYDDD",/\d{7}/]],he=[["HH:mm:ss.SSSS",/\d\d:\d\d:\d\d\.\d+/],["HH:mm:ss,SSSS",/\d\d:\d\d:\d\d,\d+/],["HH:mm:ss",/\d\d:\d\d:\d\d/],["HH:mm",/\d\d:\d\d/],["HHmmss.SSSS",/\d\d\d\d\d\d\.\d+/],["HHmmss,SSSS",/\d\d\d\d\d\d,\d+/],["HHmmss",/\d\d\d\d\d\d/],["HHmm",/\d\d\d\d/],["HH",/\d\d/]],fe=/^\/?Date\((\-?\d+)/i;function de(t){var e,n,r,i,a,o,s=t._i,c=se.exec(s)||ce.exec(s);if(c){for(p(t).iso=!0,e=0,n=le.length;en.valueOf():n.valueOf()this.clone().month(0).utcOffset()||this.utcOffset()>this.clone().month(5).utcOffset()},on.isLocal=function(){return!!this.isValid()&&!this._isUTC},on.isUtcOffset=function(){return!!this.isValid()&&this._isUTC},on.isUtc=Be,on.isUTC=Be,on.zoneAbbr=function(){return this._isUTC?"UTC":""},on.zoneName=function(){return this._isUTC?"Coordinated Universal Time":""},on.dates=C("dates accessor is deprecated. Use date instead.",Ke),on.months=C("months accessor is deprecated. Use month instead",At),on.years=C("years accessor is deprecated. Use year instead",bt),on.zone=C("moment().zone is deprecated, use moment().utcOffset instead. http://momentjs.com/guides/#/warnings/zone/",(function(t,e){return null!=t?("string"!=typeof t&&(t=-t),this.utcOffset(t,e),this):-this.utcOffset()})),on.isDSTShifted=C("isDSTShifted is deprecated. See http://momentjs.com/guides/#/warnings/dst-shifted/ for more information",(function(){if(!s(this._isDSTShifted))return this._isDSTShifted;var t={};if(m(t,this),(t=me(t))._a){var e=t._isUTC?d(t._a):xe(t._a);this._isDSTShifted=this.isValid()&&0h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},qt={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),12;case 1:return this.begin("type_directive"),13;case 2:return this.popState(),this.begin("arg_directive"),10;case 3:return this.popState(),this.popState(),15;case 4:return 14;case 5:case 6:break;case 7:this.begin("string");break;case 8:this.popState();break;case 9:return"STR";case 10:return 75;case 11:return 84;case 12:return 76;case 13:return 90;case 14:return 77;case 15:return 78;case 16:return 79;case 17:case 18:return t.lex.firstGraph()&&this.begin("dir"),24;case 19:return 38;case 20:return 42;case 21:case 22:case 23:case 24:return 87;case 25:return this.popState(),25;case 26:case 27:case 28:case 29:case 30:case 31:case 32:case 33:case 34:case 35:return this.popState(),26;case 36:return 91;case 37:return 99;case 38:return 47;case 39:return 96;case 40:return 46;case 41:return 20;case 42:return 92;case 43:return 110;case 44:case 45:case 46:return 70;case 47:case 48:case 49:return 69;case 50:return 51;case 51:return 52;case 52:return 53;case 53:return 54;case 54:return 55;case 55:return 56;case 56:return 57;case 57:return 58;case 58:return 97;case 59:return 100;case 60:return 111;case 61:return 108;case 62:return 101;case 63:case 64:return 109;case 65:return 102;case 66:return 61;case 67:return 81;case 68:return"SEP";case 69:return 80;case 70:return 95;case 71:return 63;case 72:return 62;case 73:return 65;case 74:return 64;case 75:return 106;case 76:return 107;case 77:return 71;case 78:return 49;case 79:return 50;case 80:return 40;case 81:return 41;case 82:return 59;case 83:return 60;case 84:return 117;case 85:return 21;case 86:return 22;case 87:return 23}},rules:[/^(?:%%\{)/,/^(?:((?:(?!\}%%)[^:.])*))/,/^(?::)/,/^(?:\}%%)/,/^(?:((?:(?!\}%%).|\n)*))/,/^(?:%%(?!\{)[^\n]*)/,/^(?:[^\}]%%[^\n]*)/,/^(?:["])/,/^(?:["])/,/^(?:[^"]*)/,/^(?:style\b)/,/^(?:default\b)/,/^(?:linkStyle\b)/,/^(?:interpolate\b)/,/^(?:classDef\b)/,/^(?:class\b)/,/^(?:click\b)/,/^(?:graph\b)/,/^(?:flowchart\b)/,/^(?:subgraph\b)/,/^(?:end\b\s*)/,/^(?:_self\b)/,/^(?:_blank\b)/,/^(?:_parent\b)/,/^(?:_top\b)/,/^(?:(\r?\n)*\s*\n)/,/^(?:\s*LR\b)/,/^(?:\s*RL\b)/,/^(?:\s*TB\b)/,/^(?:\s*BT\b)/,/^(?:\s*TD\b)/,/^(?:\s*BR\b)/,/^(?:\s*<)/,/^(?:\s*>)/,/^(?:\s*\^)/,/^(?:\s*v\b)/,/^(?:[0-9]+)/,/^(?:#)/,/^(?::::)/,/^(?::)/,/^(?:&)/,/^(?:;)/,/^(?:,)/,/^(?:\*)/,/^(?:\s*[xo<]?--+[-xo>]\s*)/,/^(?:\s*[xo<]?==+[=xo>]\s*)/,/^(?:\s*[xo<]?-?\.+-[xo>]?\s*)/,/^(?:\s*[xo<]?--\s*)/,/^(?:\s*[xo<]?==\s*)/,/^(?:\s*[xo<]?-\.\s*)/,/^(?:\(-)/,/^(?:-\))/,/^(?:\(\[)/,/^(?:\]\))/,/^(?:\[\[)/,/^(?:\]\])/,/^(?:\[\()/,/^(?:\)\])/,/^(?:-)/,/^(?:\.)/,/^(?:[\_])/,/^(?:\+)/,/^(?:%)/,/^(?:=)/,/^(?:=)/,/^(?:<)/,/^(?:>)/,/^(?:\^)/,/^(?:\\\|)/,/^(?:v\b)/,/^(?:[A-Za-z]+)/,/^(?:\\\])/,/^(?:\[\/)/,/^(?:\/\])/,/^(?:\[\\)/,/^(?:[!"#$%&'*+,-.`?\\_/])/,/^(?:[\u00AA\u00B5\u00BA\u00C0-\u00D6\u00D8-\u00F6]|[\u00F8-\u02C1\u02C6-\u02D1\u02E0-\u02E4\u02EC\u02EE\u0370-\u0374\u0376\u0377]|[\u037A-\u037D\u0386\u0388-\u038A\u038C\u038E-\u03A1\u03A3-\u03F5]|[\u03F7-\u0481\u048A-\u0527\u0531-\u0556\u0559\u0561-\u0587\u05D0-\u05EA]|[\u05F0-\u05F2\u0620-\u064A\u066E\u066F\u0671-\u06D3\u06D5\u06E5\u06E6\u06EE]|[\u06EF\u06FA-\u06FC\u06FF\u0710\u0712-\u072F\u074D-\u07A5\u07B1\u07CA-\u07EA]|[\u07F4\u07F5\u07FA\u0800-\u0815\u081A\u0824\u0828\u0840-\u0858\u08A0]|[\u08A2-\u08AC\u0904-\u0939\u093D\u0950\u0958-\u0961\u0971-\u0977]|[\u0979-\u097F\u0985-\u098C\u098F\u0990\u0993-\u09A8\u09AA-\u09B0\u09B2]|[\u09B6-\u09B9\u09BD\u09CE\u09DC\u09DD\u09DF-\u09E1\u09F0\u09F1\u0A05-\u0A0A]|[\u0A0F\u0A10\u0A13-\u0A28\u0A2A-\u0A30\u0A32\u0A33\u0A35\u0A36\u0A38\u0A39]|[\u0A59-\u0A5C\u0A5E\u0A72-\u0A74\u0A85-\u0A8D\u0A8F-\u0A91\u0A93-\u0AA8]|[\u0AAA-\u0AB0\u0AB2\u0AB3\u0AB5-\u0AB9\u0ABD\u0AD0\u0AE0\u0AE1\u0B05-\u0B0C]|[\u0B0F\u0B10\u0B13-\u0B28\u0B2A-\u0B30\u0B32\u0B33\u0B35-\u0B39\u0B3D\u0B5C]|[\u0B5D\u0B5F-\u0B61\u0B71\u0B83\u0B85-\u0B8A\u0B8E-\u0B90\u0B92-\u0B95\u0B99]|[\u0B9A\u0B9C\u0B9E\u0B9F\u0BA3\u0BA4\u0BA8-\u0BAA\u0BAE-\u0BB9\u0BD0]|[\u0C05-\u0C0C\u0C0E-\u0C10\u0C12-\u0C28\u0C2A-\u0C33\u0C35-\u0C39\u0C3D]|[\u0C58\u0C59\u0C60\u0C61\u0C85-\u0C8C\u0C8E-\u0C90\u0C92-\u0CA8\u0CAA-\u0CB3]|[\u0CB5-\u0CB9\u0CBD\u0CDE\u0CE0\u0CE1\u0CF1\u0CF2\u0D05-\u0D0C\u0D0E-\u0D10]|[\u0D12-\u0D3A\u0D3D\u0D4E\u0D60\u0D61\u0D7A-\u0D7F\u0D85-\u0D96\u0D9A-\u0DB1]|[\u0DB3-\u0DBB\u0DBD\u0DC0-\u0DC6\u0E01-\u0E30\u0E32\u0E33\u0E40-\u0E46\u0E81]|[\u0E82\u0E84\u0E87\u0E88\u0E8A\u0E8D\u0E94-\u0E97\u0E99-\u0E9F\u0EA1-\u0EA3]|[\u0EA5\u0EA7\u0EAA\u0EAB\u0EAD-\u0EB0\u0EB2\u0EB3\u0EBD\u0EC0-\u0EC4\u0EC6]|[\u0EDC-\u0EDF\u0F00\u0F40-\u0F47\u0F49-\u0F6C\u0F88-\u0F8C\u1000-\u102A]|[\u103F\u1050-\u1055\u105A-\u105D\u1061\u1065\u1066\u106E-\u1070\u1075-\u1081]|[\u108E\u10A0-\u10C5\u10C7\u10CD\u10D0-\u10FA\u10FC-\u1248\u124A-\u124D]|[\u1250-\u1256\u1258\u125A-\u125D\u1260-\u1288\u128A-\u128D\u1290-\u12B0]|[\u12B2-\u12B5\u12B8-\u12BE\u12C0\u12C2-\u12C5\u12C8-\u12D6\u12D8-\u1310]|[\u1312-\u1315\u1318-\u135A\u1380-\u138F\u13A0-\u13F4\u1401-\u166C]|[\u166F-\u167F\u1681-\u169A\u16A0-\u16EA\u1700-\u170C\u170E-\u1711]|[\u1720-\u1731\u1740-\u1751\u1760-\u176C\u176E-\u1770\u1780-\u17B3\u17D7]|[\u17DC\u1820-\u1877\u1880-\u18A8\u18AA\u18B0-\u18F5\u1900-\u191C]|[\u1950-\u196D\u1970-\u1974\u1980-\u19AB\u19C1-\u19C7\u1A00-\u1A16]|[\u1A20-\u1A54\u1AA7\u1B05-\u1B33\u1B45-\u1B4B\u1B83-\u1BA0\u1BAE\u1BAF]|[\u1BBA-\u1BE5\u1C00-\u1C23\u1C4D-\u1C4F\u1C5A-\u1C7D\u1CE9-\u1CEC]|[\u1CEE-\u1CF1\u1CF5\u1CF6\u1D00-\u1DBF\u1E00-\u1F15\u1F18-\u1F1D]|[\u1F20-\u1F45\u1F48-\u1F4D\u1F50-\u1F57\u1F59\u1F5B\u1F5D\u1F5F-\u1F7D]|[\u1F80-\u1FB4\u1FB6-\u1FBC\u1FBE\u1FC2-\u1FC4\u1FC6-\u1FCC\u1FD0-\u1FD3]|[\u1FD6-\u1FDB\u1FE0-\u1FEC\u1FF2-\u1FF4\u1FF6-\u1FFC\u2071\u207F]|[\u2090-\u209C\u2102\u2107\u210A-\u2113\u2115\u2119-\u211D\u2124\u2126\u2128]|[\u212A-\u212D\u212F-\u2139\u213C-\u213F\u2145-\u2149\u214E\u2183\u2184]|[\u2C00-\u2C2E\u2C30-\u2C5E\u2C60-\u2CE4\u2CEB-\u2CEE\u2CF2\u2CF3]|[\u2D00-\u2D25\u2D27\u2D2D\u2D30-\u2D67\u2D6F\u2D80-\u2D96\u2DA0-\u2DA6]|[\u2DA8-\u2DAE\u2DB0-\u2DB6\u2DB8-\u2DBE\u2DC0-\u2DC6\u2DC8-\u2DCE]|[\u2DD0-\u2DD6\u2DD8-\u2DDE\u2E2F\u3005\u3006\u3031-\u3035\u303B\u303C]|[\u3041-\u3096\u309D-\u309F\u30A1-\u30FA\u30FC-\u30FF\u3105-\u312D]|[\u3131-\u318E\u31A0-\u31BA\u31F0-\u31FF\u3400-\u4DB5\u4E00-\u9FCC]|[\uA000-\uA48C\uA4D0-\uA4FD\uA500-\uA60C\uA610-\uA61F\uA62A\uA62B]|[\uA640-\uA66E\uA67F-\uA697\uA6A0-\uA6E5\uA717-\uA71F\uA722-\uA788]|[\uA78B-\uA78E\uA790-\uA793\uA7A0-\uA7AA\uA7F8-\uA801\uA803-\uA805]|[\uA807-\uA80A\uA80C-\uA822\uA840-\uA873\uA882-\uA8B3\uA8F2-\uA8F7\uA8FB]|[\uA90A-\uA925\uA930-\uA946\uA960-\uA97C\uA984-\uA9B2\uA9CF\uAA00-\uAA28]|[\uAA40-\uAA42\uAA44-\uAA4B\uAA60-\uAA76\uAA7A\uAA80-\uAAAF\uAAB1\uAAB5]|[\uAAB6\uAAB9-\uAABD\uAAC0\uAAC2\uAADB-\uAADD\uAAE0-\uAAEA\uAAF2-\uAAF4]|[\uAB01-\uAB06\uAB09-\uAB0E\uAB11-\uAB16\uAB20-\uAB26\uAB28-\uAB2E]|[\uABC0-\uABE2\uAC00-\uD7A3\uD7B0-\uD7C6\uD7CB-\uD7FB\uF900-\uFA6D]|[\uFA70-\uFAD9\uFB00-\uFB06\uFB13-\uFB17\uFB1D\uFB1F-\uFB28\uFB2A-\uFB36]|[\uFB38-\uFB3C\uFB3E\uFB40\uFB41\uFB43\uFB44\uFB46-\uFBB1\uFBD3-\uFD3D]|[\uFD50-\uFD8F\uFD92-\uFDC7\uFDF0-\uFDFB\uFE70-\uFE74\uFE76-\uFEFC]|[\uFF21-\uFF3A\uFF41-\uFF5A\uFF66-\uFFBE\uFFC2-\uFFC7\uFFCA-\uFFCF]|[\uFFD2-\uFFD7\uFFDA-\uFFDC])/,/^(?:\|)/,/^(?:\()/,/^(?:\))/,/^(?:\[)/,/^(?:\])/,/^(?:\{)/,/^(?:\})/,/^(?:")/,/^(?:(\r?\n)+)/,/^(?:\s)/,/^(?:$)/],conditions:{close_directive:{rules:[],inclusive:!1},arg_directive:{rules:[3,4],inclusive:!1},type_directive:{rules:[2,3],inclusive:!1},open_directive:{rules:[1],inclusive:!1},vertex:{rules:[],inclusive:!1},dir:{rules:[25,26,27,28,29,30,31,32,33,34,35],inclusive:!1},string:{rules:[8,9],inclusive:!1},INITIAL:{rules:[0,5,6,7,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87],inclusive:!0}}};function Xt(){this.yy={}}return Gt.lexer=qt,Xt.prototype=Gt,Gt.Parser=Xt,new Xt}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[1,3],n=[1,5],r=[7,9,11,12,13,14,15,16,17,18,20,27,32],i=[1,15],a=[1,16],o=[1,17],s=[1,18],c=[1,19],u=[1,20],l=[1,21],h=[1,23],f=[1,25],d=[1,28],p=[5,7,9,11,12,13,14,15,16,17,18,20,27,32],g={trace:function(){},yy:{},symbols_:{error:2,start:3,directive:4,gantt:5,document:6,EOF:7,line:8,SPACE:9,statement:10,NL:11,dateFormat:12,inclusiveEndDates:13,axisFormat:14,excludes:15,todayMarker:16,title:17,section:18,clickStatement:19,taskTxt:20,taskData:21,openDirective:22,typeDirective:23,closeDirective:24,":":25,argDirective:26,click:27,callbackname:28,callbackargs:29,href:30,clickStatementDebug:31,open_directive:32,type_directive:33,arg_directive:34,close_directive:35,$accept:0,$end:1},terminals_:{2:"error",5:"gantt",7:"EOF",9:"SPACE",11:"NL",12:"dateFormat",13:"inclusiveEndDates",14:"axisFormat",15:"excludes",16:"todayMarker",17:"title",18:"section",20:"taskTxt",21:"taskData",25:":",27:"click",28:"callbackname",29:"callbackargs",30:"href",32:"open_directive",33:"type_directive",34:"arg_directive",35:"close_directive"},productions_:[0,[3,2],[3,3],[6,0],[6,2],[8,2],[8,1],[8,1],[8,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,2],[10,1],[4,4],[4,6],[19,2],[19,3],[19,3],[19,4],[19,3],[19,4],[19,2],[31,2],[31,3],[31,3],[31,4],[31,3],[31,4],[31,2],[22,1],[23,1],[26,1],[24,1]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 2:return a[s-1];case 3:this.$=[];break;case 4:a[s-1].push(a[s]),this.$=a[s-1];break;case 5:case 6:this.$=a[s];break;case 7:case 8:this.$=[];break;case 9:r.setDateFormat(a[s].substr(11)),this.$=a[s].substr(11);break;case 10:r.enableInclusiveEndDates(),this.$=a[s].substr(18);break;case 11:r.setAxisFormat(a[s].substr(11)),this.$=a[s].substr(11);break;case 12:r.setExcludes(a[s].substr(9)),this.$=a[s].substr(9);break;case 13:r.setTodayMarker(a[s].substr(12)),this.$=a[s].substr(12);break;case 14:r.setTitle(a[s].substr(6)),this.$=a[s].substr(6);break;case 15:r.addSection(a[s].substr(8)),this.$=a[s].substr(8);break;case 17:r.addTask(a[s-1],a[s]),this.$="task";break;case 21:this.$=a[s-1],r.setClickEvent(a[s-1],a[s],null);break;case 22:this.$=a[s-2],r.setClickEvent(a[s-2],a[s-1],a[s]);break;case 23:this.$=a[s-2],r.setClickEvent(a[s-2],a[s-1],null),r.setLink(a[s-2],a[s]);break;case 24:this.$=a[s-3],r.setClickEvent(a[s-3],a[s-2],a[s-1]),r.setLink(a[s-3],a[s]);break;case 25:this.$=a[s-2],r.setClickEvent(a[s-2],a[s],null),r.setLink(a[s-2],a[s-1]);break;case 26:this.$=a[s-3],r.setClickEvent(a[s-3],a[s-1],a[s]),r.setLink(a[s-3],a[s-2]);break;case 27:this.$=a[s-1],r.setLink(a[s-1],a[s]);break;case 28:case 34:this.$=a[s-1]+" "+a[s];break;case 29:case 30:case 32:this.$=a[s-2]+" "+a[s-1]+" "+a[s];break;case 31:case 33:this.$=a[s-3]+" "+a[s-2]+" "+a[s-1]+" "+a[s];break;case 35:r.parseDirective("%%{","open_directive");break;case 36:r.parseDirective(a[s],"type_directive");break;case 37:a[s]=a[s].trim().replace(/'/g,'"'),r.parseDirective(a[s],"arg_directive");break;case 38:r.parseDirective("}%%","close_directive","gantt")}},table:[{3:1,4:2,5:e,22:4,32:n},{1:[3]},{3:6,4:2,5:e,22:4,32:n},t(r,[2,3],{6:7}),{23:8,33:[1,9]},{33:[2,35]},{1:[2,1]},{4:24,7:[1,10],8:11,9:[1,12],10:13,11:[1,14],12:i,13:a,14:o,15:s,16:c,17:u,18:l,19:22,20:h,22:4,27:f,32:n},{24:26,25:[1,27],35:d},t([25,35],[2,36]),t(r,[2,8],{1:[2,2]}),t(r,[2,4]),{4:24,10:29,12:i,13:a,14:o,15:s,16:c,17:u,18:l,19:22,20:h,22:4,27:f,32:n},t(r,[2,6]),t(r,[2,7]),t(r,[2,9]),t(r,[2,10]),t(r,[2,11]),t(r,[2,12]),t(r,[2,13]),t(r,[2,14]),t(r,[2,15]),t(r,[2,16]),{21:[1,30]},t(r,[2,18]),{28:[1,31],30:[1,32]},{11:[1,33]},{26:34,34:[1,35]},{11:[2,38]},t(r,[2,5]),t(r,[2,17]),t(r,[2,21],{29:[1,36],30:[1,37]}),t(r,[2,27],{28:[1,38]}),t(p,[2,19]),{24:39,35:d},{35:[2,37]},t(r,[2,22],{30:[1,40]}),t(r,[2,23]),t(r,[2,25],{29:[1,41]}),{11:[1,42]},t(r,[2,24]),t(r,[2,26]),t(p,[2,20])],defaultActions:{5:[2,35],6:[2,1],28:[2,38],35:[2,37]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},y={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),32;case 1:return this.begin("type_directive"),33;case 2:return this.popState(),this.begin("arg_directive"),25;case 3:return this.popState(),this.popState(),35;case 4:return 34;case 5:case 6:case 7:break;case 8:return 11;case 9:case 10:case 11:break;case 12:this.begin("href");break;case 13:this.popState();break;case 14:return 30;case 15:this.begin("callbackname");break;case 16:this.popState();break;case 17:this.popState(),this.begin("callbackargs");break;case 18:return 28;case 19:this.popState();break;case 20:return 29;case 21:this.begin("click");break;case 22:this.popState();break;case 23:return 27;case 24:return 5;case 25:return 12;case 26:return 13;case 27:return 14;case 28:return 15;case 29:return 16;case 30:return"date";case 31:return 17;case 32:return 18;case 33:return 20;case 34:return 21;case 35:return 25;case 36:return 7;case 37:return"INVALID"}},rules:[/^(?:%%\{)/i,/^(?:((?:(?!\}%%)[^:.])*))/i,/^(?::)/i,/^(?:\}%%)/i,/^(?:((?:(?!\}%%).|\n)*))/i,/^(?:%%(?!\{)*[^\n]*)/i,/^(?:[^\}]%%*[^\n]*)/i,/^(?:%%*[^\n]*[\n]*)/i,/^(?:[\n]+)/i,/^(?:\s+)/i,/^(?:#[^\n]*)/i,/^(?:%[^\n]*)/i,/^(?:href[\s]+["])/i,/^(?:["])/i,/^(?:[^"]*)/i,/^(?:call[\s]+)/i,/^(?:\([\s]*\))/i,/^(?:\()/i,/^(?:[^(]*)/i,/^(?:\))/i,/^(?:[^)]*)/i,/^(?:click[\s]+)/i,/^(?:[\s\n])/i,/^(?:[^\s\n]*)/i,/^(?:gantt\b)/i,/^(?:dateFormat\s[^#\n;]+)/i,/^(?:inclusiveEndDates\b)/i,/^(?:axisFormat\s[^#\n;]+)/i,/^(?:excludes\s[^#\n;]+)/i,/^(?:todayMarker\s[^\n;]+)/i,/^(?:\d\d\d\d-\d\d-\d\d\b)/i,/^(?:title\s[^#\n;]+)/i,/^(?:section\s[^#:\n;]+)/i,/^(?:[^#:\n;]+)/i,/^(?::[^#\n;]+)/i,/^(?::)/i,/^(?:$)/i,/^(?:.)/i],conditions:{close_directive:{rules:[],inclusive:!1},arg_directive:{rules:[3,4],inclusive:!1},type_directive:{rules:[2,3],inclusive:!1},open_directive:{rules:[1],inclusive:!1},callbackargs:{rules:[19,20],inclusive:!1},callbackname:{rules:[16,17,18],inclusive:!1},href:{rules:[13,14],inclusive:!1},click:{rules:[22,23],inclusive:!1},INITIAL:{rules:[0,5,6,7,8,9,10,11,12,15,21,24,25,26,27,28,29,30,31,32,33,34,35,36,37],inclusive:!0}}};function v(){this.yy={}}return g.lexer=y,v.prototype=g,g.Parser=v,new v}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[1,2],n=[1,5],r=[6,9,11,17,18,19,21],i=[1,15],a=[1,16],o=[1,17],s=[1,21],c=[4,6,9,11,17,18,19,21],u={trace:function(){},yy:{},symbols_:{error:2,start:3,journey:4,document:5,EOF:6,directive:7,line:8,SPACE:9,statement:10,NEWLINE:11,openDirective:12,typeDirective:13,closeDirective:14,":":15,argDirective:16,title:17,section:18,taskName:19,taskData:20,open_directive:21,type_directive:22,arg_directive:23,close_directive:24,$accept:0,$end:1},terminals_:{2:"error",4:"journey",6:"EOF",9:"SPACE",11:"NEWLINE",15:":",17:"title",18:"section",19:"taskName",20:"taskData",21:"open_directive",22:"type_directive",23:"arg_directive",24:"close_directive"},productions_:[0,[3,3],[3,2],[5,0],[5,2],[8,2],[8,1],[8,1],[8,1],[7,4],[7,6],[10,1],[10,1],[10,2],[10,1],[12,1],[13,1],[16,1],[14,1]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 1:return a[s-1];case 3:this.$=[];break;case 4:a[s-1].push(a[s]),this.$=a[s-1];break;case 5:case 6:this.$=a[s];break;case 7:case 8:this.$=[];break;case 11:r.setTitle(a[s].substr(6)),this.$=a[s].substr(6);break;case 12:r.addSection(a[s].substr(8)),this.$=a[s].substr(8);break;case 13:r.addTask(a[s-1],a[s]),this.$="task";break;case 15:r.parseDirective("%%{","open_directive");break;case 16:r.parseDirective(a[s],"type_directive");break;case 17:a[s]=a[s].trim().replace(/'/g,'"'),r.parseDirective(a[s],"arg_directive");break;case 18:r.parseDirective("}%%","close_directive","journey")}},table:[{3:1,4:e,7:3,12:4,21:n},{1:[3]},t(r,[2,3],{5:6}),{3:7,4:e,7:3,12:4,21:n},{13:8,22:[1,9]},{22:[2,15]},{6:[1,10],7:18,8:11,9:[1,12],10:13,11:[1,14],12:4,17:i,18:a,19:o,21:n},{1:[2,2]},{14:19,15:[1,20],24:s},t([15,24],[2,16]),t(r,[2,8],{1:[2,1]}),t(r,[2,4]),{7:18,10:22,12:4,17:i,18:a,19:o,21:n},t(r,[2,6]),t(r,[2,7]),t(r,[2,11]),t(r,[2,12]),{20:[1,23]},t(r,[2,14]),{11:[1,24]},{16:25,23:[1,26]},{11:[2,18]},t(r,[2,5]),t(r,[2,13]),t(c,[2,9]),{14:27,24:s},{24:[2,17]},{11:[1,28]},t(c,[2,10])],defaultActions:{5:[2,15],7:[2,2],21:[2,18],26:[2,17]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},l={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),21;case 1:return this.begin("type_directive"),22;case 2:return this.popState(),this.begin("arg_directive"),15;case 3:return this.popState(),this.popState(),24;case 4:return 23;case 5:case 6:break;case 7:return 11;case 8:case 9:break;case 10:return 4;case 11:return 17;case 12:return 18;case 13:return 19;case 14:return 20;case 15:return 15;case 16:return 6;case 17:return"INVALID"}},rules:[/^(?:%%\{)/i,/^(?:((?:(?!\}%%)[^:.])*))/i,/^(?::)/i,/^(?:\}%%)/i,/^(?:((?:(?!\}%%).|\n)*))/i,/^(?:%(?!\{)[^\n]*)/i,/^(?:[^\}]%%[^\n]*)/i,/^(?:[\n]+)/i,/^(?:\s+)/i,/^(?:#[^\n]*)/i,/^(?:journey\b)/i,/^(?:title\s[^#\n;]+)/i,/^(?:section\s[^#:\n;]+)/i,/^(?:[^#:\n;]+)/i,/^(?::[^#\n;]+)/i,/^(?::)/i,/^(?:$)/i,/^(?:.)/i],conditions:{open_directive:{rules:[1],inclusive:!1},type_directive:{rules:[2,3],inclusive:!1},arg_directive:{rules:[3,4],inclusive:!1},INITIAL:{rules:[0,5,6,7,8,9,10,11,12,13,14,15,16,17],inclusive:!0}}};function h(){this.yy={}}return u.lexer=l,h.prototype=u,u.Parser=h,new h}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(15);e.default=function(t,e){return r.default.lang.round(i.default.parse(t)[e])}},function(t,e,n){var r=n(112),i=n(82),a=n(24);t.exports=function(t){return a(t)?r(t):i(t)}},function(t,e,n){var r;if(!r)try{r=n(0)}catch(t){}r||(r=window.d3),t.exports=r},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(15);e.default=function(t,e,n){var a=i.default.parse(t),o=a[e],s=r.default.channel.clamp[e](o+n);return o!==s&&(a[e]=s),i.default.stringify(a)}},function(t,e,n){var r=n(210),i=n(216);t.exports=function(t,e){var n=i(t,e);return r(n)?n:void 0}},function(t,e,n){var r=n(38),i=n(212),a=n(213),o=r?r.toStringTag:void 0;t.exports=function(t){return null==t?void 0===t?"[object Undefined]":"[object Null]":o&&o in Object(t)?i(t):a(t)}},function(t,e){t.exports=function(t){return t}},function(t,e){t.exports=function(t,e){return t===e||t!=t&&e!=e}},function(t,e,n){var r=n(34),i=n(11);t.exports=function(t){if(!i(t))return!1;var e=r(t);return"[object Function]"==e||"[object GeneratorFunction]"==e||"[object AsyncFunction]"==e||"[object Proxy]"==e}},function(t,e,n){var r=n(16).Symbol;t.exports=r},function(t,e,n){(function(t){var r=n(16),i=n(232),a=e&&!e.nodeType&&e,o=a&&"object"==typeof t&&t&&!t.nodeType&&t,s=o&&o.exports===a?r.Buffer:void 0,c=(s?s.isBuffer:void 0)||i;t.exports=c}).call(this,n(7)(t))},function(t,e,n){var r=n(112),i=n(236),a=n(24);t.exports=function(t){return a(t)?r(t,!0):i(t)}},function(t,e,n){var r=n(241),i=n(77),a=n(242),o=n(121),s=n(243),c=n(34),u=n(110),l=u(r),h=u(i),f=u(a),d=u(o),p=u(s),g=c;(r&&"[object DataView]"!=g(new r(new ArrayBuffer(1)))||i&&"[object Map]"!=g(new i)||a&&"[object Promise]"!=g(a.resolve())||o&&"[object Set]"!=g(new o)||s&&"[object WeakMap]"!=g(new s))&&(g=function(t){var e=c(t),n="[object Object]"==e?t.constructor:void 0,r=n?u(n):"";if(r)switch(r){case l:return"[object DataView]";case h:return"[object Map]";case f:return"[object Promise]";case d:return"[object Set]";case p:return"[object WeakMap]"}return e}),t.exports=g},function(t,e,n){var r=n(34),i=n(21);t.exports=function(t){return"symbol"==typeof t||i(t)&&"[object Symbol]"==r(t)}},function(t,e,n){var r;try{r={defaults:n(154),each:n(87),isFunction:n(37),isPlainObject:n(158),pick:n(161),has:n(93),range:n(162),uniqueId:n(163)}}catch(t){}r||(r=window._),t.exports=r},function(t){t.exports=JSON.parse('{"name":"mermaid","version":"8.8.2","description":"Markdownish syntax for generating flowcharts, sequence diagrams, class diagrams, gantt charts and git graphs.","main":"dist/mermaid.core.js","keywords":["diagram","markdown","flowchart","sequence diagram","gantt","class diagram","git graph"],"scripts":{"build:development":"webpack --progress --colors","build:production":"yarn build:development -p --config webpack.config.prod.babel.js","build":"yarn build:development && yarn build:production","postbuild":"documentation build src/mermaidAPI.js src/config.js --shallow -f md --markdown-toc false | sed \'1i---\\\\nsort: 3\\\\ntitle: Configurations\\\\n---\\\\n\' > docs/getting-started/Setup.md","build:watch":"yarn build --watch","minify":"minify ./dist/mermaid.js > ./dist/mermaid.min.js","release":"yarn build","lint":"eslint src","e2e:depr":"yarn lint && jest e2e --config e2e/jest.config.js","cypress":"percy exec -- cypress run","e2e":"start-server-and-test dev http://localhost:9000/ cypress","e2e-upd":"yarn lint && jest e2e -u --config e2e/jest.config.js","dev":"webpack-dev-server --config webpack.config.e2e.js","test":"yarn lint && jest src/.*","test:watch":"jest --watch src","prepublishOnly":"yarn build && yarn test","prepare":"yarn build"},"repository":{"type":"git","url":"https://github.com/knsv/mermaid"},"author":"Knut Sveidqvist","license":"MIT","standard":{"ignore":["**/parser/*.js","dist/**/*.js","cypress/**/*.js"],"globals":["page"]},"dependencies":{"@braintree/sanitize-url":"^3.1.0","babel-eslint":"^10.1.0","d3":"^5.7.0","dagre":"^0.8.4","dagre-d3":"^0.6.4","entity-decode":"^2.0.2","graphlib":"^2.1.7","he":"^1.2.0","khroma":"^1.1.0","minify":"^4.1.1","moment-mini":"^2.22.1","stylis":"^3.5.2"},"devDependencies":{"@babel/core":"^7.2.2","@babel/preset-env":"^7.8.4","@babel/register":"^7.0.0","@percy/cypress":"*","babel-core":"7.0.0-bridge.0","babel-jest":"^24.9.0","babel-loader":"^8.0.4","coveralls":"^3.0.2","css-loader":"^2.0.1","css-to-string-loader":"^0.1.3","cypress":"4.0.1","documentation":"^12.0.1","eslint":"^6.3.0","eslint-config-prettier":"^6.3.0","eslint-plugin-prettier":"^3.1.0","husky":"^1.2.1","identity-obj-proxy":"^3.0.0","jest":"^24.9.0","jison":"^0.4.18","moment":"^2.23.0","node-sass":"^4.12.0","prettier":"^1.18.2","puppeteer":"^1.17.0","sass-loader":"^7.1.0","start-server-and-test":"^1.10.6","terser-webpack-plugin":"^2.2.2","webpack":"^4.41.2","webpack-bundle-analyzer":"^3.7.0","webpack-cli":"^3.1.2","webpack-dev-server":"^3.4.1","webpack-node-externals":"^1.7.2","yarn-upgrade-all":"^0.5.0"},"files":["dist"],"yarn-upgrade-all":{"ignore":["babel-core"]},"sideEffects":["**/*.css","**/*.scss"],"husky":{"hooks":{"pre-push":"yarn test"}}}')},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=new(n(176).default)({r:0,g:0,b:0,a:0},"transparent");e.default=r},function(t,e,n){var r=n(58),i=n(59);t.exports=function(t,e,n,a){var o=!n;n||(n={});for(var s=-1,c=e.length;++s-1&&t%1==0&&t-1}(s)?s:(n=s.match(a))?(e=n[0],r.test(e)?"about:blank":s):"about:blank"}}},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[2,3],n=[1,7],r=[7,12,15,17,19,20,21],i=[7,11,12,15,17,19,20,21],a=[2,20],o=[1,32],s={trace:function(){},yy:{},symbols_:{error:2,start:3,GG:4,":":5,document:6,EOF:7,DIR:8,options:9,body:10,OPT:11,NL:12,line:13,statement:14,COMMIT:15,commit_arg:16,BRANCH:17,ID:18,CHECKOUT:19,MERGE:20,RESET:21,reset_arg:22,STR:23,HEAD:24,reset_parents:25,CARET:26,$accept:0,$end:1},terminals_:{2:"error",4:"GG",5:":",7:"EOF",8:"DIR",11:"OPT",12:"NL",15:"COMMIT",17:"BRANCH",18:"ID",19:"CHECKOUT",20:"MERGE",21:"RESET",23:"STR",24:"HEAD",26:"CARET"},productions_:[0,[3,4],[3,5],[6,0],[6,2],[9,2],[9,1],[10,0],[10,2],[13,2],[13,1],[14,2],[14,2],[14,2],[14,2],[14,2],[16,0],[16,1],[22,2],[22,2],[25,0],[25,2]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 1:return a[s-1];case 2:return r.setDirection(a[s-3]),a[s-1];case 4:r.setOptions(a[s-1]),this.$=a[s];break;case 5:a[s-1]+=a[s],this.$=a[s-1];break;case 7:this.$=[];break;case 8:a[s-1].push(a[s]),this.$=a[s-1];break;case 9:this.$=a[s-1];break;case 11:r.commit(a[s]);break;case 12:r.branch(a[s]);break;case 13:r.checkout(a[s]);break;case 14:r.merge(a[s]);break;case 15:r.reset(a[s]);break;case 16:this.$="";break;case 17:this.$=a[s];break;case 18:this.$=a[s-1]+":"+a[s];break;case 19:this.$=a[s-1]+":"+r.count,r.count=0;break;case 20:r.count=0;break;case 21:r.count+=1}},table:[{3:1,4:[1,2]},{1:[3]},{5:[1,3],8:[1,4]},{6:5,7:e,9:6,12:n},{5:[1,8]},{7:[1,9]},t(r,[2,7],{10:10,11:[1,11]}),t(i,[2,6]),{6:12,7:e,9:6,12:n},{1:[2,1]},{7:[2,4],12:[1,15],13:13,14:14,15:[1,16],17:[1,17],19:[1,18],20:[1,19],21:[1,20]},t(i,[2,5]),{7:[1,21]},t(r,[2,8]),{12:[1,22]},t(r,[2,10]),{12:[2,16],16:23,23:[1,24]},{18:[1,25]},{18:[1,26]},{18:[1,27]},{18:[1,30],22:28,24:[1,29]},{1:[2,2]},t(r,[2,9]),{12:[2,11]},{12:[2,17]},{12:[2,12]},{12:[2,13]},{12:[2,14]},{12:[2,15]},{12:a,25:31,26:o},{12:a,25:33,26:o},{12:[2,18]},{12:a,25:34,26:o},{12:[2,19]},{12:[2,21]}],defaultActions:{9:[2,1],21:[2,2],23:[2,11],24:[2,17],25:[2,12],26:[2,13],27:[2,14],28:[2,15],31:[2,18],33:[2,19],34:[2,21]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},c={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return 12;case 1:case 2:case 3:break;case 4:return 4;case 5:return 15;case 6:return 17;case 7:return 20;case 8:return 21;case 9:return 19;case 10:case 11:return 8;case 12:return 5;case 13:return 26;case 14:this.begin("options");break;case 15:this.popState();break;case 16:return 11;case 17:this.begin("string");break;case 18:this.popState();break;case 19:return 23;case 20:return 18;case 21:return 7}},rules:[/^(?:(\r?\n)+)/i,/^(?:\s+)/i,/^(?:#[^\n]*)/i,/^(?:%[^\n]*)/i,/^(?:gitGraph\b)/i,/^(?:commit\b)/i,/^(?:branch\b)/i,/^(?:merge\b)/i,/^(?:reset\b)/i,/^(?:checkout\b)/i,/^(?:LR\b)/i,/^(?:BT\b)/i,/^(?::)/i,/^(?:\^)/i,/^(?:options\r?\n)/i,/^(?:end\r?\n)/i,/^(?:[^\n]+\r?\n)/i,/^(?:["])/i,/^(?:["])/i,/^(?:[^"]*)/i,/^(?:[a-zA-Z][-_\.a-zA-Z0-9]*[-_a-zA-Z0-9])/i,/^(?:$)/i],conditions:{options:{rules:[15,16],inclusive:!1},string:{rules:[18,19],inclusive:!1},INITIAL:{rules:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,17,20,21],inclusive:!0}}};function u(){this.yy={}}return s.lexer=c,u.prototype=s,s.Parser=u,new u}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[6,9,10],n={trace:function(){},yy:{},symbols_:{error:2,start:3,info:4,document:5,EOF:6,line:7,statement:8,NL:9,showInfo:10,$accept:0,$end:1},terminals_:{2:"error",4:"info",6:"EOF",9:"NL",10:"showInfo"},productions_:[0,[3,3],[5,0],[5,2],[7,1],[7,1],[8,1]],performAction:function(t,e,n,r,i,a,o){a.length;switch(i){case 1:return r;case 4:break;case 6:r.setInfo(!0)}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:6,9:[1,7],10:[1,8]},{1:[2,1]},t(e,[2,3]),t(e,[2,4]),t(e,[2,5]),t(e,[2,6])],defaultActions:{4:[2,1]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},r={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return 4;case 1:return 9;case 2:return"space";case 3:return 10;case 4:return 6;case 5:return"TXT"}},rules:[/^(?:info\b)/i,/^(?:[\s\n\r]+)/i,/^(?:[\s]+)/i,/^(?:showInfo\b)/i,/^(?:$)/i,/^(?:.)/i],conditions:{INITIAL:{rules:[0,1,2,3,4,5],inclusive:!0}}};function i(){this.yy={}}return n.lexer=r,i.prototype=n,n.Parser=i,new i}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[1,4],n=[1,5],r=[1,6],i=[1,7],a=[1,9],o=[1,10,12,19,20,21,22],s=[1,6,10,12,19,20,21,22],c=[19,20,21],u=[1,22],l=[6,19,20,21,22],h={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,directive:5,PIE:6,document:7,line:8,statement:9,txt:10,value:11,title:12,title_value:13,openDirective:14,typeDirective:15,closeDirective:16,":":17,argDirective:18,NEWLINE:19,";":20,EOF:21,open_directive:22,type_directive:23,arg_directive:24,close_directive:25,$accept:0,$end:1},terminals_:{2:"error",6:"PIE",10:"txt",11:"value",12:"title",13:"title_value",17:":",19:"NEWLINE",20:";",21:"EOF",22:"open_directive",23:"type_directive",24:"arg_directive",25:"close_directive"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[9,0],[9,2],[9,2],[9,1],[5,3],[5,5],[4,1],[4,1],[4,1],[14,1],[15,1],[18,1],[16,1]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 6:this.$=a[s-1];break;case 8:r.addSection(a[s-1],r.cleanupValue(a[s]));break;case 9:this.$=a[s].trim(),r.setTitle(this.$);break;case 16:r.parseDirective("%%{","open_directive");break;case 17:r.parseDirective(a[s],"type_directive");break;case 18:a[s]=a[s].trim().replace(/'/g,'"'),r.parseDirective(a[s],"arg_directive");break;case 19:r.parseDirective("}%%","close_directive","pie")}},table:[{3:1,4:2,5:3,6:e,14:8,19:n,20:r,21:i,22:a},{1:[3]},{3:10,4:2,5:3,6:e,14:8,19:n,20:r,21:i,22:a},{3:11,4:2,5:3,6:e,14:8,19:n,20:r,21:i,22:a},t(o,[2,4],{7:12}),t(s,[2,13]),t(s,[2,14]),t(s,[2,15]),{15:13,23:[1,14]},{23:[2,16]},{1:[2,1]},{1:[2,2]},t(c,[2,7],{14:8,8:15,9:16,5:19,1:[2,3],10:[1,17],12:[1,18],22:a}),{16:20,17:[1,21],25:u},t([17,25],[2,17]),t(o,[2,5]),{4:23,19:n,20:r,21:i},{11:[1,24]},{13:[1,25]},t(c,[2,10]),t(l,[2,11]),{18:26,24:[1,27]},t(l,[2,19]),t(o,[2,6]),t(c,[2,8]),t(c,[2,9]),{16:28,25:u},{25:[2,18]},t(l,[2,12])],defaultActions:{9:[2,16],10:[2,1],11:[2,2],27:[2,18]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},f={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),22;case 1:return this.begin("type_directive"),23;case 2:return this.popState(),this.begin("arg_directive"),17;case 3:return this.popState(),this.popState(),25;case 4:return 24;case 5:case 6:break;case 7:return 19;case 8:case 9:break;case 10:return this.begin("title"),12;case 11:return this.popState(),"title_value";case 12:this.begin("string");break;case 13:this.popState();break;case 14:return"txt";case 15:return 6;case 16:return"value";case 17:return 21}},rules:[/^(?:%%\{)/i,/^(?:((?:(?!\}%%)[^:.])*))/i,/^(?::)/i,/^(?:\}%%)/i,/^(?:((?:(?!\}%%).|\n)*))/i,/^(?:%%(?!\{)[^\n]*)/i,/^(?:[^\}]%%[^\n]*)/i,/^(?:[\n\r]+)/i,/^(?:%%[^\n]*)/i,/^(?:[\s]+)/i,/^(?:title\b)/i,/^(?:(?!\n||)*[^\n]*)/i,/^(?:["])/i,/^(?:["])/i,/^(?:[^"]*)/i,/^(?:pie\b)/i,/^(?::[\s]*[\d]+(?:\.[\d]+)?)/i,/^(?:$)/i],conditions:{close_directive:{rules:[],inclusive:!1},arg_directive:{rules:[3,4],inclusive:!1},type_directive:{rules:[2,3],inclusive:!1},open_directive:{rules:[1],inclusive:!1},title:{rules:[11],inclusive:!1},string:{rules:[13,14],inclusive:!1},INITIAL:{rules:[0,5,6,7,8,9,10,12,15,16,17],inclusive:!0}}};function d(){this.yy={}}return h.lexer=f,d.prototype=h,h.Parser=d,new d}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){(function(t,r){var i=function(){var t=function(t,e,n,r){for(n=n||{},r=t.length;r--;n[t[r]]=e);return n},e=[1,2],n=[1,5],r=[6,9,11,20,30],i=[1,17],a=[1,20],o=[1,24],s=[1,25],c=[1,26],u=[1,27],l=[20,27,28],h=[4,6,9,11,20,30],f=[23,24,25,26],d={trace:function(){},yy:{},symbols_:{error:2,start:3,ER_DIAGRAM:4,document:5,EOF:6,directive:7,line:8,SPACE:9,statement:10,NEWLINE:11,openDirective:12,typeDirective:13,closeDirective:14,":":15,argDirective:16,entityName:17,relSpec:18,role:19,ALPHANUM:20,cardinality:21,relType:22,ZERO_OR_ONE:23,ZERO_OR_MORE:24,ONE_OR_MORE:25,ONLY_ONE:26,NON_IDENTIFYING:27,IDENTIFYING:28,WORD:29,open_directive:30,type_directive:31,arg_directive:32,close_directive:33,$accept:0,$end:1},terminals_:{2:"error",4:"ER_DIAGRAM",6:"EOF",9:"SPACE",11:"NEWLINE",15:":",20:"ALPHANUM",23:"ZERO_OR_ONE",24:"ZERO_OR_MORE",25:"ONE_OR_MORE",26:"ONLY_ONE",27:"NON_IDENTIFYING",28:"IDENTIFYING",29:"WORD",30:"open_directive",31:"type_directive",32:"arg_directive",33:"close_directive"},productions_:[0,[3,3],[3,2],[5,0],[5,2],[8,2],[8,1],[8,1],[8,1],[7,4],[7,6],[10,1],[10,5],[17,1],[18,3],[21,1],[21,1],[21,1],[21,1],[22,1],[22,1],[19,1],[19,1],[12,1],[13,1],[16,1],[14,1]],performAction:function(t,e,n,r,i,a,o){var s=a.length-1;switch(i){case 1:break;case 3:this.$=[];break;case 4:a[s-1].push(a[s]),this.$=a[s-1];break;case 5:case 6:this.$=a[s];break;case 7:case 8:this.$=[];break;case 12:r.addEntity(a[s-4]),r.addEntity(a[s-2]),r.addRelationship(a[s-4],a[s],a[s-2],a[s-3]);break;case 13:this.$=a[s];break;case 14:this.$={cardA:a[s],relType:a[s-1],cardB:a[s-2]};break;case 15:this.$=r.Cardinality.ZERO_OR_ONE;break;case 16:this.$=r.Cardinality.ZERO_OR_MORE;break;case 17:this.$=r.Cardinality.ONE_OR_MORE;break;case 18:this.$=r.Cardinality.ONLY_ONE;break;case 19:this.$=r.Identification.NON_IDENTIFYING;break;case 20:this.$=r.Identification.IDENTIFYING;break;case 21:this.$=a[s].replace(/"/g,"");break;case 22:this.$=a[s];break;case 23:r.parseDirective("%%{","open_directive");break;case 24:r.parseDirective(a[s],"type_directive");break;case 25:a[s]=a[s].trim().replace(/'/g,'"'),r.parseDirective(a[s],"arg_directive");break;case 26:r.parseDirective("}%%","close_directive","er")}},table:[{3:1,4:e,7:3,12:4,30:n},{1:[3]},t(r,[2,3],{5:6}),{3:7,4:e,7:3,12:4,30:n},{13:8,31:[1,9]},{31:[2,23]},{6:[1,10],7:15,8:11,9:[1,12],10:13,11:[1,14],12:4,17:16,20:i,30:n},{1:[2,2]},{14:18,15:[1,19],33:a},t([15,33],[2,24]),t(r,[2,8],{1:[2,1]}),t(r,[2,4]),{7:15,10:21,12:4,17:16,20:i,30:n},t(r,[2,6]),t(r,[2,7]),t(r,[2,11]),{18:22,21:23,23:o,24:s,25:c,26:u},t([15,23,24,25,26],[2,13]),{11:[1,28]},{16:29,32:[1,30]},{11:[2,26]},t(r,[2,5]),{17:31,20:i},{22:32,27:[1,33],28:[1,34]},t(l,[2,15]),t(l,[2,16]),t(l,[2,17]),t(l,[2,18]),t(h,[2,9]),{14:35,33:a},{33:[2,25]},{15:[1,36]},{21:37,23:o,24:s,25:c,26:u},t(f,[2,19]),t(f,[2,20]),{11:[1,38]},{19:39,20:[1,41],29:[1,40]},{20:[2,14]},t(h,[2,10]),t(r,[2,12]),t(r,[2,21]),t(r,[2,22])],defaultActions:{5:[2,23],7:[2,2],20:[2,26],30:[2,25],37:[2,14]},parseError:function(t,e){if(!e.recoverable){var n=new Error(t);throw n.hash=e,n}this.trace(t)},parse:function(t){var e=this,n=[0],r=[],i=[null],a=[],o=this.table,s="",c=0,u=0,l=0,h=2,f=1,d=a.slice.call(arguments,1),p=Object.create(this.lexer),g={yy:{}};for(var y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,y)&&(g.yy[y]=this.yy[y]);p.setInput(t,g.yy),g.yy.lexer=p,g.yy.parser=this,void 0===p.yylloc&&(p.yylloc={});var v=p.yylloc;a.push(v);var m=p.options&&p.options.ranges;function b(){var t;return"number"!=typeof(t=r.pop()||p.lex()||f)&&(t instanceof Array&&(t=(r=t).pop()),t=e.symbols_[t]||t),t}"function"==typeof g.yy.parseError?this.parseError=g.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var x,_,k,w,E,T,C,S,A,M={};;){if(k=n[n.length-1],this.defaultActions[k]?w=this.defaultActions[k]:(null==x&&(x=b()),w=o[k]&&o[k][x]),void 0===w||!w.length||!w[0]){var O="";for(T in A=[],o[k])this.terminals_[T]&&T>h&&A.push("'"+this.terminals_[T]+"'");O=p.showPosition?"Parse error on line "+(c+1)+":\n"+p.showPosition()+"\nExpecting "+A.join(", ")+", got '"+(this.terminals_[x]||x)+"'":"Parse error on line "+(c+1)+": Unexpected "+(x==f?"end of input":"'"+(this.terminals_[x]||x)+"'"),this.parseError(O,{text:p.match,token:this.terminals_[x]||x,line:p.yylineno,loc:v,expected:A})}if(w[0]instanceof Array&&w.length>1)throw new Error("Parse Error: multiple actions possible at state: "+k+", token: "+x);switch(w[0]){case 1:n.push(x),i.push(p.yytext),a.push(p.yylloc),n.push(w[1]),x=null,_?(x=_,_=null):(u=p.yyleng,s=p.yytext,c=p.yylineno,v=p.yylloc,l>0&&l--);break;case 2:if(C=this.productions_[w[1]][1],M.$=i[i.length-C],M._$={first_line:a[a.length-(C||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(C||1)].first_column,last_column:a[a.length-1].last_column},m&&(M._$.range=[a[a.length-(C||1)].range[0],a[a.length-1].range[1]]),void 0!==(E=this.performAction.apply(M,[s,u,c,g.yy,w[1],i,a].concat(d))))return E;C&&(n=n.slice(0,-1*C*2),i=i.slice(0,-1*C),a=a.slice(0,-1*C)),n.push(this.productions_[w[1]][0]),i.push(M.$),a.push(M._$),S=o[n[n.length-2]][n[n.length-1]],n.push(S);break;case 3:return!0}}return!0}},p={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];return this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t,t.match(/(?:\r\n?|\n).*/g)?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var n,r,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),(r=t[0].match(/(?:\r\n?|\n).*/g))&&(this.yylineno+=r.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:r?r[r.length-1].length-r[r.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],n=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),n)return n;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;var t,e,n,r;this._input||(this.done=!0),this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=n,r=a,this.options.backtrack_lexer){if(!1!==(t=this.test_match(n,i[a])))return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?!1!==(t=this.test_match(e,i[r]))&&t:""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t||this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){return this.conditionStack.length-1>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return(t=this.conditionStack.length-1-Math.abs(t||0))>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,n,r){switch(n){case 0:return this.begin("open_directive"),30;case 1:return this.begin("type_directive"),31;case 2:return this.popState(),this.begin("arg_directive"),15;case 3:return this.popState(),this.popState(),33;case 4:return 32;case 5:case 6:break;case 7:return 11;case 8:break;case 9:return 9;case 10:return 29;case 11:return 4;case 12:return 23;case 13:return 24;case 14:return 25;case 15:return 26;case 16:return 23;case 17:return 24;case 18:return 25;case 19:return 27;case 20:return 28;case 21:case 22:return 27;case 23:return 20;case 24:return e.yytext[0];case 25:return 6}},rules:[/^(?:%%\{)/i,/^(?:((?:(?!\}%%)[^:.])*))/i,/^(?::)/i,/^(?:\}%%)/i,/^(?:((?:(?!\}%%).|\n)*))/i,/^(?:%(?!\{)[^\n]*)/i,/^(?:[^\}]%%[^\n]*)/i,/^(?:[\n]+)/i,/^(?:\s+)/i,/^(?:[\s]+)/i,/^(?:"[^"]*")/i,/^(?:erDiagram\b)/i,/^(?:\|o\b)/i,/^(?:\}o\b)/i,/^(?:\}\|)/i,/^(?:\|\|)/i,/^(?:o\|)/i,/^(?:o\{)/i,/^(?:\|\{)/i,/^(?:\.\.)/i,/^(?:--)/i,/^(?:\.-)/i,/^(?:-\.)/i,/^(?:[A-Za-z][A-Za-z0-9\-]*)/i,/^(?:.)/i,/^(?:$)/i],conditions:{open_directive:{rules:[1],inclusive:!1},type_directive:{rules:[2,3],inclusive:!1},arg_directive:{rules:[3,4],inclusive:!1},INITIAL:{rules:[0,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],inclusive:!0}}};function g(){this.yy={}}return d.lexer=p,g.prototype=d,d.Parser=g,new g}();e.parser=i,e.Parser=i.Parser,e.parse=function(){return i.parse.apply(i,arguments)},e.main=function(r){r[1]||(console.log("Usage: "+r[0]+" FILE"),t.exit(1));var i=n(19).readFileSync(n(20).normalize(r[1]),"utf8");return e.parser.parse(i)},n.c[n.s]===r&&e.main(t.argv.slice(1))}).call(this,n(14),n(7)(t))},function(t,e,n){"use strict";var r;Object.defineProperty(e,"__esModule",{value:!0}),function(t){t[t.ALL=0]="ALL",t[t.RGB=1]="RGB",t[t.HSL=2]="HSL"}(r||(r={})),e.TYPE=r},function(t,e,n){"use strict";var r=n(10);t.exports=i;function i(t){this._isDirected=!r.has(t,"directed")||t.directed,this._isMultigraph=!!r.has(t,"multigraph")&&t.multigraph,this._isCompound=!!r.has(t,"compound")&&t.compound,this._label=void 0,this._defaultNodeLabelFn=r.constant(void 0),this._defaultEdgeLabelFn=r.constant(void 0),this._nodes={},this._isCompound&&(this._parent={},this._children={},this._children["\0"]={}),this._in={},this._preds={},this._out={},this._sucs={},this._edgeObjs={},this._edgeLabels={}}function a(t,e){t[e]?t[e]++:t[e]=1}function o(t,e){--t[e]||delete t[e]}function s(t,e,n,i){var a=""+e,o=""+n;if(!t&&a>o){var s=a;a=o,o=s}return a+""+o+""+(r.isUndefined(i)?"\0":i)}function c(t,e,n,r){var i=""+e,a=""+n;if(!t&&i>a){var o=i;i=a,a=o}var s={v:i,w:a};return r&&(s.name=r),s}function u(t,e){return s(t,e.v,e.w,e.name)}i.prototype._nodeCount=0,i.prototype._edgeCount=0,i.prototype.isDirected=function(){return this._isDirected},i.prototype.isMultigraph=function(){return this._isMultigraph},i.prototype.isCompound=function(){return this._isCompound},i.prototype.setGraph=function(t){return this._label=t,this},i.prototype.graph=function(){return this._label},i.prototype.setDefaultNodeLabel=function(t){return r.isFunction(t)||(t=r.constant(t)),this._defaultNodeLabelFn=t,this},i.prototype.nodeCount=function(){return this._nodeCount},i.prototype.nodes=function(){return r.keys(this._nodes)},i.prototype.sources=function(){var t=this;return r.filter(this.nodes(),(function(e){return r.isEmpty(t._in[e])}))},i.prototype.sinks=function(){var t=this;return r.filter(this.nodes(),(function(e){return r.isEmpty(t._out[e])}))},i.prototype.setNodes=function(t,e){var n=arguments,i=this;return r.each(t,(function(t){n.length>1?i.setNode(t,e):i.setNode(t)})),this},i.prototype.setNode=function(t,e){return r.has(this._nodes,t)?(arguments.length>1&&(this._nodes[t]=e),this):(this._nodes[t]=arguments.length>1?e:this._defaultNodeLabelFn(t),this._isCompound&&(this._parent[t]="\0",this._children[t]={},this._children["\0"][t]=!0),this._in[t]={},this._preds[t]={},this._out[t]={},this._sucs[t]={},++this._nodeCount,this)},i.prototype.node=function(t){return this._nodes[t]},i.prototype.hasNode=function(t){return r.has(this._nodes,t)},i.prototype.removeNode=function(t){var e=this;if(r.has(this._nodes,t)){var n=function(t){e.removeEdge(e._edgeObjs[t])};delete this._nodes[t],this._isCompound&&(this._removeFromParentsChildList(t),delete this._parent[t],r.each(this.children(t),(function(t){e.setParent(t)})),delete this._children[t]),r.each(r.keys(this._in[t]),n),delete this._in[t],delete this._preds[t],r.each(r.keys(this._out[t]),n),delete this._out[t],delete this._sucs[t],--this._nodeCount}return this},i.prototype.setParent=function(t,e){if(!this._isCompound)throw new Error("Cannot set parent in a non-compound graph");if(r.isUndefined(e))e="\0";else{for(var n=e+="";!r.isUndefined(n);n=this.parent(n))if(n===t)throw new Error("Setting "+e+" as parent of "+t+" would create a cycle");this.setNode(e)}return this.setNode(t),this._removeFromParentsChildList(t),this._parent[t]=e,this._children[e][t]=!0,this},i.prototype._removeFromParentsChildList=function(t){delete this._children[this._parent[t]][t]},i.prototype.parent=function(t){if(this._isCompound){var e=this._parent[t];if("\0"!==e)return e}},i.prototype.children=function(t){if(r.isUndefined(t)&&(t="\0"),this._isCompound){var e=this._children[t];if(e)return r.keys(e)}else{if("\0"===t)return this.nodes();if(this.hasNode(t))return[]}},i.prototype.predecessors=function(t){var e=this._preds[t];if(e)return r.keys(e)},i.prototype.successors=function(t){var e=this._sucs[t];if(e)return r.keys(e)},i.prototype.neighbors=function(t){var e=this.predecessors(t);if(e)return r.union(e,this.successors(t))},i.prototype.isLeaf=function(t){return 0===(this.isDirected()?this.successors(t):this.neighbors(t)).length},i.prototype.filterNodes=function(t){var e=new this.constructor({directed:this._isDirected,multigraph:this._isMultigraph,compound:this._isCompound});e.setGraph(this.graph());var n=this;r.each(this._nodes,(function(n,r){t(r)&&e.setNode(r,n)})),r.each(this._edgeObjs,(function(t){e.hasNode(t.v)&&e.hasNode(t.w)&&e.setEdge(t,n.edge(t))}));var i={};return this._isCompound&&r.each(e.nodes(),(function(t){e.setParent(t,function t(r){var a=n.parent(r);return void 0===a||e.hasNode(a)?(i[r]=a,a):a in i?i[a]:t(a)}(t))})),e},i.prototype.setDefaultEdgeLabel=function(t){return r.isFunction(t)||(t=r.constant(t)),this._defaultEdgeLabelFn=t,this},i.prototype.edgeCount=function(){return this._edgeCount},i.prototype.edges=function(){return r.values(this._edgeObjs)},i.prototype.setPath=function(t,e){var n=this,i=arguments;return r.reduce(t,(function(t,r){return i.length>1?n.setEdge(t,r,e):n.setEdge(t,r),r})),this},i.prototype.setEdge=function(){var t,e,n,i,o=!1,u=arguments[0];"object"==typeof u&&null!==u&&"v"in u?(t=u.v,e=u.w,n=u.name,2===arguments.length&&(i=arguments[1],o=!0)):(t=u,e=arguments[1],n=arguments[3],arguments.length>2&&(i=arguments[2],o=!0)),t=""+t,e=""+e,r.isUndefined(n)||(n=""+n);var l=s(this._isDirected,t,e,n);if(r.has(this._edgeLabels,l))return o&&(this._edgeLabels[l]=i),this;if(!r.isUndefined(n)&&!this._isMultigraph)throw new Error("Cannot set a named edge when isMultigraph = false");this.setNode(t),this.setNode(e),this._edgeLabels[l]=o?i:this._defaultEdgeLabelFn(t,e,n);var h=c(this._isDirected,t,e,n);return t=h.v,e=h.w,Object.freeze(h),this._edgeObjs[l]=h,a(this._preds[e],t),a(this._sucs[t],e),this._in[e][l]=h,this._out[t][l]=h,this._edgeCount++,this},i.prototype.edge=function(t,e,n){var r=1===arguments.length?u(this._isDirected,arguments[0]):s(this._isDirected,t,e,n);return this._edgeLabels[r]},i.prototype.hasEdge=function(t,e,n){var i=1===arguments.length?u(this._isDirected,arguments[0]):s(this._isDirected,t,e,n);return r.has(this._edgeLabels,i)},i.prototype.removeEdge=function(t,e,n){var r=1===arguments.length?u(this._isDirected,arguments[0]):s(this._isDirected,t,e,n),i=this._edgeObjs[r];return i&&(t=i.v,e=i.w,delete this._edgeLabels[r],delete this._edgeObjs[r],o(this._preds[e],t),o(this._sucs[t],e),delete this._in[e][r],delete this._out[t][r],this._edgeCount--),this},i.prototype.inEdges=function(t,e){var n=this._in[t];if(n){var i=r.values(n);return e?r.filter(i,(function(t){return t.v===e})):i}},i.prototype.outEdges=function(t,e){var n=this._out[t];if(n){var i=r.values(n);return e?r.filter(i,(function(t){return t.w===e})):i}},i.prototype.nodeEdges=function(t,e){var n=this.inEdges(t,e);if(n)return n.concat(this.outEdges(t,e))}},function(t,e,n){var r=n(33)(n(16),"Map");t.exports=r},function(t,e,n){var r=n(217),i=n(224),a=n(226),o=n(227),s=n(228);function c(t){var e=-1,n=null==t?0:t.length;for(this.clear();++e-1&&t%1==0&&t<=9007199254740991}},function(t,e,n){(function(t){var r=n(109),i=e&&!e.nodeType&&e,a=i&&"object"==typeof t&&t&&!t.nodeType&&t,o=a&&a.exports===i&&r.process,s=function(){try{var t=a&&a.require&&a.require("util").types;return t||o&&o.binding&&o.binding("util")}catch(t){}}();t.exports=s}).call(this,n(7)(t))},function(t,e,n){var r=n(62),i=n(234),a=Object.prototype.hasOwnProperty;t.exports=function(t){if(!r(t))return i(t);var e=[];for(var n in Object(t))a.call(t,n)&&"constructor"!=n&&e.push(n);return e}},function(t,e,n){var r=n(116),i=n(117),a=Object.prototype.propertyIsEnumerable,o=Object.getOwnPropertySymbols,s=o?function(t){return null==t?[]:(t=Object(t),r(o(t),(function(e){return a.call(t,e)})))}:i;t.exports=s},function(t,e){t.exports=function(t,e){for(var n=-1,r=e.length,i=t.length;++n0&&a(l)?n>1?t(l,n-1,a,o,s):r(s,l):o||(s[s.length]=l)}return s}},function(t,e,n){var r=n(42);t.exports=function(t,e,n){for(var i=-1,a=t.length;++i4,u=c?1:17,l=c?8:4,h=s?0:-1,f=c?255:15;return i.default.set({r:(r>>l*(h+3)&f)*u,g:(r>>l*(h+2)&f)*u,b:(r>>l*(h+1)&f)*u,a:s?(r&f)*u/255:1},t)}}},stringify:function(t){return t.a<1?"#"+a.DEC2HEX[Math.round(t.r)]+a.DEC2HEX[Math.round(t.g)]+a.DEC2HEX[Math.round(t.b)]+r.default.unit.frac2hex(t.a):"#"+a.DEC2HEX[Math.round(t.r)]+a.DEC2HEX[Math.round(t.g)]+a.DEC2HEX[Math.round(t.b)]}};e.default=o},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(45),a=n(15);e.default=function(t,e,n,o){void 0===o&&(o=1);var s=i.default.set({h:r.default.channel.clamp.h(t),s:r.default.channel.clamp.s(e),l:r.default.channel.clamp.l(n),a:r.default.channel.clamp.a(o)});return a.default.stringify(s)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"a")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(15);e.default=function(t){var e=i.default.parse(t),n=e.r,a=e.g,o=e.b,s=.2126*r.default.channel.toLinear(n)+.7152*r.default.channel.toLinear(a)+.0722*r.default.channel.toLinear(o);return r.default.lang.round(s)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(102);e.default=function(t){return r.default(t)>=.5}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t,e){return r.default(t,"a",e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t,e){return r.default(t,"a",-e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(15),i=n(52);e.default=function(t,e){var n=r.default.parse(t),a={};for(var o in e)e[o]&&(a[o]=n[o]+e[o]);return i.default(t,a)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(15),i=n(51);e.default=function(t,e,n){void 0===n&&(n=50);var a=r.default.parse(t),o=a.r,s=a.g,c=a.b,u=a.a,l=r.default.parse(e),h=l.r,f=l.g,d=l.b,p=l.a,g=n/100,y=2*g-1,v=u-p,m=((y*v==-1?y:(y+v)/(1+y*v))+1)/2,b=1-m,x=o*m+h*b,_=s*m+f*b,k=c*m+d*b,w=u*g+p*(1-g);return i.default(x,_,k,w)}},function(t,e,n){var r=n(53),i=n(79),a=n(58),o=n(229),s=n(235),c=n(114),u=n(115),l=n(238),h=n(239),f=n(119),d=n(240),p=n(41),g=n(244),y=n(245),v=n(124),m=n(5),b=n(39),x=n(249),_=n(11),k=n(251),w=n(30),E={};E["[object Arguments]"]=E["[object Array]"]=E["[object ArrayBuffer]"]=E["[object DataView]"]=E["[object Boolean]"]=E["[object Date]"]=E["[object Float32Array]"]=E["[object Float64Array]"]=E["[object Int8Array]"]=E["[object Int16Array]"]=E["[object Int32Array]"]=E["[object Map]"]=E["[object Number]"]=E["[object Object]"]=E["[object RegExp]"]=E["[object Set]"]=E["[object String]"]=E["[object Symbol]"]=E["[object Uint8Array]"]=E["[object Uint8ClampedArray]"]=E["[object Uint16Array]"]=E["[object Uint32Array]"]=!0,E["[object Error]"]=E["[object Function]"]=E["[object WeakMap]"]=!1,t.exports=function t(e,n,T,C,S,A){var M,O=1&n,D=2&n,N=4&n;if(T&&(M=S?T(e,C,S,A):T(e)),void 0!==M)return M;if(!_(e))return e;var B=m(e);if(B){if(M=g(e),!O)return u(e,M)}else{var L=p(e),F="[object Function]"==L||"[object GeneratorFunction]"==L;if(b(e))return c(e,O);if("[object Object]"==L||"[object Arguments]"==L||F&&!S){if(M=D||F?{}:v(e),!O)return D?h(e,s(M,e)):l(e,o(M,e))}else{if(!E[L])return S?e:{};M=y(e,L,O)}}A||(A=new r);var P=A.get(e);if(P)return P;A.set(e,M),k(e)?e.forEach((function(r){M.add(t(r,n,T,r,e,A))})):x(e)&&e.forEach((function(r,i){M.set(i,t(r,n,T,i,e,A))}));var I=N?D?d:f:D?keysIn:w,j=B?void 0:I(e);return i(j||e,(function(r,i){j&&(r=e[i=r]),a(M,i,t(r,n,T,i,e,A))})),M}},function(t,e,n){(function(e){var n="object"==typeof e&&e&&e.Object===Object&&e;t.exports=n}).call(this,n(211))},function(t,e){var n=Function.prototype.toString;t.exports=function(t){if(null!=t){try{return n.call(t)}catch(t){}try{return t+""}catch(t){}}return""}},function(t,e,n){var r=n(33),i=function(){try{var t=r(Object,"defineProperty");return t({},"",{}),t}catch(t){}}();t.exports=i},function(t,e,n){var r=n(230),i=n(47),a=n(5),o=n(39),s=n(60),c=n(48),u=Object.prototype.hasOwnProperty;t.exports=function(t,e){var n=a(t),l=!n&&i(t),h=!n&&!l&&o(t),f=!n&&!l&&!h&&c(t),d=n||l||h||f,p=d?r(t.length,String):[],g=p.length;for(var y in t)!e&&!u.call(t,y)||d&&("length"==y||h&&("offset"==y||"parent"==y)||f&&("buffer"==y||"byteLength"==y||"byteOffset"==y)||s(y,g))||p.push(y);return p}},function(t,e){t.exports=function(t,e){return function(n){return t(e(n))}}},function(t,e,n){(function(t){var r=n(16),i=e&&!e.nodeType&&e,a=i&&"object"==typeof t&&t&&!t.nodeType&&t,o=a&&a.exports===i?r.Buffer:void 0,s=o?o.allocUnsafe:void 0;t.exports=function(t,e){if(e)return t.slice();var n=t.length,r=s?s(n):new t.constructor(n);return t.copy(r),r}}).call(this,n(7)(t))},function(t,e){t.exports=function(t,e){var n=-1,r=t.length;for(e||(e=Array(r));++nl))return!1;var f=c.get(t);if(f&&c.get(e))return f==e;var d=-1,p=!0,g=2&n?new r:void 0;for(c.set(t,e),c.set(e,t);++d0&&(a=c.removeMin(),(o=s[a]).distance!==Number.POSITIVE_INFINITY);)r(a).forEach(u);return s}(t,String(e),n||a,r||function(e){return t.outEdges(e)})};var a=r.constant(1)},function(t,e,n){var r=n(10);function i(){this._arr=[],this._keyIndices={}}t.exports=i,i.prototype.size=function(){return this._arr.length},i.prototype.keys=function(){return this._arr.map((function(t){return t.key}))},i.prototype.has=function(t){return r.has(this._keyIndices,t)},i.prototype.priority=function(t){var e=this._keyIndices[t];if(void 0!==e)return this._arr[e].priority},i.prototype.min=function(){if(0===this.size())throw new Error("Queue underflow");return this._arr[0].key},i.prototype.add=function(t,e){var n=this._keyIndices;if(t=String(t),!r.has(n,t)){var i=this._arr,a=i.length;return n[t]=a,i.push({key:t,priority:e}),this._decrease(a),!0}return!1},i.prototype.removeMin=function(){this._swap(0,this._arr.length-1);var t=this._arr.pop();return delete this._keyIndices[t.key],this._heapify(0),t.key},i.prototype.decrease=function(t,e){var n=this._keyIndices[t];if(e>this._arr[n].priority)throw new Error("New priority is greater than current priority. Key: "+t+" Old: "+this._arr[n].priority+" New: "+e);this._arr[n].priority=e,this._decrease(n)},i.prototype._heapify=function(t){var e=this._arr,n=2*t,r=n+1,i=t;n>1].priority2?e[2]:void 0;for(u&&a(e[0],e[1],u)&&(r=1);++n1&&o.sort((function(t,e){var r=t.x-n.x,i=t.y-n.y,a=Math.sqrt(r*r+i*i),o=e.x-n.x,s=e.y-n.y,c=Math.sqrt(o*o+s*s);return aMath.abs(o)*u?(s<0&&(u=-u),n=0===s?0:u*o/s,r=u):(o<0&&(c=-c),n=c,r=0===o?0:c*s/o);return{x:i+n,y:a+r}}},function(t,e,n){t.exports=function t(e){"use strict";var n=/^\0+/g,r=/[\0\r\f]/g,i=/: */g,a=/zoo|gra/,o=/([,: ])(transform)/g,s=/,+\s*(?![^(]*[)])/g,c=/ +\s*(?![^(]*[)])/g,u=/ *[\0] */g,l=/,\r+?/g,h=/([\t\r\n ])*\f?&/g,f=/:global\(((?:[^\(\)\[\]]*|\[.*\]|\([^\(\)]*\))*)\)/g,d=/\W+/g,p=/@(k\w+)\s*(\S*)\s*/,g=/::(place)/g,y=/:(read-only)/g,v=/\s+(?=[{\];=:>])/g,m=/([[}=:>])\s+/g,b=/(\{[^{]+?);(?=\})/g,x=/\s{2,}/g,_=/([^\(])(:+) */g,k=/[svh]\w+-[tblr]{2}/,w=/\(\s*(.*)\s*\)/g,E=/([\s\S]*?);/g,T=/-self|flex-/g,C=/[^]*?(:[rp][el]a[\w-]+)[^]*/,S=/stretch|:\s*\w+\-(?:conte|avail)/,A=/([^-])(image-set\()/,M="-webkit-",O="-moz-",D="-ms-",N=1,B=1,L=0,F=1,P=1,I=1,j=0,R=0,Y=0,z=[],U=[],$=0,W=null,V=0,H=1,G="",q="",X="";function Z(t,e,i,a,o){for(var s,c,l=0,h=0,f=0,d=0,v=0,m=0,b=0,x=0,k=0,E=0,T=0,C=0,S=0,A=0,O=0,D=0,j=0,U=0,W=0,Q=i.length,it=Q-1,at="",ot="",st="",ct="",ut="",lt="";O0&&(ot=ot.replace(r,"")),ot.trim().length>0)){switch(b){case 32:case 9:case 59:case 13:case 10:break;default:ot+=i.charAt(O)}b=59}if(1===j)switch(b){case 123:case 125:case 59:case 34:case 39:case 40:case 41:case 44:j=0;case 9:case 13:case 10:case 32:break;default:for(j=0,W=O,v=b,O--,b=59;W0&&(++O,b=v);case 123:W=Q}}switch(b){case 123:for(v=(ot=ot.trim()).charCodeAt(0),T=1,W=++O;O0&&(ot=ot.replace(r,"")),m=ot.charCodeAt(1)){case 100:case 109:case 115:case 45:s=e;break;default:s=z}if(W=(st=Z(e,s,st,m,o+1)).length,Y>0&&0===W&&(W=ot.length),$>0&&(c=nt(3,st,s=J(z,ot,U),e,B,N,W,m,o,a),ot=s.join(""),void 0!==c&&0===(W=(st=c.trim()).length)&&(m=0,st="")),W>0)switch(m){case 115:ot=ot.replace(w,et);case 100:case 109:case 45:st=ot+"{"+st+"}";break;case 107:st=(ot=ot.replace(p,"$1 $2"+(H>0?G:"")))+"{"+st+"}",st=1===P||2===P&&tt("@"+st,3)?"@"+M+st+"@"+st:"@"+st;break;default:st=ot+st,112===a&&(ct+=st,st="")}else st="";break;default:st=Z(e,J(e,ot,U),st,a,o+1)}ut+=st,C=0,j=0,A=0,D=0,U=0,S=0,ot="",st="",b=i.charCodeAt(++O);break;case 125:case 59:if((W=(ot=(D>0?ot.replace(r,""):ot).trim()).length)>1)switch(0===A&&(45===(v=ot.charCodeAt(0))||v>96&&v<123)&&(W=(ot=ot.replace(" ",":")).length),$>0&&void 0!==(c=nt(1,ot,e,t,B,N,ct.length,a,o,a))&&0===(W=(ot=c.trim()).length)&&(ot="\0\0"),v=ot.charCodeAt(0),m=ot.charCodeAt(1),v){case 0:break;case 64:if(105===m||99===m){lt+=ot+i.charAt(O);break}default:if(58===ot.charCodeAt(W-1))break;ct+=K(ot,v,m,ot.charCodeAt(2))}C=0,j=0,A=0,D=0,U=0,ot="",b=i.charCodeAt(++O)}}switch(b){case 13:case 10:if(h+d+f+l+R===0)switch(E){case 41:case 39:case 34:case 64:case 126:case 62:case 42:case 43:case 47:case 45:case 58:case 44:case 59:case 123:case 125:break;default:A>0&&(j=1)}47===h?h=0:F+C===0&&107!==a&&ot.length>0&&(D=1,ot+="\0"),$*V>0&&nt(0,ot,e,t,B,N,ct.length,a,o,a),N=1,B++;break;case 59:case 125:if(h+d+f+l===0){N++;break}default:switch(N++,at=i.charAt(O),b){case 9:case 32:if(d+l+h===0)switch(x){case 44:case 58:case 9:case 32:at="";break;default:32!==b&&(at=" ")}break;case 0:at="\\0";break;case 12:at="\\f";break;case 11:at="\\v";break;case 38:d+h+l===0&&F>0&&(U=1,D=1,at="\f"+at);break;case 108:if(d+h+l+L===0&&A>0)switch(O-A){case 2:112===x&&58===i.charCodeAt(O-3)&&(L=x);case 8:111===k&&(L=k)}break;case 58:d+h+l===0&&(A=O);break;case 44:h+f+d+l===0&&(D=1,at+="\r");break;case 34:case 39:0===h&&(d=d===b?0:0===d?b:d);break;case 91:d+h+f===0&&l++;break;case 93:d+h+f===0&&l--;break;case 41:d+h+l===0&&f--;break;case 40:if(d+h+l===0){if(0===C)switch(2*x+3*k){case 533:break;default:T=0,C=1}f++}break;case 64:h+f+d+l+A+S===0&&(S=1);break;case 42:case 47:if(d+l+f>0)break;switch(h){case 0:switch(2*b+3*i.charCodeAt(O+1)){case 235:h=47;break;case 220:W=O,h=42}break;case 42:47===b&&42===x&&W+2!==O&&(33===i.charCodeAt(W+2)&&(ct+=i.substring(W,O+1)),at="",h=0)}}if(0===h){if(F+d+l+S===0&&107!==a&&59!==b)switch(b){case 44:case 126:case 62:case 43:case 41:case 40:if(0===C){switch(x){case 9:case 32:case 10:case 13:at+="\0";break;default:at="\0"+at+(44===b?"":"\0")}D=1}else switch(b){case 40:A+7===O&&108===x&&(A=0),C=++T;break;case 41:0==(C=--T)&&(D=1,at+="\0")}break;case 9:case 32:switch(x){case 0:case 123:case 125:case 59:case 44:case 12:case 9:case 32:case 10:case 13:break;default:0===C&&(D=1,at+="\0")}}ot+=at,32!==b&&9!==b&&(E=b)}}k=x,x=b,O++}if(W=ct.length,Y>0&&0===W&&0===ut.length&&0===e[0].length==0&&(109!==a||1===e.length&&(F>0?q:X)===e[0])&&(W=e.join(",").length+2),W>0){if(s=0===F&&107!==a?function(t){for(var e,n,i=0,a=t.length,o=Array(a);i1)){if(f=c.charCodeAt(c.length-1),d=n.charCodeAt(0),e="",0!==l)switch(f){case 42:case 126:case 62:case 43:case 32:case 40:break;default:e=" "}switch(d){case 38:n=e+q;case 126:case 62:case 43:case 32:case 41:case 40:break;case 91:n=e+n+q;break;case 58:switch(2*n.charCodeAt(1)+3*n.charCodeAt(2)){case 530:if(I>0){n=e+n.substring(8,h-1);break}default:(l<1||s[l-1].length<1)&&(n=e+q+n)}break;case 44:e="";default:n=h>1&&n.indexOf(":")>0?e+n.replace(_,"$1"+q+"$2"):e+n+q}c+=n}o[i]=c.replace(r,"").trim()}return o}(e):e,$>0&&void 0!==(c=nt(2,ct,s,t,B,N,W,a,o,a))&&0===(ct=c).length)return lt+ct+ut;if(ct=s.join(",")+"{"+ct+"}",P*L!=0){switch(2!==P||tt(ct,2)||(L=0),L){case 111:ct=ct.replace(y,":-moz-$1")+ct;break;case 112:ct=ct.replace(g,"::-webkit-input-$1")+ct.replace(g,"::-moz-$1")+ct.replace(g,":-ms-input-$1")+ct}L=0}}return lt+ct+ut}function J(t,e,n){var r=e.trim().split(l),i=r,a=r.length,o=t.length;switch(o){case 0:case 1:for(var s=0,c=0===o?"":t[0]+" ";s0&&F>0)return i.replace(f,"$1").replace(h,"$1"+X);break;default:return t.trim()+i.replace(h,"$1"+t.trim())}default:if(n*F>0&&i.indexOf("\f")>0)return i.replace(h,(58===t.charCodeAt(0)?"":"$1")+t.trim())}return t+i}function K(t,e,n,r){var u,l=0,h=t+";",f=2*e+3*n+4*r;if(944===f)return function(t){var e=t.length,n=t.indexOf(":",9)+1,r=t.substring(0,n).trim(),i=t.substring(n,e-1).trim();switch(t.charCodeAt(9)*H){case 0:break;case 45:if(110!==t.charCodeAt(10))break;default:var a=i.split((i="",s)),o=0;for(n=0,e=a.length;o64&&h<90||h>96&&h<123||95===h||45===h&&45!==u.charCodeAt(1)))switch(isNaN(parseFloat(u))+(-1!==u.indexOf("("))){case 1:switch(u){case"infinite":case"alternate":case"backwards":case"running":case"normal":case"forwards":case"both":case"none":case"linear":case"ease":case"ease-in":case"ease-out":case"ease-in-out":case"paused":case"reverse":case"alternate-reverse":case"inherit":case"initial":case"unset":case"step-start":case"step-end":break;default:u+=G}}l[n++]=u}i+=(0===o?"":",")+l.join(" ")}}return i=r+i+";",1===P||2===P&&tt(i,1)?M+i+i:i}(h);if(0===P||2===P&&!tt(h,1))return h;switch(f){case 1015:return 97===h.charCodeAt(10)?M+h+h:h;case 951:return 116===h.charCodeAt(3)?M+h+h:h;case 963:return 110===h.charCodeAt(5)?M+h+h:h;case 1009:if(100!==h.charCodeAt(4))break;case 969:case 942:return M+h+h;case 978:return M+h+O+h+h;case 1019:case 983:return M+h+O+h+D+h+h;case 883:return 45===h.charCodeAt(8)?M+h+h:h.indexOf("image-set(",11)>0?h.replace(A,"$1-webkit-$2")+h:h;case 932:if(45===h.charCodeAt(4))switch(h.charCodeAt(5)){case 103:return M+"box-"+h.replace("-grow","")+M+h+D+h.replace("grow","positive")+h;case 115:return M+h+D+h.replace("shrink","negative")+h;case 98:return M+h+D+h.replace("basis","preferred-size")+h}return M+h+D+h+h;case 964:return M+h+D+"flex-"+h+h;case 1023:if(99!==h.charCodeAt(8))break;return u=h.substring(h.indexOf(":",15)).replace("flex-","").replace("space-between","justify"),M+"box-pack"+u+M+h+D+"flex-pack"+u+h;case 1005:return a.test(h)?h.replace(i,":"+M)+h.replace(i,":"+O)+h:h;case 1e3:switch(l=(u=h.substring(13).trim()).indexOf("-")+1,u.charCodeAt(0)+u.charCodeAt(l)){case 226:u=h.replace(k,"tb");break;case 232:u=h.replace(k,"tb-rl");break;case 220:u=h.replace(k,"lr");break;default:return h}return M+h+D+u+h;case 1017:if(-1===h.indexOf("sticky",9))return h;case 975:switch(l=(h=t).length-10,f=(u=(33===h.charCodeAt(l)?h.substring(0,l):h).substring(t.indexOf(":",7)+1).trim()).charCodeAt(0)+(0|u.charCodeAt(7))){case 203:if(u.charCodeAt(8)<111)break;case 115:h=h.replace(u,M+u)+";"+h;break;case 207:case 102:h=h.replace(u,M+(f>102?"inline-":"")+"box")+";"+h.replace(u,M+u)+";"+h.replace(u,D+u+"box")+";"+h}return h+";";case 938:if(45===h.charCodeAt(5))switch(h.charCodeAt(6)){case 105:return u=h.replace("-items",""),M+h+M+"box-"+u+D+"flex-"+u+h;case 115:return M+h+D+"flex-item-"+h.replace(T,"")+h;default:return M+h+D+"flex-line-pack"+h.replace("align-content","").replace(T,"")+h}break;case 973:case 989:if(45!==h.charCodeAt(3)||122===h.charCodeAt(4))break;case 931:case 953:if(!0===S.test(t))return 115===(u=t.substring(t.indexOf(":")+1)).charCodeAt(0)?K(t.replace("stretch","fill-available"),e,n,r).replace(":fill-available",":stretch"):h.replace(u,M+u)+h.replace(u,O+u.replace("fill-",""))+h;break;case 962:if(h=M+h+(102===h.charCodeAt(5)?D+h:"")+h,n+r===211&&105===h.charCodeAt(13)&&h.indexOf("transform",10)>0)return h.substring(0,h.indexOf(";",27)+1).replace(o,"$1-webkit-$2")+h}return h}function tt(t,e){var n=t.indexOf(1===e?":":"{"),r=t.substring(0,3!==e?n:10),i=t.substring(n+1,t.length-1);return W(2!==e?r:r.replace(C,"$1"),i,e)}function et(t,e){var n=K(e,e.charCodeAt(0),e.charCodeAt(1),e.charCodeAt(2));return n!==e+";"?n.replace(E," or ($1)").substring(4):"("+e+")"}function nt(t,e,n,r,i,a,o,s,c,u){for(var l,h=0,f=e;h<$;++h)switch(l=U[h].call(at,t,f,n,r,i,a,o,s,c,u)){case void 0:case!1:case!0:case null:break;default:f=l}if(f!==e)return f}function rt(t,e,n,r){for(var i=e+1;i0&&(G=i.replace(d,91===a?"":"-")),a=1,1===F?X=i:q=i;var o,s=[X];$>0&&void 0!==(o=nt(-1,n,s,s,B,N,0,0,0,0))&&"string"==typeof o&&(n=o);var c=Z(z,s,n,0,0);return $>0&&void 0!==(o=nt(-2,c,s,s,B,N,c.length,0,0,0))&&"string"!=typeof(c=o)&&(a=0),G="",X="",q="",L=0,B=1,N=1,j*a==0?c:function(t){return t.replace(r,"").replace(v,"").replace(m,"$1").replace(b,"$1").replace(x," ")}(c)}return at.use=function t(e){switch(e){case void 0:case null:$=U.length=0;break;default:if("function"==typeof e)U[$++]=e;else if("object"==typeof e)for(var n=0,r=e.length;n=255?255:t<0?0:t},g:function(t){return t>=255?255:t<0?0:t},b:function(t){return t>=255?255:t<0?0:t},h:function(t){return t%360},s:function(t){return t>=100?100:t<0?0:t},l:function(t){return t>=100?100:t<0?0:t},a:function(t){return t>=1?1:t<0?0:t}},toLinear:function(t){var e=t/255;return t>.03928?Math.pow((e+.055)/1.055,2.4):e/12.92},hue2rgb:function(t,e,n){return n<0&&(n+=1),n>1&&(n-=1),n<1/6?t+6*(e-t)*n:n<.5?e:n<2/3?t+(e-t)*(2/3-n)*6:t},hsl2rgb:function(t,e){var n=t.h,i=t.s,a=t.l;if(100===i)return 2.55*a;n/=360,i/=100;var o=(a/=100)<.5?a*(1+i):a+i-a*i,s=2*a-o;switch(e){case"r":return 255*r.hue2rgb(s,o,n+1/3);case"g":return 255*r.hue2rgb(s,o,n);case"b":return 255*r.hue2rgb(s,o,n-1/3)}},rgb2hsl:function(t,e){var n=t.r,r=t.g,i=t.b;n/=255,r/=255,i/=255;var a=Math.max(n,r,i),o=Math.min(n,r,i),s=(a+o)/2;if("l"===e)return 100*s;if(a===o)return 0;var c=a-o;if("s"===e)return 100*(s>.5?c/(2-a-o):c/(a+o));switch(a){case n:return 60*((r-i)/c+(r1?e:"0"+e},dec2hex:function(t){var e=Math.round(t).toString(16);return e.length>1?e:"0"+e}};e.default=r},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(75),a=n(177),o=function(){function t(t,e){this.color=e,this.changed=!1,this.data=t,this.type=new a.default}return t.prototype.set=function(t,e){return this.color=e,this.changed=!1,this.data=t,this.type.type=i.TYPE.ALL,this},t.prototype._ensureHSL=function(){void 0===this.data.h&&(this.data.h=r.default.channel.rgb2hsl(this.data,"h")),void 0===this.data.s&&(this.data.s=r.default.channel.rgb2hsl(this.data,"s")),void 0===this.data.l&&(this.data.l=r.default.channel.rgb2hsl(this.data,"l"))},t.prototype._ensureRGB=function(){void 0===this.data.r&&(this.data.r=r.default.channel.hsl2rgb(this.data,"r")),void 0===this.data.g&&(this.data.g=r.default.channel.hsl2rgb(this.data,"g")),void 0===this.data.b&&(this.data.b=r.default.channel.hsl2rgb(this.data,"b"))},Object.defineProperty(t.prototype,"r",{get:function(){return this.type.is(i.TYPE.HSL)||void 0===this.data.r?(this._ensureHSL(),r.default.channel.hsl2rgb(this.data,"r")):this.data.r},set:function(t){this.type.set(i.TYPE.RGB),this.changed=!0,this.data.r=t},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,"g",{get:function(){return this.type.is(i.TYPE.HSL)||void 0===this.data.g?(this._ensureHSL(),r.default.channel.hsl2rgb(this.data,"g")):this.data.g},set:function(t){this.type.set(i.TYPE.RGB),this.changed=!0,this.data.g=t},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,"b",{get:function(){return this.type.is(i.TYPE.HSL)||void 0===this.data.b?(this._ensureHSL(),r.default.channel.hsl2rgb(this.data,"b")):this.data.b},set:function(t){this.type.set(i.TYPE.RGB),this.changed=!0,this.data.b=t},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,"h",{get:function(){return this.type.is(i.TYPE.RGB)||void 0===this.data.h?(this._ensureRGB(),r.default.channel.rgb2hsl(this.data,"h")):this.data.h},set:function(t){this.type.set(i.TYPE.HSL),this.changed=!0,this.data.h=t},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,"s",{get:function(){return this.type.is(i.TYPE.RGB)||void 0===this.data.s?(this._ensureRGB(),r.default.channel.rgb2hsl(this.data,"s")):this.data.s},set:function(t){this.type.set(i.TYPE.HSL),this.changed=!0,this.data.s=t},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,"l",{get:function(){return this.type.is(i.TYPE.RGB)||void 0===this.data.l?(this._ensureRGB(),r.default.channel.rgb2hsl(this.data,"l")):this.data.l},set:function(t){this.type.set(i.TYPE.HSL),this.changed=!0,this.data.l=t},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,"a",{get:function(){return this.data.a},set:function(t){this.changed=!0,this.data.a=t},enumerable:!0,configurable:!0}),t}();e.default=o},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(75),i=function(){function t(){this.type=r.TYPE.ALL}return t.prototype.get=function(){return this.type},t.prototype.set=function(t){if(this.type&&this.type!==t)throw new Error("Cannot change both RGB and HSL channels at the same time");this.type=t},t.prototype.reset=function(){this.type=r.TYPE.ALL},t.prototype.is=function(t){return this.type===t},t}();e.default=i},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i={};e.DEC2HEX=i;for(var a=0;a<=255;a++)i[a]=r.default.unit.dec2hex(a)},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(99),i={colors:{aliceblue:"#f0f8ff",antiquewhite:"#faebd7",aqua:"#00ffff",aquamarine:"#7fffd4",azure:"#f0ffff",beige:"#f5f5dc",bisque:"#ffe4c4",black:"#000000",blanchedalmond:"#ffebcd",blue:"#0000ff",blueviolet:"#8a2be2",brown:"#a52a2a",burlywood:"#deb887",cadetblue:"#5f9ea0",chartreuse:"#7fff00",chocolate:"#d2691e",coral:"#ff7f50",cornflowerblue:"#6495ed",cornsilk:"#fff8dc",crimson:"#dc143c",cyanaqua:"#00ffff",darkblue:"#00008b",darkcyan:"#008b8b",darkgoldenrod:"#b8860b",darkgray:"#a9a9a9",darkgreen:"#006400",darkgrey:"#a9a9a9",darkkhaki:"#bdb76b",darkmagenta:"#8b008b",darkolivegreen:"#556b2f",darkorange:"#ff8c00",darkorchid:"#9932cc",darkred:"#8b0000",darksalmon:"#e9967a",darkseagreen:"#8fbc8f",darkslateblue:"#483d8b",darkslategray:"#2f4f4f",darkslategrey:"#2f4f4f",darkturquoise:"#00ced1",darkviolet:"#9400d3",deeppink:"#ff1493",deepskyblue:"#00bfff",dimgray:"#696969",dimgrey:"#696969",dodgerblue:"#1e90ff",firebrick:"#b22222",floralwhite:"#fffaf0",forestgreen:"#228b22",fuchsia:"#ff00ff",gainsboro:"#dcdcdc",ghostwhite:"#f8f8ff",gold:"#ffd700",goldenrod:"#daa520",gray:"#808080",green:"#008000",greenyellow:"#adff2f",grey:"#808080",honeydew:"#f0fff0",hotpink:"#ff69b4",indianred:"#cd5c5c",indigo:"#4b0082",ivory:"#fffff0",khaki:"#f0e68c",lavender:"#e6e6fa",lavenderblush:"#fff0f5",lawngreen:"#7cfc00",lemonchiffon:"#fffacd",lightblue:"#add8e6",lightcoral:"#f08080",lightcyan:"#e0ffff",lightgoldenrodyellow:"#fafad2",lightgray:"#d3d3d3",lightgreen:"#90ee90",lightgrey:"#d3d3d3",lightpink:"#ffb6c1",lightsalmon:"#ffa07a",lightseagreen:"#20b2aa",lightskyblue:"#87cefa",lightslategray:"#778899",lightslategrey:"#778899",lightsteelblue:"#b0c4de",lightyellow:"#ffffe0",lime:"#00ff00",limegreen:"#32cd32",linen:"#faf0e6",magenta:"#ff00ff",maroon:"#800000",mediumaquamarine:"#66cdaa",mediumblue:"#0000cd",mediumorchid:"#ba55d3",mediumpurple:"#9370db",mediumseagreen:"#3cb371",mediumslateblue:"#7b68ee",mediumspringgreen:"#00fa9a",mediumturquoise:"#48d1cc",mediumvioletred:"#c71585",midnightblue:"#191970",mintcream:"#f5fffa",mistyrose:"#ffe4e1",moccasin:"#ffe4b5",navajowhite:"#ffdead",navy:"#000080",oldlace:"#fdf5e6",olive:"#808000",olivedrab:"#6b8e23",orange:"#ffa500",orangered:"#ff4500",orchid:"#da70d6",palegoldenrod:"#eee8aa",palegreen:"#98fb98",paleturquoise:"#afeeee",palevioletred:"#db7093",papayawhip:"#ffefd5",peachpuff:"#ffdab9",peru:"#cd853f",pink:"#ffc0cb",plum:"#dda0dd",powderblue:"#b0e0e6",purple:"#800080",rebeccapurple:"#663399",red:"#ff0000",rosybrown:"#bc8f8f",royalblue:"#4169e1",saddlebrown:"#8b4513",salmon:"#fa8072",sandybrown:"#f4a460",seagreen:"#2e8b57",seashell:"#fff5ee",sienna:"#a0522d",silver:"#c0c0c0",skyblue:"#87ceeb",slateblue:"#6a5acd",slategray:"#708090",slategrey:"#708090",snow:"#fffafa",springgreen:"#00ff7f",tan:"#d2b48c",teal:"#008080",thistle:"#d8bfd8",transparent:"#00000000",turquoise:"#40e0d0",violet:"#ee82ee",wheat:"#f5deb3",white:"#ffffff",whitesmoke:"#f5f5f5",yellow:"#ffff00",yellowgreen:"#9acd32"},parse:function(t){t=t.toLowerCase();var e=i.colors[t];if(e)return r.default.parse(e)},stringify:function(t){var e=r.default.stringify(t);for(var n in i.colors)if(i.colors[n]===e)return n}};e.default=i},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(45),a={re:/^rgba?\(\s*?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e\d+)?(%?))\s*?(?:,|\s)\s*?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e\d+)?(%?))\s*?(?:,|\s)\s*?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e\d+)?(%?))(?:\s*?(?:,|\/)\s*?\+?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e\d+)?(%?)))?\s*?\)$/i,parse:function(t){var e=t.charCodeAt(0);if(114===e||82===e){var n=t.match(a.re);if(n){var o=n[1],s=n[2],c=n[3],u=n[4],l=n[5],h=n[6],f=n[7],d=n[8];return i.default.set({r:r.default.channel.clamp.r(s?2.55*parseFloat(o):parseFloat(o)),g:r.default.channel.clamp.g(u?2.55*parseFloat(c):parseFloat(c)),b:r.default.channel.clamp.b(h?2.55*parseFloat(l):parseFloat(l)),a:f?r.default.channel.clamp.a(d?parseFloat(f)/100:parseFloat(f)):1},t)}}},stringify:function(t){return t.a<1?"rgba("+r.default.lang.round(t.r)+", "+r.default.lang.round(t.g)+", "+r.default.lang.round(t.b)+", "+r.default.lang.round(t.a)+")":"rgb("+r.default.lang.round(t.r)+", "+r.default.lang.round(t.g)+", "+r.default.lang.round(t.b)+")"}};e.default=a},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(45),a={re:/^hsla?\(\s*?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e-?\d+)?(?:deg|grad|rad|turn)?)\s*?(?:,|\s)\s*?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e-?\d+)?%)\s*?(?:,|\s)\s*?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e-?\d+)?%)(?:\s*?(?:,|\/)\s*?\+?(-?(?:\d+(?:\.\d+)?|(?:\.\d+))(?:e-?\d+)?(%)?))?\s*?\)$/i,hueRe:/^(.+?)(deg|grad|rad|turn)$/i,_hue2deg:function(t){var e=t.match(a.hueRe);if(e){var n=e[1];switch(e[2]){case"grad":return r.default.channel.clamp.h(.9*parseFloat(n));case"rad":return r.default.channel.clamp.h(180*parseFloat(n)/Math.PI);case"turn":return r.default.channel.clamp.h(360*parseFloat(n))}}return r.default.channel.clamp.h(parseFloat(t))},parse:function(t){var e=t.charCodeAt(0);if(104===e||72===e){var n=t.match(a.re);if(n){var o=n[1],s=n[2],c=n[3],u=n[4],l=n[5];return i.default.set({h:a._hue2deg(o),s:r.default.channel.clamp.s(parseFloat(s)),l:r.default.channel.clamp.l(parseFloat(c)),a:u?r.default.channel.clamp.a(l?parseFloat(u)/100:parseFloat(u)):1},t)}}},stringify:function(t){return t.a<1?"hsla("+r.default.lang.round(t.h)+", "+r.default.lang.round(t.s)+"%, "+r.default.lang.round(t.l)+"%, "+t.a+")":"hsl("+r.default.lang.round(t.h)+", "+r.default.lang.round(t.s)+"%, "+r.default.lang.round(t.l)+"%)"}};e.default=a},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"r")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"g")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"b")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"h")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"s")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(29);e.default=function(t){return r.default(t,"l")}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(103);e.default=function(t){return!r.default(t)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(15);e.default=function(t){try{return r.default.parse(t),!0}catch(t){return!1}}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t,e){return r.default(t,"s",e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t,e){return r.default(t,"s",-e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t,e){return r.default(t,"l",e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t,e){return r.default(t,"l",-e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(32);e.default=function(t){return r.default(t,"h",180)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(52);e.default=function(t){return r.default(t,{s:0})}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(15),i=n(107);e.default=function(t,e){void 0===e&&(e=100);var n=r.default.parse(t);return n.r=255-n.r,n.g=255-n.g,n.b=255-n.b,i.default(n,t,e)}},function(t,e,n){"use strict";Object.defineProperty(e,"__esModule",{value:!0});var r=n(9),i=n(15),a=n(106);e.default=function(t,e){var n,o,s,c=i.default.parse(t),u={};for(var l in e)u[l]=(n=c[l],o=e[l],s=r.default.channel.max[l],o>0?(s-n)*o/100:n*o/100);return a.default(t,u)}},function(t,e,n){t.exports={Graph:n(76),version:n(300)}},function(t,e,n){var r=n(108);t.exports=function(t){return r(t,4)}},function(t,e){t.exports=function(){this.__data__=[],this.size=0}},function(t,e,n){var r=n(55),i=Array.prototype.splice;t.exports=function(t){var e=this.__data__,n=r(e,t);return!(n<0)&&(n==e.length-1?e.pop():i.call(e,n,1),--this.size,!0)}},function(t,e,n){var r=n(55);t.exports=function(t){var e=this.__data__,n=r(e,t);return n<0?void 0:e[n][1]}},function(t,e,n){var r=n(55);t.exports=function(t){return r(this.__data__,t)>-1}},function(t,e,n){var r=n(55);t.exports=function(t,e){var n=this.__data__,i=r(n,t);return i<0?(++this.size,n.push([t,e])):n[i][1]=e,this}},function(t,e,n){var r=n(54);t.exports=function(){this.__data__=new r,this.size=0}},function(t,e){t.exports=function(t){var e=this.__data__,n=e.delete(t);return this.size=e.size,n}},function(t,e){t.exports=function(t){return this.__data__.get(t)}},function(t,e){t.exports=function(t){return this.__data__.has(t)}},function(t,e,n){var r=n(54),i=n(77),a=n(78);t.exports=function(t,e){var n=this.__data__;if(n instanceof r){var o=n.__data__;if(!i||o.length<199)return o.push([t,e]),this.size=++n.size,this;n=this.__data__=new a(o)}return n.set(t,e),this.size=n.size,this}},function(t,e,n){var r=n(37),i=n(214),a=n(11),o=n(110),s=/^\[object .+?Constructor\]$/,c=Function.prototype,u=Object.prototype,l=c.toString,h=u.hasOwnProperty,f=RegExp("^"+l.call(h).replace(/[\\^$.*+?()[\]{}|]/g,"\\$&").replace(/hasOwnProperty|(function).*?(?=\\\()| for .+?(?=\\\])/g,"$1.*?")+"$");t.exports=function(t){return!(!a(t)||i(t))&&(r(t)?f:s).test(o(t))}},function(t,e){var n;n=function(){return this}();try{n=n||new Function("return this")()}catch(t){"object"==typeof window&&(n=window)}t.exports=n},function(t,e,n){var r=n(38),i=Object.prototype,a=i.hasOwnProperty,o=i.toString,s=r?r.toStringTag:void 0;t.exports=function(t){var e=a.call(t,s),n=t[s];try{t[s]=void 0;var r=!0}catch(t){}var i=o.call(t);return r&&(e?t[s]=n:delete t[s]),i}},function(t,e){var n=Object.prototype.toString;t.exports=function(t){return n.call(t)}},function(t,e,n){var r,i=n(215),a=(r=/[^.]+$/.exec(i&&i.keys&&i.keys.IE_PROTO||""))?"Symbol(src)_1."+r:"";t.exports=function(t){return!!a&&a in t}},function(t,e,n){var r=n(16)["__core-js_shared__"];t.exports=r},function(t,e){t.exports=function(t,e){return null==t?void 0:t[e]}},function(t,e,n){var r=n(218),i=n(54),a=n(77);t.exports=function(){this.size=0,this.__data__={hash:new r,map:new(a||i),string:new r}}},function(t,e,n){var r=n(219),i=n(220),a=n(221),o=n(222),s=n(223);function c(t){var e=-1,n=null==t?0:t.length;for(this.clear();++e0){if(++e>=800)return arguments[0]}else e=0;return t.apply(void 0,arguments)}}},function(t,e,n){var r=n(131),i=n(292),a=n(296),o=n(132),s=n(297),c=n(90);t.exports=function(t,e,n){var u=-1,l=i,h=t.length,f=!0,d=[],p=d;if(n)f=!1,l=a;else if(h>=200){var g=e?null:s(t);if(g)return c(g);f=!1,l=o,p=new r}else p=e?[]:d;t:for(;++u-1}},function(t,e,n){var r=n(145),i=n(294),a=n(295);t.exports=function(t,e,n){return e==e?a(t,e,n):r(t,i,n)}},function(t,e){t.exports=function(t){return t!=t}},function(t,e){t.exports=function(t,e,n){for(var r=n-1,i=t.length;++r1||1===e.length&&t.hasEdge(e[0],e[0])}))}},function(t,e,n){var r=n(10);t.exports=function(t,e,n){return function(t,e,n){var r={},i=t.nodes();return i.forEach((function(t){r[t]={},r[t][t]={distance:0},i.forEach((function(e){t!==e&&(r[t][e]={distance:Number.POSITIVE_INFINITY})})),n(t).forEach((function(n){var i=n.v===t?n.w:n.v,a=e(n);r[t][i]={distance:a,predecessor:t}}))})),i.forEach((function(t){var e=r[t];i.forEach((function(n){var a=r[n];i.forEach((function(n){var r=a[t],i=e[n],o=a[n],s=r.distance+i.distance;s0;){if(n=c.removeMin(),r.has(s,n))o.setEdge(n,s[n]);else{if(l)throw new Error("Input graph is not connected: "+t);l=!0}t.nodeEdges(n).forEach(u)}return o}},function(t,e,n){var r;try{r=n(3)}catch(t){}r||(r=window.graphlib),t.exports=r},function(t,e,n){"use strict";var r=n(4),i=n(345),a=n(348),o=n(349),s=n(8).normalizeRanks,c=n(351),u=n(8).removeEmptyRanks,l=n(352),h=n(353),f=n(354),d=n(355),p=n(364),g=n(8),y=n(17).Graph;t.exports=function(t,e){var n=e&&e.debugTiming?g.time:g.notime;n("layout",(function(){var e=n(" buildLayoutGraph",(function(){return function(t){var e=new y({multigraph:!0,compound:!0}),n=C(t.graph());return e.setGraph(r.merge({},m,T(n,v),r.pick(n,b))),r.forEach(t.nodes(),(function(n){var i=C(t.node(n));e.setNode(n,r.defaults(T(i,x),_)),e.setParent(n,t.parent(n))})),r.forEach(t.edges(),(function(n){var i=C(t.edge(n));e.setEdge(n,r.merge({},w,T(i,k),r.pick(i,E)))})),e}(t)}));n(" runLayout",(function(){!function(t,e){e(" makeSpaceForEdgeLabels",(function(){!function(t){var e=t.graph();e.ranksep/=2,r.forEach(t.edges(),(function(n){var r=t.edge(n);r.minlen*=2,"c"!==r.labelpos.toLowerCase()&&("TB"===e.rankdir||"BT"===e.rankdir?r.width+=r.labeloffset:r.height+=r.labeloffset)}))}(t)})),e(" removeSelfEdges",(function(){!function(t){r.forEach(t.edges(),(function(e){if(e.v===e.w){var n=t.node(e.v);n.selfEdges||(n.selfEdges=[]),n.selfEdges.push({e:e,label:t.edge(e)}),t.removeEdge(e)}}))}(t)})),e(" acyclic",(function(){i.run(t)})),e(" nestingGraph.run",(function(){l.run(t)})),e(" rank",(function(){o(g.asNonCompoundGraph(t))})),e(" injectEdgeLabelProxies",(function(){!function(t){r.forEach(t.edges(),(function(e){var n=t.edge(e);if(n.width&&n.height){var r=t.node(e.v),i={rank:(t.node(e.w).rank-r.rank)/2+r.rank,e:e};g.addDummyNode(t,"edge-proxy",i,"_ep")}}))}(t)})),e(" removeEmptyRanks",(function(){u(t)})),e(" nestingGraph.cleanup",(function(){l.cleanup(t)})),e(" normalizeRanks",(function(){s(t)})),e(" assignRankMinMax",(function(){!function(t){var e=0;r.forEach(t.nodes(),(function(n){var i=t.node(n);i.borderTop&&(i.minRank=t.node(i.borderTop).rank,i.maxRank=t.node(i.borderBottom).rank,e=r.max(e,i.maxRank))})),t.graph().maxRank=e}(t)})),e(" removeEdgeLabelProxies",(function(){!function(t){r.forEach(t.nodes(),(function(e){var n=t.node(e);"edge-proxy"===n.dummy&&(t.edge(n.e).labelRank=n.rank,t.removeNode(e))}))}(t)})),e(" normalize.run",(function(){a.run(t)})),e(" parentDummyChains",(function(){c(t)})),e(" addBorderSegments",(function(){h(t)})),e(" order",(function(){d(t)})),e(" insertSelfEdges",(function(){!function(t){var e=g.buildLayerMatrix(t);r.forEach(e,(function(e){var n=0;r.forEach(e,(function(e,i){var a=t.node(e);a.order=i+n,r.forEach(a.selfEdges,(function(e){g.addDummyNode(t,"selfedge",{width:e.label.width,height:e.label.height,rank:a.rank,order:i+ ++n,e:e.e,label:e.label},"_se")})),delete a.selfEdges}))}))}(t)})),e(" adjustCoordinateSystem",(function(){f.adjust(t)})),e(" position",(function(){p(t)})),e(" positionSelfEdges",(function(){!function(t){r.forEach(t.nodes(),(function(e){var n=t.node(e);if("selfedge"===n.dummy){var r=t.node(n.e.v),i=r.x+r.width/2,a=r.y,o=n.x-i,s=r.height/2;t.setEdge(n.e,n.label),t.removeNode(e),n.label.points=[{x:i+2*o/3,y:a-s},{x:i+5*o/6,y:a-s},{x:i+o,y:a},{x:i+5*o/6,y:a+s},{x:i+2*o/3,y:a+s}],n.label.x=n.x,n.label.y=n.y}}))}(t)})),e(" removeBorderNodes",(function(){!function(t){r.forEach(t.nodes(),(function(e){if(t.children(e).length){var n=t.node(e),i=t.node(n.borderTop),a=t.node(n.borderBottom),o=t.node(r.last(n.borderLeft)),s=t.node(r.last(n.borderRight));n.width=Math.abs(s.x-o.x),n.height=Math.abs(a.y-i.y),n.x=o.x+n.width/2,n.y=i.y+n.height/2}})),r.forEach(t.nodes(),(function(e){"border"===t.node(e).dummy&&t.removeNode(e)}))}(t)})),e(" normalize.undo",(function(){a.undo(t)})),e(" fixupEdgeLabelCoords",(function(){!function(t){r.forEach(t.edges(),(function(e){var n=t.edge(e);if(r.has(n,"x"))switch("l"!==n.labelpos&&"r"!==n.labelpos||(n.width-=n.labeloffset),n.labelpos){case"l":n.x-=n.width/2+n.labeloffset;break;case"r":n.x+=n.width/2+n.labeloffset}}))}(t)})),e(" undoCoordinateSystem",(function(){f.undo(t)})),e(" translateGraph",(function(){!function(t){var e=Number.POSITIVE_INFINITY,n=0,i=Number.POSITIVE_INFINITY,a=0,o=t.graph(),s=o.marginx||0,c=o.marginy||0;function u(t){var r=t.x,o=t.y,s=t.width,c=t.height;e=Math.min(e,r-s/2),n=Math.max(n,r+s/2),i=Math.min(i,o-c/2),a=Math.max(a,o+c/2)}r.forEach(t.nodes(),(function(e){u(t.node(e))})),r.forEach(t.edges(),(function(e){var n=t.edge(e);r.has(n,"x")&&u(n)})),e-=s,i-=c,r.forEach(t.nodes(),(function(n){var r=t.node(n);r.x-=e,r.y-=i})),r.forEach(t.edges(),(function(n){var a=t.edge(n);r.forEach(a.points,(function(t){t.x-=e,t.y-=i})),r.has(a,"x")&&(a.x-=e),r.has(a,"y")&&(a.y-=i)})),o.width=n-e+s,o.height=a-i+c}(t)})),e(" assignNodeIntersects",(function(){!function(t){r.forEach(t.edges(),(function(e){var n,r,i=t.edge(e),a=t.node(e.v),o=t.node(e.w);i.points?(n=i.points[0],r=i.points[i.points.length-1]):(i.points=[],n=o,r=a),i.points.unshift(g.intersectRect(a,n)),i.points.push(g.intersectRect(o,r))}))}(t)})),e(" reversePoints",(function(){!function(t){r.forEach(t.edges(),(function(e){var n=t.edge(e);n.reversed&&n.points.reverse()}))}(t)})),e(" acyclic.undo",(function(){i.undo(t)}))}(e,n)})),n(" updateInputGraph",(function(){!function(t,e){r.forEach(t.nodes(),(function(n){var r=t.node(n),i=e.node(n);r&&(r.x=i.x,r.y=i.y,e.children(n).length&&(r.width=i.width,r.height=i.height))})),r.forEach(t.edges(),(function(n){var i=t.edge(n),a=e.edge(n);i.points=a.points,r.has(a,"x")&&(i.x=a.x,i.y=a.y)})),t.graph().width=e.graph().width,t.graph().height=e.graph().height}(t,e)}))}))};var v=["nodesep","edgesep","ranksep","marginx","marginy"],m={ranksep:50,edgesep:20,nodesep:50,rankdir:"tb"},b=["acyclicer","ranker","rankdir","align"],x=["width","height"],_={width:0,height:0},k=["minlen","weight","width","height","labeloffset"],w={minlen:1,weight:1,width:0,height:0,labeloffset:10,labelpos:"r"},E=["labelpos"];function T(t,e){return r.mapValues(r.pick(t,e),Number)}function C(t){var e={};return r.forEach(t,(function(t,n){e[n.toLowerCase()]=t})),e}},function(t,e,n){var r=n(108);t.exports=function(t){return r(t,5)}},function(t,e,n){var r=n(315)(n(316));t.exports=r},function(t,e,n){var r=n(25),i=n(24),a=n(30);t.exports=function(t){return function(e,n,o){var s=Object(e);if(!i(e)){var c=r(n,3);e=a(e),n=function(t){return c(s[t],t,s)}}var u=t(e,n,o);return u>-1?s[c?e[u]:u]:void 0}}},function(t,e,n){var r=n(145),i=n(25),a=n(317),o=Math.max;t.exports=function(t,e,n){var s=null==t?0:t.length;if(!s)return-1;var c=null==n?0:a(n);return c<0&&(c=o(s+c,0)),r(t,i(e,3),c)}},function(t,e,n){var r=n(155);t.exports=function(t){var e=r(t),n=e%1;return e==e?n?e-n:e:0}},function(t,e,n){var r=n(11),i=n(42),a=/^\s+|\s+$/g,o=/^[-+]0x[0-9a-f]+$/i,s=/^0b[01]+$/i,c=/^0o[0-7]+$/i,u=parseInt;t.exports=function(t){if("number"==typeof t)return t;if(i(t))return NaN;if(r(t)){var e="function"==typeof t.valueOf?t.valueOf():t;t=r(e)?e+"":e}if("string"!=typeof t)return 0===t?t:+t;t=t.replace(a,"");var n=s.test(t);return n||c.test(t)?u(t.slice(2),n?2:8):o.test(t)?NaN:+t}},function(t,e,n){var r=n(89),i=n(127),a=n(40);t.exports=function(t,e){return null==t?t:r(t,i(e),a)}},function(t,e){t.exports=function(t){var e=null==t?0:t.length;return e?t[e-1]:void 0}},function(t,e,n){var r=n(59),i=n(88),a=n(25);t.exports=function(t,e){var n={};return e=a(e,3),i(t,(function(t,i,a){r(n,i,e(t,i,a))})),n}},function(t,e,n){var r=n(95),i=n(323),a=n(35);t.exports=function(t){return t&&t.length?r(t,a,i):void 0}},function(t,e){t.exports=function(t,e){return t>e}},function(t,e,n){var r=n(325),i=n(328)((function(t,e,n){r(t,e,n)}));t.exports=i},function(t,e,n){var r=n(53),i=n(157),a=n(89),o=n(326),s=n(11),c=n(40),u=n(159);t.exports=function t(e,n,l,h,f){e!==n&&a(n,(function(a,c){if(f||(f=new r),s(a))o(e,n,c,l,t,h,f);else{var d=h?h(u(e,c),a,c+"",e,n,f):void 0;void 0===d&&(d=a),i(e,c,d)}}),c)}},function(t,e,n){var r=n(157),i=n(114),a=n(123),o=n(115),s=n(124),c=n(47),u=n(5),l=n(146),h=n(39),f=n(37),d=n(11),p=n(158),g=n(48),y=n(159),v=n(327);t.exports=function(t,e,n,m,b,x,_){var k=y(t,n),w=y(e,n),E=_.get(w);if(E)r(t,n,E);else{var T=x?x(k,w,n+"",t,e,_):void 0,C=void 0===T;if(C){var S=u(w),A=!S&&h(w),M=!S&&!A&&g(w);T=w,S||A||M?u(k)?T=k:l(k)?T=o(k):A?(C=!1,T=i(w,!0)):M?(C=!1,T=a(w,!0)):T=[]:p(w)||c(w)?(T=k,c(k)?T=v(k):d(k)&&!f(k)||(T=s(w))):C=!1}C&&(_.set(w,T),b(T,w,m,x,_),_.delete(w)),r(t,n,T)}}},function(t,e,n){var r=n(46),i=n(40);t.exports=function(t){return r(t,i(t))}},function(t,e,n){var r=n(67),i=n(68);t.exports=function(t){return r((function(e,n){var r=-1,a=n.length,o=a>1?n[a-1]:void 0,s=a>2?n[2]:void 0;for(o=t.length>3&&"function"==typeof o?(a--,o):void 0,s&&i(n[0],n[1],s)&&(o=a<3?void 0:o,a=1),e=Object(e);++r1&&o(t,e[0],e[1])?e=[]:n>2&&o(e[0],e[1],e[2])&&(e=[e[0]]),i(t,r(e,1),[])}));t.exports=s},function(t,e,n){var r=n(66),i=n(25),a=n(141),o=n(340),s=n(61),c=n(341),u=n(35);t.exports=function(t,e,n){var l=-1;e=r(e.length?e:[u],s(i));var h=a(t,(function(t,n,i){return{criteria:r(e,(function(e){return e(t)})),index:++l,value:t}}));return o(h,(function(t,e){return c(t,e,n)}))}},function(t,e){t.exports=function(t,e){var n=t.length;for(t.sort(e);n--;)t[n]=t[n].value;return t}},function(t,e,n){var r=n(342);t.exports=function(t,e,n){for(var i=-1,a=t.criteria,o=e.criteria,s=a.length,c=n.length;++i=c?u:u*("desc"==n[i]?-1:1)}return t.index-e.index}},function(t,e,n){var r=n(42);t.exports=function(t,e){if(t!==e){var n=void 0!==t,i=null===t,a=t==t,o=r(t),s=void 0!==e,c=null===e,u=e==e,l=r(e);if(!c&&!l&&!o&&t>e||o&&s&&u&&!c&&!l||i&&s&&u||!n&&u||!a)return 1;if(!i&&!o&&!l&&t0;--c)if(r=e[c].dequeue()){i=i.concat(s(t,e,n,r,!0));break}}return i}(n.graph,n.buckets,n.zeroIdx);return r.flatten(r.map(u,(function(e){return t.outEdges(e.v,e.w)})),!0)};var o=r.constant(1);function s(t,e,n,i,a){var o=a?[]:void 0;return r.forEach(t.inEdges(i.v),(function(r){var i=t.edge(r),s=t.node(r.v);a&&o.push({v:r.v,w:r.w}),s.out-=i,c(e,n,s)})),r.forEach(t.outEdges(i.v),(function(r){var i=t.edge(r),a=r.w,o=t.node(a);o.in-=i,c(e,n,o)})),t.removeNode(i.v),o}function c(t,e,n){n.out?n.in?t[n.out-n.in+e].enqueue(n):t[t.length-1].enqueue(n):t[0].enqueue(n)}},function(t,e){function n(){var t={};t._next=t._prev=t,this._sentinel=t}function r(t){t._prev._next=t._next,t._next._prev=t._prev,delete t._next,delete t._prev}function i(t,e){if("_next"!==t&&"_prev"!==t)return e}t.exports=n,n.prototype.dequeue=function(){var t=this._sentinel,e=t._prev;if(e!==t)return r(e),e},n.prototype.enqueue=function(t){var e=this._sentinel;t._prev&&t._next&&r(t),t._next=e._next,e._next._prev=t,e._next=t,t._prev=e},n.prototype.toString=function(){for(var t=[],e=this._sentinel,n=e._prev;n!==e;)t.push(JSON.stringify(n,i)),n=n._prev;return"["+t.join(", ")+"]"}},function(t,e,n){"use strict";var r=n(4),i=n(8);t.exports={run:function(t){t.graph().dummyChains=[],r.forEach(t.edges(),(function(e){!function(t,e){var n,r,a,o=e.v,s=t.node(o).rank,c=e.w,u=t.node(c).rank,l=e.name,h=t.edge(e),f=h.labelRank;if(u===s+1)return;for(t.removeEdge(e),a=0,++s;sc.lim&&(u=c,l=!0);var h=r.filter(e.edges(),(function(e){return l===m(t,t.node(e.v),u)&&l!==m(t,t.node(e.w),u)}));return r.minBy(h,(function(t){return a(e,t)}))}function v(t,e,n,i){var a=n.v,o=n.w;t.removeEdge(a,o),t.setEdge(i.v,i.w,{}),d(t),h(t,e),function(t,e){var n=r.find(t.nodes(),(function(t){return!e.node(t).parent})),i=s(t,n);i=i.slice(1),r.forEach(i,(function(n){var r=t.node(n).parent,i=e.edge(n,r),a=!1;i||(i=e.edge(r,n),a=!0),e.node(n).rank=e.node(r).rank+(a?i.minlen:-i.minlen)}))}(t,e)}function m(t,e,n){return n.low<=e.lim&&e.lim<=n.lim}t.exports=l,l.initLowLimValues=d,l.initCutValues=h,l.calcCutValue=f,l.leaveEdge=g,l.enterEdge=y,l.exchangeEdges=v},function(t,e,n){var r=n(4);t.exports=function(t){var e=function(t){var e={},n=0;function i(a){var o=n;r.forEach(t.children(a),i),e[a]={low:o,lim:n++}}return r.forEach(t.children(),i),e}(t);r.forEach(t.graph().dummyChains,(function(n){for(var r=t.node(n),i=r.edgeObj,a=function(t,e,n,r){var i,a,o=[],s=[],c=Math.min(e[n].low,e[r].low),u=Math.max(e[n].lim,e[r].lim);i=n;do{i=t.parent(i),o.push(i)}while(i&&(e[i].low>c||u>e[i].lim));a=i,i=r;for(;(i=t.parent(i))!==a;)s.push(i);return{path:o.concat(s.reverse()),lca:a}}(t,e,i.v,i.w),o=a.path,s=a.lca,c=0,u=o[c],l=!0;n!==i.w;){if(r=t.node(n),l){for(;(u=o[c])!==s&&t.node(u).maxRank=2),s=l.buildLayerMatrix(t);var y=a(t,s);y0;)e%2&&(n+=c[e+1]),c[e=e-1>>1]+=t.weight;u+=t.weight*n}))),u}t.exports=function(t,e){for(var n=0,r=1;r=t.barycenter)&&function(t,e){var n=0,r=0;t.weight&&(n+=t.barycenter*t.weight,r+=t.weight);e.weight&&(n+=e.barycenter*e.weight,r+=e.weight);t.vs=e.vs.concat(t.vs),t.barycenter=n/r,t.weight=r,t.i=Math.min(e.i,t.i),e.merged=!0}(t,e)}}function i(e){return function(n){n.in.push(e),0==--n.indegree&&t.push(n)}}for(;t.length;){var a=t.pop();e.push(a),r.forEach(a.in.reverse(),n(a)),r.forEach(a.out,i(a))}return r.map(r.filter(e,(function(t){return!t.merged})),(function(t){return r.pick(t,["vs","i","barycenter","weight"])}))}(r.filter(n,(function(t){return!t.indegree})))}},function(t,e,n){var r=n(4),i=n(8);function a(t,e,n){for(var i;e.length&&(i=r.last(e)).i<=n;)e.pop(),t.push(i.vs),n++;return n}t.exports=function(t,e){var n=i.partition(t,(function(t){return r.has(t,"barycenter")})),o=n.lhs,s=r.sortBy(n.rhs,(function(t){return-t.i})),c=[],u=0,l=0,h=0;o.sort((f=!!e,function(t,e){return t.barycentere.barycenter?1:f?e.i-t.i:t.i-e.i})),h=a(c,s,h),r.forEach(o,(function(t){h+=t.vs.length,c.push(t.vs),u+=t.barycenter*t.weight,l+=t.weight,h=a(c,s,h)}));var f;var d={vs:r.flatten(c,!0)};l&&(d.barycenter=u/l,d.weight=l);return d}},function(t,e,n){var r=n(4),i=n(17).Graph;t.exports=function(t,e,n){var a=function(t){var e;for(;t.hasNode(e=r.uniqueId("_root")););return e}(t),o=new i({compound:!0}).setGraph({root:a}).setDefaultNodeLabel((function(e){return t.node(e)}));return r.forEach(t.nodes(),(function(i){var s=t.node(i),c=t.parent(i);(s.rank===e||s.minRank<=e&&e<=s.maxRank)&&(o.setNode(i),o.setParent(i,c||a),r.forEach(t[n](i),(function(e){var n=e.v===i?e.w:e.v,a=o.edge(n,i),s=r.isUndefined(a)?0:a.weight;o.setEdge(n,i,{weight:t.edge(e).weight+s})})),r.has(s,"minRank")&&o.setNode(i,{borderLeft:s.borderLeft[e],borderRight:s.borderRight[e]}))})),o}},function(t,e,n){var r=n(4);t.exports=function(t,e,n){var i,a={};r.forEach(n,(function(n){for(var r,o,s=t.parent(n);s;){if((r=t.parent(s))?(o=a[r],a[r]=s):(o=i,i=s),o&&o!==s)return void e.setEdge(o,s);s=r}}))}},function(t,e,n){"use strict";var r=n(4),i=n(8),a=n(365).positionX;t.exports=function(t){(function(t){var e=i.buildLayerMatrix(t),n=t.graph().ranksep,a=0;r.forEach(e,(function(e){var i=r.max(r.map(e,(function(e){return t.node(e).height})));r.forEach(e,(function(e){t.node(e).y=a+i/2})),a+=i+n}))})(t=i.asNonCompoundGraph(t)),r.forEach(a(t),(function(e,n){t.node(n).x=e}))}},function(t,e,n){"use strict";var r=n(4),i=n(17).Graph,a=n(8);function o(t,e){var n={};return r.reduce(e,(function(e,i){var a=0,o=0,s=e.length,u=r.last(i);return r.forEach(i,(function(e,l){var h=function(t,e){if(t.node(e).dummy)return r.find(t.predecessors(e),(function(e){return t.node(e).dummy}))}(t,e),f=h?t.node(h).order:s;(h||e===u)&&(r.forEach(i.slice(o,l+1),(function(e){r.forEach(t.predecessors(e),(function(r){var i=t.node(r),o=i.order;!(os)&&c(n,e,u)}))}))}return r.reduce(e,(function(e,n){var a,o=-1,s=0;return r.forEach(n,(function(r,c){if("border"===t.node(r).dummy){var u=t.predecessors(r);u.length&&(a=t.node(u[0]).order,i(n,s,c,o,a),s=c,o=a)}i(n,s,n.length,a,e.length)})),n})),n}function c(t,e,n){if(e>n){var r=e;e=n,n=r}var i=t[e];i||(t[e]=i={}),i[n]=!0}function u(t,e,n){if(e>n){var i=e;e=n,n=i}return r.has(t[e],n)}function l(t,e,n,i){var a={},o={},s={};return r.forEach(e,(function(t){r.forEach(t,(function(t,e){a[t]=t,o[t]=t,s[t]=e}))})),r.forEach(e,(function(t){var e=-1;r.forEach(t,(function(t){var c=i(t);if(c.length)for(var l=((c=r.sortBy(c,(function(t){return s[t]}))).length-1)/2,h=Math.floor(l),f=Math.ceil(l);h<=f;++h){var d=c[h];o[t]===t&&e0}t.exports=function(t,e,r,i){var a,o,s,c,u,l,h,f,d,p,g,y,v;if(a=e.y-t.y,s=t.x-e.x,u=e.x*t.y-t.x*e.y,d=a*r.x+s*r.y+u,p=a*i.x+s*i.y+u,0!==d&&0!==p&&n(d,p))return;if(o=i.y-r.y,c=r.x-i.x,l=i.x*r.y-r.x*i.y,h=o*t.x+c*t.y+l,f=o*e.x+c*e.y+l,0!==h&&0!==f&&n(h,f))return;if(0===(g=a*c-o*s))return;return y=Math.abs(g/2),{x:(v=s*l-c*u)<0?(v-y)/g:(v+y)/g,y:(v=o*u-a*l)<0?(v-y)/g:(v+y)/g}}},function(t,e,n){var r=n(43),i=n(31),a=n(153).layout;t.exports=function(){var t=n(371),e=n(374),i=n(375),u=n(376),l=n(377),h=n(378),f=n(379),d=n(380),p=n(381),g=function(n,g){!function(t){t.nodes().forEach((function(e){var n=t.node(e);r.has(n,"label")||t.children(e).length||(n.label=e),r.has(n,"paddingX")&&r.defaults(n,{paddingLeft:n.paddingX,paddingRight:n.paddingX}),r.has(n,"paddingY")&&r.defaults(n,{paddingTop:n.paddingY,paddingBottom:n.paddingY}),r.has(n,"padding")&&r.defaults(n,{paddingLeft:n.padding,paddingRight:n.padding,paddingTop:n.padding,paddingBottom:n.padding}),r.defaults(n,o),r.each(["paddingLeft","paddingRight","paddingTop","paddingBottom"],(function(t){n[t]=Number(n[t])})),r.has(n,"width")&&(n._prevWidth=n.width),r.has(n,"height")&&(n._prevHeight=n.height)})),t.edges().forEach((function(e){var n=t.edge(e);r.has(n,"label")||(n.label=""),r.defaults(n,s)}))}(g);var y=c(n,"output"),v=c(y,"clusters"),m=c(y,"edgePaths"),b=i(c(y,"edgeLabels"),g),x=t(c(y,"nodes"),g,d);a(g),l(x,g),h(b,g),u(m,g,p);var _=e(v,g);f(_,g),function(t){r.each(t.nodes(),(function(e){var n=t.node(e);r.has(n,"_prevWidth")?n.width=n._prevWidth:delete n.width,r.has(n,"_prevHeight")?n.height=n._prevHeight:delete n.height,delete n._prevWidth,delete n._prevHeight}))}(g)};return g.createNodes=function(e){return arguments.length?(t=e,g):t},g.createClusters=function(t){return arguments.length?(e=t,g):e},g.createEdgeLabels=function(t){return arguments.length?(i=t,g):i},g.createEdgePaths=function(t){return arguments.length?(u=t,g):u},g.shapes=function(t){return arguments.length?(d=t,g):d},g.arrows=function(t){return arguments.length?(p=t,g):p},g};var o={paddingLeft:10,paddingRight:10,paddingTop:10,paddingBottom:10,rx:0,ry:0,shape:"rect"},s={arrowhead:"normal",curve:i.curveLinear};function c(t,e){var n=t.select("g."+e);return n.empty()&&(n=t.append("g").attr("class",e)),n}},function(t,e,n){"use strict";var r=n(43),i=n(97),a=n(12),o=n(31);t.exports=function(t,e,n){var s,c=e.nodes().filter((function(t){return!a.isSubgraph(e,t)})),u=t.selectAll("g.node").data(c,(function(t){return t})).classed("update",!0);u.exit().remove(),u.enter().append("g").attr("class","node").style("opacity",0),(u=t.selectAll("g.node")).each((function(t){var s=e.node(t),c=o.select(this);a.applyClass(c,s.class,(c.classed("update")?"update ":"")+"node"),c.select("g.label").remove();var u=c.append("g").attr("class","label"),l=i(u,s),h=n[s.shape],f=r.pick(l.node().getBBox(),"width","height");s.elem=this,s.id&&c.attr("id",s.id),s.labelId&&u.attr("id",s.labelId),r.has(s,"width")&&(f.width=s.width),r.has(s,"height")&&(f.height=s.height),f.width+=s.paddingLeft+s.paddingRight,f.height+=s.paddingTop+s.paddingBottom,u.attr("transform","translate("+(s.paddingLeft-s.paddingRight)/2+","+(s.paddingTop-s.paddingBottom)/2+")");var d=o.select(this);d.select(".label-container").remove();var p=h(d,f,s).classed("label-container",!0);a.applyStyle(p,s.style);var g=p.node().getBBox();s.width=g.width,s.height=g.height})),s=u.exit?u.exit():u.selectAll(null);return a.applyTransition(s,e).style("opacity",0).remove(),u}},function(t,e,n){var r=n(12);t.exports=function(t,e){for(var n=t.append("text"),i=function(t){for(var e,n="",r=!1,i=0;i0&&void 0!==arguments[0]?arguments[0]:"fatal";isNaN(t)&&(t=t.toLowerCase(),void 0!==h[t]&&(t=h[t])),f.trace=function(){},f.debug=function(){},f.info=function(){},f.warn=function(){},f.error=function(){},f.fatal=function(){},t<=h.fatal&&(f.fatal=console.error?console.error.bind(console,p("FATAL"),"color: orange"):console.log.bind(console,"",p("FATAL"))),t<=h.error&&(f.error=console.error?console.error.bind(console,p("ERROR"),"color: orange"):console.log.bind(console,"",p("ERROR"))),t<=h.warn&&(f.warn=console.warn?console.warn.bind(console,p("WARN"),"color: orange"):console.log.bind(console,"",p("WARN"))),t<=h.info&&(f.info=console.info?console.info.bind(console,p("INFO"),"color: lightblue"):console.log.bind(console,"",p("INFO"))),t<=h.debug&&(f.debug=console.debug?console.debug.bind(console,p("DEBUG"),"color: lightgreen"):console.log.bind(console,"",p("DEBUG")))},p=function(t){var e=l()().format("ss.SSS");return"%c".concat(e," : ").concat(t," : ")},g=n(70),y=function(t){for(var e="",n=0;n>=0;){if(!((n=t.indexOf("=0)){e+=t,n=-1;break}e+=t.substr(0,n),(n=(t=t.substr(n+1)).indexOf("<\/script>"))>=0&&(n+=9,t=t.substr(n))}return e},v=//gi,m=function(t){return t.replace(v,"#br#")},b=function(t){return t.replace(/#br#/g,"
")},x={getRows:function(t){if(!t)return 1;var e=m(t);return(e=e.replace(/\\n/g,"#br#")).split("#br#")},sanitizeText:function(t,e){var n=t,r=!0;if(!e.flowchart||!1!==e.flowchart.htmlLabels&&"false"!==e.flowchart.htmlLabels||(r=!1),r){var i=e.securityLevel;"antiscript"===i?n=y(n):"loose"!==i&&(n=(n=(n=m(n)).replace(//g,">")).replace(/=/g,"="),n=b(n))}return n},hasBreaks:function(t){return//gi.test(t)},splitBreaks:function(t){return t.split(//gi)},lineBreakRegex:v,removeScript:y};function _(t){return(_="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t})(t)}function k(t){return function(t){if(Array.isArray(t)){for(var e=0,n=new Array(t.length);e1&&void 0!==arguments[1]?arguments[1]:null;try{var n=new RegExp("[%]{2}(?![{]".concat(T.source,")(?=[}][%]{2}).*\n"),"ig");t=t.trim().replace(n,"").replace(/'/gm,'"'),f.debug("Detecting diagram directive".concat(null!==e?" type:"+e:""," based on the text:").concat(t));for(var r,i=[];null!==(r=E.exec(t));)if(r.index===E.lastIndex&&E.lastIndex++,r&&!e||e&&r[1]&&r[1].match(e)||e&&r[2]&&r[2].match(e)){var a=r[1]?r[1]:r[2],o=r[3]?r[3].trim():r[4]?JSON.parse(r[4].trim()):null;i.push({type:a,args:o})}return 0===i.length&&i.push({type:t,args:null}),1===i.length?i[0]:i}catch(n){return f.error("ERROR: ".concat(n.message," - Unable to parse directive").concat(null!==e?" type:"+e:""," based on the text:").concat(t)),{type:null,args:null}}},A=function(t){return t=t.replace(E,"").replace(C,"\n"),f.debug("Detecting diagram type based on the text "+t),t.match(/^\s*sequenceDiagram/)?"sequence":t.match(/^\s*gantt/)?"gantt":t.match(/^\s*classDiagram-v2/)?"classDiagram":t.match(/^\s*classDiagram/)?"class":t.match(/^\s*stateDiagram-v2/)?"stateDiagram":t.match(/^\s*stateDiagram/)?"state":t.match(/^\s*gitGraph/)?"git":t.match(/^\s*flowchart/)?"flowchart-v2":t.match(/^\s*info/)?"info":t.match(/^\s*pie/)?"pie":t.match(/^\s*erDiagram/)?"er":t.match(/^\s*journey/)?"journey":"flowchart"},M=function(t,e){var n={};return function(){for(var r=arguments.length,i=new Array(r),a=0;a"},n),x.lineBreakRegex.test(t))return t;var r=t.split(" "),i=[],a="";return r.forEach((function(t,o){var s=Y("".concat(t," "),n),c=Y(a,n);if(s>e){var u=R(t,e,"-",n),l=u.hyphenatedStrings,h=u.remainingWord;i.push.apply(i,[a].concat(k(l))),a=h}else c+s>=e?(i.push(a),a=t):a=[a,t].filter(Boolean).join(" ");o+1===r.length&&i.push(a)})),i.filter((function(t){return""!==t})).join(n.joinWith)}),(function(t,e,n){return"".concat(t,"-").concat(e,"-").concat(n.fontSize,"-").concat(n.fontWeight,"-").concat(n.fontFamily,"-").concat(n.joinWith)})),R=M((function(t,e){var n=arguments.length>2&&void 0!==arguments[2]?arguments[2]:"-",r=arguments.length>3?arguments[3]:void 0;r=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial",margin:0},r);var i=t.split(""),a=[],o="";return i.forEach((function(t,s){var c="".concat(o).concat(t);if(Y(c,r)>=e){var u=s+1,l=i.length===u,h="".concat(c).concat(n);a.push(l?c:h),o=""}else o=c})),{hyphenatedStrings:a,remainingWord:o}}),(function(t,e){var n=arguments.length>2&&void 0!==arguments[2]?arguments[2]:"-",r=arguments.length>3?arguments[3]:void 0;return"".concat(t,"-").concat(e,"-").concat(n,"-").concat(r.fontSize,"-").concat(r.fontWeight,"-").concat(r.fontFamily)})),Y=function(t,e){return e=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial"},e),z(t,e).width},z=M((function(t,e){var n=e=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial"},e),r=n.fontSize,i=n.fontFamily,a=n.fontWeight;if(!t)return{width:0,height:0};var o=["sans-serif",i],c=t.split(x.lineBreakRegex),u=[],l=Object(s.select)("body");if(!l.remove)return{width:0,height:0,lineHeight:0};for(var h=l.append("svg"),f=0,d=o;fu[1].height&&u[0].width>u[1].width&&u[0].lineHeight>u[1].lineHeight?0:1]}),(function(t,e){return"".concat(t,"-").concat(e.fontSize,"-").concat(e.fontWeight,"-").concat(e.fontFamily)})),U=function(t,e,n){var r=new Map;return r.set("height",t),n?(r.set("width","100%"),r.set("style","max-width: ".concat(e,"px;"))):r.set("width",e),r},$=function(t,e,n,r){!function(t,e){var n=!0,r=!1,i=void 0;try{for(var a,o=e[Symbol.iterator]();!(n=(a=o.next()).done);n=!0){var s=a.value;t.attr(s[0],s[1])}}catch(t){r=!0,i=t}finally{try{n||null==o.return||o.return()}finally{if(r)throw i}}}(t,U(e,n,r))},W={assignWithDepth:P,wrapLabel:j,calculateTextHeight:function(t,e){return e=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial",margin:15},e),z(t,e).height},calculateTextWidth:Y,calculateTextDimensions:z,calculateSvgSizeAttrs:U,configureSvgSize:$,detectInit:function(t){var e=S(t,/(?:init\b)|(?:initialize\b)/),n={};if(Array.isArray(e)){var r=e.map((function(t){return t.args}));n=P(n,k(r))}else n=e.args;if(n){var i=A(t);["config"].forEach((function(t){void 0!==n[t]&&("flowchart-v2"===i&&(i="flowchart"),n[i]=n[t],delete n[t])}))}return n},detectDirective:S,detectType:A,isSubstringInArray:function(t,e){for(var n=0;n=1&&(i={x:t.x,y:t.y}),a>0&&a<1&&(i={x:(1-a)*e.x+a*t.x,y:(1-a)*e.y+a*t.y})}}e=t})),i}(t)},calcCardinalityPosition:function(t,e,n){var r;f.info("our points",e),e[0]!==n&&(e=e.reverse()),e.forEach((function(t){D(t,r),r=t}));var i,a=25;r=void 0,e.forEach((function(t){if(r&&!i){var e=D(t,r);if(e=1&&(i={x:t.x,y:t.y}),n>0&&n<1&&(i={x:(1-n)*r.x+n*t.x,y:(1-n)*r.y+n*t.y})}}r=t}));var o=t?10:5,s=Math.atan2(e[0].y-i.y,e[0].x-i.x),c={x:0,y:0};return c.x=Math.sin(s)*o+(e[0].x+i.x)/2,c.y=-Math.cos(s)*o+(e[0].y+i.y)/2,c},calcTerminalLabelPosition:function(t,e,n){var r,i=JSON.parse(JSON.stringify(n));f.info("our points",i),"start_left"!==e&&"start_right"!==e&&(i=i.reverse()),i.forEach((function(t){D(t,r),r=t}));var a,o=25;r=void 0,i.forEach((function(t){if(r&&!a){var e=D(t,r);if(e=1&&(a={x:t.x,y:t.y}),n>0&&n<1&&(a={x:(1-n)*r.x+n*t.x,y:(1-n)*r.y+n*t.y})}}r=t}));var s=10,c=Math.atan2(i[0].y-a.y,i[0].x-a.x),u={x:0,y:0};return u.x=Math.sin(c)*s+(i[0].x+a.x)/2,u.y=-Math.cos(c)*s+(i[0].y+a.y)/2,"start_left"===e&&(u.x=Math.sin(c+Math.PI)*s+(i[0].x+a.x)/2,u.y=-Math.cos(c+Math.PI)*s+(i[0].y+a.y)/2),"end_right"===e&&(u.x=Math.sin(c-Math.PI)*s+(i[0].x+a.x)/2-5,u.y=-Math.cos(c-Math.PI)*s+(i[0].y+a.y)/2-5),"end_left"===e&&(u.x=Math.sin(c)*s+(i[0].x+a.x)/2-5,u.y=-Math.cos(c)*s+(i[0].y+a.y)/2-5),u},formatUrl:function(t,e){var n=t.trim();if(n)return"loose"!==e.securityLevel?Object(g.sanitizeUrl)(n):n},getStylesFromArray:N,generateId:L,random:F,memoize:M,runFunc:function(t){for(var e,n=t.split("."),r=n.length-1,i=n[r],a=window,o=0;o1?s-1:0),u=1;u=0&&(n=!0)})),n},Gt=function(t,e){var n=[];return t.nodes.forEach((function(r,i){Ht(e,r)||n.push(t.nodes[i])})),{nodes:n}},qt={parseDirective:function(t,e,n){$o.parseDirective(this,t,e,n)},defaultConfig:function(){return pt.flowchart},addVertex:function(t,e,n,r,i){var a,o=t;void 0!==o&&0!==o.trim().length&&(void 0===Mt[o]&&(Mt[o]={id:o,domId:"flowchart-"+o+"-"+St,styles:[],classes:[]}),St++,void 0!==e?(At=xt(),'"'===(a=x.sanitizeText(e.trim(),At))[0]&&'"'===a[a.length-1]&&(a=a.substring(1,a.length-1)),Mt[o].text=a):void 0===Mt[o].text&&(Mt[o].text=t),void 0!==n&&(Mt[o].type=n),null!=r&&r.forEach((function(t){Mt[o].styles.push(t)})),null!=i&&i.forEach((function(t){Mt[o].classes.push(t)})))},lookUpDomId:jt,addLink:function(t,e,n,r){var i,a;for(i=0;i/)&&(Tt="LR"),Tt.match(/.*v/)&&(Tt="TB")},setClass:Yt,getTooltip:function(t){return Lt[t]},setClickEvent:function(t,e,n){t.split(",").forEach((function(t){!function(t,e){var n=jt(t);"loose"===xt().securityLevel&&void 0!==e&&void 0!==Mt[t]&&(Mt[t].haveCallback=!0,It.push((function(){var r=document.querySelector('[id="'.concat(n,'"]'));null!==r&&r.addEventListener("click",(function(){W.runFunc(e,t)}),!1)})))}(t,e)})),zt(t,n),Yt(t,"clickable")},setLink:function(t,e,n,r){t.split(",").forEach((function(t){void 0!==Mt[t]&&(Mt[t].link=W.formatUrl(e,At),Mt[t].linkTarget=r)})),zt(t,n),Yt(t,"clickable")},bindFunctions:function(t){It.forEach((function(e){e(t)}))},getDirection:function(){return Tt.trim()},getVertices:function(){return Mt},getEdges:function(){return Ot},getClasses:function(){return Dt},clear:function(t){Mt={},Dt={},Ot=[],(It=[]).push(Ut),Nt=[],Bt={},Ft=0,Lt=[],Pt=!0,Ct=t||"gen-1"},setGen:function(t){Ct=t||"gen-1"},defaultStyle:function(){return"fill:#ffa;stroke: #f66; stroke-width: 3px; stroke-dasharray: 5, 5;fill:#ffa;stroke: #666;"},addSubGraph:function(t,e,n){var r=t.trim(),i=n;t===n&&n.match(/\s/)&&(r=void 0);var a,o,s,c=[];if(a=c.concat.apply(c,e),o={boolean:{},number:{},string:{}},s=[],c=a.filter((function(t){var e=Et(t);return""!==t.trim()&&(e in o?!o[e].hasOwnProperty(t)&&(o[e][t]=!0):!(s.indexOf(t)>=0)&&s.push(t))})),"gen-1"===Ct){f.warn("LOOKING UP");for(var u=0;u0&&function t(e,n){var r=Nt[n].nodes;if(!((Wt+=1)>2e3)){if(Vt[Wt]=n,Nt[n].id===e)return{result:!0,count:0};for(var i=0,a=1;i=0){var s=t(e,o);if(s.result)return{result:!0,count:a+s.count};a+=s.count}i+=1}return{result:!1,count:a}}}("none",Nt.length-1)},getSubGraphs:function(){return Nt},destructLink:function(t,e){var n,r=function(t){var e=t.trim(),n=e.slice(0,-1),r="arrow_open";switch(e.slice(-1)){case"x":r="arrow_cross","x"===e[0]&&(r="double_"+r,n=n.slice(1));break;case">":r="arrow_point","<"===e[0]&&(r="double_"+r,n=n.slice(1));break;case"o":r="arrow_circle","o"===e[0]&&(r="double_"+r,n=n.slice(1))}var i="normal",a=n.length-1;"="===n[0]&&(i="thick");var o=function(t,e){for(var n=e.length,r=0,i=0;in.height/2-a)){var o=a*a*(1-r*r/(i*i));0!=o&&(o=Math.sqrt(o)),o=a-o,t.y-n.y>0&&(o=-o),e.y+=o}return e},c}function fe(t,e,n,r){return t.insert("polygon",":first-child").attr("points",r.map((function(t){return t.x+","+t.y})).join(" ")).attr("transform","translate("+-e/2+","+n/2+")")}var de={addToRender:function(t){t.shapes().question=ee,t.shapes().hexagon=ne,t.shapes().stadium=ue,t.shapes().subroutine=le,t.shapes().cylinder=he,t.shapes().rect_left_inv_arrow=re,t.shapes().lean_right=ie,t.shapes().lean_left=ae,t.shapes().trapezoid=oe,t.shapes().inv_trapezoid=se,t.shapes().rect_right_inv_arrow=ce},addToRenderV2:function(t){t({question:ee}),t({hexagon:ne}),t({stadium:ue}),t({subroutine:le}),t({cylinder:he}),t({rect_left_inv_arrow:re}),t({lean_right:ie}),t({lean_left:ae}),t({trapezoid:oe}),t({inv_trapezoid:se}),t({rect_right_inv_arrow:ce})}},pe={},ge=function(t,e,n){var r=Object(s.select)('[id="'.concat(n,'"]'));Object.keys(t).forEach((function(n){var i=t[n],a="default";i.classes.length>0&&(a=i.classes.join(" "));var o,s=N(i.styles),c=void 0!==i.text?i.text:i.id;if(xt().flowchart.htmlLabels){var u={label:c.replace(/fa[lrsb]?:fa-[\w-]+/g,(function(t){return"")}))};(o=te()(r,u).node()).parentNode.removeChild(o)}else{var l=document.createElementNS("http://www.w3.org/2000/svg","text");l.setAttribute("style",s.labelStyle.replace("color:","fill:"));for(var h=c.split(x.lineBreakRegex),d=0;d').concat(a.text,"")):(l.labelType="text",l.label=a.text.replace(x.lineBreakRegex,"\n"),void 0===a.style&&(l.style=l.style||"stroke: #333; stroke-width: 1.5px;fill:none"),l.labelStyle=l.labelStyle.replace("color:","fill:"))),l.id=o,l.class=c+" "+u,l.minlen=a.length||1,e.setEdge(qt.lookUpDomId(a.start),qt.lookUpDomId(a.end),l,i)}))},ve=function(t){for(var e=Object.keys(t),n=0;n=0;h--)i=l[h],qt.addVertex(i.id,i.title,"group",void 0,i.classes);var d=qt.getVertices();f.warn("Get vertices",d);var p=qt.getEdges(),g=0;for(g=l.length-1;g>=0;g--){i=l[g],Object(s.selectAll)("cluster").append("text");for(var y=0;y"),f.info("vertexText"+i),function(t){var e,n,r=Object(s.select)(document.createElementNS("http://www.w3.org/2000/svg","foreignObject")),i=r.append("xhtml:div"),a=t.label,o=t.isNode?"nodeLabel":"edgeLabel";return i.html(''+a+""),e=i,(n=t.labelStyle)&&e.attr("style",n),i.style("display","inline-block"),i.style("white-space","nowrap"),i.attr("xmlns","http://www.w3.org/1999/xhtml"),r.node()}({isNode:r,label:i.replace(/fa[lrsb]?:fa-[\w-]+/g,(function(t){return"")}))});var a=document.createElementNS("http://www.w3.org/2000/svg","text");a.setAttribute("style",e.replace("color:","fill:"));var o=[];o="string"==typeof i?i.split(/\\n|\n|/gi):Array.isArray(i)?i:[];for(var c=0;c0)t(a,n,r,i);else{var o=n.node(a);f.info("cp ",a," to ",i," with parent ",e),r.setNode(a,o),i!==n.parent(a)&&(f.warn("Setting parent",a,n.parent(a)),r.setParent(a,n.parent(a))),e!==i&&a!==e?(f.debug("Setting parent",a,e),r.setParent(a,e)):(f.info("In copy ",e,"root",i,"data",n.node(e),i),f.debug("Not Setting parent for node=",a,"cluster!==rootId",e!==i,"node!==clusterId",a!==e));var s=n.edges(a);f.debug("Copying Edges",s),s.forEach((function(t){f.info("Edge",t);var a=n.edge(t.v,t.w,t.name);f.info("Edge data",a,i);try{!function(t,e){return f.info("Decendants of ",e," is ",Me[e]),f.info("Edge is ",t),t.v!==e&&(t.w!==e&&(Me[e]?(f.info("Here "),Me[e].indexOf(t.v)>=0||(!!De(t.v,e)||(!!De(t.w,e)||Me[e].indexOf(t.w)>=0))):(f.debug("Tilt, ",e,",not in decendants"),!1)))}(t,i)?f.info("Skipping copy of edge ",t.v,"--\x3e",t.w," rootId: ",i," clusterId:",e):(f.info("Copying as ",t.v,t.w,a,t.name),r.setEdge(t.v,t.w,a,t.name),f.info("newGraph edges ",r.edges(),r.edge(r.edges()[0])))}catch(t){f.error(t)}}))}f.debug("Removing node",a),n.removeNode(a)}))},Be=function t(e,n){f.trace("Searching",e);var r=n.children(e);if(f.trace("Searching children of id ",e,r),r.length<1)return f.trace("This is a valid node",e),e;for(var i=0;i ",a),a}},Le=function(t){return Ae[t]&&Ae[t].externalConnections&&Ae[t]?Ae[t].id:t},Fe=function(t,e){!t||e>10?f.debug("Opting out, no graph "):(f.debug("Opting in, graph "),t.nodes().forEach((function(e){t.children(e).length>0&&(f.warn("Cluster identified",e," Replacement id in edges: ",Be(e,t)),Me[e]=function t(e,n){for(var r=n.children(e),i=[].concat(r),a=0;a0?(f.debug("Cluster identified",e,Me),r.forEach((function(t){t.v!==e&&t.w!==e&&(De(t.v,e)^De(t.w,e)&&(f.warn("Edge: ",t," leaves cluster ",e),f.warn("Decendants of XXX ",e,": ",Me[e]),Ae[e].externalConnections=!0))}))):f.debug("Not a cluster ",e,Me)})),t.edges().forEach((function(e){var n=t.edge(e);f.warn("Edge "+e.v+" -> "+e.w+": "+JSON.stringify(e)),f.warn("Edge "+e.v+" -> "+e.w+": "+JSON.stringify(t.edge(e)));var r=e.v,i=e.w;f.warn("Fix XXX",Ae,"ids:",e.v,e.w,"Translateing: ",Ae[e.v]," --- ",Ae[e.w]),(Ae[e.v]||Ae[e.w])&&(f.warn("Fixing and trixing - removing XXX",e.v,e.w,e.name),r=Le(e.v),i=Le(e.w),t.removeEdge(e.v,e.w,e.name),r!==e.v&&(n.fromCluster=e.v),i!==e.w&&(n.toCluster=e.w),f.warn("Fix Replacing with XXX",r,i,e.name),t.setEdge(r,i,n,e.name))})),f.warn("Adjusted Graph",H.a.json.write(t)),Pe(t,0),f.trace(Ae))},Pe=function t(e,n){if(f.warn("extractor - ",n,H.a.json.write(e),e.children("D")),n>10)f.error("Bailing out");else{for(var r=e.nodes(),i=!1,a=0;a0}if(i){f.debug("Nodes = ",r,n);for(var c=0;c0){f.warn("Cluster without external connections, without a parent and with children",u,n);var l=e.graph(),h=new H.a.Graph({multigraph:!0,compound:!0}).setGraph({rankdir:"TB"===l.rankdir?"LR":"TB",nodesep:50,ranksep:50,marginx:8,marginy:8}).setDefaultEdgeLabel((function(){return{}}));f.warn("Old graph before copy",H.a.json.write(e)),Ne(u,e,h,u),e.setNode(u,{clusterNode:!0,id:u,clusterData:Ae[u].clusterData,labelText:Ae[u].labelText,graph:h}),f.warn("New graph after copy node: (",u,")",H.a.json.write(h)),f.debug("Old graph after copy",H.a.json.write(e))}else f.warn("Cluster ** ",u," **not meeting the criteria !externalConnections:",!Ae[u].externalConnections," no parent: ",!e.parent(u)," children ",e.children(u)&&e.children(u).length>0,e.children("D"),n),f.debug(Ae);else f.debug("Not a cluster",u,n)}r=e.nodes(),f.warn("New list of nodes",r);for(var d=0;d0}var Ue=function(t,e,n,r){var i,a,o,s,c,u,l,h,f,d,p,g,y;if(i=e.y-t.y,o=t.x-e.x,c=e.x*t.y-t.x*e.y,f=i*n.x+o*n.y+c,d=i*r.x+o*r.y+c,!(0!==f&&0!==d&&ze(f,d)||(a=r.y-n.y,s=n.x-r.x,u=r.x*n.y-n.x*r.y,l=a*t.x+s*t.y+u,h=a*e.x+s*e.y+u,0!==l&&0!==h&&ze(l,h)||0==(p=i*s-a*o))))return g=Math.abs(p/2),{x:(y=o*u-s*c)<0?(y-g)/p:(y+g)/p,y:(y=a*c-i*u)<0?(y-g)/p:(y+g)/p}},$e=function(t,e,n){var r=t.x,i=t.y,a=[],o=Number.POSITIVE_INFINITY,s=Number.POSITIVE_INFINITY;"function"==typeof e.forEach?e.forEach((function(t){o=Math.min(o,t.x),s=Math.min(s,t.y)})):(o=Math.min(o,e.x),s=Math.min(s,e.y));for(var c=r-t.width/2-o,u=i-t.height/2-s,l=0;l1&&a.sort((function(t,e){var r=t.x-n.x,i=t.y-n.y,a=Math.sqrt(r*r+i*i),o=e.x-n.x,s=e.y-n.y,c=Math.sqrt(o*o+s*s);return aMath.abs(o)*u?(s<0&&(u=-u),n=0===s?0:u*o/s,r=u):(o<0&&(c=-c),n=c,r=0===o?0:c*s/o),{x:i+n,y:a+r}},Ve={node:n.n(je).a,circle:Ye,ellipse:Re,polygon:$e,rect:We},He=function(t,e){var n=Te(t,e,"node "+e.classes,!0),r=n.shapeSvg,i=n.bbox,a=n.halfPadding;f.info("Classes = ",e.classes);var o=r.insert("rect",":first-child");return o.attr("rx",e.rx).attr("ry",e.ry).attr("x",-i.width/2-a).attr("y",-i.height/2-a).attr("width",i.width+e.padding).attr("height",i.height+e.padding),Ce(e,o),e.intersect=function(t){return Ve.rect(e,t)},r},Ge=[],qe={},Xe=0,Ze=[],Je=function(t){var e="",n=t;if(t.indexOf("~")>0){var r=t.split("~");n=r[0],e=r[1]}return{className:n,type:e}},Qe=function(t){var e=Je(t);void 0===qe[e.className]&&(qe[e.className]={id:e.className,type:e.type,cssClasses:[],methods:[],members:[],annotations:[],domId:"classid-"+e.className+"-"+Xe},Xe++)},Ke=function(t){for(var e=Object.keys(qe),n=0;n>")?r.annotations.push(i.substring(2,i.length-2)):i.indexOf(")")>0?r.methods.push(i):i&&r.members.push(i)}},en=function(t,e){t.split(",").forEach((function(t){var n=t;t[0].match(/\d/)&&(n="classid-"+n),void 0!==qe[n]&&qe[n].cssClasses.push(e)}))},nn=function(t,e,n){var r=xt(),i=t,a=Ke(i);"loose"===r.securityLevel&&void 0!==e&&void 0!==qe[i]&&(n&&(qe[i].tooltip=x.sanitizeText(n,r)),Ze.push((function(){var t=document.querySelector('[id="'.concat(a,'"]'));null!==t&&t.addEventListener("click",(function(){W.runFunc(e,a)}),!1)})))},rn={AGGREGATION:0,EXTENSION:1,COMPOSITION:2,DEPENDENCY:3},an=function(t){var e=Object(s.select)(".mermaidTooltip");null===(e._groups||e)[0][0]&&(e=Object(s.select)("body").append("div").attr("class","mermaidTooltip").style("opacity",0)),Object(s.select)(t).select("svg").selectAll("g.node").on("mouseover",(function(){var t=Object(s.select)(this);if(null!==t.attr("title")){var n=this.getBoundingClientRect();e.transition().duration(200).style("opacity",".9"),e.html(t.attr("title")).style("left",window.scrollX+n.left+(n.right-n.left)/2+"px").style("top",window.scrollY+n.top-14+document.body.scrollTop+"px"),t.classed("hover",!0)}})).on("mouseout",(function(){e.transition().duration(500).style("opacity",0),Object(s.select)(this).classed("hover",!1)}))};Ze.push(an);var on={parseDirective:function(t,e,n){$o.parseDirective(this,t,e,n)},getConfig:function(){return xt().class},addClass:Qe,bindFunctions:function(t){Ze.forEach((function(e){e(t)}))},clear:function(){Ge=[],qe={},(Ze=[]).push(an)},getClass:function(t){return qe[t]},getClasses:function(){return qe},addAnnotation:function(t,e){var n=Je(t).className;qe[n].annotations.push(e)},getRelations:function(){return Ge},addRelation:function(t){f.debug("Adding relation: "+JSON.stringify(t)),Qe(t.id1),Qe(t.id2),t.id1=Je(t.id1).className,t.id2=Je(t.id2).className,Ge.push(t)},addMember:tn,addMembers:function(t,e){Array.isArray(e)&&(e.reverse(),e.forEach((function(e){return tn(t,e)})))},cleanupLabel:function(t){return":"===t.substring(0,1)?t.substr(1).trim():t.trim()},lineType:{LINE:0,DOTTED_LINE:1},relationType:rn,setClickEvent:function(t,e,n){t.split(",").forEach((function(t){nn(t,e,n),qe[t].haveCallback=!0})),en(t,"clickable")},setCssClass:en,setLink:function(t,e,n){var r=xt();t.split(",").forEach((function(t){var i=t;t[0].match(/\d/)&&(i="classid-"+i),void 0!==qe[i]&&(qe[i].link=W.formatUrl(e,r),n&&(qe[i].tooltip=x.sanitizeText(n,r)))})),en(t,"clickable")},lookUpDomId:Ke},sn=0,cn=function(t){var e=t.match(/(\+|-|~|#)?(\w+)(~\w+~|\[\])?\s+(\w+)/),n=t.match(/^([+|\-|~|#])?(\w+) *\( *(.*)\) *(\*|\$)? *(\w*[~|[\]]*\s*\w*~?)$/);return e&&!n?un(e):n?ln(n):hn(t)},un=function(t){var e="";try{e=(t[1]?t[1].trim():"")+(t[2]?t[2].trim():"")+(t[3]?dn(t[3].trim()):"")+" "+(t[4]?t[4].trim():"")}catch(n){e=t}return{displayText:e,cssStyle:""}},ln=function(t){var e="",n="";try{var r=t[1]?t[1].trim():"",i=t[2]?t[2].trim():"",a=t[3]?dn(t[3].trim()):"",o=t[4]?t[4].trim():"";n=r+i+"("+a+")"+(t[5]?" : "+dn(t[5]).trim():""),e=pn(o)}catch(e){n=t}return{displayText:n,cssStyle:e}},hn=function(t){var e="",n="",r="",i=t.indexOf("("),a=t.indexOf(")");if(i>1&&a>i&&a<=t.length){var o="",s="",c=t.substring(0,1);c.match(/\w/)?s=t.substring(0,i).trim():(c.match(/\+|-|~|#/)&&(o=c),s=t.substring(1,i).trim());var u=t.substring(i+1,a),l=t.substring(a+1,1);n=pn(l),e=o+s+"("+dn(u.trim())+")",a<"".length&&""!==(r=t.substring(a+2).trim())&&(r=" : "+dn(r))}else e=dn(t);return{displayText:e,cssStyle:n}},fn=function(t,e,n,r){var i=cn(e),a=t.append("tspan").attr("x",r.padding).text(i.displayText);""!==i.cssStyle&&a.attr("style",i.cssStyle),n||a.attr("dy",r.textHeight)},dn=function t(e){var n=e;return-1!=e.indexOf("~")?t(n=(n=n.replace("~","<")).replace("~",">")):n},pn=function(t){switch(t){case"*":return"font-style:italic;";case"$":return"text-decoration:underline;";default:return""}},gn=function(t,e,n){f.info("Rendering class "+e);var r,i=e.id,a={id:i,label:e.id,width:0,height:0},o=t.append("g").attr("id",Ke(i)).attr("class","classGroup");r=e.link?o.append("svg:a").attr("xlink:href",e.link).attr("target","_blank").append("text").attr("y",n.textHeight+n.padding).attr("x",0):o.append("text").attr("y",n.textHeight+n.padding).attr("x",0);var s=!0;e.annotations.forEach((function(t){var e=r.append("tspan").text("«"+t+"»");s||e.attr("dy",n.textHeight),s=!1}));var c=e.id;void 0!==e.type&&""!==e.type&&(c+="<"+e.type+">");var u=r.append("tspan").text(c).attr("class","title");s||u.attr("dy",n.textHeight);var l=r.node().getBBox().height,h=o.append("line").attr("x1",0).attr("y1",n.padding+l+n.dividerMargin/2).attr("y2",n.padding+l+n.dividerMargin/2),d=o.append("text").attr("x",n.padding).attr("y",l+n.dividerMargin+n.textHeight).attr("fill","white").attr("class","classText");s=!0,e.members.forEach((function(t){fn(d,t,s,n),s=!1}));var p=d.node().getBBox(),g=o.append("line").attr("x1",0).attr("y1",n.padding+l+n.dividerMargin+p.height).attr("y2",n.padding+l+n.dividerMargin+p.height),y=o.append("text").attr("x",n.padding).attr("y",l+2*n.dividerMargin+p.height+n.textHeight).attr("fill","white").attr("class","classText");s=!0,e.methods.forEach((function(t){fn(y,t,s,n),s=!1}));var v=o.node().getBBox(),m=" ";e.cssClasses.length>0&&(m+=e.cssClasses.join(" "));var b=o.insert("rect",":first-child").attr("x",0).attr("y",0).attr("width",v.width+2*n.padding).attr("height",v.height+n.padding+.5*n.dividerMargin).attr("class",m).node().getBBox().width;return r.node().childNodes.forEach((function(t){t.setAttribute("x",(b-t.getBBox().width)/2)})),e.tooltip&&r.insert("title").text(e.tooltip),h.attr("x2",b),g.attr("x2",b),a.width=b,a.height=v.height+n.padding+.5*n.dividerMargin,a},yn=function(t,e,n,r){var i=function(t){switch(t){case rn.AGGREGATION:return"aggregation";case rn.EXTENSION:return"extension";case rn.COMPOSITION:return"composition";case rn.DEPENDENCY:return"dependency"}};e.points=e.points.filter((function(t){return!Number.isNaN(t.y)}));var a,o,c=e.points,u=Object(s.line)().x((function(t){return t.x})).y((function(t){return t.y})).curve(s.curveBasis),l=t.append("path").attr("d",u(c)).attr("id","edge"+sn).attr("class","relation"),h="";r.arrowMarkerAbsolute&&(h=(h=(h=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search).replace(/\(/g,"\\(")).replace(/\)/g,"\\)")),1==n.relation.lineType&&l.attr("class","relation dashed-line"),"none"!==n.relation.type1&&l.attr("marker-start","url("+h+"#"+i(n.relation.type1)+"Start)"),"none"!==n.relation.type2&&l.attr("marker-end","url("+h+"#"+i(n.relation.type2)+"End)");var d,p,g,y,v=e.points.length,m=W.calcLabelPosition(e.points);if(a=m.x,o=m.y,v%2!=0&&v>1){var b=W.calcCardinalityPosition("none"!==n.relation.type1,e.points,e.points[0]),x=W.calcCardinalityPosition("none"!==n.relation.type2,e.points,e.points[v-1]);f.debug("cardinality_1_point "+JSON.stringify(b)),f.debug("cardinality_2_point "+JSON.stringify(x)),d=b.x,p=b.y,g=x.x,y=x.y}if(void 0!==n.title){var _=t.append("g").attr("class","classLabel"),k=_.append("text").attr("class","label").attr("x",a).attr("y",o).attr("fill","red").attr("text-anchor","middle").text(n.title);window.label=k;var w=k.node().getBBox();_.insert("rect",":first-child").attr("class","box").attr("x",w.x-r.padding/2).attr("y",w.y-r.padding/2).attr("width",w.width+r.padding).attr("height",w.height+r.padding)}(f.info("Rendering relation "+JSON.stringify(n)),void 0!==n.relationTitle1&&"none"!==n.relationTitle1)&&t.append("g").attr("class","cardinality").append("text").attr("class","type1").attr("x",d).attr("y",p).attr("fill","black").attr("font-size","6").text(n.relationTitle1);void 0!==n.relationTitle2&&"none"!==n.relationTitle2&&t.append("g").attr("class","cardinality").append("text").attr("class","type2").attr("x",g).attr("y",y).attr("fill","black").attr("font-size","6").text(n.relationTitle2);sn++},vn=function(t,e,n){var r=t.insert("g").attr("class","node default").attr("id",e.domId||e.id),i=70,a=10;"LR"===n&&(i=10,a=70);var o=r.append("rect").style("stroke","black").style("fill","black").attr("x",-1*i/2).attr("y",-1*a/2).attr("width",i).attr("height",a).attr("class","fork-join");return Ce(e,o),e.height=e.height+e.padding/2,e.width=e.width+e.padding/2,e.intersect=function(t){return Ve.rect(e,t)},r},mn={question:function(t,e){var n=Te(t,e,void 0,!0),r=n.shapeSvg,i=n.bbox,a=i.width+e.padding+(i.height+e.padding),o=[{x:a/2,y:0},{x:a,y:-a/2},{x:a/2,y:-a},{x:0,y:-a/2}];f.info("Question main (Circle)");var s=Se(r,a,a,o);return Ce(e,s),e.intersect=function(t){return f.warn("Intersect called"),Ve.polygon(e,o,t)},r},rect:function(t,e){var n=Te(t,e,"node "+e.classes,!0),r=n.shapeSvg,i=n.bbox,a=n.halfPadding;f.trace("Classes = ",e.classes);var o=r.insert("rect",":first-child");return o.attr("class","basic label-container").attr("style",e.style).attr("rx",e.rx).attr("ry",e.ry).attr("x",-i.width/2-a).attr("y",-i.height/2-a).attr("width",i.width+e.padding).attr("height",i.height+e.padding),Ce(e,o),e.intersect=function(t){return Ve.rect(e,t)},r},rectWithTitle:function(t,e){var n;n=e.classes?"node "+e.classes:"node default";var r=t.insert("g").attr("class",n).attr("id",e.domId||e.id),i=r.insert("rect",":first-child"),a=r.insert("line"),o=r.insert("g").attr("class","label"),c=e.labelText.flat();f.info("Label text",c[0]);var u,l=o.node().appendChild(Ee(c[0],e.labelStyle,!0,!0));if(xt().flowchart.htmlLabels){var h=l.children[0],d=Object(s.select)(l);u=h.getBoundingClientRect(),d.attr("width",u.width),d.attr("height",u.height)}f.info("Text 2",c);var p=c.slice(1,c.length),g=l.getBBox(),y=o.node().appendChild(Ee(p.join("
"),e.labelStyle,!0,!0));if(xt().flowchart.htmlLabels){var v=y.children[0],m=Object(s.select)(y);u=v.getBoundingClientRect(),m.attr("width",u.width),m.attr("height",u.height)}var b=e.padding/2;return Object(s.select)(y).attr("transform","translate( "+(u.width>g.width?0:(g.width-u.width)/2)+", "+(g.height+b+5)+")"),Object(s.select)(l).attr("transform","translate( "+(u.widthe.height/2-s)){var i=s*s*(1-r*r/(o*o));0!=i&&(i=Math.sqrt(i)),i=s-i,t.y-e.y>0&&(i=-i),n.y+=i}return n},r},start:function(t,e){var n=t.insert("g").attr("class","node default").attr("id",e.domId||e.id),r=n.insert("circle",":first-child");return r.attr("class","state-start").attr("r",7).attr("width",14).attr("height",14),Ce(e,r),e.intersect=function(t){return Ve.circle(e,7,t)},n},end:function(t,e){var n=t.insert("g").attr("class","node default").attr("id",e.domId||e.id),r=n.insert("circle",":first-child"),i=n.insert("circle",":first-child");return i.attr("class","state-start").attr("r",7).attr("width",14).attr("height",14),r.attr("class","state-end").attr("r",5).attr("width",10).attr("height",10),Ce(e,i),e.intersect=function(t){return Ve.circle(e,7,t)},n},note:He,subroutine:function(t,e){var n=Te(t,e,void 0,!0),r=n.shapeSvg,i=n.bbox,a=i.width+e.padding,o=i.height+e.padding,s=Se(r,a,o,[{x:0,y:0},{x:a,y:0},{x:a,y:-o},{x:0,y:-o},{x:0,y:0},{x:-8,y:0},{x:a+8,y:0},{x:a+8,y:-o},{x:-8,y:-o},{x:-8,y:0}]);return Ce(e,s),e.intersect=function(t){return Ve.polygon(e,t)},r},fork:vn,join:vn,class_box:function(t,e){var n,r=e.padding/2;n=e.classes?"node "+e.classes:"node default";var i=t.insert("g").attr("class",n).attr("id",e.domId||e.id),a=i.insert("rect",":first-child"),o=i.insert("line"),c=i.insert("line"),u=0,l=4,h=i.insert("g").attr("class","label"),f=0,d=e.classData.annotations&&e.classData.annotations[0],p=e.classData.annotations[0]?"«"+e.classData.annotations[0]+"»":"",g=h.node().appendChild(Ee(p,e.labelStyle,!0,!0)),y=g.getBBox();if(xt().flowchart.htmlLabels){var v=g.children[0],m=Object(s.select)(g);y=v.getBoundingClientRect(),m.attr("width",y.width),m.attr("height",y.height)}e.classData.annotations[0]&&(l+=y.height+4,u+=y.width);var b=e.classData.id;void 0!==e.classData.type&&""!==e.classData.type&&(b+="<"+e.classData.type+">");var x=h.node().appendChild(Ee(b,e.labelStyle,!0,!0));Object(s.select)(x).attr("class","classTitle");var _=x.getBBox();if(xt().flowchart.htmlLabels){var k=x.children[0],w=Object(s.select)(x);_=k.getBoundingClientRect(),w.attr("width",_.width),w.attr("height",_.height)}l+=_.height+4,_.width>u&&(u=_.width);var E=[];e.classData.members.forEach((function(t){var n=cn(t).displayText,r=h.node().appendChild(Ee(n,e.labelStyle,!0,!0)),i=r.getBBox();if(xt().flowchart.htmlLabels){var a=r.children[0],o=Object(s.select)(r);i=a.getBoundingClientRect(),o.attr("width",i.width),o.attr("height",i.height)}i.width>u&&(u=i.width),l+=i.height+4,E.push(r)})),l+=8;var T=[];if(e.classData.methods.forEach((function(t){var n=cn(t).displayText,r=h.node().appendChild(Ee(n,e.labelStyle,!0,!0)),i=r.getBBox();if(xt().flowchart.htmlLabels){var a=r.children[0],o=Object(s.select)(r);i=a.getBoundingClientRect(),o.attr("width",i.width),o.attr("height",i.height)}i.width>u&&(u=i.width),l+=i.height+4,T.push(r)})),l+=8,d){var C=(u-y.width)/2;Object(s.select)(g).attr("transform","translate( "+(-1*u/2+C)+", "+-1*l/2+")"),f=y.height+4}var S=(u-_.width)/2;return Object(s.select)(x).attr("transform","translate( "+(-1*u/2+S)+", "+(-1*l/2+f)+")"),f+=_.height+4,o.attr("class","divider").attr("x1",-u/2-r).attr("x2",u/2+r).attr("y1",-l/2-r+8+f).attr("y2",-l/2-r+8+f),f+=8,E.forEach((function(t){Object(s.select)(t).attr("transform","translate( "+-u/2+", "+(-1*l/2+f+4)+")"),f+=_.height+4})),f+=8,c.attr("class","divider").attr("x1",-u/2-r).attr("x2",u/2+r).attr("y1",-l/2-r+8+f).attr("y2",-l/2-r+8+f),f+=8,T.forEach((function(t){Object(s.select)(t).attr("transform","translate( "+-u/2+", "+(-1*l/2+f)+")"),f+=_.height+4})),a.attr("class","outer title-state").attr("x",-u/2-r).attr("y",-l/2-r).attr("width",u+e.padding).attr("height",l+e.padding),Ce(e,a),e.intersect=function(t){return Ve.rect(e,t)},i}},bn={},xn=function(t){var e=bn[t.id];f.trace("Transforming node",t,"translate("+(t.x-t.width/2-5)+", "+(t.y-t.height/2-5)+")");t.clusterNode?e.attr("transform","translate("+(t.x-t.width/2-8)+", "+(t.y-t.height/2-8)+")"):e.attr("transform","translate("+t.x+", "+t.y+")")},_n={rect:function(t,e){f.trace("Creating subgraph rect for ",e.id,e);var n=t.insert("g").attr("class","cluster").attr("id",e.id),r=n.insert("rect",":first-child"),i=n.insert("g").attr("class","cluster-label"),a=i.node().appendChild(Ee(e.labelText,e.labelStyle,void 0,!0)),o=a.getBBox();if(xt().flowchart.htmlLabels){var c=a.children[0],u=Object(s.select)(a);o=c.getBoundingClientRect(),u.attr("width",o.width),u.attr("height",o.height)}var l=0*e.padding,h=l/2;f.trace("Data ",e,JSON.stringify(e)),r.attr("rx",e.rx).attr("ry",e.ry).attr("x",e.x-e.width/2-h).attr("y",e.y-e.height/2-h).attr("width",e.width+l).attr("height",e.height+l),i.attr("transform","translate("+(e.x-o.width/2)+", "+(e.y-e.height/2-e.padding/3+3)+")");var d=r.node().getBBox();return e.width=d.width,e.height=d.height,e.intersect=function(t){return We(e,t)},n},roundedWithTitle:function(t,e){var n=t.insert("g").attr("class",e.classes).attr("id",e.id),r=n.insert("rect",":first-child"),i=n.insert("g").attr("class","cluster-label"),a=n.append("rect"),o=i.node().appendChild(Ee(e.labelText,e.labelStyle,void 0,!0)),c=o.getBBox();if(xt().flowchart.htmlLabels){var u=o.children[0],l=Object(s.select)(o);c=u.getBoundingClientRect(),l.attr("width",c.width),l.attr("height",c.height)}c=o.getBBox();var h=0*e.padding,f=h/2;r.attr("class","outer").attr("x",e.x-e.width/2-f).attr("y",e.y-e.height/2-f).attr("width",e.width+h).attr("height",e.height+h),a.attr("class","inner").attr("x",e.x-e.width/2-f).attr("y",e.y-e.height/2-f+c.height-1).attr("width",e.width+h).attr("height",e.height+h-c.height-3),i.attr("transform","translate("+(e.x-c.width/2)+", "+(e.y-e.height/2-e.padding/3+(xt().flowchart.htmlLabels?5:3))+")");var d=r.node().getBBox();return e.width=d.width,e.height=d.height,e.intersect=function(t){return We(e,t)},n},noteGroup:function(t,e){var n=t.insert("g").attr("class","note-cluster").attr("id",e.id),r=n.insert("rect",":first-child"),i=0*e.padding,a=i/2;r.attr("rx",e.rx).attr("ry",e.ry).attr("x",e.x-e.width/2-a).attr("y",e.y-e.height/2-a).attr("width",e.width+i).attr("height",e.height+i).attr("fill","none");var o=r.node().getBBox();return e.width=o.width,e.height=o.height,e.intersect=function(t){return We(e,t)},n},divider:function(t,e){var n=t.insert("g").attr("class",e.classes).attr("id",e.id),r=n.insert("rect",":first-child"),i=0*e.padding,a=i/2;r.attr("class","divider").attr("x",e.x-e.width/2-a).attr("y",e.y-e.height/2).attr("width",e.width+i).attr("height",e.height+i);var o=r.node().getBBox();return e.width=o.width,e.height=o.height,e.intersect=function(t){return We(e,t)},n}},kn={},wn={},En={},Tn=function(t,e){var n=t.x,r=t.y,i=Math.abs(e.x-n),a=Math.abs(e.y-r),o=t.width/2,s=t.height/2;return i>=o||a>=s},Cn=function(t,e,n){f.warn("intersection calc o:",e," i:",n,t);var r=t.x,i=t.y,a=Math.abs(r-n.x),o=t.width/2,s=n.xMath.abs(r-e.x)*c){var y=n.y0&&f.info("Recursive edges",n.edge(n.edges()[0]));var c=o.insert("g").attr("class","clusters"),u=o.insert("g").attr("class","edgePaths"),l=o.insert("g").attr("class","edgeLabels"),h=o.insert("g").attr("class","nodes");return n.nodes().forEach((function(e){var o=n.node(e);if(void 0!==i){var s=JSON.parse(JSON.stringify(i.clusterData));f.info("Setting data for cluster XXX (",e,") ",s,i),n.setNode(i.id,s),n.parent(e)||(f.warn("Setting parent",e,i.id),n.setParent(e,i.id,s))}if(f.info("(Insert) Node XXX"+e+": "+JSON.stringify(n.node(e))),o&&o.clusterNode){f.info("Cluster identified",e,o,n.node(e));var c=t(h,o.graph,r,n.node(e));Ce(o,c),function(t,e){bn[e.id]=t}(c,o),f.warn("Recursive render complete",c,o)}else n.children(e).length>0?(f.info("Cluster - the non recursive path XXX",e,o.id,o,n),f.info(Be(o.id,n)),Ae[o.id]={id:Be(o.id,n),node:o}):(f.info("Node - the non recursive path",e,o.id,o),function(t,e,n){var r,i;e.link?(r=t.insert("svg:a").attr("xlink:href",e.link).attr("target",e.linkTarget||"_blank"),i=mn[e.shape](r,e,n)):r=i=mn[e.shape](t,e,n),e.tooltip&&i.attr("title",e.tooltip),e.class&&i.attr("class","node default "+e.class),bn[e.id]=r,e.haveCallback&&bn[e.id].attr("class",bn[e.id].attr("class")+" clickable")}(h,n.node(e),a))})),n.edges().forEach((function(t){var e=n.edge(t.v,t.w,t.name);f.info("Edge "+t.v+" -> "+t.w+": "+JSON.stringify(t)),f.info("Edge "+t.v+" -> "+t.w+": ",t," ",JSON.stringify(n.edge(t))),f.info("Fix",Ae,"ids:",t.v,t.w,"Translateing: ",Ae[t.v],Ae[t.w]),function(t,e){var n=Ee(e.label,e.labelStyle),r=t.insert("g").attr("class","edgeLabel"),i=r.insert("g").attr("class","label");i.node().appendChild(n);var a=n.getBBox();if(xt().flowchart.htmlLabels){var o=n.children[0],c=Object(s.select)(n);a=o.getBoundingClientRect(),c.attr("width",a.width),c.attr("height",a.height)}if(i.attr("transform","translate("+-a.width/2+", "+-a.height/2+")"),wn[e.id]=r,e.width=a.width,e.height=a.height,e.startLabelLeft){var u=Ee(e.startLabelLeft,e.labelStyle),l=t.insert("g").attr("class","edgeTerminals"),h=l.insert("g").attr("class","inner");h.node().appendChild(u);var f=u.getBBox();h.attr("transform","translate("+-f.width/2+", "+-f.height/2+")"),En[e.id]||(En[e.id]={}),En[e.id].startLeft=l}if(e.startLabelRight){var d=Ee(e.startLabelRight,e.labelStyle),p=t.insert("g").attr("class","edgeTerminals"),g=p.insert("g").attr("class","inner");p.node().appendChild(d),g.node().appendChild(d);var y=d.getBBox();g.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),En[e.id]||(En[e.id]={}),En[e.id].startRight=p}if(e.endLabelLeft){var v=Ee(e.endLabelLeft,e.labelStyle),m=t.insert("g").attr("class","edgeTerminals"),b=m.insert("g").attr("class","inner");b.node().appendChild(v);var x=v.getBBox();b.attr("transform","translate("+-x.width/2+", "+-x.height/2+")"),m.node().appendChild(v),En[e.id]||(En[e.id]={}),En[e.id].endLeft=m}if(e.endLabelRight){var _=Ee(e.endLabelRight,e.labelStyle),k=t.insert("g").attr("class","edgeTerminals"),w=k.insert("g").attr("class","inner");w.node().appendChild(_);var E=_.getBBox();w.attr("transform","translate("+-E.width/2+", "+-E.height/2+")"),k.node().appendChild(_),En[e.id]||(En[e.id]={}),En[e.id].endRight=k}}(l,e)})),n.edges().forEach((function(t){f.info("Edge "+t.v+" -> "+t.w+": "+JSON.stringify(t))})),f.info("#############################################"),f.info("### Layout ###"),f.info("#############################################"),f.info(n),_e.a.layout(n),f.info("Graph after layout:",H.a.json.write(n)),Ie(n).forEach((function(t){var e=n.node(t);f.info("Position "+t+": "+JSON.stringify(n.node(t))),f.info("Position "+t+": ("+e.x,","+e.y,") width: ",e.width," height: ",e.height),e&&e.clusterNode?xn(e):n.children(t).length>0?(!function(t,e){f.trace("Inserting cluster");var n=e.shape||"rect";kn[e.id]=_n[n](t,e)}(c,e),Ae[e.id].node=e):xn(e)})),n.edges().forEach((function(t){var e=n.edge(t);f.info("Edge "+t.v+" -> "+t.w+": "+JSON.stringify(e),e);var i=function(t,e,n,r,i,a){var o=n.points,c=!1,u=a.node(e.v),l=a.node(e.w);if(l.intersect&&u.intersect&&((o=o.slice(1,n.points.length-1)).unshift(u.intersect(o[0])),f.info("Last point",o[o.length-1],l,l.intersect(o[o.length-1])),o.push(l.intersect(o[o.length-1]))),n.toCluster){var h;f.trace("edge",n),f.trace("to cluster",r[n.toCluster]),o=[];var d=!1;n.points.forEach((function(t){var e=r[n.toCluster].node;if(Tn(e,t)||d)d||o.push(t);else{f.trace("inside",n.toCluster,t,h);var i=Cn(e,h,t),a=!1;o.forEach((function(t){a=a||t.x===i.x&&t.y===i.y})),o.find((function(t){return t.x===i.x&&t.y===i.y}))?f.warn("no intersect",i,o):o.push(i),d=!0}h=t})),c=!0}if(n.fromCluster){f.trace("edge",n),f.warn("from cluster",r[n.fromCluster]);for(var p,g=[],y=!1,v=o.length-1;v>=0;v--){var m=o[v],b=r[n.fromCluster].node;if(Tn(b,m)||y)f.trace("Outside point",m),y||g.unshift(m);else{f.warn("inside",n.fromCluster,m,b);var x=Cn(b,p,m);g.unshift(x),y=!0}p=m}o=g,c=!0}var _,k=o.filter((function(t){return!Number.isNaN(t.y)})),w=Object(s.line)().x((function(t){return t.x})).y((function(t){return t.y})).curve(s.curveBasis);switch(n.thickness){case"normal":_="edge-thickness-normal";break;case"thick":_="edge-thickness-thick";break;default:_=""}switch(n.pattern){case"solid":_+=" edge-pattern-solid";break;case"dotted":_+=" edge-pattern-dotted";break;case"dashed":_+=" edge-pattern-dashed"}var E=t.append("path").attr("d",w(k)).attr("id",n.id).attr("class"," "+_+(n.classes?" "+n.classes:"")),T="";switch(xt().state.arrowMarkerAbsolute&&(T=(T=(T=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search).replace(/\(/g,"\\(")).replace(/\)/g,"\\)")),f.info("arrowTypeStart",n.arrowTypeStart),f.info("arrowTypeEnd",n.arrowTypeEnd),n.arrowTypeStart){case"arrow_cross":E.attr("marker-start","url("+T+"#"+i+"-crossStart)");break;case"arrow_point":E.attr("marker-start","url("+T+"#"+i+"-pointStart)");break;case"arrow_barb":E.attr("marker-start","url("+T+"#"+i+"-barbStart)");break;case"arrow_circle":E.attr("marker-start","url("+T+"#"+i+"-circleStart)");break;case"aggregation":E.attr("marker-start","url("+T+"#"+i+"-aggregationStart)");break;case"extension":E.attr("marker-start","url("+T+"#"+i+"-extensionStart)");break;case"composition":E.attr("marker-start","url("+T+"#"+i+"-compositionStart)");break;case"dependency":E.attr("marker-start","url("+T+"#"+i+"-dependencyStart)")}switch(n.arrowTypeEnd){case"arrow_cross":E.attr("marker-end","url("+T+"#"+i+"-crossEnd)");break;case"arrow_point":E.attr("marker-end","url("+T+"#"+i+"-pointEnd)");break;case"arrow_barb":E.attr("marker-end","url("+T+"#"+i+"-barbEnd)");break;case"arrow_circle":E.attr("marker-end","url("+T+"#"+i+"-circleEnd)");break;case"aggregation":E.attr("marker-end","url("+T+"#"+i+"-aggregationEnd)");break;case"extension":E.attr("marker-end","url("+T+"#"+i+"-extensionEnd)");break;case"composition":E.attr("marker-end","url("+T+"#"+i+"-compositionEnd)");break;case"dependency":E.attr("marker-end","url("+T+"#"+i+"-dependencyEnd)")}var C={};return c&&(C.updatedPath=o),C.originalPath=n.points,C}(u,t,e,Ae,r,n);!function(t,e){f.info("Moving label",t.id,t.label,wn[t.id]);var n=e.updatedPath?e.updatedPath:e.originalPath;if(t.label){var r=wn[t.id],i=t.x,a=t.y;if(n){var o=W.calcLabelPosition(n);f.info("Moving label from (",i,",",a,") to (",o.x,",",o.y,")")}r.attr("transform","translate("+i+", "+a+")")}if(t.startLabelLeft){var s=En[t.id].startLeft,c=t.x,u=t.y;if(n){var l=W.calcTerminalLabelPosition(0,"start_left",n);c=l.x,u=l.y}s.attr("transform","translate("+c+", "+u+")")}if(t.startLabelRight){var h=En[t.id].startRight,d=t.x,p=t.y;if(n){var g=W.calcTerminalLabelPosition(0,"start_right",n);d=g.x,p=g.y}h.attr("transform","translate("+d+", "+p+")")}if(t.endLabelLeft){var y=En[t.id].endLeft,v=t.x,m=t.y;if(n){var b=W.calcTerminalLabelPosition(0,"end_left",n);v=b.x,m=b.y}y.attr("transform","translate("+v+", "+m+")")}if(t.endLabelRight){var x=En[t.id].endRight,_=t.x,k=t.y;if(n){var w=W.calcTerminalLabelPosition(0,"end_right",n);_=w.x,k=w.y}x.attr("transform","translate("+_+", "+k+")")}}(e,i)})),o},An=function(t,e,n,r,i){we(t,n,r,i),bn={},wn={},En={},kn={},Me={},Oe={},Ae={},f.warn("Graph at first:",H.a.json.write(e)),Fe(e),f.warn("Graph after:",H.a.json.write(e)),Sn(t,e,r)},Mn={},On=function(t,e,n){var r=Object(s.select)('[id="'.concat(n,'"]'));Object.keys(t).forEach((function(n){var i=t[n],a="default";i.classes.length>0&&(a=i.classes.join(" "));var o,s=N(i.styles),c=void 0!==i.text?i.text:i.id;if(xt().flowchart.htmlLabels){var u={label:c.replace(/fa[lrsb]?:fa-[\w-]+/g,(function(t){return"")}))};(o=te()(r,u).node()).parentNode.removeChild(o)}else{var l=document.createElementNS("http://www.w3.org/2000/svg","text");l.setAttribute("style",s.labelStyle.replace("color:","fill:"));for(var h=c.split(x.lineBreakRegex),d=0;d=0;h--)i=l[h],f.info("Subgraph - ",i),qt.addVertex(i.id,i.title,"group",void 0,i.classes);var d=qt.getVertices(),p=qt.getEdges();f.info(p);var g=0;for(g=l.length-1;g>=0;g--){i=l[g],Object(s.selectAll)("cluster").append("text");for(var y=0;y0)switch(e.valign){case"top":case"start":s=function(){return Math.round(e.y+e.textMargin)};break;case"middle":case"center":s=function(){return Math.round(e.y+(n+r+e.textMargin)/2)};break;case"bottom":case"end":s=function(){return Math.round(e.y+(n+r+2*e.textMargin)-e.textMargin)}}if(void 0!==e.anchor&&void 0!==e.textMargin&&void 0!==e.width)switch(e.anchor){case"left":case"start":e.x=Math.round(e.x+e.textMargin),e.anchor="start",e.dominantBaseline="text-after-edge",e.alignmentBaseline="middle";break;case"middle":case"center":e.x=Math.round(e.x+e.width/2),e.anchor="middle",e.dominantBaseline="middle",e.alignmentBaseline="middle";break;case"right":case"end":e.x=Math.round(e.x+e.width-e.textMargin),e.anchor="end",e.dominantBaseline="text-before-edge",e.alignmentBaseline="middle"}for(var c=0;c0&&(r+=(l._groups||l)[0][0].getBBox().height,n=r),a.push(l)}return a},Pn=function(t,e){var n,r,i,a,o,s=t.append("polygon");return s.attr("points",(n=e.x,r=e.y,i=e.width,a=e.height,n+","+r+" "+(n+i)+","+r+" "+(n+i)+","+(r+a-(o=7))+" "+(n+i-1.2*o)+","+(r+a)+" "+n+","+(r+a))),s.attr("class","labelBox"),e.y=e.y+e.height/2,Fn(t,e),s},In=-1,jn=function(){return{x:0,y:0,fill:void 0,anchor:void 0,style:"#666",width:void 0,height:void 0,textMargin:0,rx:0,ry:0,tspan:!0,valign:void 0}},Rn=function(){return{x:0,y:0,fill:"#EDF2AE",stroke:"#666",width:100,anchor:"start",height:100,rx:0,ry:0}},Yn=function(){function t(t,e,n,i,a,o,s){r(e.append("text").attr("x",n+a/2).attr("y",i+o/2+5).style("text-anchor","middle").text(t),s)}function e(t,e,n,i,a,o,s,c){for(var u=c.actorFontSize,l=c.actorFontFamily,h=c.actorFontWeight,f=t.split(x.lineBreakRegex),d=0;d2&&void 0!==arguments[2]?arguments[2]:{text:void 0,wrap:void 0},r=arguments.length>3?arguments[3]:void 0;if(r===nr.ACTIVE_END){var i=Kn(t.actor);if(i<1){var a=new Error("Trying to inactivate an inactive participant ("+t.actor+")");throw a.hash={text:"->>-",token:"->>-",line:"1",loc:{first_line:1,last_line:1,first_column:1,last_column:1},expected:["'ACTIVE_PARTICIPANT'"]},a}}return Hn.push({from:t,to:e,message:n.text,wrap:void 0===n.wrap&&er()||!!n.wrap,type:r}),!0},er=function(){return Jn},nr={SOLID:0,DOTTED:1,NOTE:2,SOLID_CROSS:3,DOTTED_CROSS:4,SOLID_OPEN:5,DOTTED_OPEN:6,LOOP_START:10,LOOP_END:11,ALT_START:12,ALT_ELSE:13,ALT_END:14,OPT_START:15,OPT_END:16,ACTIVE_START:17,ACTIVE_END:18,PAR_START:19,PAR_AND:20,PAR_END:21,RECT_START:22,RECT_END:23},rr=function(t,e,n){var r={actor:t,placement:e,message:n.text,wrap:void 0===n.wrap&&er()||!!n.wrap},i=[].concat(t,t);Gn.push(r),Hn.push({from:i[0],to:i[1],message:n.text,wrap:void 0===n.wrap&&er()||!!n.wrap,type:nr.NOTE,placement:e})},ir=function(t){qn=t.text,Xn=void 0===t.wrap&&er()||!!t.wrap},ar={addActor:Qn,addMessage:function(t,e,n,r){Hn.push({from:t,to:e,message:n.text,wrap:void 0===n.wrap&&er()||!!n.wrap,answer:r})},addSignal:tr,autoWrap:er,setWrap:function(t){Jn=t},enableSequenceNumbers:function(){Zn=!0},showSequenceNumbers:function(){return Zn},getMessages:function(){return Hn},getActors:function(){return Vn},getActor:function(t){return Vn[t]},getActorKeys:function(){return Object.keys(Vn)},getTitle:function(){return qn},parseDirective:function(t,e,n){$o.parseDirective(this,t,e,n)},getConfig:function(){return xt().sequence},getTitleWrapped:function(){return Xn},clear:function(){Vn={},Hn=[]},parseMessage:function(t){var e=t.trim(),n={text:e.replace(/^[:]?(?:no)?wrap:/,"").trim(),wrap:null===e.match(/^[:]?(?:no)?wrap:/)?x.hasBreaks(e)||void 0:null!==e.match(/^[:]?wrap:/)||null===e.match(/^[:]?nowrap:/)&&void 0};return f.debug("parseMessage:",n),n},LINETYPE:nr,ARROWTYPE:{FILLED:0,OPEN:1},PLACEMENT:{LEFTOF:0,RIGHTOF:1,OVER:2},addNote:rr,setTitle:ir,apply:function t(e){if(e instanceof Array)e.forEach((function(e){t(e)}));else switch(e.type){case"addActor":Qn(e.actor,e.actor,e.description);break;case"activeStart":case"activeEnd":tr(e.actor,void 0,void 0,e.signalType);break;case"addNote":rr(e.actor,e.placement,e.text);break;case"addMessage":tr(e.from,e.to,e.msg,e.signalType);break;case"loopStart":tr(void 0,void 0,e.loopText,e.signalType);break;case"loopEnd":tr(void 0,void 0,void 0,e.signalType);break;case"rectStart":tr(void 0,void 0,e.color,e.signalType);break;case"rectEnd":tr(void 0,void 0,void 0,e.signalType);break;case"optStart":tr(void 0,void 0,e.optText,e.signalType);break;case"optEnd":tr(void 0,void 0,void 0,e.signalType);break;case"altStart":case"else":tr(void 0,void 0,e.altText,e.signalType);break;case"altEnd":tr(void 0,void 0,void 0,e.signalType);break;case"setTitle":ir(e.text);break;case"parStart":case"and":tr(void 0,void 0,e.parText,e.signalType);break;case"parEnd":tr(void 0,void 0,void 0,e.signalType)}}};Un.parser.yy=ar;var or={},sr={data:{startx:void 0,stopx:void 0,starty:void 0,stopy:void 0},verticalPos:0,sequenceItems:[],activations:[],models:{getHeight:function(){return Math.max.apply(null,0===this.actors.length?[0]:this.actors.map((function(t){return t.height||0})))+(0===this.loops.length?0:this.loops.map((function(t){return t.height||0})).reduce((function(t,e){return t+e})))+(0===this.messages.length?0:this.messages.map((function(t){return t.height||0})).reduce((function(t,e){return t+e})))+(0===this.notes.length?0:this.notes.map((function(t){return t.height||0})).reduce((function(t,e){return t+e})))},clear:function(){this.actors=[],this.loops=[],this.messages=[],this.notes=[]},addActor:function(t){this.actors.push(t)},addLoop:function(t){this.loops.push(t)},addMessage:function(t){this.messages.push(t)},addNote:function(t){this.notes.push(t)},lastActor:function(){return this.actors[this.actors.length-1]},lastLoop:function(){return this.loops[this.loops.length-1]},lastMessage:function(){return this.messages[this.messages.length-1]},lastNote:function(){return this.notes[this.notes.length-1]},actors:[],loops:[],messages:[],notes:[]},init:function(){this.sequenceItems=[],this.activations=[],this.models.clear(),this.data={startx:void 0,stopx:void 0,starty:void 0,stopy:void 0},this.verticalPos=0,fr(Un.parser.yy.getConfig())},updateVal:function(t,e,n,r){void 0===t[e]?t[e]=n:t[e]=r(n,t[e])},updateBounds:function(t,e,n,r){var i=this,a=0;function o(o){return function(s){a++;var c=i.sequenceItems.length-a+1;i.updateVal(s,"starty",e-c*or.boxMargin,Math.min),i.updateVal(s,"stopy",r+c*or.boxMargin,Math.max),i.updateVal(sr.data,"startx",t-c*or.boxMargin,Math.min),i.updateVal(sr.data,"stopx",n+c*or.boxMargin,Math.max),"activation"!==o&&(i.updateVal(s,"startx",t-c*or.boxMargin,Math.min),i.updateVal(s,"stopx",n+c*or.boxMargin,Math.max),i.updateVal(sr.data,"starty",e-c*or.boxMargin,Math.min),i.updateVal(sr.data,"stopy",r+c*or.boxMargin,Math.max))}}this.sequenceItems.forEach(o()),this.activations.forEach(o("activation"))},insert:function(t,e,n,r){var i=Math.min(t,n),a=Math.max(t,n),o=Math.min(e,r),s=Math.max(e,r);this.updateVal(sr.data,"startx",i,Math.min),this.updateVal(sr.data,"starty",o,Math.min),this.updateVal(sr.data,"stopx",a,Math.max),this.updateVal(sr.data,"stopy",s,Math.max),this.updateBounds(i,o,a,s)},newActivation:function(t,e,n){var r=n[t.from.actor],i=dr(t.from.actor).length||0,a=r.x+r.width/2+(i-1)*or.activationWidth/2;this.activations.push({startx:a,starty:this.verticalPos+2,stopx:a+or.activationWidth,stopy:void 0,actor:t.from.actor,anchored:zn.anchorElement(e)})},endActivation:function(t){var e=this.activations.map((function(t){return t.actor})).lastIndexOf(t.from.actor);return this.activations.splice(e,1)[0]},createLoop:function(){var t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{message:void 0,wrap:!1,width:void 0},e=arguments.length>1?arguments[1]:void 0;return{startx:void 0,starty:this.verticalPos,stopx:void 0,stopy:void 0,title:t.message,wrap:t.wrap,width:t.width,height:0,fill:e}},newLoop:function(){var t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{message:void 0,wrap:!1,width:void 0},e=arguments.length>1?arguments[1]:void 0;this.sequenceItems.push(this.createLoop(t,e))},endLoop:function(){return this.sequenceItems.pop()},addSectionToLoop:function(t){var e=this.sequenceItems.pop();e.sections=e.sections||[],e.sectionTitles=e.sectionTitles||[],e.sections.push({y:sr.getVerticalPos(),height:0}),e.sectionTitles.push(t),this.sequenceItems.push(e)},bumpVerticalPos:function(t){this.verticalPos=this.verticalPos+t,this.data.stopy=this.verticalPos},getVerticalPos:function(){return this.verticalPos},getBounds:function(){return{bounds:this.data,models:this.models}}},cr=function(t){return{fontFamily:t.messageFontFamily,fontSize:t.messageFontSize,fontWeight:t.messageFontWeight}},ur=function(t){return{fontFamily:t.noteFontFamily,fontSize:t.noteFontSize,fontWeight:t.noteFontWeight}},lr=function(t){return{fontFamily:t.actorFontFamily,fontSize:t.actorFontSize,fontWeight:t.actorFontWeight}},hr=function(t,e,n,r){for(var i=0,a=0,o=0;o0&&o.forEach((function(r){if(n=r,i.startx===i.stopx){var a=e[t.from],o=e[t.to];n.from=Math.min(a.x-i.width/2,a.x-a.width/2,n.from),n.to=Math.max(o.x+i.width/2,o.x+a.width/2,n.to),n.width=Math.max(n.width,Math.abs(n.to-n.from))-or.labelBoxWidth}else n.from=Math.min(i.startx,n.from),n.to=Math.max(i.stopx,n.to),n.width=Math.max(n.width,i.width)-or.labelBoxWidth})))})),sr.activations=[],f.debug("Loop type widths:",a),a},br={bounds:sr,drawActors:hr,setConf:fr,draw:function(t,e){or=xt().sequence,Un.parser.yy.clear(),Un.parser.yy.setWrap(or.wrap),Un.parser.parse(t+"\n"),sr.init(),f.debug("C:".concat(JSON.stringify(or,null,2)));var n=Object(s.select)('[id="'.concat(e,'"]')),r=Un.parser.yy.getActors(),i=Un.parser.yy.getActorKeys(),a=Un.parser.yy.getMessages(),o=Un.parser.yy.getTitle(),c=yr(r,a);or.height=vr(r,c),hr(n,r,i,0);var u=mr(a,r,c);zn.insertArrowHead(n),zn.insertArrowCrossHead(n),zn.insertSequenceNumber(n);var l=1;a.forEach((function(t){var e,i,a;switch(t.type){case Un.parser.yy.LINETYPE.NOTE:i=t.noteModel,function(t,e){sr.bumpVerticalPos(or.boxMargin),e.height=or.boxMargin,e.starty=sr.getVerticalPos();var n=zn.getNoteRect();n.x=e.startx,n.y=e.starty,n.width=e.width||or.width,n.class="note";var r=t.append("g"),i=zn.drawRect(r,n),a=zn.getTextObj();a.x=e.startx,a.y=e.starty,a.width=n.width,a.dy="1em",a.text=e.message,a.class="noteText",a.fontFamily=or.noteFontFamily,a.fontSize=or.noteFontSize,a.fontWeight=or.noteFontWeight,a.anchor=or.noteAlign,a.textMargin=or.noteMargin,a.valign=or.noteAlign,a.wrap=!0;var o=Fn(r,a),s=Math.round(o.map((function(t){return(t._groups||t)[0][0].getBBox().height})).reduce((function(t,e){return t+e})));i.attr("height",s+2*or.noteMargin),e.height+=s+2*or.noteMargin,sr.bumpVerticalPos(s+2*or.noteMargin),e.stopy=e.starty+s+2*or.noteMargin,e.stopx=e.startx+n.width,sr.insert(e.startx,e.starty,e.stopx,e.stopy),sr.models.addNote(e)}(n,i);break;case Un.parser.yy.LINETYPE.ACTIVE_START:sr.newActivation(t,n,r);break;case Un.parser.yy.LINETYPE.ACTIVE_END:!function(t,e){var r=sr.endActivation(t);r.starty+18>e&&(r.starty=e-6,e+=12),zn.drawActivation(n,r,e,or,dr(t.from.actor).length),sr.insert(r.startx,e-10,r.stopx,e)}(t,sr.getVerticalPos());break;case Un.parser.yy.LINETYPE.LOOP_START:gr(u,t,or.boxMargin,or.boxMargin+or.boxTextMargin,(function(t){return sr.newLoop(t)}));break;case Un.parser.yy.LINETYPE.LOOP_END:e=sr.endLoop(),zn.drawLoop(n,e,"loop",or),sr.bumpVerticalPos(e.stopy-sr.getVerticalPos()),sr.models.addLoop(e);break;case Un.parser.yy.LINETYPE.RECT_START:gr(u,t,or.boxMargin,or.boxMargin,(function(t){return sr.newLoop(void 0,t.message)}));break;case Un.parser.yy.LINETYPE.RECT_END:e=sr.endLoop(),zn.drawBackgroundRect(n,e),sr.models.addLoop(e),sr.bumpVerticalPos(e.stopy-sr.getVerticalPos());break;case Un.parser.yy.LINETYPE.OPT_START:gr(u,t,or.boxMargin,or.boxMargin+or.boxTextMargin,(function(t){return sr.newLoop(t)}));break;case Un.parser.yy.LINETYPE.OPT_END:e=sr.endLoop(),zn.drawLoop(n,e,"opt",or),sr.bumpVerticalPos(e.stopy-sr.getVerticalPos()),sr.models.addLoop(e);break;case Un.parser.yy.LINETYPE.ALT_START:gr(u,t,or.boxMargin,or.boxMargin+or.boxTextMargin,(function(t){return sr.newLoop(t)}));break;case Un.parser.yy.LINETYPE.ALT_ELSE:gr(u,t,or.boxMargin+or.boxTextMargin,or.boxMargin,(function(t){return sr.addSectionToLoop(t)}));break;case Un.parser.yy.LINETYPE.ALT_END:e=sr.endLoop(),zn.drawLoop(n,e,"alt",or),sr.bumpVerticalPos(e.stopy-sr.getVerticalPos()),sr.models.addLoop(e);break;case Un.parser.yy.LINETYPE.PAR_START:gr(u,t,or.boxMargin,or.boxMargin+or.boxTextMargin,(function(t){return sr.newLoop(t)}));break;case Un.parser.yy.LINETYPE.PAR_AND:gr(u,t,or.boxMargin+or.boxTextMargin,or.boxMargin,(function(t){return sr.addSectionToLoop(t)}));break;case Un.parser.yy.LINETYPE.PAR_END:e=sr.endLoop(),zn.drawLoop(n,e,"par",or),sr.bumpVerticalPos(e.stopy-sr.getVerticalPos()),sr.models.addLoop(e);break;default:try{(a=t.msgModel).starty=sr.getVerticalPos(),a.sequenceIndex=l,function(t,e){sr.bumpVerticalPos(10);var n=e.startx,r=e.stopx,i=e.starty,a=e.message,o=e.type,s=e.sequenceIndex,c=e.wrap,u=x.splitBreaks(a).length,l=W.calculateTextDimensions(a,cr(or)),h=l.height/u;e.height+=h,sr.bumpVerticalPos(h);var f=zn.getTextObj();f.x=n,f.y=i+10,f.width=r-n,f.class="messageText",f.dy="1em",f.text=a,f.fontFamily=or.messageFontFamily,f.fontSize=or.messageFontSize,f.fontWeight=or.messageFontWeight,f.anchor=or.messageAlign,f.valign=or.messageAlign,f.textMargin=or.wrapPadding,f.tspan=!1,f.wrap=c,Fn(t,f);var d,p,g=l.height-10,y=l.width;if(n===r){p=sr.getVerticalPos()+g,or.rightAngles?d=t.append("path").attr("d","M ".concat(n,",").concat(p," H ").concat(n+Math.max(or.width/2,y/2)," V ").concat(p+25," H ").concat(n)):(g+=or.boxMargin,p=sr.getVerticalPos()+g,d=t.append("path").attr("d","M "+n+","+p+" C "+(n+60)+","+(p-10)+" "+(n+60)+","+(p+30)+" "+n+","+(p+20))),g+=30;var v=Math.max(y/2,or.width/2);sr.insert(n-v,sr.getVerticalPos()-10+g,r+v,sr.getVerticalPos()+30+g)}else g+=or.boxMargin,p=sr.getVerticalPos()+g,(d=t.append("line")).attr("x1",n),d.attr("y1",p),d.attr("x2",r),d.attr("y2",p),sr.insert(n,p-10,r,p);o===Un.parser.yy.LINETYPE.DOTTED||o===Un.parser.yy.LINETYPE.DOTTED_CROSS||o===Un.parser.yy.LINETYPE.DOTTED_OPEN?(d.style("stroke-dasharray","3, 3"),d.attr("class","messageLine1")):d.attr("class","messageLine0");var m="";or.arrowMarkerAbsolute&&(m=(m=(m=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search).replace(/\(/g,"\\(")).replace(/\)/g,"\\)")),d.attr("stroke-width",2),d.attr("stroke","none"),d.style("fill","none"),o!==Un.parser.yy.LINETYPE.SOLID&&o!==Un.parser.yy.LINETYPE.DOTTED||d.attr("marker-end","url("+m+"#arrowhead)"),o!==Un.parser.yy.LINETYPE.SOLID_CROSS&&o!==Un.parser.yy.LINETYPE.DOTTED_CROSS||d.attr("marker-end","url("+m+"#crosshead)"),(ar.showSequenceNumbers()||or.showSequenceNumbers)&&(d.attr("marker-start","url("+m+"#sequencenumber)"),t.append("text").attr("x",n).attr("y",p+4).attr("font-family","sans-serif").attr("font-size","12px").attr("text-anchor","middle").attr("textLength","16px").attr("class","sequenceNumber").text(s)),sr.bumpVerticalPos(g),e.height+=g,e.stopy=e.starty+e.height,sr.insert(e.fromBounds,e.starty,e.toBounds,e.stopy)}(n,a),sr.models.addMessage(a)}catch(t){f.error("error while drawing message",t)}}[Un.parser.yy.LINETYPE.SOLID_OPEN,Un.parser.yy.LINETYPE.DOTTED_OPEN,Un.parser.yy.LINETYPE.SOLID,Un.parser.yy.LINETYPE.DOTTED,Un.parser.yy.LINETYPE.SOLID_CROSS,Un.parser.yy.LINETYPE.DOTTED_CROSS].includes(t.type)&&l++})),or.mirrorActors&&(sr.bumpVerticalPos(2*or.boxMargin),hr(n,r,i,sr.getVerticalPos()));var h=sr.getBounds().bounds;f.debug("For line height fix Querying: #"+e+" .actor-line"),Object(s.selectAll)("#"+e+" .actor-line").attr("y2",h.stopy);var d=h.stopy-h.starty+2*or.diagramMarginY;or.mirrorActors&&(d=d-or.boxMargin+or.bottomMarginAdj);var p=h.stopx-h.startx+2*or.diagramMarginX;o&&n.append("text").text(o).attr("x",(h.stopx-h.startx)/2-2*or.diagramMarginX).attr("y",-25),$(n,d,p,or.useMaxWidth);var g=o?40:0;n.attr("viewBox",h.startx-or.diagramMarginX+" -"+(or.diagramMarginY+g)+" "+p+" "+(d+g)),f.debug("models:",sr.models)}},xr=n(27),_r=n.n(xr);function kr(t){return function(t){if(Array.isArray(t)){for(var e=0,n=new Array(t.length);e=6&&n.indexOf("weekends")>=0||(n.indexOf(t.format("dddd").toLowerCase())>=0||n.indexOf(t.format(e.trim()))>=0)},jr=function(t,e,n){if(n.length&&!t.manualEndTime){var r=l()(t.startTime,e,!0);r.add(1,"d");var i=l()(t.endTime,e,!0),a=Rr(r,i,e,n);t.endTime=i.toDate(),t.renderEndTime=a}},Rr=function(t,e,n,r){for(var i=!1,a=null;t<=e;)i||(a=e.toDate()),(i=Ir(t,n,r))&&e.add(1,"d"),t.add(1,"d");return a},Yr=function(t,e,n){n=n.trim();var r=/^after\s+([\d\w- ]+)/.exec(n.trim());if(null!==r){var i=null;if(r[1].split(" ").forEach((function(t){var e=Gr(t);void 0!==e&&(i?e.endTime>i.endTime&&(i=e):i=e)})),i)return i.endTime;var a=new Date;return a.setHours(0,0,0,0),a}var o=l()(n,e.trim(),!0);return o.isValid()?o.toDate():(f.debug("Invalid date:"+n),f.debug("With date format:"+e.trim()),new Date)},zr=function(t,e){if(null!==t)switch(t[2]){case"s":e.add(t[1],"seconds");break;case"m":e.add(t[1],"minutes");break;case"h":e.add(t[1],"hours");break;case"d":e.add(t[1],"days");break;case"w":e.add(t[1],"weeks")}return e.toDate()},Ur=function(t,e,n,r){r=r||!1,n=n.trim();var i=l()(n,e.trim(),!0);return i.isValid()?(r&&i.add(1,"d"),i.toDate()):zr(/^([\d]+)([wdhms])/.exec(n.trim()),l()(t))},$r=0,Wr=function(t){return void 0===t?"task"+($r+=1):t},Vr=[],Hr={},Gr=function(t){var e=Hr[t];return Vr[e]},qr=function(){for(var t=function(t){var e=Vr[t],n="";switch(Vr[t].raw.startTime.type){case"prevTaskEnd":var r=Gr(e.prevTaskId);e.startTime=r.endTime;break;case"getStartDate":(n=Yr(0,Tr,Vr[t].raw.startTime.startData))&&(Vr[t].startTime=n)}return Vr[t].startTime&&(Vr[t].endTime=Ur(Vr[t].startTime,Tr,Vr[t].raw.endTime.data,Fr),Vr[t].endTime&&(Vr[t].processed=!0,Vr[t].manualEndTime=l()(Vr[t].raw.endTime.data,"YYYY-MM-DD",!0).isValid(),jr(Vr[t],Tr,Ar))),Vr[t].processed},e=!0,n=0;nr?i=1:n0&&(e=t.classes.join(" "));for(var n=0,r=0;rn-e?n+a+1.5*ti.leftPadding>u?e+r-5:n+r+5:(n-e)/2+e+r})).attr("y",(function(t,r){return t.order*e+ti.barHeight/2+(ti.fontSize/2-2)+n})).attr("text-height",i).attr("class",(function(t){var e=o(t.startTime),n=o(t.endTime);t.milestone&&(n=e+i);var r=this.getBBox().width,a="";t.classes.length>0&&(a=t.classes.join(" "));for(var s=0,l=0;ln-e?n+r+1.5*ti.leftPadding>u?a+" taskTextOutsideLeft taskTextOutside"+s+" "+h:a+" taskTextOutsideRight taskTextOutside"+s+" "+h+" width-"+r:a+" taskText taskText"+s+" "+h+" width-"+r}))}(t,i,u,f,r,0,e),function(t,e){for(var n=[],r=0,i=0;i0&&a.setAttribute("dy","1em"),a.textContent=e[i],r.appendChild(a)}return r})).attr("x",10).attr("y",(function(i,a){if(!(a>0))return i[1]*t/2+e;for(var o=0;o "+t.w+": "+JSON.stringify(i.edge(t))),yn(r,i.edge(t),i.edge(t).relation,oi))}));var h=r.node().getBBox(),d=h.width+40,p=h.height+40;$(r,p,d,oi.useMaxWidth);var g="".concat(h.x-20," ").concat(h.y-20," ").concat(d," ").concat(p);f.debug("viewBox ".concat(g)),r.attr("viewBox",g)};ri.parser.yy=on;var li={dividerMargin:10,padding:5,textHeight:10},hi=function(t){Object.keys(t).forEach((function(e){li[e]=t[e]}))},fi=function(t,e){f.info("Drawing class"),on.clear(),ri.parser.parse(t);var n=xt().flowchart;f.info("config:",n);var r=n.nodeSpacing||50,i=n.rankSpacing||50,a=new H.a.Graph({multigraph:!0,compound:!0}).setGraph({rankdir:"TD",nodesep:r,ranksep:i,marginx:8,marginy:8}).setDefaultEdgeLabel((function(){return{}})),o=on.getClasses(),c=on.getRelations();f.info(c),function(t,e){var n=Object.keys(t);f.info("keys:",n),f.info(t),n.forEach((function(n){var r=t[n],i="";r.cssClasses.length>0&&(i=i+" "+r.cssClasses.join(" "));var a={labelStyle:""},o=void 0!==r.text?r.text:r.id,s="";switch(r.type){case"class":s="class_box";break;default:s="class_box"}e.setNode(r.id,{labelStyle:a.labelStyle,shape:s,labelText:o,classData:r,rx:0,ry:0,class:i,style:a.style,id:r.id,domId:r.domId,haveCallback:r.haveCallback,link:r.link,width:"group"===r.type?500:void 0,type:r.type,padding:xt().flowchart.padding}),f.info("setNode",{labelStyle:a.labelStyle,shape:s,labelText:o,rx:0,ry:0,class:i,style:a.style,id:r.id,width:"group"===r.type?500:void 0,type:r.type,padding:xt().flowchart.padding})}))}(o,a),function(t,e){var n=0;t.forEach((function(r){n++;var i={classes:"relation"};i.pattern=1==r.relation.lineType?"dashed":"solid",i.id="id"+n,"arrow_open"===r.type?i.arrowhead="none":i.arrowhead="normal",f.info(i,r),i.startLabelRight="none"===r.relationTitle1?"":r.relationTitle1,i.endLabelLeft="none"===r.relationTitle2?"":r.relationTitle2,i.arrowTypeStart=di(r.relation.type1),i.arrowTypeEnd=di(r.relation.type2);var a="",o="";if(void 0!==r.style){var c=N(r.style);a=c.style,o=c.labelStyle}else a="fill:none";i.style=a,i.labelStyle=o,void 0!==r.interpolate?i.curve=O(r.interpolate,s.curveLinear):void 0!==t.defaultInterpolate?i.curve=O(t.defaultInterpolate,s.curveLinear):i.curve=O(li.curve,s.curveLinear),r.text=r.title,void 0===r.text?void 0!==r.style&&(i.arrowheadStyle="fill: #333"):(i.arrowheadStyle="fill: #333",i.labelpos="c",xt().flowchart.htmlLabels,i.labelType="text",i.label=r.text.replace(x.lineBreakRegex,"\n"),void 0===r.style&&(i.style=i.style||"stroke: #333; stroke-width: 1.5px;fill:none"),i.labelStyle=i.labelStyle.replace("color:","fill:")),e.setEdge(r.id1,r.id2,i,n)}))}(c,a);var u=Object(s.select)('[id="'.concat(e,'"]'));u.attr("xmlns:xlink","http://www.w3.org/1999/xlink");var l=Object(s.select)("#"+e+" g");An(l,a,["aggregation","extension","composition","dependency"],"classDiagram",e);var h=u.node().getBBox(),d=h.width+16,p=h.height+16;if(f.debug("new ViewBox 0 0 ".concat(d," ").concat(p),"translate(".concat(8-a._label.marginx,", ").concat(8-a._label.marginy,")")),$(u,p,d,n.useMaxWidth),u.attr("viewBox","0 0 ".concat(d," ").concat(p)),u.select("g").attr("transform","translate(".concat(8-a._label.marginx,", ").concat(8-h.y,")")),!n.htmlLabels)for(var g=document.querySelectorAll('[id="'+e+'"] .edgeLabel .label'),y=0;y0&&o.length>0){var c={stmt:"state",id:L(),type:"divider",doc:yi(o)};i.push(yi(c)),n.doc=i}n.doc.forEach((function(e){return t(n,e,!0)}))}}({id:"root"},{id:"root",doc:vi},!0),{id:"root",doc:vi}},extract:function(t){var e;e=t.doc?t.doc:t,f.info(e),ki(),f.info("Extract",e),e.forEach((function(t){"state"===t.stmt&&_i(t.id,t.type,t.doc,t.description,t.note),"relation"===t.stmt&&wi(t.state1.id,t.state2.id,t.description)}))},trimColon:function(t){return t&&":"===t[0]?t.substr(1).trim():t.trim()}},Ai=n(22),Mi=n.n(Ai),Oi={},Di=function(t,e){Oi[t]=e},Ni=function(t,e){var n=t.append("text").attr("x",2*xt().state.padding).attr("y",xt().state.textHeight+1.3*xt().state.padding).attr("font-size",xt().state.fontSize).attr("class","state-title").text(e.descriptions[0]).node().getBBox(),r=n.height,i=t.append("text").attr("x",xt().state.padding).attr("y",r+.4*xt().state.padding+xt().state.dividerMargin+xt().state.textHeight).attr("class","state-description"),a=!0,o=!0;e.descriptions.forEach((function(t){a||(!function(t,e,n){var r=t.append("tspan").attr("x",2*xt().state.padding).text(e);n||r.attr("dy",xt().state.textHeight)}(i,t,o),o=!1),a=!1}));var s=t.append("line").attr("x1",xt().state.padding).attr("y1",xt().state.padding+r+xt().state.dividerMargin/2).attr("y2",xt().state.padding+r+xt().state.dividerMargin/2).attr("class","descr-divider"),c=i.node().getBBox(),u=Math.max(c.width,n.width);return s.attr("x2",u+3*xt().state.padding),t.insert("rect",":first-child").attr("x",xt().state.padding).attr("y",xt().state.padding).attr("width",u+2*xt().state.padding).attr("height",c.height+r+2*xt().state.padding).attr("rx",xt().state.radius),t},Bi=function(t,e,n){var r,i=xt().state.padding,a=2*xt().state.padding,o=t.node().getBBox(),s=o.width,c=o.x,u=t.append("text").attr("x",0).attr("y",xt().state.titleShift).attr("font-size",xt().state.fontSize).attr("class","state-title").text(e.id),l=u.node().getBBox().width+a,h=Math.max(l,s);h===s&&(h+=a);var f=t.node().getBBox();e.doc,r=c-i,l>s&&(r=(s-h)/2+i),Math.abs(c-f.x)s&&(r=c-(l-s)/2);var d=1-xt().state.textHeight;return t.insert("rect",":first-child").attr("x",r).attr("y",d).attr("class",n?"alt-composit":"composit").attr("width",h).attr("height",f.height+xt().state.textHeight+xt().state.titleShift+1).attr("rx","0"),u.attr("x",r+i),l<=s&&u.attr("x",c+(h-a)/2-l/2+i),t.insert("rect",":first-child").attr("x",r).attr("y",xt().state.titleShift-xt().state.textHeight-xt().state.padding).attr("width",h).attr("height",3*xt().state.textHeight).attr("rx",xt().state.radius),t.insert("rect",":first-child").attr("x",r).attr("y",xt().state.titleShift-xt().state.textHeight-xt().state.padding).attr("width",h).attr("height",f.height+3+2*xt().state.textHeight).attr("rx",xt().state.radius),t},Li=function(t,e){e.attr("class","state-note");var n=e.append("rect").attr("x",0).attr("y",xt().state.padding),r=function(t,e,n,r){var i=0,a=r.append("text");a.style("text-anchor","start"),a.attr("class","noteText");var o=t.replace(/\r\n/g,"
"),s=(o=o.replace(/\n/g,"
")).split(x.lineBreakRegex),c=1.25*xt().state.noteMargin,u=!0,l=!1,h=void 0;try{for(var f,d=s[Symbol.iterator]();!(u=(f=d.next()).done);u=!0){var p=f.value.trim();if(p.length>0){var g=a.append("tspan");if(g.text(p),0===c)c+=g.node().getBBox().height;i+=c,g.attr("x",e+xt().state.noteMargin),g.attr("y",n+i+1.25*xt().state.noteMargin)}}}catch(t){l=!0,h=t}finally{try{u||null==d.return||d.return()}finally{if(l)throw h}}return{textWidth:a.node().getBBox().width,textHeight:i}}(t,0,0,e.append("g")),i=r.textWidth,a=r.textHeight;return n.attr("height",a+2*xt().state.noteMargin),n.attr("width",i+2*xt().state.noteMargin),n},Fi=function(t,e){var n=e.id,r={id:n,label:e.id,width:0,height:0},i=t.append("g").attr("id",n).attr("class","stateGroup");"start"===e.type&&function(t){t.append("circle").attr("class","start-state").attr("r",xt().state.sizeUnit).attr("cx",xt().state.padding+xt().state.sizeUnit).attr("cy",xt().state.padding+xt().state.sizeUnit)}(i),"end"===e.type&&function(t){t.append("circle").attr("class","end-state-outer").attr("r",xt().state.sizeUnit+xt().state.miniPadding).attr("cx",xt().state.padding+xt().state.sizeUnit+xt().state.miniPadding).attr("cy",xt().state.padding+xt().state.sizeUnit+xt().state.miniPadding),t.append("circle").attr("class","end-state-inner").attr("r",xt().state.sizeUnit).attr("cx",xt().state.padding+xt().state.sizeUnit+2).attr("cy",xt().state.padding+xt().state.sizeUnit+2)}(i),"fork"!==e.type&&"join"!==e.type||function(t,e){var n=xt().state.forkWidth,r=xt().state.forkHeight;if(e.parentId){var i=n;n=r,r=i}t.append("rect").style("stroke","black").style("fill","black").attr("width",n).attr("height",r).attr("x",xt().state.padding).attr("y",xt().state.padding)}(i,e),"note"===e.type&&Li(e.note.text,i),"divider"===e.type&&function(t){t.append("line").style("stroke","grey").style("stroke-dasharray","3").attr("x1",xt().state.textHeight).attr("class","divider").attr("x2",2*xt().state.textHeight).attr("y1",0).attr("y2",0)}(i),"default"===e.type&&0===e.descriptions.length&&function(t,e){var n=t.append("text").attr("x",2*xt().state.padding).attr("y",xt().state.textHeight+2*xt().state.padding).attr("font-size",xt().state.fontSize).attr("class","state-title").text(e.id),r=n.node().getBBox();t.insert("rect",":first-child").attr("x",xt().state.padding).attr("y",xt().state.padding).attr("width",r.width+2*xt().state.padding).attr("height",r.height+2*xt().state.padding).attr("rx",xt().state.radius)}(i,e),"default"===e.type&&e.descriptions.length>0&&Ni(i,e);var a=i.node().getBBox();return r.width=a.width+2*xt().state.padding,r.height=a.height+2*xt().state.padding,Di(n,r),r},Pi=0;Ai.parser.yy=Si;var Ii={},ji=function t(e,n,r,i){var a,o=new H.a.Graph({compound:!0,multigraph:!0}),c=!0;for(a=0;a "+t.w+": "+JSON.stringify(o.edge(t))),function(t,e,n){e.points=e.points.filter((function(t){return!Number.isNaN(t.y)}));var r=e.points,i=Object(s.line)().x((function(t){return t.x})).y((function(t){return t.y})).curve(s.curveBasis),a=t.append("path").attr("d",i(r)).attr("id","edge"+Pi).attr("class","transition"),o="";if(xt().state.arrowMarkerAbsolute&&(o=(o=(o=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search).replace(/\(/g,"\\(")).replace(/\)/g,"\\)")),a.attr("marker-end","url("+o+"#"+function(t){switch(t){case Si.relationType.AGGREGATION:return"aggregation";case Si.relationType.EXTENSION:return"extension";case Si.relationType.COMPOSITION:return"composition";case Si.relationType.DEPENDENCY:return"dependency"}}(Si.relationType.DEPENDENCY)+"End)"),void 0!==n.title){for(var c=t.append("g").attr("class","stateLabel"),u=W.calcLabelPosition(e.points),l=u.x,h=u.y,d=x.getRows(n.title),p=0,g=[],y=0,v=0,m=0;m<=d.length;m++){var b=c.append("text").attr("text-anchor","middle").text(d[m]).attr("x",l).attr("y",h+p),_=b.node().getBBox();if(y=Math.max(y,_.width),v=Math.min(v,_.x),f.info(_.x,l,h+p),0===p){var k=b.node().getBBox();p=k.height,f.info("Title height",p,h)}g.push(b)}var w=p*d.length;if(d.length>1){var E=(d.length-1)*p*.5;g.forEach((function(t,e){return t.attr("y",h+e*p-E)})),w=p*d.length}var T=c.node().getBBox();c.insert("rect",":first-child").attr("class","box").attr("x",l-y/2-xt().state.padding/2).attr("y",h-w/2-xt().state.padding/2-3.5).attr("width",y+xt().state.padding).attr("height",w+xt().state.padding),f.info(T)}Pi++}(n,o.edge(t),o.edge(t).relation))})),w=k.getBBox();var E={id:r||"root",label:r||"root",width:0,height:0};return E.width=w.width+2*gi.padding,E.height=w.height+2*gi.padding,f.debug("Doc rendered",E,o),E},Ri=function(){},Yi=function(t,e){gi=xt().state,Ai.parser.yy.clear(),Ai.parser.parse(t),f.debug("Rendering diagram "+t);var n=Object(s.select)("[id='".concat(e,"']"));n.append("defs").append("marker").attr("id","dependencyEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 19,7 L9,13 L14,7 L9,1 Z"),new H.a.Graph({multigraph:!0,compound:!0,rankdir:"RL"}).setDefaultEdgeLabel((function(){return{}}));var r=Si.getRootDoc();ji(r,n,void 0,!1);var i=gi.padding,a=n.node().getBBox(),o=a.width+2*i,c=a.height+2*i;$(n,c,1.75*o,gi.useMaxWidth),n.attr("viewBox","".concat(a.x-gi.padding," ").concat(a.y-gi.padding," ")+o+" "+c)},zi={},Ui={},$i=function(t,e,n,r){if("root"!==n.id){var i="rect";!0===n.start&&(i="start"),!1===n.start&&(i="end"),"default"!==n.type&&(i=n.type),Ui[n.id]||(Ui[n.id]={id:n.id,shape:i,description:n.id,classes:"statediagram-state"}),n.description&&(Array.isArray(Ui[n.id].description)?(Ui[n.id].shape="rectWithTitle",Ui[n.id].description.push(n.description)):Ui[n.id].description.length>0?(Ui[n.id].shape="rectWithTitle",Ui[n.id].description===n.id?Ui[n.id].description=[n.description]:Ui[n.id].description=[Ui[n.id].description,n.description]):(Ui[n.id].shape="rect",Ui[n.id].description=n.description)),!Ui[n.id].type&&n.doc&&(f.info("Setting cluser for ",n.id),Ui[n.id].type="group",Ui[n.id].shape="divider"===n.type?"divider":"roundedWithTitle",Ui[n.id].classes=Ui[n.id].classes+" "+(r?"statediagram-cluster statediagram-cluster-alt":"statediagram-cluster"));var a={labelStyle:"",shape:Ui[n.id].shape,labelText:Ui[n.id].description,classes:Ui[n.id].classes,style:"",id:n.id,domId:"state-"+n.id+"-"+Wi,type:Ui[n.id].type,padding:15};if(n.note){var o={labelStyle:"",shape:"note",labelText:n.note.text,classes:"statediagram-note",style:"",id:n.id+"----note",domId:"state-"+n.id+"----note-"+Wi,type:Ui[n.id].type,padding:15},s={labelStyle:"",shape:"noteGroup",labelText:n.note.text,classes:Ui[n.id].classes,style:"",id:n.id+"----parent",domId:"state-"+n.id+"----parent-"+Wi,type:"group",padding:0};Wi++,t.setNode(n.id+"----parent",s),t.setNode(o.id,o),t.setNode(n.id,a),t.setParent(n.id,n.id+"----parent"),t.setParent(o.id,n.id+"----parent");var c=n.id,u=o.id;"left of"===n.note.position&&(c=o.id,u=n.id),t.setEdge(c,u,{arrowhead:"none",arrowType:"",style:"fill:none",labelStyle:"",classes:"transition note-edge",arrowheadStyle:"fill: #333",labelpos:"c",labelType:"text",thickness:"normal"})}else t.setNode(n.id,a)}e&&"root"!==e.id&&(f.info("Setting node ",n.id," to be child of its parent ",e.id),t.setParent(n.id,e.id)),n.doc&&(f.info("Adding nodes children "),Vi(t,n,n.doc,!r))},Wi=0,Vi=function(t,e,n,r){Wi=0,f.trace("items",n),n.forEach((function(n){if("state"===n.stmt||"default"===n.stmt)$i(t,e,n,r);else if("relation"===n.stmt){$i(t,e,n.state1,r),$i(t,e,n.state2,r);var i={id:"edge"+Wi,arrowhead:"normal",arrowTypeEnd:"arrow_barb",style:"fill:none",labelStyle:"",label:n.description,arrowheadStyle:"fill: #333",labelpos:"c",labelType:"text",thickness:"normal",classes:"transition"},a=n.state1.id,o=n.state2.id;t.setEdge(a,o,i,Wi),Wi++}}))},Hi=function(t){for(var e=Object.keys(t),n=0;ne.seq?t:e}),t[0]),n="";t.forEach((function(t){n+=t===e?"\t*":"\t|"}));var r,i,a,o=[n,e.id,e.seq];for(var s in Zi)Zi[s]===e.id&&o.push(s);if(f.debug(o.join(" ")),Array.isArray(e.parent)){var c=qi[e.parent[0]];ra(t,e,c),t.push(qi[e.parent[1]])}else{if(null==e.parent)return;var u=qi[e.parent];ra(t,e,u)}r=t,i=function(t){return t.id},a=Object.create(null),ia(t=r.reduce((function(t,e){var n=i(e);return a[n]||(a[n]=!0,t.push(e)),t}),[]))}var aa,oa=function(){var t=Object.keys(qi).map((function(t){return qi[t]}));return t.forEach((function(t){f.debug(t.id)})),t.sort((function(t,e){return e.seq-t.seq})),t},sa={setDirection:function(t){Qi=t},setOptions:function(t){f.debug("options str",t),t=(t=t&&t.trim())||"{}";try{na=JSON.parse(t)}catch(t){f.error("error while parsing gitGraph options",t.message)}},getOptions:function(){return na},commit:function(t){var e={id:ta(),message:t,seq:Ki++,parent:null==Xi?null:Xi.id};Xi=e,qi[e.id]=e,Zi[Ji]=e.id,f.debug("in pushCommit "+e.id)},branch:function(t){Zi[t]=null!=Xi?Xi.id:null,f.debug("in createBranch")},merge:function(t){var e=qi[Zi[Ji]],n=qi[Zi[t]];if(function(t,e){return t.seq>e.seq&&ea(e,t)}(e,n))f.debug("Already merged");else{if(ea(e,n))Zi[Ji]=Zi[t],Xi=qi[Zi[Ji]];else{var r={id:ta(),message:"merged branch "+t+" into "+Ji,seq:Ki++,parent:[null==Xi?null:Xi.id,Zi[t]]};Xi=r,qi[r.id]=r,Zi[Ji]=r.id}f.debug(Zi),f.debug("in mergeBranch")}},checkout:function(t){f.debug("in checkout");var e=Zi[Ji=t];Xi=qi[e]},reset:function(t){f.debug("in reset",t);var e=t.split(":")[0],n=parseInt(t.split(":")[1]),r="HEAD"===e?Xi:qi[Zi[e]];for(f.debug(r,n);n>0;)if(n--,!(r=qi[r.parent])){var i="Critical error - unique parent commit not found during reset";throw f.error(i),i}Xi=r,Zi[Ji]=r.id},prettyPrint:function(){f.debug(qi),ia([oa()[0]])},clear:function(){qi={},Zi={master:Xi=null},Ji="master",Ki=0},getBranchesAsObjArray:function(){var t=[];for(var e in Zi)t.push({name:e,commit:qi[Zi[e]]});return t},getBranches:function(){return Zi},getCommits:function(){return qi},getCommitsArray:oa,getCurrentBranch:function(){return Ji},getDirection:function(){return Qi},getHead:function(){return Xi}},ca=n(71),ua=n.n(ca),la={},ha={nodeSpacing:150,nodeFillColor:"yellow",nodeStrokeWidth:2,nodeStrokeColor:"grey",lineStrokeWidth:4,branchOffset:50,lineColor:"grey",leftMargin:50,branchColors:["#442f74","#983351","#609732","#AA9A39"],nodeRadius:10,nodeLabel:{width:75,height:100,x:-25,y:0}},fa={};function da(t,e,n,r){var i=O(r,s.curveBasis),a=ha.branchColors[n%ha.branchColors.length],o=Object(s.line)().x((function(t){return Math.round(t.x)})).y((function(t){return Math.round(t.y)})).curve(i);t.append("svg:path").attr("d",o(e)).style("stroke",a).style("stroke-width",ha.lineStrokeWidth).style("fill","none")}function pa(t,e){e=e||t.node().getBBox();var n=t.node().getCTM();return{left:n.e+e.x*n.a,top:n.f+e.y*n.d,width:e.width,height:e.height}}function ga(t,e,n,r,i){f.debug("svgDrawLineForCommits: ",e,n);var a=pa(t.select("#node-"+e+" circle")),o=pa(t.select("#node-"+n+" circle"));switch(r){case"LR":if(a.left-o.left>ha.nodeSpacing){var s={x:a.left-ha.nodeSpacing,y:o.top+o.height/2};da(t,[s,{x:o.left+o.width,y:o.top+o.height/2}],i,"linear"),da(t,[{x:a.left,y:a.top+a.height/2},{x:a.left-ha.nodeSpacing/2,y:a.top+a.height/2},{x:a.left-ha.nodeSpacing/2,y:s.y},s],i)}else da(t,[{x:a.left,y:a.top+a.height/2},{x:a.left-ha.nodeSpacing/2,y:a.top+a.height/2},{x:a.left-ha.nodeSpacing/2,y:o.top+o.height/2},{x:o.left+o.width,y:o.top+o.height/2}],i);break;case"BT":if(o.top-a.top>ha.nodeSpacing){var c={x:o.left+o.width/2,y:a.top+a.height+ha.nodeSpacing};da(t,[c,{x:o.left+o.width/2,y:o.top}],i,"linear"),da(t,[{x:a.left+a.width/2,y:a.top+a.height},{x:a.left+a.width/2,y:a.top+a.height+ha.nodeSpacing/2},{x:o.left+o.width/2,y:c.y-ha.nodeSpacing/2},c],i)}else da(t,[{x:a.left+a.width/2,y:a.top+a.height},{x:a.left+a.width/2,y:a.top+ha.nodeSpacing/2},{x:o.left+o.width/2,y:o.top-ha.nodeSpacing/2},{x:o.left+o.width/2,y:o.top}],i)}}function ya(t,e){return t.select(e).node().cloneNode(!0)}function va(t,e,n,r){var i,a=Object.keys(la).length;if("string"==typeof e)do{if(i=la[e],f.debug("in renderCommitHistory",i.id,i.seq),t.select("#node-"+e).size()>0)return;t.append((function(){return ya(t,"#def-commit")})).attr("class","commit").attr("id",(function(){return"node-"+i.id})).attr("transform",(function(){switch(r){case"LR":return"translate("+(i.seq*ha.nodeSpacing+ha.leftMargin)+", "+aa*ha.branchOffset+")";case"BT":return"translate("+(aa*ha.branchOffset+ha.leftMargin)+", "+(a-i.seq)*ha.nodeSpacing+")"}})).attr("fill",ha.nodeFillColor).attr("stroke",ha.nodeStrokeColor).attr("stroke-width",ha.nodeStrokeWidth);var o=void 0;for(var s in n)if(n[s].commit===i){o=n[s];break}o&&(f.debug("found branch ",o.name),t.select("#node-"+i.id+" p").append("xhtml:span").attr("class","branch-label").text(o.name+", ")),t.select("#node-"+i.id+" p").append("xhtml:span").attr("class","commit-id").text(i.id),""!==i.message&&"BT"===r&&t.select("#node-"+i.id+" p").append("xhtml:span").attr("class","commit-msg").text(", "+i.message),e=i.parent}while(e&&la[e]);Array.isArray(e)&&(f.debug("found merge commmit",e),va(t,e[0],n,r),aa++,va(t,e[1],n,r),aa--)}function ma(t,e,n,r){for(r=r||0;e.seq>0&&!e.lineDrawn;)"string"==typeof e.parent?(ga(t,e.id,e.parent,n,r),e.lineDrawn=!0,e=la[e.parent]):Array.isArray(e.parent)&&(ga(t,e.id,e.parent[0],n,r),ga(t,e.id,e.parent[1],n,r+1),ma(t,la[e.parent[1]],n,r+1),e.lineDrawn=!0,e=la[e.parent[0]])}var ba,xa=function(t){fa=t},_a=function(t,e,n){try{var r=ua.a.parser;r.yy=sa,r.yy.clear(),f.debug("in gitgraph renderer",t+"\n","id:",e,n),r.parse(t+"\n"),ha=Object.assign(ha,fa,sa.getOptions()),f.debug("effective options",ha);var i=sa.getDirection();la=sa.getCommits();var a=sa.getBranchesAsObjArray();"BT"===i&&(ha.nodeLabel.x=a.length*ha.branchOffset,ha.nodeLabel.width="100%",ha.nodeLabel.y=-2*ha.nodeRadius);var o=Object(s.select)('[id="'.concat(e,'"]'));for(var c in function(t){t.append("defs").append("g").attr("id","def-commit").append("circle").attr("r",ha.nodeRadius).attr("cx",0).attr("cy",0),t.select("#def-commit").append("foreignObject").attr("width",ha.nodeLabel.width).attr("height",ha.nodeLabel.height).attr("x",ha.nodeLabel.x).attr("y",ha.nodeLabel.y).attr("class","node-label").attr("requiredFeatures","http://www.w3.org/TR/SVG11/feature#Extensibility").append("p").html("")}(o),aa=1,a){var u=a[c];va(o,u.commit.id,a,i),ma(o,u.commit,i),aa++}o.attr("height",(function(){return"BT"===i?Object.keys(la).length*ha.nodeSpacing:(a.length+1)*ha.branchOffset}))}catch(t){f.error("Error while rendering gitgraph"),f.error(t.message)}},ka="",wa=!1,Ea={setMessage:function(t){f.debug("Setting message to: "+t),ka=t},getMessage:function(){return ka},setInfo:function(t){wa=t},getInfo:function(){return wa}},Ta=n(72),Ca=n.n(Ta),Sa={},Aa=function(t){Object.keys(t).forEach((function(e){Sa[e]=t[e]}))},Ma=function(t,e,n){try{var r=Ca.a.parser;r.yy=Ea,f.debug("Renering info diagram\n"+t),r.parse(t),f.debug("Parsed info diagram");var i=Object(s.select)("#"+e);i.append("g").append("text").attr("x",100).attr("y",40).attr("class","version").attr("font-size","32px").style("text-anchor","middle").text("v "+n),i.attr("height",100),i.attr("width",400)}catch(t){f.error("Error while rendering info diagram"),f.error(t.message)}},Oa={},Da=function(t){Object.keys(t).forEach((function(e){Oa[e]=t[e]}))},Na=function(t,e){try{f.debug("Renering svg for syntax error\n");var n=Object(s.select)("#"+t),r=n.append("g");r.append("path").attr("class","error-icon").attr("d","m411.313,123.313c6.25-6.25 6.25-16.375 0-22.625s-16.375-6.25-22.625,0l-32,32-9.375,9.375-20.688-20.688c-12.484-12.5-32.766-12.5-45.25,0l-16,16c-1.261,1.261-2.304,2.648-3.31,4.051-21.739-8.561-45.324-13.426-70.065-13.426-105.867,0-192,86.133-192,192s86.133,192 192,192 192-86.133 192-192c0-24.741-4.864-48.327-13.426-70.065 1.402-1.007 2.79-2.049 4.051-3.31l16-16c12.5-12.492 12.5-32.758 0-45.25l-20.688-20.688 9.375-9.375 32.001-31.999zm-219.313,100.687c-52.938,0-96,43.063-96,96 0,8.836-7.164,16-16,16s-16-7.164-16-16c0-70.578 57.422-128 128-128 8.836,0 16,7.164 16,16s-7.164,16-16,16z"),r.append("path").attr("class","error-icon").attr("d","m459.02,148.98c-6.25-6.25-16.375-6.25-22.625,0s-6.25,16.375 0,22.625l16,16c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688 6.25-6.25 6.25-16.375 0-22.625l-16.001-16z"),r.append("path").attr("class","error-icon").attr("d","m340.395,75.605c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688 6.25-6.25 6.25-16.375 0-22.625l-16-16c-6.25-6.25-16.375-6.25-22.625,0s-6.25,16.375 0,22.625l15.999,16z"),r.append("path").attr("class","error-icon").attr("d","m400,64c8.844,0 16-7.164 16-16v-32c0-8.836-7.156-16-16-16-8.844,0-16,7.164-16,16v32c0,8.836 7.156,16 16,16z"),r.append("path").attr("class","error-icon").attr("d","m496,96.586h-32c-8.844,0-16,7.164-16,16 0,8.836 7.156,16 16,16h32c8.844,0 16-7.164 16-16 0-8.836-7.156-16-16-16z"),r.append("path").attr("class","error-icon").attr("d","m436.98,75.605c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688l32-32c6.25-6.25 6.25-16.375 0-22.625s-16.375-6.25-22.625,0l-32,32c-6.251,6.25-6.251,16.375-0.001,22.625z"),r.append("text").attr("class","error-text").attr("x",1240).attr("y",250).attr("font-size","150px").style("text-anchor","middle").text("Syntax error in graph"),r.append("text").attr("class","error-text").attr("x",1050).attr("y",400).attr("font-size","100px").style("text-anchor","middle").text("mermaid version "+e),n.attr("height",100),n.attr("width",400),n.attr("viewBox","768 0 512 512")}catch(t){f.error("Error while rendering info diagram"),f.error(t.message)}},Ba={},La="",Fa={parseDirective:function(t,e,n){$o.parseDirective(this,t,e,n)},getConfig:function(){return xt().pie},addSection:function(t,e){void 0===Ba[t]&&(Ba[t]=e,f.debug("Added new section :",t))},getSections:function(){return Ba},cleanupValue:function(t){return":"===t.substring(0,1)?(t=t.substring(1).trim(),Number(t.trim())):Number(t.trim())},clear:function(){Ba={},La=""},setTitle:function(t){La=t},getTitle:function(){return La}},Pa=n(73),Ia=n.n(Pa),ja={},Ra=function(t){Object.keys(t).forEach((function(e){ja[e]=t[e]}))},Ya=function(t,e){try{var n=Ia.a.parser;n.yy=Fa,f.debug("Rendering info diagram\n"+t),n.yy.clear(),n.parse(t),f.debug("Parsed info diagram");var r=document.getElementById(e);void 0===(ba=r.parentElement.offsetWidth)&&(ba=1200),void 0!==ja.useWidth&&(ba=ja.useWidth);var i=Object(s.select)("#"+e);$(i,450,ba,ja.useMaxWidth),r.setAttribute("viewBox","0 0 "+ba+" 450");var a=Math.min(ba,450)/2-40,o=i.append("g").attr("transform","translate("+ba/2+",225)"),c=Fa.getSections(),u=0;Object.keys(c).forEach((function(t){u+=c[t]}));var l=Object(s.scaleOrdinal)().domain(c).range(s.schemeSet2),h=Object(s.pie)().value((function(t){return t.value}))(Object(s.entries)(c)),d=Object(s.arc)().innerRadius(0).outerRadius(a);o.selectAll("mySlices").data(h).enter().append("path").attr("d",d).attr("fill",(function(t){return l(t.data.key)})).attr("stroke","black").style("stroke-width","2px").style("opacity",.7),o.selectAll("mySlices").data(h).enter().append("text").text((function(t){return(t.data.value/u*100).toFixed(0)+"%"})).attr("transform",(function(t){return"translate("+d.centroid(t)+")"})).style("text-anchor","middle").attr("class","slice").style("font-size",17),o.append("text").text(n.yy.getTitle()).attr("x",0).attr("y",-200).attr("class","pieTitleText");var p=o.selectAll(".legend").data(l.domain()).enter().append("g").attr("class","legend").attr("transform",(function(t,e){return"translate(216,"+(22*e-22*l.domain().length/2)+")"}));p.append("rect").attr("width",18).attr("height",18).style("fill",l).style("stroke",l),p.append("text").attr("x",22).attr("y",14).text((function(t){return t}))}catch(t){f.error("Error while rendering info diagram"),f.error(t)}},za={},Ua=[],$a="",Wa={Cardinality:{ZERO_OR_ONE:"ZERO_OR_ONE",ZERO_OR_MORE:"ZERO_OR_MORE",ONE_OR_MORE:"ONE_OR_MORE",ONLY_ONE:"ONLY_ONE"},Identification:{NON_IDENTIFYING:"NON_IDENTIFYING",IDENTIFYING:"IDENTIFYING"},parseDirective:function(t,e,n){$o.parseDirective(this,t,e,n)},getConfig:function(){return xt().er},addEntity:function(t){void 0===za[t]&&(za[t]=t,f.debug("Added new entity :",t))},getEntities:function(){return za},addRelationship:function(t,e,n,r){var i={entityA:t,roleA:e,entityB:n,relSpec:r};Ua.push(i),f.debug("Added new relationship :",i)},getRelationships:function(){return Ua},clear:function(){za={},Ua=[],$a=""},setTitle:function(t){$a=t},getTitle:function(){return $a}},Va=n(74),Ha=n.n(Va),Ga={ONLY_ONE_START:"ONLY_ONE_START",ONLY_ONE_END:"ONLY_ONE_END",ZERO_OR_ONE_START:"ZERO_OR_ONE_START",ZERO_OR_ONE_END:"ZERO_OR_ONE_END",ONE_OR_MORE_START:"ONE_OR_MORE_START",ONE_OR_MORE_END:"ONE_OR_MORE_END",ZERO_OR_MORE_START:"ZERO_OR_MORE_START",ZERO_OR_MORE_END:"ZERO_OR_MORE_END"},qa=Ga,Xa=function(t,e){var n;t.append("defs").append("marker").attr("id",Ga.ONLY_ONE_START).attr("refX",0).attr("refY",9).attr("markerWidth",18).attr("markerHeight",18).attr("orient","auto").append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M9,0 L9,18 M15,0 L15,18"),t.append("defs").append("marker").attr("id",Ga.ONLY_ONE_END).attr("refX",18).attr("refY",9).attr("markerWidth",18).attr("markerHeight",18).attr("orient","auto").append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M3,0 L3,18 M9,0 L9,18"),(n=t.append("defs").append("marker").attr("id",Ga.ZERO_OR_ONE_START).attr("refX",0).attr("refY",9).attr("markerWidth",30).attr("markerHeight",18).attr("orient","auto")).append("circle").attr("stroke",e.stroke).attr("fill","white").attr("cx",21).attr("cy",9).attr("r",6),n.append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M9,0 L9,18"),(n=t.append("defs").append("marker").attr("id",Ga.ZERO_OR_ONE_END).attr("refX",30).attr("refY",9).attr("markerWidth",30).attr("markerHeight",18).attr("orient","auto")).append("circle").attr("stroke",e.stroke).attr("fill","white").attr("cx",9).attr("cy",9).attr("r",6),n.append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M21,0 L21,18"),t.append("defs").append("marker").attr("id",Ga.ONE_OR_MORE_START).attr("refX",18).attr("refY",18).attr("markerWidth",45).attr("markerHeight",36).attr("orient","auto").append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M0,18 Q 18,0 36,18 Q 18,36 0,18 M42,9 L42,27"),t.append("defs").append("marker").attr("id",Ga.ONE_OR_MORE_END).attr("refX",27).attr("refY",18).attr("markerWidth",45).attr("markerHeight",36).attr("orient","auto").append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M3,9 L3,27 M9,18 Q27,0 45,18 Q27,36 9,18"),(n=t.append("defs").append("marker").attr("id",Ga.ZERO_OR_MORE_START).attr("refX",18).attr("refY",18).attr("markerWidth",57).attr("markerHeight",36).attr("orient","auto")).append("circle").attr("stroke",e.stroke).attr("fill","white").attr("cx",48).attr("cy",18).attr("r",6),n.append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M0,18 Q18,0 36,18 Q18,36 0,18"),(n=t.append("defs").append("marker").attr("id",Ga.ZERO_OR_MORE_END).attr("refX",39).attr("refY",18).attr("markerWidth",57).attr("markerHeight",36).attr("orient","auto")).append("circle").attr("stroke",e.stroke).attr("fill","white").attr("cx",9).attr("cy",18).attr("r",6),n.append("path").attr("stroke",e.stroke).attr("fill","none").attr("d","M21,18 Q39,0 57,18 Q39,36 21,18")},Za={},Ja=function(t){return(t.entityA+t.roleA+t.entityB).replace(/\s/g,"")},Qa=0,Ka=function(t){for(var e=Object.keys(t),n=0;n/gi," "),r=t.append("text");r.attr("x",e.x),r.attr("y",e.y),r.attr("class","legend"),r.style("text-anchor",e.anchor),void 0!==e.class&&r.attr("class",e.class);var i=r.append("tspan");return i.attr("x",e.x+2*e.textMargin),i.text(n),r},go=-1,yo=function(){return{x:0,y:0,width:100,anchor:"start",height:100,rx:0,ry:0}},vo=function(){function t(t,e,n,i,a,o,s,c){r(e.append("text").attr("x",n+a/2).attr("y",i+o/2+5).style("font-color",c).style("text-anchor","middle").text(t),s)}function e(t,e,n,i,a,o,s,c,u){for(var l=c.taskFontSize,h=c.taskFontFamily,f=t.split(//gi),d=0;d3?function(t){var e=Object(s.arc)().startAngle(Math.PI/2).endAngle(Math.PI/2*3).innerRadius(7.5).outerRadius(15/2.2);t.append("path").attr("class","mouth").attr("d",e).attr("transform","translate("+o.cx+","+(o.cy+2)+")")}(c):o.score<3?function(t){var e=Object(s.arc)().startAngle(3*Math.PI/2).endAngle(Math.PI/2*5).innerRadius(7.5).outerRadius(15/2.2);t.append("path").attr("class","mouth").attr("d",e).attr("transform","translate("+o.cx+","+(o.cy+7)+")")}(c):function(t){t.append("line").attr("class","mouth").attr("stroke",2).attr("x1",o.cx-5).attr("y1",o.cy+7).attr("x2",o.cx+5).attr("y2",o.cy+7).attr("class","mouth").attr("stroke-width","1px").attr("stroke","#666")}(c);var u=yo();u.x=e.x,u.y=e.y,u.fill=e.fill,u.width=n.width,u.height=n.height,u.class="task task-type-"+e.num,u.rx=3,u.ry=3,ho(i,u);var l=e.x+14;e.people.forEach((function(t){var n=e.actors[t],r={cx:l,cy:e.y,r:7,fill:n,stroke:"#000",title:t};fo(i,r),l+=10})),vo(n)(e.task,i,u.x,u.y,u.width,u.height,{class:"task"},n,e.colour)},ko=function(t){t.append("defs").append("marker").attr("id","arrowhead").attr("refX",5).attr("refY",2).attr("markerWidth",6).attr("markerHeight",4).attr("orient","auto").append("path").attr("d","M 0,0 V 4 L6,2 Z")};eo.parser.yy=lo;var wo={leftMargin:150,diagramMarginX:50,diagramMarginY:20,taskMargin:50,width:150,height:50,taskFontSize:14,taskFontFamily:'"Open-Sans", "sans-serif"',boxMargin:10,boxTextMargin:5,noteMargin:10,messageMargin:35,messageAlign:"center",bottomMarginAdj:1,activationWidth:10,textPlacement:"fo",actorColours:["#8FBC8F","#7CFC00","#00FFFF","#20B2AA","#B0E0E6","#FFFFE0"],sectionFills:["#191970","#8B008B","#4B0082","#2F4F4F","#800000","#8B4513","#00008B"],sectionColours:["#fff"]},Eo={};var To=wo.leftMargin,Co={data:{startx:void 0,stopx:void 0,starty:void 0,stopy:void 0},verticalPos:0,sequenceItems:[],init:function(){this.sequenceItems=[],this.data={startx:void 0,stopx:void 0,starty:void 0,stopy:void 0},this.verticalPos=0},updateVal:function(t,e,n,r){void 0===t[e]?t[e]=n:t[e]=r(n,t[e])},updateBounds:function(t,e,n,r){var i,a=this,o=0;this.sequenceItems.forEach((function(s){o++;var c=a.sequenceItems.length-o+1;a.updateVal(s,"starty",e-c*wo.boxMargin,Math.min),a.updateVal(s,"stopy",r+c*wo.boxMargin,Math.max),a.updateVal(Co.data,"startx",t-c*wo.boxMargin,Math.min),a.updateVal(Co.data,"stopx",n+c*wo.boxMargin,Math.max),"activation"!==i&&(a.updateVal(s,"startx",t-c*wo.boxMargin,Math.min),a.updateVal(s,"stopx",n+c*wo.boxMargin,Math.max),a.updateVal(Co.data,"starty",e-c*wo.boxMargin,Math.min),a.updateVal(Co.data,"stopy",r+c*wo.boxMargin,Math.max))}))},insert:function(t,e,n,r){var i=Math.min(t,n),a=Math.max(t,n),o=Math.min(e,r),s=Math.max(e,r);this.updateVal(Co.data,"startx",i,Math.min),this.updateVal(Co.data,"starty",o,Math.min),this.updateVal(Co.data,"stopx",a,Math.max),this.updateVal(Co.data,"stopy",s,Math.max),this.updateBounds(i,o,a,s)},bumpVerticalPos:function(t){this.verticalPos=this.verticalPos+t,this.data.stopy=this.verticalPos},getVerticalPos:function(){return this.verticalPos},getBounds:function(){return this.data}},So=wo.sectionFills,Ao=wo.sectionColours,Mo=function(t,e,n){for(var r="",i=n+(2*wo.height+wo.diagramMarginY),a=0,o="#CCC",s="black",c=0,u=0;u tspan {\n fill: ").concat(t.actorTextColor,";\n stroke: none;\n }\n\n .actor-line {\n stroke: ").concat(t.actorLineColor,";\n }\n\n .messageLine0 {\n stroke-width: 1.5;\n stroke-dasharray: none;\n stroke: ").concat(t.signalColor,";\n }\n\n .messageLine1 {\n stroke-width: 1.5;\n stroke-dasharray: 2, 2;\n stroke: ").concat(t.signalColor,";\n }\n\n #arrowhead path {\n fill: ").concat(t.signalColor,";\n stroke: ").concat(t.signalColor,";\n }\n\n .sequenceNumber {\n fill: ").concat(t.sequenceNumberColor,";\n }\n\n #sequencenumber {\n fill: ").concat(t.signalColor,";\n }\n\n #crosshead path {\n fill: ").concat(t.signalColor,";\n stroke: ").concat(t.signalColor,";\n }\n\n .messageText {\n fill: ").concat(t.signalTextColor,";\n stroke: ").concat(t.signalTextColor,";\n }\n\n .labelBox {\n stroke: ").concat(t.labelBoxBorderColor,";\n fill: ").concat(t.labelBoxBkgColor,";\n }\n\n .labelText, .labelText > tspan {\n fill: ").concat(t.labelTextColor,";\n stroke: none;\n }\n\n .loopText, .loopText > tspan {\n fill: ").concat(t.loopTextColor,";\n stroke: none;\n }\n\n .loopLine {\n stroke-width: 2px;\n stroke-dasharray: 2, 2;\n stroke: ").concat(t.labelBoxBorderColor,";\n fill: ").concat(t.labelBoxBorderColor,";\n }\n\n .note {\n //stroke: #decc93;\n stroke: ").concat(t.noteBorderColor,";\n fill: ").concat(t.noteBkgColor,";\n }\n\n .noteText, .noteText > tspan {\n fill: ").concat(t.noteTextColor,";\n stroke: none;\n }\n\n .activation0 {\n fill: ").concat(t.activationBkgColor,";\n stroke: ").concat(t.activationBorderColor,";\n }\n\n .activation1 {\n fill: ").concat(t.activationBkgColor,";\n stroke: ").concat(t.activationBorderColor,";\n }\n\n .activation2 {\n fill: ").concat(t.activationBkgColor,";\n stroke: ").concat(t.activationBorderColor,";\n }\n")},gantt:function(t){return'\n .mermaid-main-font {\n font-family: "trebuchet ms", verdana, arial;\n font-family: var(--mermaid-font-family);\n }\n\n .section {\n stroke: none;\n opacity: 0.2;\n }\n\n .section0 {\n fill: '.concat(t.sectionBkgColor,";\n }\n\n .section2 {\n fill: ").concat(t.sectionBkgColor2,";\n }\n\n .section1,\n .section3 {\n fill: ").concat(t.altSectionBkgColor,";\n opacity: 0.2;\n }\n\n .sectionTitle0 {\n fill: ").concat(t.titleColor,";\n }\n\n .sectionTitle1 {\n fill: ").concat(t.titleColor,";\n }\n\n .sectionTitle2 {\n fill: ").concat(t.titleColor,";\n }\n\n .sectionTitle3 {\n fill: ").concat(t.titleColor,";\n }\n\n .sectionTitle {\n text-anchor: start;\n font-size: 11px;\n text-height: 14px;\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n\n }\n\n\n /* Grid and axis */\n\n .grid .tick {\n stroke: ").concat(t.gridColor,";\n opacity: 0.8;\n shape-rendering: crispEdges;\n text {\n font-family: ").concat(t.fontFamily,";\n fill: ").concat(t.textColor,";\n }\n }\n\n .grid path {\n stroke-width: 0;\n }\n\n\n /* Today line */\n\n .today {\n fill: none;\n stroke: ").concat(t.todayLineColor,";\n stroke-width: 2px;\n }\n\n\n /* Task styling */\n\n /* Default task */\n\n .task {\n stroke-width: 2;\n }\n\n .taskText {\n text-anchor: middle;\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n }\n\n .taskText:not([font-size]) {\n font-size: 11px;\n }\n\n .taskTextOutsideRight {\n fill: ").concat(t.taskTextDarkColor,";\n text-anchor: start;\n font-size: 11px;\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n\n }\n\n .taskTextOutsideLeft {\n fill: ").concat(t.taskTextDarkColor,";\n text-anchor: end;\n font-size: 11px;\n }\n\n /* Special case clickable */\n .task.clickable {\n cursor: pointer;\n }\n .taskText.clickable {\n cursor: pointer;\n fill: ").concat(t.taskTextClickableColor," !important;\n font-weight: bold;\n }\n\n .taskTextOutsideLeft.clickable {\n cursor: pointer;\n fill: ").concat(t.taskTextClickableColor," !important;\n font-weight: bold;\n }\n\n .taskTextOutsideRight.clickable {\n cursor: pointer;\n fill: ").concat(t.taskTextClickableColor," !important;\n font-weight: bold;\n }\n\n /* Specific task settings for the sections*/\n\n .taskText0,\n .taskText1,\n .taskText2,\n .taskText3 {\n fill: ").concat(t.taskTextColor,";\n }\n\n .task0,\n .task1,\n .task2,\n .task3 {\n fill: ").concat(t.taskBkgColor,";\n stroke: ").concat(t.taskBorderColor,";\n }\n\n .taskTextOutside0,\n .taskTextOutside2\n {\n fill: ").concat(t.taskTextOutsideColor,";\n }\n\n .taskTextOutside1,\n .taskTextOutside3 {\n fill: ").concat(t.taskTextOutsideColor,";\n }\n\n\n /* Active task */\n\n .active0,\n .active1,\n .active2,\n .active3 {\n fill: ").concat(t.activeTaskBkgColor,";\n stroke: ").concat(t.activeTaskBorderColor,";\n }\n\n .activeText0,\n .activeText1,\n .activeText2,\n .activeText3 {\n fill: ").concat(t.taskTextDarkColor," !important;\n }\n\n\n /* Completed task */\n\n .done0,\n .done1,\n .done2,\n .done3 {\n stroke: ").concat(t.doneTaskBorderColor,";\n fill: ").concat(t.doneTaskBkgColor,";\n stroke-width: 2;\n }\n\n .doneText0,\n .doneText1,\n .doneText2,\n .doneText3 {\n fill: ").concat(t.taskTextDarkColor," !important;\n }\n\n\n /* Tasks on the critical line */\n\n .crit0,\n .crit1,\n .crit2,\n .crit3 {\n stroke: ").concat(t.critBorderColor,";\n fill: ").concat(t.critBkgColor,";\n stroke-width: 2;\n }\n\n .activeCrit0,\n .activeCrit1,\n .activeCrit2,\n .activeCrit3 {\n stroke: ").concat(t.critBorderColor,";\n fill: ").concat(t.activeTaskBkgColor,";\n stroke-width: 2;\n }\n\n .doneCrit0,\n .doneCrit1,\n .doneCrit2,\n .doneCrit3 {\n stroke: ").concat(t.critBorderColor,";\n fill: ").concat(t.doneTaskBkgColor,";\n stroke-width: 2;\n cursor: pointer;\n shape-rendering: crispEdges;\n }\n\n .milestone {\n transform: rotate(45deg) scale(0.8,0.8);\n }\n\n .milestoneText {\n font-style: italic;\n }\n .doneCritText0,\n .doneCritText1,\n .doneCritText2,\n .doneCritText3 {\n fill: ").concat(t.taskTextDarkColor," !important;\n }\n\n .activeCritText0,\n .activeCritText1,\n .activeCritText2,\n .activeCritText3 {\n fill: ").concat(t.taskTextDarkColor," !important;\n }\n\n .titleText {\n text-anchor: middle;\n font-size: 18px;\n fill: ").concat(t.textColor," ;\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n }\n")},classDiagram:No,"classDiagram-v2":No,class:No,stateDiagram:Lo,state:Lo,git:function(){return"\n .commit-id,\n .commit-msg,\n .branch-label {\n fill: lightgrey;\n color: lightgrey;\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n }\n"},info:function(){return""},pie:function(t){return".pieTitleText {\n text-anchor: middle;\n font-size: 25px;\n fill: ".concat(t.taskTextDarkColor,";\n font-family: ").concat(t.fontFamily,";\n }\n .slice {\n font-family: ").concat(t.fontFamily,";\n fill: ").concat(t.textColor,";\n // fill: white;\n }\n .legend text {\n fill: ").concat(t.taskTextDarkColor,";\n font-family: ").concat(t.fontFamily,";\n font-size: 17px;\n }\n")},er:function(t){return"\n .entityBox {\n fill: ".concat(t.mainBkg,";\n stroke: ").concat(t.nodeBorder,";\n }\n\n .relationshipLabelBox {\n fill: ").concat(t.tertiaryColor,";\n opacity: 0.7;\n background-color: ").concat(t.tertiaryColor,";\n rect {\n opacity: 0.5;\n }\n }\n\n .relationshipLine {\n stroke: ").concat(t.lineColor,";\n }\n")},journey:function(t){return".label {\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n color: ".concat(t.textColor,";\n }\n .mouth {\n stroke: #666;\n }\n\n line {\n stroke: ").concat(t.textColor,"\n }\n\n .legend {\n fill: ").concat(t.textColor,";\n }\n\n .label text {\n fill: #333;\n }\n .label {\n color: ").concat(t.textColor,"\n }\n\n .face {\n fill: #FFF8DC;\n stroke: #999;\n }\n\n .node rect,\n .node circle,\n .node ellipse,\n .node polygon,\n .node path {\n fill: ").concat(t.mainBkg,";\n stroke: ").concat(t.nodeBorder,";\n stroke-width: 1px;\n }\n\n .node .label {\n text-align: center;\n }\n .node.clickable {\n cursor: pointer;\n }\n\n .arrowheadPath {\n fill: ").concat(t.arrowheadColor,";\n }\n\n .edgePath .path {\n stroke: ").concat(t.lineColor,";\n stroke-width: 1.5px;\n }\n\n .flowchart-link {\n stroke: ").concat(t.lineColor,";\n fill: none;\n }\n\n .edgeLabel {\n background-color: ").concat(t.edgeLabelBackground,";\n rect {\n opacity: 0.5;\n }\n text-align: center;\n }\n\n .cluster rect {\n }\n\n .cluster text {\n fill: ").concat(t.titleColor,";\n }\n\n div.mermaidTooltip {\n position: absolute;\n text-align: center;\n max-width: 200px;\n padding: 2px;\n font-family: 'trebuchet ms', verdana, arial;\n font-family: var(--mermaid-font-family);\n font-size: 12px;\n background: ").concat(t.tertiaryColor,";\n border: 1px solid ").concat(t.border2,";\n border-radius: 2px;\n pointer-events: none;\n z-index: 100;\n }\n\n .task-type-0, .section-type-0 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType0):"",";\n }\n .task-type-1, .section-type-1 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType1):"",";\n }\n .task-type-2, .section-type-2 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType2):"",";\n }\n .task-type-3, .section-type-3 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType3):"",";\n }\n .task-type-4, .section-type-4 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType4):"",";\n }\n .task-type-5, .section-type-5 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType5):"",";\n }\n .task-type-6, .section-type-6 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType6):"",";\n }\n .task-type-7, .section-type-7 {\n ").concat(t.fillType0?"fill: ".concat(t.fillType7):"",";\n }\n")}},Po=function(t,e,n){return" {\n font-family: ".concat(n.fontFamily,";\n font-size: ").concat(n.fontSize,";\n fill: ").concat(n.textColor,"\n }\n\n /* Classes common for multiple diagrams */\n\n .error-icon {\n fill: ").concat(n.errorBkgColor,";\n }\n .error-text {\n fill: ").concat(n.errorTextColor,";\n stroke: ").concat(n.errorTextColor,";\n }\n\n .edge-thickness-normal {\n stroke-width: 2px;\n }\n .edge-thickness-thick {\n stroke-width: 3.5px\n }\n .edge-pattern-solid {\n stroke-dasharray: 0;\n }\n\n .edge-pattern-dashed{\n stroke-dasharray: 3;\n }\n .edge-pattern-dotted {\n stroke-dasharray: 2;\n }\n\n .marker {\n fill: ").concat(n.lineColor,";\n }\n .marker.cross {\n stroke: ").concat(n.lineColor,";\n }\n\n svg {\n font-family: ").concat(n.fontFamily,";\n font-size: ").concat(n.fontSize,";\n }\n\n ").concat(Fo[t](n),"\n\n ").concat(e,"\n\n ").concat(t," { fill: apa;}\n")};function Io(t){return(Io="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t})(t)}var jo={},Ro=function(t,e,n){switch(f.debug("Directive type=".concat(e.type," with args:"),e.args),e.type){case"init":case"initialize":["config"].forEach((function(t){void 0!==e.args[t]&&("flowchart-v2"===n&&(n="flowchart"),e.args[n]=e.args[t],delete e.args[t])})),e.args,kt(e.args);break;case"wrap":case"nowrap":t&&t.setWrap&&t.setWrap("wrap"===e.type);break;default:f.warn("Unhandled directive: source: '%%{".concat(e.type,": ").concat(JSON.stringify(e.args?e.args:{}),"}%%"),e)}};function Yo(t){xa(t.git),ve(t.flowchart),Nn(t.flowchart),void 0!==t.sequenceDiagram&&br.setConf(P(t.sequence,t.sequenceDiagram)),br.setConf(t.sequence),ei(t.gantt),ci(t.class),Ri(t.state),Hi(t.state),Aa(t.class),Ra(t.class),Ka(t.er),Oo(t.journey),Da(t.class)}function zo(){}var Uo=Object.freeze({render:function(t,e,n,r){wt();var i=e,a=W.detectInit(i);a&&kt(a);var u=xt();if(e.length>u.maxTextSize&&(i="graph TB;a[Maximum text size in diagram exceeded];style a fill:#faa"),void 0!==r)r.innerHTML="",Object(s.select)(r).append("div").attr("id","d"+t).attr("style","font-family: "+u.fontFamily).append("svg").attr("id",t).attr("width","100%").attr("xmlns","http://www.w3.org/2000/svg").append("g");else{var l=document.getElementById(t);l&&l.remove();var h=document.querySelector("#d"+t);h&&h.remove(),Object(s.select)("body").append("div").attr("id","d"+t).append("svg").attr("id",t).attr("width","100%").attr("xmlns","http://www.w3.org/2000/svg").append("g")}window.txt=i,i=function(t){var e=t;return e=(e=(e=e.replace(/style.*:\S*#.*;/g,(function(t){return t.substring(0,t.length-1)}))).replace(/classDef.*:\S*#.*;/g,(function(t){return t.substring(0,t.length-1)}))).replace(/#\w+;/g,(function(t){var e=t.substring(1,t.length-1);return/^\+?\d+$/.test(e)?"fl°°"+e+"¶ß":"fl°"+e+"¶ß"}))}(i);var d=Object(s.select)("#d"+t).node(),p=W.detectType(i),g=d.firstChild,y=g.firstChild,v="";if(void 0!==u.themeCSS&&(v+="\n".concat(u.themeCSS)),void 0!==u.fontFamily&&(v+="\n:root { --mermaid-font-family: ".concat(u.fontFamily,"}")),void 0!==u.altFontFamily&&(v+="\n:root { --mermaid-alt-font-family: ".concat(u.altFontFamily,"}")),"flowchart"===p||"flowchart-v2"===p||"graph"===p){var m=me(i);for(var b in m)v+="\n.".concat(b," > * { ").concat(m[b].styles.join(" !important; ")," !important; }"),m[b].textStyles&&(v+="\n.".concat(b," tspan { ").concat(m[b].textStyles.join(" !important; ")," !important; }"))}var x=(new o.a)("#".concat(t),Po(p,v,u.themeVariables)),_=document.createElement("style");_.innerHTML=x,g.insertBefore(_,y);try{switch(p){case"git":u.flowchart.arrowMarkerAbsolute=u.arrowMarkerAbsolute,xa(u.git),_a(i,t,!1);break;case"flowchart":u.flowchart.arrowMarkerAbsolute=u.arrowMarkerAbsolute,ve(u.flowchart),be(i,t,!1);break;case"flowchart-v2":u.flowchart.arrowMarkerAbsolute=u.arrowMarkerAbsolute,Nn(u.flowchart),Bn(i,t,!1);break;case"sequence":u.sequence.arrowMarkerAbsolute=u.arrowMarkerAbsolute,u.sequenceDiagram?(br.setConf(Object.assign(u.sequence,u.sequenceDiagram)),console.error("`mermaid config.sequenceDiagram` has been renamed to `config.sequence`. Please update your mermaid config.")):br.setConf(u.sequence),br.draw(i,t);break;case"gantt":u.gantt.arrowMarkerAbsolute=u.arrowMarkerAbsolute,ei(u.gantt),ni(i,t);break;case"class":u.class.arrowMarkerAbsolute=u.arrowMarkerAbsolute,ci(u.class),ui(i,t);break;case"classDiagram":u.class.arrowMarkerAbsolute=u.arrowMarkerAbsolute,hi(u.class),fi(i,t);break;case"state":u.class.arrowMarkerAbsolute=u.arrowMarkerAbsolute,Ri(u.state),Yi(i,t);break;case"stateDiagram":u.class.arrowMarkerAbsolute=u.arrowMarkerAbsolute,Hi(u.state),Gi(i,t);break;case"info":u.class.arrowMarkerAbsolute=u.arrowMarkerAbsolute,Aa(u.class),Ma(i,t,c.version);break;case"pie":u.class.arrowMarkerAbsolute=u.arrowMarkerAbsolute,Ra(u.pie),Ya(i,t,c.version);break;case"er":Ka(u.er),to(i,t,c.version);break;case"journey":Oo(u.journey),Do(i,t,c.version)}}catch(e){throw Na(t,c.version),e}Object(s.select)('[id="'.concat(t,'"]')).selectAll("foreignobject > *").attr("xmlns","http://www.w3.org/1999/xhtml");var k=Object(s.select)("#d"+t).node().innerHTML;if(f.debug("cnf.arrowMarkerAbsolute",u.arrowMarkerAbsolute),u.arrowMarkerAbsolute&&"false"!==u.arrowMarkerAbsolute||(k=k.replace(/marker-end="url\(.*?#/g,'marker-end="url(#',"g")),k=function(t){var e=t;return e=(e=(e=e.replace(/fl°°/g,(function(){return"&#"}))).replace(/fl°/g,(function(){return"&"}))).replace(/¶ß/g,(function(){return";"}))}(k),void 0!==n)switch(p){case"flowchart":case"flowchart-v2":n(k,qt.bindFunctions);break;case"gantt":n(k,Jr.bindFunctions);break;case"class":case"classDiagram":n(k,on.bindFunctions);break;default:n(k)}else f.debug("CB = undefined!");var w=Object(s.select)("#d"+t).node();return null!==w&&"function"==typeof w.remove&&Object(s.select)("#d"+t).node().remove(),k},parse:function(t){var e=W.detectInit(t);e&&f.debug("reinit ",e);var n,r=W.detectType(t);switch(f.debug("Type "+r),r){case"git":(n=ua.a).parser.yy=sa;break;case"flowchart":case"flowchart-v2":qt.clear(),(n=Zt.a).parser.yy=qt;break;case"sequence":(n=$n.a).parser.yy=ar;break;case"gantt":(n=_r.a).parser.yy=Jr;break;case"class":case"classDiagram":(n=ii.a).parser.yy=on;break;case"state":case"stateDiagram":(n=Mi.a).parser.yy=Si;break;case"info":f.debug("info info info"),(n=Ca.a).parser.yy=Ea;break;case"pie":f.debug("pie"),(n=Ia.a).parser.yy=Fa;break;case"er":f.debug("er"),(n=Ha.a).parser.yy=Wa;break;case"journey":f.debug("Journey"),(n=no.a).parser.yy=lo}return n.parser.yy.graphType=r,n.parser.yy.parseError=function(t,e){throw{str:t,hash:e}},n.parse(t),n},parseDirective:function(t,e,n,r){try{if(void 0!==e)switch(e=e.trim(),n){case"open_directive":jo={};break;case"type_directive":jo.type=e.toLowerCase();break;case"arg_directive":jo.args=JSON.parse(e);break;case"close_directive":Ro(t,jo,r),jo=null}}catch(t){f.error("Error while rendering sequenceDiagram directive: ".concat(e," jison context: ").concat(n)),f.error(t.message)}},initialize:function(t){t&&t.fontFamily&&(t.themeVariables&&t.themeVariables.fontFamily||(t.themeVariables={fontFamily:t.fontFamily})),ft=P({},t),t&&t.theme&<[t.theme]?t.themeVariables=lt[t.theme].getThemeVariables(t.themeVariables):t&&(t.themeVariables=lt.default.getThemeVariables(t.themeVariables));var e="object"===Io(t)?function(t){return gt=P({},pt),gt=P(gt,t),t.theme&&(gt.themeVariables=lt[t.theme].getThemeVariables(t.themeVariables)),vt=mt(gt,yt),gt}(t):bt();Yo(e),d(e.logLevel)},reinitialize:zo,getConfig:xt,setConfig:function(t){return P(vt,t),xt()},getSiteConfig:bt,updateSiteConfig:function(t){return gt=P(gt,t),mt(gt,yt),gt},reset:function(){wt()},globalReset:function(){wt(),Yo(xt())},defaultConfig:pt});d(xt().logLevel),wt(xt());var $o=Uo,Wo=function(){Vo.startOnLoad?$o.getConfig().startOnLoad&&Vo.init():void 0===Vo.startOnLoad&&(f.debug("In start, no config"),$o.getConfig().startOnLoad&&Vo.init())};"undefined"!=typeof document&& +/*! + * Wait for document loaded before starting the execution + */ +window.addEventListener("load",(function(){Wo()}),!1);var Vo={startOnLoad:!0,htmlLabels:!0,mermaidAPI:$o,parse:$o.parse,render:$o.render,init:function(){var t,e,n,r=this,a=$o.getConfig();arguments.length>=2?( +/*! sequence config was passed as #1 */ +void 0!==arguments[0]&&(Vo.sequenceConfig=arguments[0]),t=arguments[1]):t=arguments[0],"function"==typeof arguments[arguments.length-1]?(e=arguments[arguments.length-1],f.debug("Callback function found")):void 0!==a.mermaid&&("function"==typeof a.mermaid.callback?(e=a.mermaid.callback,f.debug("Callback function found")):f.debug("No Callback function found")),t=void 0===t?document.querySelectorAll(".mermaid"):"string"==typeof t?document.querySelectorAll(t):t instanceof window.Node?[t]:t,f.debug("Start On Load before: "+Vo.startOnLoad),void 0!==Vo.startOnLoad&&(f.debug("Start On Load inner: "+Vo.startOnLoad),$o.updateSiteConfig({startOnLoad:Vo.startOnLoad})),void 0!==Vo.ganttConfig&&$o.updateSiteConfig({gantt:Vo.ganttConfig});for(var o=function(a){var o=t[a]; +/*! Check if previously processed */if(o.getAttribute("data-processed"))return"continue";o.setAttribute("data-processed",!0);var s="mermaid-".concat(Date.now());n=i(n=o.innerHTML).trim().replace(//gi,"
");var c=W.detectInit(n);c&&f.debug("Detected early reinit: ",c);try{$o.render(s,n,(function(t,n){o.innerHTML=t,void 0!==e&&e(s),n&&n(o)}),o)}catch(t){f.warn("Syntax Error rendering"),f.warn(t),r.parseError&&r.parseError(t)}},s=0;s `${match}`); + } + for (page of data) { + let [title, content] = [null, null]; + try { + if (page.title) { + title = page.title.match(regexp); + } else { + if (page.url == "/") { + page.title = ui.title; + } else { + page.title = page.url; + } + } + } catch (e) { + debug(e.message); + } + try { + if (page.content) { + page.content = $("
").html(page.content).text(); + content = page.content.match(regexp); + } + } catch (e) { + debug(e.message); + } + if (title || content) { + let result = [ + `${page.title}`, + ]; + if (content) { + let [min, max] = [content.index - 100, content.index + 100]; + let [prefix, suffix] = ["...", "..."]; + + if (min < 0) { + prefix = ""; + min = 0; + } + if (max > page.content.length) { + suffix = ""; + max = page.content.length; + } + result.push( + `

${prefix}${slice( + page.content, + min, + max + )}${suffix}

` + ); + } + results.push(`
  • ${result.join("")}
    • `); + } + } + if (results.length > 0 && text.length > 0) { + $(".search-results .content").html(results.join("")); + $(".search-results .summary").html( + ui.i18n.search_results_found.replace("#", results.length) + ); + } else { + $(".search-results .content").empty(); + $(".search-results .summary").html(ui.i18n.search_results_not_found); + } + $(".search-results h2").html(ui.i18n.search_results); +} + +function initialize(name) { + let link = $(".toctree").find(`[href="${decodeURI(name)}"]`); + + if (link.length > 0) { + $(".toctree .current").removeClass("current"); + link.addClass("current"); + link.closest(".level-1").parent().addClass("current"); + for (let i = 1; i <= 11; i++) { + link.closest(`.level-${i}`).addClass("current"); + } + } +} + +function toggleCurrent(link) { + let closest = link.closest("li"); + closest.siblings("li.current").removeClass("current"); + closest.siblings().find("li.current").removeClass("current"); + closest.find("> ul li.current").removeClass("current"); + closest.toggleClass("current"); +} + +function toc() { + $(".toctree li.current") + .append('
      ') + .html(function () { + let level = parseInt(this.dataset.level); + let temp = 0; + let stack = [$(this).find(".content-toc")]; + + $(".markdown-body") + .find("h2,h3,h4,h5,h6") + .each(function () { + let anchor = $("") + .addClass("d-flex flex-items-baseline") + .text($(this).text()) + .attr("href", `#${this.id}`); + let tagLevel = parseInt(this.tagName.slice(1)) - 1; + + if (tagLevel > temp) { + let parent = stack[0].children("li:last")[0]; + if (parent) { + stack.unshift($("
        ").appendTo(parent)); + } + } else { + stack.splice( + 0, + Math.min(temp - tagLevel, Math.max(stack.length - 1, 0)) + ); + } + temp = tagLevel; + + $("
      • ") + .addClass(`toc level-${level + tagLevel}`) + .append(anchor) + .appendTo(stack[0]); + }); + if (!stack[0].html()) { + stack[0].remove(); + } + }); +} + +function set(name, value) { + return localStorage.setItem(name, value); +} + +function get(name) { + return localStorage.getItem(name) || false; +} + +function debug() { + console.debug.apply(console, arguments); +} + +function restore() { + let scroll = get("scroll"); + let scrollTime = get("scrollTime"); + let scrollHost = get("scrollHost"); + + if (scroll && scrollTime && scrollHost) { + if (scrollHost == location.host && Date.now() - scrollTime < 6e5) { + $(".sidebar").scrollTop(scroll); + } + } + $(".sidebar").scroll(function () { + set("scroll", this.scrollTop); + set("scrollTime", Date.now()); + set("scrollHost", location.host); + }); +} + +function highlight() { + let text = new URL(location.href).searchParams.get("highlight"); + + if (text) { + $(".markdown-body") + .find("*") + .each(function () { + try { + if (this.outerHTML.match(new RegExp(text, "im"))) { + $(this).addClass("search-result"); + $(this).parentsUntil(".markdown-body").removeClass("search-result"); + } + } catch (e) { + debug(e.message); + } + }); + // last node + $(".search-result").each(function () { + $(this).html(function (i, html) { + return html.replace(text, `${text}`); + }); + }); + $(".search input").val(text); + } +} + +$(window).bind("hashchange", () => + initialize(location.hash || location.pathname) +); + +$(document).on("scroll", function () { + let start = $(this).scrollTop() + 5; + let items = []; + + $(".markdown-body") + .find("h1,h2,h3,h4,h5,h6") + .each(function () { + items.push({ + offset: $(this).offset().top, + id: this.id, + level: parseInt(this.tagName.slice(1)), + }); + }); + for (let i = 0; i < items.length; i++) { + if (start > items[i].offset) { + if (i < items.length - 1) { + if (start < items[i + 1].offset) { + if (items[i].level == 1) { + initialize(location.pathname); + } else { + initialize("#" + items[i].id); + } + } + } else { + initialize("#" + items[i].id); + } + } + } +}); + +$("#toggle").click(function () { + $(".sidebar-wrap,.content-wrap,.addons-wrap").toggleClass("shift"); +}); +$(".status").click(function () { + $(".addons").toggleClass("d-none"); +}); + +if (location.pathname == `${ui.baseurl}/search.html`) { + $.ajax(`${ui.baseurl}/data.json`) + .done(search) + .fail((xhr, message) => debug(message)); +} + +toc(); +initialize(location.pathname); +initialize(location.hash); +restore(); +highlight(); + +/* nested ul */ +$(".toc ul") + .siblings("a") + .each(function () { + let link = $(this); + let expand = $(''); + + expand.on("click", function (e) { + e.stopPropagation(); + toggleCurrent(link); + return false; + }); + link.prepend(expand); + }); + +$(".markdown-body :header").append(function () { + return ``; +}); + +$("div.highlighter-rouge").each(function () { + const match = $(this) + .attr("class") + .match(/language-(\w+)/); + if (match) { + $(this).attr("data-lang", match[1]); + } +}); + +if ("serviceWorker" in navigator) { + navigator.serviceWorker.register(`${ui.baseurl}/sw.caches.js`); +} else { + debug("Service Worker not supported!"); +} diff --git a/assets/js/theme.min.js b/assets/js/theme.min.js new file mode 100644 index 00000000000..6bf8a0cebf1 --- /dev/null +++ b/assets/js/theme.min.js @@ -0,0 +1 @@ +(()=>{function t(t,e){(null==e||e>t.length)&&(e=t.length);for(var n=0,a=new Array(e);n0){$(".toctree .current").removeClass("current"),e.addClass("current"),e.closest(".level-1").parent().addClass("current");for(var n=1;n<=11;n++)e.closest(".level-".concat(n)).addClass("current")}}function n(t,e){return localStorage.setItem(t,e)}function a(t){return localStorage.getItem(t)||!1}function r(){console.debug.apply(console,arguments)}var o,s,c,l;$(window).bind("hashchange",(function(){return e(location.hash||location.pathname)})),$(document).on("scroll",(function(){var t=$(this).scrollTop()+5,n=[];$(".markdown-body").find("h1,h2,h3,h4,h5,h6").each((function(){n.push({offset:$(this).offset().top,id:this.id,level:parseInt(this.tagName.slice(1))})}));for(var a=0;an[a].offset&&(a'.concat(t,"")}))}var c,l=function(e,n){var a;if("undefined"==typeof Symbol||null==e[Symbol.iterator]){if(Array.isArray(e)||(a=function(e,n){if(e){if("string"==typeof e)return t(e,n);var a=Object.prototype.toString.call(e).slice(8,-1);return"Object"===a&&e.constructor&&(a=e.constructor.name),"Map"===a||"Set"===a?Array.from(e):"Arguments"===a||/^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(a)?t(e,n):void 0}}(e))||n&&e&&"number"==typeof e.length){a&&(e=a);var r=0,o=function(){};return{s:o,n:function(){return r>=e.length?{done:!0}:{done:!1,value:e[r++]}},e:function(t){throw t},f:o}}throw new TypeError("Invalid attempt to iterate non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method.")}var s,c=!0,l=!1;return{s:function(){a=e[Symbol.iterator]()},n:function(){var t=a.next();return c=t.done,t},e:function(t){l=!0,s=t},f:function(){try{c||null==a.return||a.return()}finally{if(l)throw s}}}}(e);try{for(l.s();!(c=l.n()).done;){page=c.value;var i=null,u=null;try{page.title?i=page.title.match(o):"/"==page.url?page.title=ui.title:page.title=page.url}catch(t){r(t.message)}try{page.content&&(page.content=$("
        ").html(page.content).text(),u=page.content.match(o))}catch(t){r(t.message)}if(i||u){var h=['').concat(page.title,"")];if(u){var f=u.index-100,d=u.index+100,p="...",g="...";f<0&&(p="",f=0),d>page.content.length&&(g="",d=page.content.length),h.push('

        '.concat(p).concat(s(page.content,f,d)).concat(g,"

        "))}a.push('
      • '.concat(h.join(""),"
        • "))}}}catch(t){l.e(t)}finally{l.f()}a.length>0&&n.length>0?($(".search-results .content").html(a.join("")),$(".search-results .summary").html(ui.i18n.search_results_found.replace("#",a.length))):($(".search-results .content").empty(),$(".search-results .summary").html(ui.i18n.search_results_not_found)),$(".search-results h2").html(ui.i18n.search_results)})).fail((function(t,e){return r(e)})),$(".toctree li.current").append('
          ').html((function(){var t=parseInt(this.dataset.level),e=0,n=[$(this).find(".content-toc")];$(".markdown-body").find("h2,h3,h4,h5,h6").each((function(){var a=$("").addClass("d-flex flex-items-baseline").text($(this).text()).attr("href","#".concat(this.id)),r=parseInt(this.tagName.slice(1))-1;if(r>e){var o=n[0].children("li:last")[0];o&&n.unshift($("
            ").appendTo(o))}else n.splice(0,Math.min(e-r,Math.max(n.length-1,0)));e=r,$("
          • ").addClass("toc level-".concat(t+r)).append(a).appendTo(n[0])})),n[0].html()||n[0].remove()})),e(location.pathname),e(location.hash),o=a("scroll"),s=a("scrollTime"),c=a("scrollHost"),o&&s&&c&&c==location.host&&Date.now()-s<6e5&&$(".sidebar").scrollTop(o),$(".sidebar").scroll((function(){n("scroll",this.scrollTop),n("scrollTime",Date.now()),n("scrollHost",location.host)})),(l=new URL(location.href).searchParams.get("highlight"))&&($(".markdown-body").find("*").each((function(){try{this.outerHTML.match(new RegExp(l,"im"))&&($(this).addClass("search-result"),$(this).parentsUntil(".markdown-body").removeClass("search-result"))}catch(t){r(t.message)}})),$(".search-result").each((function(){$(this).html((function(t,e){return e.replace(l,''.concat(l,""))}))})),$(".search input").val(l)),$(".toc ul").siblings("a").each((function(){var t=$(this),e=$('');e.on("click",(function(e){return e.stopPropagation(),function(t){var e=t.closest("li");e.siblings("li.current").removeClass("current"),e.siblings().find("li.current").removeClass("current"),e.find("> ul li.current").removeClass("current"),e.toggleClass("current")}(t),!1})),t.prepend(e)})),$(".markdown-body :header").append((function(){return'')})),$("div.highlighter-rouge").each((function(){var t=$(this).attr("class").match(/language-(\w+)/);t&&$(this).attr("data-lang",t[1])})),"serviceWorker"in navigator?navigator.serviceWorker.register("".concat(ui.baseurl,"/sw.caches.js")):r("Service Worker not supported!")})(); \ No newline at end of file diff --git a/data.json b/data.json new file mode 100644 index 00000000000..d570dbc785c --- /dev/null +++ b/data.json @@ -0,0 +1 @@ +[{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/199138096-ab897288-10c7-4bd2-b0aa-cb7a2edac63d.png)](https://github.com/chetabahana/tensorflow/wiki/Java-SDK#skema)\n\n[![default](https://user-images.githubusercontent.com/8466209/199137158-5bbd47e0-d24d-428f-89d4-aa9d8820d5f9.png)](https://github.com/chetabahana/tensorflow/wiki/Java-SDK#pola)\n","dir":"/identition/span4/","name":"gist07.md","path":"identition/span4/gist07.md","url":"/identition/span4/gist07.html"},{"layout":"default","title":null,"content":"```\nFROM tensorflow/tensorflow:latest-gpu\n\nLABEL version=\"1.0.7\"\nLABEL homepage=\"https://eq19.github.io/\"\nLABEL maintainer=\"eq19 \"\nLABEL repository=\"https://github.com/FeedMapping/deploy\"\n\nENV DEBIAN_FRONTEND noninteractive\nENV DEBCONF_NOWARNINGS=\"yes\"\n\nRUN apt-get update -qq < /dev/null\nRUN apt-get install -qq --no-install-recommends apt-utils < /dev/null\n\nENV NVIDIA_VISIBLE_DEVICES all\nENV NVIDIA_DRIVER_CAPABILITIES compute,utility\nENV PATH=\"${PATH}:/root/.local/bin\"\n\nRUN apt-get install -qq python3.8-venv < /dev/null\nRUN python3.8 -m venv nvidia < /dev/null\nRUN chown -R root nvidia && source nvidia/bin/activate\nRUN python -m pip install -U --force-reinstall pip < /dev/null\nRUN pip install tensorflow-gpu --root-user-action=ignore --quiet\n\nENV NOKOGIRI_USE_SYSTEM_LIBRARIES=1\nENV BUNDLE_SILENCE_ROOT_WARNING=1\nENV RAILS_VERSION 5.0.1\nENV RUBYOPT=W0\n\nRUN apt-get install -qq npm < /dev/null && npm install -qq yarn < /dev/null\nRUN apt-get install -qq ruby ruby-dev ruby-bundler build-essential < /dev/null\nRUN apt-get install -qq git < /dev/null && git config --global init.defaultBranch master\n\nRUN apt-get clean && rm -rf /var/lib/apt/lists/* /tmp/* /var/tmp/* < /dev/null\nRUN gem install rails --version \"$RAILS_VERSION\" < /dev/null\n\nCOPY . .\nENTRYPOINT [\"/entrypoint.sh\"]\n\n```\n\n[![image](https://user-images.githubusercontent.com/8466209/198936863-10e3e037-6665-49c3-b147-3accda4d133b.png)](https://hub.docker.com/r/tensorflow/tensorflow)\n\n[![default](https://user-images.githubusercontent.com/8466209/199148983-8c6e4c62-8503-4412-9a48-1b8cb54b7a94.png)](https://github.com/FeedMapping/mapping/releases/tag/v1.0.7)\n\n[![default](https://user-images.githubusercontent.com/8466209/198936548-967ca221-41b7-461b-9b4b-9ff30eedea50.png)](https://github.com/eq19/grammar/actions/runs/3357023441/jobs/5562550171)\n\n[![default](https://user-images.githubusercontent.com/8466209/225285187-916bee67-a633-4917-84da-7a3187caeb03.png)](https://console.cloud.google.com/billing/018F05-BD9DB7-0A1326/reports;grouping=GROUP_BY_SKU;products=services%2F6F81-5844-456A;credits=CREDIT_TYPE_UNSPECIFIED,PROMOTION,SUSTAINED_USAGE_DISCOUNT,SPENDING_BASED_DISCOUNT?authuser=1&cloudshell=false)\n\n","dir":"/identition/span4/","name":"gist08.md","path":"identition/span4/gist08.md","url":"/identition/span4/gist08.html"},{"layout":"default","title":null,"content":"```\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n ↓\n |\n ↓ \n 114-89=139-114=25=5x5\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ ↓\n | | |\n ------------ 10 ------------- | \n | \n | \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n ```\n \n[![default](https://user-images.githubusercontent.com/8466209/199508386-69859804-9ccb-4f5d-8314-8ca0be0af235.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-pairing-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199510678-abc4b002-b54a-4a80-9e12-1ef6527ca511.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-mirror-md)\n","dir":"/identition/span6/","name":"gist08.md","path":"identition/span6/gist08.md","url":"/identition/span6/gist08.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/199272127-b1232a38-964f-49e5-83b5-ccff8da01e85.png)](https://github.com/chetabahana/chetabahana.github.io/wiki/Jekyll-Liquid#desain)\n```\n| 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ \n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n\n![default](https://user-images.githubusercontent.com/8466209/199361092-349e5aef-fe53-4601-8c17-496d945b6ac3.png)\n![default](https://user-images.githubusercontent.com/8466209/199361458-8414fe3d-c031-49ab-8167-78135c6c8cff.png)\n\n","dir":"/identition/span5/","name":"gist04.md","path":"identition/span5/gist04.md","url":"/identition/span5/gist04.html"},{"layout":"default","title":"Container-Optimized","content":"## Container-Optimized\n\n```\n$ cat /etc/os-release\n\nNAME=\"Container-Optimized OS\"\nID=cos\nPRETTY_NAME=\"Container-Optimized OS from Google\"\nHOME_URL=\"https://cloud.google.com/container-optimized-os/docs\"\nBUG_REPORT_URL=\"https://cloud.google.com/container-optimized-os/docs/resources/support-policy#contact_us\"\nGOOGLE_METRICS_PRODUCT_ID=26\nGOOGLE_CRASH_ID=Lakitu\nKERNEL_COMMIT_ID=4c0ef99fbc74bd4a4dce8851652be68038bec83e\nVERSION=105\nVERSION_ID=105\nBUILD_ID=17412.101.4\n```\n\nPipe to sort -V for sorted output. Ex: to see all executables in your PATH on your system, and all aliases, all sorted, run: compgen -c | sortsee all executables in your PATH\n\n```\n$ find ${PATH//:/ } -maxdepth 1 -executable | sort\n\nfind: ‘/usr/local/bin’: No such file or directory\nfind: ‘/opt/bin’: No such file or directory\n/bin\n/bin/attr\n/bin/basename\n/bin/bash\n/bin/bunzip2\n/bin/bzcat\n/bin/bzip2\n/bin/cat\n/bin/chacl\n/bin/chgrp\n/bin/chmod\n/bin/chown\n/bin/chroot\n/bin/cp\n/bin/cut\n/bin/dash\n/bin/date\n/bin/dd\n/bin/df\n/bin/dir\n/bin/dirname\n/bin/dmesg\n/bin/dnsdomainname\n/bin/du\n/bin/echo\n/bin/egrep\n/bin/env\n/bin/expr\n/bin/false\n/bin/fgrep\n/bin/findmnt\n/bin/getfacl\n/bin/getfattr\n/bin/getsubids\n/bin/grep\n/bin/groups\n/bin/gsed\n/bin/gunzip\n/bin/gzip\n/bin/head\n/bin/hostname\n/bin/ifconfig\n/bin/ip\n/bin/keyctl\n/bin/kill\n/bin/kmod\n/bin/ln\n/bin/login\n/bin/ls\n/bin/lsblk\n/bin/lsmod\n/bin/mkdir\n/bin/mkfifo\n/bin/mknod\n/bin/mktemp\n/bin/modinfo\n/bin/more\n/bin/mount\n/bin/mountpoint\n/bin/mv\n/bin/nano\n/bin/netstat\n/bin/ps\n/bin/pwd\n/bin/rbash\n/bin/readlink\n/bin/rm\n/bin/rmdir\n/bin/rnano\n/bin/route\n/bin/run-parts\n/bin/sed\n/bin/seq\n/bin/setfacl\n/bin/setfattr\n/bin/sh\n/bin/sleep\n/bin/sort\n/bin/stty\n/bin/su\n/bin/sync\n/bin/tail\n/bin/tar\n/bin/tempfile\n/bin/touch\n/bin/tr\n/bin/true\n/bin/tty\n/bin/umount\n/bin/uname\n/bin/vdir\n/bin/wc\n/bin/wdctl\n/bin/yes\n/bin/zcat\n/usr/bin\n/usr/bin/2to3\n/usr/bin/2to3-3.8\n/usr/bin/[\n/usr/bin/arch\n/usr/bin/argon2\n/usr/bin/aulast\n/usr/bin/aulastlog\n/usr/bin/ausyscall\n/usr/bin/auvirt\n/usr/bin/awk\n/usr/bin/b2sum\n/usr/bin/base32\n/usr/bin/base64\n/usr/bin/basename\n/usr/bin/basenc\n/usr/bin/bashbug\n/usr/bin/brotli\n/usr/bin/bsdcat\n/usr/bin/bsdcpio\n/usr/bin/bsdtar\n/usr/bin/busctl\n/usr/bin/bzcmp\n/usr/bin/bzdiff\n/usr/bin/bzegrep\n/usr/bin/bzfgrep\n/usr/bin/bzgrep\n/usr/bin/bzip2recover\n/usr/bin/bzless\n/usr/bin/bzmore\n/usr/bin/c_rehash\n/usr/bin/cal\n/usr/bin/captest\n/usr/bin/captoinfo\n/usr/bin/cbfstool\n/usr/bin/cbmem\n/usr/bin/cgpt\n/usr/bin/chage\n/usr/bin/chardetect\n/usr/bin/chattr\n/usr/bin/chcon\n/usr/bin/chfn\n/usr/bin/chmem\n/usr/bin/choom\n/usr/bin/chromeos-pgmem\n/usr/bin/chromeos-tpm-recovery\n/usr/bin/chronyc\n/usr/bin/chroot\n/usr/bin/chrt\n/usr/bin/chsh\n/usr/bin/cis_scanner\n/usr/bin/cksum\n/usr/bin/clear\n/usr/bin/cloud-id\n/usr/bin/cloud-init\n/usr/bin/cloud-init-per\n/usr/bin/cmp\n/usr/bin/col\n/usr/bin/colcrt\n/usr/bin/colrm\n/usr/bin/column\n/usr/bin/comm\n/usr/bin/compile_et\n/usr/bin/containerd\n/usr/bin/containerd-shim\n/usr/bin/containerd-shim-runc-v1\n/usr/bin/containerd-shim-runc-v2\n/usr/bin/containerd-stress\n/usr/bin/core2md\n/usr/bin/coredumpctl\n/usr/bin/coreutils\n/usr/bin/cos-extensions\n/usr/bin/crictl\n/usr/bin/cros_installer\n/usr/bin/crosid\n/usr/bin/crossystem\n/usr/bin/csplit\n/usr/bin/ctr\n/usr/bin/curl\n/usr/bin/cut\n/usr/bin/cvtsudoers\n/usr/bin/dbus-cleanup-sockets\n/usr/bin/dbus-daemon\n/usr/bin/dbus-launch\n/usr/bin/dbus-monitor\n/usr/bin/dbus-run-session\n/usr/bin/dbus-send\n/usr/bin/dbus-test-tool\n/usr/bin/dbus-update-activation-environment\n/usr/bin/dbus-uuidgen\n/usr/bin/dev_debug_vboot\n/usr/bin/diff\n/usr/bin/diff-highlight\n/usr/bin/diff3\n/usr/bin/dir\n/usr/bin/dircolors\n/usr/bin/dirname\n/usr/bin/docker\n/usr/bin/docker-containerd\n/usr/bin/docker-containerd-shim\n/usr/bin/docker-credential-gcr\n/usr/bin/docker-init\n/usr/bin/docker-proxy\n/usr/bin/docker-runc\n/usr/bin/dockerd\n/usr/bin/du\n/usr/bin/dumpRSAPublicKey\n/usr/bin/dump_fmap\n/usr/bin/dump_kernel_config\n/usr/bin/dumpsexp\n/usr/bin/easy_install\n/usr/bin/eject\n/usr/bin/elogtool\n/usr/bin/enable_dev_usb_boot\n/usr/bin/env\n/usr/bin/event_rpcgen.py\n/usr/bin/ex\n/usr/bin/expand\n/usr/bin/expiry\n/usr/bin/expr\n/usr/bin/factor\n/usr/bin/faillog\n/usr/bin/fallocate\n/usr/bin/filan\n/usr/bin/file\n/usr/bin/filecap\n/usr/bin/fincore\n/usr/bin/find\n/usr/bin/flock\n/usr/bin/fluent-bit\n/usr/bin/fmt\n/usr/bin/fold\n/usr/bin/free\n/usr/bin/ftdi_eeprom\n/usr/bin/fusermount\n/usr/bin/futility\n/usr/bin/gapplication\n/usr/bin/gbb_utility\n/usr/bin/gdbm_dump\n/usr/bin/gdbm_load\n/usr/bin/gdbmtool\n/usr/bin/gdbus\n/usr/bin/getopt\n/usr/bin/gfind\n/usr/bin/gio\n/usr/bin/gio-querymodules\n/usr/bin/git\n/usr/bin/git-cvsserver\n/usr/bin/git-receive-pack\n/usr/bin/git-shell\n/usr/bin/git-upload-archive\n/usr/bin/git-upload-pack\n/usr/bin/glib-compile-resources\n/usr/bin/glib-compile-schemas\n/usr/bin/glib-gettextize\n/usr/bin/gobject-query\n/usr/bin/google_authorized_keys\n/usr/bin/google_authorized_keys_sk\n/usr/bin/google_guest_agent\n/usr/bin/google_metadata_script_runner\n/usr/bin/google_osconfig_agent\n/usr/bin/google_oslogin_nss_cache\n/usr/bin/gpasswd\n/usr/bin/gpg-error\n/usr/bin/gsettings\n/usr/bin/gss-client\n/usr/bin/gtester\n/usr/bin/gxargs\n/usr/bin/gzexe\n/usr/bin/head\n/usr/bin/hexdump\n/usr/bin/hmac256\n/usr/bin/hostid\n/usr/bin/hostnamectl\n/usr/bin/id\n/usr/bin/idle\n/usr/bin/import-tars\n/usr/bin/infocmp\n/usr/bin/infotocap\n/usr/bin/install\n/usr/bin/inteltool\n/usr/bin/ionice\n/usr/bin/ipcmk\n/usr/bin/ipcrm\n/usr/bin/ipcs\n/usr/bin/iptables-xml\n/usr/bin/irqtop\n/usr/bin/join\n/usr/bin/journalctl\n/usr/bin/jq\n/usr/bin/jsondiff\n/usr/bin/jsonpatch\n/usr/bin/jsonpointer\n/usr/bin/jsonschema\n/usr/bin/kdestroy\n/usr/bin/kernel-install\n/usr/bin/kinit\n/usr/bin/klist\n/usr/bin/kpasswd\n/usr/bin/kubectl\n/usr/bin/kubelet\n/usr/bin/last\n/usr/bin/lastb\n/usr/bin/lastlog\n/usr/bin/less\n/usr/bin/lessecho\n/usr/bin/lesskey\n/usr/bin/lesspipe\n/usr/bin/line\n/usr/bin/link\n/usr/bin/logger\n/usr/bin/loginctl\n/usr/bin/logname\n/usr/bin/look\n/usr/bin/lsattr\n/usr/bin/lscpu\n/usr/bin/lsipc\n/usr/bin/lsirq\n/usr/bin/lslocks\n/usr/bin/lslogins\n/usr/bin/lsmem\n/usr/bin/lsns\n/usr/bin/lsof\n/usr/bin/lz4\n/usr/bin/lz4c\n/usr/bin/lz4cat\n/usr/bin/lzcat\n/usr/bin/lzcmp\n/usr/bin/lzdiff\n/usr/bin/lzegrep\n/usr/bin/lzfgrep\n/usr/bin/lzgrep\n/usr/bin/lzless\n/usr/bin/lzma\n/usr/bin/lzmadec\n/usr/bin/lzmainfo\n/usr/bin/lzmore\n/usr/bin/mawk\n/usr/bin/mcookie\n/usr/bin/md5sum\n/usr/bin/metrics_client\n/usr/bin/mk_cmds\n/usr/bin/mkfifo\n/usr/bin/mktemp\n/usr/bin/mpicalc\n/usr/bin/namei\n/usr/bin/nc\n/usr/bin/netcap\n/usr/bin/nettle-hash\n/usr/bin/nettle-lfib-stream\n/usr/bin/nettle-pbkdf2\n/usr/bin/networkctl\n/usr/bin/newgidmap\n/usr/bin/newgrp\n/usr/bin/newuidmap\n/usr/bin/nice\n/usr/bin/nl\n/usr/bin/nohup\n/usr/bin/nproc\n/usr/bin/nsenter\n/usr/bin/numfmt\n/usr/bin/nvramtool\n/usr/bin/od\n/usr/bin/oomctl\n/usr/bin/openssl\n/usr/bin/passwd\n/usr/bin/paste\n/usr/bin/pathchk\n/usr/bin/pcre2grep\n/usr/bin/pcre2test\n/usr/bin/pcregrep\n/usr/bin/pcretest\n/usr/bin/perf\n/usr/bin/perfetto\n/usr/bin/pg\n/usr/bin/pgrep\n/usr/bin/pidof\n/usr/bin/pigz\n/usr/bin/pinky\n/usr/bin/pkcs1-conv\n/usr/bin/pkill\n/usr/bin/pmap\n/usr/bin/portablectl\n/usr/bin/pr\n/usr/bin/printenv\n/usr/bin/printf\n/usr/bin/prlimit\n/usr/bin/procan\n/usr/bin/protoc-gen-go\n/usr/bin/protoc-gen-go-grpc\n/usr/bin/pscap\n/usr/bin/ptx\n/usr/bin/pv\n/usr/bin/pwdx\n/usr/bin/pwqcheck\n/usr/bin/pwqfilter\n/usr/bin/pwqgen\n/usr/bin/pydoc\n/usr/bin/pydoc3.8\n/usr/bin/pyjwt\n/usr/bin/pyserial-miniterm\n/usr/bin/pyserial-ports\n/usr/bin/python\n/usr/bin/python-exec2c\n/usr/bin/python3\n/usr/bin/python3.8\n/usr/bin/pyvenv\n/usr/bin/readlink\n/usr/bin/realpath\n/usr/bin/rename\n/usr/bin/renice\n/usr/bin/reset\n/usr/bin/resolvectl\n/usr/bin/rev\n/usr/bin/rootdev\n/usr/bin/rsync\n/usr/bin/rsync-ssl\n/usr/bin/runc\n/usr/bin/runcon\n/usr/bin/rview\n/usr/bin/rvim\n/usr/bin/scmp_sys_resolver\n/usr/bin/scp\n/usr/bin/script\n/usr/bin/scriptlive\n/usr/bin/scriptreplay\n/usr/bin/sdiff\n/usr/bin/seq\n/usr/bin/setsid\n/usr/bin/setterm\n/usr/bin/sexp-conv\n/usr/bin/sftp\n/usr/bin/sg\n/usr/bin/sha1sum\n/usr/bin/sha224sum\n/usr/bin/sha256sum\n/usr/bin/sha384sum\n/usr/bin/sha512sum\n/usr/bin/shlibsign\n/usr/bin/shred\n/usr/bin/shuf\n/usr/bin/slabtop\n/usr/bin/sleep\n/usr/bin/smbinfo\n/usr/bin/socat\n/usr/bin/sort\n/usr/bin/sos\n/usr/bin/sos-collector\n/usr/bin/sosreport\n/usr/bin/split\n/usr/bin/ssh\n/usr/bin/ssh-add\n/usr/bin/ssh-agent\n/usr/bin/ssh-copy-id\n/usr/bin/ssh-keygen\n/usr/bin/ssh-keyscan\n/usr/bin/stat\n/usr/bin/stdbuf\n/usr/bin/sudo\n/usr/bin/sudoedit\n/usr/bin/sudoreplay\n/usr/bin/sum\n/usr/bin/superiotool\n/usr/bin/systemctl\n/usr/bin/systemd-analyze\n/usr/bin/systemd-ask-password\n/usr/bin/systemd-cat\n/usr/bin/systemd-cgls\n/usr/bin/systemd-cgtop\n/usr/bin/systemd-creds\n/usr/bin/systemd-delta\n/usr/bin/systemd-detect-virt\n/usr/bin/systemd-dissect\n/usr/bin/systemd-escape\n/usr/bin/systemd-id128\n/usr/bin/systemd-inhibit\n/usr/bin/systemd-machine-id-setup\n/usr/bin/systemd-mount\n/usr/bin/systemd-notify\n/usr/bin/systemd-nspawn\n/usr/bin/systemd-path\n/usr/bin/systemd-repart\n/usr/bin/systemd-resolve\n/usr/bin/systemd-run\n/usr/bin/systemd-socket-activate\n/usr/bin/systemd-stdio-bridge\n/usr/bin/systemd-sysext\n/usr/bin/systemd-tmpfiles\n/usr/bin/systemd-tty-ask-password-agent\n/usr/bin/systemd-umount\n/usr/bin/tabs\n/usr/bin/tac\n/usr/bin/tail\n/usr/bin/taskset\n/usr/bin/tee\n/usr/bin/test\n/usr/bin/tic\n/usr/bin/timedatectl\n/usr/bin/timeout\n/usr/bin/tini\n/usr/bin/tload\n/usr/bin/toe\n/usr/bin/toolbox\n/usr/bin/top\n/usr/bin/touch\n/usr/bin/tpm-nvsize\n/usr/bin/tpmc\n/usr/bin/tput\n/usr/bin/tr\n/usr/bin/trace\n/usr/bin/traced\n/usr/bin/traced_probes\n/usr/bin/truncate\n/usr/bin/tset\n/usr/bin/tsort\n/usr/bin/tty\n/usr/bin/udevadm\n/usr/bin/ul\n/usr/bin/ulockmgr_server\n/usr/bin/uname\n/usr/bin/unexpand\n/usr/bin/uniq\n/usr/bin/unlink\n/usr/bin/unlz4\n/usr/bin/unlzma\n/usr/bin/unpigz\n/usr/bin/unshare\n/usr/bin/unxz\n/usr/bin/update_engine_client\n/usr/bin/uptime\n/usr/bin/userdbctl\n/usr/bin/users\n/usr/bin/utmpdump\n/usr/bin/uuidgen\n/usr/bin/uuidparse\n/usr/bin/vbutil_firmware\n/usr/bin/vbutil_kernel\n/usr/bin/vbutil_key\n/usr/bin/vbutil_keyblock\n/usr/bin/vdir\n/usr/bin/verity\n/usr/bin/vi\n/usr/bin/view\n/usr/bin/vim\n/usr/bin/vimdiff\n/usr/bin/vmstat\n/usr/bin/w\n/usr/bin/watch\n/usr/bin/wc\n/usr/bin/wget\n/usr/bin/whereis\n/usr/bin/which\n/usr/bin/who\n/usr/bin/whoami\n/usr/bin/x86_64-cros-linux-gnu-gio-querymodules\n/usr/bin/xargs\n/usr/bin/xmlcatalog\n/usr/bin/xmllint\n/usr/bin/xmlwf\n/usr/bin/xxd\n/usr/bin/xz\n/usr/bin/xzcat\n/usr/bin/xzcmp\n/usr/bin/xzdec\n/usr/bin/xzdiff\n/usr/bin/xzegrep\n/usr/bin/xzfgrep\n/usr/bin/xzgrep\n/usr/bin/xzless\n/usr/bin/xzmore\n/usr/bin/yat2m\n/usr/bin/yes\n/usr/bin/zcmp\n/usr/bin/zdiff\n/usr/bin/zegrep\n/usr/bin/zfgrep\n/usr/bin/zforce\n/usr/bin/zgrep\n/usr/bin/zless\n/usr/bin/zmore\n/usr/bin/znew\n```\n\n![default](https://user-images.githubusercontent.com/8466209/238171017-8d377ade-1fe0-4ef8-8594-76ca65023ca8.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198938102-de43af86-2e1a-445c-80d7-d1f4cbbbb9a7.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198938226-aa4679bc-2912-409d-9a09-642bdebfcc65.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198938652-5a366a20-08c6-4b7c-b48f-a551575dec7f.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198939140-2d553b06-c3d8-47f6-80f8-acb42e29d54d.png)\n","dir":"/identition/span3/","name":"gist05.md","path":"identition/span3/gist05.md","url":"/identition/span3/gist05.html"},{"layout":"default","title":null,"content":"\n***Φ(10,2) = 10² + 2x(10th prime) + 10¹ = 100+29 + 29+10 = 129 + 39 = 168 = π(1000)***\n\n```\nΦ = 2,10\nΔ = 5,7,17\n3': 13,18,25,42\n2' » 13 to 77, Δ = 64\n2' and 3' » 13 to 45, Δ = 32\n\n2\" + 5\" = 7\" = 77\n2\"=22, 3\"=33, 2\" + 3\" = 5\" = 55\n\n13, 16, 18, 21, 23, 25, 28, 30, 32, 34, \n36, 38, 40, 42, \n45, 47, 49, 51, 53, \n55, 57, 59, 61, \n63, 65, 67, 69, 71, 73, 75, 77\n\n```\n\n![default](https://user-images.githubusercontent.com/36441664/100138286-651e1180-2ec0-11eb-9b27-ec206498380f.jpg)\n\nThe DNA base consists of 2 groups that are in pairs between Sugar and pospat with nucleotides. Let's weighting between the two. Each of these pospats consists of three (3) groups with five (5) oxygen bonds. This sugar and pospat forms a system that moves from 5' to 3' which is anti-parallel with movement at the other end which is 3' to 5'.\n\n![default](https://user-images.githubusercontent.com/36441664/101623118-8d724800-3a4a-11eb-8773-e2fb0033fa4b.png)\n\nEach oxygen test has 2 electrons, so each group I give a weight of 2x5 or ten (10) so the total is 30. Sugar molecules are not groups so the weight is five (5) so that with a weight of 30 out of pospat the total is 35. Since there is a pair then the total is 70. Next we unite the format with nucleotides A,T,G,C paired 9+6 and 6+9 totaling 30 then the format of both is (70,30).\n\n```\n #8 |----------- 5® --------|------------ 7® --------------|\n | 1 |---------------- 77 = 4² + 5² + 6² -------------|\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78\n main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 100 - 123 ({24})\n |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30\n {98} | └── 110 - 123 (14x)» 70\n```\n\nHere we unite with the whole bond which of course is the number of the two, namely 100, then the sum of the DNA bases, namely Pospat, Sugar and Nukeotides is 200 with the format (70,30,100).\n\n***(2x5x7,2x3x5,2²x5²) = (14x5,15x2,20x5) = (70,30,100)***\n\n![default](https://user-images.githubusercontent.com/36441664/101109773-3c0d2780-360a-11eb-9f21-57e2707c7d1e.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/84743781-9d99f500-afdc-11ea-8377-e0ecee9537ea.gif)\n\n***114 - 102 = 12 » {1} & {2}***\n\n[![default](https://user-images.githubusercontent.com/8466209/198813482-ac274a00-c025-46ce-9374-f9bcb0c3fd32.png)](https://github.com/jeffreytse/jekyll-deploy-action)\n\n![default](https://user-images.githubusercontent.com/8466209/198410440-cb9003b9-ae7e-4637-aa5e-dcf968f9cb4f.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198940479-9a0d3ad0-b502-4df4-8093-fdac8e275552.png)\n","dir":"/identition/span2/","name":"gist06.md","path":"identition/span2/gist06.md","url":"/identition/span2/gist06.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/200012043-620aa039-3b72-4165-83ad-e35d3d972a1b.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/200002482-af3ef796-e71b-426c-b71d-1bd732ba5c6e.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-6_pattern-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/200007203-bdea0db7-7825-4f34-b8c2-a1b5baf99b87.png)](https://eq19.github.io/)\n\n[![default](https://user-images.githubusercontent.com/8466209/200003416-da978633-24fb-4e8d-aa12-5c18fee76667.png)](https://github.com/eq19)\n\n","dir":"/identition/span7/","name":"gist02.md","path":"identition/span7/gist02.md","url":"/identition/span7/gist02.html"},{"layout":"default","title":null,"content":"\nThis [solution](https://stackoverflow.com/a/42673938/4058484) is primary based on modules importlib and pkgutil and work with CPython 3.4 and CPython 3.5, but has no support for the CPython 2.\n\npython_modules_info.py\n```\nimport sys\nimport os\nimport shutil\nimport pkgutil\nimport importlib\nimport collections\n\nif sys.version_info.major == 2:\n raise NotImplementedError('CPython 2 is not supported yet')\n\n\ndef main():\n\n # name this file (module)\n this_module_name = os.path.basename(__file__).rsplit('.')[0]\n\n # dict for loaders with their modules\n loaders = collections.OrderedDict()\n\n # names`s of build-in modules\n for module_name in sys.builtin_module_names:\n\n # find an information about a module by name\n module = importlib.util.find_spec(module_name)\n\n # add a key about a loader in the dict, if not exists yet\n if module.loader not in loaders:\n loaders[module.loader] = []\n\n # add a name and a location about imported module in the dict\n loaders[module.loader].append((module.name, module.origin))\n\n # all available non-build-in modules\n for module_name in pkgutil.iter_modules():\n\n # ignore this module\n if this_module_name == module_name[1]:\n continue\n\n # find an information about a module by name\n module = importlib.util.find_spec(module_name[1])\n\n # add a key about a loader in the dict, if not exists yet\n loader = type(module.loader)\n if loader not in loaders:\n loaders[loader] = []\n\n # add a name and a location about imported module in the dict\n loaders[loader].append((module.name, module.origin))\n\n # pretty print\n line = '-' * shutil.get_terminal_size().columns\n for loader, modules in loaders.items():\n print('{0}\\n{1}: {2}\\n{0}'.format(line, len(modules), loader))\n for module in modules:\n print('{0:30} | {1}'.format(module[0], module[1]))\n\n\nif __name__ == '__main__':\n main()\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/199131193-34b17216-1308-4efc-953c-708e31007505.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-4_quantum-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/198928812-cab7aef3-9c41-49f4-8b89-00b8fa3fc95a.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde#file-lexer-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199133270-71ca3596-983b-435a-82f6-bcaa682ae650.png)](https://github.com/FeedMapping/prime-hexagon)\n\nA better understanding of the distribution of prime numbers would be a major breakthrough in mathematics A continued relationship with the powers of pi could indicate a connection to circular geometry Other patterns can be analyzed to determine if they are related to the distribution of primes The speed and scalability of the cluster allows Tad Gallion and other researchers to check values of numbers that are significantly higher than any individual computer could compute in a reasonable time constraint The parallelization of the algorithm achieved a 9X speedup *****using CUDA GPU programming***** Because the cluster is managed over the internet, new compute nodes can be added with minimal effort Visualization tools enable researchers to explore the prime hexagon quickly and discover patterns that can be further analyzed Understanding the pattern of prime numbers could have effects in cryptography Many modern encryption algorithms depend on the factorization of very large primes which are hard to find","dir":"/identition/span4/","name":"gist03.md","path":"identition/span4/gist03.md","url":"/identition/span4/gist03.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/199389773-2950d6e1-9bf8-488b-9192-53f8356188f0.png)](https://github.com/spacetimeengineer/spacetimeengine/tree/48924e3cf7f163d7016e2bde7518baa1bbf5e7dd/spacetimeengine)\n\n[![default](https://user-images.githubusercontent.com/8466209/199374989-188e57d5-a21e-4523-97b1-27d996223e8e.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-base-md)\n\nIf you clearly know what kind of neural networks architecture you want, you may need to dive directly into TensorFlow. Whereas Keras is preferred forfast prototyping, where you want to experiment with your ideas and see the results quickly.\n\n[![default](https://user-images.githubusercontent.com/8466209/199374038-d20dd4f9-a851-4258-a397-a3c7eac597ca.png)](https://github.com/chetabahana/tensorflow/tree/623216733f8902b0dfab1cb7e318441537dce855/tensorflow/python/keras)\n\n[![default](https://user-images.githubusercontent.com/8466209/199371855-fe818d94-f6bf-4f3d-94d0-2d18002f3888.png)](https://github.com/chetabahana/tensorflow/wiki/Trend-Analysis#template)\n\n[![default](https://user-images.githubusercontent.com/8466209/199390946-f6bc9455-2500-40e6-b8cf-30cd1aa09963.png)](https://github.com/chetabahana/tensorflow/wiki/Tensor-Kit#branching)\n[![default](https://user-images.githubusercontent.com/8466209/199371755-103f98fc-3735-42dd-81e7-089d2faf8e37.png)]()\n","dir":"/identition/span6/","name":"gist03.md","path":"identition/span6/gist03.md","url":"/identition/span6/gist03.html"},{"layout":"default","title":null,"content":"\n![cubes](https://user-images.githubusercontent.com/8466209/205804217-313e8f74-56d1-4401-be92-e3d3c95da055.jpg)\n\n![prime](https://user-images.githubusercontent.com/36441664/87958552-dea18f80-cadb-11ea-9499-6c2ee580a5ca.png)\n\n![ulam](https://upload.wikimedia.org/wikipedia/commons/2/25/Hexgrid_prime_number_spiral.svg)\n[![default](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-default-md)\n\n![lexer](https://user-images.githubusercontent.com/8466209/204159538-6f87b60c-6a32-486d-aa55-c9af2db7eda6.png)\n","dir":"/exponentiation/span14/","name":"gist02.md","path":"exponentiation/span14/gist02.md","url":"/exponentiation/span14/gist02.html"},{"layout":"default","title":"Polar Plot","content":"## Polar Plot\n\nBased on the homogeneous sorting of objects against these 114 repositories we will get the number 57 which is distributed over the pair of objects whose difference is twenty-nine (29). So everything will happen to repeat in this 29.\n\n***(114/2)! = 57! = 1653 » 1653 / 57 = 29***\n\n```\n--------+\n | ⅓\n +--- } ⅔\n Case A | ⅓\n +---------\n | ⅓ |\n-----------------+ Φ = ⅔\n | ⅓ |\n +---------\n Case B | ⅓\n +--- } ⅔\n | ⅓\n---------\n```\n\nBy this objects pairing there would exist a zone segregation numbers (28.29) on each of the pairs. Since 10 stands as the central zone then it would be a tensor between ***29-10=19*** and ***28-10=18***.\n\n***9 + 19 + 29 = 28 + 29 = (10+18) + (10+19) = 57***\n\n```\nP7:(142857)\n\n # | A | B | ∑\n------+------+------+-----\n {1} | | |\n------+ | |\n ... | 28 | 29 | 57\n------+ | |\n {57} | | |\n------+------+------+-----\n 58 | | |\n------+ | |\n ... | 29 | 28 | 57\n------+ | |\n 114 | | |\n------+------+------+-----\n | 57 | 57 | 114\n```\n\nThis zone is cenralized by the _[20 objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ while the tensor of ***19 vs 18*** is polarizing the 2x11x13=286 objects out of the pairing of 11 and 13 within the _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ and finally be composed by 20/10 = 2 numbers of 285 and 286 that having a total of 571.\n\n***Φ((13,12),(12,18)) = Φ(13,((19,18),(18,43)) = Φ(13,37,61) = Φ(6,12,18)th prime***\n\n```\n---+-----+-----+-----+-----+\n 1 |{19} | 1 |{20} | 21 |-----------------------\n---+-----+-----+-----+-----+ |\n 2 | 18 | 21 | 39 | 60 |----------------- |\n---+-----+-----+-----+-----+ | |\n 3 | 63 | 40 | 103 |{143}|----------- | |\n---+-----+-----+-----+-----+ | | |\n 4 | 37 | 104 | 141 | 245 |----- | | |\n---+-----+-----+-----+-----+ | | | |\n 5 | 10 | 142 | 152 | 294 |-{11}|{13} |{12} |{12} |{18}\n---+-----+-----+-----+-----+ | | | |\n 6 | 24 | 153 |{177}| 332 |----- | | |\n---+-----+-----+-----+-----+ | | |\n 7 | 75 | 178 | 253 | 431 |----------- | |\n---+-----+-----+-----+-----+ | |\n 8 | 30 | 254 | 284 | 538 |----------------- |\n---+-----+-----+-----+-----+ |\n 9 | 1 | 285 | 286 |{571}|-----------------------\n===+=====+=====+=====+=====+\n45 |{277}|\n---+-----+\n```\n\nHowever by the prime numbers this behaviour is not happened by the number of 57 but on the 157 as the ***19+18=37th*** prime. So on the pairing of 57 to 114 above then one of them is forced to behave as 157-57=100 which is exactly the square of 10.\n\n>157 is the 37th prime number, a balanced prime, because the arithmetic mean of those primes yields 157. The next prime is ***163*** and the previous prime is ***151***, with which ***157 forms a prime triplet***. _([Wikipedia](https://en.wikipedia.org/wiki/157_(number)))_\n\n![](https://user-images.githubusercontent.com/36441664/100333516-42494580-3005-11eb-95a2-e7360e60b60f.jpg)\n\nBy this square correlation between natural and prime numbers then the 571 would be separated by the 100 to 500 and 71 and finally by the form of (2,10) the 500 goes to 50 while 71 would be polarized to form 71x2=142 and 177 as shown on the table.\n\n***(10/2)π = 157 ⇄ (10^2)¹ + 11x7 = 177***\n\n![](https://user-images.githubusercontent.com/36441664/72922749-30ad6680-3d80-11ea-92c8-73c1fa12041b.jpg)\n\nThat is why DNA is twisted and spinning in the scope of three (3) directions in three (3) dimensions which in its entirety resembles the shape of a [trifoil](https://en.wikipedia.org/wiki/Trefoil_knot). For XX genes this lead to 1600 objects but for XY genes there are different story.\n\n> When a 3 × 3 × 3 cube is made of 27 unit cubes, 26 of them are viewable as the exterior layer. _([Wikipedia](https://en.wikipedia.org/wiki/26_(number)))_\n\n![](https://user-images.githubusercontent.com/36441664/86853354-88e2e580-c0e0-11ea-92e4-24de95335054.gif)\n\nFrom this arrangement we get the sum of all vectors with the sequence at number 247 where via the number one (1) makes 10 connected with 13 and 14 to the number twenty-seven (27).\n\n***Φ(11,13) = (114 - 10²) + 13 = 27 = 9 x 3 = 3 x 3 x 3 = 3 ^ 3***\n\n```\n----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\nseq | {1}| 2 | 3 | 4 | 5 | {6}| {7}| 8 | 9 | 10 | 11 | 12 | 13 | 14 |\n----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\nnum | {3}| {4}| 3 | 4 | 5 | 2 | 3 | 2 | 2 | 1 | 2 | 5 | 1 | 1 |{38}\n----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285\nseq x num | 3 | 8 | 9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}\n----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n |-- 11 ---| |-- 33 ---| |-- {27}--|\n```\n\nSince there are no twin primes between [26² and 28²](https://primes.utm.edu/curios/page.php?short=26) so they would goes to the rest object of 27. As you can see the formation of 69 objects from the number 29 ends in a 6 x 9 matrix centrally.\n\n***6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 72 + 42 = 114***\n\n```\nThe Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+ ---\n 7 --------- 1,2:1| 1 | 30 | 40 | 71 (2,3) ‹-------------@---- |\n | +-----+-----+-----+-----+ | |\n | 8 ‹------ 3:2| 1 | 30 | 40 | 90 | 161 (7) ‹--- | 5¨ encapsulation\n | | +-----+-----+-----+-----+ | | |\n | | 6 ‹-- 4,6:3| 1 | 30 | 200 | 231 (10,11,12) ‹--|--- | |\n | | | +-----+-----+-----+-----+ | | | ---\n --|--|-----» 7:4| 1 | 30 | 40 | 200 | 271 (13) --› | {5®} | |\n | | +-----+-----+-----+-----+ | | |\n --|---› 8,9:5| 1 | 30 | 200 | 231 (14,15) ---------› | 7¨ abstraction\n289 | +-----+-----+-----+-----+-----+ | |\n | ----› 10:6| 20 | 5 | 10 | 70 | 90 | 195 (19) --› Φ | {6®} |\n --------------------+-----+-----+-----+-----+-----+ | ---\n 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |\n | +-----+-----+-----+ | |\n | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | | +-----+-----+-----+ | | |\n | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n | | | +-----+-----+-----+ | | ---\n | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |\n | | +-----+-----+-----+ | |\n | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance\n329 | +-----+-----+-----+ |\n | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ |\n -------------------+-----+-----+ ---\n 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ |\n | +-----+-----+ |\n | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class\n | | +-----+-----+-----+-----+-----+ | |\n | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} |\n | | | +-----+-----+-----+-----+-----+ | | ---\n --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- |\n | | +-----+-----+ | |\n --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object\n168 | +-----+ |\n| 102 -› 29:18| 50 | 50(68) ---------> Δ18 |\n----------------------+-----+ ---\n```\n\nFrom this number 27, we can start the process by taking the initial vector of 69 as the number of objects that is originated from 10th prime = 29 so the _[29th=109 objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)_ out of ***the 10 objects of the central zone*** is actually decoded from _[110 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef)_ of 18th prime. Therefore the polarizing of 19 vs 18 by the prime hexagon should also involve 3 times 100+3=309 objects.\n\n[![liquid](https://user-images.githubusercontent.com/36441664/105412087-d0892300-5c66-11eb-9c3e-19d8652b478c.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md)\n\nThis pattern is raised up ***per six (6) cycles*** on the ***18+1=[19](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md)***, ***42+1=[43](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-runner-md)*** and ***72-1=[71](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)***. Since the members are limited to the sum of ***43+71=114*** so here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme.\n\n***6 x (1 + 6 + (6 + 6)) = 6 + 36 + 72 = 42 + 72 = 43 + 71 = 114***\n\n[![interpolation](https://user-images.githubusercontent.com/8466209/212487102-2f080804-9078-45c9-85ee-9977a36a5dbf.jpg)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-syntax-md)\n\nThis polarity is happened per ***six (6) cycles*** by the polar of ***six (6) to one (1)*** and ***six (6) to seven (7)*** by which we finally found if this behaviour is cascaded bilaterally within the correlation between ***61*** as [the 18th prime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef) and ***67*** as [the 19th prime](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831). \n\n_1/7 = 0,14_***285***_714_***285***_714_***285***_714_***285***_7.. cycling six (6) numbers of (1,4,2,8,5,7) infinity_\n\n![image](https://user-images.githubusercontent.com/8466209/213899448-fedc0919-f42e-49e2-aa63-a18c8b8a5e02.png)\n\nThis curve is a [polar plot](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) of _[the first 20](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ non-trivial [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) zeros including Gram points along the critical line _[ζ(1/2+t)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-fork-md)_ for real values of t running from 0 to 50. The consecutive zeros have ***[50 red plot points](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)*** between each with zeros identified by magenta _[concentric rings](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d)_ (scaled to show the relative distance between their values of t).\n\n***20x10+ ½(16×6) + ¼(12×18) + ⅛(16×16) = 200 + 48 + 32 + 6 = 286***\n\n[![RiemannZeta Zeros](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n\nSee on the left side contains of odd numbers less and equal to 19 while the right is the even number less and equal to 18. By the left side only ***[9 and 15](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)*** that are not primes. Consider these two (2) numbers are laid side by side as part of Fibonacci sequence on the [Pascal Triangle](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md). Thus the above curve is actually represesenting the pattern of _[true-prime-pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_ via _[bilateral 9 sums](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md)_.\n\n[![Fibonacci Sequence Numbers](https://user-images.githubusercontent.com/8466209/218188579-8b7abe41-3137-41fd-8620-c141a719b493.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md)\n\nMeanwhile the sum of ***28 and 35***, which is 63, has a digital root of 6+3 = 9 and is landed precisely on the _[15's cell](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)_ of the prime hexagon. So the interaction with the [seven (7) objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md) is made through the _[object of 36](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)_ which has the same digital root of 9.\n\n***36® - 9® (1,2,10,47,66,73,86,102,107) - 6°(diagram) - 12*® (pinned) = 36® - 27® = 9®**\n\n![default](https://user-images.githubusercontent.com/8466209/198753476-6871d03b-8d0f-4a44-805f-c9a9595268e1.png)\n\nAs you may see the correlation between each items could involve a complex geometry either by _[area](https://gist.github.com/eq19/80c8098f16f3e6ca06893b17a02d910e)_ or _[volume](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267)_ object that may lead to their _[tensor](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f)_ and _[gap](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288)_. So we decided to _[assign](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-portal-md)_ these behaviours one by one in to a separate group of _[repositories](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-repositories-md)_.\n\n***{10,11,12,14,15} & {26,28} = {5®} & {2®} = {7®} = {30,31,32,33,34,35,36}***\n\n![default](https://user-images.githubusercontent.com/8466209/198408830-2d2fb1ec-79e8-431c-84d4-a911b5d3fc73.png)\n\nAs conclusion to this presentation is that the structure of those prime numbers is not happened by a coincidence. It might hard to believe if they were specifically designed to become _the base algorithm_ on generating the human chromosomes from DNA.\n\n![image](https://user-images.githubusercontent.com/8466209/213899452-be32cd65-94dd-462f-bc8e-54a410be34b8.png)\n\nBy the [next parts](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde) this will go much more details. Such as the generation of the said DNA from its particular atoms and molecules from the nature of universe which may bring another conclusion if it was _initiated by a gap_.\n \n**[₠Quantum Project](https://github.com/eq19)** \nCopyright © 2022 All rights reserved.\n\nReference:\n* [Riemann Zeta](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n* [Mersenne Prime](https://en.wikipedia.org/wiki/Mersenne_prime)\n* [The Prime Hexagon](https://www.hexspin.com/)\n* [The Primes Demystified](https://www.primesdemystified.com/First1000Primes.html)\n","dir":"/identition/span2/","name":"gist09.md","path":"identition/span2/gist09.md","url":"/identition/span2/gist09.html"},{"layout":"default","title":"Why was 6 afraid of 7?","content":"## Why was 6 afraid of 7?\n\n[![default](https://user-images.githubusercontent.com/8466209/199381132-1c2beef1-d8a1-4bdf-8e11-37c71c5aaa39.png)](https://github.com/chetabahana/chetabahana.github.io/wiki/26#Skema)\n\n[![default](https://user-images.githubusercontent.com/8466209/199381827-514ef150-0ca2-4a61-8554-b69946ad2afd.png)](https://www.google.com/search?q=minor+hexagon&tbm=isch)\n\n[![default](https://user-images.githubusercontent.com/8466209/199380441-f5d66d42-3bf4-4442-afb8-3c23347dd8f1.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199380298-8f5e14a4-453a-46a9-8cfe-46859414d300.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199380073-a9657bf5-e4da-468d-9e32-d910f48de2ce.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-grammar-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199375180-51cbbd05-1884-400d-a747-3f1eb3d4057b.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-base-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199376315-60f50c75-257f-4f81-89ae-b0a05b2eb1ea.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde#file-hexagon-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199383689-383d4092-1310-4ffa-b246-d1ee5461f96c.png)](https://github.com/FeedMapping/prime-hexagon/tree/9d46dc7d05f5af89dac3abee000a0666d291e7ab/numberGenerator/python/prime_lists)\n","dir":"/identition/span6/","name":"gist02.md","path":"identition/span6/gist02.md","url":"/identition/span6/gist02.html"},{"layout":"default","title":null,"content":"\n![](https://user-images.githubusercontent.com/36441664/104337162-c1e49280-5527-11eb-9625-12b95f568aa4.png)!\n![default](https://user-images.githubusercontent.com/8466209/199362826-1f59b53a-e036-4d6c-8528-832033cd1370.png)\n![default](https://user-images.githubusercontent.com/8466209/199360397-0158fcf0-4378-4e86-93b4-9c8287c0273b.png)\n![default](https://user-images.githubusercontent.com/8466209/199359982-229c7e19-9491-44fe-bc67-9c10b14609e9.png)\n","dir":"/identition/span5/","name":"gist05.md","path":"identition/span5/gist05.md","url":"/identition/span5/gist05.html"},{"layout":"default","title":"Directory Structure","content":"## Directory Structure\n\nThis page walks through the steps required to [train an object detection model](https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/tf2_training_and_evaluation.md) with Recommended Directory Structure for Training and Evaluation for [tf2_ai_platform](https://github.com/tensorflow/models/blob/master/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile)\n\n```\n$ cat /mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile\n\nFROM tensorflow/tensorflow:latest-gpu\n\nARG DEBIAN_FRONTEND=noninteractive\n\n# Install apt dependencies\nRUN apt-get update && apt-get install -y \\\n git \\\n gpg-agent \\\n python3-cairocffi \\\n protobuf-compiler \\\n python3-pil \\\n python3-lxml \\\n python3-tk \\\n python3-opencv \\\n wget\n\n# Installs google cloud sdk, this is mostly for using gsutil to export model.\nRUN wget -nv \\\n https://dl.google.com/dl/cloudsdk/release/google-cloud-sdk.tar.gz && \\\n mkdir /root/tools && \\\n tar xvzf google-cloud-sdk.tar.gz -C /root/tools && \\\n rm google-cloud-sdk.tar.gz && \\\n /root/tools/google-cloud-sdk/install.sh --usage-reporting=false \\\n --path-update=false --bash-completion=false \\\n --disable-installation-options && \\\n rm -rf /root/.config/* && \\\n ln -s /root/.config /config && \\\n rm -rf /root/tools/google-cloud-sdk/.install/.backup\n\n# Path configuration\nENV PATH $PATH:/root/tools/google-cloud-sdk/bin\n# Make sure gsutil will use the default service account\nRUN echo '[GoogleCompute]\\nservice_account = default' > /etc/boto.cfg\n\nWORKDIR /home/tensorflow\n\n## Copy this code (make sure you are under the ../models/research directory)\nCOPY . /home/tensorflow/models\n\n# Compile protobuf configs\nRUN (cd /home/tensorflow/models/ && protoc object_detection/protos/*.proto --python_out=.)\nWORKDIR /home/tensorflow/models/\n\nRUN cp object_detection/packages/tf2/setup.py ./\nENV PATH=\"/home/tensorflow/.local/bin:${PATH}\"\n\nRUN python -m pip install -U pip\nRUN python -m pip install .\n\nENTRYPOINT [\"python\", \"object_detection/model_main_tf2.py\"]\n```\n\nGitHub allows developers to run GitHub Actions workflows on your own runners. This Docker image allows you to create your own runners on Docker. The GitHub runner (the binary) will update itself when receiving a job, if a new release is available. \n\n```\nARG FROM=debian:buster-slim\nFROM ${FROM}\n\nARG DEBIAN_FRONTEND=noninteractive\nARG GIT_VERSION=\"2.26.2\"\nARG GH_RUNNER_VERSION\nARG DOCKER_COMPOSE_VERSION=\"1.27.4\"\n\nENV RUNNER_NAME=\"\"\nENV RUNNER_WORK_DIRECTORY=\"_work\"\nENV RUNNER_TOKEN=\"\"\nENV RUNNER_REPOSITORY_URL=\"\"\nENV RUNNER_LABELS=\"\"\nENV RUNNER_ALLOW_RUNASROOT=true\nENV GITHUB_ACCESS_TOKEN=\"\"\nENV AGENT_TOOLSDIRECTORY=/opt/hostedtoolcache\n\n# Labels.\nLABEL maintainer=\"me@tcardonne.fr\" \\\n org.label-schema.schema-version=\"1.0\" \\\n org.label-schema.build-date=$BUILD_DATE \\\n org.label-schema.vcs-ref=$VCS_REF \\\n org.label-schema.name=\"tcardonne/github-runner\" \\\n org.label-schema.description=\"Dockerized GitHub Actions runner.\" \\\n org.label-schema.url=\"https://github.com/tcardonne/docker-github-runner\" \\\n org.label-schema.vcs-url=\"https://github.com/tcardonne/docker-github-runner\" \\\n org.label-schema.vendor=\"Thomas Cardonne\" \\\n org.label-schema.docker.cmd=\"docker run -it tcardonne/github-runner:latest\"\n\nRUN DEBIAN_FRONTEND=noninteractive apt-get update && \\\n apt-get install -y \\\n curl \\\n unzip \\\n apt-transport-https \\\n ca-certificates \\\n software-properties-common \\\n sudo \\\n supervisor \\\n jq \\\n iputils-ping \\\n build-essential \\\n zlib1g-dev \\\n gettext \\\n liblttng-ust0 \\\n libcurl4-openssl-dev \\\n openssh-client && \\\n rm -rf /var/lib/apt/lists/* && \\\n apt-get clean\n\nCOPY supervisord.conf /etc/supervisor/conf.d/supervisord.conf\nRUN chmod 644 /etc/supervisor/conf.d/supervisord.conf\n\n# Install Docker CLI\nRUN curl -fsSL https://get.docker.com -o- | sh && \\\n rm -rf /var/lib/apt/lists/* && \\\n apt-get clean\n\n# Install Docker-Compose\nRUN curl -L -o /usr/local/bin/docker-compose \\\n \"https://github.com/docker/compose/releases/download/${DOCKER_COMPOSE_VERSION}/docker-compose-$(uname -s)-$(uname -m)\" && \\\n chmod +x /usr/local/bin/docker-compose\n\nRUN cd /tmp && \\\n curl -sL -o git.tgz \\\n https://www.kernel.org/pub/software/scm/git/git-${GIT_VERSION}.tar.gz && \\\n tar zxf git.tgz && \\\n cd git-${GIT_VERSION} && \\\n ./configure --prefix=/usr && \\\n make && \\\n make install && \\\n rm -rf /tmp/*\n\nRUN mkdir -p /home/runner ${AGENT_TOOLSDIRECTORY}\n\nWORKDIR /home/runner\n\nRUN GH_RUNNER_VERSION=${GH_RUNNER_VERSION:-$(curl --silent \"https://api.github.com/repos/actions/runner/releases/latest\" | grep tag_name | sed -E 's/.*\"v([^\"]+)\".*/\\1/')} \\\n && curl -L -O https://github.com/actions/runner/releases/download/v${GH_RUNNER_VERSION}/actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \\\n && tar -zxf actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \\\n && rm -f actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \\\n && ./bin/installdependencies.sh \\\n && chown -R root: /home/runner \\\n && rm -rf /var/lib/apt/lists/* \\\n && apt-get clean\n\nCOPY entrypoint.sh /entrypoint.sh\nRUN chmod +x /entrypoint.sh\nENTRYPOINT [\"/entrypoint.sh\"]\nCMD [\"/usr/bin/supervisord\", \"-c\", \"/etc/supervisor/conf.d/supervisord.conf\"]\n```\n\nIn order to allow the runner to exit and restart by itself, the binary is started by a [supervisord process](https://github.com/tcardonne/docker-github-runner/blob/master/docker/Dockerfile) and [entrypoint](https://github.com/tcardonne/docker-github-runner/blob/master/docker/entrypoint.sh).\n\n```\n$ cat /etc/supervisord.conf\n\n[supervisord]\nuser=root\nnodaemon=true\nlogfile=/dev/fd/1\nlogfile_maxbytes=0\nloglevel=error\n\n[program:runner]\ndirectory=/home/runner\ncommand=/home/runner/bin/runsvc.sh\nstdout_logfile=/dev/fd/1\nstdout_logfile_maxbytes=0\nredirect_stderr=true\n```\n\nThe self-hosted runner application creates a detailed log file for each job that it processes. These files are stored in the _diag directory where you installed the runner application, and the filename begins with Worker_.\n\n```\n$ cat /home/runner/_diag/Runner_20230515-184422-utc.log\n\n[2023-05-15 18:44:22Z INFO HostContext] No proxy settings were found based on environmental variables (http_proxy/https_proxy/HTTP_PROXY/HTTPS_PROXY)\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Credentials': '/home/runner/.credentials'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Runner': '/home/runner/.runner'\n[2023-05-15 18:44:22Z INFO Listener] Runner is built for Linux (X64) - linux-x64.\n[2023-05-15 18:44:22Z INFO Listener] RuntimeInformation: Linux 5.15.109+ #1 SMP Sat May 6 10:58:50 UTC 2023.\n[2023-05-15 18:44:22Z INFO Listener] Version: 2.303.0\n[2023-05-15 18:44:22Z INFO Listener] Commit: e676c7871817c1b484299cd93fabdf4b95e70741\n[2023-05-15 18:44:22Z INFO Listener] Culture: \n[2023-05-15 18:44:22Z INFO Listener] UI Culture: \n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO Listener] Validating directory permissions for: '/home/runner'\n[2023-05-15 18:44:22Z INFO CommandLineParser] Parse\n[2023-05-15 18:44:22Z INFO CommandLineParser] Parsing 11 args\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: False\n[2023-05-15 18:44:22Z INFO CommandLineParser] Adding Command: configure\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] arg: url\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'url': 'https://github.com/FeedMapping'\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] arg: token\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'token': '***'\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] arg: name\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'name': 'Google-optimized-instance'\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] arg: work\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'work': '_work'\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] arg: replace\n[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument\n[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True\n[2023-05-15 18:44:22Z INFO CommandLineParser] arg: unattended\n[2023-05-15 18:44:22Z INFO CommandLineParser] Adding flag: replace\n[2023-05-15 18:44:22Z INFO Listener] Arguments parsed\n[2023-05-15 18:44:22Z INFO Runner] ExecuteCommand\n[2023-05-15 18:44:22Z INFO ConfigurationStore] currentAssemblyLocation: /home/runner/bin/Runner.Listener.dll\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] binPath: /home/runner/bin\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] RootFolder: /home/runner\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Runner': '/home/runner/.runner'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] ConfigFilePath: /home/runner/.runner\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Credentials': '/home/runner/.credentials'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] CredFilePath: /home/runner/.credentials\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'MigratedCredentials': '/home/runner/.credentials_migrated'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] MigratedCredFilePath: /home/runner/.credentials_migrated\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Service': '/home/runner/.service'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] ServiceConfigFilePath: /home/runner/.service\n[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'help': 'False'\n[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'version': 'False'\n[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'commit': 'False'\n[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'check': 'False'\n[2023-05-15 18:44:22Z INFO CommandSettings] Command 'configure': 'True'\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: --------------------------------------------------------------------------------\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | ____ _ _ _ _ _ _ _ _ |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | / ___(_) |_| | | |_ _| |__ / \\ ___| |_(_) ___ _ __ ___ |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | | | _| | __| |_| | | | | '_ \\ / _ \\ / __| __| |/ _ \\| '_ \\/ __| |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | | |_| | | |_| _ | |_| | |_) | / ___ \\ (__| |_| | (_) | | | \\__ \\ |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | \\____|_|\\__|_| |_|\\__,_|_.__/ /_/ \\_\\___|\\__|_|\\___/|_| |_|___/ |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE: | \n[2023-05-15 18:44:22Z INFO Terminal] WRITE: Self-hosted runner registration\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | |\n[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: --------------------------------------------------------------------------------\n[2023-05-15 18:44:22Z INFO ConfigurationManager] ConfigureAsync\n[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'generateServiceConfig': 'False'\n[2023-05-15 18:44:22Z INFO ConfigurationStore] IsConfigured()\n[2023-05-15 18:44:22Z INFO ConfigurationStore] IsConfigured: False\n[2023-05-15 18:44:22Z INFO ConfigurationManager] Is configured: False\n[2023-05-15 18:44:22Z INFO CommandSettings] Arg 'url': 'https://github.com/FeedMapping'\n[2023-05-15 18:44:22Z INFO CommandSettings] Remove url from Arg dictionary.\n[2023-05-15 18:44:22Z INFO CommandSettings] Arg 'token': '***'\n[2023-05-15 18:44:22Z INFO CommandSettings] Remove token from Arg dictionary.\n[2023-05-15 18:44:24Z INFO ConfigurationManager] Http response code: OK from 'POST https://api.github.com/actions/runner-registration' (E774:461B:1E7DC8F:3E4A2E3:64627D87)\n[2023-05-15 18:44:24Z INFO ConfigurationManager] cred retrieved via GitHub auth\n[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection\n[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 100 seconds timeout.\n[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData\n[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection\n[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 60 seconds timeout.\n[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData\n[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection\n[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 60 seconds timeout.\n[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData\n[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData\n[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData\n[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData\n[2023-05-15 18:44:25Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:25Z INFO ConfigurationManager] Test Connection complete.\n[2023-05-15 18:44:25Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:25Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:25Z INFO HostContext] Well known config file 'RSACredentials': '/home/runner/.credentials_rsaparams'\n[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Creating new RSA key using 2048-bit key length\n[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Successfully saved RSA key parameters to file /home/runner/.credentials_rsaparams\n[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Which: 'chmod'\n[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Location: '/bin/chmod'\n[2023-05-15 18:44:26Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:26Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Starting process:\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] File name: '/bin/chmod'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Arguments: '600 /home/runner/.credentials_rsaparams'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Working directory: '/home/runner'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Require exit code zero: 'False'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Encoding web name: ; code page: ''\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Force kill process on cancellation: 'False'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Redirected STDIN: 'False'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Persist current code page: 'False'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Keep redirected STDIN open: 'False'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] High priority process: 'False'\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Updated oom_score_adj to 500 for PID: 75.\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Process started with process id 75, waiting for process exit.\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.\n[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Finished process 75 with exit code 0, and elapsed time 00:00:00.2254015.\n[2023-05-15 18:44:26Z INFO RSAFileKeyManager] Successfully set permissions for RSA key parameters file /home/runner/.credentials_rsaparams\n[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'runnergroup': ''\n[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'unattended': 'True'\n[2023-05-15 18:44:26Z INFO PromptManager] ReadValue\n[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:26Z INFO ConfigurationManager] Found a self-hosted runner group with id 1 and name Default\n[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'disableupdate': 'False'\n[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'ephemeral': 'False'\n[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'name': 'Google-optimized-instance'\n[2023-05-15 18:44:26Z INFO CommandSettings] Remove name from Arg dictionary.\n[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'labels': ''\n[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'unattended': 'True'\n[2023-05-15 18:44:26Z INFO PromptManager] ReadValue\n[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:27Z INFO Terminal] WRITE LINE: A runner exists with the same name\n[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'replace': 'True'\n[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'disableupdate': 'False'\n[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'disableupdate': 'False'\n[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'ephemeral': 'False'\n[2023-05-15 18:44:27Z INFO ConfigurationStore] Saving OAuth credential @ /home/runner/.credentials\n[2023-05-15 18:44:27Z INFO ConfigurationStore] Credentials Saved.\n[2023-05-15 18:44:27Z INFO ConfigurationStore] HasCredentials()\n[2023-05-15 18:44:27Z INFO ConfigurationStore] stored True\n[2023-05-15 18:44:27Z INFO CredentialManager] GetCredentialProvider\n[2023-05-15 18:44:27Z INFO CredentialManager] Creating type OAuth\n[2023-05-15 18:44:27Z INFO CredentialManager] Creating credential type: OAuth\n[2023-05-15 18:44:27Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams\n[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection\n[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 100 seconds timeout.\n[2023-05-15 18:44:27Z INFO GitHubActionsService] Starting operation Location.GetConnectionData\n[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection\n[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 60 seconds timeout.\n[2023-05-15 18:44:27Z INFO GitHubActionsService] Starting operation Location.GetConnectionData\n[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection\n[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 60 seconds timeout.\n[2023-05-15 18:44:28Z INFO GitHubActionsService] Starting operation Location.GetConnectionData\n[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData\n[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData\n[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData\n[2023-05-15 18:44:28Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams\n[2023-05-15 18:44:28Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams\n[2023-05-15 18:44:29Z INFO GitHubActionsService] AAD Correlation ID for this token request: Unknown\n[2023-05-15 18:44:29Z INFO CommandSettings] Arg 'work': '_work'\n[2023-05-15 18:44:29Z INFO CommandSettings] Remove work from Arg dictionary.\n[2023-05-15 18:44:29Z INFO ConfigurationStore] Saving runner settings.\n[2023-05-15 18:44:29Z INFO ConfigurationStore] Settings Saved.\n[2023-05-15 18:44:29Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:29Z INFO Terminal] WRITE LINE: \n[2023-05-15 18:44:29Z INFO SystemDControlManager] Service name 'actions.runner.FeedMapping.Google-optimized-instance.service' display name 'GitHub Actions Runner (FeedMapping.Google-optimized-instance)' will be used for service configuration.\n[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'\n[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Root': '/home/runner'\n[2023-05-15 18:44:29Z INFO UnixUtil] Which: 'chmod'\n[2023-05-15 18:44:29Z INFO UnixUtil] Location: '/bin/chmod'\n[2023-05-15 18:44:29Z INFO UnixUtil] Running /bin/chmod 755 \"/home/runner/svc.sh\"\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Starting process:\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] File name: '/bin/chmod'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Arguments: '755 \"/home/runner/svc.sh\"'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Working directory: '/home/runner'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Require exit code zero: 'True'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Encoding web name: ; code page: ''\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Force kill process on cancellation: 'False'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Redirected STDIN: 'False'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Persist current code page: 'False'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Keep redirected STDIN open: 'False'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] High priority process: 'False'\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Updated oom_score_adj to 500 for PID: 79.\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Process started with process id 79, waiting for process exit.\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.\n[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Finished process 79 with exit code 0, and elapsed time 00:00:00.0022358.\n[2023-05-15 18:44:29Z INFO Listener] Runner execution has finished with return code 0\n```\n\n### System File\n\nThere is a powerful command in Linux that helps you search for files and folders called find. In this article, we will discuss the find command with some examples.\n\n```\n$ find / -type f -name \"Dockerfile*\"\n\n/mnt/disks/Linux/opt/src/github.com/google/inverting-proxy/agent/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/inverting-proxy-master/agent/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/android/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf1/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf2/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/deploycmle/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/bqtocsv/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/hypertrain/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/deployapp/Dockerfile\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/traintuned/Dockerfile\n\n/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/android/Dockerfile\n/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile\n/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf1/Dockerfile\n/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2/Dockerfile\n/mnt/disks/Linux/usr/share/man/man5/Dockerfile.5.gz\n\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.install_app\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.virtualenv.template\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.requirements_txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.preamble\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/ruby/templates/Dockerfile.template\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/php/templates/Dockerfile.template\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/php/templates/Dockerfile.entrypoint.template\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/go/data/Dockerfile\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/nodejs/data/Dockerfile\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/.kokoro/docker/docs/Dockerfile\n/mnt/disks/Linux/usr/local/go/src/crypto/elliptic/internal/fiat/Dockerfile\n\n/mnt/stateful_partition/var/lib/docker/overlay2/l5js8cyp55dvi6cah1i3gzu4k/diff/Dockerfile\n/mnt/stateful_partition/var/lib/docker/overlay2/6af1c7208063f51f2dc03dbc263eae3f4e148d6bcfd1608bfa4231ca764c5658/diff/home/runner/_work/Partition/Partition/.github/actions/intro/Dockerfile\n```\n\nNow let's say we want to find files with a particular extension like .txt. We'll modify the command like this:\n\n```\n/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/python/xds/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/src/models/official/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/src/models/official/projects/unified_detector/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/src/models/official/projects/movinet/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/src/models/research/deep_speech/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/tf2_course/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/serving/application/requirements.txt\n/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/labs/serving/application/requirements.txt\n\n/mnt/disks/Linux/usr/share/models/official/requirements.txt\n/mnt/disks/Linux/usr/share/models/official/projects/unified_detector/requirements.txt\n/mnt/disks/Linux/usr/share/models/official/projects/movinet/requirements.txt\n/mnt/disks/Linux/usr/share/models/research/deep_speech/requirements.txt\n\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/java/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/gslib/vendored/boto/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/gslib/vendored/oauth2client/docs/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/httplib2/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/requests/docs/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/pyasn1/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/pyasn1-modules/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/charset_normalizer/docs/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/gcs-oauth2-boto-plugin/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/urllib3/docs/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/.kokoro/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/testing/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/samples/cloud-client/snippets/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/system_tests/system_tests_sync/app_engine_test_app/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/mock/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/gslib/vendored/boto/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/gslib/vendored/oauth2client/docs/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/pyasn1/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/pyasn1-modules/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/gcs-oauth2-boto-plugin/requirements.txt\n/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/mock/requirements.txt\n\n/mnt/disks/Linux/usr/samples/python/network_api_pytorch_mnist/requirements.txt\n/mnt/disks/Linux/usr/samples/python/requirements.txt\n/mnt/disks/Linux/usr/samples/python/engine_refit_onnx_bidaf/requirements.txt\n/mnt/disks/Linux/usr/samples/python/introductory_parser_samples/requirements.txt\n/mnt/disks/Linux/usr/samples/python/end_to_end_tensorflow_mnist/requirements.txt\n/mnt/disks/Linux/usr/samples/python/int8_caffe_mnist/requirements.txt\n/mnt/disks/Linux/usr/samples/python/engine_refit_mnist/requirements.txt\n/mnt/disks/Linux/usr/samples/python/uff_ssd/requirements.txt\n/mnt/disks/Linux/usr/samples/python/uff_custom_plugin/requirements.txt\n/mnt/disks/Linux/usr/samples/python/yolov3_onnx/requirements.txt\n/mnt/disks/Linux/usr/samples/python/onnx_packnet/requirements.txt\n/mnt/disks/Linux/usr/samples/sampleUffMaskRCNN/converted/requirements.txt\n/mnt/disks/Linux/usr/samples/sampleSSD/requirements.txt\n\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/network_api_pytorch_mnist/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/engine_refit_onnx_bidaf/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/introductory_parser_samples/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/end_to_end_tensorflow_mnist/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/int8_caffe_mnist/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/engine_refit_mnist/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/uff_ssd/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/uff_custom_plugin/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/yolov3_onnx/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/onnx_packnet/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/sampleUffMaskRCNN/converted/requirements.txt\n/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/sampleSSD/requirements.txt\n```\n\nThe find command lets you efficiently search for files, folders, and character and block devices. Below is the basic syntax of the find command:\n\n```\n$ find / -type d -name \"tensorflow*\"\n\n/mnt/disks/Linux/opt/deeplearning/binaries/tensorflow\n/mnt/disks/Linux/opt/deeplearning/src/models/tensorflow_models\n/mnt/disks/Linux/usr/share/models/tensorflow_models\n\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_cloud-0.1.16.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_probability\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem-0.29.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/google/cloud/aiplatform/training_utils/cloud_profiler/plugins/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_datasets\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_estimator\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorboard_plugin_wit/_vendor/tensorflow_serving\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_cloud\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/xla_aot_runtime_src/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/compiler/mlir/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/include/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/include/tensorflow/compiler/mlir/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io-0.29.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_probability-0.19.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/ray/train/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/witwidget/_vendor/tensorflow_serving\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_serving_api-2.11.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_hub-0.13.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_estimator-2.11.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_transform-1.12.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/pyarrow/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/pyarrow/include/arrow/adapters/tensorflow\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow-2.11.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_metadata\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_serving\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_hub\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_transform\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_metadata-1.12.0.dist-info\n/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_datasets-4.8.2.dist-info\n\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_cloud-0.1.16.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_probability\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem-0.29.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/google/cloud/aiplatform/training_utils/cloud_profiler/plugins/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_datasets\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_estimator\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorboard_plugin_wit/_vendor/tensorflow_serving\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_cloud\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/xla_aot_runtime_src/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/compiler/mlir/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/include/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/include/tensorflow/compiler/mlir/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io-0.29.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_probability-0.19.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/ray/train/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/witwidget/_vendor/tensorflow_serving\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_serving_api-2.11.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_hub-0.13.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_estimator-2.11.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_transform-1.12.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/pyarrow/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/pyarrow/include/arrow/adapters/tensorflow\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow-2.11.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_metadata\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_serving\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_hub\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_transform\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_metadata-1.12.0.dist-info\n/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_datasets-4.8.2.dist-info\n```\n\n![default](https://user-images.githubusercontent.com/8466209/199132181-38a98bf9-9d72-4740-b96c-c57da26a6135.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/198812060-bcf0c3e5-1918-4245-b2fa-1c43c2602a90.png)](https://www.chetabahana.com/)\n\n[![default](https://user-images.githubusercontent.com/8466209/227684922-9b3190e2-879c-42e5-b404-fb975b9b8752.png)](https://cloud.google.com/sdk/gcloud/reference/compute/instances/create#--metadata)\n","dir":"/identition/span4/","name":"gist04.md","path":"identition/span4/gist04.md","url":"/identition/span4/gist04.html"},{"layout":"default","title":"Where is the 5?","content":"## Where is the 5?\n\nThe four faces additively cascade 32 four-times triangular numbers (oeis.org/A046092). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of 1000th prime.\n\n![encaptulatipn](https://user-images.githubusercontent.com/8466209/199354127-9e4d362a-933f-402b-a7a8-0010dc014747.png)\n\n```\nπ(10) = 4\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n ↓\n |\n ↓ \n 114-89=139-114=25=5x5\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ ↓\n | | |\n ------------ 10 ------------- | \n | \n | \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+===== \n \n ```\n \n![default](https://user-images.githubusercontent.com/8466209/199262407-7f8bee13-f240-4b1f-856e-ee93e97c5ddb.png)\n![default](https://user-images.githubusercontent.com/8466209/199355377-8d93057a-769d-49ed-b401-722c0b33fdab.png)\n","dir":"/identition/span5/","name":"gist02.md","path":"identition/span5/gist02.md","url":"/identition/span5/gist02.html"},{"layout":"default","title":"Binary","content":"## Binary\n\nOnce the System Properties window opens, click on the “Environment Variables” button. In the “System Variables” box, look for a variable called Path. see all executables in your PATH on your system, and all aliases, all sorted\n\n```\n$ find ${PATH//:/ } -maxdepth 1 -executable | sort\n\n/bin\n/bin/bash\n/bin/bunzip2\n/bin/bzcat\n/bin/bzcmp\n/bin/bzdiff\n/bin/bzegrep\n/bin/bzexe\n/bin/bzfgrep\n/bin/bzgrep\n/bin/bzip2\n/bin/bzip2recover\n/bin/bzless\n/bin/bzmore\n/bin/cat\n/bin/chgrp\n/bin/chmod\n/bin/chown\n/bin/cp\n/bin/dash\n/bin/date\n/bin/dd\n/bin/df\n/bin/dir\n/bin/dmesg\n/bin/dnsdomainname\n/bin/domainname\n/bin/echo\n/bin/egrep\n/bin/false\n/bin/fgrep\n/bin/findmnt\n/bin/fuser\n/bin/grep\n/bin/gunzip\n/bin/gzexe\n/bin/gzip\n/bin/hostname\n/bin/journalctl\n/bin/kill\n/bin/less\n/bin/lessecho\n/bin/lessfile\n/bin/lesskey\n/bin/lesspipe\n/bin/ln\n/bin/login\n/bin/loginctl\n/bin/ls\n/bin/lsblk\n/bin/mkdir\n/bin/mknod\n/bin/mktemp\n/bin/more\n/bin/mount\n/bin/mountpoint\n/bin/mv\n/bin/networkctl\n/bin/nisdomainname\n/bin/pidof\n/bin/ping\n/bin/ping4\n/bin/ping6\n/bin/ps\n/bin/pwd\n/bin/rbash\n/bin/readlink\n/bin/rm\n/bin/rmdir\n/bin/run-parts\n/bin/sed\n/bin/sh\n/bin/sleep\n/bin/stty\n/bin/su\n/bin/sync\n/bin/systemctl\n/bin/systemd\n/bin/systemd-ask-password\n/bin/systemd-escape\n/bin/systemd-inhibit\n/bin/systemd-machine-id-setup\n/bin/systemd-notify\n/bin/systemd-sysusers\n/bin/systemd-tmpfiles\n/bin/systemd-tty-ask-password-agent\n/bin/tar\n/bin/tempfile\n/bin/touch\n/bin/true\n/bin/umount\n/bin/uname\n/bin/uncompress\n/bin/vdir\n/bin/wdctl\n/bin/which\n/bin/ypdomainname\n/bin/zcat\n/bin/zcmp\n/bin/zdiff\n/bin/zegrep\n/bin/zfgrep\n/bin/zforce\n/bin/zgrep\n/bin/zless\n/bin/zmore\n/bin/znew\n/sbin\n/sbin/agetty\n/sbin/apparmor_parser\n/sbin/badblocks\n/sbin/blkdeactivate\n/sbin/blkdiscard\n/sbin/blkid\n/sbin/blkzone\n/sbin/blockdev\n/sbin/capsh\n/sbin/cfdisk\n/sbin/chcpu\n/sbin/ctrlaltdel\n/sbin/debugfs\n/sbin/dmsetup\n/sbin/dmstats\n/sbin/dumpe2fs\n/sbin/e2fsck\n/sbin/e2image\n/sbin/e2label\n/sbin/e2mmpstatus\n/sbin/e2undo\n/sbin/fdisk\n/sbin/findfs\n/sbin/fsck\n/sbin/fsck.cramfs\n/sbin/fsck.ext2\n/sbin/fsck.ext3\n/sbin/fsck.ext4\n/sbin/fsck.minix\n/sbin/fsfreeze\n/sbin/fstab-decode\n/sbin/fstrim\n/sbin/getcap\n/sbin/getpcaps\n/sbin/getty\n/sbin/halt\n/sbin/hwclock\n/sbin/init\n/sbin/installkernel\n/sbin/ip6tables\n/sbin/ip6tables-restore\n/sbin/ip6tables-save\n/sbin/iptables\n/sbin/iptables-restore\n/sbin/iptables-save\n/sbin/isosize\n/sbin/killall5\n/sbin/ldconfig\n/sbin/logsave\n/sbin/losetup\n/sbin/mke2fs\n/sbin/mkfs\n/sbin/mkfs.bfs\n/sbin/mkfs.cramfs\n/sbin/mkfs.ext2\n/sbin/mkfs.ext3\n/sbin/mkfs.ext4\n/sbin/mkfs.minix\n/sbin/mkhomedir_helper\n/sbin/mkswap\n/sbin/pam_tally\n/sbin/pam_tally2\n/sbin/pivot_root\n/sbin/poweroff\n/sbin/raw\n/sbin/reboot\n/sbin/resize2fs\n/sbin/runlevel\n/sbin/runuser\n/sbin/setcap\n/sbin/sfdisk\n/sbin/shadowconfig\n/sbin/shutdown\n/sbin/start-stop-daemon\n/sbin/sulogin\n/sbin/swaplabel\n/sbin/swapoff\n/sbin/swapon\n/sbin/switch_root\n/sbin/sysctl\n/sbin/telinit\n/sbin/tune2fs\n/sbin/unix_chkpwd\n/sbin/unix_update\n/sbin/wipefs\n/sbin/zramctl\n/usr/bin\n/usr/bin/2to3-2.7\n/usr/bin/[\n/usr/bin/aa-enabled\n/usr/bin/aa-exec\n/usr/bin/add-apt-repository\n/usr/bin/addpart\n/usr/bin/addr2line\n/usr/bin/apt\n/usr/bin/apt-add-repository\n/usr/bin/apt-cache\n/usr/bin/apt-cdrom\n/usr/bin/apt-config\n/usr/bin/apt-get\n/usr/bin/apt-key\n/usr/bin/apt-mark\n/usr/bin/ar\n/usr/bin/arch\n/usr/bin/as\n/usr/bin/awk\n/usr/bin/b2sum\n/usr/bin/base32\n/usr/bin/base64\n/usr/bin/basename\n/usr/bin/bashbug\n/usr/bin/bootctl\n/usr/bin/busctl\n/usr/bin/c++\n/usr/bin/c++filt\n/usr/bin/c89\n/usr/bin/c89-gcc\n/usr/bin/c99\n/usr/bin/c99-gcc\n/usr/bin/c_rehash\n/usr/bin/captoinfo\n/usr/bin/catchsegv\n/usr/bin/cc\n/usr/bin/chage\n/usr/bin/chattr\n/usr/bin/chcon\n/usr/bin/chfn\n/usr/bin/choom\n/usr/bin/chrt\n/usr/bin/chsh\n/usr/bin/cksum\n/usr/bin/clear\n/usr/bin/clear_console\n/usr/bin/cmp\n/usr/bin/comm\n/usr/bin/compose\n/usr/bin/containerd\n/usr/bin/containerd-shim\n/usr/bin/containerd-shim-runc-v1\n/usr/bin/containerd-shim-runc-v2\n/usr/bin/corelist\n/usr/bin/cpan\n/usr/bin/cpan5.28-x86_64-linux-gnu\n/usr/bin/cpp\n/usr/bin/cpp-8\n/usr/bin/csplit\n/usr/bin/ctr\n/usr/bin/curl\n/usr/bin/curl-config\n/usr/bin/cut\n/usr/bin/cvtsudoers\n/usr/bin/dbus-cleanup-sockets\n/usr/bin/dbus-daemon\n/usr/bin/dbus-monitor\n/usr/bin/dbus-run-session\n/usr/bin/dbus-send\n/usr/bin/dbus-update-activation-environment\n/usr/bin/dbus-uuidgen\n/usr/bin/deb-systemd-helper\n/usr/bin/deb-systemd-invoke\n/usr/bin/debconf\n/usr/bin/debconf-apt-progress\n/usr/bin/debconf-communicate\n/usr/bin/debconf-copydb\n/usr/bin/debconf-escape\n/usr/bin/debconf-set-selections\n/usr/bin/debconf-show\n/usr/bin/delpart\n/usr/bin/dh_python2\n/usr/bin/diff\n/usr/bin/diff3\n/usr/bin/dircolors\n/usr/bin/dirmngr\n/usr/bin/dirmngr-client\n/usr/bin/dirname\n/usr/bin/docker\n/usr/bin/docker-init\n/usr/bin/docker-proxy\n/usr/bin/dockerd\n/usr/bin/dockerd-rootless-setuptool.sh\n/usr/bin/dockerd-rootless.sh\n/usr/bin/dpkg\n/usr/bin/dpkg-architecture\n/usr/bin/dpkg-buildflags\n/usr/bin/dpkg-buildpackage\n/usr/bin/dpkg-checkbuilddeps\n/usr/bin/dpkg-deb\n/usr/bin/dpkg-distaddfile\n/usr/bin/dpkg-divert\n/usr/bin/dpkg-genbuildinfo\n/usr/bin/dpkg-genchanges\n/usr/bin/dpkg-gencontrol\n/usr/bin/dpkg-gensymbols\n/usr/bin/dpkg-maintscript-helper\n/usr/bin/dpkg-mergechangelogs\n/usr/bin/dpkg-name\n/usr/bin/dpkg-parsechangelog\n/usr/bin/dpkg-query\n/usr/bin/dpkg-scanpackages\n/usr/bin/dpkg-scansources\n/usr/bin/dpkg-shlibdeps\n/usr/bin/dpkg-source\n/usr/bin/dpkg-split\n/usr/bin/dpkg-statoverride\n/usr/bin/dpkg-trigger\n/usr/bin/dpkg-vendor\n/usr/bin/du\n/usr/bin/dwp\n/usr/bin/echo_supervisord_conf\n/usr/bin/edit\n/usr/bin/elfedit\n/usr/bin/enc2xs\n/usr/bin/encguess\n/usr/bin/env\n/usr/bin/envsubst\n/usr/bin/expand\n/usr/bin/expiry\n/usr/bin/expr\n/usr/bin/factor\n/usr/bin/faillog\n/usr/bin/faked-sysv\n/usr/bin/faked-tcp\n/usr/bin/fakeroot\n/usr/bin/fakeroot-sysv\n/usr/bin/fakeroot-tcp\n/usr/bin/fallocate\n/usr/bin/file\n/usr/bin/fincore\n/usr/bin/find\n/usr/bin/flock\n/usr/bin/fmt\n/usr/bin/fold\n/usr/bin/free\n/usr/bin/funzip\n/usr/bin/g++\n/usr/bin/g++-8\n/usr/bin/gapplication\n/usr/bin/gcc\n/usr/bin/gcc-8\n/usr/bin/gcc-ar\n/usr/bin/gcc-ar-8\n/usr/bin/gcc-nm\n/usr/bin/gcc-nm-8\n/usr/bin/gcc-ranlib\n/usr/bin/gcc-ranlib-8\n/usr/bin/gcov\n/usr/bin/gcov-8\n/usr/bin/gcov-dump\n/usr/bin/gcov-dump-8\n/usr/bin/gcov-tool\n/usr/bin/gcov-tool-8\n/usr/bin/gdbus\n/usr/bin/gencat\n/usr/bin/getconf\n/usr/bin/getent\n/usr/bin/getopt\n/usr/bin/gettext\n/usr/bin/gettext.sh\n/usr/bin/gettextize\n/usr/bin/gio\n/usr/bin/gio-querymodules\n/usr/bin/git\n/usr/bin/git-cvsserver\n/usr/bin/git-receive-pack\n/usr/bin/git-shell\n/usr/bin/git-upload-archive\n/usr/bin/git-upload-pack\n/usr/bin/gitk\n/usr/bin/glib-compile-schemas\n/usr/bin/gold\n/usr/bin/gpasswd\n/usr/bin/gpg\n/usr/bin/gpg-agent\n/usr/bin/gpg-connect-agent\n/usr/bin/gpg-wks-server\n/usr/bin/gpg-zip\n/usr/bin/gpgcompose\n/usr/bin/gpgconf\n/usr/bin/gpgparsemail\n/usr/bin/gpgsm\n/usr/bin/gpgsplit\n/usr/bin/gpgtar\n/usr/bin/gpgv\n/usr/bin/gprof\n/usr/bin/gresource\n/usr/bin/groups\n/usr/bin/gsettings\n/usr/bin/h2ph\n/usr/bin/h2xs\n/usr/bin/head\n/usr/bin/hostid\n/usr/bin/hostnamectl\n/usr/bin/i386\n/usr/bin/iconv\n/usr/bin/id\n/usr/bin/infocmp\n/usr/bin/infotocap\n/usr/bin/install\n/usr/bin/instmodsh\n/usr/bin/ionice\n/usr/bin/ipcmk\n/usr/bin/ipcrm\n/usr/bin/ipcs\n/usr/bin/iptables-xml\n/usr/bin/ischroot\n/usr/bin/join\n/usr/bin/jq\n/usr/bin/json_pp\n/usr/bin/kbxutil\n/usr/bin/kernel-install\n/usr/bin/killall\n/usr/bin/last\n/usr/bin/lastb\n/usr/bin/lastlog\n/usr/bin/lcf\n/usr/bin/ld\n/usr/bin/ld.bfd\n/usr/bin/ld.gold\n/usr/bin/ldd\n/usr/bin/less\n/usr/bin/lessecho\n/usr/bin/lessfile\n/usr/bin/lesskey\n/usr/bin/lesspipe\n/usr/bin/libnetcfg\n/usr/bin/link\n/usr/bin/linux32\n/usr/bin/linux64\n/usr/bin/locale\n/usr/bin/localectl\n/usr/bin/localedef\n/usr/bin/logger\n/usr/bin/logname\n/usr/bin/lsattr\n/usr/bin/lsb_release\n/usr/bin/lscpu\n/usr/bin/lsipc\n/usr/bin/lslocks\n/usr/bin/lslogins\n/usr/bin/lsmem\n/usr/bin/lsns\n/usr/bin/lspgpot\n/usr/bin/lzcat\n/usr/bin/lzcmp\n/usr/bin/lzdiff\n/usr/bin/lzegrep\n/usr/bin/lzfgrep\n/usr/bin/lzgrep\n/usr/bin/lzless\n/usr/bin/lzma\n/usr/bin/lzmainfo\n/usr/bin/lzmore\n/usr/bin/make\n/usr/bin/make-first-existing-target\n/usr/bin/mawk\n/usr/bin/mcookie\n/usr/bin/md5sum\n/usr/bin/md5sum.textutils\n/usr/bin/mesg\n/usr/bin/migrate-pubring-from-classic-gpg\n/usr/bin/mkfifo\n/usr/bin/msgattrib\n/usr/bin/msgcat\n/usr/bin/msgcmp\n/usr/bin/msgcomm\n/usr/bin/msgconv\n/usr/bin/msgen\n/usr/bin/msgexec\n/usr/bin/msgfilter\n/usr/bin/msgfmt\n/usr/bin/msggrep\n/usr/bin/msginit\n/usr/bin/msgmerge\n/usr/bin/msgunfmt\n/usr/bin/msguniq\n/usr/bin/mtrace\n/usr/bin/namei\n/usr/bin/nawk\n/usr/bin/newgrp\n/usr/bin/ngettext\n/usr/bin/nice\n/usr/bin/nl\n/usr/bin/nm\n/usr/bin/nohup\n/usr/bin/nproc\n/usr/bin/nsenter\n/usr/bin/numfmt\n/usr/bin/objcopy\n/usr/bin/objdump\n/usr/bin/od\n/usr/bin/openssl\n/usr/bin/pager\n/usr/bin/partx\n/usr/bin/passwd\n/usr/bin/paste\n/usr/bin/patch\n/usr/bin/pathchk\n/usr/bin/pdb\n/usr/bin/pdb2\n/usr/bin/pdb2.7\n/usr/bin/pdb3\n/usr/bin/pdb3.7\n/usr/bin/peekfd\n/usr/bin/perl\n/usr/bin/perl5.28-x86_64-linux-gnu\n/usr/bin/perl5.28.1\n/usr/bin/perlbug\n/usr/bin/perldoc\n/usr/bin/perlivp\n/usr/bin/perlthanks\n/usr/bin/pgrep\n/usr/bin/piconv\n/usr/bin/pidproxy\n/usr/bin/pigz\n/usr/bin/pinentry\n/usr/bin/pinentry-curses\n/usr/bin/pinky\n/usr/bin/pkaction\n/usr/bin/pkcheck\n/usr/bin/pkcon\n/usr/bin/pkexec\n/usr/bin/pkill\n/usr/bin/pkmon\n/usr/bin/pkttyagent\n/usr/bin/pl2pm\n/usr/bin/pldd\n/usr/bin/pmap\n/usr/bin/pod2html\n/usr/bin/pod2man\n/usr/bin/pod2text\n/usr/bin/pod2usage\n/usr/bin/podchecker\n/usr/bin/podselect\n/usr/bin/pr\n/usr/bin/print\n/usr/bin/printenv\n/usr/bin/printf\n/usr/bin/prlimit\n/usr/bin/prove\n/usr/bin/prtstat\n/usr/bin/pslog\n/usr/bin/pstree\n/usr/bin/pstree.x11\n/usr/bin/ptar\n/usr/bin/ptardiff\n/usr/bin/ptargrep\n/usr/bin/ptx\n/usr/bin/pwdx\n/usr/bin/py3clean\n/usr/bin/py3compile\n/usr/bin/py3versions\n/usr/bin/pyclean\n/usr/bin/pycompile\n/usr/bin/pydoc\n/usr/bin/pydoc2\n/usr/bin/pydoc2.7\n/usr/bin/pydoc3\n/usr/bin/pydoc3.7\n/usr/bin/pygettext\n/usr/bin/pygettext2\n/usr/bin/pygettext2.7\n/usr/bin/pygettext3\n/usr/bin/pygettext3.7\n/usr/bin/python\n/usr/bin/python2\n/usr/bin/python2.7\n/usr/bin/python3\n/usr/bin/python3.7\n/usr/bin/python3.7m\n/usr/bin/python3m\n/usr/bin/pyversions\n/usr/bin/ranlib\n/usr/bin/rcp\n/usr/bin/readelf\n/usr/bin/realpath\n/usr/bin/recode-sr-latin\n/usr/bin/rename.ul\n/usr/bin/renice\n/usr/bin/reset\n/usr/bin/resizepart\n/usr/bin/resolvectl\n/usr/bin/rev\n/usr/bin/rgrep\n/usr/bin/rlogin\n/usr/bin/rootlesskit\n/usr/bin/rootlesskit-docker-proxy\n/usr/bin/rpcgen\n/usr/bin/rsh\n/usr/bin/run-mailcap\n/usr/bin/runc\n/usr/bin/runcon\n/usr/bin/savelog\n/usr/bin/scp\n/usr/bin/script\n/usr/bin/scriptreplay\n/usr/bin/sdiff\n/usr/bin/see\n/usr/bin/select-editor\n/usr/bin/sensible-browser\n/usr/bin/sensible-editor\n/usr/bin/sensible-pager\n/usr/bin/seq\n/usr/bin/setarch\n/usr/bin/setpriv\n/usr/bin/setsid\n/usr/bin/setterm\n/usr/bin/sftp\n/usr/bin/sg\n/usr/bin/sha1sum\n/usr/bin/sha224sum\n/usr/bin/sha256sum\n/usr/bin/sha384sum\n/usr/bin/sha512sum\n/usr/bin/shasum\n/usr/bin/shred\n/usr/bin/shuf\n/usr/bin/size\n/usr/bin/skill\n/usr/bin/slabtop\n/usr/bin/slogin\n/usr/bin/snice\n/usr/bin/sort\n/usr/bin/sotruss\n/usr/bin/splain\n/usr/bin/split\n/usr/bin/sprof\n/usr/bin/ssh\n/usr/bin/ssh-add\n/usr/bin/ssh-agent\n/usr/bin/ssh-argv0\n/usr/bin/ssh-copy-id\n/usr/bin/ssh-keygen\n/usr/bin/ssh-keyscan\n/usr/bin/stat\n/usr/bin/stdbuf\n/usr/bin/strings\n/usr/bin/strip\n/usr/bin/sudo\n/usr/bin/sudoedit\n/usr/bin/sudoreplay\n/usr/bin/sum\n/usr/bin/supervisorctl\n/usr/bin/supervisord\n/usr/bin/symcryptrun\n/usr/bin/systemd-analyze\n/usr/bin/systemd-cat\n/usr/bin/systemd-cgls\n/usr/bin/systemd-cgtop\n/usr/bin/systemd-delta\n/usr/bin/systemd-detect-virt\n/usr/bin/systemd-id128\n/usr/bin/systemd-mount\n/usr/bin/systemd-path\n/usr/bin/systemd-resolve\n/usr/bin/systemd-run\n/usr/bin/systemd-socket-activate\n/usr/bin/systemd-stdio-bridge\n/usr/bin/systemd-umount\n/usr/bin/tabs\n/usr/bin/tac\n/usr/bin/tail\n/usr/bin/taskset\n/usr/bin/tee\n/usr/bin/test\n/usr/bin/tic\n/usr/bin/timedatectl\n/usr/bin/timeout\n/usr/bin/tload\n/usr/bin/toe\n/usr/bin/top\n/usr/bin/touch\n/usr/bin/tput\n/usr/bin/tr\n/usr/bin/truncate\n/usr/bin/tset\n/usr/bin/tsort\n/usr/bin/tty\n/usr/bin/tzselect\n/usr/bin/ucf\n/usr/bin/ucfq\n/usr/bin/ucfr\n/usr/bin/unattended-upgrade\n/usr/bin/unattended-upgrades\n/usr/bin/unexpand\n/usr/bin/uniq\n/usr/bin/unlink\n/usr/bin/unlzma\n/usr/bin/unpigz\n/usr/bin/unshare\n/usr/bin/unxz\n/usr/bin/unzip\n/usr/bin/unzipsfx\n/usr/bin/update-alternatives\n/usr/bin/update-mime-database\n/usr/bin/uptime\n/usr/bin/users\n/usr/bin/utmpdump\n/usr/bin/vmstat\n/usr/bin/w\n/usr/bin/w.procps\n/usr/bin/wall\n/usr/bin/watch\n/usr/bin/watchgnupg\n/usr/bin/wc\n/usr/bin/whereis\n/usr/bin/which\n/usr/bin/who\n/usr/bin/whoami\n/usr/bin/x86_64\n/usr/bin/x86_64-linux-gnu-addr2line\n/usr/bin/x86_64-linux-gnu-ar\n/usr/bin/x86_64-linux-gnu-as\n/usr/bin/x86_64-linux-gnu-c++filt\n/usr/bin/x86_64-linux-gnu-cpp\n/usr/bin/x86_64-linux-gnu-cpp-8\n/usr/bin/x86_64-linux-gnu-dwp\n/usr/bin/x86_64-linux-gnu-elfedit\n/usr/bin/x86_64-linux-gnu-g++\n/usr/bin/x86_64-linux-gnu-g++-8\n/usr/bin/x86_64-linux-gnu-gcc\n/usr/bin/x86_64-linux-gnu-gcc-8\n/usr/bin/x86_64-linux-gnu-gcc-ar\n/usr/bin/x86_64-linux-gnu-gcc-ar-8\n/usr/bin/x86_64-linux-gnu-gcc-nm\n/usr/bin/x86_64-linux-gnu-gcc-nm-8\n/usr/bin/x86_64-linux-gnu-gcc-ranlib\n/usr/bin/x86_64-linux-gnu-gcc-ranlib-8\n/usr/bin/x86_64-linux-gnu-gcov\n/usr/bin/x86_64-linux-gnu-gcov-8\n/usr/bin/x86_64-linux-gnu-gcov-dump\n/usr/bin/x86_64-linux-gnu-gcov-dump-8\n/usr/bin/x86_64-linux-gnu-gcov-tool\n/usr/bin/x86_64-linux-gnu-gcov-tool-8\n/usr/bin/x86_64-linux-gnu-gold\n/usr/bin/x86_64-linux-gnu-gprof\n/usr/bin/x86_64-linux-gnu-ld\n/usr/bin/x86_64-linux-gnu-ld.bfd\n/usr/bin/x86_64-linux-gnu-ld.gold\n/usr/bin/x86_64-linux-gnu-nm\n/usr/bin/x86_64-linux-gnu-objcopy\n/usr/bin/x86_64-linux-gnu-objdump\n/usr/bin/x86_64-linux-gnu-ranlib\n/usr/bin/x86_64-linux-gnu-readelf\n/usr/bin/x86_64-linux-gnu-size\n/usr/bin/x86_64-linux-gnu-strings\n/usr/bin/x86_64-linux-gnu-strip\n/usr/bin/xargs\n/usr/bin/xauth\n/usr/bin/xdg-user-dir\n/usr/bin/xdg-user-dirs-update\n/usr/bin/xgettext\n/usr/bin/xsubpp\n/usr/bin/xz\n/usr/bin/xzcat\n/usr/bin/xzcmp\n/usr/bin/xzdiff\n/usr/bin/xzegrep\n/usr/bin/xzfgrep\n/usr/bin/xzgrep\n/usr/bin/xzless\n/usr/bin/xzmore\n/usr/bin/yes\n/usr/bin/zdump\n/usr/bin/zipdetails\n/usr/bin/zipgrep\n/usr/bin/zipinfo\n/usr/local/bin\n/usr/local/bin/docker-compose\n/usr/local/sbin\n/usr/sbin\n/usr/sbin/aa-remove-unknown\n/usr/sbin/aa-status\n/usr/sbin/aa-teardown\n/usr/sbin/add-shell\n/usr/sbin/addgnupghome\n/usr/sbin/addgroup\n/usr/sbin/adduser\n/usr/sbin/apparmor_status\n/usr/sbin/applygnupgdefaults\n/usr/sbin/arptables\n/usr/sbin/arptables-nft\n/usr/sbin/arptables-nft-restore\n/usr/sbin/arptables-nft-save\n/usr/sbin/arptables-restore\n/usr/sbin/arptables-save\n/usr/sbin/chgpasswd\n/usr/sbin/chmem\n/usr/sbin/chpasswd\n/usr/sbin/chroot\n/usr/sbin/cpgr\n/usr/sbin/cppw\n/usr/sbin/delgroup\n/usr/sbin/deluser\n/usr/sbin/dpkg-preconfigure\n/usr/sbin/dpkg-reconfigure\n/usr/sbin/e2freefrag\n/usr/sbin/e4crypt\n/usr/sbin/e4defrag\n/usr/sbin/ebtables\n/usr/sbin/ebtables-nft\n/usr/sbin/ebtables-nft-restore\n/usr/sbin/ebtables-nft-save\n/usr/sbin/ebtables-restore\n/usr/sbin/ebtables-save\n/usr/sbin/fdformat\n/usr/sbin/filefrag\n/usr/sbin/groupadd\n/usr/sbin/groupdel\n/usr/sbin/groupmems\n/usr/sbin/groupmod\n/usr/sbin/grpck\n/usr/sbin/grpconv\n/usr/sbin/grpunconv\n/usr/sbin/iconvconfig\n/usr/sbin/invoke-rc.d\n/usr/sbin/ip6tables\n/usr/sbin/ip6tables-apply\n/usr/sbin/ip6tables-legacy\n/usr/sbin/ip6tables-legacy-restore\n/usr/sbin/ip6tables-legacy-save\n/usr/sbin/ip6tables-nft\n/usr/sbin/ip6tables-nft-restore\n/usr/sbin/ip6tables-nft-save\n/usr/sbin/ip6tables-restore\n/usr/sbin/ip6tables-restore-translate\n/usr/sbin/ip6tables-save\n/usr/sbin/ip6tables-translate\n/usr/sbin/iptables\n/usr/sbin/iptables-apply\n/usr/sbin/iptables-legacy\n/usr/sbin/iptables-legacy-restore\n/usr/sbin/iptables-legacy-save\n/usr/sbin/iptables-nft\n/usr/sbin/iptables-nft-restore\n/usr/sbin/iptables-nft-save\n/usr/sbin/iptables-restore\n/usr/sbin/iptables-restore-translate\n/usr/sbin/iptables-save\n/usr/sbin/iptables-translate\n/usr/sbin/ldattach\n/usr/sbin/mklost+found\n/usr/sbin/newusers\n/usr/sbin/nfnl_osf\n/usr/sbin/nft\n/usr/sbin/nologin\n/usr/sbin/pam-auth-update\n/usr/sbin/pam_getenv\n/usr/sbin/pam_timestamp_check\n/usr/sbin/policy-rc.d\n/usr/sbin/pwck\n/usr/sbin/pwconv\n/usr/sbin/pwunconv\n/usr/sbin/readprofile\n/usr/sbin/remove-shell\n/usr/sbin/rmt\n/usr/sbin/rmt-tar\n/usr/sbin/rtcwake\n/usr/sbin/service\n/usr/sbin/tarcat\n/usr/sbin/tzconfig\n/usr/sbin/update-ca-certificates\n/usr/sbin/update-mime\n/usr/sbin/update-passwd\n/usr/sbin/update-rc.d\n/usr/sbin/useradd\n/usr/sbin/userdel\n/usr/sbin/usermod\n/usr/sbin/vigr\n/usr/sbin/vipw\n/usr/sbin/visudo\n/usr/sbin/xtables-legacy-multi\n/usr/sbin/xtables-monitor\n/usr/sbin/xtables-nft-multi\n/usr/sbin/zic\n```\n\nThis was mostly a [fun exercise](https://unix.stackexchange.com/a/120943/158462) for myself to see if it could be done using one line of Python code without resorting to using the exec function. In a more readable form, and with some comments, the code looks like this:\n```\nimport os\nimport sys\n\n# This is just to have a function to output something on the screen.\n# I'm using Python 2.7 in which 'print' is not a function and cannot\n# be used in the 'map' function.\noutput = lambda(x) : sys.stdout.write(x + \"\\n\")\n\n# Get a list of the components in the PATH environment variable. Will\n# abort the program is PATH doesn't exist\npaths = os.environ[\"PATH\"].split(\":\")\n\n# os.listdir raises an error is something is not a path so I'm creating\n# a small function that only executes it if 'p' is a directory\nlistdir = lambda(p) : os.listdir(p) if os.path.isdir(p) else [ ]\n\n# Checks if the path specified by x[0] and x[1] is a file\nisfile = lambda(x) : True if os.path.isfile(os.path.join(x[0],x[1])) else False\n\n# Checks if the path specified by x[0] and x[1] has the executable flag set\nisexe = lambda(x) : True if os.access(os.path.join(x[0],x[1]), os.X_OK) else False\n\n# Here, I'm using a list comprehension to build a list of all executable files\n# in the PATH, and abusing the map function to write every name in the resulting\n# list to the screen.\nmap(output, [ os.path.join(p,f) for p in paths for f in listdir(p) if isfile((p,f)) and isexe((p,f)) ])\n```\n\nIf you can run Python 2 in your shell, the following (ridiculously long) one-liner can be used as well:\n\n```\n$ python2 -c 'import os;import sys;output = lambda(x) : sys.stdout.write(x + \"\\n\"); paths = os.environ[\"PATH\"].split(\":\") ; listdir = lambda(p) : os.listdir(p) if os.path.isdir(p) else [ ] ; isfile = lambda(x) : True if os.path.isfile(os.path.join(x[0],x[1])) else False ; isexe = lambda(x) : True if os.access(os.path.join(x[0],x[1]), os.X_OK) else False ; map(output,[ os.path.join(p,f) for p in paths for f in listdir(p) if isfile((p,f)) and isexe((p,f)) ])'\n```\n\n### Packages\n\nIf we need to [list the installed packages in the Python](https://stackoverflow.com/a/73958089/4058484) shell, For terminal I recommend help(\"modules\") or python -c \"help('modules')\".\n\n```\n$ python3.7 -c 'help(\"modules\")'\n\nPlease wait a moment while I gather a list of all available modules...\n\n__future__ _tracemalloc getopt rlcompleter\n_abc _uuid getpass runpy\n_ast _warnings gettext sched\n_asyncio _weakref gi secrets\n_bisect _weakrefset glob select\n_blake2 _xxtestfuzz grp selectors\n_bootlocale abc gzip shelve\n_bz2 aifc hashlib shlex\n_codecs antigravity heapq shutil\n_codecs_cn apt hmac signal\n_codecs_hk apt_inst html site\n_codecs_iso2022 apt_pkg http sitecustomize\n_codecs_jp aptsources imaplib smtpd\n_codecs_kr argparse imghdr smtplib\n_codecs_tw array imp sndhdr\n_collections ast importlib socket\n_collections_abc asynchat inspect socketserver\n_compat_pickle asyncio io softwareproperties\n_compression asyncore ipaddress spwd\n_contextvars atexit itertools sqlite3\n_crypt audioop json sre_compile\n_csv base64 keyword sre_constants\n_ctypes bdb linecache sre_parse\n_ctypes_test binascii locale ssl\n_curses binhex logging stat\n_curses_panel bisect lsb_release statistics\n_datetime builtins lzma string\n_dbm bz2 macpath stringprep\n_dbus_bindings cProfile mailbox struct\n_dbus_glib_bindings calendar mailcap subprocess\n_decimal cgi marshal sunau\n_dummy_thread cgitb math symbol\n_elementtree chunk mimetypes symtable\n_functools cmath mmap sys\n_hashlib cmd modulefinder sysconfig\n_heapq code multiprocessing syslog\n_imp codecs netrc tabnanny\n_io codeop nis tarfile\n_json collections nntplib telnetlib\n_locale colorsys ntpath tempfile\n_lsprof compileall nturl2path termios\n_lzma concurrent numbers test\n_markupbase configparser opcode textwrap\n_md5 contextlib operator this\n_multibytecodec contextvars optparse threading\n_multiprocessing copy os time\n_opcode copyreg ossaudiodev timeit\n_operator crypt parser token\n_osx_support csv pathlib tokenize\n_pickle ctypes pdb trace\n_posixsubprocess curl pickle traceback\n_py_abc curses pickletools tracemalloc\n_pydecimal dataclasses pipes tty\n_pyio datetime pkgutil turtle\n_queue dbm platform types\n_random dbus plistlib typing\n_sha1 decimal poplib unicodedata\n_sha256 difflib posix unittest\n_sha3 dis posixpath urllib\n_sha512 distro_info pprint uu\n_signal distutils profile uuid\n_sitebuiltins doctest pstats venv\n_socket dummy_threading pty warnings\n_sqlite3 email pwd wave\n_sre encodings py_compile weakref\n_ssl enum pyclbr webbrowser\n_stat errno pycurl wsgiref\n_string faulthandler pydoc xdrlib\n_strptime fcntl pydoc_data xml\n_struct filecmp pyexpat xmlrpc\n_symtable fileinput pygtkcompat xxlimited\n_sysconfigdata_m_linux_x86_64-linux-gnu fnmatch queue\n_testbuffer formatter quopri zipapp\n_testcapi fractions random zipfile\n_testimportmultiple ftplib re zipimport\n_testmultiphase functools readline zlib\n_thread gc reprlib xxsubtype\n_threading_local genericpath resource\n\nEnter any module name to get more help. Or, type \"modules spam\" to search\nfor modules whose name or summary contain the string \"spam\".\n```\n\nI'm comparing five methods to retrieve installed \"modules\", all of which I've seen in this thread\n\n```\n iter_modules help(\"modules\") builtin_module_names pip list working_set\nIncludes distributions ❌ ❌ ❌ ✔️ ✔️\nIncludes modules (No built-in) ✔️ ✔️ ❌ ❌ ❌\nIncludes built-in modules ❌ ✔️ ✔️ ❌ ❌\nIncludes frozen ✔️ ✔️ ❌ ❌ ❌\nIncludes venv ✔️ ✔️ ❌ ✔️ ✔️\nIncludes global\t ✔️ ✔️ ❌ ✔️ ✔️\nIncludes editable installs ✔️ ✔️ ❌ ✔️ ✔️\nIncludes PyCharm helpers ✔️ ❌ ❌ ❌ ❌\nLowers capital letters ❌ ❌ ❌ ❌ ✔️\nTime taken (665 modules total) 53.7 msec 1.03 sec 577 nsec 284 msec 36.2 usec\n```\nFor programmatically I recommend iter_modules + builtin_module_names to pluck the module name out of the tuples generated by [pkgutil.iter_modules()](http://docs.python.org/library/pkgutil.html#pkgutil.iter_modules) It is however very convoluted with information\n\n```\n$ python -c 'import pkgutil;print [x[1] for x in list(pkgutil.iter_modules())]'\n\n['BaseHTTPServer', 'Bastion', 'CGIHTTPServer', 'ConfigParser', 'Cookie', 'DocXMLRPCServer', 'HTMLParser', \n'MimeWriter', 'Queue', 'SimpleHTTPServer', 'SimpleXMLRPCServer', 'SocketServer', 'StringIO', 'UserDict', \n'UserList', 'UserString', '_LWPCookieJar', '_MozillaCookieJar', '__future__', '_abcoll', '_osx_support', \n'_pyio', '_strptime', '_sysconfigdata', '_threading_local', '_weakrefset', 'abc', 'aifc', 'antigravity', \n'anydbm', 'argparse', 'ast', 'asynchat', 'asyncore', 'atexit', 'audiodev', 'base64', 'bdb', 'binhex', \n'bisect', 'bsddb', 'cProfile', 'calendar', 'cgi', 'cgitb', 'chunk', 'cmd', 'code', 'codecs', 'codeop', \n'collections', 'colorsys', 'commands', 'compileall', 'compiler', 'contextlib', 'cookielib', 'copy', \n'copy_reg', 'csv', 'ctypes', 'curses', 'dbhash', 'decimal', 'difflib', 'dircache', 'dis', 'distutils', \n'doctest', 'dumbdbm', 'dummy_thread', 'dummy_threading', 'email', 'encodings', 'ensurepip', 'filecmp', \n'fileinput', 'fnmatch', 'formatter', 'fpformat', 'fractions', 'ftplib', 'functools', 'genericpath', \n'getopt', 'getpass', 'gettext', 'glob', 'gzip', 'hashlib', 'heapq', 'hmac', 'hotshot', 'htmlentitydefs', \n'htmllib', 'httplib', 'ihooks', 'imaplib', 'imghdr', 'importlib', 'imputil', 'inspect', 'io', 'json', \n'keyword', 'lib2to3', 'linecache', 'locale', 'logging', 'macpath', 'macurl2path', 'mailbox', 'mailcap', \n'markupbase', 'md5', 'mhlib', 'mimetools', 'mimetypes', 'mimify', 'modulefinder', 'multifile', \n'multiprocessing', 'mutex', 'netrc', 'new', 'nntplib', 'ntpath', 'nturl2path', 'numbers', 'opcode', \n'optparse', 'os', 'os2emxpath', 'pdb', 'pickle', 'pickletools', 'pipes', 'pkgutil', 'platform', \n'plistlib', 'popen2', 'poplib', 'posixfile', 'posixpath', 'pprint', 'profile', 'pstats', 'pty', \n'py_compile', 'pyclbr', 'pydoc', 'pydoc_data', 'quopri', 'random', 're', 'repr', 'rexec', 'rfc822', \n'rlcompleter', 'robotparser', 'runpy', 'sched', 'sets', 'sgmllib', 'sha', 'shelve', 'shlex', 'shutil', \n'site', 'sitecustomize', 'smtpd', 'smtplib', 'sndhdr', 'socket', 'sqlite3', 'sre', 'sre_compile', \n'sre_constants', 'sre_parse', 'ssl', 'stat', 'statvfs', 'string', 'stringold', 'stringprep', 'struct', \n'subprocess', 'sunau', 'sunaudio', 'symbol', 'symtable', 'sysconfig', 'tabnanny', 'tarfile', 'telnetlib', \n'tempfile', 'test', 'textwrap', 'this', 'threading', 'timeit', 'toaiff', 'token', 'tokenize', 'trace', \n'traceback', 'tty', 'types', 'unittest', 'urllib', 'urllib2', 'urlparse', 'user', 'uu', 'uuid', 'warnings', \n'wave', 'weakref', 'webbrowser', 'whichdb', 'wsgiref', 'xdrlib', 'xml', 'xmllib', 'xmlrpclib', 'zipfile', \n'CDROM', 'DLFCN', 'IN', 'TYPES', '_sysconfigdata_nd', 'Canvas', 'Dialog', 'FileDialog', 'FixTk', \n'ScrolledText', 'SimpleDialog', 'Tix', 'Tkconstants', 'Tkdnd', 'Tkinter', 'tkColorChooser', 'tkCommonDialog', \n'tkFileDialog', 'tkFont', 'tkMessageBox', 'tkSimpleDialog', 'ttk', 'turtle', '_bsddb', '_codecs_cn', \n'_codecs_hk', '_codecs_iso2022', '_codecs_jp', '_codecs_kr', '_codecs_tw', '_csv', '_ctypes', '_ctypes_test', \n'_curses', '_curses_panel', '_elementtree', '_hashlib', '_hotshot', '_json', '_lsprof', '_multibytecodec', \n'_multiprocessing', '_sqlite3', '_ssl', '_testcapi', 'audioop', 'bz2', 'crypt', 'dbm', 'future_builtins', \n'linuxaudiodev', 'mmap', 'nis', 'ossaudiodev', 'parser', 'pyexpat', 'readline', 'resource', 'termios', \n'lsb_release', 'meld3', 'pkg_resources', 'supervisor']\n```\n","dir":"/identition/span4/","name":"gist02.md","path":"identition/span4/gist02.md","url":"/identition/span4/gist02.html"},{"layout":"default","title":null,"content":"***7 x 13 x 19 = 1729***\n\n[![Centralizing](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity)\n\n***7 + 11 + 13 + 17 + 19 = 67 = 19th prime***\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\nlayer| i | f\n-----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | {7}\n-----+-----+--- } 36\n | 3 | 11\n {2} +-----+\n | 4 | {13}\n-----+-----+---------\n | 5 | 17\n 3 +-----+ } 36\n | 6 | {19}\n-----+-----+---------\n```\n\n![](https://user-images.githubusercontent.com/36441664/101619656-26529480-3a46-11eb-8498-3a7867c500a9.png)\n\n![](https://user-images.githubusercontent.com/36441664/75627425-9b18b880-5c02-11ea-97e5-7beb774079a7.png)\n\n***(12/2) th prime = 13***\n\n[![default](https://user-images.githubusercontent.com/8466209/202855806-611c6a39-e40c-4aa9-ae28-e25aea82cb19.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f)\n\n***Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)***\n\n![101093483-6ac8d500-35ed-11eb-92d1-e264d22b341f](https://user-images.githubusercontent.com/8466209/216657865-5b02d399-6e0a-49fe-a7ff-718ec7a7cb97.jpg)\n\nSo based on the difference between the numbers 25 to 29, we take the arrangement of the 25 repositories with the remaining four (4), namely 26 to 29 where we will get the vector arrangement (6,12,18) from _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n![](https://user-images.githubusercontent.com/36441664/73700083-28f2a800-4718-11ea-97b3-2e9a738dc09e.png)\n\n[![default](https://user-images.githubusercontent.com/36441664/75612568-4f5d0500-5b57-11ea-909d-856dcb7c139a.jpg)](https://blog.world-mysteries.com/science/vitruvian-man-by-leonardo-da-vinci/)\n\n![](https://user-images.githubusercontent.com/36441664/73604434-419d7980-45c3-11ea-8ad0-b62d8a27c5b0.png)\n\n***114 + 2x11x13 = 114 + 286 = 400***\n\n![image](https://user-images.githubusercontent.com/8466209/216680164-43ed465c-1c6a-45a1-b3f8-3b6d8accf996.png)\n\n***109 - (168 - 100 + 1) = 109 - (68 + 1) = 109 - 69 = 40 = 400/10 ←← π(π(π(1000th prime)))+1***\n\n```\n --------------------+-----+-----+-----+-----+-----+ | ---\n 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |\n | +-----+-----+-----+ | |\n | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | | +-----+-----+-----+ | | |\n | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n | | | +-----+-----+-----+ | | ---\n | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |\n | | +-----+-----+-----+ | |\n | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance\n329 | +-----+-----+-----+ |\n | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ |\n -------------------+-----+-----+ ---\n```\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\n```\n-----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n 2 -------------------+----+----+----+----+----+----+----+----+----+----- ←-- bilateral 9 sums\n 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n```\n\n***12 - 10 = 2***\n\n[![default](https://user-images.githubusercontent.com/36441664/128732737-81762604-0ae0-4a90-b5a8-30921cf46efb.png)](https://github.com/chetabahana/chetabahana.github.io/wiki/Mapping)\n\n![](https://user-images.githubusercontent.com/36441664/85206005-39af5d80-b349-11ea-851a-56309342b53f.png)\n\n***(114/2)! = 57! = 1653 » 1653 / 57 = 29***\n\n![](https://user-images.githubusercontent.com/36441664/101807202-6d747e80-3b47-11eb-8a6b-9e2c6408b091.jpg)\n\n***∑(13:9) = ∑(29:43) = 11x13 + 5x40x50 = 10143***\n\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n 2 -------------------+----+----+----+----+----+----+----+----+----+----- ←-- bilateral 9 sums\n 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin ↓\n |\n ↓ \n 114-89=139-114=25=5x5\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+---+----+----+---+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 |\n +----+----+----+---+----+----+---+\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n```\n\n[![Bonding Position](https://user-images.githubusercontent.com/8466209/220001571-bddc7fee-5753-4ee3-b145-b3b1bb49a354.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bonding-position)\n\n![default](https://user-images.githubusercontent.com/8466209/198418951-a84a0f30-c5d7-4fff-8139-7806e3c22b3b.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198419910-277fe92d-bb26-4b22-974f-bef1613d46c4.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198421043-9c47aeb4-176f-44be-8bf9-3daffb19001e.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198416547-0d9dbfb4-d78a-45b6-bd6c-e8846c928996.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198769947-a514bf48-0da4-46ed-a25f-c35ab94da02d.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198406080-2a29fe5f-e1c5-4c0e-aae2-78c3ce61f0c5.png)\n![default](https://user-images.githubusercontent.com/8466209/199359804-73018ae2-b497-4118-97f1-ae3d7400b21e.png)\n\n![default](https://user-images.githubusercontent.com/8466209/199354838-c5735775-58e8-4a4a-b672-59997056036a.png)\n\n![default](https://user-images.githubusercontent.com/8466209/199355198-2342b2c0-c385-4ada-af51-2effb3152005.png)\n\n![default](https://user-images.githubusercontent.com/8466209/199363218-ef852193-d9ea-4d98-916e-6d79f492d86e.png)\n","dir":"/identition/span5/","name":"gist06.md","path":"identition/span5/gist06.md","url":"/identition/span5/gist06.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | {1} | {9}\n---+-----+-----\n 2 | 10 |{32}\n---+-----+-----\n 3 | 33 | 63 \n---+-----+-----\n 4 |{64} | 101 \n---+-----+-----\n 5 |{102}| 120 \n---+-----+-----\n 6 | 121 |{189}\n---+-----+-----\n 7 | 190 |{200}\n---+-----+-----\n```\n\n```\n$ cat /etc/os-release\n\nNAME=\"Alpine Linux\"\nID=alpine\nVERSION_ID=3.18.0\nPRETTY_NAME=\"Alpine Linux v3.18\"\nHOME_URL=\"https://alpinelinux.org/\"\nBUG_REPORT_URL=\"https://gitlab.alpinelinux.org/alpine/aports/-/issues\"\n```\n\n[![](https://user-images.githubusercontent.com/8466209/200228344-9f344f49-3e5d-480f-b11c-6e30a20a8f44.jpg)](https://www.primesdemystified.com/First1000Primes.html)\n\n![flow](https://user-images.githubusercontent.com/36441664/128732737-81762604-0ae0-4a90-b5a8-30921cf46efb.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198934312-25311775-edd3-48b7-8faa-8da45c380392.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/198933986-e0c6ab91-bbb6-4413-b75b-3d11bd2ccfab.png)](https://github.com/chetabahana/tensorflow/wiki)\n\n[![default](https://user-images.githubusercontent.com/8466209/198919975-7e61e7db-06ec-4e16-bd36-10cc9048e9e7.png)](https://github.com/kaustubhcs/prime-hexagon)\n\n[![default](https://user-images.githubusercontent.com/8466209/198921109-f1e4671d-a845-4c05-8a1d-f6c05ad490a0.png)](https://github.com/kaustubhcs/prime-hexagon/tree/66b8653a102c848084e137aa614e8762b40d5c1f)\n\n[![default](https://user-images.githubusercontent.com/8466209/198920712-ebff2050-95ac-4617-bfd4-4c8ba930c65c.png)](https://github.com/spacetimeengineer/spacetimeengine)\n\n[![default](https://user-images.githubusercontent.com/8466209/198922336-f69108be-c4db-45bc-ba4e-2f09539a139c.png)](https://github.com/FeedMapping/syntax)\n\n[![default](https://user-images.githubusercontent.com/8466209/198921851-eaa9d84d-ee62-4f04-be4d-c291677acb19.png)](https://github.com/eq19)\n\nMapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).\n\n![default](https://user-images.githubusercontent.com/8466209/198928812-cab7aef3-9c41-49f4-8b89-00b8fa3fc95a.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198929326-da02dcc6-e502-4a01-a128-8c0ba03183f3.png)\n\nThere might be cases where you want to install and use Ruby with Anaconda or Miniconda. By doing this, Ruby becomes usable. however, it will not compile gems that use native extensions.\n\n>Since it is nearly impossible to use Ruby without utilizing native extensions, this method is not very practical.Instead, you can simply install Ruby from conda-forge and install the compilers package at the same time. This way, you can easily use Ruby within Conda environments like Anaconda or Miniconda _([Using Ruby with Conda](https://dev.to/kojix2/using-ruby-with-conda-1hn))_.\n\n```\nconda install -c conda-forge ruby\nconda install -c conda-forge compilers\n\nconda install -c \"conda-forge/label/broken\" ruby\nconda install -c \"conda-forge/label/cf201901\" ruby\nconda install -c \"conda-forge/label/cf202003\" ruby\nconda install -c \"conda-forge/label/gcc7\" ruby\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/239124983-1b99dc91-a1ad-498f-80a0-acb2d8b69185.png)](https://anaconda.org/conda-forge/ruby)\n\nIn gRPC, a client application can directly call a method on a server application on a different machine as if it were a local object, making it easier for you to create distributed applications and services.\n\n```\n$ find / -type f -name \"Gemfile\"\n\n/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/Gemfile\n/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/pubsub/Gemfile\n\n$ cat /mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/pubsub/Gemfile\n\nsource 'https://rubygems.org/'\n\ngem 'grpc', '~> 1.0'\ngem 'googleauth', '>= 0.5.1', '< 0.7'\n```\n\n[![gRPC and protocol buffers](https://user-images.githubusercontent.com/8466209/239118755-39dc1055-d92e-49cf-adcb-868d5a90cfa6.png)](https://grpc.io/docs/what-is-grpc/introduction/)\n\n","dir":"/identition/span3/","name":"gist07.md","path":"identition/span3/gist07.md","url":"/identition/span3/gist07.html"},{"layout":"default","title":"How to deal with cicular destination of 36?","content":"## How to deal with cicular destination of 36?\n\n```\n$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer| i | f\n -----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | 7\n -----+-----+--- } 36 » 6®\n | 3 | 11\n 2 +-----+\n | 4 | 13\n -----+-----+---------\n | 5 | 17\n 3 +-----+ } 36 » 6®\n | 6 | 19\n -----+-----+---------\n```\n![default](https://user-images.githubusercontent.com/8466209/201023835-b641450d-827b-4362-8a63-8520edb50ece.png)\n\n```\n | |-----+-----+-----+ |\n | 4 | | 11 |15,18| 29,30,31,32 ←---4x---- ←--- 35,34,33 are missing?\n | | 6 +-----+-----+\n | | | 12 | 19 | 36 --------------------------------------\n------+------+-----+-----+-----+------- |\n | | | 13 | 20 | {38} |\n | | 7 +-----+-----+ | \n | 5 | | 14 |21,22| {40,41} = (19-17)x ---- |\n | |-----+-----+-----+ | |\n | | | 15 | 23 | {42} 6x + 13x = 19x |\n 3 +------+ 8 +-----+-----+ | |\n | | | 16 |24,27| {43,44,45,46} ←- 4x -- |\n | |-----+-----+-----+ |\n | 6 | | 17 | 28 | {50} = 46 + 4 |\n | | 9 +-----+-----+ |\n | | | 18 | 29 | {68} = 32 + 36 ←- they meet here ---------\n------|------|-----+-----+------\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/201008595-9917fb26-bfea-46e6-b0e1-32db79a12e98.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md)\n\n![default](https://user-images.githubusercontent.com/8466209/201008977-b10573d2-b295-440d-82fe-c707474694ce.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201009190-a8d4dac6-5331-46c5-a704-1e02113f6e6d.png)\n","dir":"/identition/span9/","name":"gist07.md","path":"identition/span9/gist07.md","url":"/identition/span9/gist07.html"},{"layout":"default","title":null,"content":"* The direction of growth of the leading strand is 5′→3′. The direction of growth of the lagging strand is **3′→5′**.\n* The formation of leading strand begins immediately at the beginning of replication. The formation of lagging strand **begins a bit later** than that of the leading strand.\n* During the synthesis of leading strand, only one site of initiation is exposed in the template strand. During the synthesis of lagging strand, **multiple sites** of initiation are exposed in the template strand.\n\n\n[![](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-locate-md)\n\n![](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png)\n\n![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612131-b325f43c-6957-443b-b763-e357b2466f59.png)","dir":"/exponentiation/span16/","name":"gist05.md","path":"exponentiation/span16/gist05.md","url":"/exponentiation/span16/gist05.html"},{"layout":"default","title":null,"content":"```\nFROM tensorflow/tensorflow:latest-gpu\n\nLABEL version=v1.0.9\n\nENV DEBCONF_NOWARNINGS=\"yes\"\nARG DEBIAN_FRONTEND=noninteractive\n\nENV NVIDIA_VISIBLE_DEVICES all\nENV NVIDIA_DRIVER_CAPABILITIES compute,utility\n\nRUN apt-get update &>/dev/null\nRUN apt-get install python3.8-venv &>/dev/null\nRUN /usr/bin/python3.8 -m venv /maps &>/dev/null\n\nADD . /maps\nENTRYPOINT [\"/maps/entrypoint.sh\"]\n\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200241238-23d238be-9006-4ac8-b9e8-1daa48ab8d8f.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-6_pattern-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/200240844-1e76f817-775a-4cc1-9998-20e71efcc4ee.png)](https://github.com/eq19/grammar/actions/runs/3405771627/jobs/5663983028)\n\n","dir":"/identition/span8/","name":"gist03.md","path":"identition/span8/gist03.md","url":"/identition/span8/gist03.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/198918182-0d350710-64b3-48de-bd7e-a45ae4390380.png)\n![default](https://user-images.githubusercontent.com/8466209/198918275-c88e4875-938e-4f18-b1ae-696026f9fd30.png)\n![default](https://user-images.githubusercontent.com/8466209/198918564-8441195d-e47b-45e2-8e87-6d4cf8f60a84.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198918345-a1997048-4993-4934-b094-95a297992ed4.png)\n![default](https://user-images.githubusercontent.com/8466209/198918641-e33a7d60-d10a-40a4-bedf-af07b1d57d13.png)\n![default](https://user-images.githubusercontent.com/8466209/198918951-0fd19fcd-59e4-444a-8774-dcd39f3044c1.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/198917703-9e333c1b-d74d-4862-9f26-4e3f58509827.png)](https://github.com/kaustubhcs/prime-hexagon)\n\nWe color-code the six hexagons, identifying patterns in key number sequences, including the Fibonacci sequence, powers of two and three, and power of pi. For the series of consecutive powers of pi, we have found that *****no two fall within the same six-cell hexagon*****. We have computed this for pi^32, which has less than a 1/400 chance of occurring randomly.\n\n","dir":"/identition/span3/","name":"gist03.md","path":"identition/span3/gist03.md","url":"/identition/span3/gist03.html"},{"layout":"default","title":"The Bilateral 9 Sums","content":"## The Bilateral 9 Sums\n\nLet's start with the number of possible ancestors on the chromosome. A male individual has an X chromosome, which he received from his mother, and a Y chromosome, which he received from his father. \n\n![image](https://user-images.githubusercontent.com/8466209/213902684-f60e272c-8d01-4dea-ab2a-7bdb01aba32f.png)\n\nThe number of ancestors at each level, Fn, is the number of female ancestors, which is Fn−1, plus the number of male ancestors, which is Fn−2. his is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.\n\n![image](https://user-images.githubusercontent.com/8466209/213902752-fdbe6892-1089-47b1-a5ed-b301a7b0c1d6.png)\n\nIt has been noticed that the number of possible ancestors on the human X chromosome inheritance line at a given ancestral generation also follows the _[Fibonacci sequence](https://en.wikipedia.org/wiki/Fibonacci_number)_.\n\n[![image](https://user-images.githubusercontent.com/8466209/213900804-9afe17ad-601c-4713-800f-02ed204b3a7c.png)](https://en.wikipedia.org/wiki/Fibonacci_number)\n\nThis Fibonacci sequence is lied beautifully in the _[Pascal Triangle](https://en.wikipedia.org/wiki/Pascal%27s_triangle)_. Pascal's triangle has wide applications in Mathematics. We have seen that the most important applications relate to the binomial coefficients and combinatorics. \n\n![image](https://user-images.githubusercontent.com/8466209/213902359-f5fb8023-ec2b-4588-8f24-e1caafc30ef5.png)\n\n![](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png)\n\nSee that from 1 to 89 it consist of ***seven (7) steps*** which is originated by 1,15,35,28 before it goes bilateral. So that is why Y has ***1+15+35-1=50***, and only ***28-1=27*** of these are in the male-specific. This cycle is repeated through a palindromic sequence.\n\n***109th - 20th = 89th***\n\nAs the matter of fact this 89 has a symmetrical relation with the 24th Prime Number & 24th Natural Number Not Divisible by 2, 3, or 5. This is the reason that we use this primes pattern on determining the _[centralizing](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ process\n \n[![default](https://user-images.githubusercontent.com/8466209/200228973-fd99095b-aad2-4824-b3dc-d6b21fae38ea.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-write-all-md)\n\nSo the 20 objects would pair another 19 and become ***19 (sub objects) + 1 (unit object) + 19 (sub objects)=20+19=39 objects*** or it will be 40 when we put them as one (1) unit. This 40 will act as the [interface](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md) between each of containers.\n\n![default](https://user-images.githubusercontent.com/8466209/213902270-75b90edb-b94e-4844-be4a-27db66bae060.jpg)\n\nThis scheme stands as the second section of bilateral sum. By the rest sections we will discuss the above seven (7) steps one by one so all together will compromise the [nine (9) groups](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md) of project repositories as mentioned in the beginning.\n\n![default](https://user-images.githubusercontent.com/8466209/223529165-0e4c1172-47cc-422f-8e44-1dd67de25828.png)\n","dir":"/identition/span2/","name":"gist02.md","path":"identition/span2/gist02.md","url":"/identition/span2/gist02.html"},{"layout":"default","title":null,"content":"```liquid\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th → base (30)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th → maps (31)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th → feed (32)\n =======================+====+====+====+====+====+====+====+====+====+===== \n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th → lexer (33)\n -----------------------+----+----+----+----+----+----+----+----+----+----- \n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th → parser (34)\n -----------------------+----+----+----+----+----+----+----+----+----+----- \n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th → syntax (35)\n =======================+====+====+====+====+====+====+====+====+====+===== \n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th → grammar (36) \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n ```\n\n![2022-12-06 (2)](https://user-images.githubusercontent.com/8466209/205963196-7e1f4fc3-1833-4b64-9fb4-f79e6cd4637f.png)\n\n![2022-12-06 (3)](https://user-images.githubusercontent.com/8466209/205964436-c9636678-6679-48f7-938a-e307912600ef.png)\n\n![2022-12-06 (1)](https://user-images.githubusercontent.com/8466209/205947618-ef28a677-f961-4b78-9e79-e8a9ffe824c5.png)\n\n![2022-12-06 (1)](https://user-images.githubusercontent.com/8466209/205960400-3061d93a-b3cc-4cd6-84e6-359a9314869d.png)\n","dir":"/exponentiation/span14/","name":"gist03.md","path":"exponentiation/span14/gist03.md","url":"/exponentiation/span14/gist03.html"},{"layout":"default","title":null,"content":"![2022-12-06 (5)](https://user-images.githubusercontent.com/8466209/205967762-69f6aaee-f1fc-4b26-a0cc-515257b6d9e7.png)\n\n![2022-12-06 (4)](https://user-images.githubusercontent.com/8466209/205967707-254fc836-72f4-45fc-9d0e-90c5e0bda465.png)\n\n![2022-12-10 (1)](https://user-images.githubusercontent.com/8466209/206849387-d530c690-c1ed-4496-9748-355f798d44fa.png)\n","dir":"/exponentiation/span14/","name":"gist04.md","path":"exponentiation/span14/gist04.md","url":"/exponentiation/span14/gist04.html"},{"layout":"default","title":null,"content":"```liquid\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\nThe 619 is the **114th prime**. It has the last index of 6 with the prime 19 where as **6x19** is also 114. When we multiply the 114 [minor hexagon](https://www.hexspin.com/minor-hexagons/) again by six (6) minus the duplicaton within those layers we got 684-30-30-5 = 684-65 which is also 619.\n\n[![metatron](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-1_prime-md)\n\n[![gannchart](https://user-images.githubusercontent.com/8466209/206868681-2cddf780-48f1-4dc5-9ef4-981b402a15d5.png)\n](https://gist.github.com/eq19/80c8098f16f3e6ca06893b17a02d910e#file-mapping-md)\n\nDespite the correlation between the bilateral 9 sums with the Fibonacci sequence, some people has discovered many things. The sequence of ***(55, 89, 144)*** shows an almost mystical power by its mysterious accuracy in nature and even _[in trading](https://www.tradingsim.com/day-trading/fibonacci-trading)_.\n\n[![image](https://user-images.githubusercontent.com/8466209/216902149-2d017e85-3d95-4484-bc6c-59a4b2079137.png)](https://www.tradingsim.com/day-trading/fibonacci-trading)\n\n![2022-12-10](https://user-images.githubusercontent.com/8466209/206884467-05a33d48-5cdc-48fd-9b75-5be406100f06.png)\n\n[![cycle](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-default-md)\n\n![2022-12-14 (1)](https://user-images.githubusercontent.com/8466209/207418457-4db2048d-e003-492d-a78c-bc2ded725c74.png)\n","dir":"/exponentiation/span14/","name":"gist05.md","path":"exponentiation/span14/gist05.md","url":"/exponentiation/span14/gist05.html"},{"layout":"default","title":null,"content":"![gotek](https://user-images.githubusercontent.com/36441664/123180870-57f8ed80-d4b6-11eb-89e1-cf8786d0dc14.jpg)\n\n![2022-12-11](https://user-images.githubusercontent.com/8466209/206888301-0ba40a6a-2caa-4dfe-92ef-5a9db590f85d.png)\n\n![io](https://user-images.githubusercontent.com/36441664/123179535-cd16f380-d4b3-11eb-95c3-0a5b7ef21ad4.jpg)\n\n![floppies](https://user-images.githubusercontent.com/36441664/123187010-84ffcd00-d4c3-11eb-8aad-6c40553b752b.png)\n\n[![2022-12-11 (1)](https://user-images.githubusercontent.com/8466209/206888720-159281ee-1f74-4684-aca3-963dd3c882ab.png)](https://docs.github.com/en/actions/learn-github-actions/usage-limits-billing-and-administration#usage-limits)\n\n![neural](https://user-images.githubusercontent.com/36441664/123424569-377e7f80-d5eb-11eb-9c85-1f5d72f14eed.png)\n","dir":"/exponentiation/span14/","name":"gist06.md","path":"exponentiation/span14/gist06.md","url":"/exponentiation/span14/gist06.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 | 4\n---+-----+-----\n 2 |{5} |{8}\n---+-----+-----\n 3 | 9 |{17}\n---+-----+-----\n 4 |{18} |{23}\n---+-----+-----\n 5 | 24 | 27\n---+-----+-----\n 6 | 28 | 34\n---+-----+-----\n 7 |{35} |{41}\n---+-----+-----\n 8 |{42} |{52}\n---+-----+-----\n```\n\n![](https://user-images.githubusercontent.com/36441664/85040788-5e71cc80-b1b3-11ea-962f-cf26ee3419e2.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/84902333-e6ce6f80-b0d6-11ea-8289-aac5e1961cd6.gif)\n\n![equilateral](https://user-images.githubusercontent.com/8466209/205804972-0570afbc-3781-473c-bdc7-5e6927351de5.gif)\n\n![](https://user-images.githubusercontent.com/36441664/85527369-044e8c80-b635-11ea-8f32-25a6b813a9b1.gif)\n\n![](https://user-images.githubusercontent.com/36441664/85907724-ae4c3580-b83c-11ea-85c5-c9c20e13bd08.png)\n\n![](https://user-images.githubusercontent.com/36441664/85039712-32098080-b1b2-11ea-80f0-3e7e767a2ba1.jpg)\n\n>This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding. _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n\n[![Navier–Stokes Equation](https://user-images.githubusercontent.com/8466209/224287999-37cd0692-bf51-4b99-bb45-8c49e5db58e3.png)](https://www.claymath.org/millennium-problems/navier%E2%80%93stokes-equation)\n\nBy _[this paper](https://www.sciencedirect.com/science/article/pii/S0362546X23000111)_ it is derived a sufficient condition keeping energy conservation in terms of the gradient of the velocity for the weak solutions of the compressible Euler equations for both the non-vacuum and the vacuum cases.","dir":"/exponentiation/span14/","name":"gist07.md","path":"exponentiation/span14/gist07.md","url":"/exponentiation/span14/gist07.html"},{"layout":"default","title":"Electron scattering","content":"## Electron scattering\n\nElectron-electron scattering is described by one of the earliest published Feynman diagrams (featured in “Sightings,” September–October 2003). One electron (solid line at bottom right) shoots out a forcecarrying particle—a virtual photon (wavy line)—which then smacks into the second electron (solid line at bottom left). \n\n>The first electron recoils backward, while the second electron gets pushed off its original course. The diagram thus sketches a quantum-mechanical view of how particles with the same charge repel each other. As suggested by the term “Space-Time Approach” in the title of the article that accompanied this diagram, Feynman originally drew diagrams in which the dimensions were space and time; here the horizontal axis represents space. \n\n[![default](https://user-images.githubusercontent.com/8466209/224118806-b00758c2-0885-46c3-b574-566dffedf95f.png)](https://en.wikipedia.org/wiki/Feynman_diagram)\n\n![image](https://user-images.githubusercontent.com/8466209/240317298-4d42ea8d-ef95-4a33-9a6c-518149dbc02a.png)\n\n![image](https://user-images.githubusercontent.com/8466209/223643996-1ea5cb89-324e-446c-9c9f-8c94c39909b3.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/224117996-fd3f0e3b-2ef6-43f5-961d-e90b616cbccc.png)](http://web.mit.edu/dikaiser/www/FdsAmSci.pdf)\n\n![](https://user-images.githubusercontent.com/8466209/222020262-cffc624a-b92c-4137-b76a-5423df7fc5ad.png)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/207262180-7a0928a1-0c16-4193-9611-0626ad884ab1.png)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png)\n\n![207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb](https://user-images.githubusercontent.com/8466209/207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db.png)\n","dir":"/exponentiation/span15/","name":"gist02.md","path":"exponentiation/span15/gist02.md","url":"/exponentiation/span15/gist02.html"},{"layout":"default","title":null,"content":"![](https://user-images.githubusercontent.com/36441664/73700083-28f2a800-4718-11ea-97b3-2e9a738dc09e.png)\n\n![](https://user-images.githubusercontent.com/36441664/74550123-6dd1d680-4f83-11ea-8810-3b8f4f50a9c0.png)\n\n![image](https://user-images.githubusercontent.com/8466209/240316525-ac3dd580-223b-4aa9-ad42-e6bb325fd52d.png)\n\n![origin](https://user-images.githubusercontent.com/8466209/220002045-d0395b21-1f2a-4dba-992a-24bf50c480d5.png)\n\n![default](https://user-images.githubusercontent.com/8466209/224314748-3f624809-b5eb-4857-aaf1-d001eda32a4c.png)\n\n![2022-12-12](https://user-images.githubusercontent.com/8466209/206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2.png)\n\n![resize](https://user-images.githubusercontent.com/8466209/206960889-211ce865-84ad-4164-b8e5-76e1781f7071.png)\n","dir":"/exponentiation/span15/","name":"gist03.md","path":"exponentiation/span15/gist03.md","url":"/exponentiation/span15/gist03.html"},{"layout":"default","title":null,"content":"[![]()]()\n\n## Difference Between Leading Strand And Lagging Strand of DNA\n\n![Difference-Between-Lagging-and-Leading-Strand_Figure-1-768x373](https://user-images.githubusercontent.com/8466209/207424623-d099ba07-91e1-4845-adaf-64232488a2a3.png)\n\n[![Leading-Strand-And-Lagging-Strand-Of-DNA-1024x954](https://user-images.githubusercontent.com/8466209/207360880-6a772b29-f752-4972-b4ad-27de3193c62d.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md)\n\n[![](https://user-images.githubusercontent.com/8466209/207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md)\n","dir":"/exponentiation/span16/","name":"gist04.md","path":"exponentiation/span16/gist04.md","url":"/exponentiation/span16/gist04.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201015369-c6ba5c75-c2c7-415b-b424-debaa5c7f64a.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-feeding-md)\n\n![default](https://user-images.githubusercontent.com/8466209/201012946-c1b10170-a14b-46aa-8c13-4646cf7cadb4.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201013443-232335d2-af81-47eb-b93e-8005cb5fed56.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201014411-83fc0bd6-96dc-40ad-9eca-0a56695df151.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201014604-fd2d3b83-f243-4fc5-8032-ed984cb28002.png)\n","dir":"/identition/span9/","name":"gist04.md","path":"identition/span9/gist04.md","url":"/identition/span9/gist04.html"},{"layout":"default","title":null,"content":"***50 + 50 + 18 = 50 + 68 = 118***\n\n![image](https://user-images.githubusercontent.com/8466209/223748602-496016ab-db42-4f5e-a5eb-ec0b884fc4f4.png)\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+----- \n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th ←-- π(10) \n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== \n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- \n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th ←-- π(20)\n -----------------------+----+----+----+----+----+----+----+----+----+----- \n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== \n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ←-- π(30)\n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n\n```\n\n![](https://user-images.githubusercontent.com/36441664/133192153-61cad1c0-1dde-4fed-8718-840d324a7198.jpg)\n\n![resize](https://user-images.githubusercontent.com/8466209/206956260-f8c3647a-232c-470e-8c0b-e93a6fea14f7.png)\n\n![](https://user-images.githubusercontent.com/36441664/84902223-b8509480-b0d6-11ea-9763-320b38bae102.png)\n\n![action](https://user-images.githubusercontent.com/36441664/84525042-2f67e080-ad05-11ea-9f9c-e07492446240.jpg) \n\n[![Navier–Stokes](https://user-images.githubusercontent.com/8466209/224357044-f3c42fa5-b9ad-471c-85f3-6a4aa01a909e.png)](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f)\n\n![2022-12-11 (1)](https://user-images.githubusercontent.com/8466209/206918483-5016aa03-2bc1-4dcf-a7dd-29f2c4453787.png)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/206918218-95c875a7-0080-44e5-8ade-1ff776f9c30d.png)\n\n![2022-12-14 (1)](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png)\n\n![2022-12-14 (1)](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png)\n\n![](https://user-images.githubusercontent.com/36441664/104077748-9f175d00-524d-11eb-9c6d-6c0c4ee1fd93.gif)\n","dir":"/exponentiation/span15/","name":"gist04.md","path":"exponentiation/span15/gist04.md","url":"/exponentiation/span15/gist04.html"},{"layout":"default","title":null,"content":"\n```\n---+-----+-----\n 1 | 1 | 15\n---+-----+-----\n 2 | 16 | 25\n---+-----+-----\n 3 | 26 | 50\n---+-----+-----\n 4 | 51 | 84\n---+-----+-----\n 5 | 85 | 99\n---+-----+-----\n```\n\n[![Prime Identity](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity)\n\n![](https://user-images.githubusercontent.com/36441664/83051805-aef47f00-a078-11ea-87e5-d8f352e318fe.gif)\n\n***99 - 15 - 15 = 69 = 9 + 60 = 9 + (100 - 40)***\n\n![](https://user-images.githubusercontent.com/36441664/83051968-e2cfa480-a078-11ea-8ff2-316a809a8fad.jpg)\n\n![default](https://user-images.githubusercontent.com/8466209/224346485-13d27a0b-bfe3-43f0-94da-f75313dc9d77.png)\n\n```liquid \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+---+----+----+---+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 |\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n ```\n\n![](https://user-images.githubusercontent.com/36441664/74366957-992db780-4e03-11ea-8f26-cca32bd26003.png)\n\n![](https://user-images.githubusercontent.com/8466209/223616353-0e1be019-16e8-40d1-bb0c-465a9837d7bb.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/224466884-5ba87f02-e01d-45ca-a9c3-a1d535e83228.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#poincar%C3%A9-conjecture)\n\n>Experiment and computer simulations suggest the existence of a \"mass gap\" in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n\n[![Yang–Mills and Mass Gap](https://user-images.githubusercontent.com/36441664/85888653-3538e800-b814-11ea-85ba-23a56243e9e0.jpg)](https://www.claymath.org/millennium-problems/yang%E2%80%93mills-and-mass-gap)\n","dir":"/exponentiation/span15/","name":"gist05.md","path":"exponentiation/span15/gist05.md","url":"/exponentiation/span15/gist05.html"},{"layout":"default","title":null,"content":"[![84525026-2971ff80-ad05-11ea-934e-1fb3cab8cc01](https://user-images.githubusercontent.com/8466209/207610593-51e33d42-104e-47b3-ac0d-5b48ce5971dc.gif)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-target-md)\n\n![Figure_34_06_01](https://user-images.githubusercontent.com/8466209/207485796-0a0b19c6-455d-4304-bd37-cd7b6640af38.jpg)\n\n[![Leading-Strand-And-Lagging-Strand-Of-DNA-1024x954](https://user-images.githubusercontent.com/8466209/207357956-3eeeacc2-0b5f-4eeb-b2b5-71f8d22adf59.png)](https://onlyzoology.com/difference-between-leading-strand-and-lagging-strand-of-dna/)\n\n[![](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md)\n","dir":"/exponentiation/span16/","name":"gist03.md","path":"exponentiation/span16/gist03.md","url":"/exponentiation/span16/gist03.html"},{"layout":"default","title":null,"content":"[![Screenshot_2023-12-07-16-59-55-579_com google android apps docs](https://gist.github.com/assets/8466209/55c00788-ff82-4a8c-afdb-2d8d05a0ef8d)](https://arxiv.org/pdf/1812.07680.pdf)\n\n","dir":"/exponentiation/span16/","name":"gist01.md","path":"exponentiation/span16/gist01.md","url":"/exponentiation/span16/gist01.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/200699492-2ceabad2-17e9-4f8c-a87f-518a15119700.png)\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root 1 → 4 (5)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin 2 → 8 (10)\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin 5 → 7 (12)\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200107646-e12803d2-f71d-46d4-a408-a3de05ecd627.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-opposite-md)\n\n![default](https://user-images.githubusercontent.com/8466209/200103953-a6ea55a1-bb07-48d8-9d92-40050acca532.png)\n\n![default](https://user-images.githubusercontent.com/8466209/200103981-7a0d9e10-8523-4dc6-89e0-5a340b70acbe.png)\n\n![default](https://user-images.githubusercontent.com/8466209/200100113-9642fff1-8cbf-4fac-8aab-d11f7dc43f4f.png)\n\n![default](https://user-images.githubusercontent.com/8466209/200100230-92467b4d-a88f-4cee-ac81-cd32e6e5099b.png)\n\n![default](https://user-images.githubusercontent.com/8466209/200102363-1b1cc49a-1320-454b-a857-9c25956acdcf.png)\n","dir":"/identition/span7/","name":"gist06.md","path":"identition/span7/gist06.md","url":"/identition/span7/gist06.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | {1} |{43}\n---+-----+-----\n 2 | 44 |{57}\n---+-----+-----\n 3 | 58 | 59\n---+-----+-----\n 4 | 60 | 104\n---+-----+-----\n 5 | 105 |{115}\n---+-----+-----\n 6 |{116}| 134\n---+-----+-----\n 7 | 135 | 162\n---+-----+-----\n 8 | 163 | 175\n---+-----+-----\n 9 | 176 |{176}\n---+-----+-----\n```\n\nLet's say you have a defaut configuration of π(10)=2,3,5,7. How do you present your html page in order that all of the page elements are represented by the primes without any missing parts?\n\n```html\n → (29=10th prime) → next favicon\n Δ ← (10)\n | |\n (89²)\n ← (19) |\n \n \n```\n\n![image](https://user-images.githubusercontent.com/8466209/250567634-b46e7212-0bde-4934-9afa-4c02520f4bd4.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/199243558-e974f2ff-55a7-4b4d-8958-d171deecb1d9.png)](https://github.com/jonico/awesome-runners)\n\n[![default](https://user-images.githubusercontent.com/8466209/199135210-06912985-b2b0-4495-94cb-9431935dc912.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-core-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199135743-79928119-2c84-4fa4-bd85-90d77ba3d8f8.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-core-md)\n\n![default](https://user-images.githubusercontent.com/8466209/227427522-5e34043d-17b7-4cc1-84e8-2194ca408597.png)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/255234272-d951c8fc-1858-4f30-8497-b0202ed509bd.png)[![default](https://user-images.githubusercontent.com/36441664/83518550-c7dfb300-a504-11ea-9983-51c3eab2220d.jpg)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406)\n","dir":"/identition/span4/","name":"gist09.md","path":"identition/span4/gist09.md","url":"/identition/span4/gist09.html"},{"layout":"default","title":null,"content":"![73933040-31143880-490e-11ea-802f-035194e48d4b](https://user-images.githubusercontent.com/8466209/218367881-6c561132-e50c-4a72-b938-37d3eac69d45.png)\n\nAll of these coincidences are already discussed in details by previous schemes as well the existence of gap by 33's that is parsing the 102. \n\n[![sequence](https://user-images.githubusercontent.com/8466209/199844359-3f898aad-0661-4ccb-9d90-1e2aadbdf662.png)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831)\n\nPlease note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about ***19th*** as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51. From the 50 we gonna split the 15 by _bilateral 9 sums_ resulting 2 times 15+9=24 which is 48. So the total of involved objects is ***50+48=98***.\n\n***π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66***\n\n[![goes](https://user-images.githubusercontent.com/36441664/83051968-e2cfa480-a078-11ea-8ff2-316a809a8fad.jpg)](https://schoolbag.info/mathematics/numbers/38.html)\n\nSee the fact that last 15 is connected to 25 which is 24+Δ1 where as another 15 are also correlated with 24 in pairs. So here we would compound them within three (3) _[minor hexagon](https://www.hexspin.com/minor-hexagons)_ which has 24 each and one of them is carrying the (Δ1).\n\nThis cycle is repeated through a palindromic sequence.\n\n![default](https://user-images.githubusercontent.com/8466209/197364042-0c30b323-4d1b-4e13-b9d8-002d482e5a7c.png)\n\n```\n| 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ \n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n\n***67 » 66, 78, 86 ([OEIS A059756](https://oeis.org/A059756))***\n\n[![default](https://user-images.githubusercontent.com/8466209/211178117-9a879fd0-163b-442b-87bf-49d76c0b6c50.png)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831)\n\n![image](https://user-images.githubusercontent.com/8466209/195509190-6926e3cd-807a-44ef-8549-b0fc1f481a2d.png)\n\n***102 = 2+60+40 » (2,60.40)***\n\n[![default](https://user-images.githubusercontent.com/8466209/198783118-6f7890ea-aed2-495d-ae6b-acb215ad7140.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde)\n\n[![default](https://user-images.githubusercontent.com/8466209/198762875-b57d367d-2d5f-44c3-a37f-ba7a6d8dbc38.png)](https://github.com/eq19/grammar/actions/runs/3343512525/jobs/5536807573)\n\n![default](https://user-images.githubusercontent.com/8466209/225381200-cf1210c7-d2cf-4558-bab8-6152f3042244.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/198813046-300043a7-86b6-468a-b45c-a3c197f0a9f6.png)](https://www.eq19.com/)\n","dir":"/identition/span2/","name":"gist03.md","path":"identition/span2/gist03.md","url":"/identition/span2/gist03.html"},{"layout":"default","title":"Deploying containers","content":"## Deploying containers\n\nThis [Chromium Project](https://www.chromium.org/chromium-projects/) is being considered since it has an [Optimized OS](https://cloud.google.com/container-optimized-os/docs/how-to/building-from-open-source) to build containers which could be imported as image in a [_Compute Engine_](https://cloud.google.com/compute/docs/images/import-existing-image#import_image). With this scheme then the engine is able to be assigned as a runner to build inside container.\n\n[![](https://user-images.githubusercontent.com/8466209/202855623-cd58afdf-e05b-4517-b3dd-b01e70011814.gif)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-13_centralize-md)\n\nThe main reason of this requirement is because we will need to build a system that contained as [three (3) layers](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857) of primes level where the system will always be forced in to the ***[15+25=40th prime](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#mapping-scheme)*** each time we made an access to the next layer.\n\n```\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\nAlthouht the optimized os is ready with [built in images](https://cloud.google.com/container-optimized-os/docs/release-notes) however we will need to place a custom modification since the objective of this OS Project is mainly about optimizing the containers while our project is mainly about the primes behaviour.\n\n[![l8myt](https://user-images.githubusercontent.com/8466209/210317563-306111cb-5c66-4996-ad7b-47d84077175e.jpg)](https://stackoverflow.com/a/49467154/4058484)\n\nBy this modification we are going to build the three (3) layers of 19 cells with a ***cumulative sum of 1, 7 and 19*** in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66.\n\n[![](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-1_prime-md)\n\nConsider that the 1st cell is standing as (Δ1) which is eqivalent to 19. Then as per _The Δ(19 vs 18) Scenario_ the 7 cells would behave as (Δ1 to Δ7) that equivalent with 19 to 25. So by the 3rd and 4th axis it will get 102+66 = 168 primes of π(1000).\n\n```\n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+---+----+----+---+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 |\n +----+----+----+---+----+----+---+\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n```\n\nBy the 1's and 17's cells we will divide in the 0's cell in to four (4) containers shown above. You should find that the 40 primes is acting as the base rule of the current primes level also the interface between ***the grammar*** of each containers as well. Two (2) primes out of the 102 will hold the 1's and 17's cells so by the rest of 100 they will form (2,60,40).\n\n[![](https://user-images.githubusercontent.com/8466209/199135210-06912985-b2b0-4495-94cb-9431935dc912.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-runner-md)\n\nBy the scheme as we have explained above you would agree that this mapping could only be managed using a ***customizable compute service*** so the engine is easily to be created, terminated, restarted and even deleted programmatically.\n\n[![](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md)\n\nSee that all of the steps need to be done progressively. Once we [buit a container](https://github.com/chromium/chromium/blob/main/docs/linux/build_instructions.md#docker-requirements) of (2,60,40) with the three (3) inside containers then the 33's will be able to generate four (4) runners that represent ***(2,3,5,7) from the π(10)***. Let's discuss them one by one.","dir":"/exponentiation/span16/","name":"gist06.md","path":"exponentiation/span16/gist06.md","url":"/exponentiation/span16/gist06.html"},{"layout":"default","title":"Antiparallels","content":"## Antiparallels\n\nNotably, the prime five (5) is equal to the sum of the only consecutive primes, 2 + 3. However by the nature it is not going to be as simple as that. Instead they are performing to do a pairing between the _[Scheme-34](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)_ with the _[Scheme-21](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-tabulate-md)_.\n\n![](https://user-images.githubusercontent.com/36441664/85040788-5e71cc80-b1b3-11ea-962f-cf26ee3419e2.jpg)\n\nBy the structure of DNA it is clearly seen that this prime is compromizing the bilateral power of the prime two (2) and grouping power of the prime three (3). Both of these powers turn to the power of the number six (6). This number is the sum and multiplication of three (3) positive numbers in a row ***1 + 2 + 3 = 1 x 2 x 3 = 6***. \n\n[![](https://user-images.githubusercontent.com/36441664/101231659-56fd9b80-36df-11eb-87a2-6b4b211a6334.gif)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md)\n\nSo this Scheme-21 is actually coming from ***1+2+3+4+5+6 = 21***. By observing from many literatures we came to a conclution that it has something to do with a ***[golden ratio (φ)](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f#file-write-all-md)*** originated by π(π(π(1000th prime)))+1=40 that leads the _[168](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)_ to _[618 primes](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-container-md)_. So it would be antiparalel directions between _π(1000) = 168 to φ = 1000/618_ with _φ = 1000/618 to π(1000) = 168_ (vise versa).\n\n![](https://user-images.githubusercontent.com/36441664/84902333-e6ce6f80-b0d6-11ea-8289-aac5e1961cd6.gif)\n\nBy the prime hexagon it will even clearer. Both of the power goes antiparalel in their directions. As the result there would be the period when their instance was created, the period when it was terminated and the period that it shall be raised up.\n\n[![](https://user-images.githubusercontent.com/8466209/200012043-620aa039-3b72-4165-83ad-e35d3d972a1b.png)]()\n\nSuch of this movement goes from 17's and 11's then ***precissely landed on 5's cell*** within the hexagon. Each time an instance is raised up then the previous tensor is collected so it would finaly form a configuration of ***3,2 → 18+13+12 → 43*** as shown below.\n\n```\n --------------------------------------------------------------\n | | \n =======================+====+====+====+====+====+====+====+====+====+===== |\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root |\n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin |\n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th |\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin |\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th |\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin |\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th |\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin |\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ---------------\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n```\n\nBy this 43 the scheme goes to the limit of π(10) = (2,3.5,7) resulting 2 times prime levels from 10th primes of 29 to 29th prime of 109. See that they are touching the power of prime two (2) by carrying ***nine (9) cells*** of prime powers.\n\n> In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square and map their collective ***bilateral 9 sum symmetry*** _([Primesdemystified](https://www.primesdemystified.com/#primingthesquares))_\n\n[![bilateral 9 sums](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-bilateral-md)\n\nSince the prime two (2) has a bigger power of all primes combined then it will force back those power precisely as shown on the tabulation above. So from the movement of the form of (7,5,3,2) it goes to (2,3,5,7) as a ***new replication*** of π(10). \n\n```\n-----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n 2 -------------------+----+----+----+----+----+----+----+----+----+----- ←-- bilateral 9 sums\n 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n```\n\nThis replication is the one that forming _5' vs 3'_ with _3' vs 5'_ ends of DNA. One thing we should notify here is that this bilateral movements is originated by the 17's of 100 objects. So the period will cover antiparales of 2 times 100+43 or _[286 objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e)_. \n\n![212474451-c7e68350-8c80-4d67-9fb7-63fba08eb269](https://user-images.githubusercontent.com/8466209/212552402-bacfb0be-7336-4d0d-ad32-36f9cb0bfefc.jpg)\n\nIn order to facilitate this behaviour the flows within the three (3) inside containers shall have an entrance to the period when the instance was ***created***, the period when it was ***terminated*** and the period that it shall be ***raised up*** to exchange its existence. \n\n[![](https://user-images.githubusercontent.com/8466209/203874503-4276074d-3270-437f-a675-858486afd126.png)]()\n\nThe end of this formation is at fifty (50) which at the next level will carry out the regeneration process to 102 via the number one hundred (100) for its correlation with the number two (2).\n\n[![](https://user-images.githubusercontent.com/8466209/199508386-69859804-9ccb-4f5d-8314-8ca0be0af235.png)]()\n\nWith the help of a computer, we appear these two objects only those related to the intended case. Where we can do mapping or iteration with the data we prepare so that results are obtained more quickly and accurately.\n\n[![](https://user-images.githubusercontent.com/8466209/199502657-1ba96c92-29f9-41ec-90a9-cbc5adec9464.png)]()\n\nFor the series of consecutive powers of pi, it has been found that there is ***no two fall within the same six-cell hexagon***. As a matter of a fact it was computed this for pi^32, which has less than a 1/400 chance of occurring randomly.\n\n[![default](https://user-images.githubusercontent.com/8466209/203874936-9065fbff-25f6-4357-a37b-6945502161d5.png)](https://github.com/kaustubhcs/prime-hexagon)\n\nThis is a kind of connections to display the above complex relation between the individual objects and their tensors. Same case as we have expressed before we will bring further every details particulary on this scope in to another website separately. \n\n[![](https://user-images.githubusercontent.com/8466209/199359982-229c7e19-9491-44fe-bc67-9c10b14609e9.png)]()\n\nBy using this method of interpolation between the object and their tensors we finaly found that the Scheme-35 is actualy come from anti paralel behaviour of [Scheme-53](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md) which is containing _[three (3) prime pairs](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-tabulate-md)_.\n","dir":"/exponentiation/span16/","name":"gist07.md","path":"exponentiation/span16/gist07.md","url":"/exponentiation/span16/gist07.html"},{"layout":"default","title":null,"content":"![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612376-9c1b77f9-f9be-4b8e-be08-d4784b9c65cf.png)\n\n![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612583-27347639-6314-46b6-9b36-e8898e45c547.png)\n\n* Only a single RNA primer is required for the whole lagging strand to synthesize. The starting of each Okazaki fragment **requires a new RNA primer**.\n![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612733-ce46354c-7386-4bc4-84b2-e89527da7cef.png)","dir":"/exponentiation/span16/","name":"gist08.md","path":"exponentiation/span16/gist08.md","url":"/exponentiation/span16/gist08.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 |{21}\n---+-----+-----\n 2 |{22} |{34}\n---+-----+-----\n 3 |{35} |{89}\n---+-----+-----\n 4 | 90 |{119}\n---+-----+-----\n 5 | 120 | 124\n---+-----+-----\n 6 |{125}|{128}\n---+-----+-----\n```\n\n```liquid\n 26\n to\n 29\n |\n |\n |\n V \n | 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ \n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n[![](https://user-images.githubusercontent.com/8466209/206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-locate-md)\n\n![206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2](https://user-images.githubusercontent.com/8466209/207627118-3de81d9e-7f43-4a36-a4f8-fab402c487d1.png)\n\n![dualidad-onda-particula](https://user-images.githubusercontent.com/8466209/207629416-d32dd8e3-0fb5-46b1-b8cd-926060145c04.png)\n","dir":"/exponentiation/span16/","name":"gist09.md","path":"exponentiation/span16/gist09.md","url":"/exponentiation/span16/gist09.html"},{"layout":"default","title":null,"content":"\n{% include list.liquid all=true %}\n\nThe process is carried out based on a combination of the numbers 2 and 3 by multiplication and the 9th and 10th powers of the 19th identity as a boundary number that [serves distribution of the 11th](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity) by 2 to 20 and 40 to 50 in bases 10 to 100 and 1000.\n\n>19² can be written as the sum of three (3) consecutive squared triangular numbers 6²+10²+ 15²\n\n```scss\n--+-----+-----\n 1 | 1 |{15}\n---+-----+-----\n 2 |{16} |{40}\n---+-----+-----\n 3 | 41 |{50}\n---+-----+-----\n 4 | 51 | 63\n---+-----+-----\n 5 | 64 | 83\n---+-----+-----\n 6 | 84 | 98\n---+-----+-----\n```\n\nBy our mapping the prime seven (7) is forming the prime pair of (5,7) with the prime five (5) which is the only number that is part of more than one pair of twin primes, (3, 5) and (5, 7). This (5, 7) is one of the pair of that we called _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n***out (product) = in (joint) x out (last) = (1 + 5) x 19 = 6 x 19 = 114***\n\n```scss\n$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer| i | f\n -----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | 7\n -----+-----+--- } 36 » 6®\n | 3 | 11\n 2 +-----+\n | 4 | 13\n -----+-----+---------\n | 5 | 17\n 3 +-----+ } 36 » 6®\n | 6 | 19\n -----+-----+---------\n ```\n\nBy a DNA their tensor can be seen on hydrogen bonding where the form ***96 of A,T*** would pair the form ***69 of C,G***.\n \n***96 + 19 = 115 = 114 + Δ1*** \n\n![molecular_DNA](https://user-images.githubusercontent.com/8466209/212474832-bc616a25-06ad-41e7-a27d-0bec82b1f2a4.png)\n\nThis pairs is formed by the movement from the 17's and 11's and then precissely [landed on 5's](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-runner-md) explained before. So they have somethig to do with the anti paralel behaviour of Scheme-53 and Scheme-35 on a chromosom.\n\n```scss\n largest part=21 → 11+13+12=36 →| MEC30\n ↓ |\n---+-----+-----+-----+-----+ |\n 1 | 19 | 1 | 20 | 21 |-------------------|-----------\n---+-----+-----+-----+-----+ | |\n 2 | 18 | 21 | 39 | 60 |-------------------|----- |\n---+-----+-----+-----+-----+ | | |\n 3 |{63} | 40 | 103 | 143 |------------- | | |\n---+-----+-----+-----+-----+ | | | |\n 4 | 37 | 104 | 141 | 245 |------- | | | |\n---+-----+-----+-----+-----+ | | | | |\n 5 | 10* | 142 | 152 | 294 |- 11** | 13 | 12 | | 12 | 18\n---+-----+-----+-----+-----+ | | | | |\n 6 | 24 | 153 | 177 | 332 |------- | | | |\n---+-----+-----+-----+-----+ | | | |\n 7 | 75 | 178 | 253 | 431 |------------- | | |\n---+-----+-----+-----+-----+ | | |\n 8 | 30 | 254 | 284 | 538 |-------------------|----- |\n---+-----+-----+-----+-----+ | |\n 9 | 1 | 285 | 286 | 571 |-------------------|-----------\n===+=====+=====+=====+=====+ |\n45 | 277 | ← 11+13+12=36 ←| MEC30\n---+-----+ |\n\nNote:\n10* stands as the central rank\n11** stands as the central parts\n```\n\nBy toucning the bilateral way of ***96+2=98*** we came to following tabulation. This is further compromizing between the prime five (5) and the prime seven (7) represent the segregation inside the first pair (5, 7). So it shows the tensor of twelve (12) numbers. \n \n\n```scss\n\n #8 |----------- 5® --------|------------ 7® --------------|\n | 1 |---------------- 77 = 4² + 5² + 6² -------------|\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78\n main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 100 - 123 ({24})\n |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30\n {98} | └── 110 - 123 (14x)» 70\n```\n\n### Compositions\n\nSo by defining the pattern of each individual numbers with the basic rule that the 19 is _[regenerated](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d)_ out of 18 while the 7 is the _[recollection](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155)_ out of 6 and comparing with the _[Gann Chart](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-lexer-md)_ finaly we found how they look like.\n\n```scss\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\nDescription\n===========\nGetting result within a huge package (5 to 19) by spreading (11)\nthe untouched objects (7) and tunneling (13) them in to a definite scheme (17).\n\nCompositions\n============\n\nlayer| 1st | 2nd | 3rd | ∑(2,3)\n-----+------+------+------+------+------+------+------+------+------+------+------ ---\n | | 7 | {19} | 38 | 62 | 64 | 67 | 93 | 95 | 96 | 139 |\n i + 1 +------+------+------+------+------+------+------+------+------+------ 5¨\n | | 8 | 20 | 39 | 63 | 65 | 68 | 94 | 97 | 98 | |\n-----+------+------+------+------+------+------+------+------+------+------+------ ---\n | | 9 | 21 | 40 | {43} | 66 | 69 | 99 | 100 | 101 | 286 |\n + 2 +------+------+------+------+------+------+------+------+------+------ 7¨\n | | 10 | 22 | 41 | 44 | 45 | 70 | 102 | 103 | 104 | |\n q +------+------+------+------+------+------+------+------+------+------+------ ---\n | | 11 | 23 | 42 | 46 | 47 | {71} | 105 | 106 | 107 | 114 |\n + 3 +------+------+------+------+------+------+------+------+------+------ 11¨\n | | 12 | 24 | 25 | 48 | 49 | 72 | 108 | 109 | 110 | |\n-----+------+------+------+------+------+------+------+------+------+------+------ ---\n | | 13 | 26 | 27 | 50 | 51 | 73 | 74 | 111 | 112 | 247 |\n + 4 +------+------+------+------+------+------+------+------+------+------ 13¨\n | | 14 | 28 | 29 | 52 | 53 | 75 | 76 | 113 |{114} | |\n r +------+------+------+------+------+------+------+------+------+------+------ ---\n | | 15 | 30 | 31 | 54 | 55 | 77 | 78 | 79 | 80 | 157 |\n + 5 +------+------+------+------+------+------+------+------+------+------ {17¨}\n | | 16 | 32 | 33 | 56 | 57 | 81 | 82 | 83 | 84 | |\n-----+------+------+------+------+------+------+------+------+------+------+------ ---\n | | 17 | 34 | 35 | 58 | 59 | 85 | 86 | 87 | 88 | 786 |\n o + 6 +------+------+------+------+------+------+------+------+------+------ 19¨\n | | 18 | 36 | 37 | 60 | 61 | 89 | 90 | 91 | {92} | |\n-----+------+------+------+------+------+------+------+------+------+------+------ ---\n ∑ | {21} | 150 | | | | | | | | | 1729\n\n |------------------------------------------------------------- 16¨ ---|\n |----------------------------------------------- 15¨ ---|\n |--------------------------------- 14¨ ---|\n |------------------- 13¨ ---|\n |--- {12¨} ---|\n```\n\nSee that by top of pattern it goes bilateral from ***1, 7, 19, 38*** exactly shown on the _[Scheme-33](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md)_, while the rest are grouped in to the form ***69 vs 96 of A,T,C,G***. Thus each numbers are in the pattern of _[Double Helix](https://en.wikipedia.org/wiki/Nucleic_acid_double_helix)_.\n\n![image](https://user-images.githubusercontent.com/8466209/213604396-92832a7d-9122-4251-8d26-6fca720b6df7.png)\n\nThis pattern is raised up ***per six (6) cycles*** on the ***[19](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md)***, ***[43](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-runner-md)*** and ***[71](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)***. Since the members are limited to the sum of ***43+71=114*** so here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme.\n\n***[(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects***\n\n[![Polarity](https://user-images.githubusercontent.com/8466209/212487102-2f080804-9078-45c9-85ee-9977a36a5dbf.jpg)](http://www.hexspin.com/minor-hexagons/)\n\nMeanwhile the six (6) cycles would behave as _[P(7)=142857](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md)_ which is originated by the 7 out of 6. This pattern is also shown on the tabulation above by the horizontal flow of 14,28,29,.. which are then finaly terminated by the bilateral way to _[57x2=114](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#polar-plot)_.\n \n ### Bilateral way\n\nThis behaviour can be seen on the function chart of _[Riemann Zeta Zeros](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)_ as shown below where the 19 came out of 18 of 0's cell. \n\n[![](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#polar-plot)\n\nThe _P(7)=142857_ will bring the system to forms 7x13x19 = 1729 objects of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. As the impact there will be a gap raised to form ***[20 out of 18 of 0's cell](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)*** and facilitate the [_new candidate_](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md) to get an access to the next primes level.\n\n![](https://user-images.githubusercontent.com/8466209/220001571-bddc7fee-5753-4ee3-b145-b3b1bb49a354.png)\n\nThe rest of primes goes to the [33's of 15th axis](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-19_root-md) that holding 102 primes of (2,60,40). By the bilateral way the form will be [splitted](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-parser-md) to (1,30,20). Since the base frame shall be 40 so it will be forced to form ***(1,30,40) of prime 71***.\n\n[![zeta-vs-zero](https://user-images.githubusercontent.com/8466209/213628433-c7382e39-4efa-4455-867c-13652293474d.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-vs-zero)\n\nThe 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n[![default](https://user-images.githubusercontent.com/8466209/244139208-378b2229-c3e8-4f1f-8829-dee6687348fb.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n\nAs you may see the bilateral way between this 19's tensor with the (Δ1) is not easy to be understood nor explained. However at this point, you may already get an idea that as a part of the nature, the _DNA System_ and the _Prime Structure_ applies the same. \n\n>[Quantum Theory](https://gist.github.com/eq19) tells us that there are [instantaneous connections](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#instaneous-connection) between two entangled quantum objects, like _[electrons](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#electron-scattering)_. In fact, there is no separation. ***[At the quantum level, theoretically, everything is linked](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#everything-is-linked)***. This is known as the candidate for _The Theory of Everything_. Thus the Sunlight, Saturn, Moon, Saturn’s rings, [Moon’s orbit](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#moons-orbit), ocean, me and you… are all one.\n\n[![](https://user-images.githubusercontent.com/8466209/199392468-a2738235-b65f-47da-848d-ffa0340cd51b.png)](https://github.com/eq19)\n\nBroadly speaking it still remain of how this project can be developed so that it can be applied to the goals we want. Therefore we decided to bring further every details in to a group of websites. That is the background why the _[root scheme](https://gist.github.com/eq19)_ of 'eq19' is exist.\n","dir":"/exponentiation/span16/","name":"gist10.md","path":"exponentiation/span16/gist10.md","url":"/exponentiation/span16/gist10.html"},{"layout":"default","title":null,"content":"![](https://user-images.githubusercontent.com/36441664/72921817-8f71e080-3d7e-11ea-97c5-331789123a15.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/73038520-52dcdc80-3e85-11ea-95ed-91a6db884043.png)\n\n![](https://user-images.githubusercontent.com/36441664/72921751-710be500-3d7e-11ea-81c4-4923d68be691.gif)\n\n![image](https://user-images.githubusercontent.com/36441664/72533380-a9f01980-38a7-11ea-8609-6cb6f37645d1.jpg)\n\n![Fibonacci](https://user-images.githubusercontent.com/36441664/72921775-7bc67a00-3d7e-11ea-8042-c8b8ee0326b8.jpg)\n\n![image](https://user-images.githubusercontent.com/36441664/71191184-80e46500-22b8-11ea-9f97-5ce856a39820.png)\n\n![image](https://user-images.githubusercontent.com/36441664/71581711-14c7f380-2b39-11ea-9f61-8cf3df12a100.png)\n\n![image](https://user-images.githubusercontent.com/36441664/103138448-52883980-4705-11eb-85e6-5128c632f612.png)\n\n\n![](https://user-images.githubusercontent.com/36441664/82048729-58358f80-96df-11ea-8176-14c26328a12f.png)\n\n![2022-12-12](https://user-images.githubusercontent.com/8466209/206964338-fb62d060-86c7-4a2d-a64c-7da49bc70222.png)\n","dir":"/exponentiation/span16/","name":"gist12.md","path":"exponentiation/span16/gist12.md","url":"/exponentiation/span16/gist12.html"},{"layout":"default","title":null,"content":"[![screencapture-console-cloud-google-billing-018F05-BD9DB7-0A1326-2022-12-24-11_01_11](https://user-images.githubusercontent.com/8466209/209420635-7e57c4a9-1df8-4c18-8510-96aa23250516.png)](https://console.cloud.google.com/billing/018F05-BD9DB7-0A1326?authuser=1&cloudshell=false&project=chetabahana)\n\n[![screencapture-console-cloud-google-billing-018F05-BD9DB7-0A1326-reports-chartType-STACKED-BAR-grouping-GROUP-BY-SERVICE-2022-12-26-17_44_07](https://user-images.githubusercontent.com/8466209/209540338-f64c57d7-20ed-4413-baf1-0da50a730be3.png)\n](https://console.cloud.google.com/billing/018F05-BD9DB7-0A1326/reports;chartType=STACKED_BAR;grouping=GROUP_BY_SERVICE?authuser=1&cloudshell=false&project=marketleader)\n\n![image](https://user-images.githubusercontent.com/8466209/235955528-7bf82161-cacd-40a3-849e-5b09db8a5638.png)\n","dir":"/exponentiation/span17/","name":"gist03.md","path":"exponentiation/span17/gist03.md","url":"/exponentiation/span17/gist03.html"},{"layout":"default","title":null,"content":"[![2022-12-26 (4)](https://user-images.githubusercontent.com/8466209/209532746-5a09e0f6-9346-4d61-aee8-eeef1f801e5a.png)\n](https://console.cloud.google.com/iam-admin/serviceaccounts/create?authuser=1&project=marketleader&cloudshell=false)\n\n[![2022-12-26 (6)](https://user-images.githubusercontent.com/8466209/209535961-5441181b-a87b-4879-8e6a-c752eaaec587.png)\n](https://console.cloud.google.com/iam-admin/serviceaccounts/details/112927040009179159531/permissions?authuser=1&project=marketleader)\n\n[gcloud](https://developers.google.com/cloud/sdk/gcloud/reference/compute/?hl=en_US) command line\n\n```\ngcloud compute instance-templates create instance-template-ubuntu-01 \\\n--project=marketleader --machine-type=e2-micro --network-interface=network=default,network-tier=PREMIUM \\\n--maintenance-policy=MIGRATE --provisioning-model=STANDARD \\\n--service-account=project-owner@marketleader.iam.gserviceaccount.com \\\n--scopes=https://www.googleapis.com/auth/source.full_control,\\\nhttps://www.googleapis.com/auth/compute,https://www.googleapis.com/auth/servicecontrol,\\\nhttps://www.googleapis.com/auth/service.management.readonly,\\\nhttps://www.googleapis.com/auth/logging.write,https://www.googleapis.com/auth/monitoring.write,\\\nhttps://www.googleapis.com/auth/trace.append,https://www.googleapis.com/auth/devstorage.read_only \\\n--create-disk=auto-delete=yes,boot=yes,device-name=instance-template-ubuntu-2204LTS,\\\nimage=projects/ubuntu-os-cloud/global/images/ubuntu-2204-jammy-v20221206,mode=rw,size=10,type=pd-standard \\\n--no-shielded-secure-boot --shielded-vtpm --shielded-integrity-monitoring --reservation-affinity=any \\\n--tags=https-server --threads-per-core=2\n```\n\nEquivalent [REST request](https://developers.google.com/compute/docs/reference/latest?hl=en_US)\n\n```\nPOST https://www.googleapis.com/compute/v1/projects/marketleader/global/instanceTemplates\n{\n \"description\": \"\",\n \"name\": \"instance-template-ubuntu-01\",\n \"properties\": {\n \"advancedMachineFeatures\": {\n \"threadsPerCore\": 2\n },\n \"canIpForward\": false,\n \"confidentialInstanceConfig\": {\n \"enableConfidentialCompute\": false\n },\n \"description\": \"\",\n \"disks\": [\n {\n \"autoDelete\": true,\n \"boot\": true,\n \"deviceName\": \"instance-template-ubuntu-2204LTS\",\n \"diskEncryptionKey\": {},\n \"initializeParams\": {\n \"diskSizeGb\": \"10\",\n \"diskType\": \"pd-standard\",\n \"labels\": {},\n \"sourceImage\": \"projects/ubuntu-os-cloud/global/images/ubuntu-2204-jammy-v20221206\"\n },\n \"mode\": \"READ_WRITE\",\n \"type\": \"PERSISTENT\"\n }\n ],\n \"displayDevice\": {\n \"enableDisplay\": false\n },\n \"keyRevocationActionType\": \"NONE\",\n \"labels\": {},\n \"machineType\": \"e2-micro\",\n \"metadata\": {\n \"items\": []\n },\n \"networkInterfaces\": [\n {\n \"accessConfigs\": [\n {\n \"kind\": \"compute#accessConfig\",\n \"name\": \"External NAT\",\n \"networkTier\": \"PREMIUM\",\n \"type\": \"ONE_TO_ONE_NAT\"\n }\n ],\n \"network\": \"projects/marketleader/global/networks/default\",\n \"stackType\": \"IPV4_ONLY\"\n }\n ],\n \"reservationAffinity\": {\n \"consumeReservationType\": \"ANY_RESERVATION\"\n },\n \"scheduling\": {\n \"automaticRestart\": true,\n \"onHostMaintenance\": \"MIGRATE\",\n \"provisioningModel\": \"STANDARD\"\n },\n \"serviceAccounts\": [\n {\n \"email\": \"project-owner@marketleader.iam.gserviceaccount.com\",\n \"scopes\": [\n \"https://www.googleapis.com/auth/source.full_control\",\n \"https://www.googleapis.com/auth/compute\",\n \"https://www.googleapis.com/auth/servicecontrol\",\n \"https://www.googleapis.com/auth/service.management.readonly\",\n \"https://www.googleapis.com/auth/logging.write\",\n \"https://www.googleapis.com/auth/monitoring.write\",\n \"https://www.googleapis.com/auth/trace.append\",\n \"https://www.googleapis.com/auth/devstorage.read_only\"\n ]\n }\n ],\n \"shieldedInstanceConfig\": {\n \"enableIntegrityMonitoring\": true,\n \"enableSecureBoot\": false,\n \"enableVtpm\": true\n },\n \"tags\": {\n \"items\": [\n \"https-server\"\n ]\n }\n }\n}\n```\n\n[![instance-template-ubuntu-2204LTS](https://user-images.githubusercontent.com/8466209/209422018-1209129c-fc1d-4d21-baf9-3d8791c65bcb.png)\n](https://console.cloud.google.com/compute/instanceTemplates/add?authuser=1&cloudshell=false&project=marketleader)\n\n[![2022-12-24 (9)](https://user-images.githubusercontent.com/8466209/209423099-b1a94680-016a-4a05-a8d0-a8bed34ea099.png)\n](https://console.cloud.google.com/compute/instanceTemplates/add?authuser=1&cloudshell=false&project=marketleader)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/253502287-3490508a-c791-42f0-91b4-6518f6f9d384.png)\n","dir":"/exponentiation/span17/","name":"gist04.md","path":"exponentiation/span17/gist04.md","url":"/exponentiation/span17/gist04.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 | 4\n---+-----+-----\n 2 | 5 | 14\n---+-----+-----\n 3 | 15 | 26\n---+-----+-----\n 4 | 27 | 40\n---+-----+-----\n 5 | 41 |{47}\n---+-----+-----\n 6 | 48 | 54\n---+-----+-----\n 7 | 55 |{71}\n---+-----+-----\n 8 | 72 | 75\n---+-----+-----\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200224482-708a56dc-196e-4f13-865b-07585322a6b8.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-8_spinning-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-tensor-md)\n\n>The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2 _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n\n[![Riemann Hypothesis](https://user-images.githubusercontent.com/8466209/218374273-729fee09-5480-4fb3-a3a6-0dc050bdbe26.png)](https://www.claymath.org/millennium-problems/riemann-hypothesis)","dir":"/identition/span8/","name":"gist07.md","path":"identition/span8/gist07.md","url":"/identition/span8/gist07.html"},{"layout":"default","title":null,"content":"![2022-12-24 (10)](https://user-images.githubusercontent.com/8466209/209439858-be21b338-8486-470a-8a2e-6a50a4ce692a.png)\n\n[![2022-12-24 (11)](https://user-images.githubusercontent.com/8466209/209440027-a5a4dcd9-ad13-46d6-919a-7b5e4d1b966e.png)](https://console.cloud.google.com/compute/instances?authuser=1&cloudshell=false&project=marketleader&tab=instances)\n![2022-12-24 (12)](https://user-images.githubusercontent.com/8466209/209442921-774da1ac-fd91-449a-a19c-a90fbe170a7a.png)\n\n![2022-12-24 (13)](https://user-images.githubusercontent.com/8466209/209442958-440076e5-c350-4d27-8ce0-6917d8ad8426.png)\n\n[![screencapture-swaadha-how-to-create-github-organization-runner-in-kubernetes-cluster-2022-12-26-17_10_33](https://user-images.githubusercontent.com/8466209/209537509-00ed823e-817b-4a3b-a119-61cdac14cf87.png)\n](https://swaadha.com/how-to-create-github-organization-runner-in-kubernetes-cluster/)","dir":"/exponentiation/span17/","name":"gist05.md","path":"exponentiation/span17/gist05.md","url":"/exponentiation/span17/gist05.html"},{"layout":"default","title":null,"content":"[![](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png)](https://gist.github.com/eq19/dc30497160f3389546d177da901537d9#file-leading-md)\n\n![2022-12-25 (6)](https://user-images.githubusercontent.com/8466209/209474076-093cde4b-ea53-4f54-9901-5ae661106937.png)\n\n[![2022-12-25 (3)](https://user-images.githubusercontent.com/8466209/209473648-bbcb171c-e1b3-4a49-9a9f-96536dfe8c24.png)\n](https://console.cloud.google.com/compute/instancesAdd?authuser=1&cloudshell=false&project=marketleader)\n\n[![2022-12-25 (2)](https://user-images.githubusercontent.com/8466209/209473582-2c292df3-90ba-4859-bea9-25637f6c12c0.png)\n](https://console.cloud.google.com/compute/instancesAdd?authuser=1&cloudshell=false&project=marketleader)\n","dir":"/exponentiation/span17/","name":"gist07.md","path":"exponentiation/span17/gist07.md","url":"/exponentiation/span17/gist07.html"},{"layout":"default","title":null,"content":"\n[![](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-locate-md)\n\n[![2022-12-26 (1)](https://user-images.githubusercontent.com/8466209/209503644-968f7e29-ab14-4eff-abad-6a2bccd8398e.png)\n](https://github.com/FeedMapping/feedmapping.github.io)\n\n[![2022-12-26 (2)](https://user-images.githubusercontent.com/8466209/209503851-493bebbb-28e9-495b-87e5-8d9c17e24f0f.png)\n](https://docs.github.com/en/pages/getting-started-with-github-pages/configuring-a-publishing-source-for-your-github-pages-site#publishing-with-a-custom-github-actions-workflow)\n\n[![First 120 builds-minutes per day are free](https://user-images.githubusercontent.com/8466209/255348632-aa005f71-470c-4f96-bd76-02c9abfa9b16.png)](https://cloud.google.com/build/pricing#additional_costs)\n","dir":"/exponentiation/span17/","name":"gist08.md","path":"exponentiation/span17/gist08.md","url":"/exponentiation/span17/gist08.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 |{10}\n---+-----+-----\n 2 |{11} |{22}\n---+-----+-----\n 3 | 23 | 39\n---+-----+-----\n 4 |{40} |{60}\n---+-----+-----\n 5 |{61} | 70\n---+-----+-----\n 6 |{71} |{77}\n---+-----+-----\n 7 |{78} | 82\n---+-----+-----\n 8 | 83 |{100}\n---+-----+-----\n 9 | 101 | 104\n---+-----+-----\n10 | 105 |{111}\n---+-----+-----\n```\n\n![Untitled](https://user-images.githubusercontent.com/8466209/255354303-b21e4caf-b759-4319-b92c-77209ea0e1da.png)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/255354336-2c112708-3011-4e15-a51f-ad4a5998ab85.png)\n\n[![](https://user-images.githubusercontent.com/8466209/200244306-f5e5a428-83b9-46bb-a4b1-c96367e278b2.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-circular-md)\n\n","dir":"/exponentiation/span17/","name":"gist09.md","path":"exponentiation/span17/gist09.md","url":"/exponentiation/span17/gist09.html"},{"layout":"default","title":null,"content":"![](https://user-images.githubusercontent.com/8466209/204256833-d12508ae-8cb1-4381-ade5-7acfcc3f0e12.png)\n\n![](https://user-images.githubusercontent.com/36441664/125708871-db9523c3-8d32-4423-976f-59a9c56a146d.png)\n\n![2022-12-11 (3)](https://user-images.githubusercontent.com/8466209/206912519-cf441c73-314f-4056-a199-ca56110c9254.png)\n\n![2022-12-12 (1)](https://user-images.githubusercontent.com/8466209/207072690-80ab2c3d-f41a-48bd-ab64-09df6afd4a26.png)\n\n![Untitled](https://user-images.githubusercontent.com/8466209/207068091-8ee3cfa6-d68c-4f85-bb90-1597b9778f44.png)\n\n[![2022-12-24 (5)](https://user-images.githubusercontent.com/8466209/209421514-d62c776a-77c0-4cb0-a0ac-5f33ba51c161.png)](https://help.ubuntu.com)\n","dir":"/exponentiation/span17/","name":"gist10.md","path":"exponentiation/span17/gist10.md","url":"/exponentiation/span17/gist10.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/200098879-84208edb-d66b-4d46-bcfb-3889cf23801b.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/200098961-f051223d-ea39-4f8a-a7ea-a26496da988b.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md)\n\n","dir":"/identition/span7/","name":"gist05.md","path":"identition/span7/gist05.md","url":"/identition/span7/gist05.html"},{"layout":"default","title":"The Classes","content":"## [The Classes](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#objects-vs-classes)\n\nGematria is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. Single word can yield several values depending on which cipher is used. This cipher is sometimes erroneously labelled as \"Jewish\" or \"Hebrew\" by popular numerology calculators, such as Gematrix and Gematrinator.\n\n[![A mathematical formula for finding a letter's corresponding number in Mispar Gadol](https://user-images.githubusercontent.com/8466209/226222755-1aa42385-145d-4fc5-81a3-54ebefa4e272.png)](https://en.wikipedia.org/wiki/Gematria#Standard_encoding)\n\n![](https://user-images.githubusercontent.com/36441664/77167537-ce0ae980-6ae8-11ea-869d-b4164b511755.jpg)\n\n```\n------+------+-----+-----+-----+-------- 7x + 6x = 13x\n | | | 7 | 11 | 20 | |\n | | 4 +-----+-----+ | |\n | 3 | | 8 | 12 | 26 ----- | |\n | +-----+-----+-----+ | | |\n | | | 9 | 13 | 27 2x ----- |\n 2 +------| 5 +-----+-----+ | |\n | | | 10 | 14 | 28 ----- |\n | |-----+-----+-----+ |\n | 4 | | 11 |15,18| 29,30,31,32 ←---4x-----\n | | 6 +-----+-----+\n | | | 12 | 19 | 36 ←--- 35,34,33 are missing\n------+------+-----+-----+-----+-------\n | | | 13 | 20 | {38}\n | | 7 +-----+-----+\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/198756338-2bc18ae7-c431-486f-9c30-412ca28c55da.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199130173-c106f4b1-7964-4f0b-ba3f-31119d7eb39f.png)](https://www.eq19.com/)\n\n[![default](https://user-images.githubusercontent.com/8466209/199134366-a6c1a115-6f4a-466e-a542-076c6d742d4c.png)](https://www.nvidia.com/en-us/data-center/graphics-cards-for-virtualization/)\n\n[![default](https://user-images.githubusercontent.com/8466209/199134523-93606dfd-1194-4983-80d0-7dda2e8ddace.png)](https://docs.nvidia.com/deeplearning/cudnn/install-guide/index.html#install-windows)\n\n[![tensorflow](https://user-images.githubusercontent.com/36441664/128624639-b5d8c73f-79af-4433-8b7b-28a35e331d21.png)](https://github.com/chetabahana/tensorflow/wiki#grounds)\n\n[![default](https://user-images.githubusercontent.com/8466209/199136893-391bd954-44a3-4767-8002-661f33b7391f.png)](https://github.com/NVIDIA/tensorflow)\n\n[![default](https://user-images.githubusercontent.com/8466209/199136378-f0cef6b2-a422-4f33-a88d-aebe5b38a690.png)](https://github.com/NVIDIA/nvidia-docker)\n\n","dir":"/identition/span4/","name":"gist05.md","path":"identition/span4/gist05.md","url":"/identition/span4/gist05.html"},{"layout":"default","title":null,"content":"![](https://user-images.githubusercontent.com/36441664/84945795-e43d3b80-b111-11ea-900a-f0b9236d7e69.png)\n\n```\n #8 |----------- 5® --------|------------ 7® --------------|\n | 1 |---------------- 77 = 4² + 5² + 6² -------------|\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78\n main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 100 - 123 ({24})\n |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30\n {98} | └── 110 - 123 (14x)» 70\n```\n\n> [Key Difference between Python vs Ruby](https://www.guru99.com/python-vs-ruby-difference.html)\n- Python support multiple inheritance, while Ruby support single inheritance.\n- Python is mainly used for academic, AI, machine learning, and scientific programming, while Ruby is used for web development and functional programming.\n- Python is not a fully object-oriented programming language. Whereas **Ruby is a fully object-oriented programming language**.\n- In Python, once a variable is set, you can’t unset it back, while in Ruby, it will be present in the symbol table as long as the variable is in scope.\n- Python lambda functions are larger, while Ruby supports only a single-line lambda function.\n- Python is very explicit and elegant to read, while Ruby can be very hard to debug at times.\n- Python has methods, while Ruby has functions.\n\n![default](https://user-images.githubusercontent.com/8466209/199273134-783707cf-b29c-44b1-8cd9-c45ad79990f7.png)\n![default](https://user-images.githubusercontent.com/8466209/199358225-8318b692-84c5-407a-a105-2498788948d5.png)\n![default](https://user-images.githubusercontent.com/8466209/199359482-4793b2d0-c04a-4f45-8bcc-87a2f30ad511.png)\n","dir":"/identition/span5/","name":"gist03.md","path":"identition/span5/gist03.md","url":"/identition/span5/gist03.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/195963923-0796217c-7a87-4b2d-ba93-f47465304c03.png)](https://www.nausetschools.org/cms/lib/MA02212418/Centricity/Domain/204/Linkage%20Map%20Worksheet%20Genetics%202017.pdf)\n\n```\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | ° |ΔΔΔΔ ΦΦ | • ΔΔ ΔΔ ¤ | • ΔΔ ΦΦΦ Φ ΦΦ ¤¤¤¤| • ΔΔ ΦΦΦ Φ ¤¤ ΦΦ | \n \n |----- 102 ---|----- 66 ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -|\n |---2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------|\n |--------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------|\n |--------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----|\n\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/198915985-f3280a15-1ca4-45bf-855c-ac277fa2ca2e.png)](https://www.hexspin.com/defining-the-prime-hexagon/)\n\n![default](https://user-images.githubusercontent.com/8466209/198837916-57284efa-bdb7-42d8-80f6-584b3c3bbd19.png)\n\n","dir":"/identition/span3/","name":"gist02.md","path":"identition/span3/gist02.md","url":"/identition/span3/gist02.html"},{"layout":"default","title":"System Storage","content":"## System Storage\n\nGitHub allows developers to run GitHub Actions workflows on your own runners. This [Docker image](https://hub.docker.com/r/tcardonne/github-runner#!) allows you to create your own runners on Docker, you can enable Docker siblings by binding the host Docker daemon socket.\n\n```\n$ cat /etc/os-release\n\nPRETTY_NAME=\"Debian GNU/Linux 10 (buster)\"\nNAME=\"Debian GNU/Linux\"\nVERSION_ID=\"10\"\nVERSION=\"10 (buster)\"\nVERSION_CODENAME=buster\nID=debian\nHOME_URL=\"https://www.debian.org/\"\nSUPPORT_URL=\"https://www.debian.org/support\"\nBUG_REPORT_URL=\"https://bugs.debian.org/\"\n```\n\nBy default, the df command shows the disk space used and available disk space in kilobytes. To display information about disk drives in human-readable format (kilobytes, megabytes, gigabytes and so on), invoke the df command with the -h option\n\n```\n$ df -h\nFilesystem Size Used Avail Use% Mounted on\n/dev/root 2.0G 1.1G 902M 54% /\ndevtmpfs 484M 0 484M 0% /dev\ntmpfs 487M 0 487M 0% /dev/shm\ntmpfs 195M 512K 195M 1% /run\ntmpfs 487M 112K 487M 1% /etc/machine-id\ntmpfs 256K 0 256K 0% /mnt/disks\ntmpfs 487M 0 487M 0% /tmp\noverlayfs 487M 112K 487M 1% /etc\n/dev/sda8 11M 24K 11M 1% /usr/share/oem\n/dev/sda1 5.7G 3.5G 2.2G 62% /mnt/stateful_partition\ntmpfs 2.0M 128K 1.9M 7% /var/lib/cloud\n/dev/sdb1 49G 9.9G 38G 22% /mnt/disks/Linux ◄- DEEP LEARNING\n```\n\nOn Unix-like operating systems, the set command is a built-in function of the Bourne shell ( sh ), C shell ( csh ), and Korn shell ( ksh ), which is used to define and determine the values of the system environment.\n\n```\n$ set\n\nACTIONS_ID_TOKEN_REQUEST_TOKEN=***\nACTIONS_ID_TOKEN_REQUEST_URL='https://pipelines.actions.githubusercontent.com/a18hGIuIy4qbY5KTUvkKiuBNsSHDVCEtnJ8x8NEYFPEBFH2tOZ/00000000-0000-0000-0000-000000000000/_apis/distributedtask/hubs/Actions/plans/7534b9e1-5505-4cff-9f7a-440ad58fadf5/jobs/55c239b7-523f-5586-aeb6-60a00c959946/idtoken?api-version=2.0'\nAGENT_TOOLSDIRECTORY=/opt/hostedtoolcache\nBASH=/bin/bash\nBASHOPTS=checkwinsize:cmdhist:complete_fullquote:extquote:force_fignore:globasciiranges:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath\nBASH_ALIASES=()\nBASH_ARGC=()\nBASH_ARGV=()\nBASH_CMDS=()\nBASH_LINENO=([0]=\"0\")\nBASH_SOURCE=([0]=\"/home/runner/_work/_temp/b00557e9-dc1d-40fb-a211-db6869b65693.sh\")\nBASH_VERSINFO=([0]=\"5\" [1]=\"0\" [2]=\"3\" [3]=\"1\" [4]=\"release\" [5]=\"x86_64-pc-linux-gnu\")\nBASH_VERSION='5.0.3(1)-release'\nCI=true\nDIRSTACK=()\nEUID=0\nGITHUB_ACCESS_TOKEN=***\nGITHUB_ACTION=__run\nGITHUB_ACTIONS=true\nGITHUB_ACTION_REF=\nGITHUB_ACTION_REPOSITORY=\nGITHUB_ACTOR=eq19\nGITHUB_ACTOR_ID=8466209\nGITHUB_API_URL=https://api.github.com\nGITHUB_BASE_REF=\nGITHUB_ENV=/home/runner/_work/_temp/_runner_file_commands/set_env_acae127c-173c-43fd-abea-f6d3fe882641\nGITHUB_EVENT_NAME=push\nGITHUB_EVENT_PATH=/home/runner/_work/_temp/_github_workflow/event.json\nGITHUB_GRAPHQL_URL=https://api.github.com/graphql\nGITHUB_HEAD_REF=\nGITHUB_JOB=github-pages\nGITHUB_OUTPUT=/home/runner/_work/_temp/_runner_file_commands/set_output_acae127c-173c-43fd-abea-f6d3fe882641\nGITHUB_PATH=/home/runner/_work/_temp/_runner_file_commands/add_path_acae127c-173c-43fd-abea-f6d3fe882641\nGITHUB_REF=refs/heads/eQ19\nGITHUB_REF_NAME=eQ19\nGITHUB_REF_PROTECTED=false\nGITHUB_REF_TYPE=branch\nGITHUB_REPOSITORY=FeedMapping/Partition\nGITHUB_REPOSITORY_ID=550855238\nGITHUB_REPOSITORY_OWNER=FeedMapping\nGITHUB_REPOSITORY_OWNER_ID=11927583\nGITHUB_RETENTION_DAYS=90\nGITHUB_RUN_ATTEMPT=1\nGITHUB_RUN_ID=4975344786\nGITHUB_RUN_NUMBER=88\nGITHUB_SERVER_URL=https://github.com\nGITHUB_SHA=a5ee1d5f656adf586a43252afce0a4ddc838ade4\nGITHUB_STATE=/home/runner/_work/_temp/_runner_file_commands/save_state_acae127c-173c-43fd-abea-f6d3fe882641\nGITHUB_STEP_SUMMARY=/home/runner/_work/_temp/_runner_file_commands/step_summary_acae127c-173c-43fd-abea-f6d3fe882641\nGITHUB_TRIGGERING_ACTOR=eq19\nGITHUB_WORKFLOW='Build and deploy Jekyll site'\nGITHUB_WORKFLOW_REF=FeedMapping/Partition/.github/workflows/github-pages.yml@refs/heads/eQ19\nGITHUB_WORKFLOW_SHA=a5ee1d5f656adf586a43252afce0a4ddc838ade4\nGITHUB_WORKSPACE=/home/runner/_work/Partition/Partition\nGROUPS=()\nHOME=/root\nHOSTNAME=ef75abdc2b19\nHOSTTYPE=x86_64\nIFS=$' \\t\\n'\nMACHTYPE=x86_64-pc-linux-gnu\nOPTERR=1\nOPTIND=1\nOSTYPE=linux-gnu\nPATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin\nPIPESTATUS=([0]=\"0\")\nPPID=17188\nPS4='+ '\n***\nRUNNER_ALLOW_RUNASROOT=true\nRUNNER_ARCH=X64\nRUNNER_LABELS=\nRUNNER_NAME=Google-optimized-instance\nRUNNER_ORGANIZATION_URL=https://github.com/FeedMapping\nRUNNER_OS=Linux\nRUNNER_REPLACE_EXISTING=true\nRUNNER_REPOSITORY_URL=\nRUNNER_TEMP=/home/runner/_work/_temp\nRUNNER_TOKEN=ACAS6IJKEQK3RSYCNEQ3Z53EL2JM6\nRUNNER_TOOL_CACHE=/opt/hostedtoolcache\nRUNNER_TRACKING_ID=github_b2590dca-5a63-4f9a-a8e2-68924e311fdc\nRUNNER_WORKSPACE=/home/runner/_work/Partition\nRUNNER_WORK_DIRECTORY=_work\nSHELL=/bin/bash\nSHELLOPTS=braceexpand:errexit:hashall:interactive-comments\nSHLVL=1\nSUPERVISOR_ENABLED=1\nSUPERVISOR_GROUP_NAME=runner\nSUPERVISOR_PROCESS_NAME=runner\nTERM=dumb\nUID=0\n_=-V\n```\n\n[![docker-github-runner](https://user-images.githubusercontent.com/8466209/229943878-e3d1cae4-15fd-43ab-9d7f-904a343b745c.png)](https://github.com/eq19/setup)\n\n\n```\ndocker info\ndocker --version\n\ndocker logout\ndocker login\n\ngit clone https://github.com/eq19/setup\ncd setup/docker\ndocker build -t setup .\n\ndocker images\ndocker tag setup:latest eq19/setup:latest\n\ndocker push eq19/setup:latest\n```\n\nFor now, there are only Debian Buster (tagged with latest and vX.Y.Z) and Ubuntu Focal (tagged with ubuntu-20.04 and vX.Y.Z-ubuntu-20.04) images, but I may add more variants in the future. Feel free to create an issue if you want another base image.\n\n[![default](https://user-images.githubusercontent.com/8466209/238171580-d65c5bcb-7ae9-498d-841f-b645e08c49b2.png)](https://registry.hub.docker.com/r/tcardonne/github-runner/tags)\n\nWhen comparing Chromium OS vs Debian GNU/Linux, the Slant community recommends Debian GNU/Linux for most people. In the question“What are the best Linux distributions for desktops?” Debian GNU/Linux is ranked 3rd while Chromium OS is ranked 88th. The most important reason people chose Debian GNU/Linux is:\n\n> Debian offers stable and testing CD images specifically built for GNOME (the default), KDE Plasma Workspaces, Xfce and LXDE. Less common window managers such as Enlightenment, Openbox, Fluxbox, GNUstep, IceWM, Window Maker and others can also be installed _([Slant](https://www.slant.co/versus/2691/2692/~chromium-os_vs_debian-gnu-linux))_.\n\n[![chromium-os_vs_debian-gnu-linux](https://user-images.githubusercontent.com/8466209/238179595-7f087116-910c-4cf9-8b1b-1051e74f93d4.png)](https://www.slant.co/versus/2691/2692/~chromium-os_vs_debian-gnu-linux)\n\nFor most frameworks, Debian 10 is the default OS. Ubuntu 20.04 images are available for some frameworks. They are denoted by the -ubuntu-2004 suffixes in the image family name (see [Listing all available versions](https://cloud.google.com/deep-learning-vm/docs/images#listing-versions)). Debian 9 images have been deprecated.\n\n[![Deep Learning VM Images\n](https://user-images.githubusercontent.com/8466209/238179451-d71d776a-883f-4978-b60a-50a25a6c8572.png)](https://cloud.google.com/deep-learning-vm/docs/images#choosing_an_operating_system)\n\nYou can pull a container image and show the \"[history](https://stackoverflow.com/a/75291419/2023941)\" for the container. This shows you how it is built and what the original starting image. This does not mean that you access the original image. You can add to and remove parts of the image. You can also export an image to a tar archive file, modify and then reimport\n\n```\n{% raw %}\n$ docker history gcr.io/deeplearning-platform-release/tf-cpu:m96 --format \" {{.CreatedBy}}\" --no-trunc\n\nRUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c cd /opt/google/licenses && chmod +x query_licenses.sh && ./query_licenses.sh # buildkit\nRUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c BAZEL_INSTALLER_URL=\"https://github.com/bazelbuild/bazel/releases/download/0.19.0/bazel-0.19.0-installer-linux-x86_64.sh\" && BAZEL_INSTALLER_FILE=\"bazel_installer.sh\" && wget -q \"${BAZEL_INSTALLER_URL}\" -O \"${BAZEL_INSTALLER_FILE}\" && chmod +x \"${BAZEL_INSTALLER_FILE}\" && \"./${BAZEL_INSTALLER_FILE}\" && rm -rf \"./${BAZEL_INSTALLER_FILE}\" # buildkit\nRUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c export CONDA_REPOSITORY=\"/tmp/conda\" && chmod +x /opt/google/conda/install_to_env.sh && ENV_DOCKER=1 /opt/google/conda/install_to_env.sh base dlenv-tf-${VERSION}-cpu-meta # buildkit\nENV KMP_SETTINGS=1\nENV KMP_AFFINITY=granularity=fine,verbose,compact,1,0\nENV KMP_BLOCKTIME=0\nENV CONTAINER_NAME=tf-cpu/1-15\nARG CONTAINER_NAME\nLABEL com.google.environment=Container: TensorFlow 1-15\nARG VERSION\nCMD [\"/run_jupyter.sh\"]\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x run_jupyter.sh # buildkit\nCOPY build/container/run_jupyter.sh /run_jupyter.sh # buildkit\nENTRYPOINT [\"/entrypoint.sh\"]\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x entrypoint.sh # buildkit\nCOPY build/container/entrypoint.sh /entrypoint.sh # buildkit\nCOPY build/package/conda/channels.json /opt/google/conda/channels.json # buildkit\nCOPY build/package/packages/jupyter/jupyter_notebook_config.py /opt/jupyter/.jupyter/jupyter_notebook_config.py # buildkit\nCOPY build/package/packages/jupyter/ipython_kernel_config.py /etc/ipython/ipython_kernel_config.py # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chown -R \"jupyter:jupyter\" \"/home/jupyter/.\" # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c adduser --uid 1000 --gid 1001 jupyter # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c addgroup --gid 1001 jupyter # buildkit\nENV LD_LIBRARY_PATH=/usr/local/cuda/lib64:/usr/local/cuda/lib:/usr/local/lib/x86_64-linux-gnu:/usr/local/nvidia/lib:/usr/local/nvidia/lib64:\nVOLUME [/home/jupyter]\nEXPOSE map[8080/tcp:{}]\nENV SHELL=/bin/bash\nENV PATH=/opt/conda/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x /opt/google/conda/provision_conda.sh && /opt/google/conda/provision_conda.sh # buildkit\nENV DL_ANACONDA_HOME=/opt/conda\nENV ANACONDA_PYTHON_VERSION=3.7\nCOPY build/vm/packer/generic/packages /opt/google # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c cd / && gsutil cp -r gs://dl-platform-binaries-builds/openmpi-4.0.2/v20191105/openmpi.tar.gz . && tar xf openmpi.tar.gz && rm -f openmpi.tar.gz # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt update -y && apt install -y libnuma-dev # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c if dpkg -s libnccl2; then echo \"deb https://packages.cloud.google.com/apt google-fast-socket main\" | tee /etc/apt/sources.list.d/google-fast-socket.list && curl -s -L https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add - && apt-get --allow-releaseinfo-change update && apt install -y google-fast-socket; fi # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt-get --allow-releaseinfo-change update -y && apt-get install -y dirmngr && apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 8B57C5C2836F4BEB && apt-key adv --keyserver keyserver.ubuntu.com --recv-keys FEEA9169307EA071 && apt-get --allow-releaseinfo-change update -y && echo \"deb [signed-by=/usr/share/keyrings/cloud.google.gpg] https://packages.cloud.google.com/apt cloud-sdk main\" | tee -a /etc/apt/sources.list.d/google-cloud-sdk.list && curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key --keyring /usr/share/keyrings/cloud.google.gpg add - && apt-get --allow-releaseinfo-change update -y && apt-get install -y apt-transport-https ca-certificates gnupg && echo \"deb http://packages.cloud.google.com/apt gcsfuse-focal main\" | tee /etc/apt/sources.list.d/gcsfuse.list && curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add - && apt-get --allow-releaseinfo-change update -y && apt-get install -y google-cloud-sdk && apt-get install -y gcsfuse && rm -rf /var/lib/apt/lists/* # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt-get --allow-releaseinfo-change -o Acquire::Check-Valid-Until=false update -y && apt-get install --no-install-recommends -y -q $(grep -vE \"^\\s*#\" aptget-requirements.txt | tr \"\\n\" \" \") && rm -rf /var/lib/apt/lists/* && rm -rf aptget-requirements.txt # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c if [ \"${BASE_IMAGE}\" =~ \"^nvidia. *\" ]; then apt update -y || true && apt install -y wget && apt install -yq software-properties-common && wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/cuda-ubuntu2004.pin && mv cuda-ubuntu2004.pin /etc/apt/preferences.d/cuda-repository-pin-600 && apt-key adv --fetch-keys https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/3bf863cc.pub && add-apt-repository \"deb https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/ /\" && apt-get --allow-releaseinfo-change update; fi # buildkit\nCOPY build/vm/packer/base/aptget-requirements.txt /aptget-requirements.txt # buildkit\nRUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt update --allow-releaseinfo-change -y && apt upgrade -y # buildkit\nARG DEBIAN_FRONTEND=noninteractive\nENV LANG=C.UTF-8\nENV LC_ALL=C.UTF-8\nLABEL com.google.environment=Container: Minimal\n{% endraw %}\n```\n![Untitled](https://user-images.githubusercontent.com/8466209/255381318-7cd95f34-ee40-4d02-bea8-3d72ff9bb4af.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198933143-1d783ccf-22a1-4415-9a11-8effe98d1741.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198837916-57284efa-bdb7-42d8-80f6-584b3c3bbd19.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198934268-1570c3cc-5a90-48b3-a1e6-b016c2d93ab4.png)\n","dir":"/identition/span3/","name":"gist06.md","path":"identition/span3/gist06.md","url":"/identition/span3/gist06.html"},{"layout":"default","title":null,"content":"![](https://user-images.githubusercontent.com/36441664/84743844-b0acc500-afdc-11ea-8311-3affd4bf0c69.gif)\n\n![](https://user-images.githubusercontent.com/36441664/84656283-a2a76780-af3c-11ea-930d-049952522888.png)\n\n![](https://user-images.githubusercontent.com/36441664/69990325-04434e00-1578-11ea-9e5a-c86bd88fe706.png)\n\nThis recombination scheme shall be made available on each of _[instance](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ that composing _[7 blocks](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)_. Since these blocks are spread in to _[29 flats](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-mapping-md)_ that bring a total of _[77 rooms](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-portal-md)_ then the total objects per instance would become ***114***.\n\n![](https://user-images.githubusercontent.com/36441664/76367716-7211c980-6360-11ea-9f36-728b57c9ca34.png)\n\n***Φ(13:9) = Φ(29th prime) = Φ(109) = (2+69) + 68 = 71 + 68 = 139***\n\n```\n -------------------+-----+-----+ ---\n 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ |\n | +-----+-----+ |\n | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class\n | | +-----+-----+-----+-----+-----+ | |\n | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} |\n | | | +-----+-----+-----+-----+-----+ | | ---\n --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- |\n | | +-----+-----+ | |\n --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object\n168 | +-----+ |\n| 102 -› 29:18| 50 | 50(68) ---------> Δ18 |\n----------------------+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/36441664/84648825-c1ebc800-af2f-11ea-88d5-9446b711cfe5.png)\n\n![](https://user-images.githubusercontent.com/36441664/84744689-c4a4f680-afdd-11ea-80b7-6cd6566e42f9.png)\n\nIn this analogy, the basic question is: is the puzzle really as hard as we think, or are we missing something? This issue was first raised by the baffling Austrian-American mathematician Kurt Gödel. It was formulated as ***[P ≠ NP](https://en.wikipedia.org/wiki/P_versus_NP_problem)*** by Stephen Cook in 1971.\n\n![](https://user-images.githubusercontent.com/36441664/85101079-c532cc80-b22b-11ea-86a1-49ddf8b18a71.jpg)\n\nP is a polynomial and NP is a non-deterministic polynomial. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. In simpler terms, P means a problem that is easily solved by a computer, and NP means a problem that a computer is not easy to solve but is easy to check.\n\n![](https://user-images.githubusercontent.com/36441664/84743524-4b58d400-afdc-11ea-9e64-5306a5811a33.jpg)\n\n[![default](https://user-images.githubusercontent.com/8466209/198754036-1629e06f-5741-4d8d-8ff4-aa6127ecbd08.png)](https://github.com/myoung34/docker-github-actions-runner)\n\n[![default](https://user-images.githubusercontent.com/8466209/198806388-ee9c460b-0a44-4659-ab0a-35c1a68cbbb8.png)](https://docs.github.com/en/actions/hosting-your-own-runners/adding-self-hosted-runners#adding-a-self-hosted-runner-to-a-repository)\n\n[![default](https://user-images.githubusercontent.com/8466209/198812060-bcf0c3e5-1918-4245-b2fa-1c43c2602a90.png)](https://www.chetabahana.com/)\n","dir":"/identition/span2/","name":"gist07.md","path":"identition/span2/gist07.md","url":"/identition/span2/gist07.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | {1} |{11}\n---+-----+-----\n 2 | 12 | 32\n---+-----+-----\n 3 | 33 |{50}\n---+-----+-----\n 4 | 51 |{86}\n---+-----+-----\n 5 | 87 | 108\n---+-----+-----\n 6 |{109}| 120\n---+-----+----- ---\n```\n\n[![default](https://user-images.githubusercontent.com/36441664/76159498-b1b79600-6153-11ea-91e4-bc312f9456ac.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#scheme-139)\n![](https://user-images.githubusercontent.com/36441664/99020210-96c5dd00-2590-11eb-8201-7590eb31ac59.jpg)\n\n>In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in ***four-dimensional space*** _([Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture))_.\n\n![](https://user-images.githubusercontent.com/36441664/82712407-12b22d00-9cb2-11ea-9cc2-3cf392b2d35c.png)\n![default](https://user-images.githubusercontent.com/8466209/199263778-d09e3d86-c438-4447-8689-29178dbd367f.png)\n[![default](https://user-images.githubusercontent.com/8466209/199364235-ce289eeb-27ee-4d2f-a36b-1b220831f922.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155)\n","dir":"/identition/span5/","name":"gist07.md","path":"identition/span5/gist07.md","url":"/identition/span5/gist07.html"},{"layout":"default","title":null,"content":"```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/199502657-1ba96c92-29f9-41ec-90a9-cbc5adec9464.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-runner-md)\n\n","dir":"/identition/span6/","name":"gist06.md","path":"identition/span6/gist06.md","url":"/identition/span6/gist06.html"},{"layout":"default","title":"License","content":"### License\n\nEvery organization that has at least one licensed Microsoft 365 user (with an E1, E3, E5, F1, and F3 subscription) or uses Microsoft cloud services such as Azure or Intune also has an Azure Active Directory tenant.\n```\nMicrosoft 365 A3 for students use benefit\nInformation Barriers\nMicrosoft Bookings\nUniversal Print Without Seeding\nProject for Office (Plan E3)\nCommon Data Service\nInformation Protection for Office 365 - Standard\nEducation Analytics\nMicrosoft Kaizala Pro\nMicrosoft Search\nWhiteboard (Plan 2)\nMicrosoft Intune Plan 1 for Education\nMicrosoft Defender for Cloud Apps Discovery\nTo-Do (Plan 2)\nWindows 10/11 Enterprise\nMinecraft Education Edition\nMicrosoft Intune Plan 1\nMicrosoft Azure Multi-Factor Authentication\nAzure Active Directory Premium P1\nAzure Active Directory Basic for Education\nMicrosoft Stream for Office 365 E3\nSchool Data Sync (Plan 2)\nAzure Rights Management\nMicrosoft Teams\nSway\nMicrosoft StaffHub\nPower Apps for Office 365\nPower Automate for Office 365\nMicrosoft Forms (Plan 2)\nMicrosoft Planner\nYammer for Academic\nSkype for Business Online (Plan 2)\nOffice for the Web for Education\nSharePoint (Plan 2) for Education\nExchange Online (Plan 2)\nOffice 365 Cloud App Security\nThe latest desktop version of Office\n```\n\nThere are, however, different editions of Azure AD licenses that provide the organization with different capabilities: Azure AD Free/Office 365, Premium P1, and Premium P2.\n\n![default](https://user-images.githubusercontent.com/8466209/229310273-8b633a45-59f6-4366-ba19-e22522beb94b.png)\n\nThough lower tiers of AAD have certain limitations, such as with the number of apps and directory objects IT teams can manage, Azure AD Premium P2’s feature set offers admins the opportunity to thoroughly manage their users and their SSO access.\n\n### Azure AD\n\nAzure Active Directory (Azure AD) is a cloud-based identity and access management service. Azure AD enables your employees access external resources, such as Microsoft 365, the Azure portal, and thousands of other SaaS applications.\n\n>Azure Active Directory also helps them access internal resources like apps on your corporate intranet, and any cloud apps developed for your own organization _([Microsoft](https://learn.microsoft.com/en-us/azure/active-directory/fundamentals/active-directory-whatis))_.\n\n[![Azure Active Directory](https://user-images.githubusercontent.com/8466209/229262526-f13a7f1a-f2da-45e3-9cc9-3d0f70bc3b21.png)](https://learn.microsoft.com/en-us/azure/active-directory/fundamentals/active-directory-whatis)\n\nAzure AD [Premium P2](https://petri.com/azure-active-directory-premium-p1-vs-p2/#Active_Directory_Premium_P1_vs_P2_Which_plan_is_right_for_you) licenses are beneficial for organizations that are expected to demonstrate a high level of governance of identities. That implies managing privileged access and automating access reviews and responses to potentially compromised accounts.\n\n[![Azure AD Premium P2](https://user-images.githubusercontent.com/8466209/229264239-2d34a7c4-0caf-4148-8c86-d4bc1a1e0ba9.png)](https://entra.microsoft.com/)\n\nAAD Premium P2 offers the following features:\n\n```\nAll of the features listed for Azure AD Microsoft 365 apps \nLeverage SSO for an unlimited number of pre-integrated SaaS applications\nConfigure self-service application assignment to enable users to self-discover and request access to applications\nOn-prem write-back for all password changes\nAdvanced usage reporting\nHR-driven provisioning\nSelf-service group management and application management \nMicrosoft® Identity Management (MIM) CAL + MIM server for simplified lifecycle user management\nConditional access based on device state or location and group\nAutomate password rollover for group accounts\nJoin a Windows® Pro device to Azure AD to enable desktop SSO, and Administrator BitLocker recovery\nApplication proxy for on-premises, header-based, and Integrated Windows Authentication\nMDM auto-enrollment, self-service BitLocker recovery, additional local admin tooling to Windows Pro devices via Azure AD Join\nRole-based access control (RBAC)\nRisk-based Identity Protection \nPrivileged identity management\nSelf-service entitlement management (My Access)\nAccess certifications and reviews\nEntitlements management\nLifecycle Workflows (preview)\nPrivileged Identity Management (PIM), just-in-time access\nCloud app discovery (Windows Defender for cloud apps)\nIdentity Protection reporting: vulnerabilities and risky accounts\nIdentity Protection reporting: risk events investigation, SIEM connectivity\nA service-level agreement\n```\n\nAzure AD Premium P2 is most commonly used for providing insight into user activity within Azure infrastructure, Microsoft 365, and web applications. \n\n[![Azure Active Directory Premium P1 vs. P2: Features comparison](https://user-images.githubusercontent.com/8466209/229262780-3143c0e6-ad52-4dd6-8351-12be563efc8c.png)](https://petri.com/azure-active-directory-premium-p1-vs-p2/#Azure_Active_Directory_Premium_P1_vs_P2_Features_comparison)\n\n### Storage\n\n![default](https://user-images.githubusercontent.com/8466209/229309763-6b4571aa-5373-4552-93a6-7028f75cf053.png)\n[![default](https://user-images.githubusercontent.com/8466209/199137654-16103a10-3167-4a08-b128-dfdd5e169674.png)](https://user-images.githubusercontent.com/36441664/121343696-2bd55c80-c94d-11eb-9aff-76843fb799b6.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/199134564-15e8f3f8-02b6-41f7-9d89-9a000faf04bf.png)](https://github.com/chetabahana/tensorflow/wiki/Tensor-Kit#updating)\n\n","dir":"/identition/span4/","name":"gist06.md","path":"identition/span4/gist06.md","url":"/identition/span4/gist06.html"},{"layout":"default","title":"Project Repositories","content":"# Project Repositories\n\n```\n(5, 2, 1, 0)\n(7, 3, 1, 0)\n(11, 4, 1, 0)\n(13, 5, 1, 0)\n(17, 0, 1, 1)\n(19, 1, 1, 1)\n(23, 2, 1, 1)\n(29, 2, -1, 1)\n(31, 1, -1, 1)\n(37, 1, 1, 1)\n(41, 2, 1, 1)\n(43, 3, 1, 1)\n(47, 4, 1, 1)\n(53, 4, -1, 1)\n(59, 4, 1, 1)\n(61, 5, 1, 1)\n(67, 5, -1, 1)\n(71, 4, -1, 1)\n(73, 3, -1, 1)\n(79, 3, 1, 1)\n(83, 4, 1, 1)\n(89, 4, -1, 1)\n(97, 3, -1, 1)\n(101, 2, -1, 1)\n(103, 1, -1, 1)\n(107, 0, -1, 1)\n(109, 5, -1, 0)\n(113, 4, -1, 0)\n(127, 3, -1, 0)\n(131, 2, -1, 0)\n(137, 2, 1, 0)\n(139, 3, 1, 0)\n(149, 4, 1, 0)\n(151, 5, 1, 0)\n(157, 5, -1, 0)\n(163, 5, 1, 0)\n(167, 0, 1, 1)\n(173, 0, -1, 1)\n(179, 0, 1, 1)\n(181, 1, 1, 1)\n(191, 2, 1, 1)\n(193, 3, 1, 1)\n(197, 4, 1, 1)\n(199, 5, 1, 1)\n(211, 5, -1, 1)\n(223, 5, 1, 1)\n(227, 0, 1, 2)\n(229, 1, 1, 2)\n(233, 2, 1, 2)\n(239, 2, -1, 2)\n(241, 1, -1, 2)\n(251, 0, -1, 2)\n(257, 0, 1, 2)\n(263, 0, -1, 2)\n(269, 0, 1, 2)\n(271, 1, 1, 2)\n(277, 1, -1, 2)\n(281, 0, -1, 2)\n(283, 5, -1, 1)\n(293, 4, -1, 1)\n(307, 3, -1, 1)\n(311, 2, -1, 1)\n(313, 1, -1, 1)\n(317, 0, -1, 1)\n(331, 5, -1, 0)\n(337, 5, 1, 0)\n(347, 0, 1, 1)\n(349, 1, 1, 1)\n(353, 2, 1, 1)\n(359, 2, -1, 1)\n(367, 1, -1, 1)\n(373, 1, 1, 1)\n(379, 1, -1, 1)\n(383, 0, -1, 1)\n(389, 0, 1, 1)\n(397, 1, 1, 1)\n(401, 2, 1, 1)\n(409, 3, 1, 1)\n(419, 4, 1, 1)\n(421, 5, 1, 1)\n(431, 0, 1, 2)\n(433, 1, 1, 2)\n(439, 1, -1, 2)\n(443, 0, -1, 2)\n(449, 0, 1, 2)\n(457, 1, 1, 2)\n(461, 2, 1, 2)\n(463, 3, 1, 2)\n(467, 4, 1, 2)\n(479, 4, -1, 2)\n(487, 3, -1, 2)\n(491, 2, -1, 2)\n(499, 1, -1, 2)\n(503, 0, -1, 2)\n(509, 0, 1, 2)\n(521, 0, -1, 2)\n(523, 5, -1, 1)\n(541, 5, 1, 1)\n(547, 5, -1, 1)\n(557, 4, -1, 1)\n(563, 4, 1, 1)\n(569, 4, -1, 1)\n(571, 3, -1, 1)\n(577, 3, 1, 1)\n(587, 4, 1, 1)\n(593, 4, -1, 1)\n(599, 4, 1, 1)\n(601, 5, 1, 1)\n(607, 5, -1, 1)\n(613, 5, 1, 1)\n(617, 0, 1, 2)\n(619, 1, 1, 2)\n(631, 1, -1, 2)\n(641, 0, -1, 2)\n(643, 5, -1, 1)\n(647, 4, -1, 1)\n(653, 4, 1, 1)\n(659, 4, -1, 1)\n(661, 3, -1, 1)\n(673, 3, 1, 1)\n(677, 4, 1, 1)\n(683, 4, -1, 1)\n(691, 3, -1, 1)\n(701, 2, -1, 1)\n(709, 1, -1, 1)\n(719, 0, -1, 1)\n(727, 5, -1, 0)\n(733, 5, 1, 0)\n(739, 5, -1, 0)\n(743, 4, -1, 0)\n(751, 3, -1, 0)\n(757, 3, 1, 0)\n(761, 4, 1, 0)\n(769, 5, 1, 0)\n(773, 0, 1, 1)\n(787, 1, 1, 1)\n(797, 2, 1, 1)\n(809, 2, -1, 1)\n(811, 1, -1, 1)\n(821, 0, -1, 1)\n(823, 5, -1, 0)\n(827, 4, -1, 0)\n(829, 3, -1, 0)\n(839, 2, -1, 0)\n(853, 1, -1, 0)\n(857, 0, -1, 0)\n(859, 5, -1, -1)\n(863, 4, -1, -1)\n(877, 3, -1, -1)\n(881, 2, -1, -1)\n(883, 1, -1, -1)\n(887, 0, -1, -1)\n(907, 5, -1, -2)\n(911, 4, -1, -2)\n(919, 3, -1, -2)\n(929, 2, -1, -2)\n(937, 1, -1, -2)\n(941, 0, -1, -2)\n(947, 0, 1, -2)\n(953, 0, -1, -2)\n(967, 5, -1, -3)\n(971, 4, -1, -3)\n(977, 4, 1, -3)\n(983, 4, -1, -3)\n(991, 3, -1, -3)\n(997, 3, 1, -3)\n```\n\n![](https://user-images.githubusercontent.com/8466209/218319845-23639b98-a087-4bf5-afd9-2af9dfabcdfb.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/84945795-e43d3b80-b111-11ea-900a-f0b9236d7e69.png)\n\n[![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Eulerangles.svg/300px-Eulerangles.svg.png)](https://en.wikipedia.org/wiki/Euler_angles)\n\n***139 = 34th prime =(2x17)th prime***\n\n```\nScheme 13:9\n===========\n(1){1}-7: 7’\n(1){8}-13: 6‘\n(1)14-{19}: 6‘\n------------- 6+6 -------\n(2)20-24: 5’ |\n(2)25-{29}: 5’ |\n------------ 5+5 -------\n(3)30-36: 7:{70,30,10²}|\n------------ |\n(4)37-48: 12• --- |\n(5)49-59: 11° | |\n --}30° 30• |\n(6)60-78: 19° | |\n(7)79-96: 18• --- |\n-------------- |\n(8)97-109: 13 |\n(9)110-139:{30}=5x6 <--x-- (129/17-139/27)\n --\n {43}\n```\n\n![](https://user-images.githubusercontent.com/36441664/84743646-6fb4b080-afdc-11ea-86de-d072f0c047a5.gif)\n\n[![P versus NP](https://user-images.githubusercontent.com/36441664/84533710-e6b72400-ad12-11ea-9ee5-a8b57b8855fb.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-portal-md)\n\n![default](https://user-images.githubusercontent.com/8466209/218370587-ec438d91-be88-408a-a746-ff1e6324a514.png)\n\n```\nM: 6® = (2,{3}), ({29,30,31,32}) --> 2,89+29,3 = 289+329 = 618 (main)\nF: 6'® = (40,41), (43,44,45,46) --> 30+30+10+10+10+10 = 60+40 (user)\nC1: 10°® = 3*®+3*®+4® = (7,13,19),(20,27,36),({38,42,50,68}) --> 200 (main)\nC2: 7® = 5®+2® = 1®+4*®+2*® = 1®+6*® = 10,(11,12,14,15,26,28) --> 168 (user)\n```\n\n***π (Φ (329 + 289)) = π (Φ x 618) = π (1000) = 168***\n\n```\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\n## Pinned Repo\n\n### User repos\n\n```\n# pinned repos\n# https://dev.to/thomasaudo/get-started-with-github-grapql-api--1g8b\necho -e \"\\n$hr\\nPINNED REPOSITORIES\\n$hr\"\nAUTH=\"Authorization: bearer $JEKYLL_GITHUB_TOKEN\"\ncurl -L -X POST \"${GITHUB_GRAPHQL_URL}\" -H \"$AUTH\" \\\n--data-raw '{\"query\":\"{\\n user(login: \\\"'${GITHUB_REPOSITORY_OWNER}'\\\") \\\n{\\n pinnedItems(first: 6, types: REPOSITORY) {\\n nodes {\\n ... on Repository \\\n{\\n name\\n }\\n }\\n }\\n }\\n}\"'\n\n================================================================================\nPINNED REPOSITORIES\n================================================================================\n % Total % Received % Xferd Average Speed Time Time Time Current\n Dload Upload Total Spent Left Speed\n\n 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0\n100 292 100 150 100 142 1171 1109 --:--:-- --:--:-- --:--:-- 2281\n\n{\"data\":{\"user\":{\"pinnedItems\":{\"nodes\":[{\"name\":\"maps\"},{\"name\":\"feed\"},\n{\"name\":\"lexer\"},{\"name\":\"parser\"},{\"name\":\"syntax\"},{\"name\":\"grammar\"}]}}}}\n```\n\n### Organization (View as: Public\n\nGitHub graphQL API [multiple queries](https://stackoverflow.com/questions/51047292/github-graphql-api-multiple-queries-on-organizations-repositories) on organizations & \n\n```\ncurl -L -X POST \"${GITHUB_GRAPHQL_URL}\" -H \"$AUTH\" \\\n--data-raw '{\"query\":\"{\\n organization(login: \\\"'${GITHUB_REPOSITORY_OWNER}'\\\") \\ \n{\\n pinnedItems(first: 6, types: REPOSITORY) {\\n nodes {\\n ... on Repository \\ \n{\\n name\\n }\\n }\\n }\\n }\\n}\"'\n\n================================================================================\nPINNED REPOSITORIES\n================================================================================\n % Total % Received % Xferd Average Speed Time Time Time Current\n Dload Upload Total Spent Left Speed\n\n 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0\n100 292 100 150 100 142 1171 1109 --:--:-- --:--:-- --:--:-- 2281\n\n{\"data\":{\"organization\":{\"pinnedItems\":{\"nodes\":[{\"name\":\"classifier\"},\n{\"name\":\"domJSON\"},{\"name\":\"openoffice\"},{\"name\":\"landing-page-theme\"},\n{\"name\":\"asciidoc\"},{\"name\":\"recommendations-ai\"}]}}}}\n```\n\n***1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects***\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\n-----+-----+-----+-----+-----+ -----------------------------------------------\n{786}| 1,2 | 2 | 2,3 | 3,4 | {19} |\n-----+-----+-----+-----+-----+ |\n {86}| 4 | 4,5 | 5,6 |{6,7}| 17 Base Zone\n +-----+-----+-----+-----+ |\n {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ |\n +-----+-----+-----+ -----------\n {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone |\n ----+-----+-----+-----+-----+ |\n {6}|15,16|17,18|18,20|21,22| 19 Mirror Zone\n +-----+-----+-----+-----+ |\n {8}|23,25|25,27|27,29| 18 |\n +-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------\n {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------\n | 1 2 3 | 4 5 6 | 7 8 9 |\n |------ 29' ------|--------------- 139' ----------------|\n |------ 102¨ -----|--------------- 66¨ ----------------|\n```\n\n***114 = 102 + 66 - 29 - 25 = 6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 25 + 89***\n\n![image](https://user-images.githubusercontent.com/8466209/200228344-9f344f49-3e5d-480f-b11c-6e30a20a8f44.jpg)\n\n***6 x 114 - 30 - 30 - 5 = 619 = 6 x 19 = 114th prime***\n\n[![](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-1_prime-md)\n\n***π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786***\n\n[![default](https://user-images.githubusercontent.com/8466209/198191314-6ca520ed-6aea-40c0-8f89-3d1d1a83dc1e.png)](https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners#using-a-github-hosted-runner)\n\nTo make it easier to develop a program following a model, we divide the object by placing it into a smaller objects. We do this division by adopting the _[OOP (Object Oriented Programming)](https://www.google.com/search?q=object+oriented+programming&tbm=isch)_ which is an object-oriented programming method.\n\n***139 + 286 + 114 + 247 + 157 + 786 = 786 + 157 + 786 = 1729 = 7 x 13 x 19***\n\n![](https://user-images.githubusercontent.com/8466209/199355377-8d93057a-769d-49ed-b401-722c0b33fdab.png)\n\n***168 + 329 + 289 = 168 + 618 = 786***\n\n![default](https://user-images.githubusercontent.com/8466209/218931333-c4c8bd23-c05d-4af0-9b02-afa3079ef9b8.png)\n\nUsing this method then out of bilateray way of ***19 vs 18*** we could get in to _[Scheme-33](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-entrance-md)_. By a _[decomposition](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-target-md)_ the subject is divided into six (6) parts, each part is further regrouped in to 19 sub-parts so finaly we got π(1000/Φ)=π(618)=114 objects.\n\n***d(43,71,114) = d(7,8,6) » 786***\n\n[![default](https://user-images.githubusercontent.com/8466209/201287114-4819b99d-9815-4fc8-b994-7d3ca606b99e.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md)\n\nBy defining the pattern on each individual numbers against _[homogeneous sorting](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#interpolation)_ out of these 114 objects then we finally come to a scale called _[MEC30](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#identity)_ which is based on the beauty of ***Euler's identity***.\n\n>Mathematics writer Constance Reid has opined that [Euler's identity](https://en.wikipedia.org/wiki/Euler%27s_identity) is ***the most famous formula in all mathematics***. And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler's identity during a lecture, stated that the identity \"is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth\" _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity#Mathematical_beauty))_\n\n[![default](https://user-images.githubusercontent.com/8466209/219573505-52af4aec-3e02-4259-9f67-8bfe7424a8fb.png)](https://en.wikipedia.org/wiki/Euler%27s_identity)\n\nAlthough this may seem very fast, a much more sophisticated method, combined with a very powerful computer, is necessary to find very large primes. Despite there are many [studies](https://github.com/search?q=Riemann+Hypothesis&type=Repositories) and [papers](https://arxiv.org/search/advanced?advanced=&terms-0-operator=AND&terms-0-term=Riemann+Hypothesis&terms-0-field=title&terms-1-operator=AND&terms-1-term=prime&terms-1-field=abstract&classification-mathematics=y&classification-physics_archives=all&classification-include_cross_list=include&date-filter_by=all_dates&date-year=&date-from_date=&date-to_date=&date-date_type=submitted_date&abstracts=show&size=50&order=-announced_date_first) it is still an important [open problem](http://www.claymath.org/sites/default/files/official_problem_description.pdf) today.\n\n> The Millennium Prize Problems are ***seven problems*** in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved _([Wikipedia](https://en.wikipedia.org/wiki/7#Mathematics))_.\n\n![](https://user-images.githubusercontent.com/36441664/84532586-b2daff00-ad10-11ea-9880-ff7e97858cd3.gif)\n\nIn the next section we will discuss about algorithms in applications and their [relation](https://github.com/eq19/parser/files/10730998/Visualising.the.Riemann.Hypothesis.pdf) to the distribution of prime numbers.\n","dir":"/identition/span2/","name":"gist08.md","path":"identition/span2/gist08.md","url":"/identition/span2/gist08.html"},{"layout":"default","title":"Why is 7 the most feared number?","content":"## Why is 7 the most feared number?\n\n[![default](https://user-images.githubusercontent.com/8466209/199844359-3f898aad-0661-4ccb-9d90-1e2aadbdf662.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde#file-feeding-md)\n\n```\n 3 4 6 6\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↓\n 4 pairs 4 pairs\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/199874512-8d89c3b9-832c-48b7-91f3-e422bb2cc8bb.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-dockerfile-md)\n\n![default](https://user-images.githubusercontent.com/8466209/200098839-e77950cb-a21d-4103-acb6-02349fd7fdd8.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/200098936-de751345-d67a-4783-b3a7-e0326ed56051.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md)\n","dir":"/identition/span7/","name":"gist04.md","path":"identition/span7/gist04.md","url":"/identition/span7/gist04.html"},{"layout":"default","title":null,"content":"![image](https://user-images.githubusercontent.com/8466209/213899950-c5f53981-5d6e-45c8-ae66-b03ab48398e0.png)\n\n![image](https://user-images.githubusercontent.com/8466209/213900039-f2a73c24-1bc2-4953-bf0d-a52ec49b81b9.png)\n\n![image](https://user-images.githubusercontent.com/36441664/86006520-46663c80-ba40-11ea-8397-ee81ce56387c.gif)\n\n![image](https://user-images.githubusercontent.com/8466209/219372127-1fc0a0ad-5a58-4577-911f-478f7b7e5965.png)\n\n![default](https://user-images.githubusercontent.com/36441664/101850765-04175e80-3b8d-11eb-9e7a-5f049fb81347.png)\n\n96 is the smallest integer n for which [π(n) = n/4](https://primes.utm.edu/curios/page.php/96.html).\n\n***π(96) = π(4x24) = 24***\n\n![102](https://user-images.githubusercontent.com/8466209/216648703-35abad71-1395-49f5-bb9a-fa80fdf04e03.png)\n\n***139 - (25-18-18-25) = (114-18) - 18 - 25 = (96-18) - 25 = 78 - 25 = 53***\n\n![](https://user-images.githubusercontent.com/8466209/216677495-a2d66661-2ae2-4a15-aeae-93b74e2e8450.png)\n\n![](https://user-images.githubusercontent.com/36441664/101232759-35ec7900-36e6-11eb-95a5-61a838962ce2.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/101109759-357eb000-360a-11eb-8873-b9d73b7bb10d.jpg)\n\nSee that from 1 to 89 it consist of seven (7) steps which is originated by 1,15,35,28 before it goes bilateral. \n\n![default](https://user-images.githubusercontent.com/8466209/198411256-93305a08-2de1-4a1b-9d5e-dd9f0c8a1c2b.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198408322-f3829ebd-62b6-485c-a3fc-6ecced6dcf9e.png)\n\n![default](https://user-images.githubusercontent.com/8466209/198409145-f2e6fe05-595f-4d7d-922e-169b69447f0b.png)\n\nThe distribution of these scale has a bilateral symmetrical relationship along with the peculiarities of each numbers within the format (18,30,36) of prime hexagon so that it can represent the pattern of _[true-prime-pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_ systemically. \n\n***(5 + 7 + 11 + 13) + (17 + 19) = 36 + 36 = 72***\n\n[![default](https://user-images.githubusercontent.com/8466209/200475393-f3e42f0b-d291-4f17-93c4-9bec6e6943de.png)](https://github.com/chetabahana/tensorflow/wiki/Untouched-Intelligences#filosofi)\n\nThis 29 turns the finiteness position of 15 as the ***[middle zero axis](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)*** of the _MEC30_. So the next steps will start exactly with the same story as we have explained from the [beginning](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity). \n\n>MEC 30 claims to \"illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way\" via the elementary level of numbers. It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences.\n\n[![default](https://user-images.githubusercontent.com/8466209/220210334-81c62871-25a2-47ef-ae38-c7bf50a4c8e3.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)\n","dir":"/identition/span2/","name":"gist04.md","path":"identition/span2/gist04.md","url":"/identition/span2/gist04.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 | 28\n---+-----+-----\n 2 | 29 | 46\n---+-----+-----\n 3 | 47 |{56}\n---+-----+-----\n 4 |{57} | 61\n---+-----+-----\n 5 | 62 | 82\n---+-----+-----\n 6 | 83 | 94\n---+-----+-----\n 7 | 95 | 99\n---+-----+-----\n 8 |{100}|{123}\n---+-----+-----\n```\n\n![image](https://user-images.githubusercontent.com/8466209/201361949-6e99504f-b139-4fd0-8a0d-3739964927f4.png)\n\n![image](https://user-images.githubusercontent.com/8466209/201361906-52dc91d4-48fa-4701-a334-c5bdd22b8b61.png)\n\n![image](https://user-images.githubusercontent.com/8466209/201362034-7a0c83f3-d310-4b92-b3e5-fc1f832693fc.png)\n\n![image](https://user-images.githubusercontent.com/8466209/201362104-cd379833-3f1b-4def-ab0d-f5f73ea5f127.png)\n\n>Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three. _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n\n[![Birch and Swinnerton-Dyer Conjecture](https://user-images.githubusercontent.com/8466209/218376819-e17c97cf-1f1d-4363-a1ce-2b1c355591c3.png)](https://www.claymath.org/millennium-problems/birch-and-swinnerton-dyer-conjecture)\n","dir":"/identition/span11/","name":"gist09.md","path":"identition/span11/gist09.md","url":"/identition/span11/gist09.html"},{"layout":"default","title":"Poincaré Conjecture","content":"## Poincaré Conjecture\n\n```\n---+-----+-----\n 1 | {1} | {2}\n---+-----+-----\n 2 | 3 | 20\n---+-----+-----\n 3 | 21 | 46\n---+-----+-----\n 4 |{47} | 58\n---+-----+-----\n 5 | 59 | 70\n---+-----+-----\n 6 |{71} |{93}\n---+-----+-----\n 7 | 94 | 103\n---+-----+-----\n 8 | 104 |{109}\n---+-----+-----\n```\n\n![](https://user-images.githubusercontent.com/36441664/84181975-e2d99680-aab3-11ea-8cf0-7da54cf0eb3f.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/84181982-e4a35a00-aab3-11ea-848a-89c1a1f8c9cf.jpg)\n\n![default](https://user-images.githubusercontent.com/8466209/200230450-2754c2d3-2b52-429d-b1c5-48fcfdf923be.png)\n\n![](https://user-images.githubusercontent.com/36441664/86853354-88e2e580-c0e0-11ea-92e4-24de95335054.gif)\n\n![](https://user-images.githubusercontent.com/36441664/88384290-54f10b00-cdd6-11ea-878d-c687cc1afbea.gif)\n\n![](https://user-images.githubusercontent.com/36441664/84181979-e3722d00-aab3-11ea-9868-982020dcd4b3.png)\n\n![](https://user-images.githubusercontent.com/36441664/84685920-3ee56480-af65-11ea-81a4-f44ebc656a19.jpg)\n\n```\n --------------------+-----+-----+-----+-----+-----+ | ---\n 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |\n | +-----+-----+-----+ | |\n | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | | +-----+-----+-----+ | | |\n | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n | | | +-----+-----+-----+ | | ---\n | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |\n | | +-----+-----+-----+ | |\n | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance\n329 | +-----+-----+-----+ |\n | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ |\n -------------------+-----+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/36441664/82712407-12b22d00-9cb2-11ea-9cc2-3cf392b2d35c.png)\n\n![](https://user-images.githubusercontent.com/36441664/88372848-e5bcec00-cdc0-11ea-8b8a-09b579a257f9.png)\n\n![default](https://user-images.githubusercontent.com/8466209/200230504-9b543817-cb59-4bc1-8bbb-fddc059c7d6b.png)\n\n>In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n\n[![Poincaré Conjecture](https://user-images.githubusercontent.com/36441664/84187330-17515080-aabc-11ea-8e53-47f12a248d4c.jpg)](https://www.claymath.org/millennium-problems/poincar%C3%A9-conjecture)\n\nThe Ricci Flow method has now been _[developed](http://engine.scichina.com/publisher/scp/journal/SCIS/62/9/10.1007/s11432-018-9702-7)_ not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI ([Artificial intelligence](https://en.wikipedia.org/wiki/Artificial_intelligence)). No wonder now all the science leads to it.\n\n>AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence. Discussions on many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence as the golden standard for Artificial Intelligence _([Human vs AI](https://www.frontiersin.org/articles/10.3389/frai.2021.622364/full))_.\n\n[![default](https://user-images.githubusercontent.com/8466209/224466884-5ba87f02-e01d-45ca-a9c3-a1d535e83228.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#mass-gap-%CE%B4)\n\nDespite of any debated subjects regarding _Human vs AI_, the said AI would not even close to the ability of human brain without undertanding of _[GAP](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#mass-vs-gap-%CE%B4)_ functionality between left and right of the human brain. Let's find it in details on further discussion.","dir":"/identition/span10/","name":"gist10.md","path":"identition/span10/gist10.md","url":"/identition/span10/gist10.html"},{"layout":"default","title":"How to select repos?","content":"## How to select repos?\n[![default](https://user-images.githubusercontent.com/8466209/200460413-0ff244c9-04b2-49f1-86cc-cd6955d5dc6a.png)](https://github.com/eq19/grammar)\n\n[![default](https://user-images.githubusercontent.com/8466209/200459104-d508754e-cbae-4d07-b0c9-3c339ea6e917.png)](https://www.eq19.com/grammar/)\n\n[![default](https://user-images.githubusercontent.com/8466209/200458239-51004392-df2f-4e29-8cf6-04a462068331.png)](https://github.com/eq19/grammar/actions)\n\n[![default](https://user-images.githubusercontent.com/8466209/200469800-6c46fee3-5ce8-4999-b414-0a771e3fc93c.png)](https://www.eq19.com/grammar/)\n\n[![default](https://user-images.githubusercontent.com/8466209/200475393-f3e42f0b-d291-4f17-93c4-9bec6e6943de.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)\n\n[![default](https://user-images.githubusercontent.com/8466209/200472044-dab44257-7c9a-4a91-82bb-c90cb7143e91.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525)\n","dir":"/identition/span8/","name":"gist06.md","path":"identition/span8/gist06.md","url":"/identition/span8/gist06.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/201120468-f985427d-b4e8-4bf8-b39c-e5919af1f540.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201121309-7410e679-3273-4e87-9177-abeae76ffb5b.png)\n\n![image](https://user-images.githubusercontent.com/8466209/201121924-f8b105e5-0e76-4513-90c6-b561071aa699.png)\n","dir":"/identition/span10/","name":"gist04.md","path":"identition/span10/gist04.md","url":"/identition/span10/gist04.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/200121103-538c687c-0748-4e81-b40b-2de82fa3a305.png)](https://stackoverflow.com/a/59952803/4058484)\n\n[![default](https://user-images.githubusercontent.com/8466209/200120900-ad4b3617-3f7f-465c-a741-2c95dbaa8ca7.png)](https://www.tensorflow.org/install/source_windows)\n\n[![default](https://user-images.githubusercontent.com/8466209/200121011-d320bf1f-93b7-42b5-9894-f6939e5948e5.png)](https://developer.nvidia.com/cuda-10.1-download-archive-base)\n","dir":"/identition/span7/","name":"gist07.md","path":"identition/span7/gist07.md","url":"/identition/span7/gist07.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201110882-5dd8931d-a1cd-4bb7-8d82-0d3da0b58c66.png)](https://github.com/FeedMapping/feedmapping.github.io)\n\n![image](https://user-images.githubusercontent.com/8466209/201114200-db3490f8-a9b4-4bb6-bed3-dbc1677fd45e.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/201117531-d2fd8521-3056-4581-9354-f58052808e9b.png)](https://github.com/eq19/eq19.github.io/tree/eQ19)\n\n","dir":"/identition/span10/","name":"gist03.md","path":"identition/span10/gist03.md","url":"/identition/span10/gist03.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/201104906-927fddf1-bd46-43b6-8b3d-47c37657deb1.png)\n![default](https://user-images.githubusercontent.com/8466209/201105343-f8d9aec8-fd82-442d-8d6a-dcac5a61da42.png)\n![default](https://user-images.githubusercontent.com/8466209/201105576-5670bc54-46f9-4f78-b6f8-e1a3868a590e.png)\n![default](https://user-images.githubusercontent.com/8466209/201106351-89b330d9-e60f-44b4-ba72-097f04fa63c4.png)\n![default](https://user-images.githubusercontent.com/8466209/201107959-5311d9a7-0b61-4b18-8ea1-b32a36f1d804.png)\n![default](https://user-images.githubusercontent.com/8466209/201108271-9edc6b15-d4d8-469f-b7c9-797cd0abdfe4.png)\n![default](https://user-images.githubusercontent.com/8466209/201108973-71ecaec4-c47e-4b3f-bbec-4cc2343344fd.png)\n\n","dir":"/identition/span10/","name":"gist02.md","path":"identition/span10/gist02.md","url":"/identition/span10/gist02.html"},{"layout":"default","title":null,"content":"By prime hexagon we can see that seven (7), hold the power to make the prime spin remain on the track. This power is then transfered to twelve (12) spins. \n\n![image](https://user-images.githubusercontent.com/8466209/253148724-8dffc1e4-e2a9-478e-ae13-7bb1c0303406.png)\n\nSo basically there is a power transformation between an addition of 3 and 4 to 7 in to their multiplication in to 12 where this 7 will be treated as one of their member.\n\n```\n #8 |----------- 5® --------|------------ 7® --------------|\n | 1 |---------------- 77 = 4² + 5² + 6² -------------|\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78\n main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 200\n |--- A,T,G,C ---| | └── 30\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 70\n {98} | └── 100\n```\n\nTherefore the 12 will consist of 11 groups runner and 1 profile of the transformation result. Follow to the prime hexagon we collect them in [19 gists](https://gist.github.com/mine) as below.\n\n```\n$ gh api -H \"${HEADER}\" /users/eq19/gists --jq 'sort_by(.created_at)|.[].url'\n\nhttps://api.github.com/gists/c9bdc2bbe55f2d162535023c8d321831 19 grammar 36\nhttps://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 syntax\nhttps://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 parser\nhttps://api.github.com/gists/dc30497160f3389546d177da901537d9 16 lexer\nhttps://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 feed\nhttps://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 maps\nhttps://api.github.com/gists/f78d4470250720fb18111165564d555f 13 io 30\n --------\nhttps://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77\nhttps://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10\nhttps://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9\nhttps://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8\nhttps://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7\nhttps://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6\nhttps://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5\nhttps://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4\nhttps://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3\nhttps://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2\nhttps://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1\nhttps://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37\n```\n\nSince 19 is thouching the first node then the workflow will be proceeded as bilateral way\n\n```\nhttps://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77\nhttps://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10\nhttps://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9\nhttps://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8\nhttps://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7\nhttps://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6\nhttps://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5\nhttps://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4\nhttps://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3\nhttps://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2\nhttps://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1\nhttps://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37\n12 months (moon)\n-------- bilateral 9 sums\n7 days (sun)\nhttps://api.github.com/gists/c9bdc2bbe55f2d162535023c8d321831 19 grammar 36\nhttps://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 syntax\nhttps://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 parser\nhttps://api.github.com/gists/dc30497160f3389546d177da901537d9 16 lexer\nhttps://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 feed\nhttps://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 maps\nhttps://api.github.com/gists/f78d4470250720fb18111165564d555f 13 io 30\n```\n\nHere we can see that the transformation from 7 to 12 is actualy started from the prime 13. So the power of 7 is transfered to 77 by the prime pair 11 and 13.\n\n![image](https://user-images.githubusercontent.com/8466209/253148763-4a982982-4f70-4d7d-b524-51b72c6f17e9.png)\n\nThe nodes is from converted from 7 to 77 whivh is 7 times 11. By the prime pair 11 and 13, the total nodes is involving 1 + 7 + 29 + 77 = 37 + 77 = 114 nodes\n\n```\n Δ1 + Δ7 + Δ29 → | Δ37 + Δ77 = Δ114 = Δ113 + Δ1 → \n\n | 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - | 100| - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - | 101| - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - |\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - | 102| -| - | - | - |\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n | Δ Δ Δ | Φ12 | Δ Δ |\n -113 +150 = +37 +102 = +139 -113 -114\n```\n\nAs conclution the behaviour of this 7 is happen between the sequence of 30 and 36 while the 12 is happen between the sequence of 36 and 102.\n\n![default](https://user-images.githubusercontent.com/8466209/200024664-afc433a0-5f7f-4ec1-9bfc-77d672817fed.png)\n\nBy observing more detail we spread the power of 7. \n\n*****168 + 329 + 289 - 619 - 30 - 30 - 5 = 786 - 619 - 65 = 102 = (2,60,40)*****\n","dir":"/identition/span7/","name":"gist03.md","path":"identition/span7/gist03.md","url":"/identition/span7/gist03.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 |{73}\n---+-----+-----\n 2 |{74} | 94\n---+-----+-----\n 3 | 95 | 113\n---+-----+-----\n 4 |{114}| 121\n---+-----+-----\n 5 | 122 | 135\n---+-----+-----\n 6 | 136 | 156\n---+-----+-----\n 7 |{157}|{165}\n---+-----+-----\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/199369598-357b1b6f-378b-4a56-8c7b-519316418edb.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation)\n\n[![default](https://user-images.githubusercontent.com/8466209/199392998-1322a3f1-182f-4f69-9af9-f9691bcb617b.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199392725-b5483087-9b7f-4381-b73d-21849a88d295.png)](https://github.com/chetabahana/tensorflow/wiki#manuscript)\n \n[![default](https://user-images.githubusercontent.com/8466209/199392468-a2738235-b65f-47da-848d-ffa0340cd51b.png)](https://github.com/chetabahana/tensorflow/wiki#delivery)","dir":"/identition/span6/","name":"gist10.md","path":"identition/span6/gist10.md","url":"/identition/span6/gist10.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201255091-979c9ab2-18a3-467b-95b1-11c9a80bcbf4.png)](https://github.com/TheAlgorithms/Python/blob/master/requirements.txt)\n[![default](https://user-images.githubusercontent.com/8466209/201279272-a840ff2f-7eb0-48eb-8dd5-37e266a62d5a.png)](https://github.com/eq19/grammar/actions/workflows/build.yml)\n[![default](https://user-images.githubusercontent.com/8466209/201256070-85b14f71-063b-4b4a-b546-be9dec8c9c6f.png)](https://github.com/eq19/grammar/actions/runs/3441609775/jobs/5741337732)\n","dir":"/identition/span10/","name":"gist05.md","path":"identition/span10/gist05.md","url":"/identition/span10/gist05.html"},{"layout":"default","title":"Site GitHub","content":"# Site GitHub\n\nThe following sample information is exposed to Jekyll templates in the [site.github](https://github.com/jekyll/github-metadata/blob/main/docs/site.github.md#using-sitegithub) namespace:\n\n```\n{% raw %}\n{% for item in site.github %}\n * {{ item | jsonify }}: {{ site.github[item] | jsonify }}\n{% endfor %}\n{% endraw %}\n```\n\nOutput:\n```\n{\n \"versions\": {\n \"jekyll\": ,\n \"kramdown\": ,\n \"liquid\": ,\n \"maruku\": ,\n \"rdiscount\": ,\n \"redcarpet\": ,\n \"RedCloth\": ,\n \"jemoji\": ,\n \"jekyll-mentions\": ,\n \"jekyll-redirect-from\": ,\n \"jekyll-sitemap\": ,\n \"github-pages\": ,\n \"ruby\": \"\n },\n \"hostname\": \"github.com\",\n \"pages_hostname\": \"github.io\",\n \"api_url\": \"https://api.github.com\",\n \"help_url\": \"https://help.github.com\",\n \"environment\": \"dotcom\",\n \"pages_env\": \"dotcom\",\n \"public_repositories\": [ Repository Objects ],\n \"organization_members\": [ User Objects ],\n \"build_revision\": \"cbd866ebf142088896cbe71422b949de7f864bce\",\n \"project_title\": \"metadata-example\",\n \"project_tagline\": \"A GitHub Pages site to showcase repository metadata\",\n \"owner_name\": \"github\",\n \"owner_url\": \"https://github.com/github\",\n \"owner_gravatar_url\": \"https://github.com/github.png\",\n \"repository_url\": \"https://github.com/github/metadata-example\",\n \"repository_nwo\": \"github/metadata-example\",\n \"repository_name\": \"metadata-example\",\n \"zip_url\": \"https://github.com/github/metadata-example/zipball/gh-pages\",\n \"tar_url\": \"https://github.com/github/metadata-example/tarball/gh-pages\",\n \"clone_url\": \"https://github.com/github/metadata-example.git\",\n \"releases_url\": \"https://github.com/github/metadata-example/releases\",\n \"issues_url\": \"https://github.com/github/metadata-example/issues\",\n \"wiki_url\": \"https://github.com/github/metadata-example/wiki\",\n \"language\": null,\n \"is_user_page\": false,\n \"is_project_page\": true,\n \"show_downloads\": true,\n \"url\": \"http://username.github.io/metadata-example\", // (or the CNAME)\n \"baseurl\": \"/metadata-example\",\n \"contributors\": [ User Objects ],\n \"releases\": [ Release Objects ],\n \"latest_release\": [ Release Object ],\n \"private\": false,\n \"archived\": false,\n \"disabled\": false,\n \"license\": {\n \"key\": \"mit\",\n \"name\": \"MIT License\",\n \"spdx_id\": \"MIT\",\n \"url\": \"https://api.github.com/licenses/mit\"\n },\n \"source\": {\n \"branch\": \"gh-pages\",\n \"path\": \"/\"\n }\n}\n```\n\n## GitHub API\n\nJekyll supports [loading data](https://jekyllrb.com/docs/datafiles/) from YAML, JSON, CSV, and TSV files located in the _data directory. Note that CSV and TSV files must contain a header row.\n\n```bash\n gh api -H \"${HEADER}\" /user/orgs --jq '.[].login' | sort -uf | yq eval -P | sed \"s/ /, /g\" > /tmp/user_orgs\n IFS=', '; array=($(cat /tmp/user_orgs))\n\n echo \"[\" > _data/orgs.json\n for ((i=0; i < ${#array[@]}; i++)); do\n\t gh api -H \"${HEADER}\" /orgs/${array[$i]} >> _data/orgs.json\n if [[ \"$i\" -lt \"${#array[@]}-1\" ]]; then echo \",\" >> _data/orgs.json; fi\n done\n echo \"]\" >> _data/orgs.json\n fi\n```\n\n```liquid\n{% raw %}\n{% for item in site.data.orgs %}\n - {{ item.name | jsonify }}\n{% endfor %}\n{% endraw %}\n```\n\n{%- for item in site.data.orgs -%}\n - {{ item.name | jsonify }}\n{%- endfor -%}\n\n## Wotkflow Run\n\n[![default](https://user-images.githubusercontent.com/8466209/201278178-6c8eb4c9-1a45-4583-b61e-b948d9431e95.png)](https://github.com/TheAlgorithms/Python/blob/master/.github/workflows/build.yml)\n\n[![default](https://user-images.githubusercontent.com/8466209/201258756-7f1cc4e4-fc24-4061-8dbe-8610dd56a557.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-gitignore-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/201274327-f0e777ad-7226-4b86-bb1e-c21290264492.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-runner-md)\n\n","dir":"/identition/span10/","name":"gist06.md","path":"identition/span10/gist06.md","url":"/identition/span10/gist06.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201290909-61804ad4-04d9-40f6-81d3-b396909cf372.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-opposite-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/201287545-565e5907-eb35-48ba-96c8-199a70cc8fa4.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-syntax-md)\n\n[![image](https://user-images.githubusercontent.com/8466209/201288295-5b42e95b-3a67-4136-8e60-174f9bc473f8.png)](https://github.com/purcellconsult/OOP-in-Python)\n\n[![default](https://user-images.githubusercontent.com/8466209/201290477-3bfd5e72-d761-4610-acd1-c314d369d100.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md)\n\n![image](https://user-images.githubusercontent.com/8466209/201288734-8d9a1193-3b15-4501-803c-0ced1b0ef91f.png)\n","dir":"/identition/span10/","name":"gist07.md","path":"identition/span10/gist07.md","url":"/identition/span10/gist07.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201292753-842f61b5-fa45-4b0b-be17-41545774c28b.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-4_quantum-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/201289502-7a7e9c84-1bdf-4865-8eab-7117d7362afe.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-algorithm-md!)\n\n[![image](https://user-images.githubusercontent.com/8466209/201289841-81b4e930-012c-499a-b192-4e2387698f39.png)](https://github.com/tensorflow/tensorflow)\n\n[![default](https://user-images.githubusercontent.com/8466209/201290640-9f7b1e38-6fe2-4819-9fd9-e8777c6eddc4.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md)\n\n![image](https://user-images.githubusercontent.com/8466209/201288829-541df68d-fd5c-4dcc-859b-35af3a15f100.png)\n\n\n\n\n","dir":"/identition/span10/","name":"gist08.md","path":"identition/span10/gist08.md","url":"/identition/span10/gist08.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201276953-5e3f16bc-f578-4336-b4d0-9b25a658ff66.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-circular-md)\n\n[![image](https://user-images.githubusercontent.com/8466209/201293827-ed23aa2f-54a4-4e5c-9535-ddc65eaf63dc.png)](https://github.com/kamranahmedse/developer-roadmap)\n\n| Tables | Are | Cool |\n|----------|:-------------:|------:|\n| col 1 is | left-aligned | $1600 |\n| col 2 is | 📂 centered | $12 |\n| col 3 is | right-aligned | $1 |\n\n\n| Tables | Are | Cool |\n| ------------- |:-------------:| -----:|\n| col 3 is 🚀 | right-aligned | $1600 |\n| col 2 is 🔨 | centered | $12 |\n| zebra stripes | are neat | $1 |\n|
            • 💎item1
            • 💎item2
            | See the list | from the first column|\n\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
            TablesAreCool
            col 3 isright-aligned$1600
            col 2 iscentered$12
            zebra stripesare neat$1
            \n
              \n
            • item1
              • \n
            • item2
              • \n
            \n             		See the listfrom the first column
            \n\n\nThe hexagon is also found in the structure of DNA it forms the chains that produce the double-helix macromolecule. Functional description of DNA (I) comprising using a bio-oscillator which reproduces the sequence of bases, in spatial and energetic states, in the form of vibrations, is new.\n\n>This Ulam spiral serves to illustrate primes and prime factor abundances in a hexagonal spiral. Prime numbers in green; darker blue indicates numbers with more different prime factors..\n\n[![Ulam spiral](https://upload.wikimedia.org/wikipedia/commons/2/25/Hexgrid_prime_number_spiral.svg)](https://en.wikipedia.org/wiki/Ulam_spiral)\n","dir":"/identition/span10/","name":"gist09.md","path":"identition/span10/gist09.md","url":"/identition/span10/gist09.html"},{"layout":"default","title":null,"content":"\n\n[![default](https://user-images.githubusercontent.com/8466209/199505430-103ea007-46c1-462d-a508-4cb2f952533f.png)](https://github.com/MarketLeader/marketleader.github.io/tree/bb03da9405c488db8999a56d56b31081dd13ebe5)\n\n[![default](https://user-images.githubusercontent.com/8466209/199506031-040881cb-5ba0-4b9c-b217-19c6f70db625.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-runner-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/199531841-702f40e4-c1b6-434b-b0de-7cd3c721bc7f.png)](https://stackoverflow.com/a/74291357/4058484)\n\n[![default](https://user-images.githubusercontent.com/8466209/199534966-02f7e806-6cba-4c3c-829c-8886774a6b4a.png)](https://stackoverflow.com/questions/52395202/pushing-changes-in-the-git-submodule)\n","dir":"/identition/span6/","name":"gist07.md","path":"identition/span6/gist07.md","url":"/identition/span6/gist07.html"},{"layout":"default","title":null,"content":"```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n ```\n \n \n![default](https://user-images.githubusercontent.com/8466209/201350726-068c3de2-8123-43ec-9d08-6afc743ddcbe.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201355458-2ff29c7c-c35a-49ed-a9e8-f607ae5841ab.png)\n![image](https://user-images.githubusercontent.com/8466209/201383102-8ae5652f-94fd-4f09-adab-d727e3ba80f5.png)\n![image](https://user-images.githubusercontent.com/8466209/201368103-efd619a2-a608-420e-9117-40f92e68a003.png)\n","dir":"/identition/span11/","name":"gist02.md","path":"identition/span11/gist02.md","url":"/identition/span11/gist02.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/201393202-8550c8ed-ab0d-489f-8831-5eee78534713.png)\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|------------------------ Scheme-12 ------------------------|\n|------------ 6¤ -------------|------------- 6¤ ------------|\n|--------------------------- 192 ---------------------------|\n|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}|\n|--------- 5¤ ---------|------------ {96} -----------|{43}|\n|--------- {53} ---------|-------------- {139} -------------|\n|------ Scheme-53 -------|------------ Scheme-34 -----------|\n```\n![default](https://user-images.githubusercontent.com/8466209/201392901-e56d6e20-b985-46cc-815d-780e5eed4406.png)\n\n![image](https://user-images.githubusercontent.com/8466209/201362482-1581055c-0bfd-4314-a90e-1c49515cf6c3.png)\n","dir":"/identition/span11/","name":"gist04.md","path":"identition/span11/gist04.md","url":"/identition/span11/gist04.html"},{"layout":"default","title":null,"content":"*****Φ(11,13) = Φ(1,2,3) + Φ(4,2) = 123 + 42 = 165*****\n\n![default](https://user-images.githubusercontent.com/36441664/85060684-db12a400-b1cf-11ea-8f37-6b9b3bcab2f2.gif)\n\n```\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1\n```\n![default](https://user-images.githubusercontent.com/8466209/201391686-4d1fc69f-1028-496e-b674-21053d65a2c2.png)\n![default](https://user-images.githubusercontent.com/36441664/104337162-c1e49280-5527-11eb-9625-12b95f568aa4.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/201354388-dcf5e2f1-cb50-4d1b-8c93-0dd49bc7e46d.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-runner-md)\n\n![default](https://user-images.githubusercontent.com/8466209/201355214-d1e67872-d9e7-4a9f-ae64-4305238f6071.png)\n\n[![image](https://user-images.githubusercontent.com/8466209/201360527-91a03353-2eb8-4f20-ba8d-afee93fb7b3c.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-basic-md)\n","dir":"/identition/span11/","name":"gist08.md","path":"identition/span11/gist08.md","url":"/identition/span11/gist08.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/201387892-26680e27-bbd9-494c-9e8b-c14226f346d5.png)](https://en.wikipedia.org/wiki/List_of_regions_in_the_human_brain)\n\n![default](https://user-images.githubusercontent.com/36441664/72667103-cd06fe80-3a4a-11ea-85fe-c75d551fa049.jpg)\n```\n #8 |----------- 5® --------|------------ 7® --------------|\n | 1 |---------------- 77 = 4² + 5² + 6² -------------|\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78\n main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n-----+-----|-----+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 100 - 123 ({24})\n |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30\n {98} | └── 110 - 123 (14x)» 70\n```\n","dir":"/identition/span11/","name":"gist03.md","path":"identition/span11/gist03.md","url":"/identition/span11/gist03.html"},{"layout":"default","title":null,"content":"```\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\n[![default](https://user-images.githubusercontent.com/8466209/199512064-fe149c63-1c7b-4d67-b700-fb61c52382de.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406)\n\n[![default](https://user-images.githubusercontent.com/8466209/199510889-f6bca686-74cf-4fed-a7c1-bd1269058e63.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md)\n","dir":"/identition/span6/","name":"gist09.md","path":"identition/span6/gist09.md","url":"/identition/span6/gist09.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/201399105-413df8fa-f33e-43eb-969a-eebbe28d28f2.png)\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root 1 → 4 (5)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin 2 → 8 (10)\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin 5 → 7 (12)\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200474124-1643ba7d-8075-4c53-84a8-b9966a83d1c5.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)\n\n[![default](https://user-images.githubusercontent.com/8466209/201881644-15e0dd30-ffd5-479e-9a62-7f37e87a6288.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/201879992-2ee3e071-03ea-46d0-8844-31ecd11c062b.png)](https://winbuzzer.com/2020/04/15/windows-10-how-to-create-a-virtual-hard-drive-as-hdd-dvd-or-ram-disk-xcxwbt)\n\n## Manage certificates with ACME & DNS\n\nAutomatic Certificate Management Environment (ACME) is a common protocol used to automate the management certificates between a Certificate Authority (CA) and server. With automation, many users can reduce the chances of outages due to failure to renew their HTTPS certificates.\n\n[![Use HTTPS on your domain](https://user-images.githubusercontent.com/8466209/259370523-b2e4195f-bae5-433f-8d9f-16d348167546.png)](https://support.google.com/domains/answer/7630973)\n\n[Posh-ACME](https://poshac.me/) is a PowerShell module and ACME client to create publicly trusted SSL/TLS certificates from an ACME capable certificate authority such as [Let's Encrypt](https://letsencrypt.org/).\n\n[![Posh-ACME](https://user-images.githubusercontent.com/8466209/259368021-fc267e62-3890-4e9f-9940-f4a8d53a38a5.png)](https://poshac.me/docs/v4/Tutorial/#picking-a-server)\n","dir":"/identition/span11/","name":"gist05.md","path":"identition/span11/gist05.md","url":"/identition/span11/gist05.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/201396853-75d12ee6-a80f-4b1c-b3a0-c7a3a808aaca.png)\n\n\n[![default](https://user-images.githubusercontent.com/8466209/202141967-f86798ad-4aff-48ee-b09f-b1645b330276.png)](https://en.wikipedia.org/wiki/List_of_S%26P_500_companies)\n\n> The components that have increased their dividends in 25 consecutive years are known as the S&P 500 Dividend Aristocrats. The index is one of the factors in computation of the Conference Board Leading Economic Index, used to forecast the direction of the economy. _Aource: [Google Finance](https://www.google.com/finance/quote/.INX:INDEXSP)_\n\n*****50 x 10 = 500*****\n```\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n ↓\n |\n ↓ \n 114-89=139-114=25=5x5\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ ↓\n | | |\n 50 x 10 = 500 ----→ ------------- 10 ------------- | \n | \n | \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n```\n\n\n```\n//Updated on 10-6-2015 By ChrisMoody\n//Added Linebr ability, ability to turn on/off highlight Bars when crossing Swing Hi/Lo\n//Added Ability to turn on/off background highlight when bars cross swing hi/lo\n//Created 99% by Glaz and ChrisMoody Modified about 1% on 7/30/2014 for user dvk197-\n\nstudy(title=\"CM_Gann Swing HighLow V2\", shorttitle=\"CM_Gann_Swing_HL_V2\", overlay=true)\nperiods=input(3, minval=1, title=\"Moving Average Period\")\npt = input(false, title=\"Plot Up/Down Triangles at Top and Bottom of Candles/Bars?\")\npc = input(true, title=\"Plot Circles at Top and Bottom of Candles/Bars?\")\npttb = input(true, title=\"Plot Triangles at Top and Bottom of Screen?\")\nshb = input(false, title=\"Show Highlight Bars on Cross Up or Cross Down?\")\nsbh = input(true, title=\"Show Background Highlights at Cross Up or Cross Down?\")\n\n//code for Calculations\nhld = iff(close > sma(high,periods)[1], 1, iff(close shb and close > hi and close[1] < hi\nBHcloseAbove = sbh and close > hi and close[1] < hi\ncloseBelow() => shb and close < lo and close[1] > lo\nBHcloseBelow = sbh and close < lo and close[1] > lo\n\n//Highlight Bar Color Plots\nbarcolor(closeAbove() ? yellow : na)\nbarcolor(closeBelow() ? yellow : na)\n//Background Highlight Rules\nbgcolor(BHcloseAbove ? green : na, transp=60)\nbgcolor(BHcloseBelow ? red : na, transp=60)\n\n//Plot Statements for circles and Triangle Up/Down at Price Bars\nplot(pc and hi ? hi : na,title=\"Gann Swing High Plots-Circles\", color=fuchsia,style=linebr, linewidth=4)\nplot(pc and lo ? lo : na,title=\"Gann Swing Low Plots-Circles\", color=lime,style=linebr, linewidth=4)\nplotshape(pt and hi ? hi : na,title=\"Gann Swing High Plots-Triangle Down\", offset=0, style=shape.triangledown, location=location.abovebar, color=fuchsia, transp=0)\nplotshape(pt and lo ? lo : na,title=\"Gann Swing Low Plots-Triangle Up\", offset=0, style=shape.triangleup, location=location.belowbar, color=lime, transp=0)\n\n//Plot Statement for Triangles at Top and Bottom of Screen\nplotshape(pttb and hi ? hi : na,title=\"Gann Swing High Plots-Triangles Down Top of Screen\", offset=0, style=shape.triangledown, location=location.top, color=red, transp=0)\nplotshape(pttb and lo ? lo : na, title=\"Gann Swing Low Plots-Triangles Up Bottom of Screen\",offset=0, style=shape.triangleup, location=location.bottom, color=lime, transp=0)\n```\n[![2022-11-26 (1)](https://user-images.githubusercontent.com/8466209/204060638-bee5515b-9f5c-441c-b374-6027f66b7726.png)\n](https://www.tradingview.com/script/ngO3BO37-CM-Gann-Swing-High-Low-V2/)\n\n> Gann was born June 6, 1878, in Lufkin, Texas. His father was a cotton farmer. He started trading in 1902 when he was 24.[24] He was believed to be a great student of the Bible, who believed that it was the greatest book ever written Likewise, Henry W Steele[34] demonstrates in a YouTube video that the numbers in Gann's work often refer to a different subject from what they appear on the surface. For example, on page one and two of Forty-Five Years in Wall Street,[35] there is a paragraph describing the different stocks at different prices on 14 June 1949, but Steele discovered that those \"prices\" are actually astrological aspects appearing in the sky on that day. _Source [Wikipedia](https://en.wikipedia.org/wiki/William_Delbert_Gann#Bibliography)_\n\n[![default](https://user-images.githubusercontent.com/8466209/201389693-d0b4a41a-90bc-475f-89ee-ecf4e154c63e.png)](https://www.bing.com/images/search?q=gann+hexagon+chart)\n\nWD Gann is well known as the greatest market researcher of all time. He researched every possible aspect of natural laws in conjuction with variables of price and time in market movements. Find more detail _[here](https://github.com/eq19/parser/files/10151301/gann-time-factor.pdf)_ and _[here](https://github.com/eq19/parser/files/10151302/master-time-factor.pdf)_.\n","dir":"/identition/span11/","name":"gist06.md","path":"identition/span11/gist06.md","url":"/identition/span11/gist06.html"},{"layout":"default","title":null,"content":"\n![Untitled](https://user-images.githubusercontent.com/8466209/259256709-e6c0bb56-b3dc-4f7c-9a52-3ffc64d1707f.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/204060669-90a68f1a-424f-40b4-aafd-1ee862202ed4.png)](https://www.brokerxplorer.com/amp/article/what-is-the-best-ema-for-swing-trading-3336)\n\n![image](https://user-images.githubusercontent.com/8466209/201362641-b166327c-0a7d-4e2a-8170-ba4ca8dda5fe.png)\n\n","dir":"/identition/span11/","name":"gist07.md","path":"identition/span11/gist07.md","url":"/identition/span11/gist07.html"},{"text":"ABCDEFGHIJKLMNOPQRSTUVWXYZ\nabcdefghijklmnopqrstuvwxyz\n1234567890\n一二三四五六七八九十百千萬上中下左右大小春夏秋冬東南西北金木水火土\n‘?’“!”(%)[#]{@}/&\\<-+÷×=>®©$€£¥¢:;,.*\n","layout":"default","title":"Fonts Test","content":"# Fonts Test\n\n`{:.font-mono}`\n\n```\n{{ page.text -}}\n```\n\n`{:.font-body}`\n\n{:.font-body}\n{{ page.text }}\n\n`{:.font-head}`\n\n{:.font-head}\n{{ page.text }}\n\n## font-awesome\n\n```html\nchecked\nbattery\n```\n\nchecked\nbattery\n\n[![default](https://user-images.githubusercontent.com/8466209/199379682-8f7885d9-dc91-4ec2-b288-1309091034ca.png)](https://keras.io/about/)\n\n[![default](https://user-images.githubusercontent.com/8466209/199375567-b50a5317-9024-45f3-8da5-88aa3383b47b.png)](https://github.com/tensorflow/tensorflow/tree/e3ff0f63dcde80216192c41c8d921e2f44e15999/tensorflow/python/keras)\n\n[![default](https://user-images.githubusercontent.com/8466209/199370408-c29c1265-5bb0-4f38-a010-5f17e4af2c58.png)](https://hub.docker.com/layers/tensorflow/tensorflow/2.5.0-gpu/images/sha256-0cb24474909c8ef0a3772c64a0fd1cf4e5ff2b806d39fd36abf716d6ea7eefb3?context=explore)\n\n","dir":"/identition/span6/","name":"gist04.md","path":"identition/span6/gist04.md","url":"/identition/span6/gist04.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | {1} |{56}\n---+-----+-----\n 2 | 57 |{71}\n---+-----+-----\n 3 | 72 | 85\n---+-----+-----\n 4 |{86} |{89}\n---+-----+-----\n 5 | 90 | 94\n---+-----+-----\n 6 | 95 | 102\n---+-----+-----\n 7 | 103 |{171}\n---+-----+-----\n 8 | 172 | 206\n---+-----+-----\n```\n\n```\nimport pandas as pd\nimport numpy as np\n\n# Make numpy values easier to read.\nnp.set_printoptions(precision=3, suppress=True)\n\nimport tensorflow as tf\nfrom tensorflow.keras import layers\n\nabalone_train = pd.read_csv(\n \"https://storage.googleapis.com/download.tensorflow.org/data/abalone_train.csv\",\n names=[\"Length\", \"Diameter\", \"Height\", \"Whole weight\", \"Shucked weight\",\n \"Viscera weight\", \"Shell weight\", \"Age\"])\n\nabalone_train.head()\nabalone_features = abalone_train.copy()\nabalone_labels = abalone_features.pop('Age')\nabalone_features = np.array(abalone_features)\nabalone_features\n\nabalone_model = tf.keras.Sequential([\n layers.Dense(64),\n layers.Dense(1)\n])\n\nabalone_model.compile(loss = tf.keras.losses.MeanSquaredError(),\n optimizer = tf.keras.optimizers.Adam())\nabalone_model.fit(abalone_features, abalone_labels, epochs=10)\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200127121-3ead6276-c908-495d-9ddf-9c858258f8f8.png)](https://colab.research.google.com/github/tensorflow/docs/blob/master/site/en/tutorials/load_data/csv.ipynb#scrollTo=uZdpCD92SN3Z)\n\n[![default](https://user-images.githubusercontent.com/8466209/200127760-db1529e5-d019-46c3-a283-1fe8119d2fc8.png)](https://archive.ics.uci.edu/ml/datasets/abalone)\n","dir":"/identition/span7/","name":"gist08.md","path":"identition/span7/gist08.md","url":"/identition/span7/gist08.html"},{"layout":"default","title":null,"content":"![default](https://user-images.githubusercontent.com/8466209/201009382-ca13eae0-6ae9-4512-aa40-8b8c4f2f276b.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201010402-205363e4-af41-4b07-b501-22f6533a0210.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201017831-469513ee-0e92-4b27-9b3d-cb00add66966.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201019936-a8a19fe8-6a8a-4909-ae8d-063fafed564b.png)\n","dir":"/identition/span9/","name":"gist05.md","path":"identition/span9/gist05.md","url":"/identition/span9/gist05.html"},{"layout":"default","title":"The Bilateral 9 Sums","content":"## The Bilateral 9 Sums\n\n\n```\nRoot 4x\n29\n └── 30\n └── 31\n └── 32\n \nRewrite Root 4x → Twin 4x\n\nRoot 4x\n29\n └── 30\n └── 31\n └── 32\n \nTwin 4x\n33\n └── 34\n └── 35\n └── 36\n\n -----------------------+----+----+----+----+\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | \n =======================+====+====+====+====+\n 19 → π(10) | 2 | 3 | 5 | 7 | 4 x Root\n -----------------------+----+----+----+----+\n 17 → π(20) | 11 | 13 | 17 | 19 | 4 x Twin\n -----------------------+----+----+----+----+\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | ← Rewrite here\n =======================+====+====+====+====+\n```\n\n```\n# Sample workflow for building and deploying a Jekyll site to GitHub Pages\nname: Build and deploy Jekyll site to GitHub Pages\n\non:\n # 💎 Runs on pushes targeting the default branch\n push:\n branches:\n - eQ19\n - Chetabahana\n\n # Allows you to run this workflow manually from the Actions tab\n workflow_dispatch:\n\n# Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages\npermissions: write-all\n```\n \n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ←------------ Rewrite here\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n```\n## Recombimation\n[![default](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png)](https://www.primesdemystified.com/#primingthesquares)\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== ←-- Rewrite here (bilateral 9 sums)\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n```\n\n","dir":"/identition/span9/","name":"gist02.md","path":"identition/span9/gist02.md","url":"/identition/span9/gist02.html"},{"layout":"default","title":null,"content":"Because \"Ate Nine\" (89)\n\n[![default](https://user-images.githubusercontent.com/8466209/200234332-efce4c04-5f83-4cae-893f-f895eae27647.png)](https://ell.stackexchange.com/questions/115903/why-is-7-the-most-feared-number)\n\n[![11_89_109_7919_8128](https://user-images.githubusercontent.com/8466209/200228344-9f344f49-3e5d-480f-b11c-6e30a20a8f44.jpg)](https://www.primesdemystified.com/First1000Primes.html)\n\n```\n=======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n ↓\n |\n ↓ \n 114-89=139-114=25=5x5\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ ↓\n | | |\n ------------ 10 ------------- | \n | \n | \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n```\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root 1 → 4 (5)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin 2 → 8 (10)\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin 5 → 7 (12)\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n |\n ↓ \n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200474984-d0d05783-787c-460b-a80f-3f26debc0c0d.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-feeding-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/200225487-5e40102b-e8f9-4aa7-8a64-7529dfc14c7c.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-8_spinning-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/200244306-f5e5a428-83b9-46bb-a4b1-c96367e278b2.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-feeding-md)\n\n","dir":"/identition/span9/","name":"gist03.md","path":"identition/span9/gist03.md","url":"/identition/span9/gist03.html"},{"layout":"default","title":null,"content":"```\n---+-----+-----\n 1 | 1 | 28\n---+-----+-----\n 2 | 29 | 37\n---+-----+-----\n 3 | {38}| {48}\n---+-----+-----\n 4 | 49 | 127\n---+-----+-----\n 5 | 128 | 129\n---+-----+-----\n```\n\n![default](https://user-images.githubusercontent.com/8466209/201078012-9b1b1575-a598-4876-aeb4-aef6e8f6d957.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201077251-993d5ce3-a131-41a9-9f7e-36cb6e5f3b14.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201078741-00eab47a-7346-4403-a6b8-c0d52956891a.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201080070-a8895143-3188-4372-ba40-6b0452f432dd.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201080731-3b71a429-5ab0-4786-a965-4813d47a19ee.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201081540-f39e3e47-fd2c-4199-ad54-8d65bd9423d9.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201084190-f171aeb3-0464-427c-bb04-772fd7c01223.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201085311-e840b515-1764-4d26-8b2d-794016969784.png)\n\n![default](https://user-images.githubusercontent.com/8466209/201086588-c03cd0e6-fae5-4a18-b491-a34a82b28bf6.png)\n\n![default](https://user-images.githubusercontent.com/8466209/200228973-fd99095b-aad2-4824-b3dc-d6b21fae38ea.png)\n","dir":"/identition/span9/","name":"gist06.md","path":"identition/span9/gist06.md","url":"/identition/span9/gist06.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/200241752-e70d2eeb-5885-4f99-9362-4a05aeeb4435.png)](https://dev.to/thomasaudo/get-started-with-github-grapql-api--1g8b)\n\n![default](https://user-images.githubusercontent.com/8466209/200250136-7fe7a768-08a5-4bfb-ad19-c2a93cda363b.png)\n","dir":"/identition/span8/","name":"gist02.md","path":"identition/span8/gist02.md","url":"/identition/span8/gist02.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/200239492-515b374f-6180-4df0-840c-2f10ab5ef07b.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-grammar-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/200244306-f5e5a428-83b9-46bb-a4b1-c96367e278b2.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-grammar-md)\n","dir":"/identition/span8/","name":"gist05.md","path":"identition/span8/gist05.md","url":"/identition/span8/gist05.html"},{"layout":"default","title":null,"content":"[![default](https://user-images.githubusercontent.com/8466209/200248298-9c3979fa-9aa2-4283-839d-6ab4e76a667f.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-5-replicate-md)\n\n```\n=======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n=======================+====+====+====+====+====+====+====+====+====+=====\n ↓\n |\n ↓ \n 114-89=139-114=25=5x5\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ ↓\n | | |\n ------------ 10 ------------- | \n | \n | \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/200247726-5fddd4ad-210b-436b-9f22-0b93be6d01b4.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md)\n\n","dir":"/identition/span8/","name":"gist04.md","path":"identition/span8/gist04.md","url":"/identition/span8/gist04.html"},{"sort":0,"spin":null,"span":null,"suit":0,"permalink":"//","layout":"default","title":"Prime Identity","content":"

            Prime Identity

            \n\n

            We are going to assign prime identity as a standard model that attempts to stimulate a quantum field model called eQuantum for the four (4) known fundamental forces.

            \n\n
            This section is referring to _[wiki page-0](https://github.com/eq19/eq19.github.io/wiki)_ of _[zone section-0]()_ that is _[inherited ]()_ from _[the zone section-0](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Addition Zones (0-18)
              2. \n
            2. Multiplication Zones (18-30)
              3. \n
            3. Exponentiation Zones (30-36)\n
                \n
              1. Electrodynamics (maps)
                2. \n
              2. Quantum Gravity (feed)
                3. \n
              3. Chromodynamics (lexer)
                4. \n
              4. Electroweak Theory (parser)
                5. \n
              5. Grand Unified Theory (syntax)
                6. \n
              \n
              4. \n
            4. Identition Zones (36-102)\n
                \n
              1. Theory of Everything (span 12)
                2. \n
              2. Everything is Connected (span 11)
                3. \n
              3. Truncated Perturbation (span 10)
                4. \n
              4. Quadratic Polynomials (span 9)
                5. \n
              5. Fundamental Forces (span 8)
                6. \n
              6. Elementary Particles (span 7)
                7. \n
              7. Basic Transformation (span 6)
                8. \n
              8. Hidden Dimensions (span 5)
                9. \n
              9. Parallel Universes (span 4)
                10. \n
              10. Vibrating Strings (span 3)
                11. \n
              11. Series Expansion (span 2)
                12. \n
              12. Wormhole Theory (span 1)
                13. \n
              \n
              5. \n
            \n\n

            This presentation was inspired by theoretical works from Hideki Yukawa who in 1935 had predicted the existence of mesons as the carrier particles of strong nuclear force.

            \n\n

            Addition Zones

            \n\n

            Here we would like to recompile the way we take on getting the arithmetic expresion of an individual unit expression (identity) such as a taxicab number below.

            \n\n
            It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician _[GH Hardy](https://en.wikipedia.org/wiki/G._H._Hardy)_ when he visited Indian mathematician _[Srinivasa Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan)_ in hospital _([Wikipedia](https://en.wikipedia.org/wiki/1729_(number)))_.\n
            \n\n

            \"Ramanujan-Hardy

            \n\n

            These three (3) number are twin primes. We called the pairs as True Prime Pairs. Our scenario is mapping the distribution out of these pairs by taking the symmetrical behaviour of 36 as the smallest power (greater than 1) which is not a prime power.

            \n\n
            The smallest square number expressible as the sum of **four (4) consecutive primes** in two ways (5 + 7 + 11 + 13 and 17 + 19) which are also **two (2) couples** of prime twins! _([Prime Curios!](https://en.wikipedia.org/wiki/1729_(number)](https://primes.utm.edu/curios/page.php?number_id=270)))_.\n
            \n\n
            $True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer|  i  |   f\n -----+-----+---------\n      |  1  | 5\n   1  +-----+\n      |  2  | 7\n -----+-----+---  } 36 » 6®\n      |  3  | 11\n   2  +-----+\n      |  4  | 13\n -----+-----+---------\n      |  5  | 17\n   3  +-----+     } 36 » 6®\n      |  6  | 19\n -----+-----+---------\n
            \n\n

            Thus in short this is all about the method that we called as the 19 vs 18 Scenario of mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

            \n\n

            Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | \n      |      |  1  +-----+          \n      |  1   |     |  2  | (5)\n      |      |-----+-----+\n      |      |     |  3  |\n  1   +------+  2  +-----+----\n      |      |     |  4  |\n      |      +-----+-----+\n      |  2   |     |  5  | (7)\n      |      |  3  +-----+\n      |      |     |  6  |\n------+------+-----+-----+------      } (36)\n      |      |     |  7  |\n      |      |  4  +-----+\n      |  3   |     |  8  | (11)\n      |      +-----+-----+\n      |      |     |  9  |\n  2   +------|  5  +-----+-----\n      |      |     |  10 |\n      |      |-----+-----+\n      |  4   |     |  11 | (13)\n      |      |  6  +-----+\n      |      |     |  12 |\n------+------+-----+-----+------------------\n      |      |     |  13 |\n      |      |  7  +-----+\n      |  5   |     |  14 | (17)\n      |      |-----+-----+\n      |      |     |  15 |\n  3   +------+  8  +-----+-----       } (36)\n      |      |     |  16 |\n      |      |-----+-----+\n      |  6   |     |  17 | (19)\n      |      |  9  +-----+\n      |      |     |  18 |\n------|------|-----+-----+------\n
            \n\n

            The main background is that, as you may aware, the prime number theorem describes the asymptotic distribution of prime numbers which is still a major problem in mathematic.

            \n\n

            Multiplication Zones

            \n\n

            Instead of a proved formula we came to a unique expression called zeta function. This expression first appeared in a paper in 1737 entitled Variae observationes circa series infinitas.

            \n\n
            This expression states that the sum of the zeta function is equal to the product of the reciprocal of one minus the reciprocal of primes to the powers. But what has this got to do with the primes?  The answer is in the following product taken over the primes p (discovered by _[Leonhard Euler](https://en.wikipedia.org/wiki/Leonhard_Euler)_):\n
            \n\n

            \"zeta

            \n\n

            This issue is actually come from Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is considered to be the most important of unsolved problems in pure mathematics.

            \n\n
            In addition to the trivial roots, there also exist ***complex roots*** for real t. We find that the he first ten (10) non-trivial roots of the Riemann zeta function is occured when the values of t below 50. A plot of the values of ζ(1/2 + it) for t ranging from –50 to +50 is shown below. The roots occur each time ***the locus passes through the origin***. _([mathpages](https://www.mathpages.com/home/kmath738/kmath738.htm))_.\n
            \n\n

            \"trivial

            \n\n

            Meanwhile obtaining the non complex numbers it is easier to look at a graph like the one below which shows Li(x) (blue), R(x) (black), π(x) (red) and x/ln x (green); and then proclaim “R(x) is the best estimate of π(x).” Indeed it is for that range, but as we mentioned above, Li(x)-π(x) changes sign infinitely often, and near where it does, Li(x) would be the best value.

            \n\n

            \"non

            \n\n

            And we can see in the same way that the function Li(x)-(1/2)Li(x1/2) is ‘on the average’ a better approximation than Li(x) to π(x); but no importance can be attached to the latter terms in Riemann’s formula even by repeated averaging.

            \n\n

            Exponentiation Zones

            \n\n

            The problem is that the contributions from the non-trivial zeros at times swamps that of any but the main terms in these expansions.

            \n\n
            A. E. Ingham says it this way: Considerable importance was attached formerly to a function suggested by Riemann as an approximation to π(x)... This function represents π(x) with astonishing accuracy for all values of x for which π(x) has been calculated, but we now see that its superiority over Li(x) ***is illusory***... and for special values of x (as large as we please) the one approximation will deviate as widely as the other from the true value _([primes.utm.edu](https://primes.utm.edu/howmany.html#better))_.\n
            \n\n

            \"howmany

            \n\n

            Moreover in it was verified numerically, in a rigorous way using interval arithmetic, that The Riemann hypothesis is true up to 3 · 10^12. That is, all zeroes β+iγ of the Riemann zeta-function with 0<γ≤3⋅1012 have β=1/2.

            \n\n
            We have Λ ≤ 0.2. The next entry is conditional on taking H a little higher than 10*13, which of course, is not achieved by Theorem 1. This would enable one to prove Λ < 0.19. Given that our value of H falls between the entries in this table, it is possible that some extra decimals could be wrought out of the calculation. We have not pursued this _([arXiv:2004.09765](https://arxiv.org/abs/2004.09765))_.\n
            \n\n

            \"functional

            \n\n

            This Euler formula represents the distribution of a group of numbers that are positioned at regular intervals on a straight line to each other. Riemann later extended the definition of zeta(s) to all complex numbers (except the simple pole at s=1 with residue one). Euler’s product still holds if the real part of s is greater than one. Riemann derived the functional equation of zeta function.

            \n\n
            The Riemann zeta function has the trivial zeros at -2, -4, -6, ... (the poles of gamma(s/2)).  Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 < Re(s) < 1, and that they are symmetric about the critical line Re(s)=1/2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line _([primes.utm.edu](https://primes.utm.edu/notes/rh.html))_.\n
            \n\n

            \"zeta

            \n\n

            If both of the above statements are true then mathematically this Riemann Hypothesis is proven to be incorrect because it only applies to certain cases or limitations. So first of all the basis of the Riemann Hypothesis has to be considered.

            \n\n
            The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the functional equations. _([Riemann Zeta - pdf](https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf))_\n
            \n\n

            \"Riemann

            \n\n

            On the other hand, the possibility of obtaining the function of the distribution of prime numbers shall go backwards since it needs significant studies to be traced.

            \n\n

            Or may be start again from the Euleur Function.

            \n\n

            Identition Zones

            \n\n

            Freeman Dyson discovered an intriguing connection between quantum physics and Montgomery’s pair correlation conjecture about the zeros of the zeta function which dealts with the distribution of primes.

            \n\n
            The Mathematical Elementary Cell 30 (***MEC30***) standard _[unites](https://www.eq19.com/multiplication/12.html#entrypoint-of-momentum-spin-3)_ the mathematical and physical results of 1972 by _the mathematician Hugh Montgomery and the physicist Freeman Dyson_ and thus reproduces energy distribution in systems as a path plan ***more accurately than a measurement***. _([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))_\n
            \n\n

            \"The

            \n\n

            The path plan assume that a symmetric distribution of prime numbers with equal axial lengths from a middle zero axis = 15 is able to determine the distribution of primes in a given number space. This assumption finally bring us to the equation of Euler’s identity.

            \n\n
            Euler's identity is considered to be an exemplar of deep mathematical beauty as it shows a profound connection between the most fundamental numbers. Three (3) of the basic arithmetic operations occur exactly once each: ***addition***, ***multiplication***, and ***exponentiation*** _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_.\n
            \n\n

            \"Euler's

            \n\n

            The finiteness position of Euler’s identity by the said MEC30 opens up the possibility of accurately representing the self-similarity based on the distribution of True Prime Pairs so that all number would belongs together with their own identitities.

            \n\n
            See that there are multiple repetition from addition to multiplication which may lead up to the concept of [11th-dimension](https://www.eq19.com/identition/#extra-dimensions). This path is being applied as you can find on the left sidebar. (Please change the view to desktop mode if you are on mobile browser).\n
            \n\n

            \"DE102011101032A9.pdf\"

            \n\n

            Nothing is going to be easly about the nature of prime numbers but they demonstrably congruent to something organized. Let’s discuss starting with the addition zones.

            \n\n

            eQuantum Project
            \nCopyright © 2023-2024

            \n\n

            Reference:

            \n\n","dir":"/","name":"README.md","path":"README.md","url":"/"},{"sort":1,"spin":13,"layout":"default","title":"algorithm","content":"# algorithm\n\ncombined. By this 1000 primes then **168-150=Δ18** is raised on the next turn. \n```liquid\n$True Prime Pairs:\nlayer | node | sub | i | k | f\n------+------+-----+-----+-----+-----\n | | | 1 | 1,2 | 2,3 ← 2x = (13-11)x ---\n | | 1 +-----+-----+ |\n | 1 | | 2 | 3 | 7 |\n | |-----+-----+-----+ |\n | | | 3 | 4,6 | 10,11,12 -- |\n 1 +------+ 2 +-----+-----+ | |\n | | | 4 | 7 | 13 5x --- |\n | +-----+-----+-----+ | | |\n | 2 | | 5 | 8,9 | 14,15 ----- | |\n | | 3 +-----+-----+ | |\n | | | 6 | 10 | 19 | |\n------+------+-----+-----+-----+-------- 7x + 6x = 13x\n | | | 7 | 11 | 20 | |\n | | 4 +-----+-----+ | |\n | 3 | | 8 | 12 | 26 ----- | |\n | +-----+-----+-----+ | | |\n | | | 9 | 13 | 27 2x ----- |\n 2 +------| 5 +-----+-----+ | |\n | | | 10 | 14 | 28 ----- |\n | |-----+-----+-----+ |\n | 4 | | 11 |15,18| 29,30,31,32 ←---4x----\n | | 6 +-----+-----+\n | | | 12 | 19 | 36\n------+------+-----+-----+-----+-------\n | | | 13 | 20 | {38}\n | | 7 +-----+-----+\n | 5 | | 14 |21,22| {40,41} = (19-17)x ----\n | |-----+-----+-----+ |\n | | | 15 | 23 | {42} 6x + 13x = 19x\n 3 +------+ 8 +-----+-----+ |\n | | | 16 |24,27| {43,44,45,46} ←- 4x --\n | |-----+-----+-----+\n | 6 | | 17 | 28 | {50} = 46 + 4\n | | 9 +-----+-----+\n | | | 18 | 29 | {68} = 32 + 36\n------|------|-----+-----+------\n```\n\n```liquid\n| 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ \n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n\n[![eQ19](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)\n](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-entrypoint-md)\n\n![HxD](https://user-images.githubusercontent.com/8466209/205026477-b05094ce-fe6f-46d3-a579-50f407f42c70.png)\n\n","dir":"/exponentiation/span13/","name":"gist01.md","path":"exponentiation/span13/gist01.md","url":"/exponentiation/span13/gist01.html"},{"sort":1,"spin":null,"span":null,"suit":1,"permalink":"/addition/","layout":"default","title":"Addition Zones (0-18)","content":"

            Addition Zones (0-18)

            \n\n

            Addition is the form of an expression set equal to zero as the additive identity which is common practice in several areas of mathematics.

            \n\n
            This section is referring to _[wiki page-1](https://github.com/eq19/eq19.github.io/wiki)_ of _[zone section-1]()_ that is _[inherited ]()_ from _[the zone section-1](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            By the Euler’s identity this addition should form as one (1) unit of an object originated by the 18s structure. For further on let’s call this unit as the base unit.

            \n\n

            The 24 Cells Hexagon

            \n\n

            Below is the list of primes spin along with their position, the polarity of the number, and the prime hexagon’s overall rotation within 1000 numbers.

            \n\n
            [The Prime Hexagon](https://www.hexspin.com/) is a mathematical structure developed by mathematician _[Tad Gallion](https://www.hexspin.com/about-me/)_. A Prime Hexagon is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime number is encountered _([GitHub: kaustubhcs/prime-hexagon](https://github.com/kaustubhcs/prime-hexagon#prime-hexagon))_.\n
            \n\n
            5, 2, 1, 0\n7, 3, 1, 0\n11, 4, 1, 0\n13, 5, 1, 0\n17, 0, 1, 1\n19, 1, 1, 1\n23, 2, 1, 1\n29, 2, -1, 1\n31, 1, -1, 1\n37, 1, 1, 1\n41, 2, 1, 1\n43, 3, 1, 1\n47, 4, 1, 1\n53, 4, -1, 1\n59, 4, 1, 1\n61, 5, 1, 1\n67, 5, -1, 1\n71, 4, -1, 1\n73, 3, -1, 1\n79, 3, 1, 1\n83, 4, 1, 1\n89, 4, -1, 1\n97, 3, -1, 1\n101, 2, -1, 1\n103, 1, -1, 1\n107, 0, -1, 1\n109, 5, -1, 0\n113, 4, -1, 0\n127, 3, -1, 0\n131, 2, -1, 0\n137, 2, 1, 0\n139, 3, 1, 0\n149, 4, 1, 0\n151, 5, 1, 0\n157, 5, -1, 0\n163, 5, 1, 0\n167, 0, 1, 1\n173, 0, -1, 1\n179, 0, 1, 1\n181, 1, 1, 1\n191, 2, 1, 1\n193, 3, 1, 1\n197, 4, 1, 1\n199, 5, 1, 1\n211, 5, -1, 1\n223, 5, 1, 1\n227, 0, 1, 2\n229, 1, 1, 2\n233, 2, 1, 2\n239, 2, -1, 2\n241, 1, -1, 2\n251, 0, -1, 2\n257, 0, 1, 2\n263, 0, -1, 2\n269, 0, 1, 2\n271, 1, 1, 2\n277, 1, -1, 2\n281, 0, -1, 2\n283, 5, -1, 1\n293, 4, -1, 1\n307, 3, -1, 1\n311, 2, -1, 1\n313, 1, -1, 1\n317, 0, -1, 1\n331, 5, -1, 0\n337, 5, 1, 0\n347, 0, 1, 1\n349, 1, 1, 1\n353, 2, 1, 1\n359, 2, -1, 1\n367, 1, -1, 1\n373, 1, 1, 1\n379, 1, -1, 1\n383, 0, -1, 1\n389, 0, 1, 1\n397, 1, 1, 1\n401, 2, 1, 1\n409, 3, 1, 1\n419, 4, 1, 1\n421, 5, 1, 1\n431, 0, 1, 2\n433, 1, 1, 2\n439, 1, -1, 2\n443, 0, -1, 2\n449, 0, 1, 2\n457, 1, 1, 2\n461, 2, 1, 2\n463, 3, 1, 2\n467, 4, 1, 2\n479, 4, -1, 2\n487, 3, -1, 2\n491, 2, -1, 2\n499, 1, -1, 2\n503, 0, -1, 2\n509, 0, 1, 2\n521, 0, -1, 2\n523, 5, -1, 1\n541, 5, 1, 1\n547, 5, -1, 1\n557, 4, -1, 1\n563, 4, 1, 1\n569, 4, -1, 1\n571, 3, -1, 1\n577, 3, 1, 1\n587, 4, 1, 1\n593, 4, -1, 1\n599, 4, 1, 1\n601, 5, 1, 1\n607, 5, -1, 1\n613, 5, 1, 1\n617, 0, 1, 2\n619, 1, 1, 2\n631, 1, -1, 2\n641, 0, -1, 2\n643, 5, -1, 1\n647, 4, -1, 1\n653, 4, 1, 1\n659, 4, -1, 1\n661, 3, -1, 1\n673, 3, 1, 1\n677, 4, 1, 1\n683, 4, -1, 1\n691, 3, -1, 1\n701, 2, -1, 1\n709, 1, -1, 1\n719, 0, -1, 1\n727, 5, -1, 0\n733, 5, 1, 0\n739, 5, -1, 0\n743, 4, -1, 0\n751, 3, -1, 0\n757, 3, 1, 0\n761, 4, 1, 0\n769, 5, 1, 0\n773, 0, 1, 1\n787, 1, 1, 1\n797, 2, 1, 1\n809, 2, -1, 1\n811, 1, -1, 1\n821, 0, -1, 1\n823, 5, -1, 0\n827, 4, -1, 0\n829, 3, -1, 0\n839, 2, -1, 0\n853, 1, -1, 0\n857, 0, -1, 0\n859, 5, -1, -1\n863, 4, -1, -1\n877, 3, -1, -1\n881, 2, -1, -1\n883, 1, -1, -1\n887, 0, -1, -1\n907, 5, -1, -2\n911, 4, -1, -2\n919, 3, -1, -2\n929, 2, -1, -2\n937, 1, -1, -2\n941, 0, -1, -2\n947, 0, 1, -2\n953, 0, -1, -2\n967, 5, -1, -3\n971, 4, -1, -3\n977, 4, 1, -3\n983, 4, -1, -3\n991, 3, -1, -3\n997, 3, 1, -3\n
            \n\n

            Including the 1st (2) and 2nd prime (3) all together will have a total of 168 primes. The number of 168 it self is in between 39th (167) and 40th prime (173).

            \n\n

            \"247\"

            \n\n

            The most obvious interesting feature of proceeding this prime hexagon, the number line begins to coil upon itself, is it confines all numbers of primes spin!

            \n\n
            Each time a prime number is encountered, the spin or ‘wall preference’ is switched. So, from the first cell, exit from 2’s left side. This sets the spin to left and the next cell is 3, a prime, so switches to right. 4 is not prime and continues right. 5 is prime, so switch to left and so on. _([HexSpin](https://www.hexspin.com/defining-the-prime-hexagon/))_\n
            \n\n

            \"Defining

            \n\n

            As the number line winds about toward infinity, bending around prime numbers, it never exits the 24 cells. And it is the fact that 168 divided by 24 is exactly seven (7).

            \n\n
            Surprisingly, the 24-cell hexagon confines all natural numbers. The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon’s outer boundary, other than 2 and 3, the initial primes that forced the number line into this complex coil. Without a prime number in the outer set of triangles, the number line does not change to an outward course and ***remains forever contained in the 24 cells***. _([HexSpin](https://www.hexspin.com/defining-the-prime-hexagon/))_\n
            \n\n

            \"Euler

            \n\n

            So there should be a tight connection between 168 primes within 1000 with the 24-cell hexagon. Indeed it is also correlated with 1000 prime numbers.

            \n\n

            18s Structure

            \n\n

            You may learn that sets of algebraic objects has a multilinear relationship related to a vector space called tensor.

            \n\n
            Tensors may map between different objects such as vectors, scalars, even other tensors contained in a group of _[partitions](https://en.wikipedia.org/wiki/Partition_(number_theory))_.\n
            \n\n

            \"300px-Components_stress_tensor

            \n\n

            You may notice that there are twists and turns until 19 abuts 2 therefore this addition zone takes only the seven (7) primes out of the 18’s structure of True Prime Pairs.

            \n\n
            The number of primes less than or equal to a thousand (π(1000) = 168) equals the number of hours in a week (7 * 24 = 168).\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) ---------------------\n      |      |  6  +-----+\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s = f(1000) √\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | --------------------------\n------|------|-----+-----+------\n
            \n\n

            In linear algebra, there is vector is known as eigenvector, a nonzero vector that changes at most by a scalar factor when linear transformation is applied to it.

            \n\n
            The eigenvectors of the matrix (red lines) are the two special directions such that every point on them will just slide on them _([Wikipedia](https://commons.wikimedia.org/wiki/File:Eigenvectors_of_a_linear_operator.gif))_.\n
            \n\n

            \"Eigenvectors_of_a_linear_operator\"

            \n\n

            The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating 3 minor hexagons.

            \n\n
            Prime numbers are numbers that have only 2 factors: 1 and themselves.\n- For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.\n- 1 is not a prime number because it can not be divided by any other integer except for 1 and itself. The only factor of 1 is 1.\n- On the other hand, 1 is also not a composite number because it can not be divided by any other integer except for 1 and itself.\n\nIn conclusion, the number 1 is neither prime nor composite.\n
            \n\n

            π(6+11) = π(17) = 7

            \n\n

            \"\"

            \n\n

            So there would be the empty spaces for 18 - 7 = 11 numbers. By our project these spaces will be unified by all of the eleven (11) members of identition zones.

            \n\n

            (11x7) + (29+11) + (25+6) + (11+7) + (4+1) = 77+40+31+18+5 = 171

            \n\n

            \"extended

            \n\n

            The above seven (7) primes will act then as extended branes. This is what we mean by addition zones and it happens whenever a cycle is restarted.

            \n\n

            Undiscovered Features

            \n\n

            When we continue the spin within the discussed prime hexagon with the higher numbers there are the six (6) internal hexagons within the Prime Hexagon.

            \n\n
            Cell types are interesting, but they simply reflect a ***modulo 6 view of numbers***.  More interesting are the six internal hexagons within the Prime Hexagon.  Like the Prime Hexagon, they are newly discovered. The minor hexagons form solely from the order, and type, of primes along the number line _([HexSpin](https://www.hexspin.com/minor-hexagons/))_.\n
            \n\n

            \"Screen-Shot-2016-11-07-at-5

            \n\n

            So the most important thing that need to be investigated is why the prime spinned by module six (6). What is the special thing about this number six (6) in primes behaviour?

            \n\n
            Similarly, I have a six colored dice in the form of the hexagon.  If I take a known, logical sequence of numbers, say 10, 100, 1000, 10000, and look at their spins in the hexagon, the resulting colors associated with each number should appear random – ***unless the sequence I’m investigating is linked to the nature of the prime numbers***.\n
            \n\n

            \"\"

            \n\n

            Moreover there are view statements mentioned by the provider which also bring us in to an attention like the modulo 6 above. We put some of them below.

            \n\n
            That is, if the powers of 10 all returned with blue spin, or as a series of rainbows, or evenly alternating colors or other non-random results, ***then I’d say prime numbers appear to have a linkage to 10.  I may not know what the the linkage is, just that it appears to exist*** _([HexSpin](https://www.hexspin.com/minor-hexagons/))_.\n
            \n\n

            \"image\"

            \n\n

            Another is that phi and its members have a pisano period if the resulting fractional numbers are truncated.

            \n\n
            I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in. That is what I found. ***Phi and its members have a pisano period if the resulting fractional numbers are truncated***. _([HexSpin](https://www.hexspin.com/phi-not-pi-and-why-i-truncate-to-determine-integer-values/))_.\n
            \n\n

            \"truncated

            \n\n

            It would mean that there should be undiscovered things hidden within the residual of this decimal values. In fact it is the case that happen with 3-forms in 7D.

            \n\n
            In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist and in particular _[the 4D metric, is defined by the 3-form](https://www.eq19.com/identition/span12/#three-3-layers)_.\n- We would like to say that our present use of G2 structures (3-forms in 7D) is different from what one can find in the literature on Kaluza–Klein compactifications of supergravity.\n- We show that the resulting 4D theory is (Riemannian) [General Relativity](https://www.sciencedirect.com/topics/physics-and-astronomy/general-relativity) (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.\n- Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.\n\nAlso, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. _([General relativity from three-forms in seven dimensions - pdf](https://github.com/eq19/eq19.github.io/files/14064088/1-s2.0-S0370269317304926-main.pdf))_\n
            \n\n

            \"3-forms

            \n\n

            Taking 19 as a certain parameter we can see that the left handed cycles are happen on 5th-spin (forms 4th hexagon, purple) and 6th-spin (forms 5th hexagon, cyan). Both have different rotation with other spin below 9th spin (forms 6th hexagon, yellow).

            \n\n

            Dimensional Algorithms

            \n\n

            The the main reason of assigning two (2) profiles instead of only one (1) is that we have to accommodate the major type of primes numbers called twin primes.

            \n\n
            This is a necessary but not sufficient condition for N to be a prime as noted, for example, by N= 6(4)+1= 25, which is clearly composite. We note that each turn of the spiral equals an increase of six units. This means that we have a mod(6) situation allowing us to write: N mod(6)=6n+1 or N mod(6)=6n-1 (equivalent to 6n+5). _([HexSpiral-Pdf](https://mae.ufl.edu/~uhk/HEX-SPIRAL-N.pdf))_\n
            \n\n

            \"twin

            \n\n
            Proceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth (4th) hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. Twin primes ***29 and 31 define the fifth (5th) hexagon***, cyan. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon _([HexSpin](https://www.hexspin.com/defining-the-prime-hexagon/))_.\n
            \n\n

            \"IMG_20231221_074421\"

            \n\n
            Because the value 30 is the first (common) product of the first 3 primes. And this 30th order repeats itself to infinity. Even in the first 30s system, therefore, the positions are fixed in which the number information positions itself to infinity. We call it the first member of the MEC 30.\n- The numbers not divisible by 2, 3 or 5 are highlighted. We call them prime positions, hence 1, 7, 11, 13, 17, 19, 23, 29. Important for our work is that in the following the term prime refers only to prime numbers that are in the prime positions. So primes 2, 3 and 5 are always excluded.\n- These positions: 1 7 11 13 17 19 23 29. We refer to this basic system as MEC 30 - \"Mathematical Elementary Cell 30\". By repeating the positions we show the function of the basic system in the next step. If we extend the 30th order of the MEC, for example, to the number 120, the result is ***4 times a 30th order*** and thus 4 × 8 = 32 prime positions.\n- Hypothetical assumption: If the product of the primes (except 2, 3, 5,) would not fall into the prime positions, thus be divided by 2, 3 or 5, the information would have 120 = 32 primes in 32 prime positions: 1, 7, 11, 13, 17, 19, 23, 29, / 31, 37, 41, 43, 47, 49, 53, 59, / 61, 67, 71, 73, 77, 79, 83, 89, / 91, 97, 101, 103, 107, 109, 113, 119\n- These forms gives prime positions:  1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17 , 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29. The 30th order is repeated in the number space ***120 = 4 times, 4 × 8 = 32 prime positions, thus 4 terms***.\n\nFrom our consideration we can conclude that the distribution of prime numbers must have a static base structure, which is also confirmed logically in the further course. This static structure is altered by the products of the primes themselves, since these products must fall into the prime positions since they are not divisible by 2, 3 and 5. _([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))_\n
            \n\n

            \"\"

            \n\n
            All perfect squares within our domain (numbers not divisible by 2, 3 or 5) possess a digital root of 1, 4 or 7 and are congruent to either {1} or {19} modulo 30.\n- ***When the digital root of perfect squares is sequenced within a modulo 30 x 3 = modulo 90 horizon, beautiful symmetries in the form of period-24 palindromes are revealed***. Here's one modulo 90 spin on perfect squares.\n- parsing the squares by their mod 90 congruence reveals that there are ***[96 perfect squares](https://www.eq19.com/multiplication/17.html#perfect-squares)*** generated with each 4 * 90 = 360 degree cycle,\n- which distribute 16 squares to each of 6 mod 90 congruence sub-sets defined as n congruent to {1, 19, 31, 49, 61, 79} forming 4 bilateral 80 sums.\n- each of the 6 columns has 8 bilateral 360 sums, tor a total of 48 * 360 = 40 * 432 (much more on the significance of number 432, elsewhere on this site). \n\nThere's another hidden dimension of our domain worth noting involving multiples of 360, i.e., when framed as n ≌ {1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53 59, 61, 67, 71, 73, 77, 79, 83, 89} modulo 90, and taking 'bipolar' differentials of perfect squares _([PrimesDemystified](https://primesdemystified.com/#Distribution_of_Perfect_Squares))_\n
            \n\n

            16 × 6 = 96

            \n\n

            \"96

            \n\n

            The complete theory was obtained by dimensional reduction of the 11D supergravity on a seven (7) torus and realizing the exceptional symmetry group E7(7)

            \n\n
            Each of the digital root multiplication matrices produced by the six channels consists of what are known in mathematics as '[Orthogonal Latin Squares](https://en.wikipedia.org/wiki/Latin_square)' (defined in Wikipedia as \"an n x n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column\" ... in our case every row and column of the repeating 6x6 matrices possesses the six elements: 1, 2, 4, 5, 7, 8 in some order). Also, the sum of the multiplicative digital roots = 108 x 24 = 2592 = 432 x 6.\n- Note: Channels A, D, E and F combined represent the set of natural numbers not divisible by 2, 3 and 5, the first 24 elements of which form the basis of the [Magic Mirror Matrix](https://www.primesdemystified.com/magicmatrix.html).]\n- The graphic below illustrates the transformative relationships between the matrices employing their primary building blocks (one of the sixteen identical 6 x 6 (36 element) Latin Squares that constitute each matrix):[![Multiplication_Matrix_Transforms](https://github.com/eq19/eq19.github.io/assets/8466209/2b8e8a2b-4bbd-4562-a907-9cad0dc61f76)](https://www.primesdemystified.com/twinprimes.html)\n- When you rotate either the {1,4,7} or {2,5,8} magic square around its horizontal axis, i.e. columns {A,B,C} become {C,B,A}, then add the {1,4,7} {2,5,8} magic squares together, you produce a square with nine 9's. For example, ***adding the first rows of each gives us: {2,8,5} + {7,1,4} = {9,9,9}***.\n- Triangles and magic squares similar–or identical–to those shown above can be derived from the digital root sequence cycles of all three twin prime distribution channels (namely numbers ≌ to {11,13}, {17,19} and {1,29} modulo 30).\n- This is also true of dyads formed by ***paired radii of the Prime Spiral Sieve that sum to 30***, i.e., numbers ≌ to {1,29}, {7,23}, {11,19}, or {13,17} modulo 30, as well as dyads formed when {n, n + 10} are ≌ to {1, 11}, {7, 17}, {13, 23} or {19, 29} modulo 30 (note their pairing by terminating digits). One example relating to twin primes: The first three candidate pairs in the twin prime distribution channel ≌ to {11,13} modulo 30 (all three of which are indeed twin primes) sequence their digital roots as follows:\n  - **{11,13} = digital roots 2 & 4**\n  - **{41,43} = digital roots 5 & 7**\n  - **{71,73} = digital roots 8 & 1**.\n- As you can see, this is the same digital root sequence illustrated above. It appears that the triangulations and magic squares structuring the distribution of twin primes (and as it turns out, all prime numbers) have a genesis in universal principles involving symmetry groups ***rotated by the 8-dimensional algorithms*** discussed at length on this site.\n- You can see this universal principle at work, for example, with regard to the Fibonacci digital root sequence when coupled to a pair of dyads that follow certain incremental rules. As we illustrated above, the initializing dyad of ***the period-24 Fibonacci digital root sequence*** is {1,1, ...}.\n\nWe can generate triangles and magic squares by tiering the Fibonacci digital root sequence with two pairs of terms that are + 3 or + 6 from the initial terms {1,1}. The values of the 2nd and 3rd tiers, or rows, must differ, or symmetry is lost. In other words, ***the first two columns should read either {1,4,7 + 1,7,4, or vice versa} but not {1,4,7 + 1,4,7, or 1,7,4, + 1,7,4}***. _([PrimesDemystified](https://www.primesdemystified.com/twinprimes.html))_\n
            \n\n

            \"Base

            \n\n
            When these 9 squares are combined and segregated to create a 6 x 6 (36 element) square, and this square is compared to the Vedic Square minus its 3's, 6's and 9's (the result dubbed \"[Imaginary Square](https://www.primesdemystified.com/Factorization.html)\"), you'll discover that they share identical vertical and horizontal secquences, though in a different order (alternating +2 and -2 from each other), and that these can be easily made to match exactly by applying a simple function multiplier, as described and illustrated later below. _([PrimesDemystified](https://www.primesdemystified.com/magicmatrix.html))_\n
            \n\n

            \"ReciprocalTransform\"

            \n\n
            In sum, we're positing that ***Palindromagon + {9/3} Star Polygon = Regular Enneazetton***.\n- The significance of this 'chain-of-events' is that we can state with deterministic certainty that cycling the period-24 digital root dyads of both twin primes and the modulo 90 factorization sequences of numbers not divisible by 2, 3, or 5 generates an infinite progression of these complex polygons possessing stunning reflectional and translational symmetries.\n- Lastly, let's compare the above-pictured 'enneazetton' to an 18-gon 9-point star generated by the first three primes; 2, 3 and 5 (pictured below), and we see that they are identical, save for the number of sides (9 vs. 18). They are essentially convex and concave versions of each other. \n\nThis is geometric confirmation of the deep if not profound connection between the three twin prime distribution channels (which remember have 2, 3, and 5 encoded in their Prime Spiral Sieve angles) and the first three primes, 2, 3, and 5. _([PrimesDemystified](https://www.primesdemystified.com/twinprimes.html))_\n
            \n\n

            \"Theory

            \n\n

            The symmetries that come into focus when the lense aperature, of the Prime Spiral Sieve is tripled to modulo 90, synchronizing its modulus with its period-24 digital root.

            \n\n

            Prime Spiral Sieve

            \n\n

            It appears that the triangulations and magic squares structuring the distribution of all prime numbers involving symmetry groups rotated by the 8-dimensional algorithms.

            \n\n
            Focusing on just the twin prime distribution channels, we see the relationships shown below [and, directly above, we show that two of the channels (B & C) transform bi-directionally by rotating 180° around one of their principal (lower-left to upper-right) diagonal axes]:\n
            \n\n

            7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

            \n\n

            \"Twin_Primes_Channel_Matrices

            \n\n
            Another fascinating feature of this array is that any even number of–not necessarily contiguous–factors drawn from any one of ***the 32 angles in this modulo 120*** configuration distribute products to 1(mod 120) or 49 (mod 120), along with the squares.\n- We see from the graphic above that the digital roots of the Fibonacci numbers indexed to our domain (Numbers ≌ to {1,7,11,13,17,19,23,29} modulo 30) ***repeat palindromically every 32 digits (or 4 thirts) consisting of 16 pairs of bilateral 9 sums***.\n- The digital root sequence of our domain, on the other hand, repeats every 24 digits (or 3 thirts) and possesses 12 pairs of bilateral 9 sums. The entire Prime Root sequence end-to-end covering 360° has 48 pairs of bilateral 9 sums.\n- And finally, the Prime Root elements themselves within the Cirque, ***consisting of 96 elements, has 48 pairs of bilateral sums totaling 360***. Essentially, the prime number highway consists of infinitely telescoping circles ...\n- Also note, the digital roots of the Prime Root Set as well as the digital roots of Fibonnaci numbers and Lucas numbers (the latter not shown above) ***indexed to it all sum to 432 (48x9) in 360° cycles***.\n- The sequence involving Fibonacci digital roots repeats every 120°, and has been documented by the author on the On-Line Encyclopedia of Integer Sequences: [Digital root of Fibonacci numbers indexed by natural numbers not divisible by 2, 3 or 5 (A227896)](https://oeis.org/A227896).\n- The four faces of our pyramid additively cascade ***32 four-times triangular numbers*** (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of ***32^2 = 1024 = 2^10***).\n- These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of ***the 1000th prime*** within our domain, and equals the total number of 'elements' used to construct the pyramid. \n\nA thirt, in case you're wondering, is a useful unit of measure when discussing intervals in natural numbers not divisible by 2, 3 or 5. A thirt, equivalent to one rotation around the [Prime Spiral Sieve](https://www.primesdemystified.com/) is like a mile marker on the prime number highway. If we take the Modulo 30 Prime Spiral Sieve and expand it to ***Modulo 360***, we see that ***there are 12 thirts*** in one complete circle, or 'cirque' as we've dubbed it. ***Each thirt consists of 8 elements***. _([PrimesDemystified](https://www.primesdemystified.com/twinprimes.html))_\n
            \n\n

            1000 x (π(11) + 360) days = 1000 x 365 days = 1000 years

            \n\n

            \"Mystery

            \n\n

            The side of a pentagon-pentagram can clearly be seen as in relation to its diagonal as 1: (√5 +1)/2 or 1:φ , the Golden Section.

            \n\n

            \"golden-ratio-pentagram-lr\"

            \n\n

            They are the source of triangular coordinates when translated into vertices of a modulo 9 circle which by definition has 9 equidistant points each separated by 40°.

            \n\n
            When we additively sum the three period-24 digital root cycles these dyads produce, then tier them, we create six 3 x 3 matrices (each containing values 1 thru 9) separated by repetitive number tiers in the following order: {1,1,1} {5,5,5} {7,7,7} {8,8,8} {4,4,4} {2,2,2}.\n- The six (6) matrices these tiers demarcate are the source of triangular coordinates when translated into vertices of a modulo 9 circle (which ***by definition has 9 equidistant points around its circumference, each separated by 40°***).\n- The series of diagrams below show the six geometric stages culminating in a complex polygon of extraordinary beauty. We've dubbed this object a 'palindromagon' given that the coordinates of the 18 triangulations produced by the digital root dyadic cycles in the order sequenced sum to a palindrome: 639 693 963 369 396 936.\n- Remarkably, this periodic palindrome, with additive sum of 108, sequences the 6 possible permutations of values {3,6,9}. Interesting to consider a geometric object with a hidden palindromic dimension. But that's not all: When the six triadic permutations forming the palindrome are labeled A, B, C, D, E, F in the order generated, ACE and BDF form 3 x 3 Latin squares. In both cases all rows, columns and principal diagonals sum to 18:\n\n  - ***ACE ... BDF***\n  - 693 ... 639\n  - 369 ... 963\n  - 936 ... 396\n\n- The output of these algorithmically sequenced triangulations is fundamentally a geometric representation of the twin prime distribution channels (and, as we noted above, the same geometry is expressed in factorization sequencing, albeit the vertices may be ordered differently.\n- This is because each set of three generator dyads roots to the same six elements: 1, 2, 4, 5, 7, 8. Thus, for example, dyad sets ({1,2} {4,5} {7,8}) and ({2,4} {5,7} {8,1}) will generate identical complex polygons, despite their vertices being sequenced in different orders.).\n\nIt's remarkable that ***objects consisting of star polygons, spiraling irregular pentagons***, and possessing nonagon perimeters and centers, can be constructed from only ***27 coordinates pointing to 9 triangles in 3 variations***. Each period-24 cycle produces two 'palindromagons'. _([PrimesDemystified](https://www.primesdemystified.com/twinprimes.html))_\n
            \n\n

            \"Twin_Prime_Digital_Root_Polygon\"

            \n\n

            The equality between the product on the 1st-line and the formulas in the 3rd- and 4th-lines is Euler’s pentagonal number where p(33) = 10143 landed exactly by n - 7.

            \n\n
            Using Euler's method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler _([Wikipedia](https://en.wikipedia.org/wiki/Partition_function_(number_theory)#Generating_function))_.\n
            \n\n

            π(π(π(1000th prime))) + 1 = 40

            \n\n

            \"image\"\n

            \n\n

            As explicitly indicated by n - 7 within identition zones this p(33) behave reversal to the exponentiation zones so it would stand as π(π(π(1000th prime)))+1. Within these 1000 primes there will be fractions which end up with 168 identities.

            \n\n

            p(33) = p(40-7) = loop (100000) = 4 + 25 + 139 + 1091 + 8884 = 10143

            \n\n

            \"\"

            \n\n

            This will be the same structure as the seven (7) pàrtitions of addition zones. So by simple words this 11 dimensions brings us back to the root functions. The only difference is the base unit of the lexer (Id: 33). It is now carrying the above p(33) = 10143.

            \n\n
            [The published](https://github.com/eq19/eq19.github.io/files/13930690/PhysRev.76.769.pdf) diagram by [Feynman](https://physics.aps.org/story/v24/st3) helped scientists track particle movements in illustrations and visual equations rather than verbose explanations. What seemed almost improbable at the time is now one of the greatest [explanations](https://www.quantamagazine.org/why-feynman-diagrams-are-so-important-20160705/) of particle physics — the squiggly lines, diagrams, arrows, quarks, and cartoonish figures are now the established nomenclature and visual story that students, scientists, and readers will see when they learn about this field of science. _([medium.com](https://medium.com/taking-note/learning-from-the-feynman-technique-5373014ad230))_\n
            \n\n

            8 pairs = 8 x 2 = 16

            \n\n

            \"Electromagnetism\"

            \n\n

            Starting with the next chapter we are going to discuss in detail how this reversal behaviour is converting the 11 dimensions to 7 x 11 = 77 partitions.

            \n\n
            ***There are 7 hidden dimensions in 11-d Supergravity, which is the low energy approximation to M theory, which also has 7 hidden dimensions***. _([Prime Curios!](https://t5k.org/curios/page.php?curio_id=20686))_\n
            \n\n

            π(1000) - loop(1,30) - loop(31,36) = 168 - 29 - 25 = 114

            \n\n

            \"IMG_20240114_014704\"

            \n","dir":"/addition/","name":"README.md","path":"addition/README.md","url":"/addition/"},{"sort":2,"spin":1,"span":"partition","suit":"intro","layout":"default","title":"Partition function","content":"# [Partition function](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e)\n\nBased on the finiteness position of middle zero axis = 15 we have defined our _19 vs 18 Scenario_ contained in _three (3) groups of five (5) of integer number [partitions](https://en.wikipedia.org/wiki/Partition_(number_theory))_. Each groups represents ***the three (3) basic arithmetic operations*** of _[Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_.\n\n>Euler's identity is often cited as an example of deep mathematical beauty. Three (3) of the basic arithmetic operations occur exactly once each: ***addition***, ***multiplication***, and ***exponentiation*** _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_.\n\n```\n---+-----+-----\n 1 | 1 | 5 🡰--19--\n---+-----+----- |\n 2 | 6 | 8 | \n---+-----+----- |\n 3 | 9 | 26 --289-¤-exponentiation zone\n---+-----+----- |\n 4 | 27 | 28 |\n---+-----+----- |\n 5 | 29 | 29 ➤--18--\n---+-----+-----\n 6 | 30 | 31 🡰--18--\n---+-----+----- |\n 7 | 32 | 44 |\n---+-----+----- |\n 8 | 45 | 46 --329-¤-multiplication zone\n---+-----+----- |\n 9 | 47 | 49 |\n---+-----+----- |\n10 | 50 | 50 ➤--17--\n---+-----+----- \n11 | 51 | 53 🡰--17--\n---+-----+----- |\n12 | 54 | 59 | \n---+-----+----- |\n13 | 60 | 82 --168-¤-addition zone\n---+-----+----- |\n14 | 83 |{102} |\n---+-----+----- |\n15 |{103}| 110 ➤--16--\n---+-----+-----\n```\n\nThe five (5) of integer number partitions shows a profound connection between the most fundamental numbers in mathematics as it also links ***the five (5) fundamental mathematical constants***:

            (1) The number 1, the ***multiplicative identity***,
            (2) The number i, ***the imaginary unit*** of the complex numbers.
            ![image](https://user-images.githubusercontent.com/8466209/222681901-b8d2a6a4-6959-4544-b66a-74eb3efde4c1.png)
            (3) The number π = 3.1415..., the fundamental ***circle constant***, and

            ![Pi-unrolled-720](https://user-images.githubusercontent.com/8466209/222678426-29cfb16e-dca2-43eb-bd59-ff893e126a0a.gif)

            (4) The number e = 2.718..., also known as ***Euler's number***, which occurs widely in mathematical analysis.

            ![image](https://user-images.githubusercontent.com/8466209/222675476-d80e0ce8-ee1b-442c-9810-f98e29ba6961.png)

            (5) Furthermore, the equation is given in the form of an expression ***set equal to zero***, the number 0, as the ***additive identity*** which is common practice in several areas of mathematics.
            \n>Euler's identity is a special case of Euler's formula ***eix = cos x + i sin x*** when evaluated for ***x = π***, In addition, it is directly used in a proof that ***π is transcendental***, which implies the impossibility of squaring the circle. _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_

            [![Euler's identity](https://user-images.githubusercontent.com/8466209/219020102-60b526fd-273d-4c6d-8997-06254bdc5625.png)](https://en.wikipedia.org/wiki/Euler%27s_identity)\n\nIt is stated by _[DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en)_ that using Euler's identity, the [MEC30 standard](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity) is more accurately than a measurement. The distribution of prime numbers is a central point of study in _[number theory](https://en.wikipedia.org/wiki/Number_theory)_. So let's start from there.\n\n## Rational Objects\n\nIn number theory, ***[the partition functionp(n) ](https://en.wikipedia.org/wiki/Partition_function_(number_theory))*** represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (_[Diophantine geometry](https://en.wikipedia.org/wiki/Diophantine_geometry)_).\n\n>The central problem is to determine when a Diophantine equation has solutions, and if it does, how many. Two examples of an elliptic curve, that is, a curve of genus 1 having at least ***one rational point***. Either graph can be seen as a slice of a torus in four-dimensional space _([Wikipedia](https://en.wikipedia.org/wiki/Number_theory#Diophantine_geometry))_.\n\n[![Number theory](https://user-images.githubusercontent.com/8466209/227834941-50c822bc-a5b5-47df-82c1-6df288aa24ef.png)](https://en.wikipedia.org/wiki/Number_theory#Diophantine_geometry)\n\nOne of the main reason is that one does not yet have a mathematically complete example of a quantum gauge theory in four-dimensional space-time. It is even a sign that Einstein’s equations on the energy of empty space are somehow incomplete.\n\n>Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents _([Wikipedia](https://en.wikipedia.org/wiki/Albert_Einstein#Scientific_career))_.\n\n![default](https://user-images.githubusercontent.com/8466209/227863531-b8b9a02a-148c-4048-b7cb-1d1ff820b6be.png)\n\nDyson introduced the concept in the context of a study of _[certain congruence properties](https://en.wikipedia.org/wiki/Ramanujan%27s_congruences)_ of the partition function discovered by the mathematician Srinivasa Ramanujan who the one that found the interesting behaviour of the [taxicab number 1729](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity).\n\n>In _[number theory](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#number-theory)_ and combinatorics, [rank of a partition](https://en.wikipedia.org/wiki/Rank_of_a_partition) of a positive integer is a certain integer associated with the partition meanwhile the [crank of a partition](https://en.wikipedia.org/wiki/Crank_of_a_partition) of an integer is a certain integer associated with that partition _([Wikipedia](https://en.wikipedia.org/wiki/Freeman_Dyson#Crank_of_a_partition))_.\n\n[![Rank_of_a_partition](https://user-images.githubusercontent.com/8466209/227838045-3ddd5238-7beb-4023-affa-c61a054afd2b.png)](https://en.wikipedia.org/wiki/Freeman_Dyson#Rank_of_a_partition)\n\n[Young tableaux](https://en.wikipedia.org/wiki/Young_tableau) were introduced by Alfred Young, a mathematician at Cambridge University, in 1900. They were then applied to the study of the symmetric group. Their theory was further developed by many mathematicians, including [W. V. D. Hodge](https://en.wikipedia.org/wiki/Hodge_theory)\n\n### The rank of a partition\n\nBy our project, this partition stands as [the prime identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity). The tabulation below shows the [2nd prime identity](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#polar-plot) where the 20 out of the [largest part = 21](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#compositions) goes to [rank = 10](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-18_10_imaginary-md) via [crank = 20-11 = 9](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-18_09_residual-md). These 10 and 9 are associated with the ***[19th prime identitity](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-19_root-md)***.\n\n```\n largest part = 21 → 11+13+12 = 36 → MEC30\n ↓ |\n---+-----+-----+-----+-----+ ↓\n 1 | 19 | 1 | 20 | 21 |-------------------|-----\n---+-----+-----+-----+-----+ ↓ |\n 2 | 18 | 21 | 39 | 60 |------------------- |\n---+-----+-----+-----+-----+ | |\n 3 |{63} | 40 | 103 | 143 |------------- | |\n---+-----+-----+-----+-----+ | | |\n 4 | 37 | 104 | 141 | 245 |------- | | |\n---+-----+-----+-----+-----+ | | | |\n 5 | 10* | 142 | 152 | 294 |- 11** | 13 | 12 | 12 | 18\n---+-----+-----+-----+-----+ | | | |\n 6 | 24 | 153 | 177 | 332 |------- | | |\n---+-----+-----+-----+-----+ | | |\n 7 | 75 | 178 | 253 | 431 |------------- | |\n---+-----+-----+-----+-----+ | |\n 8 | 30 | 254 | 284 | 538 |------------------- |\n---+-----+-----+-----+-----+ ↓ |\n 9 | 1 | 285 | 286 | 571 |-------------------|-----\n===+=====+=====+=====+=====+ ↓\n45 | 277 | ← 11+13+12=36 ← MEC30\n---+-----+ |\n ↑\nNote:\n10* stands as the central rank\n11** stands as the central parts\n```\n\nBy having a total of 571, the congruence properties is composed in to the last of 20/10 = 2 numbers of 285 and 286 throughout the cumulative sum of [45 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#addition-zone) that are [forming](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partition) the _[10x11=110 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#partition-function)_ of ***18th prime identity***.\n\n***(71+6) + (43-6) = 77 + 37 = 11x7 + 30+13-6***\n\n[![Factorization](https://user-images.githubusercontent.com/8466209/228433870-3941279d-4740-4282-8132-f2154673b1ce.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#centralizing)\n\nThis scheme of 19 vs 18 stands as our _[19 vs 18 Scenario](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-%CE%B419-vs-18-scenario)_ while the tensor of 110 objects are obtained by observing centralizing ***the first 20 to 10 objects*** from [polarizing](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#polar-plot) of 2x11x13=286 objects out of ***the central pair 11 and 13*** within _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. \n\n### The crank of a partition\n\nIn [linear algebra](https://en.wikipedia.org/wiki/Linear_algebra), this tensor is known as _[eigenvector](https://mathworld.wolfram.com/Eigenvector.html)_, a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding _[eigenvalues](https://en.wikipedia.org/wiki/Eigenvalues)_ is the factor by which the eigenvector is scaled.\n\n>In this shear mapping the red arrow changes direction, but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it does not change direction, and since its length is unchanged, its eigenvalue is 1 _([Wikipedia](https://en.wikipedia.org/wiki/Eigenvalues#Overview))_.\n\n[![File:Mona_Lisa_eigenvector_grid](https://user-images.githubusercontent.com/8466209/229377643-ef8d94d0-d8b7-468a-8154-31c8e332edf9.jpg)](https://en.wikipedia.org/wiki/Eigenvalues#Overview)\n\nDyson discovered that _the eigenvalue_ of these matrices are spaced apart in exactly the same manner as _[Montgomery conjecture](https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture)_ of the nontrivial zeros of the [zeta function](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function). Means it also depends on _Riemann hypotesis_ which is still in a major issue. Similar case left science today many unsolved problems that associated with. \n\n[![Eigenvectors_of_a_linear_operator](https://user-images.githubusercontent.com/8466209/228168805-ab93185d-4172-4284-8459-040e2f8797d4.gif)](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors#Overview)\n\nThe rank cannot be used to prove the theorem combinatorially, Dayson wrote an arithmetical coefficient similar to, but more recondite than, the rank of a partition; and called this hypothetical coefficient as the \"crank\" of the partition.\n\n>The values p(1),,,,,,p(8)} of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the [Young diagrams](https://github.com/eq19/lexer#young-diagrams) for the partitions of the numbers from 1 to 8 _([Wikipedia](https://en.wikipedia.org/wiki/Partition_function_(number_theory)))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/230748873-6761c929-261c-429c-bf14-f30851f6a12e.png)](https://arxiv.org/pdf/2302.07971.pdf)\n\nSince 286 has the prime factors of 11 and 13 so it is also the product of the middle two numbers of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. Therefore, _the eigenvalue_ of the 11 parts also determines the equal size rotation of crank partitions of 13 prime identity.\n\n```\n$True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub | i | f\n------+------+-----+----------\n | | | 1 | ◄-----------------------------\n | | 1 +-----+ |\n | 1 | | 2 | (5) |\n | |-----+-----+ |\n | | | 3 | |\n 1 +------+ 2 +-----+---- |\n | | | 4 | |\n | +-----+-----+ |\n | 2 | | 5 | (7) |\n | | 3 +-----+ |\n | | | 6 | |\n------+------+-----+-----+------ |\n | | | 7 | |\n | | 4 +-----+\n | 3 | | 8 | (11) ◄-- 11 parts of rank 10 = 110\n | +-----+-----+\n | | | 9 | |\n 2 +------| 5 +-----+----- |\n | | | 10 | |\n | |-----+-----+ |\n | 4 | | 11 | (13) ◄----------------------------\n | | 6 +-----+\n | | | 12 |\n------+------+-----+-----+-------------------- (36)\n | | | 13 |\n | | 7 +-----+\n | 5 | | 14 | (17) ◄----------------------------\n | |-----+-----+ |\n | | | 15 | 0 axis ◄-- partitions of the (13) ◄-- rotation\n 3 +------+ 8 +-----+----- |\n | | | 16 | ◄----------------------------\n | |-----+-----+\n | 6 | | 17 | (19)\n | | 9 +-----+\n | | | 18 |\n------|------|-----+-----+-------------------- (72)\n```\n\nUnfortunately the rotation of this eigenvalues deals with [four-dimensional space-time](https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space) which was already a big issue. Speculation is that the unfinished book of Ramanujan's partition, series of Dyson's solutions and hugh of Einstein's papers tend to solve it.\n\n>On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! _([Clay Institute's - Official problem description](https://claymath.org/sites/default/files/yangmills.pdf))_.\n\n[![Geometry of 4D rotations](https://user-images.githubusercontent.com/8466209/229301443-d3b4d5a1-a586-40cd-a6a3-515bb2808335.png)](https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#Geometry_of_4D_rotations)\n\nMore generally, the central problem is to determine when an equation in n-dimensional space has solutions. However at this point, we finaly found that the prime distribution has something to do with _[the subclasses of rank and crank partitions](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-subclasses-of-each-partitions)_.\n\n## The subclasses of each partitions\n\nDayson introduced the idea of rank of a partition to accomplish the task he set for himself. He made the following conjectures which were proved in 1954 by _[Peter Swinnerton-Dyer](https://en.wikipedia.org/wiki/Peter_Swinnerton-Dyer)_ an English mathematician specialising in _[number theory](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#number-theory)_.\n\n>Dayson's friend the neurologist and author Oliver Sacks said: \"A favourite word of Freeman's about doing science and being creative is the word ***subversive*** (tending or intending to subvert or overthrow, destroy, or undermine an established or existing system, especially a legally constituted or a set of beliefs), and he's done that all his life _([Wikipedia](https://en.wikipedia.org/wiki/Freeman_Dyson#Biography))_.\n\n```\nN(0, 5, 5n + 4) = N(1, 5, 5n + 4) = N(2, 5, 5n + 4) = N(3, 5, 5n + 4) = N(4, 5, 5n + 4)\nN(0, 7, 7n + 5) = N(1, 7, 7n + 5) = N(2, 7, 7n + 5) = . . . = N(6, 7, 7n + 5)\n```\n\nThe concepts of rank and crank can both be used to classify partitions of certain integers into subclasses of equal size. The two concepts produce different subclasses of partitions. This is illustrated in the following two tables.\n\n>Although not in the form that Dayson have defined, it was found that the last problem on which Ramanujan worked on before his death was cranks. Berndt and his coauthors have given substantial evidence that Ramanujan knew about the function _([Wikipedia](https://en.wikipedia.org/wiki/Crank_of_a_partition#Ramanujan_and_cranks))_.\n\n[![default](https://user-images.githubusercontent.com/8466209/228412737-ab2f87a4-cdb1-4dc6-9a8c-907edef0ed19.png)](https://en.wikipedia.org/wiki/Crank_of_a_partition#Basic_result)\n\nThe subclasses of partitions develops characters similar to the distribution of prime numbers. This results in a fundamental causal relation to the primes, systemically the products are entered into the position system. \n\n>The approach taken is to think of the solutions of an equation as a geometric object. For example, an equation in two variables defines a curve in the plane. More generally, an equation, or system of equations, in two or more variables defines a curve, a surface or some other such object in n-dimensional space _([Wikipedia](https://en.wikipedia.org/wiki/Number_theory#Diophantine_geometry))_.\n\n![](https://user-images.githubusercontent.com/8466209/201362034-7a0c83f3-d310-4b92-b3e5-fc1f832693fc.png)\n\nDyson has many [series of formal solution](https://en.wikipedia.org/wiki/Freeman_Dyson#Dyson_series). An explicitly time-dependent _[Schrödinger equation](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#schr%C3%B6dinger-equation)_ by iteration, and the time-ordering operator {T} as entity of basic importance of quantum mechanics, are also named after Dyson .\n\n### Relation to the primes\n\nThe Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.\n\n>Both Ulam and Gardner noted that the existence of such prominent lines ***is not unexpected***, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with **major unsolved problems** in number theory such as Landau's problems _([Wikipedia](https://en.wikipedia.org/wiki/Ulam_spiral))_.\n\n[![prime Sacks_spiral](https://user-images.githubusercontent.com/8466209/229820606-b2bbd7fb-3300-4507-8080-fb27ed6fd512.png)](https://upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Sacks_spiral.svg/120px-Sacks_spiral.svg.png)\n\nAccording to the results of Princeton University USA in 1972, the distribution of the prime numbers shows in the Riemann zeta function between the position of its complex zeros and middle axis is identical with the rotation curve of energy distribution. \n\n***37 + 12 = 61 - 12 = 49 = 7 x 7 = d(13)***\n\n![image](https://user-images.githubusercontent.com/36441664/74591945-2b75cb80-504f-11ea-85dd-14d0a803ee6b.png)\n\nIn the second opposing member, the position 19 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 11 as a prime number is now forced to determine _a new axis-symmetrical zero position_.\n\n>Note that when 77 contains 'Lucky 7 and 11' as prime factors it is also the product of the middle two numbers of this sequence (11*7 = 77) _([Prime Curios!](https://t5k.org/curios/page.php/77.html))_.\n\n![MEC30 Localization](https://user-images.githubusercontent.com/36441664/74591731-f5cfe300-504c-11ea-9e04-d814c57aa969.png)\n\nWhen the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent .\n\n>It's possible to build a _[Hessian matrix](https://en.wikipedia.org/wiki/Hessian_matrix)_ for a _[Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization)_ step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector _([Tensorflow](https://www.tensorflow.org/guide/advanced_autodiff#batch_jacobian))_. \n\n[![Batch Jacobian](https://user-images.githubusercontent.com/8466209/229297019-4583e9a7-273d-4489-ab87-37c88be16adb.png)](https://www.tensorflow.org/guide/advanced_autodiff#batch_jacobian)\n\nThis idea was done as the earliest in 1960s by [Swinnerton-Dyer](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#physical-result) using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known. \n\n>From these numerical results ***the conjecture predicts that the data should form a line of slope equal to the rank of the curve***, which is 1 in this case drawn in red in red on the graph _([Wikipedia](https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture#Current_status))_.\n\n[![The Birch and Swinnerton-Dyer conjecture ](https://user-images.githubusercontent.com/8466209/218376819-e17c97cf-1f1d-4363-a1ce-2b1c355591c3.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rational-vs-irrational)\n\nIt is stated that Np for a curve E with rank r obeys an asymptotic law and is still remain unsolved. Thus it would mean that using Euler's identity to get a definite pattern of prime distribution is still a long way to go.","dir":"/identition/span1/","name":"gist02.md","path":"identition/span1/gist02.md","url":"/identition/span1/gist02.html"},{"sort":2,"spin":13,"layout":"default","title":"core","content":"# core\n[![default](https://user-images.githubusercontent.com/8466209/202907205-4c025632-44a7-4cbe-927f-166254803607.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-keyring-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/204159538-6f87b60c-6a32-486d-aa55-c9af2db7eda6.png)\n](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-feeding-md)\n","dir":"/exponentiation/span13/","name":"gist02.md","path":"exponentiation/span13/gist02.md","url":"/exponentiation/span13/gist02.html"},{"sort":2,"spin":null,"span":null,"suit":2,"layout":"default","title":"True Prime Pairs","content":"

            True Prime Pairs

            \n\n

            This is the partial of the mapping scheme of our eQuantum Project. Our mapping is simulating a recombination of the three (3) layers of these prime pairs.

            \n\n
            This section is referring to _[wiki page-2](https://github.com/eq19/eq19.github.io/wiki)_ of _[zone section-2]()_ that is _[inherited ]()_ from _[the zone section-2](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            An Independent claim is also included for the localization and determination, or their material structures, by graphical representation of base sequences on various media, based on the new assignments and the derived vibrations and amplitudes.

            \n\n

            Prime Objects

            \n\n

            In short this project is mapping the quantum way within a huge of prime objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

            \n\n
            5, 2, 1, 0\n7, 3, 1, 0\n11, 4, 1, 0\n13, 5, 1, 0\n17, 0, 1, 1\n19, 1, 1, 1\n
            \n\n

            \"default\"

            \n\n
            The 5+7+11+13 is the smallest square number expressible as the sum of four consecutive primes which are also two couples of prime twins!\n- Their sum is 36 which is [the smallest square](https://primes.utm.edu/curios/page.php?number_id=270) that is the sum of a twin prime pair {17, 19}.\n- This 36 is the smallest number expressible as the sum of consecutive prime in **two (2) ways** (5+7+11+13 and 17+19). \n
            \n\n
            $True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer|  i  |   f\n -----+-----+---------\n      |  1  | 5\n   1  +-----+\n      |  2  | 7\n -----+-----+---  } 36 » 6®\n      |  3  | 11\n   2  +-----+\n      |  4  | 13\n -----+-----+---------\n      |  5  | 17\n   3  +-----+     } 36 » 6®\n      |  6  | 19\n -----+-----+---------\n
            \n\n

            \"\"

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | \n      |      |  1  +-----+          \n      |  1   |     |  2  | (5)\n      |      |-----+-----+\n      |      |     |  3  |\n  1   +------+  2  +-----+----\n      |      |     |  4  |\n      |      +-----+-----+\n      |  2   |     |  5  | (7)\n      |      |  3  +-----+\n      |      |     |  6  |\n------+------+-----+-----+------      } (36)\n      |      |     |  7  |\n      |      |  4  +-----+\n      |  3   |     |  8  | (11)\n      |      +-----+-----+\n      |      |     |  9  |\n  2   +------|  5  +-----+-----\n      |      |     |  10 |\n      |      |-----+-----+\n      |  4   |     |  11 | (13)\n      |      |  6  +-----+\n      |      |     |  12 |\n------+------+-----+-----+------------------\n      |      |     |  13 |\n      |      |  7  +-----+\n      |  5   |     |  14 | (17)\n      |      |-----+-----+\n      |      |     |  15 |\n  3   +------+  8  +-----+-----       } (36)\n      |      |     |  16 |\n      |      |-----+-----+\n      |  6   |     |  17 | (19)\n      |      |  9  +-----+\n      |      |     |  18 |\n------|------|-----+-----+------\n
            \n\n

            \"Primes-vs-composites

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) ---------------------\n      |      |  6  +-----+        <-----------------  strip √\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s = f(1000)\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | --------------------------\n------|------|-----+-----+------# \n
            \n\n
            We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius.\n- We show that the resulting 4D theory is (Riemannian) [General Relativity](https://www.sciencedirect.com/topics/physics-and-astronomy/general-relativity) (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.\n- Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.\n\nIn our approach ***a 3-form is not an object that exist in addition to the metric, it is the only object that exist. The metric, and in particular the 4D metric, is defined by the 3-form***. _([General relativity from three-forms in seven dimensions - pdf](https://github.com/eq19/eq19.github.io/files/14064088/1-s2.0-S0370269317304926-main.pdf))_\n
            \n\n

            \"Symmetry

            \n\n
            In this article we will support this conjecture and develop a new approach to quantum gravity called smooth quantum gravity by using ***smooth 4-manifolds*** with an exotic smoothness structure.\n- In particular we discuss the appearance of a wildly embedded 3-manifold which we identify with a quantum state.\n- Furthermore, we analyze this quantum state by using foliation theory and relate it to an element in an operator algebra.\n- Then we describe a set of geometric, non-commutative operators, the skein algebra, which can be ***used to determine the geometry of a 3-manifold***.\n- This operator algebra can be understood as a deformation quantization of the classical Poisson algebra of observables given by [holonomies](https://en.wikipedia.org/wiki/Holonomy).\n- The structure of this operator algebra induces an action by using the quantized calculus of Connes. \n\nThe scaling behavior of this action is analyzed to obtain the classical theory of _General Relativity (GRT)_ for large scales. _([Smooth quantum gravity - pdf](https://github.com/eq19/eq19.github.io/files/14132472/1601.06436.pdf))_\n
            \n\n

            \"addition

            \n\n

            The holonomy tells you how to propagate MEC30. A spin network state assigns an amplitude to a set of spin half particles tracing out a path in space, merging and splitting.

            \n\n

            \"\"

            \n\n

            This kind of approach has some obvious properties: there are non-linear gravitons, a connection to lattice gauge field theory and a dimensional reduction from 4D to 2D.

            \n\n

            Construction of a State

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------    <----------------- Mobius strip √\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |\n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) ---------------------\n      |      |  6  +-----+        <----------------- Mobius strip\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s = f(1000)\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | --------------------------\n------|------|-----+-----+------  <----------------- Möbius strip √\n
            \n\n
            The funny looking ***Möbius strip***, which was also independently discovered in 1858 by the unlucky Listing whose name left the history of mathematics untouched.\n- It is a surface with only one side and only one boundary, often used to puzzle young math students. You can easily create it by taking a strip of paper, twisting it and then joining the ends of the strip.\n- Being the first example of a surface without orientation it did not shake the grounds of mathematics as much as the other discoveries of this list did, yet it provided a lot of practical applications, such as a resistant belt, and inspired mathematicians to come up with unorientable surfaces, like the ***Klein bottle***.\n\n- The name of this surface possibly comes from a double coincidence: Klein, its conceptor, originally named it Fläche, which means surface in German and sounds similar to Flasche, which means bottle. The fact that it also looked like a bottle seems to have sealed the renaming.\n\nMathematical fields were created, we got the ***Turing Machine***, fancy looking surfaces and, most importantly, the ability to re-examine our perceptions and adapt our tools accordingly. _([freeCodeCamp](https://www.freecodecamp.org/news/10-awkward-moments-in-math-history-d364706d902d/))_\n
            \n\n

            \"mobius

            \n\n

            These items are elementary parts possessing familiar properties but they never exist as free particles. Instead they join together by the strong force into bound states.

            \n\n

            f(18) = f(7) + f(11) = (1+7+29) + 11th prime = 37 + 31 = 36 + 32 = 68

            \n\n

            \"\"

            \n\n

            Bilateral 9 Sums

            \n\n
            Eigennvalue curves (right) showing a triple eigenvalue at zero for τ = 1 and double eigenvalues at 1 ± √2i for τ = √43. On the left the graph of 1/|Q(λ)| with the same eigenvalue curves plotted in the ground plane. Green stars indicate the eigenvalues of A, blue stars the roots of puv(λ) and triangles the zeroes of Q0\n(λ)\n
            \n\n

            10 + 10th prime + 10th prime = 10 + 29 + 29 = 68

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------    <----------------- Mobius strip\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |\n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- (71) √\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) ---------------------\n      |      |  6  +-----+        <----------------- Mobius strip\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- (43) √\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | --------------------------\n------|------|-----+-----+------  <----------------- Möbius strip\n
            \n\n

            This pattern is raised up per six (6) cycles on the 19, 43 and 71. Since the members are limited to the sum of 43+71=114.

            \n\n

            \"Polarity\"

            \n\n

            So here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme.

            \n\n
            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their ***collective bilateral 9 sum symmetry***). _([PrimesDemystified](https://primesdemystified.com/))_\n
            \n\n

            7 x π(89) = 7 x 24 = 168 = π(1000)

            \n\n

            \"collective

            \n\n

            Supersymmetric Multiplet

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                       MEC 30 / 2\n------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) √\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = (43-19) √\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}\n
            \n\n
            Given our domain is limited to numbers ≌ {1,7,11,13,17,19,23,29} modulo 30, only ϕ(m)/m = 8/30 or 26.66% of natural numbers N = {0, 1, 2, 3, ...} need be sieved.\n- For example, to illustrate the proportionality of this ratio, we find that 25% of the first 100 natural numbers are prime, while 72% of numbers not divisible by 2, 3, or 5 are prime (and, curiously, if we count 2, 3, and 5 in after the fact, we get 75%, or exactly 3 x 25%).\n- Also note that if you plug the number 30 into [Euler's totient function](https://en.wikipedia.org/wiki/Euler%27s_totient_function), phi(n): phi(30)= 8, with the 8 integers (known as [totatives](https://mathworld.wolfram.com/Totative.html)) smaller than and having no factors in common with 30 being: 1, 7, 11, 13, 17, 19, 23 and 29, i.e., what are called \"prime roots\" above. Thirty is the largest integer with this property.]\n- The integer 30, product of the first three prime numbers (2, 3 and 5), and thus a primorial, plays a powerful role organizing the array's perfect symmetry, viz., in the case of the 8 prime roots:\n\n1+29=30; 7+23=30; 11+19=30; and 13+17=30.\n\n- In The Number Mysteries well-known mathematician Marcus Du Sautoy writes: \"In the world of mathematics, the numbers 2, 3, and 5 are like hydrogen, helium, and lithium. That's what makes them the most important numbers in mathematics.\"\n- Although 2, 3 and 5 are the only prime numbers not included in the domain under discussion, they are nonetheless integral to it: First of all, they sieve out roughly 73% of all natural numbers, leaving only those nominally necessary to construct a geometry within which prime numbers can be optimally arrayed.\n- The remaining 26.66% (to be a bit more precise) constituting the array can be constructed with an elegantly simple interchangeable expression (or power series, if you prefer) that incorporates the first three primes. It's conjectured that this manifold series ultimately consists of all (and only) the numbers not divisible by 2, 3, or 5 (and their negatives), which inclues all prime numbers >5 (more below under the heading \"Conjectures and Facts Relating to the Prime Spiral Sieve\").\n\nWhat is critical to understand, is that the invisible hand of 2, 3 and 5, and their factorial 30, create the structure within which the balance of the prime numbers, i.e., all those greater than 5, are arrayed algorithmically–as we shall demonstrate. Primes 2, 3 and 5 play out in modulo 30-60-90 cycles (decomposing to {3,6,9} sequencing at the digital root level). Once the role of 2, 3 and 5 is properly understood, all else falls beautifully into place. _([PrimesDemystified](https://primesdemystified.com/#Distribution_of_Perfect_Squares))_\n
            \n\n

            \"One_Grand_Pyramid_Teaser\"

            \n\n","dir":"/addition/","name":"2.md","path":"addition/2.md","url":"/addition/2.html"},{"sort":2,"spin":5,"span":"parser","suit":"intro","layout":"default","title":"2.5 Parsering","content":"## 2.5 Parsering\n\n```\n---+-----+-----\n 1 | 1 | 18\n---+-----+-----\n 2 | 19 | 29\n---+-----+-----\n 3 | {30}|{43}\n---+-----+-----\n```\n\n![](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)\n\n***139 = 34th prime =(2x17)th prime***\n\n```\nScheme 13:9\n===========\n(1){1}-7: 7’\n(1){8}-13: 6‘\n(1)14-{19}: 6‘\n------------- 6+6 -------\n(2)20-24: 5’ |\n(2)25-{29}: 5’ |\n------------ 5+5 -------\n(3)30-36: 7:{70,30,10²}|\n------------ |\n(4)37-48: 12• --- |\n(5)49-59: 11° | |\n --}30° 30• |\n(6)60-78: 19° | |\n(7)79-96: 18• --- |\n-------------- |\n(8)97-109: 13 |\n(9)110-139:{30}=5x6 <--x-\n --\n {43}\n```\n\n```\n$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer| i | f\n -----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | 7\n -----+-----+--- } 36 » 6®\n | 3 | 11\n 2 +-----+\n | 4 | 13\n -----+-----+---------\n | 5 | 17\n 3 +-----+ } 36 » 6®\n | 6 | 19\n -----+-----+---------\n```\n\n### 2.5.1 The imaginary\n\n![image](https://user-images.githubusercontent.com/8466209/222680152-96bc4f1d-702d-4182-84b9-04fd9d427f49.png)\n\nThe consciousness is awaken through to the 13th central sphere of Metatron’s Cube. The 13th sphere (the central circle) represents death and rebirth, endings and beginnings through all of Creation in all directions of time and space.\n\n![](https://user-images.githubusercontent.com/8466209/202855806-611c6a39-e40c-4aa9-ae28-e25aea82cb19.png)\n\n***1155 / 5 = 286 - 55 = 200 + 31 = 231***\n\n```\nlayer| i | f\n-----+-------+------\n | 1,2:1 | (2,3)\n 1 +-------+\n | 3:2 | (7)\n-----+-------+------\n | 4,6:3 | (10,11,12) <--- 231 (3x)\n 2 +-------+\n |{7}:4 |({13})\n-----+-------+------\n | 8,9:5 | (14,{15}) <--- 231 (2x)\n 3 +-------+\n | 10:6 | (19)\n-----+-------+------\n```\n\n![](https://user-images.githubusercontent.com/36441664/100784808-5694a480-3442-11eb-80ad-04dc1100d585.png)\n\n[![partitions](https://user-images.githubusercontent.com/8466209/227838045-3ddd5238-7beb-4023-affa-c61a054afd2b.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)\n\n#### 2.5.1.1 The limit shape\n\n>We study the [limit shape](https://github.com/naa/young-diagrams#young-diagrams) of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape _([arXiv:2010.16383v4](http://arxiv.org/abs/2010.16383))_.\n\n[![Limit shape for infinite rank limit of tensor\npower decomposition for Lie algebras of series\n](https://user-images.githubusercontent.com/8466209/233841647-e7f5154c-740f-4c19-9094-abbe0a4cced6.png)](https://arxiv.org/pdf/2010.16383.pdf)\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|------------------------- Skema-12 ------------------------|\n|------------ 6¤ -------------|------------- 6¤ ------------|\n|--------------------------- 192 ---------------------------|\n|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}|\n|--------- 5¤ ---------|------------ {96} -----------|{43}|\n|--------- {53} ---------|-------------- {139} -------------|\n|------- Skema-23 -------|------------- Skema-34 -----------| \n```\n\nHere we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.\n\n![](https://user-images.githubusercontent.com/36441664/83051968-e2cfa480-a078-11ea-8ff2-316a809a8fad.jpg)\n\n>The values p(1),,,,,,p(8)} of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the [Young diagrams](https://github.com/eq19/lexer#young-diagrams) for the partitions of the numbers from onr (1) to eight (8) _([Wikipedia](https://en.wikipedia.org/wiki/Partition_function_(number_theory)))_.\n\n[![default](https://user-images.githubusercontent.com/8466209/235672220-30997c4b-0d66-4e8a-a579-44e05062ac88.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partiti)\n\n#### 2.5.1.2 The eight (8) difference sequence\n\nThe Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period ***eight (8) difference sequence*** of: {6, 4, 2, 4, 2, 4, 6, 2} _([Primesdemystified](https://primesdemystified.com/#deepsymmetries))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/219260933-4331d79b-5815-4566-82e3-1a485bb2c61f.png)](https://primesdemystified.com/#deepsymmetries)\n\n```\n Tabulate Prime by Power of 10\n loop(10) = π(10)-π(1) = 4-0 = 4\n loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\n![](https://user-images.githubusercontent.com/8466209/212930357-8cf2591b-a2be-4a2c-b6ae-dc43892efe73.png)\n\nSpeaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.\n\n[![11's additive sums](https://user-images.githubusercontent.com/8466209/221473004-867a1b50-f91f-470d-9922-e5e4f543a590.png)](https://primesdemystified.com/#deepsymmetries)\n\n### 2.5.2 The balanced prime\n\n![](https://user-images.githubusercontent.com/36441664/105412087-d0892300-5c66-11eb-9c3e-19d8652b478c.png)\n\nThese objects will then behave as a complex numbers that leads to trivial and complex roots of the _[18th prime identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_. Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as _[the balanced prime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_.\n\n***286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271***\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== bilateral 9 sums\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n```\n\n```\n\n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | 2' | 3' | 5' | 7' |\n |--------------|-------------------|------------------------------|------------------------------|\n | lexering = π(1000) | parsering = 1000/Φ |\n |--------------|-------------------|------------------------------|------------------------------|\n | mapping | feeding | syntaxing | grammaring |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+\n | 2 | 60 | 40 |\n +----+----+----+\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n\n```\n\n#### 2.5.2.1 Replicate position\n\nIt will be forced back to Δ19 making a cycle that bring back **the 12 to → 13** of 9 collumns and replicate [The Scheme 13:9](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md) through **(i=9,k=13)=9x3=27** with entry form of (100/50=2,60,40) as below:\n\n```liquid\n| 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ \n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n\nBy [the prime hexagon](https://www.hexspin.com/defining-the-prime-hexagon/) this number 114 located on [6th row vs 19th column](https://github.com/tsgallion/prime-hexagon/blob/23f35a3a18c27b5a9e9cc1ec6495d043a109c287/tests/good-0000-1000-01.txt#L112) whereas 114th prime = 619 = 618+1. Since DNA Recombination is happen when two (2) chromosomes involve then they start the position as below:\n\n```liquid\n | by the 1st chromosome | by the 2nd\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | 30 | 36 | - |\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | 20 | 21 | 22 |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n\n#### 2.5.2.2 Opposite prime position\n\nIn the second opposing member, the position 19 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 11 as a prime number is now forced to determine a new axis-symmetrical zero position.\n\n![](https://user-images.githubusercontent.com/8466209/241491860-72da956a-1740-4ed7-83ef-3844ae1ff8d2.png)\n\n![](https://user-images.githubusercontent.com/8466209/211178117-9a879fd0-163b-442b-87bf-49d76c0b6c50.png)\n \n![](https://user-images.githubusercontent.com/8466209/227791172-e09f8e43-502f-40a5-8bca-fa481edbfb79.png)\n\n### 2.5.3 Direction grammar\n\n![](https://user-images.githubusercontent.com/8466209/206868681-2cddf780-48f1-4dc5-9ef4-981b402a15d5.png)\n\n![](https://user-images.githubusercontent.com/8466209/205431468-6777265f-63a8-42ea-b454-d45227478362.png)\n\n### 2.5.4 The runner composition\n\n![](https://user-images.githubusercontent.com/8466209/226080396-235a1645-8a58-49c4-9754-8bac362a72fa.png)\n\n![](https://user-images.githubusercontent.com/8466209/222966425-9da703ef-9189-44e6-8fc1-8b766cf9f7bb.png)\n\n![](https://user-images.githubusercontent.com/36441664/71659208-5515b480-2d79-11ea-859f-a20dea0cf680.jpg)\n\n![](https://user-images.githubusercontent.com/8466209/229297019-4583e9a7-273d-4489-ab87-37c88be16adb.png)\n\n### 2.5.5 The concatenation\n\n![](https://user-images.githubusercontent.com/8466209/223529165-0e4c1172-47cc-422f-8e44-1dd67de25828.png)\n\n![](https://user-images.githubusercontent.com/8466209/228989527-2915b89f-dd8c-40d9-ae64-3d69c5217b3d.png)\n\n>The 77 is equal to the sum of ***the first eight (8) primes***. The square of 77 is 5929, the concatenation of two primes, 59 and 29. The concatenation of all palindromes from one up to 77 is prime _([Prime Curios!\n](https://t5k.org/curios/page.php/77.html))_.\n\n![](https://user-images.githubusercontent.com/8466209/223011738-7e2084bc-861b-4424-89d5-9f39643df22f.png)\n\nPrime numbers that end with \"77\" occur [more often](https://t5k.org/curios/page.php?number_id=459&submitter=Gaydos) than any other 2-digit ending among the first one million primes. The sum of the proper divisors of 77 equals 19 and the sum of primes up to 19 equals 77. Does this ever happen again?\n","dir":"/identition/span2/","name":"gist05.md","path":"identition/span2/gist05.md","url":"/identition/span2/gist05.html"},{"sort":2,"spin":1,"span":"assigning","suit":"intro","layout":"default","title":"Assigning Repositories","content":"# [Assigning Repositories](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bilateral-9-sums)\n\nBy this part we are going to assign nine (9) groups of ***[project repositories](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-repositories-md)*** including one (1) group of the central. All of them will be managed by an [instance](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#building-the-instance) to represesent the pattern of _[true-prime-pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_ via _[bilateral 9 sums](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#the-bilateral-9-sums)_.\n\n[![default](https://user-images.githubusercontent.com/8466209/201345867-d4383ae5-f951-4ea8-8794-8cc4f3e5f4e0.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e/edit)\n\nThe purpose of this instance is simulating ***[the central behaviour](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8)*** on each pairs of human chromosomes. So the nine (9) groups would consist of three (3) containers + one (1) sub central + one (1) central + one (1) sub central + three (3) containers.\n\n***(7-1) + (12x9) = 6 + 108 = 114***\n\n```\n Tabulate Prime by Power of 10\n loop(10) = π(10)-π(1) = 4-0 = 4\n loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\nLet's sum them up so we get ***9+1+9=19***. Put them as one (1) unit so the whole objects will be ***19 (sub objects)+1 (unit object)=20 objects***. Thus this sum is what we called as ***[bilateral 9 sums](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#the-bilateral-9-sums)***.\n![default](https://user-images.githubusercontent.com/8466209/201350726-068c3de2-8123-43ec-9d08-6afc743ddcbe.png)\n\nAs a matter of the fact every schemes are contained in X/Y genes where the Y gene has has hardly any genes. When we do pair them as reproduction genes then we will come again to 3 containers + 1 sub central + 1 central + 1 sub central + 3 containers.\n\n> The X bears about 1,600 genes with varied functions. But the ***Y has hardly any genes***; maybe 50, and only 27 of these are in the male-specific part of the Y.(_[The Conversation](https://theconversation.com/sex-genes-the-y-chromosome-and-the-future-of-men-32893)_)\n\n![image](https://user-images.githubusercontent.com/8466209/213841770-f61d8940-473b-473e-aa84-c711ed72d286.png)\n\n```\n --------------------------------------------------------------\n | | \n =======================+====+====+====+====+====+====+====+====+====+===== |\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root |\n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin |\n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th |\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin |\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th |\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin |\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th |\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin |\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ---------------\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n ```\n\nWhen recombination is occur then the prime **13 is forced to → 12** where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is [simulated](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation) by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (**40 nodes**).\n\n[![flowchart](https://user-images.githubusercontent.com/36441664/128732737-81762604-0ae0-4a90-b5a8-30921cf46efb.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation)\n\nThis central doesn't exist phisically. However when we were going up by the form of nine (9) subs central + one (1) central + nine (9) subs central then we will get the human brain as the central.\n\n![](https://user-images.githubusercontent.com/36441664/128795186-6f58dbf1-b148-4fc0-b0e1-d79a01ac2e07.png)\n\nObserving many literatures we finaly found that the pattern of this centralizing is done by a kind of neurotransmitter that works as a messenger by transmitting a signal. That is the way they are communicating each others.\n\n> A neurotransmitter is a signaling molecule secreted by a neuron to affect another cell across a synapse. The cell receiving the signal, any main body part or target cell, may be another neuron, but could also be a gland or muscle cell.. _[Wikipedia](https://en.m.wikipedia.org/wiki/Neurotransmitter)_\n\n![](https://user-images.githubusercontent.com/36441664/136785743-f524a425-39fd-4bdf-a085-d2fa8cdd2c4f.png)\n\nHowever it seems that determining the pattern of this signalling either going up to the top of the brain or going down to the XX or XY genes even to the bottom of that little Y is staggeringly complex. Yet science points to a much more ambiguous reality.\n\n> Determination of biological sex is staggeringly complex, involving not only anatomy but an intricate choreography of genetic and chemical factors that unfolds over time. (_[ScientificAmerica](https://www.scientificamerican.com/article/beyond-xx-and-xy-the-extraordinary-complexity-of-sex-determination/)_)\n\n[![image](https://user-images.githubusercontent.com/8466209/213841901-6eb107b1-c35a-4479-ba00-082e65e81207.png)](https://www.scientificamerican.com/article/beyond-xx-and-xy-the-extraordinary-complexity-of-sex-determination/)\n\nTherefore here we would only take the fact that ***X bears about 1,600 genes*** with varied functions while the ***Y has 50, and only 27 of these are in the male-specific*** and how their relation with the ***20 objects*** of bilateral 9 sum.\n","dir":"/identition/span2/","name":"gist01.md","path":"identition/span2/gist01.md","url":"/identition/span2/gist01.html"},{"sort":3,"spin":1,"span":"mapping","suit":"intro","layout":"default","title":"DNA Recombination","content":"# [DNA Recombination](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-18_03_residual-md)\n\nThis imajinary unit is the product of reciprocal complex numbers of the trivial and complex roots that goes recursively with ***their residual objects***. By the nature such as DNA this residual is taken as genetic exchange to generate a better recombination. \n\n>Recombination is a process that results in genetic exchange between chromosomes or regions. Recombination counteracts physical linkage between adjacent genes, thereby reducing genetic hitchhiking _([Wikipedia](https://en.wikipedia.org/wiki/Molecular_evolution#Recombination))_.\n\n![](https://user-images.githubusercontent.com/36441664/86853354-88e2e580-c0e0-11ea-92e4-24de95335054.gif)\n\nRecombination can also generate particular types of mutations if chromosomes are misaligned. Recombination involves the breakage and rejoining of two chromosomes ***(M and F)*** to produce two re-arranged chromosomes ***(C1 and C2)***.\n\n>The result of genes results in more efficient selection, meaning that regions with higher recombination will harbor fewer detrimental mutations, more selectively favored variants, and fewer errors in replication and repair _([Wikipedia](https://en.wikipedia.org/wiki/Molecular_evolution#Recombination))_.\n\n[![](https://user-images.githubusercontent.com/8466209/218370587-ec438d91-be88-408a-a746-ff1e6324a514.png)](https://en.wikipedia.org/wiki/Molecular_evolution#Recombination)\n\nConsider that by the _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ the 36 is _[the smallest square](https://primes.utm.edu/curios/page.php?number_id=270)_ expressible as the sum of consecutive prime in two (2) ways of 4 (four) primes and 2 (two) primes.\n\n***2nd identity (objects) = 500 x 2/(2+3) = 500 x 2/5 = 200 objects***\n\n```\n$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer| i | f\n -----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | 7\n -----+-----+--- } 36 » 6® by 4 primes\n | 3 | 11\n 2 +-----+\n | 4 | 13\n -----+-----+---------\n | 5 | 17\n 3 +-----+ } 36 » 6® by 2 primes --------------------\n | 6 | 19 |\n -----+-----+--------- |\n |\n |\nlayer | node | sub | i | f |\n------+------+-----+---------- \n | | | 1 | ----------------------- 71 by 2 identities √\n | | 1 +-----+ |\n | 1 | | 2 | (5) |\n | |-----+-----+ |\n | | | 3 | |\n 1 +------+ 2 +-----+---- |\n | | | 4 | |\n | +-----+-----+ |\n | 2 | | 5 | (7) |\n | | 3 +-----+ |\n | | | 6 | | 11x\n------+------+-----+-----+------ } (36) |\n | | | 7 | |\n | | 4 +-----+ |\n | 3 | | 8 | (11) |\n | +-----+-----+ |\n | | | 9 | |\n 2 +------| 5 +-----+----- |\n | | | 10 | |\n | |-----+-----+ |\n | 4 | | 11 | (13) ------------------ 71 by 4 identities √\n | | 6 +-----+\n | | | 12 |--------------------- (72 - 2) by 1 identity √\n------+------+-----+-----+\n | | | 13 |\n | | 7 +-----+\n | 5 | | 14 | (17)\n | |-----+-----+\n | | | 15 |\n 3 +------+ 8 +-----+----- \n | | | 16 |\n | |-----+-----+\n | 6 | | 17 | (19)\n | | 9 +-----+\n | | | 18 |--------------------- (72 - 4) by 1 identity √\n------|------|-----+-----+\n```\n\nSince the position of 19 acts as the ***exchange base*** then a new recombination would be re-arranged which is resulting a linkage between 2 (two) and four (4) of prime identities aligned by the residual tensor of 71.\n\n***(2 x 32 x 109) − (2 x 32 x 89) = 360***\n\n```\nlayer | node | sub | i | f\n------+------+-----+---------- ---\n | | | 1 | 71 (2,3) √ ------------ |\n | | 1 +-----+ | |\n | 1 | | 2 | | (5) \n | |-----+-----+ | |\n | | | 3 | | |\n 1 +------+ 2 +-----+---- | ---\n | | | 4 | | |\n | +-----+-----+ | |\n | 2 | | 5 | | (7) \n | | 3 +-----+ | |\n | | | 6 | | {6®} √ |\n------+------+-----+-----+------ } (36) | ---\n | | | 7 | | |\n | | 4 +-----+ | |\n | 3 | | 8 | | (11) \n | +-----+-----+ | |\n | | | 9 | | |\n 2 +------| 5 +-----+----- | ---\n | | | 10 | | |\n | |-----+-----+ | |\n | 4 | | 11 | 71 (29,30,31,32) √ ---- (13)\n | | 6 +-----+ |\n | | | 12 | {70} (36) |\n------+------+-----+-----+------------------ ---\n | | | 13 | |\n | | 7 +-----+ |\n | 5 | | 14 | (17) \n | |-----+-----+ |\n | | | 15 | |\n 3 +------+ 8 +-----+----- } (36) ---\n | | | 16 | |\n | |-----+-----+ |\n | 6 | | 17 | 100 (10 x 500/100) (19) \n | | 9 +-----+ |\n | | | 18 | 10 x 500/100 (68) |\n------|------|-----+-----+------ ---\n```\n\nBy the 2x25=500/10=50 and 10x10=11+89=100 which is identified from the factorization of 285+286=571 object. Meanwhile 32 is expanded to 32+36=68. So finally the tensor of 71 will be derived to 7×10=68+2=72-2=70 at the center of the scheme.\n\n***(10th)th prime = 29th prime = 109 = 110 - 1***\n\n```\nlayer | node | sub | i | f\n------+------+-----+---------- ---\n | | | 1 | 71 (2,3) -------------- |\n | | 1 +-----+ | |\n | 1 | | 2 | | (5) \n | |-----+-----+ | |\n | | | 3 | | |\n 1 +------+ 2 +-----+---- | ---\n | | | 4 | | |\n | +-----+-----+ | |\n | 2 | | 5 | | (7) \n | | 3 +-----+ | |\n | | | 6 | | {6®} = 11 x 30 |\n------+------+-----+-----+------ } (36) | ---\n | | | 7 | | |\n | | 4 +-----+ | |\n | 3 | | 8 |--- 109 √ --- | 110-1 by 1 identity √ (11) \n | +-----+-----+ | | |\n | | | 9 |---- 69 √ | {2®} √ | 71-2 by 1 identity √ |\n 2 +------| 5 +-----+----- | | ---\n | | | 10 |--- 109 √ --- | 110-1 by 1 identity √ |\n | |-----+-----+ | |\n | 4 | | 11 | 71 (29,30,31,32) ------ (13)\n | | 6 +-----+ |\n | | | 12 | |\n------+------+-----+-----+------------------ 329 = 330 - 1 = 309 + 20 ---\n | | | 13 | |\n | | 7 +-----+ |\n | 5 | | 14 | (17) \n | |-----+-----+ |\n | | | 15 | |\n 3 +------+ 8 +-----+----- ---\n | | | 16 | |\n | |-----+-----+ |\n | 6 | | 17 | 100(50) (19) \n168 √ | | 9 +-----+ |\n| | | | 18 | 50(68) |\n------|------|-----+-----+------ ---\n```\n\n## Palindromic behaviour\n\nThe main scheme is two (2) by five (5) objects expressed by three (3) operation of addition (2+5=7), multiplication (2x5=10) and exponentiation (5²=25 and 2^5=32). Here we correlate 11's additive sums with 3960, 7920 and the first 1000 prime numbers.\n\n[![11's additive sums](https://user-images.githubusercontent.com/8466209/225830554-007fbd06-9d7d-44e8-867d-c7b0188bf488.png)](https://www.primesdemystified.com/First1000Primes.html)\n\n![image](https://user-images.githubusercontent.com/8466209/225558112-939e068d-d179-4aa9-bd42-ee6714b53d58.png)\n\n>In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry) _([Primesdemystified](https://primesdemystified.com/#primingthesquares))_.\n\n[![Distribution of Perfect Squares](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-bilateral-md)\n\n## Deep Symmetry\n\n![default](https://user-images.githubusercontent.com/8466209/199262407-7f8bee13-f240-4b1f-856e-ee93e97c5ddb.png)\n\nDiving deeper yet, here we show the absolute value delta differences of simple reversal sets in relation to primes 89 and 109 contextualized with the first 1000 prime numbers.\n\n![image](https://user-images.githubusercontent.com/8466209/225575599-4a8ccdb1-bd46-4a78-a2f8-1535b2a021ed.png)\n\n>Achim Frenzel's popular scientific book, which is illustrated with numerous graphics, is treated as an approach that should definitely be further researched by science. In addition, as a future-oriented project, the book is intended to lead to an interdisciplinary doctorate and therefore refers to its own website as an Internet discussion platform.\n\n![](https://user-images.githubusercontent.com/36441664/74591945-2b75cb80-504f-11ea-85dd-14d0a803ee6b.png)\n\n>An Independent claim is also included for the localization and determination of (I), or their material structures, by graphical representation of base sequences on various media, based on the new assignments and the derived vibrations and amplitudes _(Open Patent Data [DE19991049059](https://www.surechembl.org/document/DE-19949059-A1))_.\n \n![](https://user-images.githubusercontent.com/36441664/74591731-f5cfe300-504c-11ea-9e04-d814c57aa969.png)\n\nSee on the left side contains of odd numbers less and equal to 19 while the right is the even number less and equal to 18. By the left side only ***[9 and 15](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)*** that are not primes\n\nSince this bilateral sums of 9 are laid on the prime spiral sieve then the symmetrical behaviour will occur by three (3) rotations of 360. By the 20 objects of [1st prime identity](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857), this 360 will then be separated to ***3x100=300*** and ***3x20=60***.\n\n***89^2 - 1 = 7921 - 1 = 7920 = 22 x 360 = 66 x 120***\n\n[![Deep Symmetries](https://user-images.githubusercontent.com/8466209/219261961-10e4d77f-ead3-43d4-9407-f01d83f1f204.png)](https://primesdemystified.com/#deepsymmetries)\n\nBy the 500 objects of the [2nd prime identity](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e), the 300 goes to the 29 while the rest of 200 goes as [3rd prime identity](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde) to the 89. So the involved objects on the both sides are ***300+29=329*** and ***200+89=289*** thus the total will be ***[329+289=618 objects](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857)***.","dir":"/identition/span3/","name":"gist01.md","path":"identition/span3/gist01.md","url":"/identition/span3/gist01.html"},{"sort":3,"spin":1,"span":"irrational","suit":"intro","layout":"default","title":"Irrational Partitions","content":"# [Irrational Partitions](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde)\n\nThis section is discussing the ***200 residual objects*** that goes irrational along the pattern within the _[4th dimension](hhttps://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#dimensional-space)_ from the 2nd to 3rd prime identity in regards to the three (3) zones where each represents the basic arithmetic operations of _[Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_.\n\n```\n---+-----+-----\n 1 | {1} | {9}\n---+-----+-----\n 2 | 10 |{32}\n---+-----+-----\n 3 | 33 | 63 \n---+-----+-----\n 4 |{64} | 101 \n---+-----+-----\n 5 |{102}| 120 \n---+-----+-----\n 6 | 121 |{189}\n---+-----+-----\n 7 | 190 |{200}\n---+-----+-----\n```\n\nThere are some mathematical shape of this residual objects. [Torus](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partition) is basically a donut shape, which has the property of of having variable Gaussian curvature. Some parts of the surface has positive curvature, others zero, others negative.\n\n>The blue parts of the torus above have positive curvature, the red parts negative and the top grey band has zero curvature. If our 3 dimensional space was like the surface areas of a 4 dimensional torus, the parts would have different angle sums.\n\n[![Torus](https://user-images.githubusercontent.com/8466209/228750971-14bb5e2a-5cc7-4b18-9d97-d77401deb55e.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partition)\n\nThese are two more bizarre shapes with strange properties. Mobius strip only has one side, if you start anywhere on its surface and follow the curvature round you will eventually return to the same place having travelled on every part of the surface.\n\n![Mobius](https://user-images.githubusercontent.com/8466209/228749895-07d0a768-8c0c-49b1-933f-beec4ce57e25.png)\n\nThe Klein bottle is in someways a 3D version of the Mobius strip and even though it exists in 3 dimensions, to make a true one you need to “fold through” the 4th dimension.\n\n[![Klein bottle](https://user-images.githubusercontent.com/8466209/228749672-e1db5df4-8843-4c73-b3a1-b16d21188c52.png)](https://ibmathsresources.com/2014/08/05/non-euclidean-geometry-v-theshapeoftheuniverse/)\n\nThe torus is actually one of the current theories of _[the shape of universe](https://ibmathsresources.com/2014/08/05/non-euclidean-geometry-v-theshapeoftheuniverse/)_ while the klein bottle is shape of the idea in theoretical physics called ***[string theory](https://en.wikipedia.org/wiki/String_theory)*** that reality is made up of infinitesimal vibrating strings, smaller than atoms, electrons or quarks\n\n>Finally, there exist scenarios in which there could actually be more than [4D of spacetime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#dimensional-space). String theories require extra dimensions of spacetime for their mathematical consistency. In string theory, spacetime is ***26-dimensional***, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional _([Wikipedia](https://en.wikipedia.org/wiki/String_theory#Extra_dimensions))_.\n\n[![String theory](https://user-images.githubusercontent.com/8466209/229411952-b42cd7a1-4962-44c7-960a-bf9077713de5.png)](https://en.wikipedia.org/wiki/String_theory)\n\nThese are situations where theories in two or three spacetime dimensions are no more useful. This classification theorem identifies several infinite families of groups as well as ***26 additional groups*** which do not fit into any family. \n\n## The three (3) zones\n\nIn order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become the [irrational partitions](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#irrational-partitions). \n\n***[(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects***\n\n```\nlayer | node | sub | i | f \n------+------+-----+---------- \n | | | 1 | ----------------------- 71 = 72-1\n | | 1 +-----+ |\n | 1 | | 2 | (5) |\n | |-----+-----+ |\n | | | 3 | --------- |\n 1 +------+ 2 +-----+---- | |\n | | | 4 | 5x --- |\n | +-----+-----+ | | |\n | 2 | | 5 | (7) ----- | |\n | | 3 +-----+ | |\n289+11=300 | | 6 | | |\n------+------+-----+-----+----- 72 x 6 7x --- 11x = 77 (rational)\n | | | 7 | | |\n | | 4 +-----+ | |\n | 3 | | 8 | (11) --- | |\n | +-----+-----+ | | |\n | | | 9 | 2x --- |\n 2 +------| 5 +-----+----- | |\n | | | 10 | --------- |\n | |-----+-----+ |\n | 4 | | 11 | (13) ------------------ 71 = 72-1\n | | 6 +-----+\n329+71=400 | | 12 |------------------------ 70 = 72-2\n------+------+-----+-----+\n | | | 13 |\n | | 7 +-----+\n | 5 | | 14 | (17) ◄---------------------------\n | |-----+-----+\n | | | 15 | ◄-- 42 x 6 partitions of 13 (irrational)\n 3 +------+ 8 +-----+----- \n | | | 16 | ◄---------------------------\n | |-----+-----+\n | 6 | | 17 | (19)\n | | 9 +-----+\n168+32=200 | | | 18 |------------------------ 68 = 72-4\n------|------|--|--+-----+\n 900 -----\n```\n\nThis irrational parts took the finiteness position of middle zero axis = 15 on our _19 vs 18 Scenario_ contained in _three (3) groups of five (5) of integer number [partitions](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#partition-function)_ where each groups represents ***the three (3) basic arithmetic operations*** of _[Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_.\n\n***329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ***\n\n[![default](https://user-images.githubusercontent.com/8466209/195963923-0796217c-7a87-4b2d-ba93-f47465304c03.png)](https://www.nausetschools.org/cms/lib/MA02212418/Centricity/Domain/204/Linkage%20Map%20Worksheet%20Genetics%202017.pdf)\n\n\nThe 200 objects that goes from the 2nd to 3rd prime identity would take position as ***multiplication zone*** by given of 100x2=200 which is then be used in turn to 100+2=102 (***addition zone***) and 100^2=10000 (***exponentiation zone***)\n\n***2 + 60 + 40 = 102***\n\n```\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\nThe Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum mechanics. It is a key result in quantum-mechanical system, and its discovery was a significant landmark in the development of the subject.\n\n>Complex plot of a wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space _([Wikipedia](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation))_.\n\n[![Wavepacket-a2k4-en](https://user-images.githubusercontent.com/8466209/227751489-e61f12f4-4ade-4473-a1d0-0ad3dbcd6c6d.gif)](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation)\n\n## The modular function\n\nConsequently, we only need to fold a 30's cycle as in the illustration 7 so that we can identify the opposite prime positions that form their specific pairs in a specific convolution.\n\n![](https://user-images.githubusercontent.com/36441664/72666121-b7410b80-3a41-11ea-9217-b37f485d5098.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/72685907-2f323300-3b21-11ea-934b-43e314157988.jpg)\n\nThese two (2) exponent are acting as the exchange zones of the MEC30 behaviour of the other two operators. This interactions is managed in between 4 identities of (26 to 29) and 2 identities (30 to 31) by means of ***Triangular waves***.\n\n![MEC30](https://user-images.githubusercontent.com/8466209/229441188-42618575-1d95-4866-a36e-192807aefeff.png)\n\nA seemingly unrelated construction is the j-function of number theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern.\n\n>Although this function appears in a branch of mathematics that seems very different from the theory of finite groups, ***the two subjects turn out to be intimately related*** _([Wikipedia](https://en.wikipedia.org/wiki/String_theory#Monstrous_moonshine))_.\n\n[![Monstrous moonshine](https://user-images.githubusercontent.com/8466209/228734448-0299ab1f-7620-4d86-adf4-1adcf4d8db86.png)](https://en.wikipedia.org/wiki/String_theory#Monstrous_moonshine)\n\nWe propose a new higher dimensional version of the McKay correspondence which enables us to understand the ***[Hodge theory](https://en.wikipedia.org/wiki/Hodge_theory)*** assigned to singular Gorenstein varieties by physicists, and so-called Higgs bundles. \n\n>Hodge theory can be extended to cohomology with coefficients in nonabelian groups between flat vector bundles which, by the Riemann-Hilbert correspondence, are the same as local systems _([Hodge Theory in String Theory](https://www.pims.math.ca/files/Hodge_Theory_in_String_Theory.pdf))_\n\n[![Hodge conjecture](https://user-images.githubusercontent.com/36441664/85226186-768a5b80-b400-11ea-8cf5-fcd57291ae81.jpg)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)\n\nOur [results](https://www.sciencedirect.com/science/article/pii/0040938395000518) lead to the conjecture that string theory indicates the existence of some new cohomology theory for algebraic varieties with Gorenstein singularities.\n","dir":"/identition/span1/","name":"gist03.md","path":"identition/span1/gist03.md","url":"/identition/span1/gist03.html"},{"sort":3,"spin":13,"layout":"default","title":"default","content":"# default\n```\n===========\n(1){1}-7: 7’\n(1){8}-13: 6‘\n(1)14-{19}: 6‘\n------------- {6+6} --→ [M+F] \n(2)20-24: 5’ |\n(2)25-{29}: 5’ |\n------------ 5+5 --------\n(3)30-36: 7:{70,30,10²} |\n------------ |\n(4)37-48: 12• --- |\n(5)49-59: 11° | |\n --}30° 30• |\n(6)60-78: 19° | |\n(7)79-96: 18• --- |\n-------------- |\n(8)97-109: 13 |\n(9)110-139:{30}=5x6 <--x-- [C1+C2]\n --\n 43\n```\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|------------------------ Scheme-12 ------------------------|\n|------------ 6¤ -------------|------------- 6¤ ------------|\n|--------------------------- 192 ---------------------------|\n|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}|\n|--------- 5¤ ---------|------------ {96} -----------|{43}|\n|--------- {53} ---------|-------------- {139} -------------|\n|------ Scheme-53 -------|------------ Scheme-34 -----------|\n```\n\n```\n Tabulate Prime by Power of 10\n loop(10) = π(10)-π(1) = 4-0 = 4\n loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n\nSequence:\n By the next layer the 89² will become 89 and 5 become 5² or 25.\n This 89 and 25 are in the same layer with total of 114 or prime 619\n So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n```\n\n[![Screenshot](https://user-images.githubusercontent.com/8466209/204251093-ade3969a-ecc5-4f78-9a19-e13439e78e31.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md)\n\n[![204159170-55a7470a-d03b-49c0-ba3c-68a64f895263](https://user-images.githubusercontent.com/8466209/204254729-71d84d54-b908-4b55-82c2-388cfbd7233c.png)\n](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-runner-md)\n\n![Screenshot_2022-11-28-16-50-17-00](https://user-images.githubusercontent.com/8466209/204253954-e7dfe758-64a8-442e-8989-67343c9d18ed.png)\n","dir":"/exponentiation/span13/","name":"gist03.md","path":"exponentiation/span13/gist03.md","url":"/exponentiation/span13/gist03.html"},{"sort":3,"spin":null,"span":null,"suit":3,"layout":"default","title":"Primes Platform","content":"

            Primes Platform

            \n\n
            This section is referring to _[wiki page-3](https://github.com/eq19/eq19.github.io/wiki)_ of _[zone section-3]()_ that is _[inherited ]()_ from _[the zone section-3](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            Prime hexagon is a mathematical structure developed by mathematician T. Gallion that is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime is encountered.

            \n\n
            This is not easy as they are linked to the nature of prime numbers, and nothing is easy about the nature of prime numbers.  But I begin with this assumption: if the hexagons participate in the Universe in any way other than haphazardly, they must be demonstrably ***congruent to something organized*** _([T. Gallion](https://www.hexspin.com/minor-hexagons/))_.\n
            \n\n
            s p i n\n0 0 0 0\n1 0 0 0\n2 0 1 0  ◄--- 1st prime\n3 1 1 0  ◄--- 2nd prime\n--------\n5 2 1 0  ◄--- 3rd prime\n7 3 1 0\n11 4 1 0\n13 5 1 0\n17 0 1 1 ◄--- 7th prime\n19 1 1 1 ◄--- 8th prime\n
            \n\n

            17 = 7th prime = (18 - 11) th prime

            \n\n

            \"\"

            \n\n
            p r i m e s\n1 0 0 0 0\n2 1 0 0 0\n3 2 0 1 0 2 ◄--- 1st prime\n4 3 1 1 0 3 ◄--- 2nd prime\n5 5 2 1 0 5 ◄--- 3rd prime\n6 7 3 1 0\n7 11 4 1 0\n8 13 5 1 0\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 19 ◄--- 8th prime\n-----\n11 23 2 1 1 23 ◄--- 9th prime √\n
            \n\n

            Residual objects

            \n\n

            You may learn that sets of algebraic objects has a multilinear relationship related to a vector space called tensor. Tensors may map between different objects such as vectors, scalars, and even other tensors.

            \n\n

            \"300px-Components_stress_tensor

            \n\n
            p r i m e s\n1 0 0 0 0\n2 1 0 0 0\n3 2 0 1 0 2 ◄--- 1st prime\n4 3 1 1 0 3 ◄--- 2nd prime\n5 5 2 1 0 5 ◄--- 3rd prime\n6 7 3 1 0\n7 11 4 1 0\n8 13 5 1 0\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 ∆1 ◄--- 8th prime ◄--- Terminating Digit\n-----\n11 23 2 1 1 √\n
            \n\n

            (17+13) + (11+19) = (7+11) + (19+23) = 60

            \n\n

            \"image\"

            \n\n

            \"image\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 √\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 √\n+29 rows √\n-----\n41 √\n
            \n\n

            In order to maintain the 36 symmetry (whether it is an addition zone or not), with this prime number 19 was found at least seven (7) pairs of truncated patterns.

            \n\n
            The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating ***3 minor hexagons***.\n
            \n\n

            π(6+11) = π(17) = 7

            \n\n

            \"\"

            \n\n

            Central Polarity

            \n\n

            This polarity is happened per six (6) cycles by the polar of six (6) to one (1) and six (6) to seven (7) that leads to the prime number 61 and 67.

            \n\n
            The above ***characteristics of primes in the hexagon suggests 0 family numbers split more than twin primes***. I speculate these numbers split all primes. That is, all primes have a partner (of the opposite family) equidistant from such a number. For instance, ***0 family member 18 splits twin primes 17 and 19***, but is also 5 more than 13 and 5 less than 23, and it is also 11 more the 7, and 11 less than 29, etc. _([Hexspin](https://www.hexspin.com/cell-types/))_\n
            \n\n

            \"\"

            \n\n

            By which we finally found if this behaviour is cascaded bilaterally within the correlation between 61 as the 18th prime and 67 as the 19th prime.

            \n\n
            The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the Functional equations of Riemann\n
            \n\n

            18 + 19 = π(61) + π(67) = 37

            \n\n

            \"\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 (spin 18) √\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 (spin 19) √\n+29 rows\n-----\n41\n
            \n
            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period ***eight (8) difference sequence*** of: {6, 4, 2, 4, 2, 4, 6, 2} \n_([Primesdemystified](https://primesdemystified.com/#deepsymmetries))_.\n
            \n\n

            \"image\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 (spin 18)\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 (spin 19)\n+29 rows\n-----\n41\n+59 rows √\n
            \n\n
            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.\n
            \n\n

            \"11's

            \n\n

            Fibonacci level-1 (29) x Fibonacci level-2 (59) = 10x10 = 💯

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Terminating Digit #0 ◄- Fibonacci Index #18 √\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Terminating Digit #1 ◄- Fibonacci Index #19 √\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄- Terminating Digit #11 ◄- Fibonacci Index #29 √\n-----\n41\n+59 rows ◄--- total 41+59 = 💯 rows = 10x10 rows √\n
            \n\n

            Numeric Symmetries

            \n\n

            (59² − 31²) = 360 x 7

            \n\n

            \"Squares_Distribution\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- 7th prime\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30 ✔️\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 ✔️\n-----\n
            \n\n

            \"\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s ✔️\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11s ✔️\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s ✔️\n-----\n
            \n\n
            These positions: 1 7 11 13 17 19 23 29. We refer to this basic system as MEC 30 - \"Mathematical Elementary Cell 30\".\n- By repeating the positions we show the function of the basic system in the next step. If we extend the 30th order of the MEC, for example, to the number 120, the result is 4 times a 30th order and thus 4 × 8 = 32 prime positions.\n- Hypothetical assumption: If the product of the primes (except 2, 3, 5,) would not fall into the prime positions, thus be divided by 2, 3 or 5, the information would have 120 = 32 primes in 32 prime positions.\n- Prime positions (not the primes) 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29, / 1, 7, 11, 13, 17 , 19, 23, 29, / 1, 7, 11, 13, 17, 19, 23, 29,\n- The 30th order is repeated in the number space 120 = 4 times, 4 × 8 = 32 prime positions, thus 4 terms. From our considerations and also from the graphic see 2 However, we can conclude that the distribution of prime numbers must have a static base structure, which is also confirmed logically in the further course. \n\nThis static structure is altered by the products of the primes themselves, since these products must fall into the prime positions since they are not divisible by 2, 3 and 5.\n
            \n\n

            \"\"

            \n\n
            The numbers not divisible by 2, 3 or 5 are highlighted. We call them prime positions, hence 1, 7, 11, 13, 17, 19, 23, 29. Important for our work is that in the following the term prime refers only to prime numbers that are in the prime positions. ***So primes 2, 3 and 5 are always excluded***.\n
            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ✔️\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7 ◄--- #23 ✔️\n7 11 4 1 0 11 ◄--- #19 ✔️\n8 13 5 1 0 13 ◄--- # 17 ✔️\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n
            In this one system, reproduced as an icon, we can show the distribution profile of the primes as well as their products over a checkerboard-like model in the 4.\n- We show this fundamental causal relationship in the MEC 30 mathematically accurate in the table 13 , The organization of this table is based on the well-known idea of Christian Goldbach. That every even number should consist of the sum of two primes.\n- All pairs of prime numbers without \"1\", 2, 3, 5, we call henceforth Goldbach pairs. The MEC 30 transforms this idea of Christian Goldbach into the structure of a numerical double-strand, into an opposing member of the MEC 30 scale.\n- We call this double strand a convolution, which results in an opposite arrangement. It represents the natural vibration, thus also the redundant vibrations in the energy transfer. In the 6 For example, in the graph, the even number 60 is folded. At folding of the even number 60 6 result in 8 prime pairs.\n- In this case, among the 8 pairs of prime pairs there are only 6 Goldbach pairs. 2 prime positions in the prime position pairs carry products of the factors \"1 × 1\" and 7 × 7. Thus, 2 prime pairs do not fulfill the requirements of the Goldbach pairs. In general, any even number larger than 30 can be represented graphically within a cycle (MEC 30) as a specific cyclic convolution. This characteristic convolution of the even numbers is a fundamental test element in the numerical table. The result Even the even numbers to infinity occupy a fixed position within the 30s system MEC 30. The even numbers thus have 15 positions: 30/2 = 15 even positions of the MEC 30.\n- There are therefore only 15 even positions for all even numbers to infinity. Every even number has a specific convolution due to its position in the 30s system. First, we have to determine the positions of the even numbers in the 30s system to make them one in the following graph 7 attributable to the 15 specific folds.\n
            \n\n

            \"\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 ✔️\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49 ✔️\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43 ✔️\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            Palindromic Sequence

            \n\n
            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their ***collective bilateral 9 sum symmetry***). _([PrimesDemystified](https://primesdemystified.com/))_\n
            \n\n

            7 x π(89) = 7 x 24 = 168 = π(1000)

            \n\n

            \"collective

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2 ✔️\n4 3 1 1 0 3 👉 61 - 1 = 60 ✔️\n5 5 2 1 0 5\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n
            The color spin addresses for numbers are generally straightforward – a composite number takes the spin of the prior prime.  4 spins blue because 3 spins blue.  8 is red because 7 is red.  However, twin primes, and the 0 type numbers between them, are open to some interpretation.\n
            \n\n

            \"base\"

            \n\n

            (43 - 19)the prime = 24th prime = 89

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                       MEC 30 / 2\n------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) √\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = (43-19) √\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}\n
            \n\n
            The number 120 has 32 prime positions minus 5 prime number products = 27 prime numbers. The information of the prime number products translates our theory into a checkerboard-like pattern using the finite 8 prime positions from the MEC 30, we call it Ikon. 8 × 8 primary positions = 64 primary positions of the checkerboard icon.\n- First, there are two main features that we use. To Ikon 1: The primes information and their products. In this left icon, the redundants (the doubles) are to be determined through the number information in the positions Impeccable.\n- Second: The product positions. In the icon, the cyclic behavior is shown in identical 8 horizontal and 8 vertical orders, we call these orders templates that would not be visible through the pure number information. The cyclical behavior of the 8 × 8 product positions continues indefinitely.\n- Since the prime positions are finite, a total of 8 positions in the 30th order, an already revolutionary system opens up, the entire infinite distribution of the prime number products in an icon as a \"checkerboard pattern\". represent and thus obtain mathematically exact results.\n- The three and 4 , Square Graphics (Ikon) will now be in the following, larger graphic 5 transfer. As stated above, we use the properties of the numbers, they consist of one information and one position. Thus we are able to calculate the redundant product positions by means of identical information in different positions.\n- And subtracting them from the total prime positions gives us the number of prime numbers. This succeeds due to the self-similarity of the 30th order of the MEC 30, as shown in the graph 5 is articulated. At the top of the following larger graphic 5 the self-similarity of the 30th order (MEC 30) can be seen.\n- This results in a fundamental causal relation to the primes, systemically the products are entered into the position system. Therefore, the distribution of primes products also determines the distribution of primes themselves. The reason lies in the one-system, since the prime number as a number itself also consists of an information and a position.\n\nWe apply the same principle as above for the determination of the prime position. Only with the difference that we move in the even positions of the MEC 30.\n
            \n\n

            7 x π(89) = 7 x 24 = 168 = π(1000)

            \n\n

            \"\"

            \n\n

            \"Theory

            \n","dir":"/addition/","name":"3.md","path":"addition/3.md","url":"/addition/3.html"},{"sort":3,"spin":4,"span":"lexer","suit":"intro","layout":"default","title":"Mass vs Gap (Δ)","content":"## [Mass vs Gap (Δ)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288)\n\nThis section will be the last one of our presentation of 18th prime identity. Here we are going to explain one more item that is still open or undiscussed which is about what the [77 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#object-orientation) are going to do within the 19 vs 18 Scenario.\n\n***15 + 35 + 28 = 15 + 63 = 78 = 77 + 1***\n\n```\n---+-----+-----\n 1 | 1 | 15\n---+-----+-----\n 2 | 16 | 25\n---+-----+-----\n 3 | 26 | 50\n---+-----+-----\n 4 | 51 | 84\n---+-----+-----\n 5 | 85 | 99\n---+-----+-----\n```\n\n```\n$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer| i | f\n -----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | 7\n -----+-----+--- } 36 » 6®\n | 3 | 11\n 2 +-----+\n | 4 | 13\n -----+-----+---------\n | 5 | 17\n 3 +-----+ } 36 » 6®\n | 6 | 19\n -----+-----+---------\n```\n\nIn many ways, a _[black hole](https://en.wikipedia.org/wiki/Black_hole)_ acts like an ideal black body, as ***it reflects no light***. Here is an animated simulation of a Schwarzschild black hole with a galaxy passing behind. Around the time of alignment, extreme gravitational lensing of the galaxy is observed.\n\n[![black hole](https://user-images.githubusercontent.com/8466209/220674107-f4b5daff-b0cb-46d0-990f-50fccd88a599.gif)](https://en.wikipedia.org/wiki/Black_hole)\n\n```\n largest part=21 → 11+13+12=36 → MEC30\n ↓ |\n---+-----+-----+-----+-----+ ↓\n 1 | 19 | 1 | 20 | 21 |-------------------|-----\n---+-----+-----+-----+-----+ ↓ |\n 2 | 18 | 21 | 39 | 60 |------------------- |\n---+-----+-----+-----+-----+ | |\n 3 |{63} | 40 | 103 | 143 |------------- | |\n---+-----+-----+-----+-----+ | | |\n 4 | 37 | 104 | 141 | 245 |------- | | |\n---+-----+-----+-----+-----+ | | | |\n 5 | 10* | 142 | 152 | 294 |- 11** | 13 | 12 | 12 | 18\n---+-----+-----+-----+-----+ | | | |\n 6 | 24 | 153 | 177 | 332 |------- | | |\n---+-----+-----+-----+-----+ | | |\n 7 | 75 | 178 | 253 | 431 |------------- | |\n---+-----+-----+-----+-----+ | |\n 8 | 30 | 254 | 284 | 538 |------------------- |\n---+-----+-----+-----+-----+ ↓ |\n 9 | 1 | 285 | 286 | 571 |-------------------|-----\n===+=====+=====+=====+=====+ ↓\n45 | 277 | ← 11+13+12=36 ← MEC30\n---+-----+ |\n ↑\nNote:\n10* stands as the central rank\n11** stands as the central parts\n```\n\nAccording to the observations made by NASA, Astronomers have uncovered ***[TON 618](https://en.wikipedia.org/wiki/TON_618#Supermassive_black_hole)*** as the record breaking supermassive black hole, weighing 66 trillion and brilliantly as 140 trillion times that of the Sun, making it one of the brightest object in the Universe. \n\n[![default](https://user-images.githubusercontent.com/8466209/223629156-8cfdfb46-1884-4f45-bbb6-d11093ac3834.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)\n\nIf the statement that it is indeed located at the center of our universe then the said black hole would behave as the exchange position between ***[twin (2) universes](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#dark-energi)***. This would for sure strengthen the syntax algorithm of our _[implementation](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation)_.\n\n***7 x 11 = 77 = 99 - 22 = 11 x (9 -2)***\n\n```\n #8 |------- 5® --------|------------ 7® --------------|\n | 1 |-------------- 77 = 4² + 5² + 6² -------------|\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n user | 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n------+---|---+---+---+---+---+---+---+---+----+----+----+ 7,78\n main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 100 - 123 ({24})\n |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30\n {98} | └── 110 - 123 (14x)» 70\n\n```\n\n```liquid\nDirection:\n- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.\n- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.\n- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.\n \nConclution:\n- All of the other primes than 2 is 1 less than the number n times the number of 2. \n- Those Mersenne primes is generated as 1 less than the power n of the number of 2. \n- Thus they will conseqently be carried out by the same scheme of this number of 2.\n```\n\nPerceptually, everything is separate and finite. But actually, everything is connected and infinite. It is this infinite connection, despite our limited finite perceptions, that makes us one with the cosmos.\n\n## Primes Platform\n\nEach result goes to the 9th object of prime 67 which is 19th prime. This ***[mass gap of (Δ > 0)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)*** is actually [the quantum way](https://gist.github.com/eq19) of our algorithm which is discused in details by the _[19th prime identity](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831)_. \n\n[![](https://user-images.githubusercontent.com/36441664/81015797-80c0bc80-8e89-11ea-905a-c6cec604f443.png)](https://en.wikipedia.org/wiki/Brun%27s_theorem)\n\nSo when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming bilateral 9 sum which facilitate them to finaly generate 1000 primes. \n\n***1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects***\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n \n-----+-----+-----+-----+-----+ -----------------------------------------------\n{786}| 1,2 | 2 | 2,3 | 3,4 | {19} |\n-----+-----+-----+-----+-----+ |\n {86}| 4 | 4,5 | 5,6 |{6,7}| 17 Base Zone\n +-----+-----+-----+-----+ |\n {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ |\n +-----+-----+-----+ -----------\n {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone |\n ----+-----+-----+-----+-----+ |\n {6}|15,16|17,18|18,20|21,22| 19 Mirror Zone\n +-----+-----+-----+-----+ |\n {8}|23,25|25,27|27,29| 18 |\n +-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------\n {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------\n | 1 2 3 | 4 5 6 | 7 8 9 |\n |------ 29' ------|--------------- 139' ----------------|\n |------ 102¨ -----|--------------- 66¨ ----------------|\n```\n\nWhen recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row \nforming the _[Primes Platform](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)_. Thus we got 109 objects including for the 7 rows back to the original stage. \n\n```\n Tabulate Prime by Power of 10\n loop(10) = π(10)-π(1) = 4-0 = 4\n loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n\nSequence:\n By the next layer the 89² will become 89 and 5 become 5² or 25.\n This 89 and 25 are in the same layer with total of 114 or prime 619\n So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n```\n\n***[(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects***\n\n```\nThe Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+ ---\n 7 --------- 1,2:1| 1 | 30 | 40 | 71 (2,3) ‹-------------@---- |\n | +-----+-----+-----+-----+ | |\n | 8 ‹------ 3:2| 1 | 30 | 40 | 90 | 161 (7) ‹--- | 5¨ encapsulation\n | | +-----+-----+-----+-----+ | | |\n | | 6 ‹-- 4,6:3| 1 | 30 | 200 | 231 (10,11,12) ‹--|--- | |\n | | | +-----+-----+-----+-----+ | | | ---\n --|--|-----» 7:4| 1 | 30 | 40 | 200 | 271 (13) --› | {5®} | |\n | | +-----+-----+-----+-----+ | | |\n --|---› 8,9:5| 1 | 30 | 200 | 231 (14,15) ---------› | 7¨ abstraction\n289 | +-----+-----+-----+-----+-----+ | |\n | ----› 10:6| 20 | 5 | 10 | 70 | 90 | 195 (19) --› Φ | {6®} |\n --------------------+-----+-----+-----+-----+-----+ | ---\n 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |\n | +-----+-----+-----+ | |\n | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | | +-----+-----+-----+ | | |\n | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n | | | +-----+-----+-----+ | | ---\n | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |\n | | +-----+-----+-----+ | |\n | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance\n329 | +-----+-----+-----+ |\n | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ |\n -------------------+-----+-----+ ---\n 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ |\n | +-----+-----+ |\n | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class\n | | +-----+-----+-----+-----+-----+ | |\n | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} |\n | | | +-----+-----+-----+-----+-----+ | | ---\n --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- |\n | | +-----+-----+ | |\n --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object\n168 | +-----+ |\n| 102 -› 29:18| 50 | 50(68) ---------> Δ18 |\n----------------------+-----+ ---\n```\n\nThe above is observed following the W0 (assumptions of relativistic quantum mechanics) for the _[Existence and Mass Gap](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap#The_Wightman_axioms)_ which transform under the homogeneous group as a _[four-vector](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#four-4-vector)_ and has a mass gap Δ > 0.\n\n>Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on \n***R^4 and has a mass gap Δ > 0*** _([Wikipedia](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap))_.\n\n![image](https://user-images.githubusercontent.com/8466209/223643996-1ea5cb89-324e-446c-9c9f-8c94c39909b3.png)\n![origin](https://user-images.githubusercontent.com/8466209/220002045-d0395b21-1f2a-4dba-992a-24bf50c480d5.png)\n![action](https://user-images.githubusercontent.com/36441664/84525042-2f67e080-ad05-11ea-9f9c-e07492446240.jpg)\n\n![default](https://user-images.githubusercontent.com/8466209/235528211-256deb9c-e31f-4560-8811-3cd38726702c.png)\n\n[![runner](https://user-images.githubusercontent.com/8466209/223616353-0e1be019-16e8-40d1-bb0c-465a9837d7bb.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#four-4-vector)\n\n![](https://user-images.githubusercontent.com/36441664/59960482-f2527f00-94f2-11e9-84aa-f7ef5eb4ae89.png)\n","dir":"/identition/span3/","name":"gist04.md","path":"identition/span3/gist04.md","url":"/identition/span3/gist04.html"},{"sort":4,"spin":1,"span":"orientation","suit":"intro","layout":"default","title":"Object Orientation","content":"# [Object Orientation](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699)\n\nHere we are going to discuss the concept of lagging and leading scheme on DNA System using four-dimensional space (4D). A mathematical extension of the concept of three-dimensional space (3D) originated by ***43 out of 89*** objects of bilateral 9 sums. \n\n```\n---+-----+-----\n 1 | {1} |{43}\n---+-----+-----\n 2 | 44 |{57}\n---+-----+-----\n 3 | 58 | 59\n---+-----+-----\n 4 | 60 | 104\n---+-----+-----\n 5 | 105 |{115}\n---+-----+-----\n 6 |{116}| 134\n---+-----+-----\n 7 | 135 | 162\n---+-----+-----\n 8 | 163 | 175\n---+-----+-----\n 9 | 176 |{176}\n---+-----+-----\n```\n\nThe geometry of four-dimensional space is much more complex than that of three-dimensional space, due to the extra degree of freedom. However in our case this 43 objects has excatly a finite fraction of four (4) axis dimensions to MEC30.\n\n![default](https://user-images.githubusercontent.com/8466209/226088008-95da40ee-aece-4ec8-86ee-cff448e15b42.png)\n\n\n***(114/2)! = 57! = 1653 » 1653 / 57 = 29***\n\n```\n--------+\n | ⅓\n +--- } ⅔\n Case A | ⅓\n +---------\n | ⅓ |\n-----------------+ Φ = ⅔\n | ⅓ |\n +---------\n Case B | ⅓\n +--- } ⅔\n | ⅓\n---------\n```\n\n***9 + 19 + 29 = 28 + 29 = 57***\n\n```\nP7:(142857)\n\n # | A | B | ∑\n------+------+------+-----\n {1} | | |\n------+ | |\n ... | 28 | 29 | 57\n------+ | |\n {57} | | |\n------+------+------+-----\n 58 | | |\n------+ | |\n ... | 29 | 28 | 57\n------+ | |\n 114 | | |\n------+------+------+-----\n | 57 | 57 | 114\n```\n\nComparatively, four-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w to describe the two additional cardinal directions of ***up toward*** and ***down from***, respectively. \n\n>The set of points in Euclidean 4-space having the same distance R from a fixed point P0 forms a hypersurface known as a 3-sphere where R is substituted by function R(t) with t meaning the cosmological age of the universe. Growing or shrinking R with time means expanding or collapsing universe, depending on the mass density inside _([Wikipedia](https://en.wikipedia.org/wiki/Four-dimensional_space#Hypersphere))_.\n\n[![Clifford-torus](https://user-images.githubusercontent.com/8466209/226084191-fbdb2d57-08bc-4d18-adea-4e165aee19a8.gif)](https://en.wikipedia.org/wiki/Four-dimensional_space#Hypersphere)\n\nBy [deploying containers](https://gist.github.com/eq19/e84a0961dc7636c01d5953d19d65e30a#file-create-md) on Compute Engine, you can simplify app deployment while controlling four dimensional space. You can configure a virtual machine (VM) instance or an instance template to [deploy and launch](https://cloud.google.com/compute/docs/containers/deploying-containers) a Docker container. \n\n## Balanced Prime\n\nThe initial objects will be a formation of a double helix driven by vectors 71 and 68 based on the arrangement of prime numbers on a cube of 10x10x10 or 1000 to the Golden Ratio.\t\n\n***π(10x10x10) + 10x10x10/Φ = π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786***\t\n\n![](https://user-images.githubusercontent.com/36441664/93509564-1d23c100-f94a-11ea-992b-78472d112f75.jpg)\t\n\n![](https://user-images.githubusercontent.com/36441664/94854538-3f900100-0457-11eb-8452-2a89a42a3da8.gif)\n\n[![image](https://user-images.githubusercontent.com/8466209/226250907-b3ad5fec-b284-476b-9a21-7b71c3cdd54b.png)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#mapping-scheme)\n\n***1/7 = 0,142857142857142857142857.. infinity***\n\n![default](https://user-images.githubusercontent.com/8466209/223204214-7dd70a63-34fd-4f9c-887e-5d3b3df87088.png)\n\nBy the prime numbers this polarizing between the objects and its tensors is identified by the 157 as the ***19+18=37th prime***. This 157 is a balanced prime of two (2) primes of ***151 + 163 = 314 = 100 x π*** by which the 100 is standing as the square of 10x10 out of the central objects of ten (10) while the π is one of the constant of _[Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_.\n\n>The number 157 is the 18+19=37th prime number, ***a balanced prime***, because the arithmetic mean of those primes yields 157. The next prime is 163 and the previous prime is 151, with which 157 forms a prime triplet _([Wikipedia](https://en.wikipedia.org/wiki/157_(number)))_.\n\n[![](https://user-images.githubusercontent.com/36441664/100333516-42494580-3005-11eb-95a2-e7360e60b60f.jpg)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-scenario-md)\n\nBy this square correlation between natural and prime numbers then the 571 would be separated by the 100 to 500 and 71 and finally by the form of (2,10) the 500 goes to 50 while 71 is polarized to 71x2=142 and 177 as shown on the table.\n\n***(10/2)π = 157 ⇄ (10^2)¹ + 11x7 = 177 = 286 - 109***\n\n[![interpolation](https://user-images.githubusercontent.com/36441664/72922749-30ad6680-3d80-11ea-92c8-73c1fa12041b.jpg)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#interpolation)\n\nSo by the above explanation of this 157's behaviour it is now left the question of where the tensor of 571 by the ***two (2) numbers*** of 285 and 286 is going. That is the ***imajinary part (i)*** of Euler's identity has something to do with the _[zeta function](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function)_.\n\n### Encapsulation Scenario\n\nThis 4D concept is conducted to get 1000 prime objects of 3rd layer within four (4) times interaction of _[triangular waves](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#triangular-waves)_ between ***26 and 28th*** prime identities starting from 11x2=22, 22x2=44, 44x2=88 that leads to 88x2=176 objecs of 4th prime identity.\t\n\n***4 x 22 of 88 rows = 4 x 528 = 2112 elements = the index of 1000th prime***\t\n\n```\t\nid: 26\t\n---+-----+-----+-----+-----+\t\n 1 | 5 | 1 | 6 | 7 |----------------------------\t\n---+-----+-----+-----+-----+ |\t\n 2 | 2 | 7 | 9 | 16 |---------------------- |\t\n---+-----+-----+-----+-----+ | |\t\n 3 | 58 | 10 | 68 | 78 |---------------- | |\t\n---+-----+-----+-----+-----+ | | |\t\n 4 | 35 | 69 | 104 | 173 |---------- | | |\t\n---+-----+-----+-----+-----+ | | | |\t\n 5 | {17}| 105 | 122 |{227}| | | | |\t\n---+-----+-----+-----+-----+- Cross {17}Δ26|43Δ30|13Δ17|30 ----\t\n 6 | {17}|{123}| 140 | 263 | | | | | |\t\n---+-----+-----+-----+-----+ | | | | |\t\n 7 | 18 | 141 | 159 | 300 |---------- | | | |\t\n---+-----+-----+-----+-----+ | | | |\t\n 8 | 15 | 160 | 175 | 335 |---------------- | | |\t\n---+-----+-----+-----+-----+ | | |\t\n 9 | 15 | 176 | 191 | 367 |---------------------- | |\t\n---+-----+-----+-----+-----+ | |\t\n10 | 35 |{192}|{227}| 419 |---------------------------- | \t\n---+-----+-----+-----+-----+ |\t\n |\t\nid: 27 {26} |\t\n | |\t\n---+-----+-----+-----+-----+ | |\t\n 1 | 5 | 1 | 6 | 7 |---------------------- {1+7} |\t\n---+-----+-----+-----+-----+ | | |\t\n 2 | 7 | 7 | 14 | 21 |---------------- | | |\t\n---+-----+-----+-----+-----+ | | {17} |\t\n 3 | 29 | 15 | 44 | 59 |---------- | | | |\t\n---+-----+-----+-----+-----+ | | | | |\t\n 4 | 8 | 45 | 53 | 98 | | | | | |\t\n---+-----+-----+-----+-----+- 4xMEC30 29 2 18 -- Cross -- MEC30\t\n 6 | 4 | 54 | 58 | 112 | | | | | |\t\n---+-----+-----+-----+-----+ | | | | |\t\n 7 | - | 59 | 59 | 118 |---------- | | | |\t\n---+-----+-----+-----+-----+ | | {17} |\t\n 7 | 9 | 60 | 69 | 129 |---------------- | | |\t\n---+-----+-----+-----+-----+ | | |\t\n 8 | 23 | 70 | 93 | 163 |---------------------- {1x7} |\t\n---+-----+-----+-----+-----+ | |\t\n | |\t\nid: 28 {28} | \t\n |\t\n---+-----+-----+-----+-----+ |\t\n 1 | 5 | 1 | 6 | 7 |---------------------------- |\t\n---+-----+-----+-----+-----+ | |\t\n 2 | 6 | 7 | 13 | 20 |---------------------- | |\t\n---+-----+-----+-----+-----+ | | |\t\n 3 | 7 | 14 | 21 | 35 |---------------- | | |\t\n---+-----+-----+-----+-----+ | | | |\t\n 4 | 6 | 22 | 28 | 50 |---------- | | | |\t\n---+-----+-----+-----+-----+ | | | | |\t\n 5 | 13 | 29 | 42 | 71 | Δ13 Δ11 Δ7 0 0 --=--- \t\n---+-----+-----+-----+-----+ | | | |\t\n 6 | 17 | 43 | 60 | 103 |---------- | | |\t\n---+-----+-----+-----+-----+ | | |\t\n 7 | 14 | 61 | 75 | 136 |---------------- | |\t\n---+-----+-----+-----+-----+ | |\t\n 8 | 6 | 76 | 82 | 158 |---------------------- |\t\n---+-----+-----+-----+-----+ |\t\n 9 | 5 | 83 | 88 | 171 |----------------------------\t\n---+-----+-----+-----+-----+\t\n```\t\n\nThis scheme could be happen by The Encapsulation behaviour of 28 which is the natural number following 27 preceding 29 and depicted as 28 balls arranged in a ***[triangular pattern with the number of layers of 7](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#triangular-pattern)*** which lead to the concept of _[Gematria](https://en.wikipedia.org/wiki/Gematria)_.\t\n\n>Twenty-eight is a composite number, its proper divisors being 1, 2, 4, 7, and 14. It is ***the only known number*** that can be expressed as a sum of the first nonnegative (or positive) integers ( 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) and a sum of the first nonprimes ( 1 + 4 + 6 + 8 + 9 ), and it is unlikely that any other number has this property _([Wikipedia](https://en.wikipedia.org/wiki/28_(number)))_..\t\n[![triangular pattern with the number of layers of 7](https://user-images.githubusercontent.com/36441664/74991882-e4863c80-5479-11ea-9dfc-f00822fe952d.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#triangular-pattern)\t\n\nHowever there was a wide discussion stating that _[Gematria is NOT numerology](https://en.wikipedia.org/wiki/Talk:28_(number)#Gematria_is_NOT_numerology)_. impacting a loss of science principal on prime interaction such as in DNA System, which occurs at a mismatch, is said to trigger a shift in the balance, for the binding of the template-primer, from the polymerase, to the exonuclease domain. So it shall use a method that [combines data and code](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rational-vs-irrational).\t\n\n>Encapsulation allows developers to present a consistent and usable interface which is independent of how a system is implemented internally. As one example, encapsulation can be used to hide the values or state of a structured data object inside a class, preventing direct access to them by clients in a way that could expose hidden implementation details or violate state invariance maintained by the methods _([Wikipedia](https://en.wikipedia.org/wiki/Encapsulation_(computer_programming)))_.\t\n![](https://user-images.githubusercontent.com/8466209/199354127-9e4d362a-933f-402b-a7a8-0010dc014747.png)\t\n\nEncapsulation is key concept in object-oriented programming (OOP) defined as a way to restrict the direct access to components of an object that users cannot access state values for all of the variables of a particular object. So let's discuss it first.\n\n### Golden Ratio\n\nSo it is converting all residual objects out of the prime recycling of _[Riemann Zeta](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function)_ in to those three (3) basic arithmetic operations of _[Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_ as well the Fibonacy constant (***φ***) to Euler's number (***e***). Thus none of residual is neglected by an assumption.\n\n![](https://user-images.githubusercontent.com/36441664/72682696-8248bd80-3b02-11ea-935f-d016e46da4fc.png)\n\nThis behaviour would come to the feature of ***golden ratio***. However it is not stand as a basic rule but as an impact of 329's vs 289's layers. That is also the reason why we could only see the three (3) digits of 618 out of the _Fibonaci_ constant.\n\n***φ = 1.618 = Fibonaci = Golden Ratio***\n\n![](https://user-images.githubusercontent.com/36441664/85039732-36ce3480-b1b2-11ea-969c-536a01c115b6.jpg)\n\nPlottng ***40th prime scheme*** of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.\n\n***89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120***\n\n[![default](https://user-images.githubusercontent.com/8466209/225589915-8f7690c8-4c17-4232-be51-63e79efb2c51.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)\n\n![](https://user-images.githubusercontent.com/8466209/199355377-8d93057a-769d-49ed-b401-722c0b33fdab.png)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n | | | 20:13 | 90 | 90 (38) ‹-------------- ¤ |\n | | 7 +----------+-----+ |\n | 5 | | 14 | ----------------------------- 17¨ class\n | |-----+----------+ | | |\n | | | 15 | | LEADING SCHEME | |\n 3 +------+ 8 +----------+----- | (Multiplication Zone) | ---\n | | | 16 | | | |\n | |-----+----------+-----+ ----------------------------- |\n | 6 | | 28:17 | 100 | 19¨ object\n168 | | 9 +----------+-----+ |\n| | | | 29:18 | 50 | 50(68) ---------> Δ18 |\n------|------|-----+----------+-----+ ---\n```\n\nThese three (3) times bilateral 9 sums will lead to 168 vs 618 exponents between 68 and 69 objects of ***50 and 27th prime identity*** that simulate the [X/Y-genes reproduction](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#assigning-repositories) of human cromosomes to the repository assignment of our project.\n\n## Registry unit\n\nYou can see that two distinct pressure zones are forming and that the spiral pattern expected from lid-driven cavity flow is beginning to form. Experiment with different values of nt to see how long the system takes to stabilize.\n\n[![12 Steps to Navier-Stokes](https://user-images.githubusercontent.com/8466209/224357044-f3c42fa5-b9ad-471c-85f3-6a4aa01a909e.png)](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f)\n\nIt is a relationship between the rate of acceleration of liquids (the increase in their speed) and the force that acts on them, widely used in moving air vehicles, and is considered the most important equation used in the application of aircraft movement.\n\n[![Navier–Stokes Equation](https://user-images.githubusercontent.com/8466209/229137105-85011ac0-9a92-4305-920c-0e76a4f315b1.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#anti-parallel)\n\nIt is considered one of the most important equations in physics. Now let's analyze how we could say this structure can be used for switching the workflow between Windows and Linux.\n","dir":"/identition/span1/","name":"gist04.md","path":"identition/span1/gist04.md","url":"/identition/span1/gist04.html"},{"sort":4,"spin":13,"layout":"default","title":"factor","content":"# factor\n\n[![factorcode](https://user-images.githubusercontent.com/8466209/205431165-24d484fc-c7a2-4482-b2c2-61de97495a67.png)](https://docs.factorcode.org/content/article-vocab-index.html)\n\n[![TA_Chart](https://user-images.githubusercontent.com/8466209/204839094-d6b1713d-af4e-4fee-b073-3fe84e1e9275.png)](https://tfhub.dev/)\n\n[![2022-11-30 (5)](https://user-images.githubusercontent.com/8466209/205431468-6777265f-63a8-42ea-b454-d45227478362.png)\n](https://github.com/factor/factor/)\n","dir":"/exponentiation/span13/","name":"gist04.md","path":"exponentiation/span13/gist04.md","url":"/exponentiation/span13/gist04.html"},{"sort":4,"spin":1,"span":"quantum","suit":"intro","layout":"default","title":"Lexer vs Parser","content":"# [Lexer vs Parser](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#objects-vs-classes)\n\n![enneatruth_anim](https://user-images.githubusercontent.com/8466209/222872175-af87d1af-a263-4cea-8d99-f667698df9fa.gif)\n\n![image](https://user-images.githubusercontent.com/8466209/222872241-0b9c2d81-14e4-4acf-a6eb-fc736f9109a0.png)\n\n>Notice how the 3, 9, and 6 is in red and does not connect at the base. That is because it is a vector. The 1,2,4,8,7,5 is the third dimension while the oscillation between the 3 and 6 demonstrates the fourth dimension, which is the higher dimensional magnetic field of an electrical coil. \n\n![image](https://user-images.githubusercontent.com/8466209/222872294-62779dd9-f263-4372-af0a-f704102037e4.png)\n\n>The 3, 9, and 6 always occur together with the 9 as the control. In fact, the Yin/Yang is not a duality but rather a trinary. This is because the 3 and 6 represent each side of the Yin/Yang and the 9 is the “S” curve between them. Everything is based on thirds. We think that the universe is based on dualities because we see the effects not the cause.\n\n![](https://user-images.githubusercontent.com/36441664/81163688-566e1c80-8fb9-11ea-9556-2c6ec6321fd8.png)\n\n![](https://user-images.githubusercontent.com/36441664/75617590-b7314100-5b93-11ea-926f-fc01910cbd11.png)\n\n### Four (4) Vector\n\n[![](https://user-images.githubusercontent.com/8466209/207483341-add0449b-3aec-4ee3-baa6-144583e60f9f.gif)](https://en.wikipedia.org/wiki/Feynman_diagram)\n\n![](https://user-images.githubusercontent.com/36441664/74104225-1697c480-4b85-11ea-8819-870981638baf.png)\n\n![](https://user-images.githubusercontent.com/36441664/81162523-874d5200-8fb7-11ea-9b66-65f476bc5427.jpg)!\n\n***Φ(11,13) = (114 - 10²) + 13 = 27***\n\n```\n1729 = 7 x 13 x 19\n1729 / 7 = 13 x 19 = 247\n\n1729 = 7 x 13 x 19\n 7 + 13 = 20 = d(2)\n └── 2 x 19 = 38\n\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n| {1}| 2 | 3 | 4 | 5 | {6}| {7}| 8 | 9 | 10 | 11 | 12 | 13 | 14 |\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n| {3}| {4}| 3 | 4 | 5 | 2 | 3 | 2 | 2 | 1 | 2 | 5 | 1 | 1 |{38}\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285\n| 3 | 8 | 9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|-- 38 ---| |-- 33 ---| |-- {27}--|\n```\n\n[![Four Spacetime Dimensions](https://user-images.githubusercontent.com/36441664/133192153-61cad1c0-1dde-4fed-8718-840d324a7198.jpg)](https://jayryablon.wordpress.com/)\n\n![](https://user-images.githubusercontent.com/8466209/206956260-f8c3647a-232c-470e-8c0b-e93a6fea14f7.png)\n\n```\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n | | | 20:13 | 90 | 90 (38) ‹-------------- ¤ |\n | | 7 +----------+-----+ |\n | 5 | | 14 | ----------------------------- 17¨ class\n | |-----+----------+ | | |\n | | | 15 | | LEADING SCHEME | |\n 3 +------+ 8 +----------+----- | (Multiplication Zone) | ---\n | | | 16 | | | |\n | |-----+----------+-----+ ----------------------------- |\n | 6 | | 28:17 | 100 | 19¨ object\n168 | | 9 +----------+-----+ |\n| | | | 29:18 | 50 | 50(68) ---------> Δ18 |\n------|------|-----+----------+-----+ ---\n```\n\n## Diagram of Classes\n\nCOS instances come pre-installed with the ***[Docker runtime](https://cloud.google.com/container-optimized-os/docs/concepts/features-and-benefits#features_and_benefits)*** and ***[cloud-init](https://www.digitalocean.com/community/tutorials/an-introduction-to-cloud-config-scripting)***. With a COS instance, you can [bring up](https://gist.github.com/higebu/b8bf07c1b99689341689ecb65d854c2f) your Docker container at the same time you create your VM, with no on-host setup required.\n\n>Note: [docker-credential-gcr](https://cloud.google.com/artifact-registry/docs/docker/authentication) writes credentials to $HOME/.docker/config.json. When running /usr/bin/docker-credential-gcr configure-docker in a unit file, ***you must set the environment variable $HOME***. Otherwise, docker-credential-gcr will try to write credentials to /root/.docker/config.json, which is not permitted on Container-Optimized OS _([Google Cloud](https://cloud.google.com/container-optimized-os/docs/how-to/run-container-instance#using_cloud-init_with))_.\n\n```\n#cloud-config\n\nusers:\n- default\n- uid: 2000\n name: runner\n groups: admin,adm,video,docker,google-sudoers\n\nwrite_files:\n- owner: root\n permissions: 0644\n path: /etc/systemd/system/runner.service\n content: |\n [Unit]\n Wants=gcr-online.target\n After=gcr-online.target\n Description=gcloud compute instances create instance-template --scopes=https://www.googleapis.com/auth/cloud-platform --network-interface=network=default,network-tier=PREMIUM --maintenance-policy=MIGRATE --provisioning-model=STANDARD --project=feedmapping --zone=us-central1-a --shielded-vtpm --shielded-integrity-monitoring --reservation-affinity=any --service-account=project-owner@feedmapping.iam.gserviceaccount.com --machine-type=e2-micro --enable-display-device --no-shielded-secure-boot --image-family cos-stable --image-project cos-cloud --metadata-from-file user-data=cloud-config --create-disk=auto-delete=yes,device-name=persistent-disk-1,boot=no,image-family=tf-ent-latest-gpu,mode=rw,size=50,type=pd-standard,image-project=deeplearning-platform-release \n\n [Service]\n Environment=\"HOME=/home/runner\"\n ExecStartPre=/usr/bin/docker-credential-gcr configure-docker\n ExecStart=/usr/bin/docker run --rm --name myrunner -e RUNNER_NAME=Google-optimized-instance -e RUNNER_ORGANIZATION_URL=https://github.com/FeedMapping -e RUNNER_WORK_DIRECTORY=/mnt/disks/Linux/tmp/_FeedMapping -e RUNNER_REPLACE_EXISTING=true -e GITHUB_ACCESS_TOKEN=ghp_XXXXXXXXXXXXXXXXXXXXXXXXXX -v /var/run/docker.sock:/var/run/docker.sock -v /mnt:/mnt eq19/setup\n ExecStop=/usr/bin/docker stop myrunner\n ExecStopPost=/usr/bin/docker rm myrunner\n\nruncmd:\n- systemctl daemon-reload\n- systemctl start runner.service\n- systemctl status runner.service\n\nbootcmd:\n- fsck.ext4 -tvy /dev/sdb1\n- mkdir -p /mnt/disks/Linux\n- mount -t ext4 -o discard,defaults /dev/sdb1 /mnt/disks/Linux\n```\n\nUsing the [advanced scenarios](https://cloud.google.com/container-optimized-os/docs/how-to/create-configure-instance#advanced) you can [deploy](https://github.com/eq19/setup#using-docker-inside-your-actions) multiple containers and [configure Docker options using cloud-init](https://cloud.google.com/container-optimized-os/docs/how-to/run-container-instance#using_cloud-init_with), you can create a Compute Engine instance with your choice of COS image then [proceed to configure](https://cloud.google.com/container-optimized-os/docs/how-to/run-container-instance) with [metadata](https://cloud.google.com/compute/docs/metadata/overview).\n\n```\ndocker run -it --name Google-optimized-instance \\\n -e RUNNER_NAME=Google-optimized-instance \\\n -e RUNNER_ORGANIZATION_URL=https://github.com/FeedMapping \\\n -e GITHUB_ACCESS_TOKEN=ghp_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx \\\n -v /var/run/docker.sock:/var/run/docker.sock \\\n tcardonne/github-runner\n```\n\nThe Google instance deployed through the Google Cloud console or the Google Cloud CLI, not the API. Use [advanced scenarios](https://cloud.google.com/container-optimized-os/docs/how-to/create-configure-instance#advanced) to deploy multiple containers, and to use [cloud-init](https://cloud.google.com/compute/docs/startupscript) for advanced [configuration](https://docs.github.com/en/actions/hosting-your-own-runners/configuring-the-self-hosted-runner-application-as-a-service).\n\n[![default](https://user-images.githubusercontent.com/8466209/226794991-716ca3ff-876b-4efb-9180-a2ea547c851b.png)](https://docs.github.com/en/actions/hosting-your-own-runners/configuring-the-self-hosted-runner-application-as-a-service)\n\n\nIt will be managed by the boot disk of 10GB represent the central of addition zone with two (2) exponential zone each represent new lagging strand DNA, whose direction of synthesis ***is opposite*** to the direction of the growing replication fork.\n\n## Deep Learning\n\nBase on above scheme here we are going to use [Deep Learning VM Images](https://cloud.google.com/deep-learning-vm/docs/images#deciding) from Google and [Windows Server Images](https://cloud.google.com/compute/docs/images/os-details#windows_server) from Microsoft by the image disks of 32GB to represent _[imajinary part (i)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rational-vs-irrational)_, and the 50GB to represent _[circle part (π)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)_.\n\n>The Cloud-init is a way to configure a COS instance when it boots up. The tool expects its configuration in the value of the ***[user-data key](https://cloud.google.com/container-optimized-os/docs/how-to/create-configure-instance#using_cloud-init_with_the_cloud_config_format)*** of the [instance metadata](https://cloud.google.com/sdk/gcloud/reference/compute/instances/create#--metadata). The cloud-init tool understands [multiple formats](https://cloudinit.readthedocs.org/en/latest/topics/format.html).\n\n[![default](https://user-images.githubusercontent.com/8466209/227417560-298c1c98-db6b-4221-b377-ebe38313cc84.png)](https://cloud.google.com/container-optimized-os/docs/how-to/create-configure-instance#using_cloud-init_with_the_cloud_config_format)\n\nThe COS Container has [limited or no support for the gsutil tool](https://cloud.google.com/compute/docs/instances/startup-scripts/linux#limitations). Passing a startup script for COS instance of _[#cloud-config](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#diagram-of-classes)_ from [Cloud Storage](https://cloud.google.com/compute/docs/instances/startup-scripts/linux#passing-storage) is not possible therefore it [needs](https://stackoverflow.com/a/74624902/4058484) to be stored in a [local file](https://cloud.google.com/compute/docs/instances/startup-scripts/linux#passing-local) and [create-disk](https://cloud.google.com/sdk/gcloud/reference/compute/instances/create#--create-disk) using _[gcloud](https://cloud.google.com/sdk/docs/cheatsheet)_.\n\n```\ngcloud compute instances create instance-template \\\n--scopes=https://www.googleapis.com/auth/cloud-platform \\\n--network-interface=network=default,network-tier=PREMIUM \\\n--maintenance-policy=MIGRATE --provisioning-model=STANDARD \\\n--project=feedmapping --zone=us-central1-a --shielded-vtpm \\\n--shielded-integrity-monitoring --reservation-affinity=any \\\n--service-account=project-owner@feedmapping.iam.gserviceaccount.com \\\n--machine-type=e2-micro --enable-display-device --no-shielded-secure-boot \\\n--image-family cos-stable --image-project cos-cloud \\ ◄- COS\n--metadata-from-file user-data=cloud-config \\\n--create-disk=auto-delete=yes,device-name=persistent-disk-1,boot=no,\\ ◄- LINUX\nimage-family=tf-ent-latest-gpu,mode=rw,size=50,type=pd-standard,\\\nimage-project=deeplearning-platform-release \\\n--create-disk=auto-delete=yes,device-name=persistent-disk-2,boot=no,\\ ◄- WINDOWS\nimage=projects/gce-uefi-images/global/images/windows-server-1909\\\n-dc-core-for-containers-v20200609,mode=rw,size=32,type=pd-standard\n```\n\n[Deep Learning VM Images](https://cloud.google.com/deep-learning-vm/docs/concepts-images) are virtual machine images optimized for data science and machine learning tasks. Built with key ML frameworks, tools pre-installed, and ***can be used out of the box on instances with GPUs*** to accelerate data processing.\n\n[![Deciding on an image family](https://user-images.githubusercontent.com/8466209/237991018-c0551de0-a3fb-40b5-abf2-b636d8a6cbd1.png)](https://cloud.google.com/deep-learning-vm/docs/images#deciding)\n\nIn Linux [dpkg](https://phoenixnap.com/kb/dpkg-command) is the primary package manager for Debian and Debian-based systems, such as Ubuntu. The tool installs, builds, removes, configures, and retrieves information for Debian packages. The command works with packages in .deb format.\n\n```\n$ dpkg -l\n\nDesired=Unknown/Install/Remove/Purge/Hold\n| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend\n|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)\n||/ Name Version Architecture Description\n+++-=============================-===========================-============-===============================================================================\nii adduser 3.118 all add and remove users and groups\nii apparmor 2.13.2-10 amd64 user-space parser utility for AppArmor\nii apt 1.8.2.3 amd64 commandline package manager\nii apt-transport-https 1.8.2.3 all transitional package for https support\nii base-files 10.3+deb10u13 amd64 Debian base system miscellaneous files\nii base-passwd 3.5.46 amd64 Debian base system master password and group files\nii bash 5.0-4 amd64 GNU Bourne Again SHell\nii binutils 2.31.1-16 amd64 GNU assembler, linker and binary utilities\nii binutils-common:amd64 2.31.1-16 amd64 Common files for the GNU assembler, linker and binary utilities\nii binutils-x86-64-linux-gnu 2.31.1-16 amd64 GNU binary utilities, for x86-64-linux-gnu target\nii bsdutils 1:2.33.1-0.1 amd64 basic utilities from 4.4BSD-Lite\nii build-essential 12.6 amd64 Informational list of build-essential packages\nii bzip2 1.0.6-9.2~deb10u2 amd64 high-quality block-sorting file compressor - utilities\nii ca-certificates 20200601~deb10u2 all Common CA certificates\nii containerd.io 1.6.20-1 amd64 An open and reliable container runtime\nii coreutils 8.30-3 amd64 GNU core utilities\nii cpp 4:8.3.0-1 amd64 GNU C preprocessor (cpp)\nii cpp-8 8.3.0-6 amd64 GNU C preprocessor\nii curl 7.64.0-4+deb10u5 amd64 command line tool for transferring data with URL syntax\nii dash 0.5.10.2-5 amd64 POSIX-compliant shell\nii dbus 1.12.24-0+deb10u1 amd64 simple interprocess messaging system (daemon and utilities)\nii dbus-user-session 1.12.24-0+deb10u1 amd64 simple interprocess messaging system (systemd --user integration)\nii debconf 1.5.71+deb10u1 all Debian configuration management system\nii debian-archive-keyring 2019.1+deb10u1 all GnuPG archive keys of the Debian archive\nii debianutils 4.8.6.1 amd64 Miscellaneous utilities specific to Debian\nii diffutils 1:3.7-3 amd64 File comparison utilities\nii dirmngr 2.2.12-1+deb10u2 amd64 GNU privacy guard - network certificate management service\nii distro-info-data 0.41+deb10u6 all information about the distributions' releases (data files)\nii dmsetup 2:1.02.155-3 amd64 Linux Kernel Device Mapper userspace library\nii docker-buildx-plugin 0.10.4-1~debian.10~buster amd64 Docker Buildx cli plugin.\nii docker-ce 5:23.0.3-1~debian.10~buster amd64 Docker: the open-source application container engine\nii docker-ce-cli 5:23.0.3-1~debian.10~buster amd64 Docker CLI: the open-source application container engine\nii docker-ce-rootless-extras 5:23.0.3-1~debian.10~buster amd64 Rootless support for Docker.\nii docker-compose-plugin 2.17.2-1~debian.10~buster amd64 Docker Compose (V2) plugin for the Docker CLI.\nii dpkg 1.19.8 amd64 Debian package management system\nii dpkg-dev 1.19.8 all Debian package development tools\nii e2fsprogs 1.44.5-1+deb10u3 amd64 ext2/ext3/ext4 file system utilities\nii fakeroot 1.23-1 amd64 tool for simulating superuser privileges\nii fdisk 2.33.1-0.1 amd64 collection of partitioning utilities\nii file 1:5.35-4+deb10u2 amd64 Recognize the type of data in a file using \"magic\" numbers\nii findutils 4.6.0+git+20190209-2 amd64 utilities for finding files--find, xargs\nii g++ 4:8.3.0-1 amd64 GNU C++ compiler\nii g++-8 8.3.0-6 amd64 GNU C++ compiler\nii gcc 4:8.3.0-1 amd64 GNU C compiler\nii gcc-8 8.3.0-6 amd64 GNU C compiler\nii gcc-8-base:amd64 8.3.0-6 amd64 GCC, the GNU Compiler Collection (base package)\nii gettext 0.19.8.1-9 amd64 GNU Internationalization utilities\nii gettext-base 0.19.8.1-9 amd64 GNU Internationalization utilities for the base system\nii gir1.2-glib-2.0:amd64 1.58.3-2 amd64 Introspection data for GLib, GObject, Gio and GModule\nii gir1.2-packagekitglib-1.0 1.1.12-5 amd64 GObject introspection data for the PackageKit GLib library\nii git 1:2.20.1-2+deb10u8 amd64 fast, scalable, distributed revision control system\nii git-man 1:2.20.1-2+deb10u8 all fast, scalable, distributed revision control system (manual pages)\nii gnupg 2.2.12-1+deb10u2 all GNU privacy guard - a free PGP replacement\nii gnupg-l10n 2.2.12-1+deb10u2 all GNU privacy guard - localization files\nii gnupg-utils 2.2.12-1+deb10u2 amd64 GNU privacy guard - utility programs\nii gpg 2.2.12-1+deb10u2 amd64 GNU Privacy Guard -- minimalist public key operations\nii gpg-agent 2.2.12-1+deb10u2 amd64 GNU privacy guard - cryptographic agent\nii gpg-wks-client 2.2.12-1+deb10u2 amd64 GNU privacy guard - Web Key Service client\nii gpg-wks-server 2.2.12-1+deb10u2 amd64 GNU privacy guard - Web Key Service server\nii gpgconf 2.2.12-1+deb10u2 amd64 GNU privacy guard - core configuration utilities\nii gpgsm 2.2.12-1+deb10u2 amd64 GNU privacy guard - S/MIME version\nii gpgv 2.2.12-1+deb10u2 amd64 GNU privacy guard - signature verification tool\nii grep 3.3-1 amd64 GNU grep, egrep and fgrep\nii gzip 1.9-3+deb10u1 amd64 GNU compression utilities\nii hostname 3.21 amd64 utility to set/show the host name or domain name\nii init-system-helpers 1.56+nmu1 all helper tools for all init systems\nii iptables 1.8.2-4 amd64 administration tools for packet filtering and NAT\nii iputils-ping 3:20180629-2+deb10u2 amd64 Tools to test the reachability of network hosts\nii iso-codes 4.2-1 all ISO language, territory, currency, script codes and their translations\nii jq 1.5+dfsg-2+b1 amd64 lightweight and flexible command-line JSON processor\nii krb5-locales 1.17-3+deb10u5 all internationalization support for MIT Kerberos\nii less 487-0.1+b1 amd64 pager program similar to more\nii libacl1:amd64 2.2.53-4 amd64 access control list - shared library\nii libalgorithm-diff-perl 1.19.03-2 all module to find differences between files\nii libalgorithm-diff-xs-perl 0.04-5+b1 amd64 module to find differences between files (XS accelerated)\nii libalgorithm-merge-perl 0.08-3 all Perl module for three-way merge of textual data\nii libapparmor1:amd64 2.13.2-10 amd64 changehat AppArmor library\nii libappstream4:amd64 0.12.5-1 amd64 Library to access AppStream services\nii libapt-inst2.0:amd64 1.8.2.3 amd64 deb package format runtime library\nii libapt-pkg5.0:amd64 1.8.2.3 amd64 package management runtime library\nii libargon2-1:amd64 0~20171227-0.2 amd64 memory-hard hashing function - runtime library\nii libasan5:amd64 8.3.0-6 amd64 AddressSanitizer -- a fast memory error detector\nii libassuan0:amd64 2.5.2-1 amd64 IPC library for the GnuPG components\nii libatomic1:amd64 8.3.0-6 amd64 support library providing __atomic built-in functions\nii libattr1:amd64 1:2.4.48-4 amd64 extended attribute handling - shared library\nii libaudit-common 1:2.8.4-3 all Dynamic library for security auditing - common files\nii libaudit1:amd64 1:2.8.4-3 amd64 Dynamic library for security auditing\nii libbinutils:amd64 2.31.1-16 amd64 GNU binary utilities (private shared library)\nii libblkid1:amd64 2.33.1-0.1 amd64 block device ID library\nii libbsd0:amd64 0.9.1-2+deb10u1 amd64 utility functions from BSD systems - shared library\nii libbz2-1.0:amd64 1.0.6-9.2~deb10u2 amd64 high-quality block-sorting file compressor library - runtime\nii libc-bin 2.28-10+deb10u2 amd64 GNU C Library: Binaries\nii libc-dev-bin 2.28-10+deb10u2 amd64 GNU C Library: Development binaries\nii libc6:amd64 2.28-10+deb10u2 amd64 GNU C Library: Shared libraries\nii libc6-dev:amd64 2.28-10+deb10u2 amd64 GNU C Library: Development Libraries and Header Files\nii libcap-ng0:amd64 0.7.9-2 amd64 An alternate POSIX capabilities library\nii libcap2:amd64 1:2.25-2 amd64 POSIX 1003.1e capabilities (library)\nii libcap2-bin 1:2.25-2 amd64 POSIX 1003.1e capabilities (utilities)\nii libcc1-0:amd64 8.3.0-6 amd64 GCC cc1 plugin for GDB\nii libcom-err2:amd64 1.44.5-1+deb10u3 amd64 common error description library\nii libcroco3:amd64 0.6.12-3 amd64 Cascading Style Sheet (CSS) parsing and manipulation toolkit\nii libcryptsetup12:amd64 2:2.1.0-5+deb10u2 amd64 disk encryption support - shared library\nii libcurl3-gnutls:amd64 7.64.0-4+deb10u5 amd64 easy-to-use client-side URL transfer library (GnuTLS flavour)\nii libcurl4:amd64 7.64.0-4+deb10u5 amd64 easy-to-use client-side URL transfer library (OpenSSL flavour)\nii libcurl4-openssl-dev:amd64 7.64.0-4+deb10u5 amd64 development files and documentation for libcurl (OpenSSL flavour)\nii libdb5.3:amd64 5.3.28+dfsg1-0.5 amd64 Berkeley v5.3 Database Libraries [runtime]\nii libdbus-1-3:amd64 1.12.24-0+deb10u1 amd64 simple interprocess messaging system (library)\nii libdebconfclient0:amd64 0.249 amd64 Debian Configuration Management System (C-implementation library)\nii libdevmapper1.02.1:amd64 2:1.02.155-3 amd64 Linux Kernel Device Mapper userspace library\nii libdpkg-perl 1.19.8 all Dpkg perl modules\nii libedit2:amd64 3.1-20181209-1 amd64 BSD editline and history libraries\nii libelf1:amd64 0.176-1.1 amd64 library to read and write ELF files\nii liberror-perl 0.17027-2 all Perl module for error/exception handling in an OO-ish way\nii libexpat1:amd64 2.2.6-2+deb10u6 amd64 XML parsing C library - runtime library\nii libext2fs2:amd64 1.44.5-1+deb10u3 amd64 ext2/ext3/ext4 file system libraries\nii libfakeroot:amd64 1.23-1 amd64 tool for simulating superuser privileges - shared libraries\nii libfdisk1:amd64 2.33.1-0.1 amd64 fdisk partitioning library\nii libffi6:amd64 3.2.1-9 amd64 Foreign Function Interface library runtime\nii libfile-fcntllock-perl 0.22-3+b5 amd64 Perl module for file locking with fcntl(2)\nii libgcc-8-dev:amd64 8.3.0-6 amd64 GCC support library (development files)\nii libgcc1:amd64 1:8.3.0-6 amd64 GCC support library\nii libgcrypt20:amd64 1.8.4-5+deb10u1 amd64 LGPL Crypto library - runtime library\nii libgdbm-compat4:amd64 1.18.1-4 amd64 GNU dbm database routines (legacy support runtime version) \nii libgdbm6:amd64 1.18.1-4 amd64 GNU dbm database routines (runtime version) \nii libgirepository-1.0-1:amd64 1.58.3-2 amd64 Library for handling GObject introspection data (runtime library)\nii libglib2.0-0:amd64 2.58.3-2+deb10u4 amd64 GLib library of C routines\nii libglib2.0-bin 2.58.3-2+deb10u4 amd64 Programs for the GLib library\nii libglib2.0-data 2.58.3-2+deb10u4 all Common files for GLib library\nii libgmp10:amd64 2:6.1.2+dfsg-4+deb10u1 amd64 Multiprecision arithmetic library\nii libgnutls30:amd64 3.6.7-4+deb10u10 amd64 GNU TLS library - main runtime library\nii libgomp1:amd64 8.3.0-6 amd64 GCC OpenMP (GOMP) support library\nii libgpg-error0:amd64 1.35-1 amd64 GnuPG development runtime library\nii libgpm2:amd64 1.20.7-5 amd64 General Purpose Mouse - shared library\nii libgssapi-krb5-2:amd64 1.17-3+deb10u5 amd64 MIT Kerberos runtime libraries - krb5 GSS-API Mechanism\nii libgstreamer1.0-0:amd64 1.14.4-1 amd64 Core GStreamer libraries and elements\nii libhogweed4:amd64 3.4.1-1+deb10u1 amd64 low level cryptographic library (public-key cryptos)\nii libicu63:amd64 63.1-6+deb10u3 amd64 International Components for Unicode\nii libidn11:amd64 1.33-2.2 amd64 GNU Libidn library, implementation of IETF IDN specifications\nii libidn2-0:amd64 2.0.5-1+deb10u1 amd64 Internationalized domain names (IDNA2008/TR46) library\nii libip4tc0:amd64 1.8.2-4 amd64 netfilter libip4tc library\nii libip6tc0:amd64 1.8.2-4 amd64 netfilter libip6tc library\nii libiptc0:amd64 1.8.2-4 amd64 netfilter libiptc library\nii libisl19:amd64 0.20-2 amd64 manipulating sets and relations of integer points bounded by linear constraints\nii libitm1:amd64 8.3.0-6 amd64 GNU Transactional Memory Library\nii libjansson4:amd64 2.12-1 amd64 C library for encoding, decoding and manipulating JSON data\nii libjq1:amd64 1.5+dfsg-2+b1 amd64 lightweight and flexible command-line JSON processor - shared library\nii libjson-c3:amd64 0.12.1+ds-2+deb10u1 amd64 JSON manipulation library - shared library\nii libk5crypto3:amd64 1.17-3+deb10u5 amd64 MIT Kerberos runtime libraries - Crypto Library\nii libkeyutils1:amd64 1.6-6 amd64 Linux Key Management Utilities (library)\nii libkmod2:amd64 26-1 amd64 libkmod shared library\nii libkrb5-3:amd64 1.17-3+deb10u5 amd64 MIT Kerberos runtime libraries\nii libkrb5support0:amd64 1.17-3+deb10u5 amd64 MIT Kerberos runtime libraries - Support library\nii libksba8:amd64 1.3.5-2+deb10u2 amd64 X.509 and CMS support library\nii libldap-2.4-2:amd64 2.4.47+dfsg-3+deb10u7 amd64 OpenLDAP libraries\nii libldap-common 2.4.47+dfsg-3+deb10u7 all OpenLDAP common files for libraries\nii liblocale-gettext-perl 1.07-3+b4 amd64 module using libc functions for internationalization in Perl\nii liblsan0:amd64 8.3.0-6 amd64 LeakSanitizer -- a memory leak detector (runtime)\nii libltdl7:amd64 2.4.6-9 amd64 System independent dlopen wrapper for GNU libtool\nii liblttng-ust-ctl4:amd64 2.10.3-1 amd64 LTTng 2.0 Userspace Tracer (trace control library)\nii liblttng-ust0:amd64 2.10.3-1 amd64 LTTng 2.0 Userspace Tracer (tracing libraries)\nii liblz4-1:amd64 1.8.3-1+deb10u1 amd64 Fast LZ compression algorithm library - runtime\nii liblzma5:amd64 5.2.4-1+deb10u1 amd64 XZ-format compression library\nii libmagic-mgc 1:5.35-4+deb10u2 amd64 File type determination library using \"magic\" numbers (compiled magic file)\nii libmagic1:amd64 1:5.35-4+deb10u2 amd64 Recognize the type of data in a file using \"magic\" numbers - library\nii libmnl0:amd64 1.0.4-2 amd64 minimalistic Netlink communication library\nii libmount1:amd64 2.33.1-0.1 amd64 device mounting library\nii libmpc3:amd64 1.1.0-1 amd64 multiple precision complex floating-point library\nii libmpdec2:amd64 2.4.2-2 amd64 library for decimal floating point arithmetic (runtime library)\nii libmpfr6:amd64 4.0.2-1 amd64 multiple precision floating-point computation\nii libmpx2:amd64 8.3.0-6 amd64 Intel memory protection extensions (runtime)\nii libncurses6:amd64 6.1+20181013-2+deb10u3 amd64 shared libraries for terminal handling\nii libncursesw6:amd64 6.1+20181013-2+deb10u3 amd64 shared libraries for terminal handling (wide character support)\nii libnetfilter-conntrack3:amd64 1.0.7-1 amd64 Netfilter netlink-conntrack library\nii libnettle6:amd64 3.4.1-1+deb10u1 amd64 low level cryptographic library (symmetric and one-way cryptos)\nii libnfnetlink0:amd64 1.0.1-3+b1 amd64 Netfilter netlink library\nii libnftables0:amd64 0.9.0-2 amd64 Netfilter nftables high level userspace API library\nii libnftnl11:amd64 1.1.2-2 amd64 Netfilter nftables userspace API library\nii libnghttp2-14:amd64 1.36.0-2+deb10u1 amd64 library implementing HTTP/2 protocol (shared library)\nii libnpth0:amd64 1.6-1 amd64 replacement for GNU Pth using system threads\nii libnss-systemd:amd64 241-7~deb10u9 amd64 nss module providing dynamic user and group name resolution\nii libonig5:amd64 6.9.1-1 amd64 regular expressions library\nii libp11-kit0:amd64 0.23.15-2+deb10u1 amd64 library for loading and coordinating access to PKCS#11 modules - runtime\nii libpackagekit-glib2-18:amd64 1.1.12-5 amd64 Library for accessing PackageKit using GLib\nii libpam-cap:amd64 1:2.25-2 amd64 POSIX 1003.1e capabilities (PAM module)\nii libpam-modules:amd64 1.3.1-5 amd64 Pluggable Authentication Modules for PAM\nii libpam-modules-bin 1.3.1-5 amd64 Pluggable Authentication Modules for PAM - helper binaries\nii libpam-runtime 1.3.1-5 all Runtime support for the PAM library\nii libpam-systemd:amd64 241-7~deb10u9 amd64 system and service manager - PAM module\nii libpam0g:amd64 1.3.1-5 amd64 Pluggable Authentication Modules library\nii libpcre2-8-0:amd64 10.32-5+deb10u1 amd64 New Perl Compatible Regular Expression Library- 8 bit runtime files\nii libpcre3:amd64 2:8.39-12 amd64 Old Perl 5 Compatible Regular Expression Library - runtime files\nii libperl5.28:amd64 5.28.1-6+deb10u1 amd64 shared Perl library\nii libpolkit-agent-1-0:amd64 0.105-25+deb10u1 amd64 PolicyKit Authentication Agent API\nii libpolkit-backend-1-0:amd64 0.105-25+deb10u1 amd64 PolicyKit backend API\nii libpolkit-gobject-1-0:amd64 0.105-25+deb10u1 amd64 PolicyKit Authorization API\nii libprocps7:amd64 2:3.3.15-2 amd64 library for accessing process information from /proc\nii libpsl5:amd64 0.20.2-2 amd64 Library for Public Suffix List (shared libraries)\nii libpython-stdlib:amd64 2.7.16-1 amd64 interactive high-level object-oriented language (Python2)\nii libpython2-stdlib:amd64 2.7.16-1 amd64 interactive high-level object-oriented language (Python2)\nii libpython2.7-minimal:amd64 2.7.16-2+deb10u1 amd64 Minimal subset of the Python language (version 2.7)\nii libpython2.7-stdlib:amd64 2.7.16-2+deb10u1 amd64 Interactive high-level object-oriented language (standard library, version 2.7)\nii libpython3-stdlib:amd64 3.7.3-1 amd64 interactive high-level object-oriented language (default python3 version)\nii libpython3.7-minimal:amd64 3.7.3-2+deb10u4 amd64 Minimal subset of the Python language (version 3.7)\nii libpython3.7-stdlib:amd64 3.7.3-2+deb10u4 amd64 Interactive high-level object-oriented language (standard library, version 3.7)\nii libquadmath0:amd64 8.3.0-6 amd64 GCC Quad-Precision Math Library\nii libreadline7:amd64 7.0-5 amd64 GNU readline and history libraries, run-time libraries\nii librtmp1:amd64 2.4+20151223.gitfa8646d.1-2 amd64 toolkit for RTMP streams (shared library)\nii libsasl2-2:amd64 2.1.27+dfsg-1+deb10u2 amd64 Cyrus SASL - authentication abstraction library\nii libsasl2-modules:amd64 2.1.27+dfsg-1+deb10u2 amd64 Cyrus SASL - pluggable authentication modules\nii libsasl2-modules-db:amd64 2.1.27+dfsg-1+deb10u2 amd64 Cyrus SASL - pluggable authentication modules (DB)\nii libseccomp2:amd64 2.3.3-4 amd64 high level interface to Linux seccomp filter\nii libselinux1:amd64 2.8-1+b1 amd64 SELinux runtime shared libraries\nii libsemanage-common 2.8-2 all Common files for SELinux policy management libraries\nii libsemanage1:amd64 2.8-2 amd64 SELinux policy management library\nii libsepol1:amd64 2.8-1 amd64 SELinux library for manipulating binary security policies\nii libsmartcols1:amd64 2.33.1-0.1 amd64 smart column output alignment library\nii libsqlite3-0:amd64 3.27.2-3+deb10u2 amd64 SQLite 3 shared library\nii libss2:amd64 1.44.5-1+deb10u3 amd64 command-line interface parsing library\nii libssh2-1:amd64 1.8.0-2.1 amd64 SSH2 client-side library\nii libssl1.1:amd64 1.1.1n-0+deb10u4 amd64 Secure Sockets Layer toolkit - shared libraries\nii libstdc++-8-dev:amd64 8.3.0-6 amd64 GNU Standard C++ Library v3 (development files)\nii libstdc++6:amd64 8.3.0-6 amd64 GNU Standard C++ Library v3\nii libstemmer0d:amd64 0+svn585-1+b2 amd64 Snowball stemming algorithms for use in Information Retrieval\nii libsystemd0:amd64 241-7~deb10u9 amd64 systemd utility library\nii libtasn1-6:amd64 4.13-3+deb10u1 amd64 Manage ASN.1 structures (runtime)\nii libtinfo6:amd64 6.1+20181013-2+deb10u3 amd64 shared low-level terminfo library for terminal handling\nii libtsan0:amd64 8.3.0-6 amd64 ThreadSanitizer -- a Valgrind-based detector of data races (runtime)\nii libubsan1:amd64 8.3.0-6 amd64 UBSan -- undefined behaviour sanitizer (runtime)\nii libudev1:amd64 241-7~deb10u8 amd64 libudev shared library\nii libunistring2:amd64 0.9.10-1 amd64 Unicode string library for C\nii liburcu6:amd64 0.10.2-1 amd64 userspace RCU (read-copy-update) library\nii libuuid1:amd64 2.33.1-0.1 amd64 Universally Unique ID library\nii libx11-6:amd64 2:1.6.7-1+deb10u2 amd64 X11 client-side library\nii libx11-data 2:1.6.7-1+deb10u2 all X11 client-side library\nii libxau6:amd64 1:1.0.8-1+b2 amd64 X11 authorisation library\nii libxcb1:amd64 1.13.1-2 amd64 X C Binding\nii libxdmcp6:amd64 1:1.1.2-3 amd64 X11 Display Manager Control Protocol library\nii libxext6:amd64 2:1.3.3-1+b2 amd64 X11 miscellaneous extension library\nii libxml2:amd64 2.9.4+dfsg1-7+deb10u5 amd64 GNOME XML library\nii libxmuu1:amd64 2:1.1.2-2+b3 amd64 X11 miscellaneous micro-utility library\nii libxtables12:amd64 1.8.2-4 amd64 netfilter xtables library\nii libyaml-0-2:amd64 0.2.1-1 amd64 Fast YAML 1.1 parser and emitter library\nii libzstd1:amd64 1.3.8+dfsg-3+deb10u2 amd64 fast lossless compression algorithm\nii linux-libc-dev:amd64 4.19.269-1 amd64 Linux support headers for userspace development\nii login 1:4.5-1.1 amd64 system login tools\nii lsb-base 10.2019051400 all Linux Standard Base init script functionality\nii lsb-release 10.2019051400 all Linux Standard Base version reporting utility\nii make 4.2.1-1.2 amd64 utility for directing compilation\nii manpages 4.16-2 all Manual pages about using a GNU/Linux system\nii manpages-dev 4.16-2 all Manual pages about using GNU/Linux for development\nii mawk 1.3.3-17+b3 amd64 a pattern scanning and text processing language\nii mime-support 3.62 all MIME files 'mime.types' & 'mailcap', and support programs\nii mount 2.33.1-0.1 amd64 tools for mounting and manipulating filesystems\nii ncurses-base 6.1+20181013-2+deb10u3 all basic terminal type definitions\nii ncurses-bin 6.1+20181013-2+deb10u3 amd64 terminal-related programs and man pages\nii netbase 5.6 all Basic TCP/IP networking system\nii nftables 0.9.0-2 amd64 Program to control packet filtering rules by Netfilter project\nii openssh-client 1:7.9p1-10+deb10u2 amd64 secure shell (SSH) client, for secure access to remote machines\nii openssl 1.1.1n-0+deb10u4 amd64 Secure Sockets Layer toolkit - cryptographic utility\nii packagekit 1.1.12-5 amd64 Provides a package management service\nii packagekit-tools 1.1.12-5 amd64 Provides PackageKit command-line tools\nii passwd 1:4.5-1.1 amd64 change and administer password and group data\nii patch 2.7.6-3+deb10u1 amd64 Apply a diff file to an original\nii perl 5.28.1-6+deb10u1 amd64 Larry Wall's Practical Extraction and Report Language\nii perl-base 5.28.1-6+deb10u1 amd64 minimal Perl system\nii perl-modules-5.28 5.28.1-6+deb10u1 all Core Perl modules\nii pigz 2.4-1 amd64 Parallel Implementation of GZip\nii pinentry-curses 1.1.0-2 amd64 curses-based PIN or pass-phrase entry dialog for GnuPG\nii policykit-1 0.105-25+deb10u1 amd64 framework for managing administrative policies and privileges\nii procps 2:3.3.15-2 amd64 /proc file system utilities\nii psmisc 23.2-1+deb10u1 amd64 utilities that use the proc file system\nii publicsuffix 20220811.1734-0+deb10u1 all accurate, machine-readable list of domain name suffixes\nii python 2.7.16-1 amd64 interactive high-level object-oriented language (Python2 version)\nii python-apt-common 1.8.4.3 all Python interface to libapt-pkg (locales)\nii python-meld3 1.0.2-2 all HTML/XML templating system for Python\nii python-minimal 2.7.16-1 amd64 minimal subset of the Python2 language\nii python-pkg-resources 40.8.0-1 all Package Discovery and Resource Access using pkg_resources\nii python2 2.7.16-1 amd64 interactive high-level object-oriented language (Python2 version)\nii python2-minimal 2.7.16-1 amd64 minimal subset of the Python2 language\nii python2.7 2.7.16-2+deb10u1 amd64 Interactive high-level object-oriented language (version 2.7)\nii python2.7-minimal 2.7.16-2+deb10u1 amd64 Minimal subset of the Python language (version 2.7)\nii python3 3.7.3-1 amd64 interactive high-level object-oriented language (default python3 version)\nii python3-apt 1.8.4.3 amd64 Python 3 interface to libapt-pkg\nii python3-dbus 1.2.8-3 amd64 simple interprocess messaging system (Python 3 interface)\nii python3-distro-info 0.21 all information about distributions' releases (Python 3 module)\nii python3-gi 3.30.4-1 amd64 Python 3 bindings for gobject-introspection libraries\nii python3-minimal 3.7.3-1 amd64 minimal subset of the Python language (default python3 version)\nii python3-pycurl 7.43.0.2-0.1 amd64 Python bindings to libcurl (Python 3)\nii python3-software-properties 0.96.20.2-2 all manage the repositories that you install software from\nii python3.7 3.7.3-2+deb10u4 amd64 Interactive high-level object-oriented language (version 3.7)\nii python3.7-minimal 3.7.3-2+deb10u4 amd64 Minimal subset of the Python language (version 3.7)\nii readline-common 7.0-5 all GNU readline and history libraries, common files\nii sed 4.7-1 amd64 GNU stream editor for filtering/transforming text\nii sensible-utils 0.0.12 all Utilities for sensible alternative selection\nii shared-mime-info 1.10-1 amd64 FreeDesktop.org shared MIME database and spec\nii software-properties-common 0.96.20.2-2 all manage the repositories that you install software from (common)\nii sudo 1.8.27-1+deb10u5 amd64 Provide limited super user privileges to specific users\nii supervisor 3.3.5-1 all System for controlling process state\nii systemd 241-7~deb10u9 amd64 system and service manager\nii systemd-sysv 241-7~deb10u9 amd64 system and service manager - SysV links\nii sysvinit-utils 2.93-8 amd64 System-V-like utilities\nii tar 1.30+dfsg-6 amd64 GNU version of the tar archiving utility\nii tzdata 2021a-0+deb10u8 all time zone and daylight-saving time data\nii ucf 3.0038+nmu1 all Update Configuration File(s): preserve user changes to config files\nii unattended-upgrades 1.11.2 all automatic installation of security upgrades\nii unzip 6.0-23+deb10u3 amd64 De-archiver for .zip files\nii util-linux 2.33.1-0.1 amd64 miscellaneous system utilities\nii xauth 1:1.0.10-1 amd64 X authentication utility\nii xdg-user-dirs 0.17-2 amd64 tool to manage well known user directories\nii xz-utils 5.2.4-1+deb10u1 amd64 XZ-format compression utilities\nii zlib1g:amd64 1:1.2.11.dfsg-1+deb10u2 amd64 compression library - runtime\nii zlib1g-dev:amd64 1:1.2.11.dfsg-1+deb10u2 amd64 compression library - development\n/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin\n/usr/bin/python\nPython 3.7.3\ncurl 7.64.0 (x86_64-pc-linux-gnu) libcurl/7.64.0 OpenSSL/1.1.1n zlib/1.2.11 libidn2/2.0.5 libpsl/0.20.2 (+libidn2/2.0.5) libssh2/1.8.0 nghttp2/1.36.0 librtmp/2.3\n```","dir":"/identition/span4/","name":"gist01.md","path":"identition/span4/gist01.md","url":"/identition/span4/gist01.html"},{"sort":4,"spin":null,"span":null,"suit":5,"layout":"default","title":"Pairwise Scenario","content":"

            Pairwise Scenario

            \n\n
            This section is referring to _[wiki page-4](https://github.com/eq19/eq19.github.io/wiki)_ of _[zone section-4]()_ that is _[inherited ]()_ from _[the zone section-5](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            \"image\"

            \n\n

            (10 - 2) th prime = 8th prime = 19

            \n\n

            \"default\"

            \n\n

            The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.

            \n\n

            \"Rank

            \n\n

            tps://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#partition-function) represents the number of possible partitions of a non-negative integer n.

            \n\n

            f(8 twins) = 60 - 23 = 37 inner partitions

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 -29 = 61 - 1 = 60 ✔️\n5 5 2 1 0 5 👉 f(37) = f(8 twins) ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            7 + 13 + 19 + 25 = 64 = 8 × 8 = 8²

            \n\n

            \"\"

            \n\n

            Subclasses of Partitions

            \n\n
            Let weighted points be given in the plane . For each point a radius is given which is the expected ideal distance from this point to a new facility. We want to find the location of a new facility such that the sum of the weighted errors between the existing points and this new facility is minimized. This is in fact a nonconvex optimization problem. We show that the optimal solution lies in an extended rectangular hull of the existing points. Based on this finding then an efficient big square small square (BSSS) procedure is proposed.\n
            \n\n

            \"A_BSSS_Algorithm_for_the_Location_Problem_with_Min.pdf\"

            \n\n

            Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            \n\n
            [Young diagrams](https://commons.wikimedia.org/wiki/Category:Young_diagrams) associated to the partitions of the positive integers ***1 through 8***. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions _([Wikipedia](https://en.wikipedia.org/wiki/Partition_(number_theory)))_.\n
            \n\n

            f(8🪟8) = 1 + 7 + 29 = 37 inner partitions

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 -29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 f(37) = f(8🪟8) ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            When these subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent .

            \n\n
            It's possible to build a _[Hessian matrix](https://en.wikipedia.org/wiki/Hessian_matrix)_ for a _[Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization)_ step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector _([Tensorflow](https://www.tensorflow.org/guide/advanced_autodiff#batch_jacobian))_. \n
            \n\n

            \"Partitioned-matrices-of-the-numbers-60-62-and-64-as-examples\"

            \n\n
            ***In summary, it has been shown that partitions into an even number of distinct parts and an odd number of distinct parts exactly cancel each other, producing null terms 0x^n, except if n is a generalized [pentagonal number](https://www.eq19.com/identition/#hidden-dimensions) n=g_{k}=k(3k-1)/2}***, in which case there is exactly one Ferrers diagram left over, producing a term (−1)kxn. But this is precisely what the right side of the identity says should happen, so we are finished. _([Wikipedia](https://en.wikipedia.org/wiki/Pentagonal_number_theorem))_\n
            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 -29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 f(37) = f(29🪟23) ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            The code is interspersed with python, shell, perl, also demonstrates how multiple languages can be integrated seamlessly.

            \n\n

            \"extended

            \n\n

            These include generating variants of their abundance profile, assigning taxonomy and finally generating a rooted phylogenetic tree.

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 f(37) = ❓ 👈 Composite ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime 👉 7s 👈 Composite ✔️\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            This behaviour in a fundamental causal relation to the primes when the products are entered into the partitions system.

            \n\n

            Composite behaviour

            \n\n

            The subclasses of partitions systemically develops characters similar to the distribution of prime numbers. It would mean that there should be some undiscovered things hidden within the residual of the decimal values.

            \n\n

            \"integer

            \n\n

            168 + 2 = 170 = (10+30)+60+70 = 40+60+70 = 40 + 60 + ∆(2~71)

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 f(37) ✔️\n          6 👉 11s Composite Partition ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime\n           18 👉 7s Composite Partition ✔️\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n
            The initial concept of this work was the Partitioned Matrix of an even number w≥ 4:\n- It was shown that ***for every even number w≥ 4*** it is possible to establish a corresponding Partitioned Matrix with a determined number of lines.\n- It was demonstrated that, fundamentally, ***the sum of the partitions is equal to the number of lines*** in the matrix: Lw = Cw + Gw + Mw.\n- It was also shown that for each and every Partitioned Matrix of an even number w ≥ 4 it is observed that\n Gw = π(w) − (Lw − Cw), which means that the number of Goldbach partitions or ***partitions of prime numbers of an even number w ≥ 4 is given by the number of prime numbers up to w minus the number of available lines*** (Lwd) calculated as follows: Lwd = Lw − Cw.\n\nTo analyze the adequacy of the proposed formulas, probabilistically calculated reference values were adopted. _([Partitions of even numbers - pdf](https://github.com/eq19/eq19.github.io/files/13722898/Partitions_of_even_numbers.pdf))_\n
            \n\n

            \"Batch

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 ✔️\n          6 👉 11s Composite Partition ◄--- 2+60+40 = 102 ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime \n           18 👉 7s Composite Partition \n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            (11x7) + (29+11) + (25+6) + (11+7) + 4 = 77+40+31+18+4 = 170

            \n\n

            \"16S

            \n","dir":"/addition/","name":"4.md","path":"addition/4.md","url":"/addition/4.html"},{"sort":5,"spin":1,"span":"bonding","suit":"intro","layout":"default","title":"Bonding Position","content":"# [Bonding Position](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406)\n\nYet another related dimension of symmetry, when you combine the terminating digit symmetries described above, capturing three (3) rotations of 120 around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry\n\n```\n---+-----+-----\n 1 | {1} |{11}\n---+-----+-----\n 2 | 12 | 32\n---+-----+-----\n 3 | 33 |{50}\n---+-----+-----\n 4 | 51 |{86}\n---+-----+-----\n 5 | 87 | 108\n---+-----+-----\n 6 |{109}| 120\n---+-----+----- \n```\n\nIn quantum mechanics, Schrödinger's cat is a thought experiment that illustrates a paradox of quantum superposition. \n\n>In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead, while it is unobserved in a closed box, as a result of its fate being linked to a random subatomic event that may or may not occur _([Wikipedia](https://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat))_.\n\n[![Schrodinger's Cat](https://user-images.githubusercontent.com/8466209/227751083-8c3c6fcf-3c69-4e94-a0ea-c2f163c6524c.png)](https://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat#/media/File:Schrodingers_cat.svg)\n\n***2x10 + 9 = 20 + 9 = 29***\n\n```\n-----+-----+-----+-----+-----+\n 1' | 1 | {2} | 3 | 4 | 4¤\n +-----+-----+-----+-----+\n 2' | 5 | 6 | 7 | 8 | 4¤\n +-----+-----+-----+-----+\n 3' | 9 |{10} | 2¤ (M dan F)\n +-----+-----+-----+ \n 4' | 11 | 12 | 13 | 3¤ <----------- d(11) = d(17+12)= d(29)\n +-----+-----+-----+-----+ \n 5' | 14 | 15 | 16 | 17 | 4¤ \n +-----+-----+-----+-----+\n 6' | 18 | 19 |{20} | 3¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+\n ∑ | 21 | 22 | 23 | 24 |{25} | 26 | 27 | 28 | 29 | 9¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+\n |----------------------- {9'} ------------------------|\n```\n\nPrimzahlentechnologie Einleitung. Wie Geht Primzahlen Technologie. [MEC 30 - Mathematical Elementary Cell 30](https://www.abebooks.com/servlet/BookDetailsPL?bi=31387652325): Die Theorie der Gravitation ist die Mathematik des Universums and MEC30.2 Method for factorization\n\n>Measuring with your limb scale is a measurement that does not intervene in the system, so also possible in the idle state of the system. Thus, the MEC 30 results in a measurement method for the energy flow in a system in which the route plan or flow plan of the energy is obtained _(German Patent [DE102011101032](https://www.freepatentsonline.com/DE102011101032A9.html) and [DE102014016656](https://www.freepatentsonline.com/DE102014016656.html))_.\n\n[![MEC 30](https://user-images.githubusercontent.com/8466209/226112677-12731dd6-b461-41ec-8672-064710f58fdc.png)](https://www.abebooks.com/servlet/BookDetailsPL?bi=31387652325)\n\n>The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period ***eight (8) difference sequence*** of: {6, 4, 2, 4, 2, 4, 6, 2} _([Primesdemystified](https://primesdemystified.com/#deepsymmetries))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/219260933-4331d79b-5815-4566-82e3-1a485bb2c61f.png)](https://primesdemystified.com/#deepsymmetries)\n\n## Symmetry Mirroring\n\nSpeaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.\n\n>The 77 is equal to the sum of the first 8 primes. The square of 77 is 5929, the concatenation of two primes, 59 and 29. The concatenation of all palindromes from one up to 77 is prime _([Prime Curios!\n](https://t5k.org/curios/page.php/77.html))_.\n\n[![11's additive sums](https://user-images.githubusercontent.com/8466209/221473004-867a1b50-f91f-470d-9922-e5e4f543a590.png)](https://primesdemystified.com/#deepsymmetries)\n\nPrime numbers that end with \"77\" occur [more often](https://t5k.org/curios/page.php?number_id=459&submitter=Gaydos) than any other 2-digit ending among the first one million primes. The sum of the proper divisors of 77 equals 19 and the sum of primes up to 19 equals 77. Does this ever happen again?\n\n```\n Tabulate Prime by Power of 10\n loop(10) = π(10)-π(1) = 4-0 = 4\n loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\nThe individual bases, depending on their sizes and spatial extents and masses, are assigned unequivocal values, situated within the vibration heights derived from (I), to define a measure from which the sequence can be counted, read or imaged.\n\n![default](https://user-images.githubusercontent.com/8466209/226264170-95bac9da-6efb-48ef-85e5-14430f60875e.png)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n | | | 20:13 | 90 | 90 (38) ‹-------------- ¤ |\n | | 7 +----------+-----+ |\n | 5 | | 14 | ----------------------------- 17¨ class\n | |-----+----------+ | | |\n | | | 15 | | LEADING SCHEME | |\n 3 +------+ 8 +----------+----- | (Multiplication Zone) | ---\n | | | 16 | | | |\n | |-----+----------+-----+ ----------------------------- |\n | 6 | | 28:17 | 100 | 19¨ object\n168 | | 9 +----------+-----+ |\n| | | | 29:18 | 50 | 50(68) ---------> Δ18 |\n------|------|-----+----------+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/36441664/123736293-1196fa80-d8cb-11eb-875c-2dc6cbda1d76.jpg)\n\n## Molecular Interactions\n\nBy the nature this behaviour can be observed from the molecular interactions of water. Water is _[intrinsically self-complementary](https://williams.chemistry.gatech.edu/structure/molecular_interactions/mol_int.html#Wat1)_ on molecular interactions. In liquid or solid water, engage in ideal hydrogen bonding. Six (6) times of the angle 109 occupied as the most while the angle of 114 and 104 are exist only once. So the one in charge here is clearly the ***29th prime identity***.\n\n***109 = 29th prime = (10th)th prime = ((114-104)th)th prime***\n\n[![Molecular Interactions](https://user-images.githubusercontent.com/36441664/101807202-6d747e80-3b47-11eb-8a6b-9e2c6408b091.jpg)](https://williams.chemistry.gatech.edu/structure/molecular_interactions/mol_int.html#Wat1)\n\nLet's assume that it is done using a material that stretches and then pops back when the stretching force goes away. It is pound for pound _[stronger than steel](https://www.nytimes.com/2020/11/04/science/spider-silk-web-self-assembly.html)_. So all of these steps are similar kind with the way a spider started to build its web.\n\n>Every web begins with a single thread, which ***[forms the basis of the rest of the structure](https://www.instagram.com/reel/Cn2UMIeomF5/?igshid=MDJmNzVkMjY=)***. To establish this bridge, the spider climbs to a suitable starting point (up a tree branch, for example) and releases a length of thread into the wind. With any luck, the free end of the thread will catch onto another branch _([howstuffworks.com](https://animals.howstuffworks.com/arachnids/spider5.htm))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/220207477-784067da-6d75-4d5f-a521-69606b49119d.png)](https://animals.howstuffworks.com/arachnids/spider5.htm)\n\nThis 29 turns the finiteness position of 15 as the ***[middle zero axis](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)*** of the _MEC30_. So the next steps will start exactly with the same story as we have explained from the [beginning](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity). \n\n>MEC 30 claims to \"illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way\" via the elementary level of numbers. It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences.\n\n[![default](https://user-images.githubusercontent.com/8466209/220210334-81c62871-25a2-47ef-ae38-c7bf50a4c8e3.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)\n\nThe only different is, instead of an _[instance](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#building-the-instance)_, it will behave as an _[inside container](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#deploying-containers)_, just like how spider built a home web as strong as steel but useless to cover them against a rainy day nor even a small breeze.\n\n[![default](https://user-images.githubusercontent.com/8466209/224466884-5ba87f02-e01d-45ca-a9c3-a1d535e83228.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#mass-gap-%CE%B4)\n\n[![Yang–Mills and Mass Gap](https://user-images.githubusercontent.com/36441664/85888653-3538e800-b814-11ea-85ba-23a56243e9e0.jpg)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#mass-vs-gap-%CE%B4)\n","dir":"/identition/span1/","name":"gist05.md","path":"identition/span1/gist05.md","url":"/identition/span1/gist05.html"},{"sort":5,"spin":1,"span":"replicate","suit":"intro","layout":"default","title":"Triangular waves","content":"# [Triangular waves](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bonding-position)\n\n>A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, ***the higher harmonics roll off much faster*** than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse) _([Wikipedia](https://en.wikipedia.org/wiki/Triangle_wave))_.\n\n[![Making Triangular Waves](https://user-images.githubusercontent.com/8466209/225824209-ba2b9fe0-1a29-4208-940e-3351243ab0ba.png)](https://www.primesdemystified.com/First1000Primes.html)\n\nHamilton's program for proving the Poincaré conjecture involves first putting a Riemannian metric on the unknown simply connected closed 3-manifold. Such mechanism is discussed in detail by _[16th prime identity](https://gist.github.com/eq19/dc30497160f3389546d177da901537d9)_.\n\n![](https://user-images.githubusercontent.com/8466209/219422862-38fd1aae-0ae7-4ba3-8e88-db10a2cf522f.png)\n\nThere are 243 prime pairs among the first 1000 primes that sum to 7920, where 243 x 7920 gives additive sum 1,924,560 (and we note that 7920 = 22 x 360 = 2(1092 − 892), which equates to 1,924,560/(2(1092 − 892) = 243.).\n\n![default](https://user-images.githubusercontent.com/8466209/225643958-7933e50d-6cd3-42b4-8de1-eca70687e713.png)\n\nConsider these two (2) numbers are laid side by side as part of Fibonacci sequence on the [Pascal Triangle](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md). Thus the above is actually represesenting the pattern of _[true-prime-pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_ via _[bilateral 9 sums](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md)_.\n\n***63 = 21 x 3 = 7 x 3 x 3***\n\n[![Fibonacci Sequence Numbers](https://user-images.githubusercontent.com/8466209/218188579-8b7abe41-3137-41fd-8620-c141a719b493.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md)\n\nMeanwhile the sum of ***28 and 35***, which is 63, has a digital root of 6+3 = 9 and is landed precisely on the _[15's cell](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)_ of the prime hexagon. So the interaction with the [seven (7) objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md) is made through the _[object of 36](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)_ which has the same digital root of 9.\n\n>la position du début de l'emplacement, dans les décimales du nombre e, de la séquence ***0719425863***, qui est la première occurrence d'une séquence de longueur ***10 contenant*** chaque chiffre une et une seule fois _([Wikipedia](https://fr.wikipedia.org/wiki/1_729_(nombre)))_.\n\n![](https://user-images.githubusercontent.com/36441664/73480257-261c4e00-43cc-11ea-8c80-b2cd7b8d98b0.png)\n\nThis _[1729 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-recycling)_ is passing the first cycle of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ so it will be located by the starting point of 286 objects of 2nd identity. This balancing will exchange ***786 and 500 objects in pair***.\n\n***1729 = 786 + 157 + 786 = 500 + 286 + 157 + 286 + 500***\n\n[![Euleur Gap](https://user-images.githubusercontent.com/8466209/220001571-bddc7fee-5753-4ee3-b145-b3b1bb49a354.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity)\n\nThe basic idea is to try to \"improve\" this metric; for example, if the metric can be improved enough so that it has constant positive curvature, then according to classical results in Riemannian geometry, it must be the 3-sphere. \n\n![](https://user-images.githubusercontent.com/8466209/195509190-6926e3cd-807a-44ef-8549-b0fc1f481a2d.png)\n\nHamilton prescribed the \"[Ricci flow equations](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#ricci-flow)\" for improving the metric. Ricci flow expands the negative curvature part of the manifold and contracts the positive curvature part. In some cases, Hamilton was able to show that this works\n\n## System Images\n\n![](https://user-images.githubusercontent.com/36441664/125712858-fd635048-1970-48f7-a063-758c9c99a3a7.png)\n\n[![](https://user-images.githubusercontent.com/8466209/209758101-c62460d5-0fb0-461a-ac64-931e07bd0828.png)](https://user-images.githubusercontent.com/8466209/205960400-3061d93a-b3cc-4cd6-84e6-359a9314869d.png)\n\nPass a startup script from Cloud Storage for the scripts greater than 256 KB. \n\n[![Startup script](https://user-images.githubusercontent.com/8466209/221899049-3a88854a-1836-4960-832c-a2f849f25f68.png)](https://cloud.google.com/compute/docs/instances/startup-scripts)\n\n**Artifact Registry** expands on the capabilities of Container Registry and is the recommended container registry for Google Cloud. \n\n![2023-03-01](https://user-images.githubusercontent.com/8466209/222013722-6c410230-2665-4636-9071-9d2453ae5758.png)\n\nA [Cloud Build trigger](https://cloud.google.com/build/docs/automating-builds/create-manage-triggers) automatically starts a build whenever you make any changes to your source code. You can configure the trigger to build your code on any changes to the source repository or only changes that match certain criteria.\n\n[![](https://user-images.githubusercontent.com/8466209/222014481-8af35f36-f6cf-4260-9e47-f22f5017ed12.png)](https://cloud.google.com/build/docs/automating-builds/create-manage-triggers)\n\n[![8d0zCSMHxpgkFZTmXCGk](https://user-images.githubusercontent.com/8466209/210665303-b56792d5-8442-4e8a-a1fb-ae95ae6235d5.png)\n](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831)\n\nCompute Engine supplies an up-to-date [Container-Optimized OS (COS)](https://cloud.google.com/container-optimized-os/docs) image with Docker installed and launches your container when your VM starts. See below the [access control](https://cloud.google.com/artifact-registry/docs/access-control) for information about private registry permissions.\n\n> DNA is read by DNA polymerase in the 3′ to 5′ direction, meaning the new strand is synthesized in the 5' to 3' direction. Since the leading and lagging strand templates are oriented in opposite directions at the replication fork, *****a major issue***** is how to achieve synthesis of new lagging strand DNA, whose direction of synthesis is opposite to the direction of the growing replication fork __(Source: [Wikipedia](https://en.wikipedia.org/wiki/DNA_replication#Replication_for))__.\n\n[![default](https://user-images.githubusercontent.com/8466209/199140400-d85fef37-1c7d-455b-bb56-6841694ed648.png)](https://en.wikipedia.org/wiki/DNA_replication#Replication_fork)\n\nMeans this field remains unthoucheable. Up to the previous topic of [quantum](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699) we brought you [AI](https://en.wikipedia.org/wiki/Artificial_intelligence). A touchable intelligence. By this project we would like to introduce a brand new intelligence called **UI** which is the abreviation of [Untouched Inteligence](https://github.com/chetabahana/tensorflow/wiki/Untouched-Intelligences)\n","dir":"/identition/span5/","name":"gist01.md","path":"identition/span5/gist01.md","url":"/identition/span5/gist01.html"},{"sort":5,"spin":13,"layout":"default","title":"grouping","content":"# grouping\n\n![integration](https://user-images.githubusercontent.com/8466209/204819549-e0190e18-035d-4093-b6c7-3315d355f160.jpg)\n\n![integration](https://user-images.githubusercontent.com/8466209/204817921-7b3cb166-dd8a-49b0-8c13-915f7aa9b210.jpg)\n\n[![default](https://user-images.githubusercontent.com/8466209/202907299-bcd8f3b9-51db-42f8-a9e6-0c9a9da0cadf.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-hexagon-md)\n\n[![default](https://user-images.githubusercontent.com/8466209/202907392-215918c3-84f5-4b14-a016-79b9d3e1f76f.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-output-md)\n\n![TA_Chart](https://user-images.githubusercontent.com/8466209/204747440-0950b4e4-724a-43c9-92ce-86838e682128.png)\n","dir":"/exponentiation/span13/","name":"gist05.md","path":"exponentiation/span13/gist05.md","url":"/exponentiation/span13/gist05.html"},{"sort":5,"spin":null,"span":null,"suit":7,"layout":"default","title":"Power of Magnitude","content":"

            Power of Magnitude

            \n\n
            This section is referring to _[wiki page-5](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-1]()_ that is _[inherited ]()_ from _[the gist section-7](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n
            ***The number 120 = MEC30 x 4 has 32 prime positions minus 5 prime number products = 27 prime numbers***. The information of the prime number products translates our theory into a checkerboard-like pattern using the finite 8 prime positions from the MEC 30, we call it Ikon. 8 × 8 primary positions = 64 primary positions of the checkerboard icon.\n
            \n\n

            \"Hebrew

            \n\n
            Note that the hexagon in the middle has 37 circles and the total figure, a star of David has 73. For this one you go around one point of the pattern in a circle until you go past a letter that you have already covered. For instance in B-R-A-Sh you will have to switch the position for the Sh because it moves more than through the alphabet. S-I-T does the same with the T.\n
            \n\n

            \"Torah

            \n\n

            Composite Contribution

            \n\n

            The above seven (7) primes will act then as extended branes. This is what we mean by addition zones and it happens whenever a cycle is restarted.

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                       MEC 30 / 2\n------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2       |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7 x 24 = 168 ✔️\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}\n
            \n\n

            This scheme goes to the unification of 11s with 7s to 18s meanwhile the 11th it self behave as residual by the 5th minor hexagon between the 30 to 36’ cells.

            \n\n

            \"74550123-6dd1d680-4f83-11ea-8810-3b8f4f50a9c0\"

            \n\n
             1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18\n---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----+----\n 19| 20| 21| 22| 23| 24| 25|\n---+---+---+---+---+---+---+\n - | - | - | 28| 29|\n
            \n\n

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0’s cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            \n\n
            You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why? Because they do not fit inside — they stick off the hexagon like a tail. Perhaps that’s where they belong. However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively. _([HexSpin](https://www.hexspin.com/0-1-and-negative-numbers/))\n
            \n\n

            0 + 30 + 36 + 102 = 168 = π(1000)

            \n\n

            \"19

            \n\n
             0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 \n---+---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----\n - | - | 20| 21| 22| 23| 24| 25|\n---+---+---+---+---+---+---+\n - | - | - | - | 28| 29|\n---+---+---+---+---+---+\n 30| 31|\n---+---+\n 36|\n
            \n\n
            This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with ***the prime distribution level*** as indicated by the _[self repetition](https://www.eq19.com/exponentiation/#self-repetition)_ on MEC30.\n
            \n\n

            7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

            \n\n

            \"IMG_20231221_074421\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin ✔️\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin ✔️\n6 7 3 1 0 7 ◄--- #23\n7 11 4 1 0 11 ◄--- #19\n8 13 5 1 0 13 ◄--- # 17 ◄--- #49\n9 17 0 1 1 17 ◄--- 7th prime\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin ✔️\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            It will be forced back to Δ19 making a cycle that bring back the 12 to → 13 of 9 collumns and replicate The Scheme 13:9 through (i=9,k=13)=9x3=27 with entry form of (100/50=2,60,40) as below:

            \n\n

            \"default\"

            \n\n

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            \n\n
            I like that 0 can occupy a center point.  Incidentally, this circular shape minus all my numbers and colors s has been called Seed of Life / Flower of Life by certain New Age groups who claim it has a sacred geometry.  Please don’t see this as an endorsement of any spiritual group or religion. _([Prime Hexagon - Circulat Form](https://www.hexspin.com/circular/))_\n
            \n\n

            \"image\"

            \n\n","dir":"/addition/","name":"5.md","path":"addition/5.md","url":"/addition/5.html"},{"sort":6,"spin":1,"span":"quantum","suit":"intro","layout":"default","title":"The Quantum Way","content":"# [The Quantum Way](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155)\n\n```\n---+-----+-----\n 1 | 1 |{73}\n---+-----+-----\n 2 |{74} | 94\n---+-----+-----\n 3 | 95 | 113\n---+-----+-----\n 4 |{114}| 121\n---+-----+-----\n 5 | 122 | 135\n---+-----+-----\n 6 | 136 | 156\n---+-----+-----\n 7 |{157}|{165}\n---+-----+-----\n```\n\nWhat is critical to understand, is that the invisible hand of 2, 3 and 5, and their factorial 30, create the structure within which the balance of the prime numbers, i.e., all those greater than 5, are arrayed algorithmically–as we shall demonstrate.\n\n>In number theory, the _[partition function p(n)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partition)_ represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. _([Wikipedia](https://en.wikipedia.org/wiki/Partition_function_(number_theory)))_.\n\n![default](https://user-images.githubusercontent.com/8466209/226643815-f8c926cd-ae36-43d3-b271-8df07272f429.png)\n\nThe integer thirty (30) is the 19th composite number, Organizing Principle of the Prime Number Sequence, provides both vertical and horizontal structure to the prime number sequence in [Prime Spiral Sieve](https://www.primesdemystified.com/).\n\n>The number 30 possesses remarkable attributes, including–and perhaps most profoundly–its role (along with its prime factors 2, 3 and 5) as a primary organizing principle in the distribution of prime numbers _([Primesdemystified](https://www.primesdemystified.com/thirty.html))_.\n\n```\n 15\n ↓\n 29\n ↓\n---+-----+-----\n 6 | 30 | 31 ------\n---+-----+----- |\n 7 | 32 | 44 |\n---+-----+----- | 4th (id:12)\n 8 | 45 | 46 |\n---+-----+----- |\n 9 | 47 | 49 --329-¤-multiplication zone\n---+-----+----- | 5th (id:13)\n10 | 50 | 50 ------\n---+-----+----- \n11 | 51 | 53 ------\n---+-----+----- |\n12 | 54 | 59 | \n---+-----+----- | 6th (id:14 - id:15)\n13 | 60 | 82 |\n---+-----+----- |\n14 | 83 |{102} --289-¤-exponentiation zone\n---+-----+----- | 7th (id:16 - id:19)\n15 |{103}| 110 ------\n---+-----+-----\n```\n\n_[Prime hexagon](http://www.hexspin.com/)_ is a mathematical structure developed by mathematician T. Gallion that is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime is encountered.\n\n![](https://user-images.githubusercontent.com/36441664/75614463-8806d980-5b6b-11ea-9b88-33808482d431.png)\n\nThe tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating 3 [minor hexagons](https://www.hexspin.com/minor-hexagons/), assigned names blue, red and green.\n\n[![default](https://user-images.githubusercontent.com/8466209/226646352-272ae724-e27f-4c21-8020-5d013227910b.png)](http://www.hexspin.com/defining-the-prime-hexagon/)\n\nMany of you with familiarity with Docker for Windows know how you currently have to switch between running either Windows or Linux Containers. Prime hexagon teaches us how to combat this limitation and run both simultaneously on the same host.\n\n## Separated segments\n\n[Functional description of DNA](https://europepmc.org/article/PAT/DE19949059), useful e.g. for identifying new coding sequences, comprises assigning characteristic values to individual bases derived from vibrational properties\n\n![default](https://user-images.githubusercontent.com/36441664/83051747-a2702680-a078-11ea-9e55-f02f057ae0db.png)\n\nThe lagging strand is the strand of new DNA whose direction of synthesis is opposite to the direction of the growing replication fork. The lagging strand is synthesized in short, separated segments.\n\n***320 + 289 + 168 = 618 + 168 = 786***\n\nCell types are interesting, but they simply reflect a ***[modulo six (6)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-18_06_quantum-md)*** view of numbers. More interesting are the six internal hexagons within the Prime Hexagon. Like the Prime Hexagon, they are newly discovered.\n\n![default](https://user-images.githubusercontent.com/8466209/227656225-bd72a9ed-47d0-4ff5-80f4-46bee4f80452.png)\n\n>Surprisingly, the ***24-cell hexagon*** confines all natural numbers. The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon’s outer boundary, other than 2 and 3. \n\n[![iMinor Hexagons](https://user-images.githubusercontent.com/8466209/227582587-c9719ef1-1643-495a-9e0e-3181285ad049.png)]()\n\n### Three dimensional sphere\n\nIn 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. \n\n>Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries _([ClayMath Institute](https://www.claymath.org/millennium-problems/poincar%C3%A9-conjecture))_.\n\n[![Poincaré Conjecture](https://user-images.githubusercontent.com/36441664/84181979-e3722d00-aab3-11ea-9868-982020dcd4b3.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#replication-fork)\n\nThe initial primes that forced the number line into this complex coil. Without a prime number in the outer set of triangles, the number line does not change to an outward course and remains forever contained in the 24 cells shown above.\n\n>The minor hexagons form solely from the order, and type, of primes along the number line. Perhaps they have no significance. however, as they do form I suspect they must connect to deeper things in mathematics _([Prime Hexagon](http://www.hexspin.com/minor-hexagons/))_.\n\n![Δ300](https://user-images.githubusercontent.com/36441664/105412087-d0892300-5c66-11eb-9c3e-19d8652b478c.png)\n\n![gif-dribbb](https://user-images.githubusercontent.com/8466209/229562944-94851029-3f80-49e5-a6bc-b4ea0a931d61.gif)\n\nPhi and its members have a pisano period if the resulting fractional numbers are truncated. If one instead rounds to the nearest number, the modular values for the first two terms are flipped compared to the 24th and 25th values as seen below.\n\n[![phi’s cousin, the Fibonacci Series](https://user-images.githubusercontent.com/8466209/229198281-8dbd72fb-cd0b-46c3-8a2c-ddc66107333e.png)](https://www.hexspin.com/phi-not-pi-and-why-i-truncate-to-determine-integer-values/)\n\nNumbers fill the hexagon by spiraling until a prime number is met, then it jumps to the next minor hexagon and begins to spiral again. As the numbers continue to fill the field, the other minor hexagons from, purple, cyan and yellow.\n\n***(2112/82) − (576/82) = 24***\n\n![image](https://user-images.githubusercontent.com/8466209/226644534-00cf4fe3-04f9-4b28-8a8b-674bcf4bd585.png)\n```\nlayer | node | sub | i | f\n------+------+-----+----------+------ ---\n | | | 1,2:1 | 71 (2,3) ------------- |\n | | 1 +----------+ | |\n | 1 | | 2 | | (5) \n | |-----+----------+ | |\n | | | 3 | | |\n 1 +------+ 2 +----------+---- | ---\n | | | 4 | | |\n | +-----+----------+ | |\n | 2 | | 5 | | (7) \n289 | | 3 +----------+ | |\n| | | | 6 | | {6®} |\n------+------+-----+----------+------ } (36) | ↓ ---\n | | | 11:7√| 50/10+9 (20) ----› ¤ √ | 29=MEC30 - Δ1 |\n | | 4 +----------+ | ↓ |\n | 3 | | 12:8√| 9+60+40 (26) √ -- | from 329-40 √ (11) \n | +-----+----------+ | | ↓ lagging |\n | | | 13:9√| 9+60 (27) √ | {2®} from 168 (Triangular) √ |\n 2 +------| 5 +----------+----- | | ↓ leading ---\n | | | 14:10√| 9+60+40 (28) √ -- | goes to 329 √ |\n | |-----+----------+ | |\n | 4 | | 15,18:11√| 71 (29,30,31,32) ------ (13)\n329 | | 6 +----------+ |\n| | | | 19:12√| {70} (36) |\n------+------+-----+----------+------------------ ---\n | | | 20:13√| (20-11)x10 (38) ‹- ¤ √ |\n | | 7 +----------+ |\n | 5 | | 14 | (17) \n | |-----+----------+ |\n | | | 15 | |\n 3 +------+ 8 +----------+----- ---\n | | | 16 | |\n | |-----+----------+ |\n | 6 | | 28:17√| 100(50) (19) \n168 | | 9 +----------+ |\n| | | | 29:18√| 50(68) |\n------|------|-----+----------+------ ---\n```\n\n## Prime factor abundances\n\nThe genetic material of a cell or an organism refers to those materials found in the nucleus, mitochondria and cytoplasm, which play a fundamental role in determining the structure of cell substances and capable of self-propagating and variation.\n\n![The genetic material](https://user-images.githubusercontent.com/36441664/160698918-395f9ba0-0c2f-418d-a2e2-b1bbbbbe058c.jpg)\n\n![torus](https://user-images.githubusercontent.com/36441664/82712407-12b22d00-9cb2-11ea-9cc2-3cf392b2d35c.png)\n\nSpirals following other tilings of the plane also generate lines rich in prime numbers, for example hexagonal spirals. Hexagonal number spiral with prime numbers in green and more highly composite numbers in darker shades of blue.\n\n![default](https://upload.wikimedia.org/wikipedia/commons/2/25/Hexgrid_prime_number_spiral.svg)\n\n### Ricci Flow\n\nFinite collections of objects are considered 0-dimensional. Objects that are \"dragged\" versions of zero-dimensional objects are then called one-dimensional. Similarly, objects which are dragged one-dimensional objects are two-dimensional, and so on. \n\n>The basic ideas leading up to this result (including the dimension invariance theorem, domain invariance theorem, and Lebesgue covering dimension) were developed by **Poincaré**, Brouwer, Lebesgue, Urysohn, and Menger _([MathWorld](https://mathworld.wolfram.com/Dimension.html))_.\n\n![default](https://user-images.githubusercontent.com/8466209/221333839-bd4edd90-9996-49a3-9d4d-20f7997004c3.png)\n\nThe Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it “rounder”, in the hope that one may draw topological conclusions from the existence of such “round” metrics.\n\n>Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere _([Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture))_\n\n![default](https://user-images.githubusercontent.com/8466209/222646190-34a8dc8b-f8f2-4a6c-b06e-5612aa00e754.png)\n\nThe Ricci Flow method has now been _[developed](http://engine.scichina.com/publisher/scp/journal/SCIS/62/9/10.1007/s11432-018-9702-7)_ not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI ([Artificial intelligence](https://en.wikipedia.org/wiki/Artificial_intelligence)). No wonder now all the science leads to it.\n\n![](https://user-images.githubusercontent.com/36441664/88372848-e5bcec00-cdc0-11ea-8b8a-09b579a257f9.png)\n\nSo what we've discussed on this wiki is entirely nothing but an embodiment of this solved [Poincare Conjecture](https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture). This is the one placed with id: 10 (ten) which stands as the basic algorithm of _[π(10)=(2,3,5,7)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#lexer-vs-parser)_.\n\n[![Poincaré Conjecture](https://user-images.githubusercontent.com/36441664/84187330-17515080-aabc-11ea-8e53-47f12a248d4c.jpg)](https://www.claymath.org/millennium-problems/poincar%C3%A9-conjecture)\n\nMany relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence.\n\n>AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence _([Human vs AI](https://www.frontiersin.org/articles/10.3389/frai.2021.622364/full))_.\n\n![](https://user-images.githubusercontent.com/8466209/200475393-f3e42f0b-d291-4f17-93c4-9bec6e6943de.png)\n\nDespite of any debated subjects regarding _Human vs AI_, the said AI would not even close to the ability of human brain without undertanding of _[GAP](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#mass-vs-gap-%CE%B4)_ functionality between left and right of the human brain. Let's find it in details on further discussion.\n","dir":"/identition/span1/","name":"gist06.md","path":"identition/span1/gist06.md","url":"/identition/span1/gist06.html"},{"sort":6,"spin":1,"span":"pattern","suit":"intro","layout":"default","title":"The Prime hexagon","content":"# [The Prime hexagon](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-quantum-way)\n\n\n### Cranks of prime\n\n[![Turbulent Combustion](https://user-images.githubusercontent.com/8466209/223621634-c0678865-f2a4-4254-b6f3-b84708ea4320.png)](https://www.slideserve.com/keziah/turbulent-combustion-conservation-equations-closure/?utm_source=slideserve&utm_medium=website&utm_campaign=auto+related+load)\n\n![default](https://user-images.githubusercontent.com/8466209/223622800-4602ad28-1622-4742-821e-d702c0fc8303.png)\n\n[![Navier–Stokes Equation](https://user-images.githubusercontent.com/8466209/224287999-37cd0692-bf51-4b99-bb45-8c49e5db58e3.png)\n\n","dir":"/identition/span6/","name":"gist01.md","path":"identition/span6/gist01.md","url":"/identition/span6/gist01.html"},{"sort":6,"spin":13,"layout":"default","title":"helix","content":"# helix\n\n![default](https://user-images.githubusercontent.com/8466209/202855806-611c6a39-e40c-4aa9-ae28-e25aea82cb19.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202854972-8fbcaef7-104c-4c51-b828-ee0e3625783a.png)\n","dir":"/exponentiation/span13/","name":"gist06.md","path":"exponentiation/span13/gist06.md","url":"/exponentiation/span13/gist06.html"},{"sort":6,"spin":null,"span":null,"suit":11,"layout":"default","title":"The Pairwise Disjoint","content":"

            The Pairwise Disjoint

            \n\n
            This section is referring to _[wiki page-6](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-2]()_ that is _[inherited ]()_ from _[the gist section-11](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            Mobius Strip

            \n\n

            There are some mathematical shape of this residual objects. Torus is basically a donut shape, which has the property of of having variable Gaussian curvature.

            \n\n
            The blue parts of the torus above have positive curvature, the red parts negative and the top grey band has zero curvature.  If our 3 dimensional space was like the surface areas of a 4 dimensional torus, the parts would have different angle sums.\n
            \n\n

            \"Torus\"

            \n\n

            Some parts of the surface has positive curvature, others zero, others negative.

            \n\n

            \"ring_tor1_anim\"

            \n\n

            If you start anywhere on its surface and follow the curvature round you will eventually return to the same place having travelled on every part of the surface.

            \n\n

            \"Mobius\"

            \n\n

            \"Fiddler_crab_mobius_strip\"

            \n\n

            Mobius strip only has one side, there are two more bizarre shapes with strange properties.

            \n\n

            The Klein bottle

            \n\n

            The Klein bottleis in someways a 3D version of the Mobius strip and even though it exists in 3 dimensions, to make a true one you need to “fold through” the 4th dimension.

            \n\n
            In [mathematics](https://en.wikipedia.org/wiki/Mathematics), the Klein bottle ([/ˈklaɪn/](https://en.wikipedia.org/wiki/Help:IPA/English)) is an example of a [non-orientable](https://en.wikipedia.org/wiki/Orientability) [surface](https://en.wikipedia.org/wiki/Surface_(topology)); that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.\n- More formally, the Klein bottle is a [two-dimensional](https://en.wikipedia.org/wiki/Two-dimensional) [manifold](https://en.wikipedia.org/wiki/Manifold) on which one cannot define a [normal vector](https://en.wikipedia.org/wiki/Normal_vector) at each point that varies [continuously](https://en.wikipedia.org/wiki/Continuous_function) over the whole manifold.\n- Other related non-orientable surfaces include the [Möbius strip](https://en.wikipedia.org/wiki/M%C3%B6bius_strip) and the [real projective plane](https://en.wikipedia.org/wiki/Real_projective_plane). \n\nWhile a Möbius strip is a surface with a [boundary](https://en.wikipedia.org/wiki/Boundary_(topology)), a Klein bottle has no boundary. For comparison, a [sphere](https://en.wikipedia.org/wiki/Sphere) is an orientable surface with no boundary.\n
            \n\n

            \"image\"

            \n\n

            \"Klein

            \n\n

            A sign inversion visualized as a vector pointing along the Möbius band when the circle is continuously rotated through a full turn of 360°.

            \n\n

            \"image\"

            \n\n

            The Spinors

            \n\n

            A spinor associated to the conformal group of the circle, exhibiting a sign inversion on a full rotation of the circle through an angle of 2π.

            \n\n

            (17+13) + (11+19) = (7+11) + (19+23) = 60

            \n\n

            \"\"

            \n\n

            \"Sipnors\"

            \n\n

            \"3-Figure1-1\"

            \n\n
            Eigennvalue curves (right) showing a triple eigenvalue at zero for τ = 1 and double eigenvalues at 1 ± √2i for τ = √43. On the left the graph of 1/|Q(λ)| with the same eigenvalue curves plotted in the ground plane. Green stars indicate the eigenvalues of A, blue stars the roots of puv(λ) and triangles the zeroes of Q0\n(λ)\n
            \n\n

            Global Properties

            \n\n

            7 + 11 + 13 = 31\n1 + (26+6) + (27+6) = 66

            \n\n

            \"9

            \n\n
             0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 \n---+---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----\n - | - | 20| 21| 22| 23| 24| 25|\n---+---+---+---+---+---+---+---+\n - | - | - | - | 28| 29| ◄--- missing 26 & 27 ✔️\n---+---+---+---+---+---+\n 30| 31| - | - | ◄--- missing 32 & 33 ✔️\n---+---+---+---+\n 36|\n
            \n\n
            This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with ***the prime distribution level*** as indicated by the _[self repetition](https://www.eq19.com/exponentiation/#self-repetition)_ on MEC30.\n
            \n\n

            7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

            \n\n

            \"IMG_20231221_074421\"

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                       MEC 30 / 2\n------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) √\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7 x 24 = 168 √\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}\n
            \n\n

            This model may explains the newly discovered prime number theorem in relatively simple layman’s terms for anyone with a slight background in theoretical physics.

            \n\n
            The property gives an in depth analysis of the not so random distribution of primes by showing how it has solved Goldbach's conjecture and the Ulam spiral.\n
            \n\n

            \"Schematic-of-the-internal-energy-ow-in-the-model-The-lines-of-ow-geodesics-circulate\"

            \n\n

            The model suggests a possible origin for both charge and half-integer spin and also reconciles the apparently contradictory criteria discussed above.

            \n\n
            ***Arbitrary sequence of three (3) consecutive nucleotides*** along a helical path whose metric distances satisfy the relationship dn,n+3\u0017dn,n+2\u0017dn,n+1.\n- Sketch showing a characteristic duplex DNA helical standing-wave pattern.\n- The vertical lines depict the cross-section projections of each bp along the helix axis, their length providing a measure of their twist magnitude.\n- Thick lines represent the sugar-phosphate profile. \n\nOptimally overlapping bps are indicated by the presence of the ovals (m) measures the \u0001overlapping resonance correlation length. _([π − π orbital resonance in twisting duplex DNA](https://github.com/eq19/eq19.github.io/files/13790206/prb_Hx2.pdf))_\n
            \n\n

            \"a-Arbitrary-sequence-of-three-consecutive-nucleotides-along-a-helical-path-whose-metric\"

            \n\n

            Under certain conditions, energy could not take on any indiscriminate value, the energy must be some multiple of a very small quantity (later to be known as a quantum).

            \n\n
            Twisted strip model for one wavelength of a photon with circular polarisation in  at space. A similar photon in a closed path in curved space with periodic boundary conditions of length \u0015C. \n\n- The B-fi\feld is in the plane of the strip and the E-field\f is perpendicular to it (a).\n- The E-fi\feld vector is radial and directed inwards, and the B-fi\feld is vertical (b). \n\nThe magnetic moment ~\u0016, angular momentum L~, and direction of propagation with velocity c are also indicated. _([Is the electron a photon with toroidal topology? - pdf](https://github.com/eq19/eq19.github.io/files/13790325/LdBelectoroid.pdf))_\n
            \n\n

            \"a-Twisted-strip-model-for-one-wavelength-of-a-photon-with-circular-polarisation-in-at\"

            \n\n

            A deeper understanding requires a uni\fcation of the aspects discussed above in terms of an underlying principle.

            \n","dir":"/addition/","name":"6.md","path":"addition/6.md","url":"/addition/6.html"},{"sort":7,"spin":1,"span":"proofreading","suit":"intro","layout":"default","title":"Proofreading Ability","content":"# [Proofreading Ability](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf)\n\n```\n---+-----+-----\n 1 | {1} |{56}\n---+-----+-----\n 2 | 57 |{71}\n---+-----+-----\n 3 | 72 | 85\n---+-----+-----\n 4 |{86} |{89}\n---+-----+-----\n 5 | 90 | 94\n---+-----+-----\n 6 | 95 | 102\n---+-----+-----\n 7 | 103 |{171}\n---+-----+-----\n 8 | 172 | 206\n---+-----+-----\n```\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\nlayer| i | f\n-----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | {7}\n-----+-----+--- } 36\n | 3 | 11\n {2} +-----+\n | 4 | {13}\n-----+-----+---------\n | 5 | 17\n 3 +-----+ } 36\n | 6 | {19}\n-----+-----+---------\n```\n\n## Infinite connection\n\n```\nΦ = 2,10\nΔ = 5,7,17\n3': 13,18,25,42\n2' » 13 to 77, Δ = 64\n2' and 3' » 13 to 45, Δ = 32\n\n2\" + 5\" = 7\" = 77\n2\"=22, 3\"=33, 2\" + 3\" = 5\" = 55\n\n13, 16, 18, 21, 23, 25, 28, 30, 32, 34, \n36, 38, 40, 42, \n45, 47, 49, 51, 53, \n55, 57, 59, 61, \n63, 65, 67, 69, 71, 73, 75, 77\n```\n\n![](https://user-images.githubusercontent.com/36441664/100138286-651e1180-2ec0-11eb-9b27-ec206498380f.jpg)\n\nNext we will discuss how to form these numbers on each screens. As explained earlier, there are all three (3) layers. The instance is going to simulate DNA polymerase with ***proofreading ability***.\t\n\n>Proofreading removes the mismatched nucleotide and extension continues. If a mismatch is accidentally incorporated, the polymerase is inhibited from further extension _([Wikipedia](https://en.wikipedia.org/wiki/DNA_polymerase#Function))_.\t\n\n[![DNA polymerases](https://user-images.githubusercontent.com/36441664/81181797-2a619400-8fd7-11ea-8462-9e1aab20c709.jpg)](https://en.wikipedia.org/wiki/DNA_polymerase)\t\n\n>A current model of meiotic recombination, initiated by ***a double-strand break or gap***, followed by pairing with an homologous chromosome and strand invasion to initiate the recombinational repair process _([Wikipedia](https://en.wikipedia.org/wiki/Genetic_recombination))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/219876965-9d76b5a9-ef31-4d52-a256-ea5e42f442fa.png)](https://en.wikipedia.org/wiki/Genetic_recombination)\n\n***π(96) = 96/4 = 24***\n\n![](https://user-images.githubusercontent.com/36441664/91654837-66fd5200-ead6-11ea-885f-26660998c1ac.png)\n\nFidelity is very important in DNA replication. Mismatches in DNA base pairing can potentially result in dysfunctional proteins and could lead to cancer. Hydrogen bonds play a key role in base pair binding and interaction. \t\n\n>The function of DNA polymerase is not quite perfect, with the enzyme making ***about one mistake for every billion base pairs copied***. Error correction is a property of some, but not all DNA polymerases. This process corrects mistakes in newly synthesized DNA _([Wikipedia](https://en.wikipedia.org/wiki/DNA_polymerase#Function))_.\t\n\n![dna-genetics-biochemistry](https://user-images.githubusercontent.com/8466209/209992678-2f9210c5-e813-4940-b7a0-4fb75dbbc255.jpg)\t\n\n### Strand Partition\n\n![ezgif com-optimize](https://user-images.githubusercontent.com/8466209/235304712-f3ed4ada-9840-4cdf-911f-f9ce53191340.gif)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n | | | 20:13 | 90 | 90 (38) ‹-------------- ¤ |\n | | 7 +----------+-----+ |\n | 5 | | 14 | ----------------------------- 17¨ class\n | |-----+----------+ | | |\n | | | 15 | | LEADING SCHEME | |\n 3 +------+ 8 +----------+----- | (Multiplication Zone) | ---\n | | | 16 | | | |\n | |-----+----------+-----+ ----------------------------- |\n | 6 | | 28:17 | 100 | 19¨ object\n168 | | 9 +----------+-----+ |\n| | | | 29:18 | 50 | 50(68) ---------> Δ18 |\n------|------|-----+----------+-----+ ---\n```\n\n## Four-vector configuration\n\nIf you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers ***[Simultaneously](https://blogs.msdn.microsoft.com/premier_developer/2018/04/20/running-docker-windows-and-linux-containers-simultaneously/)***, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel\n\n[![image](https://user-images.githubusercontent.com/8466209/222601650-8fef811d-6bd5-44de-b81f-6d39f47625ad.png)](https://blogs.msdn.microsoft.com/premier_developer/2018/04/20/running-docker-windows-and-linux-containers-simultaneously/)\n\nOn the lagging strand template, a primase \"reads\" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.\n\n[![GitHub Actions workflow](https://user-images.githubusercontent.com/8466209/222642428-fb9f183f-f4d5-43c6-a3c2-c1adebac2bad.png)](https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners#using-a-github-hosted-runner)\n\nThe leading strand is the strand of new DNA which is synthesized in the same direction as the growing replication fork. This sort of DNA replication is continuous. This workflow is assigned to Linux container (Ubuntu).\n\nThe runner is the application that runs a job from a GitHub Actions workflow. It is used by GitHub Actions in the [hosted virtual environments](https://github.com/actions/virtual-environments), or you can [self-host the runner](https://help.github.com/en/actions/automating-your-workflow-with-github-actions/about-self-hosted-runners) in your own environment. We use both of them to create [group as a four-vector](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#lexer-vs-parser).\n\n>DNA polymerase extends primed segments, forming Okazaki fragments. The RNA primers are then removed and replaced with DNA, and the fragments of DNA are joined by DNA ligase and are bound to the helicase heximer _([Wikipedia](https://en.wikipedia.org/wiki/DNA_replication#Replication_fork))_.\n\n[![DNA ligase](https://user-images.githubusercontent.com/8466209/207357956-3eeeacc2-0b5f-4eeb-b2b5-71f8d22adf59.png)](https://en.wikipedia.org/wiki/DNA_replication#Replication_fork)\n\nIn eukaryotes the helicase wraps around the leading strand, and in prokaryotes it wraps around the lagging strand. As helicase unwinds DNA at the replication fork, the DNA ahead is ***forced to rotate*** resulting a build-up of twists in the DNA ahead.\n\n>Because of its orientation, replication of the lagging strand is more complicated as compared to that of the leading strand. As a consequence, the DNA polymerase on this strand is seen to \"lag behind\".\n\n![container-diagram](https://user-images.githubusercontent.com/8466209/222651860-4259e479-7e03-45dc-bf1e-71b6246fefe8.svg)\n\n### Hamiltonian Path Problem\n\nBy [The GitHub Runner](https://github.com/actions/runner) you can [connect](https://github.com/tcardonne/docker-github-runner) to the [Google COS Instance](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#container-optimized-os). For self-hosted runners defined at the organization level, configure [runs-on.group](https://docs.github.com/en/actions/hosting-your-own-runners/using-self-hosted-runners-in-a-workflow#about-self-hosted-runner-groups) in your workflow file to target a [runner groups](https://docs.github.com/en/actions/using-jobs/choosing-the-runner-for-a-job#choosing-runners-in-a-group) or [combine groups and labels](https://docs.github.com/en/actions/hosting-your-own-runners/using-self-hosted-runners-in-a-workflow#using-default-labels-to-route-jobs).\n\n[![choosing-the-runner](https://user-images.githubusercontent.com/8466209/227559588-88480a1b-b339-46e8-9516-572f90f788f7.png)](https://docs.github.com/en/actions/using-jobs/choosing-the-runner-for-a-job#choosing-runners-in-a-group)\n\nOn the other hand, with larger systems we are able to transfer the behavior of the energy from the subatomic space into the haptic space with the scale described here (thought experiment Schröninger's cat). Thus, we are still able to apply the [Schröninger wave equation](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-three-3-zones) in the haptic space, and ***replace the Hamiltonian*** with our measurements.\n[![default](https://user-images.githubusercontent.com/8466209/228989527-2915b89f-dd8c-40d9-ae64-3d69c5217b3d.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)\n\nThe problems would arise when the Windows Container in Github deliver the _[RNA Primer](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#scenario)_ to Google instance as [Windows Image](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#system-images) because it shall read the image while the _[COS](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#diagram-of-classes)_ is run under Linux. So it will need to [proof and solve](https://mikinty.github.io/P-vs-NP/) without actually having to try.\n \n>If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the ***Hamiltonian Path Problem*** given N cities to visit, how can one do this without visiting a city twice? _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n\n[![P vs NP Problem](https://user-images.githubusercontent.com/8466209/222922021-70011b19-25e8-4851-b72a-db41f24a14c2.png)](https://www.claymath.org/millennium-problems/p-vs-np-problem)\n\nGetting the [proofreading ability](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#encapsulation-scenario) of DNA polymerase to quickly solve problem for about one mistake for every billion base pairs copied is somehow that required by one of a major unsolved problem in theoretical computer science called ***[P vs NP](https://en.wikipedia.org/wiki/P_versus_NP_problem)***.\n\n>P vs. NP deals with the gap between computers being able to quickly solve problems vs. just being able to test proposed solutions for correctness. As such, the P vs. NP problem is the search for a way to solve problems that ***require the trying of millions, billions, or trillions of combinations without actually having to try each one*** _([P vs. NP Explained](https://danielmiessler.com/study/pvsnp/#:~:text=P%20vs.%20NP%20deals%20with%20the%20gap%20between,combinations%20without%20actually%20having%20to%20try%20each%20one.))_.\n\n[![P_versus_NP_problem](https://user-images.githubusercontent.com/36441664/84743524-4b58d400-afdc-11ea-9e64-5306a5811a33.jpg)](https://en.wikipedia.org/wiki/P_versus_NP_problem)\n\nThis way will also be our approach to [Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity). By taking the correlation between ***f(π) as P*** vs ***f(i) as NP*** where ***eiπ + 1 = 0*** then theoretically they shall be correlated to get an expression of the prime distribution similar to _[MEC30](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_.\n","dir":"/identition/span1/","name":"gist07.md","path":"identition/span1/gist07.md","url":"/identition/span1/gist07.html"},{"sort":7,"spin":1,"span":"roots","suit":"intro","layout":"default","title":"Double strands","content":"# [Double strands](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#object-orientation)\n\nThe _[bilateral way](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bilateral-9-sums)_ of ***329 vs 289*** of 286 objects of 2nd prime identity will be taken as the basis that is involving 26-9=17 of other identities where the square of 17 which is ***17x17=329*** acts as the central of syntax algorithm.\n\n```\nid: 26\n\n---+-----+-----+-----+-----+\n 1 | 5 | 1 | 6 | 7 |----------------------------\n---+-----+-----+-----+-----+ |\n 2 | 2 | 7 | 9 | 16 |---------------------- |\n---+-----+-----+-----+-----+ | |\n 3 | 58 | 10 | 68 | 78 |---------------- | |\n---+-----+-----+-----+-----+ | | |\n 4 | 35 | 69 | 104 | 173 |---------- | | |\n---+-----+-----+-----+-----+ | | | |\n 5 | {17}| 105 | 122 |{227}| | | | |\n---+-----+-----+-----+-----+- Cross {17}Δ26|43Δ30|13Δ17|30\n 6 | {17}|{123}| 140 | 263 | | | | |\n---+-----+-----+-----+-----+ | | | |\n 7 | 18 | 141 | 159 | 300 |---------- | | |\n---+-----+-----+-----+-----+ | | |\n 8 | 15 | 160 | 175 | 335 |---------------- | |\n---+-----+-----+-----+-----+ | |\n 9 | 15 | 176 | 191 | 367 |---------------------- |\n---+-----+-----+-----+-----+ |\n10 | 35 |{192}|{227}| 419 |---------------------------- \n---+-----+-----+-----+-----+\n```\n\nBy taking the 200 residual objects we will get their recycing scenario which is similar to the ***leading and lagging strands*** of DNA Replication where the result is obtained on the lagging stage by initiating a DNA synthesis called RNA Primer. \n\n>RNA primers are used by living organisms in initiation of synthesizing a strand of DNA. A class of enzymes called primases add a complementary RNA primer to the reading template on both the leading and lagging strands _([Wikipedia](https://en.wikipedia.org/wiki/Primer_(molecular_biology)))_.\n\n![image](https://user-images.githubusercontent.com/8466209/226189793-03af4e0a-e95e-48b7-b9d8-2cf930b224eb.png)\n\nThere are situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics. Finally, there exist scenarios in which there could actually be more than [4D of spacetime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#dimensional-space).\n\n[![default](https://user-images.githubusercontent.com/8466209/195963923-0796217c-7a87-4b2d-ba93-f47465304c03.png)](https://www.nausetschools.org/cms/lib/MA02212418/Centricity/Domain/204/Linkage%20Map%20Worksheet%20Genetics%202017.pdf)\n\nNote that 1/109's decimal expansion is period 108 (making it a 'long period prime' in that 1/p has the maximal period of p−1 digits). This period consists of 54 bilateral 9 sums = 486, which is the number of primes in the _[243 pairs summing to 7920](https://www.primesdemystified.com/First1000Primes.html)_.\n\n***36 + 72 = 108***\n\n![](https://user-images.githubusercontent.com/36441664/73879041-52cddb00-488e-11ea-816b-04dcb0573dad.png)\n\nThis behaviour would come to the feature of ***golden ratio***. However it is not stand as a basic rule but as an impact of 329's vs 289's layers. That is also the reason why we could only see the three (3) digits of 618 out of the _Fibonaci_ constant.\n\n***φ = 1.618 = Fibonaci = Golden Ratio***\n\n![](https://user-images.githubusercontent.com/36441664/72682696-8248bd80-3b02-11ea-935f-d016e46da4fc.png)\n\nThe 200 objects that goes from the 2nd to 3rd prime identity would take position as ***multiplication zone*** by given of 100x2=200 which is then be used in turn to 100+2=102 (***addition zone***) and 100^2=10000 (***exponentiation zone***)\n\n***2 + 60 + 40 = 102***\n\n```\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\nSo it is converting all residual objects out of the prime recycling of _[Riemann Zeta](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function)_ in to those three (3) basic arithmetic operations of _[Euler's identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity)_ as well the Fibonacy constant (***φ***) to Euler's number (***e***). Thus none of residual is neglected by an assumption.\n\n![](https://user-images.githubusercontent.com/36441664/85039732-36ce3480-b1b2-11ea-969c-536a01c115b6.jpg)\n\nDNA polymerase (responsible for DNA replication) enzymes are ***only capable of adding nucleotides to the 3’-end of an existing nucleic acid***, requiring a primer be bound to the template before DNA polymerase can begin a complementary strand.\n\n>DNA polymerase adds nucleotides after binding to RNA primer and synthesizes the whole strand. Later, the RNA strands must be removed accurately and replace them with DNA nucleotides forming a gap region known as a nick that is filled in using an enzyme called ligase _([Wikipedia](https://en.wikipedia.org/wiki/Primer_(molecular_biology)))_.\n\n![](https://user-images.githubusercontent.com/36441664/160698911-1b0b94df-b50e-426b-ada8-a75c9e4080f9.png)\n\nPlottng ***40th prime scheme*** of the three (3) layers with all the features of 3rd prime identity with DNA Replication as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.\n\n***329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ***\n\n```\nlayer | node | sub | i | f\n------+------+-----+---------+------ ---\n | | | 1,2:1 √| 71 (2,3) ------------- |\n | | 1 +---------+ | |\n | 1 | | 2 | | (5) \n | |-----+---------+ | |\n | | | 3 | | |\n 1 +------+ 2 +---------+---- | ---\n | | | 4 | | |\n | +-----+---------+ | |\n | 2 | | 5 | | (7) \n289 √ | | 3 +---------+ | |\n| | | | 6 | | {6®} |\n------+------+-----+---------+------ } (36) | ↓ ---\n | | | 7 | | 29=MEC30 - Δ1 |\n | | 4 +---------+ | ↓ |\n | 3 | | 8 | 109 (26) √ -- | 9+60+40 from 329-40 √ (11) \n | +-----+---------+ | | ↓ lagging √ |\n | | | 9 | 69 (27) √ | {2®} | 9+60=40+29 from 168 √ |\n 2 +------| 5 +---------+----- | | ↓ leading √ ---\n | | | 10 | 109 (28) √ -- | 9+60+40 goes to 329 √ |\n | |-----+---------+ | ↓ |\n | 4 | | 11 | 71 (29,30,31,32) ------ ↓ (13)\n329 √ | | 6 +---------+ 9+9+9=27 (Triangular) √ |\n| | | | 12 | {70} (36) |\n------+------+-----+---------+------------------ ---\n | | | 20:13 | |\n | | 7 +---------+ |\n | 5 | | 14 | (17) \n | |-----+---------+ |\n | | | 15 | |\n 3 +------+ 8 +---------+----- ---\n | | | 16 | |\n | |-----+---------+ |\n | 6 | | 17 | 100(50) (19) \n168 | | 9 +---------+ |\n| | | | 18 | 50(68) |\n------|------|-----+---------+------ ---\n```\n","dir":"/identition/span7/","name":"gist01.md","path":"identition/span7/gist01.md","url":"/identition/span7/gist01.html"},{"sort":7,"spin":13,"layout":"default","title":"impact","content":"# impact\n![202907558-c7198082-14fd-409b-9e31-1a0440f79039](https://user-images.githubusercontent.com/8466209/204255750-5aae0f08-89ba-406b-b38f-6100a38a0280.png)![image](https://user-images.githubusercontent.com/8466209/202908203-6a7fdaa1-2e75-4658-aa9d-a298292a3065.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202907739-d8821b4d-47a8-41a8-bd43-e1dad600481c.png)\n\n[![202907558-c7198082-14fd-409b-9e31-1a0440f79039](https://user-images.githubusercontent.com/8466209/204256833-d12508ae-8cb1-4381-ade5-7acfcc3f0e12.png)](https://github.com/kaustubhcs/prime-hexagon)\n\n[![default](https://user-images.githubusercontent.com/8466209/203874936-9065fbff-25f6-4357-a37b-6945502161d5.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-keyring-md)\n","dir":"/exponentiation/span13/","name":"gist07.md","path":"exponentiation/span13/gist07.md","url":"/exponentiation/span13/gist07.html"},{"sort":7,"spin":null,"span":null,"suit":13,"layout":"default","title":"The Prime Recycling ζ(s)","content":"

            The Prime Recycling ζ(s)

            \n\n
            This section is referring to _[wiki page-7](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-3]()_ that is _[inherited ]()_ from _[the gist section-13](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            The Position Pairs

            \n\n

            \"Pauli_matrices\"

            \n\n

            36 + 36 - 6 partitions = 72 - 6 = 66 = 30+36 = 6x11

            \n\n
            $True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer|  i  |   f\n -----+-----+---------\n      |  1  | 5\n   1  +-----+\n      |  2  | 7\n -----+-----+---  } 36 » 6®\n      |  3  | 11\n   2  +-----+\n      |  4  | 13\n -----+-----+---------\n      |  5  | 17\n   3  +-----+     } 36 » 6®\n      |  6  | 19\n -----+-----+---------\n
            \n\n

            \"spinnors

            \n\n
            #!/usr/bin/env python\n\nimport numpy as np\nfrom scipy import linalg\n\nclass SU3(np.matrix):\n\tGELLMANN_MATRICES = np.array([\n\t\tnp.matrix([ #lambda_1\n\t\t\t[0, 1, 0],\n\t\t\t[1, 0, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_2\n\t\t\t[0,-1j,0],\n\t\t\t[1j,0, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_3\n\t\t\t[1, 0, 0],\n\t\t\t[0,-1, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_4\n\t\t\t[0, 0, 1],\n\t\t\t[0, 0, 0],\n\t\t\t[1, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_5\n\t\t\t[0, 0,-1j],\n\t\t\t[0, 0, 0 ],\n\t\t\t[1j,0, 0 ],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_6\n\t\t\t[0, 0, 0],\n\t\t\t[0, 0, 1],\n\t\t\t[0, 1, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_7\n\t\t\t[0, 0,  0 ],\n\t\t\t[0, 0, -1j],\n\t\t\t[0, 1j, 0 ],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_8\n\t\t\t[1, 0, 0],\n\t\t\t[0, 1, 0],\n\t\t\t[0, 0,-2],\n\t\t], dtype=np.complex) / np.sqrt(3),\n\t])\n\n\n\tdef computeLocalAction(self):\n\t\tpass\n\n\t@classmethod\n\tdef getMeasure(self):\n\t\tpass\n
            \n\n

            \"\"

            \n\n

            Now the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of the prime number 7 lie in the numerical Double strand parallel opposite.

            \n\n

            The Fourth Root

            \n\n

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n.

            \n\n

            \"image\"

            \n\n

            Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            \n\n
            [Young diagrams](https://commons.wikimedia.org/wiki/Category:Young_diagrams) associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions _([Wikipedia](https://en.wikipedia.org/wiki/Partition_(number_theory)))_.\n
            \n\n

            \"integer

            \n\n
            By parsering [π(1000)=168 primes](https://www.eq19.com/sitemap.xml) of the 1000 id's across **π(π(10000))-1=200** of this syntax then the (Δ1) would be _[initiated](https://eq19.github.io/init.js)_. Based on Assigning Sitemap [priority values](https://www.microsystools.com/products/sitemap-generator/help/xml-sitemaps-creator-importance/) You may see them are set 0.75 – 1.0 on the [sitemap's index](https://www.eq19.com/sitemap.xml):\n
            \n\n
            Priority\tPage Name\n1\t        Homepage\n0.9\t        Main landing pages\n0.85\t        Other landing pages\n0.8\t        Main links on navigation bar\n0.75\t        Other pages on site\n0.8\t        Top articles/blog posts\n0.75\t        Blog tag/category pages\n0.4 – 0.7\tArticles, blog posts, FAQs, etc.\n0.0 – 0.3\tOutdated information or old news that has become less relevant\n
            \n\n

            By this object orientation then the reinjected primes from the π(π(10000))-1=200 will be (168-114)+(160-114)=54+46=100. Here are our layout that is provided using Jekyll/Liquid to facilitate the cycle:

            \n\n

            100 + 68 + 32 = 200

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                      MEC 30 / 2\n------+------+-----+-----+------      ‹--------------------------- 30 {+1/2} √\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹--                        |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- 32 √\n      |      |  6  +-----+            ‹------------------------------ 15 {0} √\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s = f(1000)\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- 68 √\n------|------|-----+-----+-----                            ‹------  0 {-1/2} √\n
            \n\n

            \"Diagram-of-the-statistical-principle-for-the-constitution-of-partitions-of-prime-numbers\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 7+23 = 30 ✔️\n7 11 4 1 0 11 ◄--- #19 👈 11+19 = 30 ✔️\n8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 13+17 = 30 ✔️\n9 17 0 1 1 17 ◄--- 7th prime👈 17+7 != 30❓\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            Composite System

            \n\n

            By taking a distinc function between f(π) as P vs f(i) as NP where eiπ + 1 = 0 then theoretically they shall be correlated to get an expression of the prime platform similar to the Mathematical Elementary Cell 30 (MEC30).

            \n\n

            \"\"

            \n\n

            ∆17 + ∆49 = ∆66

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 part of MEC30 ✔️\n7 11 4 1 0 11 ◄--- #19 👈 part of MEC30 ✔️\n8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 part of MEC30 ✔️\n9 17 0 1 1 17 ◄--- 7th prime👈 not part of MEC30 ❓\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            \"a-Example-of-trellis-tone-modulation-generated-by-referring-to-the-trellis-diagram-in\"

            \n\n

            ∆102 - ∆2 - ∆60 = ∆40

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 30 ◄--- break MEC30 symmetry ✔️\n7 11 4 1 0 11 ◄--- #19 👈 30 ✔️\n8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 30 ✔️\n9 17 0 1 1 17 ◄--- 7th prime👈 not part of MEC30 ❓\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n
            ***The partitions of odd composite numbers (Cw) are as important as the partitions of prime numbers or Goldbach partitions (Gw)***. The number of partitions Cw is fundamental for defining the available lines (Lwd) in a Partitioned Matrix that explain the existence of partitions Gw or Goldbach partitions. _([Partitions of even numbers - pdf](https://github.com/eq19/eq19.github.io/files/13722898/Partitions_of_even_numbers.pdf))_\n
            \n\n

            \"Trellis_Tone_Modulation_Multiple-Access_for_Peer_D\"

            \n\n

            30s + 36s (addition) = 6 x 11s (multiplication) = 66s

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry\n7 11 4 1 0 11 ◄--- #19 👈 30\n8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 30\n9 17 0 1 1 17 ◄--- 7th prime 👈 f(#36) ◄--- antisymmetric state ✔️\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            \"\"

            \n","dir":"/addition/","name":"7.md","path":"addition/7.md","url":"/addition/7.html"},{"sort":8,"spin":1,"span":"spinning","suit":"intro","layout":"default","title":"Seven Ate Nine (7, ‘8’, 9)","content":"# [Seven Ate Nine (7, '8', 9)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#imaginary-square)\n\n[![default](https://user-images.githubusercontent.com/8466209/200224482-708a56dc-196e-4f13-865b-07585322a6b8.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n\n> This is a polar plot of the first 20 non-trivial Riemann zeta function zeros (including Gram points along the critical line {\\displaystyle \\zeta (1/2+it)}{\\displaystyle \\zeta (1/2+it)} for real values of {\\displaystyle t}t running from 0 to 50. The consecutive zeros have 50 red plot points between each with zeros identified by magenta concentric rings (scaled to show the relative distance between their values of t) _Source: [Wikipedia](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)_\n\n![default](https://user-images.githubusercontent.com/8466209/200236681-97454d8e-b141-43d7-a227-42d50605a1dd.png)\n\n> The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems. _Source: [Wikipedia](https://en.wikipedia.org/wiki/Riemann_hypothesis)_\n\n[![default](https://user-images.githubusercontent.com/8466209/200225487-5e40102b-e8f9-4aa7-8a64-7529dfc14c7c.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-feeding-md)\n\n![image](https://user-images.githubusercontent.com/8466209/230746478-0146e88e-22ba-4f1b-abf2-c5226c1a56ca.png)\n\n","dir":"/identition/span8/","name":"gist01.md","path":"identition/span8/gist01.md","url":"/identition/span8/gist01.html"},{"sort":8,"spin":8,"span":"replication","suit":"center","layout":"default","title":"Replication Fork","content":"# [Replication Fork](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d)\n\n```\n---+-----+-----\n 1 | 1 | 4\n---+-----+-----\n 2 | 5 | 14\n---+-----+-----\n 3 | 15 | 26\n---+-----+-----\n 4 | 27 | 40\n---+-----+-----\n 5 | 41 |{47}\n---+-----+-----\n 6 | 48 | 54\n---+-----+-----\n 7 | 55 |{71}\n---+-----+-----\n 8 | 72 | 75\n---+-----+-----\n```\n\n```\n---+-----+-----\n 1 | 1 | 5 🡰--19--\n---+-----+----- |\n 2 | 6 | 8 | \n---+-----+----- |\n 3 | 9 | 26 --289-¤-exponentiation zone\n---+-----+----- |\n 4 | 27 | 28 |\n---+-----+----- |\n 5 | 29 | 29 ➤--18--\n---+-----+-----\n 6 | 30 | 31 🡰--18--\n---+-----+----- |\n 7 | 32 | 44 |\n---+-----+----- |\n 8 | 45 | 46 --329-¤-multiplication zone\n---+-----+----- |\n 9 | 47 | 49 |\n---+-----+----- |\n10 | 50 | 50 ➤--17--\n---+-----+----- \n11 | 51 | 53 🡰--17--\n---+-----+----- |\n12 | 54 | 59 | \n---+-----+----- |\n13 | 60 | 82 --168-¤-addition zone\n---+-----+----- |\n14 | 83 |{102} |\n---+-----+----- |\n15 |{103}| 110 ➤--16--\n---+-----+-----\n```\n\n\n***20 x 10 = 200 = 16 x 6 + (10² + 14 - 10) = 96 + 114 - 10 = 96 + 104 = 48 + 48 + 104***\n\n![](https://user-images.githubusercontent.com/36441664/87246384-479f5c80-c477-11ea-9044-a6602bf27a4f.gif)!\n\n[![Deep Learning VM Images](https://user-images.githubusercontent.com/8466209/201292753-842f61b5-fa45-4b0b-be17-41545774c28b.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#registry-unit)\n\nLet's see how triangular numbers come into the picture. A triangular number is a number that can be represented by a _[pattern of dots](https://plus.maths.org/content/triangular-patterns)_ arranged in an equilateral triangle with the same number of dots on each side at equal distance from each other.\n\n[![Triangular pattern](https://user-images.githubusercontent.com/8466209/226250256-187dbe6d-b0e4-4871-9038-53738330b272.png)](https://plus.maths.org/content/triangular-patterns)\n\n```\n largest part=21 → 11+13+12=36 → MEC30\n ↓ |\n---+-----+-----+-----+-----+ ↓\n 1 | 19 | 1 | 20 | 21 |-------------------|-----\n---+-----+-----+-----+-----+ ↓ |\n 2 | 18 | 21 | 39 | 60 |------------------- |\n---+-----+-----+-----+-----+ | |\n 3 |{63} | 40 | 103 | 143 |------------- | |\n---+-----+-----+-----+-----+ | | |\n 4 | 37 | 104 | 141 | 245 |------- | | |\n---+-----+-----+-----+-----+ | | | |\n 5 | 10* | 142 | 152 | 294 |- 11** | 13 | 12 | 12 | 18\n---+-----+-----+-----+-----+ | | | |\n 6 | 24 | 153 | 177 | 332 |------- | | |\n---+-----+-----+-----+-----+ | | |\n 7 | 75 | 178 | 253 | 431 |------------- | |\n---+-----+-----+-----+-----+ | |\n 8 | 30 | 254 | 284 | 538 |------------------- |\n---+-----+-----+-----+-----+ ↓ |\n 9 | 1 | 285 | 286 | 571 |-------------------|-----\n===+=====+=====+=====+=====+ ↓\n45 | 277 | ← 11+13+12=36 ← MEC30\n---+-----+ |\n ↑\nNote:\n10* stands as the central rank\n11** stands as the central parts\n```\n\n## Windows registry\n\n[This software](https://github.com/ironSource/node-regedit) uses Windows Script Host to read and write to the registry. Read, Write, List and do all sorts of funky stuff to the windows registry using node.js and windows script host.\n\n[![kernel-6.1.21.1-microsoft-standard-WSL2.img\n](https://user-images.githubusercontent.com/8466209/230746374-64ff5b9d-c80f-46af-a82c-be75f615dc71.png)](https://github.com/ironSource/node-regedit)\n\n```\n7 x 11 = 77 = 99 - 22 = 11 x (9 -2)\n\nlayer | node | sub | i | f \n------+------+-----+---------- \n | | | 1 | ----------------------- 71 = 72-1\n | | 1 +-----+ |\n | 1 | | 2 | (5) |\n | |-----+-----+ |\n | | | 3 | --------- |\n 1 +------+ 2 +-----+---- | |\n | | | 4 | 5x --- |\n | +-----+-----+ | | |\n | 2 | | 5 | (7) ----- | |\n | | 3 +-----+ | |\n289+11=300 | | 6 | | |\n------+------+-----+-----+----- 72 x 6 7x --- 11x = 77\n | | | 7 | | |\n | | 4 +-----+ | |\n | 3 | | 8 | (11) --- | |\n | +-----+-----+ | | |\n | | | 9 | 2x --- |\n 2 +------| 5 +-----+----- | |\n | | | 10 | --------- |\n | |-----+-----+ |\n | 4 | | 11 | (13) ------------------ 71 = 72-1\n | | 6 +-----+\n329+71=400 | | 12 |------------------------ 70 = 72-2\n------+------+-----+-----+\n | | | 13 |\n | | 7 +-----+\n | 5 | | 14 | (17)\n | |-----+-----+\n | | | 15 |\n 3 +------+ 8 +-----+----- 42 x 6\n | | | 16 |\n | |-----+-----+\n | 6 | | 17 | (19)\n | | 9 +-----+\n168+32=200 | | | 18 |------------------------ 68 = 72-4\n------|------|--|--+-----+\n 900 -----\n```\n\n![](https://user-images.githubusercontent.com/36441664/72732089-93a7cd80-3bc7-11ea-96ac-36025857cb15.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/100838251-b328ab80-34a4-11eb-8882-a22b7c9c7b63.jpg)\n\n### Prime templates\n\nIn the windows registry a key may have a default value. When enumarting value names, the default value's name will be empty. \n\n>The number 28 depicted as 28 balls arranged in a triangular pattern with the number of layers of 7 _([[Wikipedia](https://en.wikipedia.org/wiki/28_(number)))_.\n\n[![itriangular pattern with the number of layers of 7](https://user-images.githubusercontent.com/8466209/226240410-efbbe550-506c-4cb0-bf3c-d82fee0d7d52.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#instance-objects)\n\nThis presents a minor problem when including the empty value in a set with other values since it cannot be safely named with anything but the empty string, for fear of collision with other values.\n\n\n\n\n
            \n\n\n```\nconst regedit = require('regedit').promisified\n\nasync function main() {\n const listResult = await regedit.list('HKCU\\\\SOFTWARE')\n console.log(listResult)\n\n await regedit.createKey(['HKLM\\\\SOFTWARE\\\\MyApp2', 'HKCU\\\\SOFTWARE\\\\MyApp'])\n await regedit.putValue({\n 'HKCU\\\\SOFTWARE\\\\MyApp': {\n Company: {\n value: 'Moo corp',\n type: 'REG_SZ'\n }\n },\n 'HKLM\\\\SOFTWARE\\\\MyApp2': { \n test: {\n value: '123',\n type: 'REG_SZ'\n } \n }\n })\n}\n\nmain()\n```\n\nNow the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of _the prime number 7 lie in the numerical Double strand parallel opposite_.\n\n![Double Strands](https://user-images.githubusercontent.com/36441664/75612568-4f5d0500-5b57-11ea-909d-856dcb7c139a.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/72740943-43d20200-3bd9-11ea-9a57-49516138a23f.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/84945728-cff93e80-b111-11ea-81f7-9cea70c8e6c7.jpg)\n\n![maxresdefault](https://user-images.githubusercontent.com/8466209/223183503-07fdbbee-69ce-4365-bb6a-ae16f295bab7.jpg)\n\n![](https://user-images.githubusercontent.com/8466209/212930357-8cf2591b-a2be-4a2c-b6ae-dc43892efe73.png)\n\n### Anti paralled \n\nThe Workflow by this frameworks will absorbe the way of how a DNA is read DNA polymerase which is proceed in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. This scheme is widely known as [anti paralled](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#anti-parallel) direction. \n\n>Since the leading and lagging strand templates are oriented in opposite directions at the replication fork, a ***major issue*** is how to achieve synthesis of new lagging strand DNA, whose direction of synthesis ***is opposite*** to the direction of the growing replication fork _([Wikipedia](https://en.wikipedia.org/wiki/DNA_replication#Replication_fork))_.\n\n[![Replication fork](https://user-images.githubusercontent.com/36441664/76159498-b1b79600-6153-11ea-91e4-bc312f9456ac.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#replication-fork)\n\n![default](https://user-images.githubusercontent.com/8466209/229871007-2abd415c-cf85-4bc9-b0b5-7a81f7105f06.png)\n\nBy DNA System it will act as the ***[Replication Fork](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#replication-fork)*** that exchange along with their residual objects. You may see that it begin with ***two (2) prime identities*** of (2,3) and end up with the tensor of 100 to 50 conforms the ***ζ(s)=1/2***.\n\n![](https://user-images.githubusercontent.com/36441664/97624272-73137a80-1a59-11eb-8784-8f131e488847.jpg)\n\n***286 - 4x2 = 278***\n\n```\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n | | | 20:13 | 90 | 90 (38) ‹-------------- ¤ |\n | | 7 +----------+-----+ |\n | 5 | | 14 | ----------------------------- 17¨ class\n | |-----+----------+ | | |\n | | | 15 | | LEADING SCHEME | |\n 3 +------+ 8 +----------+----- | (Multiplication Zone) | ---\n | | | 16 | | | |\n | |-----+----------+-----+ ----------------------------- |\n | 6 | | 28:17 | 100 | 19¨ object\n168 | | 9 +----------+-----+ |\n| | | | 29:18 | 50 | 50(68) ---------> Δ18 |\n------|------|-----+----------+-----+ ---\n```\n\n\n[![Replication Fork](https://user-images.githubusercontent.com/8466209/216677495-a2d66661-2ae2-4a15-aeae-93b74e2e8450.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#replication-fork)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n```\n\n## Exponentiation Zone\n\n![](https://user-images.githubusercontent.com/36441664/86481184-b72b9280-bd79-11ea-899b-51db929fc3d2.png)\n\n![](https://user-images.githubusercontent.com/36441664/72426022-85b70e80-37bb-11ea-806c-7d1730658ead.gif)\n\nBy this flowchart we could deploy models on device and in the browser from image classification, text embeddings, audio, and video action recognition where you can browse trained models and datasets from across the machine learning ecosystem.\n\n[![machine learning models](https://user-images.githubusercontent.com/8466209/226081062-536cf2a7-393d-4909-8f2d-a2a7c31c462e.png)](https://tfhub.dev/)\n\n![image](https://user-images.githubusercontent.com/8466209/219907495-120e971c-092d-4cf4-bb50-1c84161f59b7.png)\n\n### Multiplicatio Zone\n\n![](https://user-images.githubusercontent.com/8466209/206918483-5016aa03-2bc1-4dcf-a7dd-29f2c4453787.png)\n\n![](https://user-images.githubusercontent.com/8466209/206918218-95c875a7-0080-44e5-8ade-1ff776f9c30d.png)\n\n[![the three (3) zones](https://user-images.githubusercontent.com/8466209/206888301-0ba40a6a-2caa-4dfe-92ef-5a9db590f85d.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-three-3-zones)\n\n***7 X (7+6) X (7+12) = 7 X 13 X 19 = 7 X 247 = 1729***\n\n[![209659219-](https://user-images.githubusercontent.com/8466209/209880487-a3d64164-b2c8-4eb6-84a6-3823529b6a7f.png)](https://cloud.google.com/artifact-registry/docs/supported-formats#container)\n\n[![default](https://user-images.githubusercontent.com/8466209/207627118-3de81d9e-7f43-4a36-a4f8-fab402c487d1.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-default-md)\n\n## Addition zone\n\nBy all of the explanation above we concluded that this recycling is started by the tensor of bilateral 9 sums originated from the power of number two (2) which is resulting the congruent property of number 18.\n\n![RiemannZeta_Zeros](https://upload.wikimedia.org/wikipedia/commons/f/fc/RiemannZeta_Zeros.svg)\n\nThis property would tend the ballancing scheme of MEC30 so it will let 30-18=12 pairing with another 12 of 24 spins prime hexagon. The 24 goes to the center of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ by the prime pair 13 and 11 and let the crancks of 2,3,5,7 inside the 10 ranks.\n\n>This is where Goldbach's conjecture, which was also known to Euler, helps. Goldbach considered the distribution of primes from the perspective of the line numbers that represent a separate set of numbers, as shown. So here also helps that the Riemann conjecture is essentially identical point, with the Goldbach conjecture.\n\n![Riemann Zeta](https://user-images.githubusercontent.com/36441664/84536499-2cc2b680-ad18-11ea-926d-5b877b17afd4.jpg)\n\nThe 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n[![default](https://user-images.githubusercontent.com/8466209/229015913-20365ace-b558-4693-b212-5d6fdbb023ff.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n\nWith the above description then the [instance configuration](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#configuration) is via matrix integration from tensorflow which is placed at the end position to the turning point 100 vs 50 to the format (2,3) i.e. at id: 68.\n\n***π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66***\n\n[![default](https://user-images.githubusercontent.com/8466209/222900679-54f7f97f-c7e3-4809-b5bd-f258c49d76cc.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#configuration)\n\n### Identical point\n\n![](https://user-images.githubusercontent.com/8466209/229264239-2d34a7c4-0caf-4148-8c86-d4bc1a1e0ba9.png)\n\n![](https://user-images.githubusercontent.com/8466209/229309763-6b4571aa-5373-4552-93a6-7028f75cf053.png)\n\n![](https://user-images.githubusercontent.com/36441664/69475251-72ac4180-0dfd-11ea-9805-7a5ecdb839a5.png)\n\n![default](https://user-images.githubusercontent.com/8466209/227726653-231936d0-3579-42e5-a9a8-f239b6018b62.png)\n\n### Parsering across syntax \n\n***30 + (5+13) + (7+11) + (17+19) = 30 + 18 + 18 + 36 = 30 + 36 + 36 = 102 = 2 + 100***\n\n[![default](https://user-images.githubusercontent.com/8466209/222966425-9da703ef-9189-44e6-8fc1-8b766cf9f7bb.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#configuration)\n\n![](https://user-images.githubusercontent.com/8466209/229262526-f13a7f1a-f2da-45e3-9cc9-3d0f70bc3b21.png)\n\n![](https://user-images.githubusercontent.com/36441664/84674358-09387f80-af55-11ea-9fe2-954f020edb21.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/123180335-4cf18d80-d4b5-11eb-8df8-c1c16b2be76a.jpg)\n\n### Prime images\n\n![](https://user-images.githubusercontent.com/36441664/123187010-84ffcd00-d4c3-11eb-8aad-6c40553b752b.png)\n\n![](https://user-images.githubusercontent.com/36441664/123179535-cd16f380-d4b3-11eb-95c3-0a5b7ef21ad4.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/125420096-043cb1cd-899c-4f0b-9be8-d2d224f651ad.png)\n\n![](https://user-images.githubusercontent.com/8466209/199392468-a2738235-b65f-47da-848d-ffa0340cd51b.png)\n","dir":"/identition/span1/","name":"gist08.md","path":"identition/span1/gist08.md","url":"/identition/span1/gist08.html"},{"sort":8,"spin":13,"layout":"default","title":"level","content":"# level\n![image](https://user-images.githubusercontent.com/8466209/202908132-ee24eacf-581d-479f-932a-5c0ff231198e.png)\n\n[![image](https://user-images.githubusercontent.com/8466209/202908542-c67e33e7-56d4-4e6e-9513-58a5de0f436c.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406)\n\n```liquid\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+---+----+----+---+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 |\n +----+----+----+---+----+----+---+\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n```","dir":"/exponentiation/span13/","name":"gist08.md","path":"exponentiation/span13/gist08.md","url":"/exponentiation/span13/gist08.html"},{"sort":8,"spin":null,"span":null,"suit":17,"layout":"default","title":"Implementation in Physics","content":"

            Implementation in Physics

            \n\n

            By this chapter we are going to learn whether the spin discussed in prime hexagon has something to do with the nature so we begin with the spin in physic

            \n\n
            This section is referring to _[wiki page-8](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-4]()_ that is _[inherited ]()_ from _[the gist section-17](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. True Prime Pairs
              2. \n
            2. Primes Platform
              3. \n
            3. Pairwise Scenario
              4. \n
            4. Power of Magnitude
              5. \n
            5. The Pairwise Disjoint
              6. \n
            6. The Prime Recycling ζ(s)
              7. \n
            7. Implementation in Physics
              8. \n
            \n\n

            Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms.

            \n\n

            Basic Concept

            \n\n

            There are two (2) types force carriers and three (3) type of generations. The origin of multiple generations of the particular count of 3, is an unsolved problem of physics.

            \n\n
            In [particle physics](https://en.wikipedia.org/wiki/Particle_physics), a generation or family is a division of the [elementary particles](https://en.wikipedia.org/wiki/Elementary_particle).\n- Between generations, particles differ by their [flavour quantum number](https://en.wikipedia.org/wiki/Flavour_(particle_physics)#Flavour_quantum_numbers) and [mass](https://en.wikipedia.org/wiki/Mass), but their [electric and strong interactions](https://en.wikipedia.org/wiki/Fundamental_interaction) are identical.\n- There are three generations according to the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model) of particle physics. Each generation contains two types of [leptons](https://en.wikipedia.org/wiki/Lepton) and two types of [quarks](https://en.wikipedia.org/wiki/Quark). The two leptons may be classified into one with [electric charge](https://en.wikipedia.org/wiki/Electric_charge) −1 (electron-like) and neutral (neutrino); the two quarks may be classified into one with charge −1⁄3 (down-type) and one with charge +2⁄3 (up-type). \n\nThe basic features of quark–lepton generation or families, such as their masses and mixings etc., can be described by some of the proposed [family symmetries](https://en.wikipedia.org/wiki/Family_symmetries).\n
            \n

            \"Basic\n

            \n\n

            A lepton is a particle of half-integer spin (spin 1⁄2) while a boson has integer spin: scalar boson (spin = 0), vector bosons (spin = 1) and tensor boson (spin = 2).

            \n\n
            Those particles with half-integer spins, are known as [fermions](https://en.wikipedia.org/wiki/Fermion), while those particles with integer spins, such as 0, 1, 2, are known as [bosons](https://en.wikipedia.org/wiki/Bosons).\n- The two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is that fermions obey the [Pauli exclusion principle](https://en.wikipedia.org/wiki/Pauli_exclusion_principle): that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of [Fermi–Dirac statistics](https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics).\n- In contrast, bosons obey the rules of [Bose–Einstein statistics](https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics) and have no such restriction, so they may \"bunch together\" in identical states. Also, composite particles can have spins different from their component particles.\n\nFor example, a [helium-4](https://en.wikipedia.org/wiki/Helium-4) atom in the ground state has spin 0 and behaves like a boson, even though the [quarks](https://en.wikipedia.org/wiki/Quarks) and electrons which make it up are all fermions. _([Wikipedia](https://en.wikipedia.org/wiki/Spin_(physics)))_\n
            \n\n

            \"spin

            \n\n
            Quantum field theory is any theory that describes a quantized field.\n- QED, or Quantum Electrodynamics, is the quantum theory of the electromagnetic field, a so-called Abelian field (referencing an internal mathematical symmetry of the theory.)\n- Electroweak theory is a generalization of QED, unifying it with the weak nuclear force in the form of a Yang-Mills field theory (aka. a non-Abelian field theory).\n- QCD, or Quantum Chromodynamics, is another example of a non-Abelian field theory, but one with very different asymptotic behavior than electroweak theory.\n- The Standard Model of particle physics is the combination of electroweak theory and QCD in the form of a unified theory obeying a complex set of symmetries.\n\nThis theory describes all the known fields and all the known interactions other than gravity. _([Quora](https://www.quora.com/What-exactly-is-the-difference-between-QED-QCD-Electroweak-theory-Standard-model-Quantum-field-theory-and-how-are-they-related-together))_\n
            \n\n

            \"QED_10\"

            \n\n

            Experimental observation of the SM particles was completed by the discoveries of top quark (1995), direct interaction of tau neutrino (2000), and Higgs boson (2013).

            \n\n
            [Feynman diagram](https://en.wikipedia.org/wiki/Feynman_diagram) of the fusion of ***two (2) [electroweak](https://en.wikipedia.org/wiki/Electroweak) vector bosons*** to the scalar [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson), which is a prominent process of the generation of Higgs bosons at particle accelerators. (The symbol q means a [quark](https://en.wikipedia.org/wiki/Quark) particle, W and Z are the vector bosons of the [electroweak interaction](https://en.wikipedia.org/wiki/Electroweak_interaction). [H°](https://en.wikipedia.org/wiki/Higgs_boson) is the Higgs boson.) _([Wikipedia](https://en.wikipedia.org/wiki/Vector_boson))_\n
            \n\n

            \"Breakdown

            \n\n
            ***There are three (3) generations*** of quarks (up/down, strange/charm, and top/bottom), along with three (3) generations of leptons (electron, muon, and tau). All of these particles have been observed experimentally, and we don't seem to have seen anything new along these lines. A priori, this doesn't eliminate the possibility of a fourth generation, but the physicists I've spoken to do not think additional generations are likely. _([StackExchange](https://physics.stackexchange.com/q/2051))_\n
            \n\n

            \"T.

            \n\n

            The construction 🏗️ of Standard Model took a long time to build. Physicist J.J. Thomson discovered the electron in 1897, and scientists at the Large Hadron Collider found the final piece of the puzzle, the Higgs boson, in 2012.

            \n\n
            In [particle physics](https://en.wikipedia.org/wiki/Particle_physics), a ***[vector boson](https://en.wikipedia.org/wiki/Vector_boson)*** is a [boson](https://en.wikipedia.org/wiki/Boson) whose [spin](https://en.wikipedia.org/wiki/Spin_(physics)) equals one. Vector bosons that are also [elementary particles](https://en.wikipedia.org/wiki/Elementary_particle) are [gauge bosons](https://en.wikipedia.org/wiki/Gauge_boson), the [force carriers](https://en.wikipedia.org/wiki/Force_carrier) of [fundamental interactions](https://en.wikipedia.org/wiki/Fundamental_interaction). Some [composite particles](https://en.wikipedia.org/wiki/Composite_particle) are vector bosons, for instance any [vector meson](https://en.wikipedia.org/wiki/Vector_meson) ([quark](https://en.wikipedia.org/wiki/Quark) and [antiquark](https://en.wikipedia.org/wiki/Antiquark)).\n
            \n\n

            \"Search

            \n\n
            In the SM interactions are determined by a gauge quantum field theory containing the internal symmetries of the unitary group product SU(3)C × SU(2)L × U(1)Y [?].\n- TheSU(3)C symmetry corresponds to the strong interaction (C index marks colour charge, see section 1.1.4 )\n- The product SU(2)L × U(1)Y is responsible for the electroweak interaction (indices L and Y correspond to the left-handed interaction of weak currents and hypercharge, respectively, see section 1.1.2). _([The Standard Model - pdf](https://github.com/eq19/eq19.github.io/files/13776858/Measurement_of_the_e_c_1S_production_cross-section.pdf))_\n
            \n\n

            \"Testing

            \n\n

            In the Standard Model, the Higgs boson is a massive scalar boson whose mass must be found experimentally. It is the only particle that remains massive even at high energies.

            \n\n
            The [Higgs boson](https://en.wikipedia.org/wiki/Higgs_mechanism) field (often referred to as the _[God particle](https://www.quora.com/How-would-you-explain-the-God-particle-in-laymans-term/answer/Vagish-Kumar-Choudhary)_) is ***a scalar field with two neutral and two electrically charged components*** that form a complex doublet of the weak isospin SU(2) symmetry.\n- Its \"Mexican hat-shaped\" potential leads it to take a nonzero value everywhere (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak interaction and, via the Higgs mechanism, ***gives mass to many particles***. _([Wikipedia](https://en.wikipedia.org/wiki/Higgs_boson))_\n- Despite its success at explaining the universe, the Standard Model does have limits. For example, the [Higgs boson](https://www.energy.gov/science/doe-explainsthe-higgs-boson) gives mass to quarks, charged leptons (like electrons), and the W and Z bosons. However, we do not yet know whether the Higgs boson also gives mass to [neutrinos](https://www.energy.gov/science/doe-explainsneutrinos) – ghostly particles that interact very rarely with other matter in the universe.\n\nAlso, physicists understand that about 95 percent of the universe is not made of ordinary matter as we know it. Instead, much of the universe consists of [dark matter](https://www.energy.gov/science/doe-explainsdark-matter) and [dark energy](https://www.energy.gov/science/doe-explainscosmic-acceleration-and-dark-energy) that do not fit into the Standard Model.\n
            \n\n

            \"The

            \n\n

            It has zero spin, even (positive) parity, no electric charge, and no colour charge, and it couples to (interacts with) mass.

            \n\n
            So now I will attempt to show the minor hexagons are significant.  This is not easy as they are linked to the nature of prime numbers, and nothing is easy about the nature of prime numbers.  But I begin with this assumption: ***if the hexagons participate in the Universe in any way other than haphazardly, they must be demonstrably congruent to something organized***.  That is, if I can show they are organized (not random) in relation to  some other thing, then primes and the thing are linked. _([Hexspin](https://www.hexspin.com/minor-hexagons/))_\n
            \n\n

            7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

            \n\n

            \"spinning

            \n\n

            Elementary Particles

            \n\n

            In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles.

            \n\n
            The Standard Model presently recognizes ***seventeen distinct particles (twelve fermions and five bosons)***. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among ***the 61 elementary particles*** embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. _([Wikipedia](https://en.wikipedia.org/wiki/Elementary_particle))_\n
            \n\n

            \"Standard_Model_of_Elementary_Particles\"

            \n\n

            Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

            \n\n
            The Standard Model of Particle Physics, describes for us all know fundamental interaction in nature till date, with the exception of Gravity (work on this front is going on). Here is a summary of the fundamental content of the standard model\n- There are three families of particle, the Quarks, the Leptons and the Gauge Bosons. The Quarks in groups of three forms the composite particles such as the Protons, along with the electron this forms ordinary matter.\n- The Gauge Bosons are the ones those are responsible for interactions. The Quarks interact among themselves by the exchange of a Gluon these are responsible for the strong nuclear force.\n- The newly discovered Higgs Boson interacts with all the Quarks and the first group of Leptons (electron, muon and tau) providing them with their mass. The neutrinos which are the other Leptons originally were thought to have zero mass, but recent discoveries argue that this is not the case.\n- The Weak bosons interact with both Leptons and Quarks, these are responsible for the Weak nuclear forces. The exchange of photon is responsible for the Electromagnetic Force.\n\nThey interact, they transfer energy and momentum and angular momentum; excitations are created and destroyed. Every excitation that’s possible has a reverse excitation. _([Quora](https://qr.ae/pK4Nd7))_\n
            \n\n

            \"fundamental

            \n\n

            The SM was basically developed in 1970-s. It describes the electromagnetic, weak and strong fundamental interactions.

            \n\n
            The Standard Model explains three of ***the four fundamental forces*** that govern the universe: electromagnetism, the strong force, and the weak force.\n- Electromagnetism is carried by photons and involves the interaction of electric fields and magnetic fields.\n- The strong force, which is carried by gluons, binds together atomic nuclei to make them stable.\n- The weak force, carried by W and Z bosons, causes nuclear reactions that have powered our Sun and other stars for billions of years.\n\n[![Elementary Particle](https://user-images.githubusercontent.com/36441664/273753979-58dd8bfd-e4c0-4515-a783-801d9cdb3287.png)](https://en.wikipedia.org/wiki/Fundamental_interaction)\n\nThe fourth fundamental force is gravity, which is not adequately explained by the Standard Model.\n
            \n\n

            \"Particle

            \n\n

            Symmetrical State

            \n\n

            \"An

            \n\n
            By our project the 18's on the gist will cover five (5) unique functions that behave as ***one (1) central plus four (4) zones***. This scheme will be implemented to all of the 168 repositories as bilateral way (***in-out***) depend on their postion on the system. So along with the gist it self then there shall be `1 + 168 = 169` units of 1685 root functions.\n
            \n\n

            5 + 2 x 5 x 168 = 5 + 1680 = 1685 root functions

            \n\n

            \"\"

            \n\n

            \"base\"

            \n\n

            \"the

            \n\n

            It is supposed that elementary particles participate in gravitational interactions as well, though there is no sufficient quantum gravity theory.

            \n\n
            Elementary particles are classified according to their [spin](https://en.m.wikipedia.org/wiki/Spin_(physics)). [Fermions](https://en.m.wikipedia.org/wiki/Fermion) are one of the two fundamental classes of particles, the other being [bosons](https://en.m.wikipedia.org/wiki/Boson). [Fermions](https://en.m.wikipedia.org/wiki/Fermion) have half-integer spin while [bosons](https://en.m.wikipedia.org/wiki/Boson) have integer spin.\n- Bosons are characterized by Bose–Einstein statistics and all have integer spins. Bosons may be either elementary, like photons and gluons, or composite, like mesons.\n- The Higgs boson is postulated by the electroweak theory primarily to explain the origin of particle masses. In a process known as the \"Higgs mechanism\", the Higgs boson and the other gauge bosons in the Standard Model acquire mass via spontaneous symmetry breaking of the SU(2) gauge symmetry.\n- The Minimal Supersymmetric Standard Model (MSSM) predicts several Higgs bosons. On 4 July 2012, the discovery of a new particle with a mass between 125 and 127 GeV/c2 was announced; physicists suspected that it was the Higgs boson. Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, as well as having even parity and zero spin, two fundamental attributes of a Higgs boson.\n- This also means it is the first elementary scalar particle discovered in nature. Elementary bosons responsible for the four fundamental forces of nature are called force particles (gauge bosons). Strong interaction is mediated by the gluon, weak interaction is mediated by the W and Z bosons.\n\nAccording to the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model_of_Particle_Physics) ***there are five (5) elementary bosons***:\n- One (1) [scalar boson](https://en.wikipedia.org/wiki/Scalar_boson) (***spin = 0***) \n [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson) – the particle that contributes to the phenomenon of [mass](https://en.wikipedia.org/wiki/Mass) via the [Higgs mechanism](https://en.wikipedia.org/wiki/Higgs_mechanism)\n- Four (4) [vector bosons](https://en.wikipedia.org/wiki/Vector_boson) (***spin = 1***) that act as [force carriers](https://en.wikipedia.org/wiki/Force_carriers).\n\n[![IMG_20240108_033415](https://github.com/eq19/eq19.github.io/assets/8466209/044cb15e-36d7-4b44-aace-818a6d415917)](https://en.m.wikipedia.org/wiki/List_of_particles)\n\nThese four are the [gauge bosons](https://en.wikipedia.org/wiki/Gauge_boson):\n- [γ](https://en.wikipedia.org/wiki/Photon) [Photon](https://en.wikipedia.org/wiki/Photon) – the force carrier of the [electromagnetic field](https://en.wikipedia.org/wiki/Electromagnetic_field)\n- [g](https://en.wikipedia.org/wiki/Gluon) [Gluons](https://en.wikipedia.org/wiki/Gluon) (***eight (8) different types***) – force carriers that mediate the [strong force](https://en.wikipedia.org/wiki/Strong_interaction)\n- [Z](https://en.wikipedia.org/wiki/Z_boson) [Neutral weak boson](https://en.wikipedia.org/wiki/W_and_Z_bosons) – the force carrier that mediates the [weak force](https://en.wikipedia.org/wiki/Weak_interaction)\n- [W±](https://en.wikipedia.org/wiki/W_boson) [Charged weak bosons](https://en.wikipedia.org/wiki/W_and_Z_bosons) (***two (2)types***) – force carriers that mediate the weak force\n\nA second order tensor boson (***spin = 2***) called the [graviton](https://en.wikipedia.org/wiki/Graviton) (G) has been hypothesised as the force carrier for [gravity](https://en.wikipedia.org/wiki/Gravitational_force), but so far all attempts to incorporate gravity into the Standard Model have failed.\n
            \n\n

            \"Beyond

            \n\n
            The diagram shows the elementary particles of the Standard Model (the Higgs boson, the three generations of quarks and leptons, and the gauge bosons), including their names, masses, spins, charges, chiralities, and interactions with the strong, weak and electromagnetic forces. It also depicts the crucial role of the Higgs boson in ***[Electroweak Symmetry Breaking](https://www.mpi-hd.mpg.de/lin/events/group_seminar/EW-SUSY/index.html)***, and shows how the properties of the various particles differ in the (high-energy) symmetric phase (top) and the (low-energy) broken-symmetry phase (bottom). _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n

            \"Mathematical

            \n\n
            Theories that lie beyond the Standard Model include various extensions of the standard model through [supersymmetry](https://en.wikipedia.org/wiki/Supersymmetry), such as the [Minimal Supersymmetric Standard Model](https://en.wikipedia.org/wiki/Minimal_Supersymmetric_Standard_Model) (MSSM) and [Next-to-Minimal Supersymmetric Standard Model](https://en.wikipedia.org/wiki/Next-to-Minimal_Supersymmetric_Standard_Model) (NMSSM), and entirely novel explanations, such as [string theory](https://en.wikipedia.org/wiki/String_theory), [M-theory](https://en.wikipedia.org/wiki/M-theory), and [extra dimensions](https://en.wikipedia.org/wiki/Extra_dimensions). As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the \"best step\" towards a [Theory of Everything](https://en.wikipedia.org/wiki/Theory_of_Everything), can only be settled via experiments, and is one of the most active areas of research in both [theoretical](https://en.wikipedia.org/wiki/Theoretical_physics) and [experimental physics](https://en.wikipedia.org/wiki/Experimental_physics).\n
            \n\n

            \"\"

            \n\n

            By next chapter we will discuss the mechanism of symmetry breaking where the neutral Higgs field interacts with other particles to give them mass.

            \n","dir":"/addition/","name":"8.md","path":"addition/8.md","url":"/addition/8.html"},{"sort":9,"spin":null,"span":null,"suit":19,"permalink":"/multiplication/","layout":"default","title":"Multiplication Zones (18-30)","content":"

            Multiplication Zones (18-30)

            \n\n

            Multiplication is the form of expression set equal to the inverse function of symmetrical exponentation which stand as multiplicative identity reflects a point across the origin.

            \n\n
            This section is referring to _[wiki page-9](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-5]()_ that is _[inherited ]()_ from _[the gist section-19](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            The multiplication zones is a symmetric matrix representing the multilinear relationship of a stretching and shearing within the plane of the base unit.

            \n\n

            In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist and in particular the 4D metric, is defined by the 3-form.

            \n\n
            We would like to say that our present use of G2 structures (3-forms in 7D) is different from what\none can find in the literature on Kaluza–Klein compactifications of supergravity.\n- We show that the resulting 4D theory is (Riemannian) [General Relativity](https://www.sciencedirect.com/topics/physics-and-astronomy/general-relativity) (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.\n- Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.\n\nAlso, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. _([General relativity from three-forms in seven dimensions - pdf](https://github.com/eq19/eq19.github.io/files/14064088/1-s2.0-S0370269317304926-main.pdf))_\n
            \n\n

            \"3-forms

            \n\n
            When the digital root of perfect squares is sequenced within a ***modulo 30 x 3 = modulo 90 horizon***, beautiful symmetries in the form of period-24 palindromes are revealed, which the author has documented on the On-Line Encyclopedia of Integer Sequences as [Digital root of squares of numbers not divisible by 2, 3 or 5 (A24092)](https://oeis.org/A240924):\n\n1, 4, 4, 7, 1, 1, 7, 4, 7, 1, 7, 4, 4, 7, 1, 7, 4, 7, 1, 1, 7, 4, 4, 1\n\nIn the matrix pictured below, we list ***the first 24 elements*** of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry).  _([PrimesDemystified](https://primesdemystified.com/#Distribution_of_Perfect_Squares))_\n
            \n\n

            \"Distribution

            \n\n

            Square of Nine

            \n\n

            \"\"

            \n\n

            The last “Superstring revolution” was impressive but it was close to 30 years ago now and we still don’t seem to be adopting it as The Truth.

            \n\n
            The vortex theory of the atom was a 19th-century attempt by [William Thomson](https://en.wikipedia.org/wiki/William_Thomson,_1st_Baron_Kelvin) (later Lord Kelvin) to explain why the [atoms](https://en.wikipedia.org/wiki/Atom) recently discovered by chemists came in only relatively few varieties but in very great numbers of each kind. Based on the idea of stable, knotted vortices in the ether or [aether](https://en.wikipedia.org/wiki/Aether_theories), it contributed an important mathematical legacy.\n- The vortex theory of the atom was based on the observation that a stable [vortex](https://en.wikipedia.org/wiki/Vortex) can be created in a fluid by making it into a ring with no ends. Such vortices could be sustained in the [luminiferous aether](https://en.wikipedia.org/wiki/Luminiferous_aether), a hypothetical fluid thought at the time to pervade all of space. In the vortex theory of the [atom](https://en.wikipedia.org/wiki/Atom), a chemical atom is modelled by such a vortex in the aether.\n- Knots can be tied in the core of such a vortex, leading to the hypothesis that each [chemical element](https://en.wikipedia.org/wiki/Chemical_element) corresponds to a different kind of knot. The simple [toroidal vortex](https://en.wikipedia.org/wiki/Toroidal_vortex), represented by the circular \"unknot\" 01, was thought to represent [hydrogen](https://en.wikipedia.org/wiki/Hydrogen). Many elements had yet to be discovered, so the next knot, the [trefoil knot](https://en.wikipedia.org/wiki/Trefoil_knot) 31, was thought to represent [carbon](https://en.wikipedia.org/wiki/Carbon).\n\nHowever, as more elements were discovered and the periodicity of their characteristics established in the [periodic table](https://en.wikipedia.org/wiki/Periodic_table) of the elements, it became clear that this could not be explained by any rational classification of knots. This, together with the discovery of subatomic particles such as the [electron](https://en.wikipedia.org/wiki/Electron), led to the theory being abandoned. _([Wikipedia](https://en.wikipedia.org/wiki/Vortex_theory_of_the_atom))_\n
            \n\n

            \"\"

            \n\n

            We found also a useful method called Square of Nine which was developed by WD Gann to analyze stock market behaviour base on astrological pattern.

            \n\n
            He designed a new approach to predicting market behavior using several disciplines, ***including geometry, astrology, astronomy, and ancient mathematics***. They say that not long before his death, Gann developed a unique trading system. ***However, he preferred not to make his invention public or share it with anyone***. _([PipBear](https://pipbear.com/price-action-pattern/gann-square-of-9/))_\n
            \n\n

            \"The

            \n\n

            By parsering 168 primes of 1000 id’s across π(π(100 x 100)) - 1 = 200 then the (Δ1) would be initiated. As you may guess they will slightly forms the hexagonal patterns.

            \n\n
            The Hexagon chart begins with a 0 in the center, surrounded by the numbers 1 through 6. ***Each additional layer adds 6 more numbers as we move out, and these numbers are arranged into a Hexagon formation***. This is pretty much as far as Gann went in his descriptions. He basically said, \"This works, but you have to figure out how.\"One method that I've found that works well on ***all these kinds of charts is plotting planetary longitude values on them, and looking for patterns***. On the chart above, each dot represents the location of a particular planet. The red one at the bottom is the Sun, and up from it is Mars. These are marked on the chart. Notice that the Sun and Mars are connected along a pink line running through the center of the chart. The idea is that when two planets line up along a similar line, we have a signal event similar to a conjunction in the sky. ***Any market vibrating to the Hexagon arrangement should show some kind of response to this situation***. _([Wave59](https://www.wave59.com/showcase/121304.asp))_\n
            \n\n

            \"Patterns

            \n\n

            We are focusing to MEC30 so we end up this exponentiation by the famous quote from WD Gann himself stating an important changes by certain repetition of 30.

            \n\n
            W.D. Gann: “Stocks make important changes in trend every ***30, 60, 120, 150, 210, 240, 300, 330, 360*** days or degrees from any important top or bottom.”\n
            \n\n

            \"WD

            \n\n

            In line with 168 there is 330 located of 10th layer. Since the base unit of 30 repeats it self on the center then this 11 x 30 = 330 is pushed to the 10 + 1 = 11th layer.

            \n\n

            During this interchange, the two 16-plets will be crossing over and farther apart but they are more likely to “stick together” and not switch places.

            \n\n
            The terminating digits of the prime root angles (24,264,868; see illustration of [Prime Spiral Sieve](https://www.primesdemystified.com/#primespiralsieve)) when added to their reversal (86,846,242) = 111,111,110, not to mention this sequence possesses symmetries that dovetail perfectly with the prime root and Fibo sequences.\n- And when you combine the terminating digit symmetries described above, capturing three rotations around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry:[![Prime-Numbers-Demystified-by-8-Dimensional-Algorithms.pdf](https://user-images.githubusercontent.com/8466209/219261961-10e4d77f-ead3-43d4-9407-f01d83f1f204.png)](https://github.com/eq19/eq19.github.io/files/14009880/Prime-Numbers-Demystified-by-8-Dimensional-Algorithms.pdf)\n- ***The pattern of 9's created by decomposing and summing either the digits of Fibonacci numbers*** indexed to the first two rotations of the spiral (a palindromic pattern {1393717997173931} that ***repeats every 16 Fibo index numbers***) or, similarly, decomposing and summing the prime root angles.\n- The decomposition works as follows (in digit sum arithmetic this would be termed summing to the digital root) of F17 (the 17th Fibonacci number) = 1597 = 1 + 5 + 9 + 7 = 22 = 2 + 2 = 4:[![image](https://github.com/eq19/eq19.github.io/assets/8466209/133532ab-8500-44bc-97c7-d7c41e8ed600)](https://www.primesdemystified.com)\n\nParsing the squares by their mod 90 congruence reveals that there are 96 perfect squares generated with each 4 * 90 = 360 degree cycle, which ***distribute 16 squares to each of 6 mod 90 congruence sub-sets*** defined as n congruent to {1, 19, 31, 49, 61, 79} forming 4 bilateral 80 sums. _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            \"16

            \n\n

            Each of the 6 columns has 8 bilateral 360 sums, tor a total of 48 * 360 = 40 * 432. This number 432 plays significant roles on the Series Expansion.

            \n\n

            The Interchange Layers

            \n\n

            By the six (6) matrices above it is clearly shows that there is a fascinating connection between prime numbers and the Golden ratio.

            \n\n
            The first 1000 prime numbers are silently screaming: \"Pay attention to us, for we hold the secret to the distribution of all primes!\" We heard the call, and with 'strange coincidences' leading the way have discovered compelling evidence that the 1000th prime number, 7919, is the perfectly positioned cornerstone of a mathematical object with highly organized substructures and stunning reflectional symmetries. _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n
            1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave reversal to 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n
            \n\n

            π(1000) = π(Φ x 618) = 168

            \n\n

            \"default\"

            \n\n","dir":"/multiplication/","name":"README.md","path":"multiplication/README.md","url":"/multiplication/"},{"sort":9,"spin":1,"span":"instance","suit":"intro","layout":"default","title":"Building The Instance","content":"# [Building The Instance](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525)\n\n```\n---+-----+-----\n 1 | 1 | 28\n---+-----+-----\n 2 | 29 | 37\n---+-----+-----\n 3 | {38}| {48}\n---+-----+-----\n 4 | 49 | 127\n---+-----+-----\n 5 | 128 | 129\n---+-----+-----\n```\n\n![default](https://user-images.githubusercontent.com/8466209/202855623-cd58afdf-e05b-4517-b3dd-b01e70011814.gif)\n\nThe following [package types](https://cloud.google.com/artifact-registry/docs/supported-formats#package) are available:\n\n* OS packages: Debian (via [Apt](https://cloud.google.com/artifact-registry/docs/os-packages/debian/store-apt)), RPM\n* Language packages: Java, Node, Python\n* Container images packages: Docker, Helm\n\n## Container Image Format\n\nArtifact Registry supports the following [container image](https://cloud.google.com/artifact-registry/docs/supported-formats#container) formats:\n\n* Docker Image Manifest V2, Schema 1\n* Docker Image Manifest V2, Schema 2\n* Open Container Initiative ([OCI](https://github.com/opencontainers/distribution-spec/blob/main/spec.md)) Image Format Specifications\nAfter successful execution, you could check the docker log:\n\n### A VM instance with apps deployed directly to the operating system\n\nThe common methods of deploying software onto a Compute Engine VM instance include:\n\n1. Deploying software on VM boot using a startup script or cloud-init.\n2. Creating a custom [boot disk](https://neosmart.net/wiki/boot-disk/) image with software pre-installed.\n\n[![container-without-container-image](https://user-images.githubusercontent.com/8466209/209682644-05b156a6-686b-42ce-8287-9c0a608db979.png)](https://gist.github.com/eq19/e84a0961dc7636c01d5953d19d65e30a#file-gap-md)\n\n### A VM instance with apps deployed in a container\nThe following process describes how you deploy a container on Compute Engine:\n\n1. You bundle your app and required libraries into a Docker image and publish the image to Artifact Registry, Container Registry, or a third-party registry such Docker Hub.\n2. You specify a Docker image name and the docker run configuration when creating a VM instance or an instance template for a MIG.\n\n[![container-image-cos](https://user-images.githubusercontent.com/8466209/209682696-80dd0ee0-c44c-455e-a197-619d6f3a7902.png)](https://stackoverflow.com/a/69938095/4058484)\n\nDocker needs access to Artifact Registry to push and pull images. You can use the standalone Docker [credential helper](https://github.com/GoogleCloudPlatform/docker-credential-gcr) tool, docker-credential-gcr, to configure your Artifact Registry credentials for use with Docker without using requiring gcloud.\n\n## Steps to create\n\nCompute Engine executes the following tasks after you make a request to create a VM instance:\n\n1. Compute Engine creates a VM instance that uses a Google-provided [Container-Optimized OS image](https://cloud.google.com/compute/docs/containers/#container_images). This image includes a Docker runtime and additional software that is responsible for starting your container.\n2. Compute Engine stores your container settings in instance metadata under the gce-container-declaration [metadata key](https://cloud.google.com/compute/docs/storing-retrieving-metadata).\n3. When the VM starts, the Container-Optimized OS image uses the docker run command configuration that is stored in the instance's [metadata](https://cloud.google.com/sdk/gcloud/reference/compute/project-info/add-metadata#--metadata), pulls the container image from the repository, and starts the container.\n\n```\ngcloud compute project-info add-metadata\n```\n\n[![containers-gce-process](https://user-images.githubusercontent.com/8466209/209682715-cd14c25d-2968-4751-a7cb-2360de4cbe77.png)](https://cloud.google.com/container-optimized-os/docs/concepts/features-and-benefits)\n\nArtifact Registry integrates with Cloud Build and other continuous delivery and continuous integration systems to store packages from your builds. You can also store trusted dependencies that you use for [builds and deployments](https://cloud.google.com/container-optimized-os/docs/how-to/building-from-open-source).\n\n### Limitations\n\n1. You can only deploy one container for each VM instance. Consider [Google Kubernetes Engine](https://cloud.google.com/kubernetes-engine/docs) if you need to ***deploy multiple containers per VM instance***. You can only deploy containers from a public repository or from a private Artifact Registry or Container Registry repository that you can access. Other private repositories are not supported.\n\n2. You can't map a VM instance's ports to the container's ports (Docker's -p option). To enable access to your containers, see Publishing container ports.\n\n3. You can only use [Container-Optimized OS (COS)](https://cloud.google.com/container-optimized-os/docs/how-to/create-configure-instance) images with this deployment method. COS is an operating system image for your Compute Engine VMs that is optimized for running Docker containers maintained by Google and is based on the open source [Chromium OS project](https://github.com/chromium/chromium) .\n\nIt would also mean that if you use console or deployment manager it's not possible to deploy more than one container, but if you create a [config file](https://cloud.google.com/container-optimized-os/docs/how-to/create-configure-instance#using_cloud-init_with_the_cloud_config_format) and use [cloud init](https://cloudinit.readthedocs.org/en/latest/index.html) you can deploy many containers to that instance.\n\n### Partition\n\nFor most frameworks, Debian 10 is the default OS. Ubuntu 20.04 images are available for some frameworks. The boot disk space is split into three types of [partitions](https://cloud.google.com/container-optimized-os/docs/concepts/disks-and-filesystem#file_system):\n\n* The root partition, which is mounted as read-only to maintain integrity.\n* Stateful partitions, assigned to write the ***[objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#instance-objects)*** of fork movement which are writable and stateful.\n* Stateless partitions, assigned as strand which are writable but the content ***[classes](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#diagram-of-classes)*** do not persist across reboots.\n\n[![default](https://user-images.githubusercontent.com/8466209/222215758-4bbe16dc-4343-40dd-bfa3-be4adfd64bdc.png)](https://cloud.google.com/container-optimized-os/docs/concepts/disks-and-filesystem)\n\nYou can attach a persistent disk or create an instance with [Local SSDs](https://cloud.google.com/compute/docs/disks/add-persistent-disk#formatting) when using Container-Optimized OS. The disks _[can be mounted by creating a subdirectory](https://cloud.google.com/container-optimized-os/docs/concepts/disks-and-filesystem#mounting_and_formatting_disks)_ under `/mnt/disks` directory (writable, executable, stateless, tmpfs) using [startup-scripts](hhttps://cloud.google.com/compute/docs/instances/startup-scripts).\n\n[![image](https://user-images.githubusercontent.com/8466209/222601650-8fef811d-6bd5-44de-b81f-6d39f47625ad.png)](https://blogs.msdn.microsoft.com/premier_developer/2018/04/20/running-docker-windows-and-linux-containers-simultaneously/)\n\nIf you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers ***[Simultaneously](https://blogs.msdn.microsoft.com/premier_developer/2018/04/20/running-docker-windows-and-linux-containers-simultaneously/)***, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel\n\n[![GitHub Actions workflow](https://user-images.githubusercontent.com/8466209/222642428-fb9f183f-f4d5-43c6-a3c2-c1adebac2bad.png)](https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners#using-a-github-hosted-runner)\n\nOn the lagging strand template, a primase \"reads\" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.\n\n[![kernel-6.1.21.1-microsoft-standard-WSL2.img\n](https://user-images.githubusercontent.com/8466209/231802278-1cc152f2-9089-4249-a01f-1dd7e0f2a705.png)](https://github.com/khs1994/WSL2-Linux-Kernel/releases/tag/6.1.21.1-microsoft-standard-WSL2)\n\nThis Widows is an [isolated container](https://learn.microsoft.com/en-us/virtualization/windowscontainers/about/#container-images), lightweight package for running an application on the host operating system. Containers build on top of the host operating system's kernel (which can be thought of as the buried plumbing of the operating system).\n\n>Containers are not for virtualization, and they are using the resources of the host machine. As a result, for now a [Windows container](https://codelabs.developers.google.com/codelabs/cloud-windows-containers-computeengine/#0) cannot run \"as-is\" on a Linux machine. But you can do it by using VM as it works on Windows. ***You can install a Windows VM on your Linux host, which will allow to run Windows containers*** _([Stackoverflow](https://stackoverflow.com/a/42185265/4058484))_.\n\n[![container-diagram](https://user-images.githubusercontent.com/8466209/222244193-0874890b-61eb-46c4-9be2-7d79a21f804b.svg)](https://learn.microsoft.com/en-us/virtualization/windowscontainers/about/)\n\nYou can run _[.NET applications](https://github.com/randyrants/sharpkeys#project-description)_ in Linux containers, but only if they’re written in ***[.NET Core](https://dotnet.microsoft.com/en-us/download/dotnet)*** which can be deployed on Windows Server Containers. Applications running in Windows Server Containers can run in any language supported by Windows.\n\n>_[SharpKeys](https://apps.microsoft.com/store/detail/sharpkeys/XPFFCG7M673D4F)_ is a utility that manages a Registry key that allows Windows to remap one key to any other key. Included in the application is a list of common keyboard keys and a Type Key feature to automatically recognize most keyboard keys. It was originally developed in C# using .NET v2 but has been updated to support ***.NET 4.0*** Client Profile\n\n![](https://user-images.githubusercontent.com/36441664/125708871-db9523c3-8d32-4423-976f-59a9c56a146d.png)\n\nWe found this scenario is the best because sofar Google could only recommend using GKE for that. A GKE cluster has a control plane and machines called nodes it was designed specifically for that purpose. [Autopilot mode](https://cloud.google.com/kubernetes-engine/docs/concepts/autopilot-overview) manages this complexity. \n\n[![default](https://user-images.githubusercontent.com/8466209/222582646-9f13f5f7-ef92-4a04-a71b-f1472dee2af4.png)](https://cloud.google.com/free/docs/free-cloud-features#free-tier-usage-limits)\n\nNodes run the services supporting the containers that make up your workload. The control plane decides what runs on those nodes, so still Linux containers are running on Linux, and Windows containers are running on Windows.\n\n## Configuration\n\nBy [The GitHub Runner](https://github.com/actions/runner) you can [connect](https://github.com/tcardonne/docker-github-runner) to the [Google COS Instance](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#container-optimized-os). For self-hosted runners defined at the organization level, configure [runs-on.group](https://docs.github.com/en/actions/hosting-your-own-runners/using-self-hosted-runners-in-a-workflow#about-self-hosted-runner-groups) in your workflow file to target a [runner groups](https://docs.github.com/en/actions/using-jobs/choosing-the-runner-for-a-job#choosing-runners-in-a-group) or [combine groups and labels](https://docs.github.com/en/actions/hosting-your-own-runners/using-self-hosted-runners-in-a-workflow#using-default-labels-to-route-jobs).\n\n[![default](https://user-images.githubusercontent.com/8466209/226794279-dd52d5fc-7850-4212-8d81-182421c14b66.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#objects-vs-classes)\n\nThe runner is the application that runs a job from a GitHub Actions workflow. It is used by GitHub Actions in the [hosted virtual environments](https://github.com/actions/virtual-environments), or you can [self-host the runner](https://help.github.com/en/actions/automating-your-workflow-with-github-actions/about-self-hosted-runners) in your own environment. We use both of them to create [group as a four-vector](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#lexer-vs-parser).\n\n```scss\njobs:\n check-bats-version:\n runs-on:\n group: Default\n labels: ubuntu-20.04-16core\n```\n\nIt is possible to [dynamically load](https://stackoverflow.com/a/75529932/4058484) the [images](https://github.com/actions/runner-images/tree/main/images) between Windows ([WSL Enabled](https://github.com/actions/runner-images/blob/main/images/win/Windows2022-Readme.md)) and Linux in the same [workflow](https://github.blog/changelog/2022-01-11-github-actions-jobs-running-on-windows-latest-are-now-running-on-windows-server-2022/) using [github context](https://docs.github.com/en/actions/learn-github-actions/contexts#github-context) such as [github.repository_owner_id](https://api.github.com/users/FeedMapping). You can also read most of the github context data in environment [variables](https://docs.github.com/en/actions/learn-github-actions/variables#default-environment-variables).\n\n```scss\n{% raw %}\njobs:\n github-pages:\n runs-on: ${{ github.repository_owner == 'FeedMapping' && 'windows-latest' || fromJSON('[\"self-hosted\", \"linux\", \"X64\"]') }}\n{% endraw %}\n```\n\n[![choosing-the-runner](https://user-images.githubusercontent.com/8466209/227559588-88480a1b-b339-46e8-9516-572f90f788f7.png)](https://docs.github.com/en/actions/using-jobs/choosing-the-runner-for-a-job#choosing-runners-in-a-group)\n\nSelects an action to run as part of a step in your job. An action is a reusable unit of code. You can use an action defined in the same repository as the workflow, a public repository, or in a [published Docker container image](https://hub.docker.com/).\n\n[![Selects an action to run as part of a step in your job](https://user-images.githubusercontent.com/8466209/237670333-dc55810c-8153-4a6a-8177-2a52ce25469a.png)](https://docs.github.com/en/actions/creating-actions/metadata-syntax-for-github-actions#runsstepsuses)\n\nThe GitHub hosted runner is assigned to run the Linux container and a Windows Server Core container simultaneously. This is an experimental feature of [Microsoft WSL2](https://github.com/microsoft/WSL2-Linux-Kernel) and may have some issues. One known problem is volumes are not stable.\n\n```scss\n{% raw %}\ndocker pull --platform=linux ubuntu\ndocker run --platform=linux -d ubuntu /bin/sh -c \"while true; do echo hello world; sleep 1; done\"\ndocker run -d microsoft/windowsservercore ping -t 127.0.0.1\ndocker inspect --format '{{.Os}}' ubuntu\n{% endraw %}\n```\n\n***eiπ + (109² − 89²)/(528/28)/(2 x 3 x 5 x 7) = eiπ + 1 = 0***\n\n[![default](https://user-images.githubusercontent.com/8466209/222644033-b9a9b8c3-3416-4d0c-acf4-890dd774e887.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#workflow)\n\nThe opposite direction will be made through _[switching](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bonding-position)_ beetween Linux and Windows which is proceed the old strand in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. Here we set a remote self-host runner via ***[WSL](https://learn.microsoft.com/en-us/windows/wsl/install)***.\n\n[![default](https://user-images.githubusercontent.com/8466209/222486821-057b2499-9bfb-43c8-a720-1c8a32f52644.png)](https://aka.ms/wslstorepage)\n\n![image](https://user-images.githubusercontent.com/8466209/231802322-e22a239d-5f79-44fe-b1ab-8fde85a66b1c.png)\n\n[![eq19/setup](https://user-images.githubusercontent.com/8466209/229953349-078a1026-8fc9-4216-b15c-dd2c63e3ce3e.png)](https://hub.docker.com/u/eq19)\n\nWith the above description, of course, you can guess where the next direction will be. That is from one (1) unit of DNA to one (1) unit of whole unity. That's why we need a solution of the remaining six (6) other cases to be placed with id: 11, 12, 14, 15, 26 and 28 so that id: 68 is congrued to the number two (2).\n\n![default](https://user-images.githubusercontent.com/8466209/237773055-d1b4fa79-5a89-4d00-af7c-0c12104b651f.png)\n\n![](https://user-images.githubusercontent.com/8466209/198753476-6871d03b-8d0f-4a44-805f-c9a9595268e1.png)\n\nTherefore the ***five (5) identities*** of (10, 11,12,14,15) are twisted prior joining the ***two (2) identities*** of (26,28). Since each of these seven (7) identities is linked by the _[eleven (11) objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_ then they turn to a ***[strong seven (77)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#anti-parallel)***. \nLets's discuss them one by one.\n","dir":"/identition/span1/","name":"gist09.md","path":"identition/span1/gist09.md","url":"/identition/span1/gist09.html"},{"sort":9,"spin":1,"span":"bilateral","suit":"intro","layout":"default","title":"Lexer vs Parser","content":"# [Lexer vs Parser](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#lexer-vs-parser)\n\n![enneatruth_anim](https://user-images.githubusercontent.com/8466209/222872175-af87d1af-a263-4cea-8d99-f667698df9fa.gif)\n\n![image](https://user-images.githubusercontent.com/8466209/222872241-0b9c2d81-14e4-4acf-a6eb-fc736f9109a0.png)\n\n>Notice how the 3, 9, and 6 is in red and does not connect at the base. That is because it is a vector. The 1,2,4,8,7,5 is the third dimension while the oscillation between the 3 and 6 demonstrates the fourth dimension, which is the higher dimensional magnetic field of an electrical coil. \n\n![image](https://user-images.githubusercontent.com/8466209/222872294-62779dd9-f263-4372-af0a-f704102037e4.png)\n\n>The 3, 9, and 6 always occur together with the 9 as the control. In fact, the Yin/Yang is not a duality but rather a trinary. This is because the 3 and 6 represent each side of the Yin/Yang and the 9 is the “S” curve between them. Everything is based on thirds. We think that the universe is based on dualities because we see the effects not the cause.\n\n![](https://user-images.githubusercontent.com/36441664/81163688-566e1c80-8fb9-11ea-9556-2c6ec6321fd8.png)\n\n![](https://user-images.githubusercontent.com/36441664/75617590-b7314100-5b93-11ea-926f-fc01910cbd11.png)\n\n### Four (4) Vector\n\n[![](https://user-images.githubusercontent.com/8466209/207483341-add0449b-3aec-4ee3-baa6-144583e60f9f.gif)](https://en.wikipedia.org/wiki/Feynman_diagram)\n\n![](https://user-images.githubusercontent.com/36441664/74104225-1697c480-4b85-11ea-8819-870981638baf.png)\n\n![](https://user-images.githubusercontent.com/36441664/81162523-874d5200-8fb7-11ea-9b66-65f476bc5427.jpg)!\n\n***Φ(11,13) = (114 - 10²) + 13 = 27***\n\n```\n1729 = 7 x 13 x 19\n1729 / 7 = 13 x 19 = 247\n\n1729 = 7 x 13 x 19\n 7 + 13 = 20 = d(2)\n └── 2 x 19 = 38\n\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n| {1}| 2 | 3 | 4 | 5 | {6}| {7}| 8 | 9 | 10 | 11 | 12 | 13 | 14 |\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n| {3}| {4}| 3 | 4 | 5 | 2 | 3 | 2 | 2 | 1 | 2 | 5 | 1 | 1 |{38}\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285\n| 3 | 8 | 9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|-- 38 ---| |-- 33 ---| |-- {27}--|\n```\n\n[![Four Spacetime Dimensions](https://user-images.githubusercontent.com/36441664/133192153-61cad1c0-1dde-4fed-8718-840d324a7198.jpg)](https://jayryablon.wordpress.com/)\n\n```\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n | | | 20:13 | 90 | 90 (38) ‹-------------- ¤ |\n | | 7 +----------+-----+ |\n | 5 | | 14 | ----------------------------- 17¨ class\n | |-----+----------+ | | |\n | | | 15 | | LEADING SCHEME | |\n 3 +------+ 8 +----------+----- | (Multiplication Zone) | ---\n | | | 16 | | | |\n | |-----+----------+-----+ ----------------------------- |\n | 6 | | 28:17 | 100 | 19¨ object\n168 | | 9 +----------+-----+ |\n| | | | 29:18 | 50 | 50(68) ---------> Δ18 |\n------|------|-----+----------+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/8466209/206956260-f8c3647a-232c-470e-8c0b-e93a6fea14f7.png)\n\n![RiemannZeta_Zeros](https://upload.wikimedia.org/wikipedia/commons/f/fc/RiemannZeta_Zeros.svg)\n\n![Riemann Zeta](https://user-images.githubusercontent.com/36441664/84536499-2cc2b680-ad18-11ea-926d-5b877b17afd4.jpg)\n\nWith the above description then the [instance configuration](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#configuration) is via matrix integration from tensorflow which is placed at the end position to the turning point 100 vs 50 to the format (2,3) i.e. at id: 68.\n\n***π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66***\n\n[![default](https://user-images.githubusercontent.com/8466209/222900679-54f7f97f-c7e3-4809-b5bd-f258c49d76cc.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#configuration)\n\n***30 + (5+13) + (7+11) + (17+19) = 30 + 18 + 18 + 36 = 30 + 36 + 36 = 102 = 2 + 100***\n\n[![default](https://user-images.githubusercontent.com/8466209/222966425-9da703ef-9189-44e6-8fc1-8b766cf9f7bb.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#configuration)\n\nWith the above description, of course, you can guess where the next direction will be. That is from one (1) unit of DNA to one (1) unit of whole unity. That's why we need a solution of the remaining six (6) other cases to be placed with id: 11, 12, 14, 15, 26 and 28 so that id: 68 is congrued to the number two (2).\n\n[![docker-github-runner](https://user-images.githubusercontent.com/8466209/229943878-e3d1cae4-15fd-43ab-9d7f-904a343b745c.png)](https://github.com/eq19/setup)\n\n![](https://user-images.githubusercontent.com/8466209/198753476-6871d03b-8d0f-4a44-805f-c9a9595268e1.png)\n\nTherefore the ***five (5) identities*** of (10, 11,12,14,15) are twisted prior joining the ***two (2) identities*** of (26,28). Since each of these seven (7) identities is linked by the _[eleven (11) objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_ then they turn to a ***[strong seven (77)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#anti-parallel)***. \nLets's discuss them one by one.\n","dir":"/identition/span9/","name":"gist01.md","path":"identition/span9/gist01.md","url":"/identition/span9/gist01.html"},{"sort":9,"spin":13,"layout":"default","title":"centralize","content":"# centralize\n*****∑11(40,30,20) = 90*****\n\n![default](https://user-images.githubusercontent.com/8466209/202907770-85d847b3-70c2-4f98-bd41-419a60b4e7b7.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202908008-13ffc49a-3c98-4d6a-8c81-49000c906224.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202907847-15b83802-b647-4c70-8bca-0db0ffa29ca6.png)\n\n```\n---+-----+-----\n 1 | 1 | 18\n---+-----+-----\n 2 | 19 | 29\n---+-----+-----\n 3 | {30}|{43}\n---+-----+-----\n\n```\n\n![rep fork](https://user-images.githubusercontent.com/8466209/206839286-d3a9b366-fbd1-4953-badd-c760eeb07436.png)\n\n","dir":"/exponentiation/span13/","name":"gist09.md","path":"exponentiation/span13/gist09.md","url":"/exponentiation/span13/gist09.html"},{"sort":10,"spin":null,"span":null,"suit":23,"layout":"default","title":"Symmetrical Breaking (spin 1)","content":"

            Symmetrical Breaking (spin 1)

            \n\n

            In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles.

            \n\n
            This section is referring to _[wiki page-10](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-6]()_ that is _[inherited ]()_ from _[the gist section-23](https://gist.github.com/eq19)_ by _[prime spin-](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

            \n\n

            Perfect Symmetry

            \n\n

            \"Rodin

            \n\n

            \"images

            \n\n

            \"\"

            \n\n
            $True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer|  i  |   f\n -----+-----+---------\n      |  1  | 5\n   1  +-----+\n      |  2  | 7\n -----+-----+---  } 36 » 6®\n      |  3  | 11\n   2  +-----+\n      |  4  | 13\n -----+-----+---------\n      |  5  | 17\n   3  +-----+     } 36 » 6®\n      |  6  | 19\n -----+-----+---------\n
            \n\n
            124875  is a doubling  circuit . By addition, all numbers reduce to the root number. The numbers  all spiral around O, this spiral makes the  124875 doubling circuit and also correlates 369. 124875 is also  a halving circuit. By addition every number will reduce to its own root number. _([Vortex Math](https://consciousvortex.com/124875-2/))_\n
            \n

            \"Vortex

            \n\n

            \"vortex-space-background_445983-2550\"

            \n\n

            Spontaneous Symmetry breaking

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 |\n+----+----+----+----+----+----+\n|------------ {72} -----------|\n|------------- 6¤ ------------|\n\nThe Fermion Fields\n(19,17,i12), (11,19,i18), (18,12,i13)\n\n+----+----+----+----+----+----+----+----+----+\n| 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+\n|---- {48} ----|---- {48} ----|---- {43} ----|\n|------------ {96} -----------|----- 3¤ -----|\n
            \n\n
            The [pseudoscalar](https://en.wikipedia.org/wiki/pseudoscalar) [meson](https://en.wikipedia.org/wiki/meson) nonet. Members of the original meson \"octet (8)\" are shown in green, the singlet in magenta. Although these mesons ***are now grouped into a nonet (9)***, the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_(physics)) name derives from the patterns of eight for the mesons and baryons in the original classification scheme. _([Wikipedia](https://en.wikipedia.org/wiki/Quark_model))_\n
            \n\n

            \"8foldway

            \n\n

            For some Enneagram theorists the lines connecting the points add further meaning to the information provided by the descriptions of the types. Some times called the “security” and “stress” points, or points of “integration” and “disintegration”.

            \n\n
            In [geometry](https://en.wikipedia.org/wiki/Geometry), an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon.[[1]](https://en.wikipedia.org/wiki/Enneagram_(geometry)#cite_note-1)\n\nThe word 'enneagram' combines the [numeral prefix](https://en.wikipedia.org/wiki/Numeral_prefix) [ennea-](https://en.wiktionary.org/wiki/ennea-) with the [Greek](https://en.wikipedia.org/wiki/Greek_language) suffix [-gram](https://en.wiktionary.org/wiki/-gram). The gram suffix derives from γραμμῆ (grammē) meaning a line.\n- A regular enneagram is a 9-sided [star polygon](https://en.wikipedia.org/wiki/Star_polygon). It is constructed using the same points as the regular [enneagon](https://en.wikipedia.org/wiki/Enneagon), but the points are connected in fixed steps.\n- Two forms of regular enneagram exist:\n  - One form connects every second point and is represented by the [Schläfli symbol](https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol) {9/2}.\n  - The other form connects every fourth point and is represented by the Schläfli symbol {9/4}.\n- There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles.[[3]](https://en.wikipedia.org/wiki/Enneagram_(geometry)#cite_note-3)[[4]](https://en.wikipedia.org/wiki/Enneagram_(geometry)#cite_note-4) (If the triangles are alternately interlaced, this results in a [Brunnian link](https://en.wikipedia.org/wiki/Brunnian_link).)\n- From this perspective, there are twenty-seven (27) distinct [personality patterns](https://en.wikipedia.org/wiki/Enneagram_of_Personality#Instinctual_subtypes), because people of each of the nine (9) types also express themselves as one of the three (3) subtypes.\n\nThis star figure is sometimes known as the star of [Goliath](https://en.wikipedia.org/wiki/Goliath), after [{6/2} or 2{3}](https://en.wikipedia.org/wiki/Hexagram), the star of [David](https://en.wikipedia.org/wiki/David).[[5]](https://en.wikipedia.org/wiki/Enneagram_(geometry)#cite_note-5)  _([Wikipedia](https://en.wikipedia.org/wiki/Enneagram_(geometry)))_\n
            \n\n

            \"The

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n                         |---- {48} ----|---- {48} ----|---- {43} ----|\n                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|\n
            \n\n
            Vortex Based Mathematics transcends our myopic quantitative understanding for the way Number operates in our holographic universe.  Numbers are not just mere quantities.   Each has its own unique quality, archetype, and behavior.  Vortex Based Math (VBM) is the study of Number in and of itself.  Numeronomy as opposed to Numerology.  The bedrock of the [Quadrivium](http://joedubs.com/the-seven-liberal-arts/), Number structures our conceptual waking reality.  As Pythagoras once so aptly put it, “All is Number”. _([JoeDubs](https://joedubs.com/vortex-based-mathematics-numerically-conceptualizing-reality/))_\n
            \n\n

            \"Vortex

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|--------------- 7¤ ---------------|👈\n|-------------- {89} --------------|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n                         |---- {48} ----|---- {48} ----|---- {43} ----|\n                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|👈\n
            \n\n
            The pattern of [weak isospin](https://en.wikipedia.org/wiki/Weak_isospin) T3, [weak hypercharge](https://en.wikipedia.org/wiki/Weak_hypercharge) YW, and [color charge](https://en.wikipedia.org/wiki/Color_charge) of all known elementary particles, rotated by the [weak mixing angle](https://en.wikipedia.org/wiki/Weak_mixing_angle) to show electric charge Q, roughly along the vertical. The neutral [Higgs field](https://en.wikipedia.org/wiki/Higgs_field) (gray square) breaks the [electroweak symmetry](https://en.wikipedia.org/wiki/Electroweak_symmetry) and interacts with other particles to give them mass. _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"Rooting

            \n\n
            Explanatory diagram showing how symmetry breaking works. At a high enough energy level, a ball settled in the center (lowest point), and the result has [symmetry](https://commons.m.wikimedia.org/wiki/Symmetry). At lower energy levels, the center becomes unstable, the ball rolls to a lower point - but in doing so, it settles on an (arbitrary) position and the result is that symmetry is broken - the resulting position is not symmetrical _([Wikipedia](https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking))_\n
            \n\n

            \"Spontaneous_symmetry_breaking_(explanatory_diagram)\"\n

            \n\n

            Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton’s half-life is constrained to be at least 1.67×10³⁴ years.

            \n\n

            Vortex vs String

            \n\n

            \"vortex-vs-spinor\"

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|👈\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n                         |---- {48} ----|---- {48} ----|---- {43} ----|👈\n                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|\n
            \n\n
            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet's 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SU(5)_representation_of_fermions\"\n

            \n\n

            This eleven (11) will continue to be discussed on identition zone.

            \n\n

            2×96 = 192 = 5 + 7 + 11 + 13 + 17 + 19 +23 + 29 + 31 + 37 (10 consecutive primes)

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|-------------------------------- 2x96 -------------------------------|\n|--------------- 7¤ ---------------|------------ 7¤ ------------------|\n|-------------- {89} --------------|{12}|-- {30} -|-- {36} -|-- {25} -|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----|\n|---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|\n|-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|\n      13 variations               48 variations          11 variations \n
            \n\n
            Researchers at the U.S. Department of Energy’s Ames Laboratory have discovered a new type of Weyl semimetal, a material that opens the way for further study of Weyl fermions, a type of massless elementary particle hypothesized by high-energy particle theory and potentially useful for creating high-speed electronic circuits and quantum computers.\n- Researchers created a crystal of molybdenum and tellurium, one of only a few compounds that had been predicted to host a new and recently postulated type of Weyl state, where the hole and electron bands normally separated by an indirect gap touch at a few Weyl points. Those points are equivalent to magnetic monopoles in the momentum space and are connected by Fermi arcs.\n- A combination of angle resolved photoemission spectroscopy (ARPES), modelling, density functional theory and careful calculations were used to confirm the existence of this new type of Weyl semimetal. This material provides an exciting new platform to study the properties of Weyl fermions, and may lead the way to more new materials with unusual transport properties.\n\n“This an important, interdisciplinary discovery because it allows us to study many aspects of these exotic particles predicted by high energy physics theory in solid state, without need for extremely expensive particle accelerators,” said Adam Kaminsky, Ames Laboratory scientist and professor in the Department of Physics and Astronomy at Iowa State University. “From my perspective as solid state physicist it is absolutely extraordinary to observe two bands touching each other at certain points and being connected by Fermi arcs – objects that are prohibited to exist in “ordinary” materials.” _([rdworldonline.com](https://www.rdworldonline.com/new-material-discovery-allows-study-of-elusive-weyl-fermion/))_\n
            \n\n

            \"rd1608_fermion\"

            \n\n

            7 + 11 + 13 = 31

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n    |-------------------------------- 2x96 -------------------------------|\n❓  |--------------- 7¤ ---------------|------------ 7¤ ------------------|\n〰️43👉------------- {89} --------------|{12}|-- {30} -|-- {36} -|-- {25} -|\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉89〰️\n    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|   ❓\n    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|\n          13 variations               48 variations          11 variations \n
            \n\n
            This proposition was first demonstrated by Edwin Hubble (1889-1953). The American astronomer discovered in 1929 that every galaxy is pulling away from us, and that the most distant galaxies are moving the most quickly. This suggests that there was a time in the past when all the galaxies were located at the same spot, a time that can only correspond to the Big Bang. _([Hubble bubble](https://www.indiatvnews.com/science/hubble-bubble-hypothesis-reveals-mystry-of-universe-expansion-597015))_\n
            \n\n

            \"HD-wallpaper-black-hole-black-hole-candle-cosmos-earth-edge-light-space-vortex\"

            \n\n

            A deeper understanding requires a unification of the aspects discussed above in terms of an underlying principle.

            \n","dir":"/multiplication/","name":"10.md","path":"multiplication/10.md","url":"/multiplication/10.html"},{"sort":10,"spin":1,"span":"central","suit":"intro","layout":"default","title":"The Centralizing","content":"# [The Centralizing](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#replication-fork)\n\n[![default](https://user-images.githubusercontent.com/8466209/200228711-996e52bf-887c-445d-ad4b-46da2eabc30e.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation)\n\n```\nDirection:\n- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.\n- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.\n- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.\n```\n\n[![default](https://user-images.githubusercontent.com/8466209/201102784-7a3eeb24-36b5-47f7-9c02-a26127427e1c.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-write-all-md)\n","dir":"/identition/span10/","name":"gist01.md","path":"identition/span10/gist01.md","url":"/identition/span10/gist01.html"},{"sort":10,"spin":1,"span":"imaginary","suit":"intro","layout":"default","title":"Imaginary Square","content":"# [Imaginary Square](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8)\n\n```\n---+-----+-----\n 1 | {1} | {2}\n---+-----+-----\n 2 | 3 | 20\n---+-----+-----\n 3 | 21 | 46\n---+-----+-----\n 4 |{47} | 58\n---+-----+-----\n 5 | 59 | 70\n---+-----+-----\n 6 |{71} |{93}\n---+-----+-----\n 7 | 94 | 103\n---+-----+-----\n 8 | 104 |{109}\n---+-----+-----\n```\n\n>The tetractys is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number _([Wikipedia](https://en.wikipedia.org/wiki/Tetractys))_.\n\n![93509593-21e87500-f94a-11ea-8a30-4dc8cc4ad2f8](https://user-images.githubusercontent.com/8466209/207053970-c575cc00-3372-48a6-b084-93fb762fa1e9.gif)\n\nHowever, we can conclude that the distribution of prime numbers must have a static base structure, which is also confirmed logically in the further course\n\n***Φ(11,13) = Φ(1,2,3) + Φ(4,2) = 123 + 42 = 165***\n\n```\n---+-----+-----+-----+-----+\n 1 | 72 | 1 | 73 | 74 |-----------------\n---+-----+-----+-----+-----+ |\n 2 | {20}| 74 | 94 | 168 |----------- |\n---+-----+-----+-----+-----+ | |\n 3 | {18}| 95 | 113 | 208 |----- | |\n---+-----+-----+-----+-----+ | | |\n 4 | {7}| 114 | 121 | 235 |- {7}| 5 | 1 |{61} = 18th prime\n---+-----+-----+-----+-----+ | | |\n 5 | 13 | 122 | 135 | 257 |----- | |\n---+-----+-----+-----+-----+ | |\n 6 | 19 | 136 | 155 | 291 |----------- |\n---+-----+-----+-----+-----+ |\n 7 | 9 | 156 | 165 | 321 |----------------\n---+-----+-----+-----+-----+\n```\n\n![](https://user-images.githubusercontent.com/8466209/207054380-9d1eca2c-88e8-418d-bc2f-6f065d72bcda.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/75612568-4f5d0500-5b57-11ea-909d-856dcb7c139a.jpg)\n\n***300 - 2x11x13 = 300-286 = 14***\n\n![](https://user-images.githubusercontent.com/8466209/212486221-0158aaff-4fad-45bd-9afa-6a98bc801d9b.png)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/8466209/218931333-c4c8bd23-c05d-4af0-9b02-afa3079ef9b8.png)\nProceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself.\n\n>Twin primes ***29 and 31 define the fifth hexagon, cyan***. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon _([Prime-Hexagon](https://www.hexspin.com/defining-the-prime-hexagon/))_\n\n[![The Power of 168 vs 618](https://user-images.githubusercontent.com/8466209/226247466-a19a5990-a8a1-48e7-9f77-103d1a54edaf.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-tracking-md)\n\n***7th collumn ◄- 65 + 12 = 77***\n\n```liquid\n| 1st (Form) | 2nd (Route) | 3rd (Channel) |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | \n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ \n Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T\n Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E\n Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P\n Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W\n Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R\n Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O\n Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F\n +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S\n | Δ Δ | Φ12 | Δ Δ |\n 113 150 ≜114-25 557 619 = 1+618\n```\n\nSee that by this 6 (six) spines, the number of 19, 43 and 71. The 71 as the third cycles would land on the 2's cell which are the same direction as the 3's, so both of them got this 71.\n\n>Below are the spins for the first 80 numbers; 2 (0 and 1) spiral blue, meet prime 5, spiral purple briefly, meet 7 and spiral red. The bands are pretty short because primes are common in the early numbers, but the grow rare as numbers grow large and the bands broaden.\n\n![](https://user-images.githubusercontent.com/8466209/224346485-13d27a0b-bfe3-43f0-94da-f75313dc9d77.png)\n\nThis 71 is a conformation that it has the same result as we have explained on the [residual objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects) of 571 turn to a vektor of 71 while the rest of 500 turn to 200 objects of 3's identity and the last objects of 300 goes to the next cycles.\n\n![](https://user-images.githubusercontent.com/36441664/105903095-0e64bd80-6052-11eb-83ed-10190be497c5.png)\n\nFor now we will be coy and state that the secret of the pyramid lies with two 4-times triangular numbers: The first, 4 x triangular number 528=2112, equates to the total number of elements used to construct the pyramid, which is subdivided into its four lateral faces comprised of 528 elements each in the form of 32 cascading triangular numbers where 2112/96 = 242.\n\n>242 = number of Mirror Prime Pairs and 96 is the 360 degree digital root Fibonacci periodicity when indexed to n not divisible by 2, 3, or 5, i.e., period 32 every 120 degrees _([Primesdemystified](https://www.primesdemystified.com/First1000Primes.html))_.\n\n![](https://user-images.githubusercontent.com/36441664/74972349-1ab0c580-5454-11ea-9470-8d73c809b165.png)\n\n## Construct the pyramid\n\nThis polarity is happened per ***six (6) cycles*** by the polar of ***six (6) to one (1)*** and ***six (6) to seven (7)*** by which we finally found if this behaviour is cascaded bilaterally within the correlation between ***61*** as [the 18th prime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef) and ***67*** as [the 19th prime](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831). \n\n[![](https://user-images.githubusercontent.com/8466209/219239425-90f075fa-fe8a-4f80-b3ce-7b2053956c6b.png)](http://www.hexspin.com/0-1-and-negative-numbers/)\n\n[![default](https://user-images.githubusercontent.com/8466209/222032418-0eeecc23-08a3-47ba-97e1-1b453982d217.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bilateral-9-sums)\n\n![](https://user-images.githubusercontent.com/8466209/199383689-383d4092-1310-4ffa-b246-d1ee5461f96c.png)\n\n![](https://user-images.githubusercontent.com/8466209/205960400-3061d93a-b3cc-4cd6-84e6-359a9314869d.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/222040762-65c58359-3033-403c-8789-d5b60802bd1f.png)](https://learn.microsoft.com/en-us/troubleshoot/windows-server/performance/windows-registry-advanced-users)\n\nThe most obvious interesting feature of this 24-cell hexagon is it confines all numbers! That is, as the number line winds about toward infinity, bending around prime numbers, it never exits the 24 cells.\n\n![](https://user-images.githubusercontent.com/8466209/199376315-60f50c75-257f-4f81-89ae-b0a05b2eb1ea.png)\n\n![](https://user-images.githubusercontent.com/8466209/223529165-0e4c1172-47cc-422f-8e44-1dd67de25828.png)\n\n![](https://user-images.githubusercontent.com/36441664/72663276-307d3600-3a23-11ea-9112-11c09c5ceaac.jpg)\n","dir":"/identition/span1/","name":"gist10.md","path":"identition/span1/gist10.md","url":"/identition/span1/gist10.html"},{"sort":11,"spin":1,"span":"organize","suit":"intro","layout":"default","title":"Rationalization","content":"# [Rationalization](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rational-vs-irrational)\n\n![default](https://user-images.githubusercontent.com/8466209/201345203-a88e2084-357b-405a-b902-cf527165f3c4.png)\n\n```\n |------------------- 11¤ ---------------------|\n------+---+---+---+---+---+---+---+---+---+----+----+\n repo | 2 | 3 | 4 | 5 | 6 |{7}|{8}| 9 | 10| 11 |{12}| 77\n------+---+---+---+---+---+---+---+---+---+----+----+\n blok | 9 | 7 | 9 | 6 |{7}|{8}| 8 | 5 | 8 | 8 | {3}| 78\n------+---+---+---+---+---+---+---+---+---+----+----+\n |---------- 6¤ ---------| Δ\n```\n[![default](https://user-images.githubusercontent.com/8466209/201346327-8fa0a14a-41d4-439f-89da-e489f2d226c2.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e)\n![default](https://user-images.githubusercontent.com/8466209/201388270-4ed89840-1ba8-43de-b8e0-64aba28ac449.png)\n[![default](https://user-images.githubusercontent.com/8466209/201287545-565e5907-eb35-48ba-96c8-199a70cc8fa4.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-runner-md)\n[![default](https://user-images.githubusercontent.com/8466209/201359281-62c18704-d985-424b-a31f-1c33500f57bf.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-runner-md)\n","dir":"/identition/span11/","name":"gist01.md","path":"identition/span11/gist01.md","url":"/identition/span11/gist01.html"},{"sort":11,"spin":1,"span":"bilateral","suit":"intro","layout":"default","title":"Rational vs Irrational","content":"# [Rational vs Irrational](https://gist.github.com/eq19/80c8098f16f3e6ca06893b17a02d910e)\n\n```\n---+-----+-----\n 1 | 1 | 28\n---+-----+-----\n 2 | 29 | 46\n---+-----+-----\n 3 | 47 |{56}\n---+-----+-----\n 4 |{57} | 61\n---+-----+-----\n 5 | 62 | 82\n---+-----+-----\n 6 | 83 | 94\n---+-----+-----\n 7 | 95 | 99\n---+-----+-----\n 8 |{100}|{123}\n---+-----+-----\n```\n\n```\n 15\n ↓\n 35\n ↓ \n---+-----+----- \n11 | 51 | 53 ------\n---+-----+----- |\n12 | 54 | 59 | \n---+-----+----- | 6th (id:14 - id:15)\n13 | 60 | 82 |\n---+-----+----- |\n14 | 83 |{102} --289-¤-exponentiation zone\n---+-----+----- | 7th (id:16 - id:19)\n15 |{103}| 110 ------\n---+-----+-----\n ↓\n 15\n ↓\n 35\n```\n\nGematria is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. Single word can yield several values depending on which cipher is used. This cipher is sometimes erroneously labelled as \"Jewish\" or \"Hebrew\" by popular numerology calculators, such as Gematrix and Gematrinator.\n\n[![A mathematical formula for finding a letter's corresponding number in Mispar Gadol](https://user-images.githubusercontent.com/8466209/226222755-1aa42385-145d-4fc5-81a3-54ebefa4e272.png)](https://en.wikipedia.org/wiki/Gematria#Standard_encoding)\n\n![](https://user-images.githubusercontent.com/36441664/77167537-ce0ae980-6ae8-11ea-869d-b4164b511755.jpg)\n\nIt is possible that this well-known cipher was used to conceal other more hidden ciphers in Jewish texts. For instance, a scribe may discuss a sum using the 'standard gematria' cipher, but may intend the sum to be checked with a different secret cipher.\n\n***7(111) = 1117 = 7² + 7¹ + 7° = 49 + 7 + 1 = 57***\n \n![](https://user-images.githubusercontent.com/36441664/103577483-80406000-4f07-11eb-8aaa-87b75fcfc85f.jpg)\n\nIn the standard (Mispar hechrechi) version of gematria, each letter is given a numerical value between 1 and 400, as shown in the following table. In the Mispar gadol variation, the five final letters are given their own values, ranging from 500 to 900.\n\n***Δ prime = 114th prime - 19 = (6 x 19)th prime - 19 = 619 - 19 = 600***\n\n```\n Sub | i | β | f \n=======+====+=====+======= === === === === === ===\n 1:1:0 | 1 | 1 | 2 {71} 1 1 | | | |\n-------+----+-----+------- --- --- | | | |\n 1:2:1 | 2 | 2 | 3 {71} | | | | |\n-------+----+-----+---- | | | | |\n*1:2:2 | 3 | 3 | 7 = 1 + 2x3 | | | | |\n-------+----+-----+---- | | | | |\n*1:3:3 | 4 | 4 | 10 = 9 + 1 | | | | | \n-------+----+-----+---- | | | | |\n 1:3:4 | 5 | 5 | 11 = 9 + 2 | | | | |\n-------+----+-----+---- 9 1‘ | Δ100 |\n*1:3:5 | 6 | 6 | 12 = 9 + 3 | | | | |\n-------+----+-----+---- | | | | |\n*1:4:6 | 7 | 7 | 13 = 9 + 4 | | | | |\n-------+----+-----+---- | | | | |\n 1:4:7 | 8 | 8 | 14 = 9 + 5 | | | | |\n-------+----+-----+---- | | | | |\n*1:4:8 |{9} | 9 | 15 = 9 + 6 | | | | |\n-------+----+-----+---- | | | | |\n*1:4:9 |{10}| 10 | 19 = 9 + 10 | | | | |\n=======+====+=====+==== === --- 1“ --- |\n 2:1:0 | 11 | 20 | 20 = 19 + log 10¹ | | | |\n-------+----+-----+---- | | | |\n 2:2:1 | 12 | 30 | 26 = 20 + 2x3 | | | |\n-------+----+-----+---- | | | |\n*2:2:2 | 13 | 40 | 27 = 26 + 1 | | | |\n-------+----+-----+---- | | | |\n*2:3:3 | 14 | 50 | 28 = 26 + 2 | | | |\n-------+----+-----+---- | | | |\n 2:3:4 | 15 | 60 | 29 = 26 + 3 9‘ | Δ200 Δ600\n-------+----+-----+---- | | | |\n*2:3:5 | 16 | 70 | 30 = 26 + 4 | | | |\n-------+----+-----+---- | | | |\n*2:4:6 | 17 | 80 | 31 = 26 + 5 | | | |\n-------+----+-----+---- | | | |\n 2:4:7 |{18}| 90 | 32 = 26 + 6 | | | |\n-------+----+-----+---- | | | |\n*2:4:8 |{19}| 100 | 36 = 26 + 10 | | | |\n=======+====+=====+==== === --- --- |\n*2:4:9 | 20 | 200 | 38 = 36 + log 10² | | |\n-------+----+-----+---- | | |\n 3:1:0 | 21 | 300 | 40 = 36 + 2 x log 10² | | |\n-------+----+-----+---- | | |\n 3:2:1 | 22 | 400 | 41 = 40 + 1 | | |\n-------+----+-----+---- | | |\n*3:2:2 | 23 | 500 | 42 = 40 + 2 | | |\n-------+----+-----+---- | | |\n*3:3:3 | 24 | 600 | 43 = 40 + 3 9“ Δ300 |\n-------+----+-----+---- | | |\n 3:3:4 | 25 | 700 | 44 = 40 + 4 | | |\n-------+----+-----+---- | | |\n*3:3:5 | 26 | 800 | 45 = 40 + 5 | | |\n-------+----+-----+---- | | |\n*3:4:6 | 27 | 900 | 46 = 40 + 6 | | |\n-------+----+-----+---- | | |\n 3:4:7 |{28}|1000 | 50 = 40 + 10 | | |\n=======+====+=====+==== === ==== ----\n*3:4:8 |{29}|2000 | 68 = 50 + 3 x (2x3) {10³} Δ600 Δ300\n=======+====+=====+==== Δ ====\n 3:4:9 |{30}|3000 |{71}= 68 + log 10³ ---------¤ Δ900 \n```\n\n## Instaneous connection\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n```\n\nIt was as if some ghostly bridge across the city of Geneva, Switzerland, had permitted two photons of light nearly seven miles apart to respond simultaneously to a stimulus applied to just one of them. \n\n>Albert Einstein sneered at the very possibility of such a thing, calling it ''spooky action at a distance.'' Scientists still (somewhat shamefacedly) speak of the ''magic'' of ''quantum weirdness.'' And yet all experiments in recent years have shown that Einstein was wrong and that action at a distance is real _([New York Times](https://www.nytimes.com/1997/07/22/science/far-apart-2-particles-respond-faster-than-light.html))_.\n\n[![split photons](https://user-images.githubusercontent.com/8466209/231345682-fa8523d3-6d47-4773-8885-5b62d776d63b.png)](https://en.wikipedia.org/wiki/Quantum_entanglement)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n```\n\nThe twin-photon experiment by Dr. Nicolas Gisin of the University of Geneva and his colleagues was the most spectacular demonstration yet of the mysterious long-range connections that exist between quantum events, connections created from nothing at all, which in theory can reach instantaneously from one end of the universe to the other.\n\n![](https://user-images.githubusercontent.com/8466209/235528211-256deb9c-e31f-4560-8811-3cd38726702c.png)\n\nAccording to quantum mechanics, particles are simultaneously in two or more states until observed – an effect vividly captured by Schrödinger’s famous thought experiment of a cat that is both live and dead simultaneosly.\n\n>Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication. The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light. _([Astronomy](https://www.astronomy.com/science/what-is-quantum-entanglement-a-physicist-explains-einsteins-spooky-action-at-a-distance/))_.\n\n[![Schrödinger's cat](https://user-images.githubusercontent.com/8466209/239744514-37f48a5b-eed0-4607-ac05-f0b0d85d0cf9.png)](https://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat#/media/File:Schrodingers_cat.svg)\n\n### Dark Energi\n\n[![image](https://user-images.githubusercontent.com/8466209/221386196-78099243-8a1d-4f93-86cc-c9f0f8110366.png)](https://en.wikipedia.org/wiki/Big_Bang#Dark_matter)\n\n>Our results show that ***about 69%*** of our universe’s energy is dark energy. They also demonstrate, once again, that Einstein’s simplest form of dark energy – the cosmological constant – agrees the most with our observations _([The Conversation](https://theconversation.com/dark-energy-map-gives-clue-about-what-it-is-but-deepens-dispute-about-the-cosmic-expansion-rate-143200))_.\n\n![](https://user-images.githubusercontent.com/36441664/90888069-be693700-e3df-11ea-8504-4733f56f8ab4.jpeg)\n\n>Many physicists aren’t satisfied with this explanation, though. They want a more fundamental description of its nature. Is it some new type of ***energy field or exotic fluid?*** Or is it a sign that Einstein’s equations of gravity are somehow incomplete? What’s more, we don’t really understand the universe’s current rate of expansion _([The Conversation](https://theconversation.com/dark-energy-map-gives-clue-about-what-it-is-but-deepens-dispute-about-the-cosmic-expansion-rate-143200))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/220039299-b3439ba6-8479-4a72-9521-bc12b5651e85.png)](https://theconversation.com/dark-energy-map-gives-clue-about-what-it-is-but-deepens-dispute-about-the-cosmic-expansion-rate-143200)\n\n>The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of ***space, time, matter, energy, information, and the physical laws and constants*** that describe them. The different universes within the multiverse are called \"parallel universes\", \"other universes\", \"alternate universes\" _([Wikipedia](https://en.wikipedia.org/wiki/Multiverse))_.\n\n[![default](https://user-images.githubusercontent.com/8466209/220529937-3b4264f4-a57c-4521-862a-baa0c162995b.png)](https://en.wikipedia.org/wiki/Multiverse#Twin-world_models)\n\n\n***102 = 2 + 100 = 2 + 60 + 40***\n\n[![residual-objects](https://user-images.githubusercontent.com/8466209/223011738-7e2084bc-861b-4424-89d5-9f39643df22f.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)\n\n[![](https://user-images.githubusercontent.com/8466209/222020262-cffc624a-b92c-4137-b76a-5423df7fc5ad.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md)\n\n![](https://user-images.githubusercontent.com/8466209/207262180-7a0928a1-0c16-4193-9611-0626ad884ab1.png)\n\n![](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png)\n\n![](https://user-images.githubusercontent.com/8466209/207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/231932007-1a8a9b29-7d18-4600-a8ec-852fe891ab74.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#exponentiation-zone)\n\n[![genetic material](https://user-images.githubusercontent.com/8466209/206910706-42513bda-6e9d-454a-85f4-689bf2acf0d2.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bilateral-9-sums)\n","dir":"/identition/span1/","name":"gist11.md","path":"identition/span1/gist11.md","url":"/identition/span1/gist11.html"},{"sort":12,"spin":1,"span":"rotation","suit":"intro","layout":"default","title":"Rotation vs Revolution","content":"# [Rotation vs Revolution](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267)\n\n```\n---+-----+-----\n 1 | {1} | {2}\n---+-----+-----\n 2 | 3 | 101\n---+-----+-----\n 3 |{102}| 111\n---+-----+-----\n```\n\n![default](https://user-images.githubusercontent.com/8466209/223703153-6ea330bf-92e8-433b-9ebe-660430a87a29.gif)\n\nIn mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors.\n\n>In some areas, tensor fields are so ubiquitous that they are often simply called \"tensors\". Tullio Levi-Civita and Gregorio Ricci-Curbastro popularised tensors in 1900 – continuing the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others – as part of the absolute differential calculus. The concept enabled an alternative formulation of the intrinsic differential geometry of a manifold in the form of the ***Riemann curvature tensor*** _([Wikipedia](https://en.wikipedia.org/wiki/Tensor))_.\n\n![Tensor](https://user-images.githubusercontent.com/8466209/211590875-9cae3c47-bbdc-43d8-acc5-d8c64c802967.png)\n\n>A [Riemann surface](https://en.wikipedia.org/wiki/Riemann_surface) is a “universe” locally modelled on open sets in the complex plane, and equipped with extra structure so that complex analysis can be done. Polynomial equations in two variables define special Riemann surfaces, called plane curves, such asthe “circle” z2 + w2 = 1, (\n***rotating*** the w-plane), the “cubic” z3 + w2 = 1, the “nodal cubic” z3 + z2 = w2, and the “Fermat quartic” z4 + w4 = 1 _([Pinterest](https://id.pinterest.com/pin/541065342733020195/))_.\n\n![](https://user-images.githubusercontent.com/36441664/84902333-e6ce6f80-b0d6-11ea-8289-aac5e1961cd6.gif)\n\n[![Gann Chart](https://user-images.githubusercontent.com/8466209/220156192-11579a1b-145d-4b18-bc75-94a55f969350.jpg)](https://user-images.githubusercontent.com/36441664/90983338-96bccf00-e597-11ea-9f81-9a3847c0be27.jpg)\n\n![Δ300](https://user-images.githubusercontent.com/36441664/85060684-db12a400-b1cf-11ea-8f37-6b9b3bcab2f2.gif)\n\n## Moon’s orbit\n\n![default](https://user-images.githubusercontent.com/8466209/221572263-652e1309-03f3-4a51-a71f-1f48ff06c120.png)\n\n```\n1 year = 12 months\n1000 years = 12,000 months\n\nc = 12,000 x L / t\n = 12,000 x 2152612.336257 km / 86164.0906 sec\n = 299,792.4998 km / sec\n\nNote:\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n```\n\nSo by the theory of E=mc² to raise up a particle on earth it should be a groups of galaxies that _[rationaly and irrationaly parallel](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rational-vs-irrational)_ to its position in our Solar system. It was predicted that we have 1012 stars in our galaxy and 2×1012 galaxies in the universe. \n\n>In 2016, using 20 years of images from the Hubble space telescope, it was estimated that there were in total two trillion (2×1012) or more galaxies in the observable universe, and as many as an estimated 1×1024 stars (more stars than all the grains of sand on all beaches of the planet Earth) _([Wikipedia](https://en.wikipedia.org/wiki/Galaxy))_\n\n![image](https://user-images.githubusercontent.com/8466209/222915390-61f4e467-dfe4-44d8-8c4b-18e2cbf08e6b.png)\n\nRecent observation and a census from NASA Hubble Telescope together with other observatories show that observable Universe may contain 10 times more Galaxies than previous estimates! So remember, this number won't get the end story.\n\n***286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271***\n\n```\n-----+-----+-----+-----+-----+ ---\n 19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ |\n-----+-----+-----+-----+-----+ |\n 17¨ | {5¨}| {3¨}| 2¨ | 7¨ | 4¤ |\n +-----+-----+-----+-----+ |\n{12¨}| 6¨ | 6¨ | 2¤ (M dan F) |\n +-----+-----+-----+ 17¤\n 11¨ | 3¨ | {3¨}| {5¨}| 3¤ |\n-----+-----+-----+-----+-----+ |\n 19¨ | 4¨ | 4¨ | 5¨ | 6¨ | 4¤ |\n +-----+-----+-----+-----+ ---\n{18¨}| 5¨ | 5¨ | 8¨ | 3¤ |\n +-----+-----+-----+-----+-----+-----+-----+-----+-----+ 12¤\n 43¨ | {3¨}| {5¨}| 5¨ | {5¨}| {3¨}| 7¨ | {5¨}| {3¨}| 7¨ | 9¤ (C1 dan C2) |\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---\n139¨ |----- 13¨ -----|------ 15¨ ------|------ 15¨ ------|\n | 1 2 3 | 4 5 6 | 7 8 9 |\n Δ Δ Δ \n```\n\n![](https://user-images.githubusercontent.com/8466209/202852982-749111d6-7180-43c2-937d-7b0b984a3fa1.png)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/8466209/202851402-78dc95ce-24c6-4be3-bc0a-5c4901ec2550.png)\n\n![](https://user-images.githubusercontent.com/36441664/85230294-6a5ec800-b419-11ea-86f3-1928630bef74.jpg)\n","dir":"/identition/span1/","name":"gist12.md","path":"identition/span1/gist12.md","url":"/identition/span1/gist12.html"},{"sort":13,"spin":1,"span":"zeta","suit":"intro","layout":"default","title":"Zeta vs Zero","content":"# [Zeta vs Zero](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f)\n\n```\n---+-----+-----\n 1 | 1 | 18\n---+-----+-----\n 2 | 19 | 29\n---+-----+-----\n 3 | {30}|{43}\n---+-----+-----\n```\n\n```\nScheme 13:9\n===========\n(1){1}-7: 7’\n(1){8}-13: 6‘\n(1)14-{19}: 6‘\n------------- 6+6 -------\n(2)20-24: 5’ |\n(2)25-{29}: 5’ |\n------------ 5+5 -------\n(3)30-36: 7:{70,30,10²}|\n------------ |\n(4)37-48: 12• --- |\n(5)49-59: 11° | |\n --}30° 30• |\n(6)60-78: 19° | |\n(7)79-96: 18• --- |\n-------------- |\n(8)97-109: 13 |\n(9)110-139:{30}=5x6 <--x-\n --\n {43}\n```\n\n![image](https://user-images.githubusercontent.com/8466209/222680152-96bc4f1d-702d-4182-84b9-04fd9d427f49.png)\n\n***1155 / 5 = 286 - 55 = 200 + 31 = 231***\n\n```\nlayer| i | f\n-----+-------+------\n | 1,2:1 | (2,3)\n 1 +-------+\n | 3:2 | (7)\n-----+-------+------\n | 4,6:3 | (10,11,12) <--- 231 (3x)\n 2 +-------+\n |{7}:4 |({13})\n-----+-------+------\n | 8,9:5 | (14,{15}) <--- 231 (2x)\n 3 +-------+\n | 10:6 | (19)\n-----+-------+------\n```\n\n![](https://user-images.githubusercontent.com/36441664/100784808-5694a480-3442-11eb-80ad-04dc1100d585.png)\n\n***139 = 34th prime =(2x17)th prime***\n\n>We study the [limit shape](https://github.com/naa/young-diagrams#young-diagrams) of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape _([arXiv:2010.16383v4](http://arxiv.org/abs/2010.16383))_.\n\n[![Limit shape for infinite rank limit of tensor\npower decomposition for Lie algebras of series\n](https://user-images.githubusercontent.com/8466209/233841647-e7f5154c-740f-4c19-9094-abbe0a4cced6.png)](https://arxiv.org/pdf/2010.16383.pdf)\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|------------------------- Skema-12 ------------------------|\n|------------ 6¤ -------------|------------- 6¤ ------------|\n|--------------------------- 192 ---------------------------|\n|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}|\n|--------- 5¤ ---------|------------ {96} -----------|{43}|\n|--------- {53} ---------|-------------- {139} -------------|\n|------- Skema-23 -------|------------- Skema-34 -----------| \n```\n\n[![default](https://user-images.githubusercontent.com/8466209/235672220-30997c4b-0d66-4e8a-a579-44e05062ac88.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partition)\n\n```\n|------------ 36' --------------|----------------------------36' ----------------------------|\n| 19' | 17' | 13' | 11' | 7' | 5' |\n+---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n+---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n| 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n+---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n| ° |ΔΔΔΔ ΦΦ | • ΔΔ ΔΔ ¤ | • ΔΔ ΦΦΦ Φ ΦΦ ¤¤¤¤| • ΔΔ ΦΦΦ Φ ¤¤ ΦΦ | \n\n|---- 102 ---|----- 66 ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -|\n|--2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------|\n|-------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------|\n|-------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----|\n```\n\n***919 = 1 + 6(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17) = 1 + 6(153)***\n\n![](https://user-images.githubusercontent.com/36441664/82588608-47948600-9bc5-11ea-9935-d4123a2bddd1.jpg)\n\n***286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271***\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== ←-- bilateral 9 sums\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n```\n\nThese objects will then behave as a complex numbers that leads to trivial and complex roots of the _[18th prime identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_. Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as _[the balanced prime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_.\n\n***Input (12) + Query (15) + Result (19) + Ouput (22) = Total 68 Objects***\n\n![image](https://user-images.githubusercontent.com/8466209/219710751-e7e9d316-10f8-4598-b3f3-cad468467027.png)\n\n```\nlayer | node | sub | i | f\n------+------+-----+----------+-----+-----+-----+ ---\n | | | 1,2:1 | 1 | 30 | 40 | 71 (2,3) ‹------------------- |\n | | 1 +----------+-----+-----+-----+ | |\n | 1 | | 2 | | 5¨ encapsulation\n | |-----+----------+ ----------------------------- | |\n | | | 3 | | | | |\n 1 +------+ 2 +----------+---- | LAGGING SCHEME | | ---\n | | | 4 | | (Exponentiation Zone) | | |\n | +-----+----------+ | | | |\n | 2 | | 5 | ------------------------------ | 7¨ abstraction\n289 | | 3 +----------+ | |\n| | | | 6 | ‹---------------------------- Φ | {6®} |\n------+------+-----+----------+-----+----- | ---\n | | | 11:7 | 5 | 9 | 14 (20) --------› ¤ | |\n | | 4 +----------+-----+-----+-----+ | |\n | 3 | | 12:8 | 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | +-----+----------+-----+-----+-----+ | | |\n | | | 13:9 | 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n 2 +------| 5 +----------+-----+-----+-----+ | | ---\n | | | 14:19 | 9 | 60 | 40 | 109 (28) ------------- | |\n | |-----+----------+-----+-----+-----+ | |\n | 4 | | 15,18:11 | 1 | 30 | 40 | 71 (29,30,31,32) ------------ 13¨ inheritance\n329 | | 6 +----------+-----+-----+-----+ |\n| | | | 19:12 | 10 | 60 | {70} (36) -------› Φ |\n------+------+-----+----------+-----+-----+ ---\n```\n\nAs you can see, starting with 1, and doubling it (1+1) we got 2, again, doubling 2 (2+2) we got 4. Further doubling 32 (32+32) we got 64 and summing up 6+4 gave us 10 which again summing up the two digits gave us 1. If you keep following this pattern, It will always give us the digits 1, 2, 4, 5, 7, 8. Even summing 7+7 gives 14 which further gives 5 (1+4).\n\n![image](https://user-images.githubusercontent.com/8466209/222872757-bda0eae9-af85-4d5d-8a7d-a347210ba674.png)\n\n[![RiemannZeta Zeros](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n\nBased on Prime (7): 142857 then id: 28 from the last case will end up in id: 57 i.e. in the flowchart so that in turn they can point us to the algorithm tensor from the stop point to id: 114 on the third screen.\n\n![default](https://user-images.githubusercontent.com/8466209/221916014-7f536b3e-ba5d-4e79-9985-3f0f4c8d3d12.png)\n```\n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | mapping | feeding | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+---+----+----+---+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 |\n +----+----+----+---+----+----+---+\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n ```\n\n![2023-03-17 (2)](https://user-images.githubusercontent.com/8466209/225976499-0689bb75-34bf-4fd0-94ca-03fa2a2152fa.png)\n\n![default](https://user-images.githubusercontent.com/8466209/235939923-c5a1b158-d995-442b-bc3d-b08291ff0fc0.png)\n\n![default](https://user-images.githubusercontent.com/8466209/236091657-62397dbe-fb87-46a2-8676-f4903b6efd3f.png)\n\n![default](https://user-images.githubusercontent.com/8466209/226080396-235a1645-8a58-49c4-9754-8bac362a72fa.png)\n\nConsider that all creatures will go ***mature*** just like our body which is stop growing in a certain of condition. Therefore an [instance](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#building-the-instance) will become an inside container by leaving the central as black hole and derived all of [residual objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects) to outer level. This is what the ten (10) digits of _[0719425863](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-recycling)_ in Euler's number got something to do.\n\n***(1729 + 571 - 500) / (157 - 57) = 1800 / 100 = 18th prime identity = 110 objects***\n\n![default](https://user-images.githubusercontent.com/8466209/220014405-f9db1b2f-6068-4554-8ddf-82b9aaa3a05c.png)\n\nThe above _0719425863_ is implicity state the identity of ***seven (7) after zero (0)***. By _[the prime hexagon](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-hexagon)_, it match with the ***0th-step*** of _18 identities_ and ***1st-step*** of the _seven (7) prime identities_ from _19th to 25th_. So when it goes to _four (4) prime identities_ from _26th and end up to the 29th_ it will open up a _[gap at the 27th](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#replication-fork)_ which linkages with the _110 objects_ of the 18th.\n","dir":"/identition/span1/","name":"gist13.md","path":"identition/span1/gist13.md","url":"/identition/span1/gist13.html"},{"sort":13,"spin":112,"span":10,"suit":20,"layout":"default","title":"The Angular Momentum (spin 2)","content":"

            The Angular Momentum (spin 2)

            \n\n

            Under certain conditions, energy could not take on any indiscriminate value, the energy must be some multiple of a very small quantity (later to be known as a quantum).

            \n\n
            This section is referring to _[wiki page-13](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-9]()_ that is _[inherited ]()_ from _[the gist section-20](https://gist.github.com/eq19)_ by _[prime spin-112](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-10](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            This is also consistent with the fact that the quadratic residues for modulo 30 (making them congruent with perfect squares) are 1 and 19.

            \n\n

            Perfect Squares

            \n\n

            \"multilateral

            \n\n

            (17+13) + (11+19) = (7+11) + (19+23) = 60

            \n\n

            \"image\"

            \n\n

            \"Examples_Dyad_Sets_Congruent_1_and_71_Mod_90\"

            \n\n

            Reversal behaviour

            \n\n

            329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ

            \n\n

            \"default\"

            \n\n

            2 + 60 + 40 = 102

            \n\n
            1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave reversal to 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n
            \n\n

            The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner’s Mathematical Games column in Scientific American a short time later.

            \n\n
            Both Ulam and Gardner noted that the existence of such prominent lines ***is not unexpected***, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with **major unsolved problems** in number theory such as Landau's problems _([Wikipedia](https://en.wikipedia.org/wiki/Ulam_spiral))_.\n
            \n\n

            \"prime

            \n\n

            \"Reversal

            \n\n

            Fibonacci Retracement

            \n\n
            The weak mixing angle or Weinberg angle[[2]](https://en.wikipedia.org/wiki/Weinberg_angle#cite_note-3) is a parameter in the [Weinberg](https://en.wikipedia.org/wiki/Steven_Weinberg)–[Salam](https://en.wikipedia.org/wiki/Abdus_Salam) theory of the [electroweak interaction](https://en.wikipedia.org/wiki/Electroweak_interaction), part of the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model) of particle physics, and is usually denoted as θW. ***It is the angle by which [spontaneous symmetry breaking](https://www.eq19.com/multiplication/10.html#spontaneous-symmetry-breaking) [rotates](https://en.wikipedia.org/wiki/Rotation_matrix) the original W0 and B0 [vector boson](https://en.wikipedia.org/wiki/Vector_boson) plane, producing as a result the Z0 boson, and the [photon](https://en.wikipedia.org/wiki/Photon).[[3]](https://en.wikipedia.org/wiki/Weinberg_angle#cite_note-Cheng-Li-2006-4)***. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for _([Wikipedia](https://en.wikipedia.org/wiki/Weinberg_angle))_\n
            \n\n

            \"Weinberg_angle_(relation_between_coupling_constants\"

            \n\n

            More interesting is that, like the Prime Hexagon it self, they are newly discovered. See how these layers will behave there:

            \n\n
            This progression 41,43,47,53,61,71,83,97,113,131 whose general term is ***41+x+xx***, is as much remarkable since the ***40 first terms*** are all prime numbers _([Euler's letter to Bernoulli](https://math.stackexchange.com/a/1722188/908994))_.\n
            \n\n

            So here we are going to discuss about this number particularly with the said recombination which resulting the above Δ1 with 619.

            \n\n

            There are many other prime curiousity has been stated for this number 619 but almost none about 619-1 which is 618.

            \n\n

            (786/1000)² = 618/1000

            \n\n

            \"(786)

            \n\n

            There are set of sequence known as Fibonacci retracement. For unknown reasons, these Fibonacci ratios seem to play a role in the stock market, just as they do in nature.

            \n\n
            The mathematically significant Fibonacci sequence defines a set of ratios known as _Fibonacci retracements_ which can be used to determine probable ***[entry and exit points](https://www.eq19.com/exponentiation/#parsering-structure)*** for the equities when paired with additional momentum. The Fibonacci retracement levels are 0.236, 0.382, ***0.618, and 0.786***.\n- The key Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it. For example, 21 divided by 34 equals 0.6176, and 55 divided by 89 equals about 0.61798.\n- The 38.2% ratio is discovered by dividing a number in the series by the number located two spots to the right. For instance, 55 divided by 144 equals approximately 0.38194.\n- The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example, 8 divided by 34 equals about 0.23529.\n- The 78.6% level is given by the _[square root](https://youtu.be/K-AvE0B1KMw)_ of 61.8%, while not officially a Fibonacci ratio, 0.5 is also commonly referenced (50% is derived not from the Fibonacci sequence but rather from the idea that on average stocks retrace half their earlier movements). _([Golden Ratio - Articles](https://www.fnb.co.za/blog/investments/articles/FibonacciandtheGoldenRatio/))_\n
            \n\n

            (√0.618 - 0.618) x 1000 = (0.786 - 0.618) x 1000 = 0.168 x 1000 = 168 = π(1000)

            \n\n

            \"Fibonacci

            \n\n

            They are used to determine critical points where an asset’s momentum is likely to reverse. This study cascade culminating in the Fibonacci digital root sequence (also period-24).

            \n\n

            Truncated Perturbation

            \n\n

            \"image\"

            \n\n
            I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.\n
            \n\n
            That is what I found.  Phi and its members have a pisano period if the resulting fractional numbers are truncated.\n
            \n\n

            \"Truncate

            \n\n
            Direction:\n- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.\n- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.\n- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.\n \nConclusion:\n- All of the other primes than 2 is 1 less than the number n times the number of 2. \n- Those Mersenne primes is generated as 1 less than the power n of the number of 2. \n- Thus they will conseqently be carried out by the same scheme of this number of 2.\n
            \n\n
            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.\n
            \n\n

            \"11's

            \n\n

            103 - 43 = 60

            \n\n
                |-------------------------------- 2x96 -------------------------------|\n❓  |--------------- 7¤ ---------------|------------ 7¤ ------------------|\n〰️43👉------------- {89} --------------|-------------- {103} -------------|\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉89〰️\n    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|   ❓\n    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|\n          13 variations               48 variations          11 variations \n
            \n\n
            To date, I have found only one number sequence that visibly produces non-random results: pi and its powers, shown as truncated for display purposes. I believe these data suggest prime numbers are linked in some way to pi. _([Hexspin](https://www.hexspin.com/minor-hexagons/))_\n
            \n\n

            \"image\"

            \n","dir":"/multiplication/","name":"11.md","path":"multiplication/11.md","url":"/multiplication/11.html"},{"sort":14,"spin":1,"span":"antiparalel","suit":"intro","layout":"default","title":"Anti Parallel","content":"# [Anti Parallel](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f)\n\n```\n---+-----+-----\n 1 | 1 | 4\n---+-----+-----\n 2 |{5} |{8}\n---+-----+-----\n 3 | 9 |{17}\n---+-----+-----\n 4 |{18} |{23}\n---+-----+-----\n 5 | 24 | 27\n---+-----+-----\n 6 | 28 | 34\n---+-----+-----\n 7 |{35} |{41}\n---+-----+-----\n 8 |{42} |{52}\n---+-----+-----\n```\n\n![](https://user-images.githubusercontent.com/36441664/100797235-65845280-3454-11eb-9a1b-5c68a371f4d7.gif)\n\n![default](https://user-images.githubusercontent.com/8466209/223538255-e0b89693-009f-4506-bbba-9d5f4bd3a2cf.png)\n\n![](https://i.pinimg.com/736x/37/16/73/37167304621de46d28a2dd4c5cbf7f75--fluid-mechanics-engineering-millennium-prize-problems.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/73613129-23686580-4625-11ea-9f19-5588a3c33e80.gif)\n\n![](https://user-images.githubusercontent.com/36441664/85412349-b0d83200-b593-11ea-8cb0-15de138a96bc.gif)\t\n\n## 19 vs 18 Scenario\n\nThus in short here below is all the method that we called as the ***[19 vs 18 Scenario](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-%CE%B419-vs-18-scenario)*** of mapping [the quantum way](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-utilization-md) within a huge of [primes objects](https://github.com/eq19) (5 to 19) by [lexering](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-lexer-md) (11) the un[grammar](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md)ed feed (7) and [parsering](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md) (13) across [syntax](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-syntax-md) (17). \n\n***[(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects***\n\n```\nThe Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+ ---\n 7 --------- 1,2:1| 1 | 30 | 40 | 71 (2,3) ‹-------------@---- |\n | +-----+-----+-----+-----+ | |\n | 8 ‹------ 3:2| 1 | 30 | 40 | 90 | 161 (7) ‹--- | 5¨ encapsulation\n | | +-----+-----+-----+-----+ | | |\n | | 6 ‹-- 4,6:3| 1 | 30 | 200 | 231 (10,11,12) ‹--|--- | |\n | | | +-----+-----+-----+-----+ | | | ---\n --|--|-----» 7:4| 1 | 30 | 40 | 200 | 271 (13) --› | {5®} | |\n | | +-----+-----+-----+-----+ | | |\n --|---› 8,9:5| 1 | 30 | 200 | 231 (14,15) ---------› | 7¨ abstraction\n289 | +-----+-----+-----+ | |\n | ----› 10:6| ----------------------------› Φ | {6®} |\n --------------------+-----+-----+-----+ | ---\n 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |\n | +-----+-----+-----+ | |\n | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | | +-----+-----+-----+ | | |\n | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n | | | +-----+-----+-----+ | | ---\n | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |\n | | +-----+-----+-----+ | |\n | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance\n329 | +-----+-----+-----+ |\n | ‹--------- 19:12| 10 | 60 | {70} (36) ‹------- Φ |\n -------------------+-----+-----+ ---\n 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ |\n | +-----+-----+ |\n | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class\n | | +-----+-----+-----+-----+-----+ | |\n | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} |\n | | | +-----+-----+-----+-----+-----+ | | ---\n --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- |\n | | +-----+-----+ | |\n --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object\n168 | +-----+ |\n| 102 -› 29:18| 50 | 50(68) ---------> Δ18 |\n----------------------+-----+ ---\n```\n\n![](https://user-images.githubusercontent.com/36441664/84323508-1c3c0000-aba1-11ea-99b5-d8d0a10727c9.png)\n\n![](https://user-images.githubusercontent.com/8466209/226644534-00cf4fe3-04f9-4b28-8a8b-674bcf4bd585.png)\n\n![](https://user-images.githubusercontent.com/8466209/198918345-a1997048-4993-4934-b094-95a297992ed4.png)\n\n![](https://user-images.githubusercontent.com/8466209/198918641-e33a7d60-d10a-40a4-bedf-af07b1d57d13.png)\n\n![](https://user-images.githubusercontent.com/36441664/85039712-32098080-b1b2-11ea-80f0-3e7e767a2ba1.jpg)\n\n## Historical Events\n\n[William Delbert Gann](https://en.wikipedia.org/wiki/William_Delbert_Gann) is perhaps the most mysterious of all the famous traders in history. Known for using geometry, astrology and ancient mathematics to predict events in the financial markets and historical events, evenso influences on the weather.\n\n***11 x 30 = 330 = 329 + 1***\n\n[![](https://user-images.githubusercontent.com/8466209/206868681-2cddf780-48f1-4dc5-9ef4-981b402a15d5.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)\n\n_
            In March, Saturn was at 224° and Venus was at 344°. The corn top price was ¢137, which was around 104°,
            thus the three points loosely formed a Grand Trine (Wikipedia).
            _\n\n![default](https://user-images.githubusercontent.com/8466209/227791172-e09f8e43-502f-40a5-8bca-fa481edbfb79.png)\n\n***1 container + 7 blocks + 29 flats + 77 rooms = f(0719425863) + 7 blocks + 29 flats + 77 rooms = 114 objects***\n\n[![](https://user-images.githubusercontent.com/8466209/205431468-6777265f-63a8-42ea-b454-d45227478362.png)]\n\n![](https://user-images.githubusercontent.com/8466209/206839286-d3a9b366-fbd1-4953-badd-c760eeb07436.png)\n\n![](https://user-images.githubusercontent.com/8466209/206884467-05a33d48-5cdc-48fd-9b75-5be406100f06.png)\n\n![](https://user-images.githubusercontent.com/8466209/206964338-fb62d060-86c7-4a2d-a64c-7da49bc70222.png)\n\n![](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png)\n\n![](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png)\n\n## Balanced Structural\n\nFor starters, it possesses a perfectly balanced structural and numeric symmetries. So it conforms the intervals between the prime roots of the Prime Spiral Sieve (and every subsequent row or rotation of the sieve) with the period _[eight (8) difference sequence](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_.\n\n***Φ(10,2) = 10² + 2x(10th prime) + 10¹ = 100+29 + 29+10 = 129 + 39 = 168 = π(1000)***\n\n[![8 objects](https://user-images.githubusercontent.com/8466209/221477873-db074770-f754-4a19-b926-fe4204d4a047.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bonding-position)\n\nTo represent as a gap then this drive is supposed to not exist phisically by a computer, this could be replaced by \nspecial folders using shared drives such as _[Google Drive](https://workspace.google.com/products/drive/)_ that you can use to store, search, and access files with a team. \n\n>As of May 2022, [shared drives](https://redirect.viglink.com/?key=e7eab128eb8d1c53e14db14f4c632447&u=https%3A%2F%2Fsupport.google.com%2Fa%2Fanswer%2F7212025%3Fhl%3Den%26amp%3Bref_topic%3D7337266&cuid=xid:fr1677477323aaa) are available to Google Workspace accounts including Education Fundamentals, Teaching & Learning Upgrade, Standard, and Plus, Nonprofits, Business Standard and Plus, Enterprise, and G Suite Business; Essentials.\n\n[![Google Drive](https://user-images.githubusercontent.com/8466209/221490011-0f82561f-bde5-4700-bc09-a087f8dd9b2d.png)](https://www.howtogeek.com/802048/how-to-add-a-shared-google-drive-to-windows-file-explorer/)\n\nIt is also a form of the existence of DNA. The topology of DNA refers to the specific spatial structure formed by further distortion on the basis of the DNA double helix. Superhelical structure is the main form of topology, which can be divided into positive supercoil and negative supercoil, under corresponding conditions, they can transform each other.\n\n![The topology of DNA](https://user-images.githubusercontent.com/36441664/101093483-6ac8d500-35ed-11eb-92d1-e264d22b341f.jpg)\n\n![](https://user-images.githubusercontent.com/36441664/85040434-00dd8000-b1b3-11ea-9aa5-70add88095f2.jpg)\n\nGann was a very devout man and honestly believed that he had found the key to predictable markets because of his study of the Bible in conjunction with his (supposed) study of many esoteric math theory from Greece and Egypt and his study of astrology. \n\n![default](https://user-images.githubusercontent.com/8466209/222864121-96efc8b2-885d-426b-8af6-e7faa31d9278.png)\n\nIt may take many years of serious study to master it. And most of the methods available online doesnt have anything to do with Gann. His books are also just means to put in the right path. \n\n>Even though Gann was thought to be \"religious\", a careful analysis of his writings finds that he did not agree with the conventional Christian teachings _([Wikipedia](https://en.wikipedia.org/wiki/William_Delbert_Gann#Personal_view_on_religion))_.\n\n[![WD Gann - A Trader Legend](https://user-images.githubusercontent.com/36441664/85039095-91b35c00-b1b1-11ea-9f5e-aaef8e1d32bf.jpg)](https://github.com/MarketLeader/Stocks/files/10128472/WD.Gann.-.A.Trader.Legend.pdf)\n\nReal mastery and understanding is still programmed in such a way that only the most qualified and determined candidates could learn it and keep it remain as a secret, just as he desired.\n","dir":"/identition/span1/","name":"gist14.md","path":"identition/span1/gist14.md","url":"/identition/span1/gist14.html"},{"sort":14,"spin":111,"span":9,"suit":21,"layout":"default","title":"Entrypoint of Momentum (spin 3)","content":"

            Entrypoint of Momentum (spin 3)

            \n\n
            This section is referring to _[wiki page-14](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-10]()_ that is _[inherited ]()_ from _[the gist section-21](https://gist.github.com/eq19)_ by _[prime spin-111](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-9](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Coupling Behaviour

            \n\n
            Parameters of the Standard Model\nSymbol\tDescription\tRenormalization\nscheme (point)\tValue\tExperimental\nuncertainty\n1. me | Electron mass |   | 510.9989461 keV | ±3.1 meV\n2. mμ | Muon mass |   | 105.6583745 MeV | ±2.4 eV\n3. mτ | Tau mass |   | 1.77686 GeV | ±0.12 MeV\n4. mu | Up quark mass | μMS = 2 GeV | 2.16 MeV | +0.49 −0.26 MeV\n5. md | Down quark mass | μMS = 2 GeV | 4.67 MeV | +0.48 −0.17 MeV\n6. ms | Strange quark mass | μMS = 2 GeV | 93.4 MeV | +8.6 −3.4 MeV\n7. mc | Charm quark mass | μMS = mc | 1.27 GeV | ±0.02 GeV\n8. mb | Bottom quark mass | μMS = mb | 4.18 GeV | +0.03 −0.02 GeV\n9. mt | Top quark mass | On-shell scheme | 172.69 GeV | ±0.30 GeV\n10. θ12 | CKM 12-mixing angle |   | 13.1° |  \n11. θ23 | CKM 23-mixing angle |   | 2.4° |  \n12. θ13 | CKM 13-mixing angle |   | 0.2° |  \n13. δ | CKM CP-violating Phase |   | 0.995 |  \n14. g1 or g' | U(1) gauge coupling | μMS = mZ | 0.357 |  \n15. g2 or g | SU(2) gauge coupling | μMS = mZ | 0.652 |  \n16. g3 or gs | SU(3) gauge coupling | μMS = mZ | 1.221 |  \n17. θQCD | QCD vacuum angle |   | ~0 |  \n18. v | Higgs vacuum expectation value |   | 246.2196 GeV | ±0.2 MeV\n19. mH | Higgs mass |   | 125.18 GeV | ±0.16 GeV\n
            \n\n
            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.\n
            \n\n

            \"11's

            \n\n

            π(10) = 2,3,5,7

            \n\n

            \"IMG_20240105_140622\"

            \n\n
            [![image](https://github.com/eq19/eq19.github.io/assets/8466209/5b0282fd-8918-49ca-b676-0802699eaeef)](https://www.sciencedirect.com/science/article/abs/pii/B9780444513434501939)\n
            \n\n

            \"IMG_20240105_141215\"

            \n\n

            \"IMG_20240105_133751\"

            \n\n

            \"IMG_20240105_135516\"

            \n\n

            Within a cycle this scheme would generate the prime platform which is performing the rank of 10 shapes starting with the primes 2,3,5,7.

            \n\n
            That is, if the powers of 10 all returned with blue spin, or as a series of rainbows, or evenly alternating colors or other non-random results, ***then I’d say prime numbers appear to have a linkage to 10.  I may not know what the the linkage is, just that it appears to exist*** _([HexSpin](https://www.hexspin.com/minor-hexagons/))_.\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"IMG_20240109_004026\"

            \n\n

            Via the 11 partitions as the lexer and 13 frames as the parser we do a recombination to build the grammar in 6 periods.

            \n\n
            Twisted strip model for one wavelength of a photon with circular polarisation in  at space. A similar photon in a closed path in curved space with periodic boundary conditions of length \u0015C. \n\n- The B-fi\feld is in the plane of the strip and the E-field\f is perpendicular to it (a).\n- The E-fi\feld vector is radial and directed inwards, and the B-fi\feld is vertical (b). \n\nThe magnetic moment ~\u0016, angular momentum L~, and direction of propagation with velocity c are also indicated. _([Is the electron a photon with toroidal topology? - pdf](https://github.com/eq19/eq19.github.io/files/13790325/LdBelectoroid.pdf))_\n
            \n\n

            \"a-Twisted-strip-model-for-one-wavelength-of-a-photon-with-circular-polarisation-in-at\"

            \n\n

            Twisted Patterns

            \n\n
                |-------------------------------- 2x96 -------------------------------|\n❓  |--------------- 7¤ ---------------|------------ 7¤ ------------------|\n〰️43👉------------- {89} --------------|-------------- {103} -------------|\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89\n    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|  ✔️\n    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|\n          13 variations               48 variations          11 variations \n
            \n\n
            F11 (89): The decimal expansion of 89's reciprocal (1/89) is period-44 (see graphic below) composed of 22 bi-lateral 9 sums = 198, while 89 + 109 = 198, 7920/198 = 40 and 8,363,520/198 = 20 x 2112 (7919's index number as a member of this domain). And, curiously, 198's inverse (891) + 109 = 1000, while the sum of 89 and 109's inverses, 98 + 901, = 999. Then consider that, while it's obvious 997 of the first 1000 primes are not divisible by 2, 3, or 5, one might miss the fact that 997 minus its reverasl, 799, = 198 = 89 + 109. And for the record we note that 1/109's decimal expansion is period 108 (making it a 'long period prime' in that 1/p has the maximal period of p−1 digits). This period consists of 54 bilateral 9 sums = 486, which (coincidentally?) is the number of primes in the 243 pairs summing to 7920 (more about these, below). _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            43 + 1 = 44 periods

            \n\n

            \"The\n

            \n\n
            1092 − 892 = 3960 and 3960 x 2 = 7920; which equates to 8,363,520/(1092 − 892) = 2112, and when you plug 7919 into the formula for triangular numbers you generate 31,359,240 = 7919 x (1092 − 892). And here's another grouping that relates to these ratios: (672 − 232) = (1092 − 892) and (672 + 1092) − (232 + 892) = 7920 = 2(1092 − 892). And here we correlate 11's additive sums with 3960, 7920 and the first 1000 prime numbers. _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            \"11_3960_1st_1000_primes\"

            \n\n
            The symmetry of this supergravity theory is given by the supergroup OSp(1❕32) which gives the subgroups O(1) for the bosonic symmetry and Sp(32) for the fermion symmetry. ***This is because spinors need 32 components in 11 dimensions***. 11D supergravity can be compactified down to 4 dimensions which then has OSp(8❕4) symmetry. (We still have 8 × 4 = 32 so there are still the same number of components.) Spinors need 4 components in 4 dimensions. This gives O(8) for the gauge group which is too small to contain the Standard Model gauge group U(1) × SU(2) × SU(3) ***which would need at least O(10)***.\n_([Wikipedia](https://en.wikipedia.org/wiki/Higher-dimensional_supergravity#The_mathematics))_ 👈 π(10)\n
            \n\n

            \"M-Theory\"

            \n\n
                |-------------------------------- 2x96 -------------------------------|\n✔️  |--------------- 7¤ ---------------|------------ 7¤ ------------------|\n〰️Osp(8|4) 👉------ {89} --------------|-------------- {103} -------------|\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89\n    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|\n    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|\n          13 variations               48 variations          11 variations \n
            \n\n

            Shock wave

            \n\n

            Many physicists suspect that the fact that the observable universe contains more matter than antimatter is caused by a chiral anomaly

            \n\n
            The pion is one of the particles that mediate the residual strong interaction between a pair of [nucleons](https://en.m.wikipedia.org/wiki/Nucleons). This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the [Yukawa potential](https://en.m.wikipedia.org/wiki/Yukawa_potential).\n- The pion, being spinless, has [kinematics](https://en.m.wikipedia.org/wiki/Kinematics) described by the [Klein–Gordon](https://en.m.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation).\n- In the terms of [quantum field theory](https://en.m.wikipedia.org/wiki/Quantum_field_theory), the [effective field theory](https://en.m.wikipedia.org/wiki/Effective_field_theory) [Lagrangian](https://en.m.wikipedia.org/wiki/Lagrangian_(field_theory)) describing the pion-nucleon interaction is called the ***[Yukawa interaction](https://en.m.wikipedia.org/wiki/Yukawa_interaction)***.\n- The nearly identical masses of π± and π° indicate that there must be a symmetry at play: this symmetry is called the [SU(2)](https://en.m.wikipedia.org/wiki/SU(2)) [flavour symmetry](https://en.m.wikipedia.org/wiki/Flavour_symmetry) or [isospin](https://en.m.wikipedia.org/wiki/Isospin). The reason that there are ***three (3) pions, π+, π− and π°***, is that these are understood to belong to the triplet representation or the [adjoint representation](https://en.m.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_group) ***3 of SU(2)***.\n- By contrast, the up and down quarks transform according to the [fundamental representation](https://en.m.wikipedia.org/wiki/Fundamental_representation) ***2 of SU(2)***, whereas the anti-quarks transform according to the conjugate representation 2*.\n- With the addition of the [strange quark](https://en.m.wikipedia.org/wiki/Strange_quark), the pions participate in a larger, SU(3), flavour symmetry, in the adjoint representation, ***eight (8) of SU(3)***.\n- The other members of this [octet](https://en.m.wikipedia.org/wiki/Eightfold_way_(physics)#Meson_octet) are the four (4) [kaons](https://en.m.wikipedia.org/wiki/Kaon) and the [eta meson](https://en.m.wikipedia.org/wiki/Eta_meson).\n\nPions are [pseudoscalars](https://en.m.wikipedia.org/wiki/Pseudoscalar_(physics)) under a [parity](https://en.m.wikipedia.org/wiki/Parity_(physics)) transformation. Pion currents thus couple to the axial vector current and so participate in the [chiral anomaly](https://en.m.wikipedia.org/wiki/Chiral_anomaly). _([Wikipedia](https://en.wikipedia.org/wiki/Pion))_\n
            \n\n

            \"residual

            \n\n

            In phenomenology, Yukawa coupling can be observed in phenomenology from 6 quark masses and 4 CKM mixing parameters.

            \n\n
            Since the range of the nuclear force was known, ***Yukawa used his equation to predict the mass of the mediating particle as [about two hundreds (200) times](https://github.com/eq19/eq19.github.io/files/13961751/Yukawa.pdf) the mass of the electron***. Physicists called this particle the \"[meson](https://en.wikipedia.org/wiki/Meson),\" as its mass was in the middle of the proton and electron. Yukawa's meson was found in 1947, and came to be known as the [pion](https://en.m.wikipedia.org/wiki/Pion). _([Wikipedia](https://en.wikipedia.org/wiki/Yukawa_potential#History))_\n
            \n\n

            \"The_Minimal_Flavor_Structure_of_Quarks_and_Leptons\"

            \n\n
            It is widely accepted that audible thunder is generated by the lightning channel and the subsequent shock wave that [travels extremely rapidly (~3000 m/s)](https://en.m.wikibooks.org/wiki/Engineering_Acoustics/Thunder_acoustics#cite_note-3) a few provides a experimentally-proved thunder generation mechanism. _([Wikipedia](https://en.m.wikibooks.org/wiki/Engineering_Acoustics/Thunder_acoustics))_\n
            \n\n

            \"two

            \n\n

            The parity is associated to the shock wave (3km/s) produced after a lightning discharge (300,000km/s) propagated in 3 periods of travels to the normal speed of 1km/s.

            \n\n
            Depending on the conditions surrounding the lightning rod such as the air composition, atmospheric pressure, ***the thunder will travel at a unique velocity, pitch, frequency band and duration depending on the characteristics of the lightning rod***. Indeed, as shown in [the study](http://iopscience.iop.org/0143-0807/30/1/014) by Blanco et al. (2009) ***[the geometry plays a vital role](https://www.eq19.com/multiplication/20.html)*** in the perceived resulting sound.\n_([Wikipedia](https://en.wikibooks.org/wiki/Engineering_Acoustics/Thunder_acoustics))_\n
            \n\n

            \"Thunder_diagram\"

            \n\n
            This is typical for processes in which the so-called initial state radiation takes place. It is well known that emission of real or virtual photons from the initial colliding electrons essentially modify the shapes of the narrow resonance curves [[39]](https://www.sciencedirect.com/science/article/pii/S037026931400937X#br0390): the curves become wider, a suppression of the resonance maximum is observed and the main distinctive feature – the radiation tail – appears to the right of the resonance pole. _([Glashow resonance in neutrino–photon scattering](https://www.sciencedirect.com/science/article/pii/S037026931400937X))_\n
            \n\n

            \"1The

            \n\n

            This OSp(8❕4) will be assigned to 4xMEC30 and let the 4x30=120 numbers of 32 prime positions minus 5 types of bosons gives 27 variations of decay objects.

            \n\n","dir":"/multiplication/","name":"12.md","path":"multiplication/12.md","url":"/multiplication/12.html"},{"sort":14,"spin":1,"span":"equilateral","suit":"intro","layout":"default","title":"Turbulence","content":"# [Turbulence](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#anti-parallel)\n\nA sequence of Jupyter notebooks featuring the \"12 Steps to Navier-Stokes\"\n\n## 12 steps to Navier–Stokes\n\n[The interactive module 12 steps to Navier–Stokes](https://github.com/barbagroup/CFDPython) is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013.\n\n![image](https://user-images.githubusercontent.com/8466209/224356987-784ab074-6aba-49ad-8f73-cd56d36bf4e8.png)\n\nYou can see that two distinct pressure zones are forming and that the spiral pattern expected from lid-driven cavity flow is beginning to form. Experiment with different values of nt to see how long the system takes to stabilize.\n\n![image](https://user-images.githubusercontent.com/8466209/224357044-f3c42fa5-b9ad-471c-85f3-6a4aa01a909e.png)\n\nThe quiver plot shows the magnitude of the velocity at the discrete points in the mesh grid we created. (We're actually only showing half of the points because otherwise it's a bit of a mess. The X[::2, ::2] syntax above is a convenient way to ask for every other point.) Another way to visualize the flow in the cavity is to use a streamplot\n\n![image](https://user-images.githubusercontent.com/8466209/224357497-00fe4561-3cce-4810-a71d-4389bec36fdd.png)\n\nTo use these lessons, you need Python 3, and the standard stack of scientific Python: NumPy, Matplotlib, SciPy, Sympy. And of course, you need Jupyter—an interactive computational environment that runs on a web browser.","dir":"/exponentiation/span14/","name":"gist01.md","path":"exponentiation/span14/gist01.md","url":"/exponentiation/span14/gist01.html"},{"sort":15,"spin":1,"span":"gap","suit":"intro","layout":"default","title":"Mass vs Gap (Δ)","content":"# [Mass vs Gap (Δ)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288)\n\nThis section will be the last one of our presentation of 18th prime identity. Here we are going to explain one more item that is still open or undiscussed which is about what the [77 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#object-orientation) are going to do within the 19 vs 18 Scenario.\n\n***15 + 35 + 28 = 15 + 63 = 78 = 77 + 1***\n\n```\n---+-----+-----\n 1 | 1 | 15\n---+-----+-----\n 2 | 16 | 25\n---+-----+-----\n 3 | 26 | 50\n---+-----+-----\n 4 | 51 | 84\n---+-----+-----\n 5 | 85 | 99\n---+-----+-----\n```\n\n```\n$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer| i | f\n -----+-----+---------\n | 1 | 5\n 1 +-----+\n | 2 | 7\n -----+-----+--- } 36 » 6®\n | 3 | 11\n 2 +-----+\n | 4 | 13\n -----+-----+---------\n | 5 | 17\n 3 +-----+ } 36 » 6®\n | 6 | 19\n -----+-----+---------\n```\n\nIn many ways, a _[black hole](https://en.wikipedia.org/wiki/Black_hole)_ acts like an ideal black body, as ***it reflects no light***. Here is an animated simulation of a Schwarzschild black hole with a galaxy passing behind. Around the time of alignment, extreme gravitational lensing of the galaxy is observed.\n\n[![black hole](https://user-images.githubusercontent.com/8466209/220674107-f4b5daff-b0cb-46d0-990f-50fccd88a599.gif)](https://en.wikipedia.org/wiki/Black_hole)\n\n```\n largest part=21 → 11+13+12=36 → MEC30\n ↓ |\n---+-----+-----+-----+-----+ ↓\n 1 | 19 | 1 | 20 | 21 |-------------------|-----\n---+-----+-----+-----+-----+ ↓ |\n 2 | 18 | 21 | 39 | 60 |------------------- |\n---+-----+-----+-----+-----+ | |\n 3 |{63} | 40 | 103 | 143 |------------- | |\n---+-----+-----+-----+-----+ | | |\n 4 | 37 | 104 | 141 | 245 |------- | | |\n---+-----+-----+-----+-----+ | | | |\n 5 | 10* | 142 | 152 | 294 |- 11** | 13 | 12 | 12 | 18\n---+-----+-----+-----+-----+ | | | |\n 6 | 24 | 153 | 177 | 332 |------- | | |\n---+-----+-----+-----+-----+ | | |\n 7 | 75 | 178 | 253 | 431 |------------- | |\n---+-----+-----+-----+-----+ | |\n 8 | 30 | 254 | 284 | 538 |------------------- |\n---+-----+-----+-----+-----+ ↓ |\n 9 | 1 | 285 | 286 | 571 |-------------------|-----\n===+=====+=====+=====+=====+ ↓\n45 | 277 | ← 11+13+12=36 ← MEC30\n---+-----+ |\n ↑\nNote:\n10* stands as the central rank\n11** stands as the central parts\n```\n\nAccording to the observations made by NASA, Astronomers have uncovered ***[TON 618](https://en.wikipedia.org/wiki/TON_618#Supermassive_black_hole)*** as the record breaking supermassive black hole, weighing 66 trillion and brilliantly as 140 trillion times that of the Sun, making it one of the brightest object in the Universe. \n\n[![default](https://user-images.githubusercontent.com/8466209/223629156-8cfdfb46-1884-4f45-bbb6-d11093ac3834.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)\n\nIf the statement that it is indeed located at the center of our universe then the said black hole would behave as the exchange position between ***[twin (2) universes](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#dark-energi)***. This would for sure strengthen the syntax algorithm of our _[implementation](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation)_.\n\n***7 x 11 = 77 = 99 - 22 = 11 x (9 -2)***\n\n```\n #8 |------- 5® --------|------------ 7® --------------|\n | 1 |-------------- 77 = 4² + 5² + 6² -------------|\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n user | 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 |\n------+---|---+---+---+---+---+---+---+---+----+----+----+ 7,78\n main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - |\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n Δ | Δ | Δ | Δ\n Φ17|Φ29 | 96-99| 100 - 123 ({24})\n |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100\n Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30\n {98} | └── 110 - 123 (14x)» 70\n\n```\n\n```liquid\nDirection:\n- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.\n- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.\n- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.\n \nConclution:\n- All of the other primes than 2 is 1 less than the number n times the number of 2. \n- Those Mersenne primes is generated as 1 less than the power n of the number of 2. \n- Thus they will conseqently be carried out by the same scheme of this number of 2.\n```\n\nPerceptually, everything is separate and finite. But actually, everything is connected and infinite. It is this infinite connection, despite our limited finite perceptions, that makes us one with the cosmos.\n\n## Primes Platform\n\nEach result goes to the 9th object of prime 67 which is 19th prime. This ***[mass gap of (Δ > 0)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)*** is actually [the quantum way](https://gist.github.com/eq19) of our algorithm which is discused in details by the _[19th prime identity](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831)_. \n\n[![](https://user-images.githubusercontent.com/36441664/81015797-80c0bc80-8e89-11ea-905a-c6cec604f443.png)](https://en.wikipedia.org/wiki/Brun%27s_theorem)\n\nSo when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming bilateral 9 sum which facilitate them to finaly generate 1000 primes. \n\n***1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects***\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n \n-----+-----+-----+-----+-----+ -----------------------------------------------\n{786}| 1,2 | 2 | 2,3 | 3,4 | {19} |\n-----+-----+-----+-----+-----+ |\n {86}| 4 | 4,5 | 5,6 |{6,7}| 17 Base Zone\n +-----+-----+-----+-----+ |\n {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ |\n +-----+-----+-----+ -----------\n {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone |\n ----+-----+-----+-----+-----+ |\n {6}|15,16|17,18|18,20|21,22| 19 Mirror Zone\n +-----+-----+-----+-----+ |\n {8}|23,25|25,27|27,29| 18 |\n +-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------\n {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------\n | 1 2 3 | 4 5 6 | 7 8 9 |\n |------ 29' ------|--------------- 139' ----------------|\n |------ 102¨ -----|--------------- 66¨ ----------------|\n```\n\nWhen recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row \nforming the _[Primes Platform](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform)_. Thus we got 109 objects including for the 7 rows back to the original stage. \n\n```\n Tabulate Prime by Power of 10\n loop(10) = π(10)-π(1) = 4-0 = 4\n loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n =======================+====+====+====+====+====+====+====+====+====+=====\n Δ Δ\n 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1\n\nSequence:\n By the next layer the 89² will become 89 and 5 become 5² or 25.\n This 89 and 25 are in the same layer with total of 114 or prime 619\n So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n```\n\n***[(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects***\n\n```\nThe Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+ ---\n 7 --------- 1,2:1| 1 | 30 | 40 | 71 (2,3) ‹-------------@---- |\n | +-----+-----+-----+-----+ | |\n | 8 ‹------ 3:2| 1 | 30 | 40 | 90 | 161 (7) ‹--- | 5¨ encapsulation\n | | +-----+-----+-----+-----+ | | |\n | | 6 ‹-- 4,6:3| 1 | 30 | 200 | 231 (10,11,12) ‹--|--- | |\n | | | +-----+-----+-----+-----+ | | | ---\n --|--|-----» 7:4| 1 | 30 | 40 | 200 | 271 (13) --› | {5®} | |\n | | +-----+-----+-----+-----+ | | |\n --|---› 8,9:5| 1 | 30 | 200 | 231 (14,15) ---------› | 7¨ abstraction\n289 | +-----+-----+-----+-----+-----+ | |\n | ----› 10:6| 20 | 5 | 10 | 70 | 90 | 195 (19) --› Φ | {6®} |\n --------------------+-----+-----+-----+-----+-----+ | ---\n 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |\n | +-----+-----+-----+ | |\n | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism\n | | +-----+-----+-----+ | | |\n | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | |\n | | | +-----+-----+-----+ | | ---\n | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |\n | | +-----+-----+-----+ | |\n | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance\n329 | +-----+-----+-----+ |\n | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ |\n -------------------+-----+-----+ ---\n 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ |\n | +-----+-----+ |\n | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class\n | | +-----+-----+-----+-----+-----+ | |\n | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} |\n | | | +-----+-----+-----+-----+-----+ | | ---\n --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- |\n | | +-----+-----+ | |\n --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object\n168 | +-----+ |\n| 102 -› 29:18| 50 | 50(68) ---------> Δ18 |\n----------------------+-----+ ---\n```\n\nThe above is observed following the W0 (assumptions of relativistic quantum mechanics) for the _[Existence and Mass Gap](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap#The_Wightman_axioms)_ which transform under the homogeneous group as a _[four-vector](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#four-4-vector)_ and has a mass gap Δ > 0.\n\n>Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on \n***R^4 and has a mass gap Δ > 0*** _([Wikipedia](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap))_.\n\n![image](https://user-images.githubusercontent.com/8466209/223643996-1ea5cb89-324e-446c-9c9f-8c94c39909b3.png)\n![origin](https://user-images.githubusercontent.com/8466209/220002045-d0395b21-1f2a-4dba-992a-24bf50c480d5.png)\n![action](https://user-images.githubusercontent.com/36441664/84525042-2f67e080-ad05-11ea-9f9c-e07492446240.jpg)\n\n[![runner](https://user-images.githubusercontent.com/8466209/223616353-0e1be019-16e8-40d1-bb0c-465a9837d7bb.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#four-4-vector)\n\n## Everything is linked\n\nThe ***ζ(s)*** will behave as ***the other universe (not the twin)*** which was initiated paralelly by a [big bang](https://en.wikipedia.org/wiki/Big_Bang). While this parts are relativity young. it will continue to grow as a [four-vector](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#lexer-vs-parser). So it will need a gap between each identities to proceed the thing.\n\n>Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed _([Wikipedia](https://en.wikipedia.org/wiki/Black_hole#High-energy_collisions#Growth))_\n\n[![Infinite number](https://user-images.githubusercontent.com/8466209/222023510-e57f97a6-5026-4027-b105-25a4290ed2de.png)](https://en.wikipedia.org/wiki/Black_hole#High-energy_collisions)\n\nBy our universe it could be represented by _the central black hole_ which is very strong to throw away every objects but it has no resistance against any exchange from _[the other universe](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)_. \n\n>In quantum field theory, the ***mass gap*** is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle _([Wikipedia](https://en.wikipedia.org/wiki/Mass_gap))_.\n\n[![the central black hole_](https://user-images.githubusercontent.com/36441664/104077748-9f175d00-524d-11eb-9c6d-6c0c4ee1fd93.gif)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution)\n\nSo by the ζ(s) then our [multiverse](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#rotation-vs-revolution) is belong to a group of multiple universes inside the ***lightest particle*** of a mass gap out of one of _[the like of them](https://legacy.quran.com/65/12)_ somewhere in an infinite number of [another parallel universes](https://www.instagram.com/reel/CmrFIXpBGsV/?igshid=OWEyOTRmYTI=).\n\n>***[Prof Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking)'s [final research paper](https://arxiv.org/pdf/1810.01847.pdf) [suggests that our Universe may be one of many similar](https://link.springer.com/content/pdf/10.1007/JHEP04(2018)147.pdf)*** _([BBC News](https://www.bbc.com/news/science-environment-43976977))_.\n\n[![everything is linked](https://user-images.githubusercontent.com/8466209/221993489-2f2b5a6f-68b5-474d-88af-4babddf60df4.png)](https://www.bbc.com/news/science-environment-43976977)\n\n[Another suggestion](https://www.instagram.com/reel/Crtd99OtzoI/?igshid=NjZiM2M3MzIxNA==) which has just yet been in a topic of the science is that the similar behaviour also happen by particles such as hydrogen which is throwing all of the waves ***out of the central***. So hypothetically it suppose to have a populated infinite number of its own parallel universes because whatever [a smallest thing](https://www.instagram.com/reel/Cmy5WFzoujq/) is arised, they could only exist by _[the same law of physics](https://www.instagram.com/reel/Cqq8s4og2LV/?igshid=MDJmNzVkMjY=)_,\n\n>Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics ***cannot predict*** the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron _([Wikipedia](https://en.wikipedia.org/wiki/Quantum_physics))_.\n\n[![the electron in a hydrogen](https://user-images.githubusercontent.com/8466209/219906653-b96d4d30-6d74-4bef-b6de-f5bc9d7fefdc.png)](https://en.wikipedia.org/wiki/Quantum_physics)\n \nConsider that this law of physics would exist everywhere. So it is also one of their law when the ***[1st sequence](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bonding-position)*** of the ten (10) digits of ***0719425863*** in Euler's number ***[is zero (0)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-vs-zero)***. Thus theoretically it speaks if _an existence of everything arose from nothingness_.\n\n**[₠Quantum Project](https://github.com/eq19)** \nCopyright © 2022 All rights reserved.\n\nReference:\n* [Riemann Zeta](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n* [Mersenne Prime](https://en.wikipedia.org/wiki/Mersenne_prime)\n* [The Prime Hexagon](https://www.hexspin.com/)\n* [The Primes Demystified](https://www.primesdemystified.com/First1000Primes.html)","dir":"/identition/span1/","name":"gist15.md","path":"identition/span1/gist15.md","url":"/identition/span1/gist15.html"},{"sort":15,"spin":110,"span":8,"suit":22,"layout":"default","title":"The Mapping of Spacetime (spin 4)","content":"

            The Mapping of Spacetime (spin 4)

            \n\n
            This section is referring to _[wiki page-15](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-11]()_ that is _[inherited ]()_ from _[the gist section-22](https://gist.github.com/eq19)_ by _[prime spin-110](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-8](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Decay Frames

            \n\n
            As we've already alluded, to lay the foundation for a bijection with numbers not divisible by 2, 3, or 5, each of the pyramid's four lateral faces is constructed from a 32-step triangular number progression (oeis.org/A000217: a(n) = n(n+1)/2 ...).\n
            \n\n

            \"image\"

            \n\n

            7 = 4th prime

            \n\n
             Osp(1) |  1 |  2 |  3 |  4 \n--------+----+----+----+----\n π(10)  |  2 |  3 |  5 |  7 ✔️\n
            \n\n

            19 = 8th prime

            \n\n
             Osp(2) |  1 |  2 |  3 |  4 | th\n========+====+====+====+====+====\n π(10)  |  2 |  3 |  5 |  7 | 4th\n--------+----+----+----+----+----\n π(19)  | 11 | 13 | 17 | 19 | 8th ✔️\n
            \n\n

            29 = 10th prime

            \n\n
             Osp(3) |  1 |  2 |  3 |  4 | th\n========+====+====+====+====+====\n π(10)  |  2 |  3 |  5 |  7 | 4th\n--------+----+----+----+----+----\n π(19)  | 11 | 13 | 17 | 19 | 8th\n--------+----+----+----+----+----\n π(29)  | 23 | 29 |  - |  - | 10th ✔️\n
            \n\n

            109 = 29th prime

            \n\n
             Osp(8|4) |  1 |  2 |  3 |   4 | th\n==========+====+====+====+=====+====\n π(10)    |  2 |  3 |  5 |   7 | 4th\n----------+----+----+----+-----+----\n π(19)    | 11 | 13 | 17 |  19 | 8th\n----------+----+----+----+-----+----\n π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10) ✔️ \n==========+====+====+====+=====+====\n π(❓)    | .. | .. | .. |  .. | ❓th\n----------+----+----+----+-----+----\n π(❓)    | .. | .. | .. |  .. | ❓th\n----------+----+----+----+-----+----\n π(❓)    | .. | .. | .. |  .. | ❓th 👈 π(19) ❓\n==========+====+====+====+=====+====\n π(❓)    | .. | .. | .. |  .. | ❓th\n----------+----+----+----+-----+----\n π(❓)    | .. | .. | .. |  .. | ❓th\n----------+----+----+----+-----+----\n π(109)   | .. | .. | .. | 109 | 29th 👈 π(29) ✔️\n
            \n

            12 + 18 + 13 = 43

            \n\n
             Osp(8|4) |  1 |  2 |  3 |   4 | th\n==========+====+====+====+=====+====\n π(10)    |  2 |  3 |  5 |   7 | 4th\n----------+----+----+----+-----+----\n π(19)    | 11 | 13 | 17 |  19 | 8th\n----------+----+----+----+-----+----\n π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10)\n==========+====+====+====+=====+====\n π(29+12) | 31 | 37 | 41 |   - | 13th ✔️\n----------+----+----+----+-----+----\n π(41+18) | 43 | 47 | 53 |  59 | 17th ✔️\n----------+----+----+----+-----+----\n π(59+13) | 61 | 67 | 71 |   - | 20th 👈 π(19+1) ✔️\n==========+====+====+====+=====+====\n π(❓)    | .. | .. | .. |  .. | ❓th\n----------+----+----+----+-----+----\n π(❓)    | .. | .. | .. |  .. | ❓th\n----------+----+----+----+-----+----\n π(109)   | .. | .. | .. | 109 | 29th 👈 π(29)\n
            \n\n

            109 - 72 = 37

            \n\n
             Osp(8|4) |  1 |  2 |  3 |   4 | th\n==========+====+====+====+=====+====\n π(10)    |  2 |  3 |  5 |   7 | 4th\n----------+----+----+----+-----+----\n π(19)    | 11 | 13 | 17 |  19 | 8th\n----------+----+----+----+-----+----\n π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10)\n==========+====+====+====+=====+====\n π(41)    | 31 | 37 | 41 |   - | 13th\n----------+----+----+----+-----+----\n π(59)    | 43 | 47 | 53 |  59 | 17th \n----------+----+----+----+-----+- ---\n π(72)    | 61 | 67 | 71 |   - | 20th 👈 π(19+1)\n==========+====+====+====+=====+====\n π(72+11) | 73 | 79 | 83 |   - | 23th ✔️\n----------+----+----+----+-----+----\n π(83+18) | 89 | 97 |101 |   - | 26th ✔️\n----------+----+----+----+-----+----\n π(101+8) |103 |107 |109 |   - | 29th 👈 π(29+1) ✔️\n
            \n\n

            Decay Objects

            \n\n
            “Eliason’s work has been both praised and criticized within the academic community. Some scholars have praised his innovative approach to the study of the Torah and the insights that it has yielded. Others have criticized his methods as being overly subjective and lacking in scientific rigor. _([Torah Geometry](https://allmynoodles.com/torah-geometry/))_\n
            \n\n

            \"dreidel-letters-3\"

            \n\n
            Despite the controversy surrounding his work, Eric Eliason’s Torah geometry and gematria remain a fascinating subject of study for those interested in the mysteries of religious texts and the ways in which they can be interpreted and understood.\n
            \n\n

            \"a-tree-maze-7\"

            \n\n
            Mathematically, this type of system requires ***27 letters (1-9, 10–90, 100–900)***. In practice, the last letter, tav (which has the value 400), is used in combination with itself or other letters from qof (100) onwards to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes ***extended to 27 by using 5 sofit (final)*** forms of the [Hebrew letters](https://en.wikipedia.org/wiki/Hebrew_numerals#cite_note-7). _([Wikipedia](https://en.wikipedia.org/wiki/Hebrew_numerals))_\n
            \n\n

            \"Hebrew

            \n\n

            The first object symboled by “star” above is taken from one of the Higgs particles called neutral CP-odd (A) and behave as the base unit.

            \n\n
            The Higgs mechanism breaks electroweak symmetry in the Standard Model, giving mass to particles ***through its couplings***.\n- Current data from electroweak precision measurements points to a light Higgs {Mmggs < 199 GeV @ 95% CL [1]). However, the Higgs has never been definitively observed (MHiggs > 114 GeV at 95% CL [2]). \n- A Standard Model Higgs suffers from the so called hierarchy problem. The theory needs fine-tuned parameters to accomodate a light Higgs mass. Supersymmetry offers a solution to this problem, through a symmetry between fermions and bosons. \n- The Minimal Supersymmetric Standard Model  contains ***two Higgs doublets, leading to five physical Higgs bosons: Two neutral CP-even states (h and H), one neutral CP-odd (A), and two charged states (H+ and H~)***. \n- At tree-level, the masses are governed by two parameters, often taken to be mA and tan/3 [3]. When tan/3 > > 1 , ***A is nearly degenerate with one of the CP-even states (denoted φ)***. Where mA < 130 GeV (mA > 130), mA = mh (mA = mH).\n- In this same large tan/3 region, the cross sections for some production mechanisms such as pp -» Α(φ) and pp -» A($i)bb are enhanced by factors of tan /32(sec/32). For example, with Λ/S = 2 TeV, tan/3 = 30 and mA = 100 GeV, the cross sections for pp —>· A and pp —> φ are each of or-der 10 pb[4].\n- The cross section for pp -> Α/φΜ) is smaller, but within the same order of magnitude. In the same region, the branching ratios to Α/φ ->· bb and rr dominate, ***at ~ 90% and ~ 10%*** respectively, independent of mass. \n- Due to their similar masses, cross-sections and branching ratios in the high tan/3 region, we search for ***both A and φ simultaneously**$.\n- At the Tevatron, we search for pp —>> Α/φ —► rr (the bb final state is expected to be overwhelmed by dijet background) and pp ->· Α/φΰ) -» bbbb. \n- This search for pp -> Α/φ -> r+r~ is underway at CDF. The dominant issues for this analysis are: ***[tau identification](https://github.com/eq19/eq19.github.io/files/13852355/AndreaCardini-ICHEP2020-DeepTau.pdf), ditau mass reconstruction, irreducible background from Z —► rr, and event loss at the trigger level***. \n\nWherever not specified, we use the benchmark case of ***mA = 95 GeV and tan ß = 40*** to quote efficiencies and cross-sections. _([Search for MSSM Higgses at the Tevatron](https://github.com/eq19/eq19.github.io/files/14056796/0212016.pdf))_\n
            \n\n

            π(10) = 2,3,5,7

            \n\n

            \"SO(10)\"\n

            \n\n
            Sub  | i  |  β  | f   \n=======+====+=====+=======  ===   ===   ===   ===   ===   ===\n 1:1:0 | 1  |   1 | 2 {71}   1     1     |     |     |     |\n-------+----+-----+-------  ---   ---    |     |     |     |\n 1:2:1 | 2  |   2 | 3 {71}         |     |     |     |     |\n-------+----+-----+----            |     |     |     |     |\n*1:2:2 | 3  |   3 |                |     |     |     |     |\n-------+----+-----+----            |     |     |     |     |\n*1:3:3 | 4  |   4 |                |     |     |     |     |  \n-------+----+-----+----            |     |     |     |     |\n 1:3:4 | 5  |   5 |                |     |     |     |     |\n-------+----+-----+----            9     1‘    |    Δ100   |\n*1:3:5 | 6  |   6 |                |     |     |     |     |\n-------+----+-----+----            |     |     |     |     |\n*1:4:6 | 7  |   7 |                |     |     |     |     |\n-------+----+-----+----            |     |     |     |     |\n 1:4:7 | 8  |   8 |                |     |     |     |     |\n-------+----+-----+----            |     |     |     |     |\n*1:4:8 |{9} |   9 | 15 = 9 + 6 √   |     |     |     |     | ← 15 ✓\n=======+====+=====+====           ===   ===    1\"   ===    |\n*1:4:9 |{10}|  10 | 19 = 9 + 10 √  |     |     |     |     |\n-------+----+-----+----            |     |     |     |     |\n 2:1:0 | 11 |  20 | 20 = 19 + log 10 √   |     |     |     |\n-------+----+-----+----                  |     |     |     |\n 2:2:1 | 12 |  30 |                      |     |     |     |\n-------+----+-----+----                  |     |     |     |\n*2:2:2 | 13 |  40 |                      |     |     |     |\n-------+----+-----+----                  |     |     |     |\n*2:3:3 | 14 |  50 |                      |     |     |     |\n-------+----+-----+----                  |     |     |     |\n 2:3:4 | 15 |  60 |                      9‘    |   Δ200  Δ600\n-------+----+-----+----                  |     |     |     |\n*2:3:5 | 16 |  70 |                      |     |     |     |\n-------+----+-----+----                  |     |     |     |\n*2:4:6 | 17 |  80 |                      |     |     |     |\n-------+----+-----+----                  |     |     |     |\n 2:4:7 |{18}|  90 | 32 = 26 + 6 √        |     |     |     |← 32 = 31 + ∆1✓\n=======+====+=====+====                 ===   ===   ===    |\n*2:4:8 |{19}| 100 | 36 = 26 + 10 √       |     |     |     |\n-------+----+-----+----                  |     |     |     |\n*2:4:9 | 20 | 200 | 38 = 36 + log 100 √        |     |     |\n-------+----+-----+----                        |     |     |\n 3:1:0 | 21 | 300 |                            |     |     |\n-------+----+-----+----                        |     |     |\n 3:2:1 | 22 | 400 |                            |     |     |\n-------+----+-----+----                        |     |     |\n*3:2:2 | 23 | 500 |                            |     |     |\n-------+----+-----+----                        |     |     |\n*3:3:3 | 24 | 600 |                            9\"  Δ300    |\n-------+----+-----+----                        |     |     |\n 3:3:4 | 25 | 700 |                            |     |     |\n-------+----+-----+----                        |     |     |\n*3:3:5 | 26 | 800 |                            |     |     |\n-------+----+-----+----                        |     |     |\n*3:4:6 | 27 | 900 | 46 = 40 + 6 √              |     |     |← 46 = 45 + ∆1 ✓\n=======+====+=====+====                       ===   ===   ===\n 3:4:7 |{28}|1000 | 50 = 40 + 10 = 68 - 18 √\n
            \n\n
            [Valise adinkras](https://github.com/eq19/feed/files/13248983/2110.01665.pdf), although an important subclass, do not encode all information present when a 4D supermultiplet is reduced to 1D. We extend this to [non-valise adinkras](https://github.com/HEPTHools/Adinkra) providing a complete ***[eigenvalue classification](https://github.com/eq19/feed/files/13228760/1904.01738.pdf)*** via _Python code_.\n
            \n\n

            \"IMG_20231228_185122\"

            \n\n

            In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become the irrational partitions.

            \n\n

            Flavour and Colors

            \n\n

            \"image\"

            \n\n

            \"image\"

            \n\n
            You might imagine, right away, that there are nine gluons that are possible: one for each of the color-anticolor combinations possible. Indeed, this is what almost everyone expects, following some very straightforward logic.\n- There are three possible colors, three possible anticolors, and each possible color-anticolor combination represents one of the gluons. If you visualized what was happening inside the proton as follows:\n  - a quark emits a gluon, changing its color,\n  - and that gluon is then absorbed by another quark, changing its color,\n\nyou’d get an excellent picture for what was happening with six of the possible gluons. _([Why are there only 8 gluons](https://www.forbes.com/sites/startswithabang/2020/11/18/why-are-there-only-8-gluons/?sh=7d018fc67ad8))_\n
            \n\n

            \"Why

            \n\n

            There is also another explanation to the above color charge based on gluons transform in the adjoint representation of SU(3), which is 8-dimensional.

            \n\n

            Triangular Wave

            \n\n

            One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so one of solution would be truncated approach.

            \n\n
            The first 3 triplets are prime and form the first triangle on top. Then we do the next two and the last one on the bottom because we will sandwich the other 3 in.\n- These all match perfectly or one letter off on the bottom triangle, by sliding. The BGY slides, the YBG matches the YBR except one letter.\n- Notice that the first 3 are prime. Then the next 4 are quite factorable. The 29 (RBR) is prime and there is no 29th letter, ending the pattern. 26 and 27 lead to 28 letters. Incidentally, the first 3 primes add to 99 and the primes add to 128. The last three to cover (RYY,YBY and RBR) match up with the top triangle’s bottom (except one letter) with RYY in reverse and make a matching triangle together. RYY has the most factors. The last 3 end in 29, suggesting an end to the pattern as there is no 29th letter.\n- The final letter is B and it matches the middle letter, the two letters at the top and the two letters at the bottom if we do the BGY slide in one way.\n\n***[Only B](https://allmynoodles.com/torah-geometry/)***.\n
            \n\n

            \"a-triangle-sandwich-3\"

            \n\n
            Speculating beyond the pyramidal model just described, the ratios seem to suggest that this geometry can be conceived sinusoidally as a Fourier series forming continuous triangular waves that reverse polarity in quarter cycles. For example, the 9th harmonic of the fundamental frequency 440 Hz = 3960 Hz (and keep in mind that 3960 = 1092 − 892, their relationship to the first 1000 primes covered in detail earlier in this section). Then consider that 8,363,520 (additive sum of the pyramid)/(1092 − 892) = 2112 (index # of the 1000th prime); 8/3/6/3/5/20 x (1092 − 892) x 360 = 2112; and that 443,520 (additive sum of the pyramidion)/(1092 − 892) = 112 (index # of 419, the 81st prime [as in 92, interestingly], and in turn 7919 x 28/528 = [419]; whole number part taken). _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            Here’s a draft of what the proposed triangular wave might look like:

            \n\n

            \"Triangular

            \n\n

            Base on the above discussions we conclude that the decay frames should behave as 4 times Triangular Waves as well, let have it done by The True Primer Pairs.

            \n\n
            Surprisingly, the 24-cell hexagon confines all natural numbers. ***The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon’s outer boundary, other than 2 and 3, the initial primes that forced the number line into this complex coil***. Without a prime number in the outer set of triangles, the number line does not change to an outward course and remains forever contained in the 24 cells shown above. _([HexSpin](https://www.hexspin.com/defining-the-prime-hexagon/))_\n
            \n\n
            The True Prime Pairs\n(5,7), (11,13), (17,19)\n\nTabulate Prime by Power of 10\nloop(10) = π(10)-π(1) = 4-0 = 4\nloop(100) = π(100)-π(10)-1th = 25-4-2 = 19\nloop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n--------------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs → Δ→π  |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n==========================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(∆10) → π(10)     |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n--------------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(10+∆9) → π(19)   | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 13 → π(19+∆10) → π(29)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th\n--------------------------+----+----+----+----+----+----+----+----+----+-----\n 11 → π(29+∆12) → π(41)  | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n  7 → π(41+∆18) → π(59)  | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n--------------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n  5 → π(59+∆13) → π(72)  | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th\n==========================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n  3,2 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n==========================+====+====+====+====+====+====+====+====+====+=====\n         Δ                                                            Δ\n12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-\n
            \n\n
            Speaking of iterative digital division–a powerful tool for exposing structure–we get this astonishing equation: iteratively dividing the digital roots of the first 12 Fibonacci numbers times the divisively iterated 1000th prime, 7919, times 3604 gives us 1000.\n- Keep in mind that the first two and last two digits of the Fibo sequence below, 11 and 89, sum to 100; that 89 is the 11th Fibo number; that there are 1000 primes between 1 and 892; and that 89 has the Fibonacci sequence embedded in its decimal expansion:\n
            \n\n

            1/1/2/3/5/8/4/3/7/1/8/9 x 7/9/1/9 x 3604 = 1000

            \n\n

            \"One

            \n\n
                |-------------------------------- 2x96 -------------------------------|\n    |--------------- 7¤ ---------------|---------------- 7¤ --------------|👈❓\n〰️Osp(8|4) 👉------ {89} --------------|-------------- {103} -------------|\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |\n    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89\n    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|\n    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|\n          13 variations               48 variations          11 variations \n
            \n\n

            \"image\"

            \n\n
                |-------------------------------- 2x96 ---------------------|\n    |--------------- 7¤ ---------------|---------- 5¤ ----------| ✔️\n〰️Osp(8|4) 👉------ {89} --------------|-------- {103} ---------|\n    +----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n    +----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---👉109²-89²=11×360 ✔️\n    |---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n    |-------- Bosons --------|---------- Fermions ---------|-- Graviton\n          13 variations               48 variations           11 variations\n
            \n\n

            \"image\"

            \n","dir":"/multiplication/","name":"13.md","path":"multiplication/13.md","url":"/multiplication/13.html"},{"sort":15,"spin":1,"span":"gap","suit":"intro","layout":"default","title":"Mass Gap (Δ)","content":"# [Mass Gap (Δ)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#mass-vs-gap-%CE%B4)\n\n>In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).\n\n[![default](https://user-images.githubusercontent.com/8466209/224185881-0d1c448e-ee04-4ad2-87e2-1da3c864643c.png)](https://en.wikipedia.org/wiki/Feynman_diagram)\n\n_[FeynCalc](https://feyncalc.github.io/)_ is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics. Some of the features of FeynCalc are\n\n* Passarino-Veltman reduction of one-loop amplitudes to standard scalar integrals\n* Tools for frequently occurring tasks like Lorentz index contraction, color factor calculation, Dirac matrix manipulation and traces, etc.\n* Tensor and Dirac algebra manipulations (including traces) in 4 or D dimensions\n* Generation of Feynman rules from a Lagrangian\n* Tools for non-commutative algebra\n* SU(N) algebra\n* Tables of integrals, convolutions and Feynman rules\n* Special convolution, Mellin transform and other integral tables\n* Tools for calculating 2-loop propagator-type diagrams\n* FORM and FORTRAN code generation\n* Translation to and from FORM\n\n```\nknownResult = 2*SMP[\"e\"]^4*((s^2 + u^2)/t^2) + \n 4*SMP[\"e\"]^4*(u^2/(s*t)) + 2*SMP[\"e\"]^4*((t^2 + u^2)/s^2); \nFCCompareResults[ampSquaredMassless[0], knownResult, \n Text -> {\"\\tCheck the final result:\", \"CORRECT.\", \"WRONG!\"}, \n Interrupt -> {Hold[Quit[1]], Automatic}]; \nPrint[\"\\tCPU Time used: \", Round[N[TimeUsed[], 4], 0.001], \n \" s.\"]; \n```\n\n[![default](https://user-images.githubusercontent.com/8466209/224119544-f6819ad1-150b-48e9-a396-b51fe65a7fbe.png)](https://arxiv.org/pdf/1602.04182.pdf)\n\nToday most physicists draw Feynman diagrams in a more stylized way, highlighting the topology of propagation lines and vertices. (This diagram and Figure 4 are reproduced from Feynman 1949 (by permission of the American Physical Society.)\n\n![](https://user-images.githubusercontent.com/8466209/222644033-b9a9b8c3-3416-4d0c-acf4-890dd774e887.png)\n","dir":"/exponentiation/span15/","name":"gist01.md","path":"exponentiation/span15/gist01.md","url":"/exponentiation/span15/gist01.html"},{"sort":16,"spin":109,"span":7,"suit":23,"layout":"default","title":"Similar Order of Magnitude (spin 5)","content":"

            Similar Order of Magnitude (spin 5)

            \n\n
            This section is referring to _[wiki page-16](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-12]()_ that is _[inherited ]()_ from _[the gist section-23](https://gist.github.com/eq19)_ by _[prime spin-109](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-7](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Double Beta Decay

            \n\n

            Every second, trillions upon trillions of the tiny particles shoot down to Earth from space almost completely unaffected by any matter they come across.

            \n\n

            \"image\"

            \n\n
            Feynman diagram of neutrinoless ***double beta decay***, with two neutrons decaying to two protons.\n- The only emitted products in this process are two electrons, which can occur if the neutrino and antineutrino are the same particle (i.e. Majorana neutrinos) so the same neutrino can be emitted and absorbed within the nucleus.\n- In conventional double beta decay, two antineutrinos — one arising from each W vertex — are emitted from the nucleus, in addition to the two electrons. \n\nThe detection of neutrinoless double beta decay is thus a sensitive test of whether neutrinos are Majorana particles.  _([Wikipedia](https://en.wikipedia.org/wiki/Double_beta_decay#Neutrinoless_double_beta_decay))_\n
            \n\n

            \"Quantum

            \n\n
            We analyze a simple extension of the Standard Model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group.\n- Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sector\nand the SM particles, and generate masses for the active neutrinos via the seesaw\nmechanism.\n- We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario.\n\nWe also study the constraints from direct Dark Matter searches and the prospects for indirect detection\nvia sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV. _([Sterile Neutrino portal to Dark Matter II - pdf](https://github.com/eq19/eq19.github.io/files/13822870/1607.02373.pdf))_\n
            \n\n

            \"Sterile

            \n\n
            The current status of the nucleon decay experiments is as follows: the partial lifetime\nlimit on p → π0e+ is τ (p → π0e+) > 1.67 × 1034 years, and the bound on the partial lifetime for p → K+ν is τ (p → K+ν) > 6.6 × 1033 years [42, 43]. It is expected that a future experiment, the Hyper-Kamiokande, may achieve a sensitivity of 5-10 times the present bound. _([Proton Decay - pdf](https://github.com/eq19/eq19.github.io/files/13884072/1603.03568.pdf))_\n
            \n\n

            \"image\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry\n7 11 4 1 0 11 ◄--- #19 👈 30\n8 13 5 1 0 13 ◄--- #17 ◄--∆32-- #49 👈 30 ✔️\n9 17 0 1 1 17 ◄--- 7th prime 👈 f(#36) ◄--- antisymmetric state ✔️\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            Exact Dark Symmetry

            \n\n

            \"image\"

            \n\n

            lightning speed ÷ shockwave speed = 300000km/s ÷ 3km/s = 100000 ÷ 1

            \n\n
              Sub  | i  |     β | f   \n=======+====+=======+=======  ===   ===   ===   ===   ===   ===\n 1:1:0 | 1  |     1 | 2 {71}   1     1     |     |     |     |\n-------+----+-------+-------  ---   ---    |     |     |     |\n 1:2:1 | 2  |     2 | 3 {71}         |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:2:2 | 3  |     3 | 7 = 1 + 2x3    |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:3:3 | 4  |     4 | 10 = 9 + 1     |     |     |     |     |  \n-------+----+-------+----            |     |     |     |     |\n 1:3:4 | 5  |     5 | 11 = 9 + 2     |     |     |     |     |\n-------+----+-------+----            9     1‘    |    Δ100   |\n*1:3:5 | 6  |     6 | 12 = 9 + 3     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:4:6 | 7  |     7 | 13 = 9 + 4     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n 1:4:7 | 8  |     8 | 14 = 9 + 5     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:4:8 |{9} |     9 | 15 = 9 + 6     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:4:9 |{10}|    10 | 19 = 9 + 10    |     |     |     |     |\n=======+====+=======+====           ===   ---    1\"   ---    |\n 2:1:0 | 11 |    20 | 20 = 19 + log 10¹    |     |     |     |\n-------+----+-------+----                  |     |     |     |\n 2:2:1 | 12 |    30 | 26 = 20 + 2x3        |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:2:2 | 13 |    40 | 27 = 26 + 1          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:3:3 | 14 |    50 | 28 = 26 + 2          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n 2:3:4 | 15 |    60 | 29 = 26 + 3          9‘    |   Δ200    |\n-------+----+-------+----                  |     |     |     |\n*2:3:5 | 16 |    70 | 30 = 26 + 4          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:4:6 | 17 |    80 | 31 = 26 + 5          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n 2:4:7 |{18}|    90 | 32 = 26 + 6          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:4:8 |{19}|   100 | 36 = 26 + 10         |     |     |     |\n=======+====+=======+====                 ===   ---   ---  ∆1000\n*2:4:9 | 20 |   200 | 38 = 36 + log 10²          |     |     |\n-------+----+-------+----                        |     |     |\n 3:1:0 | 21 |   300 | 40 = 36 + 2 x log 10²      |     |     |\n-------+----+-------+----                        |     |     |\n 3:2:1 | 22 |   400 | 41 = 40 + 1                |     |     |\n-------+----+-------+----                        |     |     |\n*3:2:2 | 23 |   500 | 42 = 40 + 2                |     |     |\n-------+----+-------+----                        |     |     |\n*3:3:3 | 24 |   600 | 43 = 40 + 3                9\"  Δ300    |\n-------+----+-------+----                        |     |     |\n 3:3:4 | 25 |   700 | 44 = 40 + 4                |     |     |\n-------+----+-------+----                        |     |     |\n*3:3:5 | 26 |   800 | 45 = 40 + 5                |     |     |\n-------+----+-------+----                        |     |     |\n*3:4:6 | 27 |   900 | 46 = 40 + 6                |     |     |\n-------+----+-------+----                        |     |     |\n 3:4:7 |{28}|  1000 | 50 = 40 + 10               |     |     |\n=======+====+=======+====                       ===  ====    |\n*3:4:8 |{29}|  2000 | 68 = 50 + 3 x (2x3)      {10³}   |     |\n-------+----+-------+----                        Δ     |     |\n 3:4:9 |{30}|  3000 |{71}= 68 + log 10³                |     |   \n-------+----+-------+----                              |     |\n 3:2:1 | 31 |  4000 | 72 = 71 + 1                      |     |\n-------+----+-------+----                              |     |\n*3:2:2 | 32 |  5000 | 73 = 71 + 2                      |     |\n-------+----+-------+----                              |     |\n*3:3:3 | 33 |  6000 | 74 = 71 + 3                    Δ400    |\n-------+----+-------+----                              |     |\n 3:3:4 | 34 |  7000 | 75 = 71 + 4                      |     |\n-------+----+-------+----                              |     |\n*3:3:5 | 35 |  8000 | 76 = 71 + 5                      |     |\n-------+----+-------+----                              |     |\n*3:4:6 | 36 |  9000 |{77}= 71 + 6                      |     |\n-------+----+-------+----                              |     |\n 3:4:7 |{37}| 10000 | 81 = 71 + 10 = 100 - 19          |     |\n=======+====+=======+====                             ====  ----\n
            \n\n

            32-5 = 27 = 9x3

            \n\n
            The four faces of our pyramid additively cascade ***32 four-times triangular numbers*** (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of ***32^2 = 1024 = 2^10***). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of ***the 1000th prime*** within our domain, and equals the total number of 'elements' used to construct the pyramid. _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            \"\"

            \n\n

            109 = 29th prime = ((10th)th prime)

            \n\n
                |-------------------------------- 2x96 ---------------------|\n    |--------------- 7¤ ---------------|---------- 5¤ ----------|\n✔️👉|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n    +----+----+----+----+----+----+----+----+----+----+----+----+\n    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n    +----+----+----+----+----+----+----+----+----+----+----+----+\n    |--------- {53} ---------|---- {48} ----|---- {48} ----|---👉109²-89² ✔️\n    |---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n    |-------- Bosons --------|---------- Fermions ---------|-- Graviton\n          13 variations               48 variations           11 variations\n
            \n\n

            Parity Order

            \n\n

            \"symmetry-09-00097-ag-550\"

            \n\n
            The origin of multiple generations of fermions, and the particular count of 3, is an ***[unsolved problem of physics](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics).***\n- [String theory](https://en.wikipedia.org/wiki/String_theory) provides a cause for multiple generations, but the particular number depends on the details of the [compactification](https://en.wikipedia.org/wiki/Compactification_(physics)) of the [D-brane](https://en.wikipedia.org/wiki/D-brane) intersections.\n- Additionally, [E8](https://en.wikipedia.org/wiki/E8_(mathematics)) [grand unified theories](https://en.wikipedia.org/wiki/Grand_Unified_Theory) in 10 dimensions [compactified](https://en.wikipedia.org/wiki/Compactification_(physics)) on certain [orbifolds](https://en.wikipedia.org/wiki/Orbifold) down to 4‑D naturally contain 3 generations of matter.[[11]](https://en.wikipedia.org/wiki/Generation_(particle_physics)#cite_note-11) This includes many [heterotic string theory](https://en.wikipedia.org/wiki/Heterotic_string_theory) models.\n\nIn standard quantum field theory, under certain assumptions, a single fermion field can give rise to multiple fermion poles with mass ratios of around eπ≈23 and e2π≈535 potentially explaining the large ratios of fermion masses between successive generations and their origin. _([Wikipedia](https://en.wikipedia.org/wiki/Generation_(particle_physics)))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                       MEC 30 / 2\n------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)               ∆9 ✔️  |\n      |      +-----+-----+                    👆     |          Double\n      |      |     |  9  | ∆9+∆(89-71)=∆27= { ∆9 ✔️  |‹--109² { Beta\n  2   +------|  5* +-----+-----               👇     |          Decay\n      |      |     |  10 |                    ∆9 ✔️  |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7 x 24 = 168 √\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}\n
            \n\n

            \"matrix-folding\"

            \n\n
            Tabulate Prime by Power of 10\n  loop(10) = π(10)-π(1) = 4-0 = 4\n  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n  =======================+====+====+====+====+====+====+====+====+====+=====\n   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th\n  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th\n  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n  =======================+====+====+====+====+====+====+====+====+====+=====\n           Δ                                                            Δ\n  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1\n\nSequence:\n By the next layer the 89² will become 89 and 5 become 5² or 25.\n This 89 and 25 are in the same layer with total of 114 or prime 619\n So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n
            \n\n
            Using Euler's method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler _([Wikipedia](https://en.wikipedia.org/wiki/Partition_function_(number_theory)#Generating_function))_.\n
            \n\n

            π(π(π(1000th prime))) + 1 = 40

            \n\n

            \"image\"\n

            \n\n

            Distribution Order

            \n\n
            1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave reversal to 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n
            \n\n

            \"96

            \n\n

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycling .

            \n\n

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️\n
            \n\n

            \"223622800-4602ad28-1622-4742-821e-d702c0fc8303\"

            \n\n","dir":"/multiplication/","name":"14.md","path":"multiplication/14.md","url":"/multiplication/14.html"},{"sort":17,"spin":108,"span":6,"suit":24,"layout":"default","title":"The Search for The Graviton (spin 6)","content":"

            The Search for The Graviton (spin 6)

            \n\n

            Most theories containing gravitons suffer from severe problems. This has led theorists to make choices subjectively (as always) on what is the most elegant theory.

            \n\n
            This section is referring to _[wiki page-17](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-13]()_ that is _[inherited ]()_ from _[the gist section-24](https://gist.github.com/eq19)_ by _[prime spin-108](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-6](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way.

            \n\n

            Boson Decay

            \n\n

            Higgs boson decay process into two Z bosons, each decaying in to two leptons. When a particle decays, it transforms into other particles (called decay products).

            \n\n
            Attempts to extend the Standard Model or other quantum field theories by adding gravitons run into serious theoretical difficulties at energies close to or above the [Planck scale](https://en.wikipedia.org/wiki/Planck_scale).\n- This is because of infinities arising due to quantum effects; technically, gravitation is not [renormalizable](https://en.wikipedia.org/wiki/Renormalizable).\n- Since classical general relativity and [quantum mechanics](https://en.wikipedia.org/wiki/Quantum_mechanics) seem to be incompatible at such energies, from a theoretical point of view, this situation is not tenable.\n\nOne possible solution is to replace particles with [strings](https://en.wikipedia.org/wiki/String_theory). String theories are quantum theories of gravity in the sense that they reduce to classical general relativity plus field theory at low energies, but are fully quantum mechanical, contain a graviton, and are thought to be mathematically consistent. _([Wikipedia](https://en.wikipedia.org/wiki/Graviton))_\n
            \n\n

            \"Search

            \n\n

            There are 5 different string theories, each requiring 10 dimensions. On the other hand, string theory is supposed to be fundamental theory.

            \n\n
            Introduced earlier in GUTS: The Unification of Forces Superstring theory is an attempt to unify gravity with the other three forces and, thus, must contain quantum gravity.\n- The main tenet of Superstring theory is that fundamental particles, including the graviton that carries the gravitational force, act like one-dimensional vibrating strings.\n- Since gravity affects the time and space in which all else exists, Superstring theory is an attempt at a Theory of Everything (TOE).\n- Each independent quantum number is thought of as a separate dimension in some super space (analogous to the fact that the familiar dimensions of space are independent of one another) and is represented by a different type of Superstring.\n- As the universe evolved after the Big Bang and forces became distinct (spontaneous symmetry breaking), some of the dimensions of superspace are imagined to have curled up and become unnoticed.\n- Forces are expected to be unified only at extremely high energies and at particle separations on the order of 10^-35m. This could mean that Superstrings must have dimensions or wavelengths of this size or smaller.\n- Just as quantum gravity may imply that there are no time intervals shorter than some finite value, it also implies that there may be no sizes smaller than some tiny but finite value. That may be about 10^-35m.\n- If so, and if Superstring theory can explain all it strives to, then the structures of Superstrings are at the lower limit of the smallest possible size and can have no further substructure.\n- This would be the ultimate answer to the question the ancient Greeks considered: There is a finite lower limit to space. Not only is Superstring theory in its infancy, it deals with dimensions about 17 orders of 10^-18m magnitude smaller than the details that we have been able to observe directly.\n- It is thus relatively unconstrained by experiment, and there are a host of theoretical possibilities to choose from. This has led theorists to make choices subjectively (as always) on what is the most elegant theory, with less hope than usual that experiment will guide them.\n- It has also led to ***speculation of alternate universes***, with their Big Bangs creating each new universe with a random set of rules. These speculations may not be tested even in principle, since an alternate universe is by definition unattainable. It is something like exploring a self-consistent field of mathematics, with its axioms and rules of logic that are not consistent with nature.\n\nSuch endeavors have often given insight to mathematicians and scientists alike and occasionally have been directly related to the description of new discoveries. _([College Physics 2e - pdf page 1518](https://assets.openstax.org/oscms-prodcms/media/documents/College_Physics_2e-WEB_7Zesafu.pdf))_\n
            \n\n

            \"\"

            \n\n
            With William Thomson’s idea of _[vortex atoms](https://en.wikipedia.org/wiki/Vortex_theory_of_the_atom)_ coming of age in the shape of string and superstring theories, in recent years hopes for a $nite theory of quantum gravity have centered on the quantum superstring (QSS).\n- Although the perturbation expansion yields finite terms, the summations do involve infinities [ 2481. However, that would still be true in quantum electrodynamics (QED) ; in perturbative treatments in quantum field theory these infinities are assumed to arise because of non-perturbative solutions and are regarded as an indication of the latter’s existence. Should we then consider the search for a theory of quantum gravity as having reached its goal and should we therefore cross it out as a motivation for the study of non-Riemannian gravitational theories?\n- The basic assumption in the post- 1984 treatment of the quantum superstring [ 2381 “theory of everything” \n(TOE), an on-mass-shell S-matrix type theory, is that its truncation below Planck mass should go over smoothly into an off-mass-shell relativistic quantum (point) local field theory * (including a version of ten-dimensional supergravity, in one sector of the “heterotic string” [ 2471, for instance) thus, even if the search were over, the same geometrical-gravitational question then relates to that truncated “low-energy” field theory and its gravitational sector. \n\nMoreover, it has been pointed out [ 1051 that consistency would then require the low-energy $eid theory to be fmite by itseIf! This then implies the existence of a finite or renormalizable relativistic quantum field theory of gravity. _([Gauge theory of gravity - pdf](https://github.com/eq19/eq19.github.io/files/13804799/1-s2.0-037015739400111F-main_compressed.pdf))_\n
            \n\n

            \"476931_1_En_1\"

            \n\n

            The symmetry\n of this supergravity theory is given by the supergroup OSp(1\\32) which gives the subgroups O(1) for the bosonic and Sp(32) for the fermion.

            \n\n
            In general relativity, gravity is a force that bends and warps space-time around supermassive bodies.\n- Even though gravity is one of the four fundamental forces in nature, it is very weak compared to the other three forces (electromagnetism, weak force and strong force). So it can’t be observed or identified on the scale of subatomic particles.\n- However, [gravity](https://byjus.com/physics/gravity/) is ***very dominant in long-distance scenarios***. It controls the structure of the macro universe (galaxies, planets, stars, moons).\n- As far as [quantum mechanics](https://github.com/eq19/eq19.github.io/files/13787269/aqm.pdf)\n is concerned, gravity doesn’t have much effect. The probable nature of the quantum realm also poses a significant challenge for the induction of gravity in the quantum realm.\n- Generally, ***gravity does not act as a particle as its own***. Even if a hypothetical model is introduced to explain the particle nature of a gravity particle, it violates fundamental energy laws.\n\nIn the 1970s, theorists tried to discard the self-destructive idea of point-like gravity particles. Instead of point particles, strings were introduced. Even if strings collide, there will be no infinite energy problem. Strings can smoothly smash and rebound without implying any physically nonsense infinities.\n
            \n\n

            \"An-adinkra-for-the-chiral-multiplet\"

            \n\n

            This standard model is missing the Gravitational interaction and it is postulated that there exists a particle called the Graviton that leads to supergravity theory.

            \n\n
            Supergravity is an extension of supersymmetry, designed to include the principles of General Relativity. In order to make this possible, supersymmetry has to become local, with a spacetime-dependent spinor ǫ(x) parametrising the infinitesimal SUSY transformation.\n- The key ingredient of supergravity is the graviton hµν , a massless spin-2 elementary particle which couples to the stress-energy tensor, thus mediating gravitational interactions.\n- Its fermionic, spin-3/2 partner, the gravitino ψαµ, equipped both with a spinor index α and a spacetime index µ, is the gauge field of local supersymmetry and becomes massive when SUSY is broken, by absorbing the emerging goldstino in the so-called super-Higgs mechanism.\n- There are two ways in which the graviton can be related to the metric gµν, either through an infinitesimal expansion gµν = ηµν + hµν around the flat metric ηµν , or through the vielbein formalism.\n\nAs is well-known from General Relativity, the metric (and implicitly the graviton) has tosatisfy the Einstein’s field equations _([Holomorphic_Yukawa_Couplings - pdf](https://github.com/eq19/eq19.github.io/files/13850219/Holomorphic_Yukawa_Couplings_in_Heterotic_String_T.pdf))_\n
            \n\n

            \"NLFIW\"

            \n\n
            Think of it this way, all gravitating bodies in the universe would be surrounded at all times by a cloud of tunneling electrons. We cannot see these particles since they’re so small and since they permeate all of space. They would also tunnel to a different location about once every Planck time (about 10^-43 seconds) whenever they interact with another particle.\n- These interactions between particles amount to the exchanges of bosons between electrons and other electrons or other fermions. At each point where the electron absorbs another boson, we say that the wave function of the electron collapses, and it tunnels to a new location whereupon it interacts with yet another particle.\n- The cloud of electron surrounding gravitating objects would diminish in inverse proportion to the square of the distance; hence, if you recede from an objects’ surface, you’re less likely to find an electron tunneling from that object.\n- Electrons also make an excellent candidate for a particle of gravity since they absorb and emit photons readily, and we know from Einstein’s theory of general relativity that light interacts readily with gravitational fields, and that gravitational fields are thought to emit photons spontaneously.\n- This spontaneous emission of photons is what we refer to as the cosmological constant or dark energy, and in our current thinking on the topic we imagine that particles of antimatter are created and annihilate with particles of matter leading, occasionally, to the emission of a photon. I suspect that this is incorrect and that no such thing as antimatter really exists. I suspect that positrons are really tunneling W particles and that this Dirac Sea, or background of tunneling electrons, is really giving rise to this phenomenon of the cosmological constant, or vacuum energy, we observe inn nature.\n- As a consequence, we would need to adumbrate our standard model of particle physics by about half. This ought to be seen as a positive thing in physics. No longer do we have untestable assumptions (such as the creation and annihilation of particles) in our models, and we have a far easier means of now beginning to probe the quantum nature of gravity.\n\nThe other fascinating consequence of this way of thinking is that gravity would no longer be a fundamental force; instead it would be a secondary effect of electromagnetism. This should have been what we anticipated all along; and now, we might have a quantum theory focusing on only three forces and a theory of gravitation that is truly particle-based. _([Medium - Article](https://medium.com/@cottlesam/quantum-gravity-will-force-us-to-cut-the-standard-model-in-half-c073e2033968))_\n
            \n\n

            \"Cut

            \n\n
            There are two groups of scientists (called collaborations) looking for evidence of gravitons in proton-proton collision experiments at the Large Hadron Collider at CERN. Once a graviton has been created, it’s expected to decay in one of a few possible ways - and it’s evidence of these decays that the collaborations are looking for. ***ATLAS search for evidence that the gravitons decays into two photons, and the CMS search for evidence that the graviton decays into two jets (bursts) of hadrons (a particular class of particle)***. _([ThingsWeDontKnow.com](https://blog.thingswedontknow.com/2016/08/search-for-the-graviton.html))_\n
            \n\n

            \"fully-expanded-incl-matrices\"\n

            \n\n

            Prime Assessments

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry\n7 11 4 1 0 11 ◄--- #19 ◄--- #43 ◄--- 24s 👈 30 ✔️\n8 13 5 1 0 13 ◄--- #17 ◄--- #49 ◄--- 32s 👈 30 ✔️\n9 17 0 1 1 17 ◄--- 7th prime 👈 5 ◄--- antisymmetric state ✔️\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            \"image\"

            \n\n

            Lightning speed ÷ Shockwave speed = 300000km/s ÷ 3km/s = 100000 ÷ 1

            \n\n
              Sub  | i  |     β | f   \n=======+====+=======+=======  ===   ===   ===   ===   ===   ===\n 1:1:0 | 1  |     1 | 2 {71}   1     1     |     |     |     |\n-------+----+-------+-------  ---   ---    |     |     |     |\n 1:2:1 | 2  |     2 | 3 {71}         |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:2:2 | 3  |     3 | 7 = 1 + 2x3    |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:3:3 | 4  |     4 | 10 = 9 + 1     |     |     |     |     |  \n-------+----+-------+----            |     |     |     |     |\n 1:3:4 | 5  |     5 | 11 = 9 + 2     |     |     |     |     |\n-------+----+-------+----            9     1‘    |    Δ100   |\n*1:3:5 | 6  |     6 | 12 = 9 + 3     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:4:6 | 7  |     7 | 13 = 9 + 4     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n 1:4:7 | 8  |     8 | 14 = 9 + 5     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:4:8 |{9} |     9 | 15 = 9 + 6     |     |     |     |     |\n-------+----+-------+----            |     |     |     |     |\n*1:4:9 |{10}|    10 | 19 = 9 + 10    |     |     |     |     |\n=======+====+=======+====           ===   ---    1\"   ---    |\n 2:1:0 | 11 |    20 | 20 = 19 + log 10¹    |     |     |     |\n-------+----+-------+----                  |     |     |     |\n 2:2:1 | 12 |    30 | 26 = 20 + 2x3        |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:2:2 | 13 |    40 | 27 = 26 + 1          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:3:3 | 14 |    50 | 28 = 26 + 2          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n 2:3:4 | 15 |    60 | 29 = 26 + 3          9‘    |   Δ200    |\n-------+----+-------+----                  |     |     |     |\n*2:3:5 | 16 |    70 | 30 = 26 + 4          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:4:6 | 17 |    80 | 31 = 26 + 5          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n 2:4:7 |{18}|    90 | 32 = 26 + 6          |     |     |     |\n-------+----+-------+----                  |     |     |     |\n*2:4:8 |{19}|   100 | 36 = 26 + 10         |     |     |     |\n=======+====+=======+====                 ===   ---   ---  ∆1000\n*2:4:9 | 20 |   200 | 38 = 36 + log 10²          |     |     |\n-------+----+-------+----                        |     |     |\n 3:1:0 | 21 |   300 | 40 = 36 + 2 x log 10²      |     |     |\n-------+----+-------+----                        |     |     |\n 3:2:1 | 22 |   400 | 41 = 40 + 1                |     |     |\n-------+----+-------+----                        |     |     |\n*3:2:2 | 23 |   500 | 42 = 40 + 2                |     |     |\n-------+----+-------+----                        |     |     |\n*3:3:3 | 24 |   600 | 43 = 40 + 3                9\"  Δ300    |\n-------+----+-------+----                        |     |     |\n 3:3:4 | 25 |   700 | 44 = 40 + 4                |     |     |\n-------+----+-------+----                        |     |     |\n*3:3:5 | 26 |   800 | 45 = 40 + 5                |     |     |\n-------+----+-------+----                        |     |     |\n*3:4:6 | 27 |   900 | 46 = 40 + 6                |     |     |\n-------+----+-------+----                        |     |     |\n 3:4:7 |{28}|  1000 | 50 = 40 + 10               |     |     |\n=======+====+=======+====                       ===  ====    |\n*3:4:8 |{29}|  2000 | 68 = 50 + 3 x (2x3)      {10³}   |     |\n-------+----+-------+----                        Δ     |     |\n 3:4:9 |{30}|  3000 |{71}= 68 + log 10³                |     |   \n-------+----+-------+----                              |     |\n 3:2:1 | 31 |  4000 | 72 = 71 + 1                      |     |\n-------+----+-------+----                              |     |\n*3:2:2 | 32 |  5000 | 73 = 71 + 2                      |     |\n-------+----+-------+----                              |     |\n*3:3:3 | 33 |  6000 | 74 = 71 + 3                    Δ400    |\n-------+----+-------+----                              |     |\n 3:3:4 | 34 |  7000 | 75 = 71 + 4                      |     |\n-------+----+-------+----                              |     |\n*3:3:5 | 35 |  8000 | 76 = 71 + 5                      |     |\n-------+----+-------+----                              |     |\n*3:4:6 | 36 |  9000 |{77}= 71 + 6                      |     |\n-------+----+-------+----                              |     |\n 3:4:7 |{37}| 10000 | 81 = 71 + 10 = 100 - 19          |     |\n=======+====+=======+====                             ====  ----\n
            \n\n

            32-5 = 27 = 9x3

            \n\n
            The four faces of our pyramid additively cascade ***32 four-times triangular numbers*** (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of ***32^2 = 1024 = 2^10***). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of ***the 1000th prime*** within our domain, and equals the total number of 'elements' used to construct the pyramid. _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            \"\"

            \n\n
            While gravitons are presumed to be [massless](https://en.wikipedia.org/wiki/Massless_particle), they would still carry [energy](https://en.wikipedia.org/wiki/Energy), as does any other quantum particle. [Photon energy](https://en.wikipedia.org/wiki/Photon_energy) and [gluon energy](https://en.wikipedia.org/wiki/Gluon_energy) are also carried by massless particles.\n- ***It is unclear which variables might determine graviton energy***, the amount of energy carried by a single graviton.\n- Alternatively, [if gravitons are massive at all](https://en.wikipedia.org/wiki/Massive_gravity), the analysis of gravitational waves yielded a new upper bound on the [mass](https://en.wikipedia.org/wiki/Mass) of gravitons.\n- The graviton's [Compton wavelength](https://en.wikipedia.org/wiki/Compton_wavelength) is at least 1.6×10^16 [m](https://en.wikipedia.org/wiki/Metre), or ***about 1.6 [light-years](https://en.wikipedia.org/wiki/Light-year)***, corresponding to a graviton mass of no more than 7.7×10−23 [eV](https://en.wikipedia.org/wiki/Electronvolt)/[c](https://en.wikipedia.org/wiki/Speed_of_light)2.[[22]](https://en.wikipedia.org/wiki/Graviton#cite_note-Abbott2017-22)\n- This relation between wavelength and mass-energy is ***calculated with the [Planck–Einstein relation](https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation)***, the same formula that relates electromagnetic [wavelength](https://en.wikipedia.org/wiki/Wavelength) to [photon energy](https://en.wikipedia.org/wiki/Photon_energy).\n- However, if gravitons are the quanta of gravitational waves, then ***the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons***, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.\n- Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the [GW170104](https://en.wikipedia.org/wiki/GW170104) event, which was ~ 1,700 km. The report[[22]](https://en.wikipedia.org/wiki/Graviton#cite_note-Abbott2017-22) did not elaborate on the source of this ratio. \n\n***It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way***. _([Wikipedia](https://en.wikipedia.org/wiki/Graviton))_\n
            \n\n

            \"\"

            \n\n

            Double decay generations = 2^π(11 dimensions) = 2⁵ = 32

            \n\n
            E = mc²\nm = E/c²\n\nc = 1 light-second\n  = 1000 years x L / t\n  = 12,000 months x 2152612.336257 km / 86164.0906 sec\n  = 299,792.4998 km / sec\n\nNote:\n1 year = 12 months\n1000 years = 12,000 months\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n\nConclusion:\nπ(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (5th level) ✔️\n   👇\nπ(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown ✔️\n   👇\nπ(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe ✔️\n   👇\nπ(π(32(109²-89²))) Moon vs Sun vs Galaxies ✔️\n   👇\n|--👇---------------------------- 2x96 ---------------------|\n|--👇----------- 7¤ ---------------|---------- 5¤ ----------|\n|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown ✔️\n|---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n|-------- Bosons --------|---------- Fermions ---------|-- Graviton\n       13 variations               48 variations           11 variations\n
            \n\n

            BBC News: Prof Stephen Hawking’s final research paper suggests that our Universe may be one of many similar. This paper is the fruit of 20 years’ work.

            \n\n

            Parity Order

            \n\n
            In the second opposing term, the position 13 gives a redundant value of the template 7 of `7 × 7 = 49`. The opposite prime position 31 as the ***11th prime number*** is now forced as ***a new axis-symmetrical zero position***. _([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))_\n
            \n\n

            s(18) = 1 + 49 = 68 - 18 = 50

            \n\n

            \"\"

            \n\n

            ∆9 (local) + 2×∆9 (decay) = ∆27

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} | ✔️   |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown ✔️       |\n----------------------+-----+                                                ---\n
            \n\n

            \"\"

            \n\n
            Tabulate Prime by Power of 10:\n\n  loop(10) = π(10)-π(1) = 4-0 = 4\n  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n  =======================+====+====+====+====+====+====+====+====+====+=====\n   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th\n  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th\n  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n  =======================+====+====+====+====+====+====+====+====+====+=====\n           Δ                                                            Δ\n  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1\n\nSequence:\n By the next layer the 89² will become 89 and 5 become 5² or 25.\n This 89 and 25 are in the same layer with total of 114 or prime 619\n So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n
            \n\n
            Using Euler's method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler _([Wikipedia](https://en.wikipedia.org/wiki/Partition_function_(number_theory)#Generating_function))_.\n
            \n\n

            π(π(π(1000th prime))) + 1 = 40

            \n\n

            \"image\"\n

            \n\n

            Distribution Order

            \n\n

            169 - 1 cycle of 360° = 169 - ∆1 = 168 = π(1000)

            \n\n

            \"96

            \n\n
            The primary reason that the electron is considered to be elementary is that ***experimentally it appears to be point-like and hence structureless***.\n- At the same time we are confronted with the fact that it has a rich set of properties which are fundamental to its nature.\n- ***It has an elementary charge, a half-integral spin, a de\fnite mass, a well de\fned dipole moment, an anomalous spin factor g-2 and of course a wave-particle nature***.\n\nIt seems inappropriate to think about such things as the elementary charge as a separate building block from the elementary particle which carries it. _([Is the electron a photon with toroidal topology? - pdf](https://github.com/eq19/eq19.github.io/files/13790325/LdBelectoroid.pdf))_\n
            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️\n
            \n\n
            Folio math is similar to modular math, but instead of the numbers wrapping around or spinning around a unit circle, they turn back at different positions on both the X and Y axis. ***In other words, they never make full cycles***.\n- The Y-Axis splits at the top, and the X-Axis splits on the left. The colors help this stand out. Let’s start with the top of the Y-Axis. ***All digits at the top of the Y-Axis reduce down to 1,7,4 or 5,2,8***.\n- This is important. Using this Prime Number Folio Coordinate System, it’s easier to think of prime numbers in separate sequences across from each other and right or left-handed rather than next to each other on a number line. I see them as Chiral.\n- All digits in on the right-hand side of the Y-Axis reduce down to 5, 2 or 8. (For example 179 has 3 digits, what matters is that the numbers 1 +7+9 sum to the number 8.) So this would be considered a right-handed prime number. Or a number on the right side of the Y-Axis.\n\nThe image stands on its own. The patterns should jump off the page. Especially with the color. Right-handed numbers have different properties than the left-handed numbers. These observations are in no way mathematically rigorous.\n- The numbers on the right side `(5,2,8)|` of the Y-Axis include not only prime numbers, but the products of the prime numbers combined from both sides of the Y-axis.\n- Every product on the right-hand side of the Y-Axis is created from two primes (or semi-primes or combination of semi-primes) from both sides of the Y-axis (one from each side), which ALWAYS sum to an exact multiple of 6. These are plotted on the right side of the X-Axis. (For example `7×11=77`. While `7+11=18`.)\n\nUsing this Folio Coordinate System, it’s easy to see how the products and sums and their distribution are directly related to each other. You might want to start thinking about the Goldbach Conjecture.\n- All products and sums on the right side are indigo/purple to show how they combine with the red and blue prime numbers.\n- It looks like we are simply adding 6 to each Axis/number line, when in fact we are adding the number 1 to each consecutive number but positioning it at different points while moving around both the X and Y Axis.\n- The colors should help your eye follow the numbers. Follow the colors of the rainbow/number combination to help you move around the system. `(R-1,O-2,Y-3,G-4,B-5,I-6)`.\n\n***The number 35 is an important number***. It’s the first number on the right-hand side that’s a product of two prime factors of `5 x 7 = 35`.\n- The sum of `5 + 7 = 12`. Since the right-handed numbers are distributed evenly by 6, we can add `7 x 6 = 42` to 35 and land on the number 77.\n- So now we know that starting with the number 35 if we add 42 continuously we will ***NEVER land on a prime number***. We can also add `5 x 6 = 42` to 35 and land on 65.\n- We also know that `7 + 11 = 18`. The next number that introduces a product of two primes is `5 x 13 = 65` and `5 + 13 = 18`. So we can take `6 x 13 = 78` and add this to 65 and land on 143. Which is the product of `11 x 13 = 143`.\n- Starting with 65 we can add 78 continuously and ***NEVER land on a prime number***.\n- In the meantime 77 (The product of 7 and 11 now introduces the prime number 11 into the mix. So `77 + (6x11) = 143`.\n- ***Starting with 77 we can add 66 continuously and NEVER land on a prime number***. \n\nYou can’t add multiples of 6 until that multiple is introduced into the sequence. The primes on the left behave differently. You can still move around using multiples of 6, but there is no common starting point like the number 35.\n- You have to start with the squares of ***5 at 25 (in blue)*** for one sequence of numbers and the square of ***7 at 49 (in red)*** for the other sequence of numbers.\n- The sums of these products are also not exact multiples of 6. They sum to 10 and 14 and are matched to the split X Axis on the left-hand side of the graph.\n\nThe Prime Number Folio Coordinate System and it’s natural numbers are all you need to find a prime number or a composite number and it’s factors. ***No need for complex numbers or the Reimann Hypothesis***. _([Medium](https://medium.com/invisible-illness/prime-number-folio-coordinate-system-78b316b65cf7))_\n
            \n\n

            Being brought forth you will also begin to uncover the irrelevant role that the Riemann hypothesis plays 7 ate 9 in understanding this elegant distribution.

            \n\n

            \"The

            \n\n
            This curve is a [polar plot](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) of _[the first 20](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ non-trivial [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) zeros including Gram points along the critical line _[ζ(1/2+t)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-fork-md)_ for real values of t running from 0 to 50. The consecutive zeros have ***[50 red plot points](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)*** between each with zeros identified by magenta _[concentric rings](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d)_ (scaled to show the relative distance between their values of t). _([Wikipedia](https://en.wikipedia.org/wiki/Riemann_hypothesis))_\n
            \n\n

            20x10+ ½(16×6) + ¼(12×18) + ⅛(16×16) = 200 + 48 + 32 + 6 = 286 = 2 x 11 x 13

            \n\n

            \"RiemannZeta

            \n\n

            Despite there are many studies and papers it is still an important open problem today.

            \n\n
            The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the functional equations. _([Riemann Zeta - pdf](https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf))_\n
            \n\n

            \"Riemann

            \n\n

            Sehr leider Herr Riemann. Bis jetzt Leute können den Fall immer noch nicht lösen.

            \n","dir":"/multiplication/","name":"15.md","path":"multiplication/15.md","url":"/multiplication/15.html"},{"sort":18,"spin":107,"span":5,"suit":25,"layout":"default","title":"Elementary Retracements (spin 7)","content":"

            Elementary Retracements (spin 7)

            \n\n

            With the MEC 30 as a folding rule, we describe an application that is familiar and simple. And thus use the identical property of energy and number distribution.

            \n\n
            This section is referring to _[wiki page-18](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-14]()_ that is _[inherited ]()_ from _[the gist section-25](https://gist.github.com/eq19)_ by _[prime spin-107](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-5](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Thus, we get an unmistakable motion plan of energy, based on the number distribution on the MEC 30 as a folding rule.

            \n\n

            Spin Networks

            \n\n

            In fact spin networks constitute a basis that minimize the degree of over-completeness of the loop basis, and for trivalent intersections eliminate it entirely.

            \n\n

            \"Vertex-with-m-outgoing-and-n-ingoing-lines_Q320\"

            \n\n

            The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations.

            \n\n

            \"images

            \n\n

            \"The-action-of-the-area-operator-on-a-node-with-intertwiner-C-j-1-j-2-k-a-1-a-2-b-C-j-3-j_Q320\"

            \n\n

            \"maxwell-interaction\"

            \n\n

            \"41114_2016_3_Equ98\"

            \n\n

            Constant Area

            \n\n

            The five (5) of integer number partitions profound connection between the most fundamental as it also links the five (5) fundamental mathematical constants:

            (1) The number 1, the multiplicative identity,
            (2) The number i, the imaginary unit of the complex numbers.
            \"image\"
            (3) The number π = 3.1415…, the fundamental circle constant, and

            \"Pi-unrolled-720\"

            (4) The number e = 2.718…, also known as Euler’s number, which occurs widely in mathematical analysis.

            \"image\"

            (5) Furthermore, the equation is given in the form of an expression set equal to zero, the number 0, as the additive identity which is common practice in several areas of mathematics.

            \n
            \n

            Euler’s identity is a special case of Euler’s formula eix = cos x + i sin x when evaluated for x = π, In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia)

            \"Euler's

            \n
            \n\n

            It is stated by DE102011101032A9 that using Euler’s identity, the MEC30 standard is more accurately than a measurement.

            \n\n
            In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first [Pauli matrix](https://github.com/eq19/eq19.github.io/files/13818844/math0703448.pdf)\n
            \n\n

            \"ang5\"\n

            \n\n

            The distribution of prime numbers is a central point of study in number theory. So let’s start from there.

            \n\n
            The Lorentz group consists, unsurprisingly, of the Lorentz transformations, which are the linear transformations preserving the Minkowski dot product. Equivalently, they are the linear transformations fixing that hyperboloid of two sheets. If we discard one of the sheets, we obtain the orthochronous (time-preserving) subgroup.\n- From the perspective of the centre of the cone, the hyperboloid looks like an open disc. The orthochronous Lorentz transformations precisely correspond to distance-preserving transformations of the hyperbolic plane. These are themselves determined uniquely by a conformal (or anticonformal) transformation of the ‘circle at infinity’.\n- Adding an extra dimension, the orthochronous Lorentz group O^{+}(3,1) is isomorphic to the group of distance-preserving transformations of hyperbolic 3-space, which is again isomorphic to the group of (anti-)conformal transformations of the ‘sphere at infinity’, namely our index-2 supergroup of the Möbius group.\n\nMoreover, this nicely generalises: the group generated by geometric inversions on the n-sphere is abstractly isomorphic to the orthochronous Lorentz group O^{+}(n+1,1). ***And when n = 24, we get a very beautiful discrete subgroup, namely the automorphism group of the II(25,1)*** lattice intimately related to the [Leech lattice](http://cp4space.wordpress.com/2013/09/12/leech-lattice/). _([Complex Projective 4-Space](https://cp4space.hatsya.com/2013/10/10/what-should-this-group-be-called/))_\n
            \n\n

            \"spacetime\"

            \n\n

            Bispinor Structure

            \n\n
            The Lie group structure of the Lorentz group is explored. Its generators and its Lie algebra are exhibited, via the study of infinitesimal Lorentz transformations.\n- The exponential map is introduced and it is shown that the study of the Lorentz group can be reduced to that of its Lie algebra.\n- Finally, the link between the restricted Lorentz group and the special linear group  is established via the spinor map. \n\nThe Lie algebras of these two groups are shown to be identical (up to some isomorphism).\n
            \n\n

            \"270355_1_En_7_Fig1_HTML\"

            \n\n
            The four pairwise disjoint and non-compact connected components of the Lorentzgroup L = O(1, 3) and corresponding subgroups:\n- the proper Lorentz group L+ = SO(1, 3),\n- the orthochronous Lorentz group L↑,\n- the orthochronous Lorentz group Lo = L↑ + ∪ TL↑+ (see below) and\n- the proper orthochronous Lorentz group L↑+ = SO+(1, 3), which contains the identity element. \n\nOf course, the sets L↓−, L↑− and L↓+ do not represent groups due to the missing identity element. _([[The-four-pairwise-disjoint](https://github.com/eq19/eq19.github.io/files/13810691/weyl_majorana_dirac_aste.pdf))_\n
            \n\n

            \"The-four-pairwise-disjoint-and-non-compact-connected-components-of-the-Lorentz-group-L\"

            \n\n
            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet's 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SU(5)_representation_of_fermions\"\n

            \n\n

            Spin-½ objects are all fermions (a fact explained by the spin–statistics theorem) and satisfy the Pauli exclusion principle where\nEuler’s Identity satisfy Pauli Matrices

            \n\n

            \"Spin_half_angular_momentum\"

            \n\n

            \"5-Table1-1\"

            \n\n

            The edges are labelled by spins together with `intertwiners’ at the vertices which are prescription for how to sum over different ways the spins are rerouted.

            \n\n

            \"Euclidean-space\"

            \n\n

            Bispinor Fashion

            \n\n
            The color strong force is the strong interaction between the three [quarks](https://simple.m.wikipedia.org/wiki/Quarks) that a [proton](https://simple.m.wikipedia.org/wiki/Proton) or [neutron](https://simple.m.wikipedia.org/wiki/Neutron) is made of.\n- It is called the color strong force because, like the [electromagnetic force](https://simple.m.wikipedia.org/wiki/Electromagnetism), the strong force has [charges](https://simple.m.wikipedia.org/wiki/Electric_charge).\n- The electromagnetic force has only one type of charge, which can be either [positive](https://simple.m.wikipedia.org/wiki/Positive_charge) or [negative](https://simple.m.wikipedia.org/wiki/Negative_charge) (magnetic charges are just slow-moving electric charges), but the strong force has three types.\n- These three types of charges are named after colors: red, green, and blue. They also have anti-colors: anti-red, anti-green and anti-blue. Like the electromagnetic force's positive and negative charges, different colors attract, and the same colors repel. Some particles that have color charge are quarks and antiquarks.\n- The type of quark is not related to that quark's color charge at all. Quarks are one of the smallest particles currently known. They take up no space because they are points, and they are the only particles that we have not been able to break apart from other particles yet. This is because the nature of the strong force between particles is that it becomes stronger the further away the particles are.\n\nThe force carrier of the strong force is called the gluon. Gluons also have color charge. Both quarks and gluons have properties that make them unique from other particles, as described in the Standard Model. _([Wikipedia](https://simple.m.wikipedia.org/wiki/Strong_interaction))_.\n
            \n\n

            \"Nuclear_Force_anim\"

            \n\n
            Shortly after the existence of quarks was proposed by [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann) and [George Zweig](https://en.wikipedia.org/wiki/George_Zweig) in 1964, [Moo-Young Han](https://en.wikipedia.org/wiki/Moo-Young_Han) and [Yoichiro Nambu](https://en.wikipedia.org/wiki/Yoichiro_Nambu) introduced a hidden internal degree of freedom in which quark wave functions were antisymmetric, thus solving the spin-statistics problem of the Gell Mann-Zweig quark model.\n- Han and Nambu initially designated this degree of freedom by the group SU(3)', but it was referred to in later papers as \"the three triplet model.\" One feature of the model (which was originally preferred by Han and Nambu) was that it permitted integrally charged quarks, as well as the fractionally charged quarks initially proposed by Zweig and Gell-Mann.\n- Somewhat later, in the early 1970s, Gell-Mann, in several conference talks, coined the name \"Color\" to describe the internal degree of freedom of the three triplet model, and advocated a new field theory, designated as \"Quantum Chromodynamics\" (QCD) to describe the interaction of quarks and gluons within hadrons. In Gell-Mann's QCD, each quark and gluon had fractional electric charge, and carried what came to be called \"Color Charge\" in the space of the Color degree of freedom.\nIn quantum chromodynamics (QCD), a quark's color can take one of three values or charges: red, green, and blue. An antiquark can take one of three anticolors: called antired, antigreen, and antiblue (represented as cyan, magenta, and yellow, respectively). Gluons are mixtures of two colors, such as red and antigreen, which constitutes their color charge. QCD considers eight gluons of the possible nine color–anticolor combinations to be unique; see eight gluon colors for an explanation.\n- All three colors mixed together, or any one of these colors and its complement (or negative), is \"colorless\" or \"white\" and has a net color charge of zero. Due to a property of the strong interaction called color confinement, free particles must have a color charge of zero.\n- A baryon is composed of three quarks, which must be one each of red, green, and blue colors; likewise an antibaryon is composed of three antiquarks, one each of antired, antigreen and antiblue. A meson is made from one quark and one antiquark; the quark can be any color, and the antiquark has the matching anticolor.\n\nThe following illustrates the coupling constants for color-charged particles. In a quantum field theory, a coupling constant and a charge are different but related notions. The coupling constant sets the magnitude of the force of interaction; for example, in quantum electrodynamics, the fine-structure constant is a coupling constant. _([Wikipedia](https://en.wikipedia.org/wiki/Color_charge))_\n
            \n\n

            \"Neutron_QCD_Animation\"

            \n\n

            \"IMG_20240111_062522\"

            \n\n

            \"SO(10)\"\n

            \n\n

            This diagram is representing groupings (leptons, quarks, weak-force bosons) with 6 quarks in a way that par\nallels the 6 leptons.

            \n\n
            In [physics](https://en.wikipedia.org/wiki/Physics), and specifically in [quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory), a bispinor is a mathematical construction that is used to describe some of the [fundamental particles](https://en.wikipedia.org/wiki/Fundamental_particle) of [nature](https://en.wikipedia.org/wiki/Nature), including [quarks](https://en.wikipedia.org/wiki/Quark) and [electrons](https://en.wikipedia.org/wiki/Electron).\n- It is a specific embodiment of a [spinor](https://en.wikipedia.org/wiki/Spinor), specifically constructed so that it is consistent with the requirements of [special relativity](https://en.wikipedia.org/wiki/Special_relativity).\n- Bispinors transform in a certain \"spinorial\" fashion under the action of the [Lorentz group](https://en.wikipedia.org/wiki/Lorentz_group), which describes the symmetries of [Minkowski spacetime](https://en.wikipedia.org/wiki/Minkowski_spacetime).\n- They occur in the relativistic [spin-1/2](https://en.wikipedia.org/wiki/Spin-1/2) [wave function](https://en.wikipedia.org/wiki/Wave_function) solutions to the [Dirac equation](https://en.wikipedia.org/wiki/Dirac_equation).\n- Bispinors are so called because they are constructed out of two simpler component spinors, the [Weyl spinors](https://en.wikipedia.org/wiki/Weyl_spinor). Each of the two component spinors transform differently under the two distinct complex-conjugate spin-1/2 [representations](https://en.wikipedia.org/wiki/Representation_(mathematics)) of the Lorentz group.\n- This pairing is of fundamental importance, as it allows the represented particle to have a [mass](https://en.wikipedia.org/wiki/Mass), carry a [charge](https://en.wikipedia.org/wiki/Charge_(physics)), and represent the flow of charge as a [current](https://en.wikipedia.org/wiki/Noether_current), and perhaps most importantly, to carry [angular momentum](https://en.wikipedia.org/wiki/Angular_momentum).[![ang5](https://github.com/eq19/eq19.github.io/assets/8466209/f6dc49c5-261f-4a8d-8270-cd2f2c25a03d)\n](https://www.lancaster.ac.uk/staff/schomeru/lecturenotes/Quantum%20Mechanics/S16.html)\n- More precisely, the mass is a [Casimir invariant](https://en.wikipedia.org/wiki/Casimir_invariant) of the Lorentz group (an eigenstate of the energy), while the vector combination carries momentum and current, being [covariant](https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors) under the action of the Lorentz group.\n- The angular momentum is carried by the [Poynting vector](https://en.wikipedia.org/wiki/Poynting_vector), suitably constructed for the spin field.[[1]](https://en.wikipedia.org/wiki/Bispinor#cite_note-1)\n- A bispinor is more or less \"the same thing\" as a [Dirac spinor](https://en.wikipedia.org/wiki/Dirac_spinor). The convention used here is that the article on the Dirac spinor presents [plane-wave](https://en.wikipedia.org/wiki/Plane-wave) solutions to the Dirac equation using the Dirac convention for the [gamma matrices](https://en.wikipedia.org/wiki/Gamma_matrices). That is, the Dirac spinor is a bispinor in the Dirac convention.\n- Bispinors are elements of a 4-dimensional complex vector space (1/2, 0) ⊕ (0, 1/2) representation of the Lorentz group.\n\nDirac bispinor 6D shows ***eight (8) quantum spin eigenstates in six (6) dimensions*** of complex spacetime: 0 (the Higgs field), ±½ (fermions), ±1 (bosons), ±⅔ (anti-fermions), 2 (graviton). Top-left Minkowski diagram displays 6D spacetime curvature. Bottom-right projection displays the 2 orthogonal sinusoids of the Dirac harmonic oscillator, and their phase offsets.\n
            \n\n

            \"Dirac_bispinor_6D\"

            \n\n

            Mass vs Gap (Δ)

            \n\n

            FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.

            \n\n
            ***They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics***. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a _[perturbative approach](https://core.ac.uk/download/pdf/76996904.pdf)_ is usually implemented, this being equivalent to summing over Feynman diagrams. _([Wikiwand](https://www.wikiwand.com/en/Partition_function_%28quantum_field_theory%29))_\n
            \n\n

            \"default\"

            \n\n
              Tabulate Prime by Power of 10\n  loop(10) = π(10)-π(1) = 4-0 = 4\n  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n  =======================+====+====+====+====+====+====+====+====+====+=====\n   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th\n  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th\n  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n  =======================+====+====+====+====+====+====+====+====+====+=====\n           Δ                                                            Δ\n  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1\n
            \n\n

            So when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming bilateral 9 sum which facilitate them to finaly generate 1000 primes.

            \n\n

            \"image\"

            \n\n

            These waves have phase offsets, meaning they peak at different times. This all relates to Zitterbewegung, a term describing the jittery motion of particles in quantum mechanics.

            \n\n
            In this work, we propose a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates.\n- We take gaphene/SiC heterostructure as a role model and demonstrate experimentally the substrate modulation leads to Dirac fermion cloning and consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space.\n- Our theoretical modeling captures the cloning mechanism of Dirac states and indicates that flat bands can emerge at certain magic lattice constants of substrate when the period of modulation becomes nearly commensurate with the (√3 ×√3)R30◦ supercell of graphene.\n\nThe results show that the epitaxial monolayer graphene is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons. _(\n[Dirac Fermion Cloning - pdf](https://github.com/eq19/eq19.github.io/files/13834263/Dirac_Fermion_Cloning_Moirbfe_Flat_Bands_and_Magi.pdf))_\n
            \n\n

            \"Dirac

            \n\n
            The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the “mass gap”: the quantum particles have positive masses, even though the classical waves travel at the speed of light. ***This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view***. _([Clay Institute](https://www.claymath.org/millennium/yang-mills-the-maths-gap/))_\n
            \n
            E = mc²\nm = E/c²\n\nc = 1 light-second\n  = 1000 years x L / t\n  = 12,000 months x 2152612.336257 km / 86164.0906 sec\n  = 299,792.4998 km / sec\n\nNote:\n1 year = 12 months\n1000 years = 12,000 months\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n\nConclusion:\nπ(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (mass of matter) ✔️\n   👇\nπ(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown (gap in 2nd-level)✔️\n   👇\nπ(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level) ✔️\n   👇\nπ(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st gap via dark matter) ✔️\n   👇\n|--👇---------------------------- 2x96 ---------------------|\n|--👇----------- 7¤ ---------------|---------- 5¤ ----------|\n|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown\n|---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n|-------- Bosons --------|---------- Fermions ---------|-- Graviton\n       13 variations               48 variations           11 variations\n
            \n\n

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row \nforming the Primes Platform. Thus we got 109 objects including for the 7 rows back to the original stage.

            \n\n

            \"origin\"

            \n\n

            To conclude, we believe we have the first firm evidence of Majorana fermion, after 80 years of this whole saga of trying to find it.

            \n\n
            And we believe this discovery will have important implications in the knowledge and lives of human beings. For example, we live in a universe full of matter now, but the Big Bang created both matter and antimatter. _([Quantized signature of majorana](https://millie.pubpub.org/pub/kangwang))_\n
            \n\n

            \"majorana\"

            \n\n

            So what happened to all the antimatter? Where did it go? Perhaps the Majorana fermion can go some ways towards explaining that.

            \n\n

            \"IMG_20240109_004026\"

            \n\n

            The above is observed following the W0 (assumptions of relativistic quantum mechanics) for the Existence and Mass Gap which transform under the homogeneous group as a four-vector and has a mass gap Δ > 0.

            \n\n

            \"image\"

            \n\n
            [Yang–Mills Existence and Mass Gap](https://www.claymath.org/millennium/yang-mills-the-maths-gap/): Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on ***R^4 and has a mass gap Δ > 0***. (In [quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory), ***the mass gap is the difference in energy between the vacuum and the next lowest [energy state](https://en.wikipedia.org/wiki/Energy_state)***. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle.) _([Wikipedia](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap))_\n
            \n\n

            \"Yang–Mills

            \n","dir":"/multiplication/","name":"16.md","path":"multiplication/16.md","url":"/multiplication/16.html"},{"sort":19,"spin":106,"span":4,"suit":26,"layout":"default","title":"The Recycling Momentum (spin 8)","content":"

            The Recycling Momentum (spin 8)

            \n\n
            This section is referring to _[wiki page-19](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-15]()_ that is _[inherited ]()_ from _[the gist section-26](https://gist.github.com/eq19)_ by _[prime spin-106](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-4](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            The Extra Dimensions

            \n\n

            By this image you would see how the earth movements should actually work based on spacetime curved by mass and energy on our solar system. But it is still not enough.

            \n\n
            Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990 that they were all different limiting cases of a single theory in **11 dimensions** known as M-theory _([Wikipedia](https://en.wikipedia.org/wiki/String_theory))_.\n
            \n\n

            \"Solar

            \n\n

            Nowadays there are many scientists come in to the conclusion that there should be extra dimensions involved and typically it would take a very complicated form.

            \n\n
            1. ***Line/length***\n2. ***Plane/shapes***\n3. ***Depth***, representing a [stretching and shearing](https://www.eq19.com/multiplication/#streaching-structure) of the plane\n4. ***Time***, stands as [starting point](https://youtu.be/yPVQtvbiS4Y) to _[attemp](https://theoryofeverything.org/TOE/JGM/What%20Time%20is%20it.pdf)_ the ***[Theory Of Everything (TOE)](https://www.eq19.com/identition/#fundamental-forces)***.\n5. ***Alternate world*** (we could measure similarities and differences of what might have been). Some theories state that light is nothing but ripples of vibrations in the [fifth dimension](https://www.wattpad.com/amp/474802474)\n6. ***A plane of possible worlds*** that start with the same conditions (example: the Big Bang). Theoretically, if you were to master the sixth and seventh dimensions, you could travel through time.\n7. ***Access to different worlds*** with different initial conditions. Here, everything would have happened differently, including the beginning conditions (one universe started with the Big Bang, another with the Oscillating Universe theory).\n8. This dimension is similar to the seventh. There are ***[multiple universes](https://en.wikipedia.org/wiki/Multiverse#M-theory)*** that all started differently and histories that branch out infinitely.\n9. Here, we can compare ***all the could-have-been universes***, each with a possibly different set of laws of physics.\n10. Kinda like ***an extra room to accommodate ALL the theories***. In additions, some physicists believe that at the instant of the Big Bang, the universe(s) was fully 10 dimensional.\n
            \n\n

            \"extra

            \n\n

            The coupling dynamics of dimension d ⩾ 4 reflects to matter–antimatter annihilation that tied in with addition, multiplication and exponentiation function of Euler Indentity.

            \n\n
            In 1922, Hermann Weyl claimed that Maxwell's theory of electromagnetism can be expressed in terms of an action only for a four-dimensional manifold. Finally, Tangherlini showed in 1963 that ***when there are more than three spatial dimensions, electron orbitals around nuclei cannot be stable***; electrons would either fall into the nucleus or disperse. _([Wikipedia](https://en.wikipedia.org/wiki/Anthropic_principle#Dimensions_of_spacetime))_\n
            \n\n

            \"pairing

            \n\n

            By the exponentiation zones these annihilation relates to the fundamental circle constant π = 3.1415…. So how does it go with imajinari constant?

            \n\n
            ***Euler's identity*** is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula \ne^ix = cos x + i sin x when evaluated for x = π. _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_.\n
            \n\n

            \"Euler's

            \n\n

            Rotation vs Revolution

            \n\n

            \"85060684-db12a400-b1cf-11ea-8f37-6b9b3bcab2f2\"

            \n\n
            The full Lagrangian of the SM is rather cumbersome and can be found in _[The Physics of the Standard Model and Beyond - pdf](https://github.com/eq19/eq19.github.io/files/13793234/the-physics-of-the-standard-model-and-beyond.pdf)_. A graphical representation of elementary particle interactions is shown on Fig. 1.1\n- Three major groups of true elementary particles are distinguished in the framework of the SM: fermions, in particular quarks and leptons, gauge bosons, which are interaction carriers and the Higgs boson, responsible for the masses of elementary particles.\n- Fermions have spin equal to n/2, n = 1, 2, 3 . . . and obey Fermi-Dirac statistics. Quarks, charged leptons and neutrinos belong to the SM fermions. Bosons have an integer spin and are described by Bose-Einstein statistics. The SM interaction carriers are the gauge bosons γ, Z, W± (vectors) and the Higgs boson H (scalar).\n\nAll the particles of the [Standard Model](https://en.m.wikipedia.org/wiki/Standard_Model) have been experimentally observed, including the [Higgs boson](https://en.m.wikipedia.org/wiki/Higgs_boson) in 2012.[[2]](https://en.m.wikipedia.org/wiki/List_of_particles#cite_note-2)[[3]](https://en.m.wikipedia.org/wiki/List_of_particles#cite_note-3) Many other hypothetical elementary particles, such as the [graviton](https://en.m.wikipedia.org/wiki/Graviton), have been proposed, but not observed experimentally. _([Wikipedia](https://en.wikipedia.org/wiki/List_of_particles))_\n
            \n\n

            \"The

            \n\n

            In order to propagate this annihilation and how they interact with each other we shall attemp it using string theory that bring the concept of eleven (11) dimensions.

            \n\n
            The Milky Way is a [barred spiral galaxy](https://en.wikipedia.org/wiki/Barred_spiral_galaxy) with a [D25 isophotal diameter](https://en.wikipedia.org/wiki/Galaxy#Isophotal_diameter) estimated at 26.8 ± 1.1 [kiloparsecs](https://en.wikipedia.org/wiki/Parsec#Parsecs_and_kiloparsecs) (87,400 ± 3,600 [light-years](https://en.wikipedia.org/wiki/Light-year)),[[10]](https://en.wikipedia.org/wiki/Milky_Way#cite_note-Goodwin-11) but only about ***1,000 light-years thick at the spiral arms (more at the bulge)***.\n- Recent simulations suggest that a [dark matter](https://en.wikipedia.org/wiki/Dark_matter) area, also containing some visible stars, may extend up to a diameter of almost 2 million light-years (613 kpc).\n- The Milky Way has several ***[satellite galaxies](https://en.wikipedia.org/wiki/List_of_Milky_Way%27s_satellite_galaxies)*** and is part of the [Local Group](https://en.wikipedia.org/wiki/Local_Group) of galaxies, which form part of the [Virgo Supercluster](https://en.wikipedia.org/wiki/Virgo_Supercluster), which is itself a component of the [Laniakea Supercluster](https://en.wikipedia.org/wiki/Laniakea_Supercluster).\n- It is estimated to contain 100–400 billion stars and at least that number of planets. ***The Solar System is located at a radius of about 27,000 light-years (8.3 kpc) from the Galactic Center, on the inner edge of the Orion Arm, one of the spiral-shaped concentrations of gas and dust***. The stars in the innermost 10,000 light-years form a bulge and one or more bars that radiate from the bulge.\n- The Galactic Center is an intense radio source known as Sagittarius A, a supermassive black hole of 4.100 (± 0.034) million solar masses.[39][40] Stars and gases at a wide range of distances from the Galactic Center orbit at approximately 220 kilometers per second (136 miles per second).\n- The constant rotational speed appears to contradict the laws of Keplerian dynamics and suggests that much (about 90%) of the mass of the Milky Way is invisible to telescopes, neither emitting nor absorbing electromagnetic radiation. ***This conjectural mass has been termed \"dark matter\"***. The rotational period is about 212 million years at the radius of the Sun.[16]\n\nThe Milky Way as a whole is moving at a velocity of approximately 600 km per second (372 miles per second) with respect to extragalactic frames of reference. The oldest stars in the Milky Way are nearly as old as the Universe itself and thus probably formed shortly after the Dark Ages of the Big Bang.[42] _([Wikipedia](https://en.wikipedia.org/wiki/Milky_Way))_\n
            \n\n
            E = mc²\nm = E/c²\n\nc = 1 light-second\n  = 1000 years x L / t\n  = 12,000 months x 2152612.336257 km / 86164.0906 sec\n  = 299,792.4998 km / sec\n\nNote:\n1 year = 12 months\n1000 years = 12,000 months\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n\nConclusion:\nπ(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (mass of matter)\n   👇\nπ(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown (gap in 2nd-level)\n   👇\nπ(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level)\n   👇\nπ(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter) \n   👇\n|--👇---------------------------- 2x96 ---------------------|\n|--👇----------- 7¤ ---------------|---------- 5¤ ----------|\n|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉\n|---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n|-------- Bosons --------|---------- Fermions ---------|-- Graviton\n|----- (Sun Orbit) ------|-------- (Moon Orbit) -------| (11 Galaxies) ✔️\n|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way ✔️\n
            \n\n

            \"\"

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------  ✔️   |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |\n----------------------+-----+                                                ---\n
            \n\n

            1st Fermion Fields = 96 / 12 Moon Orbit = 8 (1st-gap)

            \n\n

            \"8

            \n\n

            Truncated Perturbation

            \n\n
            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet's 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SU(5)_representation_of_fermions\"\n

            \n\n

            10th prime = 29 = 28+1

            \n\n
                        3 x 3rd-gap\n           ∆     ∆     ∆\n           |     |     |\n-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap\n  1' |  1  | {2} |  3  |  4  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  2' |  5  |  6  |  7  |  8  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  3' |  9  |{10} |  2¤ (M dan F)\n     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      \n  4' | 11  | 12  | 13  | 3¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  5' | 14  | 15  | 16  | 17  | 4¤    \n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  6' | 18  | 19  |{20} | 3¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap\n  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap\n           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆\n           |     |     |     |     |     |     |     | P(7)=142857\n               8 x 3rd-gap inside the 2nd-gap          (Truncated)\n
            \n\n
            In 2016, using 20 years of images from the Hubble space telescope, it was estimated that there were in total two trillion (2×10<sup>12</sup>) or more galaxies in the observable universe, and as many as an estimated 1×10<sup>24</sup> stars (more stars than all the grains of sand on all beaches of the planet Earth) _([Wikipedia](https://en.wikipedia.org/wiki/Galaxy))_\n
            \n\n

            \"image\"

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ---------- ✔️      13¨  inheritance\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |\n----------------------+-----+                                                ---\n
            \n\n
            The matter representations come in ***three copies (generations) of the 16 representation***. The [Yukawa coupling](https://en.wikipedia.org/wiki/Yukawa_coupling) is 10H 16f 16f. ***This includes a right-handed neutrino**\". One may either include three copies of [singlet](https://en.wikipedia.org/wiki/Singlet_state) representations φ and a Yukawa coupling (the \"double seesaw mechanism\"); or else, add the Yukawa interaction or add the [nonrenormalizable](https://en.wikipedia.org/wiki/Nonrenormalizable) coupling. _([Wikipedia](https://en.wikipedia.org/wiki/SO(10)))_\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SO(10)_-_16_Weight_Diagram\n

            \n\n

            Each result goes to the 9th object of prime 67 which is 19th prime. This mass gap of (Δ > 0) is actually the quantum way of our eQ19-algorithm.

            \n\n
            In [mathematics](https://en.m.wikipedia.org/wiki/Mathematics) and [applied mathematics](https://en.m.wikipedia.org/wiki/Applied_mathematics), perturbation theory comprises methods for finding an [approximate solution](https://en.m.wikipedia.org/wiki/Approximation_theory) to a problem, by starting from the exact [solution](https://en.m.wikipedia.org/wiki/Solution_(equation)) of a related, simpler problem.\n- A critical feature of the technique is a middle step that breaks the problem into \"solvable\" and \"perturbative\" parts.\n- In perturbation theory, the solution is expressed as a [power series](https://en.m.wikipedia.org/wiki/Power_series) in a small parameter.\n- The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction.\n\nPerturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in [quantum field theory](https://en.m.wikipedia.org/wiki/Quantum_field_theory). [Perturbation theory (quantum mechanics)](https://en.m.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)) describes the use of this method in [quantum mechanics](https://en.m.wikipedia.org/wiki/Quantum_mechanics). The field in general remains actively and heavily researched across multiple disciplines._([Wikipedia](https://en.m.wikipedia.org/wiki/Perturbation_theory))_\n
            \n\n

            \"\"

            \n\n
                        3 x 3rd-gap\n           ∆     ∆     ∆\n           |     |     |\n-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap\n  19 |  1  | {2} |  3  |  4  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  17 |  5  |  6  |  7  |  8  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  ❓ |  9  |{10} |  2¤ (M dan F)\n     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      \n  ❓ | 11  | 12  | 13  | 3¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  ❓ | 14  | 15  | 16  | 17  | 4¤    \n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  ❓ | 18  | 19  |{20} | 3¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap\n  ❓ | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap\n           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆\n           |     |     |     |     |     |     |     | P(7)=142857\n               8 x 3rd-gap inside the 2nd-gap          (Truncated)\n
            \n\n

            \"96

            \n\n

            These waves have phase offsets, meaning they peak at different times. This all relates to Zitterbewegung, a term describing the jittery motion of particles in quantum mechanics.

            \n\n

            Expanded Structure

            \n\n

            This diagram is representing groupings (leptons, quarks, weak-force bosons) with 6 quarks in a way that parallels the 6 leptons.

            \n\n
            ***There are 8 different types of tiny particles, or 'states', that we can find in a special kind of space that has 6 dimensions*** and involves both real and imaginary numbers. These particles include:\n- ***The Higgs field***, which doesn't spin and is represented by 0.\n- ***Fermions***, which are particles like electrons, having a spin of plus or minus a half.\n- ***Bosons***, like photons, which have a spin of plus or minus 1.\n- ***Anti-fermions***, which are like fermions but have a spin of plus or minus two-thirds.\n- ***The graviton***, believed to be responsible for gravity, with a spin of 2.\n\n***In a diagram at the top left, this 6-dimensional space is shown to be curved***. In another diagram at the bottom right, we see two waves that are perpendicular to each other, representing the motion of a particle in a 'Dirac harmonic oscillator' – a concept in quantum mechanics. _([Physics In History](https://twitter.com/PhysInHistory/status/1739158977089274165))_\n
            \n\n

            \"Dirac_bispinor_6D\"

            \n\n

            Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The corresponding eigenvalue is often represented as the multiplying factor.

            \n\n
            The red vectors are not parallel to either eigenvector, so, their directions are changed by the transformation. The lengths of the purple vectors are unchanged after the transformation (due to their eigenvalue of 1), while blue vectors are three times the length of the original (due to their eigenvalue of 3). See also: An extended version, showing all four quadrants.\n
            \n\n

            \"\"

            \n\n

            Therefore this 12’s treatment will involve at least 11 groups of runner and one (1) profile of the 7’s transformation. We collect them in 11 + 7 = 18 gists as below.

            \n\n
            Gists provide a simple way to share code snippets with others. Every gist is a Git repository, which means that it can be forked and cloned. If you are signed in to GitHub when you create a gist, the gist will be associated with your account and you will see it in your list of gists when you navigate to your gist home page. _([GitHub](https://docs.github.com/en/get-started/writing-on-github/editing-and-sharing-content-with-gists/creating-gists#about-gists))_\n
            \n\n
            $ gh api -H \"${HEADER}\" /users/eq19/gists --jq '.[].url'\n\nhttps://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar 36\nhttps://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax\nhttps://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser\nhttps://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer\nhttps://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed\nhttps://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 30\n                                                           --------\nhttps://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77\nhttps://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10\nhttps://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9\nhttps://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8\nhttps://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7\nhttps://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6\nhttps://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5\nhttps://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4\nhttps://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3\nhttps://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2\nhttps://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1\nhttps://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37\n
            \n\n

            By the prime hexagon the 19th spin is touching back to the first node. So the workflow will be proceeded as bilateral way and twisted them by such a kind of double strands.

            \n\n
            Since the higher primes is more than 71 then the most logical position will be in the 11s somewhere in the third of minor hexagon. By the MEC30 we can see that they will be pushed to and ***ended up on the prime 13***.\n
            \n\n
            https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77\nhttps://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10\nhttps://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9\nhttps://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8\nhttps://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7\nhttps://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6\nhttps://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5\nhttps://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4\nhttps://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3\nhttps://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2\nhttps://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1\nhttps://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 1\n-------- bilateral\nhttps://github.com/eq19/eq19.github.io/wiki                   19 identity 37\nhttps://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar\nhttps://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax\nhttps://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser\nhttps://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer\nhttps://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed\nhttps://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 30\n
            \n\n

            We concluded later on that this bilateral would not come to be possible if only one (1) profile is assigned. Therefore we add another profile so they would be 11 + 2 = 13's.

            \n\n

            These are the ones that bring 11 + 13 = 24 cell hexagons.

            \n\n

            Orbital structure

            \n\n

            The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.

            \n\n
            The points that lie on the line through the origin, parallel to an eigenvector, remain on the line after the transformation. These lines are represented as faint blue and violet lines, matching the associated eigenvectors. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. Notice that all blue vectors are scaled by a factor of 3. This is their associated eigenvalue. The violet vectors are not scaled, so their eigenvalue is 1.\n
            \n\n

            \"streching\"

            \n\n

            By our project the scheme will be treated as the sun and the moon orbit where this 31 is the maximum days of a month:

            \n\n
            By the _[exponentiation zones](https://www.eq19.com/exponentiation/)_ and _[identition zones](https://www.eq19.com/identition/)_ they will end up as 7 days (***sun***) and 12 months (***moon***) while the 11 will represent the ones outside the orbit (***stars*** or ***galaxies***). This 7 vs 12 is the point of view from the earth which making its position is just in the right location (not too far nor to close) with the sun within the universe.\n
            \n\n
            https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 1\nhttps://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed\nhttps://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer\nhttps://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser\nhttps://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax\nhttps://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar\nhttps://github.com/eq19/eq19.github.io.wiki                   19 identity 37\n7 days (sun)\n-------- bilateral 9 sums\n12 months (moon)\nhttps://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 1\nhttps://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1\nhttps://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2\nhttps://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3\nhttps://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4\nhttps://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5\nhttps://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6\nhttps://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7\nhttps://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8\nhttps://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9\nhttps://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10\nhttps://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77\n
            \n\n

            We are going to manage the relation of all the involved things in the scheme above using wiki and gist. The main different with gist is that wiki is allowing folder. So we can sort the files regardless where the folder that contained the file is located.

            \n\n
            Gists and Wiki are actually Git repositories, which means that you can fork or clone any gist, even if you aren't the original author. _([GitHub](https://docs.github.com/en/get-started/writing-on-github/editing-and-sharing-content-with-gists/creating-gists#about-gists))_\n
            \n\n
            #!/usr/bin/env bash\n\nWIKI=https://github.com/$2/$1.wiki.git\nBASE=https://github.com/eq19/eq19.github.io.wiki.git\nrm -rf /tmp/workdir /tmp/gistdir && mkdir /tmp/gistdir\n\ngit ls-remote ${WIKI} > /dev/null 2>&1\ngit clone $([ $? == 0 ] && echo $WIKI || echo $BASE) /tmp/workdir\ngh gist clone 0ce5848f7ad62dc46dedfaa430069857 /tmp/gistdir/addition\n\ngh gist clone b32915925d9d365e2e9351f0c4ed786e /tmp/gistdir/identition/folder1\ngh gist clone 88d09204b2e5986237bd66d062406fde /tmp/gistdir/identition/folder2\ngh gist clone 8cab5e72d52ecb338a2f2187082a1699 /tmp/gistdir/identition/folder3\ngh gist clone 54600a56d20163c2da8910dd804ec406 /tmp/gistdir/identition/folder4\ngh gist clone f1af4317b619154719546e615aaa2155 /tmp/gistdir/identition/folder5\ngh gist clone 6c89c3b0f109e0ead561a452720d1ebf /tmp/gistdir/identition/folder6\ngh gist clone f21abd90f8d471390aad23d6ecc90d6d /tmp/gistdir/identition/folder7\ngh gist clone 6e2fcc2138be6fb68839a3ede32f0525 /tmp/gistdir/identition/folder8\ngh gist clone b541275ab7deda356feef32d600e44d8 /tmp/gistdir/identition/folder9\ngh gist clone 80c8098f16f3e6ca06893b17a02d910e /tmp/gistdir/identition/folder10\ngh gist clone 4ffc4d02579d5cfd336a553c6da2f267 /tmp/gistdir/identition/folder11\n\ngh gist clone f78d4470250720fb18111165564d555f /tmp/gistdir/exponentiation/folder13\ngh gist clone 765ddc69e339079a5a64b56c1d46e00f /tmp/gistdir/exponentiation/folder14\ngh gist clone b9f901cda16e8a11dd24ee6b677ca288 /tmp/gistdir/exponentiation/folder15\ngh gist clone dc30497160f3389546d177da901537d9 /tmp/gistdir/exponentiation/folder16\ngh gist clone e84a0961dc7636c01d5953d19d65e30a /tmp/gistdir/exponentiation/folder17\ngh gist clone e9832026b5b78f694e4ad22c3eb6c3ef /tmp/gistdir/exponentiation/folder18\n\nfind /tmp/workdir -type f -name \"Home.md\" -prune -exec sh -c 'mv -f \"$1\" \"${1%/*}/README.md\"' sh {} \\;\nfind /tmp/workdir -type f -name \"*zone.md\" -prune -exec sh -c 'mv -f \"$1\" \"${1%/*}/README.md\"' sh {} \\;\nfind /tmp/workdir/identition -type f -name \"*.md\" -prune -exec sh -c 'mv -f \"$1\" \"${1%/*}/README.md\"' sh {} \\;\nfind /tmp/workdir/exponentiation -type f -name \"*.md\" -prune -exec sh -c 'mv -f \"$1\" \"${1%/*}/README.md\"' sh {} \\;\nfind /tmp/gistdir -type d -name .git -prune -exec rm -rf {} \\; && find /tmp/gistdir -type f -name \"README.md\" -exec rm -rf {} \\;\n
            \n\n

            The implementation from addition folder 1 will be exposed by the exponentiation folder 7 meanwhile the folder 12 of multiplication goes to identition zone of 11 folders.

            \n\n

            So they are 4 folders (1, 7, 11, 12) remain inviolable by the gist.

            \n\n

            Section Layers

            \n\n

            The above scheme is also applied in to our project sections which is consists of four (4) zones, the 1st- layer covers addition and multiplication zones, the rest are single zones.

            \n\n

            \"Section

            \n\n

            Dayson introduced the idea of rank of a partition to accomplish the task he set for himself. He made the following conjectures which were proved in 1954 by Peter Swinnerton-Dyer an English mathematician specialising in number theory.

            \n\n
            Dayson's friend the neurologist and author Oliver Sacks said: \"A favourite word of Freeman's about doing science and being creative is the word ***subversive*** (tending or intending to subvert or overthrow, destroy, or undermine an established or existing system, especially a legally constituted or a set of beliefs), and he's done that all his life _([Wikipedia](https://en.wikipedia.org/wiki/Freeman_Dyson#Biography))_.\n
            \n\n
            N(0, 5, 5n + 4) = N(1, 5, 5n + 4) = N(2, 5, 5n + 4) = N(3, 5, 5n + 4) = N(4, 5, 5n + 4)\nN(0, 7, 7n + 5) = N(1, 7, 7n + 5) = N(2, 7, 7n + 5) = . . . = N(6, 7, 7n + 5)\n
            \n\n

            The concepts of rank and crank can both be used to classify partitions of certain integers into subclasses of equal size. The two concepts produce different subclasses of partitions. This is illustrated in the following two tables.

            \n\n
            Although not in the form that Dayson have defined, it was found that the last problem on which Ramanujan worked on before his death was cranks. Berndt and his coauthors have given substantial evidence that Ramanujan knew about the function _([Wikipedia](https://en.wikipedia.org/wiki/Crank_of_a_partition#Ramanujan_and_cranks))_.\n
            \n\n

            \"default\"

            \n\n

            The subclasses of partitions develops characters similar to the distribution of prime numbers. This results in a fundamental causal relation to the primes, systemically the products are entered into the position system.

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  current discussion               |\n-----+-----+-----+-----+-----+                                              |\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    17¤\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤        ----->  assigned to \"id:33\"              |\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                             ---\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+                12¤\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)   |\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            A seemingly unrelated construction is the j-function of number theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern.

            \n\n
            Although this function appears in a branch of mathematics that seems very different from the theory of finite groups, ***the two subjects turn out to be intimately related*** _([Wikipedia](https://en.wikipedia.org/wiki/String_theory#Monstrous_moonshine))_.\n
            \n\n

            \"Monstrous

            \n\n

            We propose a new higher dimensional version of the McKay correspondence which enables us to understand the Hodge theory assigned to singular Gorenstein varieties by physicists, and so-called Higgs bundles.

            \n\n
            Hodge theory can be extended to cohomology with coefficients in nonabelian groups between flat vector bundles which, by the Riemann-Hilbert correspondence, are the same as local systems _([Hodge Theory in String Theory](https://www.pims.math.ca/files/Hodge_Theory_in_String_Theory.pdf))_\n
            \n\n

            \"Hodge

            \n\n

            Our results lead to the conjecture that string theory indicates the existence of some new cohomology theory for algebraic varieties with Gorenstein singularities.

            \n","dir":"/multiplication/","name":"17.md","path":"multiplication/17.md","url":"/multiplication/17.html"},{"sort":20,"spin":105,"span":3,"suit":27,"layout":"default","title":"Exchange Entrypoint (spin 9)","content":"

            Exchange Entrypoint (spin 9)

            \n\n
            This section is referring to _[wiki page-20](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-16]()_ that is _[inherited ]()_ from _[the gist section-27](https://gist.github.com/eq19)_ by _[prime spin-105](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-3](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Spinors vs Antispinor

            \n\n

            One consequence of this is that, in 4 dimensions, we cannot talk about rotation about a line the only non-trivial rotation fixes a plane.

            \n\n

            \"\"

            \n\n

            \"Configuration-of-asymmetric-and-symmetric-laminates\"

            \n\n

            \"image\"

            \n\n

            Thus, these cubic monomials with one free vector index have 32 × 11 − 32 = 320 degrees\nof freedom and are in the {320} representation.

            \n\n
            In [physics](https://en.wikipedia.org/wiki/Physics), and specifically in [quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory), a bispinor is a mathematical construction that is used to describe some of the [fundamental particles](https://en.wikipedia.org/wiki/Fundamental_particle) of [nature](https://en.wikipedia.org/wiki/Nature), including [quarks](https://en.wikipedia.org/wiki/Quark) and [electrons](https://en.wikipedia.org/wiki/Electron).\n- It is a specific embodiment of a [spinor](https://en.wikipedia.org/wiki/Spinor), specifically constructed so that it is consistent with the requirements of [special relativity](https://en.wikipedia.org/wiki/Special_relativity).\n- Bispinors transform in a certain \"spinorial\" fashion under the action of the [Lorentz group](https://en.wikipedia.org/wiki/Lorentz_group), which describes the symmetries of [Minkowski spacetime](https://en.wikipedia.org/wiki/Minkowski_spacetime).\n- They occur in the relativistic [spin-1/2](https://en.wikipedia.org/wiki/Spin-1/2) [wave function](https://en.wikipedia.org/wiki/Wave_function) solutions to the [Dirac equation](https://en.wikipedia.org/wiki/Dirac_equation).\n- Bispinors are so called because they are constructed out of two simpler component spinors, the [Weyl spinors](https://en.wikipedia.org/wiki/Weyl_spinor).\n- Each of the two component spinors transform differently under the two distinct complex-conjugate spin-1/2 [representations](https://en.wikipedia.org/wiki/Representation_(mathematics)) of the Lorentz group.\n- This pairing is of fundamental importance, as it allows the represented particle to have a [mass](https://en.wikipedia.org/wiki/Mass), carry a [charge](https://en.wikipedia.org/wiki/Charge_(physics)), and represent the flow of charge as a [current](https://en.wikipedia.org/wiki/Noether_current), and perhaps most importantly, to carry [angular momentum](https://en.wikipedia.org/wiki/Angular_momentum).\n- More precisely, the mass is a [Casimir invariant](https://en.wikipedia.org/wiki/Casimir_invariant) of the Lorentz group (an eigenstate of the energy), while the vector combination carries momentum and current, being [covariant](https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors) under the action of the Lorentz group.\n- The angular momentum is carried by the [Poynting vector](https://en.wikipedia.org/wiki/Poynting_vector), suitably constructed for the spin field.[[1]](https://en.wikipedia.org/wiki/Bispinor#cite_note-1)\n- A bispinor is more or less \"the same thing\" as a [Dirac spinor](https://en.wikipedia.org/wiki/Dirac_spinor). The convention used here is that the article on the Dirac spinor presents [plane-wave](https://en.wikipedia.org/wiki/Plane-wave) solutions to the Dirac equation using the Dirac convention for the [gamma matrices](https://en.wikipedia.org/wiki/Gamma_matrices). That is, the Dirac spinor is a bispinor in the Dirac convention.\n\nBy contrast, the article below concentrates primarily on the Weyl, or chiral representation, is less focused on the Dirac equation, and more focused on the geometric structure, including the geometry of the [Lorentz group](https://en.wikipedia.org/wiki/Lorentz_group). Thus, much of what is said below can be applied to the [Majorana equation](https://en.wikipedia.org/wiki/Majorana_equation). _([Wikipedia](https://en.wikipedia.org/wiki/Bispinor))_\n
            \n\n

            \"The-electric-dipole-bispinor-as-source-of-fields-of-Matter-and-Antimatter\"

            \n\n

            Matter vs Antimatter

            \n\n
            Giving a specific example of a result obtained with data from the ATLAS experiment, Priscilla Pani, ATLAS experiment co-convener of the LHC Dark Matter Working Group, highlights how the collaboration has recently searched the full LHC dataset from the machine’s second run (Run 2), collected between 2015 and 2018, ***to [look for instances in which the Higgs boson might decay into dark-matter particles](https://atlas.cern/updates/physics-briefing/probing-dark-matter-higgs-boson). “We found no instances of this decay but we were able to set the strongest limits to date on the likelihood that it occurs,”**\" says Pani. _([CERN](https://home.cern/news/series/lhc-physics-ten/breaking-new-ground-search-dark-matter))_\n
            \n\n

            \"Map-1_Plan

            \n\n
            In order to be ***[four-spinors](https://en.wikipedia.org/wiki/Dirac_spinor#Four-spinor_for_particles)*** like the electron and other [lepton](https://en.wikipedia.org/wiki/Lepton) components, there must be one quark component for every combination of [flavour](https://en.wikipedia.org/wiki/Flavor_(particle_physics)) and [colour](https://en.wikipedia.org/wiki/Color_charge), ***bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four component [bispinor](https://en.wikipedia.org/wiki/Bispinor), for a total of [96 complex-valued components](https://github.com/eq19/eq19.github.io/files/13796986/NEUTRINOS_Mysterious_Particles_with_Fascinating_Fe.pdf) for the fermion field***. _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n

            24 x π(7) = 32 x π(π(11)) = 96

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                      MEC 30 / 2\n------+------+-----+-----+------      ‹--------------------------- 30 {+1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  | ‹-- ∆18 = (89-71)         |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- ∆32 ✔️\n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = (43-19)\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- ∆68 ✔️\n------|------|-----+-----+-----                            ‹------  0 {-1/2}\n
            \n\n

            \"IMG_20240111_062522\"

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |  169-1🌀  |  329+289  | ✔️\n-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap\n  1' |  1  | {2} |  3  |  4  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  2' |  5  |  6  |  7  |  8  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  3' |  9  |{10} |  2¤ (M dan F)\n     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      \n  4' | 11  | 12  | 13  | 3¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  5' | 14  | 15  | 16  | 17  | 4¤    \n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  6' | 18  | 19  |{20} | 3¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap\n  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap\n           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆\n           |     |     |     |     |     |     |     | P(7)=142857\n               8 x 3rd-gap inside the 2nd-gap          (Truncated)\n
            \n\n

            Rate to Infinity

            \n\n
            This is because ***[spinors](https://en.wikipedia.org/wiki/Spinor) need 32 components in 11 dimensions. 11D supergravity can be compactified down to 4 dimensions*** which then has OSp(8\\4) symmetry. (We still have 8 × 4 = 32 so there are still the same number of components.) Spinors need 4 components in 4 dimensions. ***This gives O(8) for the gauge group which is too small to contain the Standard Model gauge group U(1) × SU(2) × SU(3) which would need at least O(10)***. _([Wikipedia](https://en.wikipedia.org/wiki/Higher-dimensional_supergravity#The_mathematics))_\n
            \n\n

            32 = 8 x 4 = 2³ x 2² = 2⁵

            \n\n

            \"Global

            \n\n
            Eigenvalue curves (right) showing ***a triple eigenvalue*** at zero for τ = 1 and ***double eigenvalues*** at 1 ± √2i for τ = 4/√3. On the left the graph of 1/Q(λ) with the same eigenvalue curves plotted in the ground plane. Green stars indicate the eigenvalues of A, blue stars the roots of puv(λ) and triangles the zeroes of Q(λ) _([Global properties of eigenvalues - pdf](https://github.com/eq19/eq19.github.io/files/13251083/2007.01188.pdf))_\n
            \n\n

            Digital Root (32) = triple (3) + double (2) = 5 eigenvalues

            \n\n

            \"Eigenvalue-curves-right-showing-a-triple-eigenvalue-at-zero-for\"

            \n\n

            100 + 68 + 32 = 168 + 32 = π(1000) + 32 = 200

            \n
            The plot shows the eigenvalues of A + tuu > J for 0 ≤ t ≤ 125000 in red, and the eigenvalues of A − tuu>J for the same range of t in cyan\n- Then, one checks easily that A is J-Hamiltonian, and that u >JAu = 0, while u >JA3u = −4 6= 0.\n- The polynomial puv(λ) for v = −Ju is constant, equal to −4.\n- Hence all the four eigenvalues † of A + tuu >J ***are going to infinity*\"\", as is shown in the\nfollowing figure. \n\nNote also that the rate of convergence to infinity in this example should be as the fourth root of t, which is confirmed by the graph (***the fourth root of 125000 is about 19***). _([Global properties of eigenvalues](https://github.com/eq19/eq19.github.io/files/13251083/2007.01188.pdf))_\n
            \n\n

            4 x 8 = 32 = 2⁵

            \n\n

            \"Four

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} ✔️     |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} ✔️\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} ✔️     |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} ✔️\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |\n----------------------+-----+                                                ---\n
            \n\n

            Elementary Structure

            \n\n

            You may refer to the structure of minor hexagon it shows that this reversal behaviour is linked to the nature of the prime numbers.

            \n\n
            Aside from 2 and 3, primes come in two flavors, 1 modulo 6 and 5 modulo 6, or the dark and light blue triangles in figure 2(a).  The program determines where primes land in the hexagon by moving between the 6 possible positions where primes may land, figure 2(b) .  The 1-type primes land in python cells 1, 3, and 5.  The 5-type primes land in 0, 2, and 4 cells.   Finally, it can print output in the form of figure 2(c). _([HexSpin](https://www.hexspin.com/finding-a-number-in-the-hexagon/))_\n
            \n\n

            \"Finding

            \n\n

            Here we are using the inverse function to exponentiation by 3 x 6 = 18 spins. This is what we mean by the multiplication zones that is applied to each of addition zones.

            \n\n
            The three (3) minor hexagons are surrounded by the primes (19, 43, 71) which is close to ***the multiplication of six (6)*** with 3, 7, 12 to 18, 42, 72. One of a mysterious thing is that `19 × 6 = 43 + 71` where ∆1 is balancing and keep them to remain stay on the 18s scheme. Therefore we use the primes ***43 and 71*** as corresponding _[eigenvalues](https://en.wikipedia.org/wiki/Eigenvalues)_ which is the factor by which the eigenvector is [scaled](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors#Overview).\n
            \n

            19 x 6 = 43 + 71 = 114

            \n\n

            \"\"

            \n\n

            f(30) = 66 - 30 - 30 - 5 = 1

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin\n3 2 0 1 0 2 👉 2\n4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60\n5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 \n          6 👉 11s Composite Partition ◄--- 102 👈 4th spin\n6 7 3 1 0 7 ◄--- #23 👈 1 ◄--- break MEC30 symmetry ✔️\n7 11 4 1 0 11 ◄--- #19 ◄--- #43 ◄--- 24s 👈 30\n8 13 5 1 0 13 ◄--- #17 ◄--- #49 ◄--- 32s 👈 30\n9 17 0 1 1 17 ◄--- 7th prime 👈 5 ◄--- antisymmetric state ✔️\n           18 👉 7s Composite Partition ◄--- 168 👈 7th spin\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43\n..\n..\n40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n..\n..\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s\n-----\n
            \n\n

            These features are the solution to arrange 30 files located in in four (4) of zone folders as the lexer to cope with the Prime Spin and MEC30 Structure.

            \n\n
            Now such interaction between the elementary particles can be described by means of a field of force, just as the interaction between the charged particles is described by the electromagnetic field. The above \n considerations show that the interaction of heavy particles with this field is much larger than that of light particles with it.\n- Now the binding energy of the proton in C12, which is estimated from the difference of masses of C12 and B11, is. This corresponds to a binding energy 0,0152 in mass unit, being ***thirty (30) times the electron mass***. _(page 53)_\n- Assuming λ=5×10-¹²cm, we.obtain for me a value ***2×10² times as large as the electron mass***. As such a quantum with large mass and positive or negative charge has never been found by the experiment, the above theory seems to be on a wrong line. We can show, however, that, in the ordinary nuclear transformation, such a quantum can not be emitted into outer space. _(page 54)_\n\nThe interaction of such a quantum with the heavy particle should be far greater than that with the light particle in order to account for the large interaction of the neutron and the proton as well as the small probability of β-disintegration. _([Yukawa - pdf](https://github.com/eq19/eq19.github.io/files/13961751/Yukawa.pdf))_\n
            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|--- ✔️    |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------› ✔️    |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} |      |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |\n----------------------+-----+                                                ---\n
            \n\n

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            \n\n

            \"\"

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} |      |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹---------------------- ✔️   17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|---- ✔️    |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |\n----------------------+-----+                                                ---\n
            \n\n

            Higgs Mechanism

            \n\n

            \"360_F_60364421_ehBG4nFhe9uM5sAfvGO8uFl852OvBgmg\"

            \n\n

            \"Elementary-particles-of-standard-model-2\"

            \n\n

            \"hq720\"

            \n\n

            109 + 30 + 30 = 139 + 30 = 169

            \n\n

            \"the

            \n\n
            In a quantum system, a physical state is described by a [state vector](https://en.wikipedia.org/wiki/Quantum_state):\n- A pair of distinct state vectors are physically equivalent if they differ only by an overall phase factor, ignoring other interactions.\n- A pair of indistinguishable particles such as this have only one state.\n- ***This means that if the positions of the particles are exchanged (i.e., they undergo a permutation), this does not identify a new physical state, but rather one matching the original physical state***.\n\nIn fact, one cannot tell which particle is in which position. _([Wikipedia](https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem))_\n
            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} | ✔️   |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown ✔️       |\n----------------------+-----+                                                ---\n
            \n\n

            \"download

            \n\n

            Sun vs Moon

            \n\n

            \"1\"

            \n\n

            Thus a characteristic constant of this system depending on uniformperiods of the month and the year.

            \n\n
            Since the presence of the sun changes the geometrical properties of space and time , we must screen out its gravitational effect on the earth moon system according to the validity condition of the second postulate of special relativity, i.e. we must only consider the lunar geocentric motion without the heliocentric motion of the earth-moon system. Thus a velocity component VO=V cosO representing the net orbital velocity of the moon as shown in fig. (1) is introduced for calculating the net length L of the lunar orbit assuming a stationary earth. _([Determination Of The Greatest Speed C](https://www.islamawareness.net/Islam/speed.html))_\n
            \n\n
            E = mc²\nm = E/c²\n\nc = 1 light-second\n  = 1000 years x L / t\n  = 12,000 months x 2152612.336257 km / 86164.0906 sec\n  = 299,792.4998 km / sec\n\nNote:\n1 year = 12 months\n1000 years = 12,000 months\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n\nConclusion:\nπ(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (mass of matter)\n   👇\nπ(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown (gap in 2nd-level)\n   👇\nπ(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level)\n   👇\nπ(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter) \n   👇\n|--👇---------------------------- 2x96 ---------------------|\n|--👇----------- 7¤ ---------------|---------- 5¤ ----------|\n|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉\n|---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n|-------- Bosons --------|---------- Fermions ---------|-- Graviton\n|-- Sun Orbit (7 days) --|--- Moon Orbit (12 months) --| (11 Galaxies) ✔️\n|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way\n
            \n\n

            \"image\"

            \n\n

            \"The

            \n\n
            The number of primes less than or equal to a thousand [`π(1000) = 168`](https://www.eq19.com/addition/#prime-hexagon) equals the number of hours in a week [`24 × 7 = 168`](https://www.eq19.com/#addition-zones). The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating ***three (3)*** minor hexagons.\n
            \n\n

            ∆28 - ∆27 = 1000 - 900 + π(27/9) = 100 + 2 = 102 (Recycled to original state)

            \n\n
            $True Prime Pairs:\n(5,7),(11,13),(17,19)\n\n|------------ 7'----------------|--------------------------- 12' ----------------------------|\n|      3'     |        4'       |              6'             |              6'              |\n+---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n| 1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |\n+---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n| 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |\n+---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n| Z | W± |  γ | A   H+   H-  hH | u    c    t     g    γ  eμτ |  d    s    b     g   ν¤    γ |  \n\n|---- 102  ---|-----  66  ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -|\n|--2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------|\n|-------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------|\n|-------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----|\n
            \n\n
            In [particle physics](https://en.wikipedia.org/wiki/Particle_physics), a lepton is an [elementary particle](https://en.wikipedia.org/wiki/Elementary_particle) of [half-integer spin](https://en.wikipedia.org/wiki/Half-integer_spin) ([spin](https://en.wikipedia.org/wiki/Spin_(physics)) 1⁄2) that does not undergo [strong interactions](https://en.wikipedia.org/wiki/Strong_interaction).[[1]](https://en.wikipedia.org/wiki/Lepton#cite_note-1)\n- Two main classes of leptons exist: ***[charged](https://en.wikipedia.org/wiki/Electric_charge)*** leptons (also known as the [electron](https://en.wikipedia.org/wiki/Electron)-like leptons or muons), and neutral leptons (better known as ***[neutrinos](https://en.wikipedia.org/wiki/Neutrino))***.\n- Charged leptons can combine with other particles to form various [composite particles](https://en.wikipedia.org/wiki/Composite_particle) such as [atoms](https://en.wikipedia.org/wiki/Atom) and [positronium](https://en.wikipedia.org/wiki/Positronium), while neutrinos rarely interact with anything, and are consequently rarely observed.\n- ***The best known of all leptons is the [electron](https://en.wikipedia.org/wiki/Electron)***.\n\nThere are ***six types of leptons***, known as [flavours](https://en.wikipedia.org/wiki/Flavour_(particle_physics)), grouped in three [generations](https://en.wikipedia.org/wiki/Generation_(particle_physics)).[[2]](https://en.wikipedia.org/wiki/Lepton#cite_note-HyperphysicsLepton-2)\n- The [first-generation](https://en.wikipedia.org/wiki/Standard_Model) leptons, also called electronic leptons, comprise the [electron](https://en.wikipedia.org/wiki/Electron) (e−) and the [electron neutrino](https://en.wikipedia.org/wiki/Electron_neutrino) (νe); the second are the muonic leptons, comprising the [muon](https://en.wikipedia.org/wiki/Muon) (μ−) and the [muon neutrino](https://en.wikipedia.org/wiki/Muon_neutrino) (νμ); and the third are the tauonic leptons, comprising the [tau](https://en.wikipedia.org/wiki/Tau_(particle)) (τ−) and the [tau neutrino](https://en.wikipedia.org/wiki/Tau_neutrino) (ντ).\n- ***Electrons have the least mass of all the charged leptons***. The heavier muons and taus will rapidly change into electrons and neutrinos through a process of [particle decay](https://en.wikipedia.org/wiki/Particle_decay): the transformation from a higher mass state to a lower mass state.\n- Thus electrons are stable and the most common charged lepton in the [universe](https://en.wikipedia.org/wiki/Universe), whereas muons and taus can only be produced in [high energy](https://en.wikipedia.org/wiki/High_energy_physics) collisions (such as those involving [cosmic rays](https://en.wikipedia.org/wiki/Cosmic_ray) and those carried out in [particle accelerators](https://en.wikipedia.org/wiki/Particle_accelerator)).\n- Leptons have various [intrinsic properties](https://en.wikipedia.org/wiki/Intrinsic_properties), including [electric charge](https://en.wikipedia.org/wiki/Electric_charge), [spin](https://en.wikipedia.org/wiki/Spin_(physics)), [mass](https://en.wikipedia.org/wiki/Mass).\n- Unlike [quarks](https://en.wikipedia.org/wiki/Quark), however, leptons are not subject to the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction), but they are subject to the other three [fundamental interactions](https://en.wikipedia.org/wiki/Fundamental_interaction): [gravitation](https://en.wikipedia.org/wiki/Gravitation), the [weak interaction](https://en.wikipedia.org/wiki/Weak_interaction), and to ***[electromagnetism](https://en.wikipedia.org/wiki/Electromagnetism)***, of which the latter is proportional to charge, and is thus zero for the electrically neutral neutrinos.\n\n[![Electrodynamics](https://github.com/eq19/eq19.github.io/assets/8466209/b8629985-8996-4819-9e19-a106b98eed48)](https://www.eq19.com/multiplication/#beyond-the-96)\n\nFor every lepton flavor, there is a corresponding type of [antiparticle](https://en.wikipedia.org/wiki/Antiparticle), known as an antilepton, that differs from the lepton only in that some of its properties have [equal magnitude but opposite sign](https://en.wikipedia.org/wiki/Charge_conjugation). According to certain theories, neutrinos may be [their own antiparticle](https://en.wikipedia.org/wiki/Majorana_fermion). It is not currently known whether this is the case. _([Wikipedia](https://en.wikipedia.org/wiki/Lepton))_\n
            \n\n

            \"universe

            \n\n

            It is stated that if vector of the composite system is mathematically equivalent then the entangled states of the two particles are different (otherwise the antisymmetric state vector would vanish).

            \n\n
            The aim of this paper is to offer a conceptual analysis of Weinberg's proof of the spin-statistics theorem by comparing it with _[Pauli's original proof](https://github.com/eq19/eq19.github.io/files/13774471/Pauli.pdf)_ and with the subsequent textbook tradition, which typically resorts to the dichotomy positive energy for half-integral spin particles/micro causality for integral-spin particles.\n- In contrast to this tradition, Weinberg's proof does not directly invoke the positivity of the energy, but derives the theorem from the single relativistic requirement of micro causality. This seemingly innocuous difference marks an important change in the conceptual basis of quantum physics.\n- Its historical, theoretical, and conceptual roots are here reconstructed. The link between Weinberg's proof and Pauli's original is highlighted: Weinberg's proof turns out to do justice to Pauli's anti-Dirac lines of thought.\n\nThe work of Furry and Oppenheimer is also surveyed as a “third way” between the textbook tradition established by _[Pauli and Weinberg's approach - pdf](https://github.com/eq19/eq19.github.io/files/13774357/1-s2.0-S1355219803000662-main.pdf)_\n
            \n\n

            \"Increasing_disorder

            \n\n

            This is nothing but Pauli’s Exclusion Principle forbidding the possibility of any two indistinguishable particles being in the same dynamic state (Pauli, 1925).

            \n\n

            Irrational Partitions

            \n\n

            By this exponentiation zones we will get multiple layers of primes density. So we need to get in to the patterns of the above hexagonal forms through deep learning.

            \n\n
            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet's 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SU(5)_representation_of_fermions\"\n

            \n\n

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            \n\n
            layer | node | sub |  i  |  f                               \n------+------+-----+---------- \n      |      |     |  1  | -----------------------  71 = 72-1\n      |      |  1  +-----+                        |\n      |  1   |     |  2  | (5)                    |\n      |      |-----+-----+                        |\n      |      |     |  3  | ---------              |\n  1   +------+  2  +-----+----      |             |\n      |      |     |  4  |          5x ---        |\n      |      +-----+-----+          |     |       |\n      |  2   |     |  5  | (7) -----      |       |\n      |      |  3  +-----+                |       |\n289+11=300   |     |  6  |                |       |\n------+------+-----+-----+----- 72 x 6   7x --- 11x = 77 (rational)\n      |      |     |  7  |                |       |\n      |      |  4  +-----+                |       |\n      |  3   |     |  8  | (11)  ---      |       |\n      |      +-----+-----+          |     |       |\n      |      |     |  9  |          2x ---        |\n  2   +------|  5  +-----+-----     |             |\n      |      |     |  10 | ---------              |\n      |      |-----+-----+                        |\n      |  4   |     |  11 | (13) ------------------  71 = 72-1\n      |      |  6  +-----+\n329+71=400   |     |  12 |------------------------  70 = 72-2\n------+------+-----+-----+\n      |      |     |  13 |\n      |      |  7  +-----+\n      |  5   |     |  14 | (17) ◄---------------------------\n      |      |-----+-----+\n      |      |     |  15 | ◄-- 42 x 6 partitions of 13 (irrational)\n  3   +------+  8  +-----+----- \n      |      |     |  16 |      ◄---------------------------\n      |      |-----+-----+\n      |  6   |     |  17 | (19)\n      |      |  9  +-----+\n168+32=200   |  |  |  18 |------------------------  68 = 72-4\n------|------|--|--+-----+\n       900 -----\n
            \n\n

            The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum mechanics. It is a key result in quantum-mechanical system, and its discovery was a significant landmark in the development of the subject.

            \n\n
            Complex plot of a wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space _([Wikipedia](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation))_.\n
            \n\n

            \"Wavepacket-a2k4-en\"

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----  ✔️    |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} |      |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ------------ ✔️   13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |\n----------------------+-----+                                                ---\n
            \n\n

            A set of conceptual problems has to be solved, including a superposition principle which requires a linear vector field and quantisation of space-time itself.

            \n\n
            The approach taken is to think of the solutions of an equation as a geometric object. For example, an equation in two variables defines a curve in the plane. More generally, an equation, or system of equations, in two or more variables defines a curve, a surface or some other such object in n-dimensional space _([Wikipedia](https://en.wikipedia.org/wiki/Number_theory#Diophantine_geometry))_.\n
            \n\n

            \"\"

            \n\n

            Consider this could only be solved by prime theory. An experimental observation of the graviton, the gravitational force carrier, is extremely hard due to small coupling.

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤ ✔️ --->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ |  .. |  .. | ..  |  .. | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            This idea was taken as the earliest in 1960s Swinnerton-Dyer by using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

            \n\n
            In the early 1960s [Peter Swinnerton-Dyer](https://en.wikipedia.org/wiki/Peter_Swinnerton-Dyer) used the [EDSAC computer](https://en.wikipedia.org/wiki/EDSAC) to calculate the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.\n- Based on these numerical results, [Birch & Swinnerton-Dyer (1965)](https://en.wikipedia.org/wiki/EDSAC#CITEREFBirchSwinnerton-Dyer1965) conjectured that Np for a curve E with rank r obeys an asymptotic law.\n- ***The conjecture predicts that the data should form a line of slope equal to the rank of the curve***, which is 1 in this case drawn in red in red on the graph \n\nThe [Birch and Swinnerton-Dyer conjecture](https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture), considered one of the [top unsolved problems in mathematics](https://en.wikipedia.org/wiki/Millennium_Prize_Problems) as of 2022. _([Wikipedia](https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture#Current_status))_.\n
            \n\n

            \"The

            \n","dir":"/multiplication/","name":"18.md","path":"multiplication/18.md","url":"/multiplication/18.html"},{"sort":21,"spin":104,"span":2,"suit":28,"layout":"default","title":"The Mapping Order (spin 10)","content":"

            The Mapping Order (spin 10)

            \n\n
            This section is referring to _[wiki page-21](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-17]()_ that is _[inherited ]()_ from _[the gist section-28](https://gist.github.com/eq19)_ by _[prime spin-104](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-2](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Rational Objects

            \n\n

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            \n\n
            The central problem is to determine when a Diophantine equation has solutions, and if it does, how many. Two examples of an elliptic curve, that is, a curve of genus 1 having at least ***one rational point***. Either graph can be seen as a slice of a torus in four-dimensional space _([Wikipedia](https://en.wikipedia.org/wiki/Number_theory#Diophantine_geometry))_.\n
            \n\n

            \"Number

            \n\n

            One of the main reason is that one does not yet have a mathematically complete example of a quantum gauge theory in four-dimensional space-time. It is even a sign that Einstein’s equations on the energy of empty space are somehow incomplete.

            \n\n
            Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents _([Wikipedia](https://en.wikipedia.org/wiki/Albert_Einstein#Scientific_career))_.\n
            \n\n

            \"default\"

            \n\n

            Speculation is that the unfinished book of Ramanujan’s partition, series of Dyson’s solutions and hugh of Einstein’s papers tend to solve it.

            \n\n

            Dyson introduced the concept in the context of a study of certain congruence properties of the partition function discovered by the mathematician Srinivasa Ramanujan who the one that found the interesting behaviour of the taxicab number 1729.

            \n\n
            The concept was introduced by [Freeman Dyson](https://en.wikipedia.org/wiki/Freeman_Dyson)in a paper published in the journal [Eureka](https://en.wikipedia.org/wiki/Eureka_(University_of_Cambridge_magazine)). It was [presented](https://en.wikipedia.org/wiki/Rank_of_a_partition#cite_note-Dyson-1) in the context of a study of certain [congruence](https://en.wikipedia.org/wiki/Congruence_relation) properties of the [partition function](https://en.wikipedia.org/wiki/Partition_function_(number_theory)) discovered by the Indian mathematical genius [Srinivasa Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan). _([Wikipedia](https://e\nn.wikipedia.org/wiki/Rank_of_a_partition))_\n
            \n\n

            \"Rank_of_a_partition\"

            \n\n

            Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University, in 1900. They were then applied to the study of the symmetric group. Their theory was further developed by many mathematicians, including W. V. D. Hodge

            \n\n
            In _[number theory](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#number-theory)_ and combinatorics, [rank of a partition](https://en.wikipedia.org/wiki/Rank_of_a_partition) of a positive integer is a certain integer associated with the partition meanwhile the [crank of a partition](https://en.wikipedia.org/wiki/Crank_of_a_partition) of an integer is a certain integer associated with that partition _([Wikipedia](https://en.wikipedia.org/wiki/Freeman_Dyson#Crank_of_a_partition))_.\n
            \n\n

            \"\"

            \n\n

            Supersymmetry

            \n\n

            In mathematics, the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition.

            \n\n
            On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! _([Clay Institute's - Official problem description](https://claymath.org/sites/default/files/yangmills.pdf))_.\n
            \n\n

            \"image\"

            \n\n

            25 + 19 + 13 + 7 = 64 = 8 × 8 = 8²

            \n\n

            \"\"

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|👈\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n        ∆         ∆      |---- {48} ----|---- {48} ----|---- {43} ----|👈\n        7        13      |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|\n                            ∆                               |-- 25 ---|\n                           19                                    ∆\n                                                               5 x 5\n
            \n\n
            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet's 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SU(5)_representation_of_fermions\"\n

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ |  5¨ |  3¨ | ..  |  .. | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n
            Family Number Group +3, +6, +9 being activated by the Aetheron Flux Monopole Emanations, creating Negative Draft Counterspace, Motion and Nested Vortices.) _([RodinAerodynamics](https://rense.com/RodinAerodynamics.htm))_\n
            \n\n

            \"guest7\"

            \n\n

            This idea was taken as the earliest in 1960s Swinnerton-Dyer by using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

            \n\n
            From these numerical results ***the conjecture predicts that the data should form a line of slope equal to the rank of the curve***, which is 1 in this case drawn in red in red on the graph _([Wikipedia](https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture#Current_status))_.\n
            \n\n

            Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as _[Mo\nUnfortunately the rotation of this eigenvalues deals with four-dimensional space-time which was already a big issue.

            \n\n

            \"Geometry

            \n\n

            In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture.

            \n\n
            Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries _([ClayMath Institute](https://www.claymath.org/millennium-problems/poincar%C3%A9-conjecture))_.\n
            \n\n

            \"Poincaré

            \n\n

            More generally, the central problem is to determine when an equation in n-dimensional space has solutions. However at this point, we finaly found that the prime distribution has something to do with the subclasses of rank and crank partitions.

            \n\n

            Ricci Flow

            \n\n

            \"guest5\"

            \n\n
            p r i m e s\n1 0 0 0 0 0\n2 1 0 0 0 1\n3 2 0 1 0 2\n4 3 1 1 0 3\n5 5 2 1 0 5\n6 7 3 1 0 7\n7 11 4 1 0 11\n8 13 5 1 0 13\n9 17 0 1 1 17 ◄--- has a total of 18-7 = 11 composite √\n10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18\n-----\n11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19\n12 29 2 -1 1 ∆3 ◄--- 2nd ∆prime ◄--- Fibonacci Index #20\n13 31 1 -1 1 ∆4\n14 37 1 1 1 ∆5 ◄--- 3th ∆prime ◄--- Fibonacci Index #21\n15 41 2 1 1 ∆6\n16 43 3 1 1 ∆7 ◄--- 4th ∆prime ◄--- Fibonacci Index #22\n17 47 4 1 1 ∆8\n18 53 4 -1 1 ∆9\n19 59 4 1 1 ∆10\n20 61 5 1 1 ∆11 ◄--- 5th ∆prime ◄--- Fibonacci Index #23\n21 67 5 -1 1 ∆12\n22 71 4 -1 1 ∆13 ◄--- 6th ∆prime ◄--- Fibonacci Index #24\n23 73 3 -1 1 ∆14\n24 79 3 1 1 ∆15\n25 83 4 1 1 ∆16\n26 89 4 -1 1 ∆17 ◄--- 7th ∆prime ◄--- Fibonacci Index #25\n27 97 3 -1 1 ∆18\n28 101 2 -1 1 ∆19 ◄--- 8th ∆prime ◄--- Fibonacci Index #26\n29 103 1 -1 1 ∆20\n30 107 0 -1 1 ∆21\n31 109 5 -1 0 ∆22\n32 113 4 -1 0 ∆23 ◄--- 9th ∆prime ◄--- Fibonacci Index #27\n33 127 3 -1 0 ∆24\n34 131 2 -1 0 ∆25\n35 137 2 1 0 ∆26\n36 139 3 1 0 ∆27\n37 149 4 1 0 ∆28\n38 151 5 1 0 ∆29 ◄--- 10th ∆prime  ◄--- Fibonacci Index #28\n39 157 5 -1 0 ∆30\n40 163 5 1 0 ∆31 ◄--- 11th ∆prime ◄--- Fibonacci Index #29\n-----\n41 167 0 1 1 ∆0\n42 173 0 -1 1 ∆1\n43 179 0 1 1 ∆2 ◄--- ∆∆1\n44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30\n45 191 2 1 1 ∆4\n46 193 3 1 1 ∆5 ◄--- ∆∆3 ◄--- 2nd ∆∆prime ◄--- Fibonacci Index #31\n47 197 4 1 1 ∆6\n48 199 5 1 1 ∆7 ◄--- ∆∆4\n49 211 5 -1 1 ∆8\n50 223 5 1 1 ∆9\n51 227 0 1 2 ∆10\n52 229 1 1 2 ∆11 ◄--- ∆∆5 ◄--- 3rd ∆∆prime ◄--- Fibonacci Index #32\n53 233 2 1 2 ∆12\n54 239 2 -1 2 ∆13 ◄--- ∆∆6\n55 241 1 -1 2 ∆14\n56 251 0 -1 2 ∆15\n57 257 0 1 2 ∆16\n58 263 0 -1 2 ∆17 ◄--- ∆∆7 ◄--- 4th ∆∆prime ◄--- Fibonacci Index #33\n59 269 0 1 2 ∆18\n60 271 1 1 2 ∆19 ◄--- ∆∆8\n61 277 1 -1 2 ∆20\n62 281 0 -1 2 ∆21\n63 283 5 -1 1 ∆22\n64 293 4 -1 1 ∆23 ◄--- ∆∆9\n65 307 3 -1 1 ∆24\n66 311 2 -1 1 ∆25\n67 313 1 -1 1 ∆26\n68 317 0 -1 1 ∆27\n69 331 5 -1 0 ∆28\n70 337 5 1 0 ∆29 ◄--- ∆∆10\n71 347 0 1 1 ∆30\n72 349 1 1 1 ∆31 ◄--- ∆∆11 ◄--- 5th ∆∆prime ◄--- Fibonacci Index #34\n73 353 2 1 1 ∆32\n74 359 2 -1 1 ∆33\n75 367 1 -1 1 ∆34\n76 373 1 1 1 ∆35\n77 379 1 -1 1 ∆36\n78 383 0 -1 1 ∆37 ◄--- ∆∆12\n79 389 0 1 1 ∆38\n80 397 1 1 1 ∆39\n81 401 2 1 1 ∆40\n82 409 3 1 1 ∆41 ◄--- ∆∆13 ◄--- 6th ∆∆prime ◄--- Fibonacci Index #35\n83 419 4 1 1 ∆42\n84 421 5 1 1 ∆43 ◄--- ∆∆14\n85 431 0 1 2 ∆44\n86 433 1 1 2 ∆45\n87 439 1 -1 2 ∆46\n88 443 0 -1 2 ∆47 ◄--- ∆∆15\n89 449 0 1 2 ∆48\n90 457 1 1 2 ∆49\n91 461 2 1 2 ∆50\n92 463 3 1 2 ∆51\n93 467 4 1 2 ∆52\n94 479 4 -1 2 ∆53 ◄--- ∆∆16\n95 487 3 -1 2 ∆54\n96 491 2 -1 2 ∆55\n97 499 1 -1 2 ∆56\n98 503 0 -1 2 ∆57\n99 509 0 1 2 ∆58\n100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36\n-----\n101 523 5 -1 1 ∆2 ◄--- ∆∆18 ◄--- 1st ∆∆∆prime ◄--- Fibonacci Index #37 √\n102 541 5 1 1 ∆3 ◄--- ∆∆∆1 ◄--- 1st ÷÷÷composite ◄--- Index #(37+2)=#39 √\n103 547 5 -1 1 ∆4\n104 557 4 -1 1 ∆5 ◄--- ∆∆∆2 ◄---2nd ∆∆∆prime √\n105 563 4 1 1 ∆6\n106 569 4 -1 1 ∆7 ◄--- ∆∆∆3 ◄--- 3rd ∆∆∆prime √\n107 571 3 -1 1 ∆8\n108 577 3 1 1 ∆9\n109 587 4 1 1 ∆10\n110 593 4 -1 1 ∆11 ◄--- ∆∆∆4 ◄--- 2nd ÷÷÷composite ◄--- Index #(37+3)=#40 √\n111 599 4 1 1 ∆12\n112 601 5 1 1 ∆13 ◄--- ∆∆∆5 ◄--- 4th ∆∆∆prime √\n113 607 5 -1 1 ∆14\n114 613 5 1 1 ∆15\n115 617 0 1 2 ∆16\n116 619 1 1 2 ∆17 ◄--- ∆∆∆6 ◄--- 3rd ÷÷÷composite ◄--- Index #(37+5)=#42 √\n117 631 1 -1 2 ∆18\n118 641 0 -1 2 ∆19 ◄--- ∆∆∆7 ◄--- 5th ∆∆∆prime √\n119 643 5 -1 1 ∆20\n120 647 4 -1 1 ∆21\n121 653 4 1 1 ∆22\n122 659 4 -1 1 ∆23 ◄--- ∆∆∆8 ◄--- 4th ÷÷÷composite ◄--- Index #(37+7)=#44 √\n123 661 3 -1 1 ∆24\n124 673 3 1 1 ∆25\n125 677 4 1 1 ∆26\n126 683 4 -1 1 ∆27\n127 691 3 -1 1 ∆28\n128 701 2 -1 1 ∆29 ◄--- ∆∆∆9 ◄--- 5th ÷÷÷composite ◄--- Index #(37+11)=#48 √\n129 709 1 -1 1 ∆30\n130 719 0 -1 1 ∆31 ◄--- ∆∆∆10 ◄--- 6th ÷÷÷composite ◄--- Index #(37+13)=#50 √\n131 727 5 -1 0 ∆32\n132 733 5 1 0 ∆33\n133 739 5 -1 0 ∆34\n134 743 4 -1 0 ∆35\n135 751 3 -1 0 ∆36\n136 757 3 1 0 ∆37 ◄--- ∆∆∆11 ◄--- 6th ∆∆∆prime √\n137 761 4 1 0 ∆38\n138 769 5 1 0 ∆39\n139 773 0 1 1 ∆40\n140 787 1 1 1 ∆41 ◄--- ∆∆∆12 ◄--- 7th ÷÷÷composite ◄--- Index #(37+17)=#54 √\n141 797 2 1 1 ∆42\n142 809 2 -1 1 ∆43 ◄--- ∆∆∆13 ◄--- 7th ∆∆∆prime √\n143 811 1 -1 1 ∆44\n144 821 0 -1 1 ∆45\n145 823 5 -1 0 ∆46\n146 827 4 -1 0 ∆47 ◄--- ∆∆∆14 ◄--- 8th ÷÷÷composite ◄--- Index #(37+19)=#56 √\n147 829 3 -1 0 ∆48\n148 839 2 -1 0 ∆49\n149 853 1 -1 0 ∆50\n150 857 0 -1 0 ∆51\n151 859 5 -1 -1 ∆52\n152 863 4 -1 -1 ∆53 ◄--- ∆∆∆15 ◄--- 9th ÷÷÷composite ◄--- Index #(37+23)=#60 √\n153 877 3 -1 -1 ∆54\n154 881 2 -1 -1 ∆55\n155 883 1 -1 -1 ∆56\n156 887 0 -1 -1 ∆57\n157 907 5 -1 -2 ∆58\n158 911 4 -1 -2 ∆59 ◄--- ∆∆∆16 ◄--- 10th ÷÷÷composite ◄--- Index #(37+29)=#66 √\n159 919 3 -1 -2 ∆60\n169 929 2 -1 -2 ∆61 ◄--- ∆∆∆17 ◄--- 8th ∆∆∆prime √\n161 937 1 -1 -2 ∆62\n162 941 0 -1 -2 ∆63\n163 947 0 1 -2 ∆64\n164 953 0 -1 -2 ∆65\n165 967 5 -1 -3 ∆66\n166 971 4 -1 -3 ∆67 ◄--- ∆∆∆18 ◄--- 11th ÷÷÷composite ◄--- Index #(37+31)=#68 √\n167 977 4 1 -3 ∆68\n168 983 4 -1 -3 ∆69\n169 991 3 -1 -3 ∆70\n170 997 3 1 -32 ∆71 ◄--- ∆∆∆19 ◄--- 9th ∆∆∆prime √\n
            \n\n

            \"Scot_Number_Map_Diag\"

            \n\n

            The Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it rounder, in the hope that one may draw topological conclusions from the existence of such “round” metrics.

            \n\n
            Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere _([Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture))_\n
            \n\n

            \"default\"

            \n\n

            The Ricci Flow method has now been developed not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI (Artificial intelligence). No wonder now all the science leads to it.

            \n\n

            \"\"

            \n\n

            So what we’ve discussed on this wiki is entirely nothing but an embodiment of this solved Poincare Conjecture. This is the one placed with id: 10 (ten) which stands as the basic algorithm of π(10)=(2,3,5,7).

            \n\n
            Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence. AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence _([Human vs AI](https://www.frontiersin.org/articles/10.3389/frai.2021.622364/full))_.\n
            \n\n

            \"Poincaré

            \n\n

            Finite collections of objects are considered 0-dimensional. Objects that are “dragged” versions of zero-dimensional objects are then called one-dimensional. Similarly, objects which are dragged one-dimensional objects are two-dimensional, and so on.

            \n\n
            The basic ideas leading up to this result (including the dimension invariance theorem, domain invariance theorem, and Lebesgue covering dimension) were developed by **Poincaré**, Brouwer, Lebesgue, Urysohn, and Menger _([MathWorld](https://mathworld.wolfram.com/Dimension.html))_.\n
            \n\n

            \"default\"

            \n\n

            Spacetime Patterns

            \n\n

            \"toroid_color\"

            \n\n

            In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.

            \n\n
            It's possible to build a _[Hessian matrix](https://en.wikipedia.org/wiki/Hessian_matrix)_ for a _[Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization)_ step using the Jacobian method. ***You would first flatten out its axes into a matrix, and flatten out the gradient into a vector.*** _([Tensorflow](https://www.tensorflow.org/guide/advanced_autodiff#batch_jacobian))_\n
            \n\n

            \"Tensorflow

            \n\n

            When the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent.

            \n\n
            ***When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant***. Both the matrix and (if applicable) the determinant ad  often referred to simply as the Jacobian in literature. _([Wikipedia](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant))_\n
            \n\n

            \"Hessian

            \n\n

            Double Strands

            \n\n

            Here we adopt an analysis of variance called N/P-Integration that was applied to find the best set of environmental variables that describe the density out of distance matrices.

            \n\n
            With collaborators, we regularly work on projects where we want to understand the taxonomic and functional diversity of microbial community in the context of metadata often recorded under specific hypotheses. Integrating (***N-/P- integration***; see figure below) these datasets require a fair deal of multivariate statistical analysis for which I have shared the [code](https://userweb.eng.gla.ac.uk/umer.ijaz/bioinformatics/ecological.html) on this website. _([Umer.Ijaz](https://userweb.eng.gla.ac.uk/umer.ijaz/#intro))_\n
            \n\n

            \"N-/P-

            \n\n

            It can be used to build parsers/compilers/interpreters for various use cases ranging from simple config files to full fledged programming languages.

            \n\n
            With theoretical foundations in [Information Engineering](https://en.wikipedia.org/wiki/Information_engineering) (Discrete Mathematics, Control Theory, System Theory, Information Theory, and Statistics), my research has delivered a suite of systems and products that has allowed me to carve out a niche within an extensive collaborative network (>200 academics). _([Umer.Ijaz](https://userweb.eng.gla.ac.uk/umer.ijaz/#intro))_\n
            \n\n

            \"information

            \n\n

            Since such interactions result in a change in momentum, they can give rise to classical Newtonian forces of rotation and revolution by means of orbital structure.

            \n\n

            \"torus\"

            \n\n

            As you can see on the left sidebar (dekstop mode) a total of 102 items will be reached by the end of Id: 35.

            \n\n

            \"\"

            \n\n

            So when they transfered to Id: 36 it will cover 11 x 6 = 66 items thus the total will be 102 + 66 = 168

            \n","dir":"/multiplication/","name":"19.md","path":"multiplication/19.md","url":"/multiplication/19.html"},{"sort":21,"spin":86,"span":27,"suit":"main","layout":"default","title":"Feeding (spin 3)","content":"# Feeding (spin 3)\n\n{% include list.liquid all=true %}\n\nAs shown in [The Primes Platform](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-lexer-md) this cycle goes to **the prime 13** then reinjected through _[index 13:9](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md)_ . So it forms [The Scheme-139](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md) through the infinitely primes cycling. This scheme will be [implemented](https://chetabahana.github.io/#chetabahana-skema?pad=2) by taking the following as the syntax algorithm:\n\n[![default](https://user-images.githubusercontent.com/8466209/195963923-0796217c-7a87-4b2d-ba93-f47465304c03.png)](https://www.nausetschools.org/cms/lib/MA02212418/Centricity/Domain/204/Linkage%20Map%20Worksheet%20Genetics%202017.pdf)\n\nThe Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period ***eight (8) difference sequence*** of: {6, 4, 2, 4, 2, 4, 6, 2} _([Primesdemystified](https://primesdemystified.com/#deepsymmetries))_.\n\n[![image](https://user-images.githubusercontent.com/8466209/219260933-4331d79b-5815-4566-82e3-1a485bb2c61f.png)](https://primesdemystified.com/#deepsymmetries)\n\nSpeaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.\n\n[![11's additive sums](https://user-images.githubusercontent.com/8466209/221473004-867a1b50-f91f-470d-9922-e5e4f543a590.png)](https://primesdemystified.com/#deepsymmetries)\n\nThese objects will then behave as a complex numbers that leads to trivial and complex roots of the _[18th prime identity](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_. \n***286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271***\n\n```\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum \n =======================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10\n =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 --------\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin |\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------\n =======================+====+====+====+====+====+====+====+====+====+===== bilateral 9 sums (2)+60+40=102\n 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------\n =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin |\n 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 --------\n -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th\n```\n\nThe opposite direction will be made through switching beetween Linux and Windows which is proceed the old strand in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. Here we set a remote self-host runner via WSL.\n\n![default](https://user-images.githubusercontent.com/8466209/244855108-b80b3c2e-1a13-4b55-828a-72ed15b448dd.png)\n\nThe rest of primes goes to the [33's of 15th axis](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-19_root-md) that holding 102 primes of (2,60,40). By the bilateral way the form will be [splitted](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-parser-md) to (1,30,20). Since the base frame shall be 40 so it will be forced to form ***(1,30,40) of prime 71***.\n\n[![default](https://user-images.githubusercontent.com/8466209/202856928-45e4e5e0-4c77-45c9-af4c-5ffcacee916f.png)](https://docs.github.com/en/repositories/managing-your-repositorys-settings-and-features/managing-repository-settings/setting-repository-visibility#making-a-repository-private)\n\n","dir":"/identition/span12/","name":"gist01.md","path":"identition/span12/gist01.md","url":"/identition/span12/gist01.html"},{"sort":21,"spin":30,"span":168,"suit":2,"permalink":"/exponentiation/","layout":"default","title":"Exponentiation Zones (30-36)","content":"

            Exponentiation Zones (30-36)

            \n\n

            Exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power.

            \n\n
            This section is referring to _[wiki page-21](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-17]()_ that is _[inherited ]()_ from _[the gist section-2](https://gist.github.com/eq19)_ by _[prime spin-30](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-168](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Electrodynamics (maps)
              2. \n
            2. Quantum Gravity (feed)
              3. \n
            3. Chromodynamics (lexer)
              4. \n
            4. Electroweak Theory (parser)
              5. \n
            5. Grand Unified Theory (syntax)
              6. \n
            \n\n

            Exponentiation Zones allows multiple layers on representing recursive residues of the operands, thus promising large gain to the conventional arithmetic expression

            \n\n

            Standard Model

            \n\n

            In particle physics, study of the symmetry and its breaking play very important role in order to get useful \ninformation about the nature.

            \n\n
            Similarly the Standard Model incorporates three generations of quarks, so its fermionic content can be summarized. In addition, the Standard Model involves gauge bosons (photons for the electromagnetic interaction, W and Z for the weak interaction, and ***eight (8) gluons*** for the strong interaction), plus the (scalar) Higgs particle. This is what all known matter in the Universe consists of. _([Netrinos](https://github.com/eq19/eq19.github.io/files/13796986/NEUTRINOS_Mysterious_Particles_with_Fascinating_Fe.pdf))_\n
            \n\n

            \"Multiplets-of-the-1-2-spin-baryon-in-SU4-flavour-model

            \n\n

            Elementary particles and their interactions are considered by a theoretical framework called the Standard Model (SM) of Particle Physics.

            \n\n
            The Standard Model presently recognizes ***seventeen distinct particles (twelve fermions and five bosons)***. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have ***48 and 13 variations***, respectively. Among ***the 61 elementary particles*** embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. _([Wikipedia](https://en.wikipedia.org/wiki/Elementary_particle))_\n
            \n\n

            17 distinct particles = 12 fermions + 5 bosons = 48 + 13 = 61 variations

            \n\n

            \"Standard_Model_of_Elementary_Particles\"

            \n\n

            It is hypothesized that gravitational interactions are mediated by an as yet undiscovered elementary particle, dubbed the graviton.

            \n\n

            How many quarks?

            \n\n
            Answer-1: 3 generation x 3 color x 2 types x 2 each = 36 quarks\n
            \n\n

            \"How

            \n\n
            Answer-2: 6 flavour x 3 colors x 2 types = 36 quarks\n
            \n\n

            \"image\"

            \n\n
            Answer-3: 6 flavour x 3 colour x 4 bispinor = 72 quarks\n
            \n\n

            There are 72 quarks

            \n\n
            In order to be ***[four-spinors](https://en.wikipedia.org/wiki/Dirac_spinor#Four-spinor_for_particles)*** like the electron and other [lepton](https://en.wikipedia.org/wiki/Lepton) components, there must be one quark component for every combination of [flavour](https://en.wikipedia.org/wiki/Flavor_(particle_physics)) and [colour](https://en.wikipedia.org/wiki/Color_charge), ***bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four (4) component [bispinor](https://en.wikipedia.org/wiki/Bispinor), for a total of [96 complex-valued components](https://github.com/eq19/eq19.github.io/files/13796986/NEUTRINOS_Mysterious_Particles_with_Fascinating_Fe.pdf) for the fermion field***. _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n

            \"IMG_20240108_045902\"\n

            \n\n

            It is stated that each of the 24 components is a four component bispinor. A bispinor is constructed out 2 simpler component spinor so there are eight (8) spinors in total.

            \n\n
            Bispinors are so called because ***they are constructed out of two (2) simpler component spinors, the Weyl spinors***. Each of the two (2) component spinors transform differently under the two (2) distinct complex-conjugate spin-1/2 representations of the Lorentz group. This pairing is of fundamental importance, as it allows the represented particle to have a mass, carry a charge, and represent the flow of charge as a current, and perhaps most importantly, to carry angular momentum. _([Wikipedia](https://en.wikipedia.org/wiki/Bispinor))_\n
            \n\n

            ((3+3) + 2x(3x3)) x 4 = (3 + 3 + 18) x 4 = 24 x 4 = 96 components

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q)\n===========+=========+=========+===========+===========+============\nbispinor-1 |    2    |    3    |     3     |    18     |     24\n-----------+---------+---------+-----------+-----------+------------ } 48\nbispinor-2 |    2    |    3    |     3     |    18     |     24\n===========+=========+=========+===========+===========+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24\n-----------+---------+---------+-----------+-----------+------------ } 48\nbispinor-4 |    2    |    3    |     3     |    18     |     24\n===========+=========+=========+===========+===========+============\n     Total |    8    |   12    |    12     |    72     |     96\n
            \n\n

            Thus fermion is constructed out of eight (8) spinors that brings the total of 96 components consist of 12 charged leptons, 12 neutrinos and 72 quarks.

            \n\n

            Beyond the Quarks

            \n\n
            It has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear in 2018 that the SO(10) model is also free from all [nonperturbative global anomalies](https://en.wikipedia.org/wiki/Anomaly_(physics)#Witten_anomaly_and_Wang-Wen-Witten_anomaly) on [non-spin manifolds](https://en.wikipedia.org/wiki/Spin_structure) --- an important rule for confirming the consistency of SO(10) grand unified theory, with a Spin(10) gauge group and chiral fermions in the 16-dimensional spinor representations, defined on non-spin manifolds. _([Wikipedia](https://en.wikipedia.org/wiki/SO(10)))_\n
            \n\n

            \"SO(10)_-_16_Weight_Diagram

            \n\n
            Fermion particles are described by [Fermi–Dirac statistics](https://en.m.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics) and have [quantum numbers](https://en.m.wikipedia.org/wiki/Quantum_numbers) described by the [Pauli exclusion principle](https://en.m.wikipedia.org/wiki/Pauli_exclusion_principle). They include the [quarks](https://en.m.wikipedia.org/wiki/Quarks) and [leptons](https://en.m.wikipedia.org/wiki/Leptons), as well as any [composite particles](https://en.m.wikipedia.org/wiki/Composite_particles) consisting of an odd number of these, such as all [baryons](https://en.m.wikipedia.org/wiki/Baryons) and many atoms and nuclei. Fermions have half-integer spin; for all known elementary fermions this is 1⁄2. In the Standard Model, there are 12 types of elementary fermions: six [quarks](https://en.m.wikipedia.org/wiki/Quark) and six [leptons](https://en.m.wikipedia.org/wiki/Lepton).\n- Leptons do not interact via the strong interaction. Their respective antiparticles are the antileptons, which are identical, except that they carry the opposite electric charge and lepton number. The antiparticle of an electron is an antielectron, which is almost always called a \"positron\" for historical reasons.[![IMG_20240108_032736](https://github.com/eq19/eq19.github.io/assets/8466209/d0593a3f-0411-4ae9-94a6-7bba9e97391c)](https://en.wikipedia.org/wiki/List_of_particles)\n  - There are six leptons in total; the three charged leptons are called \"electron-like leptons\", while the neutral leptons are called \"neutrinos\".\n  - Neutrinos are known to oscillate, so that neutrinos of definite flavor do not have definite mass, rather they exist in a superposition of mass eigenstates.\n  - The hypothetical heavy right-handed neutrino, called a ***sterile neutrino***, has been omitted.\n- [Quarks](https://en.m.wikipedia.org/wiki/Quark) are the fundamental constituents of [hadrons](https://en.m.wikipedia.org/wiki/Hadron) and interact via the [strong force](https://en.m.wikipedia.org/wiki/Strong_force). Quarks are the only known carriers of [fractional charge](https://en.m.wikipedia.org/wiki/Fractional_charge), but because they combine in groups of three quarks (baryons) or in pairs of one quark and one [antiquark](https://en.m.wikipedia.org/wiki/Antiquark) (mesons), only integer charge is observed in nature.[![IMG_20240108_033012](https://github.com/eq19/eq19.github.io/assets/8466209/7427eccf-647c-4409-8f64-a144742b2fa3)](https://en.wikipedia.org/wiki/List_of_particles)\n  - Their respective [antiparticles](https://en.m.wikipedia.org/wiki/Antiparticle) are the [antiquarks](https://en.m.wikipedia.org/wiki/Antiquark), which are identical except that they carry the opposite electric charge (for example the up quark carries charge +2⁄3, while the up antiquark carries charge −2⁄3), color charge, and baryon number.\n  - There are six [flavors](https://en.m.wikipedia.org/wiki/Flavor_(particle_physics)) of quarks; the three positively charged quarks are called ***up-type quarks*** while the three negatively charged quarks are called ***down-type quarks***.\n\nAll known fermions except [neutrinos](https://en.m.wikipedia.org/wiki/Neutrinos), are also [Dirac fermions](https://en.m.wikipedia.org/wiki/Dirac_fermion); that is, each known fermion has its own distinct [antiparticle](https://en.m.wikipedia.org/wiki/Antiparticle). It is not known whether the [neutrino](https://en.m.wikipedia.org/wiki/Neutrino) is a [Dirac fermion](https://en.m.wikipedia.org/wiki/Dirac_fermion) or a [Majorana fermion](https://en.m.wikipedia.org/wiki/Majorana_fermion).[[4]](https://en.m.wikipedia.org/wiki/List_of_particles#cite_note-4) Fermions are the basic building blocks of all [matter](https://en.m.wikipedia.org/wiki/Matter). They are classified according to whether they interact via the [strong interaction](https://en.m.wikipedia.org/wiki/Strong_interaction) or not.\n
            \n\n

            \"Electrodynamics\"

            \n\n

            Free Parameters

            \n\n

            The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.

            \n\n
            The most general Lagrangian with massless neutrinos, one finds that the dynamics depend on ***19 parameters***, whose numerical values are established by experiment.\n\n- The 19 certain parameters are summarized below:\n[![IMG_20231230_232603](https://github.com/eq19/eq19.github.io/assets/8466209/2b4f5d82-d000-46f0-91ee-618ff55f01a4)](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Free_parameters)\n- The neutrino parameter values are still uncertain.\n- The value of the [vacuum energy](https://en.wikipedia.org/wiki/Vacuum_energy) (or more precisely, the [renormalization](https://en.wikipedia.org/wiki/Renormalization) scale used to calculate this energy) may also be treated as an additional free parameter.\n\nThe renormalization scale may be identified with the [Planck scale](https://en.wikipedia.org/wiki/Planck_scale) or fine-tuned to match the observed [cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant). However, both options [are problematic](https://en.wikipedia.org/wiki/Cosmological_constant_problem). _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                                       MEC 30 / 2\n------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 + ∆18 = ∆27         |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- ∆32\n      |      |  6  +-----+            ‹------------------------------ 15 {0}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = (43-19)\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19) ‹-- parameters ✔️    |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- ∆68 - ∆18 = ∆50\n------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}\n
            \n\n

            The Standard Model with massive neutrinos need 7 more parameters (3 masses and 4 PMNS matrix parameters) for a total of 26 parameters.

            \n\n
            In principle, there is one further parameter in the Standard Model; the Lagrangian\nof QCD can contain a phase that would lead to CP violation in the strong interac-\ntion.\n- Experimentally, this strong CP phase is known to be extremely small,\n θCP ≃ 0, and is usually taken to be zero.\n- If θCP is counted, then the Standard Model has ***26 free parameters***.\n- The relatively large number of free parameters is symptomatic of the StandardModel being just that; a model where the parameters are chosen to match the observations, rather than coming from a higher theoretical principle.\n- Putting aside θCP, of the 25 SM parameters, 14 are associated with the Higgs field, eight with the\nflavour sector and only three with the gauge interactions.\n\nLikewise, ***the coupling constants of the three gauge interactions*** are of a similar order of magnitude, hinting that they might be different low-energy manifestations of a Grand Unified Theory (GUT) of the forces. These patterns provide hints for, as yet unknown, physics beyond the Standard Model. _([Modern Particle Physics - pdf](https://github.com/eq19/eq19.github.io/files/13800674/Modern-Particle-Physics.pdf))_\n
            \n\n

            (24-5) + (24-17) = 19 + 7 = 26

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |     ❓\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |     ❓\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |     ❓\n
            \n\n
            Now we show the interplay of the finite system of prime positions with the ***15 finite even positions*** in the cyclic convolution. Consequently, we only need ***to fold a 30's cycle*** as so that we can identify the opposite prime positions that form their specific pairs in a specific convolution.\n
            \n\n

            13+17 = 11+19 = 30

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5 \n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |     ❓\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |     ❓\n
            \n\n

            The pairwise disjoint

            \n\n
            The Lie group structure of the Lorentz group is explored. Its generators and its Lie algebra are exhibited, via the study of infinitesimal Lorentz transformations.\n- The exponential map is introduced and it is shown that the study of the Lorentz group can be reduced to that of its Lie algebra.\n- Finally, the link between the restricted Lorentz group and the special linear group  is established via the spinor map. \n\nThe Lie algebras of these two groups are shown to be identical (up to some isomorphism).\n
            \n\n

            \"270355_1_En_7_Fig1_HTML\"

            \n\n

            19 + i(13+5) = 19 + i18

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |   66+i30 ✔️\n
            \n\n

            A bispinor is more or less “the same thing” as a Dirac spinor. The convention used here is that the article on the Dirac spinor presents plane-wave solutions to the Dirac equation.

            \n\n
            The four pairwise disjoint and non-compact connected components of the Lorentzgroup L = O(1, 3) and corresponding subgroups:\n- the proper Lorentz group L+ = SO(1, 3),\n- the orthochronous Lorentz group L↑,\n- the orthochronous Lorentz group Lo = L↑ + ∪ TL↑+ (see below) and\n- the proper orthochronous Lorentz group L↑+ = SO+(1, 3), which contains the identity element. \n\nOf course, the sets L↓−, L↑− and L↓+ do not represent groups due to the missing identity element. _([The-four-pairwise-disjoint](https://github.com/eq19/eq19.github.io/files/13810691/weyl_majorana_dirac_aste.pdf))_\n
            \n\n

            19 + 7 = 26

            \n\n

            \"The-four-pairwise-disjoint-and-non-compact-connected-components-of-the-Lorentz-group-L\"

            \n\n
             Bispinors | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i5+i7 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i13+i5 ✔️\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |   66+i30\n
            \n\n

            Thus it appears that the cosmological models] derived from compactification of 11d supergravity on a manifold with G2 holonomy have some hidden E7 symmetry.

            \n\n

            Counterpart of Bispinor

            \n\n

            A Dirac fermionis equivalent to two (2) Weyl fermions so it is not the same as bispinor. The counterpart is a Majorana fermion, a particle that must be its own antiparticle.

            \n\n
            Because particles and antiparticles have opposite conserved charges, Majorana fermions have zero charge, hence among the fundamental particles, the only fermions that could be Majorana are [sterile neutrinos](https://en.wikipedia.org/wiki/Sterile_neutrino), if they exist.\n- All the other elementary fermions of the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model) have [gauge charges](https://en.wikipedia.org/wiki/Charge_(physics)), so they cannot have fundamental [Majorana masses](https://en.wikipedia.org/wiki/Majorana_mass): Even the Standard Model's left-handed neutrinos and right-handed antineutrinos have non-zero [weak isospin](https://en.wikipedia.org/wiki/Weak_isospin),  a [charge-like](https://en.wikipedia.org/wiki/Charge_(physics)) quantum number.\n- However, if they exist, the so-called \"[sterile neutrinos](https://en.wikipedia.org/wiki/Sterile_neutrinos)\" (left-handed antineutrinos and right-handed neutrinos) would be [truly neutral particles](https://en.wikipedia.org/wiki/Truly_neutral_particle) (assuming no other, unknown gauge charges exist).\n- [Ettore Majorana](https://en.wikipedia.org/wiki/Ettore_Majorana) hypothesised the existence of Majorana fermions in 1937. The [sterile neutrinos](https://en.wikipedia.org/wiki/Sterile_neutrino) introduced to explain [neutrino oscillation](https://en.wikipedia.org/wiki/Neutrino_oscillation) and anomalously small S.M. [neutrino masses](https://en.wikipedia.org/wiki/Neutrino_mass) could have Majorana masses.\n\nIf they do, then at low energy (after [electroweak symmetry breaking](https://en.wikipedia.org/wiki/Electroweak_symmetry_breaking)), by the [seesaw mechanism](https://en.wikipedia.org/wiki/Seesaw_mechanism), ***the neutrino fields would naturally behave as six Majorana fields, with three of them expected to have very high masses (comparable to the [GUT scale](https://en.wikipedia.org/wiki/GUT_scale)) and the other three expected to have very low masses (below 1 eV)***.\n
            \n\n

            \"matrices-interpreted-2\"

            \n\n
             Majorana  | spinors | charged | neutrinos |   quark   | components | parameter\n  Fields   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   13+5\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   5+7\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    ❓     |     -     |     ❓     |   i66❓\n===========+=========+=========+===========+===========+============+===========\n     Total |   12    |    -    |    ❓     |     -     |     ❓     |   30+i66❓\n
            \n\n
            In [physics](https://en.wikipedia.org/wiki/Physics), a subatomic particle is a [particle](https://en.wikipedia.org/wiki/Particle) smaller than an [atom](https://en.wikipedia.org/wiki/Atom).[[1]](https://en.wikipedia.org/wiki/Subatomic_particle#cite_note-1)\n- According to the [Standard Model of particle physics](https://en.wikipedia.org/wiki/Standard_Model), a subatomic particle can be either a [composite particle](https://en.wikipedia.org/wiki/Composite_particle), which is composed of other particles (for example, a [baryon](https://en.wikipedia.org/wiki/Baryon), like a [proton](https://en.wikipedia.org/wiki/Proton) or a [neutron](https://en.wikipedia.org/wiki/Neutron), composed of three [quarks](https://en.wikipedia.org/wiki/Quarks); or a [meson](https://en.wikipedia.org/wiki/Meson), composed of two quarks), or an [elementary particle](https://en.wikipedia.org/wiki/Elementary_particle), which is not composed of other particles (for example, [quarks](https://en.wikipedia.org/wiki/Quarks); or [electrons](https://en.wikipedia.org/wiki/Electrons), [muons](https://en.wikipedia.org/wiki/Muons), and [tau](https://en.wikipedia.org/wiki/Tau) particles, which are called [leptons](https://en.wikipedia.org/wiki/Leptons)).[[2]](https://en.wikipedia.org/wiki/Subatomic_particle#cite_note-2)\n- [Particle physics](https://en.wikipedia.org/wiki/Particle_physics) and [nuclear physics](https://en.wikipedia.org/wiki/Nuclear_physics) study these particles and how they interact.[[3]](https://en.wikipedia.org/wiki/Subatomic_particle#cite_note-3)\n- Most force carrying particles like [photons](https://en.wikipedia.org/wiki/Photons) or [gluons](https://en.wikipedia.org/wiki/Gluons) are called [bosons](https://en.wikipedia.org/wiki/Bosons) and, although they have discrete quanta of energy, do not have rest mass or discrete diameters (other than pure energy wavelength) and are unlike the former particles that have rest mass and cannot overlap or combine which are called [fermions](https://en.wikipedia.org/wiki/Fermions).\n\n[![subatomic particles](https://github.com/eq19/eq19.github.io/assets/8466209/d54d3cd4-ee66-400b-a9cc-d7e0b888b468)](https://en.wikipedia.org/wiki/Subatomic_particle)\n\nExperiments show that light could behave like a [stream of particles](https://en.wikipedia.org/wiki/Stream_of_particles) (called [photons](https://en.wikipedia.org/wiki/Photon)) as well as exhibiting wave-like properties. This led to the concept of [wave–particle duality](https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality) to reflect that quantum-scale particles behave both like particles and like [waves](https://en.wikipedia.org/wiki/Wave); they are sometimes called wavicles to reflect this. _([Wikipedia](https://en.wikipedia.org/wiki/Subatomic_particle))_\n
            \n\n

            the 12 fermions and 5 bosons are known to have 48 and 13 variations, respectively

            \n\n
             Majorana  | spinors | charged | neutrinos |   quark   | components | parameter\n  Fields   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   13+5\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   5+7\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13 ✔️\n===========+=========+=========+===========+===========+============+===========\n     Total |   12    |    -    |    43     |     -     |     43     |  30+i13 ✔️\n
            \n\n
            [Leptons](https://en.wikipedia.org/wiki/Lepton) do not interact via the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction).\n- Their respective [antiparticles](https://en.wikipedia.org/wiki/Antiparticle) are the [antileptons](https://en.wikipedia.org/wiki/Antilepton), which are identical, except that they carry the opposite electric charge and lepton number.\n- The antiparticle of an [electron](https://en.wikipedia.org/wiki/Electron) is an antielectron, which is almost always called a \"[positron](https://en.wikipedia.org/wiki/Positron)\" for historical reasons.\n- There are six leptons in total; the three charged leptons are called \"electron-like leptons\", while the neutral leptons are called \"[neutrinos](https://en.wikipedia.org/wiki/Neutrino)\".\n- Neutrinos are known to [oscillate](https://en.wikipedia.org/wiki/Neutrino_oscillation), so that neutrinos of definite [flavor](https://en.wikipedia.org/wiki/Flavour_(particle_physics)) do not have definite mass, rather they exist in a superposition of mass [eigenstates](https://en.wikipedia.org/wiki/Eigenstate).\n\nThe hypothetical heavy right-handed neutrino, called a \"[sterile neutrino](https://en.wikipedia.org/wiki/Sterile_neutrino)\", has been omitted. _([Wikipedia](https://en.wikipedia.org/wiki/List_of_particles))_\n
            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️\n
            \n\n

            Since the total of parameters is 66+i30 then according to renormalization theory the 12 boson fields should have the total complex value of 30+i66.

            \n\n
            When describing [spacetime](https://en.wikipedia.org/wiki/Spacetime) as a continuum, certain statistical and quantum mechanical constructions are not [well-defined](https://en.wikipedia.org/wiki/Well-defined).\n- To define them, or make them unambiguous, a [continuum limit](https://en.wikipedia.org/wiki/Continuum_limit) must carefully remove \"construction scaffolding\" of lattices at various scales.\n- Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. That is, the experimental value of the physical quantity yields practical applications, but due to their empirical nature the observed measurement represents areas of quantum field theory that require deeper derivation from theoretical bases.\n- Renormalization was first developed in [quantum electrodynamics](https://en.wikipedia.org/wiki/Quantum_electrodynamics) (QED) to make sense of [infinite](https://en.wikipedia.org/wiki/Infinity) integrals in [perturbation theory](https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)).\n- Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and [self-consistent](https://en.wikipedia.org/wiki/Self-consistent) actual mechanism of scale [physics](https://en.wikipedia.org/wiki/Physics) in several fields of physics and [mathematics](https://en.wikipedia.org/wiki/Mathematics). \n\nDespite his later skepticism, it was [Paul Dirac](https://en.wikipedia.org/wiki/Paul_Dirac) who pioneered renormalization. _([Wikipedia](https://en.wikipedia.org/wiki/Renormalization))_\n
            \n\n

            \"image\"

            \n\n

            Supersymmetry

            \n\n
            The natural next step is to generalise this to D = 3, 4, 6, 10 and obtain a ‘magic pyramid’ with the D = 3 magic square at the base and Type II supergravity at the summit. On the basis of these results we speculate that the part played by octonions in string and M-theory may be more prominent than previously though. _([Super Yang-Mills - pdf](https://github.com/eq19/eq19.github.io/files/14386520/1309.0546.pdf))_\n
            \n\n

            \"images

            \n\n
            In this paper, we have extended our previous discussions about using HYMNs (height-yielding matrix numbers) which are the eigenvalues [14] of functions of the adjacency matrices associated with the L-matrics and R-matrices derived from adinkras. _([Properties of HYMNs - pdf](https://github.com/eq19/eq19.github.io/files/14386627/2010.14659.pdf))_\n
            \n\n

            \"images

            \n\n

            \"images

            \n\n

            In the forty years since 11D on-shell supergravity theory was constructed in 1978, a lot of efforts have been made to understand supergravity in superspace.

            \n\n
            Inspired by the history of how Einstein constructed ***General Relativity***, we study the linearized Nordstrom supergravity in _[10- and 11-dimensional superspaces](https://github.com/eq19/feed/files/12908714/JHEP07.2019.063.pdf)_.\n- [Valise adinkras](https://github.com/eq19/feed/files/13248983/2110.01665.pdf), although an important subclass, do not encode all information present when a 4D supermultiplet is reduced to 1D. We extend this to [non-valise adinkras](https://github.com/HEPTHools/Adinkra) providing a complete ***[eigenvalue classification](https://github.com/eq19/feed/files/13228760/1904.01738.pdf)*** via _Python code_.\n- We found no obstacles to applying the lessons we learned in _[4D to higher dimensions](https://github.com/eq19/feed/files/12908712/JHEP09.2021.202.pdf)_. We also derive infinitesimal 10D superspace Weyl transformation laws. The identification of all off-shell _[ten-dimensional supergeometrical](https://github.com/eq19/feed/files/12908716/JHEP03.2021.074.pdf)_ Weyl field strength tensors, constructed from respective torsions.\n- We realize that Lie Algebra techniques, in particular branching rules, Plethysm, and tensor product, provide the key to deciphering the complete list of independent fields that describe ***a supersymmetric multiplet in arbitrary spacetime dimensions*** efficiently.\n- Thus, _[adinkra-based arguments](https://github.com/eq19/feed/files/13227675/Adinkra_foundation_of_component_decomposition_and_.pdf)_ suggest the surprising possibility that the 11D, N=1 scalar superfield alone might describe a _[Poincare supergravity prepotential or semi-prepotential](https://github.com/eq19/feed/files/12908715/JHEP09.2020.089.pdf)_ in analogy to one of the off-shell versions of 4D, N=1.\n- All of these results strongly suggest adynkras are pointing in the direction of using ***[series expansion](https://github.com/eq19/feed/files/12924002/ATMP-2021-0025-0006-a003.pdf)*** in terms of _[Young Tableaux (YT's)](https://en.wikipedia.org/wiki/Young_tableau)_ as a tool to gain the most fundamental mathematical understanding of this class of problems.\n\nWe show the explicit one-to-one correspondence between Lorentz irreps and field variables, leading to an _adynkrafield_ formalism in which the traditional ζ (theta)-monomials are replaced by _YT's_ as shown below. _([YangruiHu.com](https://www.yangruihu.com/susy))_\n
            \n\n

            \"Higher-Dimensional

            \n\n
            In supergravity theory, supersymmetry theory and superstring theory, Adinkra symbols are a graphical representation of supersymmetry algebras. The similarity between Adinkra in supersymmetry and Adinkra symbols is that they are both graphical representations with hidden meanings (Prof. Sylvester James Gates Jr.). _([Adinkra Alphabet](https://www.adinkraalphabet.com/2018/05/30/adinkra-supersymmetry/))_\n
            \n\n

            \"Adinkrasupersymmetry\"

            \n\n
            ***All of these results strongly suggest adynkras are pointing in the direction of using series expansion*** in terms of YT’s as a tool to gain the most fundamental mathematical understanding of this class of problems. _([Higher-Dimensional Supergravity - Pdf](https://github.com/eq19/feed/files/12924002/ATMP-2021-0025-0006-a003.pdf))_\n
            \n\n

            \"Similarity\"

            \n\n
            Numerous connections have been observed between some, though not all, of these exceptional objects. Most common are objects related to [8](https://en.wikipedia.org/wiki/8_(number)) and [24](https://en.wikipedia.org/wiki/24_(number)) dimensions, noting that 24 = 8 · 3. By contrast, the [pariah groups](https://en.wikipedia.org/wiki/Pariah_group) stand apart, as the name suggests. Exceptional objects related to the number 8 include the following.\n- The octonions are 8-dimensional. The [E8 lattice](https://en.wikipedia.org/wiki/E8_lattice) can be realized as the integral octonions (up to a scale factor).\nThe exceptional Lie groups can be seen as symmetries of the octonions and structures derived from the octonions;[[19]](https://en.wikipedia.org/wiki/Exceptional_object#cite_note-19) further, the E8 algebra is related to the E8 lattice, as the notation implies (the lattice is generated by the root system of the algebra).\n- Triality occurs for Spin(8), which also connects to 8 · 3  = 24.Likewise, exceptional objects related to the number 24 include The Leech lattice is 24-dimensional.\nMost sporadic simple groups can be related to the Leech lattice, or more broadly the Monster.\nThe exceptional [Jordan algebra](https://en.wikipedia.org/wiki/Jordan_algebra) has a representation in terms of 24×24 real matrices together with the Jordan product rule.\nThese objects are connected to various other phenomena in math which may be considered surprising but not themselves \"exceptional\". For example, in [algebraic topology](https://en.wikipedia.org/wiki/Algebraic_topology), 8-fold real [Bott periodicity](https://en.wikipedia.org/wiki/Bott_periodicity) can be seen as coming from the octonions. In the theory of [modular forms](https://en.wikipedia.org/wiki/Modular_forms), the 24-dimensional nature of the Leech lattice underlies the presence of 24 in the formulas for the [Dedekind eta function](https://en.wikipedia.org/wiki/Dedekind_eta_function) and the [modular discriminant](https://en.wikipedia.org/wiki/Modular_discriminant), which connection is deepened by [Monstrous moonshine](https://en.wikipedia.org/wiki/Monstrous_moonshine), a development that related modular functions to the Monster group.\n\nIn [string theory](https://en.wikipedia.org/wiki/String_theory) and superstring theory we often find that particular dimensions are singled out as a result of exceptional algebraic phenomena. For example, [bosonic string theory](https://en.wikipedia.org/wiki/Bosonic_string_theory) requires a spacetime of dimension 26 which is directly related to the presence of 24 in the [Dedekind eta function](https://en.wikipedia.org/wiki/Dedekind_eta_function). Similarly, the possible dimensions of [supergravity](https://en.wikipedia.org/wiki/Supergravity) are related to the dimensions of the [division algebras](https://en.wikipedia.org/wiki/Division_algebras). _([Wikipedia](https://en.wikipedia.org/wiki/Exceptional_object))_\n
            \n\n

            \"1200px-Exceptionalmindmap2\"

            \n\n

            The Root System

            \n\n

            The Cartan–Weyl basis of the Lie algebra of SU(3) is obtained by another change of basis, where one defines The Root System for SU(3).

            \n\n
            In [mathematical physics](https://en.wikipedia.org/wiki/Mathematical_physics), [Clebsch–Gordan coefficients](https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients) are the expansion coefficients of [total angular momentum](https://en.wikipedia.org/wiki/Total_angular_momentum) [eigenstates](https://en.wikipedia.org/wiki/Eigenstate) in an uncoupled [tensor product](https://en.wikipedia.org/wiki/Tensor_product) basis.\n- Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a [direct sum](https://en.wikipedia.org/wiki/Direct_sum) of irreducible representations, where the type and the multiplicities of these irreducible representations are known abstractly.\n- The name derives from the German mathematicians [Alfred Clebsch](https://en.wikipedia.org/wiki/Alfred_Clebsch) (1833–1872) and [Paul Gordan](https://en.wikipedia.org/wiki/Paul_Gordan) (1837–1912), who encountered an equivalent problem in [invariant theory](https://en.wikipedia.org/wiki/Invariant_theory).\n\nGeneralization to SU(3) of Clebsch–Gordan coefficients is useful because of their utility in characterizing [hadronic decays](https://en.wikipedia.org/wiki/Hadron), where a [flavor-SU(3) symmetry](https://en.wikipedia.org/wiki/Flavour_(particle_physics)) exists (the [eightfold way](https://en.wikipedia.org/wiki/Eightfold_way_(physics))) that connects the three light [quarks](https://en.wikipedia.org/wiki/Quarks): [up](https://en.wikipedia.org/wiki/Up_quark), [down](https://en.wikipedia.org/wiki/Down_quark), and [strange](https://en.wikipedia.org/wiki/Strange_quark). _([Wikipedia](https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients_for_SU(3)))_\n
            \n\n

            \"The

            \n\n

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            \n\n

            π(π(30+37)) = π(π(67)) = π(19) = 8

            \n\n
            #!/usr/bin/env bash\n\nedit_file () {\n\n  NUM=$(($2 + 0))\n  \n  while IFS=' ' read -ra SPIN; do\n    T+=(\"${SPIN[0]}\")\n    R+=(\"${SPIN[1]}\")\n    A+=(\"${SPIN[2]}\")\n    C+=(\"${SPIN[3]}\")\n    K+=(\"${SPIN[4]}\")\n    I+=(\"${SPIN[5]}\")\n    N+=(\"${SPIN[6]}\")\n    G+=(\"${SPIN[7]}\")\n  done < /tmp/spin.txt\n\n  FRONT=\"---\\n\"\n  FRONT+=\"sort: ${K[$NUM]}\\n\"\n  FRONT+=\"span: ${I[$NUM]}\\n\"\n  FRONT+=\"spin: ${N[$NUM]}\\n\"\n  FRONT+=\"suit: ${G[$NUM]}\\n\"\n  FRONT+=\"---\\n\"\n\n  IFS=$'\\n' read -d '' -r -a LINE < _Sidebar.md\n  TEXT=\"${LINE[$NUM]}\" && TITLE=${TEXT%|*}\n  FRONT+=\"# $TITLE\\n\\n\"\n\n  [[ $NUM -le 9 ]] && sed -i \"1s|^|$FRONT|\" $1\n  if [[ $NUM -lt 2 || $NUM == 9 ]]; then\n    mv -f $1 ${1%/*}/README.md\n    sed '1,6!d' ${1%/*}/README.md\n  fi\n}\n\nFILE=${1##*/} && SORT=${FILE%.*}\n[[ $SORT =~ ^-?[0-9]+$ ]] && edit_file $1 $SORT\n
            \n\n

            These matrices are particularly important in both mathematics and physics. For example, these matrices (and their generalizations) are important in Lie theory.

            \n\n
            _[Gell-mann matrices](https://en.m.wikipedia.org/wiki/Gell-Mann_matrices)_ are a complete set of Hermitian  noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model ***the eight gluons*** that mediate the strong force quantum chromodynamics, an analogue of the _[Pauli matrices](https://mathworld.wolfram.com/PauliMatrices.html)_ well-adapted to applications in the realm of quantum mechanics. _([Wolfram](https://mathworld.wolfram.com/Gell-MannMatrix.html))_\n
            \n\n
            #!/usr/bin/env python\n\nimport numpy as np\nfrom scipy import linalg\n\nclass SU3(np.matrix):\n\tGELLMANN_MATRICES = np.array([\n\t\tnp.matrix([ #lambda_1\n\t\t\t[0, 1, 0],\n\t\t\t[1, 0, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_2\n\t\t\t[0,-1j,0],\n\t\t\t[1j,0, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_3\n\t\t\t[1, 0, 0],\n\t\t\t[0,-1, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_4\n\t\t\t[0, 0, 1],\n\t\t\t[0, 0, 0],\n\t\t\t[1, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_5\n\t\t\t[0, 0,-1j],\n\t\t\t[0, 0, 0 ],\n\t\t\t[1j,0, 0 ],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_6\n\t\t\t[0, 0, 0],\n\t\t\t[0, 0, 1],\n\t\t\t[0, 1, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_7\n\t\t\t[0, 0,  0 ],\n\t\t\t[0, 0, -1j],\n\t\t\t[0, 1j, 0 ],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_8\n\t\t\t[1, 0, 0],\n\t\t\t[0, 1, 0],\n\t\t\t[0, 0,-2],\n\t\t], dtype=np.complex) / np.sqrt(3),\n\t])\n\n\n\tdef computeLocalAction(self):\n\t\tpass\n\n\t@classmethod\n\tdef getMeasure(self):\n\t\tpass\n
            \n\n

            These representations are a curious finding. They relate particles to antiparticles by using only the complex conjugate i → −i, they fill these as of Euler’s Identity.

            \n\n
            Euler's identity is a special case of Euler's formula ***e^ix = cos x + i sin x*** when evaluated for ***x = π***, In addition, it is directly used in a proof that ***π is transcendental***, which implies the impossibility of squaring the circle. _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_\n
            \n\n

            \"Euler's

            \n\n

            Euler identity present a matrix generalization of the about exponential representation for matrix real and imaginary unit which compatible with the Pauli matrix

            \n\n
            Gell–Mann -matrices are a complete set of Hermitian 3 ⊗ 3 noncommuting trace-orthogonal matrices. They are at the heart of Quantum Chromodynamics (QCD), an integral part of the Standard Model. They are also used in quantum information theory to represent qutrits. Gell–Mann matrices are to SU(3) what the Pauli matrices are to SU(2). _([Wolfram](https://demonstrations.wolfram.com/EverythingAboutGellMannMatricesPart1UnaryOperations/))_\n
            \n\n

            \"Everything

            \n\n

            These unifying principles might come in the form of grand unified theories, supersymmetry, M-theory, or perhaps something else.

            \n\n
            The discovery of [neutrino oscillations](https://en.wikipedia.org/wiki/Neutrino_oscillation) indicates that the Standard Model is incomplete, but there is currently no clear evidence that nature is described by any _[Grand Unified Theory](https://en.wikipedia.org/wiki/Grand_Unified_Theory)_. Neutrino oscillations have led to renewed interest toward certain GUT such as _[SO(10)](https://en.wikipedia.org/wiki/SO(10))_. _([Wikipedia](https://en.wikipedia.org/wiki/Grand_Unified_Theory))_\n
            \n\n

            \"Higher-Dimensional

            \n\n

            Although, at the moment evidence do not have a complete model. However, it becomes a little more clear that this unlikely algebra is not going away.

            \n\n

            Basic Transformation

            \n\n

            The first appearance of e in a printed publication was in Euler’s Mechanica (1736). It is unknown why Euler chose the letter e.

            \n\n
            [Leonhard Euler](https://en.m.wikipedia.org/wiki/Leonhard_Euler) started to use ***the letter e*** for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and in a letter to [Christian Goldbach](https://en.m.wikipedia.org/wiki/Christian_Goldbach) on 25 November 1731. _([Wikipedia](https://en.wikipedia.org/wiki/E_(mathematical_constant)))_\n
            \n\n

            \"Letter

            \n\n

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            \n\n
            During the last few years of the 12th century, ***Fibonacci*** undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that ***it popularized the use of the Arabic numerals in Europe***, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. _([Famous Mathematicians](https://famous-mathematicians.org/leonardo-pisano-bigollo/))_\n
            \n\n

            \"MEC30

            \n\n

            Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30’s square.

            \n\n
            A square system of coupled nonlinear equations can be solved iteratively by Newton's method. This method uses the Jacobian matrix of the system of equations. _([Wikipedia](https://en.wikipedia.org/Jacobian_matrix_and_determinant))_\n
            \n\n

            \"gradien\"

            \n\n

            In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism.

            \n\n
            As usual, the images ***on the left are snapshots of the particles at different times. Those times correspond to the grey slices in the space-time diagram on the right***. You can see the specific interaction points in the space-time diagram, where the blue particle is emitted and then absorbed by the red particles. Those points will be important later, as we compare this to the situation in ***string theory***. _([Slimy.com](http://www.slimy.com/~steuard/research/StringIntro/slide13.html))_\n
            \n\n

            \"Feynman

            \n\n

            \"ezgif-4-95200c65b5\"

            \n\n
            They are at the heart of Quantum Chromodynamics (QCD), an integral part of the Standard Model. They are also used in ***quantum information*** theory to represent qutrits. _[Gell–Mann matrices](https://github.com/search?q=Gellmann+language%3APython&type=code&l=Python)_ are to SU(3) what the _[Pauli matrices](https://github.com/search?q=Pauli+language%3APython&type=code&l=Python)_ are to SU(2). _([Wolfram](https://demonstrations.wolfram.com/EverythingAboutGellMannMatricesPart1UnaryOperations/))_\n
            \n\n

            \"Gell-Mann

            \n\n

            In this paper, you may find a way to apply the Gell-Mann transformations made by the λi matrices using Geometric Algebra Cl3,0.\nSo it will need a gap between each identities to proceed the thing. Let’s discuss how it goes by the seven (7) hidden dimensions.

            \n\n

            Fundamental Forces

            \n\n
            In [particle physics](https://en.wikipedia.org/wiki/Particle_physics), a lepton is an [elementary particle](https://en.wikipedia.org/wiki/Elementary_particle) of [half-integer spin](https://en.wikipedia.org/wiki/Half-integer_spin) ([spin](https://en.wikipedia.org/wiki/Spin_(physics)) 1⁄2) that does not undergo [strong interactions](https://en.wikipedia.org/wiki/Strong_interaction).[[1]](https://en.wikipedia.org/wiki/Lepton#cite_note-1)\n- Two main classes of leptons exist: ***[charged](https://en.wikipedia.org/wiki/Electric_charge)*** leptons (also known as the [electron](https://en.wikipedia.org/wiki/Electron)-like leptons or muons), and neutral leptons (better known as ***[neutrinos](https://en.wikipedia.org/wiki/Neutrino))***.\n- Charged leptons can combine with other particles to form various [composite particles](https://en.wikipedia.org/wiki/Composite_particle) such as [atoms](https://en.wikipedia.org/wiki/Atom) and [positronium](https://en.wikipedia.org/wiki/Positronium), while neutrinos rarely interact with anything, and are consequently rarely observed.\n- ***The best known of all leptons is the [electron](https://en.wikipedia.org/wiki/Electron)***.\n\nThere are ***six types of leptons***, known as [flavours](https://en.wikipedia.org/wiki/Flavour_(particle_physics)), grouped in three [generations](https://en.wikipedia.org/wiki/Generation_(particle_physics)).[[2]](https://en.wikipedia.org/wiki/Lepton#cite_note-HyperphysicsLepton-2)\n- The [first-generation](https://en.wikipedia.org/wiki/Standard_Model) leptons, also called electronic leptons, comprise the [electron](https://en.wikipedia.org/wiki/Electron) (e−) and the [electron neutrino](https://en.wikipedia.org/wiki/Electron_neutrino) (νe); the second are the muonic leptons, comprising the [muon](https://en.wikipedia.org/wiki/Muon) (μ−) and the [muon neutrino](https://en.wikipedia.org/wiki/Muon_neutrino) (νμ); and the third are the tauonic leptons, comprising the [tau](https://en.wikipedia.org/wiki/Tau_(particle)) (τ−) and the [tau neutrino](https://en.wikipedia.org/wiki/Tau_neutrino) (ντ).\n- ***Electrons have the least mass of all the charged leptons***. The heavier muons and taus will rapidly change into electrons and neutrinos through a process of [particle decay](https://en.wikipedia.org/wiki/Particle_decay): the transformation from a higher mass state to a lower mass state.\n- Thus electrons are stable and the most common charged lepton in the [universe](https://en.wikipedia.org/wiki/Universe), whereas muons and taus can only be produced in [high energy](https://en.wikipedia.org/wiki/High_energy_physics) collisions (such as those involving [cosmic rays](https://en.wikipedia.org/wiki/Cosmic_ray) and those carried out in [particle accelerators](https://en.wikipedia.org/wiki/Particle_accelerator)).\n- Leptons have various [intrinsic properties](https://en.wikipedia.org/wiki/Intrinsic_properties), including [electric charge](https://en.wikipedia.org/wiki/Electric_charge), [spin](https://en.wikipedia.org/wiki/Spin_(physics)), [mass](https://en.wikipedia.org/wiki/Mass).\n- Unlike [quarks](https://en.wikipedia.org/wiki/Quark), however, leptons are not subject to the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction), but they are subject to the other three [fundamental interactions](https://en.wikipedia.org/wiki/Fundamental_interaction): [gravitation](https://en.wikipedia.org/wiki/Gravitation), the [weak interaction](https://en.wikipedia.org/wiki/Weak_interaction), and to ***[electromagnetism](https://en.wikipedia.org/wiki/Electromagnetism)***, of which the latter is proportional to charge, and is thus zero for the electrically neutral neutrinos.![force_chart](https://github.com/eq19/eq19.github.io/assets/8466209/dd7cc532-a84e-4921-834c-1e9939937f66)\n\nFor every lepton flavor, there is a corresponding type of [antiparticle](https://en.wikipedia.org/wiki/Antiparticle), known as an antilepton, that differs from the lepton only in that some of its properties have [equal magnitude but opposite sign](https://en.wikipedia.org/wiki/Charge_conjugation). According to certain theories, neutrinos may be [their own antiparticle](https://en.wikipedia.org/wiki/Majorana_fermion). It is not currently known whether this is the case. _([Wikipedia](https://en.wikipedia.org/wiki/Lepton))_\n
            \n\n

            \"Electrodynamics\"

            \n\n

            They are composed out of Symmetry Breaking between The True Prime Pairs versus the 139 components of The Fermion Field tabulated as below.

            \n\n

            (33+1)th prime = 139

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    | 👉 3    |     3     |    18     |     24     |   11 ✔️\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    139     |  96+i43\n
            \n\n

            Beyond the 139

            \n\n

            According to the 24 cells of Prime Hexagon, this 12 boson fields seems to be realistic. However it would need to have a total of 96 complex-valued components as well.

            \n\n
            The present particle physics or standard model based on the \"unreal gauge transformation symmetry\" and meaningless math cannot explain any actual physical mechanism at all _([biglobe.ne.jp](https://www7b.biglobe.ne.jp/~kcy05t/parph.html))_\n
            \n\n

            \"hsta1\"

            \n\n

            When we take all the forces that we understand, i.e., not including gravity, and write down the QFT version of them, we arrive at the predictions of the Standard Model.

            \n\n
            This is where the idea of ***12 fermion fields and 12 boson fields*** come from. These fields are excitations of the underlying theories (the Standard Model) that describe the known Universe in its entirety, and include:\n- The six (6): up-, down-, strange-, charm-, bottom-, top-quarks, and their antiquark counterparts,\n- The three (3) charged (electron, muon, tau) and three (3) neutral (electron neutrino, muon neutrino, tau neutrino) leptons, and their antimatter counterparts,\n- The eight (8) gluons (because of the eight possible color combinations),\n- The one (1) electromagnetic (photon) boson,\n- The two (2) weak (W-and-Z) bosons,\n- And the Higgs boson.\n\nThe quarks and leptons are fermions, which is why they have antimatter counterparts, and the W boson comes in two equal-and-opposite varieties (positively and negatively charged), but all told, ***there are 24 unique, fundamental excitations of quantum fields possible***. This is where the 24 fields idea comes from. _([Forbes](https://www.forbes.com/sites/startswithabang/2018/11/17/ask-ethan-are-quantum-fields-real/?sh=32c398b3777a))_\n
            \n\n

            \"SM-particles\"

            \n\n

            This scheme goes to the unification of 11s with 7s to 18s meanwhile the 11th it self behave as residual by the 5th minor hexagon between the 30 to 36’ cells.

            \n\n
            This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with ***the prime distribution level*** as indicated by the _[self repetition](https://www.eq19.com/exponentiation/#self-repetition)_ on MEC30.\n
            \n\n

            109 = 29th prime = (10th prime)th prime

            \n\n

            \"self

            \n\n

            The evolution of a spin foam, has a scale above the Planck length. Consequently, not just matter, but space itself, prefers an atomic structure.

            \n\n

            \"SM-SUSY-diagram\"

            \n\n

            These include generating variants of their abundance profile, assigning taxonomy and finally generating a rooted phylogenetic tree for the Standard Model.

            \n\n
            Here is an elegant model to define the elementary particles of the Standard Model in Physics.\n- The black spheres are the bosons, the green ones leptons and the rest of the colored ones Murray Gell-Mann’s quarks (red for Generation I, blue for II and orange for III).\n- Higgs Boson (aka the God particle) that does not have charge is the vertex between the matter and anti-matter particles.\n- The z-boson and its counterpart would lie in the centroids of the tetrahedrons created by folding the triangles to meet up at the Higgs particle.\n\nThe next step is to re-gigg the model to account for the collisions and annihilations. Gluons and Photons that don’t have mass are not in the model, but will be the consequences of the interactions. _([Hypercomplex-Math](https://nitinuchil.wordpress.com/2020/09/09/hypercomplex-math/))_\n
            \n\n

            \"particlephysicsmodel-1\"

            \n\n

            All 15 matter particles are mirroring their corresponding doppelgangers (anti-particles) each others that could potentially explain dark matter.

            \n\n

            Quadratic Polynomials

            \n\n

            In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns.

            \n\n
            The interaction of any pair of fermions in perturbation theory can be modelled as:\n\n***Two fermions go in → interaction by boson exchange → Two changed fermions go out.***\n\nThe exchange of bosons always carries energy and momentum between the fermions, thereby ***changing their speed and direction***. The exchange may also transport a charge between the fermions, changing the charges of the fermions in the process (e.g., turn them from one type of fermion to another). Since bosons carry one unit of angular momentum, ***the fermion's spin direction will flip from +1⁄2 to −1⁄2 (or vice versa)*** during such an exchange (in units of the reduced Planck's constant). _([Wikipedia](https://en.wikipedia.org/wiki/Fundamental_interaction))_\n
            \n\n

            36th prime - 30th prime = 151 - 113 = 1 + 37

            \n\n

            \"Defining

            \n\n
            Our ***[18s gists](https://gist.github.com/eq19)*** would form the _[18s structure of 11s and 7s](https://www.eq19.com/addition/#structure-true-prime-pairs)_ where by the 11s, the 20th prime 71 would stand as _[eigenvalue](https://www.eq19.com/multiplication/#streaching-structure)_ and by the 7s, the 11th prime 31 would stand as the _[new symmetical zero axis](https://www.eq19.com/exponentiation/#parsering-structure)_ by means of _[MEC30 Structure](https://www.eq19.com/exponentiation/#self-repetition)_. So whenever the 11s is _[compactified](https://www.eq19.com/identition/#the-powers-of-10)_ down to ***[4 dimensions](https://www.eq19.com/exponentiation/#parsering-structure)*** it will always be compactifed by the 7s as their _[extended branes](https://www.eq19.com/identition/#extra-dimensions)_ which including the _[eigenvector](https://www.eq19.com/addition/#18s-structure)_ of _[dark energy](https://www.eq19.com/identition/#string-theory)_ and finally become another level of ***[11 dimensions](https://www.eq19.com/identitionl/#the-powers-of-pi)*** that lead to the concept of _[multiple universes](https://www.eq19.com/identition/#extra-dimensions)_. \n
            \n\n

            Δ prime = 114th prime - 19 = (6 x 19)th prime - 19 = 619 - 19 = 600 = 3 x 200

            \n\n

            \"Proof

            \n\n

            Observing more detail of the discussed scheme of 168 we will get it also when we take the 19’s and 17’s cell of (31+37)+(35+65)=68+100=168.

            \n\n
            By our project the 18's on the gist will cover five (5) unique functions that behave as ***one (1) central plus four (4) zones***. This scheme will be implemented to all of the 168 repositories as bilateral way (***in-out***) depend on their postion on the system. So along with the gist it self then there shall be `1 + 168 = 169` units of 1685 root functions.\n
            \n\n

            5 + 2 x 5 x 168 = 5 + 1680 = 1685 root functions

            \n\n

            \"\"

            \n\n

            By the spin above you can see that the 4 zones of these 19's to 17's are representing the rotation 1 to 5. Such of formation can be seen on Ulam Spiral as below.

            \n\n
            The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.\n
            \n\n

            \"ulam

            \n\n

            By MEC30 we will also discuss the relation of these 4 zones with high density of 40 primes where 60 number is folded. So by the module 6 it will always return to the beginning position within 60+40=100 nodes per layer.

            \n\n
            Both Ulam and Gardner noted that the existence of such prominent lines ***is not unexpected***, as lines in ***the spiral correspond to quadratic polynomials***, and certain such polynomials, such as Euler's prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with **major unsolved problems** in number theory such as Landau's problems _([Wikipedia](https://en.wikipedia.org/wiki/Ulam_spiral))_.\n
            \n\n

            \"prime

            \n\n

            This density will bring the D3-Brane where the lexer is being assigned per MEC30. Base on the its spin as shown in the above picture this lexer is assigned by Id: 33.

            \n\n

            Parsering Structure

            \n\n

            Ploting 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            \n\n

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            \n\n
            $True Prime Pairs:\n(5,$True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer|  i  |   f\n -----+-----+---------\n      |  1  | 5\n   1  +-----+\n      |  2  | 7\n -----+-----+---  } 36 » 6®\n      |  3  | 11\n   2  +-----+\n      |  4  | 13\n -----+-----+---------\n      |  5  | 17\n   3  +-----+     } 36 » 6®\n      |  6  | 19\n -----+-----+---------\n  \nlayer | node | sub |  i  |  f                               \n------+------+-----+---------- \n      |      |     |  1  | -------------------- _site ---  71 = 72-1\n      |      |  1  +-----+                        |\n      |  1   |     |  2  | (5)                  _saas\n      |      |-----+-----+                        |\n      |      |     |  3  | ---------            _data\n  1   +------+  2  +-----+----      |             |\n      |      |     |  4  |         5x ---       _posts\n      |      +-----+-----+          |     |       |\n      |  2   |     |  5  | (7) -----      |     _drafts\n      |      |  3  +-----+                |       |\n289+11=300   |     |  6  |                |     _plugins\n------+------+-----+-----+----- 72 x 6   7x ------------ 11x = 77 (rational)◄--\n      |      |     |  7  |                |     _includes                      |\n      |      |  4  +-----+                |       |                            |\n      |  3   |     |  8  | (11)  ---      |     _layouts                       |\n      |      +-----+-----+          |     |       |                            |\n      |      |     |  9  |         2x ---        assets  (69 = 72-3)           |\n  2   +------|  5  +-----+-----     |             |                            |\n      |      |     |  10 | ---------            _saas                          |\n      |      |-----+-----+                        |                            |\n      |  4   |     |  11 | (13) ----------------_site --  71 = 72-1            |\n      |      |  6  +-----+                                                     |\n329+71=400   |     |  12 |------------------------------  70 = 72-2            |\n------+------+-----+-----+                                                    11x\n      |      |     |  13 |                                                     |\n      |      |  7  +-----+                                                     |\n      |  5   |     |  14 | (17) ◄------------------------------------------- (17)\n      |      |-----+-----+                                                     |\n      |      |     |  15 | ◄-- 42 x 6 partitions of 13 (irrational)            |\n  3   +------+  8  +-----+-----                                                +\n      |      |     |  16 |                                                     |  \n      |      |-----+-----+                                                     |\n      |  6   |     |  17 | (19) ◄------------------------------------------- (19)\n      |      |  9  +-----+                                                     |\n168+32=200   |  |  |  18 |------------------------------  68 = 72-4            |\n------|------|--|--+-----+                                                     |\n       900 -----                                                               |\n                                                                               |\n
            \n\n

            Using the javascript library from Chevotrain and data parser from Jekyll/Liquid finally we found the correlation between the lexer and parser trough the powers of pi.

            \n\n
            In this example, the content from a Markdown document `document.md` that specifies `layout: docs` gets pushed into the `{{ content }}` tag of the layout file `docs.html`. Because the docs layout itself specifies `layout: page`, the content from `docs.html` gets pushed into the `{{ content }}` tag in the layout file `page.html`. Finally because the page layout specifies `layout: default`, the content from `page.html` gets pushed into the `{{ content }}` tag of the layout file `default.html`. _([JekyllRb](https://jekyllrb.com/tutorials/convert-site-to-jekyll/#how-layouts-work))_\n
            \n\n

            \"Parsering\"

            \n\n

            Since the modulo 6 is occured all over the spin then we have defined that this 4 zones should stand as default configuration as you can see on the left sidebar.

            \n\n
            In order to maintain the 18's structure between each of repositories to correlate with the above density then we could use a hierarchical database that stores low-level settings for the operating system such as _[windows registry](https://en.wikipedia.org/wiki/Windows_Registry)_.\n
            \n\n

            \"windows

            \n\n

            Going deeper there are many things raised up as questions. So in this project we are going to analyze it using a javascript library called Chevrotain.

            \n\n
            The spin states for the powers of pi. The Prime Hexagon is an integer environment, so pi powers are truncated. I believe these data suggest ***prime numbers are linked in some way to pi***. _([HexSpin](https://www.hexspin.com/minor-hexagons/))_\n
            \n\n

            \"Lexers,

            \n\n

            It is going to setup CI/CD for up to 1000 public repositories out of millions that available on GitHub. You may visit our mapping scheme for more detail.

            \n\n

            Grand Unification

            \n\n

            The 619 is the 114th prime. By the True Prime Pairs it is laid on the last index of 6 with prime 19 where as 6x19 is also 114. Let’s put 19 hexagons within the 3 layers.

            \n\n

            168+618 - 19x6x6 = 786 - 684 = 102

            \n\n

            \"entry

            \n\n

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            \n\n
            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) _([₠Quantum](https://github.com/eq19))_.\n
            \n\n

            6+6 + 6/\\6 = 6+6 + 15 = 27-day month

            \n\n

            \"flowchart\"

            \n\n

            By this project the above would be deployed as default layout. It is set to be avalaible throughout the whole platform via a single page within a parser repository which is acting as prime 13. Their interface will be in json and xml format.

            \n\n

            Here is for the sample:

            \n\n
            {\n  \"title\":\"Mapping System\",\n  \"content\":\"<p>Hello, <strong>world</strong>.\\nI am here.</p>\\n\",\n  \"links\": [\n    {\"title\":\"Introduction\",\"url\":\"https://www.eq19.com/intro/\"},\n    {\"title\":\"Go tour on Mapping System \",\"url\":\"https://www.eq19.com/maps/\"},\n    {\"title\":\"A backed pretty display for markdown\",\"url\":\"https://www.eq19.com/gistio/\"},\n    {\"title\":\"Gist.io for programmers\",\"url\":\"https://gist.io/@eq19/d2336e28e79702acf38edd182003d5e0\"}\n  ]\n}\n
            \n\n

            Using a kind of interface such as docker then it could be developed cross platform. Evenso. Let assume that all alpabethic letter in the sequence is representing a local disk so you may build your own pattern in your PC such as shown below:

            \n\n

            \"default\"

            \n\n

            By The GitHub Runner you can connect to the Google COS Instance. For self-hosted runners defined at the organization level, configure runs-on.group in your workflow file to target a runner groups or combine groups and labels.

            \n\n
            Why collaborating with physicists?\n- Contribute to the understanding of the Universe.\n- Open methodological challenges.\n- Test bed for developing ambitious ML/AI methods, as enabled by the precise mechanistic understanding of physical processes.\n- Core problems in particle physics transfer to other fields of science (likelihood-free inference, domain adaptation, optimization, etc).\n- A high-level summary of various aspects of [machine learning in LHC](https://github.com/eq19/eq19.github.io/files/14396836/Pata.slides.pdf) data reconstruction, mostly based on CMS examples. A short summary of a particular use case: ML for combining signals across detector subsystems with particle flow. This talk is in personal capacity (not representing CMS or CERN), representing my biased views.\n\nYou can find a great and fairly complete overview of [ML papers in HEP](https://iml-wg.github.io/HEPML-LivingReview/). _([Pata Slides](https://github.com/eq19/eq19.github.io/files/14396836/Pata.slides.pdf))_\n
            \n\n

            π(10) = 2,3,5,7

            \n\n

            \"SO(10)\"\n

            \n\n

            \"teaching-machines-glouppe_compressed.pdf\"

            \n\n

            This way will also be our approach to Euler’s identity. By taking the correlation between f(π) as P vs f(i) as NP where eiπ + 1 = 0 then theoretically they shall be correlated to get an expression of the prime distribution similar to MEC30.

            \n\n
            The Minimal Supersymmetric Standard Model (MSSM) contains two Higgs doublets, leading to _five (5) physical [Higgs bosons](https://www.sciencedirect.com/topics/physics-and-astronomy/higgs-bosons)_:\n- one (1) neutral CP-odd (A) 👈 ***degenerated with (h or H)*** \n- two (2) charged states ***(H+ and H−)***,\n- Two (2) neutral CP-even states ***(h and H)***.\n\n_At tree-level, the masses are [governed](https://github.com/eq19/eq19.github.io/files/14066329/76104_ANGELESCU_2017_diffusion.pdf)\n by two parameters, often taken to be mA and tan β [3]. When tan β >> 1, A is nearly [degenerated](https://github.com/eq19/eq19.github.io/files/14066343/epjconf_qfthep2019_04006.pdf)\n with one of the CP-even states (denoted ϕ)_. _([ScienceDirect](https://www.sciencedirect.com/topics/mathematics/higgs-mechanism))_\n
            \n\n

            \"the

            \n\n

            This also introduces a lower bound of Mod 90 originated from the 4th coupling of MEC30 which is holded by five (5) cells between 13 and 17.

            \n\n
            Below we will demonstrate how factorization algorithms and twin prime dyad cycling at the digital root level rotate the vertices of ***equilateral triangles within {9/3}*** star polygons like the one pictured above. These rotations are ***encoded in 3 x 3 matrices generated by period-24 digital root dyad tri-level cycling***. We will also reveal the Latin Square reflecting {3,6,9} hidden in plain sight betwixt and between the twin prime distribution channels; ***all of its rows, columns and principal diagonals summing to 18***. _[PrimesDemystified](https://www.primesdemystified.com/twinprimes.html)_\n
            \n\n

            19 + 18 + 102 = 37 + 102 = 139 = 34th prime = (40 - 6)the prime

            \n\n

            \"exponentiation

            \n\n

            The boson, photon and gravity forces are assigned to 30, 31 and 32. Gluon force and exchange are assigned to 33 and 34 which are then standing as the lexer and parser.

            \n\n
            An overview of the various families of elementary and composite particles, and their interactions. Fermions are on the left, and Bosons are on the right.\n\n[![Elementary Particle](https://github.com/eq19/eq19.github.io/assets/8466209/b6b6ea3c-cbbc-431c-b767-ecabf1cba933)](https://en.wikipedia.org/wiki/Fundamental_interaction)\n\nAccording to the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model_of_Particle_Physics) ***there are five (5) elementary bosons with thirteen (13) variations***. These 5 and 13 will be assigned to the \"5xid's of **31~35** (sequenced)\" and \"13xid's of **36~68** (unsequenced)\", respectively (see the sidebar menu).\n- One (1) [scalar boson](https://en.wikipedia.org/wiki/Scalar_boson) (***spin = 0***) [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson) – the particle that contributes to the phenomenon of [mass](https://en.wikipedia.org/wiki/Mass) via the [Higgs mechanism](https://en.wikipedia.org/wiki/Higgs_mechanism) (assigned to \"19xid's of **2~30**\").\n- Four (4) [vector bosons](https://en.wikipedia.org/wiki/Vector_boson) (***spin = 1***) that act as [force carriers](https://en.wikipedia.org/wiki/Force_carriers). These four are the [gauge bosons](https://en.wikipedia.org/wiki/Gauge_boson), they have ***twelve (12) different types*** originated from the interaction on _[bispinor-2 and -3](https://www.eq19.com/multiplication/12.html#free-parameters)_ to the _twelve (12) spinors of majorana_:\n  - [γ](https://en.wikipedia.org/wiki/Photon) [Photon](https://en.wikipedia.org/wiki/Photon) – the force carrier of the [electromagnetic field](https://en.wikipedia.org/wiki/Electromagnetic_field) (**id:31**).\n  - [g](https://en.wikipedia.org/wiki/Gluon) [Gluons](https://en.wikipedia.org/wiki/Gluon) (***eight (8) different types***) – force carriers originated from the _eight (8) spinors of bispinor-1 to -4_ that mediate the [strong force](https://en.wikipedia.org/wiki/Strong_interaction) (**id:33**)\n  - [Z](https://en.wikipedia.org/wiki/Z_boson) [Neutral weak boson](https://en.wikipedia.org/wiki/W_and_Z_bosons) – the force carrier that mediates the [weak force](https://en.wikipedia.org/wiki/Weak_interaction) and\n  - [W±](https://en.wikipedia.org/wiki/W_boson) [Charged weak bosons](https://en.wikipedia.org/wiki/W_and_Z_bosons) (***two (2) types***) – force carriers that mediate the weak force (**id:34**).\n- A second order tensor boson (***spin = 2***) called the [graviton](https://en.wikipedia.org/wiki/Graviton) (G). It has been hypothesised as the force carrier for [gravity](https://en.wikipedia.org/wiki/Gravitational_force) (**id:32**).\n
            \n\n

            \"The

            \n\n

            This lead to a consequence of SU(5) grand unification (assigned to 35) showing a complex scalar Higgs boson of 24 gauge groups observe mass of W boson (assigned to 36).

            \n","dir":"/exponentiation/","name":"README.md","path":"exponentiation/README.md","url":"/exponentiation/"},{"sort":22,"spin":85,"span":28,"suit":"main","layout":"default","title":"Entrypoint (spin 4)","content":"# Entrypoint (spin 4)\n\n{% include list.liquid all=true %}\n\n```\nSUBMODULE=path/to/submodule\n\nrm -rf $SUBMODULE\ngit rm --cached $SUBMODULE\nrm -rf .git/modules/$SUBMODULE\ngit config -f .gitmodules --remove-section submodule.$SUBMODULE\ngit add . && git commit -m \"delete $SUBMODULE\" && git push\n```\n\nThis recombination is taking a scheme called [DNA Recombination](https://en.wikipedia.org/wiki/DNA#Genetic_recombination): **[M+F](https://github.com/eq19/quantum/blob/workflows/_layouts/feed.rb) to [C1+C2](https://github.com/eq19/quantum/blob/workflows/_includes/data/roots.rb)** which could only be happen when **two (2) chromosomes involve**. Here we found that each of their DNA will form a scheme called _The Scheme 13:9_ as shown below.\n\n![](https://user-images.githubusercontent.com/8466209/218370587-ec438d91-be88-408a-a746-ff1e6324a514.png)\n\nThe 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n![](https://user-images.githubusercontent.com/8466209/212930357-8cf2591b-a2be-4a2c-b6ae-dc43892efe73.png)\n\n>I like that 0 can occupy a center point. Incidentally, this circular shape minus all my numbers and colors s has been called Seed of Life / Flower of Life by certain New Age groups who claim it has a sacred geometry. Please don’t see this as an endorsement of any spiritual group or religion. _([Prime Hexagon - Circulat Form](https://www.hexspin.com/circular/))_\n\n[![image](https://user-images.githubusercontent.com/8466209/249753773-abe68727-cc33-4efa-a1be-23dd66141297.png)](https://www.hexspin.com/circular/)\n\nYou can use either mklink /j or junction in Windows 10 to create [junctions](https://superuser.com/a/1020825/505363). Junction not only allows you to create NTFS junctions, it allows you to see if files or directories are actually reparse points. Reparse points are the mechanism on which NTFS junctions are based, and they are used by Windows' Remote Storage Service (RSS), as well as volume mount points.\n\n```\nmklink /j .github C:\\Users\\Admin\\.github\n```\n\n[![mklink](https://user-images.githubusercontent.com/8466209/248441972-80899fea-8faf-4c03-9191-20378e704438.png)](https://superuser.com/a/1020825/505363)\n\nThe color spin addresses for numbers are generally straightforward – a composite number takes the spin of the prior prime. 4 spins blue because 3 spins blue. 8 is red because 7 is red. However, twin primes, and the 0 type numbers between them, are open to some interpretation.\n\n[![base](https://user-images.githubusercontent.com/8466209/249753163-6cfbcecf-3713-409b-8d8b-5fa5cf8489ac.png)](https://www.hexspin.com/finding-a-number-in-the-hexagon/)\n\nBy _[The Δ(19 vs 18) Scenario](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef)_ those three are exactly landed in the ***0's cell*** out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66. \n\n[![19vs18](https://user-images.githubusercontent.com/8466209/211178117-9a879fd0-163b-442b-87bf-49d76c0b6c50.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-18_feed-md)\n\nIn the second opposing member, the position 13 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the ***11th prime number*** is now forced to determine a new axis-symmetrical zero position.\n\n![default](https://user-images.githubusercontent.com/8466209/241491860-72da956a-1740-4ed7-83ef-3844ae1ff8d2.png)\n\nMany relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence.\n\n>AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence _([Human vs AI](https://www.frontiersin.org/articles/10.3389/frai.2021.622364/full))_.\n\n![](https://user-images.githubusercontent.com/8466209/200475393-f3e42f0b-d291-4f17-93c4-9bec6e6943de.png)\n\nThe next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.\n\n[![33's](https://user-images.githubusercontent.com/8466209/211838795-459a4d41-1ebf-4688-9e0f-a3fd71635ddd.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-core-md)\n\nThis process would take place all the way to three (3) layers in a more complex way involving ***114 objects*** generated by the sum of the above mentioned prime 71 and 43. This is what we will discuss further on how apply it in to a _[custom domain](https://stackoverflow.com/a/67143696/4058484)_.\n","dir":"/identition/span12/","name":"gist02.md","path":"identition/span12/gist02.md","url":"/identition/span12/gist02.html"},{"sort":22,"spin":103,"span":1,"suit":29,"layout":"default","title":"Magnitude Order (spin 11)","content":"

            Magnitude Order (spin 11)

            \n\n
            This section is referring to _[wiki page-22](https://github.com/eq19/eq19.github.io/wiki)_ of _[gist section-18]()_ that is _[inherited ]()_ from _[the gist section-29](https://gist.github.com/eq19)_ by _[prime spin-103](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-1](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Symmetrical Breaking (spin 1)
              2. \n
            2. The Angular Momentum (spin 2)
              3. \n
            3. Entrypoint of Momentum (spin 3)
              4. \n
            4. The Mapping of Spacetime (spin 4)
              5. \n
            5. Similar Order of Magnitude (spin 5)
              6. \n
            6. The Search for The Graviton (spin 6)
              7. \n
            7. Elementary Retracements (spin 7)
              8. \n
            8. The Recycling Momentum (spin 8)
              9. \n
            9. Exchange Entrypoint (spin 9)
              10. \n
            10. The Mapping Order (spin 10)
              11. \n
            11. Magnitude Order (spin 11)
              12. \n
            \n\n

            Assigning The Lexer

            \n\n

            \"image\"

            \n\n
            Φ = 2,10\nΔ = 5,7,17\n3': 13,18,25,42\n2' » 13 to 77, Δ = 64\n2' and 3' » 13 to 45, Δ = 32\n\n2\" + 5\" = 7\" = 77\n2\"=22, 3\"=33, 2\" + 3\" = 5\" = 55\n\n13, 16, 18, 21, 23, 25, 28, 30, 32, 34, \n36, 38, 40, 42, \n45, 47, 49, 51, 53, \n55, 57, 59, 61, \n63, 65, 67, 69, 71, 73, 75, 77\n
            \n\n

            \"image\"

            \n\n

            Next we will discuss how to form these numbers on each screens. As explained earlier, there are all three (3) layers. The instance is going to simulate DNA polymerase with proofreading ability.

            \n\n

            Proofreading Ability

            \n\n
            Proofreading removes the mismatched nucleotide and extension continues. If a mismatch is accidentally incorporated, the polymerase is inhibited from further extension _([Wikipedia](https://en.wikipedia.org/wiki/DNA_polymerase#Function))_.\t\n
            \n\n

            \"DNA

            \n\n
            A current model of meiotic recombination, initiated by ***a double-strand break or gap***, followed by pairing with an homologous chromosome and strand invasion to initiate the recombinational repair process _([Wikipedia](https://en.wikipedia.org/wiki/Genetic_recombination))_.\n
            \n\n

            \"image\"

            \n\n

            π(96) = 96/4 = 24

            \n\n

            \"\"

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ |  5¨ |  3¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            Strand Partition

            \n\n

            \"169-over-109-blood-pressure\"

            \n\n

            Fidelity is very important in DNA replication. Mismatches in DNA base pairing can potentially result in dysfunctional proteins and could lead to cancer. Hydrogen bonds play a key role in base pair binding and interaction.

            \n\n
            The function of DNA polymerase is not quite perfect, with the enzyme making ***about one mistake for every billion base pairs copied***. Error correction is a property of some, but not all DNA polymerases. This process corrects mistakes in newly synthesized DNA _([Wikipedia](https://en.wikipedia.org/wiki/DNA_polymerase#Function))_.\t\n
            \n\n

            \"dna-genetics-biochemistry\"

            \n\n

            \"ezgif

            \n\n

            \"Symmetry

            \n\n

            1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects

            \n\n

            \"\"

            \n\n
            Prime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\nSequence Layers:\n- By the next layer the 89² will become 89 and 5 become 5² or 25.\n- This 89 and 25 are in the same layer with total of 114 or prime 619\n- So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n\n-----+-----+-----+-----+-----+     -----------------------------------------------\n{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |\n-----+-----+-----+-----+-----+                                               |\n {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone\n     +-----+-----+-----+-----+                                               |\n {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |\n     +-----+-----+-----+                                               -----------\n {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |\n ----+-----+-----+-----+-----+                                               |\n  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone\n     +-----+-----+-----+-----+                                               |\n  {8}|23,25|25,27|27,29| 18                                                  |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------\n  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------\n     |  1     2     3  |   4     5     6 |   7     8      9  |\n     |------ 29' ------|--------------- 139' ----------------|\n     |------ 102¨ -----|---------------  66¨ ----------------|\n
            \n\n

            Four-vector configuration

            \n\n

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            \n\n

            \"image\"

            \n\n

            On the lagging strand template, a primase “reads” the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            \n\n

            \"GitHub

            \n\n

            The leading strand is the strand of new DNA which is synthesized in the same direction as the growing replication fork. This sort of DNA replication is continuous. This workflow is assigned to Linux container (Ubuntu).

            \n\n
            DNA polymerase extends primed segments, forming Okazaki fragments. The RNA primers are then removed and replaced with DNA, and the fragments of DNA are joined by DNA ligase and are bound to the helicase heximer _([Wikipedia](https://en.wikipedia.org/wiki/DNA_replication#Replication_fork))_.\n
            \n\n

            \"DNA

            \n\n

            In eukaryotes the helicase wraps around the leading strand, and in prokaryotes it wraps around the lagging strand. As helicase unwinds DNA at the replication fork, the DNA ahead is forced to rotate resulting a build-up of twists in the DNA ahead.

            \n\n
            Because of its orientation, replication of the lagging strand is more complicated as compared to that of the leading strand. As a consequence, the DNA polymerase on this strand is seen to \"lag behind\".\n
            \n\n

            \"container-diagram\"

            \n\n
            layer | node | sub |    i     |   f\n------+------+-----+----------+-----+-----+-----+                                    ---\n      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |\n      |      |  1  +----------+-----+-----+-----+                              |      |\n      |  1   |     |        2 |                                                |      5¨  encapsulation\n      |      |-----+----------+            -----------------------------       |      |\n      |      |     |        3 |           |                             |      |      |\n  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---\n      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |\n      |      +-----+----------+           |                             |      |      |\n      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction\n289   |      |  3  +----------+                                                |      |\n|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |\n------+------+-----+----------+-----+-----                                     |     ---\n      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |\n      |      |  4  +----------+-----+-----+-----+                              |      |\n      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism\n      |      +-----+----------+-----+-----+-----+                       |      |      |\n      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |\n  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---\n      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |\n      |      |-----+----------+-----+-----+-----+                              |      |\n      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance\n329   |      |  6  +----------+-----+-----+-----+                                     |\n|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |\n------+------+-----+----------+-----+-----+                                          ---\n      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |\n      |      |  7  +----------+-----+                                                 |\n      |  5   |     |       14 |            -----------------------------             17¨  class\n      |      |-----+----------+           |                             |             |\n      |      |     |       15 |           |       LEADING SCHEME        |             |\n  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---\n      |      |     |       16 |           |                             |             |\n      |      |-----+----------+-----+      -----------------------------              |\n      |  6   |     |    28:17 | 100 |                                                19¨  object\n168   |      |  9  +----------+-----+                                                 |\n|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |\n------|------|-----+----------+-----+                                                ---\n
            \n\n

            This distribution of fermion parameters are shown by [13,17], [11,19] in the coupling of MEC30. So we shall find the rest of [7,23], [1,29] in the boson field.

            \n\n
            In [physics](https://en.wikipedia.org/wiki/Physics), a ***coupling constant or gauge coupling*** parameter (or, more simply, a coupling), is a number that determines the strength of the [force](https://en.wikipedia.org/wiki/Force) exerted in an [interaction](https://en.wikipedia.org/wiki/Fundamental_interaction).\n- Originally, the coupling constant related the force acting between two static bodies to the \"[charges](https://en.wikipedia.org/wiki/Charge_(physics))\" of the bodies (i.e. the electric charge for [electrostatic](https://en.wikipedia.org/wiki/Electrostatics) and the mass for [Newtonian gravity](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation)) divided by the distance squared, r².\n- The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter\n- The solution to both these problems comes from the Higgs mechanism, which involves scalar fields (the number of which depend on the exact form of Higgs mechanism) which (to give the briefest possible description) are \"absorbed\" by the massive bosons as degrees of freedom, and which couple to the fermions via ***Yukawa coupling*** to create what looks like mass terms.\n\nThe next step is to ***couple the gauge fields to the fermions***, allowing for interactions. _([Wikipedia](https://en.wikipedia.org/wiki/Coupling_constant))_\n
            \n\n

            \"Euler's

            \n\n

            By The GitHub Runner you can connect to the Google COS Instance. For self-hosted runners defined at the organization level, configure runs-on.group in your workflow file to target a runner groups or combine groups and labels.

            \n\n

            Build Coupling Runner

            \n\n

            The runner is the application that runs a job from a GitHub Actions workflow. It is used by GitHub Actions in the hosted virtual environments, or you can self-host the runner in your own environment. We use both of them to create group as a four-vector.

            \n\n

            \"choosing-the-runner\"

            \n\n

            On the other hand, with larger systems we are able to transfer the behavior of the energy from the subatomic space into the haptic space with the scale described here (thought experiment Schröninger’s cat). Thus, we are still able to apply the Schröninger wave equation in the haptic space, and replace the Hamiltonian with our measurements.\n\"default\"

            \n\n

            The problems would arise when the Windows Container in Github deliver the RNA Primer to Google instance as Windows Image because it shall read the image while the COS is run under Linux. So it will need to proof and solve without actually having to try.

            \n\n
            If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the ***Hamiltonian Path Problem*** given N cities to visit, how can one do this without visiting a city twice? _([Clay Institute](https://www.claymath.org/millennium-problems))_.\n
            \n\n

            \"P

            \n\n

            Getting the proofreading ability of DNA polymerase to quickly solve problem for about one mistake for every billion base pairs copied is somehow that required by one of a major unsolved problem in theoretical computer science called P vs NP.

            \n\n
            P vs. NP deals with the gap between computers being able to quickly solve problems vs. just being able to test proposed solutions for correctness. As such, the [P vs. NP problem](https://en.wikipedia.org/wiki/P_versus_NP_problem) is the search for a way to solve problems that ***require the trying of millions, billions, or trillions of combinations without actually having to try each one*** _([P vs. NP Explained](https://danielmiessler.com/study/pvsnp/#:~:text=P%20vs.%20NP%20deals%20with%20the%20gap%20between,combinations%20without%20actually%20having%20to%20try%20each%20one.))_.\n
            \n\n

            \"P_versus_NP_problem\"

            \n\n

            It is stated that Np for a curve E with rank r obeys an asymptotic law and is still remain unsolved. Thus it would mean that using Euler’s identity to get a definite pattern of prime distribution is still a long way to go.

            \n","dir":"/multiplication/","name":"20.md","path":"multiplication/20.md","url":"/multiplication/20.html"},{"sort":23,"spin":84,"span":27,"suit":"main","layout":"default","title":"Mapping (spin 5)","content":"# Mapping (spin 5)\n\n{% include list.liquid all=true %}\n\nWhen we come to a mapping of a Project, is critical to look for the future of Parts Unlimited otherwise the project will massively over budget and very late. So to deal with this we shall consider to move everything to the cloud…\n\n[![phoenix](https://user-images.githubusercontent.com/8466209/246674379-6079f1cb-3a81-403b-8d5b-b876fd03ed25.png)](https://blog.marcolancini.it/2020/blog-blogging-stack/)\n\nSince version 3.2 , a new Jekyll project bootstrapped with jekyll new uses gem-based themes to define the look of the site. This results in a lighter default directory structure: _layouts, _includes and _sass are stored in the theme-gem, by default.\n\n[![default](https://user-images.githubusercontent.com/8466209/243235885-5823667b-426a-47e8-8ee3-a1afdce79d77.png)](https://jekyllrb.com/docs/structure/)\n\nYou can attach a persistent disk or create an instance with [Local SSDs](https://cloud.google.com/compute/docs/disks/add-persistent-disk#formatting) when using Container-Optimized OS. The disks _[can be mounted by creating a subdirectory](https://cloud.google.com/container-optimized-os/docs/concepts/disks-and-filesystem#mounting_and_formatting_disks)_ under `/mnt/disks` directory (writable, executable, stateless, tmpfs) using [startup-scripts](hhttps://cloud.google.com/compute/docs/instances/startup-scripts).\n\n[![image](https://user-images.githubusercontent.com/8466209/222601650-8fef811d-6bd5-44de-b81f-6d39f47625ad.png)](https://blogs.msdn.microsoft.com/premier_developer/2018/04/20/running-docker-windows-and-linux-containers-simultaneously/)\n\nIf you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers ***[Simultaneously](https://blogs.msdn.microsoft.com/premier_developer/2018/04/20/running-docker-windows-and-linux-containers-simultaneously/)***, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel\n\n[![GitHub Actions workflow](https://user-images.githubusercontent.com/8466209/222642428-fb9f183f-f4d5-43c6-a3c2-c1adebac2bad.png)](https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners#using-a-github-hosted-runner)\n\nOn the lagging strand template, a primase \"reads\" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.\n\n![default](https://user-images.githubusercontent.com/8466209/244405518-cb407b47-1409-423f-adc3-21074eb79d4d.png)\n\nYou can run .NET applications in Linux containers, but only if they’re written in .NET Core which can be deployed on Windows Server Containers. Applications running in Windows Server Containers can run in any language supported by Windows.\n\n[![kernel-6.1.21.1-microsoft-standard-WSL2.img\n](https://user-images.githubusercontent.com/8466209/231802278-1cc152f2-9089-4249-a01f-1dd7e0f2a705.png)](https://github.com/khs1994/WSL2-Linux-Kernel/releases/tag/6.1.21.1-microsoft-standard-WSL2)\n\nLet's combine them all then we will get 168 which is the total primes out of 1000 numbers. This 168 we will get it also when we combine the 1's and 17's cell of (31+37)+(35+65)=68+100=168. \n\n[![zeta-vs-zero](https://user-images.githubusercontent.com/8466209/213628433-c7382e39-4efa-4455-867c-13652293474d.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-vs-zero)\n\nThis can be remedied by re-mounting your Windows partition inside WSL with the metdata option. Edit the /etc/wsl.conf file (create it if it doesn’t exist) and add the following:\n\n```\n[automount]\noptions = \"metadata\"\n```\n\nLog out from WSL and log in again, and now the windows partition will be mounted with metadata and chmod will work against windows files. You can now chmod 600 ~/.ssh/id_rsa and everything will work correctly.\n\n![default](https://user-images.githubusercontent.com/8466209/243375484-035dc8da-0a22-4b6c-ba14-fc303e36a94e.png)\n\nBy this project we are going to use a library called [Chevrotain](https://github.com/Chevrotain/chevrotain). It can be used to build Lexers, Parsers and Interpreters for various use cases ranging from simple config files to full fledged programming languages.\n\n[![Lexers, Parsers and Interpreters with Chevrotain](https://user-images.githubusercontent.com/8466209/244846209-90a4afee-64fd-4a13-b2d7-626ae767a77c.png)](https://dev.to/codingwithadam/introduction-to-lexers-parsers-and-interpreters-with-chevrotain-5c7b)\n\nThis Widows is an [isolated container](https://learn.microsoft.com/en-us/virtualization/windowscontainers/about/#container-images), lightweight package for running an application on the host operating system. Containers build on top of the host operating system's kernel (which can be thought of as the buried plumbing of the operating system).\n","dir":"/identition/span12/","name":"gist03.md","path":"identition/span12/gist03.md","url":"/identition/span12/gist03.html"},{"sort":23,"spin":31,"span":156,"suit":17,"permalink":"/exponentiation/span17/","layout":"default","title":"Electrodynamics (maps)","content":"

            Electrodynamics (maps)

            \n\n

            It is shown that a considerable simplification can be attained in writing down matrix elements for complex processes in electrodynamics.

            \n\n
            This section is referring to _[wiki page-23](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-1]()_ that is _[inherited ]()_ from _[the spin section-17](https://gist.github.com/eq19)_ by _[prime spin-31](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-156](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist03.md
              2. \n
            2. gist04.md
              3. \n
            3. gist05.md
              4. \n
            4. gist07.md
              5. \n
            5. gist08.md
              6. \n
            6. gist09.md
              7. \n
            7. gist10.md
              8. \n
            \n\n

            All matrix elements are now finite, with the exception of those relating to problems of vacuum polarization. The more conventional Hamiltonian point of view is discussed.

            \n\n

            Basic Transformation

            \n\n

            The first appearance of e in a printed publication was in Euler’s Mechanica (1736). It is unknown why Euler chose the letter e.

            \n\n
            [Leonhard Euler](https://en.m.wikipedia.org/wiki/Leonhard_Euler) started to use ***the letter e*** for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and in a letter to [Christian Goldbach](https://en.m.wikipedia.org/wiki/Christian_Goldbach) on 25 November 1731. _([Wikipedia](https://en.wikipedia.org/wiki/E_(mathematical_constant)))_\n
            \n\n

            \"Letter

            \n\n

            \"images

            \n\n
            It turns out that the basic idea of QED can be communicated while assuming that the square of the total of the probability amplitudes mentioned above (P(A to B), E(C to D) and j) acts just like our everyday probability (a simplification made in [Feynman's book](https://github.com/eq19/eq19.github.io/files/13930690/PhysRev.76.769.pdf)). Later on, this will be corrected to include specifically quantum-style mathematics, following Feynman.\n\nThe basic rules of probability amplitudes that will be used are:\n- If an event can occur via a number of indistinguishable alternative processes (a.k.a. \"virtual\" processes), then its probability amplitude is the ***sum of the probability amplitudes of the alternatives***.\n- If a virtual process involves a number of independent or concomitant sub-processes, then the probability amplitude of the total (compound) process is the ***product of the probability amplitudes of the sub-processes***.\n\nThe indistinguishability criterion in (a) is very important: it means that there is no observable feature present in the given system that in any way \"reveals\" which alternative is taken. In such a case, one cannot observe which alternative actually takes place without changing the experimental setup in some way (e.g. by introducing a new apparatus into the system). _([Wikipedia](https://en.wikipedia.org/wiki/Quantum_electrodynamics))_\n
            \n\n

            \"First_Feynman_Diagram\"

            \n\n
            It should be remembered that the expression hides a lot of complexity. We have summed over all possible timeorderings and summed over all polarization states of the virtual photon. If we are then presented with a new Feynman diagram we don’t want to go through the full calculation again. Fortunately this isn’t necessary – can just write down matrix element using a set of simple rules Basic Feynman Rules: e+ g m+ Propagator factor for each internal line (i. e. each internal virtual particle) Dirac Spinor for each external line e–\n
            \n\n

            \"image-18\"

            \n\n

            Mapping Scheme

            \n\n

            Within a cycle this scheme would generate the prime platform which is performing the rank of 10 shapes starting with the primes 2,3,5,7.

            \n\n

            \"proton-1\"

            \n\n

            Via the 11 partitions as the lexer and 13 frames as the parser we do a recombination to build the grammar in 6 periods.

            \n\n

            \"6

            \n\n

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            \n\n
            With theoretical foundations in [Information Engineering](https://en.wikipedia.org/wiki/Information_engineering) (Discrete Mathematics, Control Theory, System Theory, Information Theory, and Statistics), my research has delivered a suite of systems and products that has allowed me to carve out a niche within an extensive collaborative network (>200 academics). _([Umer.Ijaz](https://userweb.eng.gla.ac.uk/umer.ijaz/#intro))_\n
            \n\n

            \"information

            \n\n
            \n

            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) (₠Quantum).

            \n
            \n\n

            \"flowchart\"

            \n\n

            By this project the above would be deployed as default layout. It is set to be avalaible throughout the whole platform via a single page within a parser repository which is acting as prime 13. Their interface will be in json and xml format.

            \n\n

            Here is for the sample:

            \n\n
            {\n  \"title\":\"Mapping System\",\n  \"content\":\"<p>Hello, <strong>world</strong>.\\nI am here.</p>\\n\",\n  \"links\": [\n    {\"title\":\"Introduction\",\"url\":\"https://www.eq19.com/intro/\"},\n    {\"title\":\"Go tour on Mapping System \",\"url\":\"https://www.eq19.com/maps/\"},\n    {\"title\":\"A backed pretty display for markdown\",\"url\":\"https://www.eq19.com/gistio/\"},\n    {\"title\":\"Gist.io for programmers\",\"url\":\"https://gist.io/@eq19/d2336e28e79702acf38edd182003d5e0\"}\n  ]\n}\n
            \n\n

            Using a kind of interface such as docker then it could be developed cross platform. Evenso. Let assume that all alpabethic letter in the sequence is representing a local disk so you may build your own pattern in your PC such as shown below:

            \n\n

            \"Matrices-of-prime-numbers\"

            \n\n

            The tensor product of a triplet with an octet reducing to a deciquintuplet, an anti-sextet, and a triplet appears diagrammatically as a total of 24 states.

            \n\n

            \"Young_tableaux_17\"\n\"Young_tableaux_18\"

            \n\n

            Using the same procedure, any direct product representation is easily reduced.

            \n\n

            1

            \n

            \"main-qimg-4a1f46404471a9e9efa53881ce58c091-pjlq\"

            \n

            2

            \n

            \"mqdefault\"

            \n

            3

            \n

            \"478517_2_En_18_Fig10_HTML\"

            \n

            4

            \n

            \"images

            \n\n

            6

            \n

            \"axioms-12-01058-g001\"

            \n

            7

            \n

            \"SciDACLayers_1_9_2012\"

            \n

            8

            \n

            \"hq720

            \n

            9

            \n

            \"images

            \n

            11

            \n

            \"images

            \n

            12

            \n

            \"QCD\"

            \n

            13

            \n

            \"axioms-12-01058-g002-550\"

            \n

            14

            \n

            \"axioms-12-01058-g004\"

            \n

            15

            \n

            \"qcd_together\"

            \n

            20

            \n

            \"qcd-620px\"

            \n

            22

            \n

            \"QED_16\"

            \n

            23

            \n

            \"hqdefault\"

            \n

            24

            \n

            \"1-quantum-electrodynamics-laguna-designscience-photo-library\"

            \n

            26

            \n

            \"Feynman-rules-of-NCQED\"

            \n

            27

            \n

            \"Feynman-rules-for-electron-selectron-photino-interaction-and-photino-propagators\"

            \n

            28

            \n

            \"Useful-Feynman-rules-in-VSR-QED\"

            \n

            29

            \n

            \"488px-Qed_rules\"

            \n

            30

            \n

            \"InteractionVertexOfQED\"

            \n

            31

            \n

            \"300px-Compton_qed\"

            \n

            32

            \n

            \"Diagrams-in-strong-field-quantum-electrodynamics-SFQED-versus-ordinary-quantum\"

            \n

            33

            \n

            \"Feynman-rules-for-the-PS-theory\"

            \n

            34

            \n

            \"a-Summary-of-the-Feynman-rules-Solid-line-represents-the-fermionic-propagator-G-0-pp\"

            \n

            35

            \n

            \"I15-73-Feynman\"

            \n

            37

            \n

            \"008869256_1-75ca18aad2faf65f52f4c7706d7d8bd3-768x994\"

            \n

            38

            \n

            \"bigwuethrich_figuresrules-peskin-qed-v2\"

            \n

            39

            \n

            \"1_RMV1kvtEZ-o-_8WKQLnCSA\"

            \n

            40

            \n

            \"slide_1\"

            \n","dir":"/exponentiation/span17/","name":"README.md","path":"exponentiation/span17/README.md","url":"/exponentiation/span17/"},{"sort":24,"spin":83,"span":28,"suit":"main","layout":"default","title":"Keyring (spin 6)","content":"# Keyring (spin 6)\n\n{% include list.liquid all=true %}\n\nA lexer is the part of an interpreter that turns a sequence of characters (plain text) into a sequence of tokens. The Parser which takes the tokens from the lexer and returns a syntax tree based on a grammar. The grammar is often expressed in a meta language.\n\n```\nBusyBox v1.34.1 (2022-07-19 20:11:24 UTC) multi-call binary.\n\nUsage: mv [-finT] SOURCE DEST\nor: mv [-fin] SOURCE... { -t DIRECTORY | DIRECTORY }\n\nRename SOURCE to DEST, or move SOURCEs to DIRECTORY\n\n\t-f\tDon't prompt before overwriting\n\t-i\tInteractive, prompt before overwrite\n\t-n\tDon't overwrite an existing file\n\t-T\tRefuse to move if DEST is a directory\n\t-t DIR\tMove all SOURCEs into DIR\n```\n\n![default](https://user-images.githubusercontent.com/8466209/244847966-5b73434b-c157-4c06-898d-85c6612f3538.png)\n\nBy this modification we are going to build the three (3) layers of 19 cells with a ***cumulative sum of 1, 7 and 19*** in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66.\n\n![default](https://user-images.githubusercontent.com/8466209/243738264-3847d61f-dd67-4164-ab94-dca118e5c402.png)\n\nThe next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.\n\n![image](https://user-images.githubusercontent.com/8466209/202837861-de31327a-543f-44a9-a2c9-c36cbc72a185.png)\n\nBy The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66. \n\n![default](https://user-images.githubusercontent.com/8466209/231932007-1a8a9b29-7d18-4600-a8ec-852fe891ab74.png)\n\n![default](https://user-images.githubusercontent.com/8466209/244845506-cc08a9ad-51f0-4659-aa98-3acc8f0168cb.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202854180-811302ca-ddd7-4365-a882-b146e28a7fac.png)\n\n","dir":"/identition/span12/","name":"gist04.md","path":"identition/span12/gist04.md","url":"/identition/span12/gist04.html"},{"sort":24,"spin":32,"span":155,"suit":16,"permalink":"/exponentiation/span16/","layout":"default","title":"Quantum Gravity (feed)","content":"

            Quantum Gravity (feed)

            \n\n

            Effective field theories have been a mainstay of theoretical physics since the 1930s but they haven’t helped all that much with quantum gravity.

            \n\n
            This section is referring to _[wiki page-24](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-2]()_ that is _[inherited ]()_ from _[the spin section-16](https://gist.github.com/eq19)_ by _[prime spin-32](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-155](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist05.md
              2. \n
            2. gist04.md
              3. \n
            3. gist03.md
              4. \n
            4. gist01.md
              5. \n
            5. Deploying containers
              6. \n
            6. Antiparallels
              7. \n
            7. gist08.md
              8. \n
            8. gist09.md
              9. \n
            9. gist10.md
              10. \n
            10. gist12.md
              11. \n
            \n\n

            Here we decided to take a concept that gravity enter the event horizons of black holes and tunnel out again to deposit it into the background.

            \n\n

            Event horizons

            \n\n

            18

            \n

            \"images

            \n

            19

            \n

            \"images

            \n

            22

            \n

            \"316503

            \n

            37

            \n

            \"worm\"

            \n

            22

            \n

            \"quantum_anticentrifugal_force\"

            \n\n

            Eternal Cyclic

            \n\n

            We would expect that the quantum theory reduces to Einstein’s theory of gravity. There is no way to put a black hole into the Hamiltonian.

            \n\n

            \"searching

            \n\n

            20

            \n

            \"4dfbafd3f1e223eff196f2b8691bb992\"

            \n

            21

            \n

            \"main-qimg-b18921fc2fe38539d30c68227a3b41cc-pjlq\"

            \n\n

            38

            \n

            \"IMG_20240116_151732\"

            \n\n

            \"fisica49_01\"

            \n\n

            \"maxresdefault

            \n\n

            Gravitating Objects

            \n\n
            A lot number of positive color-charges move from the positive charged particle toward the negative charged particles, and negative color-charges move from negative charged particle toward the positive charged particle and they combine in each other _([Gravity in Time space - pdf](https://github.com/eq19/eq19.github.io/files/13950511/Descriptiongravityinteractwithspace-timeatthequantumlevel.pdf))_\n
            \n\n

            \"A-lot-number-of-positive-color-charges-move-from-the-positive-charged-particle-toward-the\"

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 👈\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n
            \n\n
            Think of it this way, all gravitating bodies in the universe would be surrounded at all times by a cloud of tunneling electrons. We cannot see these particles since they’re so small and since they permeate all of space. They would also tunnel to a different location about once every Planck time (about 10^-43 seconds) whenever they interact with another particle.\n- These interactions between particles amount to the exchanges of bosons between electrons and other electrons or other fermions. At each point where the electron absorbs another boson, we say that the wave function of the electron collapses, and it tunnels to a new location whereupon it interacts with yet another particle.\n- The cloud of electron surrounding gravitating objects would diminish in inverse proportion to the square of the distance; hence, if you recede from an objects’ surface, you’re less likely to find an electron tunneling from that object.\n- Electrons also make an excellent candidate for a particle of gravity since they absorb and emit photons readily, and we know from Einstein’s theory of general relativity that light interacts readily with gravitational fields, and that gravitational fields are thought to emit photons spontaneously.\n- This spontaneous emission of photons is what we refer to as the cosmological constant or dark energy, and in our current thinking on the topic we imagine that particles of antimatter are created and annihilate with particles of matter leading, occasionally, to the emission of a photon. I suspect that this is incorrect and that no such thing as antimatter really exists. I suspect that positrons are really tunneling W particles and that this Dirac Sea, or background of tunneling electrons, is really giving rise to this phenomenon of the cosmological constant, or vacuum energy, we observe inn nature.\n- As a consequence, we would need to adumbrate our standard model of particle physics by about half. This ought to be seen as a positive thing in physics. No longer do we have untestable assumptions (such as the creation and annihilation of particles) in our models, and we have a far easier means of now beginning to probe the quantum nature of gravity.\n\nThe other fascinating consequence of this way of thinking is that gravity would no longer be a fundamental force; instead it would be a secondary effect of electromagnetism. This should have been what we anticipated all along; and now, we might have a quantum theory focusing on only three forces and a theory of gravitation that is truly particle-based. _([Medium - Article](https://medium.com/@cottlesam/quantum-gravity-will-force-us-to-cut-the-standard-model-in-half-c073e2033968))_\n
            \n\n

            \"Cut

            \n\n
            We may gain a better understanding of black hole physics; wewe may gain the insight that tunneling electrons enter the event horizons of black holes, absorb a particle there, and tunnel out again to deposit it into the background. In this way, we could explain how black holes radiate away.  _([Medium - Article](https://medium.com/@cottlesam/quantum-gravity-will-force-us-to-cut-the-standard-model-in-half-c073e2033968))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)  ✔️ ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n
            There are two groups of scientists (called collaborations) looking for evidence of gravitons in proton-proton collision experiments at the Large Hadron Collider at CERN. Once a graviton has been created, it’s expected to decay in one of a few possible ways - and it’s evidence of these decays that the collaborations are looking for. ***ATLAS search for evidence that the gravitons decays into two photons, and the CMS search for evidence that the graviton decays into two jets (bursts) of hadrons (a particular class of particle)***. _([ThingsWeDontKnow.com](https://blog.thingswedontknow.com/2016/08/search-for-the-graviton.html))_\n
            \n\n

            \"fully-expanded-incl-matrices\"\n

            \n\n

            Constructing the tableaux

            \n\n

            \"Young_tableaux_1\"

            \n\n

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36.

            \n\n

            \"\"

            \n\n

            and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            \n\n

            \"\"

            \n\n

            \"Screenshotgoogle\"

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 👈\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 👈\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 👈\n
            \n\n

            \"PRI_196247467\"

            \n","dir":"/exponentiation/span16/","name":"README.md","path":"exponentiation/span16/README.md","url":"/exponentiation/span16/"},{"sort":25,"spin":82,"span":29,"suit":"main","layout":"default","title":"Enneagram (spin 7)","content":"# Enneagram (spin 7)\n\n{% include list.liquid all=true %}\n\nFor some Enneagram theorists the lines connecting the points add further meaning to the information provided by the descriptions of the types. Sometimes called the \"security\" and \"stress\" points, or points of \"integration\" and \"disintegration\".\n\n>From this perspective, there are twenty-seven (27) distinct personality patterns, because people of each of the nine (9) types also express themselves as one of the three (3) subtypes _([Wikipedia](https://en.wikipedia.org/wiki/Enneagram_of_Personality#Instinctual_subtypes))_.\n\n![](https://user-images.githubusercontent.com/36441664/72740943-43d20200-3bd9-11ea-9a57-49516138a23f.jpg)\n\nThis is managed within _[twelve (12) flows (A: to W:)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)_. Each flows is representing a certain period which is converting ***the three (3) layers of 19 cells*** with a cumulative sum of 1, 7 and 19 in sequence as explained before.\n\n![default](https://user-images.githubusercontent.com/8466209/202852982-749111d6-7180-43c2-937d-7b0b984a3fa1.png)\n\n[![default](https://user-images.githubusercontent.com/8466209/202854626-268e084b-ed18-4439-9278-7ed19351cc9b.png)](https://stackoverflow.com/a/74439875/4058484)\n\n![default](https://user-images.githubusercontent.com/8466209/202159178-6f0c20e3-6ac5-4aaf-b026-508d54e3834e.png)\n\n![image](https://user-images.githubusercontent.com/8466209/202158795-ee46f959-8b59-42c5-adb0-4ade6a7a494d.png)\n\nIt turns out it’s actually pretty straight forward to set WSL to [use your Windows home directory](https://jeremyskinner.co.uk/2018/07/27/sharing-home-directory-between-windows-and-wsl/). First, within WSL edit the /etc/passwd file (eg with sudo nano /etc/passwd). \n\n```\neq19:x:1000:1000:eQ19:/home/eq19:/bin/bash\neq19:x:1000:1000:eQ19:/mnt/c/users/Admin:/bin/bash\n```\n\n![image](https://user-images.githubusercontent.com/8466209/243179406-3f466fdf-08fd-48e0-9ec7-b81ffcfa9f84.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202854144-cac0a371-a9b6-4b28-92bb-2f8f248bf5f0.png)\n","dir":"/identition/span12/","name":"gist05.md","path":"identition/span12/gist05.md","url":"/identition/span12/gist05.html"},{"sort":25,"spin":33,"span":154,"suit":15,"permalink":"/exponentiation/span15/","layout":"default","title":"Chromodynamics (lexer)","content":"

            Chromodynamics (lexer)

            \n\n

            This section serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks in quantum chromodynamics of colours of the gluon.

            \n\n
            This section is referring to _[wiki page-25](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-3]()_ that is _[inherited ]()_ from _[the spin section-15](https://gist.github.com/eq19)_ by _[prime spin-33](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-154](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Electron scattering
              2. \n
            2. gist03.md
              3. \n
            3. gist04.md
              4. \n
            4. gist05.md
              5. \n
            5. Mass Gap (Δ)
              6. \n
            \n\n

            A gauge colour rotation is a spacetime-dependent SU(3) group element. They span the Lie algebra of the SU(3) group in the defining representation.

            \n\n

            Feynman diagram

            \n\n
            In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).\n
            \n\n

            \"default\"

            \n\n

            \"quark-quark_scattering\"

            \n\n

            \"SmallBookPile\"

            \n\n

            So basically there is a basic transformation between addition of 3 + 4 = 7 in to their multiplication of 3 x 4 = 12 while the 7 vs 12 will be treated as exponentiation.

            \n\n

            \"images6-ezgif

            \n\n

            Matrix Scheme

            \n\n

            Quarks have three colors. Color is to the strong interaction as electric charge is to the electromagnetic interaction.

            \n\n

            \"quantum-chromodynamics-1-320\"

            \n\n
            red   anti-red,   red   anti-blue,   red   anti-green,\nblue  anti-red,   blue  anti-blue,   blue  anti-green,\ngreen anti-red,   green anti-blue,   green anti-green.\n
            \n\n

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            \n\n
            During the last few years of the 12th century, ***Fibonacci*** undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that ***it popularized the use of the Arabic numerals in Europe***, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. _([Famous Mathematicians](https://famous-mathematicians.org/leonardo-pisano-bigollo/))_\n
            \n\n

            \"MEC30

            \n\n

            Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30’s square.

            \n\n
            A square system of coupled nonlinear equations can be solved iteratively by Newton's method. This method uses the Jacobian matrix of the system of equations. _([Wikipedia](https://en.wikipedia.org/Jacobian_matrix_and_determinant))_\n
            \n\n

            \"gradien\"

            \n\n
            Fermions and bosons—fermions have quantum spin = 1/2.\n- The elementary fermions are leptons and quarks.\n- There are three generations of leptons: electron, muon, and tau, with electric charge −1, and their neutrinos with no electric charge.\n- There are three generations of quarks: (u, d); (c, s); and (t, b).\n\nThe (u, c, t) quarks have electric charge 2/3 while the (d, s, b) quarks have electric charge −1/3. _([IntechOpen](https://www.intechopen.com/chapters/71535))_\n
            \n\n

            \"UF1\"

            \n\n

            Interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used.

            \n\n

            \"UF2\"

            \n\n

            Bosons have quantum spin = 1: photon, quantum of the electromagnetic field; gluon, quantum of the strong field; and W and Z, weak field quanta, which we do not need.

            \n\n
            An animation of [color confinement](https://en.wikipedia.org/wiki/Color_confinement), a property of the strong interaction. If energy is supplied to the quarks as shown, the [gluon](https://en.wikipedia.org/wiki/Gluon) tube connecting [quarks](https://en.wikipedia.org/wiki/Quark) elongates until it reaches a point where it \"snaps\" and the energy added to the system results in the formation of a quark–[antiquark](https://en.wikipedia.org/wiki/Antiquark) pair. Thus single quarks are never seen in isolation. _([Wikipedia](https://en.wikipedia.org/wiki/Strong_interaction))_\n
            \n\n

            \"Gluon_tube-color_confinement_animation\"

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7 👈\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |   66+i30\n
            \n\n

            Interactions

            \n\n

            The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.

            \n\n
            ***Unlike the strong force, the residual strong force diminishes with distance, and does so rapidly***. The decrease is approximately as a negative exponential power of distance, though there is no simple expression known for this; see [Yukawa potential](https://en.wikipedia.org/wiki/Yukawa_potential). The rapid decrease with distance of the attractive residual force and the less rapid decrease of the repulsive electromagnetic force acting between protons within a nucleus, causes the instability of larger atomic nuclei, such as all those with [atomic numbers](https://en.wikipedia.org/wiki/Atomic_number) larger than 82 (the element lead). _([Wikipedia](https://en.wikipedia.org/wiki/Strong_interaction#Between_hadrons))_\n
            \n\n

            \"gifman\"

            \n\n
            Feynman diagram for the same process as in the animation, with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while ***multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion \"in-flight\", are not shown***. The π⁰ pion contains an anti-quark, shown to travel in the opposite direction, as per the Feynman–Stueckelberg interpretation. _([Wikipedia](https://en.wikipedia.org/wiki/Pion))_\n
            \n\n

            \"residual

            \n\n
            The Gell-Mann matrices, developed by [Murray Gell-Mann](https://en.m.wikipedia.org/wiki/Murray_Gell-Mann), are a set of eight [linearly independent](https://en.m.wikipedia.org/wiki/Linear_independence) 3×3 [traceless](https://en.wikipedia.org/wiki/Matrix_trace) [Hermitian matrices](https://en.wikipedia.org/wiki/Hermitian_matrices) used in the study of the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction) in [particle physics](https://en.wikipedia.org/wiki/Particle_physics). They span the [Lie algebra](https://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_associated_with_a_Lie_group) of the [SU(3)](https://en.wikipedia.org/wiki/Special_unitary_group#SU(3)) group in the defining representation.\n- These matrices are [traceless](https://en.wikipedia.org/wiki/Traceless), [Hermitian](https://en.wikipedia.org/wiki/Hermitian_matrix), and obey the extra trace orthonormality relation (so they can generate [unitary matrix](https://en.wikipedia.org/wiki/Unitary_matrix) group elements of [SU(3)](https://en.wikipedia.org/wiki/SU(3)) through [exponentiation](https://en.wikipedia.org/wiki/Matrix_exponential)[[1]](https://en.m.wikipedia.org/wiki/Gell-Mann_matrices#cite_note-Scherer-Schindler-1)). These properties were chosen by Gell-Mann because they then naturally generalize the [Pauli matrices](https://en.wikipedia.org/wiki/Pauli_matrices) for [SU(2)](https://en.wikipedia.org/wiki/SU(2)) to SU(3), which formed the basis for Gell-Mann's [quark model](https://en.wikipedia.org/wiki/Quark_model).[[2]](https://en.wikipedia.org/wiki/Gell-Mann_matrices#cite_note-2) Gell-Mann's generalization further [extends to general SU(n)](https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices#Construction). For their connection to the [standard basis](https://en.wikipedia.org/wiki/Root_system) of Lie algebras, see the [Weyl–Cartan basis](https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients_for_SU(3)#Standard_basis).\n- Since the eight matrices and the identity are a complete trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that [satisfied by the Pauli matrices](https://en.wikipedia.org/wiki/Pauli_matrices#Completeness_relation_2). Namely, using the dot to sum over the eight matrices and using Greek indices for their row/column indices\n- A particular choice of matrices is called a [group representation](https://en.wikipedia.org/wiki/Group_representation), because any element of SU(3) can be written in the form using the ***[Einstein notation](https://en.wikipedia.org/wiki/Einstein_notation)***, where the eight \n are real numbers and a sum over the index j is implied. Given one representation, an equivalent one may be obtained by an arbitrary unitary similarity transformation, since that leaves the commutator unchanged.\n- The matrices can be realized as a representation of the [infinitesimal generators](https://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_associated_with_a_Lie_group) of the [special unitary group](https://en.wikipedia.org/wiki/Special_unitary_group) called [SU(3)](https://en.wikipedia.org/wiki/Special_unitary_group#The_group_SU(3)). The [Lie algebra](https://en.wikipedia.org/wiki/Lie_algebra) of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight [linearly independent](https://en.wikipedia.org/wiki/Linear_independence) generators, which can be written as \ng_{i}, with i taking values from [1 to 8](https://en.wikipedia.org/wiki/Gell-Mann_matrices#cite_note-Scherer-Schindler-1)\n\nThese matrices serve to study the internal (color) rotations of the ***[gluon fields](https://en.m.wikipedia.org/wiki/Gluon_field) associated with the coloured quarks of [quantum chromodynamics](https://en.m.wikipedia.org/wiki/Quantum_chromodynamics) (cf. [colours of the gluon](https://en.m.wikipedia.org/wiki/Gluon#Eight_gluon_colours))***. A gauge colour rotation is a spacetime-dependent SU(3) group element where summation over the eight indices (8) is implied. _[Wikipedia](https://en.wikipedia.org/wiki/Gell-Mann_matrices))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ |  5¨ |  3¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            From the 50 we gonna split the 15 by bilateral 9 sums resulting 2 times 15+9=24 which is 48. So the total of involved objects is 50+48=98.

            \n\n
            Consider the evidence: scattering experiments strongly suggest a meson to be composed of a quark anti-quark pair and a baryon to be composed of three quarks. The famous 3R experiment also suggests that whatever force binds the quarks together has 3 types of charge (called the 3 colors).\n- Now, into the realm of theory: we are looking for an internal symmetry having a 3-dimensional representation which can give rise to a neutral combination of 3 particles (otherwise no color-neutral baryons).\n-  The simplest such statement is that a linear combination of each type of charge (red + green + blue) must be neutral, and following William of Occam we believe that the simplest theory describing all the facts must be the correct one.\n-  We now postulate that the particles carrying this force, called gluons, must occur in color anti-color units (i.e. nine of them).\n- BUT, red + blue + green is neutral, which means that the linear combination red anti-red + blue anti-blue + green anti-green must be non-interacting, since otherwise the colorless baryons would be able to emit these gluons and interact with each other via the strong force—contrary to the evidence.  So, there can only be ***EIGHT gluons***.\n\nThis is just Occam's razor again: a hypothetical particle that can't interact with anything, and therefore can't be detected, doesn't exist. The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra.  That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional. _([Physics FAQ](https://math.ucr.edu/home/baez/physics/ParticleAndNuclear/gluons.html))_\n
            \n\n

            \"0_kGdCmWqcFG_s8fIq\"

            \n\n

            Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.

            \n\n

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            \n\n

            \"960x0\"

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-👇--+                                             ---\n 17¨ |  5¨ |  3¨ |  ❓ |  7¨ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            \n\n
            [Young diagrams](https://commons.wikimedia.org/wiki/Category:Young_diagrams) associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions _([Wikipedia](https://en.wikipedia.org/wiki/Partition_(number_theory)))_.\n
            \n\n

            \"Hadron_colors

            \n\n
            In mathematics, orthonormality typically implies a norm which has a value of unity (1). Gell-Mann matrices, however, ***are normalized to a value of 2***.\n- Thus, the [trace](https://en.wikipedia.org/wiki/Trace_(linear_algebra)) of the pairwise product results in the ortho-normalization condition where delta is the [Kronecker delta](https://en.wikipedia.org/wiki/Kronecker_delta).\n- This is so the embedded Pauli matrices corresponding to the three embedded subalgebras of SU(2) are conventionally normalized.\n- In this three-dimensional matrix representation, the [Cartan subalgebra](https://en.wikipedia.org/wiki/Cartan_subalgebra) is the set of linear combinations (with real coefficients) of the two matrices which commute with each other.\n\nThe SU(2) Casimirs of these subalgebras ***mutually commute***. However, any unitary similarity transformation of these subalgebras will yield SU(2) subalgebras. There is an uncountable number of such transformations. _([Wikipedia](https://en.wikipedia.org/wiki/Gell-Mann_matrices))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-👇--+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"The-PMNS-Neutrino-Mixing-Matrix-The-non-diagonal-structure-and-the-smallness-of-the-U-e3\"\n\"images\n\"16-0054-07\n\"images\n\"1-neutrino-oscillation-l\"\n\"\"

            \n\n

            \"\"

            \n\n","dir":"/exponentiation/span15/","name":"README.md","path":"exponentiation/span15/README.md","url":"/exponentiation/span15/"},{"sort":26,"spin":81,"span":30,"suit":"main","layout":"default","title":"Twisting (spin 8)","content":"# Twisting (spin 8)\n\n{% include list.liquid all=true %}\n\n***1155 / 5 = 286 - 55 = 200 + 31 = 231***\n\n```\nlayer| i | f\n-----+-------+------\n | 1,2:1 | (2,3)\n 1 +-------+\n | 3:2 | (7)\n-----+-------+------\n | 4,6:3 | (10,11,12) <--- 231 (3x)\n 2 +-------+\n |{7}:4 |({13})\n-----+-------+------\n | 8,9:5 | (14,{15}) <--- 231 (2x)\n 3 +-------+\n | 10:6 | (19)\n-----+-------+------\n```\n\n>We study the [limit shape](https://github.com/naa/young-diagrams#young-diagrams) of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape _([arXiv:2010.16383v4](http://arxiv.org/abs/2010.16383))_.\n\n[![Limit shape for infinite rank limit of tensor\npower decomposition for Lie algebras of series\n](https://user-images.githubusercontent.com/8466209/233841647-e7f5154c-740f-4c19-9094-abbe0a4cced6.png)](https://arxiv.org/pdf/2010.16383.pdf)\n\nDyson discovered that _the eigenvalue_ of these matrices are spaced apart in exactly the same manner as _[Montgomery conjecture](https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture)_ of the nontrivial zeros of the [zeta function](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function). Means it also depends on _Riemann hypotesis_ which is still in a major issue. Similar case left science today many unsolved problems that associated with. \n\n[![Eigenvectors_of_a_linear_operator](https://user-images.githubusercontent.com/8466209/228168805-ab93185d-4172-4284-8459-040e2f8797d4.gif)](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors#Overview)\n\nIn order to propagate through space and interact we shall attemp it using [string theory](https://en.wikipedia.org/wiki/String_theory) One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become irrational partitions.\n\n>In turns out that quantum string theory always destroys the symmetries of the classical string theory, **except in one special case: when the number of dimensions is 10**. That's why string theory works only in 10 dimensions _([Physicsforums](https://www.physicsforums.com/threads/why-is-it-necessary-to-have-11-dimensions-in-m-theory.821762/))_.\n\n![default](https://user-images.githubusercontent.com/8466209/230748873-6761c929-261c-429c-bf14-f30851f6a12e.png)\n\n```\nTrue Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|------------------------- Skema-12 ------------------------|\n|------------ 6¤ -------------|------------- 6¤ ------------|\n|--------------------------- 192 ---------------------------|\n|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}|\n|--------- 5¤ ---------|------------ {96} -----------|{43}|\n|--------- {53} ---------|-------------- {139} -------------|\n|------- Skema-23 -------|------------- Skema-34 -----------| \n```\n\n[![default](https://user-images.githubusercontent.com/8466209/235672220-30997c4b-0d66-4e8a-a579-44e05062ac88.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#the-crank-of-a-partition)\n\nThis 23 units will form Scheme-23 as **two (2) long strands** which is known as [doble helix](https://en.wikipedia.org/wiki/Nucleic_acid_double_helix) Here we call them as Scheme-23 (71) and Scheme-23 (68). These strands are originated by the **three (3) layers** of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n[![Scheme-139](https://user-images.githubusercontent.com/36441664/99129100-38a40300-263f-11eb-8715-a657fec3aaf1.jpg)](https://github.com/chetabahana/chetabahana.github.io/wiki/139)\n\n![](https://user-images.githubusercontent.com/8466209/222032418-0eeecc23-08a3-47ba-97e1-1b453982d217.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202470200-f22486a6-0708-4e52-a486-ee9a2f50d0c6.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202154163-1f5a4b9a-322b-474c-bad1-46f51f4082f0.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202152955-944c8c9c-d161-459e-98a0-1051776fe2df.png)\n\n![](https://user-images.githubusercontent.com/8466209/222040762-65c58359-3033-403c-8789-d5b60802bd1f.png)\n\n![](https://user-images.githubusercontent.com/8466209/205960400-3061d93a-b3cc-4cd6-84e6-359a9314869d.png)\n\nSince the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as _[the balanced prime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)_.\n\n![default](https://user-images.githubusercontent.com/8466209/202857541-83a99aeb-afbb-40e0-8ccf-78d74c911545.png)\n","dir":"/identition/span12/","name":"gist06.md","path":"identition/span12/gist06.md","url":"/identition/span12/gist06.html"},{"sort":26,"spin":34,"span":153,"suit":14,"permalink":"/exponentiation/span14/","layout":"default","title":"Electroweak Theory (parser)","content":"

            Electroweak Theory (parser)

            \n\n

            Establishment theoretical framework as the standard theory of electroweak interactions: Higgs searches, quark mixing, neutrino oscillations.

            \n\n
            This section is referring to _[wiki page-26](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-4]()_ that is _[inherited ]()_ from _[the spin section-14](https://gist.github.com/eq19)_ by _[prime spin-34](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-153](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist02.md
              2. \n
            2. gist03.md
              3. \n
            3. gist04.md
              4. \n
            4. gist05.md
              5. \n
            5. gist06.md
              6. \n
            6. gist07.md
              7. \n
            7. Turbulence
              8. \n
            \n\n

            Gauge invariance is a powerful tool to determine the dynamical forces. Particle content, structure and symmetries of Lagrangian are discussed.

            \n\n

            Standard Theory

            \n\n
            ***The Higgs and the electromagnetic field have no effect on each other***, at the level of the fundamental forces (\"tree level\"), while any other combination of the hypercharge and the weak isospin must interact with the Higgs. ***This causes an apparent separation between the weak force, which interacts with the Higgs, and electromagnetism, which does not***. _([Wikipedia](https://en.wikipedia.org/wiki/Electroweak_interaction#Formulation))_\n
            \n\n

            \"image\"

            \n\n

            \"f22b28c976a4980061b601872e2faac8039dd7d8\"

            \n\n

            \"images

            \n\n

            \"images

            \n\n

            \"images

            \n\n

            Experiments have verified that the weak and electromagnetic force become identical at very small distances and provide the GUT description of the carrier particles for the forces.

            \n\n

            Interactions

            \n\n

            \"images

            \n\n

            \"boson-particle-decay-virtual-particle-w-and-z-bosons-lepton-synchrotron-hadron-particle-physics-annihilation-scattering-thumbnail\"

            \n\n

            \"TjQdBoIUDG\"

            \n\n

            \"image\"

            \n\n

            1

            \n

            \"EWT3b-600x400\"

            \n\n

            \"Figure_34_06_01\"

            \n\n

            \"w-boson-kaon-w-and-z-bosons-weak-interaction-meson-standard-model-feynman-diagram-elementary-particle-pion-boson\"

            \n\n

            \"weak-nuclear-force-1\"

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nboson-1    |    ..   |    ..   |     ..    |     ..    |      5     |    i5\n-----------+---------+---------+-----------+-----------+------------+-----------\nboson-2    |    ..   |    ..   |     ..    |     ..    |      7     |    i7\n-----------+---------+---------+-----------+-----------+------------+-----------\nboson-3    |    ..   |    ..   |     ..    |     ..    |     11     |   i11\n-----------+---------+---------+-----------+-----------+------------+-----------\nboson-4    |    ..   |    ..   |     ..    |     ..    |     13     |   i13\n-----------+---------+---------+-----------+-----------+------------+-----------\nboson-5    |    ..   |    ..   |     ..    |     ..    |     17     |   i17\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    ..   |    ..   |     ..    |     ..    |     53     |   i53\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |  66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    192     |  96+i96 ✔️\n
            \n\n

            Symmetry Breaking

            \n\n
            The pattern of [weak isospin](https://en.wikipedia.org/wiki/Weak_isospin), T3, and [weak hypercharge](https://en.wikipedia.org/wiki/Weak_hypercharge), YW, of the known elementary particles, showing electric charge along the [weak mixing angle](https://en.wikipedia.org/wiki/Weinberg_angle). The four components of the Higgs field (squares) break the electroweak symmetry and interact with other particles to give them mass, with three components becoming part of the massive W and Z bosons. Allowed decays of the neutral Higgs boson, H, (circled) satisfy electroweak charge conservation. _([Wikipedia](https://en.wikipedia.org/wiki/Electroweak_interaction))_\n
            \n\n

            \"Electroweak

            \n\n

            The Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking becomes manifest,

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"Beta-minus_Decay

            \n\n

            Unlike the strong and electromagnetic forces, the intermediary particles of the weak interaction, the W+, the W-, and the Z0 have rather large masses.

            \n\n
            A key aspect of the theory is the explanation of why three out of four of the intermediary particles of the electroweak force are massive. Illustration of two weak reactions.\n- The left panel shows beta decay while the middle panel shows how electron antineutrinos can be detected by conversion to a positron.\n- The right panel shows how W- emission works according to the quark model, ***resulting in the conversion of a down quark to an up quark and the resulting transformation of a neutron into a proton***.\n\nThe real reason for the apparent weakness of the weak force is the large mass of the intermediary particles. As we have seen, large mass translates into short range for a virtual particle at low momentum transfers. This short range is what causes the weak force to appear weak for momentum transfers much less than the masses of the W and Z particles. _([libre texts.org](https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_II_(Raymond)/20%3A_The_Standard_Model/20.03%3A_The_Electroweak_Theory))_\n
            \n\n

            \"Beta\n

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤ ✔️ --->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            Problem

            \n\n
            Consider the following contradiction in the electroweak theory of the Standard Model.\n\nThe electroweak theory of neutrino interaction uses factors like  in order to account for a complete parity violation. This factor implies a massless neutrino [1]: “Nature had the choice of an aesthetically satisfying, but a left-right, symmetry violating theory, with a neutrino which travels exactly with the same velocity of light; or alternatively a theory where left-right symmetry is preserved, but the neutrino has a tiny mass – some ten thousand times smaller than the mass of the electron.”\nThe neutrino masslessness is also stated by other authors. A review article on neutrino properties states that “two-components left-handed massless neutrino fields play a crucial role in the determination of the charged current structure of the Standard Model” (see the Abstract of [2]). Similarly, a Quantum Field Theory textbook states: “Thus, massless neutrinos are a prediction of the Standard Model” (see [4], p. 555). Indeed, a massless neutrino is the basis for the two-component Weyl neutrino, which shows parity violation (see e.g. section 2.2 of [2]). The same argument appears on p. 139 of [3].\n\nOn the other hand, a recent review article negates the foregoing ides and states that it is now admitted “that neutrinos can no longer be considered as massless particles” (see [5], p. 1307). This statement is adopted by the Particle Data Group [6], which is the authorized organization for the definition of reliable particle data. The recognition of this fact by the community was demonstrated by the 2015 Nobel Prize, awarded to the persons who have discovered this property [7].\nIt follows that the experimentally confirmed massive neutrino undermines the basis of the Standard Model electroweak theory, since the massless neutrino is a crucial element in this theory.\n\nResearch topic: Can the validity of the electroweak theory be restored?\n\nRemark: Further  contradictions are discussed in [8]. _([Research Topics](https://oprassn.org/a-problem-in-the-electroweak-theory/))_\n
            \n\n

            \"A

            \n\n
            The True Prime Pairs\n(5,7), (11,13), (17,19)\n\nTabulate Prime by Power of 10\nloop(10) = π(10)-π(1) = 4-0 = 4\nloop(100) = π(100)-π(10)-1th = 25-4-2 = 19\nloop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n--------------------------+----+----+----+----+----+----+----+----+----+-----\n True Prime Pairs → Δ→π  |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n==========================+====+====+====+====+====+====+====+====+====+=====\n 19 → π(∆10) → π(10)     |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n--------------------------+----+----+----+----+----+----+----+----+----+-----\n 17 → π(10+∆9) → π(19)   | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n 13 → π(19+∆10) → π(29)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th\n--------------------------+----+----+----+----+----+----+----+----+----+-----\n 11 → π(29+∆12) → π(41)  | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n  7 → π(41+∆18) → π(59)  | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n--------------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n  5 → π(59+∆13) → π(72)  | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th\n==========================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n  3,2 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n==========================+====+====+====+====+====+====+====+====+====+=====\n         Δ                                                            Δ\n12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-\n
            \n\n

            How do you resolve Maxwell equations as euler-lagrange equation without electromagnetic electromagnetism, lagrangian formalism, field theory, Maxwell equations, variational principle potential.

            \n\n
            Axial (e-e rES repulsions blue aggregating to black axial outward, vs weak axial inward) to generate the Bose “cylinder surface” proof of statistical mechanics.\n- Axial View of one hemisphere set of one subshell (N,1,many,-1/2) quantum number example below:\n- That gives the path from Planck strength to the Maxwell strengths. Those are not independent, but all based upon h (or h-hat*c version in this case).\n- Yes, I used Euler to get there! The weakness of the Lagrangian is that introduces errors in (a0/re)N scaling ^2 vs ^3 (extra 1/r wrongly called angular momentum by Bohr) that introduces an error correction. Hence, circling back to QED methods of error-correction (loops, re-normalization).\n\nSo, in the end, you do need. But the path can get similar when you move off arbitration x,y,z or X1,X2,X3 frame-of-reference to the quantitized hemispherical coordinates of the quantum numbers understood as (r#,theta#,phi#,z#).\n
            \n\n

            \"main-qimg-521a032d4132a419487624564dd201b2-pjlq\"

            \n\n

            \"main-qimg-5f05266cfdc63d60f86ad0852076ee00\"

            \n\n

            \"\"

            \n\n
            1729 = 7 x 13 x 19\n1729 / 7 = 13 x 19 = 247\n\n1729 = 7 x 13 x 19\n       7 + 13 = 20 = d(2)\n                     └──  2 x 19 = 38\n\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n| {1}|  2 |  3 |  4 |  5 | {6}| {7}|  8 |  9 | 10 | 11 | 12 | 13 | 14 |\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n| {3}| {4}|  3 |  4 |  5 |  2 |  3 |  2 |  2 |  1 |  2 |  5 |  1 |  1 |{38}\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285\n|  3 |  8 |  9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|-- 38 ---|              |-- 33 ---|                        |-- {27}--|\n
            \n\n

            \"1591890434759

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤ ✔️ --->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"electron

            \n\n
            True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    | ✔️\n-----+-----+-----+-----+-----+     -----------------------------------------------\n{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |\n-----+-----+-----+-----+-----+                                               |\n {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone\n     +-----+-----+-----+-----+                                               |\n {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |\n     +-----+-----+-----+                                               -----------\n {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |\n ----+-----+-----+-----+-----+                                               |\n  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone\n     +-----+-----+-----+-----+                                               |\n  {8}|23,25|25,27|27,29| 18                                                  |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------\n  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------\n     |  1     2     3  |   4     5     6 |   7     8      9  |\n     |------ 29' ------|--------------- 139' ----------------|\n     |------ 618¨ -----|--------------- 168¨ ----------------|\n
            \n\n

            \"IMG_20240118_121014\"

            \n","dir":"/exponentiation/span14/","name":"README.md","path":"exponentiation/span14/README.md","url":"/exponentiation/span14/"},{"sort":27,"spin":80,"span":31,"suit":"main","layout":"default","title":"Recycling (spin 9)","content":"# Recycling (spin 9)\n\n{% include list.liquid all=true %}\n\n>This progression 41,43,47,53,61,71,83,97,113,131 whose general term is ***41+x+xx***, is as much remarkable since the ***40 first terms*** are all prime numbers _([Euler's letter to Bernoulli](https://math.stackexchange.com/a/1722188/908994))_.\n \n```liquid\n1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n```\n\nPlottng ***40th prime scheme*** of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.\n\n***89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120***\n\n[![default](https://user-images.githubusercontent.com/8466209/225589915-8f7690c8-4c17-4232-be51-63e79efb2c51.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)\n\nI wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.\n\n>That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated.\n\n[![Truncate to Determine Integer Values](https://user-images.githubusercontent.com/8466209/229198281-8dbd72fb-cd0b-46c3-8a2c-ddc66107333e.png)](https://www.hexspin.com/phi-not-pi-and-why-i-truncate-to-determine-integer-values/)\n\n_[FeynCalc](https://feyncalc.github.io/)_ is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics. \n\n[![default](https://user-images.githubusercontent.com/8466209/224119544-f6819ad1-150b-48e9-a396-b51fe65a7fbe.png)](https://arxiv.org/pdf/1602.04182.pdf)\n\n![](https://user-images.githubusercontent.com/8466209/206918483-5016aa03-2bc1-4dcf-a7dd-29f2c4453787.png)\n\n![](https://user-images.githubusercontent.com/8466209/206918218-95c875a7-0080-44e5-8ade-1ff776f9c30d.png)\n\n![](https://user-images.githubusercontent.com/8466209/206888301-0ba40a6a-2caa-4dfe-92ef-5a9db590f85d.png)\n\n![](https://user-images.githubusercontent.com/36441664/123187010-84ffcd00-d4c3-11eb-8aad-6c40553b752b.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202152303-4b85138b-eb65-4d99-bf7a-3b52729e1f13.png)\n","dir":"/identition/span12/","name":"gist07.md","path":"identition/span12/gist07.md","url":"/identition/span12/gist07.html"},{"sort":27,"spin":36,"span":167,"suit":3,"permalink":"/identition/","layout":"default","title":"Identition Zones (36-102)","content":"

            Identition Zones (36-102)

            \n\n

            Identition is defined for a complex operation\n by extending one of the definitions of the exponential function from real exponents to complex exponents.

            \n\n
            This section is referring to _[wiki page-27](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-5]()_ that is _[inherited ]()_ from _[the spin section-3](https://gist.github.com/eq19)_ by _[prime spin-36](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-167](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Theory of Everything (span 12)
              2. \n
            2. Everything is Connected (span 11)
              3. \n
            3. Truncated Perturbation (span 10)
              4. \n
            4. Quadratic Polynomials (span 9)
              5. \n
            5. Fundamental Forces (span 8)
              6. \n
            6. Elementary Particles (span 7)
              7. \n
            7. Basic Transformation (span 6)
              8. \n
            8. Hidden Dimensions (span 5)
              9. \n
            9. Parallel Universes (span 4)
              10. \n
            10. Vibrating Strings (span 3)
              11. \n
            11. Series Expansion (span 2)
              12. \n
            12. Wormhole Theory (span 1)
              13. \n
            \n\n

            This identition zones stands as one of the solution to deal with the residual primes that is occured in the exponentation zones to become compactifiable within the base unit.

            \n\n

            Basic Concept

            \n\n

            A general mass structure for the heavy SM fermion generations has been obtained which explains the following features of SO(10):

            \n\n
            The work performed in this thesis will focus on two different models, that both can be used in the creation of a GUT. ***Both models are based on having SO(10) as the unification gauge group***.\n- Such models are more complex than the original suggestions, but can also accommodate more physics. In these two models, it is not possible ***to achieve unification among the gauge couplings with tree-level matching conditions***.\n- However, so-called threshold effects appear when matching the couplings at a higher order in perturbation theory, which are a result of particles with masses around the symmetry breaking scales.\n\nSpecifically, it will be investigated if threshold effects can save these two models, and thereby allowing unification. _([Threshold Effects in SO(10) Grand Unified Theories - pdf](https://github.com/eq19/eq19.github.io/files/14396682/FULLTEXT01.pdf))_\n
            \n\n

            \"Grand

            \n\n

            A precise measurement of the rate of the H→ bb process directly tests the Yukawa coupling of the Higgs boson to a down-type quark.

            \n\n
            Recently, the CMS and ATLAS Collaborations reported observations of the Higgs boson produced in association with a top quark pair thus representing the first direct measurements of the Higgs boson coupling to quarks. - This week the CMS Collaboration announces another major achievement and reports the [observation of Higgs boson decay to bottom quarks (H→ bb)](https://cds.cern.ch/record/2633415)\n- A precise measurement of the rate of the H→ bb process directly tests the Yukawa coupling of the Higgs boson to a down-type quark, and is necessary to solidify the Higgs boson as the possible sole source of mass generation in the fermion sector of the Standard Model (SM).\n- While the decay of the Higgs boson to bottom quarks is the most frequent of all Higgs boson decays, it has been a real experimental challenge to observe it. This is on account of the overwhelmingly large background contribution from a number of other SM processes that can mimic its experimental signature characterized by the appearance of a bottom and an anti-bottom quark.\n\nThe CMS Collaboration overcame this challenge by deploying modern sophisticated analysis tools and by focusing on particular signatures where a Higgs boson is produced in association with a vector boson V (a W or Z particle), a weak interaction process known as VH(bb), shown in the figure below, leading to a significant reduction in the background. _([CERN](https://cms.cern/news/higgs-observed-decaying-b-quarks))_\n
            \n\n

            \"down-type

            \n\n

            In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

            \n\n
            The concept of eleven dimensions is a theoretical one in physics and cosmology, specifically in the realm of string theory and M-theory.\n- ***These theories propose that our observable universe is made up of 11 dimensions, rather than the traditional three dimensions of length, width, and height, and the fourth dimension of time***.\n- The additional dimensions are thought to be compactified or curled up, meaning that they are not directly observable by us in our everyday experience.\n- ***As for the cosmic philosophy, it is important to note that these theories are still considered speculative and have not been proven through experimental evidence***.\n- However, they do offer a new perspective on the nature of our universe and the _[fundamental forces](https://www.eq19.com/exponentiation/#fundamental-forces)_ that govern it.\n- Some scientists and philosophers argue that these theories may provide new insights into the origins of the universe and the nature of reality itself. \n\nUltimately, the concept of eleven dimensions is a fascinating area of study that continues to inspire new research and discoveries in the field of physics and cosmology. _(ChatGPT)_\n
            \n\n

            \"M-theory\"

            \n\n

            Our physical space is observed to have only three large dimensions and taken together with time as the fourth dimension, a physical theory must take this into account.

            \n\n
            ***It is argued, among other things, that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring***, and that a recently conjectured duality between the heterotic string and Type IIA superstrings controls the strong coupling dynamics of the heterotic string in five, six, and seven dimensions and implies S-duality for both heterotic and Type II strings. _([String Theory - Pdf](https://github.com/eq19/feed/files/12640756/String_theory.pdf))_\n
            \n\n

            \"time

            \n\n

            String theory, superstring theory, or M-theory, or some other variant on this theme is one of the Unsolved Problem in physic as a step road to a Theory Of Everything (TOE).

            \n\n
            Nothing prevents a theory from including more than 4 dimensions. In the case of string theory, consistency requires spacetime to have 10, 11 or 26 dimensions. ***The conflict between observation and theory is resolved by making the unobserved dimensions compactified***. _([Astrophysics Research](https://astrophysicsblogs.blogspot.com/2008/01/superstring-theory_03.html))_\n
            \n\n

            \"superstring

            \n\n

            The string theory is sofar the leading candidate to the TOE however it is said that the theory may be incompatible with dark energy.

            \n\n
            It is argued that the generic formulation of string theory leads naturally to dark energy, represented by a positive cosmological constant to lowest order and the intrinsic stringy non-commutativity is the new crucial ingredient responsible for its radiative stability. _([Physic Letters](https://doi.org/10.1016/j.physletb.2019.134950))_\n
            \n\n

            \"string

            \n\n

            The finiteness position of MEC30 along with Euler’s identity opens up the possibility of accurately representing the self-singularity of True Prime Pairs.

            \n\n
            The Mathematical Elementary Cell 30 (MEC30) standard [unites](https://www.eq19.com/multiplication/12.html#entrypoint-of-momentum-spin-3) the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. ([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))\n
            \n\n

            \"Spinning

            \n\n

            By taking the correlation of these 11 partitions with the logical sequence of numbers there would be a series expansion.

            \n\n

            Visualizing TOE

            \n\n

            Assigning a specific mass, length, time, and charge metrics based on new dimensional relationships and the Planck constant (which defines Higgs mass).

            \n\n
            All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold. _([An Exceptionally  Simple Theory of Everything - pdf](https://github.com/eq19/eq19.github.io/files/14151110/0711.0770.pdf))_\n
            \n\n

            \"A-periodic-table-of-E8\"

            \n\n

            We discuss the phenomenology of doubly and singly charged Higgs bosons (of SU(2) L-triplet fields) in the simplest A 4-symmetric version of the Higgs Triplet Model.

            \n\n
            In this article, we investigated the ***phenomenology of triplet Higgs bosons in the simplest A4-symmetric version*** of the Higgs Triplet Model (A4HTM). The A4HTM is a four-Higgs- Triplet-Model (δ of 1 and (∆x, ∆y, ∆z) of 3).\n- Four mass eigenstates of [doubly charged](https://www.researchgate.net/publication/13276480_Higgs_triplets_in_the_standard_model) Higgs bosons, H±±i, are obtained explicitly from the Higgs potential.\n- We also obtained four mass eigenstates of the triplet-like singly charged Higgs bosons, H±T i, for which doublet components can be ignored because of small triplet vev’s.\n- It was shown that the A4HTM gives unique predictions about their decay branching ratios into two leptons (H−−i → ℓℓ′ and H−iT → ℓν); for example, the leptonic decays of H−−2 are only into µµ and eτ because an approximate Z3 symmetry remains, and the ratio of the branching ratios is 2 : 1 as a consequence of the A4 symmetry in the original Lagrangian.\n- Therefore, it will be possible to test the model at hadron colliders (Tevatron and LHC) if some of these Higgs bosons are light enough to be produced.\n- Even if these Higgs bosons are too heavy to be produced at hadron colliders, they can affect the lepton flavor violating decays of charged leptons if the triplet Yukawa coupling constants are large enough.\n- It was shown that there is no contribution of these Higgs bosonsto µ → eee ¯ and ℓ → ℓ′γ.\n- Thus, we can naturally expect signals of τ → µee and τ → eµµ(which are possible in this model among six τ → ℓℓ′ℓ′′) in the future in collider experiments (Super-KEKB, super B factory, super flavor factory, and LHCb) without interfering with a stringent experimental bound on µ → eee ¯ . This model will be excluded if ℓ → ℓ ′γ is observed.\n\nWe considered current experimental constraints on the model and prospects of the measurement of the non-standard neutrino interactions (NSI) in the neutrino factory. If H±±2 or H±±3 is lighter enough than other H±±i, effects of the NSI can be around the expected sensitivity in the neutrino factory. _([Triplet Higgs bosons - pdf](https://github.com/eq19/eq19.github.io/files/14442049/1005.5338.pdf))_\n
            \n\n

            \"how-we-can-constrain-various-higgs-sectors1-l\"

            \n\n

            This approach shows that there are actually four copies of the tri-rectified Coxeter-Dynkin diagram of H4, promises to open the door to as yet unexplored E8-based GUTs.

            \n\n
            There are [28 octonion Fano plane triangles](https://en.wikipedia.org/wiki/Fano_plane) that correspond directly to the [28 Trott quartic curve bitangents](https://en.wikipedia.org/wiki/Bitangents_of_a_quartic). \n- These bitangents are directly related to the Legendre functions used in the Shroedinger spherical harmonic electron orbital probability densities.\n- Shown below is a graphic of these overlaid onto the n=5, l=2, m=1 element, which is assigned to [gold (Au)](https://en.wikipedia.org/wiki/File:Stowe-Janet-Scerri_PeriodicTable.svg).\n- When using an algorithm based on the [E8 positive algebra root assignments](https://en.wikipedia.org/wiki/E8_%28mathematics%29), the “flipped” Fano plane has E8 algebra root number 79 (the atomic number of Au) and split real even group number of 228 (in Clifford/Pascal triangle order).[![FanoLegendre](https://github.com/eq19/eq19.github.io/assets/8466209/6a9f5200-6d4f-477e-979e-e84757290b28)](https://theoryofeverything.org/theToE/2013/06/15/connecting-the-octonion-fano-plane-to-the-atomic-elements/)\n- This matrix is shown to be useful in providing direct relationships between E8 and the lower dimensional Dynkin and Coxeter-Dynkin geometries contained within it, geometries that are visualized in the form of real and virtual 3 dimensional objects.\n- A direct linkage between E8, the folding matrix, fundamental physics particles in an extended Standard Model Gravi GUT, quaternions, and octonions is introduced, and its importance is investigated and described. \n- E8 and its 4D children, the[ 600-cell](https://en.wikipedia.org/wiki/600-cell) and [120-cell](https://en.wikipedia.org/wiki/120-cell) (pages on which I have some work, amongst others) and its grandkids (2 of the 3D 5 [Platonic Solids](https://en.wikipedia.org/wiki/Platonic_solid), one of which is the 3D version of the 2D Pentagon) are all related to the Fibonacci numbers and the [Golden Ratio](https://en.wikipedia.org/wiki/Golden_ratio).\n- And finally, the {7, 8} dimensions in physics can be identified with quark color, as {7} preserves the blue quark positions, while {8} moves the ***dual concentric rings of quarks*** while preserving their relative positions within the rings. It is interesting t note that the dimensions {6, 7, 8} are appropriately labeled {r, g, b} in SRE coordinates, since in this projection the SRE math coordinates are located at the afforementioned ***6 triple overlap points at center of the quark’s*** {r, g, ¯ g, b, ¯ ¯b} concentric rings (the intersection of the gluons triality lines)![6 triple overlap points](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)\n\nSo that kind of explains why most of my [2D art, 3D objects and sculptures](http://theoryofeverything.com/theToE/) (e.g. furniture like the dodecahedron table below), and 4D [youtube animations](https://www.youtube.com/@JGregoryMoxness/videos) all use the [Golden Ratio](https://en.wikipedia.org/wiki/Golden_ratio) theme. _([E8 to H4 folding matrix - pdf](https://github.com/eq19/eq19.github.io/files/14450026/E8toH4fold_compressed.pdf))_\n
            \n\n

            \"28+Octonion\"

            \n\n

            The number 28, aside from being triangular wave of perfect pyramid, is the sum of the first 5 primes and the sum of the first 7 natural numbers.

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                         MEC30/2\n------+------+-----+-----+------      ‹--------------- 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = 71-43 ✔️\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+ ‹--- vacuum energy ‹--- ∆60 ‹--- 15 {zero axis}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹-------------------- 30 {+1/2}\n
            \n\n

            The split real even E8 group used has been determined from Dynkin diagram which builds the Cartan matrix and determines the root with corresponding Hasse diagrams.

            \n\n
            It has been found recently that the expansion of N = 8 supergravity in terms of [Feynman diagrams](https://en.wikipedia.org/wiki/Feynman_diagrams) has shown that N = 8 supergravity is in some ways [[1]](https://en.wikipedia.org/wiki/N_%3D_8_supergravity#cite_note-1) a product of two [N = 4 super Yang–Mills](https://en.wikipedia.org/wiki/N_%3D_4_super_Yang%E2%80%93Mills) theories.\n- This is written schematically as: N = 8 supergravity = (N = 4 super Yang–Mills) × (N = 4 super Yang–Mills). This is not surprising, as N = 8 supergravity contains six independent representations of N = 4 super Yang–Mills.\n- The theory contains 1 [graviton](https://en.wikipedia.org/wiki/Graviton) (spin 2), 8 [gravitinos](https://en.wikipedia.org/wiki/Gravitinos) (spin 3/2), 28 [vector bosons](https://en.wikipedia.org/wiki/Vector_boson) (spin 1), 56 [fermions](https://en.wikipedia.org/wiki/Fermions) (spin 1/2), 70 [scalar fields](https://en.wikipedia.org/wiki/Scalar_fields) (spin 0) where we don't distinguish particles with negative spin.\n- These numbers are simple combinatorial numbers that come from [Pascal's Triangle](https://en.wikipedia.org/wiki/Pascal%27s_Triangle) and also the number of ways of writing n as a sum of 8 nonnegative cubes [A173681](https://oeis.org/A173681).\n- The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories). [Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking) in his [Brief History of Time](https://en.wikipedia.org/wiki/Brief_History_of_Time) speculated that this theory could be the [Theory of Everything](https://en.wikipedia.org/wiki/Theory_of_Everything).[![ToEsummary1](https://github.com/eq19/eq19.github.io/assets/8466209/d821d38a-3787-473f-a83a-23ea2afd45b9)](https://theoryofeverything.org/theToE/2013/11/15/another-look-at-integrating-the-pascal-triangle-to-clifford-algebra-e8-lie-al)\n- One reason why the theory was abandoned was that ***the 28 vector bosons*** which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the [orthogonal group](https://en.wikipedia.org/wiki/Orthogonal_group) O(10).\n\nFor model building, it has been assumed that almost all the supersymmetries would be broken in nature,[[why?](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify)] leaving just one supersymmetry (N = 1), although nowadays because of the lack of evidence for N = 1 supersymmetry higher supersymmetries are now being considered such as N = 2. _([Wikipedia](https://en.wikipedia.org/wiki/N_%3D_8_supergravity))_\n
            \n\n

            \"Pascal

            \n\n

            The Golden Ratio “symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage.”

            \n\n
            There is a fascinating connection between prime numbers and the Golden ratio. The Golden ratio is an irrational number, which means that it cannot be expressed as a ratio of two integers. However, it can be approximated by dividing consecutive Fibonacci numbers.\n- Additionally, it has been observed that the frequency of prime numbers in certain sequences related to the Golden ratio (such as the continued fraction expansion of the Golden ratio) appears to be higher than in other sequences.\n- Interestingly, the Fibonacci sequence is closely related to prime numbers, as any two consecutive Fibonacci numbers are always coprime. However, the exact nature of the relationship between primes and the Golden ratio is still an active area of research.[![phi-continued-fraction](https://github.com/eq19/eq19.github.io/assets/8466209/df218fdb-71b0-4261-a33c-a6e6f09aaf1c)](https://www.cosmic-core.org/free/article-56-geometry-the-golden-ratio-part-1-introduction/)\n- There are set of sequence known as _[Fibonacci retracement](https://www.investopedia.com/ask/answers/05/fibonacciretracement.asp#:~:text=The%20key%20Fibonacci%20ratio%20of,two%20spots%20to%20the%20right.)_. For unknown reasons, these Fibonacci ratios seem to play a role in the _[stock market](https://www.eq19.com/exponentiation/#hexagonal-patterns)_, just as they do in nature. \n- The mathematically significant Fibonacci sequence defines a set of ratios known as _Fibonacci retracements_ which can be used to determine probable ***[entry and exit points](https://www.eq19.com/exponentiation/#parsering-structure)*** for the equities when paired with additional momentum.\n- The Fibonacci retracement levels are 0.236, 0.382, ***0.618, and 0.786***.[![Fibonacci retracement](https://user-images.githubusercontent.com/36441664/277129518-a7bfc713-40f5-47a5-9a1d-37c3e3fde1ff.png)](https://www.investopedia.com/ask/answers/05/fibonacciretracement.asp#:~:text=The%20key%20Fibonacci%20ratio%20of,two%20spots%20)\n  - The key Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it. For example, 21 divided by 34 equals 0.6176, and 55 divided by 89 equals about 0.61798.\n  - The 38.2% ratio is discovered by dividing a number in the series by the number located two spots to the right. For instance, 55 divided by 144 equals approximately 0.38194.\n  - The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example, 8 divided by 34 equals about 0.23529.\n  - The 78.6% level is given by the _[square root](https://youtu.be/K-AvE0B1KMw)_ of 61.8%, while not officially a Fibonacci ratio, 0.5 is also commonly referenced (50% is derived not from the Fibonacci sequence but rather from the idea that on average stocks retrace half their earlier movements).\n\nThey are used to determine critical points where an _[asset's momentum is likely to reverse](https://www.eq19.com/identition/#the-powers-of-10)_. This study cascade culminating in the Fibonacci digital root sequence (also period-24). _([Golden Ratio - Articles](https://www.fnb.co.za/blog/investments/articles/FibonacciandtheGoldenRatio/))_\n
            \n\n

            (√0.618 - 0.618) x 1000 = (0.786 - 0.618) x 1000 = 0.168 x 1000 = 168 = π(1000)

            \n\n

            \"24-digital

            \n\n

            The simplest group is SU(5), which we will consider here, other examples include SO(10). SU(5) has 5²−1 = 24 generators which means there are 24 gauge bosons.

            \n\n
            It is known that the recently reported shift of ***the W boson mass can be easily explained by an SU(2)L triplet Higgs boson*\"\" with a zero hypercharge if it obtains a vacuum expectation value (VEV) of O(1) GeV. \n- Surprisingly, the addition of a TeV scale complex triplet Higgs boson to the standard model (SM) ***leads to a precise unification of the gauge couplings*** at around 10¹⁴GeV.\n- We consider that it is a consequence of SU(5) grand unification and show a possible potential for the Higgs fields yielding a weak scale complex SU(2) triplet scalar boson.\n- Although it seems the proton decay constraint would doom such a low-scale unification, we show that the constraint can be avoided by introducing ***vector-like fermions*** which mix with the SM fermions through mass terms involving the VEV of GUT breaking Higgs field.\n\nImportantly, the simplest viable model only requires the addition of one pair of vector-like fermions transforming 10 and 10. _([W boson mass anomaly and grand unification - pdf](https://github.com/eq19/eq19.github.io/files/14412652/2205.03877.pdf))_\n
            \n\n

            168 + 329 + 289 - 619 - 30 - 30 - 5 = 786 - 619 - 65 = 102

            \n\n

            \"W

            \n\n

            Since SU(5) has 24 generators, SU(5) GUTs have 12 new gauge bosons known as Xbosons (or X/Y bosons) in addition to the SM.

            \n\n
            The particle spectrum is completed by the Higgs particles required to give masses to fermions as well\nas to break the GUT symmetry.\n- Georgi and Glashow have chosen the SU(5) where a single gauge coupling constant is manifestly incorporated.\n- As has been discussed in the introduction, the SM gauge group has a rank four and the simple groups which contain complex representations of rank four are just ***SU(3) × SU(3) and SU(5)***.\n- Further, the fermions of the Standard Model can be arranged in terms of the fundamental ¯5 and the anti-symmetric 10 representation of the ***SU(5) [30]***.\n- To begin with, let us study the fermion masses in the prototype SU(5).\nGiven that ***fermions are in 5 and 10 representations***\n- We conclude that the scalars that form Yukawa couplings are:![IMG_20240310_205245](https://github.com/eq19/eq19.github.io/assets/8466209/78025b26-260d-4887-8aeb-c72f64b4530b)\n- It is easy to check that this combination of the representations is anomaly free. The gauge theory of SU(5) contains _[24 gauge bosons](https://www.google.com/search?q=SU%282%29+SU%285%29+SO%2810%29+GUT+grand+unification+%2224+gauge+bosons%22&newwindow=1)_.[![2-Table1-1](https://github.com/eq19/eq19.github.io/assets/8466209/7b9f3335-df95-4d8e-b9ed-4ce0f517487b)](https://github.com/eq19/eq19.github.io/files/14549460/0206268.pdf)\n- They are decomposed in terms of the standard model gauge group SU(3) × SU(2) × U(1) as: 24 = (8, 1) + (1, 3) + (1, 1) + (3, 2) + (¯3, 2) (10)\n- The first component represents the gluon fields (G) mediating the colour, the second one corresponds to the Standard Model SU(2) mediators (W) and the third component corresponds to the U(1) mediator (B).\n- The fourth and fifth components carry both colour as well as the SU(2) indices and are called the X and gauge bosons. Schematically, the gauge bosons can be represented in terms of the 5 × 5 matrix:\n![IMG_20240310_204627](https://github.com/eq19/eq19.github.io/assets/8466209/00fd6eed-d0fb-4d58-b7de-0d03cb0e62a7)\n\nNotice that in this case the couplings of the triplets to the fermions is not related to the fermion masses\nas the Higgs triplets are now a mixing between the triplets in the 5H and the triplets in the 50. Therefore\nwe have some ***unknown Yukawa coupling Y50***. _([Flavour Physics and Grand Unification - pdf](https://github.com/eq19/eq19.github.io/files/14413722/0711.2903.pdf))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                         MEC30/2\n------+------+-----+-----+------      ‹--------------- 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+ ‹--- vacuum energy ‹--- ∆60 ‹--- 15 {zero axis}\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = 43-19 ✔️\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹-------------------- 30 {+1/2}\n
            \n\n

            Series Expansion

            \n\n

            Beyond leading approx. we define mGUT as the mass of the heavy 24 gauge bosons, while mT = mHT is the mass of the triplet Higgs.

            \n\n
            The matter representations come in three copies (generations) of the 16 representation. The [Yukawa coupling](https://en.wikipedia.org/wiki/Yukawa_coupling) is 10H 16f 16f. ***This includes a right-handed neutrino**\". One may either include three copies of [singlet](https://en.wikipedia.org/wiki/Singlet_state) representations φ and a Yukawa coupling (the \"double seesaw mechanism\"); or else, add the Yukawa interaction or add the [nonrenormalizable](https://en.wikipedia.org/wiki/Nonrenormalizable) coupling. _([Wikipedia](https://en.wikipedia.org/wiki/SO(10)))_\n
            \n\n

            \"24

            \n\n

            The cleanest signature for a Higgs sector with triplet fields would be the discovery of doubly charged Higgs Bosons.

            \n\n
            Like Pauli’s bold prediction of the neutrino and GIM’s bold prediction of the charm quark, the equally bold speculation of Kobayashi and Maskawa was proved absolutely correct, when the ***fermions of the third generation*** began to be discovered one by one. First came the tau lepton in 1975, closely followed by the bottom quark in 1977. There followed a 17-year hiatus till the 1994 discovery of the top quark, and another 6 years wait till the existence of the tau neutrino νwas confirmed in 2000.\n
            \n\n

            \"12648_2023_2718_Figa_HTML\"

            \n\n

            This thesis constitutes a first attempt to derive aspects of standard model particle physics from little more than an algebra.

            \n\n
            Here, we argue that physical concepts such as particles, causality, and irreversible time may result from ***the algebra acting on itself***.\n- We then focus on a special case by considering the algebra R ⊗ C ⊗ H ⊗ O, the tensor product of the only four normed division algebras over the real numbers.\n- ***Using nothing more than R ⊗ C ⊗ H ⊗ O acting on itself***, we set out to find standard model particle representations: a task which occupies the remainder of this text.\n- From the C ⊗ H portion of the algebra, we find generalized ideals, and show that ***they describe concisely all of the Lorentz representations of the standard model***.\n- From just the C ⊗ O portion of the algebra, we find minimal left ideals, and show that ***they mirror the behaviour of a generation of quarks and leptons under su(3)c and u(1)em***.\n- These unbroken symmetries, su(3)c and u(1)em, appear uniquely in this model as particular symmetries of the ***algebra’s ladder operators***. Electric charge, here, is seen to be simply a number operator for the system.\n- We then combine the C ⊗ H and C ⊗ O portions of R ⊗ C ⊗ H ⊗ O, and focus on a leptonic subspace, so as to ***demonstrate a rudimentary electroweak model***. Here, the underlying ladder operators are found to have a symmetry generated uniquely by su(2)L and u(1)Y.\n- Furthermore, we find that this model yields a straight forward explanation as to why SU(2)L acts only on ***left-handed states***.\n- We then make progress towards a three-generation model. The action of C ⊗ O on itself can be seen to generate ***a 64-complex-dimensional*** algebra, wherein we are ***able to identify two sets of generators for SU(3)c***.\n- We apply these generators to the rest of the space, and find that it breaks down into the SU(3)c representations of ***exactly three generations of quarks and leptons***.\n\nFurthermore, we show that these three-generation results can be extended, so as to include ***all 48 fermionic U(1)em charges***. _([Standard Model from an algebra - pdf](https://github.com/eq19/eq19.github.io/files/14387513/Standard_model_physics_from_an_algebra.pdf))_\n
            \n\n

            \"The-64-dimensional-octonionic-chain-algebra-splits-into-two-sets-of-SU-3-generators\"

            \n\n

            Is the fermion red? green? blue? Does the fermion have isospin up? down? These five questions can be represented by an exterior algebra of 2⁵ or 32-complex dimensional.

            \n\n

            There are thought to be 24 separate quantum fields that permit the universe. It consists of 12 various fundamental forces including mass, 9 quarks, and 3 leptons.

            \n\n
            [String Theory](https://www.eq19.com/identition/#string-theory) which states there could be 11 dimensions (***9 dimensions of space, 1 dimension of time, and 1 dimension for other universes***) - the diagram  below can sum it up for the 9 dimensions of space. Then the Cosmos would be the 11th dimension where (+/-) Binary Universes are born from Nothingness. Where Nothingness = 0 = (+) universe of regular matter and (-) universe of dark matter. _([Quora](https://www.quora.com/Grand-Unification-Theories-predict-that-there-should-be-several-extra-dimensions-Is-it-possible-that-fields-electromagnetic-Higgs-gluon-etc-are-these-extra-dimensions-and-if-so-why/answer/George-Davros))_\n
            \n\n

            \"11

            \n\n

            Remember we must sum over all the quantum numbers of the quarks so the cross section is multiplied by Number of colours, Nc.

            \n\n
            Finally NG′ is the number of parameters of the group G′, the subgroup of G still unbroken by the flavour matrices.\n- In this case, G′ corresponds to two U(1) symmetries, baryon number conservation and lepton number conservation and therefore NG′ = 2.\n- Furthermore Eq. (79) can be applied separately to phases and moduli. In this way, and taking into account that a U(N) matrix contains n(n − 1)/2 moduli and n(n + 1)/2 phases.\n- It is straightforward to obtain that we have, Nph = 69 − 5 × 6 + 2 = 41 phases and ***Nmod = 84 − 5 × 3 = 69 moduli in the flavour sector***.\n- This amounts to a total of 123 parameters in the model4, out of which 44 are CP violating phases!!\n\nAs we know, in the SM, there is only one observable CP violating phase, the CKM phase, and therefore we have here ***43 new phases, 40 in the flavour sector and three in the flavour independent sector***. _([Flavour Physics and Grand Unification - pdf](https://github.com/eq19/eq19.github.io/files/14413722/0711.2903.pdf))_\n
            \n\n

            \"root

            \n\n

            Both 1/89 and 1/109 have the Fibonacci sequence encoded in their decimal expansions illustrates a period-24 palindromic that bring the powers of pi.

            \n\n
            In this article I am going to introduce the main results of a new theory of elemetary particle physics developed by the engineer M.S. El Nachie.\n- This theory provides a fractal model of quantum space-time, the so-called E-infinity space, that allows the precise determination of the mass-energy of most elementary particles -and much more- in close agreement with their experimental values.[![Phi_division_unity](https://github.com/eq19/eq19.github.io/assets/8466209/4d6ea7b9-e06a-4341-92fa-6edcf56ca44f)](https://www.sacred-geometry.es/?q=en/content/golden-ratio)\n- The [Golden Ratio](https://www.sacred-geometry.es/?q=en/content/golden-ratio) emerges naturally in this theory, and ***turns out to be the central piece*** that connects the fractal dimension of quantum space-time with the mass-energy of every fundamental particle, and also with several fundamental physical quantities such as the Fine Structure constant.[![Phi_Squared_Circle_Mides](https://github.com/eq19/eq19.github.io/assets/8466209/9afc48e0-326b-47ee-86fd-68697705d187)](https://www.sacred-geometry.es/?q=en/content/golden-ratio)\n- El Nachie has been severely criticised by his non-orthodoxal publication methods -he uses to publish his papers in a Journal where he is the editor in chief. Despite this fact, I think that his theory deserves consideration so I will try to summarize it in the lines that follow.\n- The intervention of the Golden Ratio can be seen as a way to enter the quantum world, the world of subtle vibrations, in which we observe increasing energy levels as we move to smaller and smaller scales.\n- El Nachie has proposed a way of calculating the fractal dimension of quantum space-time. The resulting value (Figure 7) suggests that the quantum world is composed of an infinite number or scaled copies of our ordinary 4-dimensional space-time.\n- Setting k=0 one obtains the classical dimensions of ***heterotic superstring theory***, namely 26, 16, 10, 6 and 4, as well as the constant of super-symmetric (αgs=26) and ***non super-symmetric (αg=42) unification of all fundamental forces***.\n\nAs we have seen in section 2, the above is a Fibonacci-like sequence with a very concise geometrical interpetation related to numbers ***5, 11 and φ***. _([Phi in Particle Physics](https://www.sacred-geometry.es/?q=en/content/phi-particle-physics))_\n
            \n\n

            \"PHI_Quantum_SpaceTime\"

            \n\n

            Both scheme are carrying a correlation between two (2) number of 89 and 109 which provide the bilateral of 12 to the 24 cells of prime hexagon.

            \n\n
            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their ***collective bilateral 9 sum symmetry***). _([PrimesDemystified](https://primesdemystified.com/))_\n
            \n\n

            \"collective

            \n\n

            So the 36 should behave as a central. Therefore the total files that inherited from this scheme will be 1 + 7 + 29 = 37 including one (1) main page.

            \n\n
            Every repository on GitHub.com comes equipped with a section for hosting documentation, called a wiki. You can use your repository's wiki to share long-form content about your project, such as how to use it, how you designed it, or its core principles. _([GitHub](https://docs.github.com/en/communities/documenting-your-project-with-wikis/about-wikis))_\n
            \n\n

            7 x π(89) = 7 x 24 = 168 = π(1000)

            \n\n

            \"\"

            \n\n

            Since we are discussing about prime distribution then this 18’s structure will also cover the further scheme that is inherited from the above 37 files.

            \n\n
            This web enabled demonstration shows a polar plot of ***the first 20 non-trivial Riemann zeta function zeros (including Gram points) along the critical line Zeta(1/2+it) for real values of t running from 0 to 50***. The consecutively labeled zeros have 50 red plot points between each, with zeros identified by concentric magenta rings scaled to show the relative distance between their values of t. ***Gram’s law states that the curve usually crosses the real axis once between zeros***. _([TheoryOfEverything](https://theoryofeverything.org/theToE/2016/04/23/interactive-reimann-zeta-function-zeros-demonstration/))_\n
            \n\n

            1 + 7 + 29 = 37 = 19 + 18

            \n\n

            \"Riemann

            \n\n

            By our project, these 37 files are located within the wiki of main repository and organized by the 18’s structure located per the 18 files of project gist.

            \n\n
            Spin networks constitute a basis that minimize the degree of over-completeness of the loop basis, and ***for trivalent intersections eliminate it entirely***.\n- The edges are labelled by spins together with `intertwiners' at the vertices which are prescription for how to sum over different ways the spins are rerouted.\n- The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations.\n\nSome of these relations are rooted in a relation to superstring theory and quantum gravity which is [directly related](https://www.eq19.com/identition/span12/#final-theory) to the quantization of general relativity. _([Wikipedia](https://en.wikipedia.org/wiki/Loop_representation_in_gauge_theories_and_quantum_gravity#spin_network_states))_\n
            \n\n

            \"Spin

            \n\n

            This generated a lot of interest in the approach and eventually led to the Loop Quantum Gravity (LQG). You may find that the rest of topics will concern mainly to this matter.

            \n\n

            Hidden Dimensions

            \n\n

            Assigning a specific mass, length, time, and charge metrics based on new dimensional relationships and the Planck constant (which defines Higgs mass).

            \n\n

            \"169-over-109-blood-pressure\"

            \n\n

            Consider the following 13x13 square divided into two triangles and two quadrilateral polygons. If the four pieces are restructured in the form of a rectangle, it appears that the overall area has inexplicably lost one unit! What has happened?

            \n\n

            \"13x13

            \n\n

            In the special case of a unit segment, the Golden Ratio provides the only way to divide unity in two parts that are in a geometric progression

            \n\n
            Supersymmetry and more specifically supergravity grand unification allow one to extrapolate physics from the electroweak scale up to the grand unification scale consistent with electroweak data.\n- Here we give a brief overview of their current status and show that the case for supersymmetry is stronger as a result of the Higgs boson discovery with a mass measurement at ∼ 125 GeV consistent with the supergravity grand unification prediction that the Higgs boson mass lie below 130 GeV. Thus the discovery of the Higgs boson and the measurement of its mass provide a further impetus for the search for sparticles to continue at the current and future colliders.\n- The group SO(10) as the framework for grand unification appears preferred over SU(5). The group SO(10) contains both G(4, 2, 2) and SU(5)⊗U(1) as subgroups, i.e., SO(10) has the branchings SO(10) → SU(4)C ⊗ SU(2)L ⊗ SU(2)R and SO(10) → SU(5) ⊗ U(1).[![Mystery of the First 1000 Prime Numbers](https://user-images.githubusercontent.com/8466209/225830554-007fbd06-9d7d-44e8-867d-c7b0188bf488.png)](https://www.primesdemystified.com/First1000Primes.html)\n- ***It possesses a spinor representation which is 2⁵ = 32 dimensional and which splits into 16 ⊕ 16***. A full generation of quarks and leptons can be accommodated in a single 16 plet representation. Thus the 16 plet has the decomposition in SU(5) ⊗ U(1) so that 16 =10(−1) ⊕ 5(3) ⊕ 1(−5).\n- As noted the combination 5 ⊕ 10 in SU(5) is anomaly free and further 1(−5) in the 16-plet decomposition is a right handed neutrino which is a singlet of the standard model gauge group and thus the 16-plet of matter in SO(10) is anomaly free.\n- The absence of anomaly in this case is the consequence of a more general result for SO(N) gauge theories. Thus in general anomalies arise due to the non-vanishing of the trace over the product of three group generators in some given group representation Tr ({Ta, Tb}Tc).\n- For SO(10) one will have Tr ({Σµν, Σαβ}Σλρ). However, there is no invariant tensor to which the above quantity can be proportional which then automatically guarantees vanishing of the anomaly for SO(10). This analysis extends to other SO(N) groups.\n- ***One exception is SO(6) where there does exist a six index invariant tensor*** ǫµναβλρ and so in this case vanishing of the anomaly is not automatic.\n- The group SO(10) is rank 5 where as the standard model gauge group is rank 4. The rank of the group can be reduced by either using ***16 ⊕ 16 of Higgs fields or 126 ⊕ 126 of Higgs***.\n- Since under SU(5) ⊗ U(1) one has 16 ⊃ 1(−5) we see that a VEV formation for the singlet will reduce the rank of the group. Similarly 126 ⊃ 1(−10) under the above decomposition. Thus when the singlets in 16 ⊕ 16 of Higgs or 126 ⊕ 126 get VEVs, the SO(10) gauge symmetry will break reducing its rank.\n- However, we still need to reduce the remaining group symmetry to the Standard Model gauge group. For this we need to have additional Higgs fields such as 45, 54, 210. Further to get the residual gauge group SU(3)C ⊗ U(1)em we need to have 10 -plet of Higgs fields.\n- Thus the breaking of SO(10) down to SU(3)C ⊗ U(1)em ***requires at least three (3) sets of Higgs representations***: one to reduce the rank, the second to break the rest of the gauge group to the Standard Model gauge group and then at least one 10-plet to break the electroweak symmetry.[![Higgs fields](https://github.com/eq19/eq19.github.io/assets/8466209/ac0b2608-24b2-4a0d-bae8-55473a8576d9)](https://www.nature.com/articles/s41586-022-04892-x)\n- As discussed above one can do this by a combination of fields from the set: 10, 16 ⊕ 16, 45, 54, 120, 126 ⊕ 126, 210.\n- To generate quark and lepton masses we need to couple two 16-plets of matter with Higgs fields. ***To see which Higgs fields couple we expand the product 16⊗16 as a sum over the irreducible representations of SO(10)***. \n\nHere we have ***16 ⊗ 16 = 10s ⊕ 120a ⊕ 126s***, where the s(a) refer to symmetric (anti-symmetric) under the interchange of the two 16-plets. The array of Higgs bosons available lead to a large number of possible SO(10) models. _([Superunification - pdf](https://github.com/eq19/eq19.github.io/files/14413665/1709.09718.pdf))_\n
            \n\n

            \"SO(10)_-_16_Weight_Diagram

            \n\n

            The index of 8 sign masks (sm) to the 30 fPi (each with 8 Hexadecimal masks). These can be “inverted” (0↔1) making 16×30=480 octonion permutations.

            \n\n
            I am pleased to announce the availability of [splitFano.pdf](https://theoryofeverything.org/TOE/JGM/splitFano.pdf), a 321 page pdf file with the 3840=480*8 [split octonion](http://en.wikipedia.org/wiki/Split-octonion) permutations (with Fano planes and multiplication tables). \n- These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices (sorted by Fano plane index or fPi).\n- They are assigned to the ***30 canonical sets of 7 triples**# using the maskList: {5, 8, 4, 3, 7, 6, 3, 2, 6, 5, 1, 4, 6, 7, 3, 3, 8, 6, 3, 1, 6, 6, 2, 3, 5, 8, 4, 3, 7, 6}\n- There are 7 sets of split octonions for each of the 480 “parent” octonions (each of which is defined by 30 sets of 7 triads and 16 7 bit “sign masks” which reverse the direction of the triad multiplication). The 7 split octonions are identified by selecting a triad.\n- The complement of {1,2,3,4,5,6,7} and the triad list leaves 4 elements which are the rows/colums corresponding to the negated elements in the multiplication table (highlighted with yellow background).\n- The red arrows in the Fano Plane indicate the potential reversal due to this negation that defines the split octonions. The selected triad nodes are yellow, and the other 4 are cyan (25MB).\n- These allow for the simplification of Maxwell’s four equations which define electromagnetism (aka.light) into a single equation.\n\nBelow is the first page of the comprehensive split octonion list of all 3840 Split Fano Planes with their multiplication tables available. _([8×16×30 Split Fano](https://theoryofeverything.org/theToE/2013/06/22/the-comprehensive-split-octonions-and-their-fano-planes/))_\n
            \n\n
            \nThe 30 indexed (fPi) canonical sets of 7 triples (which get sign masks applied to make valid octonions).\n1 {{1, 2, 3}, {1, 4, 5}, {1, 6, 7}, {2, 4, 6}, {2, 5, 7}, {3, 4, 7}, {3, 5, 6}}\n2 {{1, 2, 3}, {1, 4, 5}, {1, 6, 7}, {2, 4, 7}, {2, 5, 6}, {3, 4, 6}, {3, 5, 7}}\n3 {{1, 2, 3}, {1, 4, 6}, {1, 5, 7}, {2, 4, 5}, {2, 6, 7}, {3, 4, 7}, {3, 5, 6}}\n4 {{1, 2, 3}, {1, 4, 6}, {1, 5, 7}, {2, 4, 7}, {2, 5, 6}, {3, 4, 5}, {3, 6, 7}}\n5 {{1, 2, 3}, {1, 4, 7}, {1, 5, 6}, {2, 4, 5}, {2, 6, 7}, {3, 4, 6}, {3, 5, 7}}\n6 {{1, 2, 3}, {1, 4, 7}, {1, 5, 6}, {2, 4, 6}, {2, 5, 7}, {3, 4, 5}, {3, 6, 7}}\n7 {{1, 2, 4}, {1, 3, 5}, {1, 6, 7}, {2, 3, 6}, {2, 5, 7}, {3, 4, 7}, {4, 5, 6}}\n8 {{1, 2, 4}, {1, 3, 5}, {1, 6, 7}, {2, 3, 7}, {2, 5, 6}, {3, 4, 6}, {4, 5, 7}}\n9 {{1, 2, 4}, {1, 3, 6}, {1, 5, 7}, {2, 3, 5}, {2, 6, 7}, {3, 4, 7}, {4, 5, 6}}\n10 {{1, 2, 4}, {1, 3, 6}, {1, 5, 7}, {2, 3, 7}, {2, 5, 6}, {3, 4, 5}, {4, 6, 7}}\n11 {{1, 2, 4}, {1, 3, 7}, {1, 5, 6}, {2, 3, 5}, {2, 6, 7}, {3, 4, 6}, {4, 5, 7}}\n12 {{1, 2, 4}, {1, 3, 7}, {1, 5, 6}, {2, 3, 6}, {2, 5, 7}, {3, 4, 5}, {4, 6, 7}}\n13 {{1, 2, 5}, {1, 3, 4}, {1, 6, 7}, {2, 3, 6}, {2, 4, 7}, {3, 5, 7}, {4, 5, 6}}\n14 {{1, 2, 5}, {1, 3, 4}, {1, 6, 7}, {2, 3, 7}, {2, 4, 6}, {3, 5, 6}, {4, 5, 7}}\n15 {{1, 2, 5}, {1, 3, 6}, {1, 4, 7}, {2, 3, 4}, {2, 6, 7}, {3, 5, 7}, {4, 5, 6}}\n16 {{1, 2, 5}, {1, 3, 6}, {1, 4, 7}, {2, 3, 7}, {2, 4, 6}, {3, 4, 5}, {5, 6, 7}}\n17 {{1, 2, 5}, {1, 3, 7}, {1, 4, 6}, {2, 3, 4}, {2, 6, 7}, {3, 5, 6}, {4, 5, 7}}\n18 {{1, 2, 5}, {1, 3, 7}, {1, 4, 6}, {2, 3, 6}, {2, 4, 7}, {3, 4, 5}, {5, 6, 7}}\n19 {{1, 2, 6}, {1, 3, 4}, {1, 5, 7}, {2, 3, 5}, {2, 4, 7}, {3, 6, 7}, {4, 5, 6}}\n20 {{1, 2, 6}, {1, 3, 4}, {1, 5, 7}, {2, 3, 7}, {2, 4, 5}, {3, 5, 6}, {4, 6, 7}}\n21 {{1, 2, 6}, {1, 3, 5}, {1, 4, 7}, {2, 3, 4}, {2, 5, 7}, {3, 6, 7}, {4, 5, 6}}\n22 {{1, 2, 6}, {1, 3, 5}, {1, 4, 7}, {2, 3, 7}, {2, 4, 5}, {3, 4, 6}, {5, 6, 7}}\n23 {{1, 2, 6}, {1, 3, 7}, {1, 4, 5}, {2, 3, 4}, {2, 5, 7}, {3, 5, 6}, {4, 6, 7}}\n24 {{1, 2, 6}, {1, 3, 7}, {1, 4, 5}, {2, 3, 5}, {2, 4, 7}, {3, 4, 6}, {5, 6, 7}}\n25 {{1, 2, 7}, {1, 3, 4}, {1, 5, 6}, {2, 3, 5}, {2, 4, 6}, {3, 6, 7}, {4, 5, 7}}\n26 {{1, 2, 7}, {1, 3, 4}, {1, 5, 6}, {2, 3, 6}, {2, 4, 5}, {3, 5, 7}, {4, 6, 7}}\n27 {{1, 2, 7}, {1, 3, 5}, {1, 4, 6}, {2, 3, 4}, {2, 5, 6}, {3, 6, 7}, {4, 5, 7}}\n28 {{1, 2, 7}, {1, 3, 5}, {1, 4, 6}, {2, 3, 6}, {2, 4, 5}, {3, 4, 7}, {5, 6, 7}}\n29 {{1, 2, 7}, {1, 3, 6}, {1, 4, 5}, {2, 3, 4}, {2, 5, 6}, {3, 5, 7}, {4, 6, 7}}\n30 {{1, 2, 7}, {1, 3, 6}, {1, 4, 5}, {2, 3, 5}, {2, 4, 6}, {3, 4, 7}, {5, 6, 7}}\n\nThe 8 sets of sign masks. Each sign mask (or the set of 7 triples) can be permuted in a consistent way to produce isomorphic sets of 480 octonions.\n\n1 {00, 07, 19, 1E, 2A, 2D, 33, 34}\n2 {01, 06, 18, 1F, 2B, 2C, 32, 35}\n3 {02, 05, 1B, 1C, 28, 2F, 31, 36}\n4 {03, 04, 1A, 1D, 29, 2E, 30, 37}\n5 {08, 0F, 11, 16, 22, 25, 3B, 3C}\n6 {09, 0E, 10, 17, 23, 24, 3A, 3D}\n7 {0A, 0D, 13, 14, 20, 27, 39, 3E}\n8 {0B, 0C, 12, 15, 21, 26, 38, 3F\n\n
            \n\n

            \"splitFano1\"

            \n\n

            Let’s discuss more detail about this particular topic as guided by Prof Stephen Hawking in one of his greatest book: The Theory of Everything.

            \n","dir":"/identition/","name":"README.md","path":"identition/README.md","url":"/identition/"},{"sort":27,"spin":35,"span":152,"suit":13,"permalink":"/exponentiation/span13/","layout":"default","title":"Grand Unified Theory (syntax)","content":"

            Grand Unified Theory (syntax)

            \n\n

            Grand Unified Theory (GUT) is successful in describing the four forces as distinct under normal circumstances, but connected in fundamental ways.

            \n\n
            This section is referring to _[wiki page-27](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-5]()_ that is _[inherited ]()_ from _[the spin section-13](https://gist.github.com/eq19)_ by _[prime spin-35](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-152](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. algorithm
              2. \n
            2. core
              3. \n
            3. default
              4. \n
            4. factor
              5. \n
            5. grouping
              6. \n
            6. helix
              7. \n
            7. impact
              8. \n
            8. level
              9. \n
            9. centralize
              10. \n
            \n\n

            GUT is also successful in describing a system of carrier particles for all four forces, but there is much to be done, particularly in the realm of gravity.

            \n\n

            User Profiles

            \n\n

            \"Capture-49\"

            \n\n

            \"Triangle_diagram\"

            \n\n

            \"images\"

            \n\n

            \"Electroweak

            \n\n

            \"image\"

            \n\n

            \"image\"

            \n\n

            \"image\"

            \n\n
            How can the Universe be so uniform? Now, the time for light to cross a significant part of the Universe is billions of years. We call this time the light communication time, and it is the shortest time required for any changes to be felt between two parts of the Universe. (From J. Schombert)\n
            \n\n

            \"horizon_problem\"

            \n\n

            Unification

            \n\n

            GUT predicts that the other forces become identical under conditions so extreme that they cannot be tested in the laboratory, although there may be lingering evidence of them in the evolution of the universe.

            \n\n

            \"I15-53-electroweak\"

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  ❓ |  ❓ |  ❓ | 3¤ ✔️     ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"GUTs

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-👇--+-👇--+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-👇--+-👇--+----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  ❓ |  ❓ |  .. | 3¤ ✔️     ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"Figure_34_06_03\"

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-👇--+-👇--+-👇--+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-👇--+-👇--+-👇--+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  ❓ |  ❓ |  .. | 3¤ ✔️     ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"The-strong-force-is-complicated-since-observable-particles-that-feel-the-strong-force\"

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-👇--+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-👇--+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-👇--+-👇--+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  .. | 3¤ ✔️     ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"CCJanFeb23_EFT_fermi-635x206\"

            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤ ✔️     ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            Black Hole

            \n\n

            \"main-qimg-6874830a97ce37b0b02cc3ae3d2268f1\"

            \n\n

            \"1591890434759\"

            \n\n

            \"I4dae\"

            \n\n

            \"\"

            \n\n
            E = mc²\nm = E = mc²\nm = E/c²\n\nc = 1 light-second\n  = 1000 years x L / t\n  = 12,000 months x 2152612.336257 km / 86164.0906 sec\n  = 299,792.4998 km / sec\n\nNote:\n1 year = 12 months\n1000 years = 12,000 months\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n\nConclusion:\nπ(π(π(π(π(32(109²-89²)))))) Universe vs Parallel vs Multiverse (via blackhole)\n   👇\nπ(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Parallel (gap in 2nd-level)\n   👇\nπ(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level)\n   👇\nπ(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter)\n   👇\n|--👇---------------------------- 2x96 ---------------------|\n|--👇----------- 7¤ ---------------|---------- 5¤ ----------|\n|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|\n+----+----+----+----+----+----+----+----+----+----+----+----+ \n|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown\n|---------- 5¤ ----------|------------ {96} -----------|-1¤-|\n|-------- Bosons --------|---------- Fermions ---------|-- Graviton\n|-- Sun Orbit (7 days) --|--- Moon Orbit (12 months) --| (11 Galaxies)\n|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way 👉 Σ=12\n
            \n\n

            \"\"

            \n\n

            \"main-qimg-2d9e529abca58e22d8abc805a24b27bd\"

            \n\n

            How water is formed

            \n\n
            Finally, there exist scenarios in which there could actually be more than [4D of spacetime](https://en.wikipedia.org/wiki/PMNS_matrix). String theories require extra dimensions of spacetime for their mathematical consistency. In string theory, spacetime is ***[26-dimensional](https://github.com/eq19/eq19.github.io/files/13904636/0102042.pdf)***, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional.\n[![String theory](https://user-images.githubusercontent.com/8466209/229411952-b42cd7a1-4962-44c7-960a-bf9077713de5.png)](https://en.wikipedia.org/wiki/String_theory#Extra_dimensions)\n\nThese are situations where theories in two or three spacetime dimensions are no more useful. This classification theorem identifies several infinite families of groups as well as ***26 additional groups*** which do not fit into any family. _([Wikipedia](https://en.wikipedia.org/wiki/String_theory))_\n
            \n\n

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------  ✔️   |     11¨  polymorphism\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                          ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |\n----------------------+-----+                                                ---\n
            \n\n

            The only different is, instead of an instance, it will behave as an inside container, just like how spider built a home web as strong as steel but useless to cover them against a rainy day nor even a small breeze.

            \n\n

            \"default\"

            \n\n

            This would even close to the similar ability of human brain without undertanding of GAP functionality between left and right of the human brain.

            \n\n

            Final Theory

            \n\n

            \"\"

            \n\n

            \"\"

            \n\n

            \"\"

            \n\n

            \"l9mo0z1dltu61\"

            \n\n

            \"EU4RYL7UcAAzZN2\"

            \n\n

            \"final-theory\"

            \n\n

            \"\"

            \n\n

            \"ckm-angles-n\"

            \n\n

            \"HEXAHEDRONTORUS1\"

            \n\n

            \"0\"

            \n\n

            \"\"

            \n\n","dir":"/exponentiation/span13/","name":"README.md","path":"exponentiation/span13/README.md","url":"/exponentiation/span13/"},{"sort":28,"spin":37,"span":151,"suit":12,"permalink":"/identition/span12/","layout":"default","title":"Theory of Everything (span 12)","content":"

            Theory of Everything (span 12)

            \n\n

            Theory of Everything (TOE) is a final theory that links together all aspects of the universe. Finding a TOE is one of the major unsolved problems in physics.

            \n\n
            This section is referring to _[wiki page-28](https://github.com/eq19/eq19.github.io/wiki)_ of _[main section-6]()_ that is _[inherited ]()_ from _[the spin section-12](https://gist.github.com/eq19)_ by _[prime spin-37](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-151](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Feeding (spin 3)
              2. \n
            2. Entrypoint (spin 4)
              3. \n
            3. Mapping (spin 5)
              4. \n
            4. Keyring (spin 6)
              5. \n
            5. Enneagram (spin 7)
              6. \n
            6. Twisting (spin 8)
              7. \n
            7. Recycling (spin 9)
              8. \n
            8. Exchange (spin 10)
              9. \n
            9. Dimensions
              10. \n
            \n\n

            This makes it an exciting time to be a theoretical physicists but without some kind of clearer direction, it’s hard to see where the next big breakthrough will be.

            \n\n

            Tracing Method

            \n\n

            We do this division by adopting the OOP (Object Oriented Programming) which is an object-oriented programming method.

            \n\n

            \"\"

            \n\n

            To make it easier to develop a program following a model, we divide the object by placing it into a smaller objects (puzzles).

            \n\n

            π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786

            \n\n

            \"default\"

            \n\n

            As given in the following graph, to discover TOE then a theory of “quantum gravity” is needed and we don’t have it whereas its unification step leads just one level below.

            \n\n

            \"Modern

            \n\n

            Similarly our discussion for this topic is ended up with the lack of “prime distribution” which is still an open problem. Therefore we will assign each of the cases as a puzzle.

            \n\n

            \"\"

            \n\n

            However a much more sophisticated method is necessary to shed light on TOE and many of the other mysteries surrounding the distribution of prime numbers.

            \n\n
            The Millennium Prize Problems are ***seven problems*** in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved _([Wikipedia](https://en.wikipedia.org/wiki/7#Mathematics))_.\n
            \n\n

            \"\"

            \n\n

            It is suspected that the TOE should form as simple as E = mc² As usual, behind a simplest thing there shall be complex aspects. Let talk about the current status.

            \n\n
            **[How close are we to the theory of everything?](https://www.quora.com/How-close-are-we-to-the-theory-of-everything)**\n\nWell, we thought we were getting pretty close about a decade ago - but more recent experimental and observational science is making things a LOT harder for the theoreticians:\n- The final realization that ***quantum mechanics and relativity cannot both be correct*** has created a bit of a problem.\n- ***A theory of “quantum gravity” is needed - and we don’t have it***. Even more annoyingly, both quantum mechanics and relativity are very solidly proven to be true.\n- Cosmologists found dark matter and then dark energy. They can describe their observed properties - point out that about 96% of everything is dark matter/energy - and then leave particle physicists with a major problem.\n- The demands of theoreticians for more data has pushed particle colliders to somewhere ***close to the limits of our ability*** to pay for the darned things (although not yet the limits of theoretical feasibility).\n- The construction of something significantly bigger than the Large Hadron Collider does not seem likely right now  so the data we have may turn out to be the only data we’ll ever have (from particle colliders). Large space telescopes, however, are getting MUCH better and when SpaceX get their StarShip to fly - they’ll be much cheaper and MUCH larger. So getting help from cosmologists MIGHT offer assistance.\n- The great hope that String Theory could be the “Theory of Everything” has somewhat tarnished. String theory predicts that one out of 10⁵ possible realities is the one we live in but fails to mention which one! This is not exactly useful!\n- Current string theories seem ***incompatible with dark energy*** - which is definitely not good.\n\n[![Particle Physics](https://github.com/eq19/eq19.github.io/assets/8466209/916fbfbc-d514-4eb8-be7b-b67a5640d426)](https://github.com/eq19/eq19.github.io/assets/8466209/2f1fa3f5-722a-4b38-bc81-04a6b5fb78a8)\n\nThere is an additional problem called ***Background Independence*** - which is a property that Relativity requires - but which string theory does not seem to reproduce… but this is still a matter of contention. (I confess I do not understand what “Background Independence” actually is… but I Am Not A Theoretical Physicist.) _([Quora](https://www.quora.com/How-close-are-we-to-the-theory-of-everything/answer/Steve-Baker-100?ch=15&oid=1477743656568813&share=49865320&srid=Yz5Fe&target_type=answer))_\n
            \n\n

            \"elementary

            \n\n

            In the next section we will discuss about building the algorithms to find a solution in physics and their relation to the distribution of prime numbers.

            \n\n

            Three (3) Layers

            \n\n

            Our scenario of prime identity is layering three (3) prime pairs out of the symmetrical behaviour of 36 as the smallest number (greater than 1) which is not a prime.

            \n\n
            By our project this prime layering is called _[The True Prime Pairs](https://www.eq19.com/addition/2.html)_ and to be intrepeted as: Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).\n
            \n\n
            $True Prime Pairs:\n (5,7), (11,13), (17,19)\n \n layer|  i  |   f\n -----+-----+---------\n      |  1  | 5\n   1  +-----+\n      |  2  | 7\n -----+-----+---  } 36 » 6®\n      |  3  | 11\n   2  +-----+\n      |  4  | 13\n -----+-----+---------\n      |  5  | 17\n   3  +-----+     } 36 » 6®\n      |  6  | 19\n -----+-----+---------\n
            \n\n

            The (3) layers represents generation in the Standard Model of flavor that counts six (6) flavours of quarks and six (6) flavours of leptons.

            \n\n
            Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos.\n- These are conserved in strong and electromagnetic interactions, but violated by weak interactions. \n- Therefore, such flavour quantum numbers are not of great use. A separate quantum number for each [generation](https://en.wikipedia.org/wiki/Generation_(particle_physics)) is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos).\n- However, even these numbers are not absolutely conserved, as neutrinos of different generations can [mix](https://en.wikipedia.org/wiki/Quantum_superposition); that is, a neutrino of one flavour can [transform into another flavour](https://en.wikipedia.org/wiki/Neutrino_oscillation).\n\n[![PMNS Matriks](https://github.com/eq19/eq19.github.io/assets/8466209/da339619-8e78-4453-9eac-f1b5eebe547d)](https://en.wikipedia.org/wiki/Pontecorvo%E2%80%93Maki%E2%80%93Nakagawa%E2%80%93Sakata_matrix)\n\nThe strength of such mixings is specified by a matrix called the [Pontecorvo–Maki–Nakagawa–Sakata matrix](https://en.wikipedia.org/wiki/Pontecorvo%E2%80%93Maki%E2%80%93Nakagawa%E2%80%93Sakata_matrix) (PMNS matrix). _([Wikipedia](https://en.wikipedia.org/wiki/Flavour_(particle_physics)))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | \n      |      |  1  +-----+          \n      |  1   |     |  2  | (5)\n      |      |-----+-----+\n      |      |     |  3  |\n  1   +------+  2  +-----+----\n      |      |     |  4  |\n      |      +-----+-----+\n      |  2   |     |  5  | (7)\n      |      |  3  +-----+\n      |      |     |  6  |\n------+------+-----+-----+------  } (36) » 6®\n      |      |     |  7  |\n      |      |  4  +-----+\n      |  3   |     |  8  | (11)\n      |      +-----+-----+\n      |      |     |  9  |\n  2   +------|  5  +-----+-----\n      |      |     |  10 |\n      |      |-----+-----+\n      |  4   |     |  11 | (13)\n      |      |  6  +-----+\n      |      |     |  12 |\n------+------+-----+-----+------------------\n      |      |     |  13 |\n      |      |  7  +-----+\n      |  5   |     |  14 | (17)\n      |      |-----+-----+\n      |      |     |  15 |\n  3   +------+  8  +-----+-----  } (36) » 6®\n      |      |     |  16 |\n      |      |-----+-----+\n      |  6   |     |  17 | (19)\n      |      |  9  +-----+\n      |      |     |  18 |\n------|------|-----+-----+------\n
            \n\n

            While there are nine (9) possible combinations of color/anti-color pairs, due to symmetry considerations one of these combinations is eliminated. A gluon can effectively carry one of eight (8) possible color/anti-color combinations.

            \n\n

            \"color

            \n\n

            These matrices are particularly important in both mathematics and physics. For example, these matrices (and their generalizations) are important in Lie theory.

            \n\n
            _[Gell-mann matrices](https://en.m.wikipedia.org/wiki/Gell-Mann_matrices)_ are a complete set of Hermitian  noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model ***the eight gluons*** that mediate the strong force quantum chromodynamics, an analogue of the _[Pauli matrices](https://mathworld.wolfram.com/PauliMatrices.html)_ well-adapted to applications in the realm of quantum mechanics. _([Wolfram](https://mathworld.wolfram.com/Gell-MannMatrix.html))_\n
            \n\n
            #!/usr/bin/env python\n\nimport numpy as np\nfrom scipy import linalg\n\nclass SU3(np.matrix):\n\tGELLMANN_MATRICES = np.array([\n\t\tnp.matrix([ #lambda_1\n\t\t\t[0, 1, 0],\n\t\t\t[1, 0, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_2\n\t\t\t[0,-1j,0],\n\t\t\t[1j,0, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_3\n\t\t\t[1, 0, 0],\n\t\t\t[0,-1, 0],\n\t\t\t[0, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_4\n\t\t\t[0, 0, 1],\n\t\t\t[0, 0, 0],\n\t\t\t[1, 0, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_5\n\t\t\t[0, 0,-1j],\n\t\t\t[0, 0, 0 ],\n\t\t\t[1j,0, 0 ],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_6\n\t\t\t[0, 0, 0],\n\t\t\t[0, 0, 1],\n\t\t\t[0, 1, 0],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_7\n\t\t\t[0, 0,  0 ],\n\t\t\t[0, 0, -1j],\n\t\t\t[0, 1j, 0 ],\n\t\t], dtype=np.complex),\n\t\tnp.matrix([ #lambda_8\n\t\t\t[1, 0, 0],\n\t\t\t[0, 1, 0],\n\t\t\t[0, 0,-2],\n\t\t], dtype=np.complex) / np.sqrt(3),\n\t])\n\n\n\tdef computeLocalAction(self):\n\t\tpass\n\n\t@classmethod\n\tdef getMeasure(self):\n\t\tpass\n
            \n\n

            We apply these generators to the rest of the space, and find that it breaks down into the SU(3)c representations of exactly three generations of quarks and leptons.

            \n\n
            The action of C⊗O on itself can be seen to generate a ***64-complex-dimensional algebra***, wherein we are able to identify two sets of generators for SU(3)c.\n- Furthermore, we show that ***these three-generation results can be extended, so as to include all 48 fermionic U(1)em charges***.\n- The 64-dimensional octonionic chain algebra splits into ***two sets of SU (3) generators of the form iΛν and −iΛ * ν * , six SU (3) singlets j , six triplets q k , and their complex conjugates***.\n- These objects are sectioned off above into four quadrants according to their forms: νaν, ν * aν, νaν * and ν * aν * for a in the chain algebra.\n\nTransforming particles into anti-particles, and vice versa, requires only the complex conjugate ***i → −i*** in our formalism. _([Standard Model from an algebra - pdf](https://github.com/eq19/eq19.github.io/files/14387513/Standard_model_physics_from_an_algebra.pdf))_\n
            \n\n

            \"The-64-dimensional-octonionic-chain-algebra-splits-into-two-sets-of-SU-3-generators\"

            \n\n

            This quark model underlies flavor SU(3), or Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons

            \n\n
            The [pseudoscalar](https://en.wikipedia.org/wiki/pseudoscalar) [meson](https://en.wikipedia.org/wiki/meson) nonet. Members of the original meson \"octet (8)\" are shown in green, the singlet in magenta.\n- Although these mesons ***are now grouped into a nonet (9)***, the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_(physics)) name derives from the patterns of eight for the mesons and baryons in the original classification scheme.\n- The Eightfold Way classification is named after the following fact:\n  - If we take three flavors of quarks, then the quarks lie in the [fundamental representation](https://en.wikipedia.org/wiki/Fundamental_representation), 3 (called the triplet) of [flavor](https://en.wikipedia.org/wiki/Flavour_(particle_physics)) [SU(3)](https://en.wikipedia.org/wiki/SU(3)).\n  - The antiquarks lie in the complex conjugate representation 3.\n- The nine states (nonet) made out of a pair can be decomposed into the [trivial representation](https://en.wikipedia.org/wiki/Trivial_representation), 1 (called the singlet), and the [adjoint representation](https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_group), 8 (called the octet). \n- The notation for this decomposition is ***3⊗3=8⊕1***.\n\nFigure below shows the application of this decomposition to the mesons. _([Wikipedia](https://en.wikipedia.org/wiki/Quark_model))_\n
            \n\n

            \"8foldway

            \n\n

            The symmetrical states can couple to a pair of pseudoscalar mesons in a wave, and hence their widths and masses are strongly influenced by these couplings.

            \n\n
            In order to be _[four-spinors](https://en.wikipedia.org/wiki/Dirac_spinor#Four-spinor_for_particles)_ like the electron and other [lepton](https://en.wikipedia.org/wiki/Lepton) components, there must be one quark component for every combination of [flavour](https://en.wikipedia.org/wiki/Flavor_(particle_physics)) and [colour](https://en.wikipedia.org/wiki/Color_charge), _bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four (4) component [bispinor](https://en.wikipedia.org/wiki/Bispinor), for a total of [96 complex-valued components](https://github.com/eq19/eq19.github.io/files/13796986/NEUTRINOS_Mysterious_Particles_with_Fascinating_Fe.pdf) for the fermion field_. _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n

            Eightfold Way = 8 × (6®+6®) = 96®

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | \n      |      |  1  +-----+          \n      |  1   |     |  2  | (5)\n      |      |-----+-----+\n      |      |     |  3  |\n  1   +------+  2  +-----+----\n      |      |     |  4  |\n      |      +-----+-----+\n      |  2   |     |  5  | (7)\n      |      |  3  +-----+\n      |      |     |  6  |\n------+------+-----+-----+------  } (36) » 6® -------------\n      |      |     |  7  |                                 |\n      |      |  4  +-----+                                 |\n      |  3   |     |  8  | (11)                            |\n      |      +-----+-----+                                 |\n      |      |     |  9  | <--------  Eightfold Way = 8 × (6®+6®) = 96®\n  2   +------|  5  +-----+-----                               |\n      |      |     |  10 |                                    |\n      |      |-----+-----+                                    |\n      |  4   |     |  11 | (13)                               |\n      |      |  6  +-----+                                    |\n      |      |     |  12 |                                    |\n------+------+-----+-----+------------------                  |\n      |      |     |  13 |                                    |\n      |      |  7  +-----+                                    |\n      |  5   |     |  14 | (17)                               |\n      |      |-----+-----+                                    |\n      |      |     |  15 |                                    |\n  3   +------+  8  +-----+-----  } (36) » 6® -----------------\n      |      |     |  16 |\n      |      |-----+-----+\n      |  6   |     |  17 | (19)\n      |      |  9  +-----+\n      |      |     |  18 |\n------|------|-----+-----+------\n
            \n\n

            In fact this particular count of three (3) as the Eightfold Way Generation of 6 by 6 flavors is the major case of every theories in physics to get in to the TOE.

            \n\n
            The origin of multiple generations of fermions, and the particular count of 3, is an _[unsolved problem of physics](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics)_.\n- [Generations of matter](https://en.wikipedia.org/wiki/Generation_(particle_physics)): Why are there three generations of [quarks](https://en.wikipedia.org/wiki/Quark) and [leptons](https://en.wikipedia.org/wiki/Lepton)? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory of [Yukawa couplings](https://en.wikipedia.org/wiki/Yukawa_coupling))?\n- [String theory](https://en.wikipedia.org/wiki/String_theory) provides a cause for multiple generations, but the particular number depends on the details of the [compactification](https://en.wikipedia.org/wiki/Compactification_(physics)) of the [D-brane](https://en.wikipedia.org/wiki/D-brane) intersections.\n- Additionally, [E8](https://en.wikipedia.org/wiki/E8_(mathematics)) [grand unified theories](https://en.wikipedia.org/wiki/Grand_Unified_Theory) in 10 dimensions [compactified](https://en.wikipedia.org/wiki/Compactification_(physics)) on certain [orbifolds](https://en.wikipedia.org/wiki/Orbifold) down to 4‑D naturally contain 3 generations of matter.\n- This includes many [heterotic string theory](https://en.wikipedia.org/wiki/Heterotic_string_theory) models.\n\nIn standard quantum field theory, under certain assumptions, a single fermion field can give rise to multiple fermion poles with mass ratios of around eπ≈23 and e2π≈535 potentially explaining the large ratios of fermion masses between successive generations and their origin. _([Wikipedia](https://en.wikipedia.org/wiki/Generation_(particle_physics)))_\n
            \n\n

            6 x 114 - 30 - 30 - 5 = 619 = 6 x 19 = 114th prime

            \n\n

            \"\"

            \n\n

            The quark model for baryons has been very successful in describing them as qqq states, including those with nonzero internal orbital angular momentum. However, final meson-baryon states (and thus states of qq¯+qqq) play an important role as well.

            \n\n
            Why do we see certain types of strongly interacting elementary particles and not others? This question was posed over 50 years ago in the context of the quark model.\n- M. Gell-Mann and G. Zweig proposed that the known mesons were qq¯ and baryons qqq, with quarks known at the time u (“up”), d (“down”), and s (“strange”) having charges (2/3,–1/3,–1/3).\n- Mesons and baryons would then have integral charges. Mesons such as qqq¯q¯ and baryons such as qqqqq¯ would also have integral charges. Why weren’t they seen?\n- They have now been seen, but only with additional heavy quarks and under conditions which tell us a lot about the strong interactions and how they manifest themselves.\n\n[![Beyond the standard model](https://github.com/eq19/eq19.github.io/assets/8466209/0d5cee08-92b4-48e8-9b50-e55312a5736f)](https://github.com/eq19/eq19.github.io/files/13793234/the-physics-of-the-standard-model-and-beyond.pdf)\n\nThe present article describes recent progress in our understanding of such “exotic” mesons and baryons. _([Multiquark States - pdf](https://github.com/eq19/eq19.github.io/files/14322719/1711.10626.pdf))_\n
            \n\n

            \"structure-of-composite-particles-l\"

            \n\n

            There are higher dimensional numbers besides complex numbers. The classical octet meson is now nonet. Thus consequently it would go higher than E8.

            \n\n
            These are called hypercomplex numbers, such as, quaternions (4D), octonions (8D), sedenions (16D), pathions (32D), chingons (64D), routons (128D), and voudons (256D).  These names were coined by Robert P.C. de Marrais and Tony Smith.  It is an alternate naming system providing relief from the difficult Latin names, such as: trigintaduonions (32D), sexagintaquattuornions (64D), centumduodetrigintanions (128D), and ducentiquinquagintasexions (256D). _([Wordpress.com](https://nitinuchil.wordpress.com/2020/09/09/hypercomplex-math/))_ \n
            \n\n

            \"4

            \n\n

            The three (3) layers as explained above is in the 1st-term of our discussed structure. So the next step is the 2nd-term which goes to the four (4) dimensional space-time.

            \n\n

            The Four (4) Dimensions

            \n\n

            4D-dimensional space-time is much more complex due to the extra degree of freedom. Almost all of the rest of unsolved problems in physics are correlated with.

            \n\n
            The set of points in Euclidean 4-space having the same distance R from a fixed point P0 forms a hypersurface known as a 3-sphere where R is substituted by function R(t) with t meaning the cosmological age of the universe. Growing or shrinking R with time means expanding or collapsing universe, depending on the mass density inside _([Wikipedia](https://en.wikipedia.org/wiki/Four-dimensional_space#Hypersphere))_.\n
            \n\n

            \"\"

            \n\n

            The main reason is that the general relativity not consistent with quantum mechanics. It is even a sign that Einstein’s equations are somehow incomplete.

            \n\n
            Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents _([Wikipedia](https://en.wikipedia.org/wiki/Albert_Einstein#Scientific_career))_.\n
            \n\n

            \"default\"

            \n\n

            Comparatively, four-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w to describe the two additional cardinal directions of up toward and down from, respectively.

            \n\n
            On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in [4D Space vs Time](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap#Background), nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! _([Clay Institute's - Yang Mills Official problem description](https://github.com/eq19/eq19.github.io/files/14056642/yangmills.pdf))_.\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | \n      |      |  1  +-----+          \n      |  1   |     |  2  | (5)\n      |      |-----+-----+\n      |      |     |  3  |\n  1   +------+  2  +-----+----\n      |      |     |  4  |\n      |      +-----+-----+\n      |  2   |     |  5  | (7)\n      |      |  3  +-----+\n      |      |     |  6  |\n------+------+-----+-----+------  } (36) » 6® 👈 up toward ✔️\n      |      |     |  7  |\n      |      |  4  +-----+\n      |  3   |     |  8  | (11)\n      |      +-----+-----+\n      |      |     |  9  |\n  2   +------|  5  +-----+-----\n      |      |     |  10 |\n      |      |-----+-----+\n      |  4   |     |  11 | (13)\n      |      |  6  +-----+\n      |      |     |  12 |\n------+------+-----+-----+------------------\n      |      |     |  13 |\n      |      |  7  +-----+\n      |  5   |     |  14 | (17)\n      |      |-----+-----+\n      |      |     |  15 |\n  3   +------+  8  +-----+-----  } (36) » 6® 👈 down from ✔️\n      |      |     |  16 |\n      |      |-----+-----+\n      |  6   |     |  17 | (19)\n      |      |  9  +-----+\n      |      |     |  18 |\n------|------|-----+-----+------\n
            \n\n

            The Lorentz group consists, unsurprisingly, of the Lorentz transformations, which are the linear transformations preserving the Minkowski dot product.

            \n\n
            Equivalently, they are the linear transformations fixing that hyperboloid of two sheets. If we discard one of the sheets, we obtain the orthochronous (time-preserving) subgroup.\n- From the perspective of the centre of the cone, the hyperboloid looks like an open disc. The orthochronous Lorentz transformations precisely correspond to distance-preserving transformations of the hyperbolic plane. These are themselves determined uniquely by a conformal (or anticonformal) transformation of the ‘circle at infinity’.\n- Adding an extra dimension, the orthochronous Lorentz group O^{+}(3,1) is isomorphic to the group of distance-preserving transformations of hyperbolic 3-space, which is again isomorphic to the group of (anti-)conformal transformations of the ‘sphere at infinity’, namely our index-2 supergroup of the Möbius group.\n- Moreover, this nicely generalises: the group generated by geometric inversions on the n-sphere is abstractly isomorphic to the orthochronous Lorentz group O^{+}(n+1,1).\n\n***And when n = 24, we get a very beautiful discrete subgroup, namely the automorphism group of the II(25,1)*** lattice intimately related to the [Leech lattice](http://cp4space.wordpress.com/2013/09/12/leech-lattice/). _([Complex Projective 4-Space](https://cp4space.hatsya.com/2013/10/10/what-should-this-group-be-called/))_\n
            \n\n

            \"spacetime\"

            \n\n

            This diagram is representing groupings (leptons, quarks, weak-force bosons) with 6 quarks in a way that parallels the 6 leptons.

            \n\n
            ***There are 8 different types of tiny particles, or 'states', that we can find in a special kind of space that has 6 dimensions*** and involves both real and imaginary numbers. These particles include:\n- ***The Higgs field***, which doesn't spin and is represented by 0.\n- ***Fermions***, which are particles like electrons, having a spin of plus or minus a half.\n- ***Bosons***, like photons, which have a spin of plus or minus 1.\n- ***Anti-fermions***, which are like fermions but have a spin of plus or minus two-thirds.\n- ***The graviton***, believed to be responsible for gravity, with a spin of 2.\n\n***In a diagram at the top left, this 6-dimensional space is shown to be curved***. In another diagram at the bottom right, we see two waves that are perpendicular to each other, representing the motion of a particle in a 'Dirac harmonic oscillator' – a concept in quantum mechanics. _([Physics In History](https://twitter.com/PhysInHistory/status/1739158977089274165))_\n
            \n\n

            \"Dirac_bispinor_6D\"

            \n\n

            While the Dirac CP-violating phase δℓ can be determined in the future, how to probe or constrain the Majorana CP-violating phases ρ and σ is still an open question

            \n\n
            Four of the dimensions are the usual four of spacetime. The six (or perhaps seven) extra dimensions are rolled up to be almost unobservable.\n- First, let's see why they exist at all. If [N=8 Supersymmetry](https://en.wikipedia.org/wiki/N=8_Supergravity) is correct the universe must be 10 or 11 dimensional.![extra dimensions](https://github.com/eq19/eq19.github.io/assets/8466209/dc2fca4c-26be-4e52-b8e4-bf8b9ac46835)\n- Let D be the actual dimensionality of space time. Let d be the apparent dimensionality. (We know d = 4, but let's think generally.) Then there is a nice relation between D, d and N.[![Dimensional-reduction-of-supergravity-from-11D-to-4D-over-a-space-like-or-time-like](https://github.com/eq19/eq19.github.io/assets/8466209/9fb715b2-6ab2-45e6-9ae2-7ccd1e1cf38e)\n](https://www.researchgate.net/publication/273788549_10D_to_4D_Euclidean_Supergravity_over_a_Calabi-Yau_three-fold)\n- It follows from the number of spinor dimensions required by the Dirac equation, which is  The s mean round down to the nearest whole number. So plugging in d=4 and N=8 (which is the highest value N can have) we get D = 10 or 11. String theory has D=10, M-theory has D=11.[![Dirac, Weyl, and Majorana in 4D](https://github.com/eq19/eq19.github.io/assets/8466209/544aefc2-7ba5-4623-9d99-51febf61efb0)](https://www.mdpi.com/2218-1997/6/8/111)\n- One dimension is reserved for time, leaving space with 9 or 10 dimensions.\n\nWe don't see 6 (or 7) of these extra dimensions because - we assume - they are [rolled up ](https://en.m.wikipedia.org/wiki/Compactification_(physics))a la [Kaluza–Klein theory](https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory) into a 6 dimensional [Calabi–Yau space](https://en.m.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold)\n
            \n\n

            \"main-qimg-f8cd59c3b8504bdaab0977ee2704ce0e-ezgif

            \n\n

            The most promising candidate is SO(10) but it does not contain any exotic fermions (i.e. additional fermions besides the Standard Model and the right-handed neutrino), and it unifies each generation into a single irreducible representation.

            \n\n
            In [particle physics](https://en.wikipedia.org/wiki/Particle_physics), SO(10) refers to a [grand unified theory](https://en.wikipedia.org/wiki/Grand_unified_theory) (GUT) based on the [spin group](https://en.wikipedia.org/wiki/Spin_group) Spin(10). The shortened name SO(10) is conventional[[1]](https://en.wikipedia.org/wiki/SO(10)#cite_note-1) among physicists, and derives from the [Lie algebra](https://en.wikipedia.org/wiki/Lie_algebra) or less precisely the [Lie group](https://en.wikipedia.org/wiki/Lie_group) of SO(10), which is a [special orthogonal group](https://en.wikipedia.org/wiki/Special_orthogonal_group) that is [double covered](https://en.wikipedia.org/wiki/Double_covering_group) by Spin(10).\n\nSO(10) subsumes the [Georgi–Glashow](https://en.wikipedia.org/wiki/Georgi%E2%80%93Glashow_model) and [Pati–Salam models](https://en.wikipedia.org/wiki/Pati%E2%80%93Salam_model), and unifies all [fermions](https://en.wikipedia.org/wiki/Fermion) in a [generation](https://en.wikipedia.org/wiki/Generation_(particle_physics)) into a single field. This requires 12 new [gauge bosons](https://en.wikipedia.org/wiki/Gauge_boson), in addition to the 12 of [SU(5)](https://en.wikipedia.org/wiki/Georgi%E2%80%93Glashow_model) and 9 of [SU(4)×SU(2)×SU(2)](https://en.wikipedia.org/wiki/Pati%E2%80%93Salam_model).\n- Left: The pattern of [weak isospin](https://en.wikipedia.org/wiki/Weak_isospin), W, weaker isospin, W', strong g3 and g8, and baryon minus lepton, B, charges for particles in the SO(10) model, rotated to show the embedding of the [Georgi–Glashow model](https://en.wikipedia.org/wiki/Georgi%E2%80%93Glashow_model) and [Standard Model](https://en.wikipedia.org/wiki/Standard_Model), with electric charge roughly along the vertical. In addition to Standard Model particles, the theory includes 30 colored X bosons, responsible for [proton decay](https://en.wikipedia.org/wiki/Proton_decay), and two W' bosons.\n- Right: The pattern of charges for particles in the SO(10) model, rotated to show the embedding in [E6](https://en.wikipedia.org/wiki/E6_(mathematics)).\n- The matter representations come in three copies (generations) of the 16 representation. The Yukawa coupling is 10H 16f 16f. This includes a right-handed neutrino.\n\nIt has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear in 2018 that the SO(10) model is also free from all [nonperturbative global anomalies](https://en.wikipedia.org/wiki/Anomaly_(physics)#Witten_anomaly_and_Wang-Wen-Witten_anomaly) on [non-spin manifolds](https://en.wikipedia.org/wiki/Spin_structure) --- an important rule for confirming the consistency of SO(10) grand unified theory, with a Spin(10) gauge group and chiral fermions in the 16-dimensional spinor representations, defined on non-spin manifolds. _([Wikipedia](https://en.wikipedia.org/wiki/SO(10)))_\n
            \n\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
            SyntaxDescriptionLast
            \"download\"download\"download
            \n\n

            In the spin-foam formalism, the Barrett–Crane model, which was for a while the most promising state-sum model of 4D Lorentzian quantum gravity

            \n\n
            It was [based on representations](https://www.eq19.com/addition/5.html#power-of-magnitude) of the noncompact groups SO(3,1) or SL(2,C), so the spin foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks. _([Wikipedia](https://en.wikipedia.org/wiki/Lorentz_invariance_in_loop_quantum_gravity))_\n
            \n\n

            \"41114_2016_3_Equ168\"

            \n\n

            \"41114_2016_3_Equ115\"

            \n\n

            The field content of this theory is the massless N = 8 supergravity which comprises the graviton, 8 gravitinos, 28 vector fields.

            \n\n
            In four spacetime dimensions, N = 8 supergravity, speculated by [Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking), is the most [symmetric](https://en.wikipedia.org/wiki/Symmetric) quantum field theory which ***involves gravity*** and a finite number of fields.\n- It can be found from a [dimensional reduction](https://www.eq19.com/identition/span12/#the-seven-7-groups) of 11D supergravity ***by making the size of seven (7) of the dimensions go to zero***.\n- ***It has eight (8) supersymmetries***, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin −2. (The spin 2 graviton is the particle with the highest spin in this theory.)[![eight (8) supersymmetries](https://github.com/eq19/eq19.github.io/assets/8466209/3796ffd2-465f-44d7-b750-95a092537939)](https://github.com/eq19/eq19.github.io/files/14229967/0109010.pdf)\n\n- More supersymmetries would mean the particles would have [superpartners](https://en.wikipedia.org/wiki/Superpartner) with spins higher than 2.\n- The only theories with ***spins higher than 2 which are consistent*** involve an infinite number of particles (such as String Theory and Higher-Spin Theories).\n- _[Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking) in his [Brief History of Time](https://en.wikipedia.org/wiki/Brief_History_of_Time) speculated that this theory could be the [Theory of Everything](https://en.wikipedia.org/wiki/Theory_of_Everything)_.\n- However, in later years this was abandoned in favour of _[string theory](https://en.wikipedia.org/wiki/String_theory)_.\n- The theory contains 1 [graviton](https://en.wikipedia.org/wiki/Graviton) (spin 2), 8 [gravitinos](https://en.wikipedia.org/wiki/Gravitinos) (spin 3/2), 28 [vector bosons](https://en.wikipedia.org/wiki/Vector_boson) (spin 1), 56 [fermions](https://en.wikipedia.org/wiki/Fermions) (spin 1/2), 70 [scalar fields](https://en.wikipedia.org/wiki/Scalar_fields) (spin 0) where we don't distinguish particles with negative spin.\n- These numbers are simple combinatorial numbers that come from [Pascal's Triangle](https://en.wikipedia.org/wiki/Pascal%27s_Triangle) and also the number of ways of writing n as a sum of 8 nonnegative cubes [A173681](https://oeis.org/A173681).\n- One reason why the theory was abandoned was that the 28 vector bosons which form an ***O(8) gauge group is too small*** to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the [orthogonal group](https://en.wikipedia.org/wiki/Orthogonal_group) O(10).\n\nThere has been renewed interest in the 21st century, with the possibility that string theory may be finite. _([Wikipedia](https://en.wikipedia.org/wiki/N_%3D_8_supergravity))_\n
            \n\n

            \"15-Figure1-1\"

            \n\n

            One remarkable property of both string and M-theory is that seven (7) extra dimensions are required for the theory’s consistency, on top of the four dimensions in our universe.

            \n\n
            There exist scenarios in which there could actually be more than [4D of spacetime](https://en.wikipedia.org/wiki/PMNS_matrix). String theories require extra dimensions of spacetime for their mathematical consistency. These are situations where theories in two or three spacetime dimensions are no more useful.\n\nIn string theory, spacetime is _[26-dimensional](https://github.com/eq19/eq19.github.io/files/13904636/0102042.pdf)_, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional.\n\nThis classification theorem identifies several infinite families of groups as well as ***26 additional groups*** which do not fit into any family. _([Wikipedia](https://en.wikipedia.org/wiki/String_theory))_\n
            \n\n

            \"M-Theory\"

            \n\n

            So the last “Superstring revolution” was impressive but it was close to 30 years ago now - and we still don’t seem to be adopting it as “The Truth”.

            \n\n
            M Theory and/or Loop Quantum Gravity hold the promise of ***resolving the conflict between general relativity and quantum mechanics*** but lack experimental connections to predictability in physics.\n- A connection is made to these and other theories vying for the title of a “Theory of Everything” by questioning the value of the traditional Planck unit reference point for the scales at which they operate.\n- It also suggests a cosmological model which has acceleration as being fundamental.\n- It provides for an intuitive understanding of the Standard Model and its relationship to particle masses and the structure of the atom.\n\nThe prediction of particle mass and lifetimes is a good indicator for its validity. _([TOE - pdf](https://github.com/eq19/eq19.github.io/files/14378301/ToE.pdf))_\n
            \n\n

            \"string-theory-dimensions\"

            \n\n

            We suspect that using that Lorentz, all four have the same complexified Lie algebra. In loop quantum gravity it makes matters even more confusing.

            \n\n

            The Seven (7) Groups

            \n\n

            Let’s consider a prime spin theory of compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius and study its dimensional reduction to 4D.

            \n\n
            We now place integers sequentially into the lattice with a simple rule: ***Each time a prime number is encountered, the spin or ‘wall preference’ is switched***.\n\n[![19 abuts 2](https://github.com/eq19/eq19.github.io/assets/8466209/b9cef585-fcef-4090-ad5e-e820ecb29ceb)](https://www.hexspin.com/defining-the-prime-hexagon/)\n\nSo, from the first cell, exit from 2’s left side. This sets the spin to left and the next cell is 3, a prime, so switches to right. 4 is not prime and continues right. 5 is prime, so switch to left and so on. ***There are twists and turns until 19 abuts 2***. _([HexSpin](https://www.hexspin.com/defining-the-prime-hexagon/))_\n
            \n\n

            \"Defining

            \n\n

            In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist and in particular the 4D metric, is defined by the 3-form.

            \n\n
            We would like to say that our present use of G2 structures (3-forms in 7D) is different from what\none can find in the literature on Kaluza–Klein compactifications of supergravity.\n- We show that the resulting 4D theory is (Riemannian) [General Relativity](https://www.sciencedirect.com/topics/physics-and-astronomy/general-relativity) (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.\n- Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.\n\nAlso, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. _([General relativity from three-forms in seven dimensions - pdf](https://github.com/eq19/eq19.github.io/files/14064088/1-s2.0-S0370269317304926-main.pdf))_\n
            \n\n

            \"Standard

            \n\n

            The complete theory was obtained by dimensional reduction of the 11D supergravity on a seven (7) torus and realizing the exceptional symmetry group E7(7)

            \n\n
            In particular, these theories include the compactification of eleven-dimensional supergravity on the seven-sphere S7, which gives rise to a ***[four-dimensional theory](https://www.eq19.com/identition/span12/#the-four-4-dimensions)*** with compact non-abelian gauge group SO(8) _([11D Supergravity and Hidden Symmetries - pdf](https://github.com/eq19/eq19.github.io/files/14126154/2303.12682.pdf))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+---------\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ✔️\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) ---------------------\n      |      |  6  +-----+        <----------------  strip\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ✔️\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | --------------------------\n------|------|-----+-----+------\n
            \n\n

            The most general Lagrangian with massless neutrinos, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment.

            \n\n
            Straightforward extensions of the Standard Model with massive neutrinos need 7 more parameters (3 masses and 4 PMNS matrix parameters) for a total of [26 parameters](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#cite_note-Thomson499-15). The neutrino parameter values are still uncertain. The 19 certain parameters are summarized here:\n\n[![IMG_20231230_232603](https://github.com/eq19/eq19.github.io/assets/8466209/2b4f5d82-d000-46f0-91ee-618ff55f01a4)](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Free_parameters)\n\n- The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter.\n- Instead of fermion masses, dimensionless Yukawa couplings can be chosen as free parameters. For example, the electron mass depends on the Yukawa coupling of the electron to the Higgs field.\n- The value of the [vacuum energy](https://en.wikipedia.org/wiki/Vacuum_energy) (or more precisely, the [renormalization](https://en.wikipedia.org/wiki/Renormalization) scale used to calculate this energy) may also be treated as ***an additional free parameter***.\n- The renormalization scale may be identified with the [Planck scale](https://en.wikipedia.org/wiki/Planck_scale) or fine-tuned to match the observed [cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant). However, both options [are problematic](https://en.wikipedia.org/wiki/Cosmological_constant_problem).\n\nAs these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the \"best step\" towards a [Theory of Everything](https://en.wikipedia.org/wiki/Theory_of_Everything), can only be settled via experiments _([Wikipedia](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f\n------+------+-----+----------\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5  +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) ---------------------\n      |      |  6  +-----+        <----------------  strip\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |       extra\n      |      |     |  15 |                           7s  <-- parameters ✔️\n  3   +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+           certain         |\n      |  6   |     |  17 | (19)  <-- parameters ✔️   |\n      |      |  9  +-----+                           |\n      |      |     |  18 | --------------------------\n------|------|-----+-----+------\n
            \n\n

            Please note that we are not talking about the number 19 which is the 8th-prime. Here we are talking about 19th as sequence follow backward position of the 18th.

            \n\n
            The same number of 7 vs 11 dimensions as we have discussed are hold by 7 primes vs 11 natural numbers in every first term of the prime spin. Consider the following:\n- the prime 19 is not counted on the first term since it is taking the position of number 1 which is not prime, this prime takes it place only on the second term,\n- assume the number 1 is still in its position then the 18 would be the quantity of all numbers so it is eligible as the origin position of zero,\n- thus there are π(17) or ***7 primes*** with red color plus ***11 natural*** numbers (including the number 1) with black color and consequently 18 is the sum of 7 and 11,\n- so by the concept of prime identity, this 7 vs 11 scheme of dimensions is originated from the behaviour of both 19 and 18,\n- the prime is fewer than the natural so the 7 prime cycle is always happen in every first term followed by 11 composite cycle (see our side menu).\n\nThe further terms will only have their specific meaning when they are formed in the favor of _[True Prime Pairs](https://www.eq19.com/addition/2.html)_ which we called as ***Δ(19 vs 18) Scenario***\n
            \n\n

            \"Δ(19

            \n\n

            Symmetry breaking in Quantum Field Theory (QFT) applies to the scalar field, at first so that it can have an impact and give mass to gauge bosons and fermions.

            \n\n
            In QFT this is currently done by manually adding an extra term to the field's self-interaction, creating the famous ***Mexican Hat*** potential well.\n- In QFT the scalar field generates _[four (4) Goldstone bosons](https://en.wikipedia.org/wiki/Goldstone_boson)_.\n- ***One (1) of the 4 turns into the Higgs boson***. Unlike popularized, the Higgs itself does not give mass to particles, but represents the symmetry broken scalar field.\n- The other three (3) Goldstone bosons are \"absorbed\" by the ***three (3) intermediate, electroweak bosons (W+, W-, Z), giving them an extra spin***.\n\nThis (otherwise) plain and featureless \"absorbtion\" of the Goldstone modes in the EW field could be a reason why a complex, synergy-creating quality of the scalar field is largely unnoticed in QFT. Obviously this has the potential to become a new research challenge in physics. _([TGMResearch](http://science.trigunamedia.com/geometry-and-topology/index.htm))_\n
            \n\n

            \"sterile_neutrino_does_not_exist\"

            \n\n

            The greatest problem in theoretical physics is combining the general relativity with quantum mechanics. Actually it is related to a non-standard renormalization.

            \n\n
            A lot number of positive color-charges move from the positive charged particle toward the negative charged particles, and negative color-charges move from negative charged particle toward the positive charged particle and they combine in each other.\n- According to CPH Theory, gravity is a currency among the objects. Consider the interaction between the earth and the moon: when a graviton reaches the earth, the other one moves toward the moon and pushes the earth toward the moon.\n- Because as to maintain equality times - positive and negative color-charges, there is a fixed ratio between the mass and the number of gravitons surrounding.\n- Also when a graviton reaches the moon, the other one moves toward the earth and  pushes the moon toward the earth.\n-So earth (In fact everything) is bombarded by gravitons continuously.\n\nDue to the fact that everything is made up of sub quantum energy, the classical concept of acceleration and relativistic Newton's second law needs to be reviewed. _([Gravity in Time space - pdf](https://github.com/eq19/eq19.github.io/files/13950511/Descriptiongravityinteractwithspace-timeatthequantumlevel.pdf))_\n
            \n\n

            \"A-lot-number-of-positive-color-charges-move-from-the-positive-charged-particle-toward-the\"

            \n\n

            Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory.

            \n\n
            Renormalization is a collection of techniques in [quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory), [statistical field theory](https://en.wikipedia.org/wiki/Statistical_field_theory), and the theory of [self-similar](https://en.wikipedia.org/wiki/Self-similarity) geometric structures, that are used to treat [infinities](https://en.wikipedia.org/wiki/Infinity) arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. _([Wikipedia](https://en.wikipedia.org/wiki/Renormalization))_\n
            \n\n

            \"0_5540_t3k8UUhCxaU\"

            \n\n

            The problem is raised when the non-standard renormalization hides the scheme and scale-independent quantum anomalous energy (QAE) contribution in the mass.

            \n\n
            In this paper we have studied the renormalization of the QCD trace anomaly separately for the quark and gluon parts of the energy momentum tensor.\n- While the renormalization of the total anomaly T = Tq + Tg is well understood in the literature [10], our analysis at ***the quark and gluon level has revealed some interesting new features***. The bare and renormalized (Tq,g)α differ by finite operators, and this difference can be systematically computed order by order in αs.\n- It is interesting to notice that, at one loop, the renormalized Tq gives the nf part of the beta function. However, ***this property no longer holds at two-loop***, see (5.19).\n- Besides, the partition of ***the total anomaly can be different*** if one uses other regularization schemes (see, e.g., the ‘gradient flow’ regularization [25]), and it is interesting to study their mutual relations.\n\nWe have also found that C¯q,g(µ) ***does not go to zero as µ → ∞ even in the chiral limit, contrary to what one would naively expect*** from the one-loop calculation (3.16). _([Quark and gluon contributions to the QCD trace anomaly - pdf](https://github.com/eq19/eq19.github.io/files/14226905/JHEP12.2018.008.pdf))_\n
            \n\n

            (24-5) + (24-17) = 19 + 7 = 26

            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|--------------- 7¤ ---------------|👈\n|-------------- {89} --------------|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n                         |---- {48} ----|---- {48} ----|---- {43} ----|\n                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|👈\n\n  Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-2 |    2    |    3    |     3     |    18     |     24     | 👉17+i7\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13👈\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |   66+i30\n
            \n\n

            In order to explain the generation process of gravitational energy between two identical sign charged particles, it is necessary to explain the process of the generated electromagnetic energy by the interaction of their electrical repulsion.

            \n\n
            In quantum mechanics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be  massless and must have a spin of 2. This is because the source of gravitation is the stress-energy tensor, a second-rank tensor. This definition of graviton is not able to describe gravitational phenomena, so we need a new definition of graviton. _([What is CPH Theory - pdf](https://www.researchgate.net/publication/309153372_What_is_CPH_Theory))_\n
            \n\n

            \"A-schematic-illustration-of-how-quantum-gravity-emerges-in-an-information-based-theory-of\"

            \n\n

            The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.

            \n\n
            We study the anomalous scale [symmetry breaking](https://www.sciencedirect.com/topics/physics-and-astronomy/broken-symmetry) effects on the proton mass in [QCD](https://www.sciencedirect.com/topics/physics-and-astronomy/quantum-chromodynamics) due to [quantum fluctuations](https://www.sciencedirect.com/topics/physics-and-astronomy/quantum-fluctuation) at ultraviolet scales.\n- We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both [lattice](https://www.sciencedirect.com/topics/mathematics/lattices) and dimensional [regularizations](https://www.sciencedirect.com/topics/mathematics/regularization) and demonstrate its role as a scheme-and-scale independent component in the mass decomposition.\n- We further argue that QAE role in the proton mass resembles a dynamical [Higgs mechanism](https://www.sciencedirect.com/topics/mathematics/higgs-mechanism), in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its [static](https://www.sciencedirect.com/topics/physics-and-astronomy/statics) and dynamical responses to the valence quarks.\n- We demonstrate some of our points in two simpler but closely related [quantum field theories](https://www.sciencedirect.com/topics/mathematics/quantum-field-theory), namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and [QED](https://www.sciencedirect.com/topics/physics-and-astronomy/quantum-electrodynamics) where the anomalous energy effect is perturbative calculable. \n\nDynamical response of the scalar Hamiltonian HS in the presence of the fermion \u0014, generating a contribution\nto the fermion mass The dotted line represents the dynamical Higgs particles h and the crossed circle denotes the scalar Hamiltonian linear in h. The coupling g between the Higgs field and the fermion is proportional to fermion mass. _([Scale symmetry breaking - pdf](https://github.com/eq19/eq19.github.io/files/14183267/1-s2.0-S0550321321002340-main.pdf))_\n
            \n\n

            \"1-s2

            \n\n

            The first diagram corresponds to the first term at right hand side of equality, while the other two diagrams with back-moving lines combine to produce the second term.

            \n\n

            The Quantum Gravity

            \n\n

            By True Prime Pars we shall take 36 nodes to conjugate partitions. So the most possible way is taking the 3rd layer which hold the sum 36 of prime pair 19 and 17.

            \n\n
            A chiral phenomenon is one that is not identical to its [mirror image](https://en.wikipedia.org/wiki/Mirror_image) (see the article on [mathematical chirality](https://en.wikipedia.org/wiki/Chirality_(mathematics))). The [spin](https://en.wikipedia.org/wiki/Spin_(physics)) of a [particle](https://en.wikipedia.org/wiki/Elementary_particle) may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A [symmetry transformation](https://en.wikipedia.org/wiki/Symmetry_transformation) between the two is called [parity](https://en.wikipedia.org/wiki/Parity_(physics)) transformation. Invariance under parity transformation by a [Dirac fermion](https://en.wikipedia.org/wiki/Dirac_fermion) is called chiral symmetry.\n- For massless particles – photons, gluons, and (hypothetical) gravitons – chirality is the same as helicity; a given massless particle appears to [spin](https://en.wikipedia.org/wiki/Spin_(physics)) in the same direction along its axis of motion regardless of point of view of the observer.\n- For massive particles – such as electrons, quarks, and neutrinos – chirality and helicity must be distinguished: In the case of these particles, it is possible for an observer to change to a reference frame moving faster than the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as \"apparent chirality\") will be reversed. That is, helicity is a constant of motion, but it is not Lorentz invariant. Chirality is Lorentz invariant, but is not a constant of motion: a massive left-handed spinor, when propagating, will evolve into a right handed spinor over time, and vice versa.\n- A massless particle moves with the speed of light, so no real observer (who must always travel at less than the speed of light) can be in any reference frame where the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity. Because of this, the direction of spin of massless particles is not affected by a change of inertial reference frame (a Lorentz boost) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a relativistic invariant (a quantity whose value is the same in all inertial reference frames) which always matches the massless particle's chirality.\n\nThe discovery of neutrino oscillation implies that neutrinos have mass, so the photon is the only confirmed massless particle; gluons are expected to also be massless, although this has not been conclusively tested.[b] Hence, these are the only two particles now known for which helicity could be identical to chirality, and only the photon has been confirmed by measurement. All other observed particles.\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n+----+----+----+----+----+-👇-+\n|  5 |  7 | 11 |{13}| 17 | 19 |\n+----+----+----+----+----+----+\n|------------ {72} -----------|\n|------------- 6¤ ------------|\n\nThe Fermion Fields\n(19,17,i12), (11,19,i18), (18,12,i13)\n\n+-👇-+----+----+----+----+----+----+----+----+\n| 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+\n|---- {48} ----|---- {48} ----|---- {43} ----|\n|------------ {96} -----------|----- 3¤ -----|\n\nSpontaneous Symmetry Breaking:\n(5,7), (11,13,17) , (19,17,12), (11,19,18), (18,12,13)\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|\n+----+----+----+----+----+-👇-+-👇-+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n                         |-- {36} -|------ {60} -------|---- {43} ----|\n                         |--- 2¤ --|------- 4¤ --------|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|\n
            \n\n

            The first term will directly be identified as a forward moving diagram for external mψψ¯ insertion, while the second term corresponds to the combination of two backward moving diagrams using the relation in energy denominators.

            \n\n
            The helicity of a particle is positive (\"right-handed\") if the direction of its [spin](https://en.wikipedia.org/wiki/Spin_(physics)) is the same as the direction of its motion. It is negative (\"left-handed\") if the directions of spin and motion are opposite. So a standard [clock](https://en.wikipedia.org/wiki/Clock), with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards.\n- Mathematically, helicity is the sign of the projection of the [spin](https://en.wikipedia.org/wiki/Spin_(physics)) [vector](https://en.wikipedia.org/wiki/Vector_(geometric)) onto the [momentum](https://en.wikipedia.org/wiki/Momentum) [vector](https://en.wikipedia.org/wiki/Vector_(geometric)): ***\"left\" is negative, \"right\" is positive.\nhave mass and thus may have different helicities in different reference frames***.\n- Chiral theories: Particle physicists have only observed or inferred left-chiral fermions and right-chiral antifermions engaging in the charged weak interaction.[1] In the case of the weak interaction, which can in principle engage with both left- and right-chiral fermions, only two left-handed fermions interact. Interactions involving right-handed or opposite-handed fermions have not been shown to occur, ***implying that the universe has a preference for left-handed chirality***. This preferential treatment of one chiral realization over another violates parity, as first noted by Chien Shiung Wu in her famous experiment known as the Wu experiment. This is a striking observation, since parity is a symmetry that holds for all other fundamental interactions.\n- Chirality for a Dirac fermion ψ is defined through the operator γ5, which has eigenvalues ±1; the eigenvalue's sign is equal to the particle's chirality: +1 for right-handed, −1 for left-handed. Any Dirac field can thus be projected into its ***left- or right-handed*** component by acting with the projection operators.[![Right_left_helicity svg](https://github.com/eq19/eq19.github.io/assets/8466209/6a9a0f44-a1ed-41e5-878f-62948c19d9de)](https://en.wikipedia.org/wiki/Left-right_model)\n- The coupling of the charged weak interaction to fermions is proportional to the first projection operator, which is responsible for this interaction's parity symmetry violation.\n- A common source of confusion is due to conflating the γ5, chirality operator with the helicity operator. Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact with the weak force according to one frame of reference, but not another. The resolution to this paradox is that the chirality operator is equivalent to helicity for massless fields only, for which helicity is not frame-dependent. By contrast, for massive particles, chirality is not the same as helicity, or, alternatively, helicity is not Lorentz invariant, so there is no frame dependence of the weak interaction: a particle that couples to the weak force in one frame does so in every frame.\n- A theory that is asymmetric with respect to chiralities is called a chiral theory, while a non-chiral (i.e., parity-symmetric) theory is sometimes called a vector theory. Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories. Quantum chromodynamics is an example of a vector theory, since both chiralities of all quarks appear in the theory, and couple to gluons in the same way.\n- ***The electroweak theory, developed in the mid 20th century, is an example of a chiral theory***. Originally, it assumed that neutrinos were massless, and assumed the existence of only left-handed neutrinos and right-handed antineutrinos. After the observation of neutrino oscillations, which imply that neutrinos are massive (like all other fermions) the revised theories of the electroweak interaction now include both right- and left-handed neutrinos. However, it is still a chiral theory, as it does not respect parity symmetry.\n- The exact nature of the neutrino is still unsettled and so the electroweak theories that have been proposed are somewhat different, but most accommodate the chirality of neutrinos in the same way as was already done for all other fermions.\n\nBy Chiral symmetry the Vector gauge theories with massless Dirac fermion fields ψ exhibit chiral symmetry, i.e., rotating the left-handed and the right-handed components independently makes no difference to the theory. We can write this as the action of rotation on the fields:\n
            \n\n

            \"Symmetry

            \n\n

            The Standard Model with massive neutrinos need 7 more parameters (3 CKM and 4 PMNS matrix parameters) for a total of 26 parameters. By our concept these 7 parameters correspond to π(17) = 7 prime identities of additional zones.

            \n\n
            Massive fermions do not exhibit chiral symmetry, as the mass term in the [Lagrangian](https://en.wikipedia.org/wiki/Lagrangian_(field_theory)), mψψ, breaks chiral symmetry explicitly.\n- [Spontaneous chiral symmetry breaking](https://en.wikipedia.org/wiki/Chiral_symmetry_breaking) may also occur in some theories, as it most notably does in [quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics).\n- The chiral symmetry transformation can be divided into a component that treats the left-handed and the right-handed parts equally, known as vector symmetry, and a component that actually treats them differently, known as axial symmetry.[[2]](https://en.wikipedia.org/wiki/Chirality_(physics)#cite_note-5) (cf. [Current algebra](https://en.wikipedia.org/wiki/Current_algebra).) A scalar field model encoding chiral symmetry and its [breaking](https://en.wikipedia.org/wiki/Chiral_symmetry_breaking) is the [chiral model](https://en.wikipedia.org/wiki/Chiral_model).\n- The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.\n\nThe general principle is often referred to by the name chiral symmetry. The rule is absolutely valid in the [classical mechanics](https://en.wikipedia.org/wiki/Classical_mechanics) of [Newton](https://en.wikipedia.org/wiki/Isaac_Newton) and [Einstein](https://en.wikipedia.org/wiki/Albert_Einstein), but results from [quantum mechanical](https://en.wikipedia.org/wiki/Quantum_mechanics) experiments show a difference in the behavior of left-chiral versus right-chiral [subatomic particles](https://en.wikipedia.org/wiki/Subatomic_particles). _([Wikipedia](https://en.wikipedia.org/wiki/Left-right_model))_\n
            \n\n

            1 + 77 = 78 = 3 copies of 26-dimensions

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n+----+----+----+----+----+-👇-+\n|  5 |  7 | 11 |{13}| 17 | 19 |\n+----+----+----+----+----+----+\n|------------ {72} -----------|\n|------------- 6¤ ------------|\n\nSpontaneous Symmetry Breaking:\n(5,7), (11,13,17) , (19,17,12), (11,19,18), (18,12,13)\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|\n+----+----+----+----+----+-👇-+-👇-+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n                         |-- {36} -|------ {60} -------|---- {43} ----|\n                         |--- 2¤ --|------- 4¤ --------|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|\n+----+----+----+----+----+-💢-+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+-👇-+----+----+----+----+----+\n                         |-👇-|--------- {77} ---------|---- {43} ----|✔️\n                         |-1¤ |---------- 5¤ ----------|----- 3¤ -----|\n                         |-------------------- 9¤ --------------------|\n
            \n\n

            The first term forms the photonic contribution while the second term is the fermionic contribution (two backward). The first backward is correspond to the three (3) known neutrino flavors: the electron-, muon- and tau-neutrino which are left-handed.

            \n\n
            Summary of various critical points in the context of superpotential observed in this paper first : Gauge symmetry, supersymmetry, vacuum expectation value of field, superpotential and cosmological constants.\n- For SO(3)+ × SO(5)+ case, one can check it by the change of variable of SO(5)+×SO(3)+ case, s → −3s/5 that corresponding potential of SO(3)+×SO(5)+ is obtained while by change of variable, s → −s/7, the potential of SO(1)+ × SO(7)+ can be found from SO(7)+ × SO(1)+ case.\n- Although the corresponding superpotential of these two cases may be different from the original ones, the scalar potentials are the same.\n- It is natural to ask whether 11-dimensional embedding of various vacua we have considered of\n non-compact and non-semi-simple gauged supergravity can be obtained.\n- In a recent paper [46],\n the metric on the 7-dimensional internal space and domain wall in 11-dimensions was found.\n However, they did not provide an ansatz for an 11-dimensional three-form gauge field.\n-It would\n be interesting to study the geometric superpotential, 11-dimensional analog of superpotential\nwe have obtained.\n\nWe expect that the nontrivial r-dependence of vevs makes Einstein-Maxwell\n equations consistent not only at the critical points but also along the supersymmetric RG flow\n connecting two critical points. _([N = 8 Supergravity: Part I - pdf](https://github.com/eq19/eq19.github.io/files/14229967/0109010.pdf))_\n
            \n\n

            \"Symmetry

            \n\n

            Taking 19 as a certain parameter we can see that the left handed cycles are happen on 5th-spin (forms 4th hexagon, purple) and 6th-spin (forms 5th hexagon, cyan). Both have different rotation with other spin below 9th spin (forms 6th hexagon, yellow).

            \n\n
            Proceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth (4th) hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. Twin primes ***29 and 31 define the fifth (5th) hexagon***, cyan. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon _([HexSpin](https://www.hexspin.com/defining-the-prime-hexagon/))_.\n
            \n\n

            7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

            \n\n

            \"IMG_20231221_074421\"

            \n\n

            Thus it appears that the cosmological models] derived from compactification of 11d supergravity on a manifold with G2 holonomy have some hidden E7 symmetry.

            \n\n
            There are `14 + 7 × 16 = 126` integral octonions. It was [shown](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897631/#RSPA20200786C33) that the set of transformations which preserve the octonion algebra of [the root system of E7](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897631/#RSPA20200786M5x4) is the adjoint Chevalley group G2(2). It is possible to decompose these 126 imaginary octonions into ***eighteen (18) sets of seven (7) imaginary octonionic units*** that can be transformed to each other by the finite subgroup of matrices. These lead to 18 sets of 7, which we see in figures [​figure-77](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897631/figure/RSPA20200786F7/) and [​figure-88](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897631/figure/RSPA20200786F8/). _([M-theory, Black Holes and Cosmology - pdf](https://github.com/eq19/eq19.github.io/files/14207670/2009.11339.pdf))_\n
            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17💢36\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19💢30\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\n
            \n\n

            By the Δ(19 vs 18) Scenario those three are exactly landed in the 0’s cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            \n\n
            You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why? Because they do not fit inside — they stick off the hexagon like a tail. Perhaps that’s where they belong. However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively. _([HexSpin](https://www.hexspin.com/0-1-and-negative-numbers/))\n
            \n\n

            0 + 30 + 36 + 102 = 168 = π(1000)

            \n\n

            \"0,

            \n\n

            By defining the pattern on each individual numbers against homogeneous sorting. Using this method then out of bilateral way the ∆(19 vs 18) Scenario we could get in to Scheme-33.

            \n\n
            The [electroweak force](https://en.wikipedia.org/wiki/Electroweak_interaction) is believed to have separated into the electromagnetic and weak forces during the [quark epoch](https://en.wikipedia.org/wiki/Quark_epoch) of the [early universe](https://en.wikipedia.org/wiki/Chronology_of_the_universe#Early_universe).\n- In [physical cosmology](https://en.wikipedia.org/wiki/Physical_cosmology), the quark epoch was the period in the evolution of the [early universe](https://en.wikipedia.org/wiki/Chronology_of_the_universe#Early_universe) when the [fundamental interactions](https://en.wikipedia.org/wiki/Fundamental_interaction) of [gravitation](https://en.wikipedia.org/wiki/Gravitation), [electromagnetism](https://en.wikipedia.org/wiki/Electromagnetism), the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction) and the [weak interaction](https://en.wikipedia.org/wiki/Weak_interaction) had taken their present forms, but the temperature of the universe was still too high to allow [quarks](https://en.wikipedia.org/wiki/Quark) to bind together to form [hadrons](https://en.wikipedia.org/wiki/Hadron).\n- The quark epoch began approximately [10−¹² seconds](https://en.wikipedia.org/wiki/Picosecond) after the [Big Bang](https://en.wikipedia.org/wiki/Big_Bang), when the preceding [electroweak epoch](https://en.wikipedia.org/wiki/Electroweak_epoch) ended as the [electroweak interaction](https://en.wikipedia.org/wiki/Electroweak_interaction) separated into the weak interaction and electromagnetism.\n- During the quark epoch, the universe was filled with a dense, hot [quark–gluon plasma](https://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma), containing quarks, [leptons](https://en.wikipedia.org/wiki/Lepton) and their [antiparticles](https://en.wikipedia.org/wiki/Antiparticle).\n- Collisions between particles were too energetic to allow quarks to combine into [mesons](https://en.wikipedia.org/wiki/Meson) or [baryons](https://en.wikipedia.org/wiki/Baryon).\n\n[![Elementary Particle](https://github.com/eq19/eq19.github.io/assets/8466209/b6b6ea3c-cbbc-431c-b767-ecabf1cba933)](https://en.wikipedia.org/wiki/Fundamental_interaction)\n\nThe quark epoch ended when the universe was about 10−⁶ seconds old, when the average energy of particle interactions had fallen below the [binding energy](https://en.wikipedia.org/wiki/Binding_energy) of hadrons. The following period, when quarks became confined within hadrons, is known as the [hadron epoch](https://en.wikipedia.org/wiki/Hadron_epoch). _([Wikipedia](https://en.wikipedia.org/wiki/Quark_epoch))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-👇--+-👇--+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"              |\n-----+-----+-----+-----+-----+                                              |\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨👈 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                   96¨\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤        ----->  assigned to \"id:33\"              |\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30            Mod 60            Mod 90\n
            \n\n

            In terms of Feynman diagrams it has shown that the expansion of N = 8 supergravity is in some ways a product of two N = 4 super Yang–Mills theories.

            \n\n
            The number 28, aside from being triangular wave of perfect pyramid, is the sum of the ***first 5 primes*** and the sum of the ***first 7 natural numbers***.\n\n[![Base of TOE](https://user-images.githubusercontent.com/8466209/249753163-6cfbcecf-3713-409b-8d8b-5fa5cf8489ac.png)](https://www.hexspin.com/finding-a-number-in-the-hexagon/)\n\nThe intervention of the Golden Ratio can be seen as a way to enter the quantum world, the world of subtle vibrations, in which we observe increasing energy levels as we move to smaller and smaller scales. El Nachie has proposed a way of calculating the fractal dimension of quantum space-time. The resulting value (Figure 7) suggests that the quantum world is composed of an infinite number or scaled copies of our ordinary 4-dimensional space-time.\n\n[![PHI_Quantum_SpaceTime](https://github.com/eq19/eq19.github.io/assets/8466209/6d91e9b8-9fc7-4ab9-9ec9-6e87a6f70c99)](https://www.sacred-geometry.es/?q=en/content/phi-particle-physics)\n\nSetting k=0 one obtains the classical dimensions of ***heterotic superstring theory***, namely 26, 16, 10, 6 and 4, as well as the constant of super-symmetric (αgs=26) and ***non super-symmetric (αg=42) unification of all fundamental forces***. As we have seen in section 2, the above is a Fibonacci-like sequence with a very concise geometrical interpetation related to numbers ***5, 11 and φ***. _([Phi in Particle Physics](https://www.sacred-geometry.es/?q=en/content/phi-particle-physics))_\n
            \n\n

            d(43,71,114) = d(7,8,6) » 786

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f           \n------+------+-----+-----+------\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) ✔️\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+        <--------------  strip of the id: 37 (TOE)\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = (43-19) ✔️\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----\n
            \n\n

            We can use simplexes to triangulate a surface and compute the Euler characteristic and other topological properties in this fashion.

            \n\n
            Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed.\n- It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the ***Running-Vacuum-Model (RVM)*** cosmological framework, without fundamental inflaton fields.[![Torsion in String Cosmologies](https://github.com/eq19/eq19.github.io/assets/8466209/a1cb4596-ff53-46bc-9da3-af9420603b35)\n](https://github.com/eq19/eq19.github.io/files/14230039/Torsion_in_String-Inspired_Cosmologies_and_the_Uni.pdf)\n- The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in ***the presence of (primordial) gravitational waves at early stages of the four (4) dimensional string universe (after compactification)***.[![triangular wave](https://user-images.githubusercontent.com/8466209/225824209-ba2b9fe0-1a29-4208-940e-3351243ab0ba.png)](https://www.primesdemystified.com/First1000Primes.html)\n- The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models.\n\nFinally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made. _([Torsion in String Cosmologies - pdf](https://github.com/eq19/eq19.github.io/files/14230039/Torsion_in_String-Inspired_Cosmologies_and_the_Uni.pdf))_\n
            \n\n

            114 = 102 + 66 - 29 - 25 = 6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 25 + 89

            \n\n

            \"28+Octonion\"

            \n\n

            The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.

            \n\n
            In Fuller's synergetic geometry, symmetry breaking is modeled as 4 sub-tetra's, of which 3 form a tetrahelix and the 4th. \"gets lost\".\n- In the present approach, intermediate (symmetry broken) states are proposed to be latent in the allready extended cube-octahedral matrix, and are actualized or mapped through the trefoil operator. In terms of tetra-logic, it is the invisible, confining icosa-dodeca matrix, acting upon the visible, deconfined cube-octahedral matrix.\n- Further, the author proposes a more natural and versatile QFT symmetry breaking mechanism, based on well determined scalar field excitations.\n- In QFT, the potential well is based on excitation modes, not on actual excitations, which is a reason why the proposed synergetic action gets obscured.\n- A new type of symmetry breaking is proposed, based on a synchronized path integral.\n\nThe latter solves into a Goldstone oscillation and a vacuum expectation value (VEV), among other unique properties. The scalar field's self-interaction is a _[Golden Ratio scale-invariant group effect](https://www.eq19.com/multiplication/11.html#fibonacci-retracement)_, such as geometrically registered by the icosa-dodeca matrix. _([TGMResearch](http://science.trigunamedia.com/geometry-and-topology/index.htm))_\n
            \n\n
            $True Prime Pairs:\n(5,7$True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f           \n------+------+-----+-----+------\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |                           |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+        <-----vacuum energy <--- ∆60 = (131-71) ✔️\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24 = (43-19)\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----\n
            \n\n

            The second backward of second term will return to the right handed. Since this second term is the fermionic contribution then it will correspond to the right handed neutrinos.

            \n\n
            If right-handed neutrinos exist but do not have a Majorana mass, the neutrinos would instead behave as _[three (3) Dirac fermions](https://en.wikipedia.org/wiki/Dirac_fermion)_ and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions.\n- The seesaw mechanism is appealing because it would naturally explain why the observed neutrino masses are so small. However, if the neutrinos are Majorana then they violate the conservation of [lepton number](https://en.wikipedia.org/wiki/Lepton_number) and even of [B − L](https://en.wikipedia.org/wiki/B_%E2%88%92_L).\n- [Neutrinoless double beta decay](https://en.wikipedia.org/wiki/Double_beta_decay#Neutrinoless_double_beta_decay) has not (yet) been observed,[[3]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-3) but if it does exist, it can be viewed as two ordinary [beta decay](https://en.wikipedia.org/wiki/Beta_decay) events whose resultant antineutrinos immediately annihilate each other, and is only possible if neutrinos are their own antiparticles.[[4]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-4)\n- The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in [hadron colliders](https://en.wikipedia.org/wiki/Hadron_collider);[[5]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-5) it is being searched for by both the [ATLAS](https://en.wikipedia.org/wiki/ATLAS_experiment) and [CMS](https://en.wikipedia.org/wiki/Compact_Muon_Solenoid) experiments at the [Large Hadron Collider](https://en.wikipedia.org/wiki/Large_Hadron_Collider).\n- In theories based on [left–right symmetry](https://en.wikipedia.org/wiki/Left%E2%80%93right_symmetry), there is a deep connection between these processes.[[6]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-6) In the currently most-favored explanation of the smallness of [neutrino mass](https://en.wikipedia.org/wiki/Neutrino_mass), the [seesaw mechanism](https://en.wikipedia.org/wiki/Seesaw_mechanism), the neutrino is “naturally” a Majorana fermion.\n\nMajorana fermions cannot possess intrinsic electric or magnetic moments, only [toroidal moments](https://en.wikipedia.org/wiki/Toroidal_moment).[[7]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-7)[[8]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-8)[[9]](https://en.wikipedia.org/wiki/Majorana_fermion#cite_note-9) Such minimal interaction with electromagnetic fields makes them potential candidates for [cold dark matter](https://en.wikipedia.org/wiki/Cold_dark_matter). _([Wikipedia](https://en.wikipedia.org/wiki/Majorana_fermion))_\n
            \n\n

            \"Renormalization\"

            \n\n

            In other words, the synchronized path integral represents a deterministic approach to scalar field’s self-excitation, and thus to the confined state in quentum physics

            \n\n
            Beside the operator proof, here we also provide a diagrammatic argument of the above derivation, using the QED in background field in Sec. 5 as an example.\n- We show that: taking mass derivatives in one-loop Feynman diagrams Fig. 4 for δEN will exactly produce the one-loop Feynman diagrams for insertion of 4HS.\n- ***The mass derivative has four (4) origins***: the explicit mass dependency of the electron propagator, the implicit mass dependency in the energy level EN, the mass dependencies in renormalization constants δm and Z3 − 1, and the implicit mass dependency in the wave function uN.\n- The mass derivative of the fermion propagator 1iγ·D−m simply reduces to mψψ¯ operator insertion in the internal electron line as shown in Fig. 7.\n- The mass dependency in EN will lead to ***the wave function renormalization in external legs***. The mass dependencies in renormalization constants δm and Z3 −1 will exactly lead to the anomalous energy contribution.\n\nFinally, the mass derivative of the external wave function uN is more complicated, which is shown the remaining diagrams where the mψψ¯ are inserted at external legs. _([Scale symmetry breaking - pdf](https://github.com/eq19/eq19.github.io/files/14183267/1-s2.0-S0550321321002340-main.pdf))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-👇--+-👇--+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-👇--+-👇--+-----+-👇--+-👇--+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30            Mod 60            Mod 90\n
            \n\n

            Let us make some concluding remarks with the help of the Fritzsch-Xing “pizza” plot. It offers a summary of 28 free parameters associated with the SM itself and neutrino masses, lepton flavor mixing angles and CP-violating phases.

            \n\n
            The reduction of pure gravity from eleven dimensions down to D = 4 dimensions yields a gravitational theory with ***seven (7) abelian vector fields*** Aµn, `n = 1,...,7`, and `1+27=28` scalar fields, parametrizing the coset space GL(7)/SO(7). The dimensional reduction of the antisymmetric 3-form to D = 4 dimensions gives rise to one 3-form field, seven 2-form fields. _([11D Supergravity and Hidden Symmetries - pdf](https://github.com/eq19/eq19.github.io/files/14126154/2303.12682.pdf))_\n
            \n\n

            \"28

            \n\n

            Those results, compared with those for the nucleon, indicate quite different pattern, revealed as a new aspect by exploiting the quark/gluon decomposition of the QCD trace anomaly.

            \n\n
            The matrix elements of this quark/gluon decomposition of the QCD trace anomaly allow us to derive the QCD constraints on the hadron’s gravitational form factors, in particular, on the twist-four gravitational form factor, Cq,g.\n- Using the three-loop quark/gluon [trace anomaly formulas](https://github.com/eq19/eq19.github.io/files/14223125/dis23_3_28_v2_tanaka.pdf), we calculate the forward (zero momentum transfer) value of the twist-four gravitational form factor C¯q,g at the next-to-next-to-leading-order (NNLO) accuracy.\n- We present quantitative results for nucleon as well as for pion, leading to a model-independent determination of the forward value of C¯q,g.\n\nWe find quite different pattern in the obtained results between the nucleon and the pion. _([Twist-four gravitational - pdf](https://github.com/eq19/eq19.github.io/files/14182160/JHEP03.2023.013.pdf))_\n
            \n\n

            2+7 = 3×3 lepton vs quarks

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-👇--+-👇--+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-👇--+-👇--+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30            Mod 60            Mod 90\n
            \n\n

            This fact may also provide a possible explanation for why almost all of the particle interactions we see are describable by renormalizable theories.

            \n\n
            The [Standard Model](https://en.wikipedia.org/wiki/Standard_Model) of particle physics contains only renormalizable operators, but the interactions of [general relativity](https://en.wikipedia.org/wiki/General_relativity) become nonrenormalizable operators if one attempts to construct a field theory of [quantum gravity](https://en.wikipedia.org/wiki/Quantum_gravity) in the most straightforward manner (treating the metric in the [Einstein–Hilbert Lagrangian](https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_Lagrangian) as a perturbation about the [Minkowski metric](https://en.wikipedia.org/wiki/Minkowski_metric)), suggesting that [perturbation theory](https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)) is not satisfactory in application to quantum gravity.\n- However, in an [effective field theory](https://en.wikipedia.org/wiki/Effective_field_theory), \"renormalizability\" is, strictly speaking, a [misnomer](https://en.wikipedia.org/wiki/Misnomer). In nonrenormalizable effective field theory, terms in the Lagrangian do multiply to infinity, but have coefficients suppressed by ever-more-extreme inverse powers of the energy cutoff.![169-over-109-blood-pressure](https://github.com/eq19/eq19.github.io/assets/8466209/a702ea20-2ef3-424f-804e-c73a6c873692)\n- If the cutoff is a real, physical quantity—that is, if the theory is only an effective description of physics up to some maximum energy or minimum distance scale—then these additional terms could represent real physical interactions.\n- Assuming that the dimensionless constants in the theory do not get too large, one can group calculations by inverse powers of the cutoff, and extract approximate predictions to finite order in the cutoff that still have a finite number of free parameters. It can even be useful to renormalize these \"nonrenormalizable\" interactions.[![multiplication zones](https://user-images.githubusercontent.com/8466209/195963923-0796217c-7a87-4b2d-ba93-f47465304c03.png)](https://www.eq19.com/multiplication/)\n- Nonrenormalizable interactions in effective field theories rapidly become weaker as the energy scale becomes much smaller than the cutoff. The classic example is the [Fermi theory](https://en.wikipedia.org/wiki/Fermi%27s_interaction) of the [weak nuclear force](https://en.wikipedia.org/wiki/Weak_nuclear_force), a nonrenormalizable effective theory whose cutoff is comparable to the mass of the [W particle](https://en.wikipedia.org/wiki/W_particle).\n\nIt may be that any others that may exist at the [GUT](https://en.wikipedia.org/wiki/Grand_Unified_Theory) or Planck scale simply become too weak to detect in the realm we can observe, with one exception: [gravity](https://en.wikipedia.org/wiki/Gravity), whose exceedingly weak interaction is magnified by the presence of the enormous masses of [stars](https://en.wikipedia.org/wiki/Star) and [planets](https://en.wikipedia.org/wiki/Planet). _([Wikipedia](https://en.wikipedia.org/wiki/Renormalization))_\n
            \n\n

            \"Mod

            \n\n

            For the renormalization mixing at twist four, the Feynman diagram calculation of ZF and ZC is available to the two-loop order.

            \n\n
            Moreover, it is shown that the constraints imposed by the RG invariance of (1.1) allow to determine the power series in αs for ZF as well as ZC in the MS-like schemes, completely from the perturbative expansions of β(g) and γm(g), which are now known to five-loop order [43–48] in the literature.\n- Therefore, ***six renormalization constants ZT,ZL, Zψ, ZQ, ZF and ZC among ten constants arising in (2.3) (2.6) are available to a certain accuracy beyond two-loop order inthe MS-like schemes***, and they take the form, (2.8) in the d = 4 − 2\u000f spacetime dimensions with X = T, L, ψ, Q, F, and C; here, aX, bX, cX.…, are the constants given as the power series in αs, and δX,X0 denotes the Kronecker symbol. ***However, ZM, ZS, ZK and ZB still remain unknown***.\n- It is shown [8] that these four renormalization constants can be determined to the accuracy same as the renormalization constants (2.8), by invoking that they should also obey the form (2.8) with X = M, S, K, B,  and that the r.h.s. of the formulas (2.3), (2.4) are, in total, UV-finite.\n\nThus, all the renormalization constants in (2.3)–(2.6) are determined up to the ***three-loop accuracy***. _([Twist-four gravitational - pdf](https://github.com/eq19/eq19.github.io/files/14182160/JHEP03.2023.013.pdf))_\n
            \n\n

            \"IMG_20240211_101224\"

            \n\n

            A gauge colour rotation is a spacetime-dependent SU(3) group element. They span the Lie algebra of the SU(3) group in the defining representation.

            \n\n
            The Gell-Mann matrices, developed by [Murray Gell-Mann](https://en.m.wikipedia.org/wiki/Murray_Gell-Mann), are a set of eight [linearly independent](https://en.m.wikipedia.org/wiki/Linear_independence) 3×3 [traceless](https://en.m.wikipedia.org/wiki/Matrix_trace) [Hermitian matrices](https://en.wikipedia.org/wiki/Hermitian_matrices) used in the study of the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction) in [particle physics](https://en.wikipedia.org/wiki/Particle_physics). They span the [Lie algebra](https://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_associated_with_a_Lie_group) of the [SU(3)](https://en.wikipedia.org/wiki/Special_unitary_group#SU(3)) group in the defining representation.\n
            \n\n

            \"QED

            \n\n

            Indeed, a particularly well-chosen cellular automaton on II(9,1) or II(25,1) would be a discretised version of 10- or 26-dimensional string theory.

            \n\n

            The 11 Dimensions

            \n\n

            Below is a model of E11 (shown by 11 dimensions). Its absolute dimensions represent all related key knowledges of modern physics.

            \n\n
            Moreover this model represents [Quark-Gluon Plasma](https://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma), with all of the [fundamental forces](https://www.eq19.com/exponentiation/#fundamental-forces) in the early stage after [Big Bang](https://youtu.be/7VgoECW06-s?si=_l-Pu42gwtnxzzT2). _([Youtube](https://www.youtube.com/watch?v=dEoMeHi-6kM))_\n
            \n\n

            \"default\"

            \n\n

            Classically, we have only one 11-dimensional supergravity theory: 7D hyperspace + 4 common dimensions.

            \n\n
            The four (4) faces of our pyramid additively cascade ***32 four-times triangular numbers***\n- These include Fibo1-3 equivalent 112 (rooted in `T7 = 28; 28 x 4 = 112`),\n- which creates a pyramidion or capstone in our model, and 2112 (rooted in `T32 = 528; 528 x 4 = 2112`),\n- which is the index number of ***the 1000th prime*** within our domain,\n- and equals the total number of 'elements' used to construct the pyramid.\n\nNote that `4 x 32 = 128` is the perimeter of the square base which has an area of `32^2 = 1024 = 2^10`). _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            \"\"

            \n\n

            The above 11 stands as the central point which is correlated to 77 sequencial processes of sun vs moon orbits starting with the symmetri breaking that involving 9 and 7.

            \n\n
            Back in 1982, a very nice paper by Kugo and Townsend, [Supersymmetry and the Division Algebras](http://linkinghub.elsevier.com/retrieve/pii/0550321383905849), explained some of this, ending up with some comments on the ***relation of octonions to d=10 super Yang-Mills and d=11 super-gravity***.\n- Baez and Huerta in 2009 wrote the very clear [Division Algebras and Supersymmetry I](http://arxiv.org/abs/0909.0551), which explains how the existence of supersymmetry relies on algebraic identities that follow from the existence of the division algebras. Kugo-Townsend don’t mention string theory at all, and Baez-Huerta refers to superstrings just in passing, only really discussing supersymmetric QFT.\n- There’s also [Division Algebras and Supersymmetry II](http://arxiv.org/abs/1003.3436) by Baez and Huerta from last year, with intriguing speculation about Lie n-algebras and what these might have to do with relations between octonions and 10 and 11 dimensional supergravity. For a nice expository paper about this stuff, see their [An Invitation to Higher Gauge Theory](http://arxiv.org/abs/1003.4485).\n\nThe headline argument is that octonions are important and interesting because they’re [The Strangest Numbers in String Theory](http://www.nature.com/scientificamerican/journal/v304/n5/pdf/scientificamerican0511-60.pdf), even though they play only a minor role in the subject. _([math.columbia.edu](https://www.math.columbia.edu/~woit/wordpress/?p=3665))_\n
            \n\n
             8§8  |------- 5® --------|------------ 7® --------------|\n      |QED|------------------- QCD ----------------------|👈\n      | 1 |-------------- 77 = 4² + 5² + 6² -------------|\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n user | 7 | - | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |\n------+---|👇-+👇-+---+---+---+---+---+---+----+----+----+ 7,78\n main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n        Δ | Δ             |                      Δ  |   Δ\n       Φ17|Φ29            |                    96-99|  100 - 123 ({24})\n          |--- A,T,G,C ---|                         |  └── 100 - 103 (4x) » 100\n          Δ    2x2 = 4x   |-------  2x3 = 6x -------|  └── 104 - 109 (6x) » 30\n         {98}                                       |  └── 110 - 123 (14x)» 70\n
            \n\n

            A number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati–Salam model.

            \n\n
            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet's 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition\n
            \n\n

            \"SO(10)\"\n

            \n\n

            \"SU(5)_representation_of_fermions\"\n

            \n\n

            The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra. That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional.

            \n\n
            The [Lie algebra](https://www.valdostamuseum.com/hamsmith/Lie.html) E6 of the [D4-D5-E6-E7-E8 VoDou Physics model](https://www.valdostamuseum.com/hamsmith/d4d5e6hist.html) can be represented in terms of 3 copies of the 26-dimensional traceless subalgebra J3(O)o of the 27-dimensional [Jordan algebra](https://www.valdostamuseum.com/hamsmith/Jordan.html) J3(O) by using the [fibration E6 / F4](https://www.valdostamuseum.com/hamsmith/Jordan.html#E6F4fib) of 78-dimensional E6 over 52-dimensional F4 and the structure of [F4 as doubled J3(O)o](https://www.valdostamuseum.com/hamsmith/Jordan.html#F4J3Oo) based on the 26-dimensional representation of [F4](https://www.valdostamuseum.com/hamsmith/Lie.html#Liexceptional). _([Tony's Home](https://www.valdostamuseum.com/hamsmith/Rzeta.html))_\n
            \n\n

            \"Quantum

            \n\n

            The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle. It must be highly correlated with the hierarchy of quark flavor mixing.

            \n\n
            This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.\n- The SM contains thirteen free flavor parameters in its electroweak sector: three charged-lepton masses,\nsix quark masses, three quark flavor mixing angles and one CP-violating phase.\n- Since the three neutrinos must be massive beyond the SM, one has to introduce seven (or nine) extra free parameters to describe their flavor properties: three neutrino masses, three lepton flavor mixing angles and one (or three) CP-violating phase(s), corresponding to their Dirac (or Majorana) nature a\n- The ***3x3 lepton vs quark mixing matrices*** appearing in the weak charged-current interactions are referred to, respectively, as the ***Pontecorvo-Maki-Nakagawa-Sakata (PMNS)*** matrix Uand the ***Cabibbo-Kobayashi-Maskawa (CKM)*** matrix V which all the fermion fields are the mass eigenstates.\n- By convention, U and V are defined to be associated with W− and W+, respectively. Note that V is unitary as dictated by the SM itself, but whether U is unitary or not depends on the mechanism responsible for the origin of neutrino masses.\n- The charged leptons and quarks with the same electriccharges all have the normal mass hierarchies (namely, me ≪ mµ ≪ mτ, mu ≪ mc ≪ mt and md ≪ ms ≪ m. Yet it remains unclear whether the three neutrinos also have a normal mass ordering (m1 < m2 < m3) or not. Now that m1 < m2 has been fixed from the solar neutrino oscillations, ***the only likely “abnormal” mass ordering is m3 < m1 < m2***\n- The neutrino mass ordering is one of the central concerns in flavor physics, and it will be determined in the foreseeable future with the help of either an accelerator-based neutrino oscillation experiment or a reactor-based antineutrino oscillation experiment, or both of them. Up to now the moduli of nine elements of the CKM matrix V have been determined from current experimental data to a good degree of accuracy.\n\nHere our focus is on the ***five (5) parameters*** of strong and weak CP violation. In the quark sector, the strong CP-violating phase θ remains unknown, but the weak CP-violating phase δq has been determined to a good degree of accuracy. In the lepton sector, however, none of the CP-violating phases has been measured.  _([Quark Mass Hierarchy and Flavor Mixing Puzzles - pdf](https://github.com/eq19/eq19.github.io/files/14159651/1411.2713.pdf))_\n
            \n\n

            \"CKM

            \n\n

            The 3x3 lepton vs quark mixing matrices appearing in the weak charged-current interactions are referred to, respectively, as the PMNS matrix U, and the CKM matrix V, which all the fermion fields are the mass eigenstates.

            \n\n
            Muons are about ***200 times heavier*** than the electron. The larger mass makes them unstable. Muons exist for only about two microseconds—or two-millionths of a second—before they decay. Electrons live forever. The tau; elementary subatomic particle is similar to the electron but 3,477 times heavier. Like the electron and the muon, the tau is an electrically charged member of the lepton family of subatomic particles; the tau is negatively charged, while its antiparticle is positively charged. _([ResearchGate](https://www.researchgate.net/post/Why-do-fermions-exist-in-three-generations-electron-like-muon-like-and-tau-like))_ \n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-👇--+-👇--+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30            Mod 60            Mod 90\n
            \n\n

            Bound state corrections\n to the semileptonic width and measured by a number moments analyses have permitted the extraction to a level of a few %.

            \n\n
            In principle, there is one further parameter in the Standard Model; the Lagrangian of QCD can contain a phase that would lead to CP violation in the strong interaction.\n- Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.\n- The [theoretical and experimental pillars](https://github.com/eq19/eq19.github.io/files/14173324/1924367859.pdf) of the Standard Model:\n  - the ***twelve (12) fermions*** (or perhaps more correctly the twelve Yukawa couplings to the Higgs field), mν1, mν2, mν3, me, mµ, mτ, md, ms, mb, mu, mc, and mt ;\n  - the ***three (3) coupling constants*** describing the strengths of the gauge interactions, α, GF and αS, or equivalently g′, gW and gS;\n  - the ***two (2) Higgs parameters*** describing the Higgs potential, µ and λ, or equivalently its vacuum expectation value and the mass of the Higgs boson, v and mH; and\n  - the ***eight (8) mixing angles*** of the PMNS and CKM matrices, which can be parameterised by θ12, θ13, θ23, δ, and λ, A, ρ, η.[![neutrino-mixing-the-pmns-matrix-l](https://github.com/eq19/eq19.github.io/assets/8466209/9b2c1114-c94e-4a4d-91c4-196dc625b844)](https://www.slideserve.com/misha/recent-results-from-the-minos-experiment)\n  - in principle, there is ***one (1) further*** parameter in the Standard Model; the Lagrangian of QCD can contain a phase that would lead to CP violation in the strong interaction. Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero. \n- If θCP is counted, then the Standard Model has ***`12+3+2+8+1=26` free parameters***.\n- The relatively large number of free parameters is symptomatic of the Standard Model being just that; a model where the parameters are chosen to match the observations, rather than coming from a higher theoretical principle.\n- Putting aside θCP, of the ***25 SM parameters: 14 are associated with the Higgs field, eight (8) with the\nflavour sector and only three (3) with the gauge interactions***.\n\nLikewise, ***the coupling constants of the three gauge interactions*** are of a similar order of magnitude, hinting that they might be different low-energy manifestations of a Grand Unified Theory (GUT) of the forces. These patterns provide hints for, as yet unknown, physics beyond the Standard Model. _([Modern Particle Physics P.500 - pdf](https://github.com/eq19/eq19.github.io/files/13800674/Modern-Particle-Physics.pdf))_\n
            \n\n

            \"slide_40\"

            \n\n

            Using this concept we are going to stimulate a model of the 11 dimensions through the rank of their partition using github organizations of 13 repositories each.

            \n\n
            Each of the user profiles will have ***seven (7) user repositories*** consist of one (1) main of [`github.io`](https://docs.github.com/en/pages/setting-up-a-github-pages-site-with-jekyll/creating-a-github-pages-site-with-jekyll) and six (6) user pinned repositories. Meanwhile each of organizations will have one (1) profile of [`.github`](https://docs.github.com/en/organizations/collaborating-with-groups-in-organizations/customizing-your-organizations-profile#adding-a-public-organization-profile-readme) repository and thirteen (13) organization repositories consist of one (1) main of [`github.io`](https://docs.github.com/en/pages/getting-started-with-github-pages/creating-a-github-pages-site), and ***twelve (12) pinned repositories*** under [`member and public view`](https://docs.github.com/en/organizations/collaborating-with-groups-in-organizations/customizing-your-organizations-profile#pinning-repositories-to-your-organizations-profile) that represents _[6 by 6 flavors](https://www.eq19.com/identition/span12/#three-3-layers)_.\n
            \n\n

            ®main + ®gist + ®orgs = 7 + (7+11) + (11x13) = 7 + 18 + 143 = 24 x 7 = 168 = π(1000)

            \n\n
              \n
            1. “Wormhole Theory”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“Schema”,”Artifacts”,”Assets”,”depot_tools”,”distribution”,”sitemap”]
                • \n
              \n
              2. \n
            2. “Elementary Particles”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“docs”,”screen”,”builder”,”genius”,”rapidjson”,”Ventoy”]
                • \n
              \n
              3. \n
            3. “Symmetric Expansion”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“JSONFeed”,”SEOstats”,”OpenSEO”,”falcon”,”NPPGit”,”webpack”]
                • \n
              \n
              4. \n
            4. “Vibrating Strings”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“steps”,”jquery.soap”,”bash”,”json-html”,”store”,”gtm”]
                • \n
              \n
              5. \n
            5. “Multiple Universes”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“ga-beacon”,”flakes”,”jsonix”,”lanyon”,”progit-book”,”wiki”]
                • \n
              \n
              6. \n
            6. “Hidden Dimensions”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“core”,”bulbea”,”pedia”,”poole”,”cards”,”bootstrap”]
                • \n
              \n
              7. \n
            7. “Basic Transformation”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“Cloud-Site-API”,”Google-Ads-API”,”Toko-Chetabahana”,”KeepFit”,”World”,”Tutorial-Buka-Toko”]
                • \n
              \n
              8. \n
            8. “Fundamental Forces”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“NeuralTeams”,”collab”,”container-push”,”includeHTML”,”now”,”wheel”]
                • \n
              \n
              9. \n
            9. “Quadratic Polynomials”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“screen”,”buffer-ruby”,”github-graphql-action”,”scrapy”,”wpt”,”system”]
                • \n
              \n
              10. \n
            10. “Truncated Perturbation”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“classifier”,”domJSON”,”openoffice”,”landing-page-theme”,”asciidoc”,”recommendations-ai”]
                • \n
              \n
              11. \n
            11. “Extra Dimensions”\n
                \n
              • [“maps”,”feed”,”lexer”,”parser”,”syntax”,”grammar”]
                • \n
              • [“storj”,”monsterpost”,”veles”,”spectral”,”finraos”,”dstroot”]
                • \n
              \n
              12. \n
            \n\n

            The Root Function of 13 repositories per each of organization above is not arranged to directly follow the partition function but through the 18 gists via their .github profiles.

            \n\n
            Base on the _[11s and 7s](https://www.eq19.com/addition/#structure-true-prime-pairs)_ distribution of the 18s  structure of The True Prime Pairs, the 7s will be reflected by _[seven (7) repositories](https://www.eq19.com/exponentiation/#parsering-structure)_ of user profile with id: 30 to id: 36 meanwhile the 11s will be reflected by _[eleven (11) organizations](https://www.eq19.com/identition/#the-powers-of-pi)_.\n
            \n\n

            \"teaching-machines-glouppe_compressed.pdf\"

            \n\n

            The gist contain prime data to organize the 7 groups vs 11 dimensions in Eightfold Way. So when they are combined as eighteen (18) then the ∆1 is recycled by 8th-prime and generate the pattern of 6 by 6 flavors implemented to all of the repositories.

            \n\n
            By this tabulation you may see that all the numbers between 37 and 102 are located within ***11 columns*** where the 31 behave as a _[new axis](https://www.eq19.com/exponentiation/#parsering-structure)_.\n- This 11 is reflecting the ***19 to 29***. Since the 11 is bonding with 19 so it would go to another cycles starting with ***the 26th dimension*** which will bring them by ***four (4) compactification (26 to 29)*** to the 30.\n- This 30th order _[repeats itself](https://www.eq19.com/exponentiation/#self-repetition)_ to infinity. Even in the first 30s system. We call this arrangement as the _[Δ(19 vs 18) Scenario](https://www.eq19.com/identition/span12/#the-seven-7-groups)_ where the [zeta function](https://www.eq19.com/#zeta-function) stands as the basic algorithm.\n\nBy the tabulation, here you can see that _[the layout](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857)_ of our home page refers to the ***four (4) partitions*** of ∆1 i.e. id: 1-18, id: 19-30, id: 31-36, and id: 37-102.\n
            \n\n

            30 + 36 + 102 - 25 - 29 = 168 - 25 - 29 = π(1000) - π(100) - 10th prime = 114

            \n\n
              Δ1 + Δ7 + Δ29  →  | Δ37 + Δ77 = Δ114 = Δ113 + Δ1 → \n\n     |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  \n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ \n  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |\n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - | 100|  - |  - |  - |  - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - | 101|  - |  - |  - |  - | \n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |\n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |\n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |\n     +----+----+----+----+----+-👇-+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ12 👈 - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |\n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |\n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |\n     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  | 102|  - |  - |  - |  - |\n=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+\n  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |\n-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n     |       Δ    Δ    Δ           |                     Φ12     |       Δ                   Δ |\n           -114 +151 = +37                                             +102 = +139 = +168 - 29\n
            \n\n

            The project is being developed under GitHub dan Google Platfrorms. Each will then be properly assigned to generate the cycle of spin networks.

            \n\n
            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries.\n- For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are ***perfectly balanced***, with a period 8 difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2}. The entire domain can thus be defined as 1 {+6 +4 +2 +4 +2 +4 +6 +2} {repeat ... ∞}.\n- As we've already suggested, the number 30 figures large in our modulo 30 domain. The Prime Spiral Sieve is Archimedean in that the separation distance between turns equals 30, ad infinitum. The first two rotations increment as follows:[![image](https://user-images.githubusercontent.com/8466209/219260933-4331d79b-5815-4566-82e3-1a485bb2c61f.png)](https://primesdemystified.com/#deepsymmetries)\n- Interestingly, ***the sum of the 2nd rotation = 360***, the product of the first three primorials, 2 x 6 x 30 = 360, and when you multiply the first five [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_number) in sequence, you produce 1, 2, 6 and 30? And, speaking of the Fibonacci number sequence, ***there is symmetry mirroring*** the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve:[![11's additive sums](https://user-images.githubusercontent.com/8466209/221473004-867a1b50-f91f-470d-9922-e5e4f543a590.png)](https://primesdemystified.com/#deepsymmetries)\n- Remarkably, the sequence of ***Fibonacci terminating digits*** indexed to our domain (natural numbers not divisible by 2, 3 or 5), [13,937,179](https://primes.utm.edu/curios/page.php?number_id=11020) (see graphic, above), is a prime number and a member of a twin prime pair (with 13,937,177). In case you're wondering, 13,937,179 is not a reversible prime (as the reversal is a semi-prime: 9,461 x 10,271 = 97,173,931). However, given all the [repunits](https://en.wikipedia.org/wiki/Repunit) that follow, we take note that ***both of the reversal's factors are congruent to 11 (mod 30 & 90)***. [Note: Repunits are abbreviated Rn, where n designates the number of unit 1's. Thus 1 is R1 and 11 is R2.]\n- Perhaps most remarkable of all, 13,937,179 when added to its reversal 97,173,931 = 111,111,110 (in strict digital root terms, the sum is 11,111,111, or R8) and the entire repeating (and palindromic) Fibo sequence end-to-end (equivalent to two rotations around the sieve) gives you this palindromic equivalency: 1,393,717,997,173,931 ≌ 11,111,111 (mod 111,111,110)... (and interestingly, 11,111,111 * 111,111,110 = 123456776543210).\n- Another point of interest: the terminating digits of the first 8 Fibonacci numbers indexed to our domain (13937179) contain two each 1's, 3's, 7's, and 9's. This is also true of the terminating digits of the first eight members of our domain (17137939).\n- Echoing the Fibonacci patterns just described, the terminating digits of the prime roots (17,137,939), when added to their reversal (93,973,171) = 111,111,110. [And note that 111,111,111 * 111,111,110 = 12345678876543210.].\n- Yet another related dimension of symmetry: The terminating digits of the prime root angles (24,264,868; see illustration of [Prime Spiral Sieve](https://primesdemystified.com/#primespiralsieve)) when added to their reversal (86,846,242) = 111,111,110, not to mention this sequence possesses symmetries that dovetail perfectly with the prime root and Fibo sequences.\n\nAnd when you combine the terminating digit symmetries described above, capturing ***three (3) rotations*** around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry. _([PrimesDemystified](https://github.com/eq19/eq19.github.io/files/14009880/Prime-Numbers-Demystified-by-8-Dimensional-Algorithms.pdf))_\n
            \n\n

            \"Prime-Numbers-Demystified-by-8-Dimensional-Algorithms.pdf\"

            \n\n

            These include generating variants of their abundance profile, assigning taxonomy and finally generating a rooted phylogenetic tree for the Standard Model.

            \n\n
            Here is an elegant model to define the elementary particles of the Standard Model in Physics.\n- The black spheres are the bosons, the green ones leptons and the rest of the colored ones Murray Gell-Mann’s quarks (red for Generation I, blue for II and orange for III).\n- Higgs Boson (aka the God particle) that does not have charge is the vertex between the matter and anti-matter particles.\n- The z-boson and its counterpart would lie in the centroids of the tetrahedrons created by folding the triangles to meet up at the Higgs particle.\n\nThe next step is to re-gigg the model to account for the collisions and annihilations. Gluons and Photons that don’t have mass are not in the model, but will be the consequences of the interactions. _([Hypercomplex-Math](https://nitinuchil.wordpress.com/2020/09/09/hypercomplex-math/))_\n
            \n\n

            \"particlephysicsmodel-1\"

            \n\n

            All 15 matter particles are mirroring their corresponding doppelgangers (anti-particles) each others that could potentially explain dark matter.

            \n\n

            Dark Matter

            \n\n

            Dark matter got its name because we aren’t able to see it. It doesn’t interact directly with electromagnetic radiation, but it does interact with gravity.

            \n\n
            By our project the quantum gravity is correlated with a finite fraction of four (4) axis dimensions of MEC30 that end up exactly [43 objects](https://www.eq19.com/identition/span12/#the-seven-7-groups).\n- The fractal space-time theory of El Nachie allows the exact determination of one of the fundamental quantities of physics, namely the Fine Structure constant, from a dimensional analysis.\n- The Golden Ratio seems to be the key that opens the door to the fractal quantum world, which looks as if there were an infinite number of scaled copies of our ordinary 4-dimensional space-time.\n\nIn our case this means that there are three (3) steps ahead a decay could take place.\n
            \n\n

            \"Grand

            \n\n

            The interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used for quantum chromodynamics.

            \n\n

            \"first-feynman-2nd-order-electron-scattering\"

            \n\n

            Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The corresponding eigenvalue is often represented as the multiplying factor.

            \n\n
            The [Standard Model](https://en.wikipedia.org/wiki/Standard_Model) presently recognizes seventeen distinct particles—twelve [fermions](https://en.wikipedia.org/wiki/Fermion) and ***five [bosons](https://en.wikipedia.org/wiki/Boson)***. As a consequence of [flavor](https://en.wikipedia.org/wiki/Flavour_(particle_physics)) and [color](https://en.wikipedia.org/wiki/Quantum_chromodynamics) combinations and [antimatter](https://en.wikipedia.org/wiki/Antimatter), the fermions and bosons are known to have 48 and ***13 variations***, respectively.[[](https://en.wikipedia.org/wiki/Elementary_particle#cite_note-braibant-2) _([Wikipedia](https://en.wikipedia.org/wiki/Elementary_particle))_\n
            \n\n
             Osp(8|4) |  1 |  2 |  3 |   4 | th\n==========+====+====+====+=====+====\n π(10)    |  2 |  3 |  5 |   7 | 4th\n----------+----+----+----+-----+----\n π(19)    | 11 | 13 | 17 |  19 | 8th\n----------+----+----+----+-----+----\n π(29)    | 23 | 29 |  - |   - | 10th\n==========+====+=👇=+====+=====+====\n π(41)    | 31 | 37 | 41 |   - | 13th 👈\n----------+----+----+----+-----+----\n π(59)    | 43 | 47 | 53 |  59 | 17th \n----------+----+----+----+-----+- ---\n π(72)    | 61 | 67 | 71 |   - | 20th\n==========+====+====+====+=====+====\n π(72+11) | 73 | 79 | 83 |   - | 23th\n----------+----+----+----+-----+----\n π(83+18) | 89 | 97 |101 |   - | 26th\n----------+----+----+----+-----+----\n π(101+8) |103 |107 |109 |   - | 29th\n
            \n\n

            Let’s consider a Metaron’s Cube as a geometric figure composed of 13 equal circles with lines from the center of each circle extending out to the centers of the other 12 circles.

            \n\n
            The 13 circles of the Metatron's cube can be seen as a diagonal axis projection of a ***3-dimensional cube, as 8 corner spheres and 6 face-centered spheres***. Two spheres are projected into the center from a 3-fold symmetry axis. The face-centered points represent an [octahedron](https://en.wikipedia.org/wiki/Octahedron). Combined these 14 points represent the [face-centered cubic lattice cell](https://en.wikipedia.org/wiki/Cubic_crystal_system#Cubic_space_groups). _([Wikipedia](https://en.wikipedia.org/wiki/User:Tomruen/Metatron%27s_Cube))_\n
            \n\n

            \"image\"

            \n\n

            Finally we explore the indirect detection characteristics of this model, determined by the decays of the right-handed neutrinos into SM bosons and leptons.

            \n\n
            We analyze a simple extension of the Standard Model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group.\n- Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sector\nand the SM particles, and generate masses for the active neutrinos via the seesaw\nmechanism.\n- We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario.\n\nWe also study the constraints from direct Dark Matter searches and the prospects for indirect detection\nvia sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV. _([Sterile Neutrino portal to Dark Matter II - pdf](https://github.com/eq19/eq19.github.io/files/13822870/1607.02373.pdf))_\n
            \n\n

            \"Sterile

            \n\n

            It is called the mixing angle by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon. Its measured value is slightly below 30°, but also varies.

            \n\n
            If the angle was 0, the U(1) group would remain unbroken and there would be no mixing with the SU(2) group. This would lead to a single massless boson and 3 remaining massless bosons: Ws and photon. On the other hand, if the angle was 90, the SU(2) group would remain unbroken and there would be no mixing with the U(1) group. This would lead to a single massive boson and 3 remaining massless bosons: Ws and photon. _([PhysicsForums](https://www.physicsforums.com/threads/gauge-bosons-and-the-weak-mixing-angle.828525/))_\n
            \n\n

            \"Weinberg_angle_(relation_between_coupling_constants\"

            \n\n

            The coupling gives rise as the phase starts to roll down in the clockwise direction, it preferentially creates an excess of baryons over antibaryons.

            \n\n
            The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review. _([MDPI](https://www.mdpi.com/2073-8994/8/8/81))_\n
            \n\n

            \"symmetry-08-00081-g001\"

            \n\n

            Depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.

            \n\n
            When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. _If one or more [sterile neutrinos](https://en.wikipedia.org/wiki/Sterile_neutrino) are added, it is 4×4 or larger_. _([Wikipedia](https://en.wikipedia.org/wiki/Neutrino_oscillation))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-👇--+-👇--+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-👇--+-👇--+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-👇--+-👇--+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30 👈         Mod 60 👈         Mod 90 👈\n
            \n\n

            While quarks may flow within the closed surface across various open surfaces, there can be no net flux of individual quarks in to or out of any closed surface.

            \n\n
            There are four (4) main features of QCD confinement, which appear to parallel the development of the previous section.\n- These parallels are best specified with reference to baryons, as follows: Establish any closed surface over a baryon source density P. Then:\n- While gluons may flow within the closed surface across various open surfaces, there can be no net flux of gluons in to or out of any closed surface.\n- This may possibly be represented by = 0 dG , and the invariance of F → F' = F under the transformation F → F'= F − dG .\n- While quarks may flow within the closed surface across various open surfaces, there can be no net flux of individual quarks in to or out of any closed surface.\n- This may possibly be represented by the invariance of P → P'= P under the transformation F → F'= F − dG .\n- While there can be no net flux of individual quarks in to or out of any closed surface, there can indeed be a net flux of quark-antiquark pairs in to or out of any closed surface.\n- The antiquark cancels the quark, thereby averting a net flux, and in this way, quarks do flow in to or out of the closed surface, but only paired with antiquarks, as mesons.\n- This may possibly be represented as 02 ≠ i gG .\n- It does not matter how hard or in what manner one “smashes” a baryon, one can still never extract a net flux of quarks or a net flux of gluons, but only a large number of meson jets.\n- This may be possibly represented by the fact that in all of the foregoing, the volume and surface\nintegrals apply to any and all closed surfaces.\n- One can choose a small closed surface, a large closed surface, a spherical closed surface, an oblong closed surface, and indeed, a closed surface of any shape and size. The choice of closed surface does not matter.\n- These mathematical rules for what does and does not flow across any closed surface, in fact, thereby impose very stringent dynamical constraints on the behaviors of these non-Abelian magnetic sources: No matter what flows across various open surfaces, they may never be a net flux of anything across any closed\nsurface. The only exceptions, which may flow across a closed surface, are physical entities represented by.\n\nWhere is the author going with this?\n- The magnetic three-form P, and its associated third-rank antisymmetric tensorσµν P , has all\nthe characteristics of a baryon current density.\n- These σµν P , among their other properties, are naturally occurring sources containing exactly\nthree fermions. These constituent fermions are most-sensibly interpreted as quarks.\n- The surface symmetri F → F' = F under the transformation F → F'= F − dG , tells us that there is no net flow of gluons across any closed surface over the baryon density.\n- The volume symmetry \u0001P → P'= P under F → F'= F − dG , tells us that there is no net flow of quarks across any closed surface over the baryon density.\n- The physical entities represented by 2 igG , when examined in further detail, have the\ncharacteristics of mesons.\n\n[![structure-of-composite-particles-l](https://github.com/eq19/eq19.github.io/assets/8466209/2966004c-0c0d-4bca-85a9-1217d6b0237b)](https://github.com/eq19/eq19.github.io/files/14322719/1711.10626.pdf)\n\nIt tells us that mesons are the only entities which may flow across any closed\nsurface of the baryon density. _([Lab Notes](https://jayryablon.wordpress.com/2008/01/28/lab-note-3-part-1-yang-mills-theory-the-origin-of-baryons-and-confinment-and-the-mass-gap/))_\n
            \n\n

            \"image\"

            \n\n

            \"origin\"

            \n\n

            \"action\"

            \n\n

            Scientists believe there could be an anti-universe somewhere out there that acts like mirroring our own universe, reciprocating almost everything we do.

            \n\n
            Only more accurate analysis on the involved spectra and on the relative brightness of the two rings, and mainly the discovery of other ***double rings systems***, could be used to finally choose which among these two interpretations is more likely to hold. As to using ***Klein bottle holes*** to check the physical existence of other universes, it appears just a matter of time ***to find a double truncated spiral*** blurred enough to clearly show a connection with other universes. _([Observing another Universe - pdf](https://arxiv.org/pdf/1102.3784.pdf))_\n
            \n\n

            \"Gravitational-lensing-effect-produced-by-a-ringhole-from-a-single-luminous-source-a_Q320\"

            \n\n

            If this theory holds true, it could explain the presence of dark matter. Dark matter, then, could be right-handed neutrinos implied by the mirror universe.

            \n\n
            The GUT group E6 contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E6 models comes from _[E8 × E8 heterotic string theory](https://en.wikipedia.org/wiki/Heterotic_string_theory)_. _([Wikipedia](https://en.wikipedia.org/wiki/Grand_Unified_Theory#cite_note-11))_\n
            \n\n

            4² + 5² + 6² = 77

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-👇--+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-----+-----+-👇--+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-👇--+-👇--+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30            Mod 60            Mod 90\n
            \n\n

            All visible matter in the universe is made from the first generation of matter particles — up quarks, down quarks, and electrons.

            \n\n
            While gravitons are presumed to be [massless](https://en.wikipedia.org/wiki/Massless_particle), they would still carry [energy](https://en.wikipedia.org/wiki/Energy), as does any other quantum particle. [Photon energy](https://en.wikipedia.org/wiki/Photon_energy) and [gluon energy](https://en.wikipedia.org/wiki/Gluon_energy) are also carried by massless particles.\n- ***It is unclear which variables might determine graviton energy***, the amount of energy carried by a single graviton.\n- Alternatively, [if gravitons are massive at all](https://en.wikipedia.org/wiki/Massive_gravity), the analysis of gravitational waves yielded a new upper bound on the [mass](https://en.wikipedia.org/wiki/Mass) of gravitons.\n- The graviton's [Compton wavelength](https://en.wikipedia.org/wiki/Compton_wavelength) is at least 1.6×10^16 [m](https://en.wikipedia.org/wiki/Metre), or _about 1.6 [light-years](https://en.wikipedia.org/wiki/Light-year)_, corresponding to a graviton mass of no more than 7.7×10−23 [eV](https://en.wikipedia.org/wiki/Electronvolt)/[c](https://en.wikipedia.org/wiki/Speed_of_light)2.[[22]](https://en.wikipedia.org/wiki/Graviton#cite_note-Abbott2017-22)\n- This relation between wavelength and mass-energy is _calculated with the [Planck–Einstein relation](https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation)_, the same formula that relates electromagnetic [wavelength](https://en.wikipedia.org/wiki/Wavelength) to [photon energy](https://en.wikipedia.org/wiki/Photon_energy).\n- However, if gravitons are the quanta of gravitational waves, then ***the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons***, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.\n- Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the [GW170104](https://en.wikipedia.org/wiki/GW170104) event, which was ~ 1,700 km. The report[[22]](https://en.wikipedia.org/wiki/Graviton#cite_note-Abbott2017-22) did not elaborate on the source of this ratio. \n\n***It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way***. _([Wikipedia](https://en.wikipedia.org/wiki/Graviton))_\n
            \n\n

            \"image\"

            \n\n

            There even stated by the conformal cyclic cosmology that this hypothesis requires that all massive particles eventually vanish from existence.

            \n\n
            As Penrose points out, [proton decay](https://en.wikipedia.org/wiki/Proton_decay) is a possibility contemplated in various speculative extensions of the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model), but it has never been observed. _Moreover, all [electrons](https://en.wikipedia.org/wiki/Electron) must also decay, or lose their charge and/or mass, and no conventional speculations allow for this_.\n\nIn his Nobel Prize Lecture video, Roger Penrose moderated his previous requirement for no mass, beginning at 26:30 in the video, allowing some mass particles to be present as long as the amounts are insignificant with nearly all of their energy being kinetic, and in a conformal geometry dominated by photons. _([Wikipedia](https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology))_\n
            \n\n

            \"conformal

            \n\n

            This is because all second and third generation particles are unstable and quickly decay into stable first generation particles.

            \n\n

            The 27 Parameters

            \n\n

            Note that since our Universe began with a Big Bang, all its particles originate from pair creation since then.

            \n\n

            \"shilov27\"

            \n\n

            Upon reviewing the masses, the algorithms should work correctly to depict the Generation I, II & III and the charge levels of the elementary particles.

            \n\n
             Osp(8|4) |  1 |  2 |  3 |   4 | th\n==========+====+====+====+=====+====\n π(10)    |  2 |  3 |  5 |   7 | 4th\n----------+----+----+----+-----+----\n π(19)    | 11 | 13 | 17 |  19 | 8th\n----------+----+----+----+-----+----\n π(29)    | 23 | 29 |  - |   - | 10th\n==========+====+====+====+=====+====\n π(41)    | 31 | 37 | 41 |   - | 13th\n----------+----+----+----+-----+----\n π(59)    | 43 | 47 | 53 |  59 | 17th \n----------+----+----+----+-----+- ---\n π(72)    | 61 | 67 | 71 |   - | 20th\n==========+====+====+====+=====+====\n π(72+11) | 73 | 79 | 83 |   - | 23th\n----------+----+----+----+-----+----\n π(83+18) | 89 | 97 |101 |   - | 26th 👈\n----------+----+----+----+-----+----\n π(101+8) |103 |107 |109 |   - | 29th\n
            \n\n

            Bosonic String Theory of 26-dim J3(O)o is related to an M-theory based on the full 27-dimensional J3(O) and 28-dimensional J4(Q).

            \n\n

            \"String

            \n\n

            There are models of two related universes that e.g. attempt to explain the baryon asymmetry – why there was more matter than antimatter at the beginning – with a mirror anti-universe.

            \n\n
            In [physical cosmology](https://en.wikipedia.org/wiki/Physical_cosmology), the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem,[[1]](https://en.wikipedia.org/wiki/Baryon_asymmetry#cite_note-1)[[2]](https://en.wikipedia.org/wiki/Baryon_asymmetry#cite_note-2) is the observed imbalance in [baryonic matter](https://en.wikipedia.org/wiki/Baryonic_matter) (the type of matter experienced in everyday life) and [antibaryonic matter](https://en.wikipedia.org/wiki/Antibaryonic_matter) in the [observable universe](https://en.wikipedia.org/wiki/Observable_universe).\n- Neither the [standard model](https://en.wikipedia.org/wiki/Standard_Model) of [particle physics](https://en.wikipedia.org/wiki/Particle_physics) nor the theory of [general relativity](https://en.wikipedia.org/wiki/General_relativity) provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved [charges](https://en.wikipedia.org/wiki/Charge_(physics)).[[3]](https://en.wikipedia.org/wiki/Baryon_asymmetry#cite_note-3)\n- The [Big Bang](https://en.wikipedia.org/wiki/Big_Bang) should have produced equal amounts of [matter](https://en.wikipedia.org/wiki/Matter) and [antimatter](https://en.wikipedia.org/wiki/Antimatter). Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter.\n\nSeveral competing hypotheses exist to ***explain the imbalance of matter and antimatter*** that resulted in [baryogenesis](https://en.wikipedia.org/wiki/Baryogenesis). However, there is as of yet no consensus theory to explain the phenomenon, which has been described as _\"one of the [great mysteries in physics](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics)\"_. _([Wikipedia](https://en.wikipedia.org/wiki/Baryon_asymmetry))_\n
            \n\n

            \"image\"

            \n\n

            The component of the 27 dimensional gravitational field g27;27 is a scalar in the 26 dimensional theory. It is of course the dilaton.

            \n\n
            Consider a (purple) world-line String of one World of the MacroSpace of Many-Worlds and its interactions with another (gold) world-line World String, from the point of view of one point of the (purple) World String, seen so close-up that you don't see in the diagram that the (purple) and (gold) World Strings are both really closed strings when seen at very large scale:\n- massless spin-2 Gravitons travel along the (red) MacroSpace light-cones to interact with the intersection points of those (red) light-cones with the (gold) World String;\n- scalar Dilatons, with effectively real mass, travel within the (yellow) MacroSpace light-cone time-like interior to interact with the intersection region of the (yellow) light-cone time-like interior region with the (gold) World String; and\n- [Tachyons, with imaginary mass](https://www.valdostamuseum.com/hamsmith/E6StringBraneStdModelAR.pdf), travel within the (cyan) MacroSpace light-cone space-like exterior to interact with the intersection points of the (cyan) light-cone space-like exterior region with the (gold) World String.\n- Metod Saniga, inphysics/0012033 D4-D5-E6-E7-E8 VoDou Physics Model: It is a well-known fact that on a generic cubic surface, K3, the lines are seen to form three (3) separate groups.\n- The first two groups, each comprising six (6)lines, are known as Schlafli's double-six. The third group consists of ***fifteen lines***. The basics of the algebra can simply be expressed as [`27 = 12 + 15`](http://ui.adsabs.harvard.edu/abs/2001physics...2042S/abstract).\n\nNote that Gravity may not propagate in the 26 dimensions of the MacroSpace of the Many-Worlds in exactly the same way as it propagates in our 4-dimensional physical SpaceTime. _([Tony Smith's](https://www.valdostamuseum.com/hamsmith/Rzeta.html))_\n
            \n\n

            \"World

            \n\n

            Particle physicists acknowledge that the particle may exist in wave forms and yet have characteristics of matter.

            \n\n
            Supersymmetry predicts that each of the particles in the Standard Model has a partner with a spin that differs by half of a unit. \n- So bosons are accompanied by fermions and vice versa.\n- Linked to their differences in spin are differences in their collective properties.\n- Fermions are very standoffish; every one must be in a different state.\n- On the other hand, bosons are very clannish; they prefer to be in the same state. \n\nFermions and bosons seem as different as could be, yet supersymmetry brings the two types together.\n
            \n\n

            1 + 8 + 8 + 8 + 1 = 2 × (1+4+8) = 2 × 13 = 26

            \n\n

            \"standardmodel1\"

            \n\n

            The 26 dimensions of Closed Unoriented Bosonic String Theory are interpreted as the 26 dimensions of the traceless Jordan algebra J3(O)o of 3x3 Octonionic matrices.

            \n\n
            Each of the 3 Octonionic dimenisons of J3(O)o having the following physical interpretation:\n- 4-dimensional physical spacetime plus 4-dimensional internal symmetry space;\n- 8 first-generation fermion particles; 8 first-generation fermion anti-particles.\n\nThus the 26 dimensions stand as the degrees of freedom of the Worlds of the Many-Worlds. _([Tony's Web Book - pdf (800MB Size)](https://www.valdostamuseum.com/hamsmith/TonySwebBook.pdf))_.\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-👇--+-👇--+-----+                                                    |\n 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-👇--+-👇--+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-👇--+-👇--+-----+-👇--+-👇--+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ\n                  Mod 30            Mod 60            Mod 90\n
            \n\n

            At present, there is no candidate theory of everything that, at the same time, is able to calculate the fine-structure constant or the mass of the electron.

            \n\n
            In the Standard Model, elementary particles are manifestations of three “symmetry groups” — essentially, ways of interchanging subsets of the particles that leave the equations unchanged.\n- These three (3) symmetry groups, ***SU(3), SU(2) and U(1)***, correspond to the strong, weak and electromagnetic forces, respectively, and they “act” on six types of quarks, two types of leptons, plus their anti-particles, with each type of particle coming in three copies, or “generations,” that are identical except for their masses.\n- The fourth fundamental force, gravity, is described separately, and incompatibly, by Einstein’s general theory of relativity, which casts it as curves in the geometry of space-time.\n\nNote that both quarks and leptons exist in three distinct sets. Each set of quark and lepton charge types is called a generation of matter (charges +2/3, -1/3, 0, and -1 as you go down each generation). The generations are organized by increasing mass.\n
            \n\n

            \"Fundamental

            \n\n

            The solution is that many or all of these possibilities are realized in one or another of a huge number of universes, but that only a small number of them are habitable.

            \n\n

            \"\"

            \n\n

            Another suggestion which has just yet been in a topic of the science is that the similar behaviour also happen by particles such as hydrogen.

            \n\n
            Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics ***cannot predict*** the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron _([Wikipedia](https://en.wikipedia.org/wiki/Quantum_physics))_.\n
            \n\n

            \"the

            \n\n

            So hypothetically it suppose to have its own parallel universes because whatever a smallest thing is arised, they could only exist by the same law of physics.

            \n\n

            \"Infinite

            \n\n

            This law of physics would exist everywhere. So it is also one of their law when the 1st sequence of the unrepeated ten (10) digits Euler’s number is zero (0).

            \n\n
            1729th decimal digit holds significance in the decimal representation of the transcendental number e. From 1729th digit you can get the first occurrence of all ten digits consecutively and they are 0719425863. _([Ramanujan taxicab 1729 - pdf](https://github.com/eq19/eq19.github.io/files/13934098/Ramanujan2.pdf)\n)_\n
            \n\n

            139 + 286 + 114 + 247 + 157 + 786 = 786 + 157 + 786 = 1729 = 7 x 13 x 19

            \n\n

            \"0719425863\n

            \n\n

            Theoretically the zero speaks if an existence of everything arose from nothingness.

            \n\n

            By our universe it could be represented by the central black hole which is very strong to throw away every objects but it has no resistance against any exchange.

            \n\n
            Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed _([Wikipedia](https://en.wikipedia.org/wiki/Black_hole#High-energy_collisions#Growth))_\n
            \n\n

            \"the

            \n\n

            So the particle’s multiverses are obviously massive waves. It will remain untouchable as long as an experiment gives a result that it is as particle (not wave).

            \n\n
            Wave–particle duality is the concept in [quantum mechanics](https://en.m.wikipedia.org/wiki/Quantum_mechanics) that [quantum](https://en.m.wikipedia.org/wiki/Quantum) entities exhibit particle or wave properties according to the experimental circumstances.[[1]](https://en.m.wikipedia.org/wiki/Wave%E2%80%93particle_duality#cite_note-Messiah-1): 59  It expresses the inability of the [classical](https://en.m.wikipedia.org/wiki/Classical_physics) concepts such as [particle](https://en.m.wikipedia.org/wiki/Particle) or [wave](https://en.m.wikipedia.org/wiki/Wave) to fully describe the behavior of quantum objects.\n\nDuring the 19th and early 20th centuries, light was found to behave as a wave, and then later discovered to have a particulate character, whereas electrons were found to act as particles, and then later discovered to have wavelike aspects. The concept of duality arose to name these contradictions. _([Wikipedia](https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality))_\n
            \n\n

            \"Quantum-Physics\"

            \n\n

            Our results show that about 69% of our universe’s energy is dark energy. They also demonstrate, once again, that Einstein’s simplest form of dark energy – the cosmological constant – agrees the most with our observations.

            \n\n
            Dark energy is [one of the greatest mysteries](https://theconversation.com/the-experiments-trying-to-crack-physics-biggest-question-what-is-dark-energy-52917) in science today.\n- We know very little about it, other than it is invisible, it fills the whole universe, and it pushes galaxies away from each other. This is making our cosmos expand at an accelerated rate. But what is it?\n- One of the simplest explanations is that it is a ***cosmological constant*** – a result of the energy of empty space itself – an idea introduced by Albert Einstein.\n\nMany physicists aren’t satisfied with this explanation, though. They want a more fundamental description of its nature. Is it some new type of energy field or exotic fluid? _([The Conversation](https://theconversation.com/dark-energy-map-gives-clue-about-what-it-is-but-deepens-dispute-about-the-cosmic-expansion-rate-143200))_.\n
            \n\n

            \"image\"

            \n\n

            Or is it a sign that Einstein’s equations of gravity are somehow incomplete? What’s more, we don’t really understand the universe’s current rate of expansion

            \n\n
            Discussing both open and closed bosonic strings, Soo-Jong Rey, in his paper [Heterotic M(atrix) Strings and Their Interactions - pdf](https://github.com/eq19/eq19.github.io/files/14234424/9704158.pdf), says: We would like to conclude with a highly speculative remark on a possible:\n- It is well-known that The regularizedone-loop effective action of d-dimensional Yang-Mills theory. ***For d=26, the gauge kinetic term does not receive radiative correction at all***.\n- We expect that this non-renormalization remains the same even after dimensional reductions. One may wonder if it is possible to construct for bosonic string as well despite the absence of supersymmetry and BPS states.\n- M(atrix) theory description of bosonic strings bosonic Yang-Mills theory in twenty-six dimensions is rather special M(atrix)string theory. The bosonic strings also have D-brane extended solitons, whose tension scales as 1/gB for weak string coupling `gB « 1`.\n- Given the observation that the leading order string effective action of and antisymmetric tensor field ***may be derived from Einstein's Gravity in d = 27***, let us make an assumption that  the 27-th quantum dimension decompactifies as the string coupling gB becomes large. For D0-brane, the dilaton exchange force may be interpreted as ***the 27-th diagonal component*** of `d = 27` metric.\n- Gravi-photon is suppressed by compactifying 27-th direction on an rather than on a circle. Likewise, its mass may be interpreted as 27-th Kaluza-Klein momentum of a massless excitation in `d = 27`. \n\nIn the infinite boost limit, the light-front view of a bosonic string is that infinitely many D0-branes are threaded densely on the bosonic string. _([26 Dimensions of Bosonic String Theory - pdf](https://github.com/eq19/eq19.github.io/files/13904636/0102042.pdf))_\n
            \n\n

            \"Einstein’s

            \n\n

            The expected Gravitational waves spreading all over the universe, and all particles travelling in this cosmic greatest speed such as neutrinos.

            \n\n
            Einstein in 1916 proposed the existence of gravitational waves as an outgrowth of his ground-breaking general theory of relativity, which ***depicted gravity as the distortion of space and time by matter***. Until their detection in 2016, scientists had found only indirect evidence of their existence, beginning in the 1970s. The gravitational wave signal was observed in 15 years' worth of data obtained by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) Physics Frontiers Center (PFC), a collaboration of more than 190 scientists from the United States and Canada. _([Reuters](https://www.reuters.com/science/scientists-discover-that-universe-is-awash-gravitational-waves-2023-06-29/))_\n
            \n\n

            \"Sun

            \n\n

            Assuming that each fermion could be an earth in “anti-universe” then it stands as 1000 times earth moon system around the sun against the background of the 11 galaxies.

            \n\n
            Month, a measure of time corresponding or nearly corresponding to the length of time required by the [Moon](https://www.britannica.com/place/Moon) to revolve once around the Earth.\n- The [synodic month](https://www.britannica.com/science/synodic-month), or complete cycle of phases of the [Moon](https://www.britannica.com/science/moon-natural-satellite) as seen from Earth, averages 29.530588 mean solar days in length (i.e., 29 days 12 hours 44 minutes 3 seconds); because of [perturbations](https://www.britannica.com/dictionary/perturbations) in the Moon’s [orbit](https://www.britannica.com/science/orbit-astronomy), the lengths of all astronomical months vary slightly. \n- The [sidereal month](https://www.britannica.com/science/sidereal-month) is ***the time needed for the Moon to return to the same place against the background of the stars***, 27.321661 days (i.e., 27 days 7 hours 43 minutes 12 seconds); the difference between synodic and sidereal lengths is due to the orbital movement of the Earth–Moon system around the [Sun](https://www.britannica.com/place/Sun).![image](https://github.com/eq19/eq19.github.io/assets/8466209/b44edbe8-9860-4892-bc1b-0370f7c19dd6)\n- The tropical month, 27.321582 days (i.e., 27 days 7 hours 43 minutes 5 seconds), only 7 seconds shorter than the sidereal month, is the time between passages of the Moon through the same celestial longitude.\n- The [draconic](https://www.britannica.com/science/draconic-month), or nodical, month of 27.212220 days (i.e., 27 days 5 hours 5 minutes 35.8 seconds) is the time between the Moon’s passages through the same node, or intersection of its orbit with the ecliptic, the apparent pathway of the Sun.\n\nAs a calendrical period, the month is [derived](https://www.britannica.com/dictionary/derived) from the lunation—i.e., the time elapsing between successive new moons (or other phases of the moon). A total of 12 lunations amounts to 354 days and is, roughly, a [year](https://www.britannica.com/science/year). _([Britannica](https://www.britannica.com/science/month#ref225844))_\n
            \n\n

            By E24, the residual length of sidereal (7 hours, 43 minutes, 12 seconds) behave as a Fibonacci Terminating Digit. Thus it is the one that hides to Particle’s Multiverses.

            \n\n

            6+6 + 6/\\6 = 6+6 + 15 = 27-day month

            \n\n
            E = mc²\nm = E/c²\n\nc = 1 light-second\n  = 1000 years x L / t\n  = 12,000 months x 2152612.336257 km / 86164.0906 sec\n  = 299,792.4998 km / sec\n\nNote:\n1 year = 12 months\n1000 years = 12,000 months\nTe = earth revolution = 365,25636 days\nR = radius of moon rotation to earth = 384,264 km\nV = moon rotation speed = 2πR/Tm = 3682,07 km/hours\nVe = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°\nTm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours ✔️\nt = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec\nL = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km\n\nConclusion:\nπ(π(π(π(π(32(109²-89²)))))) Universe vs Parallel vs Multiverse (via blackhole)\n   👇\nπ(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Parallel (gap via expansion)\n   👇\nπ(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap via dark energy)\n   👇\nπ(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter)\n   👇\n|--👇---------------------------- 2x96 ---------------------|\n|--👇----------- 7¤ ---------------|---------- 5¤ ----------|\n|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|           \n+----+----+----+----+----+----+----+----+----+----+----+----+       Particle's\n|--------- {53} ---------|{19}|--------- {77} ---------|109²-89² 👉 Multiverses\n|---------- 5¤ ----------|------------ {96} -----------|-1¤-|      (Untouchable)\n|-------- Bosons --------|---------- Fermions ---------|-- Graviton\n|-- Sun Orbit (7 days) --|--- Moon Orbit (12 months) --| (11 Galaxies)\n|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way 👉 Sum=12\n
            \n\n

            Our Milky Way Galaxy is surrounded by the two (2) nearest Dark Matter Galaxies W-2 and W+2 with two joint gravity waveguides W+1 and W-1 and our Galaxy acquires the corresponding joint gravity potential.

            \n\n
            The described Multiverse expansion creates huge parallel Multiverse bubbles with periodic parallel +m matter and periodic –m antimatter clusters, distributed on the bubbles walls.\n- Fig. 13a shows parallel Universes/Anti-universe W2n / W2n+1.\n- Fig. 13b shows repulsive antigravity between all the nearest matter/antimatter waveguides, e.g. between  W-1 (antimatter), W+1 (antimatter) and our matter W0 Galaxies. \n- Fig. 13c shows attractive Рravitв betаeen the nearest “dark” waveguides (e.g. between W-2 Dark Matter, W+2 Dark Matter) and our Matter W0 Galaxies. \n\nThe visible W-1 (antimatter), W+1 (antimatter) Universes are adjacent to the W0 (our matter)-Universe and have two joint framing membranes M0 and M-1, carrying two joint electrostatic potentials. _([Gribov_I_2013 - pdf](https://github.com/eq19/eq19.github.io/files/14155625/Gribov_I_2013_From_the_waveguided_gravit.pdf))_\n
            \n\n

            \"From_the_waveguided\"

            \n\n

            So now we can find them as i12 in our discussions about the 26 parameters on the mechanism for fermion mass generation which end up to 139 components.

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 👈\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 👈\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️\n
            \n\n

            Thus our universe is belong to a seven (7) groups of 12 multiple universes inside a mass gap somewhere out of an infinite number of the like of them.

            \n\n
            _[Prof Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking)'s [final research paper](https://arxiv.org/pdf/1810.01847.pdf) [suggests that our Universe may be one of many similar](https://link.springer.com/content/pdf/10.1007/JHEP04(2018)147.pdf)_ _([BBC News](https://www.bbc.com/news/science-environment-43976977))_.\n
            \n\n

            \"everything

            \n\n

            This interpretation is consistent with interpreting the strings as World Lines of the Worlds of Many-Worlds Quantum Theory.

            \n\n
            The 26-dimensional traceless subalgebra J3(O)o is arepresentation of the 26-dim Theory of Unoriented Closed Bosonic Strings produces a Bohm Quantum Theory with geometry of E6 / F4. The E6 of the can be represented in terms of:\n- ***3 copies of the 26-dimensional*** traceless subalgebra J3(O)o of the 27-dimensional J3(O) by using the of ***78-dimensional E6 over 52-dimensional F4*** and the structure of based on the 26-dimensional representation of.\n- In this view, Lie algebra D4-D5-E6-E7-E8 VoDou Physics model Jordan algebra fibration E6/F4 F4 as doubled J3(O)o F4 \n\nIn order to reproduce the known spectrum of weakly coupled bosonic string theory, bosonic M theory will have to contain an additional field besides the ***27 dimensional gravitational field***, namely a three-form potential CFT. _([PhiloPhysics - pdf](https://github.com/eq19/eq19.github.io/files/14258292/PhiloPhysics.pdf))_\n
            \n\n

            6+6 + 6/\\6 = 6+6 + 15 = 27-day month

            \n\n

            \"26

            \n\n

            So we need to reformulate Einstein’s general relativity in a language closer to that of the rest of fundamental physics, specifically Yang–Mills theory.

            \n\n

            \"fully-expanded-incl-matrices\"

            \n\n

            The areas of research, which involve about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space.

            \n\n

            Loop Quantum Gravity

            \n\n

            So one of the major obstacles is simply “informing” the scientific community about the mathematical techniques of hypercomplex numbers covering at least the five (5) fundamental mathematical constants:

            \n\n

            (1) The number 1, the multiplicative identity,
            (2) The number i, the imaginary unit of the complex numbers.
            \"image\"
            (3) The number π = 3.1415…, the fundamental circle constant, and

            \"Pi-unrolled-720\"

            (4) The number e = 2.718…, also known as Euler’s number, which occurs widely in mathematical analysis.

            \"image\"

            (5) Furthermore, the equation is given in the form of an expression set equal to zero, the number 0, as the additive identity which is common practice in several areas of mathematics.

            \n
            \n

            Euler’s identity is a special case of Euler’s formula eix = cos x + i sin x when evaluated for x = π, In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia)

            \"Euler's

            \n
            \n\n

            Euler angles specify the rotation of the X, Y, and Z rotation axes. The Euler angle is the culprit of the singularities in matrix algebra.

            \n\n
            In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first [Pauli matrix](https://github.com/eq19/eq19.github.io/files/13818844/math0703448.pdf)\n
            \n\n

            \"Spin\"\n

            \n\n

            Some quantum theories of gravity posit a spin-2 quantum field that is quantized, giving rise to gravitons. Similar with how the metatron works

            \n\n
            The supposed periodic prolongation of the gravitationally bounded DM hyper-galaxies above  and below of our Milky Way galaxy realizes corresponding ***periodic hyper-galactic Milky Way-stockpile (FiР. 13a, leПt)***. \n\n![image](https://github.com/eq19/eq19.github.io/assets/8466209/ff55561b-cf19-4c56-939e-51fea15e68fd)\n\nThis short hвper-interval 10 light minutes of the Milky Way-stockpile contains near 10²⁴ hyper-civilizations inside the 10-seconds 4D-hyperslice. _([Gribov_I_2013 - pdf](https://github.com/eq19/eq19.github.io/files/14155625/Gribov_I_2013_From_the_waveguided_gravit.pdf))_\n
            \n\n

            2 × 13 × 11 = 11 galaxies × 26 dimensions/galaxy = 286

            \n\n
                       largest part = 21 → 11+13+12 = 36  →  MEC30\n                        ↓                      |\n---+-----+-----+-----+-----+                   ↓\n 1 | 19  | 1   | 20  | 21  |-------------------|-----\n---+-----+-----+-----+-----+                   ↓     |\n 2 | 18  | 21  | 39  | 60  |-------------------      |\n---+-----+-----+-----+-----+                   |     |\n 3 |{63} | 40  | 103 | 143 |-------------      |     |\n---+-----+-----+-----+-----+             |     |     |\n 4 | 37  | 104 | 141 | 245 |-------      |     |     |\n---+-----+-----+-----+-----+       |     |     |     |\n 5 | 10* | 142 | 152 | 294 |- 11👈 | 13  | 12  | 12  | 18\n---+-----+-----+-----+-----+       |     |     |     |\n 6 | 24  | 153 | 177 | 332 |-------      |     |     |\n---+-----+-----+-----+-----+             |     |     |\n 7 | 75  | 178 | 253 | 431 |-------------      |     |\n---+-----+-----+-----+-----+                   |     |\n 8 | 30  | 254 | 284 | 538 |-------------------      |\n---+-----+-----+-----+-----+                   ↓     |\n 9 | 1   | 285 | 286 | 571 |-------------------|-----\n===+=====+=====+=====+=====+                   ↓\n45 | 277 |                      ← 11+13+12=36 ←  MEC30\n---+-----+                                     |\n ↑\nNote:\n10* stands as the central rank\n11** stands as the central parts\n
            \n\n

            The finiteness position of MEC30 along with Euler’s identity opens up the possibility of accurately representing the self-singularity of True Prime Pairs.

            \n\n
            The Mathematical Elementary Cell 30 (MEC30) standard [unites](https://www.eq19.com/multiplication/12.html#entrypoint-of-momentum-spin-3) the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. ([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))\n
            \n\n

            \"Spinning

            \n\n

            These deterministic sequences intertwine like an octal helix and ultimately determine the distribution of all prime numbers greater than 5, i.e., starting with 7.

            \n\n
            Eighteen (18) of the sequences have been published on the On-Line Encyclopedia of Integer Sequences. Here's the link: [OEIS Listings for Gary W. Croft](https://oeis.org/search?q=Gary%20Croft&start=10). \n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n \nlayer | node | sub |  i  |  f.                         MEC30/2 ✔️\n------+------+-----+-----+------      ‹--------------- 0 {-1/2}\n      |      |     |  1  | --------------------------\n      |      |  1  +-----+                           |    \n      |  1   |     |  2  | (5)                       |\n      |      |-----+-----+                           |\n      |      |     |  3  |                           |\n  1   +------+  2  +-----+----                       |\n      |      |     |  4  |                           |\n      |      +-----+-----+                           |\n      |  2   |     |  5  | (7)                       |\n      |      |  3  +-----+                           |\n      |      |     |  6  |                          11s ‹-- ∆28\n------+------+-----+-----+------      } (36)         |\n      |      |     |  7  |                           |\n      |      |  4  +-----+                           |\n      |  3   |     |  8  | (11)                      |\n      |      +-----+-----+                           |\n      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |\n  2   +------|  5* +-----+-----                      |\n      |      |     |  10 |                           |\n      |      |-----+-----+                           |\n      |  4   |     |  11 | (13) --------------------- \n      |      |  6  +-----+ ‹--- vacuum energy ‹--- ∆60 ‹--- 15 {zero axis} ✔️\n      |      |     |  12 |---------------------------\n------+------+-----+-----+------------               |\n      |      |     |  13 |                           |\n      |      |  7  +-----+                           |\n      |  5   |     |  14 | (17)                      |\n      |      |-----+-----+                           |\n      |      |     |  15 |                           7s ‹-- ∆24\n  3*  +------+  8  +-----+-----       } (36)         |\n      |      |     |  16 |                           |\n      |      |-----+-----+                           |\n      |  6   |     |  17 | (19)                      |\n      |      |  9  +-----+                           |\n      |      |     |  18 | -------------------------- \n------|------|-----+-----+-----  ‹-------------------- 30 {+1/2} ✔️\n
            \n\n

            Each of the nine (9) types express themselves as one of the three (3) subtypes. So from this perspective, there are 27 distinct patterns which are usually denoted by letters.

            \n\n
            Mathematically, this type of system requires ***27 letters (1-9, 10–90, 100–900)***. In practice, the last letter, tav (which has the value 400), is used in combination with itself or other letters from qof (100) onwards to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes ***extended to 27 by using 5 sofit (final)*** forms of the [Hebrew letters](https://en.wikipedia.org/wiki/Hebrew_numerals#cite_note-7). _([Wikipedia](https://en.wikipedia.org/wiki/Hebrew_numerals))_\n
            \n\n

            \"The

            \n\n

            So it differs from string theory in that it is formulated in 3 and 4 dimensions and without supersymmetry or Kaluza–Klein extra dimensions which requires both to be true.

            \n\n
            Since Loop Quantum Grabity (LQG) has been formulated in ***4 dimensions*** (with and without supersymmetry), and M-theory requires supersymmetry and ***11 dimensions***, a direct comparison between the two has not been possible.\n- It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general relativity with supersymmetry and Kaluza–Klein extra dimensions should experimental evidence establish their existence. \n- It would therefore be desirable to have ***higher-dimensional*** Supergravity loop quantizations at one's disposal in order to compare these approaches.\n- A series of papers have been published attempting this.[[68]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013a045001-68)[[69]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013b045002-69)[[70]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013c045003-70)[[71]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013d045004-71)[[72]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013e045005-72)[[73]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2012205-73)[[74]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013f045006-74)[[75]](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2013g045007-75) Most recently, Thiemann (and alumni) have made progress toward calculating black hole entropy for supergravity in higher dimensions.\n\nIt will be useful to compare these results to the corresponding super string calculations. _([Wikipedia](https://en.wikipedia.org/wiki/Loop_quantum_gravity#cite_note-FOOTNOTEBodendorferThiemannThurn2014055002-76))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\nPrime Loops:\nπ(10) = 4 (node)\nπ(100) = 25 (partition)\nπ(1000) - 29 = 139 (section)\nπ(10000) - 29th - 29 = 1091 (segment)\nπ(100000) - 109th - 109 = 8884 (texture)\nSum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)\n\n     |    168    |    618    |\n-----+-👇--+-👇--+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨👈 4¤  ----->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n👉11¨|  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to \"id:33\"   ----->    77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n👉18¨|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n     |  1     2     3  |  4     5     6  |  7     8     9  |\n139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|\n     |--- 1 + MEC30 ---|---------- MEC30 + √(43-18) -------| ✔️\n                       Δ                 Δ                 Δ\n                     Mod 30            Mod 60            Mod 90\n
            \n\n

            Given observation that the leading action of graviton, dilaton, and antisymmetric tensor fields form a bilateral 9 sums, this patterns are indeed derived from the 27 parameters.

            \n\n
            F11 (89): The decimal expansion of 89's reciprocal (1/89) is period-44 (see graphic below) composed of 22 bi-lateral 9 sums = 198, while 89 + 109 = 198, 7920/198 = 40 and 8,363,520/198 = 20 x 2112 (7919's index number as a member of this domain).\n- And, curiously, 198's inverse (891) + 109 = 1000, while the sum of 89 and 109's inverses, 98 + 901, = 999.\n- Then consider that, while it's obvious 997 of the first 1000 primes are not divisible by 2, 3, or 5, one might miss the fact that 997 minus its reverasl, 799, = 198 = 89 + 109.\n- And for the record we note that 1/109's decimal expansion is period 108 (making it a 'long period prime' in that 1/p has the maximal period of p−1 digits).\n\n***This period consists of 2 × 27 or 54 bilateral 9 sums = 486***, which (coincidentally?) is the number of primes in the 243 pairs summing to 7920 (more about these, below). _([PrimesDemystified](https://www.primesdemystified.com/First1000Primes.html))_\n
            \n\n

            43 + 1 = 44 periods

            \n\n

            \"The\n

            \n\n

            In the other hand it is stated by DE102011101032A9 that using Euler’s identity, the MEC30 standard is more accurately than a measurement.

            \n\n
            In [physics](https://en.wikipedia.org/wiki/Physics), a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the [force](https://en.wikipedia.org/wiki/Force) exerted in an [interaction](https://en.wikipedia.org/wiki/Fundamental_interaction).\n- Originally, the coupling constant related the force acting between two static bodies to the “[charges](https://en.wikipedia.org/wiki/Charge_(physics))” of the bodies (i.e. the electric charge for [electrostatic](https://en.wikipedia.org/wiki/Electrostatics) and the mass for [Newtonian gravity](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation)) divided by the distance squared, r².\n- The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter\n- The solution to both these problems comes from the Higgs mechanism, which involves scalar fields (the number of which depend on the exact form of Higgs mechanism) which (to give the briefest possible description) are “absorbed” by the massive bosons as degrees of freedom, and which couple to the fermions via Yukawa coupling to create what looks like mass terms.\n\nThe next step is to couple the gauge fields to the fermions, allowing for interactions. ([Wikipedia](https://en.wikipedia.org/wiki/Coupling_constant))\n
            \n\n

            \"\"

            \n\n

            Another possibility opened by the scale is studying for hidden variables, knowledge of which would allow more exact predictions than quantum theory can provide.

            \n\n
            Eleven-dimensional supergravity is reformulated in a way suggested by compactifications to four dimensions. The new version has local SU(8) invariance. The bosonic quantities that pertain to the spin-0 fields constitute 56- and 133- dimensional representations of E7(+7). Some implications of our results for the S7 compactification are discussed.\n
            \n\n

            1 + 29 + 6x6 = 29 + 37 = 66 = 11x6

            \n\n

            \"True

            \n\n

            This is one of the finer points of differences between the eightfold way and the quark model which suggests the mesons should be grouped into nonets (groups of nine).

            \n\n
            In the ***second opposing term***, the position 13 gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the 11th prime number is now forced as a new axis-symmetrical zero position. ([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments)\n
            \n\n

            \"16S

            \n\n

            Particles are sorted into groups as mesons or baryons. Within each group, they are further separated by their spin angular momentum.

            \n\n
            Our sidebar is arranged to accommodate The Standard Model presently that recognizes ***seventeen (17)*** distinct particles: ***five (5) bosons and twelve (12) fermions***. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have ***13 and 48 variations***, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. ([Wikipedia](https://en.wikipedia.org/wiki/Elementary_particle))\n
            \n\n

            11 + 5 + 12 = 16 + 12 = 28-day month

            \n\n

            \"Partition

            \n\n

            In physics, the eightfold way is an organizational scheme for a class of subatomic particles known as hadrons that led to the development of the quark model.

            \n\n
            [Gell-mann matrices](https://en.m.wikipedia.org/wiki/Gell-Mann_matrices) are a complete set of Hermitian noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model the ****eight (8) gluons*** that mediate the strong force quantum chromodynamics, an analogue of the [Pauli matrices](https://mathworld.wolfram.com/PauliMatrices.html) well-adapted to applications in the realm of quantum mechanics. ([Wolfram](https://mathworld.wolfram.com/Gell-MannMatrix.html))\n
            \n\n

            \"\"

            \n\n

            In quantum chromodynamics, flavour is a conserved global symmetry. In the electroweak theory, on the other hand, this symmetry is broken, and flavour changing processes exist, such as quark decay or neutrino oscillations.

            \n\n
            [Representation theory](https://en.wikipedia.org/wiki/Representation_theory) is a mathematical theory that describes the situation where elements of a group (here, the flavour rotations A in the group SU(3)) are [automorphisms](https://en.wikipedia.org/wiki/Automorphism) of a vector space (here, the set of all possible quantum states that you get from flavour-rotating a proton).\n- Therefore, by studying the representation theory of SU(3), we can learn the possibilities for what the vector space is and how it is affected by flavour symmetry.\n- Since the flavour rotations A are approximate, not exact, symmetries, each orthogonal state in the vector space corresponds to a different particle species. In the example above, when a proton is transformed by every possible flavour rotation A, it turns out that it moves around an ***8 dimensional vector space***.\n- Those 8 dimensions correspond to the 8 particles in the so-called \"baryon octet\". \n\nThis corresponds to an 8-dimensional (\"octet\") representation of the group SU(3). Since A is an approximate symmetry, all the particles in this octet have similar mass. _([Wikipedia](https://en.wikipedia.org/wiki/Eightfold_way_(physics)))_\n
            \n\n

            \"MEC30

            \n\n

            The eight (8) steps between id:30 to 37 represents the Eightfold Way in the context of E8, a pattern developing in physics to represent the fundamental particles.

            \n\n
            E8 is at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the symmetries of E8. ***The enigmatic E8 is the largest and most complicated of the five exceptional Lie groups, and contains four subgroups that are related to the four fundamental forces of nature***: the electromagnetic force; the strong force (which binds quarks); the weak force (which controls radioactive decay); and the gravitational force. _([Wordpress.com](https://nitinuchil.wordpress.com/2020/09/09/hypercomplex-math/))_\n
            \n\n

            \"image\"

            \n\n

            Finally we found that the loop corresponds to a quadratic polynomial originated from the 4th coupling of MEC30 which is holded by five (5) cells between 13 and 17.

            \n\n
            The Minimal Supersymmetric Standard Model (MSSM) contains two Higgs doublets, leading to _five (5) physical [Higgs bosons](https://www.sciencedirect.com/topics/physics-and-astronomy/higgs-bosons)_:\n- one (1) neutral CP-odd (A) 👈 ***degenerated with (h or H)*** \n- two (2) charged states ***(H+ and H−)***,\n- Two (2) neutral CP-even states ***(h and H)***.\n\n_At tree-level, the masses are [governed](https://github.com/eq19/eq19.github.io/files/14066329/76104_ANGELESCU_2017_diffusion.pdf)\n by two parameters, often taken to be mA and tan β [3]. When tan β >> 1, A is nearly [degenerated](https://github.com/eq19/eq19.github.io/files/14066343/epjconf_qfthep2019_04006.pdf)\n with one of the CP-even states (denoted ϕ)_. _([ScienceDirect](https://www.sciencedirect.com/topics/mathematics/higgs-mechanism))_\n
            \n\n

            \"the

            \n\n

            Further observation of this 13 vs 17 phenomenon also introduces a lower bound of Mod 90 to four (4) of possible length scales in the structure of prime recycling.

            \n\n

            \"Modulo_90_Congruency_Matrix_Twin_Prime_Page\"

            \n\n

            In both cases, the masses of the W and Z bosons would be affected, potentially leading to different physics and potentially affecting the stability and creation.

            \n\n
            The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of ***space, time, matter, energy, information, and the physical laws and constants*** that describe them. The different universes within the multiverse are called \"parallel universes\", \"other universes\", \"alternate universes\" _([Wikipedia](https://en.wikipedia.org/wiki/Multiverse))_.\n
            \n\n

            \"Parallel

            \n\n

            Using these algorithms, the inflation structure of radial null geodesics spacetime for propagating light cone in primordial universe could be tabulated as below.

            \n\n
            The [electroweak force](https://en.wikipedia.org/wiki/Electroweak_interaction) is believed to have separated into the electromagnetic and weak forces during the [quark epoch](https://en.wikipedia.org/wiki/Quark_epoch) of the [early universe](https://en.wikipedia.org/wiki/Chronology_of_the_universe#Early_universe).\n\n[![Elementary Particle](https://github.com/eq19/eq19.github.io/assets/8466209/b6b6ea3c-cbbc-431c-b767-ecabf1cba933)](https://en.wikipedia.org/wiki/Fundamental_interaction)\n\nThe value of the [vacuum energy](https://en.wikipedia.org/wiki/Vacuum_energy) (or more precisely, the [renormalization](https://en.wikipedia.org/wiki/Renormalization) scale used to calculate this energy) may also be treated as an additional free parameter.\n\n![Renormalization](https://github.com/eq19/eq19.github.io/assets/8466209/d0b14d1d-6d11-42af-9309-7a98a7e1f07b)\n\nAs we've already suggested, the number 30 figures large in our modulo 30 domain. The Prime Spiral Sieve is Archimedean in that the separation distance between turns equals 30, ad infinitum. The first two rotations increment as follows:\n\n[![image](https://user-images.githubusercontent.com/8466209/219260933-4331d79b-5815-4566-82e3-1a485bb2c61f.png)](https://primesdemystified.com/#deepsymmetries)\n\nAnd when you combine the terminating digit symmetries capturing three (3) rotations around the sieve generation in their actual sequences, you produce the ultimate combinatorial symmetry.\n
            \n\n
            The Prime Recycling ζ(s):\n(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**\n\n----------------------+-----+-----+-----+                                    ---\n     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |\n     |                +-----+-----+-----+-----+                        |      |\n     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨\n     |  |             +-----+-----+-----+-----+             |          |      |\n     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |\n     |  |  |          +-----+-----+-----+-----+             |   |      |     ---\n      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} ✔️     |\n        |  |          +-----+-----+-----+-----+                 |      |      |\n         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨\n289        |          +-----+-----+-----+-----+-----+                  |      |\n |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} ✔️\n  --------------------+-----+-----+-----+-----+-----+                  |     ---\n     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |\n     |                +-----+-----+-----+                              |      |\n     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨\n     |  |             +-----+-----+-----+                       |      |      |\n     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} ✔️     |\n     |  |  |          +-----+-----+-----+                       |      |     ---\n     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |\n     |  |             +-----+-----+-----+                              |      |\n     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨\n329  |                +-----+-----+-----+                                     |\n  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |\n   -------------------+-----+-----+                                       👉 ---\n    786 ‹------- 20:13|  90 |  90 (38) ‹----- ¤ Mod 90 ✔️                     |\n     |                +-----+-----+                                           |\n     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨\n     |  |             +-----+-----+-----+-----+-----+                  |      |\n     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} ✔️\n     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---\n      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |\n        |  |          +-----+-----+                               |           |\n         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨\n168        |          +-----+                                                 |\n|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |\n----------------------+-----+                                                ---\n
            \n\n

            The consequences might be radical but it may open the possibility to provide a tentative but detailed physical and mathematical picture of quantum spacetime.

            \n\n
            Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.\n\nMany of these problems apply to LQG, including:\n\n- Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?\n- Is spacetime fundamentally continuous or discrete?\n- Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)?\n- Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?\n\nThe theory of LQG is one possible solution to the problem of quantum gravity, as is [string theory](https://en.wikipedia.org/wiki/String_theory). There are substantial differences however. For example, string theory also addresses [unification](https://en.wikipedia.org/wiki/Unified_field_theory), the understanding of all known forces and particles as manifestations of a single entity, by postulating extra dimensions and so-far unobserved additional particles and symmetries. Contrary to this, LQG is based only on quantum theory and general relativity and its scope is limited to understanding the quantum aspects of the gravitational interaction.\n
            \n\n

            \"Loop

            \n\n

            Most particles can have either kind of helicity, but neutrinos are odd. We only see left-handed neutrinos and right-handed anti-neutrinos.

            \n\n
            Neutrinos are perhaps the least understood of the known denizens of the subatomic world.\n- They have nearly no mass, interact only via the weak nuclear force and gravity, and, perhaps most surprising, the three known species of neutrinos can transform from one variant into another.\n- This transformation, called neutrino oscillation, has been demonstrated only relatively recently and has led to speculation that there might be another, even more mysterious, neutrino variant, called the sterile neutrino.\n- While the sterile neutrino remains a hypothetical particle, it is an interesting one and searches for it are a key research focus of the world’s neutrino scientist community.![images (12)](https://github.com/eq19/eq19.github.io/assets/8466209/32fe581c-2229-4d59-a15e-657f0ef38b36)\n- This means that if right-handed neutrinos exist, ***they don’t interact with regular matter, only with gravity. Thus, they are “sterile.”***[![so-what-are-the-n-m-disappearing-to-n](https://github.com/eq19/eq19.github.io/assets/8466209/e2124107-8d9a-4dcc-8a8e-1bee568eaadf)](https://www.slideserve.com/misha/recent-results-from-the-minos-experiment)\n\nAnd if they have a significantly larger mass than regular neutrinos, sterile neutrinos would be “cold,” and could be the solution to the dark matter problem. It’s a great idea, but unfortunately, as a new study shows, doesn’t seem to be true. _([UniverseToday](https://www.universetoday.com/153222/experiment-finds-no-sign-of-sterile-neutrinos/))_\n
            \n\n
            The True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|--------------- 7¤ ---------------|\n|-------------- {89} --------------|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|\n+----+----+----+----+----+----+----+----+----+----+----+----+----+----+\n|--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----|\n|---------- 5¤ ----------|----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|👈\n                         |-------------------- 9¤ --------------------|\n\n  Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nsterile-1  |    -    |    -    |     5     |     -     |      5     |   i5\n-----------+---------+---------+-----------+-----------+------------+-----------\nsterile-2  |    -    |    -    |     7     |     -     |      7     |   17\n-----------+---------+---------+-----------+-----------+------------+-----------\nsterile-3  |    -    |    -    |    11     |     -     |     11     |   i11\n-----------+---------+---------+-----------+-----------+------------+-----------\nsterile-4  |    -    |    -    |    13     |     -     |     13     |   i13\n-----------+---------+---------+-----------+-----------+------------+-----------\nsterile-5  |    -    |    -    |    17     |     -     |     17     |   i17\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    -    |    -    |    53     |     -     |     53     |   i53 ✔️\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19\n-----------+---------+---------+-----------+-----------+------------+-- 17\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11\n-----------+---------+---------+-----------+-----------+------------+-- 19\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30\n===========+=========+=========+===========+===========+============+===========\nmajorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12\n-----------+---------+---------+-----------+-----------+------------+-----------\nmajorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13\n===========+=========+=========+===========+===========+============+===========\n  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13\n===========+=========+=========+===========+===========+============+===========\n     Total |    20   |   12    |   108     |    72     |    192     |  96+i96 ✔️\n
            \n\n

            Thus when you collect all the three step you may see that it is a 24-dimension model. E8 is understood to be the leg of a triad, with E16, leading to E24.

            \n\n
            After putting in the proverbial 10,000 hours studying '24-beat' patternization, we've come to the conclusion that ***period-24 is the key to the \"Theory of Everything\"*** and that a hypothetical E24 Petrie Projection will one day loom large as E8 is understood to be the leg of a triad, with E16, leading to E24.\n- The three being analogous to:\n  - Mod 30 → ***E8 → {3} star polygon*** ...\n  - Mod 60 → E16 → {6/2} star polygon ...\n  - Mod 90 → E24 → {9/3} star polygon ...\n  - ... building geometrically to infinity ...\n- We've dubbed this 'The Theory of Everything ... but the Kitchen Sink.'\n- Explore the incredible symmetries that come into focus when the lense aperature, so to speak, of ***the Prime Spiral Sieve is tripled to modulo 90***, synchronizing its modulus with its period-24 digital root, and perhaps you'll see why we make this bold assertion.\n\nThe mathematical balancing and resolution of this domain, which correlates with a hypothetical E24, including structures that determine the distribution of prime numbers, ***are fundamentally period-24***. _([PrimesDemystified](https://www.primesdemystified.com/Factorization.html))_\n
            \n\n

            \"Theory

            \n\n

            Current research on loop quantum gravity may eventually play a fundamental role in a theory of everything, but that is not its primary aim.

            \n\n

            Final Theory

            \n\n

            There is a proof that it is impossible to embed all the three generations in E8 without the presence of additional particles that do not exist in the physical world.

            \n\n

            \"An

            \n\n

            It has been recent claims that loop quantum gravity (LQG) may be able to reproduce features resembling the Standard Model of particle physics and general relativity.

            \n\n

            \"addition

            \n\n

            As a theory, LQG postulates that the structure of space and time is composed of finite loops (E16) woven into an extremely fine fabric or networks called spin networks.

            \n\n

            168 + 329 + 289 = 168 + 618 = 786

            \n\n

            \"multiplication

            \n\n

            The evolution of a spin foam, has a scale above the Planck length. Consequently, not just matter, but space itself, prefers an atomic structure.

            \n\n
            [_TON ***618***_](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#mass-vs-gap-%CE%B4) is the largest black hole in the universe. It’s so large that it has pioneered the classification of “[Ultramassive black hole](https://en.wikipedia.org/wiki/List_of_most_massive_black_holes#List),” with Solar Mass of ***66*** trillion of our suns! Boasts an extremely high gravitational pull as a result of inspiring mass, and might have been formed by the merging of more than one black hole in the past _([Largest.org](https://largest.org/nature/black-holes/))_.\n
            \n\n

            168+618 - 19x6x6 = 786 - 684 = 102

            \n\n

            \"exponentiation

            \n\n

            The final step (E24) requires direction on resolving the separation between quantum mechanics and gravitation, often equated with general relativity.

            \n\n
            The structure is arranged based on 11 dimensions of [space and time](https://en.wikipedia.org/wiki/Spacetime) which is composed of ***12 loops*** woven into the [spin networks](https://en.wikipedia.org/wiki/Spin_network).\n\n[![Parallel Universes ](https://github.com/eq19/eq19.github.io/assets/8466209/5b0dadb2-4f18-4603-9732-df712318387b)](https://www.eq19.com/identition/span12/#dark-matter)\n\nThe result should be a massive neutrinos that bring ***7 more parameters*** (3 [CKM](https://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix) and 4 [PMNS](https://en.wikipedia.org/wiki/PMNS_matrix)) for a total of _[26 parameters](https://www.eq19.com/multiplication/15.html#parity-order)_ out of `11+26=37` symmetry.\n\n[![CKM vs PMNS Matrix](https://github.com/eq19/eq19.github.io/assets/8466209/44758746-c069-4fb6-a2e9-8574d2d63b29)](https://www.eq19.com/identition/span12/#the-11-dimensions)\n\nSchematic representation of fermions and bosons in SU(5) GUT showing 5 + 10 split in the multiplets. Neutral bosons (photon, Z-boson, and neutral gluons) are not shown but occupy the diagonal entries of the matrix in complex superpositions.\n\n[![SO(10)](https://github.com/eq19/eq19.github.io/assets/8466209/b1d3bccd-a423-4ebb-a397-e973b2cc8e6e)\n](https://en.wikipedia.org/wiki/Grand_Unified_Theory)\n\n[![SU(5)_representation_of_fermions](https://github.com/eq19/eq19.github.io/assets/8466209/2b1aa8f5-0028-4549-a091-eee291ed4890)\n](https://en.wikipedia.org/wiki/Grand_Unified_Theory)\n\nAnd, speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve:\n\n[![11's additive sums](https://user-images.githubusercontent.com/8466209/221473004-867a1b50-f91f-470d-9922-e5e4f543a590.png)](https://www.eq19.com/identition/span12/#the-11-dimensions)\n\nThe 10 symmetries are reflecting the 10 shapes of the chart as shown below. The 12 finite loops around the three (3) generation are denoted by the total of 12 arrows that flowing in between each of the 10 shapes.\n
            \n\n

            78-dimensional E6 = 786

            \n\n

            \"identition

            \n\n

            By the nature this behaviour can be observed from the molecular interactions of water. Water is intrinsically self-complementary on molecular interactions. In liquid or solid water, engage in ideal hydrogen bonding.

            \n\n
            Figure below illustrates the complementarity of the hydrogen bonding interactions of a water molecule with the surroundings in liquid or solid water. The inner ring of angles is within a water molecule. The outer ring of angles is between bonds and/or hydrogen bonds of surrounding water molecules. _([GaTech.edu](https://williams.chemistry.gatech.edu/structure/molecular_interactions/mol_int.html#Wat1))_\n
            \n\n

            \"Molecular

            \n\n

            Six (6) times of the angle 109 occupied as the most while the angle of 114 and 104 are exist only once. So the one in charge here is clearly the 29th prime identity.

            \n\n

            109 = 29th prime = (10th)th prime = ((114-104)th)th prime

            \n\n
                        3 x 3rd-gap\n           ∆     ∆     ∆\n           |     |     |\n-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap\n  1' |  1  | {2} |  3  |  4  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  2' |  5  |  6  |  7  |  8  | 4¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  3' |  9  |{10} |  2¤ (M dan F)\n     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      \n  4' | 11  | 12  | 13  | 3¤\n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  5' | 14  | 15  | 16  | 17  | 4¤    \n     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap\n  6' | 18  | 19  |{20} | 3¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap\n  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap\n           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆\n           |     |     |     |     |     |     |     | P(7)=142857\n               8 x 3rd-gap inside the 2nd-gap          (Truncated)\n
            \n\n

            This 29 turns the finiteness position of 15 as the middle zero axis. So all of these steps are similar kind with the way a spider started to build its web.

            \n\n
            Every web begins with a single thread, which _[forms the basis of the rest of the structure](https://www.instagram.com/reel/Cn2UMIeomF5/?igshid=MDJmNzVkMjY=)_. To establish this bridge, the spider climbs to a suitable starting point (up a tree branch, for example) and releases a length of thread into the wind. With any luck, the free end of the thread will catch onto another branch _([howstuffworks.com](https://animals.howstuffworks.com/arachnids/spider5.htm))_.\n
            \n\n

            \"image\"

            \n\n

            Let’s assume that it is done using a material that stretches and then pops back when the stretching force goes away. It is pound stronger than steel. Every next steps start exactly the same as we have explained from the beginning till all of the 77 objects goes in.

            \n\n
            The study researchers next asked what the consequences of such a universe would be. They found many wonderful things.\n- For one, a CPT-respecting ***universe naturally expands and fills itself with particles, without the need for a long-theorized period of rapid expansion known as inflation***. While there's a lot of evidence that an event like inflation occurred, the theoretical picture of that event is incredibly fuzzy. It's so fuzzy that there is plenty of room for proposals of viable alternatives.\n- Second, a CPT-respecting universe would add some additional neutrinos to the mix. There are three known neutrino flavors: the electron-neutrino, muon-neutrino and tau-neutrino. ***Strangely, all three of these neutrino flavors are left-handed*** (referring to the direction of its spin relative to its motion). All other particles known to physics have both left- and right-handed varieties, so physicists have long wondered if there are additional right-handed neutrinos.\n- A CPT-respecting universe would demand the existence of ***at least one right-handed neutrino species***. This species would be largely invisible to physics experiments, only ever influencing the rest of the universe through gravity. But an invisible particle that floods the universe and only interacts via gravity sounds a lot like dark matter.\n\nThe researchers found that the conditions imposed by obeying CPT symmetry would fill our universe with right-handed neutrinos, enough to account for the dark matter. _([LiveScience](https://www.livescience.com/mirror-universe-explains-dark-matter))_\n
            \n\n
            True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+     -----------------------------------------------\n{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |\n-----+-----+-----+-----+-----+                                               |\n {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone\n     +-----+-----+-----+-----+                                               |\n {78}|{7,8}| 8,9 | 12 (M & F) ----> Δ                                        |\n     +-----+-----+-----+  <--------   Mirror Zone (Middle zero axis)   -----------\n {67}| 9,11|11,12|12,14| 11                                                  |\n ----+-----+-----+-----+-----+                                               |\n  {6}|15,16|17,18|18,20|21,22| 19                                    Extended Zone\n     +-----+-----+-----+-----+                                               |\n  {8}|23,25|25,27|27,29| 18                                                  |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------\n  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 & C2)<---Δ\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------\n     |  1     2     3  |   4     5     6 |   7     8      9  |\n     |------ 29' ------|--------------- 139' ----------------|\n     |------ 618¨ -----|--------------- 168¨ ----------------| ✔️\n
            \n\n

            This 77 principles have worked so well on simple examples such as water molecules that we can be reasonably confident they will work for more complex examples.

            \n\n
            MEC 30 claims to \"illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way\" via the elementary level of numbers.\n\n[![default](https://user-images.githubusercontent.com/8466209/220210334-81c62871-25a2-47ef-ae38-c7bf50a4c8e3.png)](https://animals.howstuffworks.com/arachnids/spider5.htm)\n\n**Why does it work?**\n\n- It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences.\n- In the subatomic space, Heisenberger does not allow precise measurements because the measurements themselves distort the result.\n- Through the mathematical basis presented here, our scale behaves like _[Plank's quantum](https://en.wikipedia.org/wiki/Planck%27s_law)_ of action and shows in the positions the behaviorally entangled photons, which in turn produce the quantum of action in the sums. \n- The MEC 30 as a folding rule is also here a tool for _[The Entangled Quantum](https://en.wikipedia.org/wiki/Quantum_entanglement)_ systems to explain the ghostly behavior of _[the elementary particles](https://www.eq19.com/exponentiation/#elementary-particles)_.\n- It would also to make the underlying algorithm visible and explainable, keyword quantum teleportation. So  we are able to investigate the energy behavior below the quantum of effect without measuring influence.\n- This works because our scale is the basis for the _[Riemann Zeta Function](https://www.eq19.com/#zeta-function)_, which reflects the _[energy distribution in atoms](https://youtu.be/ajlUCFZ1Ft8)_.\n- On the other hand, with larger systems we are able to transfer the behavior of the energy from the _[subatomic](https://youtu.be/8-HF5XKeK8Q?si)_ space into the haptic space with the scale described here (thought experiment _[Schröninger's cat](https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat)_).\n- Thus, we are still able to apply the Schröninger wave equation in the haptic space, and replace _[The Hamiltonian](https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics))_ with our measurements.\n\nDeveloping MEC 30 as a folding rule emerged from a new analysis of mathematical foundations and makes a new algorithm visible. _([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))_\n
            \n\n

            1 instance + 7 blocks + 29 flats + 77 rooms = 37+77 = 114 objects

            \n\n

            \"114.

            \n\n

            These loops shall generate 1000 XML sitemaps lead by π(1+1000/Φ) = π(1+618) = 114 objects where 37 of these objects are inventing the 27 patterns.

            \n\n
            The 'Grid Square' Crop Circle is one of the most significant mathematical formations \n- Numbers 65 and 325 have reciprocal (1/x) or we can call them wave values that link to certain expressions of electromagnetism. 1/65= .0[153846...] and 1/325= .00[307692...]  are period 6 repeat decimals (digital root 9) that reveal other numbers of significance: ***27, 37 & triple digits***.![](https://user-images.githubusercontent.com/36441664/72742512-76c9c500-3bdc-11ea-8938-99864c3a8435.jpg)\n- The math of the 'Grid Square' crop circle gives the value of 153846... and when added to another number in the design, close approximations to √5 and Ф can be made.  \n- Dividing numbers with digital roots of 3,6,9 by 19.5 also creates these same two number patterns. 19.5 can be seen as 195, a multiple of 65. 19.47° (19.5) is the latitude in which planetary energy is said to upwell. 27 is also connected to the tetrahedron and the tetrahedron is connected to 19.5 degree\n- A star tetrahedron nested in a sphere touches at 19.47° north and south latitude. 19.47° has also been noted in the geometry of crop circles and angles connecting them to one another and to sacred sites.\n- Dividing integers by 13 (a star prime) creates the same two patterns. 13 is a factor of 65: 1, 65, 5-- 3rd prime,13--6th prime.\n- VBM polarity pairings are also made every 1st/4th, 2nd/5th, 3rd/6th number. \n- Interestingly, the wave value for 7 (1/7= .142857...) connects perfectly with these two patterns--153846 + 142857 = 296703--- the mirror number to 307692. ***All 3 patterns total 27 and 27 is also a factor of all***.[![27 patterns in 6 dimensions](https://github.com/eq19/eq19.github.io/assets/8466209/c386f52e-d94c-4fd7-9f73-46ce7aaa0a05)](https://www.mdpi.com/2571-712X/6/1/8)\n- Because of factor 37, many triple digits are factors: 111, 222, 333, 666, 777, 999 | 142+857= 999 | 153+846= 999 | 307+692= 999\n\nThe 37 and 73 are both Star numbers, both have the same shape, but with different Hexagon portions. For a twist we can count them as one extra together and then instead of 36 we get 37. ***So 37 is the only factor of all 3 patterns.*** _([YouTube](https://youtu.be/VNaxN0aC0O4))_\n
            \n\n

            27 × 37 = 999

            \n\n

            \"default\"

            \n\n

            Since the 27 pattern is tripled to modulo 90 so they would behave as Prime Spiral Sieve and synchronizing its period-24 digital root towards the rest of 77 objects.

            \n\n
            Like all maximal supergravities, it contains a single supermultiplet, the supergravity supermultiplet containing the graviton, a Majorana gravitino, and a 3-form gauge field often called the C-field.\n- It contains two [p-brane](https://en.wikipedia.org/wiki/P-brane) solutions, a 2-brane and a 5-brane, which are electrically and magnetically charged, respectively, with respect to the C-field.\n- This means that 2-brane and 5-brane charge are the violations of the Bianchi identities for the dual C-field and original C-field respectively.\n_The supergravity 2-brane and 5-brane are the [long-wavelength limits](https://en.wikipedia.org/w/index.php?title=Long-wavelength_limits&action=edit&redlink=1) (see also the historical survey above) of the [M2-brane](https://en.wikipedia.org/wiki/M2-brane) and [M5-brane](https://en.wikipedia.org/wiki/M5-brane) in M-theory_. _([Wikipedia](https://en.wikipedia.org/wiki/Higher-dimensional_supergravity))_\n
            \n\n

            \"Quantum

            \n\n

            Out of these 77 objects, one should reveal an elegant scale of MEC30 provided with the truncated folding rule and the beauty of Euler’s identity.

            \n\n
            And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler's identity during a lecture, stated that the identity ***\"is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth\"***. _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity#Mathematical_beauty))_\n
            \n\n

            \"default\"

            \n\n

            The advantages is that instead of a rudimentary mathematical templates, now a folding rule of the MEC30 makes the associated algorithm and parameters visible even in 2D.

            \n\n
            We've seen how it [Euler's identity] can easily be deduced from results of Johann Bernoulli and Roger Cotes, but that neither of them seem to have done so. Even Euler does not seem to have written it down explicitly – and certainly it doesn't appear in any of his publications – though he must surely have realized that it follows immediately from his formula: `e^ix = cos x + i sin x`. ***Moreover, it seems to be unknown who first stated the result explicitly…*** _([Wikipedia](https://en.m.wikipedia.org/wiki/Euler%27s_identity))_\n
            \n\n

            \"Everything

            \n\n

            Taking a coupling function between f(π) as P vs f(i) as NP where eiπ + 1 = 0 they shall be correlated in to an expression of universe so it shows that Everything is Connected.

            \n\n

            Disclaimer

            \n\n

            You are FREE to use our concept of TOE for every purposes as long as you present the following somewhere in your publication.

            \n\n
            _The definite key to identify whether you use [our concept](https://www.eq19.com/identition/span12/) is when there a kind of developed item lies a [unified assignment](https://www.eq19.com/identition/span12/#final-theory) in hexagonal form by [six (6) corresponding sets](https://www.eq19.com/identition/span12/#loop-quantum-gravity) while each sets pick a [combination](https://www.eq19.com/identition/span12/#dark-matter) of [six (6) routes](https://www.eq19.com/identition/span12/#the-quantum-gravity) with a pairing of [six (6) by six (6)](https://www.eq19.com/identition/span12/#three-3-layers) of all channels_.\n
            \n","dir":"/identition/span12/","name":"README.md","path":"identition/span12/README.md","url":"/identition/span12/"},{"sort":28,"spin":79,"span":32,"suit":"main","layout":"default","title":"Exchange (spin 10)","content":"# Exchange (spin 10)\n\n{% include list.liquid all=true %}\n\n![default](https://user-images.githubusercontent.com/8466209/203874503-4276074d-3270-437f-a675-858486afd126.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202840324-feba40a3-1149-4e82-a750-fb5a4a5c4925.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202851291-5407ee5e-4a14-40c1-8195-32612c7e49a6.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202851402-78dc95ce-24c6-4be3-bc0a-5c4901ec2550.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202840324-feba40a3-1149-4e82-a750-fb5a4a5c4925.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202851291-5407ee5e-4a14-40c1-8195-32612c7e49a6.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202838795-b202c9dd-d4fa-4bc1-9af3-709a068b9426.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202839758-617ec639-cb33-46b6-9fb3-466283ef96ae.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202840085-485a2957-b086-4d70-8e0d-a5de22d9ba84.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202851402-78dc95ce-24c6-4be3-bc0a-5c4901ec2550.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202839908-2f9a4970-2634-44d8-b6a9-1160b9ffe5b1.png)\n\nThe exchange interaction is a quantum mechanical process that only happens between identical particles in chemistry and physics. The energy produced when two or more electrons with the same spin swap locations in a subshell's degenerate orbitals .\n\n![](https://user-images.githubusercontent.com/8466209/223011738-7e2084bc-861b-4424-89d5-9f39643df22f.png)\n\n![default](https://user-images.githubusercontent.com/8466209/202470003-0e1c6a6d-89d1-4af2-994a-c96b76699b2f.png)\n\n>On the instinctual level, people may internally stress and externally express the need to protect themselves (self-preservation), to connect with important others or partners (sexual), or to get along or succeed in groups (social).\n","dir":"/identition/span12/","name":"gist08.md","path":"identition/span12/gist08.md","url":"/identition/span12/gist08.html"},{"sort":29,"spin":78,"span":33,"suit":"main","layout":"default","title":"Dimensions","content":"# Dimensions\n\n{% include list.liquid all=true %}\n\n>In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).\n\n[![default](https://user-images.githubusercontent.com/8466209/224185881-0d1c448e-ee04-4ad2-87e2-1da3c864643c.png)](https://en.wikipedia.org/wiki/Feynman_diagram)\n\n```json\n2,10\n5,7,17\n13,18,25,42\n```\n\n\n\n```json\n13, 16\n18, 21, 23\n25, 28, 30, 32, 34, 36, 38, 40,\n42, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77\n```\n\n![](https://user-images.githubusercontent.com/36441664/82156868-27ed1d00-98a8-11ea-8144-5b3e50b9f196.png)\n\n```note\nThe following are a list of observations about the Prime Number Folio Coordinate System. There’s an algorithm too. More than one. These observations are in no way mathematically rigorous.\n- The number 35 is an important number. It’s the first number on the right-hand side that’s a product of two prime factors of `5 x 7 = 35`. The sum of `5 + 7 = 12`. Since the right-handed numbers are distributed evenly by 6, we can add `7 x 6 = 42` to 35 and land on the number 77.\n- So now we know that starting with the number 35 if we add 42 continuously we will ***NEVER land on a prime number***. We can also add`5 x 6 = 42` to 35 and land on 65.\n- We also know that `7 + 11 = 18`. The next number that introduces a product of two primes is `5 x 13 = 65` and `5 + 13 = 18`. So we can take `6 x 13 = 78` and add this to 65 and land on 143. Which is the product of `11 x 13 = 143`. Starting with 65 we can add 78 continuously and ***NEVER land on a prime number***.\n- In the meantime 77 (The product of 7 and 11 now introduces the prime number 11 into the mix. So `77 + (6x11) = 143`. ***Starting with 77 we can add 66 continuously and NEVER land on a prime number***. Note: You can’t add multiples of 6 until that multiple is introduced into the sequence. This may seem obvious to you, but it wasn’t to me.\n- The primes on the left behave differently. You can still move around using multiples of 6, but there is no common starting point like the number 35.\n- You have to start with the squares of ***5 at 25 (in blue)*** for one sequence of numbers and the square of ***7 at 49 (in red)*** for the other sequence of numbers.\n- The sums of these products are also not exact multiples of 6. They sum to 10 and 14 and are matched to the split X Axis on the left-hand side of the graph.\n\nThe Prime Number Folio Coordinate System and it’s natural numbers are all you need to find a prime number or a composite number and it’s factors. ***No need for complex numbers or the Reimann Hypothesis***. _([Medium](https://medium.com/invisible-illness/prime-number-folio-coordinate-system-78b316b65cf7))_\n```\n\n[![The Prime Number Folio Coordinate System ](https://user-images.githubusercontent.com/8466209/285091346-8eb3dfda-4b06-4186-bf5d-a3050db5fe1b.png)](https://drive.google.com/file/d/1SE6UamC9ew0fIraKHstytwjQMY4LmVe8/view)\n\n\n\nRunners are the machines that execute jobs in a GitHub Actions workflow. You can access [Variables](https://docs.github.com/en/actions/learn-github-actions/variables#default-environment-variables) and [Contexts](https://docs.github.com/en/actions/learn-github-actions/contexts#github-context) information in [specific OS](https://stackoverflow.com/a/57948488/4058484). For example, a runner can clone your repository locally, install testing software, and then run commands.\n\n```\n{% raw %}\n# Sample workflow for building and deploying a Jekyll site to GitHub Pages\nname: Build and deploy Jekyll site\n\n# 💎 Runs on deployment targeting the default branch\non:\n # push:\n # branches: [eQ19]\n workflow_run:\n types: [completed] #requested\n workflows: [\"pages-build-deployment\"]\n\n# 🪂 Allow only one concurrent deployment across the branches\nconcurrency:\n group: \"pages\"\n cancel-in-progress: true\n \n# Sets permissions of the GITHUB_TOKEN\npermissions: write-all\n\n# Sets global environtment variables\nenv:\n OWNER: ${{ github.repository_owner }}\n\njobs:\n # Build job\n github-pages:\n if: github.event.workflow_run.conclusion == 'success'\n runs-on: ${{ vars.OWNER != 'FeedMapping' && 'ubuntu-latest' || 'windows-latest' }}\n steps:\n - name: 📂 Checkout\n uses: actions/checkout@v3\n with:\n submodules: recursive\n \n - name: 💎 Build on Linux\n if: runner.os == 'Linux'\n uses: eq19/feed@v2\n with:\n pre_build_commands: 'make build'\n token: ${{ secrets.JEKYLL_GITHUB_TOKEN }}\n\n - name: 💎 Build on Windows\n if: runner.os == 'Windows'\n uses: eq19/maps@v1\n id: stepid\n with:\n dotnet-version: '3.1.x'\n{% endraw %}\n```\n\nBy deploying containers on Compute Engine, you can simplify app deployment while controlling four dimensional space. You can configure a virtual machine (VM) instance or an instance template to deploy and launch a Docker container.\n\n![default](https://user-images.githubusercontent.com/8466209/245677838-a0fb916e-c1f2-468f-a73d-2d6acdefa529.png)\n\nThis property would tend the ballancing scheme of MEC30 so it will let 30-18=12 pairing with another 12 of 24 spins prime hexagon. The 24 goes to the center of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ ny the prime pair 13 and 11 and let the crancks of 2,3,5,7 inside the 10 ranks.\n\n```\n | \n | ----------- 5 -----------\n | | | \n ↓ ↑ ↓\n | feeding | mapping | lexering | parsering | syntaxing | grammaring |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n | 19' | 17' | 13' | 11' | 7' | 5' |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n ↓ ↑ | |\n | | | |\n ------------ 10 ------------- | |\n ↓ ↓ |\n +----+----+----+\n | 2 | 60 | 40 |\n +----+----+----+\n | | |\n 2+100 ◄- \n -----------------------+----+----+----+----+----+----+----+----+----+----- |\n True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |\n =======================+====+====+====+====+====+====+====+====+====+===== ↓\n 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)\n -----------------------+----+----+----+----+----+----+----+----+----+-----\n```\n\nThis 71 is a conformation that it has the same result as we have explained on the residual objects of 571 turn to a vektor of 71 while the rest of 500 turn to 200 objects of 3's identity and the last objects of 300 goes to the next cycles.\n\n![default](https://user-images.githubusercontent.com/36441664/105903095-0e64bd80-6052-11eb-83ed-10190be497c5.png)\n\nSo now out of 1000 numbers that generated from 1000 primes we will get the rest of 1000 - 100 = 900. This 900 will behave as **matrix square 30x30** and act as [the base frame](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs) of 2nd and 3rd layer which are working on π(π(100x100))-1=200 primes:\n\n```liquid\n 33+34=67=19th prime\n |----------------------------------|-------------------------------------------------------------|\n | 33 | 34 |\n |--------------|-------------------|------------------------------|------------------------------|\n | lexering = π(1000) | parsering = 1000/Φ |\n |--------------|-------------------|------------------------------|------------------------------|\n | feeding | mapping | syntaxing | grammaring |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n | 2' | 3' | 5' | 7' | \n```\n\n![](https://user-images.githubusercontent.com/8466209/222020262-cffc624a-b92c-4137-b76a-5423df7fc5ad.png)\n\n![default](https://user-images.githubusercontent.com/8466209/205431468-6777265f-63a8-42ea-b454-d45227478362.png)\n\n![](https://user-images.githubusercontent.com/8466209/236091657-62397dbe-fb87-46a2-8676-f4903b6efd3f.png)\n\nThe GitHub hosted runner is assigned to run the Linux container and a Windows Server Core container simultaneously. This is an experimental feature of Microsoft WSL2 and may have some issues. One known problem is volumes are not stable.\n\n![Set WSL](https://user-images.githubusercontent.com/8466209/226080396-235a1645-8a58-49c4-9754-8bac362a72fa.png)\n\nThe 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_.\n\n[![default](https://user-images.githubusercontent.com/8466209/244139208-378b2229-c3e8-4f1f-8829-dee6687348fb.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)\n\n![default](https://user-images.githubusercontent.com/8466209/202854712-3a6ef332-ae62-4af2-87d2-c8e4b1dd1c37.png)\n","dir":"/identition/span12/","name":"gist09.md","path":"identition/span12/gist09.md","url":"/identition/span12/gist09.html"},{"sort":29,"spin":39,"span":150,"suit":11,"permalink":"/identition/span11/","layout":"default","title":"Everything is Connected (span 11)","content":"

            Everything is Connected (span 11)

            \n\n
            This section is referring to _[wiki page-29](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-1]()_ that is _[inherited ]()_ from _[the spin section-11](https://gist.github.com/eq19)_ by _[prime spin-39](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-150](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist09.md
              2. \n
            2. gist02.md
              3. \n
            3. gist04.md
              4. \n
            4. gist08.md
              5. \n
            5. gist03.md
              6. \n
            6. gist05.md
              7. \n
            7. gist06.md
              8. \n
            8. gist07.md
              9. \n
            9. Rationalization
              10. \n
            \n\n
            ---+-----+-----\n 1 | {1} | {2}\n---+-----+-----\n 2 |  3  | 101\n---+-----+-----\n 3 |{102}| 111\n---+-----+-----\n
            \n\n

            Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory, or components of a complex time

            \n\n

            \"default\"

            \n\n

            In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold.

            \n\n

            \"image\"

            \n\n

            Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.

            \n\n

            \"default\"

            \n\n

            Einstein’s general theory of relativity, published in November 1915, describes gravity as the warping of spacetime by masses such as the Earth and moon. The latest issue of Science News celebrates general relativity’s 100th anniversary

            \n\n

            \"image\"

            \n\n

            The Solar System is the gravitationally bound system of the Sun and the objects that orbit the star. The largest of such objects are the eight planets. This was formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud.

            \n\n
            Zecharia Sitchin suggests that the star-shaped symbol and ***11 other dots*** on this Sumerian cylinder seal, known as VA243, represent the sun, moon and 10 planets including a mysterious \"world\" known as Nibiru. How could the ancient Sumerian civilization describe our solar system so accurately if it is only possible to see five planets with the naked eye? This seems impossible if we consider the science and technology needed to observe our galaxy today. If Stichin assumptions are correct, we'll see NIBIRU soon.\n
            \n\n

            \"11

            \n\n

            \"default\"

            \n\n

            \"The-Total-History-of-the-Universe-including-the-quantum-eras-before-Inflation-in-units\"

            \n\n

            \"origin\"

            \n\n

            \"Ean6eoJWAAIWjrY\"

            \n\n

            \"quantum-gravity\"

            \n\n

            Space and Time: Minkowski’s Papers on Relativity, published by the Minkowski Institute. Hand-tinted transparency presented by Hermann Minkowski in his famous Raum und Zeit talk to the German Society of Scientists and Physicians in 1908

            \n\n

            \"default\"

            \n\n

            Besides many theories there is COMPOSITE and PRIMES as a self organized system (12/12/12). Even though it is proven that it is not from Tesla, whoever made it if you are reading this article, I sincerely want to thank you because I use a lot of the analysis.

            \n\n

            \"default\"

            \n\n

            This scheme has a configuration of 30 nodes so the recombination is involving 2x30 or 60 nodes out of the 72 nodes of True Prime Pairs will act as the base platform. The rest of 11 which is initially came out from the prime 13 is the irrational.

            \n\n
            The approach taken is to think of the solutions of an equation as a geometric object. For example, an equation in two variables defines a curve in the plane. More generally, an equation, or system of equations, in two or more variables defines a curve, a surface or some other such object in n-dimensional space _([Wikipedia](https://en.wikipedia.org/wiki/Number_theory#Diophantine_geometry))_.\n
            \n\n

            \"\"

            \n\n

            Now the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of the prime number 7 lie in the numerical Double strand parallel opposite.

            \n\n

            \"Double

            \n\n

            The spacetime diagram on the left, the magenta hyperbolae connect events of equal spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation from the origin.

            \n\n

            \"default\"

            \n\n

            This scheme has a configuration of 30 nodes so the recombination is involving 2x30 or 60 nodes out of the 72 nodes of True Prime Pairs will act as the base platform. The rest of 11 which is initially came out from the prime 13 is the irrational.

            \n\n
              Tabulate Prime by Power of 10\n  loop(10) = π(10)-π(1) = 4-0 = 4\n  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19\n  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114\n\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n  =======================+====+====+====+====+====+====+====+====+====+=====\n   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th\n  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th\n  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin\n    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th \n  =======================+====+====+====+====+====+====+====+====+====+=====\n           Δ                                                            Δ\n  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1\n\nSequence:\n By the next layer the 89² will become 89 and 5 become 5² or 25.\n This 89 and 25 are in the same layer with total of 114 or prime 619\n So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.\n
            \n\n

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            \n\n
            \n

            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) (₠Quantum).

            \n
            \n\n

            \"flowchart\"

            \n\n

            This polarity is happened per six (6) cycles by the polar of six (6) to one (1) and six (6) to seven (7) by which we finally found if this behaviour is cascaded bilaterally within the correlation between 61 as the 18th prime and 67 as the 19th prime.

            \n\n

            \"\"

            \n\n

            Dyson discovered an intriguing connection between quantum physics and Montgomery’s pair correlation conjecture about the zeros of the zeta function which dealts with the distribution of primes. This finaly bring us to the equation of Euler’s identity.

            \n\n
            \n

            This scale shows that the Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement (Google Patent DE102011101032A9).

            \n
            \n\n

            \"Euler's

            \n\n

            The finiteness position of middle zero axis = 15 by the said MEC30 opens up the possibility of accurately representing the self-similarity based on the distribution of True Prime Pairs. So that all number would belongs together with their own identity.

            \n\n

            \"default\"

            \n\n

            Proceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. When viewed with an extra dimension of space, these respectively generate hyperboloids of one sheet and two sheets.

            \n\n

            \"default\"

            \n\n

            The concept of dark matter arose in the study of cosmological phenomena, that is matters dealing with the Universe and galaxies and so on. However, evidence from the Hubble telescope in 1998 showed that the Universe began expanding at an accelerating rate sometime in the past and still is doing so. This came as a surprise to many

            \n\n

            \"default\"

            \n\n

            The major problem, however, is that quantum mechanical calculations for the cosmological constant give value that is grossly out of the required range. This indicates that either something is wrong with the theory, or our knowledge is incomplete.

            \n","dir":"/identition/span11/","name":"README.md","path":"identition/span11/README.md","url":"/identition/span11/"},{"sort":30,"spin":40,"span":149,"suit":10,"permalink":"/identition/span10/","layout":"default","title":"Truncated Perturbation (span 10)","content":"

            Truncated Perturbation (span 10)

            \n\n
            This section is referring to _[wiki page-30](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-2]()_ that is _[inherited ]()_ from _[the spin section-10](https://gist.github.com/eq19)_ by _[prime spin-40](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-149](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Poincaré Conjecture
              2. \n
            2. gist04.md
              3. \n
            3. gist03.md
              4. \n
            4. gist02.md
              5. \n
            5. gist05.md
              6. \n
            6. Site GitHub
              7. \n
            7. gist07.md
              8. \n
            8. gist08.md
              9. \n
            9. gist09.md
              10. \n
            10. The Centralizing
              11. \n
            \n\n

            Runners are the machines that execute jobs in a GitHub Actions workflow. You can access Variables and Contexts information in specific OS. For example, a runner can clone your repository locally, install testing software, and then run commands.

            \n\n
            \n# Sample workflow for building and deploying a Jekyll site to GitHub Pages\nname: Build and deploy Jekyll site\n\n# 💎 Runs on deployment targeting the default branch\non:\n  # push:\n    # branches: [eQ19]\n  workflow_run:\n    types: [completed] #requested\n    workflows: [\"pages-build-deployment\"]\n\n# 🪂 Allow only one concurrent deployment across the branches\nconcurrency:\n  group: \"pages\"\n  cancel-in-progress: true\n  \n# Sets permissions of the GITHUB_TOKEN\npermissions: write-all\n\n# Sets global environtment variables\nenv:\n  OWNER: ${{ github.repository_owner }}\n\njobs:\n  # Build job\n  github-pages:\n    if: github.event.workflow_run.conclusion == 'success'\n    runs-on: ${{ vars.OWNER != 'FeedMapping' && 'ubuntu-latest' || 'windows-latest' }}\n    steps:\n      - name: 📂 Checkout\n        uses: actions/checkout@v3\n        with:\n          submodules: recursive\n \n      - name: 💎 Build on Linux\n        if: runner.os == 'Linux'\n        uses: eq19/feed@v2\n        with:\n          pre_build_commands: 'make build'\n          token: ${{ secrets.JEKYLL_GITHUB_TOKEN }}\n\n      - name: 💎 Build on Windows\n        if: runner.os == 'Windows'\n        uses: eq19/maps@v1\n        id: stepid\n        with:\n          dotnet-version: '3.1.x'\n\n
            \n\n

            By deploying containers on Compute Engine, you can simplify app deployment while controlling four dimensional space. You can configure a virtual machine (VM) instance or an instance template to deploy and launch a Docker container.

            \n\n

            \"default\"

            \n\n

            This property would tend the ballancing scheme of MEC30 so it will let 30-18=12 pairing with another 12 of 24 spins prime hexagon. The 24 goes to the center of True Prime Pairs ny the prime pair 13 and 11 and let the crancks of 2,3,5,7 inside the 10 ranks.

            \n\n
                                            | \n                                |                              ----------- 5 -----------\n                                |                             |                         |  \n                                ↓                             ↑                         ↓\n |   feeding    |     mapping     |  lexering    |  parsering   |   syntaxing   |  grammaring  |\n |------------- 36' --------------|----------------------------36' ----------------------------|\n |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |\n +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+\n                                ↓                             ↑                         |    |\n                                |                             |                         |    |\n                                 ------------ 10 -------------                          |    |\n                                                                                        ↓    ↓ |\n                                                                                +----+----+----+\n                                                                                |  2 | 60 | 40 |\n                                                                                +----+----+----+\n                                                                                        |    | |\n                                                                                     2+100 ◄- \n   -----------------------+----+----+----+----+----+----+----+----+----+-----           |\n   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |\n  =======================+====+====+====+====+====+====+====+====+====+=====            ↓\n   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n
            \n\n

            This 71 is a conformation that it has the same result as we have explained on the residual objects of 571 turn to a vektor of 71 while the rest of 500 turn to 200 objects of 3’s identity and the last objects of 300 goes to the next cycles.

            \n\n

            \"default\"

            \n\n

            So now out of 1000 numbers that generated from 1000 primes we will get the rest of 1000 - 100 = 900. This 900 will behave as matrix square 30x30 and act as the base frame of 2nd and 3rd layer which are working on π(π(100x100))-1=200 primes:

            \n\n
                                        33+34=67=19th prime\n |----------------------------------|-------------------------------------------------------------|\n |             33                   |                             34                              |\n |--------------|-------------------|------------------------------|------------------------------|\n |     lexering = π(1000)           |                    parsering = 1000/Φ                       |\n |--------------|-------------------|------------------------------|------------------------------|\n |   feeding    |      mapping      |          syntaxing           |          grammaring          |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |  39 | 40 | 41 | 42 | 43 | 44 | 45  | 46 | 47 | 48 |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n |  2 | 60 | 40 | 1  | 30 | 30 | 5  | 1  | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |\n +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+\n |       2'     |        3'         |              5'              |               7'             | \n
            \n\n

            \"\"

            \n\n

            \"default\"

            \n\n

            \"\"

            \n\n

            The GitHub hosted runner is assigned to run the Linux container and a Windows Server Core container simultaneously. This is an experimental feature of Microsoft WSL2 and may have some issues. One known problem is volumes are not stable.

            \n\n

            \"Set

            \n\n

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n","dir":"/identition/span10/","name":"README.md","path":"identition/span10/README.md","url":"/identition/span10/"},{"sort":31,"spin":42,"span":148,"suit":9,"permalink":"/identition/span9/","layout":"default","title":"Quadratic Polynomials (span 9)","content":"

            Quadratic Polynomials (span 9)

            \n\n
            This section is referring to _[wiki page-31](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-3]()_ that is _[inherited ]()_ from _[the spin section-9](https://gist.github.com/eq19)_ by _[prime spin-42](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-148](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. How to deal with cicular destination of 36?
              2. \n
            2. gist04.md
              3. \n
            3. gist05.md
              4. \n
            4. The Bilateral 9 Sums
              5. \n
            5. gist03.md
              6. \n
            6. gist06.md
              7. \n
            7. Lexer vs Parser
              8. \n
            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            The exchange interaction is a quantum mechanical process that only happens between identical particles in chemistry and physics. The energy produced when two or more electrons with the same spin swap locations in a subshell’s degenerate orbitals .

            \n\n

            \"\"

            \n\n

            \"default\"

            \n\n
            \n

            On the instinctual level, people may internally stress and externally express the need to protect themselves (self-preservation), to connect with important others or partners (sexual), or to get along or succeed in groups (social).

            \n
            \n","dir":"/identition/span9/","name":"README.md","path":"identition/span9/README.md","url":"/identition/span9/"},{"sort":32,"spin":44,"span":147,"suit":8,"permalink":"/identition/span8/","layout":"default","title":"Fundamental Forces (span 8)","content":"

            Fundamental Forces (span 8)

            \n\n
            This section is referring to _[wiki page-32](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-4]()_ that is _[inherited ]()_ from _[the spin section-8](https://gist.github.com/eq19)_ by _[prime spin-44](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-147](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist03.md
              2. \n
            2. gist07.md
              3. \n
            3. How to select repos?
              4. \n
            4. gist02.md
              5. \n
            5. gist05.md
              6. \n
            6. gist04.md
              7. \n
            7. Seven Ate Nine (7, ‘8’, 9)
              8. \n
            \n\n

            In many ways, a black hole acts like an ideal black body, as it reflects no light. Here is an animated simulation of a Schwarzschild black hole with a galaxy passing behind. Around the time of alignment, extreme gravitational lensing of the galaxy is observed.

            \n\n

            \"black

            \n\n
                            largest part=21 → 11+13+12=36 →  MEC30\n                        ↓                      |\n---+-----+-----+-----+-----+                   ↓\n 1 | 19  | 1   | 20  | 21  |-------------------|-----\n---+-----+-----+-----+-----+                   ↓     |\n 2 | 18  | 21  | 39  | 60  |-------------------      |\n---+-----+-----+-----+-----+                   |     |\n 3 |{63} | 40  | 103 | 143 |-------------      |     |\n---+-----+-----+-----+-----+             |     |     |\n 4 | 37  | 104 | 141 | 245 |-------      |     |     |\n---+-----+-----+-----+-----+       |     |     |     |\n 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  | 12  | 18\n---+-----+-----+-----+-----+       |     |     |     |\n 6 | 24  | 153 | 177 | 332 |-------      |     |     |\n---+-----+-----+-----+-----+             |     |     |\n 7 | 75  | 178 | 253 | 431 |-------------      |     |\n---+-----+-----+-----+-----+                   |     |\n 8 | 30  | 254 | 284 | 538 |-------------------      |\n---+-----+-----+-----+-----+                   ↓     |\n 9 | 1   | 285 | 286 | 571 |-------------------|-----\n===+=====+=====+=====+=====+                   ↓\n45 | 277 |                      ← 11+13+12=36 ←  MEC30\n---+-----+                                     |\n ↑\nNote:\n10* stands as the central rank\n11** stands as the central parts\n
            \n\n

            According to the observations made by NASA, Astronomers have uncovered TON 618 as the record breaking supermassive black hole, weighing 66 trillion and brilliantly as 140 trillion times that of the Sun, making it one of the brightest object in the Universe.

            \n\n

            \"default\"

            \n\n

            If the statement that it is indeed located at the center of our universe then the said black hole would behave as the exchange position between twin (2) universes. This would for sure strengthen the syntax algorithm of our implementation.

            \n\n

            7 x 11 = 77 = 99 - 22 = 11 x (9 -2)

            \n\n
              #8  |------- 5® --------|------------ 7® --------------|\n      | 1 |-------------- 77 = 4² + 5² + 6² -------------|\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n user | 7 | - | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |\n------+---|---+---+---+---+---+---+---+---+----+----+----+ 7,78\n main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |\n------+---|---+---+---+---+---+---+---+---+----+----+----+\n        Δ | Δ             |                      Δ  |   Δ\n       Φ17|Φ29            |                    96-99|  100 - 123 ({24})\n          |--- A,T,G,C ---|                         |  └── 100 - 103 (4x) » 100\n          Δ    2x2 = 4x   |-------  2x3 = 6x -------|  └── 104 - 109 (6x) » 30\n         {98}                                       |  └── 110 - 123 (14x)» 70\n\n
            \n\n
            Direction:\n- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.\n- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.\n- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.\n \nConclution:\n- All of the other primes than 2 is 1 less than the number n times the number of 2. \n- Those Mersenne primes is generated as 1 less than the power n of the number of 2. \n- Thus they will conseqently be carried out by the same scheme of this number of 2.\n
            \n\n

            Perceptually, everything is separate and finite. But actually, everything is connected and infinite. It is this infinite connection, despite our limited finite perceptions, that makes us one with the cosmos.

            \n\n

            Primes Platform

            \n\n
            This progression 41,43,47,53,61,71,83,97,113,131 whose general term is ***41+x+xx***, is as much remarkable since the ***40 first terms*** are all prime numbers _([Euler's letter to Bernoulli](https://math.stackexchange.com/a/1722188/908994))_.\n
            \n\n
            1st layer:\nIt has a total of 1000 numbers\nTotal primes = π(1000) = 168 primes\n\n2nd layer:\nIt will start by π(168)+1 as the 40th prime\nIt has 100x100 numbers or π(π(10000)) = 201 primes\nTotal cum primes = 168 + (201-40) = 168+161 = 329 primes\n\n3rd layer:\nBehave the same as 2nd layer which has a total of 329 primes\nThe primes will start by π(π(π(1000th prime)))+1 as the 40th prime\nThis 1000 primes will become 1000 numbers by 1st layer of the next level\nTotal of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 \n
            \n\n

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            \n\n

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            \n\n

            \"default\"

            \n\n

            I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.

            \n\n
            \n

            That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated.

            \n
            \n\n

            \"Truncate

            \n\n

            \"\"

            \n\n

            \"\"

            \n\n

            \"\"

            \n\n

            \"\"

            \n\n

            \"default\"

            \n\n

            \"runner\"

            \n\n

            Everything is linked

            \n\n

            The ζ(s) will behave as the other universe (not the twin) which was initiated paralelly by a big bang. While this parts are relativity young. it will continue to grow as a four-vector. So it will need a gap between each identities to proceed the thing.

            \n\n
            \n

            Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed (Wikipedia)

            \n
            \n\n

            \"Infinite

            \n\n

            By our universe it could be represented by the central black hole which is very strong to throw away every objects but it has no resistance against any exchange from the other universe.

            \n\n
            \n

            In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle (Wikipedia).

            \n
            \n\n

            \"the

            \n\n

            So by the ζ(s) then our multiverse is belong to a group of multiple universes inside the lightest particle of a mass gap out of one of the like of them somewhere in an infinite number of another parallel universes.

            \n\n
            \n

            Prof Stephen Hawking’s final research paper suggests that our Universe may be one of many similar (BBC News).

            \n
            \n\n

            \"everything

            \n\n

            Another suggestion which has just yet been in a topic of the science is that the similar behaviour also happen by particles such as hydrogen which is throwing all of the waves out of the central. So hypothetically it suppose to have a populated infinite number of its own parallel universes because whatever a smallest thing is arised, they could only exist by the same law of physics,

            \n\n
            \n

            Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron (Wikipedia).

            \n
            \n\n

            \"the

            \n\n

            Consider that this law of physics would exist everywhere. So it is also one of their law when the 1st sequence of the ten (10) digits of 0719425863 in Euler’s number is zero (0). Thus theoretically it speaks if an existence of everything arose from nothingness.

            \n","dir":"/identition/span8/","name":"README.md","path":"identition/span8/README.md","url":"/identition/span8/"},{"sort":33,"spin":48,"span":147,"suit":7,"permalink":"/identition/span7/","layout":"default","title":"Elementary Particles (span 7)","content":"

            Elementary Particles (span 7)

            \n\n
            This section is referring to _[wiki page-33](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-5]()_ that is _[inherited ]()_ from _[the spin section-7](https://gist.github.com/eq19)_ by _[prime spin-48](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-147](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist02.md
              2. \n
            2. gist06.md
              3. \n
            3. gist05.md
              4. \n
            4. Why is 7 the most feared number?
              5. \n
            5. gist07.md
              6. \n
            6. gist03.md
              7. \n
            7. gist08.md
              8. \n
            8. Double strands
              9. \n
            \n\n

            1155 / 5 = 286 - 55 = 200 + 31 = 231

            \n\n
            layer|  i    |   f\n-----+-------+------\n     | 1,2:1 | (2,3)\n  1  +-------+\n     | 3:2   | (7)\n-----+-------+------\n     | 4,6:3 | (10,11,12)  <--- 231 (3x)\n  2  +-------+\n     |{7}:4  |({13})\n-----+-------+------\n     | 8,9:5 | (14,{15})   <--- 231 (2x)\n  3  +-------+\n     | 10:6  | (19)\n-----+-------+------\n
            \n\n
            \n

            We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape (arXiv:2010.16383v4).

            \n
            \n\n

            \"Limit

            \n\n

            Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as Montgomery conjecture of the nontrivial zeros of the zeta function. Means it also depends on Riemann hypotesis which is still in a major issue. Similar case left science today many unsolved problems that associated with.

            \n\n

            \"Eigenvectors_of_a_linear_operator\"

            \n\n

            In order to propagate through space and interact we shall attemp it using string theory One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become irrational partitions.

            \n\n
            \n

            In turns out that quantum string theory always destroys the symmetries of the classical string theory, except in one special case: when the number of dimensions is 10. That’s why string theory works only in 10 dimensions (Physicsforums).

            \n
            \n\n

            \"default\"

            \n\n
            True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n|------------------------- Skema-12 ------------------------|\n|------------ 6¤ -------------|------------- 6¤ ------------|\n|--------------------------- 192 ---------------------------|\n|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |\n+----+----+----+----+----+----+----+----+----+----+----+----+\n|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|\n|---------  5¤  ---------|------------ {96} -----------|{43}|\n|--------- {53} ---------|-------------- {139} -------------|\n|------- Skema-23 -------|------------- Skema-34 -----------|    \n
            \n\n

            \"default\"

            \n\n

            This 23 units will form Scheme-23 as two (2) long strands which is known as doble helix Here we call them as Scheme-23 (71) and Scheme-23 (68). These strands are originated by the three (3) layers of True Prime Pairs.

            \n\n

            \"Scheme-139\"

            \n\n

            \"\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"\"

            \n\n

            \"\"

            \n\n

            Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as the balanced prime.

            \n\n

            \"default\"

            \n","dir":"/identition/span7/","name":"README.md","path":"identition/span7/README.md","url":"/identition/span7/"},{"sort":34,"spin":50,"span":145,"suit":6,"permalink":"/identition/span6/","layout":"default","title":"Basic Transformation (span 6)","content":"

            Basic Transformation (span 6)

            \n\n
            This section is referring to _[wiki page-34](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-6]()_ that is _[inherited ]()_ from _[the spin section-6](https://gist.github.com/eq19)_ by _[prime spin-50](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-145](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist08.md
              2. \n
            2. gist03.md
              3. \n
            3. Why was 6 afraid of 7?
              4. \n
            4. gist06.md
              5. \n
            5. gist10.md
              6. \n
            6. gist07.md
              7. \n
            7. gist09.md
              8. \n
            8. Fonts Test
              9. \n
            9. The Prime hexagon
              10. \n
            10. Markdown Elements
              11. \n
            \n\n

            For some Enneagram theorists the lines connecting the points add further meaning to the information provided by the descriptions of the types. Sometimes called the “security” and “stress” points, or points of “integration” and “disintegration”.

            \n\n
            \n

            From this perspective, there are twenty-seven (27) distinct personality patterns, because people of each of the nine (9) types also express themselves as one of the three (3) subtypes (Wikipedia).

            \n
            \n\n

            \"\"

            \n\n

            This is managed within twelve (12) flows (A: to W:). Each flows is representing a certain period which is converting the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence as explained before.

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"image\"

            \n\n

            It turns out it’s actually pretty straight forward to set WSL to use your Windows home directory. First, within WSL edit the /etc/passwd file (eg with sudo nano /etc/passwd).

            \n\n
            eq19:x:1000:1000:eQ19:/home/eq19:/bin/bash\neq19:x:1000:1000:eQ19:/mnt/c/users/Admin:/bin/bash\n
            \n\n

            \"image\"

            \n\n

            \"default\"

            \n","dir":"/identition/span6/","name":"README.md","path":"identition/span6/README.md","url":"/identition/span6/"},{"sort":35,"spin":54,"span":144,"suit":5,"permalink":"/identition/span5/","layout":"default","title":"Hidden Dimensions (span 5)","content":"

            Hidden Dimensions (span 5)

            \n\n
            This section is referring to _[wiki page-35](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-7]()_ that is _[inherited ]()_ from _[the spin section-5](https://gist.github.com/eq19)_ by _[prime spin-54](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-144](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist04.md
              2. \n
            2. gist05.md
              3. \n
            3. Where is the 5?
              4. \n
            4. gist06.md
              5. \n
            5. gist03.md
              6. \n
            6. gist07.md
              7. \n
            7. Triangular waves
              8. \n
            \n\n

            A lexer is the part of an interpreter that turns a sequence of characters (plain text) into a sequence of tokens. The Parser which takes the tokens from the lexer and returns a syntax tree based on a grammar. The grammar is often expressed in a meta language.

            \n\n
            BusyBox v1.34.1 (2022-07-19 20:11:24 UTC) multi-call binary.\n\nUsage: mv [-finT] SOURCE DEST\nor: mv [-fin] SOURCE... { -t DIRECTORY | DIRECTORY }\n\nRename SOURCE to DEST, or move SOURCEs to DIRECTORY\n\n\t-f\tDon't prompt before overwriting\n\t-i\tInteractive, prompt before overwrite\n\t-n\tDon't overwrite an existing file\n\t-T\tRefuse to move if DEST is a directory\n\t-t DIR\tMove all SOURCEs into DIR\n
            \n\n

            \"default\"

            \n\n

            By this modification we are going to build the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66.

            \n\n

            \"default\"

            \n\n

            The next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.

            \n\n

            \"image\"

            \n\n

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0’s cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n

            \"default\"

            \n\n","dir":"/identition/span5/","name":"README.md","path":"identition/span5/README.md","url":"/identition/span5/"},{"sort":36,"spin":56,"span":143,"suit":4,"permalink":"/identition/span4/","layout":"default","title":"Parallel Universes (span 4)","content":"

            Parallel Universes (span 4)

            \n\n
            This section is referring to _[wiki page-36](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-8]()_ that is _[inherited ]()_ from _[the spin section-4](https://gist.github.com/eq19)_ by _[prime spin-56](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-143](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist07.md
              2. \n
            2. gist08.md
              3. \n
            3. gist03.md
              4. \n
            4. Directory Structure
              5. \n
            5. Binary
              6. \n
            6. gist09.md
              7. \n
            7. The Classes
              8. \n
            8. License
              9. \n
            9. Lexer vs Parser
              10. \n
            \n\n

            When we come to a mapping of a Project, is critical to look for the future of Parts Unlimited otherwise the project will massively over budget and very late. So to deal with this we shall consider to move everything to the cloud…

            \n\n

            \"phoenix\"

            \n\n

            Since version 3.2 , a new Jekyll project bootstrapped with jekyll new uses gem-based themes to define the look of the site. This results in a lighter default directory structure: _layouts, _includes and _sass are stored in the theme-gem, by default.

            \n\n

            \"default\"

            \n\n
            In general relativity, gravity is a force that bends and warps space-time around supermassive bodies.\n- Even though gravity is one of the four fundamental forces in nature, it is very weak compared to the other three forces (electromagnetism, weak force and strong force). So it can’t be observed or identified on the scale of subatomic particles.\n- However, [gravity](https://byjus.com/physics/gravity/) is ***very dominant in long-distance scenarios***. It controls the structure of the macro universe (galaxies, planets, stars, moons).\n- As far as quantum mechanics is concerned, gravity doesn’t have much effect. The probable nature of the quantum realm also poses a significant challenge for the induction of gravity in the quantum realm.\n- Generally, ***gravity does not act as a particle as its own***. Even if a hypothetical model is introduced to explain the particle nature of a gravity particle, it violates fundamental energy laws.\n\nIn the 1970s, theorists tried to discard the self-destructive idea of point-like gravity particles. Instead of point particles, strings were introduced. Even if strings collide, there will be no infinite energy problem. Strings can smoothly smash and rebound without implying any physically nonsense infinities.\n
            \n\n

            \"\"

            \n\n

            You can attach a persistent disk or create an instance with Local SSDs when using Container-Optimized OS. The disks can be mounted by creating a subdirectory under /mnt/disks directory (writable, executable, stateless, tmpfs) using startup-scripts.

            \n\n

            \"image\"

            \n\n

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            \n\n

            \"GitHub

            \n\n

            On the lagging strand template, a primase “reads” the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            \n\n

            \"default\"

            \n\n

            You can run .NET applications in Linux containers, but only if they’re written in .NET Core which can be deployed on Windows Server Containers. Applications running in Windows Server Containers can run in any language supported by Windows.

            \n\n

            \"kernel-6.1.21.1-microsoft-standard-WSL2.img\n\"

            \n\n

            Let’s combine them all then we will get 168 which is the total primes out of 1000 numbers. This 168 we will get it also when we combine the 1’s and 17’s cell of (31+37)+(35+65)=68+100=168.

            \n\n

            \"zeta-vs-zero\"

            \n\n

            This can be remedied by re-mounting your Windows partition inside WSL with the metdata option. Edit the /etc/wsl.conf file (create it if it doesn’t exist) and add the following:

            \n\n
            [automount]\noptions = \"metadata\"\n
            \n\n

            Log out from WSL and log in again, and now the windows partition will be mounted with metadata and chmod will work against windows files. You can now chmod 600 ~/.ssh/id_rsa and everything will work correctly.

            \n\n

            \"default\"

            \n\n

            By this project we are going to use a library called Chevrotain. It can be used to build Lexers, Parsers and Interpreters for various use cases ranging from simple config files to full fledged programming languages.

            \n\n

            \"Lexers,

            \n\n

            This Widows is an isolated container, lightweight package for running an application on the host operating system. Containers build on top of the host operating system’s kernel (which can be thought of as the buried plumbing of the operating system).

            \n","dir":"/identition/span4/","name":"README.md","path":"identition/span4/README.md","url":"/identition/span4/"},{"sort":37,"spin":60,"span":142,"suit":3,"permalink":"/identition/span3/","layout":"default","title":"Vibrating Strings (span 3)","content":"

            Vibrating Strings (span 3)

            \n\n
            This section is referring to _[wiki page-37](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-9]()_ that is _[inherited ]()_ from _[the spin section-3](https://gist.github.com/eq19)_ by _[prime spin-60](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-142](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Container-Optimized
              2. \n
            2. gist07.md
              3. \n
            3. gist03.md
              4. \n
            4. gist02.md
              5. \n
            5. System Storage
              6. \n
            6. DNA Recombination
              7. \n
            7. Mass vs Gap (Δ)
              8. \n
            \n\n

            It turns out that quantum string theory always destroys the symmetries of classical string theory, except in one special case: when the number of dimensions is 10.

            \n\n
            Below is a model of E11 (shown by 11 dimensions). Its absolute dimensions represent all related key knowledges of modern physics. Moreover this model represents [Quark-Gluon Plasma](https://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma), with all of the [fundamental forces](https://www.eq19.com/exponentiation/#fundamental-forces) in the early stage after _[Big Bang](https://youtu.be/7VgoECW06-s?si=_l-Pu42gwtnxzzT2)_ which probably comes from [Absolute Nothingness](https://www.quora.com/What-is-the-difference-between-the-universe-the-cosmos-space-and-nothing/answer/George-Davros).\n
            \n\n

            \"default\"

            \n\n

            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period eight (8) difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2} (Primesdemystified).

            \n\n

            \"image\"

            \n\n
            Quantum field theory is any theory that describes a quantized field.\n- QED, or Quantum Electrodynamics, is the quantum theory of the electromagnetic field, a so-called Abelian field (referencing an internal mathematical symmetry of the theory.)\n- Electroweak theory is a generalization of QED, unifying it with the weak nuclear force in the form of a Yang-Mills field theory (aka. a non-Abelian field theory).\n- QCD, or Quantum Chromodynamics, is another example of a non-Abelian field theory, but one with very different asymptotic behavior than electroweak theory.\n- The Standard Model of particle physics is the combination of electroweak theory and QCD in the form of a unified theory obeying a complex set of symmetries.\n\nThis theory describes all the known fields and all the known interactions other than gravity. _([Quora](https://www.quora.com/What-exactly-is-the-difference-between-QED-QCD-Electroweak-theory-Standard-model-Quantum-field-theory-and-how-are-they-related-together))_\n
            \n\n

            \"DifferencebetweenQEDandQCD.pdf\"

            \n\n

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            \n\n

            \"11's

            \n\n

            These objects will then behave as a complex numbers that leads to trivial and complex roots of the 18th prime identity. \n286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271

            \n\n
              -----------------------+----+----+----+----+----+----+----+----+----+-----\n   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum \n  =======================+====+====+====+====+====+====+====+====+====+=====\n   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin\n  -----------------------+----+----+----+----+----+----+----+----+----+-----\n   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10\n  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin\n   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin\n    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20 --------\n  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                |\n    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------\n  =======================+====+====+====+====+====+====+====+====+====+===== bilateral 9 sums (2)+60+40=102\n    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------\n  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                |\n    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20 --------\n  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin\n    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th\n
            \n\n
            We show that the Big Bang singularity of the Friedmann-Lemaˆıtre-Robertson-Walker model does not raise major problems to General Relativity.\n- We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang.\n- The old method of resolution of singularities shows how we can “untie” the singularity of a cone and obtain a cylinder.\n- This illustrates the idea that it is not necessary to assume that, at the Big Bang singularity, the entire space was a point, but only that the space metric was 0.\n\nThese results follow from our research on singular semi-Riemannian geometry and singular General Relativity [26, 27, 29] (which we applied in previous articles to the black hole singularities [30, 31, 32, 28]).\n
            \n\n

            \"Big_Bang_singularity_in_the_Friedmann-Lemaitre-Rob.pdf\"

            \n\n

            The opposite direction will be made through switching beetween Linux and Windows which is proceed the old strand in the 3′ to 5′ direction, while the new strand is synthesized in the 5’ to 3’ direction. Here we set a remote self-host runner via WSL.

            \n\n

            \"default\"

            \n\n

            The rest of primes goes to the 33’s of 15th axis that holding 102 primes of (2,60,40). By the bilateral way the form will be splitted to (1,30,20). Since the base frame shall be 40 so it will be forced to form (1,30,40) of prime 71.

            \n\n

            \"default\"

            \n","dir":"/identition/span3/","name":"README.md","path":"identition/span3/README.md","url":"/identition/span3/"},{"sort":38,"spin":66,"span":141,"suit":2,"permalink":"/identition/span2/","layout":"default","title":"Series Expansion (span 2)","content":"

            Series Expansion (span 2)

            \n\n
            This section is referring to _[wiki page-38](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-10]()_ that is _[inherited ]()_ from _[the spin section-2](https://gist.github.com/eq19)_ by _[prime spin-66](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-141](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. gist06.md
              2. \n
            2. Polar Plot
              3. \n
            3. The Bilateral 9 Sums
              4. \n
            4. gist03.md
              5. \n
            5. gist07.md
              6. \n
            6. Project Repositories
              7. \n
            7. gist04.md
              8. \n
            8. 2.5 Parsering
              9. \n
            9. Assigning Repositories
              10. \n
            \n\n
            To be clear, these horizons are speculations based upon numerical simulations of general relativistic field equation which are inherently non-linear and notoriously difficult to solve, so more detailed computer modeling may hold surprises for us. Also, while spacetime is well-modeled by GR, at the horizons where the curvature blows up, then so does GR and speculations about _[what happens at the singularities will have to wait for quantum gravity](https://www.eq19.com/identition/#fundamental-forces)_.\n
            \n\n

            \"Answer

            \n\n

            \"\"

            \n\n
            Only more accurate analysis on the involved spectra and on the relative brightness of the two rings, and mainly the discovery of other ***double rings systems***, could be used to finally choose which among these two interpretations is more likely to hold. As to using ***Klein bottle holes*** to check the physical existence of other universes, it appears just a matter of time ***to find a double truncated spiral*** blurred enough to clearly show a connection with other universes. _([Observing another Universe through ringholes and Klein-bottle holes - pdf](https://arxiv.org/pdf/1102.3784.pdf))_\n
            \n\n

            \"Gravitational-lensing-effect-produced-by-a-ringhole-from-a-single-luminous-source-a_Q320\"

            \n\n

            \"Elementary_particle_interactions

            \n\n

            Simulating physics on a quantum computer can be reduced to solving mathematical problem using quantum mechanics.

            \n\n

            \"knots1\"

            \n\n

            The spacetime diagram on the left, the magenta hyperbolae connect events of equal spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation from the origin.

            \n\n

            \"default\"

            \n\n

            Note also that the rate of convergence to infinity in this exampleshould be as the fourth root of t, which is confirmed by the graph (the fourth root of 125000 is about 19).

            \n\n
            Four eigenvalues going to infinity. The plot shows the eigenvalues of A + tuu>J for 0 ≤ t ≤ 125000 in red, and the eigenvalues of A − tuu>J for the same range of t in cyan\n
            \n\n

            \"Four

            \n\n

            You can use either mklink /j or junction in Windows 10 to create junctions. Junction not only allows you to create NTFS junctions, it allows you to see if files or directories are actually reparse points. Reparse points are the mechanism on which NTFS junctions are based, and they are used by Windows’ Remote Storage Service (RSS), as well as volume mount points.

            \n\n
            mklink /j .github C:\\Users\\Admin\\.github\n
            \n\n

            \"mklink\"

            \n\n

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0’s cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            \n\n

            \"19vs18\"

            \n\n

            \"default\"

            \n\n

            Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence.

            \n\n
            \n

            AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence (Human vs AI).

            \n
            \n\n

            \"\"

            \n\n

            The next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.

            \n\n

            \"33's\"

            \n\n

            This process would take place all the way to three (3) layers in a more complex way involving 114 objects generated by the sum of the above mentioned prime 71 and 43. This is what we will discuss further on how apply it in to a custom domain.

            \n","dir":"/identition/span2/","name":"README.md","path":"identition/span2/README.md","url":"/identition/span2/"},{"sort":39,"spin":68,"span":140,"suit":1,"permalink":"/identition/span1/","layout":"default","title":"Wormhole Theory (span 1)","content":"

            Wormhole Theory (span 1)

            \n\n

            This section serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks in quantum chromodynamics of colours of the gluon.

            \n\n
            This section is referring to _[wiki page-39](https://github.com/eq19/eq19.github.io/wiki)_ of _[orgs section-11]()_ that is _[inherited ]()_ from _[the spin section-1](https://gist.github.com/eq19)_ by _[prime spin-68](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#file-spin-csv)_ and _[span-140](https://www.eq19.com/exponentiation/#basic-transformation)_ with _[the partitions](https://www.eq19.com/identition/#parallel-universes)_ as below.\n
            \n\n
              \n
            1. Partition function
              2. \n
            2. Irrational Partitions
              3. \n
            3. Object Orientation
              4. \n
            4. Bonding Position
              5. \n
            5. The Quantum Way
              6. \n
            6. Proofreading Ability
              7. \n
            7. Replication Fork
              8. \n
            8. Building The Instance
              9. \n
            9. Imaginary Square
              10. \n
            10. Rational vs Irrational
              11. \n
            11. Rotation vs Revolution
              12. \n
            12. Zeta vs Zero
              13. \n
            13. Anti Parallel
              14. \n
            14. Mass vs Gap (Δ)
              15. \n
            \n\n

            A gauge colour rotation is a spacetime-dependent SU(3) group element. They span the Lie algebra of the SU(3) group in the defining representation.

            \n\n

            Feynman diagram

            \n\n
            In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).\n
            \n\n

            \"default\"

            \n\n

            \"quark-quark_scattering\"

            \n\n

            \"SmallBookPile\"

            \n\n

            So basically there is a basic transformation between addition of 3 + 4 = 7 in to their multiplication of 3 x 4 = 12 while the 7 vs 12 will be treated as exponentiation.

            \n\n

            \"images6-ezgif

            \n\n

            Matrix Scheme

            \n\n

            Quarks have three colors. Color is to the strong interaction as electric charge is to the electromagnetic interaction.

            \n\n

            \"quantum-chromodynamics-1-320\"

            \n\n
            red   anti-red,   red   anti-blue,   red   anti-green,\nblue  anti-red,   blue  anti-blue,   blue  anti-green,\ngreen anti-red,   green anti-blue,   green anti-green.\n
            \n\n

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            \n\n
            During the last few years of the 12th century, ***Fibonacci*** undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that ***it popularized the use of the Arabic numerals in Europe***, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. _([Famous Mathematicians](https://famous-mathematicians.org/leonardo-pisano-bigollo/))_\n
            \n\n

            \"MEC30

            \n\n

            Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30’s square.

            \n\n
            A square system of coupled nonlinear equations can be solved iteratively by Newton's method. This method uses the Jacobian matrix of the system of equations. _([Wikipedia](https://en.wikipedia.org/Jacobian_matrix_and_determinant))_\n
            \n\n

            \"gradien\"

            \n\n
            Fermions and bosons—fermions have quantum spin = 1/2.\n- The elementary fermions are leptons and quarks.\n- There are three generations of leptons: electron, muon, and tau, with electric charge −1, and their neutrinos with no electric charge.\n- There are three generations of quarks: (u, d); (c, s); and (t, b).\n\nThe (u, c, t) quarks have electric charge 2/3 while the (d, s, b) quarks have electric charge −1/3. _([IntechOpen](https://www.intechopen.com/chapters/71535))_\n
            \n\n

            \"UF1\"

            \n\n

            Interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used.

            \n\n

            \"UF2\"

            \n\n

            Bosons have quantum spin = 1: photon, quantum of the electromagnetic field; gluon, quantum of the strong field; and W and Z, weak field quanta, which we do not need.

            \n\n
            An animation of [color confinement](https://en.wikipedia.org/wiki/Color_confinement), a property of the strong interaction. If energy is supplied to the quarks as shown, the [gluon](https://en.wikipedia.org/wiki/Gluon) tube connecting [quarks](https://en.wikipedia.org/wiki/Quark) elongates until it reaches a point where it \"snaps\" and the energy added to the system results in the formation of a quark–[antiquark](https://en.wikipedia.org/wiki/Antiquark) pair. Thus single quarks are never seen in isolation. _([Wikipedia](https://en.wikipedia.org/wiki/Strong_interaction))_\n
            \n\n

            \"Gluon_tube-color_confinement_animation\"

            \n\n
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter\n   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)\n===========+=========+=========+===========+===========+============+===========\nbispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7 👈\n===========+=========+=========+===========+===========+============+===========\nbispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13\n-----------+---------+---------+-----------+-----------+------------+-----------\nbispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5\n===========+=========+=========+===========+===========+============+===========\n     Total |    8    |   12    |    12     |    72     |     96     |   66+i30\n
            \n\n

            Interactions

            \n\n

            The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.

            \n\n
            ***Unlike the strong force, the residual strong force diminishes with distance, and does so rapidly***. The decrease is approximately as a negative exponential power of distance, though there is no simple expression known for this; see [Yukawa potential](https://en.wikipedia.org/wiki/Yukawa_potential). The rapid decrease with distance of the attractive residual force and the less rapid decrease of the repulsive electromagnetic force acting between protons within a nucleus, causes the instability of larger atomic nuclei, such as all those with [atomic numbers](https://en.wikipedia.org/wiki/Atomic_number) larger than 82 (the element lead). _([Wikipedia](https://en.wikipedia.org/wiki/Strong_interaction#Between_hadrons))_\n
            \n\n

            \"gifman\"

            \n\n
            Feynman diagram for the same process as in the animation, with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while ***multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion \"in-flight\", are not shown***. The π⁰ pion contains an anti-quark, shown to travel in the opposite direction, as per the Feynman–Stueckelberg interpretation. _([Wikipedia](https://en.wikipedia.org/wiki/Pion))_\n
            \n\n

            \"residual

            \n\n
            The Gell-Mann matrices, developed by [Murray Gell-Mann](https://en.m.wikipedia.org/wiki/Murray_Gell-Mann), are a set of eight [linearly independent](https://en.m.wikipedia.org/wiki/Linear_independence) 3×3 [traceless](https://en.wikipedia.org/wiki/Matrix_trace) [Hermitian matrices](https://en.wikipedia.org/wiki/Hermitian_matrices) used in the study of the [strong interaction](https://en.wikipedia.org/wiki/Strong_interaction) in [particle physics](https://en.wikipedia.org/wiki/Particle_physics). They span the [Lie algebra](https://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_associated_with_a_Lie_group) of the [SU(3)](https://en.wikipedia.org/wiki/Special_unitary_group#SU(3)) group in the defining representation.\n- These matrices are [traceless](https://en.wikipedia.org/wiki/Traceless), [Hermitian](https://en.wikipedia.org/wiki/Hermitian_matrix), and obey the extra trace orthonormality relation (so they can generate [unitary matrix](https://en.wikipedia.org/wiki/Unitary_matrix) group elements of [SU(3)](https://en.wikipedia.org/wiki/SU(3)) through [exponentiation](https://en.wikipedia.org/wiki/Matrix_exponential)[[1]](https://en.m.wikipedia.org/wiki/Gell-Mann_matrices#cite_note-Scherer-Schindler-1)). These properties were chosen by Gell-Mann because they then naturally generalize the [Pauli matrices](https://en.wikipedia.org/wiki/Pauli_matrices) for [SU(2)](https://en.wikipedia.org/wiki/SU(2)) to SU(3), which formed the basis for Gell-Mann's [quark model](https://en.wikipedia.org/wiki/Quark_model).[[2]](https://en.wikipedia.org/wiki/Gell-Mann_matrices#cite_note-2) Gell-Mann's generalization further [extends to general SU(n)](https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices#Construction). For their connection to the [standard basis](https://en.wikipedia.org/wiki/Root_system) of Lie algebras, see the [Weyl–Cartan basis](https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients_for_SU(3)#Standard_basis).\n- Since the eight matrices and the identity are a complete trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that [satisfied by the Pauli matrices](https://en.wikipedia.org/wiki/Pauli_matrices#Completeness_relation_2). Namely, using the dot to sum over the eight matrices and using Greek indices for their row/column indices\n- A particular choice of matrices is called a [group representation](https://en.wikipedia.org/wiki/Group_representation), because any element of SU(3) can be written in the form using the ***[Einstein notation](https://en.wikipedia.org/wiki/Einstein_notation)***, where the eight \n are real numbers and a sum over the index j is implied. Given one representation, an equivalent one may be obtained by an arbitrary unitary similarity transformation, since that leaves the commutator unchanged.\n- The matrices can be realized as a representation of the [infinitesimal generators](https://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_associated_with_a_Lie_group) of the [special unitary group](https://en.wikipedia.org/wiki/Special_unitary_group) called [SU(3)](https://en.wikipedia.org/wiki/Special_unitary_group#The_group_SU(3)). The [Lie algebra](https://en.wikipedia.org/wiki/Lie_algebra) of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight [linearly independent](https://en.wikipedia.org/wiki/Linear_independence) generators, which can be written as \ng_{i}, with i taking values from [1 to 8](https://en.wikipedia.org/wiki/Gell-Mann_matrices#cite_note-Scherer-Schindler-1)\n\nThese matrices serve to study the internal (color) rotations of the ***[gluon fields](https://en.m.wikipedia.org/wiki/Gluon_field) associated with the coloured quarks of [quantum chromodynamics](https://en.m.wikipedia.org/wiki/Quantum_chromodynamics) (cf. [colours of the gluon](https://en.m.wikipedia.org/wiki/Gluon#Eight_gluon_colours))***. A gauge colour rotation is a spacetime-dependent SU(3) group element where summation over the eight indices (8) is implied. _[Wikipedia](https://en.wikipedia.org/wiki/Gell-Mann_matrices))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-----+                                             ---\n 17¨ |  5¨ |  3¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            From the 50 we gonna split the 15 by bilateral 9 sums resulting 2 times 15+9=24 which is 48. So the total of involved objects is 50+48=98.

            \n\n
            Consider the evidence: scattering experiments strongly suggest a meson to be composed of a quark anti-quark pair and a baryon to be composed of three quarks. The famous 3R experiment also suggests that whatever force binds the quarks together has 3 types of charge (called the 3 colors).\n- Now, into the realm of theory: we are looking for an internal symmetry having a 3-dimensional representation which can give rise to a neutral combination of 3 particles (otherwise no color-neutral baryons).\n-  The simplest such statement is that a linear combination of each type of charge (red + green + blue) must be neutral, and following William of Occam we believe that the simplest theory describing all the facts must be the correct one.\n-  We now postulate that the particles carrying this force, called gluons, must occur in color anti-color units (i.e. nine of them).\n- BUT, red + blue + green is neutral, which means that the linear combination red anti-red + blue anti-blue + green anti-green must be non-interacting, since otherwise the colorless baryons would be able to emit these gluons and interact with each other via the strong force—contrary to the evidence.  So, there can only be ***EIGHT gluons***.\n\nThis is just Occam's razor again: a hypothetical particle that can't interact with anything, and therefore can't be detected, doesn't exist. The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra.  That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional. _([Physics FAQ](https://math.ucr.edu/home/baez/physics/ParticleAndNuclear/gluons.html))_\n
            \n\n

            \"0_kGdCmWqcFG_s8fIq\"

            \n\n

            Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.

            \n\n

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            \n\n

            \"960x0\"

            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-----+-👇--+                                             ---\n 17¨ |  5¨ |  3¨ |  ❓ |  7¨ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            \n\n
            [Young diagrams](https://commons.wikimedia.org/wiki/Category:Young_diagrams) associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions _([Wikipedia](https://en.wikipedia.org/wiki/Partition_(number_theory)))_.\n
            \n\n

            \"Hadron_colors

            \n\n
            In mathematics, orthonormality typically implies a norm which has a value of unity (1). Gell-Mann matrices, however, ***are normalized to a value of 2***.\n- Thus, the [trace](https://en.wikipedia.org/wiki/Trace_(linear_algebra)) of the pairwise product results in the ortho-normalization condition where delta is the [Kronecker delta](https://en.wikipedia.org/wiki/Kronecker_delta).\n- This is so the embedded Pauli matrices corresponding to the three embedded subalgebras of SU(2) are conventionally normalized.\n- In this three-dimensional matrix representation, the [Cartan subalgebra](https://en.wikipedia.org/wiki/Cartan_subalgebra) is the set of linear combinations (with real coefficients) of the two matrices which commute with each other.\n\nThe SU(2) Casimirs of these subalgebras ***mutually commute***. However, any unitary similarity transformation of these subalgebras will yield SU(2) subalgebras. There is an uncountable number of such transformations. _([Wikipedia](https://en.wikipedia.org/wiki/Gell-Mann_matrices))_\n
            \n\n
            $True Prime Pairs:\n(5,7), (11,13), (17,19)\n\n     |    168    |    618    |\n-----+-----+-----+-----+-----+                                             ---\n 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to \"id:30\"             19¨\n-----+-----+-----+-👇--+-----+                                             ---\n 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤ ✔️ --->  assigned to \"id:31\"              |\n     +-----+-----+-----+-----+                                              |\n{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to \"id:32\"              |\n     +-----+-----+-----+                                                    |\n 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to \"id:33\"  ----->  👉 77¨\n-----+-----+-----+-----+-----+                                              |\n 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to \"id:34\"              |\n     +-----+-----+-----+-----+                                              |\n{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to \"id:35\"              |\n     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨\n-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---\n139¨ |  1     2     3  |  4     5     6  |  7     8     9  |\n                    Δ                 Δ                 Δ       \n
            \n\n

            \"e72_3\"

            \n\n

            \"QCD+QUANTUM+ELECTRODYNAMICS_+is+the+quantum+theory+of+the+electromagnetic+interaction

            \n","dir":"/identition/span1/","name":"README.md","path":"identition/span1/README.md","url":"/identition/span1/"},{"sort":103,"layout":"default","title":"Markdown Elements","content":"# Markdown Elements\n\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\nThere should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs.\n\nThere should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs.\n\n> There should be no margin above this first sentence.\n>\n> Blockquotes should be a lighter gray with a gray border along the left side.\n>\n> There should be no margin below this final sentence.\n\n# Header 1\n\nThis is a normal paragraph following a header. Bacon ipsum dolor sit amet t-bone doner shank drumstick, pork belly porchetta chuck sausage brisket ham hock rump pig. Chuck kielbasa leberkas, pork bresaola ham hock filet mignon cow shoulder short ribs biltong.\n\n## Header 2\n\n> This is a blockquote following a header. Bacon ipsum dolor sit amet t-bone doner shank drumstick, pork belly porchetta chuck sausage brisket ham hock rump pig. Chuck kielbasa leberkas, pork bresaola ham hock filet mignon cow shoulder short ribs biltong.\n\n### Header 3\n\n```note\n## This is a note\n\nMarkdown is supported, Text can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines\n\n`inline code`\n\n[`inline code inside link`](./)\n```\n\n#### Header 4\n\n- This is an unordered list following a header.\n- This is an unordered list following a header.\n- This is an unordered list following a header.\n\n##### Header 5\n\n1. This is an ordered list following a header.\n2. This is an ordered list following a header.\n3. This is an ordered list following a header.\n\n###### Header 6\n\n| What | Follows |\n| ------- | -------- |\n| A table | A header |\n| A table | A header |\n| A table | A header |\n\n---\n\nThere's a horizontal rule above and below this.\n\n---\n\nHere is an unordered list:\n\n- Salt-n-Pepa\n- Bel Biv DeVoe\n- Kid 'N Play\n\nAnd an ordered list:\n\n1. Michael Jackson\n2. Michael Bolton\n3. Michael Bublé\n\nAnd an unordered task list:\n\n- [x] Create a sample markdown document\n- [x] Add task lists to it\n- [ ] Take a vacation\n\nAnd a \"mixed\" task list:\n\n- [ ] Steal underpants\n- ?\n- [ ] Profit!\n\nAnd a nested list:\n\n- Jackson 5\n - Michael\n - Tito\n - Jackie\n - Marlon\n - Jermaine\n- TMNT\n - Leonardo\n - Michelangelo\n - Donatello\n - Raphael\n\nDefinition lists can be used with HTML syntax. Definition terms are bold and italic.\n\n
            \n
            Name
            \n
            Godzilla
            \n
            Born
            \n
            1952
            \n
            Birthplace
            \n
            Japan
            \n
            Color
            \n
            Green
            \n
            \n\n---\n\nTables should have bold headings and alternating shaded rows.\n\n| Artist | Album | Year |\n| --------------- | -------------- | ---- |\n| Michael Jackson | Thriller | 1982 |\n| Prince | Purple Rain | 1984 |\n| Beastie Boys | License to Ill | 1986 |\n\nIf a table is too wide, it should condense down and/or scroll horizontally.\n\n\n\n| Artist | Album | Year | Label | Awards | Songs |\n|-------------------|-----------------|------|-------------|----------|-----------|\n| Michael Jackson | Thriller | 1982 | Epic Records | Grammy Award for Album of the Year, American Music Award for Favorite Pop/Rock Album, American Music Award for Favorite Soul/R&B Album, Brit Award for Best Selling Album, Grammy Award for Best Engineered Album, Non-Classical | Wanna Be Startin' Somethin', Baby Be Mine, The Girl Is Mine, Thriller, Beat It, Billie Jean, Human Nature, P.Y.T. (Pretty Young Thing), The Lady in My Life |\n| Prince | Purple Rain | 1984 | Warner Brothers Records | Grammy Award for Best Score Soundtrack for Visual Media, American Music Award for Favorite Pop/Rock Album, American Music Award for Favorite Soul/R&B Album, Brit Award for Best Soundtrack/Cast Recording, Grammy Award for Best Rock Performance by a Duo or Group with Vocal | Let's Go Crazy, Take Me With U, The Beautiful Ones, Computer Blue, Darling Nikki, When Doves Cry, I Would Die 4 U, Baby I'm a Star, Purple Rain |\n| Beastie Boys | License to Ill | 1986 | Mercury Records | noawardsbutthistablecelliswide | Rhymin & Stealin, The New Style, She's Crafty, Posse in Effect, Slow Ride, Girls, (You Gotta) Fight for Your Right, No Sleep Till Brooklyn, Paul Revere, Hold It Now, Hit It, Brass Monkey, Slow and Low, Time to Get Ill |\n\n\n\n---\n\nCode snippets like `var foo = \"bar\";` can be shown inline.\n\nAlso, `this should vertically align` ~~`with this`~~ ~~and this~~.\n\nCode can also be shown in a block element.\n\n```\nvar foo = \"bar\";\n```\n\nCode can also use syntax highlighting.\n\n```javascript\nvar foo = \"bar\";\n```\n\n```\nLong, single-line code blocks should not wrap. They should horizontally scroll if they are too long. This line should be long enough to demonstrate this.\n```\n\n```javascript\nvar foo =\n \"The same thing is true for code with syntax highlighting. A single line of code should horizontally scroll if it is really long.\";\n```\n\nInline code inside table cells should still be distinguishable.\n\n| Language | Code |\n| ---------- | ------------------ |\n| Javascript | `var foo = \"bar\";` |\n| Ruby | `foo = \"bar\"` |\n\n---\n\nSmall images should be shown at their actual size.\n\n![Octocat](https://github.githubassets.com/images/icons/emoji/octocat.png)\n\n\n## Mathjax Test\n\n$$\n\\begin{aligned}\n & \\phi(x,y) = \\phi \\left(\\sum_{i=1}^n x_ie_i, \\sum_{j=1}^n y_je_j \\right)\n = \\sum_{i=1}^n \\sum_{j=1}^n x_i y_j \\phi(e_i, e_j) = \\\\\n & (x_1, \\ldots, x_n) \\left( \\begin{array}{ccc}\n \\phi(e_1, e_1) & \\cdots & \\phi(e_1, e_n) \\\\\n \\vdots & \\ddots & \\vdots \\\\\n \\phi(e_n, e_1) & \\cdots & \\phi(e_n, e_n)\n \\end{array} \\right)\n \\left( \\begin{array}{c}\n y_1 \\\\\n \\vdots \\\\\n y_n\n \\end{array} \\right)\n\\end{aligned}\n$$\n\n```note\nFor documentation, see: https://kramdown.gettalong.org/syntax.html#math-blocks\n```\n\n\n## Mermaid Test\n\n ```mermaid\n graph TB\n c1-->a2\n subgraph one\n a1-->a2\n end\n subgraph two\n b1-->b2\n end\n subgraph three\n c1-->c2\n end\n ```\n\n```mermaid\ngraph TB\n c1-->a2\n subgraph one\n a1-->a2\n end\n subgraph two\n b1-->b2\n end\n subgraph three\n c1-->c2\n end\n```\n\n```mermaid\ngraph TD;\n A-->B;\n A-->C;\n B-->D;\n C-->D;\n```\n\n```mermaid\nclassDiagram\nclassA <|-- classB\nclassC *-- classD\nclassE o-- classF\nclassG <-- classH\nclassI -- classJ\nclassK <.. classL\nclassM <|.. classN\nclassO .. classP\n```\n\n```mermaid\nerDiagram\n CUSTOMER ||--o{ ORDER : places\n ORDER ||--|{ LINE-ITEM : contains\n CUSTOMER }|..|{ DELIVERY-ADDRESS : uses\n```\n\n## Primer Utilities Test\n\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.text-red}\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark}\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark.text-white}\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark.text-white.m-5}\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark.text-white.p-5.mb-6}\nText can be **bold**, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark.text-white.p-5.mb-6}\nText can be **bold**{:.h1}, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark.text-white.p-2.box-shadow-large}\nText can be **bold**{:.h1}, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n{:.bg-yellow-dark.text-white.p-5.box-shadow-large.anim-pulse}\nText can be **bold**{:.h1}, _italic_, or ~~strikethrough~~. [Links](https://github.com) should be blue with no underlines (unless hovered over).\n\n```tip\nEdit this page to see how to add this to your docs, theme can use [@primer/css utilities](https://primer.style/css/utilities)\n```\n","dir":"/identition/span6/","name":"gist05.md","path":"identition/span6/gist05.md","url":"/identition/span6/gist05.html"}] \ No newline at end of file diff --git a/exponentiation/index.html b/exponentiation/index.html new file mode 100644 index 00000000000..287466d1b92 --- /dev/null +++ b/exponentiation/index.html @@ -0,0 +1,731 @@ + Exponentiation Zones (30-36) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Exponentiation Zones (30-36)

            Exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-21 of gist section-17 that is inherited from the gist section-2 by prime spin-30 and span-168 with the partitions as below.

            +
            +
            1. Electrodynamics (maps)
            2. Quantum Gravity (feed)
            3. Chromodynamics (lexer)
            4. Electroweak Theory (parser)
            5. Grand Unified Theory (syntax)

            Exponentiation Zones allows multiple layers on representing recursive residues of the operands, thus promising large gain to the conventional arithmetic expression

            Standard Model

            In particle physics, study of the symmetry and its breaking play very important role in order to get useful information about the nature.

            +
            + + Note +
            +
            +

            Similarly the Standard Model incorporates three generations of quarks, so its fermionic content can be summarized. In addition, the Standard Model involves gauge bosons (photons for the electromagnetic interaction, W and Z for the weak interaction, and eight (8) gluons for the strong interaction), plus the (scalar) Higgs particle. This is what all known matter in the Universe consists of. (Netrinos)

            +
            +

            Multiplets-of-the-1-2-spin-baryon-in-SU4-flavour-model ppm

            Elementary particles and their interactions are considered by a theoretical framework called the Standard Model (SM) of Particle Physics.

            +
            + + Note +
            +
            +

            The Standard Model presently recognizes seventeen distinct particles (twelve fermions and five bosons). As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. (Wikipedia)

            +
            +

            17 distinct particles = 12 fermions + 5 bosons = 48 + 13 = 61 variations

            Standard_Model_of_Elementary_Particles

            It is hypothesized that gravitational interactions are mediated by an as yet undiscovered elementary particle, dubbed the graviton.

            How many quarks?

            Answer-1: 3 generation x 3 color x 2 types x 2 each = 36 quarks
+

            How many types of quarks are there and what are their names?

            Answer-2: 6 flavour x 3 colors x 2 types = 36 quarks
+

            image

            Answer-3: 6 flavour x 3 colour x 4 bispinor = 72 quarks
+

            There are 72 quarks

            +
            + + Note +
            +
            +

            In order to be four-spinors like the electron and other lepton components, there must be one quark component for every combination of flavour and colour, bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four (4) component bispinor, for a total of 96 complex-valued components for the fermion field. (Wikipedia)

            +
            +

            IMG_20240108_045902

            It is stated that each of the 24 components is a four component bispinor. A bispinor is constructed out 2 simpler component spinor so there are eight (8) spinors in total.

            +
            + + Note +
            +
            +

            Bispinors are so called because they are constructed out of two (2) simpler component spinors, the Weyl spinors. Each of the two (2) component spinors transform differently under the two (2) distinct complex-conjugate spin-1/2 representations of the Lorentz group. This pairing is of fundamental importance, as it allows the represented particle to have a mass, carry a charge, and represent the flow of charge as a current, and perhaps most importantly, to carry angular momentum. (Wikipedia)

            +
            +

            ((3+3) + 2x(3x3)) x 4 = (3 + 3 + 18) x 4 = 24 x 4 = 96 components

              Fermion  | spinors | charged | neutrinos |   quark   | components
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q)
+===========+=========+=========+===========+===========+============
+bispinor-1 |    2    |    3    |     3     |    18     |     24
+-----------+---------+---------+-----------+-----------+------------ } 48
+bispinor-2 |    2    |    3    |     3     |    18     |     24
+===========+=========+=========+===========+===========+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24
+-----------+---------+---------+-----------+-----------+------------ } 48
+bispinor-4 |    2    |    3    |     3     |    18     |     24
+===========+=========+=========+===========+===========+============
+     Total |    8    |   12    |    12     |    72     |     96
+

            Thus fermion is constructed out of eight (8) spinors that brings the total of 96 components consist of 12 charged leptons, 12 neutrinos and 72 quarks.

            Beyond the Quarks

            +
            + + Note +
            +
            +

            It has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear in 2018 that the SO(10) model is also free from all nonperturbative global anomalies on non-spin manifolds — an important rule for confirming the consistency of SO(10) grand unified theory, with a Spin(10) gauge group and chiral fermions in the 16-dimensional spinor representations, defined on non-spin manifolds. (Wikipedia)

            +
            +

            SO(10)_-_16_Weight_Diagram svg

            +
            + + Note +
            +
            +

            Fermion particles are described by Fermi–Dirac statistics and have quantum numbers described by the Pauli exclusion principle. They include the quarks and leptons, as well as any composite particles consisting of an odd number of these, such as all baryons and many atoms and nuclei. Fermions have half-integer spin; for all known elementary fermions this is 1⁄2. In the Standard Model, there are 12 types of elementary fermions: six quarks and six leptons.

            • Leptons do not interact via the strong interaction. Their respective antiparticles are the antileptons, which are identical, except that they carry the opposite electric charge and lepton number. The antiparticle of an electron is an antielectron, which is almost always called a “positron” for historical reasons.IMG_20240108_032736
              • There are six leptons in total; the three charged leptons are called “electron-like leptons”, while the neutral leptons are called “neutrinos”.
              • Neutrinos are known to oscillate, so that neutrinos of definite flavor do not have definite mass, rather they exist in a superposition of mass eigenstates.
              • The hypothetical heavy right-handed neutrino, called a sterile neutrino, has been omitted.
            • Quarks are the fundamental constituents of hadrons and interact via the strong force. Quarks are the only known carriers of fractional charge, but because they combine in groups of three quarks (baryons) or in pairs of one quark and one antiquark (mesons), only integer charge is observed in nature.IMG_20240108_033012
              • Their respective antiparticles are the antiquarks, which are identical except that they carry the opposite electric charge (for example the up quark carries charge +2⁄3, while the up antiquark carries charge −2⁄3), color charge, and baryon number.
              • There are six flavors of quarks; the three positively charged quarks are called up-type quarks while the three negatively charged quarks are called down-type quarks.

            All known fermions except neutrinos, are also Dirac fermions; that is, each known fermion has its own distinct antiparticle. It is not known whether the neutrino is a Dirac fermion or a Majorana fermion.[4] Fermions are the basic building blocks of all matter. They are classified according to whether they interact via the strong interaction or not.

            +
            +

            Electrodynamics

            Free Parameters

            The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.

            +
            + + Note +
            +
            +

            The most general Lagrangian with massless neutrinos, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment.

            • The 19 certain parameters are summarized below:IMG_20231230_232603
            • The neutrino parameter values are still uncertain.
            • The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.

            The renormalization scale may be identified with the Planck scale or fine-tuned to match the observed cosmological constant. However, both options are problematic. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                       MEC 30 / 2
+------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 + ∆18 = ∆27         |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- ∆32
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = (43-19)
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19) ‹-- parameters ✔️    |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- ∆68 - ∆18 = ∆50
+------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}
+

            The Standard Model with massive neutrinos need 7 more parameters (3 masses and 4 PMNS matrix parameters) for a total of 26 parameters.

            +
            + + Note +
            +
            +

            In principle, there is one further parameter in the Standard Model; the Lagrangianof QCD can contain a phase that would lead to CP violation in the strong interac-tion.

            • Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.
            • If θCP is counted, then the Standard Model has 26 free parameters.
            • The relatively large number of free parameters is symptomatic of the StandardModel being just that; a model where the parameters are chosen to match the observations, rather than coming from a higher theoretical principle.
            • Putting aside θCP, of the 25 SM parameters, 14 are associated with the Higgs field, eight with theflavour sector and only three with the gauge interactions.

            Likewise, the coupling constants of the three gauge interactions are of a similar order of magnitude, hinting that they might be different low-energy manifestations of a Grand Unified Theory (GUT) of the forces. These patterns provide hints for, as yet unknown, physics beyond the Standard Model. (Modern Particle Physics - pdf)

            +
            +

            (24-5) + (24-17) = 19 + 7 = 26

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |     ❓
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |     ❓
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |     ❓
+
            +
            + + Note +
            +
            +

            Now we show the interplay of the finite system of prime positions with the 15 finite even positions in the cyclic convolution. Consequently, we only need to fold a 30’s cycle as so that we can identify the opposite prime positions that form their specific pairs in a specific convolution.

            +
            +

            13+17 = 11+19 = 30

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5 
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |     ❓
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |     ❓
+

            The pairwise disjoint

            +
            + + Note +
            +
            +

            The Lie group structure of the Lorentz group is explored. Its generators and its Lie algebra are exhibited, via the study of infinitesimal Lorentz transformations.

            • The exponential map is introduced and it is shown that the study of the Lorentz group can be reduced to that of its Lie algebra.
            • Finally, the link between the restricted Lorentz group and the special linear group is established via the spinor map.

            The Lie algebras of these two groups are shown to be identical (up to some isomorphism).

            +
            +

            270355_1_En_7_Fig1_HTML

            19 + i(13+5) = 19 + i18

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |   66+i30 ✔️
+

            A bispinor is more or less "the same thing" as a Dirac spinor. The convention used here is that the article on the Dirac spinor presents plane-wave solutions to the Dirac equation.

            +
            + + Note +
            +
            +

            The four pairwise disjoint and non-compact connected components of the Lorentzgroup L = O(1, 3) and corresponding subgroups:

            • the proper Lorentz group L+ = SO(1, 3),
            • the orthochronous Lorentz group L↑,
            • the orthochronous Lorentz group Lo = L↑ + ∪ TL↑+ (see below) and
            • the proper orthochronous Lorentz group L↑+ = SO+(1, 3), which contains the identity element.

            Of course, the sets L↓−, L↑− and L↓+ do not represent groups due to the missing identity element. (The-four-pairwise-disjoint)

            +
            +

            19 + 7 = 26

            The-four-pairwise-disjoint-and-non-compact-connected-components-of-the-Lorentz-group-L

             Bispinors | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i5+i7 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i13+i5 ✔️
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |   66+i30
+

            Thus it appears that the cosmological models] derived from compactification of 11d supergravity on a manifold with G2 holonomy have some hidden E7 symmetry.

            Counterpart of Bispinor

            A Dirac fermionis equivalent to two (2) Weyl fermions so it is not the same as bispinor. The counterpart is a Majorana fermion, a particle that must be its own antiparticle.

            +
            + + Note +
            +
            +

            Because particles and antiparticles have opposite conserved charges, Majorana fermions have zero charge, hence among the fundamental particles, the only fermions that could be Majorana are sterile neutrinos, if they exist.

            If they do, then at low energy (after electroweak symmetry breaking), by the seesaw mechanism, the neutrino fields would naturally behave as six Majorana fields, with three of them expected to have very high masses (comparable to the GUT scale) and the other three expected to have very low masses (below 1 eV).

            +
            +

            matrices-interpreted-2

             Majorana  | spinors | charged | neutrinos |   quark   | components | parameter
+  Fields   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   13+5
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   5+7
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    ❓     |     -     |     ❓     |   i66❓
+===========+=========+=========+===========+===========+============+===========
+     Total |   12    |    -    |    ❓     |     -     |     ❓     |   30+i66❓
+
            +
            + + Note +
            +
            +

            In physics, a subatomic particle is a particle smaller than an atom.[1]

            subatomic particles

            Experiments show that light could behave like a stream of particles (called photons) as well as exhibiting wave-like properties. This led to the concept of wave–particle duality to reflect that quantum-scale particles behave both like particles and like waves; they are sometimes called wavicles to reflect this. (Wikipedia)

            +
            +

            the 12 fermions and 5 bosons are known to have 48 and 13 variations, respectively

             Majorana  | spinors | charged | neutrinos |   quark   | components | parameter
+  Fields   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   13+5
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   5+7
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13 ✔️
+===========+=========+=========+===========+===========+============+===========
+     Total |   12    |    -    |    43     |     -     |     43     |  30+i13 ✔️
+
            +
            + + Note +
            +
            +

            Leptons do not interact via the strong interaction.

            • Their respective antiparticles are the antileptons, which are identical, except that they carry the opposite electric charge and lepton number.
            • The antiparticle of an electron is an antielectron, which is almost always called a “positron” for historical reasons.
            • There are six leptons in total; the three charged leptons are called “electron-like leptons”, while the neutral leptons are called “neutrinos”.
            • Neutrinos are known to oscillate, so that neutrinos of definite flavor do not have definite mass, rather they exist in a superposition of mass eigenstates.

            The hypothetical heavy right-handed neutrino, called a “sterile neutrino”, has been omitted. (Wikipedia)

            +
            + 
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️
+

            Since the total of parameters is 66+i30 then according to renormalization theory the 12 boson fields should have the total complex value of 30+i66.

            +
            + + Note +
            +
            +

            When describing spacetime as a continuum, certain statistical and quantum mechanical constructions are not well-defined.

            • To define them, or make them unambiguous, a continuum limit must carefully remove “construction scaffolding” of lattices at various scales.
            • Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. That is, the experimental value of the physical quantity yields practical applications, but due to their empirical nature the observed measurement represents areas of quantum field theory that require deeper derivation from theoretical bases.
            • Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory.
            • Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics.

            Despite his later skepticism, it was Paul Dirac who pioneered renormalization. (Wikipedia)

            +
            +

            image

            Supersymmetry

            +
            + + Note +
            +
            +

            The natural next step is to generalise this to D = 3, 4, 6, 10 and obtain a ‘magic pyramid’ with the D = 3 magic square at the base and Type II supergravity at the summit. On the basis of these results we speculate that the part played by octonions in string and M-theory may be more prominent than previously though. (Super Yang-Mills - pdf)

            +
            +

            images (14)

            +
            + + Note +
            +
            +

            In this paper, we have extended our previous discussions about using HYMNs (height-yielding matrix numbers) which are the eigenvalues [14] of functions of the adjacency matrices associated with the L-matrics and R-matrices derived from adinkras. (Properties of HYMNs - pdf)

            +
            +

            images (13)

            images (15)

            In the forty years since 11D on-shell supergravity theory was constructed in 1978, a lot of efforts have been made to understand supergravity in superspace.

            +
            + + Note +
            +
            +

            Inspired by the history of how Einstein constructed General Relativity, we study the linearized Nordstrom supergravity in 10- and 11-dimensional superspaces.

            • Valise adinkras, although an important subclass, do not encode all information present when a 4D supermultiplet is reduced to 1D. We extend this to non-valise adinkras providing a complete eigenvalue classification via Python code.
            • We found no obstacles to applying the lessons we learned in 4D to higher dimensions. We also derive infinitesimal 10D superspace Weyl transformation laws. The identification of all off-shell ten-dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions.
            • We realize that Lie Algebra techniques, in particular branching rules, Plethysm, and tensor product, provide the key to deciphering the complete list of independent fields that describe a supersymmetric multiplet in arbitrary spacetime dimensions efficiently.
            • Thus, adinkra-based arguments suggest the surprising possibility that the 11D, N=1 scalar superfield alone might describe a Poincare supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, N=1.
            • All of these results strongly suggest adynkras are pointing in the direction of using series expansion in terms of Young Tableaux (YT’s) as a tool to gain the most fundamental mathematical understanding of this class of problems.

            We show the explicit one-to-one correspondence between Lorentz irreps and field variables, leading to an adynkrafield formalism in which the traditional ζ (theta)-monomials are replaced by YT’s as shown below. (YangruiHu.com)

            +
            +

            Higher-Dimensional Supergravity

            +
            + + Note +
            +
            +

            In supergravity theory, supersymmetry theory and superstring theory, Adinkra symbols are a graphical representation of supersymmetry algebras. The similarity between Adinkra in supersymmetry and Adinkra symbols is that they are both graphical representations with hidden meanings (Prof. Sylvester James Gates Jr.). (Adinkra Alphabet)

            +
            +

            Adinkrasupersymmetry

            +
            + + Note +
            +
            +

            All of these results strongly suggest adynkras are pointing in the direction of using series expansion in terms of YT’s as a tool to gain the most fundamental mathematical understanding of this class of problems. (Higher-Dimensional Supergravity - Pdf)

            +
            +

            Similarity

            +
            + + Note +
            +
            +

            Numerous connections have been observed between some, though not all, of these exceptional objects. Most common are objects related to 8 and 24 dimensions, noting that 24 = 8 · 3. By contrast, the pariah groups stand apart, as the name suggests. Exceptional objects related to the number 8 include the following.

            • The octonions are 8-dimensional. The E8 lattice can be realized as the integral octonions (up to a scale factor).The exceptional Lie groups can be seen as symmetries of the octonions and structures derived from the octonions;[19] further, the E8 algebra is related to the E8 lattice, as the notation implies (the lattice is generated by the root system of the algebra).
            • Triality occurs for Spin(8), which also connects to 8 · 3 = 24.Likewise, exceptional objects related to the number 24 include The Leech lattice is 24-dimensional.Most sporadic simple groups can be related to the Leech lattice, or more broadly the Monster.The exceptional Jordan algebra has a representation in terms of 24×24 real matrices together with the Jordan product rule.These objects are connected to various other phenomena in math which may be considered surprising but not themselves “exceptional”. For example, in algebraic topology, 8-fold real Bott periodicity can be seen as coming from the octonions. In the theory of modular forms, the 24-dimensional nature of the Leech lattice underlies the presence of 24 in the formulas for the Dedekind eta function and the modular discriminant, which connection is deepened by Monstrous moonshine, a development that related modular functions to the Monster group.

            In string theory and superstring theory we often find that particular dimensions are singled out as a result of exceptional algebraic phenomena. For example, bosonic string theory requires a spacetime of dimension 26 which is directly related to the presence of 24 in the Dedekind eta function. Similarly, the possible dimensions of supergravity are related to the dimensions of the division algebras. (Wikipedia)

            +
            +

            1200px-Exceptionalmindmap2

            The Root System

            The Cartan–Weyl basis of the Lie algebra of SU(3) is obtained by another change of basis, where one defines The Root System for SU(3).

            +
            + + Note +
            +
            +

            In mathematical physics, Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis.

            • Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations, where the type and the multiplicities of these irreducible representations are known abstractly.
            • The name derives from the German mathematicians Alfred Clebsch (1833–1872) and Paul Gordan (1837–1912), who encountered an equivalent problem in invariant theory.

            Generalization to SU(3) of Clebsch–Gordan coefficients is useful because of their utility in characterizing hadronic decays, where a flavor-SU(3) symmetry exists (the eightfold way) that connects the three light quarks: up, down, and strange. (Wikipedia)

            +
            +

            The Root System for SU(3)

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            π(π(30+37)) = π(π(67)) = π(19) = 8

            #!/usr/bin/env bash
+
+edit_file () {
+
+  NUM=$(($2 + 0))
+  
+  while IFS=' ' read -ra SPIN; do
+    T+=("${SPIN[0]}")
+    R+=("${SPIN[1]}")
+    A+=("${SPIN[2]}")
+    C+=("${SPIN[3]}")
+    K+=("${SPIN[4]}")
+    I+=("${SPIN[5]}")
+    N+=("${SPIN[6]}")
+    G+=("${SPIN[7]}")
+  done < /tmp/spin.txt
+
+  FRONT="---\n"
+  FRONT+="sort: ${K[$NUM]}\n"
+  FRONT+="span: ${I[$NUM]}\n"
+  FRONT+="spin: ${N[$NUM]}\n"
+  FRONT+="suit: ${G[$NUM]}\n"
+  FRONT+="---\n"
+
+  IFS=$'\n' read -d '' -r -a LINE < _Sidebar.md
+  TEXT="${LINE[$NUM]}" && TITLE=${TEXT%|*}
+  FRONT+="# $TITLE\n\n"
+
+  [[ $NUM -le 9 ]] && sed -i "1s|^|$FRONT|" $1
+  if [[ $NUM -lt 2 || $NUM == 9 ]]; then
+    mv -f $1 ${1%/*}/README.md
+    sed '1,6!d' ${1%/*}/README.md
+  fi
+}
+
+FILE=${1##*/} && SORT=${FILE%.*}
+[[ $SORT =~ ^-?[0-9]+$ ]] && edit_file $1 $SORT
+

            These matrices are particularly important in both mathematics and physics. For example, these matrices (and their generalizations) are important in Lie theory.

            +
            + + Note +
            +
            +

            Gell-mann matrices are a complete set of Hermitian noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model the eight gluons that mediate the strong force quantum chromodynamics, an analogue of the Pauli matrices well-adapted to applications in the realm of quantum mechanics. (Wolfram)

            +
            + 
            #!/usr/bin/env python
+
+import numpy as np
+from scipy import linalg
+
+class SU3(np.matrix):
+	GELLMANN_MATRICES = np.array([
+		np.matrix([ #lambda_1
+			[0, 1, 0],
+			[1, 0, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_2
+			[0,-1j,0],
+			[1j,0, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_3
+			[1, 0, 0],
+			[0,-1, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_4
+			[0, 0, 1],
+			[0, 0, 0],
+			[1, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_5
+			[0, 0,-1j],
+			[0, 0, 0 ],
+			[1j,0, 0 ],
+		], dtype=np.complex),
+		np.matrix([ #lambda_6
+			[0, 0, 0],
+			[0, 0, 1],
+			[0, 1, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_7
+			[0, 0,  0 ],
+			[0, 0, -1j],
+			[0, 1j, 0 ],
+		], dtype=np.complex),
+		np.matrix([ #lambda_8
+			[1, 0, 0],
+			[0, 1, 0],
+			[0, 0,-2],
+		], dtype=np.complex) / np.sqrt(3),
+	])
+
+
+	def computeLocalAction(self):
+		pass
+
+	@classmethod
+	def getMeasure(self):
+		pass
+

            These representations are a curious finding. They relate particles to antiparticles by using only the complex conjugate i → −i, they fill these as of Euler's Identity.

            +
            + + Note +
            +
            +

            Euler’s identity is a special case of Euler’s formula e^ix = cos x + i sin x when evaluated for x = π, In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia)

            +
            +

            Euler's identity

            Euler identity present a matrix generalization of the about exponential representation for matrix real and imaginary unit which compatible with the Pauli matrix

            +
            + + Note +
            +
            +

            Gell–Mann -matrices are a complete set of Hermitian 3 ⊗ 3 noncommuting trace-orthogonal matrices. They are at the heart of Quantum Chromodynamics (QCD), an integral part of the Standard Model. They are also used in quantum information theory to represent qutrits. Gell–Mann matrices are to SU(3) what the Pauli matrices are to SU(2). (Wolfram)

            +
            +

            Everything About Gell Mann Matrices Unary Operations

            These unifying principles might come in the form of grand unified theories, supersymmetry, M-theory, or perhaps something else.

            +
            + + Note +
            +
            +

            The discovery of neutrino oscillations indicates that the Standard Model is incomplete, but there is currently no clear evidence that nature is described by any Grand Unified Theory. Neutrino oscillations have led to renewed interest toward certain GUT such as SO(10). (Wikipedia)

            +
            +

            Higher-Dimensional Supergravity

            Although, at the moment evidence do not have a complete model. However, it becomes a little more clear that this unlikely algebra is not going away.

            Basic Transformation

            The first appearance of e in a printed publication was in Euler's Mechanica (1736). It is unknown why Euler chose the letter e.

            +
            + + Note +
            +
            +

            Leonhard Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and in a letter to Christian Goldbach on 25 November 1731. (Wikipedia)

            +
            +

            Letter e

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            +
            + + Note +
            +
            +

            During the last few years of the 12th century, Fibonacci undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that it popularized the use of the Arabic numerals in Europe, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. (Famous Mathematicians)

            +
            +

            MEC30 Square

            Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30's square.

            +
            + + Note +
            +
            +

            A square system of coupled nonlinear equations can be solved iteratively by Newton’s method. This method uses the Jacobian matrix of the system of equations. (Wikipedia)

            +
            +

            gradien

            In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism.

            +
            + + Note +
            +
            +

            As usual, the images on the left are snapshots of the particles at different times. Those times correspond to the grey slices in the space-time diagram on the right. You can see the specific interaction points in the space-time diagram, where the blue particle is emitted and then absorbed by the red particles. Those points will be important later, as we compare this to the situation in string theory. (Slimy.com)

            +
            +

            Feynman diagrams

            ezgif-4-95200c65b5

            +
            + + Note +
            +
            +

            They are at the heart of Quantum Chromodynamics (QCD), an integral part of the Standard Model. They are also used in quantum information theory to represent qutrits. Gell–Mann matrices are to SU(3) what the Pauli matrices are to SU(2). (Wolfram)

            +
            +

            Gell-Mann transformations

            In this paper, you may find a way to apply the Gell-Mann transformations made by the λi matrices using Geometric Algebra Cl3,0. So it will need a gap between each identities to proceed the thing. Let's discuss how it goes by the seven (7) hidden dimensions.

            Fundamental Forces

            +
            + + Note +
            +
            +

            In particle physics, a lepton is an elementary particle of half-integer spin (spin 1⁄2) that does not undergo strong interactions.[1]

            • Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutral leptons (better known as neutrinos).
            • Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed.
            • The best known of all leptons is the electron.

            There are six types of leptons, known as flavours, grouped in three generations.[2]

            For every lepton flavor, there is a corresponding type of antiparticle, known as an antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. According to certain theories, neutrinos may be their own antiparticle. It is not currently known whether this is the case. (Wikipedia)

            +
            +

            Electrodynamics

            They are composed out of Symmetry Breaking between The True Prime Pairs versus the 139 components of The Fermion Field tabulated as below.

            (33+1)th prime = 139

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    | 👉 3    |     3     |    18     |     24     |   11 ✔️
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    139     |  96+i43
+

            Beyond the 139

            According to the 24 cells of Prime Hexagon, this 12 boson fields seems to be realistic. However it would need to have a total of 96 complex-valued components as well.

            +
            + + Note +
            +
            +

            The present particle physics or standard model based on the “unreal gauge transformation symmetry” and meaningless math cannot explain any actual physical mechanism at all (biglobe.ne.jp)

            +
            +

            hsta1

            When we take all the forces that we understand, i.e., not including gravity, and write down the QFT version of them, we arrive at the predictions of the Standard Model.

            +
            + + Note +
            +
            +

            This is where the idea of 12 fermion fields and 12 boson fields come from. These fields are excitations of the underlying theories (the Standard Model) that describe the known Universe in its entirety, and include:

            • The six (6): up-, down-, strange-, charm-, bottom-, top-quarks, and their antiquark counterparts,
            • The three (3) charged (electron, muon, tau) and three (3) neutral (electron neutrino, muon neutrino, tau neutrino) leptons, and their antimatter counterparts,
            • The eight (8) gluons (because of the eight possible color combinations),
            • The one (1) electromagnetic (photon) boson,
            • The two (2) weak (W-and-Z) bosons,
            • And the Higgs boson.

            The quarks and leptons are fermions, which is why they have antimatter counterparts, and the W boson comes in two equal-and-opposite varieties (positively and negatively charged), but all told, there are 24 unique, fundamental excitations of quantum fields possible. This is where the 24 fields idea comes from. (Forbes)

            +
            +

            SM-particles

            This scheme goes to the unification of 11s with 7s to 18s meanwhile the 11th it self behave as residual by the 5th minor hexagon between the 30 to 36' cells.

            +
            + + Tip +
            +
            +

            This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with the prime distribution level as indicated by the self repetition on MEC30.

            +
            +

            109 = 29th prime = (10th prime)th prime

            self repetition

            The evolution of a spin foam, has a scale above the Planck length. Consequently, not just matter, but space itself, prefers an atomic structure.

            SM-SUSY-diagram

            These include generating variants of their abundance profile, assigning taxonomy and finally generating a rooted phylogenetic tree for the Standard Model.

            +
            + + Note +
            +
            +

            Here is an elegant model to define the elementary particles of the Standard Model in Physics.

            • The black spheres are the bosons, the green ones leptons and the rest of the colored ones Murray Gell-Mann’s quarks (red for Generation I, blue for II and orange for III).
            • Higgs Boson (aka the God particle) that does not have charge is the vertex between the matter and anti-matter particles.
            • The z-boson and its counterpart would lie in the centroids of the tetrahedrons created by folding the triangles to meet up at the Higgs particle.

            The next step is to re-gigg the model to account for the collisions and annihilations. Gluons and Photons that don’t have mass are not in the model, but will be the consequences of the interactions. (Hypercomplex-Math)

            +
            +

            particlephysicsmodel-1

            All 15 matter particles are mirroring their corresponding doppelgangers (anti-particles) each others that could potentially explain dark matter.

            Quadratic Polynomials

            In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns.

            +
            + + Note +
            +
            +

            The interaction of any pair of fermions in perturbation theory can be modelled as:

            Two fermions go in → interaction by boson exchange → Two changed fermions go out.

            The exchange of bosons always carries energy and momentum between the fermions, thereby changing their speed and direction. The exchange may also transport a charge between the fermions, changing the charges of the fermions in the process (e.g., turn them from one type of fermion to another). Since bosons carry one unit of angular momentum, the fermion’s spin direction will flip from +1⁄2 to −1⁄2 (or vice versa) during such an exchange (in units of the reduced Planck’s constant). (Wikipedia)

            +
            +

            36th prime - 30th prime = 151 - 113 = 1 + 37

            Defining the Prime Hexagon

            +
            + + Tip +
            +
            +

            Our 18s gists would form the 18s structure of 11s and 7s where by the 11s, the 20th prime 71 would stand as eigenvalue and by the 7s, the 11th prime 31 would stand as the new symmetical zero axis by means of MEC30 Structure. So whenever the 11s is compactified down to 4 dimensions it will always be compactifed by the 7s as their extended branes which including the eigenvector of dark energy and finally become another level of 11 dimensions that lead to the concept of multiple universes.

            +
            +

            Δ prime = 114th prime - 19 = (6 x 19)th prime - 19 = 619 - 19 = 600 = 3 x 200

            Proof of Confinement

            Observing more detail of the discussed scheme of 168 we will get it also when we take the 19's and 17's cell of (31+37)+(35+65)=68+100=168.

            +
            + + Tip +
            +
            +

            By our project the 18’s on the gist will cover five (5) unique functions that behave as one (1) central plus four (4) zones. This scheme will be implemented to all of the 168 repositories as bilateral way (in-out) depend on their postion on the system. So along with the gist it self then there shall be 1 + 168 = 169 units of 1685 root functions.

            +
            +

            5 + 2 x 5 x 168 = 5 + 1680 = 1685 root functions

            By the spin above you can see that the 4 zones of these 19's to 17's are representing the rotation 1 to 5. Such of formation can be seen on Ulam Spiral as below.

            +
            + + Note +
            +
            +

            The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner’s Mathematical Games column in Scientific American a short time later.

            +
            +

            ulam spiral

            By MEC30 we will also discuss the relation of these 4 zones with high density of 40 primes where 60 number is folded. So by the module 6 it will always return to the beginning position within 60+40=100 nodes per layer.

            +
            + + Note +
            +
            +

            Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler’s prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau’s problems (Wikipedia).

            +
            +

            prime Sacks_spiral

            This density will bring the D3-Brane where the lexer is being assigned per MEC30. Base on the its spin as shown in the above picture this lexer is assigned by Id: 33.

            Parsering Structure

            Ploting 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            $True Prime Pairs:
+(5,$True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+  
+layer | node | sub |  i  |  f                               
+------+------+-----+---------- 
+      |      |     |  1  | -------------------- _site ---  71 = 72-1
+      |      |  1  +-----+                        |
+      |  1   |     |  2  | (5)                  _saas
+      |      |-----+-----+                        |
+      |      |     |  3  | ---------            _data
+  1   +------+  2  +-----+----      |             |
+      |      |     |  4  |         5x ---       _posts
+      |      +-----+-----+          |     |       |
+      |  2   |     |  5  | (7) -----      |     _drafts
+      |      |  3  +-----+                |       |
+289+11=300   |     |  6  |                |     _plugins
+------+------+-----+-----+----- 72 x 6   7x ------------ 11x = 77 (rational)◄--
+      |      |     |  7  |                |     _includes                      |
+      |      |  4  +-----+                |       |                            |
+      |  3   |     |  8  | (11)  ---      |     _layouts                       |
+      |      +-----+-----+          |     |       |                            |
+      |      |     |  9  |         2x ---        assets  (69 = 72-3)           |
+  2   +------|  5  +-----+-----     |             |                            |
+      |      |     |  10 | ---------            _saas                          |
+      |      |-----+-----+                        |                            |
+      |  4   |     |  11 | (13) ----------------_site --  71 = 72-1            |
+      |      |  6  +-----+                                                     |
+329+71=400   |     |  12 |------------------------------  70 = 72-2            |
+------+------+-----+-----+                                                    11x
+      |      |     |  13 |                                                     |
+      |      |  7  +-----+                                                     |
+      |  5   |     |  14 | (17) ◄------------------------------------------- (17)
+      |      |-----+-----+                                                     |
+      |      |     |  15 | ◄-- 42 x 6 partitions of 13 (irrational)            |
+  3   +------+  8  +-----+-----                                                +
+      |      |     |  16 |                                                     |  
+      |      |-----+-----+                                                     |
+      |  6   |     |  17 | (19) ◄------------------------------------------- (19)
+      |      |  9  +-----+                                                     |
+168+32=200   |  |  |  18 |------------------------------  68 = 72-4            |
+------|------|--|--+-----+                                                     |
+       900 -----                                                               |
+                                                                               |
+

            Using the javascript library from Chevotrain and data parser from Jekyll/Liquid finally we found the correlation between the lexer and parser trough the powers of pi.

            +
            + + Note +
            +
            +

            In this example, the content from a Markdown document document.md that specifies layout: docs gets pushed into the {{ content }} tag of the layout file docs.html. Because the docs layout itself specifies layout: page, the content from docs.html gets pushed into the {{ content }} tag in the layout file page.html. Finally because the page layout specifies layout: default, the content from page.html gets pushed into the {{ content }} tag of the layout file default.html. (JekyllRb)

            +
            +

            Parsering

            Since the modulo 6 is occured all over the spin then we have defined that this 4 zones should stand as default configuration as you can see on the left sidebar.

            +
            + + Tip +
            +
            +

            In order to maintain the 18’s structure between each of repositories to correlate with the above density then we could use a hierarchical database that stores low-level settings for the operating system such as windows registry.

            +
            +

            windows registry

            Going deeper there are many things raised up as questions. So in this project we are going to analyze it using a javascript library called Chevrotain.

            +
            + + Note +
            +
            +

            The spin states for the powers of pi. The Prime Hexagon is an integer environment, so pi powers are truncated. I believe these data suggest prime numbers are linked in some way to pi. (HexSpin)

            +
            +

            Lexers, Parsers and Interpreters with Chevrotain

            It is going to setup CI/CD for up to 1000 public repositories out of millions that available on GitHub. You may visit our mapping scheme for more detail.

            Grand Unification

            The 619 is the 114th prime. By the True Prime Pairs it is laid on the last index of 6 with prime 19 where as 6x19 is also 114. Let's put 19 hexagons within the 3 layers.

            168+618 - 19x6x6 = 786 - 684 = 102

            entry and exit point

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            +
            + + Note +
            +
            +

            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) (₠Quantum).

            +
            +

            6+6 + 6/\6 = 6+6 + 15 = 27-day month

            flowchart

            By this project the above would be deployed as default layout. It is set to be avalaible throughout the whole platform via a single page within a parser repository which is acting as prime 13. Their interface will be in json and xml format.

            Here is for the sample:

            {
+  "title":"Mapping System",
+  "content":"<p>Hello, <strong>world</strong>.\nI am here.</p>\n",
+  "links": [
+    {"title":"Introduction","url":"https://www.eq19.com/intro/"},
+    {"title":"Go tour on Mapping System ","url":"https://www.eq19.com/maps/"},
+    {"title":"A backed pretty display for markdown","url":"https://www.eq19.com/gistio/"},
+    {"title":"Gist.io for programmers","url":"https://gist.io/@eq19/d2336e28e79702acf38edd182003d5e0"}
+  ]
+}
+

            Using a kind of interface such as docker then it could be developed cross platform. Evenso. Let assume that all alpabethic letter in the sequence is representing a local disk so you may build your own pattern in your PC such as shown below:

            default

            By The GitHub Runner you can connect to the Google COS Instance. For self-hosted runners defined at the organization level, configure runs-on.group in your workflow file to target a runner groups or combine groups and labels.

            +
            + + Note +
            +
            +

            Why collaborating with physicists?

            • Contribute to the understanding of the Universe.
            • Open methodological challenges.
            • Test bed for developing ambitious ML/AI methods, as enabled by the precise mechanistic understanding of physical processes.
            • Core problems in particle physics transfer to other fields of science (likelihood-free inference, domain adaptation, optimization, etc).
            • A high-level summary of various aspects of machine learning in LHC data reconstruction, mostly based on CMS examples. A short summary of a particular use case: ML for combining signals across detector subsystems with particle flow. This talk is in personal capacity (not representing CMS or CERN), representing my biased views.

            You can find a great and fairly complete overview of ML papers in HEP. (Pata Slides)

            +
            +

            π(10) = 2,3,5,7

            SO(10)

            teaching-machines-glouppe_compressed.pdf

            This way will also be our approach to Euler's identity. By taking the correlation between f(π) as P vs f(i) as NP where eiπ + 1 = 0 then theoretically they shall be correlated to get an expression of the prime distribution similar to MEC30.

            +
            + + Note +
            +
            +

            The Minimal Supersymmetric Standard Model (MSSM) contains two Higgs doublets, leading to five (5) physical Higgs bosons:

            • one (1) neutral CP-odd (A) 👈 degenerated with (h or H)
            • two (2) charged states (H+ and H−),
            • Two (2) neutral CP-even states (h and H).

            At tree-level, the masses are governed by two parameters, often taken to be mA and tan β [3]. When tan β >> 1, A is nearly degenerated with one of the CP-even states (denoted ϕ). (ScienceDirect)

            +
            +

            the 5 cells

            This also introduces a lower bound of Mod 90 originated from the 4th coupling of MEC30 which is holded by five (5) cells between 13 and 17.

            +
            + + Note +
            +
            +

            Below we will demonstrate how factorization algorithms and twin prime dyad cycling at the digital root level rotate the vertices of equilateral triangles within {9/3} star polygons like the one pictured above. These rotations are encoded in 3 x 3 matrices generated by period-24 digital root dyad tri-level cycling. We will also reveal the Latin Square reflecting {3,6,9} hidden in plain sight betwixt and between the twin prime distribution channels; all of its rows, columns and principal diagonals summing to 18. PrimesDemystified

            +
            +

            19 + 18 + 102 = 37 + 102 = 139 = 34th prime = (40 - 6)the prime

            exponentiation zones

            The boson, photon and gravity forces are assigned to 30, 31 and 32. Gluon force and exchange are assigned to 33 and 34 which are then standing as the lexer and parser.

            +
            + + Tip +
            +
            +

            An overview of the various families of elementary and composite particles, and their interactions. Fermions are on the left, and Bosons are on the right.

            Elementary Particle

            According to the Standard Model there are five (5) elementary bosons with thirteen (13) variations. These 5 and 13 will be assigned to the “5xid’s of 31~35 (sequenced)” and “13xid’s of 36~68 (unsequenced)”, respectively (see the sidebar menu).

            +
            +

            The exchange of virtual pions

            This lead to a consequence of SU(5) grand unification (assigned to 35) showing a complex scalar Higgs boson of 24 gauge groups observe mass of W boson (assigned to 36).

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist01.html b/exponentiation/span13/gist01.html new file mode 100644 index 00000000000..b945685a53a --- /dev/null +++ b/exponentiation/span13/gist01.html @@ -0,0 +1,84 @@ + algorithm · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            algorithm

            combined. By this 1000 primes then 168-150=Δ18 is raised on the next turn.

            $True Prime Pairs:
+layer | node | sub |  i  |  k  |  f
+------+------+-----+-----+-----+-----
+      |      |     |  1  | 1,2 |  2,3 ← 2x = (13-11)x ---
+      |      |  1  +-----+-----+                         |
+      |  1   |     |  2  |  3  |  7                      |
+      |      |-----+-----+-----+                         |
+      |      |     |  3  | 4,6 |  10,11,12 --            |
+  1   +------+  2  +-----+-----+             |           |
+      |      |     |  4  |  7  |  13         5x ---      |
+      |      +-----+-----+-----+             |     |     |
+      |  2   |     |  5  | 8,9 |  14,15 -----      |     |
+      |      |  3  +-----+-----+                   |     |
+      |      |     |  6  |  10 |  19               |     |
+------+------+-----+-----+-----+--------           7x + 6x = 13x
+      |      |     |  7  |  11 |  20               |     |
+      |      |  4  +-----+-----+                   |     |
+      |  3   |     |  8  |  12 |  26  -----        |     |
+      |      +-----+-----+-----+           |       |     |
+      |      |     |  9  |  13 |  27       2x -----      |
+  2   +------|  5  +-----+-----+           |             |
+      |      |     |  10 |  14 |  28 -----               |
+      |      |-----+-----+-----+                         |
+      |  4   |     |  11 |15,18|  29,30,31,32 ←---4x----
+      |      |  6  +-----+-----+
+      |      |     |  12 |  19 |  36
+------+------+-----+-----+-----+-------
+      |      |     |  13 |  20 | {38}
+      |      |  7  +-----+-----+
+      |  5   |     |  14 |21,22| {40,41} = (19-17)x ----
+      |      |-----+-----+-----+                         |
+      |      |     |  15 |  23 | {42}                   6x + 13x = 19x
+  3   +------+  8  +-----+-----+                         |
+      |      |     |  16 |24,27| {43,44,45,46} ←- 4x --
+      |      |-----+-----+-----+
+      |  6   |     |  17 |  28 | {50} = 46 + 4
+      |      |  9  +-----+-----+
+      |      |     |  18 |  29 | {68} = 32 + 36
+------|------|-----+-----+------
+
            |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - |100 |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - |101 |  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   T
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |   H
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   E
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   P
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |   O
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   W
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |   E
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   R
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   O
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |   F
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | ∑=168
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |   V
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   S
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            eQ19

            HxD

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist02.html b/exponentiation/span13/gist02.html new file mode 100644 index 00000000000..32ce69ee7bb --- /dev/null +++ b/exponentiation/span13/gist02.html @@ -0,0 +1 @@ + core · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            core

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist03.html b/exponentiation/span13/gist03.html new file mode 100644 index 00000000000..17a3f6ab698 --- /dev/null +++ b/exponentiation/span13/gist03.html @@ -0,0 +1,64 @@ + default · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            ===========
+(1){1}-7:   7'
+(1){8}-13:  6‘
+(1)14-{19}: 6‘
+------------- {6+6} --→ [M+F] 
+(2)20-24:   5'            |
+(2)25-{29}: 5'            |
+------------  5+5 --------
+(3)30-36:   7:{70,30,10²} |
+------------              |
+(4)37-48:   12• ---       |
+(5)49-59:   11°    |      |
+            --}30° 30•    |
+(6)60-78:   19°    |      |
+(7)79-96:   18• ---       |
+--------------            |
+(8)97-109:  13            |
+(9)110-139:{30}=5x6 <--x-- [C1+C2]
+            --
+            43
+
            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|------------------------ Scheme-12 ------------------------|
+|------------ 6¤ -------------|------------- 6¤ ------------|
+|--------------------------- 192 ---------------------------|
+|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
++----+----+----+----+----+----+----+----+----+----+----+----+
+|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|
+|---------  5¤  ---------|------------ {96} -----------|{43}|
+|--------- {53} ---------|-------------- {139} -------------|
+|------ Scheme-53 -------|------------ Scheme-34 -----------|
+
              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+Sequence:
+ By the next layer the 89² will become 89 and 5 become 5² or 25.
+ This 89 and 25 are in the same layer with total of 114 or prime 619
+ So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+

            Screenshot

            204159170-55a7470a-d03b-49c0-ba3c-68a64f895263

            Screenshot_2022-11-28-16-50-17-00

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist04.html b/exponentiation/span13/gist04.html new file mode 100644 index 00000000000..9a96624b61b --- /dev/null +++ b/exponentiation/span13/gist04.html @@ -0,0 +1 @@ + factor · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            factor

            factorcode

            TA_Chart

            2022-11-30 (5)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist05.html b/exponentiation/span13/gist05.html new file mode 100644 index 00000000000..6772e0ee2d9 --- /dev/null +++ b/exponentiation/span13/gist05.html @@ -0,0 +1 @@ + grouping · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            grouping

            integration

            integration

            default

            default

            TA_Chart

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist06.html b/exponentiation/span13/gist06.html new file mode 100644 index 00000000000..4d220dda284 --- /dev/null +++ b/exponentiation/span13/gist06.html @@ -0,0 +1 @@ + helix · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            helix

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist07.html b/exponentiation/span13/gist07.html new file mode 100644 index 00000000000..fea8b1fbe19 --- /dev/null +++ b/exponentiation/span13/gist07.html @@ -0,0 +1 @@ + impact · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            impact

            202907558-c7198082-14fd-409b-9e31-1a0440f79039image

            default

            202907558-c7198082-14fd-409b-9e31-1a0440f79039

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist08.html b/exponentiation/span13/gist08.html new file mode 100644 index 00000000000..277e46ef2d2 --- /dev/null +++ b/exponentiation/span13/gist08.html @@ -0,0 +1,27 @@ + level · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            level

            image

            image

                                            | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                |  2 | 60 | 40 | 1 | 30 | 30 | 5 |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/gist09.html b/exponentiation/span13/gist09.html new file mode 100644 index 00000000000..42b307fe3ad --- /dev/null +++ b/exponentiation/span13/gist09.html @@ -0,0 +1,9 @@ + centralize · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            centralize

            **∑11(40,30,20) = 90**

            default

            default

            default

            ---+-----+-----
+ 1 | 1   | 18
+---+-----+-----
+ 2 | 19  | 29
+---+-----+-----
+ 3 | {30}|{43}
+---+-----+-----
+
+

            rep fork

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span13/index.html b/exponentiation/span13/index.html new file mode 100644 index 00000000000..bafeff40ac7 --- /dev/null +++ b/exponentiation/span13/index.html @@ -0,0 +1,214 @@ + Grand Unified Theory (syntax) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Grand Unified Theory (syntax)

            Grand Unified Theory (GUT) is successful in describing the four forces as distinct under normal circumstances, but connected in fundamental ways.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-27 of main section-5 that is inherited from the spin section-13 by prime spin-35 and span-152 with the partitions as below.

            +
            +
            1. algorithm
            2. core
            3. default
            4. factor
            5. grouping
            6. helix
            7. impact
            8. level
            9. centralize

            GUT is also successful in describing a system of carrier particles for all four forces, but there is much to be done, particularly in the realm of gravity.

            User Profiles

            Capture-49

            Triangle_diagram

            images

            Electroweak svg (1)

            image

            image

            image

            +
            + + Note +
            +
            +

            How can the Universe be so uniform? Now, the time for light to cross a significant part of the Universe is billions of years. We call this time the light communication time, and it is the shortest time required for any changes to be felt between two parts of the Universe. (From J. Schombert)

            +
            +

            horizon_problem

            Unification

            GUT predicts that the other forces become identical under conditions so extreme that they cannot be tested in the laboratory, although there may be lingering evidence of them in the evolution of the universe.

            I15-53-electroweak

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  ❓ |  ❓ |  ❓ | 3¤ ✔️     ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            GUTs - The Unification of Forces.pdf

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-👇--+-👇--+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-👇--+-👇--+----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  ❓ |  ❓ |  .. | 3¤ ✔️     ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            Figure_34_06_03

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-👇--+-👇--+-👇--+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-👇--+-👇--+-👇--+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  ❓ |  ❓ |  .. | 3¤ ✔️     ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            The-strong-force-is-complicated-since-observable-particles-that-feel-the-strong-force

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-👇--+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-👇--+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-👇--+-👇--+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  .. | 3¤ ✔️     ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            CCJanFeb23_EFT_fermi-635x206

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤ ✔️     ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            Black Hole

            main-qimg-6874830a97ce37b0b02cc3ae3d2268f1

            1591890434759

            I4dae

            E = mc²
+m = E = mc²
+m = E/c²
+
+c = 1 light-second
+  = 1000 years x L / t
+  = 12,000 months x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+1 year = 12 months
+1000 years = 12,000 months
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+
+Conclusion:
+π(π(π(π(π(32(109²-89²)))))) Universe vs Parallel vs Multiverse (via blackhole)
+   👇
+π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Parallel (gap in 2nd-level)
+   👇
+π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level)
+   👇
+π(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter)
+   👇
+|--👇---------------------------- 2x96 ---------------------|
+|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
+|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
++----+----+----+----+----+----+----+----+----+----+----+----+ 
+|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown
+|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+|-------- Bosons --------|---------- Fermions ---------|-- Graviton
+|-- Sun Orbit (7 days) --|--- Moon Orbit (12 months) --| (11 Galaxies)
+|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way 👉 Σ=12
+

            main-qimg-2d9e529abca58e22d8abc805a24b27bd

            How water is formed

            +
            + + Note +
            +
            +

            Finally, there exist scenarios in which there could actually be more than 4D of spacetime. String theories require extra dimensions of spacetime for their mathematical consistency. In string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional.String theory

            These are situations where theories in two or three spacetime dimensions are no more useful. This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family. (Wikipedia)

            +
            +

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------  ✔️   |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            The only different is, instead of an instance, it will behave as an inside container, just like how spider built a home web as strong as steel but useless to cover them against a rainy day nor even a small breeze.

            default

            This would even close to the similar ability of human brain without undertanding of GAP functionality between left and right of the human brain.

            Final Theory

            l9mo0z1dltu61

            EU4RYL7UcAAzZN2

            final-theory

            ckm-angles-n

            HEXAHEDRONTORUS1

            0

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist01.html b/exponentiation/span14/gist01.html new file mode 100644 index 00000000000..2a616a699f1 --- /dev/null +++ b/exponentiation/span14/gist01.html @@ -0,0 +1 @@ + Turbulence · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Turbulence

            A sequence of Jupyter notebooks featuring the "12 Steps to Navier-Stokes"

            12 steps to Navier–Stokes

            The interactive module 12 steps to Navier–Stokes is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013.

            image

            You can see that two distinct pressure zones are forming and that the spiral pattern expected from lid-driven cavity flow is beginning to form. Experiment with different values of nt to see how long the system takes to stabilize.

            image

            The quiver plot shows the magnitude of the velocity at the discrete points in the mesh grid we created. (We're actually only showing half of the points because otherwise it's a bit of a mess. The X[::2, ::2] syntax above is a convenient way to ask for every other point.) Another way to visualize the flow in the cavity is to use a streamplot

            image

            To use these lessons, you need Python 3, and the standard stack of scientific Python: NumPy, Matplotlib, SciPy, Sympy. And of course, you need Jupyter—an interactive computational environment that runs on a web browser.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist02.html b/exponentiation/span14/gist02.html new file mode 100644 index 00000000000..7ab54f15fed --- /dev/null +++ b/exponentiation/span14/gist02.html @@ -0,0 +1 @@ + gist02.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            cubes

            prime

            ulam default

            lexer

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist02.md b/exponentiation/span14/gist02.md new file mode 100644 index 00000000000..7a4400476fc --- /dev/null +++ b/exponentiation/span14/gist02.md @@ -0,0 +1,9 @@ + +![cubes](https://user-images.githubusercontent.com/8466209/205804217-313e8f74-56d1-4401-be92-e3d3c95da055.jpg) + +![prime](https://user-images.githubusercontent.com/36441664/87958552-dea18f80-cadb-11ea-9499-6c2ee580a5ca.png) + +![ulam](https://upload.wikimedia.org/wikipedia/commons/2/25/Hexgrid_prime_number_spiral.svg) +[![default](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-default-md) + +![lexer](https://user-images.githubusercontent.com/8466209/204159538-6f87b60c-6a32-486d-aa55-c9af2db7eda6.png) diff --git a/exponentiation/span14/gist03.html b/exponentiation/span14/gist03.html new file mode 100644 index 00000000000..1fe96da7c0b --- /dev/null +++ b/exponentiation/span14/gist03.html @@ -0,0 +1,20 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  → base (30)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  → maps (31)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th  → feed (32)
+  =======================+====+====+====+====+====+====+====+====+====+===== 
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th  → lexer (33)
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th  → parser (34)
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th  → syntax (35)
+  =======================+====+====+====+====+====+====+====+====+====+===== 
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th  → grammar (36)        
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            2022-12-06 (2)

            2022-12-06 (3)

            2022-12-06 (1)

            2022-12-06 (1)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist03.md b/exponentiation/span14/gist03.md new file mode 100644 index 00000000000..9d95facab57 --- /dev/null +++ b/exponentiation/span14/gist03.md @@ -0,0 +1,29 @@ +```liquid + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th → base (30) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th → maps (31) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th → feed (32) + =======================+====+====+====+====+====+====+====+====+====+===== + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th → lexer (33) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th → parser (34) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th → syntax (35) + =======================+====+====+====+====+====+====+====+====+====+===== + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th → grammar (36) + =======================+====+====+====+====+====+====+====+====+====+===== + Δ Δ + 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1 + ``` + +![2022-12-06 (2)](https://user-images.githubusercontent.com/8466209/205963196-7e1f4fc3-1833-4b64-9fb4-f79e6cd4637f.png) + +![2022-12-06 (3)](https://user-images.githubusercontent.com/8466209/205964436-c9636678-6679-48f7-938a-e307912600ef.png) + +![2022-12-06 (1)](https://user-images.githubusercontent.com/8466209/205947618-ef28a677-f961-4b78-9e79-e8a9ffe824c5.png) + +![2022-12-06 (1)](https://user-images.githubusercontent.com/8466209/205960400-3061d93a-b3cc-4cd6-84e6-359a9314869d.png) diff --git a/exponentiation/span14/gist04.html b/exponentiation/span14/gist04.html new file mode 100644 index 00000000000..9a1be55decc --- /dev/null +++ b/exponentiation/span14/gist04.html @@ -0,0 +1 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            2022-12-06 (5)

            2022-12-06 (4)

            2022-12-10 (1)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist04.md b/exponentiation/span14/gist04.md new file mode 100644 index 00000000000..b33b2bb760b --- /dev/null +++ b/exponentiation/span14/gist04.md @@ -0,0 +1,5 @@ +![2022-12-06 (5)](https://user-images.githubusercontent.com/8466209/205967762-69f6aaee-f1fc-4b26-a0cc-515257b6d9e7.png) + +![2022-12-06 (4)](https://user-images.githubusercontent.com/8466209/205967707-254fc836-72f4-45fc-9d0e-90c5e0bda465.png) + +![2022-12-10 (1)](https://user-images.githubusercontent.com/8466209/206849387-d530c690-c1ed-4496-9748-355f798d44fa.png) diff --git a/exponentiation/span14/gist05.html b/exponentiation/span14/gist05.html new file mode 100644 index 00000000000..ad3ce582cde --- /dev/null +++ b/exponentiation/span14/gist05.html @@ -0,0 +1,15 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            The 619 is the 114th prime. It has the last index of 6 with the prime 19 where as 6x19 is also 114. When we multiply the 114 minor hexagon again by six (6) minus the duplicaton within those layers we got 684-30-30-5 = 684-65 which is also 619.

            metatron

            gannchart

            Despite the correlation between the bilateral 9 sums with the Fibonacci sequence, some people has discovered many things. The sequence of (55, 89, 144) shows an almost mystical power by its mysterious accuracy in nature and even in trading.

            image

            2022-12-10

            cycle

            2022-12-14 (1)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist05.md b/exponentiation/span14/gist05.md new file mode 100644 index 00000000000..b1f363c5e1e --- /dev/null +++ b/exponentiation/span14/gist05.md @@ -0,0 +1,33 @@ +```liquid +1st layer: +It has a total of 1000 numbers +Total primes = π(1000) = 168 primes + +2nd layer: +It will start by π(168)+1 as the 40th prime +It has 100x100 numbers or π(π(10000)) = 201 primes +Total cum primes = 168 + (201-40) = 168+161 = 329 primes + +3rd layer: +Behave the same as 2nd layer which has a total of 329 primes +The primes will start by π(π(π(1000th prime)))+1 as the 40th prime +This 1000 primes will become 1000 numbers by 1st layer of the next level +Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 +``` + +The 619 is the **114th prime**. It has the last index of 6 with the prime 19 where as **6x19** is also 114. When we multiply the 114 [minor hexagon](https://www.hexspin.com/minor-hexagons/) again by six (6) minus the duplicaton within those layers we got 684-30-30-5 = 684-65 which is also 619. + +[![metatron](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-1_prime-md) + +[![gannchart](https://user-images.githubusercontent.com/8466209/206868681-2cddf780-48f1-4dc5-9ef4-981b402a15d5.png) +](https://gist.github.com/eq19/80c8098f16f3e6ca06893b17a02d910e#file-mapping-md) + +Despite the correlation between the bilateral 9 sums with the Fibonacci sequence, some people has discovered many things. The sequence of ***(55, 89, 144)*** shows an almost mystical power by its mysterious accuracy in nature and even _[in trading](https://www.tradingsim.com/day-trading/fibonacci-trading)_. + +[![image](https://user-images.githubusercontent.com/8466209/216902149-2d017e85-3d95-4484-bc6c-59a4b2079137.png)](https://www.tradingsim.com/day-trading/fibonacci-trading) + +![2022-12-10](https://user-images.githubusercontent.com/8466209/206884467-05a33d48-5cdc-48fd-9b75-5be406100f06.png) + +[![cycle](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-default-md) + +![2022-12-14 (1)](https://user-images.githubusercontent.com/8466209/207418457-4db2048d-e003-492d-a78c-bc2ded725c74.png) diff --git a/exponentiation/span14/gist06.html b/exponentiation/span14/gist06.html new file mode 100644 index 00000000000..37b9bcdee52 --- /dev/null +++ b/exponentiation/span14/gist06.html @@ -0,0 +1 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            gotek

            2022-12-11

            io

            floppies

            2022-12-11 (1)

            neural

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist06.md b/exponentiation/span14/gist06.md new file mode 100644 index 00000000000..b501761b660 --- /dev/null +++ b/exponentiation/span14/gist06.md @@ -0,0 +1,11 @@ +![gotek](https://user-images.githubusercontent.com/36441664/123180870-57f8ed80-d4b6-11eb-89e1-cf8786d0dc14.jpg) + +![2022-12-11](https://user-images.githubusercontent.com/8466209/206888301-0ba40a6a-2caa-4dfe-92ef-5a9db590f85d.png) + +![io](https://user-images.githubusercontent.com/36441664/123179535-cd16f380-d4b3-11eb-95c3-0a5b7ef21ad4.jpg) + +![floppies](https://user-images.githubusercontent.com/36441664/123187010-84ffcd00-d4c3-11eb-8aad-6c40553b752b.png) + +[![2022-12-11 (1)](https://user-images.githubusercontent.com/8466209/206888720-159281ee-1f74-4684-aca3-963dd3c882ab.png)](https://docs.github.com/en/actions/learn-github-actions/usage-limits-billing-and-administration#usage-limits) + +![neural](https://user-images.githubusercontent.com/36441664/123424569-377e7f80-d5eb-11eb-9c85-1f5d72f14eed.png) diff --git a/exponentiation/span14/gist07.html b/exponentiation/span14/gist07.html new file mode 100644 index 00000000000..87a3edbe35d --- /dev/null +++ b/exponentiation/span14/gist07.html @@ -0,0 +1,18 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | 1   | 4
+---+-----+-----
+ 2 |{5}  |{8}
+---+-----+-----
+ 3 | 9   |{17}
+---+-----+-----
+ 4 |{18} |{23}
+---+-----+-----
+ 5 | 24  | 27
+---+-----+-----
+ 6 | 28  | 34
+---+-----+-----
+ 7 |{35} |{41}
+---+-----+-----
+ 8 |{42} |{52}
+---+-----+-----
+

            equilateral

            This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding. (Clay Institute).

            Navier–Stokes Equation

            By this paper it is derived a sufficient condition keeping energy conservation in terms of the gradient of the velocity for the weak solutions of the compressible Euler equations for both the non-vacuum and the vacuum cases.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span14/gist07.md b/exponentiation/span14/gist07.md new file mode 100644 index 00000000000..adbc43e58de --- /dev/null +++ b/exponentiation/span14/gist07.md @@ -0,0 +1,37 @@ +``` +---+-----+----- + 1 | 1 | 4 +---+-----+----- + 2 |{5} |{8} +---+-----+----- + 3 | 9 |{17} +---+-----+----- + 4 |{18} |{23} +---+-----+----- + 5 | 24 | 27 +---+-----+----- + 6 | 28 | 34 +---+-----+----- + 7 |{35} |{41} +---+-----+----- + 8 |{42} |{52} +---+-----+----- +``` + +![](https://user-images.githubusercontent.com/36441664/85040788-5e71cc80-b1b3-11ea-962f-cf26ee3419e2.jpg) + +![](https://user-images.githubusercontent.com/36441664/84902333-e6ce6f80-b0d6-11ea-8289-aac5e1961cd6.gif) + +![equilateral](https://user-images.githubusercontent.com/8466209/205804972-0570afbc-3781-473c-bdc7-5e6927351de5.gif) + +![](https://user-images.githubusercontent.com/36441664/85527369-044e8c80-b635-11ea-8f32-25a6b813a9b1.gif) + +![](https://user-images.githubusercontent.com/36441664/85907724-ae4c3580-b83c-11ea-85c5-c9c20e13bd08.png) + +![](https://user-images.githubusercontent.com/36441664/85039712-32098080-b1b2-11ea-80f0-3e7e767a2ba1.jpg) + +>This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding. _([Clay Institute](https://www.claymath.org/millennium-problems))_. + +[![Navier–Stokes Equation](https://user-images.githubusercontent.com/8466209/224287999-37cd0692-bf51-4b99-bb45-8c49e5db58e3.png)](https://www.claymath.org/millennium-problems/navier%E2%80%93stokes-equation) + +By _[this paper](https://www.sciencedirect.com/science/article/pii/S0362546X23000111)_ it is derived a sufficient condition keeping energy conservation in terms of the gradient of the velocity for the weak solutions of the compressible Euler equations for both the non-vacuum and the vacuum cases. \ No newline at end of file diff --git a/exponentiation/span14/index.html b/exponentiation/span14/index.html new file mode 100644 index 00000000000..1870150d4e8 --- /dev/null +++ b/exponentiation/span14/index.html @@ -0,0 +1,214 @@ + Electroweak Theory (parser) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Electroweak Theory (parser)

            Establishment theoretical framework as the standard theory of electroweak interactions: Higgs searches, quark mixing, neutrino oscillations.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-26 of main section-4 that is inherited from the spin section-14 by prime spin-34 and span-153 with the partitions as below.

            +
            +
            1. gist02.md
            2. gist03.md
            3. gist04.md
            4. gist05.md
            5. gist06.md
            6. gist07.md
            7. Turbulence

            Gauge invariance is a powerful tool to determine the dynamical forces. Particle content, structure and symmetries of Lagrangian are discussed.

            Standard Theory

            +
            + + Note +
            +
            +

            The Higgs and the electromagnetic field have no effect on each other, at the level of the fundamental forces (“tree level”), while any other combination of the hypercharge and the weak isospin must interact with the Higgs. This causes an apparent separation between the weak force, which interacts with the Higgs, and electromagnetism, which does not. (Wikipedia)

            +
            +

            image

            f22b28c976a4980061b601872e2faac8039dd7d8

            images (2)

            images (4)

            images (3)

            Experiments have verified that the weak and electromagnetic force become identical at very small distances and provide the GUT description of the carrier particles for the forces.

            Interactions

            images (1)

            boson-particle-decay-virtual-particle-w-and-z-bosons-lepton-synchrotron-hadron-particle-physics-annihilation-scattering-thumbnail

            TjQdBoIUDG

            image

            1

            EWT3b-600x400

            Figure_34_06_01

            w-boson-kaon-w-and-z-bosons-weak-interaction-meson-standard-model-feynman-diagram-elementary-particle-pion-boson

            weak-nuclear-force-1

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+boson-1    |    ..   |    ..   |     ..    |     ..    |      5     |    i5
+-----------+---------+---------+-----------+-----------+------------+-----------
+boson-2    |    ..   |    ..   |     ..    |     ..    |      7     |    i7
+-----------+---------+---------+-----------+-----------+------------+-----------
+boson-3    |    ..   |    ..   |     ..    |     ..    |     11     |   i11
+-----------+---------+---------+-----------+-----------+------------+-----------
+boson-4    |    ..   |    ..   |     ..    |     ..    |     13     |   i13
+-----------+---------+---------+-----------+-----------+------------+-----------
+boson-5    |    ..   |    ..   |     ..    |     ..    |     17     |   i17
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    ..   |    ..   |     ..    |     ..    |     53     |   i53
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |  66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    192     |  96+i96 ✔️
+

            Symmetry Breaking

            +
            + + Note +
            +
            +

            The pattern of weak isospin, T3, and weak hypercharge, YW, of the known elementary particles, showing electric charge along the weak mixing angle. The four components of the Higgs field (squares) break the electroweak symmetry and interact with other particles to give them mass, with three components becoming part of the massive W and Z bosons. Allowed decays of the neutral Higgs boson, H, (circled) satisfy electroweak charge conservation. (Wikipedia)

            +
            +

            Electroweak svg (2)

            The Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking becomes manifest,

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            Beta-minus_Decay svg

            Unlike the strong and electromagnetic forces, the intermediary particles of the weak interaction, the W+, the W-, and the Z0 have rather large masses.

            +
            + + Note +
            +
            +

            A key aspect of the theory is the explanation of why three out of four of the intermediary particles of the electroweak force are massive. Illustration of two weak reactions.

            • The left panel shows beta decay while the middle panel shows how electron antineutrinos can be detected by conversion to a positron.
            • The right panel shows how W- emission works according to the quark model, resulting in the conversion of a down quark to an up quark and the resulting transformation of a neutron into a proton.

            The real reason for the apparent weakness of the weak force is the large mass of the intermediary particles. As we have seen, large mass translates into short range for a virtual particle at low momentum transfers. This short range is what causes the weak force to appear weak for momentum transfers much less than the masses of the W and Z particles. (libre texts.org)

            +
            +

            Beta decay 

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤ ✔️ --->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            Problem

            +
            + + Note +
            +
            +

            Consider the following contradiction in the electroweak theory of the Standard Model.

            The electroweak theory of neutrino interaction uses factors like in order to account for a complete parity violation. This factor implies a massless neutrino [1]: “Nature had the choice of an aesthetically satisfying, but a left-right, symmetry violating theory, with a neutrino which travels exactly with the same velocity of light; or alternatively a theory where left-right symmetry is preserved, but the neutrino has a tiny mass – some ten thousand times smaller than the mass of the electron.”The neutrino masslessness is also stated by other authors. A review article on neutrino properties states that “two-components left-handed massless neutrino fields play a crucial role in the determination of the charged current structure of the Standard Model” (see the Abstract of [2]). Similarly, a Quantum Field Theory textbook states: “Thus, massless neutrinos are a prediction of the Standard Model” (see [4], p. 555). Indeed, a massless neutrino is the basis for the two-component Weyl neutrino, which shows parity violation (see e.g. section 2.2 of [2]). The same argument appears on p. 139 of [3].

            On the other hand, a recent review article negates the foregoing ides and states that it is now admitted “that neutrinos can no longer be considered as massless particles” (see [5], p. 1307). This statement is adopted by the Particle Data Group [6], which is the authorized organization for the definition of reliable particle data. The recognition of this fact by the community was demonstrated by the 2015 Nobel Prize, awarded to the persons who have discovered this property [7].It follows that the experimentally confirmed massive neutrino undermines the basis of the Standard Model electroweak theory, since the massless neutrino is a crucial element in this theory.

            Research topic: Can the validity of the electroweak theory be restored?

            Remark: Further contradictions are discussed in [8]. (Research Topics)

            +
            +

            A Problem with the Electroweak Theory

            The True Prime Pairs
+(5,7), (11,13), (17,19)
+
+Tabulate Prime by Power of 10
+loop(10) = π(10)-π(1) = 4-0 = 4
+loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+--------------------------+----+----+----+----+----+----+----+----+----+-----
+ True Prime Pairs → Δ→π  |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+==========================+====+====+====+====+====+====+====+====+====+=====
+ 19 → π(∆10) → π(10)     |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+--------------------------+----+----+----+----+----+----+----+----+----+-----
+ 17 → π(10+∆9) → π(19)   | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+ 13 → π(19+∆10) → π(29)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+--------------------------+----+----+----+----+----+----+----+----+----+-----
+ 11 → π(29+∆12) → π(41)  | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+  7 → π(41+∆18) → π(59)  | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+--------------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+  5 → π(59+∆13) → π(72)  | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+==========================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+  3,2 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+==========================+====+====+====+====+====+====+====+====+====+=====
+         Δ                                                            Δ
+12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-
+

            How do you resolve Maxwell equations as euler-lagrange equation without electromagnetic electromagnetism, lagrangian formalism, field theory, Maxwell equations, variational principle potential.

            +
            + + Note +
            +
            +

            Axial (e-e rES repulsions blue aggregating to black axial outward, vs weak axial inward) to generate the Bose “cylinder surface” proof of statistical mechanics.

            • Axial View of one hemisphere set of one subshell (N,1,many,-1/2) quantum number example below:
            • That gives the path from Planck strength to the Maxwell strengths. Those are not independent, but all based upon h (or h-hat*c version in this case).
            • Yes, I used Euler to get there! The weakness of the Lagrangian is that introduces errors in (a0/re)N scaling ^2 vs ^3 (extra 1/r wrongly called angular momentum by Bohr) that introduces an error correction. Hence, circling back to QED methods of error-correction (loops, re-normalization).

            So, in the end, you do need. But the path can get similar when you move off arbitration x,y,z or X1,X2,X3 frame-of-reference to the quantitized hemispherical coordinates of the quantum numbers understood as (r#,theta#,phi#,z#).

            +
            +

            main-qimg-521a032d4132a419487624564dd201b2-pjlq

            main-qimg-5f05266cfdc63d60f86ad0852076ee00

            1729 = 7 x 13 x 19
+1729 / 7 = 13 x 19 = 247
+
+1729 = 7 x 13 x 19
+       7 + 13 = 20 = d(2)
+                     └──  2 x 19 = 38
+
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+| {1}|  2 |  3 |  4 |  5 | {6}| {7}|  8 |  9 | 10 | 11 | 12 | 13 | 14 |
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+| {3}| {4}|  3 |  4 |  5 |  2 |  3 |  2 |  2 |  1 |  2 |  5 |  1 |  1 |{38}
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285
+|  3 |  8 |  9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|-- 38 ---|              |-- 33 ---|                        |-- {27}--|
+

            1591890434759 (1)

            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤ ✔️ --->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            electron orbit

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    | ✔️
+-----+-----+-----+-----+-----+     -----------------------------------------------
+{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |
+-----+-----+-----+-----+-----+                                               |
+ {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone
+     +-----+-----+-----+-----+                                               |
+ {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |
+     +-----+-----+-----+                                               -----------
+ {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |
+ ----+-----+-----+-----+-----+                                               |
+  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone
+     +-----+-----+-----+-----+                                               |
+  {8}|23,25|25,27|27,29| 18                                                  |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+     |  1     2     3  |   4     5     6 |   7     8      9  |
+     |------ 29' ------|--------------- 139' ----------------|
+     |------ 618¨ -----|--------------- 168¨ ----------------|
+

            IMG_20240118_121014

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span15/gist01.html b/exponentiation/span15/gist01.html new file mode 100644 index 00000000000..5bd0deab4c8 --- /dev/null +++ b/exponentiation/span15/gist01.html @@ -0,0 +1,8 @@ + Mass Gap (Δ) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Mass Gap (Δ)

            In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).

            default

            FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics. Some of the features of FeynCalc are

            • Passarino-Veltman reduction of one-loop amplitudes to standard scalar integrals
            • Tools for frequently occurring tasks like Lorentz index contraction, color factor calculation, Dirac matrix manipulation and traces, etc.
            • Tensor and Dirac algebra manipulations (including traces) in 4 or D dimensions
            • Generation of Feynman rules from a Lagrangian
            • Tools for non-commutative algebra
            • SU(N) algebra
            • Tables of integrals, convolutions and Feynman rules
            • Special convolution, Mellin transform and other integral tables
            • Tools for calculating 2-loop propagator-type diagrams
            • FORM and FORTRAN code generation
            • Translation to and from FORM
            knownResult = 2*SMP["e"]^4*((s^2 + u^2)/t^2) + 
+       4*SMP["e"]^4*(u^2/(s*t)) + 2*SMP["e"]^4*((t^2 + u^2)/s^2); 
+FCCompareResults[ampSquaredMassless[0], knownResult, 
+     Text -> {"\tCheck the final result:", "CORRECT.", "WRONG!"}, 
+     Interrupt -> {Hold[Quit[1]], Automatic}]; 
+Print["\tCPU Time used: ", Round[N[TimeUsed[], 4], 0.001], 
+     " s."]; 
+

            default

            Today most physicists draw Feynman diagrams in a more stylized way, highlighting the topology of propagation lines and vertices. (This diagram and Figure 4 are reproduced from Feynman 1949 (by permission of the American Physical Society.)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span15/gist02.html b/exponentiation/span15/gist02.html new file mode 100644 index 00000000000..a2e0936652a --- /dev/null +++ b/exponentiation/span15/gist02.html @@ -0,0 +1 @@ + Electron scattering · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Electron scattering

            Electron-electron scattering is described by one of the earliest published Feynman diagrams (featured in "Sightings," September–October 2003). One electron (solid line at bottom right) shoots out a forcecarrying particle—a virtual photon (wavy line)—which then smacks into the second electron (solid line at bottom left).

            The first electron recoils backward, while the second electron gets pushed off its original course. The diagram thus sketches a quantum-mechanical view of how particles with the same charge repel each other. As suggested by the term "Space-Time Approach" in the title of the article that accompanied this diagram, Feynman originally drew diagrams in which the dimensions were space and time; here the horizontal axis represents space.

            default

            image

            image

            default

            Untitled

            Untitled

            207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span15/gist02.md b/exponentiation/span15/gist02.md new file mode 100644 index 00000000000..5caa267234e --- /dev/null +++ b/exponentiation/span15/gist02.md @@ -0,0 +1,21 @@ +## Electron scattering + +Electron-electron scattering is described by one of the earliest published Feynman diagrams (featured in “Sightings,” September–October 2003). One electron (solid line at bottom right) shoots out a forcecarrying particle—a virtual photon (wavy line)—which then smacks into the second electron (solid line at bottom left). + +>The first electron recoils backward, while the second electron gets pushed off its original course. The diagram thus sketches a quantum-mechanical view of how particles with the same charge repel each other. As suggested by the term “Space-Time Approach” in the title of the article that accompanied this diagram, Feynman originally drew diagrams in which the dimensions were space and time; here the horizontal axis represents space. + +[![default](https://user-images.githubusercontent.com/8466209/224118806-b00758c2-0885-46c3-b574-566dffedf95f.png)](https://en.wikipedia.org/wiki/Feynman_diagram) + +![image](https://user-images.githubusercontent.com/8466209/240317298-4d42ea8d-ef95-4a33-9a6c-518149dbc02a.png) + +![image](https://user-images.githubusercontent.com/8466209/223643996-1ea5cb89-324e-446c-9c9f-8c94c39909b3.png) + +[![default](https://user-images.githubusercontent.com/8466209/224117996-fd3f0e3b-2ef6-43f5-961d-e90b616cbccc.png)](http://web.mit.edu/dikaiser/www/FdsAmSci.pdf) + +![](https://user-images.githubusercontent.com/8466209/222020262-cffc624a-b92c-4137-b76a-5423df7fc5ad.png) + +![Untitled](https://user-images.githubusercontent.com/8466209/207262180-7a0928a1-0c16-4193-9611-0626ad884ab1.png) + +![Untitled](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png) + +![207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb](https://user-images.githubusercontent.com/8466209/207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db.png) diff --git a/exponentiation/span15/gist03.html b/exponentiation/span15/gist03.html new file mode 100644 index 00000000000..8ff6abdf494 --- /dev/null +++ b/exponentiation/span15/gist03.html @@ -0,0 +1 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            image

            origin

            default

            2022-12-12

            resize

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span15/gist03.md b/exponentiation/span15/gist03.md new file mode 100644 index 00000000000..45446fac47a --- /dev/null +++ b/exponentiation/span15/gist03.md @@ -0,0 +1,13 @@ +![](https://user-images.githubusercontent.com/36441664/73700083-28f2a800-4718-11ea-97b3-2e9a738dc09e.png) + +![](https://user-images.githubusercontent.com/36441664/74550123-6dd1d680-4f83-11ea-8810-3b8f4f50a9c0.png) + +![image](https://user-images.githubusercontent.com/8466209/240316525-ac3dd580-223b-4aa9-ad42-e6bb325fd52d.png) + +![origin](https://user-images.githubusercontent.com/8466209/220002045-d0395b21-1f2a-4dba-992a-24bf50c480d5.png) + +![default](https://user-images.githubusercontent.com/8466209/224314748-3f624809-b5eb-4857-aaf1-d001eda32a4c.png) + +![2022-12-12](https://user-images.githubusercontent.com/8466209/206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2.png) + +![resize](https://user-images.githubusercontent.com/8466209/206960889-211ce865-84ad-4164-b8e5-76e1781f7071.png) diff --git a/exponentiation/span15/gist04.html b/exponentiation/span15/gist04.html new file mode 100644 index 00000000000..247eeb40c10 --- /dev/null +++ b/exponentiation/span15/gist04.html @@ -0,0 +1,21 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            50 + 50 + 18 = 50 + 68 = 118

            image

              -----------------------+----+----+----+----+----+----+----+----+----+----- 
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th    ←-- π(10) 
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th    ←-- π(20)
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th    ←-- π(30)
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+

            resize

            action

            Navier–Stokes

            2022-12-11 (1)

            Untitled

            2022-12-14 (1)

            2022-12-14 (1)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span15/gist04.md b/exponentiation/span15/gist04.md new file mode 100644 index 00000000000..984b67f07a7 --- /dev/null +++ b/exponentiation/span15/gist04.md @@ -0,0 +1,46 @@ +***50 + 50 + 18 = 50 + 68 = 118*** + +![image](https://user-images.githubusercontent.com/8466209/223748602-496016ab-db42-4f5e-a5eb-ec0b884fc4f4.png) + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th ←-- π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th ←-- π(20) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ←-- π(30) + =======================+====+====+====+====+====+====+====+====+====+===== + Δ Δ + 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1 + +``` + +![](https://user-images.githubusercontent.com/36441664/133192153-61cad1c0-1dde-4fed-8718-840d324a7198.jpg) + +![resize](https://user-images.githubusercontent.com/8466209/206956260-f8c3647a-232c-470e-8c0b-e93a6fea14f7.png) + +![](https://user-images.githubusercontent.com/36441664/84902223-b8509480-b0d6-11ea-9763-320b38bae102.png) + +![action](https://user-images.githubusercontent.com/36441664/84525042-2f67e080-ad05-11ea-9f9c-e07492446240.jpg) + +[![Navier–Stokes](https://user-images.githubusercontent.com/8466209/224357044-f3c42fa5-b9ad-471c-85f3-6a4aa01a909e.png)](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f) + +![2022-12-11 (1)](https://user-images.githubusercontent.com/8466209/206918483-5016aa03-2bc1-4dcf-a7dd-29f2c4453787.png) + +![Untitled](https://user-images.githubusercontent.com/8466209/206918218-95c875a7-0080-44e5-8ade-1ff776f9c30d.png) + +![2022-12-14 (1)](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png) + +![2022-12-14 (1)](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png) + +![](https://user-images.githubusercontent.com/36441664/104077748-9f175d00-524d-11eb-9c6d-6c0c4ee1fd93.gif) diff --git a/exponentiation/span15/gist05.html b/exponentiation/span15/gist05.html new file mode 100644 index 00000000000..8fee8c6ae8f --- /dev/null +++ b/exponentiation/span15/gist05.html @@ -0,0 +1,36 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | 1   | 15
+---+-----+-----
+ 2 | 16  | 25
+---+-----+-----
+ 3 | 26  | 50
+---+-----+-----
+ 4 | 51  | 84
+---+-----+-----
+ 5 | 85  | 99
+---+-----+-----
+

            Prime Identity

            99 - 15 - 15 = 69 = 9 + 60 = 9 + (100 - 40)

            default

                                            |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                |  2 | 60 | 40 | 1 | 30 | 30 | 5 |
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            default

            Experiment and computer simulations suggest the existence of a "mass gap" in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known (Clay Institute).

            Yang–Mills and Mass Gap

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span15/gist05.md b/exponentiation/span15/gist05.md new file mode 100644 index 00000000000..77749e99077 --- /dev/null +++ b/exponentiation/span15/gist05.md @@ -0,0 +1,61 @@ + +``` +---+-----+----- + 1 | 1 | 15 +---+-----+----- + 2 | 16 | 25 +---+-----+----- + 3 | 26 | 50 +---+-----+----- + 4 | 51 | 84 +---+-----+----- + 5 | 85 | 99 +---+-----+----- +``` + +[![Prime Identity](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity) + +![](https://user-images.githubusercontent.com/36441664/83051805-aef47f00-a078-11ea-87e5-d8f352e318fe.gif) + +***99 - 15 - 15 = 69 = 9 + 60 = 9 + (100 - 40)*** + +![](https://user-images.githubusercontent.com/36441664/83051968-e2cfa480-a078-11ea-8ff2-316a809a8fad.jpg) + +![default](https://user-images.githubusercontent.com/8466209/224346485-13d27a0b-bfe3-43f0-94da-f75313dc9d77.png) + +```liquid + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ | | + | | | | + ------------ 10 ------------- | | + ↓ ↓ | + +----+----+----+---+----+----+---+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | + | | | + 2+100 ◄- + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- + ``` + +![](https://user-images.githubusercontent.com/36441664/74366957-992db780-4e03-11ea-8f26-cca32bd26003.png) + +![](https://user-images.githubusercontent.com/8466209/223616353-0e1be019-16e8-40d1-bb0c-465a9837d7bb.png) + +[![default](https://user-images.githubusercontent.com/8466209/224466884-5ba87f02-e01d-45ca-a9c3-a1d535e83228.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#poincar%C3%A9-conjecture) + +>Experiment and computer simulations suggest the existence of a "mass gap" in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known _([Clay Institute](https://www.claymath.org/millennium-problems))_. + +[![Yang–Mills and Mass Gap](https://user-images.githubusercontent.com/36441664/85888653-3538e800-b814-11ea-85ba-23a56243e9e0.jpg)](https://www.claymath.org/millennium-problems/yang%E2%80%93mills-and-mass-gap) diff --git a/exponentiation/span15/index.html b/exponentiation/span15/index.html new file mode 100644 index 00000000000..67b404f09c5 --- /dev/null +++ b/exponentiation/span15/index.html @@ -0,0 +1,175 @@ + Chromodynamics (lexer) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Chromodynamics (lexer)

            This section serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks in quantum chromodynamics of colours of the gluon.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-25 of main section-3 that is inherited from the spin section-15 by prime spin-33 and span-154 with the partitions as below.

            +
            +
            1. Electron scattering
            2. gist03.md
            3. gist04.md
            4. gist05.md
            5. Mass Gap (Δ)

            A gauge colour rotation is a spacetime-dependent SU(3) group element. They span the Lie algebra of the SU(3) group in the defining representation.

            Feynman diagram

            +
            + + Note +
            +
            +

            In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).

            +
            +

            default

            quark-quark_scattering

            SmallBookPile

            So basically there is a basic transformation between addition of 3 + 4 = 7 in to their multiplication of 3 x 4 = 12 while the 7 vs 12 will be treated as exponentiation.

            images6-ezgif com-resize

            Matrix Scheme

            Quarks have three colors. Color is to the strong interaction as electric charge is to the electromagnetic interaction.

            quantum-chromodynamics-1-320

            red   anti-red,   red   anti-blue,   red   anti-green,
+blue  anti-red,   blue  anti-blue,   blue  anti-green,
+green anti-red,   green anti-blue,   green anti-green.
+

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            +
            + + Note +
            +
            +

            During the last few years of the 12th century, Fibonacci undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that it popularized the use of the Arabic numerals in Europe, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. (Famous Mathematicians)

            +
            +

            MEC30 Square

            Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30's square.

            +
            + + Note +
            +
            +

            A square system of coupled nonlinear equations can be solved iteratively by Newton’s method. This method uses the Jacobian matrix of the system of equations. (Wikipedia)

            +
            +

            gradien

            +
            + + Note +
            +
            +

            Fermions and bosons—fermions have quantum spin = 1/2.

            • The elementary fermions are leptons and quarks.
            • There are three generations of leptons: electron, muon, and tau, with electric charge −1, and their neutrinos with no electric charge.
            • There are three generations of quarks: (u, d); (c, s); and (t, b).

            The (u, c, t) quarks have electric charge 2/3 while the (d, s, b) quarks have electric charge −1/3. (IntechOpen)

            +
            +

            UF1

            Interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used.

            UF2

            Bosons have quantum spin = 1: photon, quantum of the electromagnetic field; gluon, quantum of the strong field; and W and Z, weak field quanta, which we do not need.

            +
            + + Note +
            +
            +

            An animation of color confinement, a property of the strong interaction. If energy is supplied to the quarks as shown, the gluon tube connecting quarks elongates until it reaches a point where it “snaps” and the energy added to the system results in the formation of a quark–antiquark pair. Thus single quarks are never seen in isolation. (Wikipedia)

            +
            +

            Gluon_tube-color_confinement_animation

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7 👈
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |   66+i30
+

            Interactions

            The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.

            +
            + + Note +
            +
            +

            Unlike the strong force, the residual strong force diminishes with distance, and does so rapidly. The decrease is approximately as a negative exponential power of distance, though there is no simple expression known for this; see Yukawa potential. The rapid decrease with distance of the attractive residual force and the less rapid decrease of the repulsive electromagnetic force acting between protons within a nucleus, causes the instability of larger atomic nuclei, such as all those with atomic numbers larger than 82 (the element lead). (Wikipedia)

            +
            +

            gifman

            +
            + + Note +
            +
            +

            Feynman diagram for the same process as in the animation, with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion “in-flight”, are not shown. The π⁰ pion contains an anti-quark, shown to travel in the opposite direction, as per the Feynman–Stueckelberg interpretation. (Wikipedia)

            +
            +

            residual strong force

            +
            + + Note +
            +
            +

            The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.

            • These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation (so they can generate unitary matrix group elements of SU(3) through exponentiation[1]). These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann’s quark model.[2] Gell-Mann’s generalization further extends to general SU(n). For their connection to the standard basis of Lie algebras, see the Weyl–Cartan basis.
            • Since the eight matrices and the identity are a complete trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that satisfied by the Pauli matrices. Namely, using the dot to sum over the eight matrices and using Greek indices for their row/column indices
            • A particular choice of matrices is called a group representation, because any element of SU(3) can be written in the form using the Einstein notation, where the eight are real numbers and a sum over the index j is implied. Given one representation, an equivalent one may be obtained by an arbitrary unitary similarity transformation, since that leaves the commutator unchanged.
            • The matrices can be realized as a representation of the infinitesimal generators of the special unitary group called SU(3). The Lie algebra of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight linearly independent generators, which can be written as g_{i}, with i taking values from 1 to 8

            These matrices serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks of quantum chromodynamics (cf. colours of the gluon). A gauge colour rotation is a spacetime-dependent SU(3) group element where summation over the eight indices (8) is implied. Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ |  5¨ |  3¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            From the 50 we gonna split the 15 by bilateral 9 sums resulting 2 times 15+9=24 which is 48. So the total of involved objects is 50+48=98.

            +
            + + Note +
            +
            +

            Consider the evidence: scattering experiments strongly suggest a meson to be composed of a quark anti-quark pair and a baryon to be composed of three quarks. The famous 3R experiment also suggests that whatever force binds the quarks together has 3 types of charge (called the 3 colors).

            • Now, into the realm of theory: we are looking for an internal symmetry having a 3-dimensional representation which can give rise to a neutral combination of 3 particles (otherwise no color-neutral baryons).
            • The simplest such statement is that a linear combination of each type of charge (red + green + blue) must be neutral, and following William of Occam we believe that the simplest theory describing all the facts must be the correct one.
            • We now postulate that the particles carrying this force, called gluons, must occur in color anti-color units (i.e. nine of them).
            • BUT, red + blue + green is neutral, which means that the linear combination red anti-red + blue anti-blue + green anti-green must be non-interacting, since otherwise the colorless baryons would be able to emit these gluons and interact with each other via the strong force—contrary to the evidence. So, there can only be EIGHT gluons.

            This is just Occam’s razor again: a hypothetical particle that can’t interact with anything, and therefore can’t be detected, doesn’t exist. The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra. That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional. (Physics FAQ)

            +
            +

            0_kGdCmWqcFG_s8fIq

            Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            960x0

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-👇--+                                             ---
+ 17¨ |  5¨ |  3¨ |  ❓ |  7¨ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            +
            + + Note +
            +
            +

            Young diagrams associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia).

            +
            +

            Hadron_colors svg

            +
            + + Note +
            +
            +

            In mathematics, orthonormality typically implies a norm which has a value of unity (1). Gell-Mann matrices, however, are normalized to a value of 2.

            • Thus, the trace of the pairwise product results in the ortho-normalization condition where delta is the Kronecker delta.
            • This is so the embedded Pauli matrices corresponding to the three embedded subalgebras of SU(2) are conventionally normalized.
            • In this three-dimensional matrix representation, the Cartan subalgebra is the set of linear combinations (with real coefficients) of the two matrices which commute with each other.

            The SU(2) Casimirs of these subalgebras mutually commute. However, any unitary similarity transformation of these subalgebras will yield SU(2) subalgebras. There is an uncountable number of such transformations. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-👇--+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            The-PMNS-Neutrino-Mixing-Matrix-The-non-diagonal-structure-and-the-smallness-of-the-U-e3 images (8) 16-0054-07 hr-web images (12) 1-neutrino-oscillation-l

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist01.html b/exponentiation/span16/gist01.html new file mode 100644 index 00000000000..e94d4178c07 --- /dev/null +++ b/exponentiation/span16/gist01.html @@ -0,0 +1 @@ + gist01.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Screenshot_2023-12-07-16-59-55-579_com google android apps docs

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist01.md b/exponentiation/span16/gist01.md new file mode 100644 index 00000000000..2ee9543d3a6 --- /dev/null +++ b/exponentiation/span16/gist01.md @@ -0,0 +1,2 @@ +[![Screenshot_2023-12-07-16-59-55-579_com google android apps docs](https://gist.github.com/assets/8466209/55c00788-ff82-4a8c-afdb-2d8d05a0ef8d)](https://arxiv.org/pdf/1812.07680.pdf) + diff --git a/exponentiation/span16/gist02.py b/exponentiation/span16/gist02.py new file mode 100644 index 00000000000..b56476cdd19 --- /dev/null +++ b/exponentiation/span16/gist02.py @@ -0,0 +1,127 @@ +from sympy import * +import sympy as sp +import numpy as np + +# define output file +5 file = open(’GR (4 ,4) - Feb27_36864_output .txt ’, ’w’) + +# calculate eigenvalues of B matrices for one adinkra +def calculation_Bmatrix_eigenvalue ( L1 , L2 , L3 , L4 ): +10 # Get R matrix +R1 = np . transpose ( L1 ) +R2 = np . transpose ( L2 ) +R3 = np . transpose ( L3 ) +15 R4 = np . transpose ( L4 ) + +# define m_i, nu_i = mu_i^{−1} +m1 = sp . Symbol (’m’) +20 m2 = sp . Symbol (’m’) +m3 = sp . Symbol (’m’) +m4 = sp . Symbol (’m’) +nu1 = sp . Symbol (’nu ’) +nu2 = sp . Symbol (’nu ’) +25 nu3 = sp . Symbol (’nu ’) +nu4 = sp . Symbol (’nu ’) + +# define lifting matrice +P_L_1 = np . diag (( m1 ,1 ,1 ,1)) +30 P_L_2 = np . diag ((1 , m2 ,1 ,1)) +P_L_3 = np . diag ((1 ,1 , m3 ,1)) +P_L_4 = np . diag ((1 ,1 ,1 , m4 )) +P_R_1 = np . diag (( nu1 ,1 ,1 ,1)) +P_R_2 = np . diag ((1 , nu2 ,1 ,1)) +35 P_R_3 = np . diag ((1 ,1 , nu3 ,1)) +P_R_4 = np . diag ((1 ,1 ,1 , nu4 )) + +# calculate B1, B2 matrix for 1+4+6+4+1 cases 40 and output their eigenvalues +#B1 = L4∗R3∗L2∗R1 +#B2 = R4∗L3∗R2∗L1 + +# lift zero boson +45 B1_lift0 = np . mat ( L4 )* np . mat ( R3 )* np . mat ( L2 )* np . mat ( R1 ) +B2_lift0 = np . mat ( R4 )* np . mat ( L3 )* np . mat ( R2 )* np . mat ( L1 ) +file . wr ite (’lift zero boson : \n’) +B1_lift0_eigen1 , B1_lift0_eigen2 , B1_lift0_eigen3 , +50 B1_lift0_eigen4 , diag1 = calculate_eigenvalues ( B1_lift0 ) +B2_lift0_eigen1 , B2_lift0_eigen2 , B2_lift0_eigen3 , +B2_lift0_eigen4 , diag2 = calculate_eigenvalues ( B2_lift0 ) +file . wr ite (’ eigenvalues for B1:’+ ’ ’ ++ str ( B1_lift0_eigen1 )+ ’ ’ + str ( B1_lift0_eigen2 ) +55 + ’ ’ + str ( B1_lift0_eigen3 )+ ’ ’ ++ str ( B1_lift0_eigen4 ) + "\n") +file . wr ite (’ eigenvalues for B2:’+ ’ ’ ++ str ( B2_lift0_eigen1 )+ ’ ’ + str ( B2_lift0_eigen2 ) ++ ’ ’ + str ( B2_lift0_eigen3 )+ ’ ’ +60 + str ( B2_lift0_eigen4 ) + "\n") + +#lift i−th boson (i = 1,2,3,4) +f o r i in (1 ,2 ,3 ,4): +65 locals ()[ ’B1_lift ’ + str ( i )] = np . mat ( locals () +[’P_L_ ’ + str ( i )])* np . mat ( L4 )* np . mat ( R3 )* +np . mat ( locals ()[ ’P_R_ ’ + str ( i )])* np . mat ( locals +()[ ’P_L_ ’ + str ( i )])* np . mat ( L2 )* np . mat ( R1 ) +* np . mat ( locals ()[ ’P_R_ ’ + str ( i )]) +70 locals ()[ ’B2_lift ’ + str ( i )] = np . mat ( R4 ) +* np . mat ( locals ()[ ’P_R_ ’ + str ( i )]) +* np . mat ( locals ()[ ’P_L_ ’ + str ( i )]) +* np . mat ( L3 )* np . mat ( R2 )* np . mat ( locals () +[’P_R_ ’ + str ( i )])* np . mat ( locals () +75 [’P_L_ ’ + str ( i )])* np . mat ( L1 ) +file . wr ite (’lift %d-th boson : \n’% i ) +locals ()[ ’B1_lift ’ + str ( i ) + ’_eigen1 ’] , +locals ()[ ’B1_lift ’ + str ( i ) + ’_eigen2 ’] , +80 locals ()[ ’B1_lift ’ + str ( i ) + ’_eigen3 ’] , +locals ()[ ’B1_lift ’ + str ( i ) + ’_eigen4 ’] , +d = calculate_eigenvalues ( locals ()[ ’B1_lift ’ + str ( i )]) +locals ()[ ’B2_lift ’ + str ( i ) + ’_eigen1 ’] , +locals ()[ ’B2_lift ’ + str ( i ) + ’_eigen2 ’] , +85 locals ()[ ’B2_lift ’ + str ( i ) + ’_eigen3 ’] , +locals ()[ ’B2_lift ’ + str ( i ) + ’_eigen4 ’] , +d = calculate_eigenvalues ( locals ()[ ’B2_lift ’ + str ( i )]) +file . wr ite (’eigenvalues for B1:’+ ’ ’ ++ str ( locals ()[ ’B1_lift ’ + str ( i ) + +90 + ’_eigen1 ’])+ ’ ’ + str ( locals () +[’B1_lift ’ + str ( i ) + ’_eigen2 ’]) ++ ’ ’ + str ( locals ()[ ’B1_lift ’ ++ str ( i ) + ’_eigen3 ’])+ ’ ’ ++ str ( locals ()[ ’B1_lift ’ + str ( i ) +95 + ’_eigen4 ’]) + "\n") +file . wr ite (’eigenvalues for B2:’+ ’ ’ ++ str ( locals ()[ ’B2_lift ’ + str ( i ) ++ ’_eigen1 ’])+ ’ ’ + str ( locals () +[’B2_lift ’ + str ( i ) + ’_eigen2 ’]) +100 + ’ ’ + str ( locals ()[ ’B2_lift ’ ++ str ( i ) + ’_eigen3 ’])+ ’ ’ ++ str ( locals ()[ ’B2_lift ’ + str ( i ) ++ ’_eigen4 ’]) + "\n") +105 + +#lift (1,2) (1,3) (1,4) (2,3) (2,4) (3,4) bosons +f o r i in (1 ,2 ,3): +f o r j in (2 ,3 ,4): +i f i < j : +110 +locals ()[ ’B1_lift ’ + str ( i )+ str ( j )] = +np . mat ( locals ()[ ’P_L_ ’ + str ( i )]) +* np . mat ( locals ()[ ’P_L_ ’ + str ( j )]) +* np . mat ( L4 )* np . mat ( R3 )* np . mat ( locals () +115 [’P_R_ ’ + str ( i )])* np . mat ( locals () +[’P_R_ ’ + str ( j )])* np . mat ( locals () +[’P_L_ ’ + str ( i )])* np . mat ( locals () +[’P_L_ ’ + str ( j )])* np . mat ( L2 )* np . mat ( R1 ) +* np . mat ( locals ()[ ’P_R_ ’ + str ( i )]) +120 * np . mat ( locals ()[ ’P_R_ ’ + str ( j )]) +locals ()[ ’B2_lift ’ + str ( i )+ str ( j )] = +np . mat ( R4 )* np . mat ( locals ()[ ’P_R_ ’ ++ str ( i )])* np . mat ( locals ()[ ’P_R_ ’ ++ str ( j )])* np . mat ( locals ()[ ’P_L_ ’ +125 + str ( i )])* np . mat ( locals ()[ ’P_L_ ’ ++ str ( j )])* np . mat ( L3 )* np . mat ( R2 ) +* np . mat ( locals ()[ ’P_R_ ’ + str ( i )]) +* np . mat ( locals ()[ ’P_R_ ’ + str ( j )]) +* np . mat ( locals ()[ ’P_L_ ’ + str ( i )]) +130 * np . mat ( locals ()[ ’P_L_ ’ + str ( j )]) +* np . mat ( L1 ) +file . wr ite (’lift (%d, %d) -th bosons : \n’%( i , j )) +135 locals ()[ ’B1_lift ’ + str ( i ) + str ( j ) + ’_eigen1 ’] , \ No newline at end of file diff --git a/exponentiation/span16/gist03.html b/exponentiation/span16/gist03.html new file mode 100644 index 00000000000..99697ad5bf3 --- /dev/null +++ b/exponentiation/span16/gist03.html @@ -0,0 +1 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            84525026-2971ff80-ad05-11ea-934e-1fb3cab8cc01

            Figure_34_06_01

            Leading-Strand-And-Lagging-Strand-Of-DNA-1024x954

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist03.md b/exponentiation/span16/gist03.md new file mode 100644 index 00000000000..7e0e2b72d98 --- /dev/null +++ b/exponentiation/span16/gist03.md @@ -0,0 +1,7 @@ +[![84525026-2971ff80-ad05-11ea-934e-1fb3cab8cc01](https://user-images.githubusercontent.com/8466209/207610593-51e33d42-104e-47b3-ac0d-5b48ce5971dc.gif)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-target-md) + +![Figure_34_06_01](https://user-images.githubusercontent.com/8466209/207485796-0a0b19c6-455d-4304-bd37-cd7b6640af38.jpg) + +[![Leading-Strand-And-Lagging-Strand-Of-DNA-1024x954](https://user-images.githubusercontent.com/8466209/207357956-3eeeacc2-0b5f-4eeb-b2b5-71f8d22adf59.png)](https://onlyzoology.com/difference-between-leading-strand-and-lagging-strand-of-dna/) + +[![](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md) diff --git a/exponentiation/span16/gist04.html b/exponentiation/span16/gist04.html new file mode 100644 index 00000000000..0aaeb2d1f00 --- /dev/null +++ b/exponentiation/span16/gist04.html @@ -0,0 +1 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Difference Between Leading Strand And Lagging Strand of DNA

            Difference-Between-Lagging-and-Leading-Strand_Figure-1-768x373

            Leading-Strand-And-Lagging-Strand-Of-DNA-1024x954

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist04.md b/exponentiation/span16/gist04.md new file mode 100644 index 00000000000..096795d6633 --- /dev/null +++ b/exponentiation/span16/gist04.md @@ -0,0 +1,9 @@ +[![]()]() + +## Difference Between Leading Strand And Lagging Strand of DNA + +![Difference-Between-Lagging-and-Leading-Strand_Figure-1-768x373](https://user-images.githubusercontent.com/8466209/207424623-d099ba07-91e1-4845-adaf-64232488a2a3.png) + +[![Leading-Strand-And-Lagging-Strand-Of-DNA-1024x954](https://user-images.githubusercontent.com/8466209/207360880-6a772b29-f752-4972-b4ad-27de3193c62d.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md) + +[![](https://user-images.githubusercontent.com/8466209/207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md) diff --git a/exponentiation/span16/gist05.html b/exponentiation/span16/gist05.html new file mode 100644 index 00000000000..22a8ac0218e --- /dev/null +++ b/exponentiation/span16/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum
            • The direction of growth of the leading strand is 5′→3′. The direction of growth of the lagging strand is 3′→5′.
            • The formation of leading strand begins immediately at the beginning of replication. The formation of lagging strand begins a bit later than that of the leading strand.
            • During the synthesis of leading strand, only one site of initiation is exposed in the template strand. During the synthesis of lagging strand, multiple sites of initiation are exposed in the template strand.

            207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist05.md b/exponentiation/span16/gist05.md new file mode 100644 index 00000000000..528df489a9a --- /dev/null +++ b/exponentiation/span16/gist05.md @@ -0,0 +1,10 @@ +* The direction of growth of the leading strand is 5′→3′. The direction of growth of the lagging strand is **3′→5′**. +* The formation of leading strand begins immediately at the beginning of replication. The formation of lagging strand **begins a bit later** than that of the leading strand. +* During the synthesis of leading strand, only one site of initiation is exposed in the template strand. During the synthesis of lagging strand, **multiple sites** of initiation are exposed in the template strand. + + +[![](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-locate-md) + +![](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png) + +![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612131-b325f43c-6957-443b-b763-e357b2466f59.png) \ No newline at end of file diff --git a/exponentiation/span16/gist06.html b/exponentiation/span16/gist06.html new file mode 100644 index 00000000000..689ca791fee --- /dev/null +++ b/exponentiation/span16/gist06.html @@ -0,0 +1,40 @@ + Deploying containers · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Deploying containers

            This Chromium Project is being considered since it has an Optimized OS to build containers which could be imported as image in a Compute Engine. With this scheme then the engine is able to be assigned as a runner to build inside container.

            The main reason of this requirement is because we will need to build a system that contained as three (3) layers of primes level where the system will always be forced in to the 15+25=40th prime each time we made an access to the next layer.

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            Althouht the optimized os is ready with built in images however we will need to place a custom modification since the objective of this OS Project is mainly about optimizing the containers while our project is mainly about the primes behaviour.

            l8myt

            By this modification we are going to build the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66.

            Consider that the 1st cell is standing as (Δ1) which is eqivalent to 19. Then as per The Δ(19 vs 18) Scenario the 7 cells would behave as (Δ1 to Δ7) that equivalent with 19 to 25. So by the 3rd and 4th axis it will get 102+66 = 168 primes of π(1000).

                                            |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                |  2 | 60 | 40 | 1 | 30 | 30 | 5 |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+  -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            By the 1's and 17's cells we will divide in the 0's cell in to four (4) containers shown above. You should find that the 40 primes is acting as the base rule of the current primes level also the interface between the grammar of each containers as well. Two (2) primes out of the 102 will hold the 1's and 17's cells so by the rest of 100 they will form (2,60,40).

            By the scheme as we have explained above you would agree that this mapping could only be managed using a customizable compute service so the engine is easily to be created, terminated, restarted and even deleted programmatically.

            See that all of the steps need to be done progressively. Once we buit a container of (2,60,40) with the three (3) inside containers then the 33's will be able to generate four (4) runners that represent (2,3,5,7) from the π(10). Let's discuss them one by one.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist06.md b/exponentiation/span16/gist06.md new file mode 100644 index 00000000000..aa71a5ef296 --- /dev/null +++ b/exponentiation/span16/gist06.md @@ -0,0 +1,72 @@ +## Deploying containers + +This [Chromium Project](https://www.chromium.org/chromium-projects/) is being considered since it has an [Optimized OS](https://cloud.google.com/container-optimized-os/docs/how-to/building-from-open-source) to build containers which could be imported as image in a [_Compute Engine_](https://cloud.google.com/compute/docs/images/import-existing-image#import_image). With this scheme then the engine is able to be assigned as a runner to build inside container. + +[![](https://user-images.githubusercontent.com/8466209/202855623-cd58afdf-e05b-4517-b3dd-b01e70011814.gif)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-13_centralize-md) + +The main reason of this requirement is because we will need to build a system that contained as [three (3) layers](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857) of primes level where the system will always be forced in to the ***[15+25=40th prime](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#mapping-scheme)*** each time we made an access to the next layer. + +``` +1st layer: +It has a total of 1000 numbers +Total primes = π(1000) = 168 primes + +2nd layer: +It will start by π(168)+1 as the 40th prime +It has 100x100 numbers or π(π(10000)) = 201 primes +Total cum primes = 168 + (201-40) = 168+161 = 329 primes + +3rd layer: +Behave the same as 2nd layer which has a total of 329 primes +The primes will start by π(π(π(1000th prime)))+1 as the 40th prime +This 1000 primes will become 1000 numbers by 1st layer of the next level +Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 +``` + +Althouht the optimized os is ready with [built in images](https://cloud.google.com/container-optimized-os/docs/release-notes) however we will need to place a custom modification since the objective of this OS Project is mainly about optimizing the containers while our project is mainly about the primes behaviour. + +[![l8myt](https://user-images.githubusercontent.com/8466209/210317563-306111cb-5c66-4996-ad7b-47d84077175e.jpg)](https://stackoverflow.com/a/49467154/4058484) + +By this modification we are going to build the three (3) layers of 19 cells with a ***cumulative sum of 1, 7 and 19*** in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66. + +[![](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-1_prime-md) + +Consider that the 1st cell is standing as (Δ1) which is eqivalent to 19. Then as per _The Δ(19 vs 18) Scenario_ the 7 cells would behave as (Δ1 to Δ7) that equivalent with 19 to 25. So by the 3rd and 4th axis it will get 102+66 = 168 primes of π(1000). + +``` + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ | | + | | | | + ------------ 10 ------------- | | + ↓ ↓ | + +----+----+----+---+----+----+---+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | + +----+----+----+---+----+----+---+ + | | | + 2+100 ◄- + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- +``` + +By the 1's and 17's cells we will divide in the 0's cell in to four (4) containers shown above. You should find that the 40 primes is acting as the base rule of the current primes level also the interface between ***the grammar*** of each containers as well. Two (2) primes out of the 102 will hold the 1's and 17's cells so by the rest of 100 they will form (2,60,40). + +[![](https://user-images.githubusercontent.com/8466209/199135210-06912985-b2b0-4495-94cb-9431935dc912.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-runner-md) + +By the scheme as we have explained above you would agree that this mapping could only be managed using a ***customizable compute service*** so the engine is easily to be created, terminated, restarted and even deleted programmatically. + +[![](https://user-images.githubusercontent.com/8466209/207363317-e8816b5d-c7b4-43e3-a120-0509641de4eb.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-recycle-md) + +See that all of the steps need to be done progressively. Once we [buit a container](https://github.com/chromium/chromium/blob/main/docs/linux/build_instructions.md#docker-requirements) of (2,60,40) with the three (3) inside containers then the 33's will be able to generate four (4) runners that represent ***(2,3,5,7) from the π(10)***. Let's discuss them one by one. \ No newline at end of file diff --git a/exponentiation/span16/gist07.html b/exponentiation/span16/gist07.html new file mode 100644 index 00000000000..cf7a24933bb --- /dev/null +++ b/exponentiation/span16/gist07.html @@ -0,0 +1,40 @@ + Antiparallels · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Antiparallels

            Notably, the prime five (5) is equal to the sum of the only consecutive primes, 2 + 3. However by the nature it is not going to be as simple as that. Instead they are performing to do a pairing between the Scheme-34 with the Scheme-21.

            By the structure of DNA it is clearly seen that this prime is compromizing the bilateral power of the prime two (2) and grouping power of the prime three (3). Both of these powers turn to the power of the number six (6). This number is the sum and multiplication of three (3) positive numbers in a row 1 + 2 + 3 = 1 x 2 x 3 = 6.

            So this Scheme-21 is actually coming from 1+2+3+4+5+6 = 21. By observing from many literatures we came to a conclution that it has something to do with a golden ratio (φ) originated by π(π(π(1000th prime)))+1=40 that leads the 168 to 618 primes. So it would be antiparalel directions between π(1000) = 168 to φ = 1000/618 with φ = 1000/618 to π(1000) = 168 (vise versa).

            By the prime hexagon it will even clearer. Both of the power goes antiparalel in their directions. As the result there would be the period when their instance was created, the period when it was terminated and the period that it shall be raised up.

            Such of this movement goes from 17's and 11's then precissely landed on 5's cell within the hexagon. Each time an instance is raised up then the previous tensor is collected so it would finaly form a configuration of 3,2 → 18+13+12 → 43 as shown below.

                                         --------------------------------------------------------------
+                            |                                                              | 
+  =======================+====+====+====+====+====+====+====+====+====+=====               |
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root      |
+  -----------------------+----+----+----+----+----+----+----+----+----+-----               |
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin      |
+  -----------------------+----+----+----+----+----+----+----+----+----+-----               |
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th                |
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin      |
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th                |
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin      |
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th                |
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin      |
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ---------------
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+

            By this 43 the scheme goes to the limit of π(10) = (2,3.5,7) resulting 2 times prime levels from 10th primes of 29 to 29th prime of 109. See that they are touching the power of prime two (2) by carrying nine (9) cells of prime powers.

            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square and map their collective bilateral 9 sum symmetry (Primesdemystified)

            bilateral 9 sums

            Since the prime two (2) has a bigger power of all primes combined then it will force back those power precisely as shown on the tabulation above. So from the movement of the form of (7,5,3,2) it goes to (2,3,5,7) as a new replication of π(10).

            -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+    2 -------------------+----+----+----+----+----+----+----+----+----+-----  ←-- bilateral 9 sums
+    3 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+

            This replication is the one that forming 5' vs 3' with 3' vs 5' ends of DNA. One thing we should notify here is that this bilateral movements is originated by the 17's of 100 objects. So the period will cover antiparales of 2 times 100+43 or 286 objects.

            212474451-c7e68350-8c80-4d67-9fb7-63fba08eb269

            In order to facilitate this behaviour the flows within the three (3) inside containers shall have an entrance to the period when the instance was created, the period when it was terminated and the period that it shall be raised up to exchange its existence.

            The end of this formation is at fifty (50) which at the next level will carry out the regeneration process to 102 via the number one hundred (100) for its correlation with the number two (2).

            With the help of a computer, we appear these two objects only those related to the intended case. Where we can do mapping or iteration with the data we prepare so that results are obtained more quickly and accurately.

            For the series of consecutive powers of pi, it has been found that there is no two fall within the same six-cell hexagon. As a matter of a fact it was computed this for pi^32, which has less than a 1/400 chance of occurring randomly.

            default

            This is a kind of connections to display the above complex relation between the individual objects and their tensors. Same case as we have expressed before we will bring further every details particulary on this scope in to another website separately.

            By using this method of interpolation between the object and their tensors we finaly found that the Scheme-35 is actualy come from anti paralel behaviour of Scheme-53 which is containing three (3) prime pairs.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist07.md b/exponentiation/span16/gist07.md new file mode 100644 index 00000000000..4b49b87bc71 --- /dev/null +++ b/exponentiation/span16/gist07.md @@ -0,0 +1,98 @@ +## Antiparallels + +Notably, the prime five (5) is equal to the sum of the only consecutive primes, 2 + 3. However by the nature it is not going to be as simple as that. Instead they are performing to do a pairing between the _[Scheme-34](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)_ with the _[Scheme-21](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-tabulate-md)_. + +![](https://user-images.githubusercontent.com/36441664/85040788-5e71cc80-b1b3-11ea-962f-cf26ee3419e2.jpg) + +By the structure of DNA it is clearly seen that this prime is compromizing the bilateral power of the prime two (2) and grouping power of the prime three (3). Both of these powers turn to the power of the number six (6). This number is the sum and multiplication of three (3) positive numbers in a row ***1 + 2 + 3 = 1 x 2 x 3 = 6***. + +[![](https://user-images.githubusercontent.com/36441664/101231659-56fd9b80-36df-11eb-87a2-6b4b211a6334.gif)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md) + +So this Scheme-21 is actually coming from ***1+2+3+4+5+6 = 21***. By observing from many literatures we came to a conclution that it has something to do with a ***[golden ratio (φ)](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f#file-write-all-md)*** originated by π(π(π(1000th prime)))+1=40 that leads the _[168](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)_ to _[618 primes](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-container-md)_. So it would be antiparalel directions between _π(1000) = 168 to φ = 1000/618_ with _φ = 1000/618 to π(1000) = 168_ (vise versa). + +![](https://user-images.githubusercontent.com/36441664/84902333-e6ce6f80-b0d6-11ea-8289-aac5e1961cd6.gif) + +By the prime hexagon it will even clearer. Both of the power goes antiparalel in their directions. As the result there would be the period when their instance was created, the period when it was terminated and the period that it shall be raised up. + +[![](https://user-images.githubusercontent.com/8466209/200012043-620aa039-3b72-4165-83ad-e35d3d972a1b.png)]() + +Such of this movement goes from 17's and 11's then ***precissely landed on 5's cell*** within the hexagon. Each time an instance is raised up then the previous tensor is collected so it would finaly form a configuration of ***3,2 → 18+13+12 → 43*** as shown below. + +``` + -------------------------------------------------------------- + | | + =======================+====+====+====+====+====+====+====+====+====+===== | + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th | + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin | + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th | + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin | + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th | + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin | + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th --------------- + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== +``` + +By this 43 the scheme goes to the limit of π(10) = (2,3.5,7) resulting 2 times prime levels from 10th primes of 29 to 29th prime of 109. See that they are touching the power of prime two (2) by carrying ***nine (9) cells*** of prime powers. + +> In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square and map their collective ***bilateral 9 sum symmetry*** _([Primesdemystified](https://www.primesdemystified.com/#primingthesquares))_ + +[![bilateral 9 sums](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-bilateral-md) + +Since the prime two (2) has a bigger power of all primes combined then it will force back those power precisely as shown on the tabulation above. So from the movement of the form of (7,5,3,2) it goes to (2,3,5,7) as a ***new replication*** of π(10). + +``` +-----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10 + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + 2 -------------------+----+----+----+----+----+----+----+----+----+----- ←-- bilateral 9 sums + 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th +``` + +This replication is the one that forming _5' vs 3'_ with _3' vs 5'_ ends of DNA. One thing we should notify here is that this bilateral movements is originated by the 17's of 100 objects. So the period will cover antiparales of 2 times 100+43 or _[286 objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e)_. + +![212474451-c7e68350-8c80-4d67-9fb7-63fba08eb269](https://user-images.githubusercontent.com/8466209/212552402-bacfb0be-7336-4d0d-ad32-36f9cb0bfefc.jpg) + +In order to facilitate this behaviour the flows within the three (3) inside containers shall have an entrance to the period when the instance was ***created***, the period when it was ***terminated*** and the period that it shall be ***raised up*** to exchange its existence. + +[![](https://user-images.githubusercontent.com/8466209/203874503-4276074d-3270-437f-a675-858486afd126.png)]() + +The end of this formation is at fifty (50) which at the next level will carry out the regeneration process to 102 via the number one hundred (100) for its correlation with the number two (2). + +[![](https://user-images.githubusercontent.com/8466209/199508386-69859804-9ccb-4f5d-8314-8ca0be0af235.png)]() + +With the help of a computer, we appear these two objects only those related to the intended case. Where we can do mapping or iteration with the data we prepare so that results are obtained more quickly and accurately. + +[![](https://user-images.githubusercontent.com/8466209/199502657-1ba96c92-29f9-41ec-90a9-cbc5adec9464.png)]() + +For the series of consecutive powers of pi, it has been found that there is ***no two fall within the same six-cell hexagon***. As a matter of a fact it was computed this for pi^32, which has less than a 1/400 chance of occurring randomly. + +[![default](https://user-images.githubusercontent.com/8466209/203874936-9065fbff-25f6-4357-a37b-6945502161d5.png)](https://github.com/kaustubhcs/prime-hexagon) + +This is a kind of connections to display the above complex relation between the individual objects and their tensors. Same case as we have expressed before we will bring further every details particulary on this scope in to another website separately. + +[![](https://user-images.githubusercontent.com/8466209/199359982-229c7e19-9491-44fe-bc67-9c10b14609e9.png)]() + +By using this method of interpolation between the object and their tensors we finaly found that the Scheme-35 is actualy come from anti paralel behaviour of [Scheme-53](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md) which is containing _[three (3) prime pairs](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-tabulate-md)_. diff --git a/exponentiation/span16/gist08.html b/exponentiation/span16/gist08.html new file mode 100644 index 00000000000..32032eb8548 --- /dev/null +++ b/exponentiation/span16/gist08.html @@ -0,0 +1 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db

            207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db

            • Only a single RNA primer is required for the whole lagging strand to synthesize. The starting of each Okazaki fragment requires a new RNA primer. 207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist08.md b/exponentiation/span16/gist08.md new file mode 100644 index 00000000000..8943e706381 --- /dev/null +++ b/exponentiation/span16/gist08.md @@ -0,0 +1,6 @@ +![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612376-9c1b77f9-f9be-4b8e-be08-d4784b9c65cf.png) + +![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612583-27347639-6314-46b6-9b36-e8898e45c547.png) + +* Only a single RNA primer is required for the whole lagging strand to synthesize. The starting of each Okazaki fragment **requires a new RNA primer**. +![207490064-f96db6e0-33fe-4c71-9fd9-9f13e71410db](https://user-images.githubusercontent.com/8466209/207612733-ce46354c-7386-4bc4-84b2-e89527da7cef.png) \ No newline at end of file diff --git a/exponentiation/span16/gist09.html b/exponentiation/span16/gist09.html new file mode 100644 index 00000000000..2d88488f33d --- /dev/null +++ b/exponentiation/span16/gist09.html @@ -0,0 +1,65 @@ + gist09.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | 1   |{21}
+---+-----+-----
+ 2 |{22} |{34}
+---+-----+-----
+ 3 |{35} |{89}
+---+-----+-----
+ 4 | 90  |{119}
+---+-----+-----
+ 5 | 120 | 124
+---+-----+-----
+ 6 |{125}|{128}
+---+-----+-----
+
                       26
+           to
+           29
+            |
+            |
+            |
+            V            
+     |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - |100 |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - |101 |  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   T
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |   H
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   E
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   P
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |   O
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   W
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |   E
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   R
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   O
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |   F
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | ∑=168
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |   V
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   S
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2

            dualidad-onda-particula

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist09.md b/exponentiation/span16/gist09.md new file mode 100644 index 00000000000..45318c0d29f --- /dev/null +++ b/exponentiation/span16/gist09.md @@ -0,0 +1,74 @@ +``` +---+-----+----- + 1 | 1 |{21} +---+-----+----- + 2 |{22} |{34} +---+-----+----- + 3 |{35} |{89} +---+-----+----- + 4 | 90 |{119} +---+-----+----- + 5 | 120 | 124 +---+-----+----- + 6 |{125}|{128} +---+-----+----- +``` + +```liquid + 26 + to + 29 + | + | + | + V + | 1st (Form) | 2nd (Route) | 3rd (Channel) | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T + Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E + Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P + Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W + Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R + Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O + Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168 +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S + | Δ Δ | Φ12 | Δ Δ | + 113 150 ≜114-25 557 619 = 1+618 +``` +[![](https://user-images.githubusercontent.com/8466209/206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-locate-md) + +![206955057-ac0d9318-08e6-4e9d-9a37-0c752ceb9fe2](https://user-images.githubusercontent.com/8466209/207627118-3de81d9e-7f43-4a36-a4f8-fab402c487d1.png) + +![dualidad-onda-particula](https://user-images.githubusercontent.com/8466209/207629416-d32dd8e3-0fb5-46b1-b8cd-926060145c04.png) diff --git a/exponentiation/span16/gist10.html b/exponentiation/span16/gist10.html new file mode 100644 index 00000000000..b55b3a272d1 --- /dev/null +++ b/exponentiation/span16/gist10.html @@ -0,0 +1,125 @@ + gist10.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum
            +
            + + Tip +
            +
            +

            This section is referring to wiki page- of zone section-0 that is inherited from the zone section- by prime spin- and span- with the partitions as below.

            +
            +
            1. gist05.md
            2. gist04.md
            3. gist03.md
            4. gist01.md
            5. Deploying containers
            6. Antiparallels
            7. gist08.md
            8. gist09.md
            9. gist10.md
            10. gist12.md

            The process is carried out based on a combination of the numbers 2 and 3 by multiplication and the 9th and 10th powers of the 19th identity as a boundary number that serves distribution of the 11th by 2 to 20 and 40 to 50 in bases 10 to 100 and 1000.

            19² can be written as the sum of three (3) consecutive squared triangular numbers 6²+10²+ 15²

            --+-----+-----
+ 1 | 1   |{15}
+---+-----+-----
+ 2 |{16} |{40}
+---+-----+-----
+ 3 | 41  |{50}
+---+-----+-----
+ 4 | 51  | 63
+---+-----+-----
+ 5 | 64  | 83
+---+-----+-----
+ 6 | 84  | 98
+---+-----+-----
+

            By our mapping the prime seven (7) is forming the prime pair of (5,7) with the prime five (5) which is the only number that is part of more than one pair of twin primes, (3, 5) and (5, 7). This (5, 7) is one of the pair of that we called True Prime Pairs.

            out (product) = in (joint) x out (last) = (1 + 5) x 19 = 6 x 19 = 114

            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            By a DNA their tensor can be seen on hydrogen bonding where the form 96 of A,T would pair the form 69 of C,G.

            96 + 19 = 115 = 114 + Δ1

            molecular_DNA

            This pairs is formed by the movement from the 17's and 11's and then precissely landed on 5's explained before. So they have somethig to do with the anti paralel behaviour of Scheme-53 and Scheme-35 on a chromosom.

                            largest part=21 → 11+13+12=36 →| MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   |
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----------
+---+-----+-----+-----+-----+                   |           |
+ 2 | 18  | 21  | 39  | 60  |-------------------|-----      |
+---+-----+-----+-----+-----+                   |     |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |     |
+---+-----+-----+-----+-----+             |     |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |     |
+---+-----+-----+-----+-----+       |     |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  |     | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |     |
+---+-----+-----+-----+-----+             |     |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |     |
+---+-----+-----+-----+-----+                   |     |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------|-----      |
+---+-----+-----+-----+-----+                   |           |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----------
+===+=====+=====+=====+=====+                   |
+45 | 277 |                      ← 11+13+12=36 ←| MEC30
+---+-----+                                     |
+
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            By toucning the bilateral way of 96+2=98 we came to following tabulation. This is further compromizing between the prime five (5) and the prime seven (7) represent the segregation inside the first pair (5, 7). So it shows the tensor of twelve (12) numbers.

            
+  #8 |----------- 5® --------|------------ 7® --------------|
+     |  1  |---------------- 77 = 4² + 5² + 6² -------------|
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ user|  7  |  -  | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main|  -  |  9  | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+               Δ | Δ             |                       Δ  | Δ
+              Φ17|Φ29            |                     96-99| 100 - 123 ({24})
+                 |--- A,T,G,C ---|                          | └── 100 - 103 (4x) » 100
+                 Δ    2x2 = 4x   |-------  2x3 = 6x  -------| └── 104 - 109 (6x) »  30
+                {98}                                        | └── 110 - 123 (14x)»  70
+

            Compositions

            So by defining the pattern of each individual numbers with the basic rule that the 19 is regenerated out of 18 while the 7 is the recollection out of 6 and comparing with the Gann Chart finaly we found how they look like.

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Description
+===========
+Getting result within a huge package (5 to 19) by spreading (11)
+the untouched objects (7) and tunneling (13) them in to a definite scheme (17).
+
+Compositions
+============
+
+layer| 1st  |         2nd        |                   3rd                   | ∑(2,3)
+-----+------+------+------+------+------+------+------+------+------+------+------      ---
+     |      |   7  | {19} |  38  |  62  |  64  |  67  |  93  |  95  |  96  |  139        |
+  i  +  1   +------+------+------+------+------+------+------+------+------+------       5¨
+     |      |   8  |  20  |  39  |  63  |  65  |  68  |  94  |  97  |  98  |             |
+-----+------+------+------+------+------+------+------+------+------+------+------      ---
+     |      |   9  |  21  |  40  | {43} |  66  |  69  |  99  | 100  | 101  |  286        |
+     +  2   +------+------+------+------+------+------+------+------+------+------       7¨
+     |      |  10  |  22  |  41  |  44  |  45  |  70  | 102  | 103  | 104  |             |
+  q  +------+------+------+------+------+------+------+------+------+------+------      ---
+     |      |  11  |  23  |  42  |  46  |  47  | {71} | 105  | 106  | 107  |  114        |
+     +  3   +------+------+------+------+------+------+------+------+------+------      11¨
+     |      |  12  |  24  |  25  |  48  |  49  |  72  | 108  | 109  | 110  |             |
+-----+------+------+------+------+------+------+------+------+------+------+------      ---
+     |      |  13  |  26  |  27  |  50  |  51  |  73  |  74  | 111  | 112  |  247        |
+     +  4   +------+------+------+------+------+------+------+------+------+------      13¨
+     |      |  14  |  28  |  29  |  52  |  53  |  75  |  76  | 113  |{114} |             |
+  r  +------+------+------+------+------+------+------+------+------+------+------      ---
+     |      |  15  |  30  |  31  |  54  |  55  |  77  |  78  |  79  |  80  |  157        |
+     +  5   +------+------+------+------+------+------+------+------+------+------     {17¨}
+     |      |  16  |  32  |  33  |  56  |  57  |  81  |  82  |  83  |  84  |             |
+-----+------+------+------+------+------+------+------+------+------+------+------      ---
+     |      |  17  |  34  |  35  |  58  |  59  |  85  |  86  |  87  |  88  |  786        |
+  o  +  6   +------+------+------+------+------+------+------+------+------+------      19¨
+     |      |  18  |  36  |  37  |  60  |  61  |  89  |  90  |  91  | {92} |             |
+-----+------+------+------+------+------+------+------+------+------+------+------      ---
+  ∑  | {21} | 150  |      |      |      |      |      |      |      |      | 1729
+
+     |------------------------------------------------------------- 16¨ ---|
+     |----------------------------------------------- 15¨ ---|
+     |--------------------------------- 14¨ ---|
+     |------------------- 13¨ ---|
+     |--- {12¨} ---|
+

            See that by top of pattern it goes bilateral from 1, 7, 19, 38 exactly shown on the Scheme-33, while the rest are grouped in to the form 69 vs 96 of A,T,C,G. Thus each numbers are in the pattern of Double Helix.

            image

            This pattern is raised up per six (6) cycles on the 19, 43 and 71. Since the members are limited to the sum of 43+71=114 so here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme.

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            Polarity

            Meanwhile the six (6) cycles would behave as P(7)=142857 which is originated by the 7 out of 6. This pattern is also shown on the tabulation above by the horizontal flow of 14,28,29,.. which are then finaly terminated by the bilateral way to 57x2=114.

            ### Bilateral way

            This behaviour can be seen on the function chart of Riemann Zeta Zeros as shown below where the 19 came out of 18 of 0's cell.

            The P(7)=142857 will bring the system to forms 7x13x19 = 1729 objects of True Prime Pairs. As the impact there will be a gap raised to form 20 out of 18 of 0's cell and facilitate the new candidate to get an access to the next primes level.

            The rest of primes goes to the 33's of 15th axis that holding 102 primes of (2,60,40). By the bilateral way the form will be splitted to (1,30,20). Since the base frame shall be 40 so it will be forced to form (1,30,40) of prime 71.

            zeta-vs-zero

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            default

            As you may see the bilateral way between this 19's tensor with the (Δ1) is not easy to be understood nor explained. However at this point, you may already get an idea that as a part of the nature, the DNA System and the Prime Structure applies the same.

            Quantum Theory tells us that there are instantaneous connections between two entangled quantum objects, like electrons. In fact, there is no separation. At the quantum level, theoretically, everything is linked. This is known as the candidate for The Theory of Everything. Thus the Sunlight, Saturn, Moon, Saturn's rings, Moon's orbit, ocean, me and you… are all one.

            Broadly speaking it still remain of how this project can be developed so that it can be applied to the goals we want. Therefore we decided to bring further every details in to a group of websites. That is the background why the root scheme of ‘eq19' is exist.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist10.md b/exponentiation/span16/gist10.md new file mode 100644 index 00000000000..93d057699e4 --- /dev/null +++ b/exponentiation/span16/gist10.md @@ -0,0 +1,194 @@ + +{% include list.liquid all=true %} + +The process is carried out based on a combination of the numbers 2 and 3 by multiplication and the 9th and 10th powers of the 19th identity as a boundary number that [serves distribution of the 11th](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#eulers-identity) by 2 to 20 and 40 to 50 in bases 10 to 100 and 1000. + +>19² can be written as the sum of three (3) consecutive squared triangular numbers 6²+10²+ 15² + +```scss +--+-----+----- + 1 | 1 |{15} +---+-----+----- + 2 |{16} |{40} +---+-----+----- + 3 | 41 |{50} +---+-----+----- + 4 | 51 | 63 +---+-----+----- + 5 | 64 | 83 +---+-----+----- + 6 | 84 | 98 +---+-----+----- +``` + +By our mapping the prime seven (7) is forming the prime pair of (5,7) with the prime five (5) which is the only number that is part of more than one pair of twin primes, (3, 5) and (5, 7). This (5, 7) is one of the pair of that we called _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. + +***out (product) = in (joint) x out (last) = (1 + 5) x 19 = 6 x 19 = 114*** + +```scss +$True Prime Pairs: + (5,7), (11,13), (17,19) + + layer| i | f + -----+-----+--------- + | 1 | 5 + 1 +-----+ + | 2 | 7 + -----+-----+--- } 36 » 6® + | 3 | 11 + 2 +-----+ + | 4 | 13 + -----+-----+--------- + | 5 | 17 + 3 +-----+ } 36 » 6® + | 6 | 19 + -----+-----+--------- + ``` + +By a DNA their tensor can be seen on hydrogen bonding where the form ***96 of A,T*** would pair the form ***69 of C,G***. + +***96 + 19 = 115 = 114 + Δ1*** + +![molecular_DNA](https://user-images.githubusercontent.com/8466209/212474832-bc616a25-06ad-41e7-a27d-0bec82b1f2a4.png) + +This pairs is formed by the movement from the 17's and 11's and then precissely [landed on 5's](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-runner-md) explained before. So they have somethig to do with the anti paralel behaviour of Scheme-53 and Scheme-35 on a chromosom. + +```scss + largest part=21 → 11+13+12=36 →| MEC30 + ↓ | +---+-----+-----+-----+-----+ | + 1 | 19 | 1 | 20 | 21 |-------------------|----------- +---+-----+-----+-----+-----+ | | + 2 | 18 | 21 | 39 | 60 |-------------------|----- | +---+-----+-----+-----+-----+ | | | + 3 |{63} | 40 | 103 | 143 |------------- | | | +---+-----+-----+-----+-----+ | | | | + 4 | 37 | 104 | 141 | 245 |------- | | | | +---+-----+-----+-----+-----+ | | | | | + 5 | 10* | 142 | 152 | 294 |- 11** | 13 | 12 | | 12 | 18 +---+-----+-----+-----+-----+ | | | | | + 6 | 24 | 153 | 177 | 332 |------- | | | | +---+-----+-----+-----+-----+ | | | | + 7 | 75 | 178 | 253 | 431 |------------- | | | +---+-----+-----+-----+-----+ | | | + 8 | 30 | 254 | 284 | 538 |-------------------|----- | +---+-----+-----+-----+-----+ | | + 9 | 1 | 285 | 286 | 571 |-------------------|----------- +===+=====+=====+=====+=====+ | +45 | 277 | ← 11+13+12=36 ←| MEC30 +---+-----+ | + +Note: +10* stands as the central rank +11** stands as the central parts +``` + +By toucning the bilateral way of ***96+2=98*** we came to following tabulation. This is further compromizing between the prime five (5) and the prime seven (7) represent the segregation inside the first pair (5, 7). So it shows the tensor of twelve (12) numbers. + + +```scss + + #8 |----------- 5® --------|------------ 7® --------------| + | 1 |---------------- 77 = 4² + 5² + 6² -------------| +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77 +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78 + main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + Δ | Δ | Δ | Δ + Φ17|Φ29 | 96-99| 100 - 123 ({24}) + |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100 + Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30 + {98} | └── 110 - 123 (14x)» 70 +``` + +### Compositions + +So by defining the pattern of each individual numbers with the basic rule that the 19 is _[regenerated](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d)_ out of 18 while the 7 is the _[recollection](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155)_ out of 6 and comparing with the _[Gann Chart](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-lexer-md)_ finaly we found how they look like. + +```scss +True Prime Pairs: +(5,7), (11,13), (17,19) + +Description +=========== +Getting result within a huge package (5 to 19) by spreading (11) +the untouched objects (7) and tunneling (13) them in to a definite scheme (17). + +Compositions +============ + +layer| 1st | 2nd | 3rd | ∑(2,3) +-----+------+------+------+------+------+------+------+------+------+------+------ --- + | | 7 | {19} | 38 | 62 | 64 | 67 | 93 | 95 | 96 | 139 | + i + 1 +------+------+------+------+------+------+------+------+------+------ 5¨ + | | 8 | 20 | 39 | 63 | 65 | 68 | 94 | 97 | 98 | | +-----+------+------+------+------+------+------+------+------+------+------+------ --- + | | 9 | 21 | 40 | {43} | 66 | 69 | 99 | 100 | 101 | 286 | + + 2 +------+------+------+------+------+------+------+------+------+------ 7¨ + | | 10 | 22 | 41 | 44 | 45 | 70 | 102 | 103 | 104 | | + q +------+------+------+------+------+------+------+------+------+------+------ --- + | | 11 | 23 | 42 | 46 | 47 | {71} | 105 | 106 | 107 | 114 | + + 3 +------+------+------+------+------+------+------+------+------+------ 11¨ + | | 12 | 24 | 25 | 48 | 49 | 72 | 108 | 109 | 110 | | +-----+------+------+------+------+------+------+------+------+------+------+------ --- + | | 13 | 26 | 27 | 50 | 51 | 73 | 74 | 111 | 112 | 247 | + + 4 +------+------+------+------+------+------+------+------+------+------ 13¨ + | | 14 | 28 | 29 | 52 | 53 | 75 | 76 | 113 |{114} | | + r +------+------+------+------+------+------+------+------+------+------+------ --- + | | 15 | 30 | 31 | 54 | 55 | 77 | 78 | 79 | 80 | 157 | + + 5 +------+------+------+------+------+------+------+------+------+------ {17¨} + | | 16 | 32 | 33 | 56 | 57 | 81 | 82 | 83 | 84 | | +-----+------+------+------+------+------+------+------+------+------+------+------ --- + | | 17 | 34 | 35 | 58 | 59 | 85 | 86 | 87 | 88 | 786 | + o + 6 +------+------+------+------+------+------+------+------+------+------ 19¨ + | | 18 | 36 | 37 | 60 | 61 | 89 | 90 | 91 | {92} | | +-----+------+------+------+------+------+------+------+------+------+------+------ --- + ∑ | {21} | 150 | | | | | | | | | 1729 + + |------------------------------------------------------------- 16¨ ---| + |----------------------------------------------- 15¨ ---| + |--------------------------------- 14¨ ---| + |------------------- 13¨ ---| + |--- {12¨} ---| +``` + +See that by top of pattern it goes bilateral from ***1, 7, 19, 38*** exactly shown on the _[Scheme-33](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md)_, while the rest are grouped in to the form ***69 vs 96 of A,T,C,G***. Thus each numbers are in the pattern of _[Double Helix](https://en.wikipedia.org/wiki/Nucleic_acid_double_helix)_. + +![image](https://user-images.githubusercontent.com/8466209/213604396-92832a7d-9122-4251-8d26-6fca720b6df7.png) + +This pattern is raised up ***per six (6) cycles*** on the ***[19](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md)***, ***[43](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-runner-md)*** and ***[71](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)***. Since the members are limited to the sum of ***43+71=114*** so here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme. + +***[(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects*** + +[![Polarity](https://user-images.githubusercontent.com/8466209/212487102-2f080804-9078-45c9-85ee-9977a36a5dbf.jpg)](http://www.hexspin.com/minor-hexagons/) + +Meanwhile the six (6) cycles would behave as _[P(7)=142857](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md)_ which is originated by the 7 out of 6. This pattern is also shown on the tabulation above by the horizontal flow of 14,28,29,.. which are then finaly terminated by the bilateral way to _[57x2=114](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#polar-plot)_. + + ### Bilateral way + +This behaviour can be seen on the function chart of _[Riemann Zeta Zeros](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg)_ as shown below where the 19 came out of 18 of 0's cell. + +[![](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#polar-plot) + +The _P(7)=142857_ will bring the system to forms 7x13x19 = 1729 objects of _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. As the impact there will be a gap raised to form ***[20 out of 18 of 0's cell](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)*** and facilitate the [_new candidate_](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md) to get an access to the next primes level. + +![](https://user-images.githubusercontent.com/8466209/220001571-bddc7fee-5753-4ee3-b145-b3b1bb49a354.png) + +The rest of primes goes to the [33's of 15th axis](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-19_root-md) that holding 102 primes of (2,60,40). By the bilateral way the form will be [splitted](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-parser-md) to (1,30,20). Since the base frame shall be 40 so it will be forced to form ***(1,30,40) of prime 71***. + +[![zeta-vs-zero](https://user-images.githubusercontent.com/8466209/213628433-c7382e39-4efa-4455-867c-13652293474d.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-vs-zero) + +The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. + +[![default](https://user-images.githubusercontent.com/8466209/244139208-378b2229-c3e8-4f1f-8829-dee6687348fb.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) + +As you may see the bilateral way between this 19's tensor with the (Δ1) is not easy to be understood nor explained. However at this point, you may already get an idea that as a part of the nature, the _DNA System_ and the _Prime Structure_ applies the same. + +>[Quantum Theory](https://gist.github.com/eq19) tells us that there are [instantaneous connections](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#instaneous-connection) between two entangled quantum objects, like _[electrons](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#electron-scattering)_. In fact, there is no separation. ***[At the quantum level, theoretically, everything is linked](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#everything-is-linked)***. This is known as the candidate for _The Theory of Everything_. Thus the Sunlight, Saturn, Moon, Saturn’s rings, [Moon’s orbit](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#moons-orbit), ocean, me and you… are all one. + +[![](https://user-images.githubusercontent.com/8466209/199392468-a2738235-b65f-47da-848d-ffa0340cd51b.png)](https://github.com/eq19) + +Broadly speaking it still remain of how this project can be developed so that it can be applied to the goals we want. Therefore we decided to bring further every details in to a group of websites. That is the background why the _[root scheme](https://gist.github.com/eq19)_ of 'eq19' is exist. diff --git a/exponentiation/span16/gist12.html b/exponentiation/span16/gist12.html new file mode 100644 index 00000000000..0e74d11028c --- /dev/null +++ b/exponentiation/span16/gist12.html @@ -0,0 +1 @@ + gist12.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            image

            Fibonacci

            image

            image

            image

            2022-12-12

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span16/gist12.md b/exponentiation/span16/gist12.md new file mode 100644 index 00000000000..36ce316d6cf --- /dev/null +++ b/exponentiation/span16/gist12.md @@ -0,0 +1,20 @@ +![](https://user-images.githubusercontent.com/36441664/72921817-8f71e080-3d7e-11ea-97c5-331789123a15.jpg) + +![](https://user-images.githubusercontent.com/36441664/73038520-52dcdc80-3e85-11ea-95ed-91a6db884043.png) + +![](https://user-images.githubusercontent.com/36441664/72921751-710be500-3d7e-11ea-81c4-4923d68be691.gif) + +![image](https://user-images.githubusercontent.com/36441664/72533380-a9f01980-38a7-11ea-8609-6cb6f37645d1.jpg) + +![Fibonacci](https://user-images.githubusercontent.com/36441664/72921775-7bc67a00-3d7e-11ea-8042-c8b8ee0326b8.jpg) + +![image](https://user-images.githubusercontent.com/36441664/71191184-80e46500-22b8-11ea-9f97-5ce856a39820.png) + +![image](https://user-images.githubusercontent.com/36441664/71581711-14c7f380-2b39-11ea-9f61-8cf3df12a100.png) + +![image](https://user-images.githubusercontent.com/36441664/103138448-52883980-4705-11eb-85e6-5128c632f612.png) + + +![](https://user-images.githubusercontent.com/36441664/82048729-58358f80-96df-11ea-8176-14c26328a12f.png) + +![2022-12-12](https://user-images.githubusercontent.com/8466209/206964338-fb62d060-86c7-4a2d-a64c-7da49bc70222.png) diff --git a/exponentiation/span16/index.html b/exponentiation/span16/index.html new file mode 100644 index 00000000000..c67efe4bdb4 --- /dev/null +++ b/exponentiation/span16/index.html @@ -0,0 +1,96 @@ + Quantum Gravity (feed) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Quantum Gravity (feed)

            Effective field theories have been a mainstay of theoretical physics since the 1930s but they haven't helped all that much with quantum gravity.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-24 of main section-2 that is inherited from the spin section-16 by prime spin-32 and span-155 with the partitions as below.

            +
            +
            1. gist05.md
            2. gist04.md
            3. gist03.md
            4. gist01.md
            5. Deploying containers
            6. Antiparallels
            7. gist08.md
            8. gist09.md
            9. gist10.md
            10. gist12.md

            Here we decided to take a concept that gravity enter the event horizons of black holes and tunnel out again to deposit it into the background.

            Event horizons

            18

            images (7)

            19

            images (6)

            22

            316503 image0

            37

            worm

            22

            quantum_anticentrifugal_force

            Eternal Cyclic

            We would expect that the quantum theory reduces to Einstein's theory of gravity. There is no way to put a black hole into the Hamiltonian.

            searching graviton

            20

            4dfbafd3f1e223eff196f2b8691bb992

            21

            main-qimg-b18921fc2fe38539d30c68227a3b41cc-pjlq

            38

            IMG_20240116_151732

            fisica49_01

            maxresdefault (1)

            Gravitating Objects

            +
            + + Note +
            +
            +

            A lot number of positive color-charges move from the positive charged particle toward the negative charged particles, and negative color-charges move from negative charged particle toward the positive charged particle and they combine in each other (Gravity in Time space - pdf)

            +
            +

            A-lot-number-of-positive-color-charges-move-from-the-positive-charged-particle-toward-the

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 👈
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+
            +
            + + Note +
            +
            +

            Think of it this way, all gravitating bodies in the universe would be surrounded at all times by a cloud of tunneling electrons. We cannot see these particles since they’re so small and since they permeate all of space. They would also tunnel to a different location about once every Planck time (about 10^-43 seconds) whenever they interact with another particle.

            • These interactions between particles amount to the exchanges of bosons between electrons and other electrons or other fermions. At each point where the electron absorbs another boson, we say that the wave function of the electron collapses, and it tunnels to a new location whereupon it interacts with yet another particle.
            • The cloud of electron surrounding gravitating objects would diminish in inverse proportion to the square of the distance; hence, if you recede from an objects’ surface, you’re less likely to find an electron tunneling from that object.
            • Electrons also make an excellent candidate for a particle of gravity since they absorb and emit photons readily, and we know from Einstein’s theory of general relativity that light interacts readily with gravitational fields, and that gravitational fields are thought to emit photons spontaneously.
            • This spontaneous emission of photons is what we refer to as the cosmological constant or dark energy, and in our current thinking on the topic we imagine that particles of antimatter are created and annihilate with particles of matter leading, occasionally, to the emission of a photon. I suspect that this is incorrect and that no such thing as antimatter really exists. I suspect that positrons are really tunneling W particles and that this Dirac Sea, or background of tunneling electrons, is really giving rise to this phenomenon of the cosmological constant, or vacuum energy, we observe inn nature.
            • As a consequence, we would need to adumbrate our standard model of particle physics by about half. This ought to be seen as a positive thing in physics. No longer do we have untestable assumptions (such as the creation and annihilation of particles) in our models, and we have a far easier means of now beginning to probe the quantum nature of gravity.

            The other fascinating consequence of this way of thinking is that gravity would no longer be a fundamental force; instead it would be a secondary effect of electromagnetism. This should have been what we anticipated all along; and now, we might have a quantum theory focusing on only three forces and a theory of gravitation that is truly particle-based. (Medium - Article)

            +
            +

            Cut the Standard Model

            +
            + + Note +
            +
            +

            We may gain a better understanding of black hole physics; wewe may gain the insight that tunneling electrons enter the event horizons of black holes, absorb a particle there, and tunnel out again to deposit it into the background. In this way, we could explain how black holes radiate away. (Medium - Article)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)  ✔️ ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+
            +
            + + Note +
            +
            +

            There are two groups of scientists (called collaborations) looking for evidence of gravitons in proton-proton collision experiments at the Large Hadron Collider at CERN. Once a graviton has been created, it’s expected to decay in one of a few possible ways - and it’s evidence of these decays that the collaborations are looking for. ATLAS search for evidence that the gravitons decays into two photons, and the CMS search for evidence that the graviton decays into two jets (bursts) of hadrons (a particular class of particle). (ThingsWeDontKnow.com)

            +
            +

            fully-expanded-incl-matrices

            Constructing the tableaux

            Young_tableaux_1

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36.

            and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            Screenshotgoogle

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 👈
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 👈
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 👈
+

            PRI_196247467

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist03.html b/exponentiation/span17/gist03.html new file mode 100644 index 00000000000..01448445c32 --- /dev/null +++ b/exponentiation/span17/gist03.html @@ -0,0 +1 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist03.md b/exponentiation/span17/gist03.md new file mode 100644 index 00000000000..8e474f94cf0 --- /dev/null +++ b/exponentiation/span17/gist03.md @@ -0,0 +1,6 @@ +[![screencapture-console-cloud-google-billing-018F05-BD9DB7-0A1326-2022-12-24-11_01_11](https://user-images.githubusercontent.com/8466209/209420635-7e57c4a9-1df8-4c18-8510-96aa23250516.png)](https://console.cloud.google.com/billing/018F05-BD9DB7-0A1326?authuser=1&cloudshell=false&project=chetabahana) + +[![screencapture-console-cloud-google-billing-018F05-BD9DB7-0A1326-reports-chartType-STACKED-BAR-grouping-GROUP-BY-SERVICE-2022-12-26-17_44_07](https://user-images.githubusercontent.com/8466209/209540338-f64c57d7-20ed-4413-baf1-0da50a730be3.png) +](https://console.cloud.google.com/billing/018F05-BD9DB7-0A1326/reports;chartType=STACKED_BAR;grouping=GROUP_BY_SERVICE?authuser=1&cloudshell=false&project=marketleader) + +![image](https://user-images.githubusercontent.com/8466209/235955528-7bf82161-cacd-40a3-849e-5b09db8a5638.png) diff --git a/exponentiation/span17/gist04.html b/exponentiation/span17/gist04.html new file mode 100644 index 00000000000..6d8577c9716 --- /dev/null +++ b/exponentiation/span17/gist04.html @@ -0,0 +1,101 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            2022-12-26 (4)

            2022-12-26 (6)

            gcloud command line

            gcloud compute instance-templates create instance-template-ubuntu-01 \
+--project=marketleader --machine-type=e2-micro --network-interface=network=default,network-tier=PREMIUM \
+--maintenance-policy=MIGRATE --provisioning-model=STANDARD \
+--service-account=project-owner@marketleader.iam.gserviceaccount.com \
+--scopes=https://www.googleapis.com/auth/source.full_control,\
+https://www.googleapis.com/auth/compute,https://www.googleapis.com/auth/servicecontrol,\
+https://www.googleapis.com/auth/service.management.readonly,\
+https://www.googleapis.com/auth/logging.write,https://www.googleapis.com/auth/monitoring.write,\
+https://www.googleapis.com/auth/trace.append,https://www.googleapis.com/auth/devstorage.read_only \
+--create-disk=auto-delete=yes,boot=yes,device-name=instance-template-ubuntu-2204LTS,\
+image=projects/ubuntu-os-cloud/global/images/ubuntu-2204-jammy-v20221206,mode=rw,size=10,type=pd-standard \
+--no-shielded-secure-boot --shielded-vtpm --shielded-integrity-monitoring --reservation-affinity=any \
+--tags=https-server --threads-per-core=2
+

            Equivalent REST request

            POST https://www.googleapis.com/compute/v1/projects/marketleader/global/instanceTemplates
+{
+  "description": "",
+  "name": "instance-template-ubuntu-01",
+  "properties": {
+    "advancedMachineFeatures": {
+      "threadsPerCore": 2
+    },
+    "canIpForward": false,
+    "confidentialInstanceConfig": {
+      "enableConfidentialCompute": false
+    },
+    "description": "",
+    "disks": [
+      {
+        "autoDelete": true,
+        "boot": true,
+        "deviceName": "instance-template-ubuntu-2204LTS",
+        "diskEncryptionKey": {},
+        "initializeParams": {
+          "diskSizeGb": "10",
+          "diskType": "pd-standard",
+          "labels": {},
+          "sourceImage": "projects/ubuntu-os-cloud/global/images/ubuntu-2204-jammy-v20221206"
+        },
+        "mode": "READ_WRITE",
+        "type": "PERSISTENT"
+      }
+    ],
+    "displayDevice": {
+      "enableDisplay": false
+    },
+    "keyRevocationActionType": "NONE",
+    "labels": {},
+    "machineType": "e2-micro",
+    "metadata": {
+      "items": []
+    },
+    "networkInterfaces": [
+      {
+        "accessConfigs": [
+          {
+            "kind": "compute#accessConfig",
+            "name": "External NAT",
+            "networkTier": "PREMIUM",
+            "type": "ONE_TO_ONE_NAT"
+          }
+        ],
+        "network": "projects/marketleader/global/networks/default",
+        "stackType": "IPV4_ONLY"
+      }
+    ],
+    "reservationAffinity": {
+      "consumeReservationType": "ANY_RESERVATION"
+    },
+    "scheduling": {
+      "automaticRestart": true,
+      "onHostMaintenance": "MIGRATE",
+      "provisioningModel": "STANDARD"
+    },
+    "serviceAccounts": [
+      {
+        "email": "project-owner@marketleader.iam.gserviceaccount.com",
+        "scopes": [
+          "https://www.googleapis.com/auth/source.full_control",
+          "https://www.googleapis.com/auth/compute",
+          "https://www.googleapis.com/auth/servicecontrol",
+          "https://www.googleapis.com/auth/service.management.readonly",
+          "https://www.googleapis.com/auth/logging.write",
+          "https://www.googleapis.com/auth/monitoring.write",
+          "https://www.googleapis.com/auth/trace.append",
+          "https://www.googleapis.com/auth/devstorage.read_only"
+        ]
+      }
+    ],
+    "shieldedInstanceConfig": {
+      "enableIntegrityMonitoring": true,
+      "enableSecureBoot": false,
+      "enableVtpm": true
+    },
+    "tags": {
+      "items": [
+        "https-server"
+      ]
+    }
+  }
+}
+

            instance-template-ubuntu-2204LTS

            2022-12-24 (9)

            Untitled

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist04.md b/exponentiation/span17/gist04.md new file mode 100644 index 00000000000..cfafe222803 --- /dev/null +++ b/exponentiation/span17/gist04.md @@ -0,0 +1,123 @@ +[![2022-12-26 (4)](https://user-images.githubusercontent.com/8466209/209532746-5a09e0f6-9346-4d61-aee8-eeef1f801e5a.png) +](https://console.cloud.google.com/iam-admin/serviceaccounts/create?authuser=1&project=marketleader&cloudshell=false) + +[![2022-12-26 (6)](https://user-images.githubusercontent.com/8466209/209535961-5441181b-a87b-4879-8e6a-c752eaaec587.png) +](https://console.cloud.google.com/iam-admin/serviceaccounts/details/112927040009179159531/permissions?authuser=1&project=marketleader) + +[gcloud](https://developers.google.com/cloud/sdk/gcloud/reference/compute/?hl=en_US) command line + +``` +gcloud compute instance-templates create instance-template-ubuntu-01 \ +--project=marketleader --machine-type=e2-micro --network-interface=network=default,network-tier=PREMIUM \ +--maintenance-policy=MIGRATE --provisioning-model=STANDARD \ +--service-account=project-owner@marketleader.iam.gserviceaccount.com \ +--scopes=https://www.googleapis.com/auth/source.full_control,\ +https://www.googleapis.com/auth/compute,https://www.googleapis.com/auth/servicecontrol,\ +https://www.googleapis.com/auth/service.management.readonly,\ +https://www.googleapis.com/auth/logging.write,https://www.googleapis.com/auth/monitoring.write,\ +https://www.googleapis.com/auth/trace.append,https://www.googleapis.com/auth/devstorage.read_only \ +--create-disk=auto-delete=yes,boot=yes,device-name=instance-template-ubuntu-2204LTS,\ +image=projects/ubuntu-os-cloud/global/images/ubuntu-2204-jammy-v20221206,mode=rw,size=10,type=pd-standard \ +--no-shielded-secure-boot --shielded-vtpm --shielded-integrity-monitoring --reservation-affinity=any \ +--tags=https-server --threads-per-core=2 +``` + +Equivalent [REST request](https://developers.google.com/compute/docs/reference/latest?hl=en_US) + +``` +POST https://www.googleapis.com/compute/v1/projects/marketleader/global/instanceTemplates +{ + "description": "", + "name": "instance-template-ubuntu-01", + "properties": { + "advancedMachineFeatures": { + "threadsPerCore": 2 + }, + "canIpForward": false, + "confidentialInstanceConfig": { + "enableConfidentialCompute": false + }, + "description": "", + "disks": [ + { + "autoDelete": true, + "boot": true, + "deviceName": "instance-template-ubuntu-2204LTS", + "diskEncryptionKey": {}, + "initializeParams": { + "diskSizeGb": "10", + "diskType": "pd-standard", + "labels": {}, + "sourceImage": "projects/ubuntu-os-cloud/global/images/ubuntu-2204-jammy-v20221206" + }, + "mode": "READ_WRITE", + "type": "PERSISTENT" + } + ], + "displayDevice": { + "enableDisplay": false + }, + "keyRevocationActionType": "NONE", + "labels": {}, + "machineType": "e2-micro", + "metadata": { + "items": [] + }, + "networkInterfaces": [ + { + "accessConfigs": [ + { + "kind": "compute#accessConfig", + "name": "External NAT", + "networkTier": "PREMIUM", + "type": "ONE_TO_ONE_NAT" + } + ], + "network": "projects/marketleader/global/networks/default", + "stackType": "IPV4_ONLY" + } + ], + "reservationAffinity": { + "consumeReservationType": "ANY_RESERVATION" + }, + "scheduling": { + "automaticRestart": true, + "onHostMaintenance": "MIGRATE", + "provisioningModel": "STANDARD" + }, + "serviceAccounts": [ + { + "email": "project-owner@marketleader.iam.gserviceaccount.com", + "scopes": [ + "https://www.googleapis.com/auth/source.full_control", + "https://www.googleapis.com/auth/compute", + "https://www.googleapis.com/auth/servicecontrol", + "https://www.googleapis.com/auth/service.management.readonly", + "https://www.googleapis.com/auth/logging.write", + "https://www.googleapis.com/auth/monitoring.write", + "https://www.googleapis.com/auth/trace.append", + "https://www.googleapis.com/auth/devstorage.read_only" + ] + } + ], + "shieldedInstanceConfig": { + "enableIntegrityMonitoring": true, + "enableSecureBoot": false, + "enableVtpm": true + }, + "tags": { + "items": [ + "https-server" + ] + } + } +} +``` + +[![instance-template-ubuntu-2204LTS](https://user-images.githubusercontent.com/8466209/209422018-1209129c-fc1d-4d21-baf9-3d8791c65bcb.png) +](https://console.cloud.google.com/compute/instanceTemplates/add?authuser=1&cloudshell=false&project=marketleader) + +[![2022-12-24 (9)](https://user-images.githubusercontent.com/8466209/209423099-b1a94680-016a-4a05-a8d0-a8bed34ea099.png) +](https://console.cloud.google.com/compute/instanceTemplates/add?authuser=1&cloudshell=false&project=marketleader) + +![Untitled](https://user-images.githubusercontent.com/8466209/253502287-3490508a-c791-42f0-91b4-6518f6f9d384.png) diff --git a/exponentiation/span17/gist05.html b/exponentiation/span17/gist05.html new file mode 100644 index 00000000000..04935f21e69 --- /dev/null +++ b/exponentiation/span17/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist05.md b/exponentiation/span17/gist05.md new file mode 100644 index 00000000000..537abd4749f --- /dev/null +++ b/exponentiation/span17/gist05.md @@ -0,0 +1,9 @@ +![2022-12-24 (10)](https://user-images.githubusercontent.com/8466209/209439858-be21b338-8486-470a-8a2e-6a50a4ce692a.png) + +[![2022-12-24 (11)](https://user-images.githubusercontent.com/8466209/209440027-a5a4dcd9-ad13-46d6-919a-7b5e4d1b966e.png)](https://console.cloud.google.com/compute/instances?authuser=1&cloudshell=false&project=marketleader&tab=instances) +![2022-12-24 (12)](https://user-images.githubusercontent.com/8466209/209442921-774da1ac-fd91-449a-a19c-a90fbe170a7a.png) + +![2022-12-24 (13)](https://user-images.githubusercontent.com/8466209/209442958-440076e5-c350-4d27-8ce0-6917d8ad8426.png) + +[![screencapture-swaadha-how-to-create-github-organization-runner-in-kubernetes-cluster-2022-12-26-17_10_33](https://user-images.githubusercontent.com/8466209/209537509-00ed823e-817b-4a3b-a119-61cdac14cf87.png) +](https://swaadha.com/how-to-create-github-organization-runner-in-kubernetes-cluster/) \ No newline at end of file diff --git a/exponentiation/span17/gist07.html b/exponentiation/span17/gist07.html new file mode 100644 index 00000000000..fe0d53124fe --- /dev/null +++ b/exponentiation/span17/gist07.html @@ -0,0 +1 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist07.md b/exponentiation/span17/gist07.md new file mode 100644 index 00000000000..99d295330fa --- /dev/null +++ b/exponentiation/span17/gist07.md @@ -0,0 +1,9 @@ +[![](https://user-images.githubusercontent.com/8466209/207415917-58daf976-3f9a-496d-af56-99039253c1e8.png)](https://gist.github.com/eq19/dc30497160f3389546d177da901537d9#file-leading-md) + +![2022-12-25 (6)](https://user-images.githubusercontent.com/8466209/209474076-093cde4b-ea53-4f54-9901-5ae661106937.png) + +[![2022-12-25 (3)](https://user-images.githubusercontent.com/8466209/209473648-bbcb171c-e1b3-4a49-9a9f-96536dfe8c24.png) +](https://console.cloud.google.com/compute/instancesAdd?authuser=1&cloudshell=false&project=marketleader) + +[![2022-12-25 (2)](https://user-images.githubusercontent.com/8466209/209473582-2c292df3-90ba-4859-bea9-25637f6c12c0.png) +](https://console.cloud.google.com/compute/instancesAdd?authuser=1&cloudshell=false&project=marketleader) diff --git a/exponentiation/span17/gist08.html b/exponentiation/span17/gist08.html new file mode 100644 index 00000000000..687dfc76be9 --- /dev/null +++ b/exponentiation/span17/gist08.html @@ -0,0 +1 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist08.md b/exponentiation/span17/gist08.md new file mode 100644 index 00000000000..3acd057f207 --- /dev/null +++ b/exponentiation/span17/gist08.md @@ -0,0 +1,10 @@ + +[![](https://user-images.githubusercontent.com/8466209/207416875-064d5b66-e577-4dde-a329-123f9325d974.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-locate-md) + +[![2022-12-26 (1)](https://user-images.githubusercontent.com/8466209/209503644-968f7e29-ab14-4eff-abad-6a2bccd8398e.png) +](https://github.com/FeedMapping/feedmapping.github.io) + +[![2022-12-26 (2)](https://user-images.githubusercontent.com/8466209/209503851-493bebbb-28e9-495b-87e5-8d9c17e24f0f.png) +](https://docs.github.com/en/pages/getting-started-with-github-pages/configuring-a-publishing-source-for-your-github-pages-site#publishing-with-a-custom-github-actions-workflow) + +[![First 120 builds-minutes per day are free](https://user-images.githubusercontent.com/8466209/255348632-aa005f71-470c-4f96-bd76-02c9abfa9b16.png)](https://cloud.google.com/build/pricing#additional_costs) diff --git a/exponentiation/span17/gist09.html b/exponentiation/span17/gist09.html new file mode 100644 index 00000000000..268e911c22e --- /dev/null +++ b/exponentiation/span17/gist09.html @@ -0,0 +1,22 @@ + gist09.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | 1   |{10}
+---+-----+-----
+ 2 |{11} |{22}
+---+-----+-----
+ 3 | 23  | 39
+---+-----+-----
+ 4 |{40} |{60}
+---+-----+-----
+ 5 |{61} | 70
+---+-----+-----
+ 6 |{71} |{77}
+---+-----+-----
+ 7 |{78} | 82
+---+-----+-----
+ 8 | 83  |{100}
+---+-----+-----
+ 9 | 101 | 104
+---+-----+-----
+10 | 105 |{111}
+---+-----+-----
+

            Untitled

            Untitled

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist09.md b/exponentiation/span17/gist09.md new file mode 100644 index 00000000000..9872c4db87c --- /dev/null +++ b/exponentiation/span17/gist09.md @@ -0,0 +1,30 @@ +``` +---+-----+----- + 1 | 1 |{10} +---+-----+----- + 2 |{11} |{22} +---+-----+----- + 3 | 23 | 39 +---+-----+----- + 4 |{40} |{60} +---+-----+----- + 5 |{61} | 70 +---+-----+----- + 6 |{71} |{77} +---+-----+----- + 7 |{78} | 82 +---+-----+----- + 8 | 83 |{100} +---+-----+----- + 9 | 101 | 104 +---+-----+----- +10 | 105 |{111} +---+-----+----- +``` + +![Untitled](https://user-images.githubusercontent.com/8466209/255354303-b21e4caf-b759-4319-b92c-77209ea0e1da.png) + +![Untitled](https://user-images.githubusercontent.com/8466209/255354336-2c112708-3011-4e15-a51f-ad4a5998ab85.png) + +[![](https://user-images.githubusercontent.com/8466209/200244306-f5e5a428-83b9-46bb-a4b1-c96367e278b2.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-circular-md) + diff --git a/exponentiation/span17/gist10.html b/exponentiation/span17/gist10.html new file mode 100644 index 00000000000..baf82180f8e --- /dev/null +++ b/exponentiation/span17/gist10.html @@ -0,0 +1 @@ + gist10.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            2022-12-11 (3)

            2022-12-12 (1)

            Untitled

            2022-12-24 (5)

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/gist10.md b/exponentiation/span17/gist10.md new file mode 100644 index 00000000000..6202d395643 --- /dev/null +++ b/exponentiation/span17/gist10.md @@ -0,0 +1,11 @@ +![](https://user-images.githubusercontent.com/8466209/204256833-d12508ae-8cb1-4381-ade5-7acfcc3f0e12.png) + +![](https://user-images.githubusercontent.com/36441664/125708871-db9523c3-8d32-4423-976f-59a9c56a146d.png) + +![2022-12-11 (3)](https://user-images.githubusercontent.com/8466209/206912519-cf441c73-314f-4056-a199-ca56110c9254.png) + +![2022-12-12 (1)](https://user-images.githubusercontent.com/8466209/207072690-80ab2c3d-f41a-48bd-ab64-09df6afd4a26.png) + +![Untitled](https://user-images.githubusercontent.com/8466209/207068091-8ee3cfa6-d68c-4f85-bb90-1597b9778f44.png) + +[![2022-12-24 (5)](https://user-images.githubusercontent.com/8466209/209421514-d62c776a-77c0-4cb0-a0ac-5f33ba51c161.png)](https://help.ubuntu.com) diff --git a/exponentiation/span17/index.html b/exponentiation/span17/index.html new file mode 100644 index 00000000000..b92ba98dad5 --- /dev/null +++ b/exponentiation/span17/index.html @@ -0,0 +1,51 @@ + Electrodynamics (maps) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Electrodynamics (maps)

            It is shown that a considerable simplification can be attained in writing down matrix elements for complex processes in electrodynamics.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-23 of main section-1 that is inherited from the spin section-17 by prime spin-31 and span-156 with the partitions as below.

            +
            +
            1. gist03.md
            2. gist04.md
            3. gist05.md
            4. gist07.md
            5. gist08.md
            6. gist09.md
            7. gist10.md

            All matrix elements are now finite, with the exception of those relating to problems of vacuum polarization. The more conventional Hamiltonian point of view is discussed.

            Basic Transformation

            The first appearance of e in a printed publication was in Euler's Mechanica (1736). It is unknown why Euler chose the letter e.

            +
            + + Note +
            +
            +

            Leonhard Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and in a letter to Christian Goldbach on 25 November 1731. (Wikipedia)

            +
            +

            Letter e

            images (5)

            +
            + + Note +
            +
            +

            It turns out that the basic idea of QED can be communicated while assuming that the square of the total of the probability amplitudes mentioned above (P(A to B), E(C to D) and j) acts just like our everyday probability (a simplification made in Feynman’s book). Later on, this will be corrected to include specifically quantum-style mathematics, following Feynman.

            The basic rules of probability amplitudes that will be used are:

            • If an event can occur via a number of indistinguishable alternative processes (a.k.a. “virtual” processes), then its probability amplitude is the sum of the probability amplitudes of the alternatives.
            • If a virtual process involves a number of independent or concomitant sub-processes, then the probability amplitude of the total (compound) process is the product of the probability amplitudes of the sub-processes.

            The indistinguishability criterion in (a) is very important: it means that there is no observable feature present in the given system that in any way “reveals” which alternative is taken. In such a case, one cannot observe which alternative actually takes place without changing the experimental setup in some way (e.g. by introducing a new apparatus into the system). (Wikipedia)

            +
            +

            First_Feynman_Diagram

            +
            + + Note +
            +
            +

            It should be remembered that the expression hides a lot of complexity. We have summed over all possible timeorderings and summed over all polarization states of the virtual photon. If we are then presented with a new Feynman diagram we don’t want to go through the full calculation again. Fortunately this isn’t necessary – can just write down matrix element using a set of simple rules Basic Feynman Rules: e+ g m+ Propagator factor for each internal line (i. e. each internal virtual particle) Dirac Spinor for each external line e–

            +
            +

            image-18

            Mapping Scheme

            Within a cycle this scheme would generate the prime platform which is performing the rank of 10 shapes starting with the primes 2,3,5,7.

            proton-1

            Via the 11 partitions as the lexer and 13 frames as the parser we do a recombination to build the grammar in 6 periods.

            6 minor hexagons

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            +
            + + Note +
            +
            +

            With theoretical foundations in Information Engineering (Discrete Mathematics, Control Theory, System Theory, Information Theory, and Statistics), my research has delivered a suite of systems and products that has allowed me to carve out a niche within an extensive collaborative network (>200 academics). (Umer.Ijaz)

            +
            +

            information engineering

            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) (₠Quantum).

            flowchart

            By this project the above would be deployed as default layout. It is set to be avalaible throughout the whole platform via a single page within a parser repository which is acting as prime 13. Their interface will be in json and xml format.

            Here is for the sample:

            {
+  "title":"Mapping System",
+  "content":"<p>Hello, <strong>world</strong>.\nI am here.</p>\n",
+  "links": [
+    {"title":"Introduction","url":"https://www.eq19.com/intro/"},
+    {"title":"Go tour on Mapping System ","url":"https://www.eq19.com/maps/"},
+    {"title":"A backed pretty display for markdown","url":"https://www.eq19.com/gistio/"},
+    {"title":"Gist.io for programmers","url":"https://gist.io/@eq19/d2336e28e79702acf38edd182003d5e0"}
+  ]
+}
+

            Using a kind of interface such as docker then it could be developed cross platform. Evenso. Let assume that all alpabethic letter in the sequence is representing a local disk so you may build your own pattern in your PC such as shown below:

            Matrices-of-prime-numbers

            The tensor product of a triplet with an octet reducing to a deciquintuplet, an anti-sextet, and a triplet appears diagrammatically as a total of 24 states.

            Young_tableaux_17 Young_tableaux_18

            Using the same procedure, any direct product representation is easily reduced.

            1

            main-qimg-4a1f46404471a9e9efa53881ce58c091-pjlq

            2

            mqdefault

            3

            478517_2_En_18_Fig10_HTML

            4

            images (11)

            6

            axioms-12-01058-g001

            7

            SciDACLayers_1_9_2012

            8

            hq720 (1)

            9

            images (5)

            11

            images (10)

            12

            QCD

            13

            axioms-12-01058-g002-550

            14

            axioms-12-01058-g004

            15

            qcd_together

            20

            qcd-620px

            22

            QED_16

            23

            hqdefault

            24

            1-quantum-electrodynamics-laguna-designscience-photo-library

            26

            Feynman-rules-of-NCQED

            27

            Feynman-rules-for-electron-selectron-photino-interaction-and-photino-propagators

            28

            Useful-Feynman-rules-in-VSR-QED

            29

            488px-Qed_rules

            30

            InteractionVertexOfQED

            31

            300px-Compton_qed

            32

            Diagrams-in-strong-field-quantum-electrodynamics-SFQED-versus-ordinary-quantum

            33

            Feynman-rules-for-the-PS-theory

            34

            a-Summary-of-the-Feynman-rules-Solid-line-represents-the-fermionic-propagator-G-0-pp

            35

            I15-73-Feynman

            37

            008869256_1-75ca18aad2faf65f52f4c7706d7d8bd3-768x994

            38

            bigwuethrich_figuresrules-peskin-qed-v2

            39

            1_RMV1kvtEZ-o-_8WKQLnCSA

            40

            slide_1

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/exponentiation/span17/spin_5.txt b/exponentiation/span17/spin_5.txt new file mode 100644 index 00000000000..185ff0aa739 --- /dev/null +++ b/exponentiation/span17/spin_5.txt @@ -0,0 +1,33 @@ +1009 3 -1 -3 +1013 2 -1 -3 +1019 2 1 -3 +1021 3 1 -3 +1031 4 1 -3 +1033 5 1 -3 +1039 5 -1 -3 +1049 4 -1 -3 +1051 3 -1 -3 +1061 2 -1 -3 +1063 1 -1 -3 +1069 1 1 -3 +1087 1 -1 -3 +1091 0 -1 -3 +1093 5 -1 -4 +1097 4 -1 -4 +1103 4 1 -4 +1109 4 -1 -4 +1117 3 -1 -4 +1123 3 1 -4 +1129 3 -1 -4 +1151 2 -1 -4 +1153 1 -1 -4 +1163 0 -1 -4 +1171 5 -1 -5 +1181 4 -1 -5 +1187 4 1 -5 +1193 4 -1 -5 +1201 3 -1 -5 +1213 3 1 -5 +1217 4 1 -5 +1223 4 -1 -5 +1229 4 1 -5 diff --git a/exponentiation/span17/spin_6.txt b/exponentiation/span17/spin_6.txt new file mode 100644 index 00000000000..c3605570ccd --- /dev/null +++ b/exponentiation/span17/spin_6.txt @@ -0,0 +1,800 @@ +1231 5 1 -5 +1237 5 -1 -5 +1249 5 1 -5 +1259 0 1 -4 +1277 0 -1 -4 +1279 5 -1 -5 +1283 4 -1 -5 +1289 4 1 -5 +1291 5 1 -5 +1297 5 -1 -5 +1301 4 -1 -5 +1303 3 -1 -5 +1307 2 -1 -5 +1319 2 1 -5 +1321 3 1 -5 +1327 3 -1 -5 +1361 2 -1 -5 +1367 2 1 -5 +1373 2 -1 -5 +1381 1 -1 -5 +1399 1 1 -5 +1409 2 1 -5 +1423 3 1 -5 +1427 4 1 -5 +1429 5 1 -5 +1433 0 1 -4 +1439 0 -1 -4 +1447 5 -1 -5 +1451 4 -1 -5 +1453 3 -1 -5 +1459 3 1 -5 +1471 3 -1 -5 +1481 2 -1 -5 +1483 1 -1 -5 +1487 0 -1 -5 +1489 5 -1 -6 +1493 4 -1 -6 +1499 4 1 -6 +1511 4 -1 -6 +1523 4 1 -6 +1531 5 1 -6 +1543 5 -1 -6 +1549 5 1 -6 +1553 0 1 -5 +1559 0 -1 -5 +1567 5 -1 -6 +1571 4 -1 -6 +1579 3 -1 -6 +1583 2 -1 -6 +1597 1 -1 -6 +1601 0 -1 -6 +1607 0 1 -6 +1609 1 1 -6 +1613 2 1 -6 +1619 2 -1 -6 +1621 1 -1 -6 +1627 1 1 -6 +1637 2 1 -6 +1657 3 1 -6 +1663 3 -1 -6 +1667 2 -1 -6 +1669 1 -1 -6 +1693 1 1 -6 +1697 2 1 -6 +1699 3 1 -6 +1709 4 1 -6 +1721 4 -1 -6 +1723 3 -1 -6 +1733 2 -1 -6 +1741 1 -1 -6 +1747 1 1 -6 +1753 1 -1 -6 +1759 1 1 -6 +1777 1 -1 -6 +1783 1 1 -6 +1787 2 1 -6 +1789 3 1 -6 +1801 3 -1 -6 +1811 2 -1 -6 +1823 2 1 -6 +1831 3 1 -6 +1847 4 1 -6 +1861 5 1 -6 +1867 5 -1 -6 +1871 4 -1 -6 +1873 3 -1 -6 +1877 2 -1 -6 +1879 1 -1 -6 +1889 0 -1 -6 +1901 0 1 -6 +1907 0 -1 -6 +1913 0 1 -6 +1931 0 -1 -6 +1933 5 -1 -7 +1949 4 -1 -7 +1951 3 -1 -7 +1973 2 -1 -7 +1979 2 1 -7 +1987 3 1 -7 +1993 3 -1 -7 +1997 2 -1 -7 +1999 1 -1 -7 +2003 0 -1 -7 +2011 5 -1 -8 +2017 5 1 -8 +2027 0 1 -7 +2029 1 1 -7 +2039 2 1 -7 +2053 3 1 -7 +2063 4 1 -7 +2069 4 -1 -7 +2081 4 1 -7 +2083 5 1 -7 +2087 0 1 -6 +2089 1 1 -6 +2099 2 1 -6 +2111 2 -1 -6 +2113 1 -1 -6 +2129 0 -1 -6 +2131 5 -1 -7 +2137 5 1 -7 +2141 0 1 -6 +2143 1 1 -6 +2153 2 1 -6 +2161 3 1 -6 +2179 3 -1 -6 +2203 3 1 -6 +2207 4 1 -6 +2213 4 -1 -6 +2221 3 -1 -6 +2237 2 -1 -6 +2239 1 -1 -6 +2243 0 -1 -6 +2251 5 -1 -7 +2267 4 -1 -7 +2269 3 -1 -7 +2273 2 -1 -7 +2281 1 -1 -7 +2287 1 1 -7 +2293 1 -1 -7 +2297 0 -1 -7 +2309 0 1 -7 +2311 1 1 -7 +2333 2 1 -7 +2339 2 -1 -7 +2341 1 -1 -7 +2347 1 1 -7 +2351 2 1 -7 +2357 2 -1 -7 +2371 1 -1 -7 +2377 1 1 -7 +2381 2 1 -7 +2383 3 1 -7 +2389 3 -1 -7 +2393 2 -1 -7 +2399 2 1 -7 +2411 2 -1 -7 +2417 2 1 -7 +2423 2 -1 -7 +2437 1 -1 -7 +2441 0 -1 -7 +2447 0 1 -7 +2459 0 -1 -7 +2467 5 -1 -8 +2473 5 1 -8 +2477 0 1 -7 +2503 1 1 -7 +2521 1 -1 -7 +2531 0 -1 -7 +2539 5 -1 -8 +2543 4 -1 -8 +2549 4 1 -8 +2551 5 1 -8 +2557 5 -1 -8 +2579 4 -1 -8 +2591 4 1 -8 +2593 5 1 -8 +2609 0 1 -7 +2617 1 1 -7 +2621 2 1 -7 +2633 2 -1 -7 +2647 1 -1 -7 +2657 0 -1 -7 +2659 5 -1 -8 +2663 4 -1 -8 +2671 3 -1 -8 +2677 3 1 -8 +2683 3 -1 -8 +2687 2 -1 -8 +2689 1 -1 -8 +2693 0 -1 -8 +2699 0 1 -8 +2707 1 1 -8 +2711 2 1 -8 +2713 3 1 -8 +2719 3 -1 -8 +2729 2 -1 -8 +2731 1 -1 -8 +2741 0 -1 -8 +2749 5 -1 -9 +2753 4 -1 -9 +2767 3 -1 -9 +2777 2 -1 -9 +2789 2 1 -9 +2791 3 1 -9 +2797 3 -1 -9 +2801 2 -1 -9 +2803 1 -1 -9 +2819 0 -1 -9 +2833 5 -1 -10 +2837 4 -1 -10 +2843 4 1 -10 +2851 5 1 -10 +2857 5 -1 -10 +2861 4 -1 -10 +2879 4 1 -10 +2887 5 1 -10 +2897 0 1 -9 +2903 0 -1 -9 +2909 0 1 -9 +2917 1 1 -9 +2927 2 1 -9 +2939 2 -1 -9 +2953 1 -1 -9 +2957 0 -1 -9 +2963 0 1 -9 +2969 0 -1 -9 +2971 5 -1 -10 +2999 4 -1 -10 +3001 3 -1 -10 +3011 2 -1 -10 +3019 1 -1 -10 +3023 0 -1 -10 +3037 5 -1 -11 +3041 4 -1 -11 +3049 3 -1 -11 +3061 3 1 -11 +3067 3 -1 -11 +3079 3 1 -11 +3083 4 1 -11 +3089 4 -1 -11 +3109 3 -1 -11 +3119 2 -1 -11 +3121 1 -1 -11 +3137 0 -1 -11 +3163 5 -1 -12 +3167 4 -1 -12 +3169 3 -1 -12 +3181 3 1 -12 +3187 3 -1 -12 +3191 2 -1 -12 +3203 2 1 -12 +3209 2 -1 -12 +3217 1 -1 -12 +3221 0 -1 -12 +3229 5 -1 -13 +3251 4 -1 -13 +3253 3 -1 -13 +3257 2 -1 -13 +3259 1 -1 -13 +3271 1 1 -13 +3299 2 1 -13 +3301 3 1 -13 +3307 3 -1 -13 +3313 3 1 -13 +3319 3 -1 -13 +3323 2 -1 -13 +3329 2 1 -13 +3331 3 1 -13 +3343 3 -1 -13 +3347 2 -1 -13 +3359 2 1 -13 +3361 3 1 -13 +3371 4 1 -13 +3373 5 1 -13 +3389 0 1 -12 +3391 1 1 -12 +3407 2 1 -12 +3413 2 -1 -12 +3433 1 -1 -12 +3449 0 -1 -12 +3457 5 -1 -13 +3461 4 -1 -13 +3463 3 -1 -13 +3467 2 -1 -13 +3469 1 -1 -13 +3491 0 -1 -13 +3499 5 -1 -14 +3511 5 1 -14 +3517 5 -1 -14 +3527 4 -1 -14 +3529 3 -1 -14 +3533 2 -1 -14 +3539 2 1 -14 +3541 3 1 -14 +3547 3 -1 -14 +3557 2 -1 -14 +3559 1 -1 -14 +3571 1 1 -14 +3581 2 1 -14 +3583 3 1 -14 +3593 4 1 -14 +3607 5 1 -14 +3613 5 -1 -14 +3617 4 -1 -14 +3623 4 1 -14 +3631 5 1 -14 +3637 5 -1 -14 +3643 5 1 -14 +3659 0 1 -13 +3671 0 -1 -13 +3673 5 -1 -14 +3677 4 -1 -14 +3691 3 -1 -14 +3697 3 1 -14 +3701 4 1 -14 +3709 5 1 -14 +3719 0 1 -13 +3727 1 1 -13 +3733 1 -1 -13 +3739 1 1 -13 +3761 2 1 -13 +3767 2 -1 -13 +3769 1 -1 -13 +3779 0 -1 -13 +3793 5 -1 -14 +3797 4 -1 -14 +3803 4 1 -14 +3821 4 -1 -14 +3823 3 -1 -14 +3833 2 -1 -14 +3847 1 -1 -14 +3851 0 -1 -14 +3853 5 -1 -15 +3863 4 -1 -15 +3877 3 -1 -15 +3881 2 -1 -15 +3889 1 -1 -15 +3907 1 1 -15 +3911 2 1 -15 +3917 2 -1 -15 +3919 1 -1 -15 +3923 0 -1 -15 +3929 0 1 -15 +3931 1 1 -15 +3943 1 -1 -15 +3947 0 -1 -15 +3967 5 -1 -16 +3989 4 -1 -16 +4001 4 1 -16 +4003 5 1 -16 +4007 0 1 -15 +4013 0 -1 -15 +4019 0 1 -15 +4021 1 1 -15 +4027 1 -1 -15 +4049 0 -1 -15 +4051 5 -1 -16 +4057 5 1 -16 +4073 0 1 -15 +4079 0 -1 -15 +4091 0 1 -15 +4093 1 1 -15 +4099 1 -1 -15 +4111 1 1 -15 +4127 2 1 -15 +4129 3 1 -15 +4133 4 1 -15 +4139 4 -1 -15 +4153 3 -1 -15 +4157 2 -1 -15 +4159 1 -1 -15 +4177 1 1 -15 +4201 1 -1 -15 +4211 0 -1 -15 +4217 0 1 -15 +4219 1 1 -15 +4229 2 1 -15 +4231 3 1 -15 +4241 4 1 -15 +4243 5 1 -15 +4253 0 1 -14 +4259 0 -1 -14 +4261 5 -1 -15 +4271 4 -1 -15 +4273 3 -1 -15 +4283 2 -1 -15 +4289 2 1 -15 +4297 3 1 -15 +4327 3 -1 -15 +4337 2 -1 -15 +4339 1 -1 -15 +4349 0 -1 -15 +4357 5 -1 -16 +4363 5 1 -16 +4373 0 1 -15 +4391 0 -1 -15 +4397 0 1 -15 +4409 0 -1 -15 +4421 0 1 -15 +4423 1 1 -15 +4441 1 -1 -15 +4447 1 1 -15 +4451 2 1 -15 +4457 2 -1 -15 +4463 2 1 -15 +4481 2 -1 -15 +4483 1 -1 -15 +4493 0 -1 -15 +4507 5 -1 -16 +4513 5 1 -16 +4517 0 1 -15 +4519 1 1 -15 +4523 2 1 -15 +4547 2 -1 -15 +4549 1 -1 -15 +4561 1 1 -15 +4567 1 -1 -15 +4583 0 -1 -15 +4591 5 -1 -16 +4597 5 1 -16 +4603 5 -1 -16 +4621 5 1 -16 +4637 0 1 -15 +4639 1 1 -15 +4643 2 1 -15 +4649 2 -1 -15 +4651 1 -1 -15 +4657 1 1 -15 +4663 1 -1 -15 +4673 0 -1 -15 +4679 0 1 -15 +4691 0 -1 -15 +4703 0 1 -15 +4721 0 -1 -15 +4723 5 -1 -16 +4729 5 1 -16 +4733 0 1 -15 +4751 0 -1 -15 +4759 5 -1 -16 +4783 5 1 -16 +4787 0 1 -15 +4789 1 1 -15 +4793 2 1 -15 +4799 2 -1 -15 +4801 1 -1 -15 +4813 1 1 -15 +4817 2 1 -15 +4831 3 1 -15 +4861 3 -1 -15 +4871 2 -1 -15 +4877 2 1 -15 +4889 2 -1 -15 +4903 1 -1 -15 +4909 1 1 -15 +4919 2 1 -15 +4931 2 -1 -15 +4933 1 -1 -15 +4937 0 -1 -15 +4943 0 1 -15 +4951 1 1 -15 +4957 1 -1 -15 +4967 0 -1 -15 +4969 5 -1 -16 +4973 4 -1 -16 +4987 3 -1 -16 +4993 3 1 -16 +4999 3 -1 -16 +5003 2 -1 -16 +5009 2 1 -16 +5011 3 1 -16 +5021 4 1 -16 +5023 5 1 -16 +5039 0 1 -15 +5051 0 -1 -15 +5059 5 -1 -16 +5077 5 1 -16 +5081 0 1 -15 +5087 0 -1 -15 +5099 0 1 -15 +5101 1 1 -15 +5107 1 -1 -15 +5113 1 1 -15 +5119 1 -1 -15 +5147 0 -1 -15 +5153 0 1 -15 +5167 1 1 -15 +5171 2 1 -15 +5179 3 1 -15 +5189 4 1 -15 +5197 5 1 -15 +5209 5 -1 -15 +5227 5 1 -15 +5231 0 1 -14 +5233 1 1 -14 +5237 2 1 -14 +5261 2 -1 -14 +5273 2 1 -14 +5279 2 -1 -14 +5281 1 -1 -14 +5297 0 -1 -14 +5303 0 1 -14 +5309 0 -1 -14 +5323 5 -1 -15 +5333 4 -1 -15 +5347 3 -1 -15 +5351 2 -1 -15 +5381 2 1 -15 +5387 2 -1 -15 +5393 2 1 -15 +5399 2 -1 -15 +5407 1 -1 -15 +5413 1 1 -15 +5417 2 1 -15 +5419 3 1 -15 +5431 3 -1 -15 +5437 3 1 -15 +5441 4 1 -15 +5443 5 1 -15 +5449 5 -1 -15 +5471 4 -1 -15 +5477 4 1 -15 +5479 5 1 -15 +5483 0 1 -14 +5501 0 -1 -14 +5503 5 -1 -15 +5507 4 -1 -15 +5519 4 1 -15 +5521 5 1 -15 +5527 5 -1 -15 +5531 4 -1 -15 +5557 3 -1 -15 +5563 3 1 -15 +5569 3 -1 -15 +5573 2 -1 -15 +5581 1 -1 -15 +5591 0 -1 -15 +5623 5 -1 -16 +5639 4 -1 -16 +5641 3 -1 -16 +5647 3 1 -16 +5651 4 1 -16 +5653 5 1 -16 +5657 0 1 -15 +5659 1 1 -15 +5669 2 1 -15 +5683 3 1 -15 +5689 3 -1 -15 +5693 2 -1 -15 +5701 1 -1 -15 +5711 0 -1 -15 +5717 0 1 -15 +5737 1 1 -15 +5741 2 1 -15 +5743 3 1 -15 +5749 3 -1 -15 +5779 3 1 -15 +5783 4 1 -15 +5791 5 1 -15 +5801 0 1 -14 +5807 0 -1 -14 +5813 0 1 -14 +5821 1 1 -14 +5827 1 -1 -14 +5839 1 1 -14 +5843 2 1 -14 +5849 2 -1 -14 +5851 1 -1 -14 +5857 1 1 -14 +5861 2 1 -14 +5867 2 -1 -14 +5869 1 -1 -14 +5879 0 -1 -14 +5881 5 -1 -15 +5897 4 -1 -15 +5903 4 1 -15 +5923 5 1 -15 +5927 0 1 -14 +5939 0 -1 -14 +5953 5 -1 -15 +5981 4 -1 -15 +5987 4 1 -15 +6007 5 1 -15 +6011 0 1 -14 +6029 0 -1 -14 +6037 5 -1 -15 +6043 5 1 -15 +6047 0 1 -14 +6053 0 -1 -14 +6067 5 -1 -15 +6073 5 1 -15 +6079 5 -1 -15 +6089 4 -1 -15 +6091 3 -1 -15 +6101 2 -1 -15 +6113 2 1 -15 +6121 3 1 -15 +6131 4 1 -15 +6133 5 1 -15 +6143 0 1 -14 +6151 1 1 -14 +6163 1 -1 -14 +6173 0 -1 -14 +6197 0 1 -14 +6199 1 1 -14 +6203 2 1 -14 +6211 3 1 -14 +6217 3 -1 -14 +6221 2 -1 -14 +6229 1 -1 -14 +6247 1 1 -14 +6257 2 1 -14 +6263 2 -1 -14 +6269 2 1 -14 +6271 3 1 -14 +6277 3 -1 -14 +6287 2 -1 -14 +6299 2 1 -14 +6301 3 1 -14 +6311 4 1 -14 +6317 4 -1 -14 +6323 4 1 -14 +6329 4 -1 -14 +6337 3 -1 -14 +6343 3 1 -14 +6353 4 1 -14 +6359 4 -1 -14 +6361 3 -1 -14 +6367 3 1 -14 +6373 3 -1 -14 +6379 3 1 -14 +6389 4 1 -14 +6397 5 1 -14 +6421 5 -1 -14 +6427 5 1 -14 +6449 0 1 -13 +6451 1 1 -13 +6469 1 -1 -13 +6473 0 -1 -13 +6481 5 -1 -14 +6491 4 -1 -14 +6521 4 1 -14 +6529 5 1 -14 +6547 5 -1 -14 +6551 4 -1 -14 +6553 3 -1 -14 +6563 2 -1 -14 +6569 2 1 -14 +6571 3 1 -14 +6577 3 -1 -14 +6581 2 -1 -14 +6599 2 1 -14 +6607 3 1 -14 +6619 3 -1 -14 +6637 3 1 -14 +6653 4 1 -14 +6659 4 -1 -14 +6661 3 -1 -14 +6673 3 1 -14 +6679 3 -1 -14 +6689 2 -1 -14 +6691 1 -1 -14 +6701 0 -1 -14 +6703 5 -1 -15 +6709 5 1 -15 +6719 0 1 -14 +6733 1 1 -14 +6737 2 1 -14 +6761 2 -1 -14 +6763 1 -1 -14 +6779 0 -1 -14 +6781 5 -1 -15 +6791 4 -1 -15 +6793 3 -1 -15 +6803 2 -1 -15 +6823 1 -1 -15 +6827 0 -1 -15 +6829 5 -1 -16 +6833 4 -1 -16 +6841 3 -1 -16 +6857 2 -1 -16 +6863 2 1 -16 +6869 2 -1 -16 +6871 1 -1 -16 +6883 1 1 -16 +6899 2 1 -16 +6907 3 1 -16 +6911 4 1 -16 +6917 4 -1 -16 +6947 4 1 -16 +6949 5 1 -16 +6959 0 1 -15 +6961 1 1 -15 +6967 1 -1 -15 +6971 0 -1 -15 +6977 0 1 -15 +6983 0 -1 -15 +6991 5 -1 -16 +6997 5 1 -16 +7001 0 1 -15 +7013 0 -1 -15 +7019 0 1 -15 +7027 1 1 -15 +7039 1 -1 -15 +7043 0 -1 -15 +7057 5 -1 -16 +7069 5 1 -16 +7079 0 1 -15 +7103 0 -1 -15 +7109 0 1 -15 +7121 0 -1 -15 +7127 0 1 -15 +7129 1 1 -15 +7151 2 1 -15 +7159 3 1 -15 +7177 3 -1 -15 +7187 2 -1 -15 +7193 2 1 -15 +7207 3 1 -15 +7211 4 1 -15 +7213 5 1 -15 +7219 5 -1 -15 +7229 4 -1 -15 +7237 3 -1 -15 +7243 3 1 -15 +7247 4 1 -15 +7253 4 -1 -15 +7283 4 1 -15 +7297 5 1 -15 +7307 0 1 -14 +7309 1 1 -14 +7321 1 -1 -14 +7331 0 -1 -14 +7333 5 -1 -15 +7349 4 -1 -15 +7351 3 -1 -15 +7369 3 1 -15 +7393 3 -1 -15 +7411 3 1 -15 +7417 3 -1 -15 +7433 2 -1 -15 +7451 2 1 -15 +7457 2 -1 -15 +7459 1 -1 -15 +7477 1 1 -15 +7481 2 1 -15 +7487 2 -1 -15 +7489 1 -1 -15 +7499 0 -1 -15 +7507 5 -1 -16 +7517 4 -1 -16 +7523 4 1 -16 +7529 4 -1 -16 +7537 3 -1 -16 +7541 2 -1 -16 +7547 2 1 -16 +7549 3 1 -16 +7559 4 1 -16 +7561 5 1 -16 +7573 5 -1 -16 +7577 4 -1 -16 +7583 4 1 -16 +7589 4 -1 -16 +7591 3 -1 -16 +7603 3 1 -16 +7607 4 1 -16 +7621 5 1 -16 +7639 5 -1 -16 +7643 4 -1 -16 +7649 4 1 -16 +7669 5 1 -16 +7673 0 1 -15 +7681 1 1 -15 +7687 1 -1 -15 +7691 0 -1 -15 +7699 5 -1 -16 +7703 4 -1 -16 +7717 3 -1 -16 +7723 3 1 -16 +7727 4 1 -16 +7741 5 1 -16 +7753 5 -1 -16 +7757 4 -1 -16 +7759 3 -1 -16 +7789 3 1 -16 +7793 4 1 -16 +7817 4 -1 -16 +7823 4 1 -16 +7829 4 -1 -16 +7841 4 1 -16 +7853 4 -1 -16 +7867 3 -1 -16 +7873 3 1 -16 +7877 4 1 -16 +7879 5 1 -16 +7883 0 1 -15 +7901 0 -1 -15 +7907 0 1 -15 +7919 0 -1 -15 +7927 5 -1 -16 diff --git a/exponentiation/span18/spin_1.txt b/exponentiation/span18/spin_1.txt new file mode 100644 index 00000000000..bd007e8a659 --- /dev/null +++ b/exponentiation/span18/spin_1.txt @@ -0,0 +1,10 @@ +0 0 0 0 +1 0 0 0 +2 0 1 0 +3 1 1 0 +5 2 1 0 +7 3 1 0 +11 4 1 0 +13 5 1 0 +17 0 1 1 +19 1 1 1 diff --git a/exponentiation/span18/spin_2.txt b/exponentiation/span18/spin_2.txt new file mode 100644 index 00000000000..8d1f1b472c4 --- /dev/null +++ b/exponentiation/span18/spin_2.txt @@ -0,0 +1,30 @@ +23 2 1 1 +29 2 -1 1 +31 1 -1 1 +37 1 1 1 +41 2 1 1 +43 3 1 1 +47 4 1 1 +53 4 -1 1 +59 4 1 1 +61 5 1 1 +67 5 -1 1 +71 4 -1 1 +73 3 -1 1 +79 3 1 1 +83 4 1 1 +89 4 -1 1 +97 3 -1 1 +101 2 -1 1 +103 1 -1 1 +107 0 -1 1 +109 5 -1 0 +113 4 -1 0 +127 3 -1 0 +131 2 -1 0 +137 2 1 0 +139 3 1 0 +149 4 1 0 +151 5 1 0 +157 5 -1 0 +163 5 1 0 diff --git a/exponentiation/span18/spin_3.txt b/exponentiation/span18/spin_3.txt new file mode 100644 index 00000000000..5f8960301f0 --- /dev/null +++ b/exponentiation/span18/spin_3.txt @@ -0,0 +1,60 @@ +167 0 1 1 +173 0 -1 1 +179 0 1 1 +181 1 1 1 +191 2 1 1 +193 3 1 1 +197 4 1 1 +199 5 1 1 +211 5 -1 1 +223 5 1 1 +227 0 1 2 +229 1 1 2 +233 2 1 2 +239 2 -1 2 +241 1 -1 2 +251 0 -1 2 +257 0 1 2 +263 0 -1 2 +269 0 1 2 +271 1 1 2 +277 1 -1 2 +281 0 -1 2 +283 5 -1 1 +293 4 -1 1 +307 3 -1 1 +311 2 -1 1 +313 1 -1 1 +317 0 -1 1 +331 5 -1 0 +337 5 1 0 +347 0 1 1 +349 1 1 1 +353 2 1 1 +359 2 -1 1 +367 1 -1 1 +373 1 1 1 +379 1 -1 1 +383 0 -1 1 +389 0 1 1 +397 1 1 1 +401 2 1 1 +409 3 1 1 +419 4 1 1 +421 5 1 1 +431 0 1 2 +433 1 1 2 +439 1 -1 2 +443 0 -1 2 +449 0 1 2 +457 1 1 2 +461 2 1 2 +463 3 1 2 +467 4 1 2 +479 4 -1 2 +487 3 -1 2 +491 2 -1 2 +499 1 -1 2 +503 0 -1 2 +509 0 1 2 +521 0 -1 2 diff --git a/exponentiation/span18/spin_4.txt b/exponentiation/span18/spin_4.txt new file mode 100644 index 00000000000..153f4bd7ce4 --- /dev/null +++ b/exponentiation/span18/spin_4.txt @@ -0,0 +1,70 @@ +523 5 -1 1 +541 5 1 1 +547 5 -1 1 +557 4 -1 1 +563 4 1 1 +569 4 -1 1 +571 3 -1 1 +577 3 1 1 +587 4 1 1 +593 4 -1 1 +599 4 1 1 +601 5 1 1 +607 5 -1 1 +613 5 1 1 +617 0 1 2 +619 1 1 2 +631 1 -1 2 +641 0 -1 2 +643 5 -1 1 +647 4 -1 1 +653 4 1 1 +659 4 -1 1 +661 3 -1 1 +673 3 1 1 +677 4 1 1 +683 4 -1 1 +691 3 -1 1 +701 2 -1 1 +709 1 -1 1 +719 0 -1 1 +727 5 -1 0 +733 5 1 0 +739 5 -1 0 +743 4 -1 0 +751 3 -1 0 +757 3 1 0 +761 4 1 0 +769 5 1 0 +773 0 1 1 +787 1 1 1 +797 2 1 1 +809 2 -1 1 +811 1 -1 1 +821 0 -1 1 +823 5 -1 0 +827 4 -1 0 +829 3 -1 0 +839 2 -1 0 +853 1 -1 0 +857 0 -1 0 +859 5 -1 -1 +863 4 -1 -1 +877 3 -1 -1 +881 2 -1 -1 +883 1 -1 -1 +887 0 -1 -1 +907 5 -1 -2 +911 4 -1 -2 +919 3 -1 -2 +929 2 -1 -2 +937 1 -1 -2 +941 0 -1 -2 +947 0 1 -2 +953 0 -1 -2 +967 5 -1 -3 +971 4 -1 -3 +977 4 1 -3 +983 4 -1 -3 +991 3 -1 -3 +997 3 1 -3 diff --git a/exponentiation/span18/spin_5.liquid b/exponentiation/span18/spin_5.liquid new file mode 100644 index 00000000000..9c329cb6e97 --- /dev/null +++ b/exponentiation/span18/spin_5.liquid @@ -0,0 +1,6 @@ +{% assign test1="virtual/file68.md" %} +{% assign test2="virtual/file50.md" %} + +{% include {{ test1 }} all=true %} +{% include {{ test2 }} all=true %} + diff --git a/identition/index.html b/identition/index.html new file mode 100644 index 00000000000..e5b0ff92516 --- /dev/null +++ b/identition/index.html @@ -0,0 +1,343 @@ + Identition Zones (36-102) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Identition Zones (36-102)

            Identition is defined for a complex operation by extending one of the definitions of the exponential function from real exponents to complex exponents.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-27 of main section-5 that is inherited from the spin section-3 by prime spin-36 and span-167 with the partitions as below.

            +
            +
            1. Theory of Everything (span 12)
            2. Everything is Connected (span 11)
            3. Truncated Perturbation (span 10)
            4. Quadratic Polynomials (span 9)
            5. Fundamental Forces (span 8)
            6. Elementary Particles (span 7)
            7. Basic Transformation (span 6)
            8. Hidden Dimensions (span 5)
            9. Parallel Universes (span 4)
            10. Vibrating Strings (span 3)
            11. Series Expansion (span 2)
            12. Wormhole Theory (span 1)

            This identition zones stands as one of the solution to deal with the residual primes that is occured in the exponentation zones to become compactifiable within the base unit.

            Basic Concept

            A general mass structure for the heavy SM fermion generations has been obtained which explains the following features of SO(10):

            +
            + + Note +
            +
            +

            The work performed in this thesis will focus on two different models, that both can be used in the creation of a GUT. Both models are based on having SO(10) as the unification gauge group.

            • Such models are more complex than the original suggestions, but can also accommodate more physics. In these two models, it is not possible to achieve unification among the gauge couplings with tree-level matching conditions.
            • However, so-called threshold effects appear when matching the couplings at a higher order in perturbation theory, which are a result of particles with masses around the symmetry breaking scales.

            Specifically, it will be investigated if threshold effects can save these two models, and thereby allowing unification. (Threshold Effects in SO(10) Grand Unified Theories - pdf)

            +
            +

            Grand Unification

            A precise measurement of the rate of the H→ bb process directly tests the Yukawa coupling of the Higgs boson to a down-type quark.

            +
            + + Note +
            +
            +

            Recently, the CMS and ATLAS Collaborations reported observations of the Higgs boson produced in association with a top quark pair thus representing the first direct measurements of the Higgs boson coupling to quarks. - This week the CMS Collaboration announces another major achievement and reports the observation of Higgs boson decay to bottom quarks (H→ bb)

            • A precise measurement of the rate of the H→ bb process directly tests the Yukawa coupling of the Higgs boson to a down-type quark, and is necessary to solidify the Higgs boson as the possible sole source of mass generation in the fermion sector of the Standard Model (SM).
            • While the decay of the Higgs boson to bottom quarks is the most frequent of all Higgs boson decays, it has been a real experimental challenge to observe it. This is on account of the overwhelmingly large background contribution from a number of other SM processes that can mimic its experimental signature characterized by the appearance of a bottom and an anti-bottom quark.

            The CMS Collaboration overcame this challenge by deploying modern sophisticated analysis tools and by focusing on particular signatures where a Higgs boson is produced in association with a vector boson V (a W or Z particle), a weak interaction process known as VH(bb), shown in the figure below, leading to a significant reduction in the background. (CERN)

            +
            +

            down-type quark

            In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

            +
            + + Warning +
            +
            +

            The concept of eleven dimensions is a theoretical one in physics and cosmology, specifically in the realm of string theory and M-theory.

            • These theories propose that our observable universe is made up of 11 dimensions, rather than the traditional three dimensions of length, width, and height, and the fourth dimension of time.
            • The additional dimensions are thought to be compactified or curled up, meaning that they are not directly observable by us in our everyday experience.
            • As for the cosmic philosophy, it is important to note that these theories are still considered speculative and have not been proven through experimental evidence.
            • However, they do offer a new perspective on the nature of our universe and the fundamental forces that govern it.
            • Some scientists and philosophers argue that these theories may provide new insights into the origins of the universe and the nature of reality itself.

            Ultimately, the concept of eleven dimensions is a fascinating area of study that continues to inspire new research and discoveries in the field of physics and cosmology. (ChatGPT)

            +
            +

            M-theory

            Our physical space is observed to have only three large dimensions and taken together with time as the fourth dimension, a physical theory must take this into account.

            +
            + + Danger +
            +
            +

            It is argued, among other things, that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring, and that a recently conjectured duality between the heterotic string and Type IIA superstrings controls the strong coupling dynamics of the heterotic string in five, six, and seven dimensions and implies S-duality for both heterotic and Type II strings. (String Theory - Pdf)

            +
            +

            time evolution

            String theory, superstring theory, or M-theory, or some other variant on this theme is one of the Unsolved Problem in physic as a step road to a Theory Of Everything (TOE).

            +
            + + Note +
            +
            +

            Nothing prevents a theory from including more than 4 dimensions. In the case of string theory, consistency requires spacetime to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compactified. (Astrophysics Research)

            +
            +

            superstring theory

            The string theory is sofar the leading candidate to the TOE however it is said that the theory may be incompatible with dark energy.

            +
            + + Danger +
            +
            +

            It is argued that the generic formulation of string theory leads naturally to dark energy, represented by a positive cosmological constant to lowest order and the intrinsic stringy non-commutativity is the new crucial ingredient responsible for its radiative stability. (Physic Letters)

            +
            +

            string theory and dark energy

            The finiteness position of MEC30 along with Euler's identity opens up the possibility of accurately representing the self-singularity of True Prime Pairs.

            +
            + + Note +
            +
            +

            The Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. (Google Patent DE102011101032A9)

            +
            +

            Spinning the MEC30

            By taking the correlation of these 11 partitions with the logical sequence of numbers there would be a series expansion.

            Visualizing TOE

            Assigning a specific mass, length, time, and charge metrics based on new dimensional relationships and the Planck constant (which defines Higgs mass).

            +
            + + Note +
            +
            +

            All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold. (An Exceptionally Simple Theory of Everything - pdf)

            +
            +

            A-periodic-table-of-E8

            We discuss the phenomenology of doubly and singly charged Higgs bosons (of SU(2) L-triplet fields) in the simplest A 4-symmetric version of the Higgs Triplet Model.

            +
            + + Note +
            +
            +

            In this article, we investigated the phenomenology of triplet Higgs bosons in the simplest A4-symmetric version of the Higgs Triplet Model (A4HTM). The A4HTM is a four-Higgs- Triplet-Model (δ of 1 and (∆x, ∆y, ∆z) of 3).

            • Four mass eigenstates of doubly charged Higgs bosons, H±±i, are obtained explicitly from the Higgs potential.
            • We also obtained four mass eigenstates of the triplet-like singly charged Higgs bosons, H±T i, for which doublet components can be ignored because of small triplet vev’s.
            • It was shown that the A4HTM gives unique predictions about their decay branching ratios into two leptons (H−−i → ℓℓ′ and H−iT → ℓν); for example, the leptonic decays of H−−2 are only into µµ and eτ because an approximate Z3 symmetry remains, and the ratio of the branching ratios is 2 : 1 as a consequence of the A4 symmetry in the original Lagrangian.
            • Therefore, it will be possible to test the model at hadron colliders (Tevatron and LHC) if some of these Higgs bosons are light enough to be produced.
            • Even if these Higgs bosons are too heavy to be produced at hadron colliders, they can affect the lepton flavor violating decays of charged leptons if the triplet Yukawa coupling constants are large enough.
            • It was shown that there is no contribution of these Higgs bosonsto µ → eee ¯ and ℓ → ℓ′γ.
            • Thus, we can naturally expect signals of τ → µee and τ → eµµ(which are possible in this model among six τ → ℓℓ′ℓ′′) in the future in collider experiments (Super-KEKB, super B factory, super flavor factory, and LHCb) without interfering with a stringent experimental bound on µ → eee ¯ . This model will be excluded if ℓ → ℓ ′γ is observed.

            We considered current experimental constraints on the model and prospects of the measurement of the non-standard neutrino interactions (NSI) in the neutrino factory. If H±±2 or H±±3 is lighter enough than other H±±i, effects of the NSI can be around the expected sensitivity in the neutrino factory. (Triplet Higgs bosons - pdf)

            +
            +

            how-we-can-constrain-various-higgs-sectors1-l

            This approach shows that there are actually four copies of the tri-rectified Coxeter-Dynkin diagram of H4, promises to open the door to as yet unexplored E8-based GUTs.

            +
            + + Note +
            +
            +

            There are 28 octonion Fano plane triangles that correspond directly to the 28 Trott quartic curve bitangents.

            • These bitangents are directly related to the Legendre functions used in the Shroedinger spherical harmonic electron orbital probability densities.
            • Shown below is a graphic of these overlaid onto the n=5, l=2, m=1 element, which is assigned to gold (Au).
            • When using an algorithm based on the E8 positive algebra root assignments, the “flipped” Fano plane has E8 algebra root number 79 (the atomic number of Au) and split real even group number of 228 (in Clifford/Pascal triangle order).FanoLegendre
            • This matrix is shown to be useful in providing direct relationships between E8 and the lower dimensional Dynkin and Coxeter-Dynkin geometries contained within it, geometries that are visualized in the form of real and virtual 3 dimensional objects.
            • A direct linkage between E8, the folding matrix, fundamental physics particles in an extended Standard Model Gravi GUT, quaternions, and octonions is introduced, and its importance is investigated and described.
            • E8 and its 4D children, the 600-cell and 120-cell (pages on which I have some work, amongst others) and its grandkids (2 of the 3D 5 Platonic Solids, one of which is the 3D version of the 2D Pentagon) are all related to the Fibonacci numbers and the Golden Ratio.
            • And finally, the {7, 8} dimensions in physics can be identified with quark color, as {7} preserves the blue quark positions, while {8} moves the dual concentric rings of quarks while preserving their relative positions within the rings. It is interesting t note that the dimensions {6, 7, 8} are appropriately labeled {r, g, b} in SRE coordinates, since in this projection the SRE math coordinates are located at the afforementioned 6 triple overlap points at center of the quark’s {r, g, ¯ g, b, ¯ ¯b} concentric rings (the intersection of the gluons triality lines)6 triple overlap points

            So that kind of explains why most of my 2D art, 3D objects and sculptures (e.g. furniture like the dodecahedron table below), and 4D youtube animations all use the Golden Ratio theme. (E8 to H4 folding matrix - pdf)

            +
            +

            28+Octonion

            The number 28, aside from being triangular wave of perfect pyramid, is the sum of the first 5 primes and the sum of the first 7 natural numbers.

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                         MEC30/2
+------+------+-----+-----+------      ‹--------------- 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = 71-43 ✔️
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+ ‹--- vacuum energy ‹--- ∆60 ‹--- 15 {zero axis}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹-------------------- 30 {+1/2}
+

            The split real even E8 group used has been determined from Dynkin diagram which builds the Cartan matrix and determines the root with corresponding Hasse diagrams.

            +
            + + Note +
            +
            +

            It has been found recently that the expansion of N = 8 supergravity in terms of Feynman diagrams has shown that N = 8 supergravity is in some ways [1] a product of two N = 4 super Yang–Mills theories.

            • This is written schematically as: N = 8 supergravity = (N = 4 super Yang–Mills) × (N = 4 super Yang–Mills). This is not surprising, as N = 8 supergravity contains six independent representations of N = 4 super Yang–Mills.
            • The theory contains 1 graviton (spin 2), 8 gravitinos (spin 3/2), 28 vector bosons (spin 1), 56 fermions (spin 1/2), 70 scalar fields (spin 0) where we don’t distinguish particles with negative spin.
            • These numbers are simple combinatorial numbers that come from Pascal’s Triangle and also the number of ways of writing n as a sum of 8 nonnegative cubes A173681.
            • The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories). Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything.ToEsummary1
            • One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the orthogonal group O(10).

            For model building, it has been assumed that almost all the supersymmetries would be broken in nature,[why?] leaving just one supersymmetry (N = 1), although nowadays because of the lack of evidence for N = 1 supersymmetry higher supersymmetries are now being considered such as N = 2. (Wikipedia)

            +
            +

            Pascal Octonion

            The Golden Ratio "symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage."

            +
            + + Note +
            +
            +

            There is a fascinating connection between prime numbers and the Golden ratio. The Golden ratio is an irrational number, which means that it cannot be expressed as a ratio of two integers. However, it can be approximated by dividing consecutive Fibonacci numbers.

            • Additionally, it has been observed that the frequency of prime numbers in certain sequences related to the Golden ratio (such as the continued fraction expansion of the Golden ratio) appears to be higher than in other sequences.
            • Interestingly, the Fibonacci sequence is closely related to prime numbers, as any two consecutive Fibonacci numbers are always coprime. However, the exact nature of the relationship between primes and the Golden ratio is still an active area of research.phi-continued-fraction
            • There are set of sequence known as Fibonacci retracement. For unknown reasons, these Fibonacci ratios seem to play a role in the stock market, just as they do in nature.
            • The mathematically significant Fibonacci sequence defines a set of ratios known as Fibonacci retracements which can be used to determine probable entry and exit points for the equities when paired with additional momentum.
            • The Fibonacci retracement levels are 0.236, 0.382, 0.618, and 0.786.Fibonacci retracement
              • The key Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it. For example, 21 divided by 34 equals 0.6176, and 55 divided by 89 equals about 0.61798.
              • The 38.2% ratio is discovered by dividing a number in the series by the number located two spots to the right. For instance, 55 divided by 144 equals approximately 0.38194.
              • The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example, 8 divided by 34 equals about 0.23529.
              • The 78.6% level is given by the square root of 61.8%, while not officially a Fibonacci ratio, 0.5 is also commonly referenced (50% is derived not from the Fibonacci sequence but rather from the idea that on average stocks retrace half their earlier movements).

            They are used to determine critical points where an asset’s momentum is likely to reverse. This study cascade culminating in the Fibonacci digital root sequence (also period-24). (Golden Ratio - Articles)

            +
            +

            (√0.618 - 0.618) x 1000 = (0.786 - 0.618) x 1000 = 0.168 x 1000 = 168 = π(1000)

            24-digital root

            The simplest group is SU(5), which we will consider here, other examples include SO(10). SU(5) has 5²−1 = 24 generators which means there are 24 gauge bosons.

            +
            + + Note +
            +
            +

            It is known that the recently reported shift of **the W boson mass can be easily explained by an SU(2)L triplet Higgs boson”” with a zero hypercharge if it obtains a vacuum expectation value (VEV) of O(1) GeV.

            • Surprisingly, the addition of a TeV scale complex triplet Higgs boson to the standard model (SM) leads to a precise unification of the gauge couplings at around 10¹⁴GeV.
            • We consider that it is a consequence of SU(5) grand unification and show a possible potential for the Higgs fields yielding a weak scale complex SU(2) triplet scalar boson.
            • Although it seems the proton decay constraint would doom such a low-scale unification, we show that the constraint can be avoided by introducing vector-like fermions which mix with the SM fermions through mass terms involving the VEV of GUT breaking Higgs field.

            Importantly, the simplest viable model only requires the addition of one pair of vector-like fermions transforming 10 and 10. (W boson mass anomaly and grand unification - pdf)

            +
            +

            168 + 329 + 289 - 619 - 30 - 30 - 5 = 786 - 619 - 65 = 102

            W Mass Shift

            Since SU(5) has 24 generators, SU(5) GUTs have 12 new gauge bosons known as Xbosons (or X/Y bosons) in addition to the SM.

            +
            + + Note +
            +
            +

            The particle spectrum is completed by the Higgs particles required to give masses to fermions as wellas to break the GUT symmetry.

            • Georgi and Glashow have chosen the SU(5) where a single gauge coupling constant is manifestly incorporated.
            • As has been discussed in the introduction, the SM gauge group has a rank four and the simple groups which contain complex representations of rank four are just SU(3) × SU(3) and SU(5).
            • Further, the fermions of the Standard Model can be arranged in terms of the fundamental ¯5 and the anti-symmetric 10 representation of the SU(5) [30].
            • To begin with, let us study the fermion masses in the prototype SU(5).Given that fermions are in 5 and 10 representations
            • We conclude that the scalars that form Yukawa couplings are:IMG_20240310_205245
            • It is easy to check that this combination of the representations is anomaly free. The gauge theory of SU(5) contains 24 gauge bosons.2-Table1-1
            • They are decomposed in terms of the standard model gauge group SU(3) × SU(2) × U(1) as: 24 = (8, 1) + (1, 3) + (1, 1) + (3, 2) + (¯3, 2) (10)
            • The first component represents the gluon fields (G) mediating the colour, the second one corresponds to the Standard Model SU(2) mediators (W) and the third component corresponds to the U(1) mediator (B).
            • The fourth and fifth components carry both colour as well as the SU(2) indices and are called the X and gauge bosons. Schematically, the gauge bosons can be represented in terms of the 5 × 5 matrix:IMG_20240310_204627

            Notice that in this case the couplings of the triplets to the fermions is not related to the fermion massesas the Higgs triplets are now a mixing between the triplets in the 5H and the triplets in the 50. Thereforewe have some unknown Yukawa coupling Y50. (Flavour Physics and Grand Unification - pdf)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                         MEC30/2
+------+------+-----+-----+------      ‹--------------- 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+ ‹--- vacuum energy ‹--- ∆60 ‹--- 15 {zero axis}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = 43-19 ✔️
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹-------------------- 30 {+1/2}
+

            Series Expansion

            Beyond leading approx. we define mGUT as the mass of the heavy 24 gauge bosons, while mT = mHT is the mass of the triplet Higgs.

            +
            + + Note +
            +
            +

            The matter representations come in three copies (generations) of the 16 representation. The Yukawa coupling is 10H 16f 16f. *This includes a right-handed neutrino”. One may either include three copies of singlet representations φ and a Yukawa coupling (the “double seesaw mechanism”); or else, add the Yukawa interaction or add the nonrenormalizable coupling. (Wikipedia)

            +
            +

            24 matriks

            The cleanest signature for a Higgs sector with triplet fields would be the discovery of doubly charged Higgs Bosons.

            +
            + + Note +
            +
            +

            Like Pauli’s bold prediction of the neutrino and GIM’s bold prediction of the charm quark, the equally bold speculation of Kobayashi and Maskawa was proved absolutely correct, when the fermions of the third generation began to be discovered one by one. First came the tau lepton in 1975, closely followed by the bottom quark in 1977. There followed a 17-year hiatus till the 1994 discovery of the top quark, and another 6 years wait till the existence of the tau neutrino νwas confirmed in 2000.

            +
            +

            12648_2023_2718_Figa_HTML

            This thesis constitutes a first attempt to derive aspects of standard model particle physics from little more than an algebra.

            +
            + + Note +
            +
            +

            Here, we argue that physical concepts such as particles, causality, and irreversible time may result from the algebra acting on itself.

            • We then focus on a special case by considering the algebra R ⊗ C ⊗ H ⊗ O, the tensor product of the only four normed division algebras over the real numbers.
            • Using nothing more than R ⊗ C ⊗ H ⊗ O acting on itself, we set out to find standard model particle representations: a task which occupies the remainder of this text.
            • From the C ⊗ H portion of the algebra, we find generalized ideals, and show that they describe concisely all of the Lorentz representations of the standard model.
            • From just the C ⊗ O portion of the algebra, we find minimal left ideals, and show that they mirror the behaviour of a generation of quarks and leptons under su(3)c and u(1)em.
            • These unbroken symmetries, su(3)c and u(1)em, appear uniquely in this model as particular symmetries of the algebra’s ladder operators. Electric charge, here, is seen to be simply a number operator for the system.
            • We then combine the C ⊗ H and C ⊗ O portions of R ⊗ C ⊗ H ⊗ O, and focus on a leptonic subspace, so as to demonstrate a rudimentary electroweak model. Here, the underlying ladder operators are found to have a symmetry generated uniquely by su(2)L and u(1)Y.
            • Furthermore, we find that this model yields a straight forward explanation as to why SU(2)L acts only on left-handed states.
            • We then make progress towards a three-generation model. The action of C ⊗ O on itself can be seen to generate a 64-complex-dimensional algebra, wherein we are able to identify two sets of generators for SU(3)c.
            • We apply these generators to the rest of the space, and find that it breaks down into the SU(3)c representations of exactly three generations of quarks and leptons.

            Furthermore, we show that these three-generation results can be extended, so as to include all 48 fermionic U(1)em charges. (Standard Model from an algebra - pdf)

            +
            +

            The-64-dimensional-octonionic-chain-algebra-splits-into-two-sets-of-SU-3-generators

            Is the fermion red? green? blue? Does the fermion have isospin up? down? These five questions can be represented by an exterior algebra of 2⁵ or 32-complex dimensional.

            There are thought to be 24 separate quantum fields that permit the universe. It consists of 12 various fundamental forces including mass, 9 quarks, and 3 leptons.

            +
            + + Note +
            +
            +

            String Theory which states there could be 11 dimensions (9 dimensions of space, 1 dimension of time, and 1 dimension for other universes) - the diagram below can sum it up for the 9 dimensions of space. Then the Cosmos would be the 11th dimension where (+/-) Binary Universes are born from Nothingness. Where Nothingness = 0 = (+) universe of regular matter and (-) universe of dark matter. (Quora)

            +
            +

            11 dimensions

            Remember we must sum over all the quantum numbers of the quarks so the cross section is multiplied by Number of colours, Nc.

            +
            + + Note +
            +
            +

            Finally NG′ is the number of parameters of the group G′, the subgroup of G still unbroken by the flavour matrices.

            • In this case, G′ corresponds to two U(1) symmetries, baryon number conservation and lepton number conservation and therefore NG′ = 2.
            • Furthermore Eq. (79) can be applied separately to phases and moduli. In this way, and taking into account that a U(N) matrix contains n(n − 1)/2 moduli and n(n + 1)/2 phases.
            • It is straightforward to obtain that we have, Nph = 69 − 5 × 6 + 2 = 41 phases and Nmod = 84 − 5 × 3 = 69 moduli in the flavour sector.
            • This amounts to a total of 123 parameters in the model4, out of which 44 are CP violating phases!!

            As we know, in the SM, there is only one observable CP violating phase, the CKM phase, and therefore we have here 43 new phases, 40 in the flavour sector and three in the flavour independent sector. (Flavour Physics and Grand Unification - pdf)

            +
            +

            root profiles

            Both 1/89 and 1/109 have the Fibonacci sequence encoded in their decimal expansions illustrates a period-24 palindromic that bring the powers of pi.

            +
            + + Note +
            +
            +

            In this article I am going to introduce the main results of a new theory of elemetary particle physics developed by the engineer M.S. El Nachie.

            • This theory provides a fractal model of quantum space-time, the so-called E-infinity space, that allows the precise determination of the mass-energy of most elementary particles -and much more- in close agreement with their experimental values.Phi_division_unity
            • The Golden Ratio emerges naturally in this theory, and turns out to be the central piece that connects the fractal dimension of quantum space-time with the mass-energy of every fundamental particle, and also with several fundamental physical quantities such as the Fine Structure constant.Phi_Squared_Circle_Mides
            • El Nachie has been severely criticised by his non-orthodoxal publication methods -he uses to publish his papers in a Journal where he is the editor in chief. Despite this fact, I think that his theory deserves consideration so I will try to summarize it in the lines that follow.
            • The intervention of the Golden Ratio can be seen as a way to enter the quantum world, the world of subtle vibrations, in which we observe increasing energy levels as we move to smaller and smaller scales.
            • El Nachie has proposed a way of calculating the fractal dimension of quantum space-time. The resulting value (Figure 7) suggests that the quantum world is composed of an infinite number or scaled copies of our ordinary 4-dimensional space-time.
            • Setting k=0 one obtains the classical dimensions of heterotic superstring theory, namely 26, 16, 10, 6 and 4, as well as the constant of super-symmetric (αgs=26) and non super-symmetric (αg=42) unification of all fundamental forces.

            As we have seen in section 2, the above is a Fibonacci-like sequence with a very concise geometrical interpetation related to numbers 5, 11 and φ. (Phi in Particle Physics)

            +
            +

            PHI_Quantum_SpaceTime

            Both scheme are carrying a correlation between two (2) number of 89 and 109 which provide the bilateral of 12 to the 24 cells of prime hexagon.

            +
            + + Note +
            +
            +

            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry). (PrimesDemystified)

            +
            +

            collective bilateral 9 sum symmetry

            So the 36 should behave as a central. Therefore the total files that inherited from this scheme will be 1 + 7 + 29 = 37 including one (1) main page.

            +
            + + Note +
            +
            +

            Every repository on GitHub.com comes equipped with a section for hosting documentation, called a wiki. You can use your repository’s wiki to share long-form content about your project, such as how to use it, how you designed it, or its core principles. (GitHub)

            +
            +

            7 x π(89) = 7 x 24 = 168 = π(1000)

            Since we are discussing about prime distribution then this 18's structure will also cover the further scheme that is inherited from the above 37 files.

            +
            + + Note +
            +
            +

            This web enabled demonstration shows a polar plot of the first 20 non-trivial Riemann zeta function zeros (including Gram points) along the critical line Zeta(1/2+it) for real values of t running from 0 to 50. The consecutively labeled zeros have 50 red plot points between each, with zeros identified by concentric magenta rings scaled to show the relative distance between their values of t. Gram’s law states that the curve usually crosses the real axis once between zeros. (TheoryOfEverything)

            +
            +

            1 + 7 + 29 = 37 = 19 + 18

            Riemann Zeta_Zeros

            By our project, these 37 files are located within the wiki of main repository and organized by the 18's structure located per the 18 files of project gist.

            +
            + + Note +
            +
            +

            Spin networks constitute a basis that minimize the degree of over-completeness of the loop basis, and for trivalent intersections eliminate it entirely.

            • The edges are labelled by spins together with `intertwiners’ at the vertices which are prescription for how to sum over different ways the spins are rerouted.
            • The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations.

            Some of these relations are rooted in a relation to superstring theory and quantum gravity which is directly related to the quantization of general relativity. (Wikipedia)

            +
            +

            Spin network states

            This generated a lot of interest in the approach and eventually led to the Loop Quantum Gravity (LQG). You may find that the rest of topics will concern mainly to this matter.

            Hidden Dimensions

            Assigning a specific mass, length, time, and charge metrics based on new dimensional relationships and the Planck constant (which defines Higgs mass).

            169-over-109-blood-pressure

            Consider the following 13x13 square divided into two triangles and two quadrilateral polygons. If the four pieces are restructured in the form of a rectangle, it appears that the overall area has inexplicably lost one unit! What has happened?

            13x13 square divided into two triangles and two quadrilateral polygons

            In the special case of a unit segment, the Golden Ratio provides the only way to divide unity in two parts that are in a geometric progression

            +
            + + Note +
            +
            +

            Supersymmetry and more specifically supergravity grand unification allow one to extrapolate physics from the electroweak scale up to the grand unification scale consistent with electroweak data.

            • Here we give a brief overview of their current status and show that the case for supersymmetry is stronger as a result of the Higgs boson discovery with a mass measurement at ∼ 125 GeV consistent with the supergravity grand unification prediction that the Higgs boson mass lie below 130 GeV. Thus the discovery of the Higgs boson and the measurement of its mass provide a further impetus for the search for sparticles to continue at the current and future colliders.
            • The group SO(10) as the framework for grand unification appears preferred over SU(5). The group SO(10) contains both G(4, 2, 2) and SU(5)⊗U(1) as subgroups, i.e., SO(10) has the branchings SO(10) → SU(4)C ⊗ SU(2)L ⊗ SU(2)R and SO(10) → SU(5) ⊗ U(1).Mystery of the First 1000 Prime Numbers
            • It possesses a spinor representation which is 2⁵ = 32 dimensional and which splits into 16 ⊕ 16. A full generation of quarks and leptons can be accommodated in a single 16 plet representation. Thus the 16 plet has the decomposition in SU(5) ⊗ U(1) so that 16 =10(−1) ⊕ 5(3) ⊕ 1(−5).
            • As noted the combination 5 ⊕ 10 in SU(5) is anomaly free and further 1(−5) in the 16-plet decomposition is a right handed neutrino which is a singlet of the standard model gauge group and thus the 16-plet of matter in SO(10) is anomaly free.
            • The absence of anomaly in this case is the consequence of a more general result for SO(N) gauge theories. Thus in general anomalies arise due to the non-vanishing of the trace over the product of three group generators in some given group representation Tr ({Ta, Tb}Tc).
            • For SO(10) one will have Tr ({Σµν, Σαβ}Σλρ). However, there is no invariant tensor to which the above quantity can be proportional which then automatically guarantees vanishing of the anomaly for SO(10). This analysis extends to other SO(N) groups.
            • One exception is SO(6) where there does exist a six index invariant tensor ǫµναβλρ and so in this case vanishing of the anomaly is not automatic.
            • The group SO(10) is rank 5 where as the standard model gauge group is rank 4. The rank of the group can be reduced by either using 16 ⊕ 16 of Higgs fields or 126 ⊕ 126 of Higgs.
            • Since under SU(5) ⊗ U(1) one has 16 ⊃ 1(−5) we see that a VEV formation for the singlet will reduce the rank of the group. Similarly 126 ⊃ 1(−10) under the above decomposition. Thus when the singlets in 16 ⊕ 16 of Higgs or 126 ⊕ 126 get VEVs, the SO(10) gauge symmetry will break reducing its rank.
            • However, we still need to reduce the remaining group symmetry to the Standard Model gauge group. For this we need to have additional Higgs fields such as 45, 54, 210. Further to get the residual gauge group SU(3)C ⊗ U(1)em we need to have 10 -plet of Higgs fields.
            • Thus the breaking of SO(10) down to SU(3)C ⊗ U(1)em requires at least three (3) sets of Higgs representations: one to reduce the rank, the second to break the rest of the gauge group to the Standard Model gauge group and then at least one 10-plet to break the electroweak symmetry.Higgs fields
            • As discussed above one can do this by a combination of fields from the set: 10, 16 ⊕ 16, 45, 54, 120, 126 ⊕ 126, 210.
            • To generate quark and lepton masses we need to couple two 16-plets of matter with Higgs fields. To see which Higgs fields couple we expand the product 16⊗16 as a sum over the irreducible representations of SO(10).

            Here we have 16 ⊗ 16 = 10s ⊕ 120a ⊕ 126s, where the s(a) refer to symmetric (anti-symmetric) under the interchange of the two 16-plets. The array of Higgs bosons available lead to a large number of possible SO(10) models. (Superunification - pdf)

            +
            +

            SO(10)_-_16_Weight_Diagram svg

            The index of 8 sign masks (sm) to the 30 fPi (each with 8 Hexadecimal masks). These can be "inverted" (0↔1) making 16×30=480 octonion permutations.

            +
            + + Note +
            +
            +

            I am pleased to announce the availability of splitFano.pdf, a 321 page pdf file with the 3840=480*8 split octonion permutations (with Fano planes and multiplication tables).

            • These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices (sorted by Fano plane index or fPi).
            • They are assigned to the *30 canonical sets of 7 triples# using the maskList: {5, 8, 4, 3, 7, 6, 3, 2, 6, 5, 1, 4, 6, 7, 3, 3, 8, 6, 3, 1, 6, 6, 2, 3, 5, 8, 4, 3, 7, 6}
            • There are 7 sets of split octonions for each of the 480 “parent” octonions (each of which is defined by 30 sets of 7 triads and 16 7 bit “sign masks” which reverse the direction of the triad multiplication). The 7 split octonions are identified by selecting a triad.
            • The complement of {1,2,3,4,5,6,7} and the triad list leaves 4 elements which are the rows/colums corresponding to the negated elements in the multiplication table (highlighted with yellow background).
            • The red arrows in the Fano Plane indicate the potential reversal due to this negation that defines the split octonions. The selected triad nodes are yellow, and the other 4 are cyan (25MB).
            • These allow for the simplification of Maxwell’s four equations which define electromagnetism (aka.light) into a single equation.

            Below is the first page of the comprehensive split octonion list of all 3840 Split Fano Planes with their multiplication tables available. (8×16×30 Split Fano)

            +
            + 
            
+The 30 indexed (fPi) canonical sets of 7 triples (which get sign masks applied to make valid octonions).
+1 {{1, 2, 3}, {1, 4, 5}, {1, 6, 7}, {2, 4, 6}, {2, 5, 7}, {3, 4, 7}, {3, 5, 6}}
+2 {{1, 2, 3}, {1, 4, 5}, {1, 6, 7}, {2, 4, 7}, {2, 5, 6}, {3, 4, 6}, {3, 5, 7}}
+3 {{1, 2, 3}, {1, 4, 6}, {1, 5, 7}, {2, 4, 5}, {2, 6, 7}, {3, 4, 7}, {3, 5, 6}}
+4 {{1, 2, 3}, {1, 4, 6}, {1, 5, 7}, {2, 4, 7}, {2, 5, 6}, {3, 4, 5}, {3, 6, 7}}
+5 {{1, 2, 3}, {1, 4, 7}, {1, 5, 6}, {2, 4, 5}, {2, 6, 7}, {3, 4, 6}, {3, 5, 7}}
+6 {{1, 2, 3}, {1, 4, 7}, {1, 5, 6}, {2, 4, 6}, {2, 5, 7}, {3, 4, 5}, {3, 6, 7}}
+7 {{1, 2, 4}, {1, 3, 5}, {1, 6, 7}, {2, 3, 6}, {2, 5, 7}, {3, 4, 7}, {4, 5, 6}}
+8 {{1, 2, 4}, {1, 3, 5}, {1, 6, 7}, {2, 3, 7}, {2, 5, 6}, {3, 4, 6}, {4, 5, 7}}
+9 {{1, 2, 4}, {1, 3, 6}, {1, 5, 7}, {2, 3, 5}, {2, 6, 7}, {3, 4, 7}, {4, 5, 6}}
+10 {{1, 2, 4}, {1, 3, 6}, {1, 5, 7}, {2, 3, 7}, {2, 5, 6}, {3, 4, 5}, {4, 6, 7}}
+11 {{1, 2, 4}, {1, 3, 7}, {1, 5, 6}, {2, 3, 5}, {2, 6, 7}, {3, 4, 6}, {4, 5, 7}}
+12 {{1, 2, 4}, {1, 3, 7}, {1, 5, 6}, {2, 3, 6}, {2, 5, 7}, {3, 4, 5}, {4, 6, 7}}
+13 {{1, 2, 5}, {1, 3, 4}, {1, 6, 7}, {2, 3, 6}, {2, 4, 7}, {3, 5, 7}, {4, 5, 6}}
+14 {{1, 2, 5}, {1, 3, 4}, {1, 6, 7}, {2, 3, 7}, {2, 4, 6}, {3, 5, 6}, {4, 5, 7}}
+15 {{1, 2, 5}, {1, 3, 6}, {1, 4, 7}, {2, 3, 4}, {2, 6, 7}, {3, 5, 7}, {4, 5, 6}}
+16 {{1, 2, 5}, {1, 3, 6}, {1, 4, 7}, {2, 3, 7}, {2, 4, 6}, {3, 4, 5}, {5, 6, 7}}
+17 {{1, 2, 5}, {1, 3, 7}, {1, 4, 6}, {2, 3, 4}, {2, 6, 7}, {3, 5, 6}, {4, 5, 7}}
+18 {{1, 2, 5}, {1, 3, 7}, {1, 4, 6}, {2, 3, 6}, {2, 4, 7}, {3, 4, 5}, {5, 6, 7}}
+19 {{1, 2, 6}, {1, 3, 4}, {1, 5, 7}, {2, 3, 5}, {2, 4, 7}, {3, 6, 7}, {4, 5, 6}}
+20 {{1, 2, 6}, {1, 3, 4}, {1, 5, 7}, {2, 3, 7}, {2, 4, 5}, {3, 5, 6}, {4, 6, 7}}
+21 {{1, 2, 6}, {1, 3, 5}, {1, 4, 7}, {2, 3, 4}, {2, 5, 7}, {3, 6, 7}, {4, 5, 6}}
+22 {{1, 2, 6}, {1, 3, 5}, {1, 4, 7}, {2, 3, 7}, {2, 4, 5}, {3, 4, 6}, {5, 6, 7}}
+23 {{1, 2, 6}, {1, 3, 7}, {1, 4, 5}, {2, 3, 4}, {2, 5, 7}, {3, 5, 6}, {4, 6, 7}}
+24 {{1, 2, 6}, {1, 3, 7}, {1, 4, 5}, {2, 3, 5}, {2, 4, 7}, {3, 4, 6}, {5, 6, 7}}
+25 {{1, 2, 7}, {1, 3, 4}, {1, 5, 6}, {2, 3, 5}, {2, 4, 6}, {3, 6, 7}, {4, 5, 7}}
+26 {{1, 2, 7}, {1, 3, 4}, {1, 5, 6}, {2, 3, 6}, {2, 4, 5}, {3, 5, 7}, {4, 6, 7}}
+27 {{1, 2, 7}, {1, 3, 5}, {1, 4, 6}, {2, 3, 4}, {2, 5, 6}, {3, 6, 7}, {4, 5, 7}}
+28 {{1, 2, 7}, {1, 3, 5}, {1, 4, 6}, {2, 3, 6}, {2, 4, 5}, {3, 4, 7}, {5, 6, 7}}
+29 {{1, 2, 7}, {1, 3, 6}, {1, 4, 5}, {2, 3, 4}, {2, 5, 6}, {3, 5, 7}, {4, 6, 7}}
+30 {{1, 2, 7}, {1, 3, 6}, {1, 4, 5}, {2, 3, 5}, {2, 4, 6}, {3, 4, 7}, {5, 6, 7}}
+
+The 8 sets of sign masks. Each sign mask (or the set of 7 triples) can be permuted in a consistent way to produce isomorphic sets of 480 octonions.
+
+1 {00, 07, 19, 1E, 2A, 2D, 33, 34}
+2 {01, 06, 18, 1F, 2B, 2C, 32, 35}
+3 {02, 05, 1B, 1C, 28, 2F, 31, 36}
+4 {03, 04, 1A, 1D, 29, 2E, 30, 37}
+5 {08, 0F, 11, 16, 22, 25, 3B, 3C}
+6 {09, 0E, 10, 17, 23, 24, 3A, 3D}
+7 {0A, 0D, 13, 14, 20, 27, 39, 3E}
+8 {0B, 0C, 12, 15, 21, 26, 38, 3F
+
+

            splitFano1

            Let's discuss more detail about this particular topic as guided by Prof Stephen Hawking in one of his greatest book: The Theory of Everything.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist02.html b/identition/span1/gist02.html new file mode 100644 index 00000000000..6cb1144e8f1 --- /dev/null +++ b/identition/span1/gist02.html @@ -0,0 +1,102 @@ + Partition function · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Partition function

            Based on the finiteness position of middle zero axis = 15 we have defined our 19 vs 18 Scenario contained in three (3) groups of five (5) of integer number partitions. Each groups represents the three (3) basic arithmetic operations of Euler's identity.

            Euler's identity is often cited as an example of deep mathematical beauty. Three (3) of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation (Wikipedia).

            ---+-----+-----
+ 1 | 1   | 5    🡰--19--
+---+-----+-----        |
+ 2 | 6   | 8           | 
+---+-----+-----        |
+ 3 | 9   | 26    --289-¤-exponentiation zone
+---+-----+-----        |
+ 4 | 27  | 28          |
+---+-----+-----        |
+ 5 | 29  | 29   ➤--18--
+---+-----+-----
+ 6 | 30  | 31   🡰--18--
+---+-----+-----        |
+ 7 | 32  | 44          |
+---+-----+-----        |
+ 8 | 45  | 46    --329-¤-multiplication zone
+---+-----+-----        |
+ 9 | 47  | 49          |
+---+-----+-----        |
+10 | 50  | 50   ➤--17--
+---+-----+-----         
+11 | 51  | 53   🡰--17--
+---+-----+-----        |
+12 | 54  | 59          |    
+---+-----+-----        |
+13 | 60  | 82    --168-¤-addition zone
+---+-----+-----        |
+14 | 83  |{102}        |
+---+-----+-----        |
+15 |{103}| 110  ➤--16--
+---+-----+-----
+

            The five (5) of integer number partitions shows a profound connection between the most fundamental numbers in mathematics as it also links the five (5) fundamental mathematical constants:

            (1) The number 1, the multiplicative identity,
            (2) The number i, the imaginary unit of the complex numbers.
            image
            (3) The number π = 3.1415…, the fundamental circle constant, and

            Pi-unrolled-720

            (4) The number e = 2.718…, also known as Euler's number, which occurs widely in mathematical analysis.

            image

            (5) Furthermore, the equation is given in the form of an expression set equal to zero, the number 0, as the additive identity which is common practice in several areas of mathematics.

            Euler's identity is a special case of Euler's formula eix = cos x + i sin x when evaluated for x = π, In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia)

            Euler's identity

            It is stated by DE102011101032A9 that using Euler's identity, the MEC30 standard is more accurately than a measurement. The distribution of prime numbers is a central point of study in number theory. So let's start from there.

            Rational Objects

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            The central problem is to determine when a Diophantine equation has solutions, and if it does, how many. Two examples of an elliptic curve, that is, a curve of genus 1 having at least one rational point. Either graph can be seen as a slice of a torus in four-dimensional space (Wikipedia).

            Number theory

            One of the main reason is that one does not yet have a mathematically complete example of a quantum gauge theory in four-dimensional space-time. It is even a sign that Einstein's equations on the energy of empty space are somehow incomplete.

            Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents (Wikipedia).

            default

            Dyson introduced the concept in the context of a study of certain congruence properties of the partition function discovered by the mathematician Srinivasa Ramanujan who the one that found the interesting behaviour of the taxicab number 1729.

            In number theory and combinatorics, rank of a partition of a positive integer is a certain integer associated with the partition meanwhile the crank of a partition of an integer is a certain integer associated with that partition (Wikipedia).

            Rank_of_a_partition

            Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University, in 1900. They were then applied to the study of the symmetric group. Their theory was further developed by many mathematicians, including W. V. D. Hodge

            The rank of a partition

            By our project, this partition stands as the prime identity. The tabulation below shows the 2nd prime identity where the 20 out of the largest part = 21 goes to rank = 10 via crank = 20-11 = 9. These 10 and 9 are associated with the 19th prime identitity.

                       largest part = 21 → 11+13+12 = 36  →  MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   ↓
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----
+---+-----+-----+-----+-----+                   ↓     |
+ 2 | 18  | 21  | 39  | 60  |-------------------      |
+---+-----+-----+-----+-----+                   |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |
+---+-----+-----+-----+-----+             |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |
+---+-----+-----+-----+-----+       |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |
+---+-----+-----+-----+-----+             |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |
+---+-----+-----+-----+-----+                   |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------      |
+---+-----+-----+-----+-----+                   ↓     |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----
+===+=====+=====+=====+=====+                   ↓
+45 | 277 |                      ← 11+13+12=36 ←  MEC30
+---+-----+                                     |
+ ↑
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            By having a total of 571, the congruence properties is composed in to the last of 20/10 = 2 numbers of 285 and 286 throughout the cumulative sum of 45 objects that are forming the 10x11=110 objects of 18th prime identity.

            (71+6) + (43-6) = 77 + 37 = 11x7 + 30+13-6

            Factorization

            This scheme of 19 vs 18 stands as our 19 vs 18 Scenario while the tensor of 110 objects are obtained by observing centralizing the first 20 to 10 objects from polarizing of 2x11x13=286 objects out of the central pair 11 and 13 within True Prime Pairs.

            The crank of a partition

            In linear algebra, this tensor is known as eigenvector, a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalues is the factor by which the eigenvector is scaled.

            In this shear mapping the red arrow changes direction, but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it does not change direction, and since its length is unchanged, its eigenvalue is 1 (Wikipedia).

            File:Mona_Lisa_eigenvector_grid

            Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as Montgomery conjecture of the nontrivial zeros of the zeta function. Means it also depends on Riemann hypotesis which is still in a major issue. Similar case left science today many unsolved problems that associated with.

            Eigenvectors_of_a_linear_operator

            The rank cannot be used to prove the theorem combinatorially, Dayson wrote an arithmetical coefficient similar to, but more recondite than, the rank of a partition; and called this hypothetical coefficient as the "crank" of the partition.

            The values p(1),,,,,,p(8)} of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the Young diagrams for the partitions of the numbers from 1 to 8 (Wikipedia).

            image

            Since 286 has the prime factors of 11 and 13 so it is also the product of the middle two numbers of True Prime Pairs. Therefore, the eigenvalue of the 11 parts also determines the equal size rotation of crank partitions of 13 prime identity.

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  |     ◄-----------------------------
+      |      |  1  +-----+                                   |
+      |  1   |     |  2  | (5)                               |
+      |      |-----+-----+                                   |
+      |      |     |  3  |                                   |
+  1   +------+  2  +-----+----                               |
+      |      |     |  4  |                                   |
+      |      +-----+-----+                                   |
+      |  2   |     |  5  | (7)                               |
+      |      |  3  +-----+                                   |
+      |      |     |  6  |                                   |
+------+------+-----+-----+------                             |
+      |      |     |  7  |                                   |
+      |      |  4  +-----+
+      |  3   |     |  8  | (11) ◄-- 11 parts of rank 10 = 110
+      |      +-----+-----+
+      |      |     |  9  |                                   |
+  2   +------|  5  +-----+-----                              |
+      |      |     |  10 |                                   |
+      |      |-----+-----+                                   |
+      |  4   |     |  11 | (13) ◄----------------------------
+      |      |  6  +-----+
+      |      |     |  12 |
+------+------+-----+-----+-------------------- (36)
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17) ◄----------------------------
+      |      |-----+-----+                                   |
+      |      |     |  15 | 0 axis ◄-- partitions of the (13) ◄-- rotation
+  3   +------+  8  +-----+-----                              |
+      |      |     |  16 |      ◄----------------------------
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |
+------|------|-----+-----+-------------------- (72)
+

            Unfortunately the rotation of this eigenvalues deals with four-dimensional space-time which was already a big issue. Speculation is that the unfinished book of Ramanujan's partition, series of Dyson's solutions and hugh of Einstein's papers tend to solve it.

            On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! (Clay Institute's - Official problem description).

            Geometry of 4D rotations

            More generally, the central problem is to determine when an equation in n-dimensional space has solutions. However at this point, we finaly found that the prime distribution has something to do with the subclasses of rank and crank partitions.

            The subclasses of each partitions

            Dayson introduced the idea of rank of a partition to accomplish the task he set for himself. He made the following conjectures which were proved in 1954 by Peter Swinnerton-Dyer an English mathematician specialising in number theory.

            Dayson's friend the neurologist and author Oliver Sacks said: "A favourite word of Freeman's about doing science and being creative is the word subversive (tending or intending to subvert or overthrow, destroy, or undermine an established or existing system, especially a legally constituted or a set of beliefs), and he's done that all his life (Wikipedia).

            N(0, 5, 5n + 4) = N(1, 5, 5n + 4) = N(2, 5, 5n + 4) = N(3, 5, 5n + 4) = N(4, 5, 5n + 4)
+N(0, 7, 7n + 5) = N(1, 7, 7n + 5) = N(2, 7, 7n + 5) = . . . = N(6, 7, 7n + 5)
+

            The concepts of rank and crank can both be used to classify partitions of certain integers into subclasses of equal size. The two concepts produce different subclasses of partitions. This is illustrated in the following two tables.

            Although not in the form that Dayson have defined, it was found that the last problem on which Ramanujan worked on before his death was cranks. Berndt and his coauthors have given substantial evidence that Ramanujan knew about the function (Wikipedia).

            default

            The subclasses of partitions develops characters similar to the distribution of prime numbers. This results in a fundamental causal relation to the primes, systemically the products are entered into the position system.

            The approach taken is to think of the solutions of an equation as a geometric object. For example, an equation in two variables defines a curve in the plane. More generally, an equation, or system of equations, in two or more variables defines a curve, a surface or some other such object in n-dimensional space (Wikipedia).

            Dyson has many series of formal solution. An explicitly time-dependent Schrödinger equation by iteration, and the time-ordering operator {T} as entity of basic importance of quantum mechanics, are also named after Dyson .

            Relation to the primes

            The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.

            Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems (Wikipedia).

            prime Sacks_spiral

            According to the results of Princeton University USA in 1972, the distribution of the prime numbers shows in the Riemann zeta function between the position of its complex zeros and middle axis is identical with the rotation curve of energy distribution.

            37 + 12 = 61 - 12 = 49 = 7 x 7 = d(13)

            image

            In the second opposing member, the position 19 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 11 as a prime number is now forced to determine a new axis-symmetrical zero position.

            Note that when 77 contains ‘Lucky 7 and 11' as prime factors it is also the product of the middle two numbers of this sequence (11*7 = 77) (Prime Curios!).

            MEC30 Localization

            When the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent .

            It's possible to build a Hessian matrix for a Newton's method step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector (Tensorflow).

            Batch Jacobian

            This idea was done as the earliest in 1960s by Swinnerton-Dyer using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

            From these numerical results the conjecture predicts that the data should form a line of slope equal to the rank of the curve, which is 1 in this case drawn in red in red on the graph (Wikipedia).

            The Birch and Swinnerton-Dyer conjecture

            It is stated that Np for a curve E with rank r obeys an asymptotic law and is still remain unsolved. Thus it would mean that using Euler's identity to get a definite pattern of prime distribution is still a long way to go.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist03.html b/identition/span1/gist03.html new file mode 100644 index 00000000000..673069cb332 --- /dev/null +++ b/identition/span1/gist03.html @@ -0,0 +1,69 @@ + Irrational Partitions · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Irrational Partitions

            This section is discussing the 200 residual objects that goes irrational along the pattern within the 4th dimension from the 2nd to 3rd prime identity in regards to the three (3) zones where each represents the basic arithmetic operations of Euler's identity.

            ---+-----+-----
+ 1 | {1} | {9}
+---+-----+-----
+ 2 | 10  |{32}
+---+-----+-----
+ 3 | 33  | 63  
+---+-----+-----
+ 4 |{64} | 101 
+---+-----+-----
+ 5 |{102}| 120 
+---+-----+-----
+ 6 | 121 |{189}
+---+-----+-----
+ 7 | 190 |{200}
+---+-----+-----
+

            There are some mathematical shape of this residual objects. Torus is basically a donut shape, which has the property of of having variable Gaussian curvature. Some parts of the surface has positive curvature, others zero, others negative.

            The blue parts of the torus above have positive curvature, the red parts negative and the top grey band has zero curvature. If our 3 dimensional space was like the surface areas of a 4 dimensional torus, the parts would have different angle sums.

            Torus

            These are two more bizarre shapes with strange properties. Mobius strip only has one side, if you start anywhere on its surface and follow the curvature round you will eventually return to the same place having travelled on every part of the surface.

            Mobius

            The Klein bottle is in someways a 3D version of the Mobius strip and even though it exists in 3 dimensions, to make a true one you need to "fold through" the 4th dimension.

            Klein bottle

            The torus is actually one of the current theories of the shape of universe while the klein bottle is shape of the idea in theoretical physics called string theory that reality is made up of infinitesimal vibrating strings, smaller than atoms, electrons or quarks

            Finally, there exist scenarios in which there could actually be more than 4D of spacetime. String theories require extra dimensions of spacetime for their mathematical consistency. In string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional (Wikipedia).

            String theory

            These are situations where theories in two or three spacetime dimensions are no more useful. This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family.

            The three (3) zones

            In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become the irrational partitions.

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            layer | node | sub |  i  |  f                               
+------+------+-----+---------- 
+      |      |     |  1  | -----------------------  71 = 72-1
+      |      |  1  +-----+                        |
+      |  1   |     |  2  | (5)                    |
+      |      |-----+-----+                        |
+      |      |     |  3  | ---------              |
+  1   +------+  2  +-----+----      |             |
+      |      |     |  4  |          5x ---        |
+      |      +-----+-----+          |     |       |
+      |  2   |     |  5  | (7) -----      |       |
+      |      |  3  +-----+                |       |
+289+11=300   |     |  6  |                |       |
+------+------+-----+-----+----- 72 x 6   7x --- 11x = 77 (rational)
+      |      |     |  7  |                |       |
+      |      |  4  +-----+                |       |
+      |  3   |     |  8  | (11)  ---      |       |
+      |      +-----+-----+          |     |       |
+      |      |     |  9  |          2x ---        |
+  2   +------|  5  +-----+-----     |             |
+      |      |     |  10 | ---------              |
+      |      |-----+-----+                        |
+      |  4   |     |  11 | (13) ------------------  71 = 72-1
+      |      |  6  +-----+
+329+71=400   |     |  12 |------------------------  70 = 72-2
+------+------+-----+-----+
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17) ◄---------------------------
+      |      |-----+-----+
+      |      |     |  15 | ◄-- 42 x 6 partitions of 13 (irrational)
+  3   +------+  8  +-----+----- 
+      |      |     |  16 |      ◄---------------------------
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+168+32=200   |  |  |  18 |------------------------  68 = 72-4
+------|------|--|--+-----+
+       900 -----
+

            This irrational parts took the finiteness position of middle zero axis = 15 on our 19 vs 18 Scenario contained in three (3) groups of five (5) of integer number partitions where each groups represents the three (3) basic arithmetic operations of Euler's identity.

            329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ

            default

            The 200 objects that goes from the 2nd to 3rd prime identity would take position as multiplication zone by given of 100x2=200 which is then be used in turn to 100+2=102 (addition zone) and 100^2=10000 (exponentiation zone)

            2 + 60 + 40 = 102

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum mechanics. It is a key result in quantum-mechanical system, and its discovery was a significant landmark in the development of the subject.

            Complex plot of a wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space (Wikipedia).

            Wavepacket-a2k4-en

            The modular function

            Consequently, we only need to fold a 30's cycle as in the illustration 7 so that we can identify the opposite prime positions that form their specific pairs in a specific convolution.

            These two (2) exponent are acting as the exchange zones of the MEC30 behaviour of the other two operators. This interactions is managed in between 4 identities of (26 to 29) and 2 identities (30 to 31) by means of Triangular waves.

            MEC30

            A seemingly unrelated construction is the j-function of number theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern.

            Although this function appears in a branch of mathematics that seems very different from the theory of finite groups, the two subjects turn out to be intimately related (Wikipedia).

            Monstrous moonshine

            We propose a new higher dimensional version of the McKay correspondence which enables us to understand the Hodge theory assigned to singular Gorenstein varieties by physicists, and so-called Higgs bundles.

            Hodge theory can be extended to cohomology with coefficients in nonabelian groups between flat vector bundles which, by the Riemann-Hilbert correspondence, are the same as local systems (Hodge Theory in String Theory)

            Hodge conjecture

            Our results lead to the conjecture that string theory indicates the existence of some new cohomology theory for algebraic varieties with Gorenstein singularities.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist04.html b/identition/span1/gist04.html new file mode 100644 index 00000000000..4f5ce09e7b8 --- /dev/null +++ b/identition/span1/gist04.html @@ -0,0 +1,152 @@ + Object Orientation · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Object Orientation

            Here we are going to discuss the concept of lagging and leading scheme on DNA System using four-dimensional space (4D). A mathematical extension of the concept of three-dimensional space (3D) originated by 43 out of 89 objects of bilateral 9 sums.

            ---+-----+-----
+ 1 | {1} |{43}
+---+-----+-----
+ 2 | 44  |{57}
+---+-----+-----
+ 3 | 58  | 59
+---+-----+-----
+ 4 | 60  | 104
+---+-----+-----
+ 5 | 105 |{115}
+---+-----+-----
+ 6 |{116}| 134
+---+-----+-----
+ 7 | 135 | 162
+---+-----+-----
+ 8 | 163 | 175
+---+-----+-----
+ 9 | 176 |{176}
+---+-----+-----
+

            The geometry of four-dimensional space is much more complex than that of three-dimensional space, due to the extra degree of freedom. However in our case this 43 objects has excatly a finite fraction of four (4) axis dimensions to MEC30.

            default

            (114/2)! = 57! = 1653 » 1653 / 57 = 29

            --------+
+        | ⅓
+        +---   } ⅔
+ Case A | ⅓
+        +---------
+        | ⅓      |
+-----------------+  Φ = ⅔
+        | ⅓      |
+        +---------
+ Case B | ⅓
+        +---   } ⅔
+        | ⅓
+---------
+

            9 + 19 + 29 = 28 + 29 = 57

            P7:(142857)
+
+   #  |  A   |  B   | ∑
+------+------+------+-----
+  {1} |      |      |
+------+      |      |
+ ...  |  28  |  29  | 57
+------+      |      |
+ {57} |      |      |
+------+------+------+-----
+  58  |      |      |
+------+      |      |
+  ... |  29  |  28  | 57
+------+      |      |
+ 114  |      |      |
+------+------+------+-----
+      |  57  |  57  | 114
+

            Comparatively, four-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w to describe the two additional cardinal directions of up toward and down from, respectively.

            The set of points in Euclidean 4-space having the same distance R from a fixed point P0 forms a hypersurface known as a 3-sphere where R is substituted by function R(t) with t meaning the cosmological age of the universe. Growing or shrinking R with time means expanding or collapsing universe, depending on the mass density inside (Wikipedia).

            Clifford-torus

            By deploying containers on Compute Engine, you can simplify app deployment while controlling four dimensional space. You can configure a virtual machine (VM) instance or an instance template to deploy and launch a Docker container.

            Balanced Prime

            The initial objects will be a formation of a double helix driven by vectors 71 and 68 based on the arrangement of prime numbers on a cube of 10x10x10 or 1000 to the Golden Ratio.

            π(10x10x10) + 10x10x10/Φ = π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786

            image

            1/7 = 0,142857142857142857142857.. infinity

            default

            By the prime numbers this polarizing between the objects and its tensors is identified by the 157 as the 19+18=37th prime. This 157 is a balanced prime of two (2) primes of 151 + 163 = 314 = 100 x π by which the 100 is standing as the square of 10x10 out of the central objects of ten (10) while the π is one of the constant of Euler's identity.

            The number 157 is the 18+19=37th prime number, a balanced prime, because the arithmetic mean of those primes yields 157. The next prime is 163 and the previous prime is 151, with which 157 forms a prime triplet (Wikipedia).

            By this square correlation between natural and prime numbers then the 571 would be separated by the 100 to 500 and 71 and finally by the form of (2,10) the 500 goes to 50 while 71 is polarized to 71x2=142 and 177 as shown on the table.

            (10/2)π = 157 ⇄ (10^2)¹ + 11x7 = 177 = 286 - 109

            interpolation

            So by the above explanation of this 157's behaviour it is now left the question of where the tensor of 571 by the two (2) numbers of 285 and 286 is going. That is the imajinary part (i) of Euler's identity has something to do with the zeta function.

            Encapsulation Scenario

            This 4D concept is conducted to get 1000 prime objects of 3rd layer within four (4) times interaction of triangular waves between 26 and 28th prime identities starting from 11x2=22, 22x2=44, 44x2=88 that leads to 88x2=176 objecs of 4th prime identity.

            4 x 22 of 88 rows = 4 x 528 = 2112 elements = the index of 1000th prime

            id: 26	
+---+-----+-----+-----+-----+	
+ 1 |   5 |   1 |  6  |   7 |----------------------------	
+---+-----+-----+-----+-----+                            |	
+ 2 |   2 |   7 |  9  |  16 |----------------------      |	
+---+-----+-----+-----+-----+                      |     |	
+ 3 |  58 |  10 |  68 |  78 |----------------      |     |	
+---+-----+-----+-----+-----+                |     |     |	
+ 4 |  35 |  69 | 104 | 173 |----------      |     |     |	
+---+-----+-----+-----+-----+          |     |     |     |	
+ 5 | {17}| 105 | 122 |{227}|          |     |     |     |	
+---+-----+-----+-----+-----+- Cross  {17}Δ26|43Δ30|13Δ17|30 ----	
+ 6 | {17}|{123}| 140 | 263 |          |     |     |     |       |	
+---+-----+-----+-----+-----+          |     |     |     |       |	
+ 7 |  18 | 141 | 159 | 300 |----------      |     |     |       |	
+---+-----+-----+-----+-----+                |     |     |       |	
+ 8 |  15 | 160 | 175 | 335 |----------------      |     |       |	
+---+-----+-----+-----+-----+                      |     |       |	
+ 9 |  15 | 176 | 191 | 367 |----------------------      |       |	
+---+-----+-----+-----+-----+                            |       |	
+10 |  35 |{192}|{227}| 419 |----------------------------        |  	
+---+-----+-----+-----+-----+                                    |	
+                                                                |	
+id: 27                                                {26}      |	
+                                                        |       |	
+---+-----+-----+-----+-----+                            |       |	
+ 1 |   5 |   1 |   6 |   7 |----------------------    {1+7}     |	
+---+-----+-----+-----+-----+                      |     |       |	
+ 2 |   7 |   7 |  14 |  21 |----------------      |     |       |	
+---+-----+-----+-----+-----+                |     |   {17}      |	
+ 3 |  29 |  15 |  44 |  59 |----------      |     |     |       |	
+---+-----+-----+-----+-----+          |     |     |     |       |	
+ 4 |   8 |  45 |  53 |  98 |          |     |     |     |       |	
+---+-----+-----+-----+-----+- 4xMEC30 29    2    18 -- Cross -- MEC30	
+ 6 |   4 |  54 |  58 | 112 |          |     |     |     |       |	
+---+-----+-----+-----+-----+          |     |     |     |       |	
+ 7 |   - |  59 |  59 | 118 |----------      |     |     |       |	
+---+-----+-----+-----+-----+                |     |   {17}      |	
+ 7 |   9 |  60 |  69 | 129 |----------------      |     |       |	
+---+-----+-----+-----+-----+                      |     |       |	
+ 8 |  23 |  70 |  93 | 163 |----------------------    {1x7}     |	
+---+-----+-----+-----+-----+                            |       |	
+                                                        |       |	
+id: 28                                                {28}      |                                                       	
+                                                                |	
+---+-----+-----+-----+-----+                                    |	
+ 1 |   5 |  1  |  6  |   7 |----------------------------        |	
+---+-----+-----+-----+-----+                            |       |	
+ 2 |   6 |  7  | 13  |  20 |----------------------      |       |	
+---+-----+-----+-----+-----+                      |     |       |	
+ 3 |   7 | 14  | 21  |  35 |----------------      |     |       |	
+---+-----+-----+-----+-----+                |     |     |       |	
+ 4 |   6 | 22  | 28  |  50 |----------      |     |     |       |	
+---+-----+-----+-----+-----+          |     |     |     |       |	
+ 5 |  13 | 29  | 42  |  71 | Δ13     Δ11   Δ7     0     0 --=--- 	
+---+-----+-----+-----+-----+          |     |     |     |	
+ 6 |  17 | 43  | 60  | 103 |----------      |     |     |	
+---+-----+-----+-----+-----+                |     |     |	
+ 7 |  14 | 61  | 75  | 136 |----------------      |     |	
+---+-----+-----+-----+-----+                      |     |	
+ 8 |   6 | 76  | 82  | 158 |----------------------      |	
+---+-----+-----+-----+-----+                            |	
+ 9 |   5 | 83  | 88  | 171 |----------------------------	
+---+-----+-----+-----+-----+	
+

            This scheme could be happen by The Encapsulation behaviour of 28 which is the natural number following 27 preceding 29 and depicted as 28 balls arranged in a triangular pattern with the number of layers of 7 which lead to the concept of Gematria.

            Twenty-eight is a composite number, its proper divisors being 1, 2, 4, 7, and 14. It is the only known number that can be expressed as a sum of the first nonnegative (or positive) integers ( 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) and a sum of the first nonprimes ( 1 + 4 + 6 + 8 + 9 ), and it is unlikely that any other number has this property (Wikipedia).. triangular pattern with the number of layers of 7

            However there was a wide discussion stating that Gematria is NOT numerology. impacting a loss of science principal on prime interaction such as in DNA System, which occurs at a mismatch, is said to trigger a shift in the balance, for the binding of the template-primer, from the polymerase, to the exonuclease domain. So it shall use a method that combines data and code.

            Encapsulation allows developers to present a consistent and usable interface which is independent of how a system is implemented internally. As one example, encapsulation can be used to hide the values or state of a structured data object inside a class, preventing direct access to them by clients in a way that could expose hidden implementation details or violate state invariance maintained by the methods (Wikipedia).

            Encapsulation is key concept in object-oriented programming (OOP) defined as a way to restrict the direct access to components of an object that users cannot access state values for all of the variables of a particular object. So let's discuss it first.

            Golden Ratio

            So it is converting all residual objects out of the prime recycling of Riemann Zeta in to those three (3) basic arithmetic operations of Euler's identity as well the Fibonacy constant (φ) to Euler's number (e). Thus none of residual is neglected by an assumption.

            This behaviour would come to the feature of golden ratio. However it is not stand as a basic rule but as an impact of 329's vs 289's layers. That is also the reason why we could only see the three (3) digits of 618 out of the Fibonaci constant.

            φ = 1.618 = Fibonaci = Golden Ratio

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            default

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            These three (3) times bilateral 9 sums will lead to 168 vs 618 exponents between 68 and 69 objects of 50 and 27th prime identity that simulate the X/Y-genes reproduction of human cromosomes to the repository assignment of our project.

            Registry unit

            You can see that two distinct pressure zones are forming and that the spiral pattern expected from lid-driven cavity flow is beginning to form. Experiment with different values of nt to see how long the system takes to stabilize.

            12 Steps to Navier-Stokes

            It is a relationship between the rate of acceleration of liquids (the increase in their speed) and the force that acts on them, widely used in moving air vehicles, and is considered the most important equation used in the application of aircraft movement.

            Navier–Stokes Equation

            It is considered one of the most important equations in physics. Now let's analyze how we could say this structure can be used for switching the workflow between Windows and Linux.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist05.html b/identition/span1/gist05.html new file mode 100644 index 00000000000..2e403f1e8d3 --- /dev/null +++ b/identition/span1/gist05.html @@ -0,0 +1,92 @@ + Bonding Position · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Bonding Position

            Yet another related dimension of symmetry, when you combine the terminating digit symmetries described above, capturing three (3) rotations of 120 around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry

            ---+-----+-----
+ 1 | {1} |{11}
+---+-----+-----
+ 2 | 12  | 32
+---+-----+-----
+ 3 | 33  |{50}
+---+-----+-----
+ 4 | 51  |{86}
+---+-----+-----
+ 5 | 87  | 108
+---+-----+-----
+ 6 |{109}| 120
+---+-----+-----   
+

            In quantum mechanics, Schrödinger's cat is a thought experiment that illustrates a paradox of quantum superposition.

            In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead, while it is unobserved in a closed box, as a result of its fate being linked to a random subatomic event that may or may not occur (Wikipedia).

            Schrodinger's Cat

            2x10 + 9 = 20 + 9 = 29

            -----+-----+-----+-----+-----+
+  1' |  1  | {2} |  3  |  4  | 4¤
+     +-----+-----+-----+-----+
+  2' |  5  |  6  |  7  |  8  | 4¤
+     +-----+-----+-----+-----+
+  3' |  9  |{10} |  2¤ (M dan F)
+     +-----+-----+-----+      
+  4' | 11  | 12  | 13  | 3¤  <----------- d(11) = d(17+12)= d(29)
+     +-----+-----+-----+-----+                                        
+  5' | 14  | 15  | 16  | 17  | 4¤    
+     +-----+-----+-----+-----+
+  6' | 18  | 19  |{20} | 3¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
+  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
+     |----------------------- {9'} ------------------------|
+

            Primzahlentechnologie Einleitung. Wie Geht Primzahlen Technologie. MEC 30 - Mathematical Elementary Cell 30: Die Theorie der Gravitation ist die Mathematik des Universums and MEC30.2 Method for factorization

            Measuring with your limb scale is a measurement that does not intervene in the system, so also possible in the idle state of the system. Thus, the MEC 30 results in a measurement method for the energy flow in a system in which the route plan or flow plan of the energy is obtained (German Patent DE102011101032 and DE102014016656).

            MEC 30

            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period eight (8) difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2} (Primesdemystified).

            image

            Symmetry Mirroring

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            The 77 is equal to the sum of the first 8 primes. The square of 77 is 5929, the concatenation of two primes, 59 and 29. The concatenation of all palindromes from one up to 77 is prime (Prime Curios! ).

            11's additive sums

            Prime numbers that end with "77" occur more often than any other 2-digit ending among the first one million primes. The sum of the proper divisors of 77 equals 19 and the sum of primes up to 19 equals 77. Does this ever happen again?

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            The individual bases, depending on their sizes and spatial extents and masses, are assigned unequivocal values, situated within the vibration heights derived from (I), to define a measure from which the sequence can be counted, read or imaged.

            default

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            Molecular Interactions

            By the nature this behaviour can be observed from the molecular interactions of water. Water is intrinsically self-complementary on molecular interactions. In liquid or solid water, engage in ideal hydrogen bonding. Six (6) times of the angle 109 occupied as the most while the angle of 114 and 104 are exist only once. So the one in charge here is clearly the 29th prime identity.

            109 = 29th prime = (10th)th prime = ((114-104)th)th prime

            Molecular Interactions

            Let's assume that it is done using a material that stretches and then pops back when the stretching force goes away. It is pound for pound stronger than steel. So all of these steps are similar kind with the way a spider started to build its web.

            Every web begins with a single thread, which forms the basis of the rest of the structure. To establish this bridge, the spider climbs to a suitable starting point (up a tree branch, for example) and releases a length of thread into the wind. With any luck, the free end of the thread will catch onto another branch (howstuffworks.com).

            image

            This 29 turns the finiteness position of 15 as the middle zero axis of the MEC30. So the next steps will start exactly with the same story as we have explained from the beginning.

            MEC 30 claims to "illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way" via the elementary level of numbers. It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences.

            default

            The only different is, instead of an instance, it will behave as an inside container, just like how spider built a home web as strong as steel but useless to cover them against a rainy day nor even a small breeze.

            default

            Yang–Mills and Mass Gap

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist06.html b/identition/span1/gist06.html new file mode 100644 index 00000000000..eb424daf1ab --- /dev/null +++ b/identition/span1/gist06.html @@ -0,0 +1,79 @@ + The Quantum Way · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Quantum Way

            ---+-----+-----
+ 1 | 1   |{73}
+---+-----+-----
+ 2 |{74} | 94
+---+-----+-----
+ 3 | 95  | 113
+---+-----+-----
+ 4 |{114}| 121
+---+-----+-----
+ 5 | 122 | 135
+---+-----+-----
+ 6 | 136 | 156
+---+-----+-----
+ 7 |{157}|{165}
+---+-----+-----
+

            What is critical to understand, is that the invisible hand of 2, 3 and 5, and their factorial 30, create the structure within which the balance of the prime numbers, i.e., all those greater than 5, are arrayed algorithmically–as we shall demonstrate.

            In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. (Wikipedia).

            default

            The integer thirty (30) is the 19th composite number, Organizing Principle of the Prime Number Sequence, provides both vertical and horizontal structure to the prime number sequence in Prime Spiral Sieve.

            The number 30 possesses remarkable attributes, including–and perhaps most profoundly–its role (along with its prime factors 2, 3 and 5) as a primary organizing principle in the distribution of prime numbers (Primesdemystified).

                       15
+           ↓
+           29
+           ↓
+---+-----+-----
+ 6 | 30  | 31   ------
+---+-----+-----       |
+ 7 | 32  | 44         |
+---+-----+-----       | 4th (id:12)
+ 8 | 45  | 46         |
+---+-----+-----       |
+ 9 | 47  | 49   --329-¤-multiplication zone
+---+-----+-----       | 5th (id:13)
+10 | 50  | 50   ------
+---+-----+-----         
+11 | 51  | 53   ------
+---+-----+-----       |
+12 | 54  | 59         |    
+---+-----+-----       | 6th (id:14 - id:15)
+13 | 60  | 82         |
+---+-----+-----       |
+14 | 83  |{102} --289-¤-exponentiation zone
+---+-----+-----       | 7th (id:16 - id:19)
+15 |{103}| 110  ------
+---+-----+-----
+

            Prime hexagon is a mathematical structure developed by mathematician T. Gallion that is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime is encountered.

            The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating 3 minor hexagons, assigned names blue, red and green.

            default

            Many of you with familiarity with Docker for Windows know how you currently have to switch between running either Windows or Linux Containers. Prime hexagon teaches us how to combat this limitation and run both simultaneously on the same host.

            Separated segments

            Functional description of DNA, useful e.g. for identifying new coding sequences, comprises assigning characteristic values to individual bases derived from vibrational properties

            default

            The lagging strand is the strand of new DNA whose direction of synthesis is opposite to the direction of the growing replication fork. The lagging strand is synthesized in short, separated segments.

            320 + 289 + 168 = 618 + 168 = 786

            Cell types are interesting, but they simply reflect a modulo six (6) view of numbers. More interesting are the six internal hexagons within the Prime Hexagon. Like the Prime Hexagon, they are newly discovered.

            default

            Surprisingly, the 24-cell hexagon confines all natural numbers. The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon's outer boundary, other than 2 and 3.

            iMinor Hexagons

            Three dimensional sphere

            In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture.

            Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries (ClayMath Institute).

            Poincaré Conjecture

            The initial primes that forced the number line into this complex coil. Without a prime number in the outer set of triangles, the number line does not change to an outward course and remains forever contained in the 24 cells shown above.

            The minor hexagons form solely from the order, and type, of primes along the number line. Perhaps they have no significance. however, as they do form I suspect they must connect to deeper things in mathematics (Prime Hexagon).

            Δ300

            gif-dribbb

            Phi and its members have a pisano period if the resulting fractional numbers are truncated. If one instead rounds to the nearest number, the modular values for the first two terms are flipped compared to the 24th and 25th values as seen below.

            phi's cousin, the Fibonacci Series

            Numbers fill the hexagon by spiraling until a prime number is met, then it jumps to the next minor hexagon and begins to spiral again. As the numbers continue to fill the field, the other minor hexagons from, purple, cyan and yellow.

            (2112/82) − (576/82) = 24

            image

            layer | node | sub |     i    |   f
+------+------+-----+----------+------                                             ---
+      |      |     |    1,2:1 |  71 (2,3) -------------                            |
+      |      |  1  +----------+                        |                           |
+      |  1   |     |        2 |                        |                          (5) 
+      |      |-----+----------+                        |                           |
+      |      |     |        3 |                        |                           |
+  1   +------+  2  +----------+----                    |                          ---
+      |      |     |        4 |                        |                           |
+      |      +-----+----------+                        |                           |
+      |  2   |     |        5 |                        |                          (7) 
+289   |      |  3  +----------+                        |                           |
+|     |      |     |        6 |                        | {6®}                      |
+------+------+-----+----------+------      } (36)      | ↓                        ---
+      |      |     |     11:7√| 50/10+9 (20) ----› ¤ √ | 29=MEC30 - Δ1             |
+      |      |  4  +----------+                        | ↓                         |
+      |  3   |     |     12:8√| 9+60+40 (26) √ --      | from 329-40 √           (11) 
+      |      +-----+----------+                  |     | ↓ lagging                 |
+      |      |     |     13:9√| 9+60 (27) √      | {2®} from 168 (Triangular) √    |
+  2   +------|  5  +----------+-----             |     | ↓ leading                ---
+      |      |     |    14:10√| 9+60+40 (28) √ --      | goes to 329 √             |
+      |      |-----+----------+                        |                           |
+      |  4   |     | 15,18:11√| 71 (29,30,31,32) ------                          (13)
+329   |      |  6  +----------+                                                    |
+|     |      |     |    19:12√| {70} (36)                                          |
+------+------+-----+----------+------------------                                 ---
+      |      |     |    20:13√| (20-11)x10 (38) ‹- ¤ √                             |
+      |      |  7  +----------+                                                    |
+      |  5   |     |       14 |                                                  (17) 
+      |      |-----+----------+                                                    |
+      |      |     |       15 |                                                    |
+  3   +------+  8  +----------+-----                                              ---
+      |      |     |       16 |                                                    |
+      |      |-----+----------+                                                    |
+      |  6   |     |    28:17√| 100(50)                                          (19) 
+168   |      |  9  +----------+                                                    |
+|     |      |     |    29:18√| 50(68)                                             |
+------|------|-----+----------+------                                             ---
+

            Prime factor abundances

            The genetic material of a cell or an organism refers to those materials found in the nucleus, mitochondria and cytoplasm, which play a fundamental role in determining the structure of cell substances and capable of self-propagating and variation.

            The genetic material

            torus

            Spirals following other tilings of the plane also generate lines rich in prime numbers, for example hexagonal spirals. Hexagonal number spiral with prime numbers in green and more highly composite numbers in darker shades of blue.

            default

            Ricci Flow

            Finite collections of objects are considered 0-dimensional. Objects that are "dragged" versions of zero-dimensional objects are then called one-dimensional. Similarly, objects which are dragged one-dimensional objects are two-dimensional, and so on.

            The basic ideas leading up to this result (including the dimension invariance theorem, domain invariance theorem, and Lebesgue covering dimension) were developed by Poincaré, Brouwer, Lebesgue, Urysohn, and Menger (MathWorld).

            default

            The Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it "rounder", in the hope that one may draw topological conclusions from the existence of such "round" metrics.

            Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere (Wikipedia)

            default

            The Ricci Flow method has now been developed not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI (Artificial intelligence). No wonder now all the science leads to it.

            So what we've discussed on this wiki is entirely nothing but an embodiment of this solved Poincare Conjecture. This is the one placed with id: 10 (ten) which stands as the basic algorithm of π(10)=(2,3,5,7).

            Poincaré Conjecture

            Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence.

            AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence (Human vs AI).

            Despite of any debated subjects regarding Human vs AI, the said AI would not even close to the ability of human brain without undertanding of GAP functionality between left and right of the human brain. Let's find it in details on further discussion.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist07.html b/identition/span1/gist07.html new file mode 100644 index 00000000000..3af59ec644b --- /dev/null +++ b/identition/span1/gist07.html @@ -0,0 +1,87 @@ + Proofreading Ability · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Proofreading Ability

            ---+-----+-----
+ 1 | {1} |{56}
+---+-----+-----
+ 2 | 57  |{71}
+---+-----+-----
+ 3 | 72  | 85
+---+-----+-----
+ 4 |{86} |{89}
+---+-----+-----
+ 5 | 90  | 94
+---+-----+-----
+ 6 | 95  | 102
+---+-----+-----
+ 7 | 103 |{171}
+---+-----+-----
+ 8 | 172 | 206
+---+-----+-----
+
            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+layer|  i  |   f
+-----+-----+---------
+     |  1  |   5
+  1  +-----+
+     |  2  |  {7}
+-----+-----+---    } 36
+     |  3  |  11
+ {2} +-----+
+     |  4  | {13}
+-----+-----+---------
+     |  5  |  17
+  3  +-----+       } 36
+     |  6  | {19}
+-----+-----+---------
+

            Infinite connection

            Φ = 2,10
+Δ = 5,7,17
+3': 13,18,25,42
+2' » 13 to 77, Δ = 64
+2' and 3' » 13 to 45, Δ = 32
+
+2" + 5" = 7" = 77
+2"=22, 3"=33, 2" + 3" = 5" = 55
+
+13, 16, 18, 21, 23, 25, 28, 30, 32, 34, 
+36, 38, 40, 42, 
+45, 47, 49, 51, 53, 
+55, 57, 59, 61, 
+63, 65, 67, 69, 71, 73, 75, 77
+

            Next we will discuss how to form these numbers on each screens. As explained earlier, there are all three (3) layers. The instance is going to simulate DNA polymerase with proofreading ability.

            Proofreading removes the mismatched nucleotide and extension continues. If a mismatch is accidentally incorporated, the polymerase is inhibited from further extension (Wikipedia).

            DNA polymerases

            A current model of meiotic recombination, initiated by a double-strand break or gap, followed by pairing with an homologous chromosome and strand invasion to initiate the recombinational repair process (Wikipedia).

            image

            π(96) = 96/4 = 24

            Fidelity is very important in DNA replication. Mismatches in DNA base pairing can potentially result in dysfunctional proteins and could lead to cancer. Hydrogen bonds play a key role in base pair binding and interaction.

            The function of DNA polymerase is not quite perfect, with the enzyme making about one mistake for every billion base pairs copied. Error correction is a property of some, but not all DNA polymerases. This process corrects mistakes in newly synthesized DNA (Wikipedia).

            dna-genetics-biochemistry

            Strand Partition

            ezgif com-optimize

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            Four-vector configuration

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            image

            On the lagging strand template, a primase "reads" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            GitHub Actions workflow

            The leading strand is the strand of new DNA which is synthesized in the same direction as the growing replication fork. This sort of DNA replication is continuous. This workflow is assigned to Linux container (Ubuntu).

            The runner is the application that runs a job from a GitHub Actions workflow. It is used by GitHub Actions in the hosted virtual environments, or you can self-host the runner in your own environment. We use both of them to create group as a four-vector.

            DNA polymerase extends primed segments, forming Okazaki fragments. The RNA primers are then removed and replaced with DNA, and the fragments of DNA are joined by DNA ligase and are bound to the helicase heximer (Wikipedia).

            DNA ligase

            In eukaryotes the helicase wraps around the leading strand, and in prokaryotes it wraps around the lagging strand. As helicase unwinds DNA at the replication fork, the DNA ahead is forced to rotate resulting a build-up of twists in the DNA ahead.

            Because of its orientation, replication of the lagging strand is more complicated as compared to that of the leading strand. As a consequence, the DNA polymerase on this strand is seen to "lag behind".

            container-diagram

            Hamiltonian Path Problem

            By The GitHub Runner you can connect to the Google COS Instance. For self-hosted runners defined at the organization level, configure runs-on.group in your workflow file to target a runner groups or combine groups and labels.

            choosing-the-runner

            On the other hand, with larger systems we are able to transfer the behavior of the energy from the subatomic space into the haptic space with the scale described here (thought experiment Schröninger's cat). Thus, we are still able to apply the Schröninger wave equation in the haptic space, and replace the Hamiltonian with our measurements. default

            The problems would arise when the Windows Container in Github deliver the RNA Primer to Google instance as Windows Image because it shall read the image while the COS is run under Linux. So it will need to proof and solve without actually having to try.

            If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem given N cities to visit, how can one do this without visiting a city twice? (Clay Institute).

            P vs NP Problem

            Getting the proofreading ability of DNA polymerase to quickly solve problem for about one mistake for every billion base pairs copied is somehow that required by one of a major unsolved problem in theoretical computer science called P vs NP.

            P vs. NP deals with the gap between computers being able to quickly solve problems vs. just being able to test proposed solutions for correctness. As such, the P vs. NP problem is the search for a way to solve problems that require the trying of millions, billions, or trillions of combinations without actually having to try each one (P vs. NP Explained).

            P_versus_NP_problem

            This way will also be our approach to Euler's identity. By taking the correlation between f(π) as P vs f(i) as NP where eiπ + 1 = 0 then theoretically they shall be correlated to get an expression of the prime distribution similar to MEC30.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist08.html b/identition/span1/gist08.html new file mode 100644 index 00000000000..82de6c412b2 --- /dev/null +++ b/identition/span1/gist08.html @@ -0,0 +1,170 @@ + Replication Fork · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Replication Fork

            ---+-----+-----
+ 1 |  1  |  4
+---+-----+-----
+ 2 |  5  | 14
+---+-----+-----
+ 3 | 15  | 26
+---+-----+-----
+ 4 | 27  | 40
+---+-----+-----
+ 5 | 41  |{47}
+---+-----+-----
+ 6 | 48  | 54
+---+-----+-----
+ 7 | 55  |{71}
+---+-----+-----
+ 8 | 72  | 75
+---+-----+-----
+
            ---+-----+-----
+ 1 | 1   | 5    🡰--19--
+---+-----+-----        |
+ 2 | 6   | 8           | 
+---+-----+-----        |
+ 3 | 9   | 26    --289-¤-exponentiation zone
+---+-----+-----        |
+ 4 | 27  | 28          |
+---+-----+-----        |
+ 5 | 29  | 29   ➤--18--
+---+-----+-----
+ 6 | 30  | 31   🡰--18--
+---+-----+-----        |
+ 7 | 32  | 44          |
+---+-----+-----        |
+ 8 | 45  | 46    --329-¤-multiplication zone
+---+-----+-----        |
+ 9 | 47  | 49          |
+---+-----+-----        |
+10 | 50  | 50   ➤--17--
+---+-----+-----         
+11 | 51  | 53   🡰--17--
+---+-----+-----        |
+12 | 54  | 59          |    
+---+-----+-----        |
+13 | 60  | 82    --168-¤-addition zone
+---+-----+-----        |
+14 | 83  |{102}        |
+---+-----+-----        |
+15 |{103}| 110  ➤--16--
+---+-----+-----
+

            20 x 10 = 200 = 16 x 6 + (10² + 14 - 10) = 96 + 114 - 10 = 96 + 104 = 48 + 48 + 104

            !

            Deep Learning VM Images

            Let's see how triangular numbers come into the picture. A triangular number is a number that can be represented by a pattern of dots arranged in an equilateral triangle with the same number of dots on each side at equal distance from each other.

            Triangular pattern

                            largest part=21 → 11+13+12=36 →  MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   ↓
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----
+---+-----+-----+-----+-----+                   ↓     |
+ 2 | 18  | 21  | 39  | 60  |-------------------      |
+---+-----+-----+-----+-----+                   |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |
+---+-----+-----+-----+-----+             |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |
+---+-----+-----+-----+-----+       |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |
+---+-----+-----+-----+-----+             |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |
+---+-----+-----+-----+-----+                   |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------      |
+---+-----+-----+-----+-----+                   ↓     |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----
+===+=====+=====+=====+=====+                   ↓
+45 | 277 |                      ← 11+13+12=36 ←  MEC30
+---+-----+                                     |
+ ↑
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            Windows registry

            This software uses Windows Script Host to read and write to the registry. Read, Write, List and do all sorts of funky stuff to the windows registry using node.js and windows script host.

            kernel-6.1.21.1-microsoft-standard-WSL2.img 

            7 x 11 = 77 = 99 - 22 = 11 x (9 -2)
+
+layer | node | sub |  i  |  f                               
+------+------+-----+---------- 
+      |      |     |  1  | -----------------------  71 = 72-1
+      |      |  1  +-----+                        |
+      |  1   |     |  2  | (5)                    |
+      |      |-----+-----+                        |
+      |      |     |  3  | ---------              |
+  1   +------+  2  +-----+----      |             |
+      |      |     |  4  |          5x ---        |
+      |      +-----+-----+          |     |       |
+      |  2   |     |  5  | (7) -----      |       |
+      |      |  3  +-----+                |       |
+289+11=300   |     |  6  |                |       |
+------+------+-----+-----+----- 72 x 6    7x --- 11x = 77
+      |      |     |  7  |                |       |
+      |      |  4  +-----+                |       |
+      |  3   |     |  8  | (11)  ---      |       |
+      |      +-----+-----+          |     |       |
+      |      |     |  9  |          2x ---        |
+  2   +------|  5  +-----+-----     |             |
+      |      |     |  10 | ---------              |
+      |      |-----+-----+                        |
+      |  4   |     |  11 | (13) ------------------  71 = 72-1
+      |      |  6  +-----+
+329+71=400   |     |  12 |------------------------  70 = 72-2
+------+------+-----+-----+
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17)
+      |      |-----+-----+
+      |      |     |  15 |
+  3   +------+  8  +-----+----- 42 x 6
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+168+32=200   |  |  |  18 |------------------------  68 = 72-4
+------|------|--|--+-----+
+       900 -----
+

            Prime templates

            In the windows registry a key may have a default value. When enumarting value names, the default value's name will be empty.

            The number 28 depicted as 28 balls arranged in a triangular pattern with the number of layers of 7 ([Wikipedia).

            itriangular pattern with the number of layers of 7

            This presents a minor problem when including the empty value in a set with other values since it cannot be safely named with anything but the empty string, for fear of collision with other values.

            <img src=https://user-images.githubusercontent.com/36441664/87292656-521b2e00-c52b-11ea-9102-e7839feda3f7.gif> <img src=https://user-images.githubusercontent.com/36441664/82119386-453ac200-97a8-11ea-8dde-3af7628c01ae.gif> 
            const regedit = require('regedit').promisified
+
+async function main() {
+  const listResult = await regedit.list('HKCU\\SOFTWARE')
+  console.log(listResult)
+
+  await regedit.createKey(['HKLM\\SOFTWARE\\MyApp2', 'HKCU\\SOFTWARE\\MyApp'])
+  await regedit.putValue({
+    'HKCU\\SOFTWARE\\MyApp': {
+        Company: {
+            value: 'Moo corp',
+            type: 'REG_SZ'
+        }
+    },
+    'HKLM\\SOFTWARE\\MyApp2': { 
+      test: {
+        value: '123',
+        type: 'REG_SZ'
+      } 
+    }
+  })
+}
+
+main()
+

            Now the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of the prime number 7 lie in the numerical Double strand parallel opposite.

            Double Strands

            maxresdefault

            Anti paralled

            The Workflow by this frameworks will absorbe the way of how a DNA is read DNA polymerase which is proceed in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. This scheme is widely known as anti paralled direction.

            Since the leading and lagging strand templates are oriented in opposite directions at the replication fork, a major issue is how to achieve synthesis of new lagging strand DNA, whose direction of synthesis is opposite to the direction of the growing replication fork (Wikipedia).

            Replication fork

            default

            By DNA System it will act as the Replication Fork that exchange along with their residual objects. You may see that it begin with two (2) prime identities of (2,3) and end up with the tensor of 100 to 50 conforms the ζ(s)=1/2.

            286 - 4x2 = 278

            329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            Replication Fork

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+

            Exponentiation Zone

            By this flowchart we could deploy models on device and in the browser from image classification, text embeddings, audio, and video action recognition where you can browse trained models and datasets from across the machine learning ecosystem.

            machine learning models

            image

            Multiplicatio Zone

            the three (3) zones

            7 X (7+6) X (7+12) = 7 X 13 X 19 = 7 X 247 = 1729

            209659219-

            default

            Addition zone

            By all of the explanation above we concluded that this recycling is started by the tensor of bilateral 9 sums originated from the power of number two (2) which is resulting the congruent property of number 18.

            RiemannZeta_Zeros

            This property would tend the ballancing scheme of MEC30 so it will let 30-18=12 pairing with another 12 of 24 spins prime hexagon. The 24 goes to the center of True Prime Pairs by the prime pair 13 and 11 and let the crancks of 2,3,5,7 inside the 10 ranks.

            This is where Goldbach's conjecture, which was also known to Euler, helps. Goldbach considered the distribution of primes from the perspective of the line numbers that represent a separate set of numbers, as shown. So here also helps that the Riemann conjecture is essentially identical point, with the Goldbach conjecture.

            Riemann Zeta

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            default

            With the above description then the instance configuration is via matrix integration from tensorflow which is placed at the end position to the turning point 100 vs 50 to the format (2,3) i.e. at id: 68.

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            default

            Identical point

            default

            Parsering across syntax

            30 + (5+13) + (7+11) + (17+19) = 30 + 18 + 18 + 36 = 30 + 36 + 36 = 102 = 2 + 100

            default

            Prime images

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist09.html b/identition/span1/gist09.html new file mode 100644 index 00000000000..3464dadc4cf --- /dev/null +++ b/identition/span1/gist09.html @@ -0,0 +1,29 @@ + Building The Instance · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Building The Instance

            ---+-----+-----
+ 1 |  1  |  28
+---+-----+-----
+ 2 |  29 |  37
+---+-----+-----
+ 3 | {38}| {48}
+---+-----+-----
+ 4 |  49 | 127
+---+-----+-----
+ 5 | 128 | 129
+---+-----+-----
+

            default

            The following package types are available:

            • OS packages: Debian (via Apt), RPM
            • Language packages: Java, Node, Python
            • Container images packages: Docker, Helm

            Container Image Format

            Artifact Registry supports the following container image formats:

            • Docker Image Manifest V2, Schema 1
            • Docker Image Manifest V2, Schema 2
            • Open Container Initiative (OCI) Image Format Specifications After successful execution, you could check the docker log:

            A VM instance with apps deployed directly to the operating system

            The common methods of deploying software onto a Compute Engine VM instance include:

            1. Deploying software on VM boot using a startup script or cloud-init.
            2. Creating a custom boot disk image with software pre-installed.

            container-without-container-image

            A VM instance with apps deployed in a container

            The following process describes how you deploy a container on Compute Engine:

            1. You bundle your app and required libraries into a Docker image and publish the image to Artifact Registry, Container Registry, or a third-party registry such Docker Hub.
            2. You specify a Docker image name and the docker run configuration when creating a VM instance or an instance template for a MIG.

            container-image-cos

            Docker needs access to Artifact Registry to push and pull images. You can use the standalone Docker credential helper tool, docker-credential-gcr, to configure your Artifact Registry credentials for use with Docker without using requiring gcloud.

            Steps to create

            Compute Engine executes the following tasks after you make a request to create a VM instance:

            1. Compute Engine creates a VM instance that uses a Google-provided Container-Optimized OS image. This image includes a Docker runtime and additional software that is responsible for starting your container.
            2. Compute Engine stores your container settings in instance metadata under the gce-container-declaration metadata key.
            3. When the VM starts, the Container-Optimized OS image uses the docker run command configuration that is stored in the instance's metadata, pulls the container image from the repository, and starts the container.
            gcloud compute project-info add-metadata
+

            containers-gce-process

            Artifact Registry integrates with Cloud Build and other continuous delivery and continuous integration systems to store packages from your builds. You can also store trusted dependencies that you use for builds and deployments.

            Limitations

            1. You can only deploy one container for each VM instance. Consider Google Kubernetes Engine if you need to deploy multiple containers per VM instance. You can only deploy containers from a public repository or from a private Artifact Registry or Container Registry repository that you can access. Other private repositories are not supported.

            2. You can't map a VM instance's ports to the container's ports (Docker's -p option). To enable access to your containers, see Publishing container ports.

            3. You can only use Container-Optimized OS (COS) images with this deployment method. COS is an operating system image for your Compute Engine VMs that is optimized for running Docker containers maintained by Google and is based on the open source Chromium OS project .

            It would also mean that if you use console or deployment manager it's not possible to deploy more than one container, but if you create a config file and use cloud init you can deploy many containers to that instance.

            Partition

            For most frameworks, Debian 10 is the default OS. Ubuntu 20.04 images are available for some frameworks. The boot disk space is split into three types of partitions:

            • The root partition, which is mounted as read-only to maintain integrity.
            • Stateful partitions, assigned to write the objects of fork movement which are writable and stateful.
            • Stateless partitions, assigned as strand which are writable but the content classes do not persist across reboots.

            default

            You can attach a persistent disk or create an instance with Local SSDs when using Container-Optimized OS. The disks can be mounted by creating a subdirectory under /mnt/disks directory (writable, executable, stateless, tmpfs) using startup-scripts.

            image

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            GitHub Actions workflow

            On the lagging strand template, a primase "reads" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            kernel-6.1.21.1-microsoft-standard-WSL2.img

            This Widows is an isolated container, lightweight package for running an application on the host operating system. Containers build on top of the host operating system's kernel (which can be thought of as the buried plumbing of the operating system).

            Containers are not for virtualization, and they are using the resources of the host machine. As a result, for now a Windows container cannot run "as-is" on a Linux machine. But you can do it by using VM as it works on Windows. You can install a Windows VM on your Linux host, which will allow to run Windows containers (Stackoverflow).

            container-diagram

            You can run .NET applications in Linux containers, but only if they're written in .NET Core which can be deployed on Windows Server Containers. Applications running in Windows Server Containers can run in any language supported by Windows.

            SharpKeys is a utility that manages a Registry key that allows Windows to remap one key to any other key. Included in the application is a list of common keyboard keys and a Type Key feature to automatically recognize most keyboard keys. It was originally developed in C# using .NET v2 but has been updated to support .NET 4.0 Client Profile

            We found this scenario is the best because sofar Google could only recommend using GKE for that. A GKE cluster has a control plane and machines called nodes it was designed specifically for that purpose. Autopilot mode manages this complexity.

            default

            Nodes run the services supporting the containers that make up your workload. The control plane decides what runs on those nodes, so still Linux containers are running on Linux, and Windows containers are running on Windows.

            Configuration

            By The GitHub Runner you can connect to the Google COS Instance. For self-hosted runners defined at the organization level, configure runs-on.group in your workflow file to target a runner groups or combine groups and labels.

            default

            The runner is the application that runs a job from a GitHub Actions workflow. It is used by GitHub Actions in the hosted virtual environments, or you can self-host the runner in your own environment. We use both of them to create group as a four-vector.

            jobs:
+  check-bats-version:
+    runs-on:
+      group: Default
+      labels: ubuntu-20.04-16core
+

            It is possible to dynamically load the images between Windows (WSL Enabled) and Linux in the same workflow using github context such as github.repository_owner_id. You can also read most of the github context data in environment variables.

            
+jobs:
+  github-pages:
+    runs-on: ${{ github.repository_owner == 'FeedMapping' && 'windows-latest' || fromJSON('["self-hosted", "linux", "X64"]') }}
+
+

            choosing-the-runner

            Selects an action to run as part of a step in your job. An action is a reusable unit of code. You can use an action defined in the same repository as the workflow, a public repository, or in a published Docker container image.

            Selects an action to run as part of a step in your job

            The GitHub hosted runner is assigned to run the Linux container and a Windows Server Core container simultaneously. This is an experimental feature of Microsoft WSL2 and may have some issues. One known problem is volumes are not stable.

            
+docker pull --platform=linux ubuntu
+docker run --platform=linux -d ubuntu /bin/sh -c "while true; do echo hello world; sleep 1; done"
+docker run -d microsoft/windowsservercore ping -t 127.0.0.1
+docker inspect --format '{{.Os}}' ubuntu
+
+

            eiπ + (109² − 89²)/(528/28)/(2 x 3 x 5 x 7) = eiπ + 1 = 0

            default

            The opposite direction will be made through switching beetween Linux and Windows which is proceed the old strand in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. Here we set a remote self-host runner via WSL.

            default

            image

            eq19/setup

            With the above description, of course, you can guess where the next direction will be. That is from one (1) unit of DNA to one (1) unit of whole unity. That's why we need a solution of the remaining six (6) other cases to be placed with id: 11, 12, 14, 15, 26 and 28 so that id: 68 is congrued to the number two (2).

            default

            Therefore the five (5) identities of (10, 11,12,14,15) are twisted prior joining the two (2) identities of (26,28). Since each of these seven (7) identities is linked by the eleven (11) objects then they turn to a strong seven (77). Lets's discuss them one by one.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist10.html b/identition/span1/gist10.html new file mode 100644 index 00000000000..c79f5ffce19 --- /dev/null +++ b/identition/span1/gist10.html @@ -0,0 +1,103 @@ + Imaginary Square · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Imaginary Square

            ---+-----+-----
+ 1 | {1} | {2}
+---+-----+-----
+ 2 |  3  | 20
+---+-----+-----
+ 3 | 21  | 46
+---+-----+-----
+ 4 |{47} | 58
+---+-----+-----
+ 5 | 59  | 70
+---+-----+-----
+ 6 |{71} |{93}
+---+-----+-----
+ 7 | 94  | 103
+---+-----+-----
+ 8 | 104 |{109}
+---+-----+-----
+

            The tetractys is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number (Wikipedia).

            93509593-21e87500-f94a-11ea-8a30-4dc8cc4ad2f8

            However, we can conclude that the distribution of prime numbers must have a static base structure, which is also confirmed logically in the further course

            Φ(11,13) = Φ(1,2,3) + Φ(4,2) = 123 + 42 = 165

            ---+-----+-----+-----+-----+
+ 1 |  72 | 1   | 73  |  74 |-----------------
+---+-----+-----+-----+-----+                 |
+ 2 | {20}| 74  | 94  | 168 |-----------      |
+---+-----+-----+-----+-----+           |     |
+ 3 | {18}| 95  | 113 | 208 |-----      |     |
+---+-----+-----+-----+-----+     |     |     |
+ 4 |  {7}| 114 | 121 | 235 |- {7}| 5   |  1  |{61} = 18th prime
+---+-----+-----+-----+-----+     |     |     |
+ 5 |  13 | 122 | 135 | 257 |-----      |     |
+---+-----+-----+-----+-----+           |     |
+ 6 |  19 | 136 | 155 | 291 |-----------      |
+---+-----+-----+-----+-----+                 |
+ 7 |   9 | 156 | 165 | 321 |----------------
+---+-----+-----+-----+-----+
+

            300 - 2x11x13 = 300-286 = 14

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+

            Proceeding, the number line begins to coil upon itself; 20 lands on 2's cell, 21 on 3's cell. Prime number 23 sends the number line left to form the fourth hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself.

            Twin primes 29 and 31 define the fifth hexagon, cyan. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon (Prime-Hexagon)

            The Power of 168 vs 618

            7th collumn ◄- 65 + 12 = 77

            |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - |100 |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - |101 |  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   T
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |   H
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   E
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   P
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |   O
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   W
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |   E
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   R
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   O
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |   F
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | ∑=168
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |   V
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   S
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            See that by this 6 (six) spines, the number of 19, 43 and 71. The 71 as the third cycles would land on the 2's cell which are the same direction as the 3's, so both of them got this 71.

            Below are the spins for the first 80 numbers; 2 (0 and 1) spiral blue, meet prime 5, spiral purple briefly, meet 7 and spiral red. The bands are pretty short because primes are common in the early numbers, but the grow rare as numbers grow large and the bands broaden.

            This 71 is a conformation that it has the same result as we have explained on the residual objects of 571 turn to a vektor of 71 while the rest of 500 turn to 200 objects of 3's identity and the last objects of 300 goes to the next cycles.

            For now we will be coy and state that the secret of the pyramid lies with two 4-times triangular numbers: The first, 4 x triangular number 528=2112, equates to the total number of elements used to construct the pyramid, which is subdivided into its four lateral faces comprised of 528 elements each in the form of 32 cascading triangular numbers where 2112/96 = 242.

            242 = number of Mirror Prime Pairs and 96 is the 360 degree digital root Fibonacci periodicity when indexed to n not divisible by 2, 3, or 5, i.e., period 32 every 120 degrees (Primesdemystified).

            Construct the pyramid

            This polarity is happened per six (6) cycles by the polar of six (6) to one (1) and six (6) to seven (7) by which we finally found if this behaviour is cascaded bilaterally within the correlation between 61 as the 18th prime and 67 as the 19th prime.

            default

            default

            The most obvious interesting feature of this 24-cell hexagon is it confines all numbers! That is, as the number line winds about toward infinity, bending around prime numbers, it never exits the 24 cells.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist11.html b/identition/span1/gist11.html new file mode 100644 index 00000000000..72741201fe2 --- /dev/null +++ b/identition/span1/gist11.html @@ -0,0 +1,143 @@ + Rational vs Irrational · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Rational vs Irrational

            ---+-----+-----
+ 1 |  1  | 28
+---+-----+-----
+ 2 | 29  | 46
+---+-----+-----
+ 3 | 47  |{56}
+---+-----+-----
+ 4 |{57} | 61
+---+-----+-----
+ 5 | 62  | 82
+---+-----+-----
+ 6 | 83  | 94
+---+-----+-----
+ 7 | 95  | 99
+---+-----+-----
+ 8 |{100}|{123}
+---+-----+-----
+
                       15
+           ↓
+           35
+           ↓ 
+---+-----+-----         
+11 | 51  | 53   ------
+---+-----+-----       |
+12 | 54  | 59         |    
+---+-----+-----       | 6th (id:14 - id:15)
+13 | 60  | 82         |
+---+-----+-----       |
+14 | 83  |{102} --289-¤-exponentiation zone
+---+-----+-----       | 7th (id:16 - id:19)
+15 |{103}| 110  ------
+---+-----+-----
+           ↓
+           15
+           ↓
+           35
+

            Gematria is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. Single word can yield several values depending on which cipher is used. This cipher is sometimes erroneously labelled as "Jewish" or "Hebrew" by popular numerology calculators, such as Gematrix and Gematrinator.

            A mathematical formula for finding a letter's corresponding number in Mispar Gadol

            It is possible that this well-known cipher was used to conceal other more hidden ciphers in Jewish texts. For instance, a scribe may discuss a sum using the ‘standard gematria' cipher, but may intend the sum to be checked with a different secret cipher.

            7(111) = 1117 = 7² + 7¹ + 7° = 49 + 7 + 1 = 57

            In the standard (Mispar hechrechi) version of gematria, each letter is given a numerical value between 1 and 400, as shown in the following table. In the Mispar gadol variation, the five final letters are given their own values, ranging from 500 to 900.

            Δ prime = 114th prime - 19 = (6 x 19)th prime - 19 = 619 - 19 = 600

              Sub  | i  |  β  | f   
+=======+====+=====+=======  ===   ===   ===   ===   ===   ===
+ 1:1:0 | 1  |   1 | 2 {71}   1     1     |     |     |     |
+-------+----+-----+-------  ---   ---    |     |     |     |
+ 1:2:1 | 2  |   2 | 3 {71}         |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:2:2 | 3  |   3 | 7 = 1 + 2x3    |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:3:3 | 4  |   4 | 10 = 9 + 1     |     |     |     |     |  
+-------+----+-----+----            |     |     |     |     |
+ 1:3:4 | 5  |   5 | 11 = 9 + 2     |     |     |     |     |
+-------+----+-----+----            9     1‘    |    Δ100   |
+*1:3:5 | 6  |   6 | 12 = 9 + 3     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:6 | 7  |   7 | 13 = 9 + 4     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+ 1:4:7 | 8  |   8 | 14 = 9 + 5     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:8 |{9} |   9 | 15 = 9 + 6     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:9 |{10}|  10 | 19 = 9 + 10    |     |     |     |     |
+=======+====+=====+====           ===   ---    1"   ---    |
+ 2:1:0 | 11 |  20 | 20 = 19 + log 10¹    |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:2:1 | 12 |  30 | 26 = 20 + 2x3        |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:2:2 | 13 |  40 | 27 = 26 + 1          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:3:3 | 14 |  50 | 28 = 26 + 2          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:3:4 | 15 |  60 | 29 = 26 + 3          9‘    |   Δ200  Δ600
+-------+----+-----+----                  |     |     |     |
+*2:3:5 | 16 |  70 | 30 = 26 + 4          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:4:6 | 17 |  80 | 31 = 26 + 5          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:4:7 |{18}|  90 | 32 = 26 + 6          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:4:8 |{19}| 100 | 36 = 26 + 10         |     |     |     |
+=======+====+=====+====                 ===   ---   ---    |
+*2:4:9 | 20 | 200 | 38 = 36 + log 10²          |     |     |
+-------+----+-----+----                        |     |     |
+ 3:1:0 | 21 | 300 | 40 = 36 + 2 x log 10²      |     |     |
+-------+----+-----+----                        |     |     |
+ 3:2:1 | 22 | 400 | 41 = 40 + 1                |     |     |
+-------+----+-----+----                        |     |     |
+*3:2:2 | 23 | 500 | 42 = 40 + 2                |     |     |
+-------+----+-----+----                        |     |     |
+*3:3:3 | 24 | 600 | 43 = 40 + 3                9"  Δ300    |
+-------+----+-----+----                        |     |     |
+ 3:3:4 | 25 | 700 | 44 = 40 + 4                |     |     |
+-------+----+-----+----                        |     |     |
+*3:3:5 | 26 | 800 | 45 = 40 + 5                |     |     |
+-------+----+-----+----                        |     |     |
+*3:4:6 | 27 | 900 | 46 = 40 + 6                |     |     |
+-------+----+-----+----                        |     |     |
+ 3:4:7 |{28}|1000 | 50 = 40 + 10               |     |     |
+=======+====+=====+====                       ===  ====  ----
+*3:4:8 |{29}|2000 | 68 = 50 + 3 x (2x3)      {10³} Δ600  Δ300
+=======+====+=====+====                        Δ         ====
+ 3:4:9 |{30}|3000 |{71}= 68 + log 10³ ---------¤         Δ900   
+

            Instaneous connection

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            It was as if some ghostly bridge across the city of Geneva, Switzerland, had permitted two photons of light nearly seven miles apart to respond simultaneously to a stimulus applied to just one of them.

            Albert Einstein sneered at the very possibility of such a thing, calling it ‘‘spooky action at a distance.'' Scientists still (somewhat shamefacedly) speak of the ‘‘magic'' of ‘‘quantum weirdness.'' And yet all experiments in recent years have shown that Einstein was wrong and that action at a distance is real (New York Times).

            split photons

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+

            The twin-photon experiment by Dr. Nicolas Gisin of the University of Geneva and his colleagues was the most spectacular demonstration yet of the mysterious long-range connections that exist between quantum events, connections created from nothing at all, which in theory can reach instantaneously from one end of the universe to the other.

            According to quantum mechanics, particles are simultaneously in two or more states until observed – an effect vividly captured by Schrödinger's famous thought experiment of a cat that is both live and dead simultaneosly.

            Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication. The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light. (Astronomy).

            Schrödinger's cat

            Dark Energi

            image

            Our results show that about 69% of our universe's energy is dark energy. They also demonstrate, once again, that Einstein's simplest form of dark energy – the cosmological constant – agrees the most with our observations (The Conversation).

            Many physicists aren't satisfied with this explanation, though. They want a more fundamental description of its nature. Is it some new type of energy field or exotic fluid? Or is it a sign that Einstein's equations of gravity are somehow incomplete? What's more, we don't really understand the universe's current rate of expansion (The Conversation).

            image

            The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The different universes within the multiverse are called "parallel universes", "other universes", "alternate universes" (Wikipedia).

            default

            102 = 2 + 100 = 2 + 60 + 40

            residual-objects

            default

            genetic material

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist12.html b/identition/span1/gist12.html new file mode 100644 index 00000000000..1b3245f98c2 --- /dev/null +++ b/identition/span1/gist12.html @@ -0,0 +1,67 @@ + Rotation vs Revolution · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Rotation vs Revolution

            ---+-----+-----
+ 1 | {1} | {2}
+---+-----+-----
+ 2 |  3  | 101
+---+-----+-----
+ 3 |{102}| 111
+---+-----+-----
+

            default

            In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors.

            In some areas, tensor fields are so ubiquitous that they are often simply called "tensors". Tullio Levi-Civita and Gregorio Ricci-Curbastro popularised tensors in 1900 – continuing the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others – as part of the absolute differential calculus. The concept enabled an alternative formulation of the intrinsic differential geometry of a manifold in the form of the Riemann curvature tensor (Wikipedia).

            Tensor

            A Riemann surface is a "universe" locally modelled on open sets in the complex plane, and equipped with extra structure so that complex analysis can be done. Polynomial equations in two variables define special Riemann surfaces, called plane curves, such asthe "circle" z2 + w2 = 1, ( rotating the w-plane), the "cubic" z3 + w2 = 1, the "nodal cubic" z3 + z2 = w2, and the "Fermat quartic" z4 + w4 = 1 (Pinterest).

            Gann Chart

            Δ300

            Moon's orbit

            default

            1 year = 12 months
+1000 years = 12,000 months
+
+c = 12,000 x L / t
+  = 12,000 x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+

            So by the theory of E=mc² to raise up a particle on earth it should be a groups of galaxies that rationaly and irrationaly parallel to its position in our Solar system. It was predicted that we have 1012 stars in our galaxy and 2×1012 galaxies in the universe.

            In 2016, using 20 years of images from the Hubble space telescope, it was estimated that there were in total two trillion (2×1012) or more galaxies in the observable universe, and as many as an estimated 1×1024 stars (more stars than all the grains of sand on all beaches of the planet Earth) (Wikipedia)

            image

            Recent observation and a census from NASA Hubble Telescope together with other observatories show that observable Universe may contain 10 times more Galaxies than previous estimates! So remember, this number won't get the end story.

            286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271

            -----+-----+-----+-----+-----+                                               ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤                                             |
+-----+-----+-----+-----+-----+                                                |
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤                                             |
+     +-----+-----+-----+-----+                                                |
+{12¨}|  6¨ |  6¨ |  2¤ (M dan F)                                              |
+     +-----+-----+-----+                                                     17¤
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤                                                   |
+-----+-----+-----+-----+-----+                                                |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤                                             |
+     +-----+-----+-----+-----+                                               ---
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤                                                   |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+                 12¤
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 dan C2)   |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+                 ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist13.html b/identition/span1/gist13.html new file mode 100644 index 00000000000..d2b6fcee5ab --- /dev/null +++ b/identition/span1/gist13.html @@ -0,0 +1,143 @@ + Zeta vs Zero · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Zeta vs Zero

            ---+-----+-----
+ 1 | 1   | 18
+---+-----+-----
+ 2 | 19  | 29
+---+-----+-----
+ 3 | {30}|{43}
+---+-----+-----
+
            Scheme 13:9
+===========
+(1){1}-7:   7'
+(1){8}-13:  6‘
+(1)14-{19}: 6‘
+------------- 6+6 -------
+(2)20-24:   5'           |
+(2)25-{29}: 5'           |
+------------  5+5 -------
+(3)30-36:   7:{70,30,10²}|
+------------             |
+(4)37-48:   12• ---      |
+(5)49-59:   11°    |     |
+            --}30° 30•   |
+(6)60-78:   19°    |     |
+(7)79-96:   18• ---      |
+--------------           |
+(8)97-109:  13           |
+(9)110-139:{30}=5x6 <--x-
+            --
+           {43}
+

            image

            1155 / 5 = 286 - 55 = 200 + 31 = 231

            layer|  i    |   f
+-----+-------+------
+     | 1,2:1 | (2,3)
+  1  +-------+
+     | 3:2   | (7)
+-----+-------+------
+     | 4,6:3 | (10,11,12)  <--- 231 (3x)
+  2  +-------+
+     |{7}:4  |({13})
+-----+-------+------
+     | 8,9:5 | (14,{15})   <--- 231 (2x)
+  3  +-------+
+     | 10:6  | (19)
+-----+-------+------
+

            139 = 34th prime =(2x17)th prime

            We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape (arXiv:2010.16383v4).

            Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series 

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|------------------------- Skema-12 ------------------------|
+|------------ 6¤ -------------|------------- 6¤ ------------|
+|--------------------------- 192 ---------------------------|
+|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
++----+----+----+----+----+----+----+----+----+----+----+----+
+|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|
+|---------  5¤  ---------|------------ {96} -----------|{43}|
+|--------- {53} ---------|-------------- {139} -------------|
+|------- Skema-23 -------|------------- Skema-34 -----------|    
+

            default

            |------------ 36' --------------|----------------------------36' ----------------------------|
+|     19'     |        17'      |      13'     |      11'     |       7'      |       5'     |
++---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+| 1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
++---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+| 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
++---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+| ° |ΔΔΔΔ  ΦΦ | •   ΔΔ   ΔΔ   ¤ | •   ΔΔ   ΦΦΦ    Φ   ΦΦ  ¤¤¤¤|  •   ΔΔ   ΦΦΦ    Φ   ¤¤   ΦΦ |  
+
+|---- 102  ---|-----  66  ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -|
+|--2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------|
+|-------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------|
+|-------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----|
+

            919 = 1 + 6(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17) = 1 + 6(153)

            286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+=====  ←-- bilateral 9 sums
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+

            These objects will then behave as a complex numbers that leads to trivial and complex roots of the 18th prime identity. Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as the balanced prime.

            Input (12) + Query (15) + Result (19) + Ouput (22) = Total 68 Objects

            image

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+

            As you can see, starting with 1, and doubling it (1+1) we got 2, again, doubling 2 (2+2) we got 4. Further doubling 32 (32+32) we got 64 and summing up 6+4 gave us 10 which again summing up the two digits gave us 1. If you keep following this pattern, It will always give us the digits 1, 2, 4, 5, 7, 8. Even summing 7+7 gives 14 which further gives 5 (1+4).

            image

            RiemannZeta Zeros

            Based on Prime (7): 142857 then id: 28 from the last case will end up in id: 57 i.e. in the flowchart so that in turn they can point us to the algorithm tensor from the stop point to id: 114 on the third screen.

            default

                                            |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                |  2 | 60 | 40 | 1 | 30 | 30 | 5 |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            2023-03-17 (2)

            default

            default

            default

            Consider that all creatures will go mature just like our body which is stop growing in a certain of condition. Therefore an instance will become an inside container by leaving the central as black hole and derived all of residual objects to outer level. This is what the ten (10) digits of 0719425863 in Euler's number got something to do.

            (1729 + 571 - 500) / (157 - 57) = 1800 / 100 = 18th prime identity = 110 objects

            default

            The above 0719425863 is implicity state the identity of seven (7) after zero (0). By the prime hexagon, it match with the 0th-step of 18 identities and 1st-step of the seven (7) prime identities from 19th to 25th. So when it goes to four (4) prime identities from 26th and end up to the 29th it will open up a gap at the 27th which linkages with the 110 objects of the 18th.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist14.html b/identition/span1/gist14.html new file mode 100644 index 00000000000..b9bc72015c5 --- /dev/null +++ b/identition/span1/gist14.html @@ -0,0 +1,57 @@ + Anti Parallel · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Anti Parallel

            ---+-----+-----
+ 1 | 1   | 4
+---+-----+-----
+ 2 |{5}  |{8}
+---+-----+-----
+ 3 | 9   |{17}
+---+-----+-----
+ 4 |{18} |{23}
+---+-----+-----
+ 5 | 24  | 27
+---+-----+-----
+ 6 | 28  | 34
+---+-----+-----
+ 7 |{35} |{41}
+---+-----+-----
+ 8 |{42} |{52}
+---+-----+-----
+

            default

            19 vs 18 Scenario

            Thus in short here below is all the method that we called as the 19 vs 18 Scenario of mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+                              |      |
+ |          ----› 10:6|  ----------------------------› Φ               | {6®} |
+  --------------------+-----+-----+-----+                              |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹------- Φ                      |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            Historical Events

            William Delbert Gann is perhaps the most mysterious of all the famous traders in history. Known for using geometry, astrology and ancient mathematics to predict events in the financial markets and historical events, evenso influences on the weather.

            11 x 30 = 330 = 329 + 1

            <div align="center">In March, Saturn was at 224° and Venus was at 344°. The corn top price was ¢137, which was around 104°,
            thus the three points loosely formed a Grand Trine (Wikipedia).</div>

            default

            1 container + 7 blocks + 29 flats + 77 rooms = f(0719425863) + 7 blocks + 29 flats + 77 rooms = 114 objects

            []

            Balanced Structural

            For starters, it possesses a perfectly balanced structural and numeric symmetries. So it conforms the intervals between the prime roots of the Prime Spiral Sieve (and every subsequent row or rotation of the sieve) with the period eight (8) difference sequence.

            Φ(10,2) = 10² + 2x(10th prime) + 10¹ = 100+29 + 29+10 = 129 + 39 = 168 = π(1000)

            8 objects

            To represent as a gap then this drive is supposed to not exist phisically by a computer, this could be replaced by special folders using shared drives such as Google Drive that you can use to store, search, and access files with a team.

            As of May 2022, shared drives are available to Google Workspace accounts including Education Fundamentals, Teaching & Learning Upgrade, Standard, and Plus, Nonprofits, Business Standard and Plus, Enterprise, and G Suite Business; Essentials.

            Google Drive

            It is also a form of the existence of DNA. The topology of DNA refers to the specific spatial structure formed by further distortion on the basis of the DNA double helix. Superhelical structure is the main form of topology, which can be divided into positive supercoil and negative supercoil, under corresponding conditions, they can transform each other.

            The topology of DNA

            Gann was a very devout man and honestly believed that he had found the key to predictable markets because of his study of the Bible in conjunction with his (supposed) study of many esoteric math theory from Greece and Egypt and his study of astrology.

            default

            It may take many years of serious study to master it. And most of the methods available online doesnt have anything to do with Gann. His books are also just means to put in the right path.

            Even though Gann was thought to be "religious", a careful analysis of his writings finds that he did not agree with the conventional Christian teachings (Wikipedia).

            WD Gann - A Trader Legend

            Real mastery and understanding is still programmed in such a way that only the most qualified and determined candidates could learn it and keep it remain as a secret, just as he desired.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/gist15.html b/identition/span1/gist15.html new file mode 100644 index 00000000000..16e16eefa17 --- /dev/null +++ b/identition/span1/gist15.html @@ -0,0 +1,169 @@ + Mass vs Gap (Δ) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Mass vs Gap (Δ)

            This section will be the last one of our presentation of 18th prime identity. Here we are going to explain one more item that is still open or undiscussed which is about what the 77 objects are going to do within the 19 vs 18 Scenario.

            15 + 35 + 28 = 15 + 63 = 78 = 77 + 1

            ---+-----+-----
+ 1 | 1   | 15
+---+-----+-----
+ 2 | 16  | 25
+---+-----+-----
+ 3 | 26  | 50
+---+-----+-----
+ 4 | 51  | 84
+---+-----+-----
+ 5 | 85  | 99
+---+-----+-----
+
            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            In many ways, a black hole acts like an ideal black body, as it reflects no light. Here is an animated simulation of a Schwarzschild black hole with a galaxy passing behind. Around the time of alignment, extreme gravitational lensing of the galaxy is observed.

            black hole

                            largest part=21 → 11+13+12=36 →  MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   ↓
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----
+---+-----+-----+-----+-----+                   ↓     |
+ 2 | 18  | 21  | 39  | 60  |-------------------      |
+---+-----+-----+-----+-----+                   |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |
+---+-----+-----+-----+-----+             |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |
+---+-----+-----+-----+-----+       |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |
+---+-----+-----+-----+-----+             |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |
+---+-----+-----+-----+-----+                   |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------      |
+---+-----+-----+-----+-----+                   ↓     |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----
+===+=====+=====+=====+=====+                   ↓
+45 | 277 |                      ← 11+13+12=36 ←  MEC30
+---+-----+                                     |
+ ↑
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            According to the observations made by NASA, Astronomers have uncovered TON 618 as the record breaking supermassive black hole, weighing 66 trillion and brilliantly as 140 trillion times that of the Sun, making it one of the brightest object in the Universe.

            default

            If the statement that it is indeed located at the center of our universe then the said black hole would behave as the exchange position between twin (2) universes. This would for sure strengthen the syntax algorithm of our implementation.

            7 x 11 = 77 = 99 - 22 = 11 x (9 -2)

              #8  |------- 5® --------|------------ 7® --------------|
+      | 1 |-------------- 77 = 4² + 5² + 6² -------------|
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ user | 7 | - | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+------+---|---+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+        Δ | Δ             |                      Δ  |   Δ
+       Φ17|Φ29            |                    96-99|  100 - 123 ({24})
+          |--- A,T,G,C ---|                         |  └── 100 - 103 (4x) » 100
+          Δ    2x2 = 4x   |-------  2x3 = 6x -------|  └── 104 - 109 (6x) » 30
+         {98}                                       |  └── 110 - 123 (14x)» 70
+
+
            Direction:
+- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.
+- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.
+- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.
+ 
+Conclution:
+- All of the other primes than 2 is 1 less than the number n times the number of 2. 
+- Those Mersenne primes is generated as 1 less than the power n of the number of 2. 
+- Thus they will conseqently be carried out by the same scheme of this number of 2.
+

            Perceptually, everything is separate and finite. But actually, everything is connected and infinite. It is this infinite connection, despite our limited finite perceptions, that makes us one with the cosmos.

            Primes Platform

            Each result goes to the 9th object of prime 67 which is 19th prime. This mass gap of (Δ > 0) is actually the quantum way of our algorithm which is discused in details by the 19th prime identity.

            So when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming bilateral 9 sum which facilitate them to finaly generate 1000 primes.

            1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+                
+-----+-----+-----+-----+-----+     -----------------------------------------------
+{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |
+-----+-----+-----+-----+-----+                                               |
+ {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone
+     +-----+-----+-----+-----+                                               |
+ {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |
+     +-----+-----+-----+                                               -----------
+ {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |
+ ----+-----+-----+-----+-----+                                               |
+  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone
+     +-----+-----+-----+-----+                                               |
+  {8}|23,25|25,27|27,29| 18                                                  |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+     |  1     2     3  |   4     5     6 |   7     8      9  |
+     |------ 29' ------|--------------- 139' ----------------|
+     |------ 102¨ -----|---------------  66¨ ----------------|
+

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row forming the Primes Platform. Thus we got 109 objects including for the 7 rows back to the original stage.

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+Sequence:
+ By the next layer the 89² will become 89 and 5 become 5² or 25.
+ This 89 and 25 are in the same layer with total of 114 or prime 619
+ So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            The above is observed following the W0 (assumptions of relativistic quantum mechanics) for the Existence and Mass Gap which transform under the homogeneous group as a four-vector and has a mass gap Δ > 0.

            Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R^4 and has a mass gap Δ > 0 (Wikipedia).

            image origin action

            runner

            Everything is linked

            The ζ(s) will behave as the other universe (not the twin) which was initiated paralelly by a big bang. While this parts are relativity young. it will continue to grow as a four-vector. So it will need a gap between each identities to proceed the thing.

            Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed (Wikipedia)

            Infinite number

            By our universe it could be represented by the central black hole which is very strong to throw away every objects but it has no resistance against any exchange from the other universe.

            In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle (Wikipedia).

            the central black hole_

            So by the ζ(s) then our multiverse is belong to a group of multiple universes inside the lightest particle of a mass gap out of one of the like of them somewhere in an infinite number of another parallel universes.

            Prof Stephen Hawking's final research paper suggests that our Universe may be one of many similar (BBC News).

            everything is linked

            Another suggestion which has just yet been in a topic of the science is that the similar behaviour also happen by particles such as hydrogen which is throwing all of the waves out of the central. So hypothetically it suppose to have a populated infinite number of its own parallel universes because whatever a smallest thing is arised, they could only exist by the same law of physics,

            Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron (Wikipedia).

            the electron in a hydrogen

            Consider that this law of physics would exist everywhere. So it is also one of their law when the 1st sequence of the ten (10) digits of 0719425863 in Euler's number is zero (0). Thus theoretically it speaks if an existence of everything arose from nothingness.

            ₠Quantum Project
            Copyright © 2022 All rights reserved.

            Reference:

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span1/index.html b/identition/span1/index.html new file mode 100644 index 00000000000..e6a65aa39b8 --- /dev/null +++ b/identition/span1/index.html @@ -0,0 +1,175 @@ + Wormhole Theory (span 1) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Wormhole Theory (span 1)

            This section serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks in quantum chromodynamics of colours of the gluon.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-39 of orgs section-11 that is inherited from the spin section-1 by prime spin-68 and span-140 with the partitions as below.

            +
            +
            1. Partition function
            2. Irrational Partitions
            3. Object Orientation
            4. Bonding Position
            5. The Quantum Way
            6. Proofreading Ability
            7. Replication Fork
            8. Building The Instance
            9. Imaginary Square
            10. Rational vs Irrational
            11. Rotation vs Revolution
            12. Zeta vs Zero
            13. Anti Parallel
            14. Mass vs Gap (Δ)

            A gauge colour rotation is a spacetime-dependent SU(3) group element. They span the Lie algebra of the SU(3) group in the defining representation.

            Feynman diagram

            +
            + + Note +
            +
            +

            In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).

            +
            +

            default

            quark-quark_scattering

            SmallBookPile

            So basically there is a basic transformation between addition of 3 + 4 = 7 in to their multiplication of 3 x 4 = 12 while the 7 vs 12 will be treated as exponentiation.

            images6-ezgif com-resize

            Matrix Scheme

            Quarks have three colors. Color is to the strong interaction as electric charge is to the electromagnetic interaction.

            quantum-chromodynamics-1-320

            red   anti-red,   red   anti-blue,   red   anti-green,
+blue  anti-red,   blue  anti-blue,   blue  anti-green,
+green anti-red,   green anti-blue,   green anti-green.
+

            This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent

            +
            + + Note +
            +
            +

            During the last few years of the 12th century, Fibonacci undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that it popularized the use of the Arabic numerals in Europe, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. (Famous Mathematicians)

            +
            +

            MEC30 Square

            Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30's square.

            +
            + + Note +
            +
            +

            A square system of coupled nonlinear equations can be solved iteratively by Newton’s method. This method uses the Jacobian matrix of the system of equations. (Wikipedia)

            +
            +

            gradien

            +
            + + Note +
            +
            +

            Fermions and bosons—fermions have quantum spin = 1/2.

            • The elementary fermions are leptons and quarks.
            • There are three generations of leptons: electron, muon, and tau, with electric charge −1, and their neutrinos with no electric charge.
            • There are three generations of quarks: (u, d); (c, s); and (t, b).

            The (u, c, t) quarks have electric charge 2/3 while the (d, s, b) quarks have electric charge −1/3. (IntechOpen)

            +
            +

            UF1

            Interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used.

            UF2

            Bosons have quantum spin = 1: photon, quantum of the electromagnetic field; gluon, quantum of the strong field; and W and Z, weak field quanta, which we do not need.

            +
            + + Note +
            +
            +

            An animation of color confinement, a property of the strong interaction. If energy is supplied to the quarks as shown, the gluon tube connecting quarks elongates until it reaches a point where it “snaps” and the energy added to the system results in the formation of a quark–antiquark pair. Thus single quarks are never seen in isolation. (Wikipedia)

            +
            +

            Gluon_tube-color_confinement_animation

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   17+i7 👈
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |   66+i30
+

            Interactions

            The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.

            +
            + + Note +
            +
            +

            Unlike the strong force, the residual strong force diminishes with distance, and does so rapidly. The decrease is approximately as a negative exponential power of distance, though there is no simple expression known for this; see Yukawa potential. The rapid decrease with distance of the attractive residual force and the less rapid decrease of the repulsive electromagnetic force acting between protons within a nucleus, causes the instability of larger atomic nuclei, such as all those with atomic numbers larger than 82 (the element lead). (Wikipedia)

            +
            +

            gifman

            +
            + + Note +
            +
            +

            Feynman diagram for the same process as in the animation, with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion “in-flight”, are not shown. The π⁰ pion contains an anti-quark, shown to travel in the opposite direction, as per the Feynman–Stueckelberg interpretation. (Wikipedia)

            +
            +

            residual strong force

            +
            + + Note +
            +
            +

            The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.

            • These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation (so they can generate unitary matrix group elements of SU(3) through exponentiation[1]). These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann’s quark model.[2] Gell-Mann’s generalization further extends to general SU(n). For their connection to the standard basis of Lie algebras, see the Weyl–Cartan basis.
            • Since the eight matrices and the identity are a complete trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that satisfied by the Pauli matrices. Namely, using the dot to sum over the eight matrices and using Greek indices for their row/column indices
            • A particular choice of matrices is called a group representation, because any element of SU(3) can be written in the form using the Einstein notation, where the eight are real numbers and a sum over the index j is implied. Given one representation, an equivalent one may be obtained by an arbitrary unitary similarity transformation, since that leaves the commutator unchanged.
            • The matrices can be realized as a representation of the infinitesimal generators of the special unitary group called SU(3). The Lie algebra of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight linearly independent generators, which can be written as g_{i}, with i taking values from 1 to 8

            These matrices serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks of quantum chromodynamics (cf. colours of the gluon). A gauge colour rotation is a spacetime-dependent SU(3) group element where summation over the eight indices (8) is implied. Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ |  5¨ |  3¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            From the 50 we gonna split the 15 by bilateral 9 sums resulting 2 times 15+9=24 which is 48. So the total of involved objects is 50+48=98.

            +
            + + Note +
            +
            +

            Consider the evidence: scattering experiments strongly suggest a meson to be composed of a quark anti-quark pair and a baryon to be composed of three quarks. The famous 3R experiment also suggests that whatever force binds the quarks together has 3 types of charge (called the 3 colors).

            • Now, into the realm of theory: we are looking for an internal symmetry having a 3-dimensional representation which can give rise to a neutral combination of 3 particles (otherwise no color-neutral baryons).
            • The simplest such statement is that a linear combination of each type of charge (red + green + blue) must be neutral, and following William of Occam we believe that the simplest theory describing all the facts must be the correct one.
            • We now postulate that the particles carrying this force, called gluons, must occur in color anti-color units (i.e. nine of them).
            • BUT, red + blue + green is neutral, which means that the linear combination red anti-red + blue anti-blue + green anti-green must be non-interacting, since otherwise the colorless baryons would be able to emit these gluons and interact with each other via the strong force—contrary to the evidence. So, there can only be EIGHT gluons.

            This is just Occam’s razor again: a hypothetical particle that can’t interact with anything, and therefore can’t be detected, doesn’t exist. The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra. That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional. (Physics FAQ)

            +
            +

            0_kGdCmWqcFG_s8fIq

            Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            960x0

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-👇--+                                             ---
+ 17¨ |  5¨ |  3¨ |  ❓ |  7¨ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            +
            + + Note +
            +
            +

            Young diagrams associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia).

            +
            +

            Hadron_colors svg

            +
            + + Note +
            +
            +

            In mathematics, orthonormality typically implies a norm which has a value of unity (1). Gell-Mann matrices, however, are normalized to a value of 2.

            • Thus, the trace of the pairwise product results in the ortho-normalization condition where delta is the Kronecker delta.
            • This is so the embedded Pauli matrices corresponding to the three embedded subalgebras of SU(2) are conventionally normalized.
            • In this three-dimensional matrix representation, the Cartan subalgebra is the set of linear combinations (with real coefficients) of the two matrices which commute with each other.

            The SU(2) Casimirs of these subalgebras mutually commute. However, any unitary similarity transformation of these subalgebras will yield SU(2) subalgebras. There is an uncountable number of such transformations. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-👇--+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            e72_3

            QCD+QUANTUM+ELECTRODYNAMICS_+is+the+quantum+theory+of+the+electromagnetic+interaction +mediated+by+massless+photons

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist01.html b/identition/span10/gist01.html new file mode 100644 index 00000000000..65d35e3c595 --- /dev/null +++ b/identition/span10/gist01.html @@ -0,0 +1,5 @@ + The Centralizing · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Centralizing

            default

            Direction:
+- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.
+- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.
+- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.
+

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist02.html b/identition/span10/gist02.html new file mode 100644 index 00000000000..e3643e8f904 --- /dev/null +++ b/identition/span10/gist02.html @@ -0,0 +1 @@ + gist02.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default default default default default default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist02.md b/identition/span10/gist02.md new file mode 100644 index 00000000000..c846b0cd2c7 --- /dev/null +++ b/identition/span10/gist02.md @@ -0,0 +1,8 @@ +![default](https://user-images.githubusercontent.com/8466209/201104906-927fddf1-bd46-43b6-8b3d-47c37657deb1.png) +![default](https://user-images.githubusercontent.com/8466209/201105343-f8d9aec8-fd82-442d-8d6a-dcac5a61da42.png) +![default](https://user-images.githubusercontent.com/8466209/201105576-5670bc54-46f9-4f78-b6f8-e1a3868a590e.png) +![default](https://user-images.githubusercontent.com/8466209/201106351-89b330d9-e60f-44b4-ba72-097f04fa63c4.png) +![default](https://user-images.githubusercontent.com/8466209/201107959-5311d9a7-0b61-4b18-8ea1-b32a36f1d804.png) +![default](https://user-images.githubusercontent.com/8466209/201108271-9edc6b15-d4d8-469f-b7c9-797cd0abdfe4.png) +![default](https://user-images.githubusercontent.com/8466209/201108973-71ecaec4-c47e-4b3f-bbec-4cc2343344fd.png) + diff --git a/identition/span10/gist03.html b/identition/span10/gist03.html new file mode 100644 index 00000000000..2eecf43c8ff --- /dev/null +++ b/identition/span10/gist03.html @@ -0,0 +1 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            image

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist03.md b/identition/span10/gist03.md new file mode 100644 index 00000000000..c316ac5f239 --- /dev/null +++ b/identition/span10/gist03.md @@ -0,0 +1,6 @@ +[![default](https://user-images.githubusercontent.com/8466209/201110882-5dd8931d-a1cd-4bb7-8d82-0d3da0b58c66.png)](https://github.com/FeedMapping/feedmapping.github.io) + +![image](https://user-images.githubusercontent.com/8466209/201114200-db3490f8-a9b4-4bb6-bed3-dbc1677fd45e.png) + +[![default](https://user-images.githubusercontent.com/8466209/201117531-d2fd8521-3056-4581-9354-f58052808e9b.png)](https://github.com/eq19/eq19.github.io/tree/eQ19) + diff --git a/identition/span10/gist04.html b/identition/span10/gist04.html new file mode 100644 index 00000000000..5900940687d --- /dev/null +++ b/identition/span10/gist04.html @@ -0,0 +1 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist04.md b/identition/span10/gist04.md new file mode 100644 index 00000000000..b4d36588378 --- /dev/null +++ b/identition/span10/gist04.md @@ -0,0 +1,5 @@ +![default](https://user-images.githubusercontent.com/8466209/201120468-f985427d-b4e8-4bf8-b39c-e5919af1f540.png) + +![default](https://user-images.githubusercontent.com/8466209/201121309-7410e679-3273-4e87-9177-abeae76ffb5b.png) + +![image](https://user-images.githubusercontent.com/8466209/201121924-f8b105e5-0e76-4513-90c6-b561071aa699.png) diff --git a/identition/span10/gist05.html b/identition/span10/gist05.html new file mode 100644 index 00000000000..dd4e14be42e --- /dev/null +++ b/identition/span10/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist05.md b/identition/span10/gist05.md new file mode 100644 index 00000000000..b6e3ce588cb --- /dev/null +++ b/identition/span10/gist05.md @@ -0,0 +1,3 @@ +[![default](https://user-images.githubusercontent.com/8466209/201255091-979c9ab2-18a3-467b-95b1-11c9a80bcbf4.png)](https://github.com/TheAlgorithms/Python/blob/master/requirements.txt) +[![default](https://user-images.githubusercontent.com/8466209/201279272-a840ff2f-7eb0-48eb-8dd5-37e266a62d5a.png)](https://github.com/eq19/grammar/actions/workflows/build.yml) +[![default](https://user-images.githubusercontent.com/8466209/201256070-85b14f71-063b-4b4a-b546-be9dec8c9c6f.png)](https://github.com/eq19/grammar/actions/runs/3441609775/jobs/5741337732) diff --git a/identition/span10/gist06.html b/identition/span10/gist06.html new file mode 100644 index 00000000000..fc49072e8bf --- /dev/null +++ b/identition/span10/gist06.html @@ -0,0 +1,78 @@ + Site GitHub · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Site GitHub

            The following sample information is exposed to Jekyll templates in the site.github namespace:

            
+{% for item in site.github %}
+  * {{ item | jsonify }}: {{ site.github[item] | jsonify }}
+{% endfor %}
+
+

            Output:

            {
+    "versions": {
+        "jekyll": <version>,
+        "kramdown": <version>,
+        "liquid": <version>,
+        "maruku": <version>,
+        "rdiscount": <version>,
+        "redcarpet": <version>,
+        "RedCloth": <version>,
+        "jemoji": <version>,
+        "jekyll-mentions": <version>,
+        "jekyll-redirect-from": <version>,
+        "jekyll-sitemap": <version>,
+        "github-pages": <version>,
+        "ruby": <version>"
+    },
+    "hostname": "github.com",
+    "pages_hostname": "github.io",
+    "api_url": "https://api.github.com",
+    "help_url": "https://help.github.com",
+    "environment": "dotcom",
+    "pages_env": "dotcom",
+    "public_repositories": [ Repository Objects ],
+    "organization_members": [ User Objects ],
+    "build_revision": "cbd866ebf142088896cbe71422b949de7f864bce",
+    "project_title": "metadata-example",
+    "project_tagline": "A GitHub Pages site to showcase repository metadata",
+    "owner_name": "github",
+    "owner_url": "https://github.com/github",
+    "owner_gravatar_url": "https://github.com/github.png",
+    "repository_url": "https://github.com/github/metadata-example",
+    "repository_nwo": "github/metadata-example",
+    "repository_name": "metadata-example",
+    "zip_url": "https://github.com/github/metadata-example/zipball/gh-pages",
+    "tar_url": "https://github.com/github/metadata-example/tarball/gh-pages",
+    "clone_url": "https://github.com/github/metadata-example.git",
+    "releases_url": "https://github.com/github/metadata-example/releases",
+    "issues_url": "https://github.com/github/metadata-example/issues",
+    "wiki_url": "https://github.com/github/metadata-example/wiki",
+    "language": null,
+    "is_user_page": false,
+    "is_project_page": true,
+    "show_downloads": true,
+    "url": "http://username.github.io/metadata-example", // (or the CNAME)
+    "baseurl": "/metadata-example",
+    "contributors": [ User Objects ],
+    "releases": [ Release Objects ],
+    "latest_release": [ Release Object ],
+    "private": false,
+    "archived": false,
+    "disabled": false,
+    "license": {
+      "key": "mit",
+      "name": "MIT License",
+      "spdx_id": "MIT",
+      "url": "https://api.github.com/licenses/mit"
+    },
+    "source": {
+      "branch": "gh-pages",
+      "path": "/"
+    }
+}
+

            GitHub API

            Jekyll supports loading data from YAML, JSON, CSV, and TSV files located in the _data directory. Note that CSV and TSV files must contain a header row.

                gh api -H "${HEADER}" /user/orgs  --jq '.[].login' | sort -uf | yq eval -P | sed "s/ /, /g" > /tmp/user_orgs
+    IFS=', '; array=($(cat /tmp/user_orgs))
+
+    echo "[" > _data/orgs.json
+    for ((i=0; i < ${#array[@]}; i++)); do
+	  gh api -H "${HEADER}" /orgs/${array[$i]} >> _data/orgs.json
+      if [[ "$i" -lt "${#array[@]}-1" ]]; then echo "," >> _data/orgs.json; fi
+    done
+    echo "]" >> _data/orgs.json
+  fi
+

            ```liquid

            {% for item in site.data.orgs %}

            • {{ item.name | jsonify }} {% endfor %}

            ```- "Wormhole Theory"- "Elementary Particles"- "Symmetric Expansion"- "Vibrating Strings"- "Multiple Universes"- "Hidden Dimensions"- "Basic Transformation"- "Fundamental Forces"- "Quadratic Polynomials"- "Truncated Perturbation"- "Extra Dimensions"## Wotkflow Run

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist06.md b/identition/span10/gist06.md new file mode 100644 index 00000000000..7159888cac0 --- /dev/null +++ b/identition/span10/gist06.md @@ -0,0 +1,115 @@ +# Site GitHub + +The following sample information is exposed to Jekyll templates in the [site.github](https://github.com/jekyll/github-metadata/blob/main/docs/site.github.md#using-sitegithub) namespace: + +``` +{% raw %} +{% for item in site.github %} + * {{ item | jsonify }}: {{ site.github[item] | jsonify }} +{% endfor %} +{% endraw %} +``` + +Output: +``` +{ + "versions": { + "jekyll": , + "kramdown": , + "liquid": , + "maruku": , + "rdiscount": , + "redcarpet": , + "RedCloth": , + "jemoji": , + "jekyll-mentions": , + "jekyll-redirect-from": , + "jekyll-sitemap": , + "github-pages": , + "ruby": " + }, + "hostname": "github.com", + "pages_hostname": "github.io", + "api_url": "https://api.github.com", + "help_url": "https://help.github.com", + "environment": "dotcom", + "pages_env": "dotcom", + "public_repositories": [ Repository Objects ], + "organization_members": [ User Objects ], + "build_revision": "cbd866ebf142088896cbe71422b949de7f864bce", + "project_title": "metadata-example", + "project_tagline": "A GitHub Pages site to showcase repository metadata", + "owner_name": "github", + "owner_url": "https://github.com/github", + "owner_gravatar_url": "https://github.com/github.png", + "repository_url": "https://github.com/github/metadata-example", + "repository_nwo": "github/metadata-example", + "repository_name": "metadata-example", + "zip_url": "https://github.com/github/metadata-example/zipball/gh-pages", + "tar_url": "https://github.com/github/metadata-example/tarball/gh-pages", + "clone_url": "https://github.com/github/metadata-example.git", + "releases_url": "https://github.com/github/metadata-example/releases", + "issues_url": "https://github.com/github/metadata-example/issues", + "wiki_url": "https://github.com/github/metadata-example/wiki", + "language": null, + "is_user_page": false, + "is_project_page": true, + "show_downloads": true, + "url": "http://username.github.io/metadata-example", // (or the CNAME) + "baseurl": "/metadata-example", + "contributors": [ User Objects ], + "releases": [ Release Objects ], + "latest_release": [ Release Object ], + "private": false, + "archived": false, + "disabled": false, + "license": { + "key": "mit", + "name": "MIT License", + "spdx_id": "MIT", + "url": "https://api.github.com/licenses/mit" + }, + "source": { + "branch": "gh-pages", + "path": "/" + } +} +``` + +## GitHub API + +Jekyll supports [loading data](https://jekyllrb.com/docs/datafiles/) from YAML, JSON, CSV, and TSV files located in the _data directory. Note that CSV and TSV files must contain a header row. + +```bash + gh api -H "${HEADER}" /user/orgs --jq '.[].login' | sort -uf | yq eval -P | sed "s/ /, /g" > /tmp/user_orgs + IFS=', '; array=($(cat /tmp/user_orgs)) + + echo "[" > _data/orgs.json + for ((i=0; i < ${#array[@]}; i++)); do + gh api -H "${HEADER}" /orgs/${array[$i]} >> _data/orgs.json + if [[ "$i" -lt "${#array[@]}-1" ]]; then echo "," >> _data/orgs.json; fi + done + echo "]" >> _data/orgs.json + fi +``` + +```liquid +{% raw %} +{% for item in site.data.orgs %} + - {{ item.name | jsonify }} +{% endfor %} +{% endraw %} +``` + +{%- for item in site.data.orgs -%} + - {{ item.name | jsonify }} +{%- endfor -%} + +## Wotkflow Run + +[![default](https://user-images.githubusercontent.com/8466209/201278178-6c8eb4c9-1a45-4583-b61e-b948d9431e95.png)](https://github.com/TheAlgorithms/Python/blob/master/.github/workflows/build.yml) + +[![default](https://user-images.githubusercontent.com/8466209/201258756-7f1cc4e4-fc24-4061-8dbe-8610dd56a557.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-gitignore-md) + +[![default](https://user-images.githubusercontent.com/8466209/201274327-f0e777ad-7226-4b86-bb1e-c21290264492.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-runner-md) + diff --git a/identition/span10/gist07.html b/identition/span10/gist07.html new file mode 100644 index 00000000000..78975934724 --- /dev/null +++ b/identition/span10/gist07.html @@ -0,0 +1 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            image

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist07.md b/identition/span10/gist07.md new file mode 100644 index 00000000000..b3bfd7166ef --- /dev/null +++ b/identition/span10/gist07.md @@ -0,0 +1,9 @@ +[![default](https://user-images.githubusercontent.com/8466209/201290909-61804ad4-04d9-40f6-81d3-b396909cf372.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-opposite-md) + +[![default](https://user-images.githubusercontent.com/8466209/201287545-565e5907-eb35-48ba-96c8-199a70cc8fa4.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-syntax-md) + +[![image](https://user-images.githubusercontent.com/8466209/201288295-5b42e95b-3a67-4136-8e60-174f9bc473f8.png)](https://github.com/purcellconsult/OOP-in-Python) + +[![default](https://user-images.githubusercontent.com/8466209/201290477-3bfd5e72-d761-4610-acd1-c314d369d100.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md) + +![image](https://user-images.githubusercontent.com/8466209/201288734-8d9a1193-3b15-4501-803c-0ced1b0ef91f.png) diff --git a/identition/span10/gist08.html b/identition/span10/gist08.html new file mode 100644 index 00000000000..9217210720e --- /dev/null +++ b/identition/span10/gist08.html @@ -0,0 +1 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            image

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist08.md b/identition/span10/gist08.md new file mode 100644 index 00000000000..00bcf879571 --- /dev/null +++ b/identition/span10/gist08.md @@ -0,0 +1,13 @@ +[![default](https://user-images.githubusercontent.com/8466209/201292753-842f61b5-fa45-4b0b-be17-41545774c28b.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-4_quantum-md) + +[![default](https://user-images.githubusercontent.com/8466209/201289502-7a7e9c84-1bdf-4865-8eab-7117d7362afe.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-algorithm-md!) + +[![image](https://user-images.githubusercontent.com/8466209/201289841-81b4e930-012c-499a-b192-4e2387698f39.png)](https://github.com/tensorflow/tensorflow) + +[![default](https://user-images.githubusercontent.com/8466209/201290640-9f7b1e38-6fe2-4819-9fd9-e8777c6eddc4.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md) + +![image](https://user-images.githubusercontent.com/8466209/201288829-541df68d-fd5c-4dcc-859b-35af3a15f100.png) + + + + diff --git a/identition/span10/gist09.html b/identition/span10/gist09.html new file mode 100644 index 00000000000..086a95ef1f5 --- /dev/null +++ b/identition/span10/gist09.html @@ -0,0 +1 @@ + gist09.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            image

            Tables Are Cool
            col 1 is left-aligned $1600
            col 2 is 📂 centered $12
            col 3 is right-aligned $1
            Tables Are Cool
            col 3 is 🚀 right-aligned $1600
            col 2 is 🔨 centered $12
            zebra stripes are neat $1
            <ul><li>💎item1</li><li>💎item2</li></ul> See the list from the first column
            Tables Are Cool
            col 3 is right-aligned $1600
            col 2 is centered $12
            zebra stripes are neat $1
            • item1
            • item2
            		 See the list from the first column

            The hexagon is also found in the structure of DNA it forms the chains that produce the double-helix macromolecule. Functional description of DNA (I) comprising using a bio-oscillator which reproduces the sequence of bases, in spatial and energetic states, in the form of vibrations, is new.

            This Ulam spiral serves to illustrate primes and prime factor abundances in a hexagonal spiral. Prime numbers in green; darker blue indicates numbers with more different prime factors..

            Ulam spiral

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist09.md b/identition/span10/gist09.md new file mode 100644 index 00000000000..a342321008c --- /dev/null +++ b/identition/span10/gist09.md @@ -0,0 +1,59 @@ +[![default](https://user-images.githubusercontent.com/8466209/201276953-5e3f16bc-f578-4336-b4d0-9b25a658ff66.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-circular-md) + +[![image](https://user-images.githubusercontent.com/8466209/201293827-ed23aa2f-54a4-4e5c-9535-ddc65eaf63dc.png)](https://github.com/kamranahmedse/developer-roadmap) + +| Tables | Are | Cool | +|----------|:-------------:|------:| +| col 1 is | left-aligned | $1600 | +| col 2 is | 📂 centered | $12 | +| col 3 is | right-aligned | $1 | + + +| Tables | Are | Cool | +| ------------- |:-------------:| -----:| +| col 3 is 🚀 | right-aligned | $1600 | +| col 2 is 🔨 | centered | $12 | +| zebra stripes | are neat | $1 | +|
            • 💎item1
            • 💎item2
            | See the list | from the first column| + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
            TablesAreCool
            col 3 isright-aligned$1600
            col 2 iscentered$12
            zebra stripesare neat$1
            +
              +
            • item1
              • +
            • item2
              • +
            +             		See the listfrom the first column
            + + +The hexagon is also found in the structure of DNA it forms the chains that produce the double-helix macromolecule. Functional description of DNA (I) comprising using a bio-oscillator which reproduces the sequence of bases, in spatial and energetic states, in the form of vibrations, is new. + +>This Ulam spiral serves to illustrate primes and prime factor abundances in a hexagonal spiral. Prime numbers in green; darker blue indicates numbers with more different prime factors.. + +[![Ulam spiral](https://upload.wikimedia.org/wikipedia/commons/2/25/Hexgrid_prime_number_spiral.svg)](https://en.wikipedia.org/wiki/Ulam_spiral) diff --git a/identition/span10/gist10.html b/identition/span10/gist10.html new file mode 100644 index 00000000000..874abfbfb3c --- /dev/null +++ b/identition/span10/gist10.html @@ -0,0 +1,31 @@ + Poincaré Conjecture · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Poincaré Conjecture

            ---+-----+-----
+ 1 | {1} | {2}
+---+-----+-----
+ 2 |  3  | 20
+---+-----+-----
+ 3 | 21  | 46
+---+-----+-----
+ 4 |{47} | 58
+---+-----+-----
+ 5 | 59  | 70
+---+-----+-----
+ 6 |{71} |{93}
+---+-----+-----
+ 7 | 94  | 103
+---+-----+-----
+ 8 | 104 |{109}
+---+-----+-----
+

            default

              --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+

            default

            In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries (Clay Institute).

            Poincaré Conjecture

            The Ricci Flow method has now been developed not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI (Artificial intelligence). No wonder now all the science leads to it.

            AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence. Discussions on many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence as the golden standard for Artificial Intelligence (Human vs AI).

            default

            Despite of any debated subjects regarding Human vs AI, the said AI would not even close to the ability of human brain without undertanding of GAP functionality between left and right of the human brain. Let's find it in details on further discussion.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span10/gist10.md b/identition/span10/gist10.md new file mode 100644 index 00000000000..ab864959254 --- /dev/null +++ b/identition/span10/gist10.md @@ -0,0 +1,69 @@ +## Poincaré Conjecture + +``` +---+-----+----- + 1 | {1} | {2} +---+-----+----- + 2 | 3 | 20 +---+-----+----- + 3 | 21 | 46 +---+-----+----- + 4 |{47} | 58 +---+-----+----- + 5 | 59 | 70 +---+-----+----- + 6 |{71} |{93} +---+-----+----- + 7 | 94 | 103 +---+-----+----- + 8 | 104 |{109} +---+-----+----- +``` + +![](https://user-images.githubusercontent.com/36441664/84181975-e2d99680-aab3-11ea-8cf0-7da54cf0eb3f.jpg) + +![](https://user-images.githubusercontent.com/36441664/84181982-e4a35a00-aab3-11ea-848a-89c1a1f8c9cf.jpg) + +![default](https://user-images.githubusercontent.com/8466209/200230450-2754c2d3-2b52-429d-b1c5-48fcfdf923be.png) + +![](https://user-images.githubusercontent.com/36441664/86853354-88e2e580-c0e0-11ea-92e4-24de95335054.gif) + +![](https://user-images.githubusercontent.com/36441664/88384290-54f10b00-cdd6-11ea-878d-c687cc1afbea.gif) + +![](https://user-images.githubusercontent.com/36441664/84181979-e3722d00-aab3-11ea-9868-982020dcd4b3.png) + +![](https://user-images.githubusercontent.com/36441664/84685920-3ee56480-af65-11ea-81a4-f44ebc656a19.jpg) + +``` + --------------------+-----+-----+-----+-----+-----+ | --- + 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | | + | +-----+-----+-----+ | | + | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism + | | +-----+-----+-----+ | | | + | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | | + | | | +-----+-----+-----+ | | --- + | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | | + | | +-----+-----+-----+ | | + | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance +329 | +-----+-----+-----+ | + | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ | + -------------------+-----+-----+ --- +``` + +![](https://user-images.githubusercontent.com/36441664/82712407-12b22d00-9cb2-11ea-9cc2-3cf392b2d35c.png) + +![](https://user-images.githubusercontent.com/36441664/88372848-e5bcec00-cdc0-11ea-8b8a-09b579a257f9.png) + +![default](https://user-images.githubusercontent.com/8466209/200230504-9b543817-cb59-4bc1-8bbb-fddc059c7d6b.png) + +>In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries _([Clay Institute](https://www.claymath.org/millennium-problems))_. + +[![Poincaré Conjecture](https://user-images.githubusercontent.com/36441664/84187330-17515080-aabc-11ea-8e53-47f12a248d4c.jpg)](https://www.claymath.org/millennium-problems/poincar%C3%A9-conjecture) + +The Ricci Flow method has now been _[developed](http://engine.scichina.com/publisher/scp/journal/SCIS/62/9/10.1007/s11432-018-9702-7)_ not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI ([Artificial intelligence](https://en.wikipedia.org/wiki/Artificial_intelligence)). No wonder now all the science leads to it. + +>AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence. Discussions on many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence as the golden standard for Artificial Intelligence _([Human vs AI](https://www.frontiersin.org/articles/10.3389/frai.2021.622364/full))_. + +[![default](https://user-images.githubusercontent.com/8466209/224466884-5ba87f02-e01d-45ca-a9c3-a1d535e83228.png)](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#mass-gap-%CE%B4) + +Despite of any debated subjects regarding _Human vs AI_, the said AI would not even close to the ability of human brain without undertanding of _[GAP](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#mass-vs-gap-%CE%B4)_ functionality between left and right of the human brain. Let's find it in details on further discussion. \ No newline at end of file diff --git a/identition/span10/index.html b/identition/span10/index.html new file mode 100644 index 00000000000..f17b9d8c559 --- /dev/null +++ b/identition/span10/index.html @@ -0,0 +1,97 @@ + Truncated Perturbation (span 10) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Truncated Perturbation (span 10)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-30 of orgs section-2 that is inherited from the spin section-10 by prime spin-40 and span-149 with the partitions as below.

            +
            +
            1. Poincaré Conjecture
            2. gist04.md
            3. gist03.md
            4. gist02.md
            5. gist05.md
            6. Site GitHub
            7. gist07.md
            8. gist08.md
            9. gist09.md
            10. The Centralizing

            Runners are the machines that execute jobs in a GitHub Actions workflow. You can access Variables and Contexts information in specific OS. For example, a runner can clone your repository locally, install testing software, and then run commands.

            
+# Sample workflow for building and deploying a Jekyll site to GitHub Pages
+name: Build and deploy Jekyll site
+
+# 💎 Runs on deployment targeting the default branch
+on:
+  # push:
+    # branches: [eQ19]
+  workflow_run:
+    types: [completed] #requested
+    workflows: ["pages-build-deployment"]
+
+# 🪂 Allow only one concurrent deployment across the branches
+concurrency:
+  group: "pages"
+  cancel-in-progress: true
+  
+# Sets permissions of the GITHUB_TOKEN
+permissions: write-all
+
+# Sets global environtment variables
+env:
+  OWNER: ${{ github.repository_owner }}
+
+jobs:
+  # Build job
+  github-pages:
+    if: github.event.workflow_run.conclusion == 'success'
+    runs-on: ${{ vars.OWNER != 'FeedMapping' && 'ubuntu-latest' || 'windows-latest' }}
+    steps:
+      - name: 📂 Checkout
+        uses: actions/checkout@v3
+        with:
+          submodules: recursive
+ 
+      - name: 💎 Build on Linux
+        if: runner.os == 'Linux'
+        uses: eq19/feed@v2
+        with:
+          pre_build_commands: 'make build'
+          token: ${{ secrets.JEKYLL_GITHUB_TOKEN }}
+
+      - name: 💎 Build on Windows
+        if: runner.os == 'Windows'
+        uses: eq19/maps@v1
+        id: stepid
+        with:
+          dotnet-version: '3.1.x'
+
+

            By deploying containers on Compute Engine, you can simplify app deployment while controlling four dimensional space. You can configure a virtual machine (VM) instance or an instance template to deploy and launch a Docker container.

            default

            This property would tend the ballancing scheme of MEC30 so it will let 30-18=12 pairing with another 12 of 24 spins prime hexagon. The 24 goes to the center of True Prime Pairs ny the prime pair 13 and 11 and let the crancks of 2,3,5,7 inside the 10 ranks.

                                            | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   feeding    |     mapping     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+
+                                                                                |  2 | 60 | 40 |
+                                                                                +----+----+----+
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            This 71 is a conformation that it has the same result as we have explained on the residual objects of 571 turn to a vektor of 71 while the rest of 500 turn to 200 objects of 3's identity and the last objects of 300 goes to the next cycles.

            default

            So now out of 1000 numbers that generated from 1000 primes we will get the rest of 1000 - 100 = 900. This 900 will behave as matrix square 30x30 and act as the base frame of 2nd and 3rd layer which are working on π(π(100x100))-1=200 primes:

                                        33+34=67=19th prime
+ |----------------------------------|-------------------------------------------------------------|
+ |             33                   |                             34                              |
+ |--------------|-------------------|------------------------------|------------------------------|
+ |     lexering = π(1000)           |                    parsering = 1000/Φ                       |
+ |--------------|-------------------|------------------------------|------------------------------|
+ |   feeding    |      mapping      |          syntaxing           |          grammaring          |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |  39 | 40 | 41 | 42 | 43 | 44 | 45  | 46 | 47 | 48 |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1  | 30 | 30 | 5  | 1  | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ |       2'     |        3'         |              5'              |               7'             | 
+

            default

            The GitHub hosted runner is assigned to run the Linux container and a Windows Server Core container simultaneously. This is an experimental feature of Microsoft WSL2 and may have some issues. One known problem is volumes are not stable.

            Set WSL

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist01.html b/identition/span11/gist01.html new file mode 100644 index 00000000000..c36b5bea2e3 --- /dev/null +++ b/identition/span11/gist01.html @@ -0,0 +1,8 @@ + Rationalization · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Rationalization

            default

                  |------------------- 11¤ ---------------------|
+------+---+---+---+---+---+---+---+---+---+----+----+
+ repo | 2 | 3 | 4 | 5 | 6 |{7}|{8}| 9 | 10| 11 |{12}| 77
+------+---+---+---+---+---+---+---+---+---+----+----+
+ blok | 9 | 7 | 9 | 6 |{7}|{8}| 8 | 5 | 8 |  8 | {3}| 78
+------+---+---+---+---+---+---+---+---+---+----+----+
+      |---------- 6¤ ---------|                   Δ
+

            default default default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist02.html b/identition/span11/gist02.html new file mode 100644 index 00000000000..e42a29971d8 --- /dev/null +++ b/identition/span11/gist02.html @@ -0,0 +1,10 @@ + gist02.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+

            default

            default image image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist02.md b/identition/span11/gist02.md new file mode 100644 index 00000000000..3a82723bc67 --- /dev/null +++ b/identition/span11/gist02.md @@ -0,0 +1,18 @@ +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + ``` + + +![default](https://user-images.githubusercontent.com/8466209/201350726-068c3de2-8123-43ec-9d08-6afc743ddcbe.png) + +![default](https://user-images.githubusercontent.com/8466209/201355458-2ff29c7c-c35a-49ed-a9e8-f607ae5841ab.png) +![image](https://user-images.githubusercontent.com/8466209/201383102-8ae5652f-94fd-4f09-adab-d727e3ba80f5.png) +![image](https://user-images.githubusercontent.com/8466209/201368103-efd619a2-a608-420e-9117-40f92e68a003.png) diff --git a/identition/span11/gist03.html b/identition/span11/gist03.html new file mode 100644 index 00000000000..ce3bc5bed10 --- /dev/null +++ b/identition/span11/gist03.html @@ -0,0 +1,15 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

              #8 |----------- 5® --------|------------ 7® --------------|
+     |  1  |---------------- 77 = 4² + 5² + 6² -------------|
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ user|  7  |  -  | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main|  -  |  9  | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+               Δ | Δ             |                       Δ  |   Δ
+              Φ17|Φ29            |                     96-99|  100 - 123 ({24})
+                 |--- A,T,G,C ---|                          |  └── 100 - 103 (4x) » 100
+                 Δ    2x2 = 4x   |-------  2x3 = 6x  -------|  └── 104 - 109 (6x) » 30
+                {98}                                        |  └── 110 - 123 (14x)» 70
+
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist03.md b/identition/span11/gist03.md new file mode 100644 index 00000000000..392c88936e8 --- /dev/null +++ b/identition/span11/gist03.md @@ -0,0 +1,19 @@ +[![default](https://user-images.githubusercontent.com/8466209/201387892-26680e27-bbd9-494c-9e8b-c14226f346d5.png)](https://en.wikipedia.org/wiki/List_of_regions_in_the_human_brain) + +![default](https://user-images.githubusercontent.com/36441664/72667103-cd06fe80-3a4a-11ea-85fe-c75d551fa049.jpg) +``` + #8 |----------- 5® --------|------------ 7® --------------| + | 1 |---------------- 77 = 4² + 5² + 6² -------------| +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77 +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78 + main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + Δ | Δ | Δ | Δ + Φ17|Φ29 | 96-99| 100 - 123 ({24}) + |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100 + Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30 + {98} | └── 110 - 123 (14x)» 70 +``` diff --git a/identition/span11/gist04.html b/identition/span11/gist04.html new file mode 100644 index 00000000000..78dc0605523 --- /dev/null +++ b/identition/span11/gist04.html @@ -0,0 +1,15 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|------------------------ Scheme-12 ------------------------|
+|------------ 6¤ -------------|------------- 6¤ ------------|
+|--------------------------- 192 ---------------------------|
+|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
++----+----+----+----+----+----+----+----+----+----+----+----+
+|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|
+|---------  5¤  ---------|------------ {96} -----------|{43}|
+|--------- {53} ---------|-------------- {139} -------------|
+|------ Scheme-53 -------|------------ Scheme-34 -----------|
+

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist04.md b/identition/span11/gist04.md new file mode 100644 index 00000000000..d83a04ba2e5 --- /dev/null +++ b/identition/span11/gist04.md @@ -0,0 +1,21 @@ +![default](https://user-images.githubusercontent.com/8466209/201393202-8550c8ed-ab0d-489f-8831-5eee78534713.png) + +``` +True Prime Pairs: +(5,7), (11,13), (17,19) + +|------------------------ Scheme-12 ------------------------| +|------------ 6¤ -------------|------------- 6¤ ------------| +|--------------------------- 192 ---------------------------| +|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---| ++----+----+----+----+----+----+----+----+----+----+----+----+ +| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 | ++----+----+----+----+----+----+----+----+----+----+----+----+ +|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}| +|--------- 5¤ ---------|------------ {96} -----------|{43}| +|--------- {53} ---------|-------------- {139} -------------| +|------ Scheme-53 -------|------------ Scheme-34 -----------| +``` +![default](https://user-images.githubusercontent.com/8466209/201392901-e56d6e20-b985-46cc-815d-780e5eed4406.png) + +![image](https://user-images.githubusercontent.com/8466209/201362482-1581055c-0bfd-4314-a90e-1c49515cf6c3.png) diff --git a/identition/span11/gist05.html b/identition/span11/gist05.html new file mode 100644 index 00000000000..d14889ba69f --- /dev/null +++ b/identition/span11/gist05.html @@ -0,0 +1,18 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root    1 → 4 (5)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin    2 → 8 (10)
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin    5 → 7 (12)
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+

            default

            default

            default

            Manage certificates with ACME & DNS

            Automatic Certificate Management Environment (ACME) is a common protocol used to automate the management certificates between a Certificate Authority (CA) and server. With automation, many users can reduce the chances of outages due to failure to renew their HTTPS certificates.

            Use HTTPS on your domain

            Posh-ACME is a PowerShell module and ACME client to create publicly trusted SSL/TLS certificates from an ACME capable certificate authority such as Let's Encrypt.

            Posh-ACME

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist05.md b/identition/span11/gist05.md new file mode 100644 index 00000000000..a0721945e4c --- /dev/null +++ b/identition/span11/gist05.md @@ -0,0 +1,37 @@ +![default](https://user-images.githubusercontent.com/8466209/201399105-413df8fa-f33e-43eb-969a-eebbe28d28f2.png) + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root 1 → 4 (5) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin 2 → 8 (10) + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin 5 → 7 (12) + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== +``` + +[![default](https://user-images.githubusercontent.com/8466209/200474124-1643ba7d-8075-4c53-84a8-b9966a83d1c5.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform) + +[![default](https://user-images.githubusercontent.com/8466209/201881644-15e0dd30-ffd5-479e-9a62-7f37e87a6288.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md) + +[![default](https://user-images.githubusercontent.com/8466209/201879992-2ee3e071-03ea-46d0-8844-31ecd11c062b.png)](https://winbuzzer.com/2020/04/15/windows-10-how-to-create-a-virtual-hard-drive-as-hdd-dvd-or-ram-disk-xcxwbt) + +## Manage certificates with ACME & DNS + +Automatic Certificate Management Environment (ACME) is a common protocol used to automate the management certificates between a Certificate Authority (CA) and server. With automation, many users can reduce the chances of outages due to failure to renew their HTTPS certificates. + +[![Use HTTPS on your domain](https://user-images.githubusercontent.com/8466209/259370523-b2e4195f-bae5-433f-8d9f-16d348167546.png)](https://support.google.com/domains/answer/7630973) + +[Posh-ACME](https://poshac.me/) is a PowerShell module and ACME client to create publicly trusted SSL/TLS certificates from an ACME capable certificate authority such as [Let's Encrypt](https://letsencrypt.org/). + +[![Posh-ACME](https://user-images.githubusercontent.com/8466209/259368021-fc267e62-3890-4e9f-9940-f4a8d53a38a5.png)](https://poshac.me/docs/v4/Tutorial/#picking-a-server) diff --git a/identition/span11/gist06.html b/identition/span11/gist06.html new file mode 100644 index 00000000000..b982a4550df --- /dev/null +++ b/identition/span11/gist06.html @@ -0,0 +1,75 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            The components that have increased their dividends in 25 consecutive years are known as the S&P 500 Dividend Aristocrats. The index is one of the factors in computation of the Conference Board Leading Economic Index, used to forecast the direction of the economy. Aource: Google Finance

            **50 x 10 = 500**

              -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+                                           ↓
+                                           |
+                                           ↓                                          
+                            114-89=139-114=25=5x5
+                                | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         ↓
+                                |                             |                         |
+             50 x 10 = 500 ----→ ------------- 10 -------------                          | 
+                                                                                        | 
+                                                                                        | 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+
            //Updated on 10-6-2015 By ChrisMoody
+//Added Linebr ability, ability to turn on/off highlight Bars when crossing Swing Hi/Lo
+//Added Ability to turn on/off background highlight when bars cross swing hi/lo
+//Created 99% by Glaz and ChrisMoody Modified about 1% on 7/30/2014 for user dvk197-
+
+study(title="CM_Gann Swing HighLow V2", shorttitle="CM_Gann_Swing_HL_V2", overlay=true)
+periods=input(3, minval=1, title="Moving Average Period")
+pt = input(false, title="Plot Up/Down Triangles at Top and Bottom of Candles/Bars?")
+pc = input(true, title="Plot Circles at Top and Bottom of Candles/Bars?")
+pttb = input(true, title="Plot Triangles at Top and Bottom of Screen?")
+shb = input(false, title="Show Highlight Bars on Cross Up or Cross Down?")
+sbh = input(true, title="Show Background Highlights at Cross Up or Cross Down?")
+
+//code for Calculations
+hld = iff(close > sma(high,periods)[1], 1, iff(close<sma(low,periods)[1],-1, 0))
+hlv = valuewhen(hld != 0, hld, 1)
+
+//code for Plot Statements
+hi = hlv == -1 ? sma(high, periods) : na
+lo = hlv == 1 ? sma(low,periods) : na
+
+//Rules for coloring Background highlights & Highlight Bars
+closeAbove() => shb and close > hi and close[1] < hi
+BHcloseAbove = sbh and close > hi and close[1] < hi
+closeBelow() => shb and close < lo and close[1] > lo
+BHcloseBelow = sbh and close < lo and close[1] > lo
+
+//Highlight Bar Color Plots
+barcolor(closeAbove() ? yellow : na)
+barcolor(closeBelow() ? yellow : na)
+//Background Highlight Rules
+bgcolor(BHcloseAbove ? green : na, transp=60)
+bgcolor(BHcloseBelow ? red : na, transp=60)
+
+//Plot Statements for circles and Triangle Up/Down at Price Bars
+plot(pc and hi ? hi : na,title="Gann Swing High Plots-Circles", color=fuchsia,style=linebr, linewidth=4)
+plot(pc and lo ? lo : na,title="Gann Swing Low Plots-Circles", color=lime,style=linebr, linewidth=4)
+plotshape(pt and hi ? hi : na,title="Gann Swing High Plots-Triangle Down", offset=0, style=shape.triangledown, location=location.abovebar, color=fuchsia, transp=0)
+plotshape(pt and lo ? lo : na,title="Gann Swing Low Plots-Triangle Up", offset=0, style=shape.triangleup, location=location.belowbar, color=lime, transp=0)
+
+//Plot Statement for Triangles at Top and Bottom of Screen
+plotshape(pttb and hi ? hi : na,title="Gann Swing High Plots-Triangles Down Top of Screen", offset=0, style=shape.triangledown, location=location.top, color=red, transp=0)
+plotshape(pttb and lo ? lo : na, title="Gann Swing Low Plots-Triangles Up Bottom of Screen",offset=0, style=shape.triangleup, location=location.bottom, color=lime, transp=0)
+

            2022-11-26 (1)

            Gann was born June 6, 1878, in Lufkin, Texas. His father was a cotton farmer. He started trading in 1902 when he was 24.[24] He was believed to be a great student of the Bible, who believed that it was the greatest book ever written Likewise, Henry W Steele[34] demonstrates in a YouTube video that the numbers in Gann's work often refer to a different subject from what they appear on the surface. For example, on page one and two of Forty-Five Years in Wall Street,[35] there is a paragraph describing the different stocks at different prices on 14 June 1949, but Steele discovered that those "prices" are actually astrological aspects appearing in the sky on that day. Source Wikipedia

            default

            WD Gann is well known as the greatest market researcher of all time. He researched every possible aspect of natural laws in conjuction with variables of price and time in market movements. Find more detail here and here.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist06.md b/identition/span11/gist06.md new file mode 100644 index 00000000000..45d8ae27ff0 --- /dev/null +++ b/identition/span11/gist06.md @@ -0,0 +1,96 @@ +![default](https://user-images.githubusercontent.com/8466209/201396853-75d12ee6-a80f-4b1c-b3a0-c7a3a808aaca.png) + + +[![default](https://user-images.githubusercontent.com/8466209/202141967-f86798ad-4aff-48ee-b09f-b1645b330276.png)](https://en.wikipedia.org/wiki/List_of_S%26P_500_companies) + +> The components that have increased their dividends in 25 consecutive years are known as the S&P 500 Dividend Aristocrats. The index is one of the factors in computation of the Conference Board Leading Economic Index, used to forecast the direction of the economy. _Aource: [Google Finance](https://www.google.com/finance/quote/.INX:INDEXSP)_ + +*****50 x 10 = 500***** +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + ↓ + | + ↓ + 114-89=139-114=25=5x5 + | + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ ↓ + | | | + 50 x 10 = 500 ----→ ------------- 10 ------------- | + | + | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- +``` + + +``` +//Updated on 10-6-2015 By ChrisMoody +//Added Linebr ability, ability to turn on/off highlight Bars when crossing Swing Hi/Lo +//Added Ability to turn on/off background highlight when bars cross swing hi/lo +//Created 99% by Glaz and ChrisMoody Modified about 1% on 7/30/2014 for user dvk197- + +study(title="CM_Gann Swing HighLow V2", shorttitle="CM_Gann_Swing_HL_V2", overlay=true) +periods=input(3, minval=1, title="Moving Average Period") +pt = input(false, title="Plot Up/Down Triangles at Top and Bottom of Candles/Bars?") +pc = input(true, title="Plot Circles at Top and Bottom of Candles/Bars?") +pttb = input(true, title="Plot Triangles at Top and Bottom of Screen?") +shb = input(false, title="Show Highlight Bars on Cross Up or Cross Down?") +sbh = input(true, title="Show Background Highlights at Cross Up or Cross Down?") + +//code for Calculations +hld = iff(close > sma(high,periods)[1], 1, iff(close shb and close > hi and close[1] < hi +BHcloseAbove = sbh and close > hi and close[1] < hi +closeBelow() => shb and close < lo and close[1] > lo +BHcloseBelow = sbh and close < lo and close[1] > lo + +//Highlight Bar Color Plots +barcolor(closeAbove() ? yellow : na) +barcolor(closeBelow() ? yellow : na) +//Background Highlight Rules +bgcolor(BHcloseAbove ? green : na, transp=60) +bgcolor(BHcloseBelow ? red : na, transp=60) + +//Plot Statements for circles and Triangle Up/Down at Price Bars +plot(pc and hi ? hi : na,title="Gann Swing High Plots-Circles", color=fuchsia,style=linebr, linewidth=4) +plot(pc and lo ? lo : na,title="Gann Swing Low Plots-Circles", color=lime,style=linebr, linewidth=4) +plotshape(pt and hi ? hi : na,title="Gann Swing High Plots-Triangle Down", offset=0, style=shape.triangledown, location=location.abovebar, color=fuchsia, transp=0) +plotshape(pt and lo ? lo : na,title="Gann Swing Low Plots-Triangle Up", offset=0, style=shape.triangleup, location=location.belowbar, color=lime, transp=0) + +//Plot Statement for Triangles at Top and Bottom of Screen +plotshape(pttb and hi ? hi : na,title="Gann Swing High Plots-Triangles Down Top of Screen", offset=0, style=shape.triangledown, location=location.top, color=red, transp=0) +plotshape(pttb and lo ? lo : na, title="Gann Swing Low Plots-Triangles Up Bottom of Screen",offset=0, style=shape.triangleup, location=location.bottom, color=lime, transp=0) +``` +[![2022-11-26 (1)](https://user-images.githubusercontent.com/8466209/204060638-bee5515b-9f5c-441c-b374-6027f66b7726.png) +](https://www.tradingview.com/script/ngO3BO37-CM-Gann-Swing-High-Low-V2/) + +> Gann was born June 6, 1878, in Lufkin, Texas. His father was a cotton farmer. He started trading in 1902 when he was 24.[24] He was believed to be a great student of the Bible, who believed that it was the greatest book ever written Likewise, Henry W Steele[34] demonstrates in a YouTube video that the numbers in Gann's work often refer to a different subject from what they appear on the surface. For example, on page one and two of Forty-Five Years in Wall Street,[35] there is a paragraph describing the different stocks at different prices on 14 June 1949, but Steele discovered that those "prices" are actually astrological aspects appearing in the sky on that day. _Source [Wikipedia](https://en.wikipedia.org/wiki/William_Delbert_Gann#Bibliography)_ + +[![default](https://user-images.githubusercontent.com/8466209/201389693-d0b4a41a-90bc-475f-89ee-ecf4e154c63e.png)](https://www.bing.com/images/search?q=gann+hexagon+chart) + +WD Gann is well known as the greatest market researcher of all time. He researched every possible aspect of natural laws in conjuction with variables of price and time in market movements. Find more detail _[here](https://github.com/eq19/parser/files/10151301/gann-time-factor.pdf)_ and _[here](https://github.com/eq19/parser/files/10151302/master-time-factor.pdf)_. diff --git a/identition/span11/gist07.html b/identition/span11/gist07.html new file mode 100644 index 00000000000..9288637756c --- /dev/null +++ b/identition/span11/gist07.html @@ -0,0 +1 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Untitled

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist07.md b/identition/span11/gist07.md new file mode 100644 index 00000000000..cee56801724 --- /dev/null +++ b/identition/span11/gist07.md @@ -0,0 +1,7 @@ + +![Untitled](https://user-images.githubusercontent.com/8466209/259256709-e6c0bb56-b3dc-4f7c-9a52-3ffc64d1707f.png) + +[![default](https://user-images.githubusercontent.com/8466209/204060669-90a68f1a-424f-40b4-aafd-1ee862202ed4.png)](https://www.brokerxplorer.com/amp/article/what-is-the-best-ema-for-swing-trading-3336) + +![image](https://user-images.githubusercontent.com/8466209/201362641-b166327c-0a7d-4e2a-8170-ba4ca8dda5fe.png) + diff --git a/identition/span11/gist08.html b/identition/span11/gist08.html new file mode 100644 index 00000000000..de21aabb34c --- /dev/null +++ b/identition/span11/gist08.html @@ -0,0 +1,15 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            **Φ(11,13) = Φ(1,2,3) + Φ(4,2) = 123 + 42 = 165**

            default

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1
+

            default default

            default

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist08.md b/identition/span11/gist08.md new file mode 100644 index 00000000000..30184a24c26 --- /dev/null +++ b/identition/span11/gist08.md @@ -0,0 +1,28 @@ +*****Φ(11,13) = Φ(1,2,3) + Φ(4,2) = 123 + 42 = 165***** + +![default](https://user-images.githubusercontent.com/36441664/85060684-db12a400-b1cf-11ea-8f37-6b9b3bcab2f2.gif) + +``` +1st layer: +It has a total of 1000 numbers +Total primes = π(1000) = 168 primes + +2nd layer: +It will start by π(168)+1 as the 40th prime +It has 100x100 numbers or π(π(10000)) = 201 primes +Total cum primes = 168 + (201-40) = 168+161 = 329 primes + +3rd layer: +Behave the same as 2nd layer which has a total of 329 primes +The primes will start by π(π(π(1000th prime)))+1 as the 40th prime +This 1000 primes will become 1000 numbers by 1st layer of the next level +Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 +``` +![default](https://user-images.githubusercontent.com/8466209/201391686-4d1fc69f-1028-496e-b674-21053d65a2c2.png) +![default](https://user-images.githubusercontent.com/36441664/104337162-c1e49280-5527-11eb-9625-12b95f568aa4.png) + +[![default](https://user-images.githubusercontent.com/8466209/201354388-dcf5e2f1-cb50-4d1b-8c93-0dd49bc7e46d.png)](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-runner-md) + +![default](https://user-images.githubusercontent.com/8466209/201355214-d1e67872-d9e7-4a9f-ae64-4305238f6071.png) + +[![image](https://user-images.githubusercontent.com/8466209/201360527-91a03353-2eb8-4f20-ba8d-afee93fb7b3c.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-basic-md) diff --git a/identition/span11/gist09.html b/identition/span11/gist09.html new file mode 100644 index 00000000000..20e853980e5 --- /dev/null +++ b/identition/span11/gist09.html @@ -0,0 +1,18 @@ + gist09.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 |  1  | 28
+---+-----+-----
+ 2 | 29  | 46
+---+-----+-----
+ 3 | 47  |{56}
+---+-----+-----
+ 4 |{57} | 61
+---+-----+-----
+ 5 | 62  | 82
+---+-----+-----
+ 6 | 83  | 94
+---+-----+-----
+ 7 | 95  | 99
+---+-----+-----
+ 8 |{100}|{123}
+---+-----+-----
+

            image

            image

            image

            image

            Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three. (Clay Institute).

            Birch and Swinnerton-Dyer Conjecture

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span11/gist09.md b/identition/span11/gist09.md new file mode 100644 index 00000000000..b9506333f26 --- /dev/null +++ b/identition/span11/gist09.md @@ -0,0 +1,31 @@ +``` +---+-----+----- + 1 | 1 | 28 +---+-----+----- + 2 | 29 | 46 +---+-----+----- + 3 | 47 |{56} +---+-----+----- + 4 |{57} | 61 +---+-----+----- + 5 | 62 | 82 +---+-----+----- + 6 | 83 | 94 +---+-----+----- + 7 | 95 | 99 +---+-----+----- + 8 |{100}|{123} +---+-----+----- +``` + +![image](https://user-images.githubusercontent.com/8466209/201361949-6e99504f-b139-4fd0-8a0d-3739964927f4.png) + +![image](https://user-images.githubusercontent.com/8466209/201361906-52dc91d4-48fa-4701-a334-c5bdd22b8b61.png) + +![image](https://user-images.githubusercontent.com/8466209/201362034-7a0c83f3-d310-4b92-b3e5-fc1f832693fc.png) + +![image](https://user-images.githubusercontent.com/8466209/201362104-cd379833-3f1b-4def-ab0d-f5f73ea5f127.png) + +>Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three. _([Clay Institute](https://www.claymath.org/millennium-problems))_. + +[![Birch and Swinnerton-Dyer Conjecture](https://user-images.githubusercontent.com/8466209/218376819-e17c97cf-1f1d-4363-a1ce-2b1c355591c3.png)](https://www.claymath.org/millennium-problems/birch-and-swinnerton-dyer-conjecture) diff --git a/identition/span11/index.html b/identition/span11/index.html new file mode 100644 index 00000000000..c580f70c20b --- /dev/null +++ b/identition/span11/index.html @@ -0,0 +1,61 @@ + Everything is Connected (span 11) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Everything is Connected (span 11)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-29 of orgs section-1 that is inherited from the spin section-11 by prime spin-39 and span-150 with the partitions as below.

            +
            +
            1. gist09.md
            2. gist02.md
            3. gist04.md
            4. gist08.md
            5. gist03.md
            6. gist05.md
            7. gist06.md
            8. gist07.md
            9. Rationalization
            ---+-----+-----
+ 1 | {1} | {2}
+---+-----+-----
+ 2 |  3  | 101
+---+-----+-----
+ 3 |{102}| 111
+---+-----+-----
+

            Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory, or components of a complex time

            default

            In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold.

            image

            Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.

            default

            Einstein's general theory of relativity, published in November 1915, describes gravity as the warping of spacetime by masses such as the Earth and moon. The latest issue of Science News celebrates general relativity's 100th anniversary

            image

            The Solar System is the gravitationally bound system of the Sun and the objects that orbit the star. The largest of such objects are the eight planets. This was formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud.

            +
            + + Note +
            +
            +

            Zecharia Sitchin suggests that the star-shaped symbol and 11 other dots on this Sumerian cylinder seal, known as VA243, represent the sun, moon and 10 planets including a mysterious “world” known as Nibiru. How could the ancient Sumerian civilization describe our solar system so accurately if it is only possible to see five planets with the naked eye? This seems impossible if we consider the science and technology needed to observe our galaxy today. If Stichin assumptions are correct, we’ll see NIBIRU soon.

            +
            +

            11 dots

            default

            The-Total-History-of-the-Universe-including-the-quantum-eras-before-Inflation-in-units

            origin

            Ean6eoJWAAIWjrY

            quantum-gravity

            Space and Time: Minkowski's Papers on Relativity, published by the Minkowski Institute. Hand-tinted transparency presented by Hermann Minkowski in his famous Raum und Zeit talk to the German Society of Scientists and Physicians in 1908

            default

            Besides many theories there is COMPOSITE and PRIMES as a self organized system (12/12/12). Even though it is proven that it is not from Tesla, whoever made it if you are reading this article, I sincerely want to thank you because I use a lot of the analysis.

            default

            This scheme has a configuration of 30 nodes so the recombination is involving 2x30 or 60 nodes out of the 72 nodes of True Prime Pairs will act as the base platform. The rest of 11 which is initially came out from the prime 13 is the irrational.

            +
            + + Note +
            +
            +

            The approach taken is to think of the solutions of an equation as a geometric object. For example, an equation in two variables defines a curve in the plane. More generally, an equation, or system of equations, in two or more variables defines a curve, a surface or some other such object in n-dimensional space (Wikipedia).

            +
            +

            Now the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of the prime number 7 lie in the numerical Double strand parallel opposite.

            Double Strands

            The spacetime diagram on the left, the magenta hyperbolae connect events of equal spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation from the origin.

            default

            This scheme has a configuration of 30 nodes so the recombination is involving 2x30 or 60 nodes out of the 72 nodes of True Prime Pairs will act as the base platform. The rest of 11 which is initially came out from the prime 13 is the irrational.

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+Sequence:
+ By the next layer the 89² will become 89 and 5 become 5² or 25.
+ This 89 and 25 are in the same layer with total of 114 or prime 619
+ So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) (₠Quantum).

            flowchart

            This polarity is happened per six (6) cycles by the polar of six (6) to one (1) and six (6) to seven (7) by which we finally found if this behaviour is cascaded bilaterally within the correlation between 61 as the 18th prime and 67 as the 19th prime.

            Dyson discovered an intriguing connection between quantum physics and Montgomery's pair correlation conjecture about the zeros of the zeta function which dealts with the distribution of primes. This finaly bring us to the equation of Euler's identity.

            This scale shows that the Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement (Google Patent DE102011101032A9).

            Euler's identity

            The finiteness position of middle zero axis = 15 by the said MEC30 opens up the possibility of accurately representing the self-similarity based on the distribution of True Prime Pairs. So that all number would belongs together with their own identity.

            default

            Proceeding, the number line begins to coil upon itself; 20 lands on 2's cell, 21 on 3's cell. Prime number 23 sends the number line left to form the fourth hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. When viewed with an extra dimension of space, these respectively generate hyperboloids of one sheet and two sheets.

            default

            The concept of dark matter arose in the study of cosmological phenomena, that is matters dealing with the Universe and galaxies and so on. However, evidence from the Hubble telescope in 1998 showed that the Universe began expanding at an accelerating rate sometime in the past and still is doing so. This came as a surprise to many

            default

            The major problem, however, is that quantum mechanical calculations for the cosmological constant give value that is grossly out of the required range. This indicates that either something is wrong with the theory, or our knowledge is incomplete.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist01.html b/identition/span12/gist01.html new file mode 100644 index 00000000000..70c200de105 --- /dev/null +++ b/identition/span12/gist01.html @@ -0,0 +1,31 @@ + Feeding (spin 3) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Feeding (spin 3)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-21 of gist section-17 that is inherited from the gist section-main by prime spin-86 and span-27 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            As shown in The Primes Platform this cycle goes to the prime 13 then reinjected through index 13:9 . So it forms The Scheme-139 through the infinitely primes cycling. This scheme will be implemented by taking the following as the syntax algorithm:

            default

            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period eight (8) difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2} (Primesdemystified).

            image

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            11's additive sums

            These objects will then behave as a complex numbers that leads to trivial and complex roots of the 18th prime identity. 286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20 --------
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                |
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------
+  =======================+====+====+====+====+====+====+====+====+====+===== bilateral 9 sums (2)+60+40=102
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                |
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20 --------
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+

            The opposite direction will be made through switching beetween Linux and Windows which is proceed the old strand in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. Here we set a remote self-host runner via WSL.

            default

            The rest of primes goes to the 33's of 15th axis that holding 102 primes of (2,60,40). By the bilateral way the form will be splitted to (1,30,20). Since the base frame shall be 40 so it will be forced to form (1,30,40) of prime 71.

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist02.html b/identition/span12/gist02.html new file mode 100644 index 00000000000..291e827ad60 --- /dev/null +++ b/identition/span12/gist02.html @@ -0,0 +1,17 @@ + Entrypoint (spin 4) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Entrypoint (spin 4)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-22 of gist section-18 that is inherited from the gist section-main by prime spin-85 and span-28 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions
            SUBMODULE=path/to/submodule
+
+rm -rf $SUBMODULE
+git rm --cached $SUBMODULE
+rm -rf .git/modules/$SUBMODULE
+git config -f .gitmodules --remove-section submodule.$SUBMODULE
+git add . && git commit -m "delete $SUBMODULE" && git push
+

            This recombination is taking a scheme called DNA Recombination: M+F to C1+C2 which could only be happen when two (2) chromosomes involve. Here we found that each of their DNA will form a scheme called The Scheme 13:9 as shown below.

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            I like that 0 can occupy a center point. Incidentally, this circular shape minus all my numbers and colors s has been called Seed of Life / Flower of Life by certain New Age groups who claim it has a sacred geometry. Please don't see this as an endorsement of any spiritual group or religion. (Prime Hexagon - Circulat Form)

            image

            You can use either mklink /j or junction in Windows 10 to create junctions. Junction not only allows you to create NTFS junctions, it allows you to see if files or directories are actually reparse points. Reparse points are the mechanism on which NTFS junctions are based, and they are used by Windows' Remote Storage Service (RSS), as well as volume mount points.

            mklink /j .github C:\Users\Admin\.github
+

            mklink

            The color spin addresses for numbers are generally straightforward – a composite number takes the spin of the prior prime. 4 spins blue because 3 spins blue. 8 is red because 7 is red. However, twin primes, and the 0 type numbers between them, are open to some interpretation.

            base

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            19vs18

            In the second opposing member, the position 13 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the 11th prime number is now forced to determine a new axis-symmetrical zero position.

            default

            Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence.

            AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence (Human vs AI).

            The next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.

            33's

            This process would take place all the way to three (3) layers in a more complex way involving 114 objects generated by the sum of the above mentioned prime 71 and 43. This is what we will discuss further on how apply it in to a custom domain.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist03.html b/identition/span12/gist03.html new file mode 100644 index 00000000000..2a60d8d974c --- /dev/null +++ b/identition/span12/gist03.html @@ -0,0 +1,11 @@ + Mapping (spin 5) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Mapping (spin 5)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-23 of main section-1 that is inherited from the spin section-main by prime spin-84 and span-27 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            When we come to a mapping of a Project, is critical to look for the future of Parts Unlimited otherwise the project will massively over budget and very late. So to deal with this we shall consider to move everything to the cloud…

            phoenix

            Since version 3.2 , a new Jekyll project bootstrapped with jekyll new uses gem-based themes to define the look of the site. This results in a lighter default directory structure: _layouts, _includes and _sass are stored in the theme-gem, by default.

            default

            You can attach a persistent disk or create an instance with Local SSDs when using Container-Optimized OS. The disks can be mounted by creating a subdirectory under /mnt/disks directory (writable, executable, stateless, tmpfs) using startup-scripts.

            image

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            GitHub Actions workflow

            On the lagging strand template, a primase "reads" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            default

            You can run .NET applications in Linux containers, but only if they're written in .NET Core which can be deployed on Windows Server Containers. Applications running in Windows Server Containers can run in any language supported by Windows.

            kernel-6.1.21.1-microsoft-standard-WSL2.img

            Let's combine them all then we will get 168 which is the total primes out of 1000 numbers. This 168 we will get it also when we combine the 1's and 17's cell of (31+37)+(35+65)=68+100=168.

            zeta-vs-zero

            This can be remedied by re-mounting your Windows partition inside WSL with the metdata option. Edit the /etc/wsl.conf file (create it if it doesn't exist) and add the following:

            [automount]
+options = "metadata"
+

            Log out from WSL and log in again, and now the windows partition will be mounted with metadata and chmod will work against windows files. You can now chmod 600 ~/.ssh/id_rsa and everything will work correctly.

            default

            By this project we are going to use a library called Chevrotain. It can be used to build Lexers, Parsers and Interpreters for various use cases ranging from simple config files to full fledged programming languages.

            Lexers, Parsers and Interpreters with Chevrotain

            This Widows is an isolated container, lightweight package for running an application on the host operating system. Containers build on top of the host operating system's kernel (which can be thought of as the buried plumbing of the operating system).

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist04.html b/identition/span12/gist04.html new file mode 100644 index 00000000000..01bd354577d --- /dev/null +++ b/identition/span12/gist04.html @@ -0,0 +1,21 @@ + Keyring (spin 6) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Keyring (spin 6)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-24 of main section-2 that is inherited from the spin section-main by prime spin-83 and span-28 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            A lexer is the part of an interpreter that turns a sequence of characters (plain text) into a sequence of tokens. The Parser which takes the tokens from the lexer and returns a syntax tree based on a grammar. The grammar is often expressed in a meta language.

            BusyBox v1.34.1 (2022-07-19 20:11:24 UTC) multi-call binary.
+
+Usage: mv [-finT] SOURCE DEST
+or: mv [-fin] SOURCE... { -t DIRECTORY | DIRECTORY }
+
+Rename SOURCE to DEST, or move SOURCEs to DIRECTORY
+
+	-f	Don't prompt before overwriting
+	-i	Interactive, prompt before overwrite
+	-n	Don't overwrite an existing file
+	-T	Refuse to move if DEST is a directory
+	-t DIR	Move all SOURCEs into DIR
+

            default

            By this modification we are going to build the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66.

            default

            The next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.

            image

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist05.html b/identition/span12/gist05.html new file mode 100644 index 00000000000..32aad5c585d --- /dev/null +++ b/identition/span12/gist05.html @@ -0,0 +1,40 @@ + Enneagram (spin 7) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Enneagram (spin 7)

            +
            +
            + + Tip +
            +
            +

            This section is referring to wiki page-25 of main section-3 that is inherited from the spin section-main by prime spin-82 and span-29 with the partitions as below.

            +
            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            For some Enneagram theorists the lines connecting the points add further meaning to the information provided by the descriptions of the types. Sometimes called the "security" and "stress" points, or points of "integration" and "disintegration".

            From this perspective, there are twenty-seven (27) distinct personality patterns, because people of each of the nine (9) types also express themselves as one of the three (3) subtypes (Wikipedia).

            This is managed within twelve (12) flows (A: to W:). Each flows is representing a certain period which is converting the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence as explained before.

            default

            default

            default

            image

            It turns out it's actually pretty straight forward to set WSL to use your Windows home directory. First, within WSL edit the /etc/passwd file (eg with sudo nano /etc/passwd).

            +
            eq19:x:1000:1000:eQ19:/home/eq19:/bin/bash
+eq19:x:1000:1000:eQ19:/mnt/c/users/Admin:/bin/bash
+

            image

            default

            +
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist06.html b/identition/span12/gist06.html new file mode 100644 index 00000000000..334fe14e73b --- /dev/null +++ b/identition/span12/gist06.html @@ -0,0 +1,37 @@ + Twisting (spin 8) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Twisting (spin 8)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-26 of main section-4 that is inherited from the spin section-main by prime spin-81 and span-30 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            1155 / 5 = 286 - 55 = 200 + 31 = 231

            layer|  i    |   f
+-----+-------+------
+     | 1,2:1 | (2,3)
+  1  +-------+
+     | 3:2   | (7)
+-----+-------+------
+     | 4,6:3 | (10,11,12)  <--- 231 (3x)
+  2  +-------+
+     |{7}:4  |({13})
+-----+-------+------
+     | 8,9:5 | (14,{15})   <--- 231 (2x)
+  3  +-------+
+     | 10:6  | (19)
+-----+-------+------
+

            We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape (arXiv:2010.16383v4).

            Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series

            Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as Montgomery conjecture of the nontrivial zeros of the zeta function. Means it also depends on Riemann hypotesis which is still in a major issue. Similar case left science today many unsolved problems that associated with.

            Eigenvectors_of_a_linear_operator

            In order to propagate through space and interact we shall attemp it using string theory One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become irrational partitions.

            In turns out that quantum string theory always destroys the symmetries of the classical string theory, except in one special case: when the number of dimensions is 10. That's why string theory works only in 10 dimensions (Physicsforums).

            default

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|------------------------- Skema-12 ------------------------|
+|------------ 6¤ -------------|------------- 6¤ ------------|
+|--------------------------- 192 ---------------------------|
+|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
++----+----+----+----+----+----+----+----+----+----+----+----+
+|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|
+|---------  5¤  ---------|------------ {96} -----------|{43}|
+|--------- {53} ---------|-------------- {139} -------------|
+|------- Skema-23 -------|------------- Skema-34 -----------|    
+

            default

            This 23 units will form Scheme-23 as two (2) long strands which is known as doble helix Here we call them as Scheme-23 (71) and Scheme-23 (68). These strands are originated by the three (3) layers of True Prime Pairs.

            Scheme-139

            default

            default

            default

            Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as the balanced prime.

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist07.html b/identition/span12/gist07.html new file mode 100644 index 00000000000..40520f54293 --- /dev/null +++ b/identition/span12/gist07.html @@ -0,0 +1,23 @@ + Recycling (spin 9) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Recycling (spin 9)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-27 of main section-5 that is inherited from the spin section-main by prime spin-80 and span-31 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            This progression 41,43,47,53,61,71,83,97,113,131 whose general term is 41+x+xx, is as much remarkable since the 40 first terms are all prime numbers (Euler's letter to Bernoulli).

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            default

            I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.

            That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated.

            Truncate to Determine Integer Values

            FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist08.html b/identition/span12/gist08.html new file mode 100644 index 00000000000..bd50c722222 --- /dev/null +++ b/identition/span12/gist08.html @@ -0,0 +1,9 @@ + Exchange (spin 10) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Exchange (spin 10)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-28 of main section-6 that is inherited from the spin section-main by prime spin-79 and span-32 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            default

            default

            default

            default

            default

            default

            default

            default

            default

            default

            default

            The exchange interaction is a quantum mechanical process that only happens between identical particles in chemistry and physics. The energy produced when two or more electrons with the same spin swap locations in a subshell's degenerate orbitals .

            default

            On the instinctual level, people may internally stress and externally express the need to protect themselves (self-preservation), to connect with important others or partners (sexual), or to get along or succeed in groups (social).

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/gist09.html b/identition/span12/gist09.html new file mode 100644 index 00000000000..1fce82526ce --- /dev/null +++ b/identition/span12/gist09.html @@ -0,0 +1,112 @@ + Dimensions · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Dimensions

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-29 of orgs section-1 that is inherited from the spin section-main by prime spin-78 and span-33 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).

            default

            2,10
+5,7,17
+13,18,25,42
+
            13, 16
+18, 21, 23
+25, 28, 30, 32, 34, 36, 38, 40,
+42, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77
+

            +
            + + Note +
            +
            +

            The following are a list of observations about the Prime Number Folio Coordinate System. There’s an algorithm too. More than one. These observations are in no way mathematically rigorous.

            • The number 35 is an important number. It’s the first number on the right-hand side that’s a product of two prime factors of 5 x 7 = 35. The sum of 5 + 7 = 12. Since the right-handed numbers are distributed evenly by 6, we can add 7 x 6 = 42 to 35 and land on the number 77.
            • So now we know that starting with the number 35 if we add 42 continuously we will NEVER land on a prime number. We can also add5 x 6 = 42 to 35 and land on 65.
            • We also know that 7 + 11 = 18. The next number that introduces a product of two primes is 5 x 13 = 65 and 5 + 13 = 18. So we can take 6 x 13 = 78 and add this to 65 and land on 143. Which is the product of 11 x 13 = 143. Starting with 65 we can add 78 continuously and NEVER land on a prime number.
            • In the meantime 77 (The product of 7 and 11 now introduces the prime number 11 into the mix. So 77 + (6x11) = 143. Starting with 77 we can add 66 continuously and NEVER land on a prime number. Note: You can’t add multiples of 6 until that multiple is introduced into the sequence. This may seem obvious to you, but it wasn’t to me.
            • The primes on the left behave differently. You can still move around using multiples of 6, but there is no common starting point like the number 35.
            • You have to start with the squares of 5 at 25 (in blue) for one sequence of numbers and the square of 7 at 49 (in red) for the other sequence of numbers.
            • The sums of these products are also not exact multiples of 6. They sum to 10 and 14 and are matched to the split X Axis on the left-hand side of the graph.

            The Prime Number Folio Coordinate System and it’s natural numbers are all you need to find a prime number or a composite number and it’s factors. No need for complex numbers or the Reimann Hypothesis. (Medium)

            +
            +

            The Prime Number Folio Coordinate System

            Runners are the machines that execute jobs in a GitHub Actions workflow. You can access Variables and Contexts information in specific OS. For example, a runner can clone your repository locally, install testing software, and then run commands.

            
+# Sample workflow for building and deploying a Jekyll site to GitHub Pages
+name: Build and deploy Jekyll site
+
+# 💎 Runs on deployment targeting the default branch
+on:
+  # push:
+    # branches: [eQ19]
+  workflow_run:
+    types: [completed] #requested
+    workflows: ["pages-build-deployment"]
+
+# 🪂 Allow only one concurrent deployment across the branches
+concurrency:
+  group: "pages"
+  cancel-in-progress: true
+  
+# Sets permissions of the GITHUB_TOKEN
+permissions: write-all
+
+# Sets global environtment variables
+env:
+  OWNER: ${{ github.repository_owner }}
+
+jobs:
+  # Build job
+  github-pages:
+    if: github.event.workflow_run.conclusion == 'success'
+    runs-on: ${{ vars.OWNER != 'FeedMapping' && 'ubuntu-latest' || 'windows-latest' }}
+    steps:
+      - name: 📂 Checkout
+        uses: actions/checkout@v3
+        with:
+          submodules: recursive
+ 
+      - name: 💎 Build on Linux
+        if: runner.os == 'Linux'
+        uses: eq19/feed@v2
+        with:
+          pre_build_commands: 'make build'
+          token: ${{ secrets.JEKYLL_GITHUB_TOKEN }}
+
+      - name: 💎 Build on Windows
+        if: runner.os == 'Windows'
+        uses: eq19/maps@v1
+        id: stepid
+        with:
+          dotnet-version: '3.1.x'
+
+

            By deploying containers on Compute Engine, you can simplify app deployment while controlling four dimensional space. You can configure a virtual machine (VM) instance or an instance template to deploy and launch a Docker container.

            default

            This property would tend the ballancing scheme of MEC30 so it will let 30-18=12 pairing with another 12 of 24 spins prime hexagon. The 24 goes to the center of True Prime Pairs ny the prime pair 13 and 11 and let the crancks of 2,3,5,7 inside the 10 ranks.

                                            | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   feeding    |     mapping     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+
+                                                                                |  2 | 60 | 40 |
+                                                                                +----+----+----+
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            This 71 is a conformation that it has the same result as we have explained on the residual objects of 571 turn to a vektor of 71 while the rest of 500 turn to 200 objects of 3's identity and the last objects of 300 goes to the next cycles.

            default

            So now out of 1000 numbers that generated from 1000 primes we will get the rest of 1000 - 100 = 900. This 900 will behave as matrix square 30x30 and act as the base frame of 2nd and 3rd layer which are working on π(π(100x100))-1=200 primes:

                                        33+34=67=19th prime
+ |----------------------------------|-------------------------------------------------------------|
+ |             33                   |                             34                              |
+ |--------------|-------------------|------------------------------|------------------------------|
+ |     lexering = π(1000)           |                    parsering = 1000/Φ                       |
+ |--------------|-------------------|------------------------------|------------------------------|
+ |   feeding    |      mapping      |          syntaxing           |          grammaring          |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |  39 | 40 | 41 | 42 | 43 | 44 | 45  | 46 | 47 | 48 |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1  | 30 | 30 | 5  | 1  | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ |       2'     |        3'         |              5'              |               7'             | 
+

            default

            The GitHub hosted runner is assigned to run the Linux container and a Windows Server Core container simultaneously. This is an experimental feature of Microsoft WSL2 and may have some issues. One known problem is volumes are not stable.

            Set WSL

            The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span12/index.html b/identition/span12/index.html new file mode 100644 index 00000000000..c78678b8074 --- /dev/null +++ b/identition/span12/index.html @@ -0,0 +1,2055 @@ + Theory of Everything (span 12) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Theory of Everything (span 12)

            Theory of Everything (TOE) is a final theory that links together all aspects of the universe. Finding a TOE is one of the major unsolved problems in physics.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-28 of main section-6 that is inherited from the spin section-12 by prime spin-37 and span-151 with the partitions as below.

            +
            +
            1. Feeding (spin 3)
            2. Entrypoint (spin 4)
            3. Mapping (spin 5)
            4. Keyring (spin 6)
            5. Enneagram (spin 7)
            6. Twisting (spin 8)
            7. Recycling (spin 9)
            8. Exchange (spin 10)
            9. Dimensions

            This makes it an exciting time to be a theoretical physicists but without some kind of clearer direction, it's hard to see where the next big breakthrough will be.

            Tracing Method

            We do this division by adopting the OOP (Object Oriented Programming) which is an object-oriented programming method.

            To make it easier to develop a program following a model, we divide the object by placing it into a smaller objects (puzzles).

            π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786

            default

            As given in the following graph, to discover TOE then a theory of "quantum gravity" is needed and we don't have it whereas its unification step leads just one level below.

            Modern physics

            Similarly our discussion for this topic is ended up with the lack of "prime distribution" which is still an open problem. Therefore we will assign each of the cases as a puzzle.

            However a much more sophisticated method is necessary to shed light on TOE and many of the other mysteries surrounding the distribution of prime numbers.

            +
            + + Note +
            +
            +

            The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved (Wikipedia).

            +
            +

            It is suspected that the TOE should form as simple as E = mc² As usual, behind a simplest thing there shall be complex aspects. Let talk about the current status.

            +
            + + Note +
            +
            +

            How close are we to the theory of everything?

            Well, we thought we were getting pretty close about a decade ago - but more recent experimental and observational science is making things a LOT harder for the theoreticians:

            • The final realization that quantum mechanics and relativity cannot both be correct has created a bit of a problem.
            • A theory of “quantum gravity” is needed - and we don’t have it. Even more annoyingly, both quantum mechanics and relativity are very solidly proven to be true.
            • Cosmologists found dark matter and then dark energy. They can describe their observed properties - point out that about 96% of everything is dark matter/energy - and then leave particle physicists with a major problem.
            • The demands of theoreticians for more data has pushed particle colliders to somewhere close to the limits of our ability to pay for the darned things (although not yet the limits of theoretical feasibility).
            • The construction of something significantly bigger than the Large Hadron Collider does not seem likely right now so the data we have may turn out to be the only data we’ll ever have (from particle colliders). Large space telescopes, however, are getting MUCH better and when SpaceX get their StarShip to fly - they’ll be much cheaper and MUCH larger. So getting help from cosmologists MIGHT offer assistance.
            • The great hope that String Theory could be the “Theory of Everything” has somewhat tarnished. String theory predicts that one out of 10⁵ possible realities is the one we live in but fails to mention which one! This is not exactly useful!
            • Current string theories seem incompatible with dark energy - which is definitely not good.

            Particle Physics

            There is an additional problem called Background Independence - which is a property that Relativity requires - but which string theory does not seem to reproduce… but this is still a matter of contention. (I confess I do not understand what “Background Independence” actually is… but I Am Not A Theoretical Physicist.) (Quora)

            +
            +

            elementary particles

            In the next section we will discuss about building the algorithms to find a solution in physics and their relation to the distribution of prime numbers.

            Three (3) Layers

            Our scenario of prime identity is layering three (3) prime pairs out of the symmetrical behaviour of 36 as the smallest number (greater than 1) which is not a prime.

            +
            + + Tip +
            +
            +

            By our project this prime layering is called The True Prime Pairs and to be intrepeted as: Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

            +
            + 
            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            The (3) layers represents generation in the Standard Model of flavor that counts six (6) flavours of quarks and six (6) flavours of leptons.

            +
            + + Note +
            +
            +

            Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos.

            • These are conserved in strong and electromagnetic interactions, but violated by weak interactions.
            • Therefore, such flavour quantum numbers are not of great use. A separate quantum number for each generation is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos).
            • However, even these numbers are not absolutely conserved, as neutrinos of different generations can mix; that is, a neutrino of one flavour can transform into another flavour.

            PMNS Matriks

            The strength of such mixings is specified by a matrix called the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix). (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | 
+      |      |  1  +-----+          
+      |  1   |     |  2  | (5)
+      |      |-----+-----+
+      |      |     |  3  |
+  1   +------+  2  +-----+----
+      |      |     |  4  |
+      |      +-----+-----+
+      |  2   |     |  5  | (7)
+      |      |  3  +-----+
+      |      |     |  6  |
+------+------+-----+-----+------  } (36) » 6®
+      |      |     |  7  |
+      |      |  4  +-----+
+      |  3   |     |  8  | (11)
+      |      +-----+-----+
+      |      |     |  9  |
+  2   +------|  5  +-----+-----
+      |      |     |  10 |
+      |      |-----+-----+
+      |  4   |     |  11 | (13)
+      |      |  6  +-----+
+      |      |     |  12 |
+------+------+-----+-----+------------------
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17)
+      |      |-----+-----+
+      |      |     |  15 |
+  3   +------+  8  +-----+-----  } (36) » 6®
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |
+------|------|-----+-----+------
+

            While there are nine (9) possible combinations of color/anti-color pairs, due to symmetry considerations one of these combinations is eliminated. A gluon can effectively carry one of eight (8) possible color/anti-color combinations.

            color charge and confinement

            These matrices are particularly important in both mathematics and physics. For example, these matrices (and their generalizations) are important in Lie theory.

            +
            + + Note +
            +
            +

            Gell-mann matrices are a complete set of Hermitian noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model the eight gluons that mediate the strong force quantum chromodynamics, an analogue of the Pauli matrices well-adapted to applications in the realm of quantum mechanics. (Wolfram)

            +
            + 
            #!/usr/bin/env python
+
+import numpy as np
+from scipy import linalg
+
+class SU3(np.matrix):
+	GELLMANN_MATRICES = np.array([
+		np.matrix([ #lambda_1
+			[0, 1, 0],
+			[1, 0, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_2
+			[0,-1j,0],
+			[1j,0, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_3
+			[1, 0, 0],
+			[0,-1, 0],
+			[0, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_4
+			[0, 0, 1],
+			[0, 0, 0],
+			[1, 0, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_5
+			[0, 0,-1j],
+			[0, 0, 0 ],
+			[1j,0, 0 ],
+		], dtype=np.complex),
+		np.matrix([ #lambda_6
+			[0, 0, 0],
+			[0, 0, 1],
+			[0, 1, 0],
+		], dtype=np.complex),
+		np.matrix([ #lambda_7
+			[0, 0,  0 ],
+			[0, 0, -1j],
+			[0, 1j, 0 ],
+		], dtype=np.complex),
+		np.matrix([ #lambda_8
+			[1, 0, 0],
+			[0, 1, 0],
+			[0, 0,-2],
+		], dtype=np.complex) / np.sqrt(3),
+	])
+
+
+	def computeLocalAction(self):
+		pass
+
+	@classmethod
+	def getMeasure(self):
+		pass
+

            We apply these generators to the rest of the space, and find that it breaks down into the SU(3)c representations of exactly three generations of quarks and leptons.

            +
            + + Note +
            +
            +

            The action of C⊗O on itself can be seen to generate a 64-complex-dimensional algebra, wherein we are able to identify two sets of generators for SU(3)c.

            • Furthermore, we show that these three-generation results can be extended, so as to include all 48 fermionic U(1)em charges.
            • The 64-dimensional octonionic chain algebra splits into two sets of SU (3) generators of the form iΛν and −iΛ * ν * , six SU (3) singlets j , six triplets q k , and their complex conjugates.
            • These objects are sectioned off above into four quadrants according to their forms: νaν, ν * aν, νaν * and ν * aν * for a in the chain algebra.

            Transforming particles into anti-particles, and vice versa, requires only the complex conjugate i → −i in our formalism. (Standard Model from an algebra - pdf)

            +
            +

            The-64-dimensional-octonionic-chain-algebra-splits-into-two-sets-of-SU-3-generators

            This quark model underlies flavor SU(3), or Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons

            +
            + + Note +
            +
            +

            The pseudoscalar meson nonet. Members of the original meson “octet (8)” are shown in green, the singlet in magenta.

            • Although these mesons are now grouped into a nonet (9), the Eightfold Way name derives from the patterns of eight for the mesons and baryons in the original classification scheme.
            • The Eightfold Way classification is named after the following fact:
              • If we take three flavors of quarks, then the quarks lie in the fundamental representation, 3 (called the triplet) of flavor SU(3).
              • The antiquarks lie in the complex conjugate representation 3.
            • The nine states (nonet) made out of a pair can be decomposed into the trivial representation, 1 (called the singlet), and the adjoint representation, 8 (called the octet).
            • The notation for this decomposition is 3⊗3=8⊕1.

            Figure below shows the application of this decomposition to the mesons. (Wikipedia)

            +
            +

            8foldway svg

            The symmetrical states can couple to a pair of pseudoscalar mesons in a wave, and hence their widths and masses are strongly influenced by these couplings.

            +
            + + Note +
            +
            +

            In order to be four-spinors like the electron and other lepton components, there must be one quark component for every combination of flavour and colour, bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four (4) component bispinor, for a total of 96 complex-valued components for the fermion field. (Wikipedia)

            +
            +

            Eightfold Way = 8 × (6®+6®) = 96®

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | 
+      |      |  1  +-----+          
+      |  1   |     |  2  | (5)
+      |      |-----+-----+
+      |      |     |  3  |
+  1   +------+  2  +-----+----
+      |      |     |  4  |
+      |      +-----+-----+
+      |  2   |     |  5  | (7)
+      |      |  3  +-----+
+      |      |     |  6  |
+------+------+-----+-----+------  } (36) » 6® -------------
+      |      |     |  7  |                                 |
+      |      |  4  +-----+                                 |
+      |  3   |     |  8  | (11)                            |
+      |      +-----+-----+                                 |
+      |      |     |  9  | <--------  Eightfold Way = 8 × (6®+6®) = 96®
+  2   +------|  5  +-----+-----                               |
+      |      |     |  10 |                                    |
+      |      |-----+-----+                                    |
+      |  4   |     |  11 | (13)                               |
+      |      |  6  +-----+                                    |
+      |      |     |  12 |                                    |
+------+------+-----+-----+------------------                  |
+      |      |     |  13 |                                    |
+      |      |  7  +-----+                                    |
+      |  5   |     |  14 | (17)                               |
+      |      |-----+-----+                                    |
+      |      |     |  15 |                                    |
+  3   +------+  8  +-----+-----  } (36) » 6® -----------------
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |
+------|------|-----+-----+------
+

            In fact this particular count of three (3) as the Eightfold Way Generation of 6 by 6 flavors is the major case of every theories in physics to get in to the TOE.

            +
            + + Note +
            +
            +

            The origin of multiple generations of fermions, and the particular count of 3, is an unsolved problem of physics.

            In standard quantum field theory, under certain assumptions, a single fermion field can give rise to multiple fermion poles with mass ratios of around eπ≈23 and e2π≈535 potentially explaining the large ratios of fermion masses between successive generations and their origin. (Wikipedia)

            +
            +

            6 x 114 - 30 - 30 - 5 = 619 = 6 x 19 = 114th prime

            The quark model for baryons has been very successful in describing them as qqq states, including those with nonzero internal orbital angular momentum. However, final meson-baryon states (and thus states of qq¯+qqq) play an important role as well.

            +
            + + Note +
            +
            +

            Why do we see certain types of strongly interacting elementary particles and not others? This question was posed over 50 years ago in the context of the quark model.

            • M. Gell-Mann and G. Zweig proposed that the known mesons were qq¯ and baryons qqq, with quarks known at the time u (“up”), d (“down”), and s (“strange”) having charges (2/3,–1/3,–1/3).
            • Mesons and baryons would then have integral charges. Mesons such as qqq¯q¯ and baryons such as qqqqq¯ would also have integral charges. Why weren’t they seen?
            • They have now been seen, but only with additional heavy quarks and under conditions which tell us a lot about the strong interactions and how they manifest themselves.

            Beyond the standard model

            The present article describes recent progress in our understanding of such “exotic” mesons and baryons. (Multiquark States - pdf)

            +
            +

            structure-of-composite-particles-l

            There are higher dimensional numbers besides complex numbers. The classical octet meson is now nonet. Thus consequently it would go higher than E8.

            +
            + + Note +
            +
            +

            These are called hypercomplex numbers, such as, quaternions (4D), octonions (8D), sedenions (16D), pathions (32D), chingons (64D), routons (128D), and voudons (256D). These names were coined by Robert P.C. de Marrais and Tony Smith. It is an alternate naming system providing relief from the difficult Latin names, such as: trigintaduonions (32D), sexagintaquattuornions (64D), centumduodetrigintanions (128D), and ducentiquinquagintasexions (256D). (Wordpress.com)

            +
            +

            4 types of numbers

            The three (3) layers as explained above is in the 1st-term of our discussed structure. So the next step is the 2nd-term which goes to the four (4) dimensional space-time.

            The Four (4) Dimensions

            4D-dimensional space-time is much more complex due to the extra degree of freedom. Almost all of the rest of unsolved problems in physics are correlated with.

            +
            + + Note +
            +
            +

            The set of points in Euclidean 4-space having the same distance R from a fixed point P0 forms a hypersurface known as a 3-sphere where R is substituted by function R(t) with t meaning the cosmological age of the universe. Growing or shrinking R with time means expanding or collapsing universe, depending on the mass density inside (Wikipedia).

            +
            +

            The main reason is that the general relativity not consistent with quantum mechanics. It is even a sign that Einstein's equations are somehow incomplete.

            +
            + + Note +
            +
            +

            Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein’s papers, comprising more than 30,000 unique documents (Wikipedia).

            +
            +

            default

            Comparatively, four-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w to describe the two additional cardinal directions of up toward and down from, respectively.

            +
            + + Note +
            +
            +

            On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! (Clay Institute’s - Yang Mills Official problem description).

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | 
+      |      |  1  +-----+          
+      |  1   |     |  2  | (5)
+      |      |-----+-----+
+      |      |     |  3  |
+  1   +------+  2  +-----+----
+      |      |     |  4  |
+      |      +-----+-----+
+      |  2   |     |  5  | (7)
+      |      |  3  +-----+
+      |      |     |  6  |
+------+------+-----+-----+------  } (36) » 6® 👈 up toward ✔️
+      |      |     |  7  |
+      |      |  4  +-----+
+      |  3   |     |  8  | (11)
+      |      +-----+-----+
+      |      |     |  9  |
+  2   +------|  5  +-----+-----
+      |      |     |  10 |
+      |      |-----+-----+
+      |  4   |     |  11 | (13)
+      |      |  6  +-----+
+      |      |     |  12 |
+------+------+-----+-----+------------------
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17)
+      |      |-----+-----+
+      |      |     |  15 |
+  3   +------+  8  +-----+-----  } (36) » 6® 👈 down from ✔️
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |
+------|------|-----+-----+------
+

            The Lorentz group consists, unsurprisingly, of the Lorentz transformations, which are the linear transformations preserving the Minkowski dot product.

            +
            + + Note +
            +
            +

            Equivalently, they are the linear transformations fixing that hyperboloid of two sheets. If we discard one of the sheets, we obtain the orthochronous (time-preserving) subgroup.

            • From the perspective of the centre of the cone, the hyperboloid looks like an open disc. The orthochronous Lorentz transformations precisely correspond to distance-preserving transformations of the hyperbolic plane. These are themselves determined uniquely by a conformal (or anticonformal) transformation of the ‘circle at infinity’.
            • Adding an extra dimension, the orthochronous Lorentz group O^{+}(3,1) is isomorphic to the group of distance-preserving transformations of hyperbolic 3-space, which is again isomorphic to the group of (anti-)conformal transformations of the ‘sphere at infinity’, namely our index-2 supergroup of the Möbius group.
            • Moreover, this nicely generalises: the group generated by geometric inversions on the n-sphere is abstractly isomorphic to the orthochronous Lorentz group O^{+}(n+1,1).

            And when n = 24, we get a very beautiful discrete subgroup, namely the automorphism group of the II(25,1) lattice intimately related to the Leech lattice. (Complex Projective 4-Space)

            +
            +

            spacetime

            This diagram is representing groupings (leptons, quarks, weak-force bosons) with 6 quarks in a way that parallels the 6 leptons.

            +
            + + Note +
            +
            +

            There are 8 different types of tiny particles, or ‘states’, that we can find in a special kind of space that has 6 dimensions and involves both real and imaginary numbers. These particles include:

            • The Higgs field, which doesn’t spin and is represented by 0.
            • Fermions, which are particles like electrons, having a spin of plus or minus a half.
            • Bosons, like photons, which have a spin of plus or minus 1.
            • Anti-fermions, which are like fermions but have a spin of plus or minus two-thirds.
            • The graviton, believed to be responsible for gravity, with a spin of 2.

            In a diagram at the top left, this 6-dimensional space is shown to be curved. In another diagram at the bottom right, we see two waves that are perpendicular to each other, representing the motion of a particle in a ‘Dirac harmonic oscillator’ – a concept in quantum mechanics. (Physics In History)

            +
            +

            Dirac_bispinor_6D

            While the Dirac CP-violating phase δℓ can be determined in the future, how to probe or constrain the Majorana CP-violating phases ρ and σ is still an open question

            +
            + + Note +
            +
            +

            Four of the dimensions are the usual four of spacetime. The six (or perhaps seven) extra dimensions are rolled up to be almost unobservable.

            • First, let’s see why they exist at all. If N=8 Supersymmetry is correct the universe must be 10 or 11 dimensional.extra dimensions
            • Let D be the actual dimensionality of space time. Let d be the apparent dimensionality. (We know d = 4, but let’s think generally.) Then there is a nice relation between D, d and N.Dimensional-reduction-of-supergravity-from-11D-to-4D-over-a-space-like-or-time-like
            • It follows from the number of spinor dimensions required by the Dirac equation, which is The s mean round down to the nearest whole number. So plugging in d=4 and N=8 (which is the highest value N can have) we get D = 10 or 11. String theory has D=10, M-theory has D=11.Dirac, Weyl, and Majorana in 4D
            • One dimension is reserved for time, leaving space with 9 or 10 dimensions.

            We don’t see 6 (or 7) of these extra dimensions because - we assume - they are rolled up a la Kaluza–Klein theory into a 6 dimensional Calabi–Yau space

            +
            +

            main-qimg-f8cd59c3b8504bdaab0977ee2704ce0e-ezgif com-webp-to-png-converter

            The most promising candidate is SO(10) but it does not contain any exotic fermions (i.e. additional fermions besides the Standard Model and the right-handed neutrino), and it unifies each generation into a single irreducible representation.

            +
            + + Note +
            +
            +

            In particle physics, SO(10) refers to a grand unified theory (GUT) based on the spin group Spin(10). The shortened name SO(10) is conventional[1] among physicists, and derives from the Lie algebra or less precisely the Lie group of SO(10), which is a special orthogonal group that is double covered by Spin(10).

            SO(10) subsumes the Georgi–Glashow and Pati–Salam models, and unifies all fermions in a generation into a single field. This requires 12 new gauge bosons, in addition to the 12 of SU(5) and 9 of SU(4)×SU(2)×SU(2).

            • Left: The pattern of weak isospin, W, weaker isospin, W’, strong g3 and g8, and baryon minus lepton, B, charges for particles in the SO(10) model, rotated to show the embedding of the Georgi–Glashow model and Standard Model, with electric charge roughly along the vertical. In addition to Standard Model particles, the theory includes 30 colored X bosons, responsible for proton decay, and two W’ bosons.
            • Right: The pattern of charges for particles in the SO(10) model, rotated to show the embedding in E6.
            • The matter representations come in three copies (generations) of the 16 representation. The Yukawa coupling is 10H 16f 16f. This includes a right-handed neutrino.

            It has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear in 2018 that the SO(10) model is also free from all nonperturbative global anomalies on non-spin manifolds — an important rule for confirming the consistency of SO(10) grand unified theory, with a Spin(10) gauge group and chiral fermions in the 16-dimensional spinor representations, defined on non-spin manifolds. (Wikipedia)

            +
            +
            Syntax Description Last
            download (3) download (4) download (2)

            In the spin-foam formalism, the Barrett–Crane model, which was for a while the most promising state-sum model of 4D Lorentzian quantum gravity

            +
            + + Note +
            +
            +

            It was based on representations of the noncompact groups SO(3,1) or SL(2,C), so the spin foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks. (Wikipedia)

            +
            +

            41114_2016_3_Equ168

            41114_2016_3_Equ115

            The field content of this theory is the massless N = 8 supergravity which comprises the graviton, 8 gravitinos, 28 vector fields.

            +
            + + Note +
            +
            +

            In four spacetime dimensions, N = 8 supergravity, speculated by Stephen Hawking, is the most symmetric quantum field theory which involves gravity and a finite number of fields.

            • It can be found from a dimensional reduction of 11D supergravity by making the size of seven (7) of the dimensions go to zero.

            • It has eight (8) supersymmetries, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin −2. (The spin 2 graviton is the particle with the highest spin in this theory.)eight (8) supersymmetries

            • More supersymmetries would mean the particles would have superpartners with spins higher than 2.
            • The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories).
            • Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything.
            • However, in later years this was abandoned in favour of string theory.
            • The theory contains 1 graviton (spin 2), 8 gravitinos (spin 3/2), 28 vector bosons (spin 1), 56 fermions (spin 1/2), 70 scalar fields (spin 0) where we don’t distinguish particles with negative spin.
            • These numbers are simple combinatorial numbers that come from Pascal’s Triangle and also the number of ways of writing n as a sum of 8 nonnegative cubes A173681.
            • One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the orthogonal group O(10).

            There has been renewed interest in the 21st century, with the possibility that string theory may be finite. (Wikipedia)

            +
            +

            15-Figure1-1

            One remarkable property of both string and M-theory is that seven (7) extra dimensions are required for the theory's consistency, on top of the four dimensions in our universe.

            +
            + + Note +
            +
            +

            There exist scenarios in which there could actually be more than 4D of spacetime. String theories require extra dimensions of spacetime for their mathematical consistency. These are situations where theories in two or three spacetime dimensions are no more useful.

            In string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional.

            This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family. (Wikipedia)

            +
            +

            M-Theory

            So the last "Superstring revolution" was impressive but it was close to 30 years ago now - and we still don't seem to be adopting it as "The Truth".

            +
            + + Note +
            +
            +

            M Theory and/or Loop Quantum Gravity hold the promise of resolving the conflict between general relativity and quantum mechanics but lack experimental connections to predictability in physics.

            • A connection is made to these and other theories vying for the title of a “Theory of Everything” by questioning the value of the traditional Planck unit reference point for the scales at which they operate.
            • It also suggests a cosmological model which has acceleration as being fundamental.
            • It provides for an intuitive understanding of the Standard Model and its relationship to particle masses and the structure of the atom.

            The prediction of particle mass and lifetimes is a good indicator for its validity. (TOE - pdf)

            +
            +

            string-theory-dimensions

            We suspect that using that Lorentz, all four have the same complexified Lie algebra. In loop quantum gravity it makes matters even more confusing.

            The Seven (7) Groups

            Let's consider a prime spin theory of compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius and study its dimensional reduction to 4D.

            +
            + + Note +
            +
            +

            We now place integers sequentially into the lattice with a simple rule: Each time a prime number is encountered, the spin or ‘wall preference’ is switched.

            19 abuts 2

            So, from the first cell, exit from 2’s left side. This sets the spin to left and the next cell is 3, a prime, so switches to right. 4 is not prime and continues right. 5 is prime, so switch to left and so on. There are twists and turns until 19 abuts 2. (HexSpin)

            +
            +

            Defining the Prime Hexagon

            In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist and in particular the 4D metric, is defined by the 3-form.

            +
            + + Note +
            +
            +

            We would like to say that our present use of G2 structures (3-forms in 7D) is different from whatone can find in the literature on Kaluza–Klein compactifications of supergravity.

            • We show that the resulting 4D theory is (Riemannian) General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.
            • Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.

            Also, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. (General relativity from three-forms in seven dimensions - pdf)

            +
            +

            Standard Spin

            The complete theory was obtained by dimensional reduction of the 11D supergravity on a seven (7) torus and realizing the exceptional symmetry group E7(7)

            +
            + + Note +
            +
            +

            In particular, these theories include the compactification of eleven-dimensional supergravity on the seven-sphere S7, which gives rise to a four-dimensional theory with compact non-abelian gauge group SO(8) (11D Supergravity and Hidden Symmetries - pdf)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+---------
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ✔️
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) ---------------------
+      |      |  6  +-----+        <----------------  strip
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ✔️
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | --------------------------
+------|------|-----+-----+------
+

            The most general Lagrangian with massless neutrinos, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment.

            +
            + + Note +
            +
            +

            Straightforward extensions of the Standard Model with massive neutrinos need 7 more parameters (3 masses and 4 PMNS matrix parameters) for a total of 26 parameters. The neutrino parameter values are still uncertain. The 19 certain parameters are summarized here:

            IMG_20231230_232603

            • The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter.
            • Instead of fermion masses, dimensionless Yukawa couplings can be chosen as free parameters. For example, the electron mass depends on the Yukawa coupling of the electron to the Higgs field.
            • The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.
            • The renormalization scale may be identified with the Planck scale or fine-tuned to match the observed cosmological constant. However, both options are problematic.

            As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the “best step” towards a Theory of Everything, can only be settled via experiments (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5  +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) ---------------------
+      |      |  6  +-----+        <----------------  strip
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |       extra
+      |      |     |  15 |                           7s  <-- parameters ✔️
+  3   +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+           certain         |
+      |  6   |     |  17 | (19)  <-- parameters ✔️   |
+      |      |  9  +-----+                           |
+      |      |     |  18 | --------------------------
+------|------|-----+-----+------
+

            Please note that we are not talking about the number 19 which is the 8th-prime. Here we are talking about 19th as sequence follow backward position of the 18th.

            +
            + + Tip +
            +
            +

            The same number of 7 vs 11 dimensions as we have discussed are hold by 7 primes vs 11 natural numbers in every first term of the prime spin. Consider the following:

            • the prime 19 is not counted on the first term since it is taking the position of number 1 which is not prime, this prime takes it place only on the second term,
            • assume the number 1 is still in its position then the 18 would be the quantity of all numbers so it is eligible as the origin position of zero,
            • thus there are π(17) or 7 primes with red color plus 11 natural numbers (including the number 1) with black color and consequently 18 is the sum of 7 and 11,
            • so by the concept of prime identity, this 7 vs 11 scheme of dimensions is originated from the behaviour of both 19 and 18,
            • the prime is fewer than the natural so the 7 prime cycle is always happen in every first term followed by 11 composite cycle (see our side menu).

            The further terms will only have their specific meaning when they are formed in the favor of True Prime Pairs which we called as Δ(19 vs 18) Scenario

            +
            +

            Δ(19 vs 18) Scenario

            Symmetry breaking in Quantum Field Theory (QFT) applies to the scalar field, at first so that it can have an impact and give mass to gauge bosons and fermions.

            +
            + + Note +
            +
            +

            In QFT this is currently done by manually adding an extra term to the field’s self-interaction, creating the famous Mexican Hat potential well.

            • In QFT the scalar field generates four (4) Goldstone bosons.
            • One (1) of the 4 turns into the Higgs boson. Unlike popularized, the Higgs itself does not give mass to particles, but represents the symmetry broken scalar field.
            • The other three (3) Goldstone bosons are “absorbed” by the three (3) intermediate, electroweak bosons (W+, W-, Z), giving them an extra spin.

            This (otherwise) plain and featureless “absorbtion” of the Goldstone modes in the EW field could be a reason why a complex, synergy-creating quality of the scalar field is largely unnoticed in QFT. Obviously this has the potential to become a new research challenge in physics. (TGMResearch)

            +
            +

            sterile_neutrino_does_not_exist

            The greatest problem in theoretical physics is combining the general relativity with quantum mechanics. Actually it is related to a non-standard renormalization.

            +
            + + Note +
            +
            +

            A lot number of positive color-charges move from the positive charged particle toward the negative charged particles, and negative color-charges move from negative charged particle toward the positive charged particle and they combine in each other.

            • According to CPH Theory, gravity is a currency among the objects. Consider the interaction between the earth and the moon: when a graviton reaches the earth, the other one moves toward the moon and pushes the earth toward the moon.
            • Because as to maintain equality times - positive and negative color-charges, there is a fixed ratio between the mass and the number of gravitons surrounding.
            • Also when a graviton reaches the moon, the other one moves toward the earth and pushes the moon toward the earth.-So earth (In fact everything) is bombarded by gravitons continuously.

            Due to the fact that everything is made up of sub quantum energy, the classical concept of acceleration and relativistic Newton’s second law needs to be reviewed. (Gravity in Time space - pdf)

            +
            +

            A-lot-number-of-positive-color-charges-move-from-the-positive-charged-particle-toward-the

            Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory.

            +
            + + Note +
            +
            +

            Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. (Wikipedia)

            +
            +

            0_5540_t3k8UUhCxaU

            The problem is raised when the non-standard renormalization hides the scheme and scale-independent quantum anomalous energy (QAE) contribution in the mass.

            +
            + + Note +
            +
            +

            In this paper we have studied the renormalization of the QCD trace anomaly separately for the quark and gluon parts of the energy momentum tensor.

            • While the renormalization of the total anomaly T = Tq + Tg is well understood in the literature [10], our analysis at the quark and gluon level has revealed some interesting new features. The bare and renormalized (Tq,g)α differ by finite operators, and this difference can be systematically computed order by order in αs.
            • It is interesting to notice that, at one loop, the renormalized Tq gives the nf part of the beta function. However, this property no longer holds at two-loop, see (5.19).
            • Besides, the partition of the total anomaly can be different if one uses other regularization schemes (see, e.g., the ‘gradient flow’ regularization [25]), and it is interesting to study their mutual relations.

            We have also found that C¯q,g(µ) does not go to zero as µ → ∞ even in the chiral limit, contrary to what one would naively expect from the one-loop calculation (3.16). (Quark and gluon contributions to the QCD trace anomaly - pdf)

            +
            +

            (24-5) + (24-17) = 19 + 7 = 26

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|--------------- 7¤ ---------------|👈
+|-------------- {89} --------------|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+                         |---- {48} ----|---- {48} ----|---- {43} ----|
+                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|👈
+
+  Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19+i5
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-2 |    2    |    3    |     3     |    18     |     24     | 👉17+i7
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11+i13👈
+-----------+---------+---------+-----------+-----------+------------+-----------
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   19+i5
+===========+=========+=========+===========+===========+============+===========
+     Total |    8    |   12    |    12     |    72     |     96     |   66+i30
+

            In order to explain the generation process of gravitational energy between two identical sign charged particles, it is necessary to explain the process of the generated electromagnetic energy by the interaction of their electrical repulsion.

            +
            + + Note +
            +
            +

            In quantum mechanics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2. This is because the source of gravitation is the stress-energy tensor, a second-rank tensor. This definition of graviton is not able to describe gravitational phenomena, so we need a new definition of graviton. (What is CPH Theory - pdf)

            +
            +

            A-schematic-illustration-of-how-quantum-gravity-emerges-in-an-information-based-theory-of

            The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.

            +
            + + Note +
            +
            +

            We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales.

            • We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition.
            • We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks.
            • We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.

            Dynamical response of the scalar Hamiltonian HS in the presence of the fermion , generating a contributionto the fermion mass The dotted line represents the dynamical Higgs particles h and the crossed circle denotes the scalar Hamiltonian linear in h. The coupling g between the Higgs field and the fermion is proportional to fermion mass. (Scale symmetry breaking - pdf)

            +
            +

            1-s2 0-S0550321321002340-gr008_lrg

            The first diagram corresponds to the first term at right hand side of equality, while the other two diagrams with back-moving lines combine to produce the second term.

            The Quantum Gravity

            By True Prime Pars we shall take 36 nodes to conjugate partitions. So the most possible way is taking the 3rd layer which hold the sum 36 of prime pair 19 and 17.

            +
            + + Note +
            +
            +

            A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.

            • For massless particles – photons, gluons, and (hypothetical) gravitons – chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer.
            • For massive particles – such as electrons, quarks, and neutrinos – chirality and helicity must be distinguished: In the case of these particles, it is possible for an observer to change to a reference frame moving faster than the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as “apparent chirality”) will be reversed. That is, helicity is a constant of motion, but it is not Lorentz invariant. Chirality is Lorentz invariant, but is not a constant of motion: a massive left-handed spinor, when propagating, will evolve into a right handed spinor over time, and vice versa.
            • A massless particle moves with the speed of light, so no real observer (who must always travel at less than the speed of light) can be in any reference frame where the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity. Because of this, the direction of spin of massless particles is not affected by a change of inertial reference frame (a Lorentz boost) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a relativistic invariant (a quantity whose value is the same in all inertial reference frames) which always matches the massless particle’s chirality.

            The discovery of neutrino oscillation implies that neutrinos have mass, so the photon is the only confirmed massless particle; gluons are expected to also be massless, although this has not been conclusively tested.[b] Hence, these are the only two particles now known for which helicity could be identical to chirality, and only the photon has been confirmed by measurement. All other observed particles.

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
++----+----+----+----+----+-👇-+
+|  5 |  7 | 11 |{13}| 17 | 19 |
++----+----+----+----+----+----+
+|------------ {72} -----------|
+|------------- 6¤ ------------|
+
+The Fermion Fields
+(19,17,i12), (11,19,i18), (18,12,i13)
+
++-👇-+----+----+----+----+----+----+----+----+
+| 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+
+|---- {48} ----|---- {48} ----|---- {43} ----|
+|------------ {96} -----------|----- 3¤ -----|
+
+Spontaneous Symmetry Breaking:
+(5,7), (11,13,17) , (19,17,12), (11,19,18), (18,12,13)
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|
++----+----+----+----+----+-👇-+-👇-+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+                         |-- {36} -|------ {60} -------|---- {43} ----|
+                         |--- 2¤ --|------- 4¤ --------|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|
+

            The first term will directly be identified as a forward moving diagram for external mψψ¯ insertion, while the second term corresponds to the combination of two backward moving diagrams using the relation in energy denominators.

            +
            + + Note +
            +
            +

            The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion. It is negative (“left-handed”) if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards.

            • Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: “left” is negative, “right” is positive.have mass and thus may have different helicities in different reference frames.
            • Chiral theories: Particle physicists have only observed or inferred left-chiral fermions and right-chiral antifermions engaging in the charged weak interaction.[1] In the case of the weak interaction, which can in principle engage with both left- and right-chiral fermions, only two left-handed fermions interact. Interactions involving right-handed or opposite-handed fermions have not been shown to occur, implying that the universe has a preference for left-handed chirality. This preferential treatment of one chiral realization over another violates parity, as first noted by Chien Shiung Wu in her famous experiment known as the Wu experiment. This is a striking observation, since parity is a symmetry that holds for all other fundamental interactions.
            • Chirality for a Dirac fermion ψ is defined through the operator γ5, which has eigenvalues ±1; the eigenvalue’s sign is equal to the particle’s chirality: +1 for right-handed, −1 for left-handed. Any Dirac field can thus be projected into its left- or right-handed component by acting with the projection operators.Right_left_helicity svg
            • The coupling of the charged weak interaction to fermions is proportional to the first projection operator, which is responsible for this interaction’s parity symmetry violation.
            • A common source of confusion is due to conflating the γ5, chirality operator with the helicity operator. Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact with the weak force according to one frame of reference, but not another. The resolution to this paradox is that the chirality operator is equivalent to helicity for massless fields only, for which helicity is not frame-dependent. By contrast, for massive particles, chirality is not the same as helicity, or, alternatively, helicity is not Lorentz invariant, so there is no frame dependence of the weak interaction: a particle that couples to the weak force in one frame does so in every frame.
            • A theory that is asymmetric with respect to chiralities is called a chiral theory, while a non-chiral (i.e., parity-symmetric) theory is sometimes called a vector theory. Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories. Quantum chromodynamics is an example of a vector theory, since both chiralities of all quarks appear in the theory, and couple to gluons in the same way.
            • The electroweak theory, developed in the mid 20th century, is an example of a chiral theory. Originally, it assumed that neutrinos were massless, and assumed the existence of only left-handed neutrinos and right-handed antineutrinos. After the observation of neutrino oscillations, which imply that neutrinos are massive (like all other fermions) the revised theories of the electroweak interaction now include both right- and left-handed neutrinos. However, it is still a chiral theory, as it does not respect parity symmetry.
            • The exact nature of the neutrino is still unsettled and so the electroweak theories that have been proposed are somewhat different, but most accommodate the chirality of neutrinos in the same way as was already done for all other fermions.

            By Chiral symmetry the Vector gauge theories with massless Dirac fermion fields ψ exhibit chiral symmetry, i.e., rotating the left-handed and the right-handed components independently makes no difference to the theory. We can write this as the action of rotation on the fields:

            +
            +

            Symmetry State

            The Standard Model with massive neutrinos need 7 more parameters (3 CKM and 4 PMNS matrix parameters) for a total of 26 parameters. By our concept these 7 parameters correspond to π(17) = 7 prime identities of additional zones.

            +
            + + Note +
            +
            +

            Massive fermions do not exhibit chiral symmetry, as the mass term in the Lagrangian, mψψ, breaks chiral symmetry explicitly.

            • Spontaneous chiral symmetry breaking may also occur in some theories, as it most notably does in quantum chromodynamics.
            • The chiral symmetry transformation can be divided into a component that treats the left-handed and the right-handed parts equally, known as vector symmetry, and a component that actually treats them differently, known as axial symmetry.[2] (cf. Current algebra.) A scalar field model encoding chiral symmetry and its breaking is the chiral model.
            • The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.

            The general principle is often referred to by the name chiral symmetry. The rule is absolutely valid in the classical mechanics of Newton and Einstein, but results from quantum mechanical experiments show a difference in the behavior of left-chiral versus right-chiral subatomic particles. (Wikipedia)

            +
            +

            1 + 77 = 78 = 3 copies of 26-dimensions

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
++----+----+----+----+----+-👇-+
+|  5 |  7 | 11 |{13}| 17 | 19 |
++----+----+----+----+----+----+
+|------------ {72} -----------|
+|------------- 6¤ ------------|
+
+Spontaneous Symmetry Breaking:
+(5,7), (11,13,17) , (19,17,12), (11,19,18), (18,12,13)
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|
++----+----+----+----+----+-👇-+-👇-+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+                         |-- {36} -|------ {60} -------|---- {43} ----|
+                         |--- 2¤ --|------- 4¤ --------|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|
++----+----+----+----+----+-💢-+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+-👇-+----+----+----+----+----+
+                         |-👇-|--------- {77} ---------|---- {43} ----|✔️
+                         |-1¤ |---------- 5¤ ----------|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|
+

            The first term forms the photonic contribution while the second term is the fermionic contribution (two backward). The first backward is correspond to the three (3) known neutrino flavors: the electron-, muon- and tau-neutrino which are left-handed.

            +
            + + Note +
            +
            +

            Summary of various critical points in the context of superpotential observed in this paper first : Gauge symmetry, supersymmetry, vacuum expectation value of field, superpotential and cosmological constants.

            • For SO(3)+ × SO(5)+ case, one can check it by the change of variable of SO(5)+×SO(3)+ case, s → −3s/5 that corresponding potential of SO(3)+×SO(5)+ is obtained while by change of variable, s → −s/7, the potential of SO(1)+ × SO(7)+ can be found from SO(7)+ × SO(1)+ case.
            • Although the corresponding superpotential of these two cases may be different from the original ones, the scalar potentials are the same.
            • It is natural to ask whether 11-dimensional embedding of various vacua we have considered of non-compact and non-semi-simple gauged supergravity can be obtained.
            • In a recent paper [46], the metric on the 7-dimensional internal space and domain wall in 11-dimensions was found. However, they did not provide an ansatz for an 11-dimensional three-form gauge field.-It would be interesting to study the geometric superpotential, 11-dimensional analog of superpotentialwe have obtained.

            We expect that the nontrivial r-dependence of vevs makes Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric RG flow connecting two critical points. (N = 8 Supergravity: Part I - pdf)

            +
            +

            Symmetry Breaking

            Taking 19 as a certain parameter we can see that the left handed cycles are happen on 5th-spin (forms 4th hexagon, purple) and 6th-spin (forms 5th hexagon, cyan). Both have different rotation with other spin below 9th spin (forms 6th hexagon, yellow).

            +
            + + Note +
            +
            +

            Proceeding, the number line begins to coil upon itself; 20 lands on 2’s cell, 21 on 3’s cell. Prime number 23 sends the number line left to form the fourth (4th) hexagon, purple. As it is not a twin, the clockwise progression (rotation) reverses itself. Twin primes 29 and 31 define the fifth (5th) hexagon, cyan. Finally, 37, again not a twin, reverses the rotation of the system, so 47 can define the yellow hexagon (HexSpin).

            +
            +

            7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s

            IMG_20231221_074421

            Thus it appears that the cosmological models] derived from compactification of 11d supergravity on a manifold with G2 holonomy have some hidden E7 symmetry.

            +
            + + Note +
            +
            +

            There are 14 + 7 × 16 = 126 integral octonions. It was shown that the set of transformations which preserve the octonion algebra of the root system of E7 is the adjoint Chevalley group G2(2). It is possible to decompose these 126 imaginary octonions into eighteen (18) sets of seven (7) imaginary octonionic units that can be transformed to each other by the finite subgroup of matrices. These lead to 18 sets of 7, which we see in figures ​figure-77 and ​figure-88. (M-theory, Black Holes and Cosmology - pdf)

            +
            + 
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17💢36
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19💢30
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+

            By the Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            +
            + + Note +
            +
            +

            You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why? Because they do not fit inside — they stick off the hexagon like a tail. Perhaps that’s where they belong. However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively. _(HexSpin)

            +
            +

            0 + 30 + 36 + 102 = 168 = π(1000)

            0, 1 and negative numbers

            By defining the pattern on each individual numbers against homogeneous sorting. Using this method then out of bilateral way the ∆(19 vs 18) Scenario we could get in to Scheme-33.

            +
            + + Note +
            +
            +

            The electroweak force is believed to have separated into the electromagnetic and weak forces during the quark epoch of the early universe.

            Elementary Particle

            The quark epoch ended when the universe was about 10−⁶ seconds old, when the average energy of particle interactions had fallen below the binding energy of hadrons. The following period, when quarks became confined within hadrons, is known as the hadron epoch. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-👇--+-👇--+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"              |
+-----+-----+-----+-----+-----+                                              |
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨👈 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                   96¨
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤        ----->  assigned to "id:33"              |
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30            Mod 60            Mod 90
+

            In terms of Feynman diagrams it has shown that the expansion of N = 8 supergravity is in some ways a product of two N = 4 super Yang–Mills theories.

            +
            + + Note +
            +
            +

            The number 28, aside from being triangular wave of perfect pyramid, is the sum of the first 5 primes and the sum of the first 7 natural numbers.

            Base of TOE

            The intervention of the Golden Ratio can be seen as a way to enter the quantum world, the world of subtle vibrations, in which we observe increasing energy levels as we move to smaller and smaller scales. El Nachie has proposed a way of calculating the fractal dimension of quantum space-time. The resulting value (Figure 7) suggests that the quantum world is composed of an infinite number or scaled copies of our ordinary 4-dimensional space-time.

            PHI_Quantum_SpaceTime

            Setting k=0 one obtains the classical dimensions of heterotic superstring theory, namely 26, 16, 10, 6 and 4, as well as the constant of super-symmetric (αgs=26) and non super-symmetric (αg=42) unification of all fundamental forces. As we have seen in section 2, the above is a Fibonacci-like sequence with a very concise geometrical interpetation related to numbers 5, 11 and φ. (Phi in Particle Physics)

            +
            +

            d(43,71,114) = d(7,8,6) » 786

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f           
+------+------+-----+-----+------
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43) ✔️
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+        <--------------  strip of the id: 37 (TOE)
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = (43-19) ✔️
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----
+

            We can use simplexes to triangulate a surface and compute the Euler characteristic and other topological properties in this fashion.

            +
            + + Note +
            +
            +

            Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed.

            • It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the Running-Vacuum-Model (RVM) cosmological framework, without fundamental inflaton fields.Torsion in String Cosmologies
            • The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in the presence of (primordial) gravitational waves at early stages of the four (4) dimensional string universe (after compactification).triangular wave
            • The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models.

            Finally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made. (Torsion in String Cosmologies - pdf)

            +
            +

            114 = 102 + 66 - 29 - 25 = 6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 25 + 89

            28+Octonion

            The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.

            +
            + + Note +
            +
            +

            In Fuller’s synergetic geometry, symmetry breaking is modeled as 4 sub-tetra’s, of which 3 form a tetrahelix and the 4th. “gets lost”.

            • In the present approach, intermediate (symmetry broken) states are proposed to be latent in the allready extended cube-octahedral matrix, and are actualized or mapped through the trefoil operator. In terms of tetra-logic, it is the invisible, confining icosa-dodeca matrix, acting upon the visible, deconfined cube-octahedral matrix.
            • Further, the author proposes a more natural and versatile QFT symmetry breaking mechanism, based on well determined scalar field excitations.
            • In QFT, the potential well is based on excitation modes, not on actual excitations, which is a reason why the proposed synergetic action gets obscured.
            • A new type of symmetry breaking is proposed, based on a synchronized path integral.

            The latter solves into a Goldstone oscillation and a vacuum expectation value (VEV), among other unique properties. The scalar field’s self-interaction is a Golden Ratio scale-invariant group effect, such as geometrically registered by the icosa-dodeca matrix. (TGMResearch)

            +
            + 
            $True Prime Pairs:
+(5,7$True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f           
+------+------+-----+-----+------
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |                           |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+        <-----vacuum energy <--- ∆60 = (131-71) ✔️
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = (43-19)
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----
+

            The second backward of second term will return to the right handed. Since this second term is the fermionic contribution then it will correspond to the right handed neutrinos.

            +
            + + Note +
            +
            +

            If right-handed neutrinos exist but do not have a Majorana mass, the neutrinos would instead behave as three (3) Dirac fermions and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions.

            • The seesaw mechanism is appealing because it would naturally explain why the observed neutrino masses are so small. However, if the neutrinos are Majorana then they violate the conservation of lepton number and even of B − L.
            • Neutrinoless double beta decay has not (yet) been observed,[3] but if it does exist, it can be viewed as two ordinary beta decay events whose resultant antineutrinos immediately annihilate each other, and is only possible if neutrinos are their own antiparticles.[4]
            • The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in hadron colliders;[5] it is being searched for by both the ATLAS and CMS experiments at the Large Hadron Collider.
            • In theories based on left–right symmetry, there is a deep connection between these processes.[6] In the currently most-favored explanation of the smallness of neutrino mass, the seesaw mechanism, the neutrino is “naturally” a Majorana fermion.

            Majorana fermions cannot possess intrinsic electric or magnetic moments, only toroidal moments.[7][8][9] Such minimal interaction with electromagnetic fields makes them potential candidates for cold dark matter. (Wikipedia)

            +
            +

            Renormalization

            In other words, the synchronized path integral represents a deterministic approach to scalar field's self-excitation, and thus to the confined state in quentum physics

            +
            + + Note +
            +
            +

            Beside the operator proof, here we also provide a diagrammatic argument of the above derivation, using the QED in background field in Sec. 5 as an example.

            • We show that: taking mass derivatives in one-loop Feynman diagrams Fig. 4 for δEN will exactly produce the one-loop Feynman diagrams for insertion of 4HS.
            • The mass derivative has four (4) origins: the explicit mass dependency of the electron propagator, the implicit mass dependency in the energy level EN, the mass dependencies in renormalization constants δm and Z3 − 1, and the implicit mass dependency in the wave function uN.
            • The mass derivative of the fermion propagator 1iγ·D−m simply reduces to mψψ¯ operator insertion in the internal electron line as shown in Fig. 7.
            • The mass dependency in EN will lead to the wave function renormalization in external legs. The mass dependencies in renormalization constants δm and Z3 −1 will exactly lead to the anomalous energy contribution.

            Finally, the mass derivative of the external wave function uN is more complicated, which is shown the remaining diagrams where the mψψ¯ are inserted at external legs. (Scale symmetry breaking - pdf)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-👇--+-👇--+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-👇--+-👇--+-----+-👇--+-👇--+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30            Mod 60            Mod 90
+

            Let us make some concluding remarks with the help of the Fritzsch-Xing "pizza" plot. It offers a summary of 28 free parameters associated with the SM itself and neutrino masses, lepton flavor mixing angles and CP-violating phases.

            +
            + + Note +
            +
            +

            The reduction of pure gravity from eleven dimensions down to D = 4 dimensions yields a gravitational theory with seven (7) abelian vector fields Aµn, n = 1,...,7, and 1+27=28 scalar fields, parametrizing the coset space GL(7)/SO(7). The dimensional reduction of the antisymmetric 3-form to D = 4 dimensions gives rise to one 3-form field, seven 2-form fields. (11D Supergravity and Hidden Symmetries - pdf)

            +
            +

            28 free parameters

            Those results, compared with those for the nucleon, indicate quite different pattern, revealed as a new aspect by exploiting the quark/gluon decomposition of the QCD trace anomaly.

            +
            + + Note +
            +
            +

            The matrix elements of this quark/gluon decomposition of the QCD trace anomaly allow us to derive the QCD constraints on the hadron’s gravitational form factors, in particular, on the twist-four gravitational form factor, Cq,g.

            • Using the three-loop quark/gluon trace anomaly formulas, we calculate the forward (zero momentum transfer) value of the twist-four gravitational form factor C¯q,g at the next-to-next-to-leading-order (NNLO) accuracy.
            • We present quantitative results for nucleon as well as for pion, leading to a model-independent determination of the forward value of C¯q,g.

            We find quite different pattern in the obtained results between the nucleon and the pion. (Twist-four gravitational - pdf)

            +
            +

            2+7 = 3×3 lepton vs quarks

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-👇--+-👇--+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-👇--+-👇--+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30            Mod 60            Mod 90
+

            This fact may also provide a possible explanation for why almost all of the particle interactions we see are describable by renormalizable theories.

            +
            + + Note +
            +
            +

            The Standard Model of particle physics contains only renormalizable operators, but the interactions of general relativity become nonrenormalizable operators if one attempts to construct a field theory of quantum gravity in the most straightforward manner (treating the metric in the Einstein–Hilbert Lagrangian as a perturbation about the Minkowski metric), suggesting that perturbation theory is not satisfactory in application to quantum gravity.

            • However, in an effective field theory, “renormalizability” is, strictly speaking, a misnomer. In nonrenormalizable effective field theory, terms in the Lagrangian do multiply to infinity, but have coefficients suppressed by ever-more-extreme inverse powers of the energy cutoff.169-over-109-blood-pressure
            • If the cutoff is a real, physical quantity—that is, if the theory is only an effective description of physics up to some maximum energy or minimum distance scale—then these additional terms could represent real physical interactions.
            • Assuming that the dimensionless constants in the theory do not get too large, one can group calculations by inverse powers of the cutoff, and extract approximate predictions to finite order in the cutoff that still have a finite number of free parameters. It can even be useful to renormalize these “nonrenormalizable” interactions.multiplication zones
            • Nonrenormalizable interactions in effective field theories rapidly become weaker as the energy scale becomes much smaller than the cutoff. The classic example is the Fermi theory of the weak nuclear force, a nonrenormalizable effective theory whose cutoff is comparable to the mass of the W particle.

            It may be that any others that may exist at the GUT or Planck scale simply become too weak to detect in the realm we can observe, with one exception: gravity, whose exceedingly weak interaction is magnified by the presence of the enormous masses of stars and planets. (Wikipedia)

            +
            +

            Mod 60

            For the renormalization mixing at twist four, the Feynman diagram calculation of ZF and ZC is available to the two-loop order.

            +
            + + Note +
            +
            +

            Moreover, it is shown that the constraints imposed by the RG invariance of (1.1) allow to determine the power series in αs for ZF as well as ZC in the MS-like schemes, completely from the perturbative expansions of β(g) and γm(g), which are now known to five-loop order [43–48] in the literature.

            • Therefore, six renormalization constants ZT,ZL, Zψ, ZQ, ZF and ZC among ten constants arising in (2.3) (2.6) are available to a certain accuracy beyond two-loop order inthe MS-like schemes, and they take the form, (2.8) in the d = 4 − 2 spacetime dimensions with X = T, L, ψ, Q, F, and C; here, aX, bX, cX.…, are the constants given as the power series in αs, and δX,X0 denotes the Kronecker symbol. However, ZM, ZS, ZK and ZB still remain unknown.
            • It is shown [8] that these four renormalization constants can be determined to the accuracy same as the renormalization constants (2.8), by invoking that they should also obey the form (2.8) with X = M, S, K, B, and that the r.h.s. of the formulas (2.3), (2.4) are, in total, UV-finite.

            Thus, all the renormalization constants in (2.3)–(2.6) are determined up to the three-loop accuracy. (Twist-four gravitational - pdf)

            +
            +

            IMG_20240211_101224

            A gauge colour rotation is a spacetime-dependent SU(3) group element. They span the Lie algebra of the SU(3) group in the defining representation.

            +
            + + Note +
            +
            +

            The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.

            +
            +

            QED vs QCD

            Indeed, a particularly well-chosen cellular automaton on II(9,1) or II(25,1) would be a discretised version of 10- or 26-dimensional string theory.

            The 11 Dimensions

            Below is a model of E11 (shown by 11 dimensions). Its absolute dimensions represent all related key knowledges of modern physics.

            +
            + + Note +
            +
            +

            Moreover this model represents Quark-Gluon Plasma, with all of the fundamental forces in the early stage after Big Bang. (Youtube)

            +
            +

            default

            Classically, we have only one 11-dimensional supergravity theory: 7D hyperspace + 4 common dimensions.

            +
            + + Note +
            +
            +

            The four (4) faces of our pyramid additively cascade 32 four-times triangular numbers

            • These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112),
            • which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112),
            • which is the index number of the 1000th prime within our domain,
            • and equals the total number of ‘elements’ used to construct the pyramid.

            Note that 4 x 32 = 128 is the perimeter of the square base which has an area of 32^2 = 1024 = 2^10). (PrimesDemystified)

            +
            +

            The above 11 stands as the central point which is correlated to 77 sequencial processes of sun vs moon orbits starting with the symmetri breaking that involving 9 and 7.

            +
            + + Note +
            +
            +

            Back in 1982, a very nice paper by Kugo and Townsend, Supersymmetry and the Division Algebras, explained some of this, ending up with some comments on the relation of octonions to d=10 super Yang-Mills and d=11 super-gravity.

            • Baez and Huerta in 2009 wrote the very clear Division Algebras and Supersymmetry I, which explains how the existence of supersymmetry relies on algebraic identities that follow from the existence of the division algebras. Kugo-Townsend don’t mention string theory at all, and Baez-Huerta refers to superstrings just in passing, only really discussing supersymmetric QFT.
            • There’s also Division Algebras and Supersymmetry II by Baez and Huerta from last year, with intriguing speculation about Lie n-algebras and what these might have to do with relations between octonions and 10 and 11 dimensional supergravity. For a nice expository paper about this stuff, see their An Invitation to Higher Gauge Theory.

            The headline argument is that octonions are important and interesting because they’re The Strangest Numbers in String Theory, even though they play only a minor role in the subject. (math.columbia.edu)

            +
            + 
             8§8  |------- 5® --------|------------ 7® --------------|
+      |QED|------------------- QCD ----------------------|👈
+      | 1 |-------------- 77 = 4² + 5² + 6² -------------|
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ user | 7 | - | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+------+---|👇-+👇-+---+---+---+---+---+---+----+----+----+ 7,78
+ main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+        Δ | Δ             |                      Δ  |   Δ
+       Φ17|Φ29            |                    96-99|  100 - 123 ({24})
+          |--- A,T,G,C ---|                         |  └── 100 - 103 (4x) » 100
+          Δ    2x2 = 4x   |-------  2x3 = 6x -------|  └── 104 - 109 (6x) » 30
+         {98}                                       |  └── 110 - 123 (14x)» 70
+

            A number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati–Salam model.

            +
            + + Note +
            +
            +

            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

            +
            +

            SO(10)

            SU(5)_representation_of_fermions

            The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra. That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional.

            +
            + + Note +
            +
            +

            The Lie algebra E6 of the D4-D5-E6-E7-E8 VoDou Physics model can be represented in terms of 3 copies of the 26-dimensional traceless subalgebra J3(O)o of the 27-dimensional Jordan algebra J3(O) by using the fibration E6 / F4 of 78-dimensional E6 over 52-dimensional F4 and the structure of F4 as doubled J3(O)o based on the 26-dimensional representation of F4. (Tony’s Home)

            +
            +

            Quantum Chromodynamics

            The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle. It must be highly correlated with the hierarchy of quark flavor mixing.

            +
            + + Note +
            +
            +

            This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.

            • The SM contains thirteen free flavor parameters in its electroweak sector: three charged-lepton masses,six quark masses, three quark flavor mixing angles and one CP-violating phase.
            • Since the three neutrinos must be massive beyond the SM, one has to introduce seven (or nine) extra free parameters to describe their flavor properties: three neutrino masses, three lepton flavor mixing angles and one (or three) CP-violating phase(s), corresponding to their Dirac (or Majorana) nature a
            • The 3x3 lepton vs quark mixing matrices appearing in the weak charged-current interactions are referred to, respectively, as the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix Uand the Cabibbo-Kobayashi-Maskawa (CKM) matrix V which all the fermion fields are the mass eigenstates.
            • By convention, U and V are defined to be associated with W− and W+, respectively. Note that V is unitary as dictated by the SM itself, but whether U is unitary or not depends on the mechanism responsible for the origin of neutrino masses.
            • The charged leptons and quarks with the same electriccharges all have the normal mass hierarchies (namely, me ≪ mµ ≪ mτ, mu ≪ mc ≪ mt and md ≪ ms ≪ m. Yet it remains unclear whether the three neutrinos also have a normal mass ordering (m1 < m2 < m3) or not. Now that m1 < m2 has been fixed from the solar neutrino oscillations, the only likely “abnormal” mass ordering is m3 < m1 < m2
            • The neutrino mass ordering is one of the central concerns in flavor physics, and it will be determined in the foreseeable future with the help of either an accelerator-based neutrino oscillation experiment or a reactor-based antineutrino oscillation experiment, or both of them. Up to now the moduli of nine elements of the CKM matrix V have been determined from current experimental data to a good degree of accuracy.

            Here our focus is on the five (5) parameters of strong and weak CP violation. In the quark sector, the strong CP-violating phase θ remains unknown, but the weak CP-violating phase δq has been determined to a good degree of accuracy. In the lepton sector, however, none of the CP-violating phases has been measured. (Quark Mass Hierarchy and Flavor Mixing Puzzles - pdf)

            +
            +

            CKM vs PMNS

            The 3x3 lepton vs quark mixing matrices appearing in the weak charged-current interactions are referred to, respectively, as the PMNS matrix U, and the CKM matrix V, which all the fermion fields are the mass eigenstates.

            +
            + + Note +
            +
            +

            Muons are about 200 times heavier than the electron. The larger mass makes them unstable. Muons exist for only about two microseconds—or two-millionths of a second—before they decay. Electrons live forever. The tau; elementary subatomic particle is similar to the electron but 3,477 times heavier. Like the electron and the muon, the tau is an electrically charged member of the lepton family of subatomic particles; the tau is negatively charged, while its antiparticle is positively charged. (ResearchGate)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-👇--+-👇--+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30            Mod 60            Mod 90
+

            Bound state corrections to the semileptonic width and measured by a number moments analyses have permitted the extraction to a level of a few %.

            +
            + + Note +
            +
            +

            In principle, there is one further parameter in the Standard Model; the Lagrangian of QCD can contain a phase that would lead to CP violation in the strong interaction.

            • Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.
            • The theoretical and experimental pillars of the Standard Model:
              • the twelve (12) fermions (or perhaps more correctly the twelve Yukawa couplings to the Higgs field), mν1, mν2, mν3, me, mµ, mτ, md, ms, mb, mu, mc, and mt ;
              • the three (3) coupling constants describing the strengths of the gauge interactions, α, GF and αS, or equivalently g′, gW and gS;
              • the two (2) Higgs parameters describing the Higgs potential, µ and λ, or equivalently its vacuum expectation value and the mass of the Higgs boson, v and mH; and
              • the eight (8) mixing angles of the PMNS and CKM matrices, which can be parameterised by θ12, θ13, θ23, δ, and λ, A, ρ, η.neutrino-mixing-the-pmns-matrix-l
              • in principle, there is one (1) further parameter in the Standard Model; the Lagrangian of QCD can contain a phase that would lead to CP violation in the strong interaction. Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.
            • If θCP is counted, then the Standard Model has 12+3+2+8+1=26 free parameters.
            • The relatively large number of free parameters is symptomatic of the Standard Model being just that; a model where the parameters are chosen to match the observations, rather than coming from a higher theoretical principle.
            • Putting aside θCP, of the 25 SM parameters: 14 are associated with the Higgs field, eight (8) with theflavour sector and only three (3) with the gauge interactions.

            Likewise, the coupling constants of the three gauge interactions are of a similar order of magnitude, hinting that they might be different low-energy manifestations of a Grand Unified Theory (GUT) of the forces. These patterns provide hints for, as yet unknown, physics beyond the Standard Model. (Modern Particle Physics P.500 - pdf)

            +
            +

            slide_40

            Using this concept we are going to stimulate a model of the 11 dimensions through the rank of their partition using github organizations of 13 repositories each.

            +
            + + Tip +
            +
            +

            Each of the user profiles will have seven (7) user repositories consist of one (1) main of github.io and six (6) user pinned repositories. Meanwhile each of organizations will have one (1) profile of .github repository and thirteen (13) organization repositories consist of one (1) main of github.io, and twelve (12) pinned repositories under member and public view that represents 6 by 6 flavors.

            +
            +

            ®main + ®gist + ®orgs = 7 + (7+11) + (11x13) = 7 + 18 + 143 = 24 x 7 = 168 = π(1000)

            1. "Wormhole Theory"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["Schema","Artifacts","Assets","depot_tools","distribution","sitemap"]
            2. "Elementary Particles"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["docs","screen","builder","genius","rapidjson","Ventoy"]
            3. "Symmetric Expansion"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["JSONFeed","SEOstats","OpenSEO","falcon","NPPGit","webpack"]
            4. "Vibrating Strings"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["steps","jquery.soap","bash","json-html","store","gtm"]
            5. "Multiple Universes"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["ga-beacon","flakes","jsonix","lanyon","progit-book","wiki"]
            6. "Hidden Dimensions"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["core","bulbea","pedia","poole","cards","bootstrap"]
            7. "Basic Transformation"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["Cloud-Site-API","Google-Ads-API","Toko-Chetabahana","KeepFit","World","Tutorial-Buka-Toko"]
            8. "Fundamental Forces"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["NeuralTeams","collab","container-push","includeHTML","now","wheel"]
            9. "Quadratic Polynomials"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["screen","buffer-ruby","github-graphql-action","scrapy","wpt","system"]
            10. "Truncated Perturbation"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["classifier","domJSON","openoffice","landing-page-theme","asciidoc","recommendations-ai"]
            11. "Extra Dimensions"
              • ["maps","feed","lexer","parser","syntax","grammar"]
              • ["storj","monsterpost","veles","spectral","finraos","dstroot"]

            The Root Function of 13 repositories per each of organization above is not arranged to directly follow the partition function but through the 18 gists via their .github profiles.

            +
            + + Tip +
            +
            +

            Base on the 11s and 7s distribution of the 18s structure of The True Prime Pairs, the 7s will be reflected by seven (7) repositories of user profile with id: 30 to id: 36 meanwhile the 11s will be reflected by eleven (11) organizations.

            +
            +

            teaching-machines-glouppe_compressed.pdf

            The gist contain prime data to organize the 7 groups vs 11 dimensions in Eightfold Way. So when they are combined as eighteen (18) then the ∆1 is recycled by 8th-prime and generate the pattern of 6 by 6 flavors implemented to all of the repositories.

            +
            + + Tip +
            +
            +

            By this tabulation you may see that all the numbers between 37 and 102 are located within 11 columns where the 31 behave as a new axis.

            • This 11 is reflecting the 19 to 29. Since the 11 is bonding with 19 so it would go to another cycles starting with the 26th dimension which will bring them by four (4) compactification (26 to 29) to the 30.
            • This 30th order repeats itself to infinity. Even in the first 30s system. We call this arrangement as the Δ(19 vs 18) Scenario where the zeta function stands as the basic algorithm.

            By the tabulation, here you can see that the layout of our home page refers to the four (4) partitions of ∆1 i.e. id: 1-18, id: 19-30, id: 31-36, and id: 37-102.

            +
            +

            30 + 36 + 102 - 25 - 29 = 168 - 25 - 29 = π(1000) - π(100) - 10th prime = 114

              Δ1 + Δ7 + Δ29  →  | Δ37 + Δ77 = Δ114 = Δ113 + Δ1 → 
+
+     |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - | 100|  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - | 101|  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+-👇-+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ12 👈 - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  | 102|  - |  - |  - |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+     |       Δ    Δ    Δ           |                     Φ12     |       Δ                   Δ |
+           -114 +151 = +37                                             +102 = +139 = +168 - 29
+

            The project is being developed under GitHub dan Google Platfrorms. Each will then be properly assigned to generate the cycle of spin networks.

            +
            + + Note +
            +
            +

            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries.

            • For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period 8 difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2}. The entire domain can thus be defined as 1 {+6 +4 +2 +4 +2 +4 +6 +2} {repeat … ∞}.
            • As we’ve already suggested, the number 30 figures large in our modulo 30 domain. The Prime Spiral Sieve is Archimedean in that the separation distance between turns equals 30, ad infinitum. The first two rotations increment as follows:image
            • Interestingly, the sum of the 2nd rotation = 360, the product of the first three primorials, 2 x 6 x 30 = 360, and when you multiply the first five Fibonacci numbers in sequence, you produce 1, 2, 6 and 30? And, speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve:11's additive sums
            • Remarkably, the sequence of Fibonacci terminating digits indexed to our domain (natural numbers not divisible by 2, 3 or 5), 13,937,179 (see graphic, above), is a prime number and a member of a twin prime pair (with 13,937,177). In case you’re wondering, 13,937,179 is not a reversible prime (as the reversal is a semi-prime: 9,461 x 10,271 = 97,173,931). However, given all the repunits that follow, we take note that both of the reversal’s factors are congruent to 11 (mod 30 & 90). [Note: Repunits are abbreviated Rn, where n designates the number of unit 1’s. Thus 1 is R1 and 11 is R2.]
            • Perhaps most remarkable of all, 13,937,179 when added to its reversal 97,173,931 = 111,111,110 (in strict digital root terms, the sum is 11,111,111, or R8) and the entire repeating (and palindromic) Fibo sequence end-to-end (equivalent to two rotations around the sieve) gives you this palindromic equivalency: 1,393,717,997,173,931 ≌ 11,111,111 (mod 111,111,110)… (and interestingly, 11,111,111 * 111,111,110 = 123456776543210).
            • Another point of interest: the terminating digits of the first 8 Fibonacci numbers indexed to our domain (13937179) contain two each 1’s, 3’s, 7’s, and 9’s. This is also true of the terminating digits of the first eight members of our domain (17137939).
            • Echoing the Fibonacci patterns just described, the terminating digits of the prime roots (17,137,939), when added to their reversal (93,973,171) = 111,111,110. [And note that 111,111,111 * 111,111,110 = 12345678876543210.].
            • Yet another related dimension of symmetry: The terminating digits of the prime root angles (24,264,868; see illustration of Prime Spiral Sieve) when added to their reversal (86,846,242) = 111,111,110, not to mention this sequence possesses symmetries that dovetail perfectly with the prime root and Fibo sequences.

            And when you combine the terminating digit symmetries described above, capturing three (3) rotations around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry. (PrimesDemystified)

            +
            +

            Prime-Numbers-Demystified-by-8-Dimensional-Algorithms.pdf

            These include generating variants of their abundance profile, assigning taxonomy and finally generating a rooted phylogenetic tree for the Standard Model.

            +
            + + Note +
            +
            +

            Here is an elegant model to define the elementary particles of the Standard Model in Physics.

            • The black spheres are the bosons, the green ones leptons and the rest of the colored ones Murray Gell-Mann’s quarks (red for Generation I, blue for II and orange for III).
            • Higgs Boson (aka the God particle) that does not have charge is the vertex between the matter and anti-matter particles.
            • The z-boson and its counterpart would lie in the centroids of the tetrahedrons created by folding the triangles to meet up at the Higgs particle.

            The next step is to re-gigg the model to account for the collisions and annihilations. Gluons and Photons that don’t have mass are not in the model, but will be the consequences of the interactions. (Hypercomplex-Math)

            +
            +

            particlephysicsmodel-1

            All 15 matter particles are mirroring their corresponding doppelgangers (anti-particles) each others that could potentially explain dark matter.

            Dark Matter

            Dark matter got its name because we aren't able to see it. It doesn't interact directly with electromagnetic radiation, but it does interact with gravity.

            +
            + + Tip +
            +
            +

            By our project the quantum gravity is correlated with a finite fraction of four (4) axis dimensions of MEC30 that end up exactly 43 objects.

            • The fractal space-time theory of El Nachie allows the exact determination of one of the fundamental quantities of physics, namely the Fine Structure constant, from a dimensional analysis.
            • The Golden Ratio seems to be the key that opens the door to the fractal quantum world, which looks as if there were an infinite number of scaled copies of our ordinary 4-dimensional space-time.

            In our case this means that there are three (3) steps ahead a decay could take place.

            +
            +

            Grand Unification

            The interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used for quantum chromodynamics.

            first-feynman-2nd-order-electron-scattering

            Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The corresponding eigenvalue is often represented as the multiplying factor.

            +
            + + Note +
            +
            +

            The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively.[ (Wikipedia)

            +
            + 
             Osp(8|4) |  1 |  2 |  3 |   4 | th
+==========+====+====+====+=====+====
+ π(10)    |  2 |  3 |  5 |   7 | 4th
+----------+----+----+----+-----+----
+ π(19)    | 11 | 13 | 17 |  19 | 8th
+----------+----+----+----+-----+----
+ π(29)    | 23 | 29 |  - |   - | 10th
+==========+====+=👇=+====+=====+====
+ π(41)    | 31 | 37 | 41 |   - | 13th 👈
+----------+----+----+----+-----+----
+ π(59)    | 43 | 47 | 53 |  59 | 17th 
+----------+----+----+----+-----+- ---
+ π(72)    | 61 | 67 | 71 |   - | 20th
+==========+====+====+====+=====+====
+ π(72+11) | 73 | 79 | 83 |   - | 23th
+----------+----+----+----+-----+----
+ π(83+18) | 89 | 97 |101 |   - | 26th
+----------+----+----+----+-----+----
+ π(101+8) |103 |107 |109 |   - | 29th
+

            Let's consider a Metaron's Cube as a geometric figure composed of 13 equal circles with lines from the center of each circle extending out to the centers of the other 12 circles.

            +
            + + Note +
            +
            +

            The 13 circles of the Metatron’s cube can be seen as a diagonal axis projection of a 3-dimensional cube, as 8 corner spheres and 6 face-centered spheres. Two spheres are projected into the center from a 3-fold symmetry axis. The face-centered points represent an octahedron. Combined these 14 points represent the face-centered cubic lattice cell. (Wikipedia)

            +
            +

            image

            Finally we explore the indirect detection characteristics of this model, determined by the decays of the right-handed neutrinos into SM bosons and leptons.

            +
            + + Note +
            +
            +

            We analyze a simple extension of the Standard Model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group.

            • Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sectorand the SM particles, and generate masses for the active neutrinos via the seesawmechanism.
            • We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario.

            We also study the constraints from direct Dark Matter searches and the prospects for indirect detectionvia sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV. (Sterile Neutrino portal to Dark Matter II - pdf)

            +
            +

            Sterile Neutrino portal to Dark Matter II

            It is called the mixing angle by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon. Its measured value is slightly below 30°, but also varies.

            +
            + + Note +
            +
            +

            If the angle was 0, the U(1) group would remain unbroken and there would be no mixing with the SU(2) group. This would lead to a single massless boson and 3 remaining massless bosons: Ws and photon. On the other hand, if the angle was 90, the SU(2) group would remain unbroken and there would be no mixing with the U(1) group. This would lead to a single massive boson and 3 remaining massless bosons: Ws and photon. (PhysicsForums)

            +
            +

            Weinberg_angle_(relation_between_coupling_constants

            The coupling gives rise as the phase starts to roll down in the clockwise direction, it preferentially creates an excess of baryons over antibaryons.

            +
            + + Note +
            +
            +

            The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review. (MDPI)

            +
            +

            symmetry-08-00081-g001

            Depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.

            +
            + + Note +
            +
            +

            When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. If one or more sterile neutrinos are added, it is 4×4 or larger. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-👇--+-👇--+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-👇--+-👇--+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-👇--+-👇--+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30 👈         Mod 60 👈         Mod 90 👈
+

            While quarks may flow within the closed surface across various open surfaces, there can be no net flux of individual quarks in to or out of any closed surface.

            +
            + + Note +
            +
            +

            There are four (4) main features of QCD confinement, which appear to parallel the development of the previous section.

            • These parallels are best specified with reference to baryons, as follows: Establish any closed surface over a baryon source density P. Then:
            • While gluons may flow within the closed surface across various open surfaces, there can be no net flux of gluons in to or out of any closed surface.
            • This may possibly be represented by = 0 dG , and the invariance of F → F’ = F under the transformation F → F’= F − dG .
            • While quarks may flow within the closed surface across various open surfaces, there can be no net flux of individual quarks in to or out of any closed surface.
            • This may possibly be represented by the invariance of P → P’= P under the transformation F → F’= F − dG .
            • While there can be no net flux of individual quarks in to or out of any closed surface, there can indeed be a net flux of quark-antiquark pairs in to or out of any closed surface.
            • The antiquark cancels the quark, thereby averting a net flux, and in this way, quarks do flow in to or out of the closed surface, but only paired with antiquarks, as mesons.
            • This may possibly be represented as 02 ≠ i gG .
            • It does not matter how hard or in what manner one “smashes” a baryon, one can still never extract a net flux of quarks or a net flux of gluons, but only a large number of meson jets.
            • This may be possibly represented by the fact that in all of the foregoing, the volume and surfaceintegrals apply to any and all closed surfaces.
            • One can choose a small closed surface, a large closed surface, a spherical closed surface, an oblong closed surface, and indeed, a closed surface of any shape and size. The choice of closed surface does not matter.
            • These mathematical rules for what does and does not flow across any closed surface, in fact, thereby impose very stringent dynamical constraints on the behaviors of these non-Abelian magnetic sources: No matter what flows across various open surfaces, they may never be a net flux of anything across any closedsurface. The only exceptions, which may flow across a closed surface, are physical entities represented by.

            Where is the author going with this?

            • The magnetic three-form P, and its associated third-rank antisymmetric tensorσµν P , has allthe characteristics of a baryon current density.
            • These σµν P , among their other properties, are naturally occurring sources containing exactlythree fermions. These constituent fermions are most-sensibly interpreted as quarks.
            • The surface symmetri F → F’ = F under the transformation F → F’= F − dG , tells us that there is no net flow of gluons across any closed surface over the baryon density.
            • The volume symmetry P → P’= P under F → F’= F − dG , tells us that there is no net flow of quarks across any closed surface over the baryon density.
            • The physical entities represented by 2 igG , when examined in further detail, have thecharacteristics of mesons.

            structure-of-composite-particles-l

            It tells us that mesons are the only entities which may flow across any closedsurface of the baryon density. (Lab Notes)

            +
            +

            image

            origin

            action

            Scientists believe there could be an anti-universe somewhere out there that acts like mirroring our own universe, reciprocating almost everything we do.

            +
            + + Note +
            +
            +

            Only more accurate analysis on the involved spectra and on the relative brightness of the two rings, and mainly the discovery of other double rings systems, could be used to finally choose which among these two interpretations is more likely to hold. As to using Klein bottle holes to check the physical existence of other universes, it appears just a matter of time to find a double truncated spiral blurred enough to clearly show a connection with other universes. (Observing another Universe - pdf)

            +
            +

            Gravitational-lensing-effect-produced-by-a-ringhole-from-a-single-luminous-source-a_Q320

            If this theory holds true, it could explain the presence of dark matter. Dark matter, then, could be right-handed neutrinos implied by the mirror universe.

            +
            + + Note +
            +
            +

            The GUT group E6 contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E6 models comes from E8 × E8 heterotic string theory. (Wikipedia)

            +
            +

            4² + 5² + 6² = 77

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-👇--+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-----+-----+-👇--+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-👇--+-👇--+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30            Mod 60            Mod 90
+

            All visible matter in the universe is made from the first generation of matter particles — up quarks, down quarks, and electrons.

            +
            + + Note +
            +
            +

            While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles.

            • It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton.
            • Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons.
            • The graviton’s Compton wavelength is at least 1.6×10^16 m, or about 1.6 light-years, corresponding to a graviton mass of no more than 7.7×10−23 eV/c2.[22]
            • This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation, the same formula that relates electromagnetic wavelength to photon energy.
            • However, if gravitons are the quanta of gravitational waves, then the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.
            • Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the GW170104 event, which was ~ 1,700 km. The report[22] did not elaborate on the source of this ratio.

            It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way. (Wikipedia)

            +
            +

            image

            There even stated by the conformal cyclic cosmology that this hypothesis requires that all massive particles eventually vanish from existence.

            +
            + + Note +
            +
            +

            As Penrose points out, proton decay is a possibility contemplated in various speculative extensions of the Standard Model, but it has never been observed. Moreover, all electrons must also decay, or lose their charge and/or mass, and no conventional speculations allow for this.

            In his Nobel Prize Lecture video, Roger Penrose moderated his previous requirement for no mass, beginning at 26:30 in the video, allowing some mass particles to be present as long as the amounts are insignificant with nearly all of their energy being kinetic, and in a conformal geometry dominated by photons. (Wikipedia)

            +
            +

            conformal cyclic cosmology

            This is because all second and third generation particles are unstable and quickly decay into stable first generation particles.

            The 27 Parameters

            Note that since our Universe began with a Big Bang, all its particles originate from pair creation since then.

            shilov27

            Upon reviewing the masses, the algorithms should work correctly to depict the Generation I, II & III and the charge levels of the elementary particles.

             Osp(8|4) |  1 |  2 |  3 |   4 | th
+==========+====+====+====+=====+====
+ π(10)    |  2 |  3 |  5 |   7 | 4th
+----------+----+----+----+-----+----
+ π(19)    | 11 | 13 | 17 |  19 | 8th
+----------+----+----+----+-----+----
+ π(29)    | 23 | 29 |  - |   - | 10th
+==========+====+====+====+=====+====
+ π(41)    | 31 | 37 | 41 |   - | 13th
+----------+----+----+----+-----+----
+ π(59)    | 43 | 47 | 53 |  59 | 17th 
+----------+----+----+----+-----+- ---
+ π(72)    | 61 | 67 | 71 |   - | 20th
+==========+====+====+====+=====+====
+ π(72+11) | 73 | 79 | 83 |   - | 23th
+----------+----+----+----+-----+----
+ π(83+18) | 89 | 97 |101 |   - | 26th 👈
+----------+----+----+----+-----+----
+ π(101+8) |103 |107 |109 |   - | 29th
+

            Bosonic String Theory of 26-dim J3(O)o is related to an M-theory based on the full 27-dimensional J3(O) and 28-dimensional J4(Q).

            String theory

            There are models of two related universes that e.g. attempt to explain the baryon asymmetry – why there was more matter than antimatter at the beginning – with a mirror anti-universe.

            +
            + + Note +
            +
            +

            In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem,[1][2] is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antibaryonic matter in the observable universe.

            • Neither the standard model of particle physics nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges.[3]
            • The Big Bang should have produced equal amounts of matter and antimatter. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter.

            Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon, which has been described as “one of the great mysteries in physics“. (Wikipedia)

            +
            +

            image

            The component of the 27 dimensional gravitational field g27;27 is a scalar in the 26 dimensional theory. It is of course the dilaton.

            +
            + + Note +
            +
            +

            Consider a (purple) world-line String of one World of the MacroSpace of Many-Worlds and its interactions with another (gold) world-line World String, from the point of view of one point of the (purple) World String, seen so close-up that you don’t see in the diagram that the (purple) and (gold) World Strings are both really closed strings when seen at very large scale:

            • massless spin-2 Gravitons travel along the (red) MacroSpace light-cones to interact with the intersection points of those (red) light-cones with the (gold) World String;
            • scalar Dilatons, with effectively real mass, travel within the (yellow) MacroSpace light-cone time-like interior to interact with the intersection region of the (yellow) light-cone time-like interior region with the (gold) World String; and
            • Tachyons, with imaginary mass, travel within the (cyan) MacroSpace light-cone space-like exterior to interact with the intersection points of the (cyan) light-cone space-like exterior region with the (gold) World String.
            • Metod Saniga, inphysics/0012033 D4-D5-E6-E7-E8 VoDou Physics Model: It is a well-known fact that on a generic cubic surface, K3, the lines are seen to form three (3) separate groups.
            • The first two groups, each comprising six (6)lines, are known as Schlafli’s double-six. The third group consists of fifteen lines. The basics of the algebra can simply be expressed as 27 = 12 + 15.

            Note that Gravity may not propagate in the 26 dimensions of the MacroSpace of the Many-Worlds in exactly the same way as it propagates in our 4-dimensional physical SpaceTime. (Tony Smith’s)

            +
            +

            World String

            Particle physicists acknowledge that the particle may exist in wave forms and yet have characteristics of matter.

            +
            + + Note +
            +
            +

            Supersymmetry predicts that each of the particles in the Standard Model has a partner with a spin that differs by half of a unit.

            • So bosons are accompanied by fermions and vice versa.
            • Linked to their differences in spin are differences in their collective properties.
            • Fermions are very standoffish; every one must be in a different state.
            • On the other hand, bosons are very clannish; they prefer to be in the same state.

            Fermions and bosons seem as different as could be, yet supersymmetry brings the two types together.

            +
            +

            1 + 8 + 8 + 8 + 1 = 2 × (1+4+8) = 2 × 13 = 26

            standardmodel1

            The 26 dimensions of Closed Unoriented Bosonic String Theory are interpreted as the 26 dimensions of the traceless Jordan algebra J3(O)o of 3x3 Octonionic matrices.

            +
            + + Note +
            +
            +

            Each of the 3 Octonionic dimenisons of J3(O)o having the following physical interpretation:

            • 4-dimensional physical spacetime plus 4-dimensional internal symmetry space;
            • 8 first-generation fermion particles; 8 first-generation fermion anti-particles.

            Thus the 26 dimensions stand as the degrees of freedom of the Worlds of the Many-Worlds. (Tony’s Web Book - pdf (800MB Size)).

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-👇--+-👇--+-----+                                                    |
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-👇--+-👇--+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-👇--+-👇--+-----+-👇--+-👇--+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ
+                  Mod 30            Mod 60            Mod 90
+

            At present, there is no candidate theory of everything that, at the same time, is able to calculate the fine-structure constant or the mass of the electron.

            +
            + + Note +
            +
            +

            In the Standard Model, elementary particles are manifestations of three “symmetry groups” — essentially, ways of interchanging subsets of the particles that leave the equations unchanged.

            • These three (3) symmetry groups, SU(3), SU(2) and U(1), correspond to the strong, weak and electromagnetic forces, respectively, and they “act” on six types of quarks, two types of leptons, plus their anti-particles, with each type of particle coming in three copies, or “generations,” that are identical except for their masses.
            • The fourth fundamental force, gravity, is described separately, and incompatibly, by Einstein’s general theory of relativity, which casts it as curves in the geometry of space-time.

            Note that both quarks and leptons exist in three distinct sets. Each set of quark and lepton charge types is called a generation of matter (charges +2/3, -1/3, 0, and -1 as you go down each generation). The generations are organized by increasing mass.

            +
            +

            Fundamental Forces

            The solution is that many or all of these possibilities are realized in one or another of a huge number of universes, but that only a small number of them are habitable.

            Another suggestion which has just yet been in a topic of the science is that the similar behaviour also happen by particles such as hydrogen.

            +
            + + Note +
            +
            +

            Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron (Wikipedia).

            +
            +

            the electron in a hydrogen

            So hypothetically it suppose to have its own parallel universes because whatever a smallest thing is arised, they could only exist by the same law of physics.

            Infinite number

            This law of physics would exist everywhere. So it is also one of their law when the 1st sequence of the unrepeated ten (10) digits Euler's number is zero (0).

            +
            + + Note +
            +
            +

            1729th decimal digit holds significance in the decimal representation of the transcendental number e. From 1729th digit you can get the first occurrence of all ten digits consecutively and they are 0719425863. (Ramanujan taxicab 1729 - pdf)

            +
            +

            139 + 286 + 114 + 247 + 157 + 786 = 786 + 157 + 786 = 1729 = 7 x 13 x 19

            0719425863 in 1729th position of Euler's number

            Theoretically the zero speaks if an existence of everything arose from nothingness.

            By our universe it could be represented by the central black hole which is very strong to throw away every objects but it has no resistance against any exchange.

            +
            + + Note +
            +
            +

            Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed (Wikipedia)

            +
            +

            the central black hole_

            So the particle's multiverses are obviously massive waves. It will remain untouchable as long as an experiment gives a result that it is as particle (not wave).

            +
            + + Note +
            +
            +

            Wave–particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances.[1]: 59  It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects.

            During the 19th and early 20th centuries, light was found to behave as a wave, and then later discovered to have a particulate character, whereas electrons were found to act as particles, and then later discovered to have wavelike aspects. The concept of duality arose to name these contradictions. (Wikipedia)

            +
            +

            Quantum-Physics

            Our results show that about 69% of our universe's energy is dark energy. They also demonstrate, once again, that Einstein's simplest form of dark energy – the cosmological constant – agrees the most with our observations.

            +
            + + Note +
            +
            +

            Dark energy is one of the greatest mysteries in science today.

            • We know very little about it, other than it is invisible, it fills the whole universe, and it pushes galaxies away from each other. This is making our cosmos expand at an accelerated rate. But what is it?
            • One of the simplest explanations is that it is a cosmological constant – a result of the energy of empty space itself – an idea introduced by Albert Einstein.

            Many physicists aren’t satisfied with this explanation, though. They want a more fundamental description of its nature. Is it some new type of energy field or exotic fluid? (The Conversation).

            +
            +

            image

            Or is it a sign that Einstein's equations of gravity are somehow incomplete? What's more, we don't really understand the universe's current rate of expansion

            +
            + + Note +
            +
            +

            Discussing both open and closed bosonic strings, Soo-Jong Rey, in his paper Heterotic M(atrix) Strings and Their Interactions - pdf, says: We would like to conclude with a highly speculative remark on a possible:

            • It is well-known that The regularizedone-loop effective action of d-dimensional Yang-Mills theory. For d=26, the gauge kinetic term does not receive radiative correction at all.
            • We expect that this non-renormalization remains the same even after dimensional reductions. One may wonder if it is possible to construct for bosonic string as well despite the absence of supersymmetry and BPS states.
            • M(atrix) theory description of bosonic strings bosonic Yang-Mills theory in twenty-six dimensions is rather special M(atrix)string theory. The bosonic strings also have D-brane extended solitons, whose tension scales as 1/gB for weak string coupling gB « 1.
            • Given the observation that the leading order string effective action of and antisymmetric tensor field may be derived from Einstein’s Gravity in d = 27, let us make an assumption that the 27-th quantum dimension decompactifies as the string coupling gB becomes large. For D0-brane, the dilaton exchange force may be interpreted as the 27-th diagonal component of d = 27 metric.
            • Gravi-photon is suppressed by compactifying 27-th direction on an rather than on a circle. Likewise, its mass may be interpreted as 27-th Kaluza-Klein momentum of a massless excitation in d = 27.

            In the infinite boost limit, the light-front view of a bosonic string is that infinitely many D0-branes are threaded densely on the bosonic string. (26 Dimensions of Bosonic String Theory - pdf)

            +
            +

            Einstein's equations

            The expected Gravitational waves spreading all over the universe, and all particles travelling in this cosmic greatest speed such as neutrinos.

            +
            + + Note +
            +
            +

            Einstein in 1916 proposed the existence of gravitational waves as an outgrowth of his ground-breaking general theory of relativity, which depicted gravity as the distortion of space and time by matter. Until their detection in 2016, scientists had found only indirect evidence of their existence, beginning in the 1970s. The gravitational wave signal was observed in 15 years’ worth of data obtained by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) Physics Frontiers Center (PFC), a collaboration of more than 190 scientists from the United States and Canada. (Reuters)

            +
            +

            Sun vs Moon

            Assuming that each fermion could be an earth in "anti-universe" then it stands as 1000 times earth moon system around the sun against the background of the 11 galaxies.

            +
            + + Note +
            +
            +

            Month, a measure of time corresponding or nearly corresponding to the length of time required by the Moon to revolve once around the Earth.

            • The synodic month, or complete cycle of phases of the Moon as seen from Earth, averages 29.530588 mean solar days in length (i.e., 29 days 12 hours 44 minutes 3 seconds); because of perturbations in the Moon’s orbit, the lengths of all astronomical months vary slightly.
            • The sidereal month is the time needed for the Moon to return to the same place against the background of the stars, 27.321661 days (i.e., 27 days 7 hours 43 minutes 12 seconds); the difference between synodic and sidereal lengths is due to the orbital movement of the Earth–Moon system around the Sun.image
            • The tropical month, 27.321582 days (i.e., 27 days 7 hours 43 minutes 5 seconds), only 7 seconds shorter than the sidereal month, is the time between passages of the Moon through the same celestial longitude.
            • The draconic, or nodical, month of 27.212220 days (i.e., 27 days 5 hours 5 minutes 35.8 seconds) is the time between the Moon’s passages through the same node, or intersection of its orbit with the ecliptic, the apparent pathway of the Sun.

            As a calendrical period, the month is derived from the lunation—i.e., the time elapsing between successive new moons (or other phases of the moon). A total of 12 lunations amounts to 354 days and is, roughly, a year. (Britannica)

            +
            +

            By E24, the residual length of sidereal (7 hours, 43 minutes, 12 seconds) behave as a Fibonacci Terminating Digit. Thus it is the one that hides to Particle's Multiverses.

            6+6 + 6/\6 = 6+6 + 15 = 27-day month

            E = mc²
+m = E/c²
+
+c = 1 light-second
+  = 1000 years x L / t
+  = 12,000 months x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+1 year = 12 months
+1000 years = 12,000 months
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours ✔️
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+
+Conclusion:
+π(π(π(π(π(32(109²-89²)))))) Universe vs Parallel vs Multiverse (via blackhole)
+   👇
+π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Parallel (gap via expansion)
+   👇
+π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap via dark energy)
+   👇
+π(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter)
+   👇
+|--👇---------------------------- 2x96 ---------------------|
+|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
+|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|           
++----+----+----+----+----+----+----+----+----+----+----+----+       Particle's
+|--------- {53} ---------|{19}|--------- {77} ---------|109²-89² 👉 Multiverses
+|---------- 5¤ ----------|------------ {96} -----------|-1¤-|      (Untouchable)
+|-------- Bosons --------|---------- Fermions ---------|-- Graviton
+|-- Sun Orbit (7 days) --|--- Moon Orbit (12 months) --| (11 Galaxies)
+|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way 👉 Sum=12
+

            Our Milky Way Galaxy is surrounded by the two (2) nearest Dark Matter Galaxies W-2 and W+2 with two joint gravity waveguides W+1 and W-1 and our Galaxy acquires the corresponding joint gravity potential.

            +
            + + Note +
            +
            +

            The described Multiverse expansion creates huge parallel Multiverse bubbles with periodic parallel +m matter and periodic –m antimatter clusters, distributed on the bubbles walls.

            • Fig. 13a shows parallel Universes/Anti-universe W2n / W2n+1.
            • Fig. 13b shows repulsive antigravity between all the nearest matter/antimatter waveguides, e.g. between W-1 (antimatter), W+1 (antimatter) and our matter W0 Galaxies.
            • Fig. 13c shows attractive Рravitв betаeen the nearest “dark” waveguides (e.g. between W-2 Dark Matter, W+2 Dark Matter) and our Matter W0 Galaxies.

            The visible W-1 (antimatter), W+1 (antimatter) Universes are adjacent to the W0 (our matter)-Universe and have two joint framing membranes M0 and M-1, carrying two joint electrostatic potentials. (Gribov_I_2013 - pdf)

            +
            +

            From_the_waveguided

            So now we can find them as i12 in our discussions about the 26 parameters on the mechanism for fermion mass generation which end up to 139 components.

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 👈
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 👈
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️
+

            Thus our universe is belong to a seven (7) groups of 12 multiple universes inside a mass gap somewhere out of an infinite number of the like of them.

            +
            + + Note +
            +
            +

            Prof Stephen Hawking’s final research paper suggests that our Universe may be one of many similar (BBC News).

            +
            +

            everything is linked

            This interpretation is consistent with interpreting the strings as World Lines of the Worlds of Many-Worlds Quantum Theory.

            +
            + + Note +
            +
            +

            The 26-dimensional traceless subalgebra J3(O)o is arepresentation of the 26-dim Theory of Unoriented Closed Bosonic Strings produces a Bohm Quantum Theory with geometry of E6 / F4. The E6 of the can be represented in terms of:

            • 3 copies of the 26-dimensional traceless subalgebra J3(O)o of the 27-dimensional J3(O) by using the of 78-dimensional E6 over 52-dimensional F4 and the structure of based on the 26-dimensional representation of.
            • In this view, Lie algebra D4-D5-E6-E7-E8 VoDou Physics model Jordan algebra fibration E6/F4 F4 as doubled J3(O)o F4

            In order to reproduce the known spectrum of weakly coupled bosonic string theory, bosonic M theory will have to contain an additional field besides the 27 dimensional gravitational field, namely a three-form potential CFT. (PhiloPhysics - pdf)

            +
            +

            6+6 + 6/\6 = 6+6 + 15 = 27-day month

            26 Dimensions of Bosonic String Theory

            So we need to reformulate Einstein's general relativity in a language closer to that of the rest of fundamental physics, specifically Yang–Mills theory.

            fully-expanded-incl-matrices

            The areas of research, which involve about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space.

            Loop Quantum Gravity

            So one of the major obstacles is simply "informing" the scientific community about the mathematical techniques of hypercomplex numbers covering at least the five (5) fundamental mathematical constants:

            (1) The number 1, the multiplicative identity,
            (2) The number i, the imaginary unit of the complex numbers.
            image
            (3) The number π = 3.1415…, the fundamental circle constant, and

            Pi-unrolled-720

            (4) The number e = 2.718…, also known as Euler's number, which occurs widely in mathematical analysis.

            image

            (5) Furthermore, the equation is given in the form of an expression set equal to zero, the number 0, as the additive identity which is common practice in several areas of mathematics.

            Euler's identity is a special case of Euler's formula eix = cos x + i sin x when evaluated for x = π, In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia)

            Euler's identity

            Euler angles specify the rotation of the X, Y, and Z rotation axes. The Euler angle is the culprit of the singularities in matrix algebra.

            +
            + + Note +
            +
            +

            In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix

            +
            +

            Spin

            Some quantum theories of gravity posit a spin-2 quantum field that is quantized, giving rise to gravitons. Similar with how the metatron works

            +
            + + Note +
            +
            +

            The supposed periodic prolongation of the gravitationally bounded DM hyper-galaxies above and below of our Milky Way galaxy realizes corresponding periodic hyper-galactic Milky Way-stockpile (FiР. 13a, leПt).

            image

            This short hвper-interval 10 light minutes of the Milky Way-stockpile contains near 10²⁴ hyper-civilizations inside the 10-seconds 4D-hyperslice. (Gribov_I_2013 - pdf)

            +
            +

            2 × 13 × 11 = 11 galaxies × 26 dimensions/galaxy = 286

                       largest part = 21 → 11+13+12 = 36  →  MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   ↓
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----
+---+-----+-----+-----+-----+                   ↓     |
+ 2 | 18  | 21  | 39  | 60  |-------------------      |
+---+-----+-----+-----+-----+                   |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |
+---+-----+-----+-----+-----+             |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |
+---+-----+-----+-----+-----+       |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11👈 | 13  | 12  | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |
+---+-----+-----+-----+-----+             |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |
+---+-----+-----+-----+-----+                   |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------      |
+---+-----+-----+-----+-----+                   ↓     |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----
+===+=====+=====+=====+=====+                   ↓
+45 | 277 |                      ← 11+13+12=36 ←  MEC30
+---+-----+                                     |
+ ↑
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            The finiteness position of MEC30 along with Euler's identity opens up the possibility of accurately representing the self-singularity of True Prime Pairs.

            +
            + + Note +
            +
            +

            The Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. (Google Patent DE102011101032A9)

            +
            +

            Spinning the MEC30

            These deterministic sequences intertwine like an octal helix and ultimately determine the distribution of all prime numbers greater than 5, i.e., starting with 7.

            +
            + + Tip +
            +
            +

            Eighteen (18) of the sequences have been published on the On-Line Encyclopedia of Integer Sequences. Here’s the link: OEIS Listings for Gary W. Croft.

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                         MEC30/2 ✔️
+------+------+-----+-----+------      ‹--------------- 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  |‹-- ∆9 = (89-71) / 2 √     |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+ ‹--- vacuum energy ‹--- ∆60 ‹--- 15 {zero axis} ✔️
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹-------------------- 30 {+1/2} ✔️
+

            Each of the nine (9) types express themselves as one of the three (3) subtypes. So from this perspective, there are 27 distinct patterns which are usually denoted by letters.

            +
            + + Note +
            +
            +

            Mathematically, this type of system requires 27 letters (1-9, 10–90, 100–900). In practice, the last letter, tav (which has the value 400), is used in combination with itself or other letters from qof (100) onwards to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit (final) forms of the Hebrew letters. (Wikipedia)

            +
            +

            The Parameter Zones

            So it differs from string theory in that it is formulated in 3 and 4 dimensions and without supersymmetry or Kaluza–Klein extra dimensions which requires both to be true.

            +
            + + Note +
            +
            +

            Since Loop Quantum Grabity (LQG) has been formulated in 4 dimensions (with and without supersymmetry), and M-theory requires supersymmetry and 11 dimensions, a direct comparison between the two has not been possible.

            • It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general relativity with supersymmetry and Kaluza–Klein extra dimensions should experimental evidence establish their existence.
            • It would therefore be desirable to have higher-dimensional Supergravity loop quantizations at one’s disposal in order to compare these approaches.
            • A series of papers have been published attempting this.[68][69][70][71][72][73][74][75] Most recently, Thiemann (and alumni) have made progress toward calculating black hole entropy for supergravity in higher dimensions.

            It will be useful to compare these results to the corresponding super string calculations. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+     |    168    |    618    |
+-----+-👇--+-👇--+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨👈 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+👉11¨|  3¨ | {3¨}| {5¨}| 3¤  --->  Np(33)  assigned to "id:33"   ----->    77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+👉18¨|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |--- 1 + MEC30 ---|---------- MEC30 + √(43-18) -------| ✔️
+                       Δ                 Δ                 Δ
+                     Mod 30            Mod 60            Mod 90
+

            Given observation that the leading action of graviton, dilaton, and antisymmetric tensor fields form a bilateral 9 sums, this patterns are indeed derived from the 27 parameters.

            +
            + + Note +
            +
            +

            F11 (89): The decimal expansion of 89’s reciprocal (1/89) is period-44 (see graphic below) composed of 22 bi-lateral 9 sums = 198, while 89 + 109 = 198, 7920/198 = 40 and 8,363,520/198 = 20 x 2112 (7919’s index number as a member of this domain).

            • And, curiously, 198’s inverse (891) + 109 = 1000, while the sum of 89 and 109’s inverses, 98 + 901, = 999.
            • Then consider that, while it’s obvious 997 of the first 1000 primes are not divisible by 2, 3, or 5, one might miss the fact that 997 minus its reverasl, 799, = 198 = 89 + 109.
            • And for the record we note that 1/109’s decimal expansion is period 108 (making it a ‘long period prime’ in that 1/p has the maximal period of p−1 digits).

            This period consists of 2 × 27 or 54 bilateral 9 sums = 486, which (coincidentally?) is the number of primes in the 243 pairs summing to 7920 (more about these, below). (PrimesDemystified)

            +
            +

            43 + 1 = 44 periods

            The decimal expansion of 89's reciprocal (1/89)

            In the other hand it is stated by DE102011101032A9 that using Euler's identity, the MEC30 standard is more accurately than a measurement.

            +
            + + Note +
            +
            +

            In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction.

            • Originally, the coupling constant related the force acting between two static bodies to the “charges” of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r².
            • The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter
            • The solution to both these problems comes from the Higgs mechanism, which involves scalar fields (the number of which depend on the exact form of Higgs mechanism) which (to give the briefest possible description) are “absorbed” by the massive bosons as degrees of freedom, and which couple to the fermions via Yukawa coupling to create what looks like mass terms.

            The next step is to couple the gauge fields to the fermions, allowing for interactions. (Wikipedia)

            +
            +

            Another possibility opened by the scale is studying for hidden variables, knowledge of which would allow more exact predictions than quantum theory can provide.

            +
            + + Note +
            +
            +

            Eleven-dimensional supergravity is reformulated in a way suggested by compactifications to four dimensions. The new version has local SU(8) invariance. The bosonic quantities that pertain to the spin-0 fields constitute 56- and 133- dimensional representations of E7(+7). Some implications of our results for the S7 compactification are discussed.

            +
            +

            1 + 29 + 6x6 = 29 + 37 = 66 = 11x6

            True Prime Pairs

            This is one of the finer points of differences between the eightfold way and the quark model which suggests the mesons should be grouped into nonets (groups of nine).

            +
            + + Note +
            +
            +

            In the second opposing term, the position 13 gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the 11th prime number is now forced as a new axis-symmetrical zero position. (Google Patent DE102011101032A9

            +
            +

            16S rRNA amplicons study

            Particles are sorted into groups as mesons or baryons. Within each group, they are further separated by their spin angular momentum.

            +
            + + Note +
            +
            +

            Our sidebar is arranged to accommodate The Standard Model presently that recognizes seventeen (17) distinct particles: five (5) bosons and twelve (12) fermions. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 13 and 48 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. (Wikipedia)

            +
            +

            11 + 5 + 12 = 16 + 12 = 28-day month

            Partition Function

            In physics, the eightfold way is an organizational scheme for a class of subatomic particles known as hadrons that led to the development of the quark model.

            +
            + + Note +
            +
            +

            Gell-mann matrices are a complete set of Hermitian noncommuting trace-orthogonal matrices. In addition, they also play an important role in physics where they can be thought to model the **eight (8) gluons* that mediate the strong force quantum chromodynamics, an analogue of the Pauli matrices well-adapted to applications in the realm of quantum mechanics. (Wolfram)

            +
            +

            In quantum chromodynamics, flavour is a conserved global symmetry. In the electroweak theory, on the other hand, this symmetry is broken, and flavour changing processes exist, such as quark decay or neutrino oscillations.

            +
            + + Note +
            +
            +

            Representation theory is a mathematical theory that describes the situation where elements of a group (here, the flavour rotations A in the group SU(3)) are automorphisms of a vector space (here, the set of all possible quantum states that you get from flavour-rotating a proton).

            • Therefore, by studying the representation theory of SU(3), we can learn the possibilities for what the vector space is and how it is affected by flavour symmetry.
            • Since the flavour rotations A are approximate, not exact, symmetries, each orthogonal state in the vector space corresponds to a different particle species. In the example above, when a proton is transformed by every possible flavour rotation A, it turns out that it moves around an 8 dimensional vector space.
            • Those 8 dimensions correspond to the 8 particles in the so-called “baryon octet”.

            This corresponds to an 8-dimensional (“octet”) representation of the group SU(3). Since A is an approximate symmetry, all the particles in this octet have similar mass. (Wikipedia)

            +
            +

            MEC30 Structure

            The eight (8) steps between id:30 to 37 represents the Eightfold Way in the context of E8, a pattern developing in physics to represent the fundamental particles.

            +
            + + Note +
            +
            +

            E8 is at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the symmetries of E8. The enigmatic E8 is the largest and most complicated of the five exceptional Lie groups, and contains four subgroups that are related to the four fundamental forces of nature: the electromagnetic force; the strong force (which binds quarks); the weak force (which controls radioactive decay); and the gravitational force. (Wordpress.com)

            +
            +

            image

            Finally we found that the loop corresponds to a quadratic polynomial originated from the 4th coupling of MEC30 which is holded by five (5) cells between 13 and 17.

            +
            + + Note +
            +
            +

            The Minimal Supersymmetric Standard Model (MSSM) contains two Higgs doublets, leading to five (5) physical Higgs bosons:

            • one (1) neutral CP-odd (A) 👈 degenerated with (h or H)
            • two (2) charged states (H+ and H−),
            • Two (2) neutral CP-even states (h and H).

            At tree-level, the masses are governed by two parameters, often taken to be mA and tan β [3]. When tan β >> 1, A is nearly degenerated with one of the CP-even states (denoted ϕ). (ScienceDirect)

            +
            +

            the 5 cells

            Further observation of this 13 vs 17 phenomenon also introduces a lower bound of Mod 90 to four (4) of possible length scales in the structure of prime recycling.

            Modulo_90_Congruency_Matrix_Twin_Prime_Page

            In both cases, the masses of the W and Z bosons would be affected, potentially leading to different physics and potentially affecting the stability and creation.

            +
            + + Note +
            +
            +

            The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The different universes within the multiverse are called “parallel universes”, “other universes”, “alternate universes” (Wikipedia).

            +
            +

            Parallel Universes

            Using these algorithms, the inflation structure of radial null geodesics spacetime for propagating light cone in primordial universe could be tabulated as below.

            +
            + + Tip +
            +
            +

            The electroweak force is believed to have separated into the electromagnetic and weak forces during the quark epoch of the early universe.

            Elementary Particle

            The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.

            Renormalization

            As we’ve already suggested, the number 30 figures large in our modulo 30 domain. The Prime Spiral Sieve is Archimedean in that the separation distance between turns equals 30, ad infinitum. The first two rotations increment as follows:

            image

            And when you combine the terminating digit symmetries capturing three (3) rotations around the sieve generation in their actual sequences, you produce the ultimate combinatorial symmetry.

            +
            + 
            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} ✔️     |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} ✔️
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} ✔️     |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                       👉 ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹----- ¤ Mod 90 ✔️                     |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} ✔️
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |
+----------------------+-----+                                                ---
+

            The consequences might be radical but it may open the possibility to provide a tentative but detailed physical and mathematical picture of quantum spacetime.

            +
            + + Note +
            +
            +

            Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

            Many of these problems apply to LQG, including:

            • Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?
            • Is spacetime fundamentally continuous or discrete?
            • Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)?
            • Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?

            The theory of LQG is one possible solution to the problem of quantum gravity, as is string theory. There are substantial differences however. For example, string theory also addresses unification, the understanding of all known forces and particles as manifestations of a single entity, by postulating extra dimensions and so-far unobserved additional particles and symmetries. Contrary to this, LQG is based only on quantum theory and general relativity and its scope is limited to understanding the quantum aspects of the gravitational interaction.

            +
            +

            Loop Quantum Gravity

            Most particles can have either kind of helicity, but neutrinos are odd. We only see left-handed neutrinos and right-handed anti-neutrinos.

            +
            + + Note +
            +
            +

            Neutrinos are perhaps the least understood of the known denizens of the subatomic world.

            • They have nearly no mass, interact only via the weak nuclear force and gravity, and, perhaps most surprising, the three known species of neutrinos can transform from one variant into another.
            • This transformation, called neutrino oscillation, has been demonstrated only relatively recently and has led to speculation that there might be another, even more mysterious, neutrino variant, called the sterile neutrino.
            • While the sterile neutrino remains a hypothetical particle, it is an interesting one and searches for it are a key research focus of the world’s neutrino scientist community.images (12)
            • This means that if right-handed neutrinos exist, they don’t interact with regular matter, only with gravity. Thus, they are “sterile.”so-what-are-the-n-m-disappearing-to-n

            And if they have a significantly larger mass than regular neutrinos, sterile neutrinos would be “cold,” and could be the solution to the dark matter problem. It’s a great idea, but unfortunately, as a new study shows, doesn’t seem to be true. (UniverseToday)

            +
            + 
            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----|
+|---------- 5¤ ----------|----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|👈
+                         |-------------------- 9¤ --------------------|
+
+  Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+sterile-1  |    -    |    -    |     5     |     -     |      5     |   i5
+-----------+---------+---------+-----------+-----------+------------+-----------
+sterile-2  |    -    |    -    |     7     |     -     |      7     |   17
+-----------+---------+---------+-----------+-----------+------------+-----------
+sterile-3  |    -    |    -    |    11     |     -     |     11     |   i11
+-----------+---------+---------+-----------+-----------+------------+-----------
+sterile-4  |    -    |    -    |    13     |     -     |     13     |   i13
+-----------+---------+---------+-----------+-----------+------------+-----------
+sterile-5  |    -    |    -    |    17     |     -     |     17     |   i17
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    -    |    -    |    53     |     -     |     53     |   i53 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |   108     |    72     |    192     |  96+i96 ✔️
+

            Thus when you collect all the three step you may see that it is a 24-dimension model. E8 is understood to be the leg of a triad, with E16, leading to E24.

            +
            + + Note +
            +
            +

            After putting in the proverbial 10,000 hours studying ‘24-beat’ patternization, we’ve come to the conclusion that period-24 is the key to the “Theory of Everything” and that a hypothetical E24 Petrie Projection will one day loom large as E8 is understood to be the leg of a triad, with E16, leading to E24.

            • The three being analogous to:
              • Mod 30 → E8 → {3} star polygon …
              • Mod 60 → E16 → {6/2} star polygon …
              • Mod 90 → E24 → {9/3} star polygon …
              • … building geometrically to infinity …
            • We’ve dubbed this ‘The Theory of Everything … but the Kitchen Sink.’
            • Explore the incredible symmetries that come into focus when the lense aperature, so to speak, of the Prime Spiral Sieve is tripled to modulo 90, synchronizing its modulus with its period-24 digital root, and perhaps you’ll see why we make this bold assertion.

            The mathematical balancing and resolution of this domain, which correlates with a hypothetical E24, including structures that determine the distribution of prime numbers, are fundamentally period-24. (PrimesDemystified)

            +
            +

            Theory of Everything

            Current research on loop quantum gravity may eventually play a fundamental role in a theory of everything, but that is not its primary aim.

            Final Theory

            There is a proof that it is impossible to embed all the three generations in E8 without the presence of additional particles that do not exist in the physical world.

            An Exceptionally Simple Theory of Everything

            It has been recent claims that loop quantum gravity (LQG) may be able to reproduce features resembling the Standard Model of particle physics and general relativity.

            addition zones

            As a theory, LQG postulates that the structure of space and time is composed of finite loops (E16) woven into an extremely fine fabric or networks called spin networks.

            168 + 329 + 289 = 168 + 618 = 786

            multiplication zones

            The evolution of a spin foam, has a scale above the Planck length. Consequently, not just matter, but space itself, prefers an atomic structure.

            +
            + + Note +
            +
            +

            TON *618* is the largest black hole in the universe. It’s so large that it has pioneered the classification of “Ultramassive black hole,” with Solar Mass of 66 trillion of our suns! Boasts an extremely high gravitational pull as a result of inspiring mass, and might have been formed by the merging of more than one black hole in the past (Largest.org).

            +
            +

            168+618 - 19x6x6 = 786 - 684 = 102

            exponentiation zones

            The final step (E24) requires direction on resolving the separation between quantum mechanics and gravitation, often equated with general relativity.

            +
            + + Tip +
            +
            +

            The structure is arranged based on 11 dimensions of space and time which is composed of 12 loops woven into the spin networks.

            Parallel Universes

            The result should be a massive neutrinos that bring 7 more parameters (3 CKM and 4 PMNS) for a total of 26 parameters out of 11+26=37 symmetry.

            CKM vs PMNS Matrix

            Schematic representation of fermions and bosons in SU(5) GUT showing 5 + 10 split in the multiplets. Neutral bosons (photon, Z-boson, and neutral gluons) are not shown but occupy the diagonal entries of the matrix in complex superpositions.

            SO(10)

            SU(5)_representation_of_fermions

            And, speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve:

            11's additive sums

            The 10 symmetries are reflecting the 10 shapes of the chart as shown below. The 12 finite loops around the three (3) generation are denoted by the total of 12 arrows that flowing in between each of the 10 shapes.

            +
            +

            78-dimensional E6 = 786

            identition zones

            By the nature this behaviour can be observed from the molecular interactions of water. Water is intrinsically self-complementary on molecular interactions. In liquid or solid water, engage in ideal hydrogen bonding.

            +
            + + Note +
            +
            +

            Figure below illustrates the complementarity of the hydrogen bonding interactions of a water molecule with the surroundings in liquid or solid water. The inner ring of angles is within a water molecule. The outer ring of angles is between bonds and/or hydrogen bonds of surrounding water molecules. (GaTech.edu)

            +
            +

            Molecular Interactions

            Six (6) times of the angle 109 occupied as the most while the angle of 114 and 104 are exist only once. So the one in charge here is clearly the 29th prime identity.

            109 = 29th prime = (10th)th prime = ((114-104)th)th prime

                        3 x 3rd-gap
+           ∆     ∆     ∆
+           |     |     |
+-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap
+  1' |  1  | {2} |  3  |  4  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  2' |  5  |  6  |  7  |  8  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  3' |  9  |{10} |  2¤ (M dan F)
+     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      
+  4' | 11  | 12  | 13  | 3¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  5' | 14  | 15  | 16  | 17  | 4¤    
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  6' | 18  | 19  |{20} | 3¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap
+  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap
+           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆
+           |     |     |     |     |     |     |     | P(7)=142857
+               8 x 3rd-gap inside the 2nd-gap          (Truncated)
+

            This 29 turns the finiteness position of 15 as the middle zero axis. So all of these steps are similar kind with the way a spider started to build its web.

            +
            + + Note +
            +
            +

            Every web begins with a single thread, which forms the basis of the rest of the structure. To establish this bridge, the spider climbs to a suitable starting point (up a tree branch, for example) and releases a length of thread into the wind. With any luck, the free end of the thread will catch onto another branch (howstuffworks.com).

            +
            +

            image

            Let's assume that it is done using a material that stretches and then pops back when the stretching force goes away. It is pound stronger than steel. Every next steps start exactly the same as we have explained from the beginning till all of the 77 objects goes in.

            +
            + + Note +
            +
            +

            The study researchers next asked what the consequences of such a universe would be. They found many wonderful things.

            • For one, a CPT-respecting universe naturally expands and fills itself with particles, without the need for a long-theorized period of rapid expansion known as inflation. While there’s a lot of evidence that an event like inflation occurred, the theoretical picture of that event is incredibly fuzzy. It’s so fuzzy that there is plenty of room for proposals of viable alternatives.
            • Second, a CPT-respecting universe would add some additional neutrinos to the mix. There are three known neutrino flavors: the electron-neutrino, muon-neutrino and tau-neutrino. Strangely, all three of these neutrino flavors are left-handed (referring to the direction of its spin relative to its motion). All other particles known to physics have both left- and right-handed varieties, so physicists have long wondered if there are additional right-handed neutrinos.
            • A CPT-respecting universe would demand the existence of at least one right-handed neutrino species. This species would be largely invisible to physics experiments, only ever influencing the rest of the universe through gravity. But an invisible particle that floods the universe and only interacts via gravity sounds a lot like dark matter.

            The researchers found that the conditions imposed by obeying CPT symmetry would fill our universe with right-handed neutrinos, enough to account for the dark matter. (LiveScience)

            +
            + 
            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+     -----------------------------------------------
+{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |
+-----+-----+-----+-----+-----+                                               |
+ {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone
+     +-----+-----+-----+-----+                                               |
+ {78}|{7,8}| 8,9 | 12 (M & F) ----> Δ                                        |
+     +-----+-----+-----+  <--------   Mirror Zone (Middle zero axis)   -----------
+ {67}| 9,11|11,12|12,14| 11                                                  |
+ ----+-----+-----+-----+-----+                                               |
+  {6}|15,16|17,18|18,20|21,22| 19                                    Extended Zone
+     +-----+-----+-----+-----+                                               |
+  {8}|23,25|25,27|27,29| 18                                                  |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 & C2)<---Δ
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+     |  1     2     3  |   4     5     6 |   7     8      9  |
+     |------ 29' ------|--------------- 139' ----------------|
+     |------ 618¨ -----|--------------- 168¨ ----------------| ✔️
+

            This 77 principles have worked so well on simple examples such as water molecules that we can be reasonably confident they will work for more complex examples.

            +
            + + Note +
            +
            +

            MEC 30 claims to “illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way” via the elementary level of numbers.

            default

            Why does it work?

            • It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences.
            • In the subatomic space, Heisenberger does not allow precise measurements because the measurements themselves distort the result.
            • Through the mathematical basis presented here, our scale behaves like Plank’s quantum of action and shows in the positions the behaviorally entangled photons, which in turn produce the quantum of action in the sums.
            • The MEC 30 as a folding rule is also here a tool for The Entangled Quantum systems to explain the ghostly behavior of the elementary particles.
            • It would also to make the underlying algorithm visible and explainable, keyword quantum teleportation. So we are able to investigate the energy behavior below the quantum of effect without measuring influence.
            • This works because our scale is the basis for the Riemann Zeta Function, which reflects the energy distribution in atoms.
            • On the other hand, with larger systems we are able to transfer the behavior of the energy from the subatomic space into the haptic space with the scale described here (thought experiment Schröninger’s cat).
            • Thus, we are still able to apply the Schröninger wave equation in the haptic space, and replace The Hamiltonian with our measurements.

            Developing MEC 30 as a folding rule emerged from a new analysis of mathematical foundations and makes a new algorithm visible. (Google Patent DE102011101032A9)

            +
            +

            1 instance + 7 blocks + 29 flats + 77 rooms = 37+77 = 114 objects

            114 Nodes.

            These loops shall generate 1000 XML sitemaps lead by π(1+1000/Φ) = π(1+618) = 114 objects where 37 of these objects are inventing the 27 patterns.

            +
            + + Note +
            +
            +

            The ‘Grid Square’ Crop Circle is one of the most significant mathematical formations

            • Numbers 65 and 325 have reciprocal (1/x) or we can call them wave values that link to certain expressions of electromagnetism. 1/65= .0[153846…] and 1/325= .00[307692…]  are period 6 repeat decimals (digital root 9) that reveal other numbers of significance: 27, 37 & triple digits.
            • The math of the ‘Grid Square’ crop circle gives the value of 153846… and when added to another number in the design, close approximations to √5 and Ф can be made.  
            • Dividing numbers with digital roots of 3,6,9 by 19.5 also creates these same two number patterns. 19.5 can be seen as 195, a multiple of 65. 19.47° (19.5) is the latitude in which planetary energy is said to upwell. 27 is also connected to the tetrahedron and the tetrahedron is connected to 19.5 degree
            • A star tetrahedron nested in a sphere touches at 19.47° north and south latitude. 19.47° has also been noted in the geometry of crop circles and angles connecting them to one another and to sacred sites.
            • Dividing integers by 13 (a star prime) creates the same two patterns. 13 is a factor of 65: 1, 65, 5– 3rd prime,13–6th prime.
            • VBM polarity pairings are also made every 1st/4th, 2nd/5th, 3rd/6th number. 
            • Interestingly, the wave value for 7 (1/7= .142857…) connects perfectly with these two patterns–153846 + 142857 = 296703— the mirror number to 307692. All 3 patterns total 27 and 27 is also a factor of all.27 patterns in 6 dimensions
            • Because of factor 37, many triple digits are factors: 111, 222, 333, 666, 777, 999 142+857= 999 153+846= 999 307+692= 999

            The 37 and 73 are both Star numbers, both have the same shape, but with different Hexagon portions. For a twist we can count them as one extra together and then instead of 36 we get 37. So 37 is the only factor of all 3 patterns. (YouTube)

            +
            +

            27 × 37 = 999

            default

            Since the 27 pattern is tripled to modulo 90 so they would behave as Prime Spiral Sieve and synchronizing its period-24 digital root towards the rest of 77 objects.

            +
            + + Note +
            +
            +

            Like all maximal supergravities, it contains a single supermultiplet, the supergravity supermultiplet containing the graviton, a Majorana gravitino, and a 3-form gauge field often called the C-field.

            • It contains two p-brane solutions, a 2-brane and a 5-brane, which are electrically and magnetically charged, respectively, with respect to the C-field.
            • This means that 2-brane and 5-brane charge are the violations of the Bianchi identities for the dual C-field and original C-field respectively.The supergravity 2-brane and 5-brane are the long-wavelength limits (see also the historical survey above) of the M2-brane and M5-brane in M-theory. (Wikipedia)
            +
            +

            Quantum Gravity

            Out of these 77 objects, one should reveal an elegant scale of MEC30 provided with the truncated folding rule and the beauty of Euler's identity.

            +
            + + Note +
            +
            +

            And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler’s identity during a lecture, stated that the identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”. (Wikipedia)

            +
            +

            default

            The advantages is that instead of a rudimentary mathematical templates, now a folding rule of the MEC30 makes the associated algorithm and parameters visible even in 2D.

            +
            + + Note +
            +
            +

            We’ve seen how it [Euler’s identity] can easily be deduced from results of Johann Bernoulli and Roger Cotes, but that neither of them seem to have done so. Even Euler does not seem to have written it down explicitly – and certainly it doesn’t appear in any of his publications – though he must surely have realized that it follows immediately from his formula: e^ix = cos x + i sin x. Moreover, it seems to be unknown who first stated the result explicitly… (Wikipedia)

            +
            +

            Everything is Connected

            Taking a coupling function between f(π) as P vs f(i) as NP where eiπ + 1 = 0 they shall be correlated in to an expression of universe so it shows that Everything is Connected.

            Disclaimer

            You are FREE to use our concept of TOE for every purposes as long as you present the following somewhere in your publication.

            +
            + + Warning +
            +
            +

            The definite key to identify whether you use our concept is when there a kind of developed item lies a unified assignment in hexagonal form by six (6) corresponding sets while each sets pick a combination of six (6) routes with a pairing of six (6) by six (6) of all channels.

            +
            +
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist01.html b/identition/span2/gist01.html new file mode 100644 index 00000000000..eb7ff98a4ff --- /dev/null +++ b/identition/span2/gist01.html @@ -0,0 +1,42 @@ + Assigning Repositories · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Assigning Repositories

            By this part we are going to assign nine (9) groups of project repositories including one (1) group of the central. All of them will be managed by an instance to represesent the pattern of true-prime-pairs via bilateral 9 sums.

            default

            The purpose of this instance is simulating the central behaviour on each pairs of human chromosomes. So the nine (9) groups would consist of three (3) containers + one (1) sub central + one (1) central + one (1) sub central + three (3) containers.

            (7-1) + (12x9) = 6 + 108 = 114

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            Let's sum them up so we get 9+1+9=19. Put them as one (1) unit so the whole objects will be 19 (sub objects)+1 (unit object)=20 objects. Thus this sum is what we called as bilateral 9 sums. default

            As a matter of the fact every schemes are contained in X/Y genes where the Y gene has has hardly any genes. When we do pair them as reproduction genes then we will come again to 3 containers + 1 sub central + 1 central + 1 sub central + 3 containers.

            The X bears about 1,600 genes with varied functions. But the Y has hardly any genes; maybe 50, and only 27 of these are in the male-specific part of the Y.(The Conversation)

            image

                                         --------------------------------------------------------------
+                            |                                                              | 
+  =======================+====+====+====+====+====+====+====+====+====+=====               |
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root      |
+  -----------------------+----+----+----+----+----+----+----+----+----+-----               |
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin      |
+  -----------------------+----+----+----+----+----+----+----+----+----+-----               |
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th                |
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin      |
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th                |
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin      |
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th                |
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin      |
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ---------------
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row. This sequence is simulated by a flowchart having 12 arrows flowing on 10 (ten) shapes of prime 31 up to 71 (40 nodes).

            flowchart

            This central doesn't exist phisically. However when we were going up by the form of nine (9) subs central + one (1) central + nine (9) subs central then we will get the human brain as the central.

            Observing many literatures we finaly found that the pattern of this centralizing is done by a kind of neurotransmitter that works as a messenger by transmitting a signal. That is the way they are communicating each others.

            A neurotransmitter is a signaling molecule secreted by a neuron to affect another cell across a synapse. The cell receiving the signal, any main body part or target cell, may be another neuron, but could also be a gland or muscle cell.. Wikipedia

            However it seems that determining the pattern of this signalling either going up to the top of the brain or going down to the XX or XY genes even to the bottom of that little Y is staggeringly complex. Yet science points to a much more ambiguous reality.

            Determination of biological sex is staggeringly complex, involving not only anatomy but an intricate choreography of genetic and chemical factors that unfolds over time. (ScientificAmerica)

            image

            Therefore here we would only take the fact that X bears about 1,600 genes with varied functions while the Y has 50, and only 27 of these are in the male-specific and how their relation with the 20 objects of bilateral 9 sum.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist02.html b/identition/span2/gist02.html new file mode 100644 index 00000000000..bbeb7ba278a --- /dev/null +++ b/identition/span2/gist02.html @@ -0,0 +1 @@ + The Bilateral 9 Sums · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Bilateral 9 Sums

            Let's start with the number of possible ancestors on the chromosome. A male individual has an X chromosome, which he received from his mother, and a Y chromosome, which he received from his father.

            image

            The number of ancestors at each level, Fn, is the number of female ancestors, which is Fn−1, plus the number of male ancestors, which is Fn−2. his is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.

            image

            It has been noticed that the number of possible ancestors on the human X chromosome inheritance line at a given ancestral generation also follows the Fibonacci sequence.

            image

            This Fibonacci sequence is lied beautifully in the Pascal Triangle. Pascal's triangle has wide applications in Mathematics. We have seen that the most important applications relate to the binomial coefficients and combinatorics.

            image

            See that from 1 to 89 it consist of seven (7) steps which is originated by 1,15,35,28 before it goes bilateral. So that is why Y has 1+15+35-1=50, and only 28-1=27 of these are in the male-specific. This cycle is repeated through a palindromic sequence.

            109th - 20th = 89th

            As the matter of fact this 89 has a symmetrical relation with the 24th Prime Number & 24th Natural Number Not Divisible by 2, 3, or 5. This is the reason that we use this primes pattern on determining the centralizing process

            default

            So the 20 objects would pair another 19 and become 19 (sub objects) + 1 (unit object) + 19 (sub objects)=20+19=39 objects or it will be 40 when we put them as one (1) unit. This 40 will act as the interface between each of containers.

            default

            This scheme stands as the second section of bilateral sum. By the rest sections we will discuss the above seven (7) steps one by one so all together will compromise the nine (9) groups of project repositories as mentioned in the beginning.

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist02.md b/identition/span2/gist02.md new file mode 100644 index 00000000000..43f0b214975 --- /dev/null +++ b/identition/span2/gist02.md @@ -0,0 +1,35 @@ +## The Bilateral 9 Sums + +Let's start with the number of possible ancestors on the chromosome. A male individual has an X chromosome, which he received from his mother, and a Y chromosome, which he received from his father. + +![image](https://user-images.githubusercontent.com/8466209/213902684-f60e272c-8d01-4dea-ab2a-7bdb01aba32f.png) + +The number of ancestors at each level, Fn, is the number of female ancestors, which is Fn−1, plus the number of male ancestors, which is Fn−2. his is under the unrealistic assumption that the ancestors at each level are otherwise unrelated. + +![image](https://user-images.githubusercontent.com/8466209/213902752-fdbe6892-1089-47b1-a5ed-b301a7b0c1d6.png) + +It has been noticed that the number of possible ancestors on the human X chromosome inheritance line at a given ancestral generation also follows the _[Fibonacci sequence](https://en.wikipedia.org/wiki/Fibonacci_number)_. + +[![image](https://user-images.githubusercontent.com/8466209/213900804-9afe17ad-601c-4713-800f-02ed204b3a7c.png)](https://en.wikipedia.org/wiki/Fibonacci_number) + +This Fibonacci sequence is lied beautifully in the _[Pascal Triangle](https://en.wikipedia.org/wiki/Pascal%27s_triangle)_. Pascal's triangle has wide applications in Mathematics. We have seen that the most important applications relate to the binomial coefficients and combinatorics. + +![image](https://user-images.githubusercontent.com/8466209/213902359-f5fb8023-ec2b-4588-8f24-e1caafc30ef5.png) + +![](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png) + +See that from 1 to 89 it consist of ***seven (7) steps*** which is originated by 1,15,35,28 before it goes bilateral. So that is why Y has ***1+15+35-1=50***, and only ***28-1=27*** of these are in the male-specific. This cycle is repeated through a palindromic sequence. + +***109th - 20th = 89th*** + +As the matter of fact this 89 has a symmetrical relation with the 24th Prime Number & 24th Natural Number Not Divisible by 2, 3, or 5. This is the reason that we use this primes pattern on determining the _[centralizing](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ process + +[![default](https://user-images.githubusercontent.com/8466209/200228973-fd99095b-aad2-4824-b3dc-d6b21fae38ea.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525#file-write-all-md) + +So the 20 objects would pair another 19 and become ***19 (sub objects) + 1 (unit object) + 19 (sub objects)=20+19=39 objects*** or it will be 40 when we put them as one (1) unit. This 40 will act as the [interface](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md) between each of containers. + +![default](https://user-images.githubusercontent.com/8466209/213902270-75b90edb-b94e-4844-be4a-27db66bae060.jpg) + +This scheme stands as the second section of bilateral sum. By the rest sections we will discuss the above seven (7) steps one by one so all together will compromise the [nine (9) groups](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md) of project repositories as mentioned in the beginning. + +![default](https://user-images.githubusercontent.com/8466209/223529165-0e4c1172-47cc-422f-8e44-1dd67de25828.png) diff --git a/identition/span2/gist03.html b/identition/span2/gist03.html new file mode 100644 index 00000000000..d37c9182a70 --- /dev/null +++ b/identition/span2/gist03.html @@ -0,0 +1,45 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            73933040-31143880-490e-11ea-802f-035194e48d4b

            All of these coincidences are already discussed in details by previous schemes as well the existence of gap by 33's that is parsing the 102.

            sequence

            Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51. From the 50 we gonna split the 15 by bilateral 9 sums resulting 2 times 15+9=24 which is 48. So the total of involved objects is 50+48=98.

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            goes

            See the fact that last 15 is connected to 25 which is 24+Δ1 where as another 15 are also correlated with 24 in pairs. So here we would compound them within three (3) minor hexagon which has 24 each and one of them is carrying the (Δ1).

            This cycle is repeated through a palindromic sequence.

            default

            |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - |100 |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - |101 |  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   T
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |   H
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   E
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   P
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |   O
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   W
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |   E
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   R
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   O
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |   F
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | ∑=168
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |   V
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   S
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            67 » 66, 78, 86 (OEIS A059756)

            default

            image

            102 = 2+60+40 » (2,60.40)

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist03.md b/identition/span2/gist03.md new file mode 100644 index 00000000000..ea3df5daf8c --- /dev/null +++ b/identition/span2/gist03.md @@ -0,0 +1,80 @@ +![73933040-31143880-490e-11ea-802f-035194e48d4b](https://user-images.githubusercontent.com/8466209/218367881-6c561132-e50c-4a72-b938-37d3eac69d45.png) + +All of these coincidences are already discussed in details by previous schemes as well the existence of gap by 33's that is parsing the 102. + +[![sequence](https://user-images.githubusercontent.com/8466209/199844359-3f898aad-0661-4ccb-9d90-1e2aadbdf662.png)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831) + +Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about ***19th*** as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51. From the 50 we gonna split the 15 by _bilateral 9 sums_ resulting 2 times 15+9=24 which is 48. So the total of involved objects is ***50+48=98***. + +***π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66*** + +[![goes](https://user-images.githubusercontent.com/36441664/83051968-e2cfa480-a078-11ea-8ff2-316a809a8fad.jpg)](https://schoolbag.info/mathematics/numbers/38.html) + +See the fact that last 15 is connected to 25 which is 24+Δ1 where as another 15 are also correlated with 24 in pairs. So here we would compound them within three (3) _[minor hexagon](https://www.hexspin.com/minor-hexagons)_ which has 24 each and one of them is carrying the (Δ1). + +This cycle is repeated through a palindromic sequence. + +![default](https://user-images.githubusercontent.com/8466209/197364042-0c30b323-4d1b-4e13-b9d8-002d482e5a7c.png) + +``` +| 1st (Form) | 2nd (Route) | 3rd (Channel) | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T + Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E + Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P + Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W + Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R + Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O + Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168 +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S + | Δ Δ | Φ12 | Δ Δ | + 113 150 ≜114-25 557 619 = 1+618 +``` + +***67 » 66, 78, 86 ([OEIS A059756](https://oeis.org/A059756))*** + +[![default](https://user-images.githubusercontent.com/8466209/211178117-9a879fd0-163b-442b-87bf-49d76c0b6c50.png)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831) + +![image](https://user-images.githubusercontent.com/8466209/195509190-6926e3cd-807a-44ef-8549-b0fc1f481a2d.png) + +***102 = 2+60+40 » (2,60.40)*** + +[![default](https://user-images.githubusercontent.com/8466209/198783118-6f7890ea-aed2-495d-ae6b-acb215ad7140.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde) + +[![default](https://user-images.githubusercontent.com/8466209/198762875-b57d367d-2d5f-44c3-a37f-ba7a6d8dbc38.png)](https://github.com/eq19/grammar/actions/runs/3343512525/jobs/5536807573) + +![default](https://user-images.githubusercontent.com/8466209/225381200-cf1210c7-d2cf-4558-bab8-6152f3042244.png) + +[![default](https://user-images.githubusercontent.com/8466209/198813046-300043a7-86b6-468a-b45c-a3c197f0a9f6.png)](https://www.eq19.com/) diff --git a/identition/span2/gist04.html b/identition/span2/gist04.html new file mode 100644 index 00000000000..7feb50e9f7b --- /dev/null +++ b/identition/span2/gist04.html @@ -0,0 +1 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            image

            image

            image

            image

            default

            96 is the smallest integer n for which π(n) = n/4.

            π(96) = π(4x24) = 24

            102

            139 - (25-18-18-25) = (114-18) - 18 - 25 = (96-18) - 25 = 78 - 25 = 53

            See that from 1 to 89 it consist of seven (7) steps which is originated by 1,15,35,28 before it goes bilateral.

            default

            default

            default

            The distribution of these scale has a bilateral symmetrical relationship along with the peculiarities of each numbers within the format (18,30,36) of prime hexagon so that it can represent the pattern of true-prime-pairs systemically.

            (5 + 7 + 11 + 13) + (17 + 19) = 36 + 36 = 72

            default

            This 29 turns the finiteness position of 15 as the middle zero axis of the MEC30. So the next steps will start exactly with the same story as we have explained from the beginning.

            MEC 30 claims to "illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way" via the elementary level of numbers. It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences.

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist04.md b/identition/span2/gist04.md new file mode 100644 index 00000000000..1594566a97a --- /dev/null +++ b/identition/span2/gist04.md @@ -0,0 +1,43 @@ +![image](https://user-images.githubusercontent.com/8466209/213899950-c5f53981-5d6e-45c8-ae66-b03ab48398e0.png) + +![image](https://user-images.githubusercontent.com/8466209/213900039-f2a73c24-1bc2-4953-bf0d-a52ec49b81b9.png) + +![image](https://user-images.githubusercontent.com/36441664/86006520-46663c80-ba40-11ea-8397-ee81ce56387c.gif) + +![image](https://user-images.githubusercontent.com/8466209/219372127-1fc0a0ad-5a58-4577-911f-478f7b7e5965.png) + +![default](https://user-images.githubusercontent.com/36441664/101850765-04175e80-3b8d-11eb-9e7a-5f049fb81347.png) + +96 is the smallest integer n for which [π(n) = n/4](https://primes.utm.edu/curios/page.php/96.html). + +***π(96) = π(4x24) = 24*** + +![102](https://user-images.githubusercontent.com/8466209/216648703-35abad71-1395-49f5-bb9a-fa80fdf04e03.png) + +***139 - (25-18-18-25) = (114-18) - 18 - 25 = (96-18) - 25 = 78 - 25 = 53*** + +![](https://user-images.githubusercontent.com/8466209/216677495-a2d66661-2ae2-4a15-aeae-93b74e2e8450.png) + +![](https://user-images.githubusercontent.com/36441664/101232759-35ec7900-36e6-11eb-95a5-61a838962ce2.jpg) + +![](https://user-images.githubusercontent.com/36441664/101109759-357eb000-360a-11eb-8873-b9d73b7bb10d.jpg) + +See that from 1 to 89 it consist of seven (7) steps which is originated by 1,15,35,28 before it goes bilateral. + +![default](https://user-images.githubusercontent.com/8466209/198411256-93305a08-2de1-4a1b-9d5e-dd9f0c8a1c2b.png) + +![default](https://user-images.githubusercontent.com/8466209/198408322-f3829ebd-62b6-485c-a3fc-6ecced6dcf9e.png) + +![default](https://user-images.githubusercontent.com/8466209/198409145-f2e6fe05-595f-4d7d-922e-169b69447f0b.png) + +The distribution of these scale has a bilateral symmetrical relationship along with the peculiarities of each numbers within the format (18,30,36) of prime hexagon so that it can represent the pattern of _[true-prime-pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_ systemically. + +***(5 + 7 + 11 + 13) + (17 + 19) = 36 + 36 = 72*** + +[![default](https://user-images.githubusercontent.com/8466209/200475393-f3e42f0b-d291-4f17-93c4-9bec6e6943de.png)](https://github.com/chetabahana/tensorflow/wiki/Untouched-Intelligences#filosofi) + +This 29 turns the finiteness position of 15 as the ***[middle zero axis](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects)*** of the _MEC30_. So the next steps will start exactly with the same story as we have explained from the [beginning](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity). + +>MEC 30 claims to "illustrate and convey the connections between quantum mechanics, gravitation and mathematics in a new way" via the elementary level of numbers. It starts with a theory about the structure of light, which is then transferred to various areas of the natural sciences. + +[![default](https://user-images.githubusercontent.com/8466209/220210334-81c62871-25a2-47ef-ae38-c7bf50a4c8e3.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#residual-objects) diff --git a/identition/span2/gist05.html b/identition/span2/gist05.html new file mode 100644 index 00000000000..a417e355d56 --- /dev/null +++ b/identition/span2/gist05.html @@ -0,0 +1,201 @@ + 2.5 Parsering · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            2.5 Parsering

            ---+-----+-----
+ 1 | 1   | 18
+---+-----+-----
+ 2 | 19  | 29
+---+-----+-----
+ 3 | {30}|{43}
+---+-----+-----
+

            139 = 34th prime =(2x17)th prime

            Scheme 13:9
+===========
+(1){1}-7:   7'
+(1){8}-13:  6‘
+(1)14-{19}: 6‘
+------------- 6+6 -------
+(2)20-24:   5'           |
+(2)25-{29}: 5'           |
+------------  5+5 -------
+(3)30-36:   7:{70,30,10²}|
+------------             |
+(4)37-48:   12• ---      |
+(5)49-59:   11°    |     |
+            --}30° 30•   |
+(6)60-78:   19°    |     |
+(7)79-96:   18• ---      |
+--------------           |
+(8)97-109:  13           |
+(9)110-139:{30}=5x6 <--x-
+            --
+           {43}
+
            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            2.5.1 The imaginary

            image

            The consciousness is awaken through to the 13th central sphere of Metatron's Cube. The 13th sphere (the central circle) represents death and rebirth, endings and beginnings through all of Creation in all directions of time and space.

            1155 / 5 = 286 - 55 = 200 + 31 = 231

            layer|  i    |   f
+-----+-------+------
+     | 1,2:1 | (2,3)
+  1  +-------+
+     | 3:2   | (7)
+-----+-------+------
+     | 4,6:3 | (10,11,12)  <--- 231 (3x)
+  2  +-------+
+     |{7}:4  |({13})
+-----+-------+------
+     | 8,9:5 | (14,{15})   <--- 231 (2x)
+  3  +-------+
+     | 10:6  | (19)
+-----+-------+------
+

            partitions

            2.5.1.1 The limit shape

            We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape (arXiv:2010.16383v4).

            Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series 

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|------------------------- Skema-12 ------------------------|
+|------------ 6¤ -------------|------------- 6¤ ------------|
+|--------------------------- 192 ---------------------------|
+|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
++----+----+----+----+----+----+----+----+----+----+----+----+
+|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|
+|---------  5¤  ---------|------------ {96} -----------|{43}|
+|--------- {53} ---------|-------------- {139} -------------|
+|------- Skema-23 -------|------------- Skema-34 -----------|    
+

            Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.

            The values p(1),,,,,,p(8)} of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the Young diagrams for the partitions of the numbers from onr (1) to eight (8) (Wikipedia).

            default

            2.5.1.2 The eight (8) difference sequence

            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period eight (8) difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2} (Primesdemystified).

            image

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            11's additive sums

            2.5.2 The balanced prime

            These objects will then behave as a complex numbers that leads to trivial and complex roots of the 18th prime identity. Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as the balanced prime.

            286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+=====   bilateral 9 sums
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+
            
+                                  |                              ----------- 5 -----------
+                                  |                             |                         |  
+                                  ↓                             ↑                         ↓
+ |       2'     |        3'         |              5'              |               7'             |
+ |--------------|-------------------|------------------------------|------------------------------|
+ |     lexering = π(1000)           |                    parsering = 1000/Φ                       |
+ |--------------|-------------------|------------------------------|------------------------------|
+ |   mapping    |     feeding       |          syntaxing           |          grammaring          |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |  39 | 40 | 41 | 42 | 43 | 44 | 45  | 46 | 47 | 48 |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1  | 30 | 30 |  5 |  1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+-----+----+----+----+
+                                  ↓                             ↑                         |    |
+                                  |                             |                         |    |
+                                   ------------ 10 -------------                          |    |
+                                                                                          ↓    ↓  |
+                                                                                   +----+----+----+
+                                                                                   |  2 | 60 | 40 |
+                                                                                   +----+----+----+
+                                                                                          |    |  |
+                                                                                       2+100 ◄- 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+
+

            2.5.2.1 Replicate position

            It will be forced back to Δ19 making a cycle that bring back the 12 to → 13 of 9 collumns and replicate The Scheme 13:9 through (i=9,k=13)=9x3=27 with entry form of (100/50=2,60,40) as below:

            |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - |100 |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - |101 |  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   T
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |   H
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   E
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   P
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |   O
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   W
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |   E
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   R
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   O
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |   F
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | ∑=168
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |   V
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   S
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            By the prime hexagon this number 114 located on 6th row vs 19th column whereas 114th prime = 619 = 618+1. Since DNA Recombination is happen when two (2) chromosomes involve then they start the position as below:

                                                                   |               by the 1st chromosome   |  by the 2nd
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | 30 | 36 |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 | 20 | 21 | 22 |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            2.5.2.2 Opposite prime position

            In the second opposing member, the position 19 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 11 as a prime number is now forced to determine a new axis-symmetrical zero position.

            2.5.3 Direction grammar

            2.5.4 The runner composition

            2.5.5 The concatenation

            The 77 is equal to the sum of the first eight (8) primes. The square of 77 is 5929, the concatenation of two primes, 59 and 29. The concatenation of all palindromes from one up to 77 is prime (Prime Curios! ).

            Prime numbers that end with "77" occur more often than any other 2-digit ending among the first one million primes. The sum of the proper divisors of 77 equals 19 and the sum of primes up to 19 equals 77. Does this ever happen again?

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist06.html b/identition/span2/gist06.html new file mode 100644 index 00000000000..b0311777455 --- /dev/null +++ b/identition/span2/gist06.html @@ -0,0 +1,30 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Φ(10,2) = 10² + 2x(10th prime) + 10¹ = 100+29 + 29+10 = 129 + 39 = 168 = π(1000)

            Φ = 2,10
+Δ = 5,7,17
+3': 13,18,25,42
+2' » 13 to 77, Δ = 64
+2' and 3' » 13 to 45, Δ = 32
+
+2" + 5" = 7" = 77
+2"=22, 3"=33, 2" + 3" = 5" = 55
+
+13, 16, 18, 21, 23, 25, 28, 30, 32, 34, 
+36, 38, 40, 42, 
+45, 47, 49, 51, 53, 
+55, 57, 59, 61, 
+63, 65, 67, 69, 71, 73, 75, 77
+
+

            default

            The DNA base consists of 2 groups that are in pairs between Sugar and pospat with nucleotides. Let's weighting between the two. Each of these pospats consists of three (3) groups with five (5) oxygen bonds. This sugar and pospat forms a system that moves from 5' to 3' which is anti-parallel with movement at the other end which is 3' to 5'.

            default

            Each oxygen test has 2 electrons, so each group I give a weight of 2x5 or ten (10) so the total is 30. Sugar molecules are not groups so the weight is five (5) so that with a weight of 30 out of pospat the total is 35. Since there is a pair then the total is 70. Next we unite the format with nucleotides A,T,G,C paired 9+6 and 6+9 totaling 30 then the format of both is (70,30).

              #8 |----------- 5® --------|------------ 7® --------------|
+     |  1  |---------------- 77 = 4² + 5² + 6² -------------|
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ user|  7  |  -  | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main|  -  |  9  | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+               Δ | Δ             |                       Δ  |   Δ
+              Φ17|Φ29            |                     96-99|  100 - 123 ({24})
+                 |--- A,T,G,C ---|                          |  └── 100 - 103 (4x) » 100
+                 Δ    2x2 = 4x   |-------  2x3 = 6x  -------|  └── 104 - 109 (6x) » 30
+                {98}                                        |  └── 110 - 123 (14x)» 70
+

            Here we unite with the whole bond which of course is the number of the two, namely 100, then the sum of the DNA bases, namely Pospat, Sugar and Nukeotides is 200 with the format (70,30,100).

            (2x5x7,2x3x5,2²x5²) = (14x5,15x2,20x5) = (70,30,100)

            default

            114 - 102 = 12 » {1} & {2}

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist06.md b/identition/span2/gist06.md new file mode 100644 index 00000000000..2743dc2f86c --- /dev/null +++ b/identition/span2/gist06.md @@ -0,0 +1,61 @@ + +***Φ(10,2) = 10² + 2x(10th prime) + 10¹ = 100+29 + 29+10 = 129 + 39 = 168 = π(1000)*** + +``` +Φ = 2,10 +Δ = 5,7,17 +3': 13,18,25,42 +2' » 13 to 77, Δ = 64 +2' and 3' » 13 to 45, Δ = 32 + +2" + 5" = 7" = 77 +2"=22, 3"=33, 2" + 3" = 5" = 55 + +13, 16, 18, 21, 23, 25, 28, 30, 32, 34, +36, 38, 40, 42, +45, 47, 49, 51, 53, +55, 57, 59, 61, +63, 65, 67, 69, 71, 73, 75, 77 + +``` + +![default](https://user-images.githubusercontent.com/36441664/100138286-651e1180-2ec0-11eb-9b27-ec206498380f.jpg) + +The DNA base consists of 2 groups that are in pairs between Sugar and pospat with nucleotides. Let's weighting between the two. Each of these pospats consists of three (3) groups with five (5) oxygen bonds. This sugar and pospat forms a system that moves from 5' to 3' which is anti-parallel with movement at the other end which is 3' to 5'. + +![default](https://user-images.githubusercontent.com/36441664/101623118-8d724800-3a4a-11eb-8773-e2fb0033fa4b.png) + +Each oxygen test has 2 electrons, so each group I give a weight of 2x5 or ten (10) so the total is 30. Sugar molecules are not groups so the weight is five (5) so that with a weight of 30 out of pospat the total is 35. Since there is a pair then the total is 70. Next we unite the format with nucleotides A,T,G,C paired 9+6 and 6+9 totaling 30 then the format of both is (70,30). + +``` + #8 |----------- 5® --------|------------ 7® --------------| + | 1 |---------------- 77 = 4² + 5² + 6² -------------| +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77 +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78 + main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + Δ | Δ | Δ | Δ + Φ17|Φ29 | 96-99| 100 - 123 ({24}) + |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100 + Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30 + {98} | └── 110 - 123 (14x)» 70 +``` + +Here we unite with the whole bond which of course is the number of the two, namely 100, then the sum of the DNA bases, namely Pospat, Sugar and Nukeotides is 200 with the format (70,30,100). + +***(2x5x7,2x3x5,2²x5²) = (14x5,15x2,20x5) = (70,30,100)*** + +![default](https://user-images.githubusercontent.com/36441664/101109773-3c0d2780-360a-11eb-9f21-57e2707c7d1e.jpg) + +![](https://user-images.githubusercontent.com/36441664/84743781-9d99f500-afdc-11ea-8377-e0ecee9537ea.gif) + +***114 - 102 = 12 » {1} & {2}*** + +[![default](https://user-images.githubusercontent.com/8466209/198813482-ac274a00-c025-46ce-9374-f9bcb0c3fd32.png)](https://github.com/jeffreytse/jekyll-deploy-action) + +![default](https://user-images.githubusercontent.com/8466209/198410440-cb9003b9-ae7e-4637-aa5e-dcf968f9cb4f.png) + +![default](https://user-images.githubusercontent.com/8466209/198940479-9a0d3ad0-b502-4df4-8093-fdac8e275552.png) diff --git a/identition/span2/gist07.html b/identition/span2/gist07.html new file mode 100644 index 00000000000..4c8d9c58f50 --- /dev/null +++ b/identition/span2/gist07.html @@ -0,0 +1,14 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            This recombination scheme shall be made available on each of instance that composing 7 blocks. Since these blocks are spread in to 29 flats that bring a total of 77 rooms then the total objects per instance would become 114.

            Φ(13:9) = Φ(29th prime) = Φ(109) = (2+69) + 68 = 71 + 68 = 139

               -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            In this analogy, the basic question is: is the puzzle really as hard as we think, or are we missing something? This issue was first raised by the baffling Austrian-American mathematician Kurt Gödel. It was formulated as P ≠ NP by Stephen Cook in 1971.

            P is a polynomial and NP is a non-deterministic polynomial. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. In simpler terms, P means a problem that is easily solved by a computer, and NP means a problem that a computer is not easy to solve but is easy to check.

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist07.md b/identition/span2/gist07.md new file mode 100644 index 00000000000..e10e20010d2 --- /dev/null +++ b/identition/span2/gist07.md @@ -0,0 +1,45 @@ +![](https://user-images.githubusercontent.com/36441664/84743844-b0acc500-afdc-11ea-8311-3affd4bf0c69.gif) + +![](https://user-images.githubusercontent.com/36441664/84656283-a2a76780-af3c-11ea-930d-049952522888.png) + +![](https://user-images.githubusercontent.com/36441664/69990325-04434e00-1578-11ea-9e5a-c86bd88fe706.png) + +This recombination scheme shall be made available on each of _[instance](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ that composing _[7 blocks](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)_. Since these blocks are spread in to _[29 flats](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-mapping-md)_ that bring a total of _[77 rooms](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-portal-md)_ then the total objects per instance would become ***114***. + +![](https://user-images.githubusercontent.com/36441664/76367716-7211c980-6360-11ea-9f36-728b57c9ca34.png) + +***Φ(13:9) = Φ(29th prime) = Φ(109) = (2+69) + 68 = 71 + 68 = 139*** + +``` + -------------------+-----+-----+ --- + 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ | + | +-----+-----+ | + | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class + | | +-----+-----+-----+-----+-----+ | | + | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} | + | | | +-----+-----+-----+-----+-----+ | | --- + --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- | + | | +-----+-----+ | | + --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object +168 | +-----+ | +| 102 -› 29:18| 50 | 50(68) ---------> Δ18 | +----------------------+-----+ --- +``` + +![](https://user-images.githubusercontent.com/36441664/84648825-c1ebc800-af2f-11ea-88d5-9446b711cfe5.png) + +![](https://user-images.githubusercontent.com/36441664/84744689-c4a4f680-afdd-11ea-80b7-6cd6566e42f9.png) + +In this analogy, the basic question is: is the puzzle really as hard as we think, or are we missing something? This issue was first raised by the baffling Austrian-American mathematician Kurt Gödel. It was formulated as ***[P ≠ NP](https://en.wikipedia.org/wiki/P_versus_NP_problem)*** by Stephen Cook in 1971. + +![](https://user-images.githubusercontent.com/36441664/85101079-c532cc80-b22b-11ea-86a1-49ddf8b18a71.jpg) + +P is a polynomial and NP is a non-deterministic polynomial. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. In simpler terms, P means a problem that is easily solved by a computer, and NP means a problem that a computer is not easy to solve but is easy to check. + +![](https://user-images.githubusercontent.com/36441664/84743524-4b58d400-afdc-11ea-9e64-5306a5811a33.jpg) + +[![default](https://user-images.githubusercontent.com/8466209/198754036-1629e06f-5741-4d8d-8ff4-aa6127ecbd08.png)](https://github.com/myoung34/docker-github-actions-runner) + +[![default](https://user-images.githubusercontent.com/8466209/198806388-ee9c460b-0a44-4659-ab0a-35c1a68cbbb8.png)](https://docs.github.com/en/actions/hosting-your-own-runners/adding-self-hosted-runners#adding-a-self-hosted-runner-to-a-repository) + +[![default](https://user-images.githubusercontent.com/8466209/198812060-bcf0c3e5-1918-4245-b2fa-1c43c2602a90.png)](https://www.chetabahana.com/) diff --git a/identition/span2/gist08.html b/identition/span2/gist08.html new file mode 100644 index 00000000000..5e651c70343 --- /dev/null +++ b/identition/span2/gist08.html @@ -0,0 +1,264 @@ + Project Repositories · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Project Repositories

            (5, 2, 1, 0)
+(7, 3, 1, 0)
+(11, 4, 1, 0)
+(13, 5, 1, 0)
+(17, 0, 1, 1)
+(19, 1, 1, 1)
+(23, 2, 1, 1)
+(29, 2, -1, 1)
+(31, 1, -1, 1)
+(37, 1, 1, 1)
+(41, 2, 1, 1)
+(43, 3, 1, 1)
+(47, 4, 1, 1)
+(53, 4, -1, 1)
+(59, 4, 1, 1)
+(61, 5, 1, 1)
+(67, 5, -1, 1)
+(71, 4, -1, 1)
+(73, 3, -1, 1)
+(79, 3, 1, 1)
+(83, 4, 1, 1)
+(89, 4, -1, 1)
+(97, 3, -1, 1)
+(101, 2, -1, 1)
+(103, 1, -1, 1)
+(107, 0, -1, 1)
+(109, 5, -1, 0)
+(113, 4, -1, 0)
+(127, 3, -1, 0)
+(131, 2, -1, 0)
+(137, 2, 1, 0)
+(139, 3, 1, 0)
+(149, 4, 1, 0)
+(151, 5, 1, 0)
+(157, 5, -1, 0)
+(163, 5, 1, 0)
+(167, 0, 1, 1)
+(173, 0, -1, 1)
+(179, 0, 1, 1)
+(181, 1, 1, 1)
+(191, 2, 1, 1)
+(193, 3, 1, 1)
+(197, 4, 1, 1)
+(199, 5, 1, 1)
+(211, 5, -1, 1)
+(223, 5, 1, 1)
+(227, 0, 1, 2)
+(229, 1, 1, 2)
+(233, 2, 1, 2)
+(239, 2, -1, 2)
+(241, 1, -1, 2)
+(251, 0, -1, 2)
+(257, 0, 1, 2)
+(263, 0, -1, 2)
+(269, 0, 1, 2)
+(271, 1, 1, 2)
+(277, 1, -1, 2)
+(281, 0, -1, 2)
+(283, 5, -1, 1)
+(293, 4, -1, 1)
+(307, 3, -1, 1)
+(311, 2, -1, 1)
+(313, 1, -1, 1)
+(317, 0, -1, 1)
+(331, 5, -1, 0)
+(337, 5, 1, 0)
+(347, 0, 1, 1)
+(349, 1, 1, 1)
+(353, 2, 1, 1)
+(359, 2, -1, 1)
+(367, 1, -1, 1)
+(373, 1, 1, 1)
+(379, 1, -1, 1)
+(383, 0, -1, 1)
+(389, 0, 1, 1)
+(397, 1, 1, 1)
+(401, 2, 1, 1)
+(409, 3, 1, 1)
+(419, 4, 1, 1)
+(421, 5, 1, 1)
+(431, 0, 1, 2)
+(433, 1, 1, 2)
+(439, 1, -1, 2)
+(443, 0, -1, 2)
+(449, 0, 1, 2)
+(457, 1, 1, 2)
+(461, 2, 1, 2)
+(463, 3, 1, 2)
+(467, 4, 1, 2)
+(479, 4, -1, 2)
+(487, 3, -1, 2)
+(491, 2, -1, 2)
+(499, 1, -1, 2)
+(503, 0, -1, 2)
+(509, 0, 1, 2)
+(521, 0, -1, 2)
+(523, 5, -1, 1)
+(541, 5, 1, 1)
+(547, 5, -1, 1)
+(557, 4, -1, 1)
+(563, 4, 1, 1)
+(569, 4, -1, 1)
+(571, 3, -1, 1)
+(577, 3, 1, 1)
+(587, 4, 1, 1)
+(593, 4, -1, 1)
+(599, 4, 1, 1)
+(601, 5, 1, 1)
+(607, 5, -1, 1)
+(613, 5, 1, 1)
+(617, 0, 1, 2)
+(619, 1, 1, 2)
+(631, 1, -1, 2)
+(641, 0, -1, 2)
+(643, 5, -1, 1)
+(647, 4, -1, 1)
+(653, 4, 1, 1)
+(659, 4, -1, 1)
+(661, 3, -1, 1)
+(673, 3, 1, 1)
+(677, 4, 1, 1)
+(683, 4, -1, 1)
+(691, 3, -1, 1)
+(701, 2, -1, 1)
+(709, 1, -1, 1)
+(719, 0, -1, 1)
+(727, 5, -1, 0)
+(733, 5, 1, 0)
+(739, 5, -1, 0)
+(743, 4, -1, 0)
+(751, 3, -1, 0)
+(757, 3, 1, 0)
+(761, 4, 1, 0)
+(769, 5, 1, 0)
+(773, 0, 1, 1)
+(787, 1, 1, 1)
+(797, 2, 1, 1)
+(809, 2, -1, 1)
+(811, 1, -1, 1)
+(821, 0, -1, 1)
+(823, 5, -1, 0)
+(827, 4, -1, 0)
+(829, 3, -1, 0)
+(839, 2, -1, 0)
+(853, 1, -1, 0)
+(857, 0, -1, 0)
+(859, 5, -1, -1)
+(863, 4, -1, -1)
+(877, 3, -1, -1)
+(881, 2, -1, -1)
+(883, 1, -1, -1)
+(887, 0, -1, -1)
+(907, 5, -1, -2)
+(911, 4, -1, -2)
+(919, 3, -1, -2)
+(929, 2, -1, -2)
+(937, 1, -1, -2)
+(941, 0, -1, -2)
+(947, 0, 1, -2)
+(953, 0, -1, -2)
+(967, 5, -1, -3)
+(971, 4, -1, -3)
+(977, 4, 1, -3)
+(983, 4, -1, -3)
+(991, 3, -1, -3)
+(997, 3, 1, -3)
+

            139 = 34th prime =(2x17)th prime

            Scheme 13:9
+===========
+(1){1}-7:   7'
+(1){8}-13:  6‘
+(1)14-{19}: 6‘
+------------- 6+6 -------
+(2)20-24:   5'           |
+(2)25-{29}: 5'           |
+------------  5+5 -------
+(3)30-36:   7:{70,30,10²}|
+------------             |
+(4)37-48:   12• ---      |
+(5)49-59:   11°    |     |
+            --}30° 30•   |
+(6)60-78:   19°    |     |
+(7)79-96:   18• ---      |
+--------------           |
+(8)97-109:  13           |
+(9)110-139:{30}=5x6 <--x-- (129/17-139/27)
+            --
+           {43}
+

            P versus NP

            default

            M: 6® = (2,{3}), ({29,30,31,32}) --> 2,89+29,3 = 289+329 = 618 (main)
+F: 6'® = (40,41), (43,44,45,46) --> 30+30+10+10+10+10 = 60+40 (user)
+C1: 10°® = 3*®+3*®+4® = (7,13,19),(20,27,36),({38,42,50,68}) --> 200 (main)
+C2: 7® = 5®+2® = 1®+4*®+2*® = 1®+6*® = 10,(11,12,14,15,26,28) --> 168 (user)
+

            π (Φ (329 + 289)) = π (Φ x 618) = π (1000) = 168

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            Pinned Repo

            User repos

            # pinned repos
+# https://dev.to/thomasaudo/get-started-with-github-grapql-api--1g8b
+echo -e "\n$hr\nPINNED  REPOSITORIES\n$hr"
+AUTH="Authorization: bearer $JEKYLL_GITHUB_TOKEN"
+curl -L -X POST "${GITHUB_GRAPHQL_URL}" -H "$AUTH" \
+--data-raw '{"query":"{\n  user(login: \"'${GITHUB_REPOSITORY_OWNER}'\") \
+{\n pinnedItems(first: 6, types: REPOSITORY) {\n nodes {\n ... on Repository \
+{\n name\n }\n }\n }\n }\n}"'
+
+================================================================================
+PINNED  REPOSITORIES
+================================================================================
+  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
+                                 Dload  Upload   Total   Spent    Left  Speed
+
+  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0
+100   292  100   150  100   142   1171   1109 --:--:-- --:--:-- --:--:--  2281
+
+{"data":{"user":{"pinnedItems":{"nodes":[{"name":"maps"},{"name":"feed"},
+{"name":"lexer"},{"name":"parser"},{"name":"syntax"},{"name":"grammar"}]}}}}
+

            Organization (View as: Public

            GitHub graphQL API multiple queries on organizations &

            curl -L -X POST "${GITHUB_GRAPHQL_URL}" -H "$AUTH" \
+--data-raw '{"query":"{\n  organization(login: \"'${GITHUB_REPOSITORY_OWNER}'\") \ 
+{\n pinnedItems(first: 6, types: REPOSITORY) {\n nodes {\n ... on Repository \ 
+{\n name\n }\n }\n }\n }\n}"'
+
+================================================================================
+PINNED  REPOSITORIES
+================================================================================
+  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
+                                 Dload  Upload   Total   Spent    Left  Speed
+
+  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0
+100   292  100   150  100   142   1171   1109 --:--:-- --:--:-- --:--:--  2281
+
+{"data":{"organization":{"pinnedItems":{"nodes":[{"name":"classifier"},
+{"name":"domJSON"},{"name":"openoffice"},{"name":"landing-page-theme"},
+{"name":"asciidoc"},{"name":"recommendations-ai"}]}}}}
+

            1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+-----+-----+-----+-----+-----+     -----------------------------------------------
+{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |
+-----+-----+-----+-----+-----+                                               |
+ {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone
+     +-----+-----+-----+-----+                                               |
+ {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |
+     +-----+-----+-----+                                               -----------
+ {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |
+ ----+-----+-----+-----+-----+                                               |
+  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone
+     +-----+-----+-----+-----+                                               |
+  {8}|23,25|25,27|27,29| 18                                                  |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+     |  1     2     3  |   4     5     6 |   7     8      9  |
+     |------ 29' ------|--------------- 139' ----------------|
+     |------ 102¨ -----|---------------  66¨ ----------------|
+

            114 = 102 + 66 - 29 - 25 = 6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 25 + 89

            image

            6 x 114 - 30 - 30 - 5 = 619 = 6 x 19 = 114th prime

            π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786

            default

            To make it easier to develop a program following a model, we divide the object by placing it into a smaller objects. We do this division by adopting the OOP (Object Oriented Programming) which is an object-oriented programming method.

            139 + 286 + 114 + 247 + 157 + 786 = 786 + 157 + 786 = 1729 = 7 x 13 x 19

            168 + 329 + 289 = 168 + 618 = 786

            default

            Using this method then out of bilateray way of 19 vs 18 we could get in to Scheme-33. By a decomposition the subject is divided into six (6) parts, each part is further regrouped in to 19 sub-parts so finaly we got π(1000/Φ)=π(618)=114 objects.

            d(43,71,114) = d(7,8,6) » 786

            default

            By defining the pattern on each individual numbers against homogeneous sorting out of these 114 objects then we finally come to a scale called MEC30 which is based on the beauty of Euler's identity.

            Mathematics writer Constance Reid has opined that Euler's identity is the most famous formula in all mathematics. And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler's identity during a lecture, stated that the identity "is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth" (Wikipedia)

            default

            Although this may seem very fast, a much more sophisticated method, combined with a very powerful computer, is necessary to find very large primes. Despite there are many studies and papers it is still an important open problem today.

            The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved (Wikipedia).

            In the next section we will discuss about algorithms in applications and their relation to the distribution of prime numbers.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist08.md b/identition/span2/gist08.md new file mode 100644 index 00000000000..39d20bec9dd --- /dev/null +++ b/identition/span2/gist08.md @@ -0,0 +1,353 @@ +# Project Repositories + +``` +(5, 2, 1, 0) +(7, 3, 1, 0) +(11, 4, 1, 0) +(13, 5, 1, 0) +(17, 0, 1, 1) +(19, 1, 1, 1) +(23, 2, 1, 1) +(29, 2, -1, 1) +(31, 1, -1, 1) +(37, 1, 1, 1) +(41, 2, 1, 1) +(43, 3, 1, 1) +(47, 4, 1, 1) +(53, 4, -1, 1) +(59, 4, 1, 1) +(61, 5, 1, 1) +(67, 5, -1, 1) +(71, 4, -1, 1) +(73, 3, -1, 1) +(79, 3, 1, 1) +(83, 4, 1, 1) +(89, 4, -1, 1) +(97, 3, -1, 1) +(101, 2, -1, 1) +(103, 1, -1, 1) +(107, 0, -1, 1) +(109, 5, -1, 0) +(113, 4, -1, 0) +(127, 3, -1, 0) +(131, 2, -1, 0) +(137, 2, 1, 0) +(139, 3, 1, 0) +(149, 4, 1, 0) +(151, 5, 1, 0) +(157, 5, -1, 0) +(163, 5, 1, 0) +(167, 0, 1, 1) +(173, 0, -1, 1) +(179, 0, 1, 1) +(181, 1, 1, 1) +(191, 2, 1, 1) +(193, 3, 1, 1) +(197, 4, 1, 1) +(199, 5, 1, 1) +(211, 5, -1, 1) +(223, 5, 1, 1) +(227, 0, 1, 2) +(229, 1, 1, 2) +(233, 2, 1, 2) +(239, 2, -1, 2) +(241, 1, -1, 2) +(251, 0, -1, 2) +(257, 0, 1, 2) +(263, 0, -1, 2) +(269, 0, 1, 2) +(271, 1, 1, 2) +(277, 1, -1, 2) +(281, 0, -1, 2) +(283, 5, -1, 1) +(293, 4, -1, 1) +(307, 3, -1, 1) +(311, 2, -1, 1) +(313, 1, -1, 1) +(317, 0, -1, 1) +(331, 5, -1, 0) +(337, 5, 1, 0) +(347, 0, 1, 1) +(349, 1, 1, 1) +(353, 2, 1, 1) +(359, 2, -1, 1) +(367, 1, -1, 1) +(373, 1, 1, 1) +(379, 1, -1, 1) +(383, 0, -1, 1) +(389, 0, 1, 1) +(397, 1, 1, 1) +(401, 2, 1, 1) +(409, 3, 1, 1) +(419, 4, 1, 1) +(421, 5, 1, 1) +(431, 0, 1, 2) +(433, 1, 1, 2) +(439, 1, -1, 2) +(443, 0, -1, 2) +(449, 0, 1, 2) +(457, 1, 1, 2) +(461, 2, 1, 2) +(463, 3, 1, 2) +(467, 4, 1, 2) +(479, 4, -1, 2) +(487, 3, -1, 2) +(491, 2, -1, 2) +(499, 1, -1, 2) +(503, 0, -1, 2) +(509, 0, 1, 2) +(521, 0, -1, 2) +(523, 5, -1, 1) +(541, 5, 1, 1) +(547, 5, -1, 1) +(557, 4, -1, 1) +(563, 4, 1, 1) +(569, 4, -1, 1) +(571, 3, -1, 1) +(577, 3, 1, 1) +(587, 4, 1, 1) +(593, 4, -1, 1) +(599, 4, 1, 1) +(601, 5, 1, 1) +(607, 5, -1, 1) +(613, 5, 1, 1) +(617, 0, 1, 2) +(619, 1, 1, 2) +(631, 1, -1, 2) +(641, 0, -1, 2) +(643, 5, -1, 1) +(647, 4, -1, 1) +(653, 4, 1, 1) +(659, 4, -1, 1) +(661, 3, -1, 1) +(673, 3, 1, 1) +(677, 4, 1, 1) +(683, 4, -1, 1) +(691, 3, -1, 1) +(701, 2, -1, 1) +(709, 1, -1, 1) +(719, 0, -1, 1) +(727, 5, -1, 0) +(733, 5, 1, 0) +(739, 5, -1, 0) +(743, 4, -1, 0) +(751, 3, -1, 0) +(757, 3, 1, 0) +(761, 4, 1, 0) +(769, 5, 1, 0) +(773, 0, 1, 1) +(787, 1, 1, 1) +(797, 2, 1, 1) +(809, 2, -1, 1) +(811, 1, -1, 1) +(821, 0, -1, 1) +(823, 5, -1, 0) +(827, 4, -1, 0) +(829, 3, -1, 0) +(839, 2, -1, 0) +(853, 1, -1, 0) +(857, 0, -1, 0) +(859, 5, -1, -1) +(863, 4, -1, -1) +(877, 3, -1, -1) +(881, 2, -1, -1) +(883, 1, -1, -1) +(887, 0, -1, -1) +(907, 5, -1, -2) +(911, 4, -1, -2) +(919, 3, -1, -2) +(929, 2, -1, -2) +(937, 1, -1, -2) +(941, 0, -1, -2) +(947, 0, 1, -2) +(953, 0, -1, -2) +(967, 5, -1, -3) +(971, 4, -1, -3) +(977, 4, 1, -3) +(983, 4, -1, -3) +(991, 3, -1, -3) +(997, 3, 1, -3) +``` + +![](https://user-images.githubusercontent.com/8466209/218319845-23639b98-a087-4bf5-afd9-2af9dfabcdfb.jpg) + +![](https://user-images.githubusercontent.com/36441664/84945795-e43d3b80-b111-11ea-900a-f0b9236d7e69.png) + +[![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Eulerangles.svg/300px-Eulerangles.svg.png)](https://en.wikipedia.org/wiki/Euler_angles) + +***139 = 34th prime =(2x17)th prime*** + +``` +Scheme 13:9 +=========== +(1){1}-7: 7’ +(1){8}-13: 6‘ +(1)14-{19}: 6‘ +------------- 6+6 ------- +(2)20-24: 5’ | +(2)25-{29}: 5’ | +------------ 5+5 ------- +(3)30-36: 7:{70,30,10²}| +------------ | +(4)37-48: 12• --- | +(5)49-59: 11° | | + --}30° 30• | +(6)60-78: 19° | | +(7)79-96: 18• --- | +-------------- | +(8)97-109: 13 | +(9)110-139:{30}=5x6 <--x-- (129/17-139/27) + -- + {43} +``` + +![](https://user-images.githubusercontent.com/36441664/84743646-6fb4b080-afdc-11ea-86de-d072f0c047a5.gif) + +[![P versus NP](https://user-images.githubusercontent.com/36441664/84533710-e6b72400-ad12-11ea-9ee5-a8b57b8855fb.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-portal-md) + +![default](https://user-images.githubusercontent.com/8466209/218370587-ec438d91-be88-408a-a746-ff1e6324a514.png) + +``` +M: 6® = (2,{3}), ({29,30,31,32}) --> 2,89+29,3 = 289+329 = 618 (main) +F: 6'® = (40,41), (43,44,45,46) --> 30+30+10+10+10+10 = 60+40 (user) +C1: 10°® = 3*®+3*®+4® = (7,13,19),(20,27,36),({38,42,50,68}) --> 200 (main) +C2: 7® = 5®+2® = 1®+4*®+2*® = 1®+6*® = 10,(11,12,14,15,26,28) --> 168 (user) +``` + +***π (Φ (329 + 289)) = π (Φ x 618) = π (1000) = 168*** + +``` +1st layer: +It has a total of 1000 numbers +Total primes = π(1000) = 168 primes + +2nd layer: +It will start by π(168)+1 as the 40th prime +It has 100x100 numbers or π(π(10000)) = 201 primes +Total cum primes = 168 + (201-40) = 168+161 = 329 primes + +3rd layer: +Behave the same as 2nd layer which has a total of 329 primes +The primes will start by π(π(π(1000th prime)))+1 as the 40th prime +This 1000 primes will become 1000 numbers by 1st layer of the next level +Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 +``` + +## Pinned Repo + +### User repos + +``` +# pinned repos +# https://dev.to/thomasaudo/get-started-with-github-grapql-api--1g8b +echo -e "\n$hr\nPINNED REPOSITORIES\n$hr" +AUTH="Authorization: bearer $JEKYLL_GITHUB_TOKEN" +curl -L -X POST "${GITHUB_GRAPHQL_URL}" -H "$AUTH" \ +--data-raw '{"query":"{\n user(login: \"'${GITHUB_REPOSITORY_OWNER}'\") \ +{\n pinnedItems(first: 6, types: REPOSITORY) {\n nodes {\n ... on Repository \ +{\n name\n }\n }\n }\n }\n}"' + +================================================================================ +PINNED REPOSITORIES +================================================================================ + % Total % Received % Xferd Average Speed Time Time Time Current + Dload Upload Total Spent Left Speed + + 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0 +100 292 100 150 100 142 1171 1109 --:--:-- --:--:-- --:--:-- 2281 + +{"data":{"user":{"pinnedItems":{"nodes":[{"name":"maps"},{"name":"feed"}, +{"name":"lexer"},{"name":"parser"},{"name":"syntax"},{"name":"grammar"}]}}}} +``` + +### Organization (View as: Public + +GitHub graphQL API [multiple queries](https://stackoverflow.com/questions/51047292/github-graphql-api-multiple-queries-on-organizations-repositories) on organizations & + +``` +curl -L -X POST "${GITHUB_GRAPHQL_URL}" -H "$AUTH" \ +--data-raw '{"query":"{\n organization(login: \"'${GITHUB_REPOSITORY_OWNER}'\") \ +{\n pinnedItems(first: 6, types: REPOSITORY) {\n nodes {\n ... on Repository \ +{\n name\n }\n }\n }\n }\n}"' + +================================================================================ +PINNED REPOSITORIES +================================================================================ + % Total % Received % Xferd Average Speed Time Time Time Current + Dload Upload Total Spent Left Speed + + 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0 +100 292 100 150 100 142 1171 1109 --:--:-- --:--:-- --:--:-- 2281 + +{"data":{"organization":{"pinnedItems":{"nodes":[{"name":"classifier"}, +{"name":"domJSON"},{"name":"openoffice"},{"name":"landing-page-theme"}, +{"name":"asciidoc"},{"name":"recommendations-ai"}]}}}} +``` + +***1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects*** + +``` +True Prime Pairs: +(5,7), (11,13), (17,19) + +-----+-----+-----+-----+-----+ ----------------------------------------------- +{786}| 1,2 | 2 | 2,3 | 3,4 | {19} | +-----+-----+-----+-----+-----+ | + {86}| 4 | 4,5 | 5,6 |{6,7}| 17 Base Zone + +-----+-----+-----+-----+ | + {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ | + +-----+-----+-----+ ----------- + {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone | + ----+-----+-----+-----+-----+ | + {6}|15,16|17,18|18,20|21,22| 19 Mirror Zone + +-----+-----+-----+-----+ | + {8}|23,25|25,27|27,29| 18 | + +-----+-----+-----+-----+-----+-----+-----+-----+-------+ ----------- + {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ +-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+ ----------- + | 1 2 3 | 4 5 6 | 7 8 9 | + |------ 29' ------|--------------- 139' ----------------| + |------ 102¨ -----|--------------- 66¨ ----------------| +``` + +***114 = 102 + 66 - 29 - 25 = 6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 25 + 89*** + +![image](https://user-images.githubusercontent.com/8466209/200228344-9f344f49-3e5d-480f-b11c-6e30a20a8f44.jpg) + +***6 x 114 - 30 - 30 - 5 = 619 = 6 x 19 = 114th prime*** + +[![](https://user-images.githubusercontent.com/8466209/90985852-ca542500-e5a8-11ea-9027-9bfdcbe37966.jpg)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-1_prime-md) + +***π(1000) + 1000/Φ = 168 + 618 = (7x71) + (17x17) = 786*** + +[![default](https://user-images.githubusercontent.com/8466209/198191314-6ca520ed-6aea-40c0-8f89-3d1d1a83dc1e.png)](https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners#using-a-github-hosted-runner) + +To make it easier to develop a program following a model, we divide the object by placing it into a smaller objects. We do this division by adopting the _[OOP (Object Oriented Programming)](https://www.google.com/search?q=object+oriented+programming&tbm=isch)_ which is an object-oriented programming method. + +***139 + 286 + 114 + 247 + 157 + 786 = 786 + 157 + 786 = 1729 = 7 x 13 x 19*** + +![](https://user-images.githubusercontent.com/8466209/199355377-8d93057a-769d-49ed-b401-722c0b33fdab.png) + +***168 + 329 + 289 = 168 + 618 = 786*** + +![default](https://user-images.githubusercontent.com/8466209/218931333-c4c8bd23-c05d-4af0-9b02-afa3079ef9b8.png) + +Using this method then out of bilateray way of ***19 vs 18*** we could get in to _[Scheme-33](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-entrance-md)_. By a _[decomposition](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288#file-target-md)_ the subject is divided into six (6) parts, each part is further regrouped in to 19 sub-parts so finaly we got π(1000/Φ)=π(618)=114 objects. + +***d(43,71,114) = d(7,8,6) » 786*** + +[![default](https://user-images.githubusercontent.com/8466209/201287114-4819b99d-9815-4fc8-b994-7d3ca606b99e.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md) + +By defining the pattern on each individual numbers against _[homogeneous sorting](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#interpolation)_ out of these 114 objects then we finally come to a scale called _[MEC30](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#identity)_ which is based on the beauty of ***Euler's identity***. + +>Mathematics writer Constance Reid has opined that [Euler's identity](https://en.wikipedia.org/wiki/Euler%27s_identity) is ***the most famous formula in all mathematics***. And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler's identity during a lecture, stated that the identity "is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth" _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity#Mathematical_beauty))_ + +[![default](https://user-images.githubusercontent.com/8466209/219573505-52af4aec-3e02-4259-9f67-8bfe7424a8fb.png)](https://en.wikipedia.org/wiki/Euler%27s_identity) + +Although this may seem very fast, a much more sophisticated method, combined with a very powerful computer, is necessary to find very large primes. Despite there are many [studies](https://github.com/search?q=Riemann+Hypothesis&type=Repositories) and [papers](https://arxiv.org/search/advanced?advanced=&terms-0-operator=AND&terms-0-term=Riemann+Hypothesis&terms-0-field=title&terms-1-operator=AND&terms-1-term=prime&terms-1-field=abstract&classification-mathematics=y&classification-physics_archives=all&classification-include_cross_list=include&date-filter_by=all_dates&date-year=&date-from_date=&date-to_date=&date-date_type=submitted_date&abstracts=show&size=50&order=-announced_date_first) it is still an important [open problem](http://www.claymath.org/sites/default/files/official_problem_description.pdf) today. + +> The Millennium Prize Problems are ***seven problems*** in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved _([Wikipedia](https://en.wikipedia.org/wiki/7#Mathematics))_. + +![](https://user-images.githubusercontent.com/36441664/84532586-b2daff00-ad10-11ea-9880-ff7e97858cd3.gif) + +In the next section we will discuss about algorithms in applications and their [relation](https://github.com/eq19/parser/files/10730998/Visualising.the.Riemann.Hypothesis.pdf) to the distribution of prime numbers. diff --git a/identition/span2/gist09.html b/identition/span2/gist09.html new file mode 100644 index 00000000000..27cb3818fc2 --- /dev/null +++ b/identition/span2/gist09.html @@ -0,0 +1,99 @@ + Polar Plot · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Polar Plot

            Based on the homogeneous sorting of objects against these 114 repositories we will get the number 57 which is distributed over the pair of objects whose difference is twenty-nine (29). So everything will happen to repeat in this 29.

            (114/2)! = 57! = 1653 » 1653 / 57 = 29

            --------+
+        | ⅓
+        +---   } ⅔
+ Case A | ⅓
+        +---------
+        | ⅓      |
+-----------------+  Φ = ⅔
+        | ⅓      |
+        +---------
+ Case B | ⅓
+        +---   } ⅔
+        | ⅓
+---------
+

            By this objects pairing there would exist a zone segregation numbers (28.29) on each of the pairs. Since 10 stands as the central zone then it would be a tensor between 29-10=19 and 28-10=18.

            9 + 19 + 29 = 28 + 29 = (10+18) + (10+19) = 57

            P7:(142857)
+
+   #  |  A   |  B   | ∑
+------+------+------+-----
+  {1} |      |      |
+------+      |      |
+ ...  |  28  |  29  | 57
+------+      |      |
+ {57} |      |      |
+------+------+------+-----
+  58  |      |      |
+------+      |      |
+  ... |  29  |  28  | 57
+------+      |      |
+ 114  |      |      |
+------+------+------+-----
+      |  57  |  57  | 114
+

            This zone is cenralized by the 20 objects while the tensor of 19 vs 18 is polarizing the 2x11x13=286 objects out of the pairing of 11 and 13 within the True Prime Pairs and finally be composed by 20/10 = 2 numbers of 285 and 286 that having a total of 571.

            Φ((13,12),(12,18)) = Φ(13,((19,18),(18,43)) = Φ(13,37,61) = Φ(6,12,18)th prime

            ---+-----+-----+-----+-----+
+ 1 |{19} | 1   |{20} | 21  |-----------------------
+---+-----+-----+-----+-----+                       |
+ 2 | 18  | 21  | 39  | 60  |-----------------      |
+---+-----+-----+-----+-----+                 |     |
+ 3 | 63  | 40  | 103 |{143}|-----------      |     |
+---+-----+-----+-----+-----+           |     |     |
+ 4 | 37  | 104 | 141 | 245 |-----      |     |     |
+---+-----+-----+-----+-----+     |     |     |     |
+ 5 | 10  | 142 | 152 | 294 |-{11}|{13} |{12} |{12} |{18}
+---+-----+-----+-----+-----+     |     |     |     |
+ 6 | 24  | 153 |{177}| 332 |-----      |     |     |
+---+-----+-----+-----+-----+           |     |     |
+ 7 | 75  | 178 | 253 | 431 |-----------      |     |
+---+-----+-----+-----+-----+                 |     |
+ 8 | 30  | 254 | 284 | 538 |-----------------      |
+---+-----+-----+-----+-----+                       |
+ 9 | 1   | 285 | 286 |{571}|-----------------------
+===+=====+=====+=====+=====+
+45 |{277}|
+---+-----+
+

            However by the prime numbers this behaviour is not happened by the number of 57 but on the 157 as the 19+18=37th prime. So on the pairing of 57 to 114 above then one of them is forced to behave as 157-57=100 which is exactly the square of 10.

            157 is the 37th prime number, a balanced prime, because the arithmetic mean of those primes yields 157. The next prime is 163 and the previous prime is 151, with which 157 forms a prime triplet. (Wikipedia)

            By this square correlation between natural and prime numbers then the 571 would be separated by the 100 to 500 and 71 and finally by the form of (2,10) the 500 goes to 50 while 71 would be polarized to form 71x2=142 and 177 as shown on the table.

            (10/2)π = 157 ⇄ (10^2)¹ + 11x7 = 177

            That is why DNA is twisted and spinning in the scope of three (3) directions in three (3) dimensions which in its entirety resembles the shape of a trifoil. For XX genes this lead to 1600 objects but for XY genes there are different story.

            When a 3 × 3 × 3 cube is made of 27 unit cubes, 26 of them are viewable as the exterior layer. (Wikipedia)

            From this arrangement we get the sum of all vectors with the sequence at number 247 where via the number one (1) makes 10 connected with 13 and 14 to the number twenty-seven (27).

            Φ(11,13) = (114 - 10²) + 13 = 27 = 9 x 3 = 3 x 3 x 3 = 3 ^ 3

            ----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+seq       | {1}|  2 |  3 |  4 |  5 | {6}| {7}|  8 |  9 | 10 | 11 | 12 | 13 | 14 |
+----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+num       | {3}| {4}|  3 |  4 |  5 |  2 |  3 |  2 |  2 |  1 |  2 |  5 |  1 |  1 |{38}
+----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285
+seq x num |  3 |  8 |  9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}
+----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+          |-- 11 ---|              |-- 33 ---|                        |-- {27}--|
+

            Since there are no twin primes between 26² and 28² so they would goes to the rest object of 27. As you can see the formation of 69 objects from the number 29 ends in a 6 x 9 matrix centrally.

            6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 72 + 42 = 114

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            From this number 27, we can start the process by taking the initial vector of 69 as the number of objects that is originated from 10th prime = 29 so the 29th=109 objects out of the 10 objects of the central zone is actually decoded from 110 objects of 18th prime. Therefore the polarizing of 19 vs 18 by the prime hexagon should also involve 3 times 100+3=309 objects.

            liquid

            This pattern is raised up per six (6) cycles on the 18+1=19, 42+1=43 and 72-1=71. Since the members are limited to the sum of 43+71=114 so here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme.

            6 x (1 + 6 + (6 + 6)) = 6 + 36 + 72 = 42 + 72 = 43 + 71 = 114

            interpolation

            This polarity is happened per six (6) cycles by the polar of six (6) to one (1) and six (6) to seven (7) by which we finally found if this behaviour is cascaded bilaterally within the correlation between 61 as the 18th prime and 67 as the 19th prime.

            1/7 = 0,142857142857142857142857.. cycling six (6) numbers of (1,4,2,8,5,7) infinity

            image

            This curve is a polar plot of the first 20 non-trivial Riemann zeta function zeros including Gram points along the critical line ζ(1/2+t) for real values of t running from 0 to 50. The consecutive zeros have 50 red plot points between each with zeros identified by magenta concentric rings (scaled to show the relative distance between their values of t).

            20x10+ ½(16×6) + ¼(12×18) + ⅛(16×16) = 200 + 48 + 32 + 6 = 286

            RiemannZeta Zeros

            See on the left side contains of odd numbers less and equal to 19 while the right is the even number less and equal to 18. By the left side only 9 and 15 that are not primes. Consider these two (2) numbers are laid side by side as part of Fibonacci sequence on the Pascal Triangle. Thus the above curve is actually represesenting the pattern of true-prime-pairs via bilateral 9 sums.

            Fibonacci Sequence Numbers

            Meanwhile the sum of 28 and 35, which is 63, has a digital root of 6+3 = 9 and is landed precisely on the 15's cell of the prime hexagon. So the interaction with the seven (7) objects is made through the object of 36 which has the same digital root of 9.

            36® - 9® (1,2,10,47,66,73,86,102,107) - 6°(diagram) - 12® (pinned) = 36® - 27® = 9®

            default

            As you may see the correlation between each items could involve a complex geometry either by area or volume object that may lead to their tensor and gap. So we decided to assign these behaviours one by one in to a separate group of repositories.

            {10,11,12,14,15} & {26,28} = {5®} & {2®} = {7®} = {30,31,32,33,34,35,36}

            default

            As conclusion to this presentation is that the structure of those prime numbers is not happened by a coincidence. It might hard to believe if they were specifically designed to become the base algorithm on generating the human chromosomes from DNA.

            image

            By the next parts this will go much more details. Such as the generation of the said DNA from its particular atoms and molecules from the nature of universe which may bring another conclusion if it was initiated by a gap.

            ₠Quantum Project
            Copyright © 2022 All rights reserved.

            Reference:

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span2/gist09.md b/identition/span2/gist09.md new file mode 100644 index 00000000000..0a4c4ffddfd --- /dev/null +++ b/identition/span2/gist09.md @@ -0,0 +1,205 @@ +## Polar Plot + +Based on the homogeneous sorting of objects against these 114 repositories we will get the number 57 which is distributed over the pair of objects whose difference is twenty-nine (29). So everything will happen to repeat in this 29. + +***(114/2)! = 57! = 1653 » 1653 / 57 = 29*** + +``` +--------+ + | ⅓ + +--- } ⅔ + Case A | ⅓ + +--------- + | ⅓ | +-----------------+ Φ = ⅔ + | ⅓ | + +--------- + Case B | ⅓ + +--- } ⅔ + | ⅓ +--------- +``` + +By this objects pairing there would exist a zone segregation numbers (28.29) on each of the pairs. Since 10 stands as the central zone then it would be a tensor between ***29-10=19*** and ***28-10=18***. + +***9 + 19 + 29 = 28 + 29 = (10+18) + (10+19) = 57*** + +``` +P7:(142857) + + # | A | B | ∑ +------+------+------+----- + {1} | | | +------+ | | + ... | 28 | 29 | 57 +------+ | | + {57} | | | +------+------+------+----- + 58 | | | +------+ | | + ... | 29 | 28 | 57 +------+ | | + 114 | | | +------+------+------+----- + | 57 | 57 | 114 +``` + +This zone is cenralized by the _[20 objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ while the tensor of ***19 vs 18*** is polarizing the 2x11x13=286 objects out of the pairing of 11 and 13 within the _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_ and finally be composed by 20/10 = 2 numbers of 285 and 286 that having a total of 571. + +***Φ((13,12),(12,18)) = Φ(13,((19,18),(18,43)) = Φ(13,37,61) = Φ(6,12,18)th prime*** + +``` +---+-----+-----+-----+-----+ + 1 |{19} | 1 |{20} | 21 |----------------------- +---+-----+-----+-----+-----+ | + 2 | 18 | 21 | 39 | 60 |----------------- | +---+-----+-----+-----+-----+ | | + 3 | 63 | 40 | 103 |{143}|----------- | | +---+-----+-----+-----+-----+ | | | + 4 | 37 | 104 | 141 | 245 |----- | | | +---+-----+-----+-----+-----+ | | | | + 5 | 10 | 142 | 152 | 294 |-{11}|{13} |{12} |{12} |{18} +---+-----+-----+-----+-----+ | | | | + 6 | 24 | 153 |{177}| 332 |----- | | | +---+-----+-----+-----+-----+ | | | + 7 | 75 | 178 | 253 | 431 |----------- | | +---+-----+-----+-----+-----+ | | + 8 | 30 | 254 | 284 | 538 |----------------- | +---+-----+-----+-----+-----+ | + 9 | 1 | 285 | 286 |{571}|----------------------- +===+=====+=====+=====+=====+ +45 |{277}| +---+-----+ +``` + +However by the prime numbers this behaviour is not happened by the number of 57 but on the 157 as the ***19+18=37th*** prime. So on the pairing of 57 to 114 above then one of them is forced to behave as 157-57=100 which is exactly the square of 10. + +>157 is the 37th prime number, a balanced prime, because the arithmetic mean of those primes yields 157. The next prime is ***163*** and the previous prime is ***151***, with which ***157 forms a prime triplet***. _([Wikipedia](https://en.wikipedia.org/wiki/157_(number)))_ + +![](https://user-images.githubusercontent.com/36441664/100333516-42494580-3005-11eb-95a2-e7360e60b60f.jpg) + +By this square correlation between natural and prime numbers then the 571 would be separated by the 100 to 500 and 71 and finally by the form of (2,10) the 500 goes to 50 while 71 would be polarized to form 71x2=142 and 177 as shown on the table. + +***(10/2)π = 157 ⇄ (10^2)¹ + 11x7 = 177*** + +![](https://user-images.githubusercontent.com/36441664/72922749-30ad6680-3d80-11ea-92c8-73c1fa12041b.jpg) + +That is why DNA is twisted and spinning in the scope of three (3) directions in three (3) dimensions which in its entirety resembles the shape of a [trifoil](https://en.wikipedia.org/wiki/Trefoil_knot). For XX genes this lead to 1600 objects but for XY genes there are different story. + +> When a 3 × 3 × 3 cube is made of 27 unit cubes, 26 of them are viewable as the exterior layer. _([Wikipedia](https://en.wikipedia.org/wiki/26_(number)))_ + +![](https://user-images.githubusercontent.com/36441664/86853354-88e2e580-c0e0-11ea-92e4-24de95335054.gif) + +From this arrangement we get the sum of all vectors with the sequence at number 247 where via the number one (1) makes 10 connected with 13 and 14 to the number twenty-seven (27). + +***Φ(11,13) = (114 - 10²) + 13 = 27 = 9 x 3 = 3 x 3 x 3 = 3 ^ 3*** + +``` +----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ +seq | {1}| 2 | 3 | 4 | 5 | {6}| {7}| 8 | 9 | 10 | 11 | 12 | 13 | 14 | +----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ +num | {3}| {4}| 3 | 4 | 5 | 2 | 3 | 2 | 2 | 1 | 2 | 5 | 1 | 1 |{38} +----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285 +seq x num | 3 | 8 | 9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247} +----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + |-- 11 ---| |-- 33 ---| |-- {27}--| +``` + +Since there are no twin primes between [26² and 28²](https://primes.utm.edu/curios/page.php?short=26) so they would goes to the rest object of 27. As you can see the formation of 69 objects from the number 29 ends in a 6 x 9 matrix centrally. + +***6 + (6x6) + 6 x (6+6) = 6 x (6+6) + 6 + (6x6) = 72 + 42 = 114*** + +``` +The Prime Recycling ζ(s): +(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity** +----------------------+-----+-----+-----+ --- + 7 --------- 1,2:1| 1 | 30 | 40 | 71 (2,3) ‹-------------@---- | + | +-----+-----+-----+-----+ | | + | 8 ‹------ 3:2| 1 | 30 | 40 | 90 | 161 (7) ‹--- | 5¨ encapsulation + | | +-----+-----+-----+-----+ | | | + | | 6 ‹-- 4,6:3| 1 | 30 | 200 | 231 (10,11,12) ‹--|--- | | + | | | +-----+-----+-----+-----+ | | | --- + --|--|-----» 7:4| 1 | 30 | 40 | 200 | 271 (13) --› | {5®} | | + | | +-----+-----+-----+-----+ | | | + --|---› 8,9:5| 1 | 30 | 200 | 231 (14,15) ---------› | 7¨ abstraction +289 | +-----+-----+-----+-----+-----+ | | + | ----› 10:6| 20 | 5 | 10 | 70 | 90 | 195 (19) --› Φ | {6®} | + --------------------+-----+-----+-----+-----+-----+ | --- + 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | | + | +-----+-----+-----+ | | + | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism + | | +-----+-----+-----+ | | | + | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | | + | | | +-----+-----+-----+ | | --- + | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | | + | | +-----+-----+-----+ | | + | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance +329 | +-----+-----+-----+ | + | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ | + -------------------+-----+-----+ --- + 786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ | + | +-----+-----+ | + | 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class + | | +-----+-----+-----+-----+-----+ | | + | | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} | + | | | +-----+-----+-----+-----+-----+ | | --- + --|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- | + | | +-----+-----+ | | + --|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object +168 | +-----+ | +| 102 -› 29:18| 50 | 50(68) ---------> Δ18 | +----------------------+-----+ --- +``` + +From this number 27, we can start the process by taking the initial vector of 69 as the number of objects that is originated from 10th prime = 29 so the _[29th=109 objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)_ out of ***the 10 objects of the central zone*** is actually decoded from _[110 objects](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef)_ of 18th prime. Therefore the polarizing of 19 vs 18 by the prime hexagon should also involve 3 times 100+3=309 objects. + +[![liquid](https://user-images.githubusercontent.com/36441664/105412087-d0892300-5c66-11eb-9c3e-19d8652b478c.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md) + +This pattern is raised up ***per six (6) cycles*** on the ***18+1=[19](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-instance-md)***, ***42+1=[43](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-runner-md)*** and ***72-1=[71](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-grammar-md)***. Since the members are limited to the sum of ***43+71=114*** so here the bilateral way of 19 that originated by the (Δ1) is clearly the one that controls the scheme. + +***6 x (1 + 6 + (6 + 6)) = 6 + 36 + 72 = 42 + 72 = 43 + 71 = 114*** + +[![interpolation](https://user-images.githubusercontent.com/8466209/212487102-2f080804-9078-45c9-85ee-9977a36a5dbf.jpg)](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831#file-syntax-md) + +This polarity is happened per ***six (6) cycles*** by the polar of ***six (6) to one (1)*** and ***six (6) to seven (7)*** by which we finally found if this behaviour is cascaded bilaterally within the correlation between ***61*** as [the 18th prime](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef) and ***67*** as [the 19th prime](https://gist.github.com/eq19/c9bdc2bbe55f2d162535023c8d321831). + +_1/7 = 0,14_***285***_714_***285***_714_***285***_714_***285***_7.. cycling six (6) numbers of (1,4,2,8,5,7) infinity_ + +![image](https://user-images.githubusercontent.com/8466209/213899448-fedc0919-f42e-49e2-aa63-a18c8b8a5e02.png) + +This curve is a [polar plot](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) of _[the first 20](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md)_ non-trivial [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) zeros including Gram points along the critical line _[ζ(1/2+t)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-fork-md)_ for real values of t running from 0 to 50. The consecutive zeros have ***[50 red plot points](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-layers-md)*** between each with zeros identified by magenta _[concentric rings](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d)_ (scaled to show the relative distance between their values of t). + +***20x10+ ½(16×6) + ¼(12×18) + ⅛(16×16) = 200 + 48 + 32 + 6 = 286*** + +[![RiemannZeta Zeros](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) + +See on the left side contains of odd numbers less and equal to 19 while the right is the even number less and equal to 18. By the left side only ***[9 and 15](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)*** that are not primes. Consider these two (2) numbers are laid side by side as part of Fibonacci sequence on the [Pascal Triangle](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md). Thus the above curve is actually represesenting the pattern of _[true-prime-pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_ via _[bilateral 9 sums](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md)_. + +[![Fibonacci Sequence Numbers](https://user-images.githubusercontent.com/8466209/218188579-8b7abe41-3137-41fd-8620-c141a719b493.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md) + +Meanwhile the sum of ***28 and 35***, which is 63, has a digital root of 6+3 = 9 and is landed precisely on the _[15's cell](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)_ of the prime hexagon. So the interaction with the [seven (7) objects](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-bilateral-md) is made through the _[object of 36](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-default-md)_ which has the same digital root of 9. + +***36® - 9® (1,2,10,47,66,73,86,102,107) - 6°(diagram) - 12*® (pinned) = 36® - 27® = 9®** + +![default](https://user-images.githubusercontent.com/8466209/198753476-6871d03b-8d0f-4a44-805f-c9a9595268e1.png) + +As you may see the correlation between each items could involve a complex geometry either by _[area](https://gist.github.com/eq19/80c8098f16f3e6ca06893b17a02d910e)_ or _[volume](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267)_ object that may lead to their _[tensor](https://gist.github.com/eq19/765ddc69e339079a5a64b56c1d46e00f)_ and _[gap](https://gist.github.com/eq19/b9f901cda16e8a11dd24ee6b677ca288)_. So we decided to _[assign](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-portal-md)_ these behaviours one by one in to a separate group of _[repositories](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-repositories-md)_. + +***{10,11,12,14,15} & {26,28} = {5®} & {2®} = {7®} = {30,31,32,33,34,35,36}*** + +![default](https://user-images.githubusercontent.com/8466209/198408830-2d2fb1ec-79e8-431c-84d4-a911b5d3fc73.png) + +As conclusion to this presentation is that the structure of those prime numbers is not happened by a coincidence. It might hard to believe if they were specifically designed to become _the base algorithm_ on generating the human chromosomes from DNA. + +![image](https://user-images.githubusercontent.com/8466209/213899452-be32cd65-94dd-462f-bc8e-54a410be34b8.png) + +By the [next parts](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde) this will go much more details. Such as the generation of the said DNA from its particular atoms and molecules from the nature of universe which may bring another conclusion if it was _initiated by a gap_. + +**[₠Quantum Project](https://github.com/eq19)** +Copyright © 2022 All rights reserved. + +Reference: +* [Riemann Zeta](https://commons.wikimedia.org/wiki/File:RiemannZeta_Zeros.svg) +* [Mersenne Prime](https://en.wikipedia.org/wiki/Mersenne_prime) +* [The Prime Hexagon](https://www.hexspin.com/) +* [The Primes Demystified](https://www.primesdemystified.com/First1000Primes.html) diff --git a/identition/span2/index.html b/identition/span2/index.html new file mode 100644 index 00000000000..c3278e83446 --- /dev/null +++ b/identition/span2/index.html @@ -0,0 +1,34 @@ + Series Expansion (span 2) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Series Expansion (span 2)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-38 of orgs section-10 that is inherited from the spin section-2 by prime spin-66 and span-141 with the partitions as below.

            +
            +
            1. gist06.md
            2. Polar Plot
            3. The Bilateral 9 Sums
            4. gist03.md
            5. gist07.md
            6. Project Repositories
            7. gist04.md
            8. 2.5 Parsering
            9. Assigning Repositories
            +
            + + Note +
            +
            +

            To be clear, these horizons are speculations based upon numerical simulations of general relativistic field equation which are inherently non-linear and notoriously difficult to solve, so more detailed computer modeling may hold surprises for us. Also, while spacetime is well-modeled by GR, at the horizons where the curvature blows up, then so does GR and speculations about what happens at the singularities will have to wait for quantum gravity.

            +
            +

            Answer to How do infalling/outflying singularities form inside a black hole

            +
            + + Note +
            +
            +

            Only more accurate analysis on the involved spectra and on the relative brightness of the two rings, and mainly the discovery of other double rings systems, could be used to finally choose which among these two interpretations is more likely to hold. As to using Klein bottle holes to check the physical existence of other universes, it appears just a matter of time to find a double truncated spiral blurred enough to clearly show a connection with other universes. (Observing another Universe through ringholes and Klein-bottle holes - pdf)

            +
            +

            Gravitational-lensing-effect-produced-by-a-ringhole-from-a-single-luminous-source-a_Q320

            Elementary_particle_interactions svg

            Simulating physics on a quantum computer can be reduced to solving mathematical problem using quantum mechanics.

            knots1

            The spacetime diagram on the left, the magenta hyperbolae connect events of equal spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation from the origin.

            default

            Note also that the rate of convergence to infinity in this exampleshould be as the fourth root of t, which is confirmed by the graph (the fourth root of 125000 is about 19).

            +
            + + Note +
            +
            +

            Four eigenvalues going to infinity. The plot shows the eigenvalues of A + tuu>J for 0 ≤ t ≤ 125000 in red, and the eigenvalues of A − tuu>J for the same range of t in cyan

            +
            +

            Four eigenvalues going to infinity

            You can use either mklink /j or junction in Windows 10 to create junctions. Junction not only allows you to create NTFS junctions, it allows you to see if files or directories are actually reparse points. Reparse points are the mechanism on which NTFS junctions are based, and they are used by Windows' Remote Storage Service (RSS), as well as volume mount points.

            mklink /j .github C:\Users\Admin\.github
+

            mklink

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            19vs18

            default

            Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence.

            AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence (Human vs AI).

            The next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.

            33's

            This process would take place all the way to three (3) layers in a more complex way involving 114 objects generated by the sum of the above mentioned prime 71 and 43. This is what we will discuss further on how apply it in to a custom domain.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist01.html b/identition/span3/gist01.html new file mode 100644 index 00000000000..44d6d0619cd --- /dev/null +++ b/identition/span3/gist01.html @@ -0,0 +1,134 @@ + DNA Recombination · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            DNA Recombination

            This imajinary unit is the product of reciprocal complex numbers of the trivial and complex roots that goes recursively with their residual objects. By the nature such as DNA this residual is taken as genetic exchange to generate a better recombination.

            Recombination is a process that results in genetic exchange between chromosomes or regions. Recombination counteracts physical linkage between adjacent genes, thereby reducing genetic hitchhiking (Wikipedia).

            Recombination can also generate particular types of mutations if chromosomes are misaligned. Recombination involves the breakage and rejoining of two chromosomes (M and F) to produce two re-arranged chromosomes (C1 and C2).

            The result of genes results in more efficient selection, meaning that regions with higher recombination will harbor fewer detrimental mutations, more selectively favored variants, and fewer errors in replication and repair (Wikipedia).

            Consider that by the True Prime Pairs the 36 is the smallest square expressible as the sum of consecutive prime in two (2) ways of 4 (four) primes and 2 (two) primes.

            2nd identity (objects) = 500 x 2/(2+3) = 500 x 2/5 = 200 objects

            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6® by 4 primes
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6® by 2 primes --------------------
+      |  6  | 19                                            |
+ -----+-----+---------                                      |
+                                                            |
+                                                            |
+layer | node | sub |  i  |  f                               |
+------+------+-----+---------- 
+      |      |     |  1  | -----------------------   71 by 2 identities √
+      |      |  1  +-----+                        |
+      |  1   |     |  2  | (5)                    |
+      |      |-----+-----+                        |
+      |      |     |  3  |                        |
+  1   +------+  2  +-----+----                    |
+      |      |     |  4  |                        |
+      |      +-----+-----+                        |
+      |  2   |     |  5  | (7)                    |
+      |      |  3  +-----+                        |
+      |      |     |  6  |                        | 11x
+------+------+-----+-----+------      } (36)      |
+      |      |     |  7  |                        |
+      |      |  4  +-----+                        |
+      |  3   |     |  8  | (11)                   |
+      |      +-----+-----+                        |
+      |      |     |  9  |                        |
+  2   +------|  5  +-----+-----                   |
+      |      |     |  10 |                        |
+      |      |-----+-----+                        |
+      |  4   |     |  11 | (13) ------------------   71 by 4 identities √
+      |      |  6  +-----+
+      |      |     |  12 |---------------------  (72 - 2) by 1 identity √
+------+------+-----+-----+
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17)
+      |      |-----+-----+
+      |      |     |  15 |
+  3   +------+  8  +-----+-----  
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |---------------------  (72 - 4) by 1 identity √
+------|------|-----+-----+
+

            Since the position of 19 acts as the exchange base then a new recombination would be re-arranged which is resulting a linkage between 2 (two) and four (4) of prime identities aligned by the residual tensor of 71.

            (2 x 32 x 109) − (2 x 32 x 89) = 360

            layer | node | sub |  i  |  f
+------+------+-----+----------                                               ---
+      |      |     |  1  | 71 (2,3) √ ------------                            |
+      |      |  1  +-----+                        |                           |
+      |  1   |     |  2  |                        |                          (5) 
+      |      |-----+-----+                        |                           |
+      |      |     |  3  |                        |                           |
+  1   +------+  2  +-----+----                    |                          ---
+      |      |     |  4  |                        |                           |
+      |      +-----+-----+                        |                           |
+      |  2   |     |  5  |                        |                          (7) 
+      |      |  3  +-----+                        |                           |
+      |      |     |  6  |                        | {6®} √                    |
+------+------+-----+-----+------      } (36)      |                          ---
+      |      |     |  7  |                        |                           |
+      |      |  4  +-----+                        |                           |
+      |  3   |     |  8  |                        |                         (11) 
+      |      +-----+-----+                        |                           |
+      |      |     |  9  |                        |                           |
+  2   +------|  5  +-----+-----                   |                          ---
+      |      |     |  10 |                        |                           |
+      |      |-----+-----+                        |                           |
+      |  4   |     |  11 | 71 (29,30,31,32) √ ----                          (13)
+      |      |  6  +-----+                                                    |
+      |      |     |  12 | {70} (36)                                          |
+------+------+-----+-----+------------------                                 ---
+      |      |     |  13 |                                                    |
+      |      |  7  +-----+                                                    |
+      |  5   |     |  14 |                                                  (17) 
+      |      |-----+-----+                                                    |
+      |      |     |  15 |                                                    |
+  3   +------+  8  +-----+-----       } (36)                                 ---
+      |      |     |  16 |                                                    |
+      |      |-----+-----+                                                    |
+      |  6   |     |  17 | 100 (10 x 500/100)                                (19) 
+      |      |  9  +-----+                                                    |
+      |      |     |  18 | 10 x 500/100 (68)                                  |
+------|------|-----+-----+------                                             ---
+

            By the 2x25=500/10=50 and 10x10=11+89=100 which is identified from the factorization of 285+286=571 object. Meanwhile 32 is expanded to 32+36=68. So finally the tensor of 71 will be derived to 7×10=68+2=72-2=70 at the center of the scheme.

            (10th)th prime = 29th prime = 109 = 110 - 1

            layer | node | sub |  i  |  f
+------+------+-----+----------                                               ---
+      |      |     |  1  | 71 (2,3) --------------                            |
+      |      |  1  +-----+                        |                           |
+      |  1   |     |  2  |                        |                          (5) 
+      |      |-----+-----+                        |                           |
+      |      |     |  3  |                        |                           |
+  1   +------+  2  +-----+----                    |                          ---
+      |      |     |  4  |                        |                           |
+      |      +-----+-----+                        |                           |
+      |  2   |     |  5  |                        |                          (7) 
+      |      |  3  +-----+                        |                           |
+      |      |     |  6  |                        | {6®} = 11 x 30            |
+------+------+-----+-----+------      } (36)      |                          ---
+      |      |     |  7  |                        |                           |
+      |      |  4  +-----+                        |                           |
+      |  3   |     |  8  |--- 109 √ ---           | 110-1 by 1 identity √    (11) 
+      |      +-----+-----+             |          |                           |
+      |      |     |  9  |---- 69 √    | {2®} √   |  71-2 by 1 identity √     |
+  2   +------|  5  +-----+-----        |          |                          ---
+      |      |     |  10 |--- 109 √ ---           | 110-1 by 1 identity √     |
+      |      |-----+-----+                        |                           |
+      |  4   |     |  11 | 71 (29,30,31,32) ------                          (13)
+      |      |  6  +-----+                                                    |
+      |      |     |  12 |                                                    |
+------+------+-----+-----+------------------ 329 = 330 - 1 = 309 + 20        ---
+      |      |     |  13 |                                                    |
+      |      |  7  +-----+                                                    |
+      |  5   |     |  14 |                                                  (17) 
+      |      |-----+-----+                                                    |
+      |      |     |  15 |                                                    |
+  3   +------+  8  +-----+-----                                              ---
+      |      |     |  16 |                                                    |
+      |      |-----+-----+                                                    |
+      |  6   |     |  17 | 100(50)                                          (19) 
+168 √ |      |  9  +-----+                                                    |
+|     |      |     |  18 | 50(68)                                             |
+------|------|-----+-----+------                                             ---
+

            Palindromic behaviour

            The main scheme is two (2) by five (5) objects expressed by three (3) operation of addition (2+5=7), multiplication (2x5=10) and exponentiation (5²=25 and 2^5=32). Here we correlate 11's additive sums with 3960, 7920 and the first 1000 prime numbers.

            11's additive sums

            image

            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry) (Primesdemystified).

            Distribution of Perfect Squares

            Deep Symmetry

            default

            Diving deeper yet, here we show the absolute value delta differences of simple reversal sets in relation to primes 89 and 109 contextualized with the first 1000 prime numbers.

            image

            Achim Frenzel's popular scientific book, which is illustrated with numerous graphics, is treated as an approach that should definitely be further researched by science. In addition, as a future-oriented project, the book is intended to lead to an interdisciplinary doctorate and therefore refers to its own website as an Internet discussion platform.

            An Independent claim is also included for the localization and determination of (I), or their material structures, by graphical representation of base sequences on various media, based on the new assignments and the derived vibrations and amplitudes (Open Patent Data DE19991049059).

            See on the left side contains of odd numbers less and equal to 19 while the right is the even number less and equal to 18. By the left side only 9 and 15 that are not primes

            Since this bilateral sums of 9 are laid on the prime spiral sieve then the symmetrical behaviour will occur by three (3) rotations of 360. By the 20 objects of 1st prime identity, this 360 will then be separated to 3x100=300 and 3x20=60.

            89^2 - 1 = 7921 - 1 = 7920 = 22 x 360 = 66 x 120

            Deep Symmetries

            By the 500 objects of the 2nd prime identity, the 300 goes to the 29 while the rest of 200 goes as 3rd prime identity to the 89. So the involved objects on the both sides are 300+29=329 and 200+89=289 thus the total will be 329+289=618 objects.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist02.html b/identition/span3/gist02.html new file mode 100644 index 00000000000..2b5f4d68d21 --- /dev/null +++ b/identition/span3/gist02.html @@ -0,0 +1,16 @@ + gist02.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

             |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  ° |ΔΔΔΔ  ΦΦ | •   ΔΔ   ΔΔ   ¤ | •   ΔΔ   ΦΦΦ    Φ   ΦΦ  ¤¤¤¤|  •   ΔΔ   ΦΦΦ    Φ   ¤¤   ΦΦ |  
+ 
+ |----- 102  ---|-----  66  ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -|
+ |---2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------|
+ |--------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------|
+ |--------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----|
+
+

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist02.md b/identition/span3/gist02.md new file mode 100644 index 00000000000..f909576d22b --- /dev/null +++ b/identition/span3/gist02.md @@ -0,0 +1,24 @@ +[![default](https://user-images.githubusercontent.com/8466209/195963923-0796217c-7a87-4b2d-ba93-f47465304c03.png)](https://www.nausetschools.org/cms/lib/MA02212418/Centricity/Domain/204/Linkage%20Map%20Worksheet%20Genetics%202017.pdf) + +``` + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | ° |ΔΔΔΔ ΦΦ | • ΔΔ ΔΔ ¤ | • ΔΔ ΦΦΦ Φ ΦΦ ¤¤¤¤| • ΔΔ ΦΦΦ Φ ¤¤ ΦΦ | + + |----- 102 ---|----- 66 ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -| + |---2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------| + |--------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------| + |--------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----| + +``` + +[![default](https://user-images.githubusercontent.com/8466209/198915985-f3280a15-1ca4-45bf-855c-ac277fa2ca2e.png)](https://www.hexspin.com/defining-the-prime-hexagon/) + +![default](https://user-images.githubusercontent.com/8466209/198837916-57284efa-bdb7-42d8-80f6-584b3c3bbd19.png) + diff --git a/identition/span3/gist03.html b/identition/span3/gist03.html new file mode 100644 index 00000000000..3947bcc516f --- /dev/null +++ b/identition/span3/gist03.html @@ -0,0 +1 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default default default

            default default default

            default

            We color-code the six hexagons, identifying patterns in key number sequences, including the Fibonacci sequence, powers of two and three, and power of pi. For the series of consecutive powers of pi, we have found that **no two fall within the same six-cell hexagon**. We have computed this for pi^32, which has less than a 1/400 chance of occurring randomly.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist03.md b/identition/span3/gist03.md new file mode 100644 index 00000000000..91ea480d44e --- /dev/null +++ b/identition/span3/gist03.md @@ -0,0 +1,12 @@ +![default](https://user-images.githubusercontent.com/8466209/198918182-0d350710-64b3-48de-bd7e-a45ae4390380.png) +![default](https://user-images.githubusercontent.com/8466209/198918275-c88e4875-938e-4f18-b1ae-696026f9fd30.png) +![default](https://user-images.githubusercontent.com/8466209/198918564-8441195d-e47b-45e2-8e87-6d4cf8f60a84.png) + +![default](https://user-images.githubusercontent.com/8466209/198918345-a1997048-4993-4934-b094-95a297992ed4.png) +![default](https://user-images.githubusercontent.com/8466209/198918641-e33a7d60-d10a-40a4-bedf-af07b1d57d13.png) +![default](https://user-images.githubusercontent.com/8466209/198918951-0fd19fcd-59e4-444a-8774-dcd39f3044c1.png) + +[![default](https://user-images.githubusercontent.com/8466209/198917703-9e333c1b-d74d-4862-9f26-4e3f58509827.png)](https://github.com/kaustubhcs/prime-hexagon) + +We color-code the six hexagons, identifying patterns in key number sequences, including the Fibonacci sequence, powers of two and three, and power of pi. For the series of consecutive powers of pi, we have found that *****no two fall within the same six-cell hexagon*****. We have computed this for pi^32, which has less than a 1/400 chance of occurring randomly. + diff --git a/identition/span3/gist04.html b/identition/span3/gist04.html new file mode 100644 index 00000000000..dd237823409 --- /dev/null +++ b/identition/span3/gist04.html @@ -0,0 +1,169 @@ + Mass vs Gap (Δ) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Mass vs Gap (Δ)

            This section will be the last one of our presentation of 18th prime identity. Here we are going to explain one more item that is still open or undiscussed which is about what the 77 objects are going to do within the 19 vs 18 Scenario.

            15 + 35 + 28 = 15 + 63 = 78 = 77 + 1

            ---+-----+-----
+ 1 | 1   | 15
+---+-----+-----
+ 2 | 16  | 25
+---+-----+-----
+ 3 | 26  | 50
+---+-----+-----
+ 4 | 51  | 84
+---+-----+-----
+ 5 | 85  | 99
+---+-----+-----
+
            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            In many ways, a black hole acts like an ideal black body, as it reflects no light. Here is an animated simulation of a Schwarzschild black hole with a galaxy passing behind. Around the time of alignment, extreme gravitational lensing of the galaxy is observed.

            black hole

                            largest part=21 → 11+13+12=36 →  MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   ↓
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----
+---+-----+-----+-----+-----+                   ↓     |
+ 2 | 18  | 21  | 39  | 60  |-------------------      |
+---+-----+-----+-----+-----+                   |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |
+---+-----+-----+-----+-----+             |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |
+---+-----+-----+-----+-----+       |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |
+---+-----+-----+-----+-----+             |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |
+---+-----+-----+-----+-----+                   |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------      |
+---+-----+-----+-----+-----+                   ↓     |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----
+===+=====+=====+=====+=====+                   ↓
+45 | 277 |                      ← 11+13+12=36 ←  MEC30
+---+-----+                                     |
+ ↑
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            According to the observations made by NASA, Astronomers have uncovered TON 618 as the record breaking supermassive black hole, weighing 66 trillion and brilliantly as 140 trillion times that of the Sun, making it one of the brightest object in the Universe.

            default

            If the statement that it is indeed located at the center of our universe then the said black hole would behave as the exchange position between twin (2) universes. This would for sure strengthen the syntax algorithm of our implementation.

            7 x 11 = 77 = 99 - 22 = 11 x (9 -2)

              #8  |------- 5® --------|------------ 7® --------------|
+      | 1 |-------------- 77 = 4² + 5² + 6² -------------|
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ user | 7 | - | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+------+---|---+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+        Δ | Δ             |                      Δ  |   Δ
+       Φ17|Φ29            |                    96-99|  100 - 123 ({24})
+          |--- A,T,G,C ---|                         |  └── 100 - 103 (4x) » 100
+          Δ    2x2 = 4x   |-------  2x3 = 6x -------|  └── 104 - 109 (6x) » 30
+         {98}                                       |  └── 110 - 123 (14x)» 70
+
+
            Direction:
+- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.
+- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.
+- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.
+ 
+Conclution:
+- All of the other primes than 2 is 1 less than the number n times the number of 2. 
+- Those Mersenne primes is generated as 1 less than the power n of the number of 2. 
+- Thus they will conseqently be carried out by the same scheme of this number of 2.
+

            Perceptually, everything is separate and finite. But actually, everything is connected and infinite. It is this infinite connection, despite our limited finite perceptions, that makes us one with the cosmos.

            Primes Platform

            Each result goes to the 9th object of prime 67 which is 19th prime. This mass gap of (Δ > 0) is actually the quantum way of our algorithm which is discused in details by the 19th prime identity.

            So when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming bilateral 9 sum which facilitate them to finaly generate 1000 primes.

            1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+                
+-----+-----+-----+-----+-----+     -----------------------------------------------
+{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |
+-----+-----+-----+-----+-----+                                               |
+ {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone
+     +-----+-----+-----+-----+                                               |
+ {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |
+     +-----+-----+-----+                                               -----------
+ {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |
+ ----+-----+-----+-----+-----+                                               |
+  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone
+     +-----+-----+-----+-----+                                               |
+  {8}|23,25|25,27|27,29| 18                                                  |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+     |  1     2     3  |   4     5     6 |   7     8      9  |
+     |------ 29' ------|--------------- 139' ----------------|
+     |------ 102¨ -----|---------------  66¨ ----------------|
+

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row forming the Primes Platform. Thus we got 109 objects including for the 7 rows back to the original stage.

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+Sequence:
+ By the next layer the 89² will become 89 and 5 become 5² or 25.
+ This 89 and 25 are in the same layer with total of 114 or prime 619
+ So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            The above is observed following the W0 (assumptions of relativistic quantum mechanics) for the Existence and Mass Gap which transform under the homogeneous group as a four-vector and has a mass gap Δ > 0.

            Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R^4 and has a mass gap Δ > 0 (Wikipedia).

            image origin action

            default

            runner

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist05.html b/identition/span3/gist05.html new file mode 100644 index 00000000000..fb5aff625c2 --- /dev/null +++ b/identition/span3/gist05.html @@ -0,0 +1,594 @@ + Container-Optimized · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Container-Optimized

            $ cat /etc/os-release
+
+NAME="Container-Optimized OS"
+ID=cos
+PRETTY_NAME="Container-Optimized OS from Google"
+HOME_URL="https://cloud.google.com/container-optimized-os/docs"
+BUG_REPORT_URL="https://cloud.google.com/container-optimized-os/docs/resources/support-policy#contact_us"
+GOOGLE_METRICS_PRODUCT_ID=26
+GOOGLE_CRASH_ID=Lakitu
+KERNEL_COMMIT_ID=4c0ef99fbc74bd4a4dce8851652be68038bec83e
+VERSION=105
+VERSION_ID=105
+BUILD_ID=17412.101.4
+
            Pipe to sort -V for sorted output. Ex: to see all executables in your PATH on your system, and all aliases, all sorted, run: compgen -c sortsee all executables in your PATH 
            $ find ${PATH//:/ } -maxdepth 1 -executable | sort
+
+find: ‘/usr/local/bin': No such file or directory
+find: ‘/opt/bin': No such file or directory
+/bin
+/bin/attr
+/bin/basename
+/bin/bash
+/bin/bunzip2
+/bin/bzcat
+/bin/bzip2
+/bin/cat
+/bin/chacl
+/bin/chgrp
+/bin/chmod
+/bin/chown
+/bin/chroot
+/bin/cp
+/bin/cut
+/bin/dash
+/bin/date
+/bin/dd
+/bin/df
+/bin/dir
+/bin/dirname
+/bin/dmesg
+/bin/dnsdomainname
+/bin/du
+/bin/echo
+/bin/egrep
+/bin/env
+/bin/expr
+/bin/false
+/bin/fgrep
+/bin/findmnt
+/bin/getfacl
+/bin/getfattr
+/bin/getsubids
+/bin/grep
+/bin/groups
+/bin/gsed
+/bin/gunzip
+/bin/gzip
+/bin/head
+/bin/hostname
+/bin/ifconfig
+/bin/ip
+/bin/keyctl
+/bin/kill
+/bin/kmod
+/bin/ln
+/bin/login
+/bin/ls
+/bin/lsblk
+/bin/lsmod
+/bin/mkdir
+/bin/mkfifo
+/bin/mknod
+/bin/mktemp
+/bin/modinfo
+/bin/more
+/bin/mount
+/bin/mountpoint
+/bin/mv
+/bin/nano
+/bin/netstat
+/bin/ps
+/bin/pwd
+/bin/rbash
+/bin/readlink
+/bin/rm
+/bin/rmdir
+/bin/rnano
+/bin/route
+/bin/run-parts
+/bin/sed
+/bin/seq
+/bin/setfacl
+/bin/setfattr
+/bin/sh
+/bin/sleep
+/bin/sort
+/bin/stty
+/bin/su
+/bin/sync
+/bin/tail
+/bin/tar
+/bin/tempfile
+/bin/touch
+/bin/tr
+/bin/true
+/bin/tty
+/bin/umount
+/bin/uname
+/bin/vdir
+/bin/wc
+/bin/wdctl
+/bin/yes
+/bin/zcat
+/usr/bin
+/usr/bin/2to3
+/usr/bin/2to3-3.8
+/usr/bin/[
+/usr/bin/arch
+/usr/bin/argon2
+/usr/bin/aulast
+/usr/bin/aulastlog
+/usr/bin/ausyscall
+/usr/bin/auvirt
+/usr/bin/awk
+/usr/bin/b2sum
+/usr/bin/base32
+/usr/bin/base64
+/usr/bin/basename
+/usr/bin/basenc
+/usr/bin/bashbug
+/usr/bin/brotli
+/usr/bin/bsdcat
+/usr/bin/bsdcpio
+/usr/bin/bsdtar
+/usr/bin/busctl
+/usr/bin/bzcmp
+/usr/bin/bzdiff
+/usr/bin/bzegrep
+/usr/bin/bzfgrep
+/usr/bin/bzgrep
+/usr/bin/bzip2recover
+/usr/bin/bzless
+/usr/bin/bzmore
+/usr/bin/c_rehash
+/usr/bin/cal
+/usr/bin/captest
+/usr/bin/captoinfo
+/usr/bin/cbfstool
+/usr/bin/cbmem
+/usr/bin/cgpt
+/usr/bin/chage
+/usr/bin/chardetect
+/usr/bin/chattr
+/usr/bin/chcon
+/usr/bin/chfn
+/usr/bin/chmem
+/usr/bin/choom
+/usr/bin/chromeos-pgmem
+/usr/bin/chromeos-tpm-recovery
+/usr/bin/chronyc
+/usr/bin/chroot
+/usr/bin/chrt
+/usr/bin/chsh
+/usr/bin/cis_scanner
+/usr/bin/cksum
+/usr/bin/clear
+/usr/bin/cloud-id
+/usr/bin/cloud-init
+/usr/bin/cloud-init-per
+/usr/bin/cmp
+/usr/bin/col
+/usr/bin/colcrt
+/usr/bin/colrm
+/usr/bin/column
+/usr/bin/comm
+/usr/bin/compile_et
+/usr/bin/containerd
+/usr/bin/containerd-shim
+/usr/bin/containerd-shim-runc-v1
+/usr/bin/containerd-shim-runc-v2
+/usr/bin/containerd-stress
+/usr/bin/core2md
+/usr/bin/coredumpctl
+/usr/bin/coreutils
+/usr/bin/cos-extensions
+/usr/bin/crictl
+/usr/bin/cros_installer
+/usr/bin/crosid
+/usr/bin/crossystem
+/usr/bin/csplit
+/usr/bin/ctr
+/usr/bin/curl
+/usr/bin/cut
+/usr/bin/cvtsudoers
+/usr/bin/dbus-cleanup-sockets
+/usr/bin/dbus-daemon
+/usr/bin/dbus-launch
+/usr/bin/dbus-monitor
+/usr/bin/dbus-run-session
+/usr/bin/dbus-send
+/usr/bin/dbus-test-tool
+/usr/bin/dbus-update-activation-environment
+/usr/bin/dbus-uuidgen
+/usr/bin/dev_debug_vboot
+/usr/bin/diff
+/usr/bin/diff-highlight
+/usr/bin/diff3
+/usr/bin/dir
+/usr/bin/dircolors
+/usr/bin/dirname
+/usr/bin/docker
+/usr/bin/docker-containerd
+/usr/bin/docker-containerd-shim
+/usr/bin/docker-credential-gcr
+/usr/bin/docker-init
+/usr/bin/docker-proxy
+/usr/bin/docker-runc
+/usr/bin/dockerd
+/usr/bin/du
+/usr/bin/dumpRSAPublicKey
+/usr/bin/dump_fmap
+/usr/bin/dump_kernel_config
+/usr/bin/dumpsexp
+/usr/bin/easy_install
+/usr/bin/eject
+/usr/bin/elogtool
+/usr/bin/enable_dev_usb_boot
+/usr/bin/env
+/usr/bin/event_rpcgen.py
+/usr/bin/ex
+/usr/bin/expand
+/usr/bin/expiry
+/usr/bin/expr
+/usr/bin/factor
+/usr/bin/faillog
+/usr/bin/fallocate
+/usr/bin/filan
+/usr/bin/file
+/usr/bin/filecap
+/usr/bin/fincore
+/usr/bin/find
+/usr/bin/flock
+/usr/bin/fluent-bit
+/usr/bin/fmt
+/usr/bin/fold
+/usr/bin/free
+/usr/bin/ftdi_eeprom
+/usr/bin/fusermount
+/usr/bin/futility
+/usr/bin/gapplication
+/usr/bin/gbb_utility
+/usr/bin/gdbm_dump
+/usr/bin/gdbm_load
+/usr/bin/gdbmtool
+/usr/bin/gdbus
+/usr/bin/getopt
+/usr/bin/gfind
+/usr/bin/gio
+/usr/bin/gio-querymodules
+/usr/bin/git
+/usr/bin/git-cvsserver
+/usr/bin/git-receive-pack
+/usr/bin/git-shell
+/usr/bin/git-upload-archive
+/usr/bin/git-upload-pack
+/usr/bin/glib-compile-resources
+/usr/bin/glib-compile-schemas
+/usr/bin/glib-gettextize
+/usr/bin/gobject-query
+/usr/bin/google_authorized_keys
+/usr/bin/google_authorized_keys_sk
+/usr/bin/google_guest_agent
+/usr/bin/google_metadata_script_runner
+/usr/bin/google_osconfig_agent
+/usr/bin/google_oslogin_nss_cache
+/usr/bin/gpasswd
+/usr/bin/gpg-error
+/usr/bin/gsettings
+/usr/bin/gss-client
+/usr/bin/gtester
+/usr/bin/gxargs
+/usr/bin/gzexe
+/usr/bin/head
+/usr/bin/hexdump
+/usr/bin/hmac256
+/usr/bin/hostid
+/usr/bin/hostnamectl
+/usr/bin/id
+/usr/bin/idle
+/usr/bin/import-tars
+/usr/bin/infocmp
+/usr/bin/infotocap
+/usr/bin/install
+/usr/bin/inteltool
+/usr/bin/ionice
+/usr/bin/ipcmk
+/usr/bin/ipcrm
+/usr/bin/ipcs
+/usr/bin/iptables-xml
+/usr/bin/irqtop
+/usr/bin/join
+/usr/bin/journalctl
+/usr/bin/jq
+/usr/bin/jsondiff
+/usr/bin/jsonpatch
+/usr/bin/jsonpointer
+/usr/bin/jsonschema
+/usr/bin/kdestroy
+/usr/bin/kernel-install
+/usr/bin/kinit
+/usr/bin/klist
+/usr/bin/kpasswd
+/usr/bin/kubectl
+/usr/bin/kubelet
+/usr/bin/last
+/usr/bin/lastb
+/usr/bin/lastlog
+/usr/bin/less
+/usr/bin/lessecho
+/usr/bin/lesskey
+/usr/bin/lesspipe
+/usr/bin/line
+/usr/bin/link
+/usr/bin/logger
+/usr/bin/loginctl
+/usr/bin/logname
+/usr/bin/look
+/usr/bin/lsattr
+/usr/bin/lscpu
+/usr/bin/lsipc
+/usr/bin/lsirq
+/usr/bin/lslocks
+/usr/bin/lslogins
+/usr/bin/lsmem
+/usr/bin/lsns
+/usr/bin/lsof
+/usr/bin/lz4
+/usr/bin/lz4c
+/usr/bin/lz4cat
+/usr/bin/lzcat
+/usr/bin/lzcmp
+/usr/bin/lzdiff
+/usr/bin/lzegrep
+/usr/bin/lzfgrep
+/usr/bin/lzgrep
+/usr/bin/lzless
+/usr/bin/lzma
+/usr/bin/lzmadec
+/usr/bin/lzmainfo
+/usr/bin/lzmore
+/usr/bin/mawk
+/usr/bin/mcookie
+/usr/bin/md5sum
+/usr/bin/metrics_client
+/usr/bin/mk_cmds
+/usr/bin/mkfifo
+/usr/bin/mktemp
+/usr/bin/mpicalc
+/usr/bin/namei
+/usr/bin/nc
+/usr/bin/netcap
+/usr/bin/nettle-hash
+/usr/bin/nettle-lfib-stream
+/usr/bin/nettle-pbkdf2
+/usr/bin/networkctl
+/usr/bin/newgidmap
+/usr/bin/newgrp
+/usr/bin/newuidmap
+/usr/bin/nice
+/usr/bin/nl
+/usr/bin/nohup
+/usr/bin/nproc
+/usr/bin/nsenter
+/usr/bin/numfmt
+/usr/bin/nvramtool
+/usr/bin/od
+/usr/bin/oomctl
+/usr/bin/openssl
+/usr/bin/passwd
+/usr/bin/paste
+/usr/bin/pathchk
+/usr/bin/pcre2grep
+/usr/bin/pcre2test
+/usr/bin/pcregrep
+/usr/bin/pcretest
+/usr/bin/perf
+/usr/bin/perfetto
+/usr/bin/pg
+/usr/bin/pgrep
+/usr/bin/pidof
+/usr/bin/pigz
+/usr/bin/pinky
+/usr/bin/pkcs1-conv
+/usr/bin/pkill
+/usr/bin/pmap
+/usr/bin/portablectl
+/usr/bin/pr
+/usr/bin/printenv
+/usr/bin/printf
+/usr/bin/prlimit
+/usr/bin/procan
+/usr/bin/protoc-gen-go
+/usr/bin/protoc-gen-go-grpc
+/usr/bin/pscap
+/usr/bin/ptx
+/usr/bin/pv
+/usr/bin/pwdx
+/usr/bin/pwqcheck
+/usr/bin/pwqfilter
+/usr/bin/pwqgen
+/usr/bin/pydoc
+/usr/bin/pydoc3.8
+/usr/bin/pyjwt
+/usr/bin/pyserial-miniterm
+/usr/bin/pyserial-ports
+/usr/bin/python
+/usr/bin/python-exec2c
+/usr/bin/python3
+/usr/bin/python3.8
+/usr/bin/pyvenv
+/usr/bin/readlink
+/usr/bin/realpath
+/usr/bin/rename
+/usr/bin/renice
+/usr/bin/reset
+/usr/bin/resolvectl
+/usr/bin/rev
+/usr/bin/rootdev
+/usr/bin/rsync
+/usr/bin/rsync-ssl
+/usr/bin/runc
+/usr/bin/runcon
+/usr/bin/rview
+/usr/bin/rvim
+/usr/bin/scmp_sys_resolver
+/usr/bin/scp
+/usr/bin/script
+/usr/bin/scriptlive
+/usr/bin/scriptreplay
+/usr/bin/sdiff
+/usr/bin/seq
+/usr/bin/setsid
+/usr/bin/setterm
+/usr/bin/sexp-conv
+/usr/bin/sftp
+/usr/bin/sg
+/usr/bin/sha1sum
+/usr/bin/sha224sum
+/usr/bin/sha256sum
+/usr/bin/sha384sum
+/usr/bin/sha512sum
+/usr/bin/shlibsign
+/usr/bin/shred
+/usr/bin/shuf
+/usr/bin/slabtop
+/usr/bin/sleep
+/usr/bin/smbinfo
+/usr/bin/socat
+/usr/bin/sort
+/usr/bin/sos
+/usr/bin/sos-collector
+/usr/bin/sosreport
+/usr/bin/split
+/usr/bin/ssh
+/usr/bin/ssh-add
+/usr/bin/ssh-agent
+/usr/bin/ssh-copy-id
+/usr/bin/ssh-keygen
+/usr/bin/ssh-keyscan
+/usr/bin/stat
+/usr/bin/stdbuf
+/usr/bin/sudo
+/usr/bin/sudoedit
+/usr/bin/sudoreplay
+/usr/bin/sum
+/usr/bin/superiotool
+/usr/bin/systemctl
+/usr/bin/systemd-analyze
+/usr/bin/systemd-ask-password
+/usr/bin/systemd-cat
+/usr/bin/systemd-cgls
+/usr/bin/systemd-cgtop
+/usr/bin/systemd-creds
+/usr/bin/systemd-delta
+/usr/bin/systemd-detect-virt
+/usr/bin/systemd-dissect
+/usr/bin/systemd-escape
+/usr/bin/systemd-id128
+/usr/bin/systemd-inhibit
+/usr/bin/systemd-machine-id-setup
+/usr/bin/systemd-mount
+/usr/bin/systemd-notify
+/usr/bin/systemd-nspawn
+/usr/bin/systemd-path
+/usr/bin/systemd-repart
+/usr/bin/systemd-resolve
+/usr/bin/systemd-run
+/usr/bin/systemd-socket-activate
+/usr/bin/systemd-stdio-bridge
+/usr/bin/systemd-sysext
+/usr/bin/systemd-tmpfiles
+/usr/bin/systemd-tty-ask-password-agent
+/usr/bin/systemd-umount
+/usr/bin/tabs
+/usr/bin/tac
+/usr/bin/tail
+/usr/bin/taskset
+/usr/bin/tee
+/usr/bin/test
+/usr/bin/tic
+/usr/bin/timedatectl
+/usr/bin/timeout
+/usr/bin/tini
+/usr/bin/tload
+/usr/bin/toe
+/usr/bin/toolbox
+/usr/bin/top
+/usr/bin/touch
+/usr/bin/tpm-nvsize
+/usr/bin/tpmc
+/usr/bin/tput
+/usr/bin/tr
+/usr/bin/trace
+/usr/bin/traced
+/usr/bin/traced_probes
+/usr/bin/truncate
+/usr/bin/tset
+/usr/bin/tsort
+/usr/bin/tty
+/usr/bin/udevadm
+/usr/bin/ul
+/usr/bin/ulockmgr_server
+/usr/bin/uname
+/usr/bin/unexpand
+/usr/bin/uniq
+/usr/bin/unlink
+/usr/bin/unlz4
+/usr/bin/unlzma
+/usr/bin/unpigz
+/usr/bin/unshare
+/usr/bin/unxz
+/usr/bin/update_engine_client
+/usr/bin/uptime
+/usr/bin/userdbctl
+/usr/bin/users
+/usr/bin/utmpdump
+/usr/bin/uuidgen
+/usr/bin/uuidparse
+/usr/bin/vbutil_firmware
+/usr/bin/vbutil_kernel
+/usr/bin/vbutil_key
+/usr/bin/vbutil_keyblock
+/usr/bin/vdir
+/usr/bin/verity
+/usr/bin/vi
+/usr/bin/view
+/usr/bin/vim
+/usr/bin/vimdiff
+/usr/bin/vmstat
+/usr/bin/w
+/usr/bin/watch
+/usr/bin/wc
+/usr/bin/wget
+/usr/bin/whereis
+/usr/bin/which
+/usr/bin/who
+/usr/bin/whoami
+/usr/bin/x86_64-cros-linux-gnu-gio-querymodules
+/usr/bin/xargs
+/usr/bin/xmlcatalog
+/usr/bin/xmllint
+/usr/bin/xmlwf
+/usr/bin/xxd
+/usr/bin/xz
+/usr/bin/xzcat
+/usr/bin/xzcmp
+/usr/bin/xzdec
+/usr/bin/xzdiff
+/usr/bin/xzegrep
+/usr/bin/xzfgrep
+/usr/bin/xzgrep
+/usr/bin/xzless
+/usr/bin/xzmore
+/usr/bin/yat2m
+/usr/bin/yes
+/usr/bin/zcmp
+/usr/bin/zdiff
+/usr/bin/zegrep
+/usr/bin/zfgrep
+/usr/bin/zforce
+/usr/bin/zgrep
+/usr/bin/zless
+/usr/bin/zmore
+/usr/bin/znew
+

            default

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist05.md b/identition/span3/gist05.md new file mode 100644 index 00000000000..34a470b63a1 --- /dev/null +++ b/identition/span3/gist05.md @@ -0,0 +1,612 @@ +## Container-Optimized + +``` +$ cat /etc/os-release + +NAME="Container-Optimized OS" +ID=cos +PRETTY_NAME="Container-Optimized OS from Google" +HOME_URL="https://cloud.google.com/container-optimized-os/docs" +BUG_REPORT_URL="https://cloud.google.com/container-optimized-os/docs/resources/support-policy#contact_us" +GOOGLE_METRICS_PRODUCT_ID=26 +GOOGLE_CRASH_ID=Lakitu +KERNEL_COMMIT_ID=4c0ef99fbc74bd4a4dce8851652be68038bec83e +VERSION=105 +VERSION_ID=105 +BUILD_ID=17412.101.4 +``` + +Pipe to sort -V for sorted output. Ex: to see all executables in your PATH on your system, and all aliases, all sorted, run: compgen -c | sortsee all executables in your PATH + +``` +$ find ${PATH//:/ } -maxdepth 1 -executable | sort + +find: ‘/usr/local/bin’: No such file or directory +find: ‘/opt/bin’: No such file or directory +/bin +/bin/attr +/bin/basename +/bin/bash +/bin/bunzip2 +/bin/bzcat +/bin/bzip2 +/bin/cat +/bin/chacl +/bin/chgrp +/bin/chmod +/bin/chown +/bin/chroot +/bin/cp +/bin/cut +/bin/dash +/bin/date +/bin/dd +/bin/df +/bin/dir +/bin/dirname +/bin/dmesg +/bin/dnsdomainname +/bin/du +/bin/echo +/bin/egrep +/bin/env +/bin/expr +/bin/false +/bin/fgrep +/bin/findmnt +/bin/getfacl +/bin/getfattr +/bin/getsubids +/bin/grep +/bin/groups +/bin/gsed +/bin/gunzip +/bin/gzip +/bin/head +/bin/hostname +/bin/ifconfig +/bin/ip +/bin/keyctl +/bin/kill +/bin/kmod +/bin/ln +/bin/login +/bin/ls +/bin/lsblk +/bin/lsmod +/bin/mkdir +/bin/mkfifo +/bin/mknod +/bin/mktemp +/bin/modinfo +/bin/more +/bin/mount +/bin/mountpoint +/bin/mv +/bin/nano +/bin/netstat +/bin/ps +/bin/pwd +/bin/rbash +/bin/readlink +/bin/rm +/bin/rmdir +/bin/rnano +/bin/route +/bin/run-parts +/bin/sed +/bin/seq +/bin/setfacl +/bin/setfattr +/bin/sh +/bin/sleep +/bin/sort +/bin/stty +/bin/su +/bin/sync +/bin/tail +/bin/tar +/bin/tempfile +/bin/touch +/bin/tr +/bin/true +/bin/tty +/bin/umount +/bin/uname +/bin/vdir +/bin/wc +/bin/wdctl +/bin/yes +/bin/zcat +/usr/bin +/usr/bin/2to3 +/usr/bin/2to3-3.8 +/usr/bin/[ +/usr/bin/arch +/usr/bin/argon2 +/usr/bin/aulast +/usr/bin/aulastlog +/usr/bin/ausyscall +/usr/bin/auvirt +/usr/bin/awk +/usr/bin/b2sum +/usr/bin/base32 +/usr/bin/base64 +/usr/bin/basename +/usr/bin/basenc +/usr/bin/bashbug +/usr/bin/brotli +/usr/bin/bsdcat +/usr/bin/bsdcpio +/usr/bin/bsdtar +/usr/bin/busctl +/usr/bin/bzcmp +/usr/bin/bzdiff +/usr/bin/bzegrep +/usr/bin/bzfgrep +/usr/bin/bzgrep +/usr/bin/bzip2recover +/usr/bin/bzless +/usr/bin/bzmore +/usr/bin/c_rehash +/usr/bin/cal +/usr/bin/captest +/usr/bin/captoinfo +/usr/bin/cbfstool +/usr/bin/cbmem +/usr/bin/cgpt +/usr/bin/chage +/usr/bin/chardetect +/usr/bin/chattr +/usr/bin/chcon +/usr/bin/chfn +/usr/bin/chmem +/usr/bin/choom +/usr/bin/chromeos-pgmem +/usr/bin/chromeos-tpm-recovery +/usr/bin/chronyc +/usr/bin/chroot +/usr/bin/chrt +/usr/bin/chsh +/usr/bin/cis_scanner +/usr/bin/cksum +/usr/bin/clear +/usr/bin/cloud-id +/usr/bin/cloud-init +/usr/bin/cloud-init-per +/usr/bin/cmp +/usr/bin/col +/usr/bin/colcrt +/usr/bin/colrm +/usr/bin/column +/usr/bin/comm +/usr/bin/compile_et +/usr/bin/containerd +/usr/bin/containerd-shim +/usr/bin/containerd-shim-runc-v1 +/usr/bin/containerd-shim-runc-v2 +/usr/bin/containerd-stress +/usr/bin/core2md +/usr/bin/coredumpctl +/usr/bin/coreutils +/usr/bin/cos-extensions +/usr/bin/crictl +/usr/bin/cros_installer +/usr/bin/crosid +/usr/bin/crossystem +/usr/bin/csplit +/usr/bin/ctr +/usr/bin/curl +/usr/bin/cut +/usr/bin/cvtsudoers +/usr/bin/dbus-cleanup-sockets +/usr/bin/dbus-daemon +/usr/bin/dbus-launch +/usr/bin/dbus-monitor +/usr/bin/dbus-run-session +/usr/bin/dbus-send +/usr/bin/dbus-test-tool +/usr/bin/dbus-update-activation-environment +/usr/bin/dbus-uuidgen +/usr/bin/dev_debug_vboot +/usr/bin/diff +/usr/bin/diff-highlight +/usr/bin/diff3 +/usr/bin/dir +/usr/bin/dircolors +/usr/bin/dirname +/usr/bin/docker +/usr/bin/docker-containerd +/usr/bin/docker-containerd-shim +/usr/bin/docker-credential-gcr +/usr/bin/docker-init +/usr/bin/docker-proxy +/usr/bin/docker-runc +/usr/bin/dockerd +/usr/bin/du +/usr/bin/dumpRSAPublicKey +/usr/bin/dump_fmap +/usr/bin/dump_kernel_config +/usr/bin/dumpsexp +/usr/bin/easy_install +/usr/bin/eject +/usr/bin/elogtool +/usr/bin/enable_dev_usb_boot +/usr/bin/env +/usr/bin/event_rpcgen.py +/usr/bin/ex +/usr/bin/expand +/usr/bin/expiry +/usr/bin/expr +/usr/bin/factor +/usr/bin/faillog +/usr/bin/fallocate +/usr/bin/filan +/usr/bin/file +/usr/bin/filecap +/usr/bin/fincore +/usr/bin/find +/usr/bin/flock +/usr/bin/fluent-bit +/usr/bin/fmt +/usr/bin/fold +/usr/bin/free +/usr/bin/ftdi_eeprom +/usr/bin/fusermount +/usr/bin/futility +/usr/bin/gapplication +/usr/bin/gbb_utility +/usr/bin/gdbm_dump +/usr/bin/gdbm_load +/usr/bin/gdbmtool +/usr/bin/gdbus +/usr/bin/getopt +/usr/bin/gfind +/usr/bin/gio +/usr/bin/gio-querymodules +/usr/bin/git +/usr/bin/git-cvsserver +/usr/bin/git-receive-pack +/usr/bin/git-shell +/usr/bin/git-upload-archive +/usr/bin/git-upload-pack +/usr/bin/glib-compile-resources +/usr/bin/glib-compile-schemas +/usr/bin/glib-gettextize +/usr/bin/gobject-query +/usr/bin/google_authorized_keys +/usr/bin/google_authorized_keys_sk +/usr/bin/google_guest_agent +/usr/bin/google_metadata_script_runner +/usr/bin/google_osconfig_agent +/usr/bin/google_oslogin_nss_cache +/usr/bin/gpasswd +/usr/bin/gpg-error +/usr/bin/gsettings +/usr/bin/gss-client +/usr/bin/gtester +/usr/bin/gxargs +/usr/bin/gzexe +/usr/bin/head +/usr/bin/hexdump +/usr/bin/hmac256 +/usr/bin/hostid +/usr/bin/hostnamectl +/usr/bin/id +/usr/bin/idle +/usr/bin/import-tars +/usr/bin/infocmp +/usr/bin/infotocap +/usr/bin/install +/usr/bin/inteltool +/usr/bin/ionice +/usr/bin/ipcmk +/usr/bin/ipcrm +/usr/bin/ipcs +/usr/bin/iptables-xml +/usr/bin/irqtop +/usr/bin/join +/usr/bin/journalctl +/usr/bin/jq +/usr/bin/jsondiff +/usr/bin/jsonpatch +/usr/bin/jsonpointer +/usr/bin/jsonschema +/usr/bin/kdestroy +/usr/bin/kernel-install +/usr/bin/kinit +/usr/bin/klist +/usr/bin/kpasswd +/usr/bin/kubectl +/usr/bin/kubelet +/usr/bin/last +/usr/bin/lastb +/usr/bin/lastlog +/usr/bin/less +/usr/bin/lessecho +/usr/bin/lesskey +/usr/bin/lesspipe +/usr/bin/line +/usr/bin/link +/usr/bin/logger +/usr/bin/loginctl +/usr/bin/logname +/usr/bin/look +/usr/bin/lsattr +/usr/bin/lscpu +/usr/bin/lsipc +/usr/bin/lsirq +/usr/bin/lslocks +/usr/bin/lslogins +/usr/bin/lsmem +/usr/bin/lsns +/usr/bin/lsof +/usr/bin/lz4 +/usr/bin/lz4c +/usr/bin/lz4cat +/usr/bin/lzcat +/usr/bin/lzcmp +/usr/bin/lzdiff +/usr/bin/lzegrep +/usr/bin/lzfgrep +/usr/bin/lzgrep +/usr/bin/lzless +/usr/bin/lzma +/usr/bin/lzmadec +/usr/bin/lzmainfo +/usr/bin/lzmore +/usr/bin/mawk +/usr/bin/mcookie +/usr/bin/md5sum +/usr/bin/metrics_client +/usr/bin/mk_cmds +/usr/bin/mkfifo +/usr/bin/mktemp +/usr/bin/mpicalc +/usr/bin/namei +/usr/bin/nc +/usr/bin/netcap +/usr/bin/nettle-hash +/usr/bin/nettle-lfib-stream +/usr/bin/nettle-pbkdf2 +/usr/bin/networkctl +/usr/bin/newgidmap +/usr/bin/newgrp +/usr/bin/newuidmap +/usr/bin/nice +/usr/bin/nl +/usr/bin/nohup +/usr/bin/nproc +/usr/bin/nsenter +/usr/bin/numfmt +/usr/bin/nvramtool +/usr/bin/od +/usr/bin/oomctl +/usr/bin/openssl +/usr/bin/passwd +/usr/bin/paste +/usr/bin/pathchk +/usr/bin/pcre2grep +/usr/bin/pcre2test +/usr/bin/pcregrep +/usr/bin/pcretest +/usr/bin/perf +/usr/bin/perfetto +/usr/bin/pg +/usr/bin/pgrep +/usr/bin/pidof +/usr/bin/pigz +/usr/bin/pinky +/usr/bin/pkcs1-conv +/usr/bin/pkill +/usr/bin/pmap +/usr/bin/portablectl +/usr/bin/pr +/usr/bin/printenv +/usr/bin/printf +/usr/bin/prlimit +/usr/bin/procan +/usr/bin/protoc-gen-go +/usr/bin/protoc-gen-go-grpc +/usr/bin/pscap +/usr/bin/ptx +/usr/bin/pv +/usr/bin/pwdx +/usr/bin/pwqcheck +/usr/bin/pwqfilter +/usr/bin/pwqgen +/usr/bin/pydoc +/usr/bin/pydoc3.8 +/usr/bin/pyjwt +/usr/bin/pyserial-miniterm +/usr/bin/pyserial-ports +/usr/bin/python +/usr/bin/python-exec2c +/usr/bin/python3 +/usr/bin/python3.8 +/usr/bin/pyvenv +/usr/bin/readlink +/usr/bin/realpath +/usr/bin/rename +/usr/bin/renice +/usr/bin/reset +/usr/bin/resolvectl +/usr/bin/rev +/usr/bin/rootdev +/usr/bin/rsync +/usr/bin/rsync-ssl +/usr/bin/runc +/usr/bin/runcon +/usr/bin/rview +/usr/bin/rvim +/usr/bin/scmp_sys_resolver +/usr/bin/scp +/usr/bin/script +/usr/bin/scriptlive +/usr/bin/scriptreplay +/usr/bin/sdiff +/usr/bin/seq +/usr/bin/setsid +/usr/bin/setterm +/usr/bin/sexp-conv +/usr/bin/sftp +/usr/bin/sg +/usr/bin/sha1sum +/usr/bin/sha224sum +/usr/bin/sha256sum +/usr/bin/sha384sum +/usr/bin/sha512sum +/usr/bin/shlibsign +/usr/bin/shred +/usr/bin/shuf +/usr/bin/slabtop +/usr/bin/sleep +/usr/bin/smbinfo +/usr/bin/socat +/usr/bin/sort +/usr/bin/sos +/usr/bin/sos-collector +/usr/bin/sosreport +/usr/bin/split +/usr/bin/ssh +/usr/bin/ssh-add +/usr/bin/ssh-agent +/usr/bin/ssh-copy-id +/usr/bin/ssh-keygen +/usr/bin/ssh-keyscan +/usr/bin/stat +/usr/bin/stdbuf +/usr/bin/sudo +/usr/bin/sudoedit +/usr/bin/sudoreplay +/usr/bin/sum +/usr/bin/superiotool +/usr/bin/systemctl +/usr/bin/systemd-analyze +/usr/bin/systemd-ask-password +/usr/bin/systemd-cat +/usr/bin/systemd-cgls +/usr/bin/systemd-cgtop +/usr/bin/systemd-creds +/usr/bin/systemd-delta +/usr/bin/systemd-detect-virt +/usr/bin/systemd-dissect +/usr/bin/systemd-escape +/usr/bin/systemd-id128 +/usr/bin/systemd-inhibit +/usr/bin/systemd-machine-id-setup +/usr/bin/systemd-mount +/usr/bin/systemd-notify +/usr/bin/systemd-nspawn +/usr/bin/systemd-path +/usr/bin/systemd-repart +/usr/bin/systemd-resolve +/usr/bin/systemd-run +/usr/bin/systemd-socket-activate +/usr/bin/systemd-stdio-bridge +/usr/bin/systemd-sysext +/usr/bin/systemd-tmpfiles +/usr/bin/systemd-tty-ask-password-agent +/usr/bin/systemd-umount +/usr/bin/tabs +/usr/bin/tac +/usr/bin/tail +/usr/bin/taskset +/usr/bin/tee +/usr/bin/test +/usr/bin/tic +/usr/bin/timedatectl +/usr/bin/timeout +/usr/bin/tini +/usr/bin/tload +/usr/bin/toe +/usr/bin/toolbox +/usr/bin/top +/usr/bin/touch +/usr/bin/tpm-nvsize +/usr/bin/tpmc +/usr/bin/tput +/usr/bin/tr +/usr/bin/trace +/usr/bin/traced +/usr/bin/traced_probes +/usr/bin/truncate +/usr/bin/tset +/usr/bin/tsort +/usr/bin/tty +/usr/bin/udevadm +/usr/bin/ul +/usr/bin/ulockmgr_server +/usr/bin/uname +/usr/bin/unexpand +/usr/bin/uniq +/usr/bin/unlink +/usr/bin/unlz4 +/usr/bin/unlzma +/usr/bin/unpigz +/usr/bin/unshare +/usr/bin/unxz +/usr/bin/update_engine_client +/usr/bin/uptime +/usr/bin/userdbctl +/usr/bin/users +/usr/bin/utmpdump +/usr/bin/uuidgen +/usr/bin/uuidparse +/usr/bin/vbutil_firmware +/usr/bin/vbutil_kernel +/usr/bin/vbutil_key +/usr/bin/vbutil_keyblock +/usr/bin/vdir +/usr/bin/verity +/usr/bin/vi +/usr/bin/view +/usr/bin/vim +/usr/bin/vimdiff +/usr/bin/vmstat +/usr/bin/w +/usr/bin/watch +/usr/bin/wc +/usr/bin/wget +/usr/bin/whereis +/usr/bin/which +/usr/bin/who +/usr/bin/whoami +/usr/bin/x86_64-cros-linux-gnu-gio-querymodules +/usr/bin/xargs +/usr/bin/xmlcatalog +/usr/bin/xmllint +/usr/bin/xmlwf +/usr/bin/xxd +/usr/bin/xz +/usr/bin/xzcat +/usr/bin/xzcmp +/usr/bin/xzdec +/usr/bin/xzdiff +/usr/bin/xzegrep +/usr/bin/xzfgrep +/usr/bin/xzgrep +/usr/bin/xzless +/usr/bin/xzmore +/usr/bin/yat2m +/usr/bin/yes +/usr/bin/zcmp +/usr/bin/zdiff +/usr/bin/zegrep +/usr/bin/zfgrep +/usr/bin/zforce +/usr/bin/zgrep +/usr/bin/zless +/usr/bin/zmore +/usr/bin/znew +``` + +![default](https://user-images.githubusercontent.com/8466209/238171017-8d377ade-1fe0-4ef8-8594-76ca65023ca8.png) + +![default](https://user-images.githubusercontent.com/8466209/198938102-de43af86-2e1a-445c-80d7-d1f4cbbbb9a7.png) + +![default](https://user-images.githubusercontent.com/8466209/198938226-aa4679bc-2912-409d-9a09-642bdebfcc65.png) + +![default](https://user-images.githubusercontent.com/8466209/198938652-5a366a20-08c6-4b7c-b48f-a551575dec7f.png) + +![default](https://user-images.githubusercontent.com/8466209/198939140-2d553b06-c3d8-47f6-80f8-acb42e29d54d.png) diff --git a/identition/span3/gist06.html b/identition/span3/gist06.html new file mode 100644 index 00000000000..03411995f1b --- /dev/null +++ b/identition/span3/gist06.html @@ -0,0 +1,180 @@ + System Storage · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            System Storage

            GitHub allows developers to run GitHub Actions workflows on your own runners. This Docker image allows you to create your own runners on Docker, you can enable Docker siblings by binding the host Docker daemon socket.

            $ cat /etc/os-release
+
+PRETTY_NAME="Debian GNU/Linux 10 (buster)"
+NAME="Debian GNU/Linux"
+VERSION_ID="10"
+VERSION="10 (buster)"
+VERSION_CODENAME=buster
+ID=debian
+HOME_URL="https://www.debian.org/"
+SUPPORT_URL="https://www.debian.org/support"
+BUG_REPORT_URL="https://bugs.debian.org/"
+

            By default, the df command shows the disk space used and available disk space in kilobytes. To display information about disk drives in human-readable format (kilobytes, megabytes, gigabytes and so on), invoke the df command with the -h option

            $ df -h
+Filesystem      Size  Used Avail Use% Mounted on
+/dev/root       2.0G  1.1G  902M  54% /
+devtmpfs        484M     0  484M   0% /dev
+tmpfs           487M     0  487M   0% /dev/shm
+tmpfs           195M  512K  195M   1% /run
+tmpfs           487M  112K  487M   1% /etc/machine-id
+tmpfs           256K     0  256K   0% /mnt/disks
+tmpfs           487M     0  487M   0% /tmp
+overlayfs       487M  112K  487M   1% /etc
+/dev/sda8        11M   24K   11M   1% /usr/share/oem
+/dev/sda1       5.7G  3.5G  2.2G  62% /mnt/stateful_partition
+tmpfs           2.0M  128K  1.9M   7% /var/lib/cloud
+/dev/sdb1        49G  9.9G   38G  22% /mnt/disks/Linux              ◄- DEEP LEARNING
+

            On Unix-like operating systems, the set command is a built-in function of the Bourne shell ( sh ), C shell ( csh ), and Korn shell ( ksh ), which is used to define and determine the values of the system environment.

            $ set
+
+ACTIONS_ID_TOKEN_REQUEST_TOKEN=***
+ACTIONS_ID_TOKEN_REQUEST_URL='https://pipelines.actions.githubusercontent.com/a18hGIuIy4qbY5KTUvkKiuBNsSHDVCEtnJ8x8NEYFPEBFH2tOZ/00000000-0000-0000-0000-000000000000/_apis/distributedtask/hubs/Actions/plans/7534b9e1-5505-4cff-9f7a-440ad58fadf5/jobs/55c239b7-523f-5586-aeb6-60a00c959946/idtoken?api-version=2.0'
+AGENT_TOOLSDIRECTORY=/opt/hostedtoolcache
+BASH=/bin/bash
+BASHOPTS=checkwinsize:cmdhist:complete_fullquote:extquote:force_fignore:globasciiranges:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath
+BASH_ALIASES=()
+BASH_ARGC=()
+BASH_ARGV=()
+BASH_CMDS=()
+BASH_LINENO=([0]="0")
+BASH_SOURCE=([0]="/home/runner/_work/_temp/b00557e9-dc1d-40fb-a211-db6869b65693.sh")
+BASH_VERSINFO=([0]="5" [1]="0" [2]="3" [3]="1" [4]="release" [5]="x86_64-pc-linux-gnu")
+BASH_VERSION='5.0.3(1)-release'
+CI=true
+DIRSTACK=()
+EUID=0
+GITHUB_ACCESS_TOKEN=***
+GITHUB_ACTION=__run
+GITHUB_ACTIONS=true
+GITHUB_ACTION_REF=
+GITHUB_ACTION_REPOSITORY=
+GITHUB_ACTOR=eq19
+GITHUB_ACTOR_ID=8466209
+GITHUB_API_URL=https://api.github.com
+GITHUB_BASE_REF=
+GITHUB_ENV=/home/runner/_work/_temp/_runner_file_commands/set_env_acae127c-173c-43fd-abea-f6d3fe882641
+GITHUB_EVENT_NAME=push
+GITHUB_EVENT_PATH=/home/runner/_work/_temp/_github_workflow/event.json
+GITHUB_GRAPHQL_URL=https://api.github.com/graphql
+GITHUB_HEAD_REF=
+GITHUB_JOB=github-pages
+GITHUB_OUTPUT=/home/runner/_work/_temp/_runner_file_commands/set_output_acae127c-173c-43fd-abea-f6d3fe882641
+GITHUB_PATH=/home/runner/_work/_temp/_runner_file_commands/add_path_acae127c-173c-43fd-abea-f6d3fe882641
+GITHUB_REF=refs/heads/eQ19
+GITHUB_REF_NAME=eQ19
+GITHUB_REF_PROTECTED=false
+GITHUB_REF_TYPE=branch
+GITHUB_REPOSITORY=FeedMapping/Partition
+GITHUB_REPOSITORY_ID=550855238
+GITHUB_REPOSITORY_OWNER=FeedMapping
+GITHUB_REPOSITORY_OWNER_ID=11927583
+GITHUB_RETENTION_DAYS=90
+GITHUB_RUN_ATTEMPT=1
+GITHUB_RUN_ID=4975344786
+GITHUB_RUN_NUMBER=88
+GITHUB_SERVER_URL=https://github.com
+GITHUB_SHA=a5ee1d5f656adf586a43252afce0a4ddc838ade4
+GITHUB_STATE=/home/runner/_work/_temp/_runner_file_commands/save_state_acae127c-173c-43fd-abea-f6d3fe882641
+GITHUB_STEP_SUMMARY=/home/runner/_work/_temp/_runner_file_commands/step_summary_acae127c-173c-43fd-abea-f6d3fe882641
+GITHUB_TRIGGERING_ACTOR=eq19
+GITHUB_WORKFLOW='Build and deploy Jekyll site'
+GITHUB_WORKFLOW_REF=FeedMapping/Partition/.github/workflows/github-pages.yml@refs/heads/eQ19
+GITHUB_WORKFLOW_SHA=a5ee1d5f656adf586a43252afce0a4ddc838ade4
+GITHUB_WORKSPACE=/home/runner/_work/Partition/Partition
+GROUPS=()
+HOME=/root
+HOSTNAME=ef75abdc2b19
+HOSTTYPE=x86_64
+IFS=$' \t\n'
+MACHTYPE=x86_64-pc-linux-gnu
+OPTERR=1
+OPTIND=1
+OSTYPE=linux-gnu
+PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+PIPESTATUS=([0]="0")
+PPID=17188
+PS4='+ '
+***
+RUNNER_ALLOW_RUNASROOT=true
+RUNNER_ARCH=X64
+RUNNER_LABELS=
+RUNNER_NAME=Google-optimized-instance
+RUNNER_ORGANIZATION_URL=https://github.com/FeedMapping
+RUNNER_OS=Linux
+RUNNER_REPLACE_EXISTING=true
+RUNNER_REPOSITORY_URL=
+RUNNER_TEMP=/home/runner/_work/_temp
+RUNNER_TOKEN=ACAS6IJKEQK3RSYCNEQ3Z53EL2JM6
+RUNNER_TOOL_CACHE=/opt/hostedtoolcache
+RUNNER_TRACKING_ID=github_b2590dca-5a63-4f9a-a8e2-68924e311fdc
+RUNNER_WORKSPACE=/home/runner/_work/Partition
+RUNNER_WORK_DIRECTORY=_work
+SHELL=/bin/bash
+SHELLOPTS=braceexpand:errexit:hashall:interactive-comments
+SHLVL=1
+SUPERVISOR_ENABLED=1
+SUPERVISOR_GROUP_NAME=runner
+SUPERVISOR_PROCESS_NAME=runner
+TERM=dumb
+UID=0
+_=-V
+

            docker-github-runner

            docker info
+docker --version
+
+docker logout
+docker login
+
+git clone https://github.com/eq19/setup
+cd setup/docker
+docker build -t setup .
+
+docker images
+docker tag setup:latest eq19/setup:latest
+
+docker push eq19/setup:latest
+

            For now, there are only Debian Buster (tagged with latest and vX.Y.Z) and Ubuntu Focal (tagged with ubuntu-20.04 and vX.Y.Z-ubuntu-20.04) images, but I may add more variants in the future. Feel free to create an issue if you want another base image.

            default

            When comparing Chromium OS vs Debian GNU/Linux, the Slant community recommends Debian GNU/Linux for most people. In the question"What are the best Linux distributions for desktops?" Debian GNU/Linux is ranked 3rd while Chromium OS is ranked 88th. The most important reason people chose Debian GNU/Linux is:

            Debian offers stable and testing CD images specifically built for GNOME (the default), KDE Plasma Workspaces, Xfce and LXDE. Less common window managers such as Enlightenment, Openbox, Fluxbox, GNUstep, IceWM, Window Maker and others can also be installed (Slant).

            chromium-os_vs_debian-gnu-linux

            For most frameworks, Debian 10 is the default OS. Ubuntu 20.04 images are available for some frameworks. They are denoted by the -ubuntu-2004 suffixes in the image family name (see Listing all available versions). Debian 9 images have been deprecated.

            Deep Learning VM Images

            You can pull a container image and show the "history" for the container. This shows you how it is built and what the original starting image. This does not mean that you access the original image. You can add to and remove parts of the image. You can also export an image to a tar archive file, modify and then reimport

            
+$ docker history  gcr.io/deeplearning-platform-release/tf-cpu:m96 --format  " {{.CreatedBy}}" --no-trunc
+
+RUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c cd /opt/google/licenses &&     chmod +x query_licenses.sh &&     ./query_licenses.sh # buildkit
+RUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c BAZEL_INSTALLER_URL="https://github.com/bazelbuild/bazel/releases/download/0.19.0/bazel-0.19.0-installer-linux-x86_64.sh" &&     BAZEL_INSTALLER_FILE="bazel_installer.sh" &&     wget -q "${BAZEL_INSTALLER_URL}" -O "${BAZEL_INSTALLER_FILE}" &&     chmod +x "${BAZEL_INSTALLER_FILE}" &&     "./${BAZEL_INSTALLER_FILE}" &&     rm -rf "./${BAZEL_INSTALLER_FILE}" # buildkit
+RUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c export CONDA_REPOSITORY="/tmp/conda" &&     chmod +x /opt/google/conda/install_to_env.sh &&     ENV_DOCKER=1 /opt/google/conda/install_to_env.sh base dlenv-tf-${VERSION}-cpu-meta # buildkit
+ENV KMP_SETTINGS=1
+ENV KMP_AFFINITY=granularity=fine,verbose,compact,1,0
+ENV KMP_BLOCKTIME=0
+ENV CONTAINER_NAME=tf-cpu/1-15
+ARG CONTAINER_NAME
+LABEL com.google.environment=Container: TensorFlow 1-15
+ARG VERSION
+CMD ["/run_jupyter.sh"]
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x run_jupyter.sh # buildkit
+COPY build/container/run_jupyter.sh /run_jupyter.sh # buildkit
+ENTRYPOINT ["/entrypoint.sh"]
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x entrypoint.sh # buildkit
+COPY build/container/entrypoint.sh /entrypoint.sh # buildkit
+COPY build/package/conda/channels.json /opt/google/conda/channels.json # buildkit
+COPY build/package/packages/jupyter/jupyter_notebook_config.py /opt/jupyter/.jupyter/jupyter_notebook_config.py # buildkit
+COPY build/package/packages/jupyter/ipython_kernel_config.py /etc/ipython/ipython_kernel_config.py # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chown -R "jupyter:jupyter" "/home/jupyter/." # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c adduser --uid 1000 --gid 1001 jupyter # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c addgroup --gid 1001 jupyter # buildkit
+ENV LD_LIBRARY_PATH=/usr/local/cuda/lib64:/usr/local/cuda/lib:/usr/local/lib/x86_64-linux-gnu:/usr/local/nvidia/lib:/usr/local/nvidia/lib64:
+VOLUME [/home/jupyter]
+EXPOSE map[8080/tcp:{}]
+ENV SHELL=/bin/bash
+ENV PATH=/opt/conda/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x /opt/google/conda/provision_conda.sh && /opt/google/conda/provision_conda.sh # buildkit
+ENV DL_ANACONDA_HOME=/opt/conda
+ENV ANACONDA_PYTHON_VERSION=3.7
+COPY build/vm/packer/generic/packages /opt/google # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c cd / &&     gsutil cp -r gs://dl-platform-binaries-builds/openmpi-4.0.2/v20191105/openmpi.tar.gz  . &&     tar xf openmpi.tar.gz &&     rm -f openmpi.tar.gz # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt update -y &&     apt install -y libnuma-dev # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c if dpkg -s libnccl2; then         echo "deb https://packages.cloud.google.com/apt google-fast-socket main" | tee /etc/apt/sources.list.d/google-fast-socket.list &&         curl -s -L https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add - &&         apt-get --allow-releaseinfo-change update && apt install -y google-fast-socket;     fi # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt-get --allow-releaseinfo-change update -y &&     apt-get install -y dirmngr &&     apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 8B57C5C2836F4BEB &&     apt-key adv --keyserver keyserver.ubuntu.com --recv-keys FEEA9169307EA071 &&     apt-get --allow-releaseinfo-change update -y &&     echo "deb [signed-by=/usr/share/keyrings/cloud.google.gpg] https://packages.cloud.google.com/apt cloud-sdk main" | tee -a /etc/apt/sources.list.d/google-cloud-sdk.list &&     curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key --keyring /usr/share/keyrings/cloud.google.gpg add - &&     apt-get --allow-releaseinfo-change update -y &&     apt-get install -y apt-transport-https ca-certificates gnupg &&     echo "deb http://packages.cloud.google.com/apt gcsfuse-focal main" | tee /etc/apt/sources.list.d/gcsfuse.list &&     curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add - &&     apt-get --allow-releaseinfo-change update -y &&     apt-get install -y google-cloud-sdk && apt-get install -y gcsfuse &&     rm -rf /var/lib/apt/lists/* # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt-get --allow-releaseinfo-change -o Acquire::Check-Valid-Until=false update -y &&     apt-get install --no-install-recommends -y -q        $(grep -vE "^\s*#" aptget-requirements.txt | tr "\n" " ") &&     rm -rf /var/lib/apt/lists/* &&     rm -rf aptget-requirements.txt # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c if [ "${BASE_IMAGE}" =~ "^nvidia. *" ]; then       apt update -y || true && apt install -y wget && apt install -yq software-properties-common &&       wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/cuda-ubuntu2004.pin &&       mv cuda-ubuntu2004.pin /etc/apt/preferences.d/cuda-repository-pin-600 &&       apt-key adv --fetch-keys https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/3bf863cc.pub &&       add-apt-repository "deb https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/ /" &&       apt-get --allow-releaseinfo-change update;     fi # buildkit
+COPY build/vm/packer/base/aptget-requirements.txt /aptget-requirements.txt # buildkit
+RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt update --allow-releaseinfo-change -y &&     apt upgrade -y # buildkit
+ARG DEBIAN_FRONTEND=noninteractive
+ENV LANG=C.UTF-8
+ENV LC_ALL=C.UTF-8
+LABEL com.google.environment=Container: Minimal
+
+

            Untitled

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist06.md b/identition/span3/gist06.md new file mode 100644 index 00000000000..53736c12c2f --- /dev/null +++ b/identition/span3/gist06.md @@ -0,0 +1,228 @@ +## System Storage + +GitHub allows developers to run GitHub Actions workflows on your own runners. This [Docker image](https://hub.docker.com/r/tcardonne/github-runner#!) allows you to create your own runners on Docker, you can enable Docker siblings by binding the host Docker daemon socket. + +``` +$ cat /etc/os-release + +PRETTY_NAME="Debian GNU/Linux 10 (buster)" +NAME="Debian GNU/Linux" +VERSION_ID="10" +VERSION="10 (buster)" +VERSION_CODENAME=buster +ID=debian +HOME_URL="https://www.debian.org/" +SUPPORT_URL="https://www.debian.org/support" +BUG_REPORT_URL="https://bugs.debian.org/" +``` + +By default, the df command shows the disk space used and available disk space in kilobytes. To display information about disk drives in human-readable format (kilobytes, megabytes, gigabytes and so on), invoke the df command with the -h option + +``` +$ df -h +Filesystem Size Used Avail Use% Mounted on +/dev/root 2.0G 1.1G 902M 54% / +devtmpfs 484M 0 484M 0% /dev +tmpfs 487M 0 487M 0% /dev/shm +tmpfs 195M 512K 195M 1% /run +tmpfs 487M 112K 487M 1% /etc/machine-id +tmpfs 256K 0 256K 0% /mnt/disks +tmpfs 487M 0 487M 0% /tmp +overlayfs 487M 112K 487M 1% /etc +/dev/sda8 11M 24K 11M 1% /usr/share/oem +/dev/sda1 5.7G 3.5G 2.2G 62% /mnt/stateful_partition +tmpfs 2.0M 128K 1.9M 7% /var/lib/cloud +/dev/sdb1 49G 9.9G 38G 22% /mnt/disks/Linux ◄- DEEP LEARNING +``` + +On Unix-like operating systems, the set command is a built-in function of the Bourne shell ( sh ), C shell ( csh ), and Korn shell ( ksh ), which is used to define and determine the values of the system environment. + +``` +$ set + +ACTIONS_ID_TOKEN_REQUEST_TOKEN=*** +ACTIONS_ID_TOKEN_REQUEST_URL='https://pipelines.actions.githubusercontent.com/a18hGIuIy4qbY5KTUvkKiuBNsSHDVCEtnJ8x8NEYFPEBFH2tOZ/00000000-0000-0000-0000-000000000000/_apis/distributedtask/hubs/Actions/plans/7534b9e1-5505-4cff-9f7a-440ad58fadf5/jobs/55c239b7-523f-5586-aeb6-60a00c959946/idtoken?api-version=2.0' +AGENT_TOOLSDIRECTORY=/opt/hostedtoolcache +BASH=/bin/bash +BASHOPTS=checkwinsize:cmdhist:complete_fullquote:extquote:force_fignore:globasciiranges:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath +BASH_ALIASES=() +BASH_ARGC=() +BASH_ARGV=() +BASH_CMDS=() +BASH_LINENO=([0]="0") +BASH_SOURCE=([0]="/home/runner/_work/_temp/b00557e9-dc1d-40fb-a211-db6869b65693.sh") +BASH_VERSINFO=([0]="5" [1]="0" [2]="3" [3]="1" [4]="release" [5]="x86_64-pc-linux-gnu") +BASH_VERSION='5.0.3(1)-release' +CI=true +DIRSTACK=() +EUID=0 +GITHUB_ACCESS_TOKEN=*** +GITHUB_ACTION=__run +GITHUB_ACTIONS=true +GITHUB_ACTION_REF= +GITHUB_ACTION_REPOSITORY= +GITHUB_ACTOR=eq19 +GITHUB_ACTOR_ID=8466209 +GITHUB_API_URL=https://api.github.com +GITHUB_BASE_REF= +GITHUB_ENV=/home/runner/_work/_temp/_runner_file_commands/set_env_acae127c-173c-43fd-abea-f6d3fe882641 +GITHUB_EVENT_NAME=push +GITHUB_EVENT_PATH=/home/runner/_work/_temp/_github_workflow/event.json +GITHUB_GRAPHQL_URL=https://api.github.com/graphql +GITHUB_HEAD_REF= +GITHUB_JOB=github-pages +GITHUB_OUTPUT=/home/runner/_work/_temp/_runner_file_commands/set_output_acae127c-173c-43fd-abea-f6d3fe882641 +GITHUB_PATH=/home/runner/_work/_temp/_runner_file_commands/add_path_acae127c-173c-43fd-abea-f6d3fe882641 +GITHUB_REF=refs/heads/eQ19 +GITHUB_REF_NAME=eQ19 +GITHUB_REF_PROTECTED=false +GITHUB_REF_TYPE=branch +GITHUB_REPOSITORY=FeedMapping/Partition +GITHUB_REPOSITORY_ID=550855238 +GITHUB_REPOSITORY_OWNER=FeedMapping +GITHUB_REPOSITORY_OWNER_ID=11927583 +GITHUB_RETENTION_DAYS=90 +GITHUB_RUN_ATTEMPT=1 +GITHUB_RUN_ID=4975344786 +GITHUB_RUN_NUMBER=88 +GITHUB_SERVER_URL=https://github.com +GITHUB_SHA=a5ee1d5f656adf586a43252afce0a4ddc838ade4 +GITHUB_STATE=/home/runner/_work/_temp/_runner_file_commands/save_state_acae127c-173c-43fd-abea-f6d3fe882641 +GITHUB_STEP_SUMMARY=/home/runner/_work/_temp/_runner_file_commands/step_summary_acae127c-173c-43fd-abea-f6d3fe882641 +GITHUB_TRIGGERING_ACTOR=eq19 +GITHUB_WORKFLOW='Build and deploy Jekyll site' +GITHUB_WORKFLOW_REF=FeedMapping/Partition/.github/workflows/github-pages.yml@refs/heads/eQ19 +GITHUB_WORKFLOW_SHA=a5ee1d5f656adf586a43252afce0a4ddc838ade4 +GITHUB_WORKSPACE=/home/runner/_work/Partition/Partition +GROUPS=() +HOME=/root +HOSTNAME=ef75abdc2b19 +HOSTTYPE=x86_64 +IFS=$' \t\n' +MACHTYPE=x86_64-pc-linux-gnu +OPTERR=1 +OPTIND=1 +OSTYPE=linux-gnu +PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin +PIPESTATUS=([0]="0") +PPID=17188 +PS4='+ ' +*** +RUNNER_ALLOW_RUNASROOT=true +RUNNER_ARCH=X64 +RUNNER_LABELS= +RUNNER_NAME=Google-optimized-instance +RUNNER_ORGANIZATION_URL=https://github.com/FeedMapping +RUNNER_OS=Linux +RUNNER_REPLACE_EXISTING=true +RUNNER_REPOSITORY_URL= +RUNNER_TEMP=/home/runner/_work/_temp +RUNNER_TOKEN=ACAS6IJKEQK3RSYCNEQ3Z53EL2JM6 +RUNNER_TOOL_CACHE=/opt/hostedtoolcache +RUNNER_TRACKING_ID=github_b2590dca-5a63-4f9a-a8e2-68924e311fdc +RUNNER_WORKSPACE=/home/runner/_work/Partition +RUNNER_WORK_DIRECTORY=_work +SHELL=/bin/bash +SHELLOPTS=braceexpand:errexit:hashall:interactive-comments +SHLVL=1 +SUPERVISOR_ENABLED=1 +SUPERVISOR_GROUP_NAME=runner +SUPERVISOR_PROCESS_NAME=runner +TERM=dumb +UID=0 +_=-V +``` + +[![docker-github-runner](https://user-images.githubusercontent.com/8466209/229943878-e3d1cae4-15fd-43ab-9d7f-904a343b745c.png)](https://github.com/eq19/setup) + + +``` +docker info +docker --version + +docker logout +docker login + +git clone https://github.com/eq19/setup +cd setup/docker +docker build -t setup . + +docker images +docker tag setup:latest eq19/setup:latest + +docker push eq19/setup:latest +``` + +For now, there are only Debian Buster (tagged with latest and vX.Y.Z) and Ubuntu Focal (tagged with ubuntu-20.04 and vX.Y.Z-ubuntu-20.04) images, but I may add more variants in the future. Feel free to create an issue if you want another base image. + +[![default](https://user-images.githubusercontent.com/8466209/238171580-d65c5bcb-7ae9-498d-841f-b645e08c49b2.png)](https://registry.hub.docker.com/r/tcardonne/github-runner/tags) + +When comparing Chromium OS vs Debian GNU/Linux, the Slant community recommends Debian GNU/Linux for most people. In the question“What are the best Linux distributions for desktops?” Debian GNU/Linux is ranked 3rd while Chromium OS is ranked 88th. The most important reason people chose Debian GNU/Linux is: + +> Debian offers stable and testing CD images specifically built for GNOME (the default), KDE Plasma Workspaces, Xfce and LXDE. Less common window managers such as Enlightenment, Openbox, Fluxbox, GNUstep, IceWM, Window Maker and others can also be installed _([Slant](https://www.slant.co/versus/2691/2692/~chromium-os_vs_debian-gnu-linux))_. + +[![chromium-os_vs_debian-gnu-linux](https://user-images.githubusercontent.com/8466209/238179595-7f087116-910c-4cf9-8b1b-1051e74f93d4.png)](https://www.slant.co/versus/2691/2692/~chromium-os_vs_debian-gnu-linux) + +For most frameworks, Debian 10 is the default OS. Ubuntu 20.04 images are available for some frameworks. They are denoted by the -ubuntu-2004 suffixes in the image family name (see [Listing all available versions](https://cloud.google.com/deep-learning-vm/docs/images#listing-versions)). Debian 9 images have been deprecated. + +[![Deep Learning VM Images +](https://user-images.githubusercontent.com/8466209/238179451-d71d776a-883f-4978-b60a-50a25a6c8572.png)](https://cloud.google.com/deep-learning-vm/docs/images#choosing_an_operating_system) + +You can pull a container image and show the "[history](https://stackoverflow.com/a/75291419/2023941)" for the container. This shows you how it is built and what the original starting image. This does not mean that you access the original image. You can add to and remove parts of the image. You can also export an image to a tar archive file, modify and then reimport + +``` +{% raw %} +$ docker history gcr.io/deeplearning-platform-release/tf-cpu:m96 --format " {{.CreatedBy}}" --no-trunc + +RUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c cd /opt/google/licenses && chmod +x query_licenses.sh && ./query_licenses.sh # buildkit +RUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c BAZEL_INSTALLER_URL="https://github.com/bazelbuild/bazel/releases/download/0.19.0/bazel-0.19.0-installer-linux-x86_64.sh" && BAZEL_INSTALLER_FILE="bazel_installer.sh" && wget -q "${BAZEL_INSTALLER_URL}" -O "${BAZEL_INSTALLER_FILE}" && chmod +x "${BAZEL_INSTALLER_FILE}" && "./${BAZEL_INSTALLER_FILE}" && rm -rf "./${BAZEL_INSTALLER_FILE}" # buildkit +RUN |2 VERSION=1-15 CONTAINER_NAME=tf-cpu/1-15 /bin/sh -c export CONDA_REPOSITORY="/tmp/conda" && chmod +x /opt/google/conda/install_to_env.sh && ENV_DOCKER=1 /opt/google/conda/install_to_env.sh base dlenv-tf-${VERSION}-cpu-meta # buildkit +ENV KMP_SETTINGS=1 +ENV KMP_AFFINITY=granularity=fine,verbose,compact,1,0 +ENV KMP_BLOCKTIME=0 +ENV CONTAINER_NAME=tf-cpu/1-15 +ARG CONTAINER_NAME +LABEL com.google.environment=Container: TensorFlow 1-15 +ARG VERSION +CMD ["/run_jupyter.sh"] +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x run_jupyter.sh # buildkit +COPY build/container/run_jupyter.sh /run_jupyter.sh # buildkit +ENTRYPOINT ["/entrypoint.sh"] +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x entrypoint.sh # buildkit +COPY build/container/entrypoint.sh /entrypoint.sh # buildkit +COPY build/package/conda/channels.json /opt/google/conda/channels.json # buildkit +COPY build/package/packages/jupyter/jupyter_notebook_config.py /opt/jupyter/.jupyter/jupyter_notebook_config.py # buildkit +COPY build/package/packages/jupyter/ipython_kernel_config.py /etc/ipython/ipython_kernel_config.py # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chown -R "jupyter:jupyter" "/home/jupyter/." # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c adduser --uid 1000 --gid 1001 jupyter # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c addgroup --gid 1001 jupyter # buildkit +ENV LD_LIBRARY_PATH=/usr/local/cuda/lib64:/usr/local/cuda/lib:/usr/local/lib/x86_64-linux-gnu:/usr/local/nvidia/lib:/usr/local/nvidia/lib64: +VOLUME [/home/jupyter] +EXPOSE map[8080/tcp:{}] +ENV SHELL=/bin/bash +ENV PATH=/opt/conda/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c chmod +x /opt/google/conda/provision_conda.sh && /opt/google/conda/provision_conda.sh # buildkit +ENV DL_ANACONDA_HOME=/opt/conda +ENV ANACONDA_PYTHON_VERSION=3.7 +COPY build/vm/packer/generic/packages /opt/google # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c cd / && gsutil cp -r gs://dl-platform-binaries-builds/openmpi-4.0.2/v20191105/openmpi.tar.gz . && tar xf openmpi.tar.gz && rm -f openmpi.tar.gz # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt update -y && apt install -y libnuma-dev # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c if dpkg -s libnccl2; then echo "deb https://packages.cloud.google.com/apt google-fast-socket main" | tee /etc/apt/sources.list.d/google-fast-socket.list && curl -s -L https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add - && apt-get --allow-releaseinfo-change update && apt install -y google-fast-socket; fi # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt-get --allow-releaseinfo-change update -y && apt-get install -y dirmngr && apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 8B57C5C2836F4BEB && apt-key adv --keyserver keyserver.ubuntu.com --recv-keys FEEA9169307EA071 && apt-get --allow-releaseinfo-change update -y && echo "deb [signed-by=/usr/share/keyrings/cloud.google.gpg] https://packages.cloud.google.com/apt cloud-sdk main" | tee -a /etc/apt/sources.list.d/google-cloud-sdk.list && curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key --keyring /usr/share/keyrings/cloud.google.gpg add - && apt-get --allow-releaseinfo-change update -y && apt-get install -y apt-transport-https ca-certificates gnupg && echo "deb http://packages.cloud.google.com/apt gcsfuse-focal main" | tee /etc/apt/sources.list.d/gcsfuse.list && curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add - && apt-get --allow-releaseinfo-change update -y && apt-get install -y google-cloud-sdk && apt-get install -y gcsfuse && rm -rf /var/lib/apt/lists/* # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt-get --allow-releaseinfo-change -o Acquire::Check-Valid-Until=false update -y && apt-get install --no-install-recommends -y -q $(grep -vE "^\s*#" aptget-requirements.txt | tr "\n" " ") && rm -rf /var/lib/apt/lists/* && rm -rf aptget-requirements.txt # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c if [ "${BASE_IMAGE}" =~ "^nvidia. *" ]; then apt update -y || true && apt install -y wget && apt install -yq software-properties-common && wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/cuda-ubuntu2004.pin && mv cuda-ubuntu2004.pin /etc/apt/preferences.d/cuda-repository-pin-600 && apt-key adv --fetch-keys https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/3bf863cc.pub && add-apt-repository "deb https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/ /" && apt-get --allow-releaseinfo-change update; fi # buildkit +COPY build/vm/packer/base/aptget-requirements.txt /aptget-requirements.txt # buildkit +RUN |1 DEBIAN_FRONTEND=noninteractive /bin/sh -c apt update --allow-releaseinfo-change -y && apt upgrade -y # buildkit +ARG DEBIAN_FRONTEND=noninteractive +ENV LANG=C.UTF-8 +ENV LC_ALL=C.UTF-8 +LABEL com.google.environment=Container: Minimal +{% endraw %} +``` +![Untitled](https://user-images.githubusercontent.com/8466209/255381318-7cd95f34-ee40-4d02-bea8-3d72ff9bb4af.png) + +![default](https://user-images.githubusercontent.com/8466209/198933143-1d783ccf-22a1-4415-9a11-8effe98d1741.png) + +![default](https://user-images.githubusercontent.com/8466209/198837916-57284efa-bdb7-42d8-80f6-584b3c3bbd19.png) + +![default](https://user-images.githubusercontent.com/8466209/198934268-1570c3cc-5a90-48b3-a1e6-b016c2d93ab4.png) diff --git a/identition/span3/gist07.html b/identition/span3/gist07.html new file mode 100644 index 00000000000..83b8132e263 --- /dev/null +++ b/identition/span3/gist07.html @@ -0,0 +1,42 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | {1} | {9}
+---+-----+-----
+ 2 | 10  |{32}
+---+-----+-----
+ 3 | 33  | 63  
+---+-----+-----
+ 4 |{64} | 101 
+---+-----+-----
+ 5 |{102}| 120 
+---+-----+-----
+ 6 | 121 |{189}
+---+-----+-----
+ 7 | 190 |{200}
+---+-----+-----
+
            $ cat /etc/os-release
+
+NAME="Alpine Linux"
+ID=alpine
+VERSION_ID=3.18.0
+PRETTY_NAME="Alpine Linux v3.18"
+HOME_URL="https://alpinelinux.org/"
+BUG_REPORT_URL="https://gitlab.alpinelinux.org/alpine/aports/-/issues"
+

            flow

            default

            default

            default

            default

            default

            default

            default

            Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

            default

            default

            There might be cases where you want to install and use Ruby with Anaconda or Miniconda. By doing this, Ruby becomes usable. however, it will not compile gems that use native extensions.

            Since it is nearly impossible to use Ruby without utilizing native extensions, this method is not very practical.Instead, you can simply install Ruby from conda-forge and install the compilers package at the same time. This way, you can easily use Ruby within Conda environments like Anaconda or Miniconda (Using Ruby with Conda).

            conda install -c conda-forge ruby
+conda install -c conda-forge compilers
+
+conda install -c "conda-forge/label/broken" ruby
+conda install -c "conda-forge/label/cf201901" ruby
+conda install -c "conda-forge/label/cf202003" ruby
+conda install -c "conda-forge/label/gcc7" ruby
+

            default

            In gRPC, a client application can directly call a method on a server application on a different machine as if it were a local object, making it easier for you to create distributed applications and services.

            $ find / -type f -name "Gemfile"
+
+/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/Gemfile
+/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/pubsub/Gemfile
+
+$ cat /mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/pubsub/Gemfile
+
+source 'https://rubygems.org/'
+
+gem 'grpc', '~> 1.0'
+gem 'googleauth', '>= 0.5.1', '< 0.7'
+

            gRPC and protocol buffers

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span3/gist07.md b/identition/span3/gist07.md new file mode 100644 index 00000000000..6d9b14652aa --- /dev/null +++ b/identition/span3/gist07.md @@ -0,0 +1,87 @@ +``` +---+-----+----- + 1 | {1} | {9} +---+-----+----- + 2 | 10 |{32} +---+-----+----- + 3 | 33 | 63 +---+-----+----- + 4 |{64} | 101 +---+-----+----- + 5 |{102}| 120 +---+-----+----- + 6 | 121 |{189} +---+-----+----- + 7 | 190 |{200} +---+-----+----- +``` + +``` +$ cat /etc/os-release + +NAME="Alpine Linux" +ID=alpine +VERSION_ID=3.18.0 +PRETTY_NAME="Alpine Linux v3.18" +HOME_URL="https://alpinelinux.org/" +BUG_REPORT_URL="https://gitlab.alpinelinux.org/alpine/aports/-/issues" +``` + +[![](https://user-images.githubusercontent.com/8466209/200228344-9f344f49-3e5d-480f-b11c-6e30a20a8f44.jpg)](https://www.primesdemystified.com/First1000Primes.html) + +![flow](https://user-images.githubusercontent.com/36441664/128732737-81762604-0ae0-4a90-b5a8-30921cf46efb.png) + +![default](https://user-images.githubusercontent.com/8466209/198934312-25311775-edd3-48b7-8faa-8da45c380392.png) + +[![default](https://user-images.githubusercontent.com/8466209/198933986-e0c6ab91-bbb6-4413-b75b-3d11bd2ccfab.png)](https://github.com/chetabahana/tensorflow/wiki) + +[![default](https://user-images.githubusercontent.com/8466209/198919975-7e61e7db-06ec-4e16-bd36-10cc9048e9e7.png)](https://github.com/kaustubhcs/prime-hexagon) + +[![default](https://user-images.githubusercontent.com/8466209/198921109-f1e4671d-a845-4c05-8a1d-f6c05ad490a0.png)](https://github.com/kaustubhcs/prime-hexagon/tree/66b8653a102c848084e137aa614e8762b40d5c1f) + +[![default](https://user-images.githubusercontent.com/8466209/198920712-ebff2050-95ac-4617-bfd4-4c8ba930c65c.png)](https://github.com/spacetimeengineer/spacetimeengine) + +[![default](https://user-images.githubusercontent.com/8466209/198922336-f69108be-c4db-45bc-ba4e-2f09539a139c.png)](https://github.com/FeedMapping/syntax) + +[![default](https://user-images.githubusercontent.com/8466209/198921851-eaa9d84d-ee62-4f04-be4d-c291677acb19.png)](https://github.com/eq19) + +Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17). + +![default](https://user-images.githubusercontent.com/8466209/198928812-cab7aef3-9c41-49f4-8b89-00b8fa3fc95a.png) + +![default](https://user-images.githubusercontent.com/8466209/198929326-da02dcc6-e502-4a01-a128-8c0ba03183f3.png) + +There might be cases where you want to install and use Ruby with Anaconda or Miniconda. By doing this, Ruby becomes usable. however, it will not compile gems that use native extensions. + +>Since it is nearly impossible to use Ruby without utilizing native extensions, this method is not very practical.Instead, you can simply install Ruby from conda-forge and install the compilers package at the same time. This way, you can easily use Ruby within Conda environments like Anaconda or Miniconda _([Using Ruby with Conda](https://dev.to/kojix2/using-ruby-with-conda-1hn))_. + +``` +conda install -c conda-forge ruby +conda install -c conda-forge compilers + +conda install -c "conda-forge/label/broken" ruby +conda install -c "conda-forge/label/cf201901" ruby +conda install -c "conda-forge/label/cf202003" ruby +conda install -c "conda-forge/label/gcc7" ruby +``` + +[![default](https://user-images.githubusercontent.com/8466209/239124983-1b99dc91-a1ad-498f-80a0-acb2d8b69185.png)](https://anaconda.org/conda-forge/ruby) + +In gRPC, a client application can directly call a method on a server application on a different machine as if it were a local object, making it easier for you to create distributed applications and services. + +``` +$ find / -type f -name "Gemfile" + +/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/Gemfile +/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/pubsub/Gemfile + +$ cat /mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/ruby/pubsub/Gemfile + +source 'https://rubygems.org/' + +gem 'grpc', '~> 1.0' +gem 'googleauth', '>= 0.5.1', '< 0.7' +``` + +[![gRPC and protocol buffers](https://user-images.githubusercontent.com/8466209/239118755-39dc1055-d92e-49cf-adcb-868d5a90cfa6.png)](https://grpc.io/docs/what-is-grpc/introduction/) + diff --git a/identition/span3/index.html b/identition/span3/index.html new file mode 100644 index 00000000000..f4f433399c1 --- /dev/null +++ b/identition/span3/index.html @@ -0,0 +1,55 @@ + Vibrating Strings (span 3) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Vibrating Strings (span 3)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-37 of orgs section-9 that is inherited from the spin section-3 by prime spin-60 and span-142 with the partitions as below.

            +
            +
            1. Container-Optimized
            2. gist07.md
            3. gist03.md
            4. gist02.md
            5. System Storage
            6. DNA Recombination
            7. Mass vs Gap (Δ)

            It turns out that quantum string theory always destroys the symmetries of classical string theory, except in one special case: when the number of dimensions is 10.

            +
            + + Note +
            +
            +

            Below is a model of E11 (shown by 11 dimensions). Its absolute dimensions represent all related key knowledges of modern physics. Moreover this model represents Quark-Gluon Plasma, with all of the fundamental forces in the early stage after Big Bang which probably comes from Absolute Nothingness.

            +
            +

            default

            The Prime Spiral Sieve possesses remarkable structural and numeric symmetries. For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period eight (8) difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2} (Primesdemystified).

            image

            +
            + + Note +
            +
            +

            Quantum field theory is any theory that describes a quantized field.

            • QED, or Quantum Electrodynamics, is the quantum theory of the electromagnetic field, a so-called Abelian field (referencing an internal mathematical symmetry of the theory.)
            • Electroweak theory is a generalization of QED, unifying it with the weak nuclear force in the form of a Yang-Mills field theory (aka. a non-Abelian field theory).
            • QCD, or Quantum Chromodynamics, is another example of a non-Abelian field theory, but one with very different asymptotic behavior than electroweak theory.
            • The Standard Model of particle physics is the combination of electroweak theory and QCD in the form of a unified theory obeying a complex set of symmetries.

            This theory describes all the known fields and all the known interactions other than gravity. (Quora)

            +
            +

            DifferencebetweenQEDandQCD.pdf

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            11's additive sums

            These objects will then behave as a complex numbers that leads to trivial and complex roots of the 18th prime identity. 286 - (231x5)/(11x7) = 286 - 1155/77 = 286 - 15 = 200 + 71 = 271

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20 --------
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                |
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------
+  =======================+====+====+====+====+====+====+====+====+====+===== bilateral 9 sums (2)+60+40=102
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 --------
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                |
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20 --------
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+
            +
            + + Note +
            +
            +

            We show that the Big Bang singularity of the Friedmann-Lemaˆıtre-Robertson-Walker model does not raise major problems to General Relativity.

            • We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang.
            • The old method of resolution of singularities shows how we can “untie” the singularity of a cone and obtain a cylinder.
            • This illustrates the idea that it is not necessary to assume that, at the Big Bang singularity, the entire space was a point, but only that the space metric was 0.

            These results follow from our research on singular semi-Riemannian geometry and singular General Relativity [26, 27, 29] (which we applied in previous articles to the black hole singularities [30, 31, 32, 28]).

            +
            +

            Big_Bang_singularity_in_the_Friedmann-Lemaitre-Rob.pdf

            The opposite direction will be made through switching beetween Linux and Windows which is proceed the old strand in the 3′ to 5′ direction, while the new strand is synthesized in the 5' to 3' direction. Here we set a remote self-host runner via WSL.

            default

            The rest of primes goes to the 33's of 15th axis that holding 102 primes of (2,60,40). By the bilateral way the form will be splitted to (1,30,20). Since the base frame shall be 40 so it will be forced to form (1,30,40) of prime 71.

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist01.html b/identition/span4/gist01.html new file mode 100644 index 00000000000..3f06df72073 --- /dev/null +++ b/identition/span4/gist01.html @@ -0,0 +1,420 @@ + Lexer vs Parser · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Lexer vs Parser

            enneatruth_anim

            image

            Notice how the 3, 9, and 6 is in red and does not connect at the base. That is because it is a vector. The 1,2,4,8,7,5 is the third dimension while the oscillation between the 3 and 6 demonstrates the fourth dimension, which is the higher dimensional magnetic field of an electrical coil.

            image

            The 3, 9, and 6 always occur together with the 9 as the control. In fact, the Yin/Yang is not a duality but rather a trinary. This is because the 3 and 6 represent each side of the Yin/Yang and the 9 is the "S" curve between them. Everything is based on thirds. We think that the universe is based on dualities because we see the effects not the cause.

            Four (4) Vector

            !

            Φ(11,13) = (114 - 10²) + 13 = 27

            1729 = 7 x 13 x 19
+1729 / 7 = 13 x 19 = 247
+
+1729 = 7 x 13 x 19
+       7 + 13 = 20 = d(2)
+                     └──  2 x 19 = 38
+
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+| {1}|  2 |  3 |  4 |  5 | {6}| {7}|  8 |  9 | 10 | 11 | 12 | 13 | 14 |
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+| {3}| {4}|  3 |  4 |  5 |  2 |  3 |  2 |  2 |  1 |  2 |  5 |  1 |  1 |{38}
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285
+|  3 |  8 |  9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|-- 38 ---|              |-- 33 ---|                        |-- {27}--|
+

            Four Spacetime Dimensions

            ------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            Diagram of Classes

            COS instances come pre-installed with the Docker runtime and cloud-init. With a COS instance, you can bring up your Docker container at the same time you create your VM, with no on-host setup required.

            Note: docker-credential-gcr writes credentials to $HOME/.docker/config.json. When running /usr/bin/docker-credential-gcr configure-docker in a unit file, you must set the environment variable $HOME. Otherwise, docker-credential-gcr will try to write credentials to /root/.docker/config.json, which is not permitted on Container-Optimized OS (Google Cloud).

            #cloud-config
+
+users:
+- default
+- uid: 2000
+  name: runner
+  groups: admin,adm,video,docker,google-sudoers
+
+write_files:
+- owner: root
+  permissions: 0644
+  path: /etc/systemd/system/runner.service
+  content: |
+    [Unit]
+    Wants=gcr-online.target
+    After=gcr-online.target
+    Description=gcloud compute instances create instance-template --scopes=https://www.googleapis.com/auth/cloud-platform --network-interface=network=default,network-tier=PREMIUM --maintenance-policy=MIGRATE --provisioning-model=STANDARD --project=feedmapping --zone=us-central1-a --shielded-vtpm --shielded-integrity-monitoring --reservation-affinity=any --service-account=project-owner@feedmapping.iam.gserviceaccount.com --machine-type=e2-micro --enable-display-device --no-shielded-secure-boot --image-family cos-stable --image-project cos-cloud --metadata-from-file user-data=cloud-config --create-disk=auto-delete=yes,device-name=persistent-disk-1,boot=no,image-family=tf-ent-latest-gpu,mode=rw,size=50,type=pd-standard,image-project=deeplearning-platform-release 
+
+    [Service]
+    Environment="HOME=/home/runner"
+    ExecStartPre=/usr/bin/docker-credential-gcr configure-docker
+    ExecStart=/usr/bin/docker run --rm --name myrunner -e RUNNER_NAME=Google-optimized-instance -e RUNNER_ORGANIZATION_URL=https://github.com/FeedMapping -e RUNNER_WORK_DIRECTORY=/mnt/disks/Linux/tmp/_FeedMapping -e RUNNER_REPLACE_EXISTING=true -e GITHUB_ACCESS_TOKEN=ghp_XXXXXXXXXXXXXXXXXXXXXXXXXX -v /var/run/docker.sock:/var/run/docker.sock -v /mnt:/mnt eq19/setup
+    ExecStop=/usr/bin/docker stop myrunner
+    ExecStopPost=/usr/bin/docker rm myrunner
+
+runcmd:
+- systemctl daemon-reload
+- systemctl start runner.service
+- systemctl status runner.service
+
+bootcmd:
+- fsck.ext4 -tvy /dev/sdb1
+- mkdir -p /mnt/disks/Linux
+- mount -t ext4 -o discard,defaults /dev/sdb1 /mnt/disks/Linux
+

            Using the advanced scenarios you can deploy multiple containers and configure Docker options using cloud-init, you can create a Compute Engine instance with your choice of COS image then proceed to configure with metadata.

            docker run -it --name Google-optimized-instance \
+    -e RUNNER_NAME=Google-optimized-instance \
+    -e RUNNER_ORGANIZATION_URL=https://github.com/FeedMapping \
+    -e GITHUB_ACCESS_TOKEN=ghp_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx \
+    -v /var/run/docker.sock:/var/run/docker.sock \
+    tcardonne/github-runner
+

            The Google instance deployed through the Google Cloud console or the Google Cloud CLI, not the API. Use advanced scenarios to deploy multiple containers, and to use cloud-init for advanced configuration.

            default

            It will be managed by the boot disk of 10GB represent the central of addition zone with two (2) exponential zone each represent new lagging strand DNA, whose direction of synthesis is opposite to the direction of the growing replication fork.

            Deep Learning

            Base on above scheme here we are going to use Deep Learning VM Images from Google and Windows Server Images from Microsoft by the image disks of 32GB to represent imajinary part (i), and the 50GB to represent circle part (π).

            The Cloud-init is a way to configure a COS instance when it boots up. The tool expects its configuration in the value of the user-data key of the instance metadata. The cloud-init tool understands multiple formats.

            default

            The COS Container has limited or no support for the gsutil tool. Passing a startup script for COS instance of #cloud-config from Cloud Storage is not possible therefore it needs to be stored in a local file and create-disk using gcloud.

            gcloud compute instances create instance-template \
+--scopes=https://www.googleapis.com/auth/cloud-platform \
+--network-interface=network=default,network-tier=PREMIUM \
+--maintenance-policy=MIGRATE --provisioning-model=STANDARD \
+--project=feedmapping --zone=us-central1-a --shielded-vtpm \
+--shielded-integrity-monitoring --reservation-affinity=any \
+--service-account=project-owner@feedmapping.iam.gserviceaccount.com \
+--machine-type=e2-micro --enable-display-device --no-shielded-secure-boot \
+--image-family cos-stable --image-project cos-cloud \                          ◄- COS
+--metadata-from-file user-data=cloud-config \
+--create-disk=auto-delete=yes,device-name=persistent-disk-1,boot=no,\          ◄- LINUX
+image-family=tf-ent-latest-gpu,mode=rw,size=50,type=pd-standard,\
+image-project=deeplearning-platform-release \
+--create-disk=auto-delete=yes,device-name=persistent-disk-2,boot=no,\          ◄- WINDOWS
+image=projects/gce-uefi-images/global/images/windows-server-1909\
+-dc-core-for-containers-v20200609,mode=rw,size=32,type=pd-standard
+

            Deep Learning VM Images are virtual machine images optimized for data science and machine learning tasks. Built with key ML frameworks, tools pre-installed, and can be used out of the box on instances with GPUs to accelerate data processing.

            Deciding on an image family

            In Linux dpkg is the primary package manager for Debian and Debian-based systems, such as Ubuntu. The tool installs, builds, removes, configures, and retrieves information for Debian packages. The command works with packages in .deb format.

            $ dpkg -l
+
+Desired=Unknown/Install/Remove/Purge/Hold
+| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
+|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
+||/ Name                          Version                     Architecture Description
++++-=============================-===========================-============-===============================================================================
+ii  adduser                       3.118                       all          add and remove users and groups
+ii  apparmor                      2.13.2-10                   amd64        user-space parser utility for AppArmor
+ii  apt                           1.8.2.3                     amd64        commandline package manager
+ii  apt-transport-https           1.8.2.3                     all          transitional package for https support
+ii  base-files                    10.3+deb10u13               amd64        Debian base system miscellaneous files
+ii  base-passwd                   3.5.46                      amd64        Debian base system master password and group files
+ii  bash                          5.0-4                       amd64        GNU Bourne Again SHell
+ii  binutils                      2.31.1-16                   amd64        GNU assembler, linker and binary utilities
+ii  binutils-common:amd64         2.31.1-16                   amd64        Common files for the GNU assembler, linker and binary utilities
+ii  binutils-x86-64-linux-gnu     2.31.1-16                   amd64        GNU binary utilities, for x86-64-linux-gnu target
+ii  bsdutils                      1:2.33.1-0.1                amd64        basic utilities from 4.4BSD-Lite
+ii  build-essential               12.6                        amd64        Informational list of build-essential packages
+ii  bzip2                         1.0.6-9.2~deb10u2           amd64        high-quality block-sorting file compressor - utilities
+ii  ca-certificates               20200601~deb10u2            all          Common CA certificates
+ii  containerd.io                 1.6.20-1                    amd64        An open and reliable container runtime
+ii  coreutils                     8.30-3                      amd64        GNU core utilities
+ii  cpp                           4:8.3.0-1                   amd64        GNU C preprocessor (cpp)
+ii  cpp-8                         8.3.0-6                     amd64        GNU C preprocessor
+ii  curl                          7.64.0-4+deb10u5            amd64        command line tool for transferring data with URL syntax
+ii  dash                          0.5.10.2-5                  amd64        POSIX-compliant shell
+ii  dbus                          1.12.24-0+deb10u1           amd64        simple interprocess messaging system (daemon and utilities)
+ii  dbus-user-session             1.12.24-0+deb10u1           amd64        simple interprocess messaging system (systemd --user integration)
+ii  debconf                       1.5.71+deb10u1              all          Debian configuration management system
+ii  debian-archive-keyring        2019.1+deb10u1              all          GnuPG archive keys of the Debian archive
+ii  debianutils                   4.8.6.1                     amd64        Miscellaneous utilities specific to Debian
+ii  diffutils                     1:3.7-3                     amd64        File comparison utilities
+ii  dirmngr                       2.2.12-1+deb10u2            amd64        GNU privacy guard - network certificate management service
+ii  distro-info-data              0.41+deb10u6                all          information about the distributions' releases (data files)
+ii  dmsetup                       2:1.02.155-3                amd64        Linux Kernel Device Mapper userspace library
+ii  docker-buildx-plugin          0.10.4-1~debian.10~buster   amd64        Docker Buildx cli plugin.
+ii  docker-ce                     5:23.0.3-1~debian.10~buster amd64        Docker: the open-source application container engine
+ii  docker-ce-cli                 5:23.0.3-1~debian.10~buster amd64        Docker CLI: the open-source application container engine
+ii  docker-ce-rootless-extras     5:23.0.3-1~debian.10~buster amd64        Rootless support for Docker.
+ii  docker-compose-plugin         2.17.2-1~debian.10~buster   amd64        Docker Compose (V2) plugin for the Docker CLI.
+ii  dpkg                          1.19.8                      amd64        Debian package management system
+ii  dpkg-dev                      1.19.8                      all          Debian package development tools
+ii  e2fsprogs                     1.44.5-1+deb10u3            amd64        ext2/ext3/ext4 file system utilities
+ii  fakeroot                      1.23-1                      amd64        tool for simulating superuser privileges
+ii  fdisk                         2.33.1-0.1                  amd64        collection of partitioning utilities
+ii  file                          1:5.35-4+deb10u2            amd64        Recognize the type of data in a file using "magic" numbers
+ii  findutils                     4.6.0+git+20190209-2        amd64        utilities for finding files--find, xargs
+ii  g++                           4:8.3.0-1                   amd64        GNU C++ compiler
+ii  g++-8                         8.3.0-6                     amd64        GNU C++ compiler
+ii  gcc                           4:8.3.0-1                   amd64        GNU C compiler
+ii  gcc-8                         8.3.0-6                     amd64        GNU C compiler
+ii  gcc-8-base:amd64              8.3.0-6                     amd64        GCC, the GNU Compiler Collection (base package)
+ii  gettext                       0.19.8.1-9                  amd64        GNU Internationalization utilities
+ii  gettext-base                  0.19.8.1-9                  amd64        GNU Internationalization utilities for the base system
+ii  gir1.2-glib-2.0:amd64         1.58.3-2                    amd64        Introspection data for GLib, GObject, Gio and GModule
+ii  gir1.2-packagekitglib-1.0     1.1.12-5                    amd64        GObject introspection data for the PackageKit GLib library
+ii  git                           1:2.20.1-2+deb10u8          amd64        fast, scalable, distributed revision control system
+ii  git-man                       1:2.20.1-2+deb10u8          all          fast, scalable, distributed revision control system (manual pages)
+ii  gnupg                         2.2.12-1+deb10u2            all          GNU privacy guard - a free PGP replacement
+ii  gnupg-l10n                    2.2.12-1+deb10u2            all          GNU privacy guard - localization files
+ii  gnupg-utils                   2.2.12-1+deb10u2            amd64        GNU privacy guard - utility programs
+ii  gpg                           2.2.12-1+deb10u2            amd64        GNU Privacy Guard -- minimalist public key operations
+ii  gpg-agent                     2.2.12-1+deb10u2            amd64        GNU privacy guard - cryptographic agent
+ii  gpg-wks-client                2.2.12-1+deb10u2            amd64        GNU privacy guard - Web Key Service client
+ii  gpg-wks-server                2.2.12-1+deb10u2            amd64        GNU privacy guard - Web Key Service server
+ii  gpgconf                       2.2.12-1+deb10u2            amd64        GNU privacy guard - core configuration utilities
+ii  gpgsm                         2.2.12-1+deb10u2            amd64        GNU privacy guard - S/MIME version
+ii  gpgv                          2.2.12-1+deb10u2            amd64        GNU privacy guard - signature verification tool
+ii  grep                          3.3-1                       amd64        GNU grep, egrep and fgrep
+ii  gzip                          1.9-3+deb10u1               amd64        GNU compression utilities
+ii  hostname                      3.21                        amd64        utility to set/show the host name or domain name
+ii  init-system-helpers           1.56+nmu1                   all          helper tools for all init systems
+ii  iptables                      1.8.2-4                     amd64        administration tools for packet filtering and NAT
+ii  iputils-ping                  3:20180629-2+deb10u2        amd64        Tools to test the reachability of network hosts
+ii  iso-codes                     4.2-1                       all          ISO language, territory, currency, script codes and their translations
+ii  jq                            1.5+dfsg-2+b1               amd64        lightweight and flexible command-line JSON processor
+ii  krb5-locales                  1.17-3+deb10u5              all          internationalization support for MIT Kerberos
+ii  less                          487-0.1+b1                  amd64        pager program similar to more
+ii  libacl1:amd64                 2.2.53-4                    amd64        access control list - shared library
+ii  libalgorithm-diff-perl        1.19.03-2                   all          module to find differences between files
+ii  libalgorithm-diff-xs-perl     0.04-5+b1                   amd64        module to find differences between files (XS accelerated)
+ii  libalgorithm-merge-perl       0.08-3                      all          Perl module for three-way merge of textual data
+ii  libapparmor1:amd64            2.13.2-10                   amd64        changehat AppArmor library
+ii  libappstream4:amd64           0.12.5-1                    amd64        Library to access AppStream services
+ii  libapt-inst2.0:amd64          1.8.2.3                     amd64        deb package format runtime library
+ii  libapt-pkg5.0:amd64           1.8.2.3                     amd64        package management runtime library
+ii  libargon2-1:amd64             0~20171227-0.2              amd64        memory-hard hashing function - runtime library
+ii  libasan5:amd64                8.3.0-6                     amd64        AddressSanitizer -- a fast memory error detector
+ii  libassuan0:amd64              2.5.2-1                     amd64        IPC library for the GnuPG components
+ii  libatomic1:amd64              8.3.0-6                     amd64        support library providing __atomic built-in functions
+ii  libattr1:amd64                1:2.4.48-4                  amd64        extended attribute handling - shared library
+ii  libaudit-common               1:2.8.4-3                   all          Dynamic library for security auditing - common files
+ii  libaudit1:amd64               1:2.8.4-3                   amd64        Dynamic library for security auditing
+ii  libbinutils:amd64             2.31.1-16                   amd64        GNU binary utilities (private shared library)
+ii  libblkid1:amd64               2.33.1-0.1                  amd64        block device ID library
+ii  libbsd0:amd64                 0.9.1-2+deb10u1             amd64        utility functions from BSD systems - shared library
+ii  libbz2-1.0:amd64              1.0.6-9.2~deb10u2           amd64        high-quality block-sorting file compressor library - runtime
+ii  libc-bin                      2.28-10+deb10u2             amd64        GNU C Library: Binaries
+ii  libc-dev-bin                  2.28-10+deb10u2             amd64        GNU C Library: Development binaries
+ii  libc6:amd64                   2.28-10+deb10u2             amd64        GNU C Library: Shared libraries
+ii  libc6-dev:amd64               2.28-10+deb10u2             amd64        GNU C Library: Development Libraries and Header Files
+ii  libcap-ng0:amd64              0.7.9-2                     amd64        An alternate POSIX capabilities library
+ii  libcap2:amd64                 1:2.25-2                    amd64        POSIX 1003.1e capabilities (library)
+ii  libcap2-bin                   1:2.25-2                    amd64        POSIX 1003.1e capabilities (utilities)
+ii  libcc1-0:amd64                8.3.0-6                     amd64        GCC cc1 plugin for GDB
+ii  libcom-err2:amd64             1.44.5-1+deb10u3            amd64        common error description library
+ii  libcroco3:amd64               0.6.12-3                    amd64        Cascading Style Sheet (CSS) parsing and manipulation toolkit
+ii  libcryptsetup12:amd64         2:2.1.0-5+deb10u2           amd64        disk encryption support - shared library
+ii  libcurl3-gnutls:amd64         7.64.0-4+deb10u5            amd64        easy-to-use client-side URL transfer library (GnuTLS flavour)
+ii  libcurl4:amd64                7.64.0-4+deb10u5            amd64        easy-to-use client-side URL transfer library (OpenSSL flavour)
+ii  libcurl4-openssl-dev:amd64    7.64.0-4+deb10u5            amd64        development files and documentation for libcurl (OpenSSL flavour)
+ii  libdb5.3:amd64                5.3.28+dfsg1-0.5            amd64        Berkeley v5.3 Database Libraries [runtime]
+ii  libdbus-1-3:amd64             1.12.24-0+deb10u1           amd64        simple interprocess messaging system (library)
+ii  libdebconfclient0:amd64       0.249                       amd64        Debian Configuration Management System (C-implementation library)
+ii  libdevmapper1.02.1:amd64      2:1.02.155-3                amd64        Linux Kernel Device Mapper userspace library
+ii  libdpkg-perl                  1.19.8                      all          Dpkg perl modules
+ii  libedit2:amd64                3.1-20181209-1              amd64        BSD editline and history libraries
+ii  libelf1:amd64                 0.176-1.1                   amd64        library to read and write ELF files
+ii  liberror-perl                 0.17027-2                   all          Perl module for error/exception handling in an OO-ish way
+ii  libexpat1:amd64               2.2.6-2+deb10u6             amd64        XML parsing C library - runtime library
+ii  libext2fs2:amd64              1.44.5-1+deb10u3            amd64        ext2/ext3/ext4 file system libraries
+ii  libfakeroot:amd64             1.23-1                      amd64        tool for simulating superuser privileges - shared libraries
+ii  libfdisk1:amd64               2.33.1-0.1                  amd64        fdisk partitioning library
+ii  libffi6:amd64                 3.2.1-9                     amd64        Foreign Function Interface library runtime
+ii  libfile-fcntllock-perl        0.22-3+b5                   amd64        Perl module for file locking with fcntl(2)
+ii  libgcc-8-dev:amd64            8.3.0-6                     amd64        GCC support library (development files)
+ii  libgcc1:amd64                 1:8.3.0-6                   amd64        GCC support library
+ii  libgcrypt20:amd64             1.8.4-5+deb10u1             amd64        LGPL Crypto library - runtime library
+ii  libgdbm-compat4:amd64         1.18.1-4                    amd64        GNU dbm database routines (legacy support runtime version) 
+ii  libgdbm6:amd64                1.18.1-4                    amd64        GNU dbm database routines (runtime version) 
+ii  libgirepository-1.0-1:amd64   1.58.3-2                    amd64        Library for handling GObject introspection data (runtime library)
+ii  libglib2.0-0:amd64            2.58.3-2+deb10u4            amd64        GLib library of C routines
+ii  libglib2.0-bin                2.58.3-2+deb10u4            amd64        Programs for the GLib library
+ii  libglib2.0-data               2.58.3-2+deb10u4            all          Common files for GLib library
+ii  libgmp10:amd64                2:6.1.2+dfsg-4+deb10u1      amd64        Multiprecision arithmetic library
+ii  libgnutls30:amd64             3.6.7-4+deb10u10            amd64        GNU TLS library - main runtime library
+ii  libgomp1:amd64                8.3.0-6                     amd64        GCC OpenMP (GOMP) support library
+ii  libgpg-error0:amd64           1.35-1                      amd64        GnuPG development runtime library
+ii  libgpm2:amd64                 1.20.7-5                    amd64        General Purpose Mouse - shared library
+ii  libgssapi-krb5-2:amd64        1.17-3+deb10u5              amd64        MIT Kerberos runtime libraries - krb5 GSS-API Mechanism
+ii  libgstreamer1.0-0:amd64       1.14.4-1                    amd64        Core GStreamer libraries and elements
+ii  libhogweed4:amd64             3.4.1-1+deb10u1             amd64        low level cryptographic library (public-key cryptos)
+ii  libicu63:amd64                63.1-6+deb10u3              amd64        International Components for Unicode
+ii  libidn11:amd64                1.33-2.2                    amd64        GNU Libidn library, implementation of IETF IDN specifications
+ii  libidn2-0:amd64               2.0.5-1+deb10u1             amd64        Internationalized domain names (IDNA2008/TR46) library
+ii  libip4tc0:amd64               1.8.2-4                     amd64        netfilter libip4tc library
+ii  libip6tc0:amd64               1.8.2-4                     amd64        netfilter libip6tc library
+ii  libiptc0:amd64                1.8.2-4                     amd64        netfilter libiptc library
+ii  libisl19:amd64                0.20-2                      amd64        manipulating sets and relations of integer points bounded by linear constraints
+ii  libitm1:amd64                 8.3.0-6                     amd64        GNU Transactional Memory Library
+ii  libjansson4:amd64             2.12-1                      amd64        C library for encoding, decoding and manipulating JSON data
+ii  libjq1:amd64                  1.5+dfsg-2+b1               amd64        lightweight and flexible command-line JSON processor - shared library
+ii  libjson-c3:amd64              0.12.1+ds-2+deb10u1         amd64        JSON manipulation library - shared library
+ii  libk5crypto3:amd64            1.17-3+deb10u5              amd64        MIT Kerberos runtime libraries - Crypto Library
+ii  libkeyutils1:amd64            1.6-6                       amd64        Linux Key Management Utilities (library)
+ii  libkmod2:amd64                26-1                        amd64        libkmod shared library
+ii  libkrb5-3:amd64               1.17-3+deb10u5              amd64        MIT Kerberos runtime libraries
+ii  libkrb5support0:amd64         1.17-3+deb10u5              amd64        MIT Kerberos runtime libraries - Support library
+ii  libksba8:amd64                1.3.5-2+deb10u2             amd64        X.509 and CMS support library
+ii  libldap-2.4-2:amd64           2.4.47+dfsg-3+deb10u7       amd64        OpenLDAP libraries
+ii  libldap-common                2.4.47+dfsg-3+deb10u7       all          OpenLDAP common files for libraries
+ii  liblocale-gettext-perl        1.07-3+b4                   amd64        module using libc functions for internationalization in Perl
+ii  liblsan0:amd64                8.3.0-6                     amd64        LeakSanitizer -- a memory leak detector (runtime)
+ii  libltdl7:amd64                2.4.6-9                     amd64        System independent dlopen wrapper for GNU libtool
+ii  liblttng-ust-ctl4:amd64       2.10.3-1                    amd64        LTTng 2.0 Userspace Tracer (trace control library)
+ii  liblttng-ust0:amd64           2.10.3-1                    amd64        LTTng 2.0 Userspace Tracer (tracing libraries)
+ii  liblz4-1:amd64                1.8.3-1+deb10u1             amd64        Fast LZ compression algorithm library - runtime
+ii  liblzma5:amd64                5.2.4-1+deb10u1             amd64        XZ-format compression library
+ii  libmagic-mgc                  1:5.35-4+deb10u2            amd64        File type determination library using "magic" numbers (compiled magic file)
+ii  libmagic1:amd64               1:5.35-4+deb10u2            amd64        Recognize the type of data in a file using "magic" numbers - library
+ii  libmnl0:amd64                 1.0.4-2                     amd64        minimalistic Netlink communication library
+ii  libmount1:amd64               2.33.1-0.1                  amd64        device mounting library
+ii  libmpc3:amd64                 1.1.0-1                     amd64        multiple precision complex floating-point library
+ii  libmpdec2:amd64               2.4.2-2                     amd64        library for decimal floating point arithmetic (runtime library)
+ii  libmpfr6:amd64                4.0.2-1                     amd64        multiple precision floating-point computation
+ii  libmpx2:amd64                 8.3.0-6                     amd64        Intel memory protection extensions (runtime)
+ii  libncurses6:amd64             6.1+20181013-2+deb10u3      amd64        shared libraries for terminal handling
+ii  libncursesw6:amd64            6.1+20181013-2+deb10u3      amd64        shared libraries for terminal handling (wide character support)
+ii  libnetfilter-conntrack3:amd64 1.0.7-1                     amd64        Netfilter netlink-conntrack library
+ii  libnettle6:amd64              3.4.1-1+deb10u1             amd64        low level cryptographic library (symmetric and one-way cryptos)
+ii  libnfnetlink0:amd64           1.0.1-3+b1                  amd64        Netfilter netlink library
+ii  libnftables0:amd64            0.9.0-2                     amd64        Netfilter nftables high level userspace API library
+ii  libnftnl11:amd64              1.1.2-2                     amd64        Netfilter nftables userspace API library
+ii  libnghttp2-14:amd64           1.36.0-2+deb10u1            amd64        library implementing HTTP/2 protocol (shared library)
+ii  libnpth0:amd64                1.6-1                       amd64        replacement for GNU Pth using system threads
+ii  libnss-systemd:amd64          241-7~deb10u9               amd64        nss module providing dynamic user and group name resolution
+ii  libonig5:amd64                6.9.1-1                     amd64        regular expressions library
+ii  libp11-kit0:amd64             0.23.15-2+deb10u1           amd64        library for loading and coordinating access to PKCS#11 modules - runtime
+ii  libpackagekit-glib2-18:amd64  1.1.12-5                    amd64        Library for accessing PackageKit using GLib
+ii  libpam-cap:amd64              1:2.25-2                    amd64        POSIX 1003.1e capabilities (PAM module)
+ii  libpam-modules:amd64          1.3.1-5                     amd64        Pluggable Authentication Modules for PAM
+ii  libpam-modules-bin            1.3.1-5                     amd64        Pluggable Authentication Modules for PAM - helper binaries
+ii  libpam-runtime                1.3.1-5                     all          Runtime support for the PAM library
+ii  libpam-systemd:amd64          241-7~deb10u9               amd64        system and service manager - PAM module
+ii  libpam0g:amd64                1.3.1-5                     amd64        Pluggable Authentication Modules library
+ii  libpcre2-8-0:amd64            10.32-5+deb10u1             amd64        New Perl Compatible Regular Expression Library- 8 bit runtime files
+ii  libpcre3:amd64                2:8.39-12                   amd64        Old Perl 5 Compatible Regular Expression Library - runtime files
+ii  libperl5.28:amd64             5.28.1-6+deb10u1            amd64        shared Perl library
+ii  libpolkit-agent-1-0:amd64     0.105-25+deb10u1            amd64        PolicyKit Authentication Agent API
+ii  libpolkit-backend-1-0:amd64   0.105-25+deb10u1            amd64        PolicyKit backend API
+ii  libpolkit-gobject-1-0:amd64   0.105-25+deb10u1            amd64        PolicyKit Authorization API
+ii  libprocps7:amd64              2:3.3.15-2                  amd64        library for accessing process information from /proc
+ii  libpsl5:amd64                 0.20.2-2                    amd64        Library for Public Suffix List (shared libraries)
+ii  libpython-stdlib:amd64        2.7.16-1                    amd64        interactive high-level object-oriented language (Python2)
+ii  libpython2-stdlib:amd64       2.7.16-1                    amd64        interactive high-level object-oriented language (Python2)
+ii  libpython2.7-minimal:amd64    2.7.16-2+deb10u1            amd64        Minimal subset of the Python language (version 2.7)
+ii  libpython2.7-stdlib:amd64     2.7.16-2+deb10u1            amd64        Interactive high-level object-oriented language (standard library, version 2.7)
+ii  libpython3-stdlib:amd64       3.7.3-1                     amd64        interactive high-level object-oriented language (default python3 version)
+ii  libpython3.7-minimal:amd64    3.7.3-2+deb10u4             amd64        Minimal subset of the Python language (version 3.7)
+ii  libpython3.7-stdlib:amd64     3.7.3-2+deb10u4             amd64        Interactive high-level object-oriented language (standard library, version 3.7)
+ii  libquadmath0:amd64            8.3.0-6                     amd64        GCC Quad-Precision Math Library
+ii  libreadline7:amd64            7.0-5                       amd64        GNU readline and history libraries, run-time libraries
+ii  librtmp1:amd64                2.4+20151223.gitfa8646d.1-2 amd64        toolkit for RTMP streams (shared library)
+ii  libsasl2-2:amd64              2.1.27+dfsg-1+deb10u2       amd64        Cyrus SASL - authentication abstraction library
+ii  libsasl2-modules:amd64        2.1.27+dfsg-1+deb10u2       amd64        Cyrus SASL - pluggable authentication modules
+ii  libsasl2-modules-db:amd64     2.1.27+dfsg-1+deb10u2       amd64        Cyrus SASL - pluggable authentication modules (DB)
+ii  libseccomp2:amd64             2.3.3-4                     amd64        high level interface to Linux seccomp filter
+ii  libselinux1:amd64             2.8-1+b1                    amd64        SELinux runtime shared libraries
+ii  libsemanage-common            2.8-2                       all          Common files for SELinux policy management libraries
+ii  libsemanage1:amd64            2.8-2                       amd64        SELinux policy management library
+ii  libsepol1:amd64               2.8-1                       amd64        SELinux library for manipulating binary security policies
+ii  libsmartcols1:amd64           2.33.1-0.1                  amd64        smart column output alignment library
+ii  libsqlite3-0:amd64            3.27.2-3+deb10u2            amd64        SQLite 3 shared library
+ii  libss2:amd64                  1.44.5-1+deb10u3            amd64        command-line interface parsing library
+ii  libssh2-1:amd64               1.8.0-2.1                   amd64        SSH2 client-side library
+ii  libssl1.1:amd64               1.1.1n-0+deb10u4            amd64        Secure Sockets Layer toolkit - shared libraries
+ii  libstdc++-8-dev:amd64         8.3.0-6                     amd64        GNU Standard C++ Library v3 (development files)
+ii  libstdc++6:amd64              8.3.0-6                     amd64        GNU Standard C++ Library v3
+ii  libstemmer0d:amd64            0+svn585-1+b2               amd64        Snowball stemming algorithms for use in Information Retrieval
+ii  libsystemd0:amd64             241-7~deb10u9               amd64        systemd utility library
+ii  libtasn1-6:amd64              4.13-3+deb10u1              amd64        Manage ASN.1 structures (runtime)
+ii  libtinfo6:amd64               6.1+20181013-2+deb10u3      amd64        shared low-level terminfo library for terminal handling
+ii  libtsan0:amd64                8.3.0-6                     amd64        ThreadSanitizer -- a Valgrind-based detector of data races (runtime)
+ii  libubsan1:amd64               8.3.0-6                     amd64        UBSan -- undefined behaviour sanitizer (runtime)
+ii  libudev1:amd64                241-7~deb10u8               amd64        libudev shared library
+ii  libunistring2:amd64           0.9.10-1                    amd64        Unicode string library for C
+ii  liburcu6:amd64                0.10.2-1                    amd64        userspace RCU (read-copy-update) library
+ii  libuuid1:amd64                2.33.1-0.1                  amd64        Universally Unique ID library
+ii  libx11-6:amd64                2:1.6.7-1+deb10u2           amd64        X11 client-side library
+ii  libx11-data                   2:1.6.7-1+deb10u2           all          X11 client-side library
+ii  libxau6:amd64                 1:1.0.8-1+b2                amd64        X11 authorisation library
+ii  libxcb1:amd64                 1.13.1-2                    amd64        X C Binding
+ii  libxdmcp6:amd64               1:1.1.2-3                   amd64        X11 Display Manager Control Protocol library
+ii  libxext6:amd64                2:1.3.3-1+b2                amd64        X11 miscellaneous extension library
+ii  libxml2:amd64                 2.9.4+dfsg1-7+deb10u5       amd64        GNOME XML library
+ii  libxmuu1:amd64                2:1.1.2-2+b3                amd64        X11 miscellaneous micro-utility library
+ii  libxtables12:amd64            1.8.2-4                     amd64        netfilter xtables library
+ii  libyaml-0-2:amd64             0.2.1-1                     amd64        Fast YAML 1.1 parser and emitter library
+ii  libzstd1:amd64                1.3.8+dfsg-3+deb10u2        amd64        fast lossless compression algorithm
+ii  linux-libc-dev:amd64          4.19.269-1                  amd64        Linux support headers for userspace development
+ii  login                         1:4.5-1.1                   amd64        system login tools
+ii  lsb-base                      10.2019051400               all          Linux Standard Base init script functionality
+ii  lsb-release                   10.2019051400               all          Linux Standard Base version reporting utility
+ii  make                          4.2.1-1.2                   amd64        utility for directing compilation
+ii  manpages                      4.16-2                      all          Manual pages about using a GNU/Linux system
+ii  manpages-dev                  4.16-2                      all          Manual pages about using GNU/Linux for development
+ii  mawk                          1.3.3-17+b3                 amd64        a pattern scanning and text processing language
+ii  mime-support                  3.62                        all          MIME files 'mime.types' & 'mailcap', and support programs
+ii  mount                         2.33.1-0.1                  amd64        tools for mounting and manipulating filesystems
+ii  ncurses-base                  6.1+20181013-2+deb10u3      all          basic terminal type definitions
+ii  ncurses-bin                   6.1+20181013-2+deb10u3      amd64        terminal-related programs and man pages
+ii  netbase                       5.6                         all          Basic TCP/IP networking system
+ii  nftables                      0.9.0-2                     amd64        Program to control packet filtering rules by Netfilter project
+ii  openssh-client                1:7.9p1-10+deb10u2          amd64        secure shell (SSH) client, for secure access to remote machines
+ii  openssl                       1.1.1n-0+deb10u4            amd64        Secure Sockets Layer toolkit - cryptographic utility
+ii  packagekit                    1.1.12-5                    amd64        Provides a package management service
+ii  packagekit-tools              1.1.12-5                    amd64        Provides PackageKit command-line tools
+ii  passwd                        1:4.5-1.1                   amd64        change and administer password and group data
+ii  patch                         2.7.6-3+deb10u1             amd64        Apply a diff file to an original
+ii  perl                          5.28.1-6+deb10u1            amd64        Larry Wall's Practical Extraction and Report Language
+ii  perl-base                     5.28.1-6+deb10u1            amd64        minimal Perl system
+ii  perl-modules-5.28             5.28.1-6+deb10u1            all          Core Perl modules
+ii  pigz                          2.4-1                       amd64        Parallel Implementation of GZip
+ii  pinentry-curses               1.1.0-2                     amd64        curses-based PIN or pass-phrase entry dialog for GnuPG
+ii  policykit-1                   0.105-25+deb10u1            amd64        framework for managing administrative policies and privileges
+ii  procps                        2:3.3.15-2                  amd64        /proc file system utilities
+ii  psmisc                        23.2-1+deb10u1              amd64        utilities that use the proc file system
+ii  publicsuffix                  20220811.1734-0+deb10u1     all          accurate, machine-readable list of domain name suffixes
+ii  python                        2.7.16-1                    amd64        interactive high-level object-oriented language (Python2 version)
+ii  python-apt-common             1.8.4.3                     all          Python interface to libapt-pkg (locales)
+ii  python-meld3                  1.0.2-2                     all          HTML/XML templating system for Python
+ii  python-minimal                2.7.16-1                    amd64        minimal subset of the Python2 language
+ii  python-pkg-resources          40.8.0-1                    all          Package Discovery and Resource Access using pkg_resources
+ii  python2                       2.7.16-1                    amd64        interactive high-level object-oriented language (Python2 version)
+ii  python2-minimal               2.7.16-1                    amd64        minimal subset of the Python2 language
+ii  python2.7                     2.7.16-2+deb10u1            amd64        Interactive high-level object-oriented language (version 2.7)
+ii  python2.7-minimal             2.7.16-2+deb10u1            amd64        Minimal subset of the Python language (version 2.7)
+ii  python3                       3.7.3-1                     amd64        interactive high-level object-oriented language (default python3 version)
+ii  python3-apt                   1.8.4.3                     amd64        Python 3 interface to libapt-pkg
+ii  python3-dbus                  1.2.8-3                     amd64        simple interprocess messaging system (Python 3 interface)
+ii  python3-distro-info           0.21                        all          information about distributions' releases (Python 3 module)
+ii  python3-gi                    3.30.4-1                    amd64        Python 3 bindings for gobject-introspection libraries
+ii  python3-minimal               3.7.3-1                     amd64        minimal subset of the Python language (default python3 version)
+ii  python3-pycurl                7.43.0.2-0.1                amd64        Python bindings to libcurl (Python 3)
+ii  python3-software-properties   0.96.20.2-2                 all          manage the repositories that you install software from
+ii  python3.7                     3.7.3-2+deb10u4             amd64        Interactive high-level object-oriented language (version 3.7)
+ii  python3.7-minimal             3.7.3-2+deb10u4             amd64        Minimal subset of the Python language (version 3.7)
+ii  readline-common               7.0-5                       all          GNU readline and history libraries, common files
+ii  sed                           4.7-1                       amd64        GNU stream editor for filtering/transforming text
+ii  sensible-utils                0.0.12                      all          Utilities for sensible alternative selection
+ii  shared-mime-info              1.10-1                      amd64        FreeDesktop.org shared MIME database and spec
+ii  software-properties-common    0.96.20.2-2                 all          manage the repositories that you install software from (common)
+ii  sudo                          1.8.27-1+deb10u5            amd64        Provide limited super user privileges to specific users
+ii  supervisor                    3.3.5-1                     all          System for controlling process state
+ii  systemd                       241-7~deb10u9               amd64        system and service manager
+ii  systemd-sysv                  241-7~deb10u9               amd64        system and service manager - SysV links
+ii  sysvinit-utils                2.93-8                      amd64        System-V-like utilities
+ii  tar                           1.30+dfsg-6                 amd64        GNU version of the tar archiving utility
+ii  tzdata                        2021a-0+deb10u8             all          time zone and daylight-saving time data
+ii  ucf                           3.0038+nmu1                 all          Update Configuration File(s): preserve user changes to config files
+ii  unattended-upgrades           1.11.2                      all          automatic installation of security upgrades
+ii  unzip                         6.0-23+deb10u3              amd64        De-archiver for .zip files
+ii  util-linux                    2.33.1-0.1                  amd64        miscellaneous system utilities
+ii  xauth                         1:1.0.10-1                  amd64        X authentication utility
+ii  xdg-user-dirs                 0.17-2                      amd64        tool to manage well known user directories
+ii  xz-utils                      5.2.4-1+deb10u1             amd64        XZ-format compression utilities
+ii  zlib1g:amd64                  1:1.2.11.dfsg-1+deb10u2     amd64        compression library - runtime
+ii  zlib1g-dev:amd64              1:1.2.11.dfsg-1+deb10u2     amd64        compression library - development
+/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+/usr/bin/python
+Python 3.7.3
+curl 7.64.0 (x86_64-pc-linux-gnu) libcurl/7.64.0 OpenSSL/1.1.1n zlib/1.2.11 libidn2/2.0.5 libpsl/0.20.2 (+libidn2/2.0.5) libssh2/1.8.0 nghttp2/1.36.0 librtmp/2.3
+
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist02.html b/identition/span4/gist02.html new file mode 100644 index 00000000000..6e74436401f --- /dev/null +++ b/identition/span4/gist02.html @@ -0,0 +1,1043 @@ + Binary · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Binary

            Once the System Properties window opens, click on the "Environment Variables" button. In the "System Variables" box, look for a variable called Path. see all executables in your PATH on your system, and all aliases, all sorted

            $ find ${PATH//:/ } -maxdepth 1 -executable | sort
+
+/bin
+/bin/bash
+/bin/bunzip2
+/bin/bzcat
+/bin/bzcmp
+/bin/bzdiff
+/bin/bzegrep
+/bin/bzexe
+/bin/bzfgrep
+/bin/bzgrep
+/bin/bzip2
+/bin/bzip2recover
+/bin/bzless
+/bin/bzmore
+/bin/cat
+/bin/chgrp
+/bin/chmod
+/bin/chown
+/bin/cp
+/bin/dash
+/bin/date
+/bin/dd
+/bin/df
+/bin/dir
+/bin/dmesg
+/bin/dnsdomainname
+/bin/domainname
+/bin/echo
+/bin/egrep
+/bin/false
+/bin/fgrep
+/bin/findmnt
+/bin/fuser
+/bin/grep
+/bin/gunzip
+/bin/gzexe
+/bin/gzip
+/bin/hostname
+/bin/journalctl
+/bin/kill
+/bin/less
+/bin/lessecho
+/bin/lessfile
+/bin/lesskey
+/bin/lesspipe
+/bin/ln
+/bin/login
+/bin/loginctl
+/bin/ls
+/bin/lsblk
+/bin/mkdir
+/bin/mknod
+/bin/mktemp
+/bin/more
+/bin/mount
+/bin/mountpoint
+/bin/mv
+/bin/networkctl
+/bin/nisdomainname
+/bin/pidof
+/bin/ping
+/bin/ping4
+/bin/ping6
+/bin/ps
+/bin/pwd
+/bin/rbash
+/bin/readlink
+/bin/rm
+/bin/rmdir
+/bin/run-parts
+/bin/sed
+/bin/sh
+/bin/sleep
+/bin/stty
+/bin/su
+/bin/sync
+/bin/systemctl
+/bin/systemd
+/bin/systemd-ask-password
+/bin/systemd-escape
+/bin/systemd-inhibit
+/bin/systemd-machine-id-setup
+/bin/systemd-notify
+/bin/systemd-sysusers
+/bin/systemd-tmpfiles
+/bin/systemd-tty-ask-password-agent
+/bin/tar
+/bin/tempfile
+/bin/touch
+/bin/true
+/bin/umount
+/bin/uname
+/bin/uncompress
+/bin/vdir
+/bin/wdctl
+/bin/which
+/bin/ypdomainname
+/bin/zcat
+/bin/zcmp
+/bin/zdiff
+/bin/zegrep
+/bin/zfgrep
+/bin/zforce
+/bin/zgrep
+/bin/zless
+/bin/zmore
+/bin/znew
+/sbin
+/sbin/agetty
+/sbin/apparmor_parser
+/sbin/badblocks
+/sbin/blkdeactivate
+/sbin/blkdiscard
+/sbin/blkid
+/sbin/blkzone
+/sbin/blockdev
+/sbin/capsh
+/sbin/cfdisk
+/sbin/chcpu
+/sbin/ctrlaltdel
+/sbin/debugfs
+/sbin/dmsetup
+/sbin/dmstats
+/sbin/dumpe2fs
+/sbin/e2fsck
+/sbin/e2image
+/sbin/e2label
+/sbin/e2mmpstatus
+/sbin/e2undo
+/sbin/fdisk
+/sbin/findfs
+/sbin/fsck
+/sbin/fsck.cramfs
+/sbin/fsck.ext2
+/sbin/fsck.ext3
+/sbin/fsck.ext4
+/sbin/fsck.minix
+/sbin/fsfreeze
+/sbin/fstab-decode
+/sbin/fstrim
+/sbin/getcap
+/sbin/getpcaps
+/sbin/getty
+/sbin/halt
+/sbin/hwclock
+/sbin/init
+/sbin/installkernel
+/sbin/ip6tables
+/sbin/ip6tables-restore
+/sbin/ip6tables-save
+/sbin/iptables
+/sbin/iptables-restore
+/sbin/iptables-save
+/sbin/isosize
+/sbin/killall5
+/sbin/ldconfig
+/sbin/logsave
+/sbin/losetup
+/sbin/mke2fs
+/sbin/mkfs
+/sbin/mkfs.bfs
+/sbin/mkfs.cramfs
+/sbin/mkfs.ext2
+/sbin/mkfs.ext3
+/sbin/mkfs.ext4
+/sbin/mkfs.minix
+/sbin/mkhomedir_helper
+/sbin/mkswap
+/sbin/pam_tally
+/sbin/pam_tally2
+/sbin/pivot_root
+/sbin/poweroff
+/sbin/raw
+/sbin/reboot
+/sbin/resize2fs
+/sbin/runlevel
+/sbin/runuser
+/sbin/setcap
+/sbin/sfdisk
+/sbin/shadowconfig
+/sbin/shutdown
+/sbin/start-stop-daemon
+/sbin/sulogin
+/sbin/swaplabel
+/sbin/swapoff
+/sbin/swapon
+/sbin/switch_root
+/sbin/sysctl
+/sbin/telinit
+/sbin/tune2fs
+/sbin/unix_chkpwd
+/sbin/unix_update
+/sbin/wipefs
+/sbin/zramctl
+/usr/bin
+/usr/bin/2to3-2.7
+/usr/bin/[
+/usr/bin/aa-enabled
+/usr/bin/aa-exec
+/usr/bin/add-apt-repository
+/usr/bin/addpart
+/usr/bin/addr2line
+/usr/bin/apt
+/usr/bin/apt-add-repository
+/usr/bin/apt-cache
+/usr/bin/apt-cdrom
+/usr/bin/apt-config
+/usr/bin/apt-get
+/usr/bin/apt-key
+/usr/bin/apt-mark
+/usr/bin/ar
+/usr/bin/arch
+/usr/bin/as
+/usr/bin/awk
+/usr/bin/b2sum
+/usr/bin/base32
+/usr/bin/base64
+/usr/bin/basename
+/usr/bin/bashbug
+/usr/bin/bootctl
+/usr/bin/busctl
+/usr/bin/c++
+/usr/bin/c++filt
+/usr/bin/c89
+/usr/bin/c89-gcc
+/usr/bin/c99
+/usr/bin/c99-gcc
+/usr/bin/c_rehash
+/usr/bin/captoinfo
+/usr/bin/catchsegv
+/usr/bin/cc
+/usr/bin/chage
+/usr/bin/chattr
+/usr/bin/chcon
+/usr/bin/chfn
+/usr/bin/choom
+/usr/bin/chrt
+/usr/bin/chsh
+/usr/bin/cksum
+/usr/bin/clear
+/usr/bin/clear_console
+/usr/bin/cmp
+/usr/bin/comm
+/usr/bin/compose
+/usr/bin/containerd
+/usr/bin/containerd-shim
+/usr/bin/containerd-shim-runc-v1
+/usr/bin/containerd-shim-runc-v2
+/usr/bin/corelist
+/usr/bin/cpan
+/usr/bin/cpan5.28-x86_64-linux-gnu
+/usr/bin/cpp
+/usr/bin/cpp-8
+/usr/bin/csplit
+/usr/bin/ctr
+/usr/bin/curl
+/usr/bin/curl-config
+/usr/bin/cut
+/usr/bin/cvtsudoers
+/usr/bin/dbus-cleanup-sockets
+/usr/bin/dbus-daemon
+/usr/bin/dbus-monitor
+/usr/bin/dbus-run-session
+/usr/bin/dbus-send
+/usr/bin/dbus-update-activation-environment
+/usr/bin/dbus-uuidgen
+/usr/bin/deb-systemd-helper
+/usr/bin/deb-systemd-invoke
+/usr/bin/debconf
+/usr/bin/debconf-apt-progress
+/usr/bin/debconf-communicate
+/usr/bin/debconf-copydb
+/usr/bin/debconf-escape
+/usr/bin/debconf-set-selections
+/usr/bin/debconf-show
+/usr/bin/delpart
+/usr/bin/dh_python2
+/usr/bin/diff
+/usr/bin/diff3
+/usr/bin/dircolors
+/usr/bin/dirmngr
+/usr/bin/dirmngr-client
+/usr/bin/dirname
+/usr/bin/docker
+/usr/bin/docker-init
+/usr/bin/docker-proxy
+/usr/bin/dockerd
+/usr/bin/dockerd-rootless-setuptool.sh
+/usr/bin/dockerd-rootless.sh
+/usr/bin/dpkg
+/usr/bin/dpkg-architecture
+/usr/bin/dpkg-buildflags
+/usr/bin/dpkg-buildpackage
+/usr/bin/dpkg-checkbuilddeps
+/usr/bin/dpkg-deb
+/usr/bin/dpkg-distaddfile
+/usr/bin/dpkg-divert
+/usr/bin/dpkg-genbuildinfo
+/usr/bin/dpkg-genchanges
+/usr/bin/dpkg-gencontrol
+/usr/bin/dpkg-gensymbols
+/usr/bin/dpkg-maintscript-helper
+/usr/bin/dpkg-mergechangelogs
+/usr/bin/dpkg-name
+/usr/bin/dpkg-parsechangelog
+/usr/bin/dpkg-query
+/usr/bin/dpkg-scanpackages
+/usr/bin/dpkg-scansources
+/usr/bin/dpkg-shlibdeps
+/usr/bin/dpkg-source
+/usr/bin/dpkg-split
+/usr/bin/dpkg-statoverride
+/usr/bin/dpkg-trigger
+/usr/bin/dpkg-vendor
+/usr/bin/du
+/usr/bin/dwp
+/usr/bin/echo_supervisord_conf
+/usr/bin/edit
+/usr/bin/elfedit
+/usr/bin/enc2xs
+/usr/bin/encguess
+/usr/bin/env
+/usr/bin/envsubst
+/usr/bin/expand
+/usr/bin/expiry
+/usr/bin/expr
+/usr/bin/factor
+/usr/bin/faillog
+/usr/bin/faked-sysv
+/usr/bin/faked-tcp
+/usr/bin/fakeroot
+/usr/bin/fakeroot-sysv
+/usr/bin/fakeroot-tcp
+/usr/bin/fallocate
+/usr/bin/file
+/usr/bin/fincore
+/usr/bin/find
+/usr/bin/flock
+/usr/bin/fmt
+/usr/bin/fold
+/usr/bin/free
+/usr/bin/funzip
+/usr/bin/g++
+/usr/bin/g++-8
+/usr/bin/gapplication
+/usr/bin/gcc
+/usr/bin/gcc-8
+/usr/bin/gcc-ar
+/usr/bin/gcc-ar-8
+/usr/bin/gcc-nm
+/usr/bin/gcc-nm-8
+/usr/bin/gcc-ranlib
+/usr/bin/gcc-ranlib-8
+/usr/bin/gcov
+/usr/bin/gcov-8
+/usr/bin/gcov-dump
+/usr/bin/gcov-dump-8
+/usr/bin/gcov-tool
+/usr/bin/gcov-tool-8
+/usr/bin/gdbus
+/usr/bin/gencat
+/usr/bin/getconf
+/usr/bin/getent
+/usr/bin/getopt
+/usr/bin/gettext
+/usr/bin/gettext.sh
+/usr/bin/gettextize
+/usr/bin/gio
+/usr/bin/gio-querymodules
+/usr/bin/git
+/usr/bin/git-cvsserver
+/usr/bin/git-receive-pack
+/usr/bin/git-shell
+/usr/bin/git-upload-archive
+/usr/bin/git-upload-pack
+/usr/bin/gitk
+/usr/bin/glib-compile-schemas
+/usr/bin/gold
+/usr/bin/gpasswd
+/usr/bin/gpg
+/usr/bin/gpg-agent
+/usr/bin/gpg-connect-agent
+/usr/bin/gpg-wks-server
+/usr/bin/gpg-zip
+/usr/bin/gpgcompose
+/usr/bin/gpgconf
+/usr/bin/gpgparsemail
+/usr/bin/gpgsm
+/usr/bin/gpgsplit
+/usr/bin/gpgtar
+/usr/bin/gpgv
+/usr/bin/gprof
+/usr/bin/gresource
+/usr/bin/groups
+/usr/bin/gsettings
+/usr/bin/h2ph
+/usr/bin/h2xs
+/usr/bin/head
+/usr/bin/hostid
+/usr/bin/hostnamectl
+/usr/bin/i386
+/usr/bin/iconv
+/usr/bin/id
+/usr/bin/infocmp
+/usr/bin/infotocap
+/usr/bin/install
+/usr/bin/instmodsh
+/usr/bin/ionice
+/usr/bin/ipcmk
+/usr/bin/ipcrm
+/usr/bin/ipcs
+/usr/bin/iptables-xml
+/usr/bin/ischroot
+/usr/bin/join
+/usr/bin/jq
+/usr/bin/json_pp
+/usr/bin/kbxutil
+/usr/bin/kernel-install
+/usr/bin/killall
+/usr/bin/last
+/usr/bin/lastb
+/usr/bin/lastlog
+/usr/bin/lcf
+/usr/bin/ld
+/usr/bin/ld.bfd
+/usr/bin/ld.gold
+/usr/bin/ldd
+/usr/bin/less
+/usr/bin/lessecho
+/usr/bin/lessfile
+/usr/bin/lesskey
+/usr/bin/lesspipe
+/usr/bin/libnetcfg
+/usr/bin/link
+/usr/bin/linux32
+/usr/bin/linux64
+/usr/bin/locale
+/usr/bin/localectl
+/usr/bin/localedef
+/usr/bin/logger
+/usr/bin/logname
+/usr/bin/lsattr
+/usr/bin/lsb_release
+/usr/bin/lscpu
+/usr/bin/lsipc
+/usr/bin/lslocks
+/usr/bin/lslogins
+/usr/bin/lsmem
+/usr/bin/lsns
+/usr/bin/lspgpot
+/usr/bin/lzcat
+/usr/bin/lzcmp
+/usr/bin/lzdiff
+/usr/bin/lzegrep
+/usr/bin/lzfgrep
+/usr/bin/lzgrep
+/usr/bin/lzless
+/usr/bin/lzma
+/usr/bin/lzmainfo
+/usr/bin/lzmore
+/usr/bin/make
+/usr/bin/make-first-existing-target
+/usr/bin/mawk
+/usr/bin/mcookie
+/usr/bin/md5sum
+/usr/bin/md5sum.textutils
+/usr/bin/mesg
+/usr/bin/migrate-pubring-from-classic-gpg
+/usr/bin/mkfifo
+/usr/bin/msgattrib
+/usr/bin/msgcat
+/usr/bin/msgcmp
+/usr/bin/msgcomm
+/usr/bin/msgconv
+/usr/bin/msgen
+/usr/bin/msgexec
+/usr/bin/msgfilter
+/usr/bin/msgfmt
+/usr/bin/msggrep
+/usr/bin/msginit
+/usr/bin/msgmerge
+/usr/bin/msgunfmt
+/usr/bin/msguniq
+/usr/bin/mtrace
+/usr/bin/namei
+/usr/bin/nawk
+/usr/bin/newgrp
+/usr/bin/ngettext
+/usr/bin/nice
+/usr/bin/nl
+/usr/bin/nm
+/usr/bin/nohup
+/usr/bin/nproc
+/usr/bin/nsenter
+/usr/bin/numfmt
+/usr/bin/objcopy
+/usr/bin/objdump
+/usr/bin/od
+/usr/bin/openssl
+/usr/bin/pager
+/usr/bin/partx
+/usr/bin/passwd
+/usr/bin/paste
+/usr/bin/patch
+/usr/bin/pathchk
+/usr/bin/pdb
+/usr/bin/pdb2
+/usr/bin/pdb2.7
+/usr/bin/pdb3
+/usr/bin/pdb3.7
+/usr/bin/peekfd
+/usr/bin/perl
+/usr/bin/perl5.28-x86_64-linux-gnu
+/usr/bin/perl5.28.1
+/usr/bin/perlbug
+/usr/bin/perldoc
+/usr/bin/perlivp
+/usr/bin/perlthanks
+/usr/bin/pgrep
+/usr/bin/piconv
+/usr/bin/pidproxy
+/usr/bin/pigz
+/usr/bin/pinentry
+/usr/bin/pinentry-curses
+/usr/bin/pinky
+/usr/bin/pkaction
+/usr/bin/pkcheck
+/usr/bin/pkcon
+/usr/bin/pkexec
+/usr/bin/pkill
+/usr/bin/pkmon
+/usr/bin/pkttyagent
+/usr/bin/pl2pm
+/usr/bin/pldd
+/usr/bin/pmap
+/usr/bin/pod2html
+/usr/bin/pod2man
+/usr/bin/pod2text
+/usr/bin/pod2usage
+/usr/bin/podchecker
+/usr/bin/podselect
+/usr/bin/pr
+/usr/bin/print
+/usr/bin/printenv
+/usr/bin/printf
+/usr/bin/prlimit
+/usr/bin/prove
+/usr/bin/prtstat
+/usr/bin/pslog
+/usr/bin/pstree
+/usr/bin/pstree.x11
+/usr/bin/ptar
+/usr/bin/ptardiff
+/usr/bin/ptargrep
+/usr/bin/ptx
+/usr/bin/pwdx
+/usr/bin/py3clean
+/usr/bin/py3compile
+/usr/bin/py3versions
+/usr/bin/pyclean
+/usr/bin/pycompile
+/usr/bin/pydoc
+/usr/bin/pydoc2
+/usr/bin/pydoc2.7
+/usr/bin/pydoc3
+/usr/bin/pydoc3.7
+/usr/bin/pygettext
+/usr/bin/pygettext2
+/usr/bin/pygettext2.7
+/usr/bin/pygettext3
+/usr/bin/pygettext3.7
+/usr/bin/python
+/usr/bin/python2
+/usr/bin/python2.7
+/usr/bin/python3
+/usr/bin/python3.7
+/usr/bin/python3.7m
+/usr/bin/python3m
+/usr/bin/pyversions
+/usr/bin/ranlib
+/usr/bin/rcp
+/usr/bin/readelf
+/usr/bin/realpath
+/usr/bin/recode-sr-latin
+/usr/bin/rename.ul
+/usr/bin/renice
+/usr/bin/reset
+/usr/bin/resizepart
+/usr/bin/resolvectl
+/usr/bin/rev
+/usr/bin/rgrep
+/usr/bin/rlogin
+/usr/bin/rootlesskit
+/usr/bin/rootlesskit-docker-proxy
+/usr/bin/rpcgen
+/usr/bin/rsh
+/usr/bin/run-mailcap
+/usr/bin/runc
+/usr/bin/runcon
+/usr/bin/savelog
+/usr/bin/scp
+/usr/bin/script
+/usr/bin/scriptreplay
+/usr/bin/sdiff
+/usr/bin/see
+/usr/bin/select-editor
+/usr/bin/sensible-browser
+/usr/bin/sensible-editor
+/usr/bin/sensible-pager
+/usr/bin/seq
+/usr/bin/setarch
+/usr/bin/setpriv
+/usr/bin/setsid
+/usr/bin/setterm
+/usr/bin/sftp
+/usr/bin/sg
+/usr/bin/sha1sum
+/usr/bin/sha224sum
+/usr/bin/sha256sum
+/usr/bin/sha384sum
+/usr/bin/sha512sum
+/usr/bin/shasum
+/usr/bin/shred
+/usr/bin/shuf
+/usr/bin/size
+/usr/bin/skill
+/usr/bin/slabtop
+/usr/bin/slogin
+/usr/bin/snice
+/usr/bin/sort
+/usr/bin/sotruss
+/usr/bin/splain
+/usr/bin/split
+/usr/bin/sprof
+/usr/bin/ssh
+/usr/bin/ssh-add
+/usr/bin/ssh-agent
+/usr/bin/ssh-argv0
+/usr/bin/ssh-copy-id
+/usr/bin/ssh-keygen
+/usr/bin/ssh-keyscan
+/usr/bin/stat
+/usr/bin/stdbuf
+/usr/bin/strings
+/usr/bin/strip
+/usr/bin/sudo
+/usr/bin/sudoedit
+/usr/bin/sudoreplay
+/usr/bin/sum
+/usr/bin/supervisorctl
+/usr/bin/supervisord
+/usr/bin/symcryptrun
+/usr/bin/systemd-analyze
+/usr/bin/systemd-cat
+/usr/bin/systemd-cgls
+/usr/bin/systemd-cgtop
+/usr/bin/systemd-delta
+/usr/bin/systemd-detect-virt
+/usr/bin/systemd-id128
+/usr/bin/systemd-mount
+/usr/bin/systemd-path
+/usr/bin/systemd-resolve
+/usr/bin/systemd-run
+/usr/bin/systemd-socket-activate
+/usr/bin/systemd-stdio-bridge
+/usr/bin/systemd-umount
+/usr/bin/tabs
+/usr/bin/tac
+/usr/bin/tail
+/usr/bin/taskset
+/usr/bin/tee
+/usr/bin/test
+/usr/bin/tic
+/usr/bin/timedatectl
+/usr/bin/timeout
+/usr/bin/tload
+/usr/bin/toe
+/usr/bin/top
+/usr/bin/touch
+/usr/bin/tput
+/usr/bin/tr
+/usr/bin/truncate
+/usr/bin/tset
+/usr/bin/tsort
+/usr/bin/tty
+/usr/bin/tzselect
+/usr/bin/ucf
+/usr/bin/ucfq
+/usr/bin/ucfr
+/usr/bin/unattended-upgrade
+/usr/bin/unattended-upgrades
+/usr/bin/unexpand
+/usr/bin/uniq
+/usr/bin/unlink
+/usr/bin/unlzma
+/usr/bin/unpigz
+/usr/bin/unshare
+/usr/bin/unxz
+/usr/bin/unzip
+/usr/bin/unzipsfx
+/usr/bin/update-alternatives
+/usr/bin/update-mime-database
+/usr/bin/uptime
+/usr/bin/users
+/usr/bin/utmpdump
+/usr/bin/vmstat
+/usr/bin/w
+/usr/bin/w.procps
+/usr/bin/wall
+/usr/bin/watch
+/usr/bin/watchgnupg
+/usr/bin/wc
+/usr/bin/whereis
+/usr/bin/which
+/usr/bin/who
+/usr/bin/whoami
+/usr/bin/x86_64
+/usr/bin/x86_64-linux-gnu-addr2line
+/usr/bin/x86_64-linux-gnu-ar
+/usr/bin/x86_64-linux-gnu-as
+/usr/bin/x86_64-linux-gnu-c++filt
+/usr/bin/x86_64-linux-gnu-cpp
+/usr/bin/x86_64-linux-gnu-cpp-8
+/usr/bin/x86_64-linux-gnu-dwp
+/usr/bin/x86_64-linux-gnu-elfedit
+/usr/bin/x86_64-linux-gnu-g++
+/usr/bin/x86_64-linux-gnu-g++-8
+/usr/bin/x86_64-linux-gnu-gcc
+/usr/bin/x86_64-linux-gnu-gcc-8
+/usr/bin/x86_64-linux-gnu-gcc-ar
+/usr/bin/x86_64-linux-gnu-gcc-ar-8
+/usr/bin/x86_64-linux-gnu-gcc-nm
+/usr/bin/x86_64-linux-gnu-gcc-nm-8
+/usr/bin/x86_64-linux-gnu-gcc-ranlib
+/usr/bin/x86_64-linux-gnu-gcc-ranlib-8
+/usr/bin/x86_64-linux-gnu-gcov
+/usr/bin/x86_64-linux-gnu-gcov-8
+/usr/bin/x86_64-linux-gnu-gcov-dump
+/usr/bin/x86_64-linux-gnu-gcov-dump-8
+/usr/bin/x86_64-linux-gnu-gcov-tool
+/usr/bin/x86_64-linux-gnu-gcov-tool-8
+/usr/bin/x86_64-linux-gnu-gold
+/usr/bin/x86_64-linux-gnu-gprof
+/usr/bin/x86_64-linux-gnu-ld
+/usr/bin/x86_64-linux-gnu-ld.bfd
+/usr/bin/x86_64-linux-gnu-ld.gold
+/usr/bin/x86_64-linux-gnu-nm
+/usr/bin/x86_64-linux-gnu-objcopy
+/usr/bin/x86_64-linux-gnu-objdump
+/usr/bin/x86_64-linux-gnu-ranlib
+/usr/bin/x86_64-linux-gnu-readelf
+/usr/bin/x86_64-linux-gnu-size
+/usr/bin/x86_64-linux-gnu-strings
+/usr/bin/x86_64-linux-gnu-strip
+/usr/bin/xargs
+/usr/bin/xauth
+/usr/bin/xdg-user-dir
+/usr/bin/xdg-user-dirs-update
+/usr/bin/xgettext
+/usr/bin/xsubpp
+/usr/bin/xz
+/usr/bin/xzcat
+/usr/bin/xzcmp
+/usr/bin/xzdiff
+/usr/bin/xzegrep
+/usr/bin/xzfgrep
+/usr/bin/xzgrep
+/usr/bin/xzless
+/usr/bin/xzmore
+/usr/bin/yes
+/usr/bin/zdump
+/usr/bin/zipdetails
+/usr/bin/zipgrep
+/usr/bin/zipinfo
+/usr/local/bin
+/usr/local/bin/docker-compose
+/usr/local/sbin
+/usr/sbin
+/usr/sbin/aa-remove-unknown
+/usr/sbin/aa-status
+/usr/sbin/aa-teardown
+/usr/sbin/add-shell
+/usr/sbin/addgnupghome
+/usr/sbin/addgroup
+/usr/sbin/adduser
+/usr/sbin/apparmor_status
+/usr/sbin/applygnupgdefaults
+/usr/sbin/arptables
+/usr/sbin/arptables-nft
+/usr/sbin/arptables-nft-restore
+/usr/sbin/arptables-nft-save
+/usr/sbin/arptables-restore
+/usr/sbin/arptables-save
+/usr/sbin/chgpasswd
+/usr/sbin/chmem
+/usr/sbin/chpasswd
+/usr/sbin/chroot
+/usr/sbin/cpgr
+/usr/sbin/cppw
+/usr/sbin/delgroup
+/usr/sbin/deluser
+/usr/sbin/dpkg-preconfigure
+/usr/sbin/dpkg-reconfigure
+/usr/sbin/e2freefrag
+/usr/sbin/e4crypt
+/usr/sbin/e4defrag
+/usr/sbin/ebtables
+/usr/sbin/ebtables-nft
+/usr/sbin/ebtables-nft-restore
+/usr/sbin/ebtables-nft-save
+/usr/sbin/ebtables-restore
+/usr/sbin/ebtables-save
+/usr/sbin/fdformat
+/usr/sbin/filefrag
+/usr/sbin/groupadd
+/usr/sbin/groupdel
+/usr/sbin/groupmems
+/usr/sbin/groupmod
+/usr/sbin/grpck
+/usr/sbin/grpconv
+/usr/sbin/grpunconv
+/usr/sbin/iconvconfig
+/usr/sbin/invoke-rc.d
+/usr/sbin/ip6tables
+/usr/sbin/ip6tables-apply
+/usr/sbin/ip6tables-legacy
+/usr/sbin/ip6tables-legacy-restore
+/usr/sbin/ip6tables-legacy-save
+/usr/sbin/ip6tables-nft
+/usr/sbin/ip6tables-nft-restore
+/usr/sbin/ip6tables-nft-save
+/usr/sbin/ip6tables-restore
+/usr/sbin/ip6tables-restore-translate
+/usr/sbin/ip6tables-save
+/usr/sbin/ip6tables-translate
+/usr/sbin/iptables
+/usr/sbin/iptables-apply
+/usr/sbin/iptables-legacy
+/usr/sbin/iptables-legacy-restore
+/usr/sbin/iptables-legacy-save
+/usr/sbin/iptables-nft
+/usr/sbin/iptables-nft-restore
+/usr/sbin/iptables-nft-save
+/usr/sbin/iptables-restore
+/usr/sbin/iptables-restore-translate
+/usr/sbin/iptables-save
+/usr/sbin/iptables-translate
+/usr/sbin/ldattach
+/usr/sbin/mklost+found
+/usr/sbin/newusers
+/usr/sbin/nfnl_osf
+/usr/sbin/nft
+/usr/sbin/nologin
+/usr/sbin/pam-auth-update
+/usr/sbin/pam_getenv
+/usr/sbin/pam_timestamp_check
+/usr/sbin/policy-rc.d
+/usr/sbin/pwck
+/usr/sbin/pwconv
+/usr/sbin/pwunconv
+/usr/sbin/readprofile
+/usr/sbin/remove-shell
+/usr/sbin/rmt
+/usr/sbin/rmt-tar
+/usr/sbin/rtcwake
+/usr/sbin/service
+/usr/sbin/tarcat
+/usr/sbin/tzconfig
+/usr/sbin/update-ca-certificates
+/usr/sbin/update-mime
+/usr/sbin/update-passwd
+/usr/sbin/update-rc.d
+/usr/sbin/useradd
+/usr/sbin/userdel
+/usr/sbin/usermod
+/usr/sbin/vigr
+/usr/sbin/vipw
+/usr/sbin/visudo
+/usr/sbin/xtables-legacy-multi
+/usr/sbin/xtables-monitor
+/usr/sbin/xtables-nft-multi
+/usr/sbin/zic
+

            This was mostly a fun exercise for myself to see if it could be done using one line of Python code without resorting to using the exec function. In a more readable form, and with some comments, the code looks like this:

            import os
+import sys
+
+# This is just to have a function to output something on the screen.
+# I'm using Python 2.7 in which 'print' is not a function and cannot
+# be used in the 'map' function.
+output = lambda(x) : sys.stdout.write(x + "\n")
+
+# Get a list of the components in the PATH environment variable. Will
+# abort the program is PATH doesn't exist
+paths = os.environ["PATH"].split(":")
+
+# os.listdir raises an error is something is not a path so I'm creating
+# a small function that only executes it if 'p' is a directory
+listdir = lambda(p) : os.listdir(p) if os.path.isdir(p) else [ ]
+
+# Checks if the path specified by x[0] and x[1] is a file
+isfile = lambda(x) : True if os.path.isfile(os.path.join(x[0],x[1])) else False
+
+# Checks if the path specified by x[0] and x[1] has the executable flag set
+isexe = lambda(x) : True if os.access(os.path.join(x[0],x[1]), os.X_OK) else False
+
+# Here, I'm using a list comprehension to build a list of all executable files
+# in the PATH, and abusing the map function to write every name in the resulting
+# list to the screen.
+map(output, [ os.path.join(p,f) for p in paths for f in listdir(p) if isfile((p,f)) and isexe((p,f)) ])
+

            If you can run Python 2 in your shell, the following (ridiculously long) one-liner can be used as well:

            $ python2 -c 'import os;import sys;output = lambda(x) : sys.stdout.write(x + "\n"); paths = os.environ["PATH"].split(":") ; listdir = lambda(p) : os.listdir(p) if os.path.isdir(p) else [ ] ; isfile = lambda(x) : True if os.path.isfile(os.path.join(x[0],x[1])) else False ; isexe = lambda(x) : True if os.access(os.path.join(x[0],x[1]), os.X_OK) else False ; map(output,[ os.path.join(p,f) for p in paths for f in listdir(p) if isfile((p,f)) and isexe((p,f)) ])'
+

            Packages

            If we need to list the installed packages in the Python shell, For terminal I recommend help("modules") or python -c "help(‘modules')".

            $ python3.7 -c 'help("modules")'
+
+Please wait a moment while I gather a list of all available modules...
+
+__future__          _tracemalloc        getopt              rlcompleter
+_abc                _uuid               getpass             runpy
+_ast                _warnings           gettext             sched
+_asyncio            _weakref            gi                  secrets
+_bisect             _weakrefset         glob                select
+_blake2             _xxtestfuzz         grp                 selectors
+_bootlocale         abc                 gzip                shelve
+_bz2                aifc                hashlib             shlex
+_codecs             antigravity         heapq               shutil
+_codecs_cn          apt                 hmac                signal
+_codecs_hk          apt_inst            html                site
+_codecs_iso2022     apt_pkg             http                sitecustomize
+_codecs_jp          aptsources          imaplib             smtpd
+_codecs_kr          argparse            imghdr              smtplib
+_codecs_tw          array               imp                 sndhdr
+_collections        ast                 importlib           socket
+_collections_abc    asynchat            inspect             socketserver
+_compat_pickle      asyncio             io                  softwareproperties
+_compression        asyncore            ipaddress           spwd
+_contextvars        atexit              itertools           sqlite3
+_crypt              audioop             json                sre_compile
+_csv                base64              keyword             sre_constants
+_ctypes             bdb                 linecache           sre_parse
+_ctypes_test        binascii            locale              ssl
+_curses             binhex              logging             stat
+_curses_panel       bisect              lsb_release         statistics
+_datetime           builtins            lzma                string
+_dbm                bz2                 macpath             stringprep
+_dbus_bindings      cProfile            mailbox             struct
+_dbus_glib_bindings calendar            mailcap             subprocess
+_decimal            cgi                 marshal             sunau
+_dummy_thread       cgitb               math                symbol
+_elementtree        chunk               mimetypes           symtable
+_functools          cmath               mmap                sys
+_hashlib            cmd                 modulefinder        sysconfig
+_heapq              code                multiprocessing     syslog
+_imp                codecs              netrc               tabnanny
+_io                 codeop              nis                 tarfile
+_json               collections         nntplib             telnetlib
+_locale             colorsys            ntpath              tempfile
+_lsprof             compileall          nturl2path          termios
+_lzma               concurrent          numbers             test
+_markupbase         configparser        opcode              textwrap
+_md5                contextlib          operator            this
+_multibytecodec     contextvars         optparse            threading
+_multiprocessing    copy                os                  time
+_opcode             copyreg             ossaudiodev         timeit
+_operator           crypt               parser              token
+_osx_support        csv                 pathlib             tokenize
+_pickle             ctypes              pdb                 trace
+_posixsubprocess    curl                pickle              traceback
+_py_abc             curses              pickletools         tracemalloc
+_pydecimal          dataclasses         pipes               tty
+_pyio               datetime            pkgutil             turtle
+_queue              dbm                 platform            types
+_random             dbus                plistlib            typing
+_sha1               decimal             poplib              unicodedata
+_sha256             difflib             posix               unittest
+_sha3               dis                 posixpath           urllib
+_sha512             distro_info         pprint              uu
+_signal             distutils           profile             uuid
+_sitebuiltins       doctest             pstats              venv
+_socket             dummy_threading     pty                 warnings
+_sqlite3            email               pwd                 wave
+_sre                encodings           py_compile          weakref
+_ssl                enum                pyclbr              webbrowser
+_stat               errno               pycurl              wsgiref
+_string             faulthandler        pydoc               xdrlib
+_strptime           fcntl               pydoc_data          xml
+_struct             filecmp             pyexpat             xmlrpc
+_symtable           fileinput           pygtkcompat         xxlimited
+_sysconfigdata_m_linux_x86_64-linux-gnu fnmatch             queue
+_testbuffer         formatter           quopri              zipapp
+_testcapi           fractions           random              zipfile
+_testimportmultiple ftplib              re                  zipimport
+_testmultiphase     functools           readline            zlib
+_thread             gc                  reprlib             xxsubtype
+_threading_local    genericpath         resource
+
+Enter any module name to get more help.  Or, type "modules spam" to search
+for modules whose name or summary contain the string "spam".
+

            I'm comparing five methods to retrieve installed "modules", all of which I've seen in this thread

                                            iter_modules help("modules") builtin_module_names pip list working_set
+Includes distributions               ❌            ❌                ❌               ✔️         ✔️
+Includes modules (No built-in)       ✔️            ✔️                ❌               ❌         ❌
+Includes built-in modules            ❌            ✔️                ✔️               ❌         ❌
+Includes frozen                      ✔️            ✔️                ❌               ❌         ❌
+Includes venv                        ✔️            ✔️                ❌               ✔️         ✔️
+Includes global	                     ✔️            ✔️                ❌               ✔️         ✔️
+Includes editable installs           ✔️            ✔️                ❌               ✔️         ✔️
+Includes PyCharm helpers             ✔️            ❌                ❌               ❌         ❌
+Lowers capital letters               ❌            ❌                ❌               ❌         ✔️
+Time taken (665 modules total)    53.7 msec    1.03 sec           577 nsec         284 msec  36.2 usec
+

            For programmatically I recommend iter_modules + builtin_module_names to pluck the module name out of the tuples generated by pkgutil.iter_modules() It is however very convoluted with information

            $ python -c 'import pkgutil;print [x[1] for x in list(pkgutil.iter_modules())]'
+
+['BaseHTTPServer', 'Bastion', 'CGIHTTPServer', 'ConfigParser', 'Cookie', 'DocXMLRPCServer', 'HTMLParser', 
+'MimeWriter', 'Queue', 'SimpleHTTPServer', 'SimpleXMLRPCServer', 'SocketServer', 'StringIO', 'UserDict', 
+'UserList', 'UserString', '_LWPCookieJar', '_MozillaCookieJar', '__future__', '_abcoll', '_osx_support', 
+'_pyio', '_strptime', '_sysconfigdata', '_threading_local', '_weakrefset', 'abc', 'aifc', 'antigravity', 
+'anydbm', 'argparse', 'ast', 'asynchat', 'asyncore', 'atexit', 'audiodev', 'base64', 'bdb', 'binhex', 
+'bisect', 'bsddb', 'cProfile', 'calendar', 'cgi', 'cgitb', 'chunk', 'cmd', 'code', 'codecs', 'codeop', 
+'collections', 'colorsys', 'commands', 'compileall', 'compiler', 'contextlib', 'cookielib', 'copy', 
+'copy_reg', 'csv', 'ctypes', 'curses', 'dbhash', 'decimal', 'difflib', 'dircache', 'dis', 'distutils', 
+'doctest', 'dumbdbm', 'dummy_thread', 'dummy_threading', 'email', 'encodings', 'ensurepip', 'filecmp', 
+'fileinput', 'fnmatch', 'formatter', 'fpformat', 'fractions', 'ftplib', 'functools', 'genericpath', 
+'getopt', 'getpass', 'gettext', 'glob', 'gzip', 'hashlib', 'heapq', 'hmac', 'hotshot', 'htmlentitydefs', 
+'htmllib', 'httplib', 'ihooks', 'imaplib', 'imghdr', 'importlib', 'imputil', 'inspect', 'io', 'json', 
+'keyword', 'lib2to3', 'linecache', 'locale', 'logging', 'macpath', 'macurl2path', 'mailbox', 'mailcap', 
+'markupbase', 'md5', 'mhlib', 'mimetools', 'mimetypes', 'mimify', 'modulefinder', 'multifile', 
+'multiprocessing', 'mutex', 'netrc', 'new', 'nntplib', 'ntpath', 'nturl2path', 'numbers', 'opcode', 
+'optparse', 'os', 'os2emxpath', 'pdb', 'pickle', 'pickletools', 'pipes', 'pkgutil', 'platform', 
+'plistlib', 'popen2', 'poplib', 'posixfile', 'posixpath', 'pprint', 'profile', 'pstats', 'pty', 
+'py_compile', 'pyclbr', 'pydoc', 'pydoc_data', 'quopri', 'random', 're', 'repr', 'rexec', 'rfc822', 
+'rlcompleter', 'robotparser', 'runpy', 'sched', 'sets', 'sgmllib', 'sha', 'shelve', 'shlex', 'shutil', 
+'site', 'sitecustomize', 'smtpd', 'smtplib', 'sndhdr', 'socket', 'sqlite3', 'sre', 'sre_compile', 
+'sre_constants', 'sre_parse', 'ssl', 'stat', 'statvfs', 'string', 'stringold', 'stringprep', 'struct', 
+'subprocess', 'sunau', 'sunaudio', 'symbol', 'symtable', 'sysconfig', 'tabnanny', 'tarfile', 'telnetlib', 
+'tempfile', 'test', 'textwrap', 'this', 'threading', 'timeit', 'toaiff', 'token', 'tokenize', 'trace', 
+'traceback', 'tty', 'types', 'unittest', 'urllib', 'urllib2', 'urlparse', 'user', 'uu', 'uuid', 'warnings', 
+'wave', 'weakref', 'webbrowser', 'whichdb', 'wsgiref', 'xdrlib', 'xml', 'xmllib', 'xmlrpclib', 'zipfile', 
+'CDROM', 'DLFCN', 'IN', 'TYPES', '_sysconfigdata_nd', 'Canvas', 'Dialog', 'FileDialog', 'FixTk', 
+'ScrolledText', 'SimpleDialog', 'Tix', 'Tkconstants', 'Tkdnd', 'Tkinter', 'tkColorChooser', 'tkCommonDialog', 
+'tkFileDialog', 'tkFont', 'tkMessageBox', 'tkSimpleDialog', 'ttk', 'turtle', '_bsddb', '_codecs_cn', 
+'_codecs_hk', '_codecs_iso2022', '_codecs_jp', '_codecs_kr', '_codecs_tw', '_csv', '_ctypes', '_ctypes_test', 
+'_curses', '_curses_panel', '_elementtree', '_hashlib', '_hotshot', '_json', '_lsprof', '_multibytecodec', 
+'_multiprocessing', '_sqlite3', '_ssl', '_testcapi', 'audioop', 'bz2', 'crypt', 'dbm', 'future_builtins', 
+'linuxaudiodev', 'mmap', 'nis', 'ossaudiodev', 'parser', 'pyexpat', 'readline', 'resource', 'termios', 
+'lsb_release', 'meld3', 'pkg_resources', 'supervisor']
+
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist02.md b/identition/span4/gist02.md new file mode 100644 index 00000000000..807bb118c25 --- /dev/null +++ b/identition/span4/gist02.md @@ -0,0 +1,1073 @@ +## Binary + +Once the System Properties window opens, click on the “Environment Variables” button. In the “System Variables” box, look for a variable called Path. see all executables in your PATH on your system, and all aliases, all sorted + +``` +$ find ${PATH//:/ } -maxdepth 1 -executable | sort + +/bin +/bin/bash +/bin/bunzip2 +/bin/bzcat +/bin/bzcmp +/bin/bzdiff +/bin/bzegrep +/bin/bzexe +/bin/bzfgrep +/bin/bzgrep +/bin/bzip2 +/bin/bzip2recover +/bin/bzless +/bin/bzmore +/bin/cat +/bin/chgrp +/bin/chmod +/bin/chown +/bin/cp +/bin/dash +/bin/date +/bin/dd +/bin/df +/bin/dir +/bin/dmesg +/bin/dnsdomainname +/bin/domainname +/bin/echo +/bin/egrep +/bin/false +/bin/fgrep +/bin/findmnt +/bin/fuser +/bin/grep +/bin/gunzip +/bin/gzexe +/bin/gzip +/bin/hostname +/bin/journalctl +/bin/kill +/bin/less +/bin/lessecho +/bin/lessfile +/bin/lesskey +/bin/lesspipe +/bin/ln +/bin/login +/bin/loginctl +/bin/ls +/bin/lsblk +/bin/mkdir +/bin/mknod +/bin/mktemp +/bin/more +/bin/mount +/bin/mountpoint +/bin/mv +/bin/networkctl +/bin/nisdomainname +/bin/pidof +/bin/ping +/bin/ping4 +/bin/ping6 +/bin/ps +/bin/pwd +/bin/rbash +/bin/readlink +/bin/rm +/bin/rmdir +/bin/run-parts +/bin/sed +/bin/sh +/bin/sleep +/bin/stty +/bin/su +/bin/sync +/bin/systemctl +/bin/systemd +/bin/systemd-ask-password +/bin/systemd-escape +/bin/systemd-inhibit +/bin/systemd-machine-id-setup +/bin/systemd-notify +/bin/systemd-sysusers +/bin/systemd-tmpfiles +/bin/systemd-tty-ask-password-agent +/bin/tar +/bin/tempfile +/bin/touch +/bin/true +/bin/umount +/bin/uname +/bin/uncompress +/bin/vdir +/bin/wdctl +/bin/which +/bin/ypdomainname +/bin/zcat +/bin/zcmp +/bin/zdiff +/bin/zegrep +/bin/zfgrep +/bin/zforce +/bin/zgrep +/bin/zless +/bin/zmore +/bin/znew +/sbin +/sbin/agetty +/sbin/apparmor_parser +/sbin/badblocks +/sbin/blkdeactivate +/sbin/blkdiscard +/sbin/blkid +/sbin/blkzone +/sbin/blockdev +/sbin/capsh +/sbin/cfdisk +/sbin/chcpu +/sbin/ctrlaltdel +/sbin/debugfs +/sbin/dmsetup +/sbin/dmstats +/sbin/dumpe2fs +/sbin/e2fsck +/sbin/e2image +/sbin/e2label +/sbin/e2mmpstatus +/sbin/e2undo +/sbin/fdisk +/sbin/findfs +/sbin/fsck +/sbin/fsck.cramfs +/sbin/fsck.ext2 +/sbin/fsck.ext3 +/sbin/fsck.ext4 +/sbin/fsck.minix +/sbin/fsfreeze +/sbin/fstab-decode +/sbin/fstrim +/sbin/getcap +/sbin/getpcaps +/sbin/getty +/sbin/halt +/sbin/hwclock +/sbin/init +/sbin/installkernel +/sbin/ip6tables +/sbin/ip6tables-restore +/sbin/ip6tables-save +/sbin/iptables +/sbin/iptables-restore +/sbin/iptables-save +/sbin/isosize +/sbin/killall5 +/sbin/ldconfig +/sbin/logsave +/sbin/losetup +/sbin/mke2fs +/sbin/mkfs +/sbin/mkfs.bfs +/sbin/mkfs.cramfs +/sbin/mkfs.ext2 +/sbin/mkfs.ext3 +/sbin/mkfs.ext4 +/sbin/mkfs.minix +/sbin/mkhomedir_helper +/sbin/mkswap +/sbin/pam_tally +/sbin/pam_tally2 +/sbin/pivot_root +/sbin/poweroff +/sbin/raw +/sbin/reboot +/sbin/resize2fs +/sbin/runlevel +/sbin/runuser +/sbin/setcap +/sbin/sfdisk +/sbin/shadowconfig +/sbin/shutdown +/sbin/start-stop-daemon +/sbin/sulogin +/sbin/swaplabel +/sbin/swapoff +/sbin/swapon +/sbin/switch_root +/sbin/sysctl +/sbin/telinit +/sbin/tune2fs +/sbin/unix_chkpwd +/sbin/unix_update +/sbin/wipefs +/sbin/zramctl +/usr/bin +/usr/bin/2to3-2.7 +/usr/bin/[ +/usr/bin/aa-enabled +/usr/bin/aa-exec +/usr/bin/add-apt-repository +/usr/bin/addpart +/usr/bin/addr2line +/usr/bin/apt +/usr/bin/apt-add-repository +/usr/bin/apt-cache +/usr/bin/apt-cdrom +/usr/bin/apt-config +/usr/bin/apt-get +/usr/bin/apt-key +/usr/bin/apt-mark +/usr/bin/ar +/usr/bin/arch +/usr/bin/as +/usr/bin/awk +/usr/bin/b2sum +/usr/bin/base32 +/usr/bin/base64 +/usr/bin/basename +/usr/bin/bashbug +/usr/bin/bootctl +/usr/bin/busctl +/usr/bin/c++ +/usr/bin/c++filt +/usr/bin/c89 +/usr/bin/c89-gcc +/usr/bin/c99 +/usr/bin/c99-gcc +/usr/bin/c_rehash +/usr/bin/captoinfo +/usr/bin/catchsegv +/usr/bin/cc +/usr/bin/chage +/usr/bin/chattr +/usr/bin/chcon +/usr/bin/chfn +/usr/bin/choom +/usr/bin/chrt +/usr/bin/chsh +/usr/bin/cksum +/usr/bin/clear +/usr/bin/clear_console +/usr/bin/cmp +/usr/bin/comm +/usr/bin/compose +/usr/bin/containerd +/usr/bin/containerd-shim +/usr/bin/containerd-shim-runc-v1 +/usr/bin/containerd-shim-runc-v2 +/usr/bin/corelist +/usr/bin/cpan +/usr/bin/cpan5.28-x86_64-linux-gnu +/usr/bin/cpp +/usr/bin/cpp-8 +/usr/bin/csplit +/usr/bin/ctr +/usr/bin/curl +/usr/bin/curl-config +/usr/bin/cut +/usr/bin/cvtsudoers +/usr/bin/dbus-cleanup-sockets +/usr/bin/dbus-daemon +/usr/bin/dbus-monitor +/usr/bin/dbus-run-session +/usr/bin/dbus-send +/usr/bin/dbus-update-activation-environment +/usr/bin/dbus-uuidgen +/usr/bin/deb-systemd-helper +/usr/bin/deb-systemd-invoke +/usr/bin/debconf +/usr/bin/debconf-apt-progress +/usr/bin/debconf-communicate +/usr/bin/debconf-copydb +/usr/bin/debconf-escape +/usr/bin/debconf-set-selections +/usr/bin/debconf-show +/usr/bin/delpart +/usr/bin/dh_python2 +/usr/bin/diff +/usr/bin/diff3 +/usr/bin/dircolors +/usr/bin/dirmngr +/usr/bin/dirmngr-client +/usr/bin/dirname +/usr/bin/docker +/usr/bin/docker-init +/usr/bin/docker-proxy +/usr/bin/dockerd +/usr/bin/dockerd-rootless-setuptool.sh +/usr/bin/dockerd-rootless.sh +/usr/bin/dpkg +/usr/bin/dpkg-architecture +/usr/bin/dpkg-buildflags +/usr/bin/dpkg-buildpackage +/usr/bin/dpkg-checkbuilddeps +/usr/bin/dpkg-deb +/usr/bin/dpkg-distaddfile +/usr/bin/dpkg-divert +/usr/bin/dpkg-genbuildinfo +/usr/bin/dpkg-genchanges +/usr/bin/dpkg-gencontrol +/usr/bin/dpkg-gensymbols +/usr/bin/dpkg-maintscript-helper +/usr/bin/dpkg-mergechangelogs +/usr/bin/dpkg-name +/usr/bin/dpkg-parsechangelog +/usr/bin/dpkg-query +/usr/bin/dpkg-scanpackages +/usr/bin/dpkg-scansources +/usr/bin/dpkg-shlibdeps +/usr/bin/dpkg-source +/usr/bin/dpkg-split +/usr/bin/dpkg-statoverride +/usr/bin/dpkg-trigger +/usr/bin/dpkg-vendor +/usr/bin/du +/usr/bin/dwp +/usr/bin/echo_supervisord_conf +/usr/bin/edit +/usr/bin/elfedit +/usr/bin/enc2xs +/usr/bin/encguess +/usr/bin/env +/usr/bin/envsubst +/usr/bin/expand +/usr/bin/expiry +/usr/bin/expr +/usr/bin/factor +/usr/bin/faillog +/usr/bin/faked-sysv +/usr/bin/faked-tcp +/usr/bin/fakeroot +/usr/bin/fakeroot-sysv +/usr/bin/fakeroot-tcp +/usr/bin/fallocate +/usr/bin/file +/usr/bin/fincore +/usr/bin/find +/usr/bin/flock +/usr/bin/fmt +/usr/bin/fold +/usr/bin/free +/usr/bin/funzip +/usr/bin/g++ +/usr/bin/g++-8 +/usr/bin/gapplication +/usr/bin/gcc +/usr/bin/gcc-8 +/usr/bin/gcc-ar +/usr/bin/gcc-ar-8 +/usr/bin/gcc-nm +/usr/bin/gcc-nm-8 +/usr/bin/gcc-ranlib +/usr/bin/gcc-ranlib-8 +/usr/bin/gcov +/usr/bin/gcov-8 +/usr/bin/gcov-dump +/usr/bin/gcov-dump-8 +/usr/bin/gcov-tool +/usr/bin/gcov-tool-8 +/usr/bin/gdbus +/usr/bin/gencat +/usr/bin/getconf +/usr/bin/getent +/usr/bin/getopt +/usr/bin/gettext +/usr/bin/gettext.sh +/usr/bin/gettextize +/usr/bin/gio +/usr/bin/gio-querymodules +/usr/bin/git +/usr/bin/git-cvsserver +/usr/bin/git-receive-pack +/usr/bin/git-shell +/usr/bin/git-upload-archive +/usr/bin/git-upload-pack +/usr/bin/gitk +/usr/bin/glib-compile-schemas +/usr/bin/gold +/usr/bin/gpasswd +/usr/bin/gpg +/usr/bin/gpg-agent +/usr/bin/gpg-connect-agent +/usr/bin/gpg-wks-server +/usr/bin/gpg-zip +/usr/bin/gpgcompose +/usr/bin/gpgconf +/usr/bin/gpgparsemail +/usr/bin/gpgsm +/usr/bin/gpgsplit +/usr/bin/gpgtar +/usr/bin/gpgv +/usr/bin/gprof +/usr/bin/gresource +/usr/bin/groups +/usr/bin/gsettings +/usr/bin/h2ph +/usr/bin/h2xs +/usr/bin/head +/usr/bin/hostid +/usr/bin/hostnamectl +/usr/bin/i386 +/usr/bin/iconv +/usr/bin/id +/usr/bin/infocmp +/usr/bin/infotocap +/usr/bin/install +/usr/bin/instmodsh +/usr/bin/ionice +/usr/bin/ipcmk +/usr/bin/ipcrm +/usr/bin/ipcs +/usr/bin/iptables-xml +/usr/bin/ischroot +/usr/bin/join +/usr/bin/jq +/usr/bin/json_pp +/usr/bin/kbxutil +/usr/bin/kernel-install +/usr/bin/killall +/usr/bin/last +/usr/bin/lastb +/usr/bin/lastlog +/usr/bin/lcf +/usr/bin/ld +/usr/bin/ld.bfd +/usr/bin/ld.gold +/usr/bin/ldd +/usr/bin/less +/usr/bin/lessecho +/usr/bin/lessfile +/usr/bin/lesskey +/usr/bin/lesspipe +/usr/bin/libnetcfg +/usr/bin/link +/usr/bin/linux32 +/usr/bin/linux64 +/usr/bin/locale +/usr/bin/localectl +/usr/bin/localedef +/usr/bin/logger +/usr/bin/logname +/usr/bin/lsattr +/usr/bin/lsb_release +/usr/bin/lscpu +/usr/bin/lsipc +/usr/bin/lslocks +/usr/bin/lslogins +/usr/bin/lsmem +/usr/bin/lsns +/usr/bin/lspgpot +/usr/bin/lzcat +/usr/bin/lzcmp +/usr/bin/lzdiff +/usr/bin/lzegrep +/usr/bin/lzfgrep +/usr/bin/lzgrep +/usr/bin/lzless +/usr/bin/lzma +/usr/bin/lzmainfo +/usr/bin/lzmore +/usr/bin/make +/usr/bin/make-first-existing-target +/usr/bin/mawk +/usr/bin/mcookie +/usr/bin/md5sum +/usr/bin/md5sum.textutils +/usr/bin/mesg +/usr/bin/migrate-pubring-from-classic-gpg +/usr/bin/mkfifo +/usr/bin/msgattrib +/usr/bin/msgcat +/usr/bin/msgcmp +/usr/bin/msgcomm +/usr/bin/msgconv +/usr/bin/msgen +/usr/bin/msgexec +/usr/bin/msgfilter +/usr/bin/msgfmt +/usr/bin/msggrep +/usr/bin/msginit +/usr/bin/msgmerge +/usr/bin/msgunfmt +/usr/bin/msguniq +/usr/bin/mtrace +/usr/bin/namei +/usr/bin/nawk +/usr/bin/newgrp +/usr/bin/ngettext +/usr/bin/nice +/usr/bin/nl +/usr/bin/nm +/usr/bin/nohup +/usr/bin/nproc +/usr/bin/nsenter +/usr/bin/numfmt +/usr/bin/objcopy +/usr/bin/objdump +/usr/bin/od +/usr/bin/openssl +/usr/bin/pager +/usr/bin/partx +/usr/bin/passwd +/usr/bin/paste +/usr/bin/patch +/usr/bin/pathchk +/usr/bin/pdb +/usr/bin/pdb2 +/usr/bin/pdb2.7 +/usr/bin/pdb3 +/usr/bin/pdb3.7 +/usr/bin/peekfd +/usr/bin/perl +/usr/bin/perl5.28-x86_64-linux-gnu +/usr/bin/perl5.28.1 +/usr/bin/perlbug +/usr/bin/perldoc +/usr/bin/perlivp +/usr/bin/perlthanks +/usr/bin/pgrep +/usr/bin/piconv +/usr/bin/pidproxy +/usr/bin/pigz +/usr/bin/pinentry +/usr/bin/pinentry-curses +/usr/bin/pinky +/usr/bin/pkaction +/usr/bin/pkcheck +/usr/bin/pkcon +/usr/bin/pkexec +/usr/bin/pkill +/usr/bin/pkmon +/usr/bin/pkttyagent +/usr/bin/pl2pm +/usr/bin/pldd +/usr/bin/pmap +/usr/bin/pod2html +/usr/bin/pod2man +/usr/bin/pod2text +/usr/bin/pod2usage +/usr/bin/podchecker +/usr/bin/podselect +/usr/bin/pr +/usr/bin/print +/usr/bin/printenv +/usr/bin/printf +/usr/bin/prlimit +/usr/bin/prove +/usr/bin/prtstat +/usr/bin/pslog +/usr/bin/pstree +/usr/bin/pstree.x11 +/usr/bin/ptar +/usr/bin/ptardiff +/usr/bin/ptargrep +/usr/bin/ptx +/usr/bin/pwdx +/usr/bin/py3clean +/usr/bin/py3compile +/usr/bin/py3versions +/usr/bin/pyclean +/usr/bin/pycompile +/usr/bin/pydoc +/usr/bin/pydoc2 +/usr/bin/pydoc2.7 +/usr/bin/pydoc3 +/usr/bin/pydoc3.7 +/usr/bin/pygettext +/usr/bin/pygettext2 +/usr/bin/pygettext2.7 +/usr/bin/pygettext3 +/usr/bin/pygettext3.7 +/usr/bin/python +/usr/bin/python2 +/usr/bin/python2.7 +/usr/bin/python3 +/usr/bin/python3.7 +/usr/bin/python3.7m +/usr/bin/python3m +/usr/bin/pyversions +/usr/bin/ranlib +/usr/bin/rcp +/usr/bin/readelf +/usr/bin/realpath +/usr/bin/recode-sr-latin +/usr/bin/rename.ul +/usr/bin/renice +/usr/bin/reset +/usr/bin/resizepart +/usr/bin/resolvectl +/usr/bin/rev +/usr/bin/rgrep +/usr/bin/rlogin +/usr/bin/rootlesskit +/usr/bin/rootlesskit-docker-proxy +/usr/bin/rpcgen +/usr/bin/rsh +/usr/bin/run-mailcap +/usr/bin/runc +/usr/bin/runcon +/usr/bin/savelog +/usr/bin/scp +/usr/bin/script +/usr/bin/scriptreplay +/usr/bin/sdiff +/usr/bin/see +/usr/bin/select-editor +/usr/bin/sensible-browser +/usr/bin/sensible-editor +/usr/bin/sensible-pager +/usr/bin/seq +/usr/bin/setarch +/usr/bin/setpriv +/usr/bin/setsid +/usr/bin/setterm +/usr/bin/sftp +/usr/bin/sg +/usr/bin/sha1sum +/usr/bin/sha224sum +/usr/bin/sha256sum +/usr/bin/sha384sum +/usr/bin/sha512sum +/usr/bin/shasum +/usr/bin/shred +/usr/bin/shuf +/usr/bin/size +/usr/bin/skill +/usr/bin/slabtop +/usr/bin/slogin +/usr/bin/snice +/usr/bin/sort +/usr/bin/sotruss +/usr/bin/splain +/usr/bin/split +/usr/bin/sprof +/usr/bin/ssh +/usr/bin/ssh-add +/usr/bin/ssh-agent +/usr/bin/ssh-argv0 +/usr/bin/ssh-copy-id +/usr/bin/ssh-keygen +/usr/bin/ssh-keyscan +/usr/bin/stat +/usr/bin/stdbuf +/usr/bin/strings +/usr/bin/strip +/usr/bin/sudo +/usr/bin/sudoedit +/usr/bin/sudoreplay +/usr/bin/sum +/usr/bin/supervisorctl +/usr/bin/supervisord +/usr/bin/symcryptrun +/usr/bin/systemd-analyze +/usr/bin/systemd-cat +/usr/bin/systemd-cgls +/usr/bin/systemd-cgtop +/usr/bin/systemd-delta +/usr/bin/systemd-detect-virt +/usr/bin/systemd-id128 +/usr/bin/systemd-mount +/usr/bin/systemd-path +/usr/bin/systemd-resolve +/usr/bin/systemd-run +/usr/bin/systemd-socket-activate +/usr/bin/systemd-stdio-bridge +/usr/bin/systemd-umount +/usr/bin/tabs +/usr/bin/tac +/usr/bin/tail +/usr/bin/taskset +/usr/bin/tee +/usr/bin/test +/usr/bin/tic +/usr/bin/timedatectl +/usr/bin/timeout +/usr/bin/tload +/usr/bin/toe +/usr/bin/top +/usr/bin/touch +/usr/bin/tput +/usr/bin/tr +/usr/bin/truncate +/usr/bin/tset +/usr/bin/tsort +/usr/bin/tty +/usr/bin/tzselect +/usr/bin/ucf +/usr/bin/ucfq +/usr/bin/ucfr +/usr/bin/unattended-upgrade +/usr/bin/unattended-upgrades +/usr/bin/unexpand +/usr/bin/uniq +/usr/bin/unlink +/usr/bin/unlzma +/usr/bin/unpigz +/usr/bin/unshare +/usr/bin/unxz +/usr/bin/unzip +/usr/bin/unzipsfx +/usr/bin/update-alternatives +/usr/bin/update-mime-database +/usr/bin/uptime +/usr/bin/users +/usr/bin/utmpdump +/usr/bin/vmstat +/usr/bin/w +/usr/bin/w.procps +/usr/bin/wall +/usr/bin/watch +/usr/bin/watchgnupg +/usr/bin/wc +/usr/bin/whereis +/usr/bin/which +/usr/bin/who +/usr/bin/whoami +/usr/bin/x86_64 +/usr/bin/x86_64-linux-gnu-addr2line +/usr/bin/x86_64-linux-gnu-ar +/usr/bin/x86_64-linux-gnu-as +/usr/bin/x86_64-linux-gnu-c++filt +/usr/bin/x86_64-linux-gnu-cpp +/usr/bin/x86_64-linux-gnu-cpp-8 +/usr/bin/x86_64-linux-gnu-dwp +/usr/bin/x86_64-linux-gnu-elfedit +/usr/bin/x86_64-linux-gnu-g++ +/usr/bin/x86_64-linux-gnu-g++-8 +/usr/bin/x86_64-linux-gnu-gcc +/usr/bin/x86_64-linux-gnu-gcc-8 +/usr/bin/x86_64-linux-gnu-gcc-ar +/usr/bin/x86_64-linux-gnu-gcc-ar-8 +/usr/bin/x86_64-linux-gnu-gcc-nm +/usr/bin/x86_64-linux-gnu-gcc-nm-8 +/usr/bin/x86_64-linux-gnu-gcc-ranlib +/usr/bin/x86_64-linux-gnu-gcc-ranlib-8 +/usr/bin/x86_64-linux-gnu-gcov +/usr/bin/x86_64-linux-gnu-gcov-8 +/usr/bin/x86_64-linux-gnu-gcov-dump +/usr/bin/x86_64-linux-gnu-gcov-dump-8 +/usr/bin/x86_64-linux-gnu-gcov-tool +/usr/bin/x86_64-linux-gnu-gcov-tool-8 +/usr/bin/x86_64-linux-gnu-gold +/usr/bin/x86_64-linux-gnu-gprof +/usr/bin/x86_64-linux-gnu-ld +/usr/bin/x86_64-linux-gnu-ld.bfd +/usr/bin/x86_64-linux-gnu-ld.gold +/usr/bin/x86_64-linux-gnu-nm +/usr/bin/x86_64-linux-gnu-objcopy +/usr/bin/x86_64-linux-gnu-objdump +/usr/bin/x86_64-linux-gnu-ranlib +/usr/bin/x86_64-linux-gnu-readelf +/usr/bin/x86_64-linux-gnu-size +/usr/bin/x86_64-linux-gnu-strings +/usr/bin/x86_64-linux-gnu-strip +/usr/bin/xargs +/usr/bin/xauth +/usr/bin/xdg-user-dir +/usr/bin/xdg-user-dirs-update +/usr/bin/xgettext +/usr/bin/xsubpp +/usr/bin/xz +/usr/bin/xzcat +/usr/bin/xzcmp +/usr/bin/xzdiff +/usr/bin/xzegrep +/usr/bin/xzfgrep +/usr/bin/xzgrep +/usr/bin/xzless +/usr/bin/xzmore +/usr/bin/yes +/usr/bin/zdump +/usr/bin/zipdetails +/usr/bin/zipgrep +/usr/bin/zipinfo +/usr/local/bin +/usr/local/bin/docker-compose +/usr/local/sbin +/usr/sbin +/usr/sbin/aa-remove-unknown +/usr/sbin/aa-status +/usr/sbin/aa-teardown +/usr/sbin/add-shell +/usr/sbin/addgnupghome +/usr/sbin/addgroup +/usr/sbin/adduser +/usr/sbin/apparmor_status +/usr/sbin/applygnupgdefaults +/usr/sbin/arptables +/usr/sbin/arptables-nft +/usr/sbin/arptables-nft-restore +/usr/sbin/arptables-nft-save +/usr/sbin/arptables-restore +/usr/sbin/arptables-save +/usr/sbin/chgpasswd +/usr/sbin/chmem +/usr/sbin/chpasswd +/usr/sbin/chroot +/usr/sbin/cpgr +/usr/sbin/cppw +/usr/sbin/delgroup +/usr/sbin/deluser +/usr/sbin/dpkg-preconfigure +/usr/sbin/dpkg-reconfigure +/usr/sbin/e2freefrag +/usr/sbin/e4crypt +/usr/sbin/e4defrag +/usr/sbin/ebtables +/usr/sbin/ebtables-nft +/usr/sbin/ebtables-nft-restore +/usr/sbin/ebtables-nft-save +/usr/sbin/ebtables-restore +/usr/sbin/ebtables-save +/usr/sbin/fdformat +/usr/sbin/filefrag +/usr/sbin/groupadd +/usr/sbin/groupdel +/usr/sbin/groupmems +/usr/sbin/groupmod +/usr/sbin/grpck +/usr/sbin/grpconv +/usr/sbin/grpunconv +/usr/sbin/iconvconfig +/usr/sbin/invoke-rc.d +/usr/sbin/ip6tables +/usr/sbin/ip6tables-apply +/usr/sbin/ip6tables-legacy +/usr/sbin/ip6tables-legacy-restore +/usr/sbin/ip6tables-legacy-save +/usr/sbin/ip6tables-nft +/usr/sbin/ip6tables-nft-restore +/usr/sbin/ip6tables-nft-save +/usr/sbin/ip6tables-restore +/usr/sbin/ip6tables-restore-translate +/usr/sbin/ip6tables-save +/usr/sbin/ip6tables-translate +/usr/sbin/iptables +/usr/sbin/iptables-apply +/usr/sbin/iptables-legacy +/usr/sbin/iptables-legacy-restore +/usr/sbin/iptables-legacy-save +/usr/sbin/iptables-nft +/usr/sbin/iptables-nft-restore +/usr/sbin/iptables-nft-save +/usr/sbin/iptables-restore +/usr/sbin/iptables-restore-translate +/usr/sbin/iptables-save +/usr/sbin/iptables-translate +/usr/sbin/ldattach +/usr/sbin/mklost+found +/usr/sbin/newusers +/usr/sbin/nfnl_osf +/usr/sbin/nft +/usr/sbin/nologin +/usr/sbin/pam-auth-update +/usr/sbin/pam_getenv +/usr/sbin/pam_timestamp_check +/usr/sbin/policy-rc.d +/usr/sbin/pwck +/usr/sbin/pwconv +/usr/sbin/pwunconv +/usr/sbin/readprofile +/usr/sbin/remove-shell +/usr/sbin/rmt +/usr/sbin/rmt-tar +/usr/sbin/rtcwake +/usr/sbin/service +/usr/sbin/tarcat +/usr/sbin/tzconfig +/usr/sbin/update-ca-certificates +/usr/sbin/update-mime +/usr/sbin/update-passwd +/usr/sbin/update-rc.d +/usr/sbin/useradd +/usr/sbin/userdel +/usr/sbin/usermod +/usr/sbin/vigr +/usr/sbin/vipw +/usr/sbin/visudo +/usr/sbin/xtables-legacy-multi +/usr/sbin/xtables-monitor +/usr/sbin/xtables-nft-multi +/usr/sbin/zic +``` + +This was mostly a [fun exercise](https://unix.stackexchange.com/a/120943/158462) for myself to see if it could be done using one line of Python code without resorting to using the exec function. In a more readable form, and with some comments, the code looks like this: +``` +import os +import sys + +# This is just to have a function to output something on the screen. +# I'm using Python 2.7 in which 'print' is not a function and cannot +# be used in the 'map' function. +output = lambda(x) : sys.stdout.write(x + "\n") + +# Get a list of the components in the PATH environment variable. Will +# abort the program is PATH doesn't exist +paths = os.environ["PATH"].split(":") + +# os.listdir raises an error is something is not a path so I'm creating +# a small function that only executes it if 'p' is a directory +listdir = lambda(p) : os.listdir(p) if os.path.isdir(p) else [ ] + +# Checks if the path specified by x[0] and x[1] is a file +isfile = lambda(x) : True if os.path.isfile(os.path.join(x[0],x[1])) else False + +# Checks if the path specified by x[0] and x[1] has the executable flag set +isexe = lambda(x) : True if os.access(os.path.join(x[0],x[1]), os.X_OK) else False + +# Here, I'm using a list comprehension to build a list of all executable files +# in the PATH, and abusing the map function to write every name in the resulting +# list to the screen. +map(output, [ os.path.join(p,f) for p in paths for f in listdir(p) if isfile((p,f)) and isexe((p,f)) ]) +``` + +If you can run Python 2 in your shell, the following (ridiculously long) one-liner can be used as well: + +``` +$ python2 -c 'import os;import sys;output = lambda(x) : sys.stdout.write(x + "\n"); paths = os.environ["PATH"].split(":") ; listdir = lambda(p) : os.listdir(p) if os.path.isdir(p) else [ ] ; isfile = lambda(x) : True if os.path.isfile(os.path.join(x[0],x[1])) else False ; isexe = lambda(x) : True if os.access(os.path.join(x[0],x[1]), os.X_OK) else False ; map(output,[ os.path.join(p,f) for p in paths for f in listdir(p) if isfile((p,f)) and isexe((p,f)) ])' +``` + +### Packages + +If we need to [list the installed packages in the Python](https://stackoverflow.com/a/73958089/4058484) shell, For terminal I recommend help("modules") or python -c "help('modules')". + +``` +$ python3.7 -c 'help("modules")' + +Please wait a moment while I gather a list of all available modules... + +__future__ _tracemalloc getopt rlcompleter +_abc _uuid getpass runpy +_ast _warnings gettext sched +_asyncio _weakref gi secrets +_bisect _weakrefset glob select +_blake2 _xxtestfuzz grp selectors +_bootlocale abc gzip shelve +_bz2 aifc hashlib shlex +_codecs antigravity heapq shutil +_codecs_cn apt hmac signal +_codecs_hk apt_inst html site +_codecs_iso2022 apt_pkg http sitecustomize +_codecs_jp aptsources imaplib smtpd +_codecs_kr argparse imghdr smtplib +_codecs_tw array imp sndhdr +_collections ast importlib socket +_collections_abc asynchat inspect socketserver +_compat_pickle asyncio io softwareproperties +_compression asyncore ipaddress spwd +_contextvars atexit itertools sqlite3 +_crypt audioop json sre_compile +_csv base64 keyword sre_constants +_ctypes bdb linecache sre_parse +_ctypes_test binascii locale ssl +_curses binhex logging stat +_curses_panel bisect lsb_release statistics +_datetime builtins lzma string +_dbm bz2 macpath stringprep +_dbus_bindings cProfile mailbox struct +_dbus_glib_bindings calendar mailcap subprocess +_decimal cgi marshal sunau +_dummy_thread cgitb math symbol +_elementtree chunk mimetypes symtable +_functools cmath mmap sys +_hashlib cmd modulefinder sysconfig +_heapq code multiprocessing syslog +_imp codecs netrc tabnanny +_io codeop nis tarfile +_json collections nntplib telnetlib +_locale colorsys ntpath tempfile +_lsprof compileall nturl2path termios +_lzma concurrent numbers test +_markupbase configparser opcode textwrap +_md5 contextlib operator this +_multibytecodec contextvars optparse threading +_multiprocessing copy os time +_opcode copyreg ossaudiodev timeit +_operator crypt parser token +_osx_support csv pathlib tokenize +_pickle ctypes pdb trace +_posixsubprocess curl pickle traceback +_py_abc curses pickletools tracemalloc +_pydecimal dataclasses pipes tty +_pyio datetime pkgutil turtle +_queue dbm platform types +_random dbus plistlib typing +_sha1 decimal poplib unicodedata +_sha256 difflib posix unittest +_sha3 dis posixpath urllib +_sha512 distro_info pprint uu +_signal distutils profile uuid +_sitebuiltins doctest pstats venv +_socket dummy_threading pty warnings +_sqlite3 email pwd wave +_sre encodings py_compile weakref +_ssl enum pyclbr webbrowser +_stat errno pycurl wsgiref +_string faulthandler pydoc xdrlib +_strptime fcntl pydoc_data xml +_struct filecmp pyexpat xmlrpc +_symtable fileinput pygtkcompat xxlimited +_sysconfigdata_m_linux_x86_64-linux-gnu fnmatch queue +_testbuffer formatter quopri zipapp +_testcapi fractions random zipfile +_testimportmultiple ftplib re zipimport +_testmultiphase functools readline zlib +_thread gc reprlib xxsubtype +_threading_local genericpath resource + +Enter any module name to get more help. Or, type "modules spam" to search +for modules whose name or summary contain the string "spam". +``` + +I'm comparing five methods to retrieve installed "modules", all of which I've seen in this thread + +``` + iter_modules help("modules") builtin_module_names pip list working_set +Includes distributions ❌ ❌ ❌ ✔️ ✔️ +Includes modules (No built-in) ✔️ ✔️ ❌ ❌ ❌ +Includes built-in modules ❌ ✔️ ✔️ ❌ ❌ +Includes frozen ✔️ ✔️ ❌ ❌ ❌ +Includes venv ✔️ ✔️ ❌ ✔️ ✔️ +Includes global ✔️ ✔️ ❌ ✔️ ✔️ +Includes editable installs ✔️ ✔️ ❌ ✔️ ✔️ +Includes PyCharm helpers ✔️ ❌ ❌ ❌ ❌ +Lowers capital letters ❌ ❌ ❌ ❌ ✔️ +Time taken (665 modules total) 53.7 msec 1.03 sec 577 nsec 284 msec 36.2 usec +``` +For programmatically I recommend iter_modules + builtin_module_names to pluck the module name out of the tuples generated by [pkgutil.iter_modules()](http://docs.python.org/library/pkgutil.html#pkgutil.iter_modules) It is however very convoluted with information + +``` +$ python -c 'import pkgutil;print [x[1] for x in list(pkgutil.iter_modules())]' + +['BaseHTTPServer', 'Bastion', 'CGIHTTPServer', 'ConfigParser', 'Cookie', 'DocXMLRPCServer', 'HTMLParser', +'MimeWriter', 'Queue', 'SimpleHTTPServer', 'SimpleXMLRPCServer', 'SocketServer', 'StringIO', 'UserDict', +'UserList', 'UserString', '_LWPCookieJar', '_MozillaCookieJar', '__future__', '_abcoll', '_osx_support', +'_pyio', '_strptime', '_sysconfigdata', '_threading_local', '_weakrefset', 'abc', 'aifc', 'antigravity', +'anydbm', 'argparse', 'ast', 'asynchat', 'asyncore', 'atexit', 'audiodev', 'base64', 'bdb', 'binhex', +'bisect', 'bsddb', 'cProfile', 'calendar', 'cgi', 'cgitb', 'chunk', 'cmd', 'code', 'codecs', 'codeop', +'collections', 'colorsys', 'commands', 'compileall', 'compiler', 'contextlib', 'cookielib', 'copy', +'copy_reg', 'csv', 'ctypes', 'curses', 'dbhash', 'decimal', 'difflib', 'dircache', 'dis', 'distutils', +'doctest', 'dumbdbm', 'dummy_thread', 'dummy_threading', 'email', 'encodings', 'ensurepip', 'filecmp', +'fileinput', 'fnmatch', 'formatter', 'fpformat', 'fractions', 'ftplib', 'functools', 'genericpath', +'getopt', 'getpass', 'gettext', 'glob', 'gzip', 'hashlib', 'heapq', 'hmac', 'hotshot', 'htmlentitydefs', +'htmllib', 'httplib', 'ihooks', 'imaplib', 'imghdr', 'importlib', 'imputil', 'inspect', 'io', 'json', +'keyword', 'lib2to3', 'linecache', 'locale', 'logging', 'macpath', 'macurl2path', 'mailbox', 'mailcap', +'markupbase', 'md5', 'mhlib', 'mimetools', 'mimetypes', 'mimify', 'modulefinder', 'multifile', +'multiprocessing', 'mutex', 'netrc', 'new', 'nntplib', 'ntpath', 'nturl2path', 'numbers', 'opcode', +'optparse', 'os', 'os2emxpath', 'pdb', 'pickle', 'pickletools', 'pipes', 'pkgutil', 'platform', +'plistlib', 'popen2', 'poplib', 'posixfile', 'posixpath', 'pprint', 'profile', 'pstats', 'pty', +'py_compile', 'pyclbr', 'pydoc', 'pydoc_data', 'quopri', 'random', 're', 'repr', 'rexec', 'rfc822', +'rlcompleter', 'robotparser', 'runpy', 'sched', 'sets', 'sgmllib', 'sha', 'shelve', 'shlex', 'shutil', +'site', 'sitecustomize', 'smtpd', 'smtplib', 'sndhdr', 'socket', 'sqlite3', 'sre', 'sre_compile', +'sre_constants', 'sre_parse', 'ssl', 'stat', 'statvfs', 'string', 'stringold', 'stringprep', 'struct', +'subprocess', 'sunau', 'sunaudio', 'symbol', 'symtable', 'sysconfig', 'tabnanny', 'tarfile', 'telnetlib', +'tempfile', 'test', 'textwrap', 'this', 'threading', 'timeit', 'toaiff', 'token', 'tokenize', 'trace', +'traceback', 'tty', 'types', 'unittest', 'urllib', 'urllib2', 'urlparse', 'user', 'uu', 'uuid', 'warnings', +'wave', 'weakref', 'webbrowser', 'whichdb', 'wsgiref', 'xdrlib', 'xml', 'xmllib', 'xmlrpclib', 'zipfile', +'CDROM', 'DLFCN', 'IN', 'TYPES', '_sysconfigdata_nd', 'Canvas', 'Dialog', 'FileDialog', 'FixTk', +'ScrolledText', 'SimpleDialog', 'Tix', 'Tkconstants', 'Tkdnd', 'Tkinter', 'tkColorChooser', 'tkCommonDialog', +'tkFileDialog', 'tkFont', 'tkMessageBox', 'tkSimpleDialog', 'ttk', 'turtle', '_bsddb', '_codecs_cn', +'_codecs_hk', '_codecs_iso2022', '_codecs_jp', '_codecs_kr', '_codecs_tw', '_csv', '_ctypes', '_ctypes_test', +'_curses', '_curses_panel', '_elementtree', '_hashlib', '_hotshot', '_json', '_lsprof', '_multibytecodec', +'_multiprocessing', '_sqlite3', '_ssl', '_testcapi', 'audioop', 'bz2', 'crypt', 'dbm', 'future_builtins', +'linuxaudiodev', 'mmap', 'nis', 'ossaudiodev', 'parser', 'pyexpat', 'readline', 'resource', 'termios', +'lsb_release', 'meld3', 'pkg_resources', 'supervisor'] +``` diff --git a/identition/span4/gist03.html b/identition/span4/gist03.html new file mode 100644 index 00000000000..160fe22460f --- /dev/null +++ b/identition/span4/gist03.html @@ -0,0 +1,61 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            This solution is primary based on modules importlib and pkgutil and work with CPython 3.4 and CPython 3.5, but has no support for the CPython 2.

            python_modules_info.py

            import sys
+import os
+import shutil
+import pkgutil
+import importlib
+import collections
+
+if sys.version_info.major == 2:
+    raise NotImplementedError('CPython 2 is not supported yet')
+
+
+def main():
+
+    # name this file (module)
+    this_module_name = os.path.basename(__file__).rsplit('.')[0]
+
+    # dict for loaders with their modules
+    loaders = collections.OrderedDict()
+
+    # names`s of build-in modules
+    for module_name in sys.builtin_module_names:
+
+        # find an information about a module by name
+        module = importlib.util.find_spec(module_name)
+
+        # add a key about a loader in the dict, if not exists yet
+        if module.loader not in loaders:
+            loaders[module.loader] = []
+
+        # add a name and a location about imported module in the dict
+        loaders[module.loader].append((module.name, module.origin))
+
+    # all available non-build-in modules
+    for module_name in pkgutil.iter_modules():
+
+        # ignore this module
+        if this_module_name == module_name[1]:
+            continue
+
+        # find an information about a module by name
+        module = importlib.util.find_spec(module_name[1])
+
+        # add a key about a loader in the dict, if not exists yet
+        loader = type(module.loader)
+        if loader not in loaders:
+            loaders[loader] = []
+
+        # add a name and a location about imported module in the dict
+        loaders[loader].append((module.name, module.origin))
+
+    # pretty print
+    line = '-' * shutil.get_terminal_size().columns
+    for loader, modules in loaders.items():
+        print('{0}\n{1}: {2}\n{0}'.format(line, len(modules), loader))
+        for module in modules:
+            print('{0:30} | {1}'.format(module[0], module[1]))
+
+
+if __name__ == '__main__':
+    main()
+

            default

            default

            default

            A better understanding of the distribution of prime numbers would be a major breakthrough in mathematics A continued relationship with the powers of pi could indicate a connection to circular geometry Other patterns can be analyzed to determine if they are related to the distribution of primes The speed and scalability of the cluster allows Tad Gallion and other researchers to check values of numbers that are significantly higher than any individual computer could compute in a reasonable time constraint The parallelization of the algorithm achieved a 9X speedup **using CUDA GPU programming** Because the cluster is managed over the internet, new compute nodes can be added with minimal effort Visualization tools enable researchers to explore the prime hexagon quickly and discover patterns that can be further analyzed Understanding the pattern of prime numbers could have effects in cryptography Many modern encryption algorithms depend on the factorization of very large primes which are hard to find

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist03.md b/identition/span4/gist03.md new file mode 100644 index 00000000000..222e23ef441 --- /dev/null +++ b/identition/span4/gist03.md @@ -0,0 +1,74 @@ + +This [solution](https://stackoverflow.com/a/42673938/4058484) is primary based on modules importlib and pkgutil and work with CPython 3.4 and CPython 3.5, but has no support for the CPython 2. + +python_modules_info.py +``` +import sys +import os +import shutil +import pkgutil +import importlib +import collections + +if sys.version_info.major == 2: + raise NotImplementedError('CPython 2 is not supported yet') + + +def main(): + + # name this file (module) + this_module_name = os.path.basename(__file__).rsplit('.')[0] + + # dict for loaders with their modules + loaders = collections.OrderedDict() + + # names`s of build-in modules + for module_name in sys.builtin_module_names: + + # find an information about a module by name + module = importlib.util.find_spec(module_name) + + # add a key about a loader in the dict, if not exists yet + if module.loader not in loaders: + loaders[module.loader] = [] + + # add a name and a location about imported module in the dict + loaders[module.loader].append((module.name, module.origin)) + + # all available non-build-in modules + for module_name in pkgutil.iter_modules(): + + # ignore this module + if this_module_name == module_name[1]: + continue + + # find an information about a module by name + module = importlib.util.find_spec(module_name[1]) + + # add a key about a loader in the dict, if not exists yet + loader = type(module.loader) + if loader not in loaders: + loaders[loader] = [] + + # add a name and a location about imported module in the dict + loaders[loader].append((module.name, module.origin)) + + # pretty print + line = '-' * shutil.get_terminal_size().columns + for loader, modules in loaders.items(): + print('{0}\n{1}: {2}\n{0}'.format(line, len(modules), loader)) + for module in modules: + print('{0:30} | {1}'.format(module[0], module[1])) + + +if __name__ == '__main__': + main() +``` + +[![default](https://user-images.githubusercontent.com/8466209/199131193-34b17216-1308-4efc-953c-708e31007505.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-4_quantum-md) + +[![default](https://user-images.githubusercontent.com/8466209/198928812-cab7aef3-9c41-49f4-8b89-00b8fa3fc95a.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde#file-lexer-md) + +[![default](https://user-images.githubusercontent.com/8466209/199133270-71ca3596-983b-435a-82f6-bcaa682ae650.png)](https://github.com/FeedMapping/prime-hexagon) + +A better understanding of the distribution of prime numbers would be a major breakthrough in mathematics A continued relationship with the powers of pi could indicate a connection to circular geometry Other patterns can be analyzed to determine if they are related to the distribution of primes The speed and scalability of the cluster allows Tad Gallion and other researchers to check values of numbers that are significantly higher than any individual computer could compute in a reasonable time constraint The parallelization of the algorithm achieved a 9X speedup *****using CUDA GPU programming***** Because the cluster is managed over the internet, new compute nodes can be added with minimal effort Visualization tools enable researchers to explore the prime hexagon quickly and discover patterns that can be further analyzed Understanding the pattern of prime numbers could have effects in cryptography Many modern encryption algorithms depend on the factorization of very large primes which are hard to find \ No newline at end of file diff --git a/identition/span4/gist04.html b/identition/span4/gist04.html new file mode 100644 index 00000000000..814d16c2bff --- /dev/null +++ b/identition/span4/gist04.html @@ -0,0 +1,548 @@ + Directory Structure · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Directory Structure

            This page walks through the steps required to train an object detection model with Recommended Directory Structure for Training and Evaluation for tf2_ai_platform

            $ cat /mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile
+
+FROM tensorflow/tensorflow:latest-gpu
+
+ARG DEBIAN_FRONTEND=noninteractive
+
+# Install apt dependencies
+RUN apt-get update && apt-get install -y \
+    git \
+    gpg-agent \
+    python3-cairocffi \
+    protobuf-compiler \
+    python3-pil \
+    python3-lxml \
+    python3-tk \
+    python3-opencv \
+    wget
+
+# Installs google cloud sdk, this is mostly for using gsutil to export model.
+RUN wget -nv \
+    https://dl.google.com/dl/cloudsdk/release/google-cloud-sdk.tar.gz && \
+    mkdir /root/tools && \
+    tar xvzf google-cloud-sdk.tar.gz -C /root/tools && \
+    rm google-cloud-sdk.tar.gz && \
+    /root/tools/google-cloud-sdk/install.sh --usage-reporting=false \
+        --path-update=false --bash-completion=false \
+        --disable-installation-options && \
+    rm -rf /root/.config/* && \
+    ln -s /root/.config /config && \
+    rm -rf /root/tools/google-cloud-sdk/.install/.backup
+
+# Path configuration
+ENV PATH $PATH:/root/tools/google-cloud-sdk/bin
+# Make sure gsutil will use the default service account
+RUN echo '[GoogleCompute]\nservice_account = default' > /etc/boto.cfg
+
+WORKDIR /home/tensorflow
+
+## Copy this code (make sure you are under the ../models/research directory)
+COPY . /home/tensorflow/models
+
+# Compile protobuf configs
+RUN (cd /home/tensorflow/models/ && protoc object_detection/protos/*.proto --python_out=.)
+WORKDIR /home/tensorflow/models/
+
+RUN cp object_detection/packages/tf2/setup.py ./
+ENV PATH="/home/tensorflow/.local/bin:${PATH}"
+
+RUN python -m pip install -U pip
+RUN python -m pip install .
+
+ENTRYPOINT ["python", "object_detection/model_main_tf2.py"]
+

            GitHub allows developers to run GitHub Actions workflows on your own runners. This Docker image allows you to create your own runners on Docker. The GitHub runner (the binary) will update itself when receiving a job, if a new release is available.

            ARG FROM=debian:buster-slim
+FROM ${FROM}
+
+ARG DEBIAN_FRONTEND=noninteractive
+ARG GIT_VERSION="2.26.2"
+ARG GH_RUNNER_VERSION
+ARG DOCKER_COMPOSE_VERSION="1.27.4"
+
+ENV RUNNER_NAME=""
+ENV RUNNER_WORK_DIRECTORY="_work"
+ENV RUNNER_TOKEN=""
+ENV RUNNER_REPOSITORY_URL=""
+ENV RUNNER_LABELS=""
+ENV RUNNER_ALLOW_RUNASROOT=true
+ENV GITHUB_ACCESS_TOKEN=""
+ENV AGENT_TOOLSDIRECTORY=/opt/hostedtoolcache
+
+# Labels.
+LABEL maintainer="me@tcardonne.fr" \
+    org.label-schema.schema-version="1.0" \
+    org.label-schema.build-date=$BUILD_DATE \
+    org.label-schema.vcs-ref=$VCS_REF \
+    org.label-schema.name="tcardonne/github-runner" \
+    org.label-schema.description="Dockerized GitHub Actions runner." \
+    org.label-schema.url="https://github.com/tcardonne/docker-github-runner" \
+    org.label-schema.vcs-url="https://github.com/tcardonne/docker-github-runner" \
+    org.label-schema.vendor="Thomas Cardonne" \
+    org.label-schema.docker.cmd="docker run -it tcardonne/github-runner:latest"
+
+RUN DEBIAN_FRONTEND=noninteractive apt-get update && \
+    apt-get install -y \
+        curl \
+        unzip \
+        apt-transport-https \
+        ca-certificates \
+        software-properties-common \
+        sudo \
+        supervisor \
+        jq \
+        iputils-ping \
+        build-essential \
+        zlib1g-dev \
+        gettext \
+        liblttng-ust0 \
+        libcurl4-openssl-dev \
+        openssh-client && \
+    rm -rf /var/lib/apt/lists/* && \
+    apt-get clean
+
+COPY supervisord.conf /etc/supervisor/conf.d/supervisord.conf
+RUN chmod 644 /etc/supervisor/conf.d/supervisord.conf
+
+# Install Docker CLI
+RUN curl -fsSL https://get.docker.com -o- | sh && \
+    rm -rf /var/lib/apt/lists/* && \
+    apt-get clean
+
+# Install Docker-Compose
+RUN curl -L -o /usr/local/bin/docker-compose \
+    "https://github.com/docker/compose/releases/download/${DOCKER_COMPOSE_VERSION}/docker-compose-$(uname -s)-$(uname -m)" && \
+    chmod +x /usr/local/bin/docker-compose
+
+RUN cd /tmp && \
+    curl -sL -o git.tgz \
+    https://www.kernel.org/pub/software/scm/git/git-${GIT_VERSION}.tar.gz && \
+    tar zxf git.tgz  && \
+    cd git-${GIT_VERSION}  && \
+    ./configure --prefix=/usr  && \
+    make && \
+    make install && \
+    rm -rf /tmp/*
+
+RUN mkdir -p /home/runner ${AGENT_TOOLSDIRECTORY}
+
+WORKDIR /home/runner
+
+RUN GH_RUNNER_VERSION=${GH_RUNNER_VERSION:-$(curl --silent "https://api.github.com/repos/actions/runner/releases/latest" | grep tag_name | sed -E 's/.*"v([^"]+)".*/\1/')} \
+    && curl -L -O https://github.com/actions/runner/releases/download/v${GH_RUNNER_VERSION}/actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \
+    && tar -zxf actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \
+    && rm -f actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \
+    && ./bin/installdependencies.sh \
+    && chown -R root: /home/runner \
+    && rm -rf /var/lib/apt/lists/* \
+    && apt-get clean
+
+COPY entrypoint.sh /entrypoint.sh
+RUN chmod +x /entrypoint.sh
+ENTRYPOINT ["/entrypoint.sh"]
+CMD ["/usr/bin/supervisord", "-c", "/etc/supervisor/conf.d/supervisord.conf"]
+

            In order to allow the runner to exit and restart by itself, the binary is started by a supervisord process and entrypoint.

            $ cat /etc/supervisord.conf
+
+[supervisord]
+user=root
+nodaemon=true
+logfile=/dev/fd/1
+logfile_maxbytes=0
+loglevel=error
+
+[program:runner]
+directory=/home/runner
+command=/home/runner/bin/runsvc.sh
+stdout_logfile=/dev/fd/1
+stdout_logfile_maxbytes=0
+redirect_stderr=true
+

            The self-hosted runner application creates a detailed log file for each job that it processes. These files are stored in the diag directory where you installed the runner application, and the filename begins with Worker.

            $ cat /home/runner/_diag/Runner_20230515-184422-utc.log
+
+[2023-05-15 18:44:22Z INFO HostContext] No proxy settings were found based on environmental variables (http_proxy/https_proxy/HTTP_PROXY/HTTPS_PROXY)
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Credentials': '/home/runner/.credentials'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Runner': '/home/runner/.runner'
+[2023-05-15 18:44:22Z INFO Listener] Runner is built for Linux (X64) - linux-x64.
+[2023-05-15 18:44:22Z INFO Listener] RuntimeInformation: Linux 5.15.109+ #1 SMP Sat May 6 10:58:50 UTC 2023.
+[2023-05-15 18:44:22Z INFO Listener] Version: 2.303.0
+[2023-05-15 18:44:22Z INFO Listener] Commit: e676c7871817c1b484299cd93fabdf4b95e70741
+[2023-05-15 18:44:22Z INFO Listener] Culture: 
+[2023-05-15 18:44:22Z INFO Listener] UI Culture: 
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO Listener] Validating directory permissions for: '/home/runner'
+[2023-05-15 18:44:22Z INFO CommandLineParser] Parse
+[2023-05-15 18:44:22Z INFO CommandLineParser] Parsing 11 args
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: False
+[2023-05-15 18:44:22Z INFO CommandLineParser] Adding Command: configure
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] arg: url
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'url': 'https://github.com/FeedMapping'
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] arg: token
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'token': '***'
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] arg: name
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'name': 'Google-optimized-instance'
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] arg: work
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'work': '_work'
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] arg: replace
+[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument
+[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True
+[2023-05-15 18:44:22Z INFO CommandLineParser] arg: unattended
+[2023-05-15 18:44:22Z INFO CommandLineParser] Adding flag: replace
+[2023-05-15 18:44:22Z INFO Listener] Arguments parsed
+[2023-05-15 18:44:22Z INFO Runner] ExecuteCommand
+[2023-05-15 18:44:22Z INFO ConfigurationStore] currentAssemblyLocation: /home/runner/bin/Runner.Listener.dll
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] binPath: /home/runner/bin
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] RootFolder: /home/runner
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Runner': '/home/runner/.runner'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] ConfigFilePath: /home/runner/.runner
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Credentials': '/home/runner/.credentials'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] CredFilePath: /home/runner/.credentials
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'MigratedCredentials': '/home/runner/.credentials_migrated'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] MigratedCredFilePath: /home/runner/.credentials_migrated
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Service': '/home/runner/.service'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] ServiceConfigFilePath: /home/runner/.service
+[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'help': 'False'
+[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'version': 'False'
+[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'commit': 'False'
+[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'check': 'False'
+[2023-05-15 18:44:22Z INFO CommandSettings] Command 'configure': 'True'
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: --------------------------------------------------------------------------------
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |        ____ _ _   _   _       _          _        _   _                      |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |       / ___(_) |_| | | |_   _| |__      / \   ___| |_(_) ___  _ __  ___      |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |      | |  _| | __| |_| | | | | '_ \    / _ \ / __| __| |/ _ \| '_ \/ __|     |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |      | |_| | | |_|  _  | |_| | |_) |  / ___ \ (__| |_| | (_) | | | \__ \     |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |       \____|_|\__|_| |_|\__,_|_.__/  /_/   \_\___|\__|_|\___/|_| |_|___/     |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |                                                                              |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE: |                       
+[2023-05-15 18:44:22Z INFO Terminal] WRITE: Self-hosted runner registration
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE:                         |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: |                                                                              |
+[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: --------------------------------------------------------------------------------
+[2023-05-15 18:44:22Z INFO ConfigurationManager] ConfigureAsync
+[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'generateServiceConfig': 'False'
+[2023-05-15 18:44:22Z INFO ConfigurationStore] IsConfigured()
+[2023-05-15 18:44:22Z INFO ConfigurationStore] IsConfigured: False
+[2023-05-15 18:44:22Z INFO ConfigurationManager] Is configured: False
+[2023-05-15 18:44:22Z INFO CommandSettings] Arg 'url': 'https://github.com/FeedMapping'
+[2023-05-15 18:44:22Z INFO CommandSettings] Remove url from Arg dictionary.
+[2023-05-15 18:44:22Z INFO CommandSettings] Arg 'token': '***'
+[2023-05-15 18:44:22Z INFO CommandSettings] Remove token from Arg dictionary.
+[2023-05-15 18:44:24Z INFO ConfigurationManager] Http response code: OK from 'POST https://api.github.com/actions/runner-registration' (E774:461B:1E7DC8F:3E4A2E3:64627D87)
+[2023-05-15 18:44:24Z INFO ConfigurationManager] cred retrieved via GitHub auth
+[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection
+[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 100 seconds timeout.
+[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData
+[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection
+[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 60 seconds timeout.
+[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData
+[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection
+[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 60 seconds timeout.
+[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData
+[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData
+[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData
+[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData
+[2023-05-15 18:44:25Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:25Z INFO ConfigurationManager] Test Connection complete.
+[2023-05-15 18:44:25Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:25Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:25Z INFO HostContext] Well known config file 'RSACredentials': '/home/runner/.credentials_rsaparams'
+[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Creating new RSA key using 2048-bit key length
+[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Successfully saved RSA key parameters to file /home/runner/.credentials_rsaparams
+[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Which: 'chmod'
+[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Location: '/bin/chmod'
+[2023-05-15 18:44:26Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:26Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Starting process:
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   File name: '/bin/chmod'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Arguments: '600 /home/runner/.credentials_rsaparams'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Working directory: '/home/runner'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Require exit code zero: 'False'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Encoding web name:  ; code page: ''
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Force kill process on cancellation: 'False'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Redirected STDIN: 'False'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Persist current code page: 'False'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   Keep redirected STDIN open: 'False'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper]   High priority process: 'False'
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Updated oom_score_adj to 500 for PID: 75.
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Process started with process id 75, waiting for process exit.
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.
+[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Finished process 75 with exit code 0, and elapsed time 00:00:00.2254015.
+[2023-05-15 18:44:26Z INFO RSAFileKeyManager] Successfully set permissions for RSA key parameters file /home/runner/.credentials_rsaparams
+[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'runnergroup': ''
+[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'unattended': 'True'
+[2023-05-15 18:44:26Z INFO PromptManager] ReadValue
+[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:26Z INFO ConfigurationManager] Found a self-hosted runner group with id 1 and name Default
+[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'disableupdate': 'False'
+[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'ephemeral': 'False'
+[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'name': 'Google-optimized-instance'
+[2023-05-15 18:44:26Z INFO CommandSettings] Remove name from Arg dictionary.
+[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'labels': ''
+[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'unattended': 'True'
+[2023-05-15 18:44:26Z INFO PromptManager] ReadValue
+[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:27Z INFO Terminal] WRITE LINE: A runner exists with the same name
+[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'replace': 'True'
+[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'disableupdate': 'False'
+[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'disableupdate': 'False'
+[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'ephemeral': 'False'
+[2023-05-15 18:44:27Z INFO ConfigurationStore] Saving OAuth credential @ /home/runner/.credentials
+[2023-05-15 18:44:27Z INFO ConfigurationStore] Credentials Saved.
+[2023-05-15 18:44:27Z INFO ConfigurationStore] HasCredentials()
+[2023-05-15 18:44:27Z INFO ConfigurationStore] stored True
+[2023-05-15 18:44:27Z INFO CredentialManager] GetCredentialProvider
+[2023-05-15 18:44:27Z INFO CredentialManager] Creating type OAuth
+[2023-05-15 18:44:27Z INFO CredentialManager] Creating credential type: OAuth
+[2023-05-15 18:44:27Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams
+[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection
+[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 100 seconds timeout.
+[2023-05-15 18:44:27Z INFO GitHubActionsService] Starting operation Location.GetConnectionData
+[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection
+[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 60 seconds timeout.
+[2023-05-15 18:44:27Z INFO GitHubActionsService] Starting operation Location.GetConnectionData
+[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection
+[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 60 seconds timeout.
+[2023-05-15 18:44:28Z INFO GitHubActionsService] Starting operation Location.GetConnectionData
+[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData
+[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData
+[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData
+[2023-05-15 18:44:28Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams
+[2023-05-15 18:44:28Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams
+[2023-05-15 18:44:29Z INFO GitHubActionsService] AAD Correlation ID for this token request: Unknown
+[2023-05-15 18:44:29Z INFO CommandSettings] Arg 'work': '_work'
+[2023-05-15 18:44:29Z INFO CommandSettings] Remove work from Arg dictionary.
+[2023-05-15 18:44:29Z INFO ConfigurationStore] Saving runner settings.
+[2023-05-15 18:44:29Z INFO ConfigurationStore] Settings Saved.
+[2023-05-15 18:44:29Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:29Z INFO Terminal] WRITE LINE: 
+[2023-05-15 18:44:29Z INFO SystemDControlManager] Service name 'actions.runner.FeedMapping.Google-optimized-instance.service' display name 'GitHub Actions Runner (FeedMapping.Google-optimized-instance)' will be used for service configuration.
+[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin'
+[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Root': '/home/runner'
+[2023-05-15 18:44:29Z INFO UnixUtil] Which: 'chmod'
+[2023-05-15 18:44:29Z INFO UnixUtil] Location: '/bin/chmod'
+[2023-05-15 18:44:29Z INFO UnixUtil] Running /bin/chmod 755 "/home/runner/svc.sh"
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Starting process:
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   File name: '/bin/chmod'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Arguments: '755 "/home/runner/svc.sh"'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Working directory: '/home/runner'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Require exit code zero: 'True'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Encoding web name:  ; code page: ''
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Force kill process on cancellation: 'False'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Redirected STDIN: 'False'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Persist current code page: 'False'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   Keep redirected STDIN open: 'False'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper]   High priority process: 'False'
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Updated oom_score_adj to 500 for PID: 79.
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Process started with process id 79, waiting for process exit.
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished.
+[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Finished process 79 with exit code 0, and elapsed time 00:00:00.0022358.
+[2023-05-15 18:44:29Z INFO Listener] Runner execution has finished with return code 0
+

            System File

            There is a powerful command in Linux that helps you search for files and folders called find. In this article, we will discuss the find command with some examples.

            $ find / -type f -name "Dockerfile*"
+
+/mnt/disks/Linux/opt/src/github.com/google/inverting-proxy/agent/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/inverting-proxy-master/agent/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/android/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf1/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf2/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/deploycmle/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/bqtocsv/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/hypertrain/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/deployapp/Dockerfile
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/traintuned/Dockerfile
+
+/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/android/Dockerfile
+/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile
+/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf1/Dockerfile
+/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2/Dockerfile
+/mnt/disks/Linux/usr/share/man/man5/Dockerfile.5.gz
+
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.install_app
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.virtualenv.template
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.requirements_txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.preamble
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/ruby/templates/Dockerfile.template
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/php/templates/Dockerfile.template
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/php/templates/Dockerfile.entrypoint.template
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/go/data/Dockerfile
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/nodejs/data/Dockerfile
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/.kokoro/docker/docs/Dockerfile
+/mnt/disks/Linux/usr/local/go/src/crypto/elliptic/internal/fiat/Dockerfile
+
+/mnt/stateful_partition/var/lib/docker/overlay2/l5js8cyp55dvi6cah1i3gzu4k/diff/Dockerfile
+/mnt/stateful_partition/var/lib/docker/overlay2/6af1c7208063f51f2dc03dbc263eae3f4e148d6bcfd1608bfa4231ca764c5658/diff/home/runner/_work/Partition/Partition/.github/actions/intro/Dockerfile
+

            Now let's say we want to find files with a particular extension like .txt. We'll modify the command like this:

            /mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/python/xds/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/src/models/official/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/src/models/official/projects/unified_detector/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/src/models/official/projects/movinet/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/src/models/research/deep_speech/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/tf2_course/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/serving/application/requirements.txt
+/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/labs/serving/application/requirements.txt
+
+/mnt/disks/Linux/usr/share/models/official/requirements.txt
+/mnt/disks/Linux/usr/share/models/official/projects/unified_detector/requirements.txt
+/mnt/disks/Linux/usr/share/models/official/projects/movinet/requirements.txt
+/mnt/disks/Linux/usr/share/models/research/deep_speech/requirements.txt
+
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/java/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/gslib/vendored/boto/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/gslib/vendored/oauth2client/docs/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/httplib2/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/requests/docs/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/pyasn1/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/pyasn1-modules/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/charset_normalizer/docs/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/gcs-oauth2-boto-plugin/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/urllib3/docs/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/.kokoro/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/testing/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/samples/cloud-client/snippets/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/system_tests/system_tests_sync/app_engine_test_app/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/mock/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/gslib/vendored/boto/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/gslib/vendored/oauth2client/docs/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/pyasn1/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/pyasn1-modules/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/gcs-oauth2-boto-plugin/requirements.txt
+/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/mock/requirements.txt
+
+/mnt/disks/Linux/usr/samples/python/network_api_pytorch_mnist/requirements.txt
+/mnt/disks/Linux/usr/samples/python/requirements.txt
+/mnt/disks/Linux/usr/samples/python/engine_refit_onnx_bidaf/requirements.txt
+/mnt/disks/Linux/usr/samples/python/introductory_parser_samples/requirements.txt
+/mnt/disks/Linux/usr/samples/python/end_to_end_tensorflow_mnist/requirements.txt
+/mnt/disks/Linux/usr/samples/python/int8_caffe_mnist/requirements.txt
+/mnt/disks/Linux/usr/samples/python/engine_refit_mnist/requirements.txt
+/mnt/disks/Linux/usr/samples/python/uff_ssd/requirements.txt
+/mnt/disks/Linux/usr/samples/python/uff_custom_plugin/requirements.txt
+/mnt/disks/Linux/usr/samples/python/yolov3_onnx/requirements.txt
+/mnt/disks/Linux/usr/samples/python/onnx_packnet/requirements.txt
+/mnt/disks/Linux/usr/samples/sampleUffMaskRCNN/converted/requirements.txt
+/mnt/disks/Linux/usr/samples/sampleSSD/requirements.txt
+
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/network_api_pytorch_mnist/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/engine_refit_onnx_bidaf/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/introductory_parser_samples/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/end_to_end_tensorflow_mnist/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/int8_caffe_mnist/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/engine_refit_mnist/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/uff_ssd/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/uff_custom_plugin/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/yolov3_onnx/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/onnx_packnet/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/sampleUffMaskRCNN/converted/requirements.txt
+/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/sampleSSD/requirements.txt
+

            The find command lets you efficiently search for files, folders, and character and block devices. Below is the basic syntax of the find command:

            $ find / -type d -name "tensorflow*"
+
+/mnt/disks/Linux/opt/deeplearning/binaries/tensorflow
+/mnt/disks/Linux/opt/deeplearning/src/models/tensorflow_models
+/mnt/disks/Linux/usr/share/models/tensorflow_models
+
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_cloud-0.1.16.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_probability
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem-0.29.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/google/cloud/aiplatform/training_utils/cloud_profiler/plugins/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_datasets
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_estimator
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorboard_plugin_wit/_vendor/tensorflow_serving
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_cloud
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/xla_aot_runtime_src/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/compiler/mlir/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/include/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/include/tensorflow/compiler/mlir/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io-0.29.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_probability-0.19.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/ray/train/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/witwidget/_vendor/tensorflow_serving
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_serving_api-2.11.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_hub-0.13.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_estimator-2.11.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_transform-1.12.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/pyarrow/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/pyarrow/include/arrow/adapters/tensorflow
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow-2.11.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_metadata
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_serving
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_hub
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_transform
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_metadata-1.12.0.dist-info
+/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_datasets-4.8.2.dist-info
+
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_cloud-0.1.16.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_probability
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem-0.29.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/google/cloud/aiplatform/training_utils/cloud_profiler/plugins/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_datasets
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_estimator
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorboard_plugin_wit/_vendor/tensorflow_serving
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_cloud
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/xla_aot_runtime_src/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/compiler/mlir/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/include/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/include/tensorflow/compiler/mlir/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io-0.29.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_probability-0.19.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/ray/train/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/witwidget/_vendor/tensorflow_serving
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_serving_api-2.11.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_hub-0.13.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_estimator-2.11.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_transform-1.12.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/pyarrow/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/pyarrow/include/arrow/adapters/tensorflow
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow-2.11.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_metadata
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_serving
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_hub
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_transform
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_metadata-1.12.0.dist-info
+/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_datasets-4.8.2.dist-info
+

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist04.md b/identition/span4/gist04.md new file mode 100644 index 00000000000..798e2d4fe6c --- /dev/null +++ b/identition/span4/gist04.md @@ -0,0 +1,591 @@ +## Directory Structure + +This page walks through the steps required to [train an object detection model](https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/tf2_training_and_evaluation.md) with Recommended Directory Structure for Training and Evaluation for [tf2_ai_platform](https://github.com/tensorflow/models/blob/master/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile) + +``` +$ cat /mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile + +FROM tensorflow/tensorflow:latest-gpu + +ARG DEBIAN_FRONTEND=noninteractive + +# Install apt dependencies +RUN apt-get update && apt-get install -y \ + git \ + gpg-agent \ + python3-cairocffi \ + protobuf-compiler \ + python3-pil \ + python3-lxml \ + python3-tk \ + python3-opencv \ + wget + +# Installs google cloud sdk, this is mostly for using gsutil to export model. +RUN wget -nv \ + https://dl.google.com/dl/cloudsdk/release/google-cloud-sdk.tar.gz && \ + mkdir /root/tools && \ + tar xvzf google-cloud-sdk.tar.gz -C /root/tools && \ + rm google-cloud-sdk.tar.gz && \ + /root/tools/google-cloud-sdk/install.sh --usage-reporting=false \ + --path-update=false --bash-completion=false \ + --disable-installation-options && \ + rm -rf /root/.config/* && \ + ln -s /root/.config /config && \ + rm -rf /root/tools/google-cloud-sdk/.install/.backup + +# Path configuration +ENV PATH $PATH:/root/tools/google-cloud-sdk/bin +# Make sure gsutil will use the default service account +RUN echo '[GoogleCompute]\nservice_account = default' > /etc/boto.cfg + +WORKDIR /home/tensorflow + +## Copy this code (make sure you are under the ../models/research directory) +COPY . /home/tensorflow/models + +# Compile protobuf configs +RUN (cd /home/tensorflow/models/ && protoc object_detection/protos/*.proto --python_out=.) +WORKDIR /home/tensorflow/models/ + +RUN cp object_detection/packages/tf2/setup.py ./ +ENV PATH="/home/tensorflow/.local/bin:${PATH}" + +RUN python -m pip install -U pip +RUN python -m pip install . + +ENTRYPOINT ["python", "object_detection/model_main_tf2.py"] +``` + +GitHub allows developers to run GitHub Actions workflows on your own runners. This Docker image allows you to create your own runners on Docker. The GitHub runner (the binary) will update itself when receiving a job, if a new release is available. + +``` +ARG FROM=debian:buster-slim +FROM ${FROM} + +ARG DEBIAN_FRONTEND=noninteractive +ARG GIT_VERSION="2.26.2" +ARG GH_RUNNER_VERSION +ARG DOCKER_COMPOSE_VERSION="1.27.4" + +ENV RUNNER_NAME="" +ENV RUNNER_WORK_DIRECTORY="_work" +ENV RUNNER_TOKEN="" +ENV RUNNER_REPOSITORY_URL="" +ENV RUNNER_LABELS="" +ENV RUNNER_ALLOW_RUNASROOT=true +ENV GITHUB_ACCESS_TOKEN="" +ENV AGENT_TOOLSDIRECTORY=/opt/hostedtoolcache + +# Labels. +LABEL maintainer="me@tcardonne.fr" \ + org.label-schema.schema-version="1.0" \ + org.label-schema.build-date=$BUILD_DATE \ + org.label-schema.vcs-ref=$VCS_REF \ + org.label-schema.name="tcardonne/github-runner" \ + org.label-schema.description="Dockerized GitHub Actions runner." \ + org.label-schema.url="https://github.com/tcardonne/docker-github-runner" \ + org.label-schema.vcs-url="https://github.com/tcardonne/docker-github-runner" \ + org.label-schema.vendor="Thomas Cardonne" \ + org.label-schema.docker.cmd="docker run -it tcardonne/github-runner:latest" + +RUN DEBIAN_FRONTEND=noninteractive apt-get update && \ + apt-get install -y \ + curl \ + unzip \ + apt-transport-https \ + ca-certificates \ + software-properties-common \ + sudo \ + supervisor \ + jq \ + iputils-ping \ + build-essential \ + zlib1g-dev \ + gettext \ + liblttng-ust0 \ + libcurl4-openssl-dev \ + openssh-client && \ + rm -rf /var/lib/apt/lists/* && \ + apt-get clean + +COPY supervisord.conf /etc/supervisor/conf.d/supervisord.conf +RUN chmod 644 /etc/supervisor/conf.d/supervisord.conf + +# Install Docker CLI +RUN curl -fsSL https://get.docker.com -o- | sh && \ + rm -rf /var/lib/apt/lists/* && \ + apt-get clean + +# Install Docker-Compose +RUN curl -L -o /usr/local/bin/docker-compose \ + "https://github.com/docker/compose/releases/download/${DOCKER_COMPOSE_VERSION}/docker-compose-$(uname -s)-$(uname -m)" && \ + chmod +x /usr/local/bin/docker-compose + +RUN cd /tmp && \ + curl -sL -o git.tgz \ + https://www.kernel.org/pub/software/scm/git/git-${GIT_VERSION}.tar.gz && \ + tar zxf git.tgz && \ + cd git-${GIT_VERSION} && \ + ./configure --prefix=/usr && \ + make && \ + make install && \ + rm -rf /tmp/* + +RUN mkdir -p /home/runner ${AGENT_TOOLSDIRECTORY} + +WORKDIR /home/runner + +RUN GH_RUNNER_VERSION=${GH_RUNNER_VERSION:-$(curl --silent "https://api.github.com/repos/actions/runner/releases/latest" | grep tag_name | sed -E 's/.*"v([^"]+)".*/\1/')} \ + && curl -L -O https://github.com/actions/runner/releases/download/v${GH_RUNNER_VERSION}/actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \ + && tar -zxf actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \ + && rm -f actions-runner-linux-x64-${GH_RUNNER_VERSION}.tar.gz \ + && ./bin/installdependencies.sh \ + && chown -R root: /home/runner \ + && rm -rf /var/lib/apt/lists/* \ + && apt-get clean + +COPY entrypoint.sh /entrypoint.sh +RUN chmod +x /entrypoint.sh +ENTRYPOINT ["/entrypoint.sh"] +CMD ["/usr/bin/supervisord", "-c", "/etc/supervisor/conf.d/supervisord.conf"] +``` + +In order to allow the runner to exit and restart by itself, the binary is started by a [supervisord process](https://github.com/tcardonne/docker-github-runner/blob/master/docker/Dockerfile) and [entrypoint](https://github.com/tcardonne/docker-github-runner/blob/master/docker/entrypoint.sh). + +``` +$ cat /etc/supervisord.conf + +[supervisord] +user=root +nodaemon=true +logfile=/dev/fd/1 +logfile_maxbytes=0 +loglevel=error + +[program:runner] +directory=/home/runner +command=/home/runner/bin/runsvc.sh +stdout_logfile=/dev/fd/1 +stdout_logfile_maxbytes=0 +redirect_stderr=true +``` + +The self-hosted runner application creates a detailed log file for each job that it processes. These files are stored in the _diag directory where you installed the runner application, and the filename begins with Worker_. + +``` +$ cat /home/runner/_diag/Runner_20230515-184422-utc.log + +[2023-05-15 18:44:22Z INFO HostContext] No proxy settings were found based on environmental variables (http_proxy/https_proxy/HTTP_PROXY/HTTPS_PROXY) +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Credentials': '/home/runner/.credentials' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Runner': '/home/runner/.runner' +[2023-05-15 18:44:22Z INFO Listener] Runner is built for Linux (X64) - linux-x64. +[2023-05-15 18:44:22Z INFO Listener] RuntimeInformation: Linux 5.15.109+ #1 SMP Sat May 6 10:58:50 UTC 2023. +[2023-05-15 18:44:22Z INFO Listener] Version: 2.303.0 +[2023-05-15 18:44:22Z INFO Listener] Commit: e676c7871817c1b484299cd93fabdf4b95e70741 +[2023-05-15 18:44:22Z INFO Listener] Culture: +[2023-05-15 18:44:22Z INFO Listener] UI Culture: +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO Listener] Validating directory permissions for: '/home/runner' +[2023-05-15 18:44:22Z INFO CommandLineParser] Parse +[2023-05-15 18:44:22Z INFO CommandLineParser] Parsing 11 args +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: False +[2023-05-15 18:44:22Z INFO CommandLineParser] Adding Command: configure +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] arg: url +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'url': 'https://github.com/FeedMapping' +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] arg: token +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'token': '***' +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] arg: name +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'name': 'Google-optimized-instance' +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] arg: work +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] Adding option 'work': '_work' +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] arg: replace +[2023-05-15 18:44:22Z INFO CommandLineParser] parsing argument +[2023-05-15 18:44:22Z INFO CommandLineParser] HasArgs: True +[2023-05-15 18:44:22Z INFO CommandLineParser] arg: unattended +[2023-05-15 18:44:22Z INFO CommandLineParser] Adding flag: replace +[2023-05-15 18:44:22Z INFO Listener] Arguments parsed +[2023-05-15 18:44:22Z INFO Runner] ExecuteCommand +[2023-05-15 18:44:22Z INFO ConfigurationStore] currentAssemblyLocation: /home/runner/bin/Runner.Listener.dll +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO ConfigurationStore] binPath: /home/runner/bin +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO ConfigurationStore] RootFolder: /home/runner +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Runner': '/home/runner/.runner' +[2023-05-15 18:44:22Z INFO ConfigurationStore] ConfigFilePath: /home/runner/.runner +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Credentials': '/home/runner/.credentials' +[2023-05-15 18:44:22Z INFO ConfigurationStore] CredFilePath: /home/runner/.credentials +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'MigratedCredentials': '/home/runner/.credentials_migrated' +[2023-05-15 18:44:22Z INFO ConfigurationStore] MigratedCredFilePath: /home/runner/.credentials_migrated +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:22Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:22Z INFO HostContext] Well known config file 'Service': '/home/runner/.service' +[2023-05-15 18:44:22Z INFO ConfigurationStore] ServiceConfigFilePath: /home/runner/.service +[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'help': 'False' +[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'version': 'False' +[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'commit': 'False' +[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'check': 'False' +[2023-05-15 18:44:22Z INFO CommandSettings] Command 'configure': 'True' +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: -------------------------------------------------------------------------------- +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | ____ _ _ _ _ _ _ _ _ | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | / ___(_) |_| | | |_ _| |__ / \ ___| |_(_) ___ _ __ ___ | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | | | _| | __| |_| | | | | '_ \ / _ \ / __| __| |/ _ \| '_ \/ __| | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | | |_| | | |_| _ | |_| | |_) | / ___ \ (__| |_| | (_) | | | \__ \ | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | \____|_|\__|_| |_|\__,_|_.__/ /_/ \_\___|\__|_|\___/|_| |_|___/ | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | | +[2023-05-15 18:44:22Z INFO Terminal] WRITE: | +[2023-05-15 18:44:22Z INFO Terminal] WRITE: Self-hosted runner registration +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: | | +[2023-05-15 18:44:22Z INFO Terminal] WRITE LINE: -------------------------------------------------------------------------------- +[2023-05-15 18:44:22Z INFO ConfigurationManager] ConfigureAsync +[2023-05-15 18:44:22Z INFO CommandSettings] Flag 'generateServiceConfig': 'False' +[2023-05-15 18:44:22Z INFO ConfigurationStore] IsConfigured() +[2023-05-15 18:44:22Z INFO ConfigurationStore] IsConfigured: False +[2023-05-15 18:44:22Z INFO ConfigurationManager] Is configured: False +[2023-05-15 18:44:22Z INFO CommandSettings] Arg 'url': 'https://github.com/FeedMapping' +[2023-05-15 18:44:22Z INFO CommandSettings] Remove url from Arg dictionary. +[2023-05-15 18:44:22Z INFO CommandSettings] Arg 'token': '***' +[2023-05-15 18:44:22Z INFO CommandSettings] Remove token from Arg dictionary. +[2023-05-15 18:44:24Z INFO ConfigurationManager] Http response code: OK from 'POST https://api.github.com/actions/runner-registration' (E774:461B:1E7DC8F:3E4A2E3:64627D87) +[2023-05-15 18:44:24Z INFO ConfigurationManager] cred retrieved via GitHub auth +[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection +[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 100 seconds timeout. +[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData +[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection +[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 60 seconds timeout. +[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData +[2023-05-15 18:44:24Z INFO RunnerServer] EstablishVssConnection +[2023-05-15 18:44:24Z INFO RunnerServer] Establish connection with 60 seconds timeout. +[2023-05-15 18:44:24Z INFO GitHubActionsService] Starting operation Location.GetConnectionData +[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData +[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData +[2023-05-15 18:44:24Z INFO GitHubActionsService] Finished operation Location.GetConnectionData +[2023-05-15 18:44:25Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:25Z INFO ConfigurationManager] Test Connection complete. +[2023-05-15 18:44:25Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:25Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:25Z INFO HostContext] Well known config file 'RSACredentials': '/home/runner/.credentials_rsaparams' +[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Creating new RSA key using 2048-bit key length +[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Successfully saved RSA key parameters to file /home/runner/.credentials_rsaparams +[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Which: 'chmod' +[2023-05-15 18:44:25Z INFO RSAFileKeyManager] Location: '/bin/chmod' +[2023-05-15 18:44:26Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:26Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Starting process: +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] File name: '/bin/chmod' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Arguments: '600 /home/runner/.credentials_rsaparams' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Working directory: '/home/runner' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Require exit code zero: 'False' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Encoding web name: ; code page: '' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Force kill process on cancellation: 'False' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Redirected STDIN: 'False' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Persist current code page: 'False' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Keep redirected STDIN open: 'False' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] High priority process: 'False' +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Updated oom_score_adj to 500 for PID: 75. +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Process started with process id 75, waiting for process exit. +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished. +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished. +[2023-05-15 18:44:26Z INFO ProcessInvokerWrapper] Finished process 75 with exit code 0, and elapsed time 00:00:00.2254015. +[2023-05-15 18:44:26Z INFO RSAFileKeyManager] Successfully set permissions for RSA key parameters file /home/runner/.credentials_rsaparams +[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'runnergroup': '' +[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'unattended': 'True' +[2023-05-15 18:44:26Z INFO PromptManager] ReadValue +[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:26Z INFO ConfigurationManager] Found a self-hosted runner group with id 1 and name Default +[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'disableupdate': 'False' +[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'ephemeral': 'False' +[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'name': 'Google-optimized-instance' +[2023-05-15 18:44:26Z INFO CommandSettings] Remove name from Arg dictionary. +[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:26Z INFO CommandSettings] Arg 'labels': '' +[2023-05-15 18:44:26Z INFO CommandSettings] Flag 'unattended': 'True' +[2023-05-15 18:44:26Z INFO PromptManager] ReadValue +[2023-05-15 18:44:26Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:27Z INFO Terminal] WRITE LINE: A runner exists with the same name +[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'replace': 'True' +[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'disableupdate': 'False' +[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'disableupdate': 'False' +[2023-05-15 18:44:27Z INFO CommandSettings] Flag 'ephemeral': 'False' +[2023-05-15 18:44:27Z INFO ConfigurationStore] Saving OAuth credential @ /home/runner/.credentials +[2023-05-15 18:44:27Z INFO ConfigurationStore] Credentials Saved. +[2023-05-15 18:44:27Z INFO ConfigurationStore] HasCredentials() +[2023-05-15 18:44:27Z INFO ConfigurationStore] stored True +[2023-05-15 18:44:27Z INFO CredentialManager] GetCredentialProvider +[2023-05-15 18:44:27Z INFO CredentialManager] Creating type OAuth +[2023-05-15 18:44:27Z INFO CredentialManager] Creating credential type: OAuth +[2023-05-15 18:44:27Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams +[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection +[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 100 seconds timeout. +[2023-05-15 18:44:27Z INFO GitHubActionsService] Starting operation Location.GetConnectionData +[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection +[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 60 seconds timeout. +[2023-05-15 18:44:27Z INFO GitHubActionsService] Starting operation Location.GetConnectionData +[2023-05-15 18:44:27Z INFO RunnerServer] EstablishVssConnection +[2023-05-15 18:44:27Z INFO RunnerServer] Establish connection with 60 seconds timeout. +[2023-05-15 18:44:28Z INFO GitHubActionsService] Starting operation Location.GetConnectionData +[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData +[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData +[2023-05-15 18:44:28Z INFO GitHubActionsService] Finished operation Location.GetConnectionData +[2023-05-15 18:44:28Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams +[2023-05-15 18:44:28Z INFO RSAFileKeyManager] Loading RSA key parameters from file /home/runner/.credentials_rsaparams +[2023-05-15 18:44:29Z INFO GitHubActionsService] AAD Correlation ID for this token request: Unknown +[2023-05-15 18:44:29Z INFO CommandSettings] Arg 'work': '_work' +[2023-05-15 18:44:29Z INFO CommandSettings] Remove work from Arg dictionary. +[2023-05-15 18:44:29Z INFO ConfigurationStore] Saving runner settings. +[2023-05-15 18:44:29Z INFO ConfigurationStore] Settings Saved. +[2023-05-15 18:44:29Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:29Z INFO Terminal] WRITE LINE: +[2023-05-15 18:44:29Z INFO SystemDControlManager] Service name 'actions.runner.FeedMapping.Google-optimized-instance.service' display name 'GitHub Actions Runner (FeedMapping.Google-optimized-instance)' will be used for service configuration. +[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Bin': '/home/runner/bin' +[2023-05-15 18:44:29Z INFO HostContext] Well known directory 'Root': '/home/runner' +[2023-05-15 18:44:29Z INFO UnixUtil] Which: 'chmod' +[2023-05-15 18:44:29Z INFO UnixUtil] Location: '/bin/chmod' +[2023-05-15 18:44:29Z INFO UnixUtil] Running /bin/chmod 755 "/home/runner/svc.sh" +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Starting process: +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] File name: '/bin/chmod' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Arguments: '755 "/home/runner/svc.sh"' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Working directory: '/home/runner' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Require exit code zero: 'True' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Encoding web name: ; code page: '' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Force kill process on cancellation: 'False' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Redirected STDIN: 'False' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Persist current code page: 'False' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Keep redirected STDIN open: 'False' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] High priority process: 'False' +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Updated oom_score_adj to 500 for PID: 79. +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Process started with process id 79, waiting for process exit. +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished. +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] STDOUT/STDERR stream read finished. +[2023-05-15 18:44:29Z INFO ProcessInvokerWrapper] Finished process 79 with exit code 0, and elapsed time 00:00:00.0022358. +[2023-05-15 18:44:29Z INFO Listener] Runner execution has finished with return code 0 +``` + +### System File + +There is a powerful command in Linux that helps you search for files and folders called find. In this article, we will discuss the find command with some examples. + +``` +$ find / -type f -name "Dockerfile*" + +/mnt/disks/Linux/opt/src/github.com/google/inverting-proxy/agent/Dockerfile +/mnt/disks/Linux/opt/deeplearning/inverting-proxy-master/agent/Dockerfile +/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/android/Dockerfile +/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile +/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf1/Dockerfile +/mnt/disks/Linux/opt/deeplearning/src/models/research/object_detection/dockerfiles/tf2/Dockerfile +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/deploycmle/Dockerfile +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/bqtocsv/Dockerfile +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/hypertrain/Dockerfile +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/deployapp/Dockerfile +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/pipelines/containers/traintuned/Dockerfile + +/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/android/Dockerfile +/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2_ai_platform/Dockerfile +/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf1/Dockerfile +/mnt/disks/Linux/usr/share/models/research/object_detection/dockerfiles/tf2/Dockerfile +/mnt/disks/Linux/usr/share/man/man5/Dockerfile.5.gz + +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.install_app +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.virtualenv.template +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.requirements_txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/python/data/Dockerfile.preamble +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/ruby/templates/Dockerfile.template +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/php/templates/Dockerfile.template +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/php/templates/Dockerfile.entrypoint.template +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/go/data/Dockerfile +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/nodejs/data/Dockerfile +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/.kokoro/docker/docs/Dockerfile +/mnt/disks/Linux/usr/local/go/src/crypto/elliptic/internal/fiat/Dockerfile + +/mnt/stateful_partition/var/lib/docker/overlay2/l5js8cyp55dvi6cah1i3gzu4k/diff/Dockerfile +/mnt/stateful_partition/var/lib/docker/overlay2/6af1c7208063f51f2dc03dbc263eae3f4e148d6bcfd1608bfa4231ca764c5658/diff/home/runner/_work/Partition/Partition/.github/actions/intro/Dockerfile +``` + +Now let's say we want to find files with a particular extension like .txt. We'll modify the command like this: + +``` +/mnt/disks/Linux/opt/conda/pkgs/grpc-cpp-1.48.1-hc2bec63_1/info/test/examples/python/xds/requirements.txt +/mnt/disks/Linux/opt/deeplearning/src/models/official/requirements.txt +/mnt/disks/Linux/opt/deeplearning/src/models/official/projects/unified_detector/requirements.txt +/mnt/disks/Linux/opt/deeplearning/src/models/official/projects/movinet/requirements.txt +/mnt/disks/Linux/opt/deeplearning/src/models/research/deep_speech/requirements.txt +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/tf2_course/requirements.txt +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/serving/application/requirements.txt +/mnt/disks/Linux/opt/deeplearning/workspace/tutorials/machine_learning_deepdive/06_structured/labs/serving/application/requirements.txt + +/mnt/disks/Linux/usr/share/models/official/requirements.txt +/mnt/disks/Linux/usr/share/models/official/projects/unified_detector/requirements.txt +/mnt/disks/Linux/usr/share/models/official/projects/movinet/requirements.txt +/mnt/disks/Linux/usr/share/models/research/deep_speech/requirements.txt + +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/ext-runtime/java/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/gslib/vendored/boto/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/gslib/vendored/oauth2client/docs/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/httplib2/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/requests/docs/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/pyasn1/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/pyasn1-modules/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/charset_normalizer/docs/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/gcs-oauth2-boto-plugin/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/urllib3/docs/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/.kokoro/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/testing/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/samples/cloud-client/snippets/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/google-auth-library-python/system_tests/system_tests_sync/app_engine_test_app/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil/third_party/mock/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/gslib/vendored/boto/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/gslib/vendored/oauth2client/docs/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/pyasn1/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/pyasn1-modules/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/gcs-oauth2-boto-plugin/requirements.txt +/mnt/disks/Linux/usr/lib/google-cloud-sdk/platform/gsutil_py2/third_party/mock/requirements.txt + +/mnt/disks/Linux/usr/samples/python/network_api_pytorch_mnist/requirements.txt +/mnt/disks/Linux/usr/samples/python/requirements.txt +/mnt/disks/Linux/usr/samples/python/engine_refit_onnx_bidaf/requirements.txt +/mnt/disks/Linux/usr/samples/python/introductory_parser_samples/requirements.txt +/mnt/disks/Linux/usr/samples/python/end_to_end_tensorflow_mnist/requirements.txt +/mnt/disks/Linux/usr/samples/python/int8_caffe_mnist/requirements.txt +/mnt/disks/Linux/usr/samples/python/engine_refit_mnist/requirements.txt +/mnt/disks/Linux/usr/samples/python/uff_ssd/requirements.txt +/mnt/disks/Linux/usr/samples/python/uff_custom_plugin/requirements.txt +/mnt/disks/Linux/usr/samples/python/yolov3_onnx/requirements.txt +/mnt/disks/Linux/usr/samples/python/onnx_packnet/requirements.txt +/mnt/disks/Linux/usr/samples/sampleUffMaskRCNN/converted/requirements.txt +/mnt/disks/Linux/usr/samples/sampleSSD/requirements.txt + +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/network_api_pytorch_mnist/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/engine_refit_onnx_bidaf/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/introductory_parser_samples/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/end_to_end_tensorflow_mnist/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/int8_caffe_mnist/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/engine_refit_mnist/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/uff_ssd/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/uff_custom_plugin/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/yolov3_onnx/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/python/onnx_packnet/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/sampleUffMaskRCNN/converted/requirements.txt +/mnt/disks/Linux/usr/targets/x86_64-linux-gnu/samples/sampleSSD/requirements.txt +``` + +The find command lets you efficiently search for files, folders, and character and block devices. Below is the basic syntax of the find command: + +``` +$ find / -type d -name "tensorflow*" + +/mnt/disks/Linux/opt/deeplearning/binaries/tensorflow +/mnt/disks/Linux/opt/deeplearning/src/models/tensorflow_models +/mnt/disks/Linux/usr/share/models/tensorflow_models + +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_cloud-0.1.16.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_probability +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem-0.29.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/google/cloud/aiplatform/training_utils/cloud_profiler/plugins/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_datasets +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_estimator +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorboard_plugin_wit/_vendor/tensorflow_serving +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_cloud +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/xla_aot_runtime_src/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/compiler/mlir/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/include/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow/include/tensorflow/compiler/mlir/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_io-0.29.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_probability-0.19.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/ray/train/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/witwidget/_vendor/tensorflow_serving +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_serving_api-2.11.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_hub-0.13.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_estimator-2.11.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_transform-1.12.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/pyarrow/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/pyarrow/include/arrow/adapters/tensorflow +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow-2.11.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_metadata +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_serving +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_hub +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_transform +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_metadata-1.12.0.dist-info +/mnt/disks/Linux/opt/conda/lib/python3.7/site-packages/tensorflow_datasets-4.8.2.dist-info + +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_cloud-0.1.16.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorboard/compat/tensorflow_stub +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_probability +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem-0.29.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/google/cloud/aiplatform/training_utils/cloud_profiler/plugins/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io_gcs_filesystem +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_datasets +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_estimator +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorboard_plugin_wit/_vendor/tensorflow_serving +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_cloud +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/xla_aot_runtime_src/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/compiler/mlir/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/include/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow/include/tensorflow/compiler/mlir/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_io-0.29.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_probability-0.19.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/ray/train/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/witwidget/_vendor/tensorflow_serving +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_serving_api-2.11.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_hub-0.13.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_estimator-2.11.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_transform-1.12.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/pyarrow/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/pyarrow/include/arrow/adapters/tensorflow +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow-2.11.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_metadata +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_serving +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_hub +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_transform +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_metadata-1.12.0.dist-info +/mnt/disks/Linux/opt/conda/pkgs/dlenv-tf-2-11-gpu-1.0.20230429-py37hfd508a8_0/lib/python3.7/site-packages/tensorflow_datasets-4.8.2.dist-info +``` + +![default](https://user-images.githubusercontent.com/8466209/199132181-38a98bf9-9d72-4740-b96c-c57da26a6135.png) + +[![default](https://user-images.githubusercontent.com/8466209/198812060-bcf0c3e5-1918-4245-b2fa-1c43c2602a90.png)](https://www.chetabahana.com/) + +[![default](https://user-images.githubusercontent.com/8466209/227684922-9b3190e2-879c-42e5-b404-fb975b9b8752.png)](https://cloud.google.com/sdk/gcloud/reference/compute/instances/create#--metadata) diff --git a/identition/span4/gist05.html b/identition/span4/gist05.html new file mode 100644 index 00000000000..e2860911e97 --- /dev/null +++ b/identition/span4/gist05.html @@ -0,0 +1,16 @@ + The Classes · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Classes

            Gematria is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. Single word can yield several values depending on which cipher is used. This cipher is sometimes erroneously labelled as "Jewish" or "Hebrew" by popular numerology calculators, such as Gematrix and Gematrinator.

            A mathematical formula for finding a letter's corresponding number in Mispar Gadol

            ------+------+-----+-----+-----+--------           7x + 6x = 13x
+      |      |     |  7  |  11 |  20               |     |
+      |      |  4  +-----+-----+                   |     |
+      |  3   |     |  8  |  12 |  26  -----        |     |
+      |      +-----+-----+-----+           |       |     |
+      |      |     |  9  |  13 |  27       2x -----      |
+  2   +------|  5  +-----+-----+           |             |
+      |      |     |  10 |  14 |  28 -----               |
+      |      |-----+-----+-----+                         |
+      |  4   |     |  11 |15,18|  29,30,31,32 ←---4x-----
+      |      |  6  +-----+-----+
+      |      |     |  12 |  19 |  36                         ←--- 35,34,33 are missing
+------+------+-----+-----+-----+-------
+      |      |     |  13 |  20 | {38}
+      |      |  7  +-----+-----+
+

            default

            default

            default

            default

            tensorflow

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist05.md b/identition/span4/gist05.md new file mode 100644 index 00000000000..d3092cb6f7c --- /dev/null +++ b/identition/span4/gist05.md @@ -0,0 +1,40 @@ +## [The Classes](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#objects-vs-classes) + +Gematria is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. Single word can yield several values depending on which cipher is used. This cipher is sometimes erroneously labelled as "Jewish" or "Hebrew" by popular numerology calculators, such as Gematrix and Gematrinator. + +[![A mathematical formula for finding a letter's corresponding number in Mispar Gadol](https://user-images.githubusercontent.com/8466209/226222755-1aa42385-145d-4fc5-81a3-54ebefa4e272.png)](https://en.wikipedia.org/wiki/Gematria#Standard_encoding) + +![](https://user-images.githubusercontent.com/36441664/77167537-ce0ae980-6ae8-11ea-869d-b4164b511755.jpg) + +``` +------+------+-----+-----+-----+-------- 7x + 6x = 13x + | | | 7 | 11 | 20 | | + | | 4 +-----+-----+ | | + | 3 | | 8 | 12 | 26 ----- | | + | +-----+-----+-----+ | | | + | | | 9 | 13 | 27 2x ----- | + 2 +------| 5 +-----+-----+ | | + | | | 10 | 14 | 28 ----- | + | |-----+-----+-----+ | + | 4 | | 11 |15,18| 29,30,31,32 ←---4x----- + | | 6 +-----+-----+ + | | | 12 | 19 | 36 ←--- 35,34,33 are missing +------+------+-----+-----+-----+------- + | | | 13 | 20 | {38} + | | 7 +-----+-----+ +``` + +[![default](https://user-images.githubusercontent.com/8466209/198756338-2bc18ae7-c431-486f-9c30-412ca28c55da.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md) + +[![default](https://user-images.githubusercontent.com/8466209/199130173-c106f4b1-7964-4f0b-ba3f-31119d7eb39f.png)](https://www.eq19.com/) + +[![default](https://user-images.githubusercontent.com/8466209/199134366-a6c1a115-6f4a-466e-a542-076c6d742d4c.png)](https://www.nvidia.com/en-us/data-center/graphics-cards-for-virtualization/) + +[![default](https://user-images.githubusercontent.com/8466209/199134523-93606dfd-1194-4983-80d0-7dda2e8ddace.png)](https://docs.nvidia.com/deeplearning/cudnn/install-guide/index.html#install-windows) + +[![tensorflow](https://user-images.githubusercontent.com/36441664/128624639-b5d8c73f-79af-4433-8b7b-28a35e331d21.png)](https://github.com/chetabahana/tensorflow/wiki#grounds) + +[![default](https://user-images.githubusercontent.com/8466209/199136893-391bd954-44a3-4767-8002-661f33b7391f.png)](https://github.com/NVIDIA/tensorflow) + +[![default](https://user-images.githubusercontent.com/8466209/199136378-f0cef6b2-a422-4f33-a88d-aebe5b38a690.png)](https://github.com/NVIDIA/nvidia-docker) + diff --git a/identition/span4/gist06.html b/identition/span4/gist06.html new file mode 100644 index 00000000000..8ebbeb8413e --- /dev/null +++ b/identition/span4/gist06.html @@ -0,0 +1,63 @@ + License · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            License

            Every organization that has at least one licensed Microsoft 365 user (with an E1, E3, E5, F1, and F3 subscription) or uses Microsoft cloud services such as Azure or Intune also has an Azure Active Directory tenant.

            Microsoft 365 A3 for students use benefit
+Information Barriers
+Microsoft Bookings
+Universal Print Without Seeding
+Project for Office (Plan E3)
+Common Data Service
+Information Protection for Office 365 - Standard
+Education Analytics
+Microsoft Kaizala Pro
+Microsoft Search
+Whiteboard (Plan 2)
+Microsoft Intune Plan 1 for Education
+Microsoft Defender for Cloud Apps Discovery
+To-Do (Plan 2)
+Windows 10/11 Enterprise
+Minecraft Education Edition
+Microsoft Intune Plan 1
+Microsoft Azure Multi-Factor Authentication
+Azure Active Directory Premium P1
+Azure Active Directory Basic for Education
+Microsoft Stream for Office 365 E3
+School Data Sync (Plan 2)
+Azure Rights Management
+Microsoft Teams
+Sway
+Microsoft StaffHub
+Power Apps for Office 365
+Power Automate for Office 365
+Microsoft Forms (Plan 2)
+Microsoft Planner
+Yammer for Academic
+Skype for Business Online (Plan 2)
+Office for the Web for Education
+SharePoint (Plan 2) for Education
+Exchange Online (Plan 2)
+Office 365 Cloud App Security
+The latest desktop version of Office
+

            There are, however, different editions of Azure AD licenses that provide the organization with different capabilities: Azure AD Free/Office 365, Premium P1, and Premium P2.

            default

            Though lower tiers of AAD have certain limitations, such as with the number of apps and directory objects IT teams can manage, Azure AD Premium P2's feature set offers admins the opportunity to thoroughly manage their users and their SSO access.

            Azure AD

            Azure Active Directory (Azure AD) is a cloud-based identity and access management service. Azure AD enables your employees access external resources, such as Microsoft 365, the Azure portal, and thousands of other SaaS applications.

            Azure Active Directory also helps them access internal resources like apps on your corporate intranet, and any cloud apps developed for your own organization (Microsoft).

            Azure Active Directory

            Azure AD Premium P2 licenses are beneficial for organizations that are expected to demonstrate a high level of governance of identities. That implies managing privileged access and automating access reviews and responses to potentially compromised accounts.

            Azure AD Premium P2

            AAD Premium P2 offers the following features:

            All of the features listed for Azure AD Microsoft 365 apps 
+Leverage SSO for an unlimited number of pre-integrated SaaS applications
+Configure self-service application assignment to enable users to self-discover and request access to applications
+On-prem write-back for all password changes
+Advanced usage reporting
+HR-driven provisioning
+Self-service group management and application management 
+Microsoft® Identity Management (MIM) CAL + MIM server for simplified lifecycle user management
+Conditional access based on device state or location and group
+Automate password rollover for group accounts
+Join a Windows® Pro device to Azure AD to enable desktop SSO, and Administrator BitLocker recovery
+Application proxy for on-premises, header-based, and Integrated Windows Authentication
+MDM auto-enrollment, self-service BitLocker recovery, additional local admin tooling to Windows Pro devices via Azure AD Join
+Role-based access control (RBAC)
+Risk-based Identity Protection 
+Privileged identity management
+Self-service entitlement management (My Access)
+Access certifications and reviews
+Entitlements management
+Lifecycle Workflows (preview)
+Privileged Identity Management (PIM), just-in-time access
+Cloud app discovery (Windows Defender for cloud apps)
+Identity Protection reporting: vulnerabilities and risky accounts
+Identity Protection reporting: risk events investigation, SIEM connectivity
+A service-level agreement
+

            Azure AD Premium P2 is most commonly used for providing insight into user activity within Azure infrastructure, Microsoft 365, and web applications.

            Azure Active Directory Premium P1 vs. P2: Features comparison

            Storage

            default default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist06.md b/identition/span4/gist06.md new file mode 100644 index 00000000000..de7046a0034 --- /dev/null +++ b/identition/span4/gist06.md @@ -0,0 +1,102 @@ +### License + +Every organization that has at least one licensed Microsoft 365 user (with an E1, E3, E5, F1, and F3 subscription) or uses Microsoft cloud services such as Azure or Intune also has an Azure Active Directory tenant. +``` +Microsoft 365 A3 for students use benefit +Information Barriers +Microsoft Bookings +Universal Print Without Seeding +Project for Office (Plan E3) +Common Data Service +Information Protection for Office 365 - Standard +Education Analytics +Microsoft Kaizala Pro +Microsoft Search +Whiteboard (Plan 2) +Microsoft Intune Plan 1 for Education +Microsoft Defender for Cloud Apps Discovery +To-Do (Plan 2) +Windows 10/11 Enterprise +Minecraft Education Edition +Microsoft Intune Plan 1 +Microsoft Azure Multi-Factor Authentication +Azure Active Directory Premium P1 +Azure Active Directory Basic for Education +Microsoft Stream for Office 365 E3 +School Data Sync (Plan 2) +Azure Rights Management +Microsoft Teams +Sway +Microsoft StaffHub +Power Apps for Office 365 +Power Automate for Office 365 +Microsoft Forms (Plan 2) +Microsoft Planner +Yammer for Academic +Skype for Business Online (Plan 2) +Office for the Web for Education +SharePoint (Plan 2) for Education +Exchange Online (Plan 2) +Office 365 Cloud App Security +The latest desktop version of Office +``` + +There are, however, different editions of Azure AD licenses that provide the organization with different capabilities: Azure AD Free/Office 365, Premium P1, and Premium P2. + +![default](https://user-images.githubusercontent.com/8466209/229310273-8b633a45-59f6-4366-ba19-e22522beb94b.png) + +Though lower tiers of AAD have certain limitations, such as with the number of apps and directory objects IT teams can manage, Azure AD Premium P2’s feature set offers admins the opportunity to thoroughly manage their users and their SSO access. + +### Azure AD + +Azure Active Directory (Azure AD) is a cloud-based identity and access management service. Azure AD enables your employees access external resources, such as Microsoft 365, the Azure portal, and thousands of other SaaS applications. + +>Azure Active Directory also helps them access internal resources like apps on your corporate intranet, and any cloud apps developed for your own organization _([Microsoft](https://learn.microsoft.com/en-us/azure/active-directory/fundamentals/active-directory-whatis))_. + +[![Azure Active Directory](https://user-images.githubusercontent.com/8466209/229262526-f13a7f1a-f2da-45e3-9cc9-3d0f70bc3b21.png)](https://learn.microsoft.com/en-us/azure/active-directory/fundamentals/active-directory-whatis) + +Azure AD [Premium P2](https://petri.com/azure-active-directory-premium-p1-vs-p2/#Active_Directory_Premium_P1_vs_P2_Which_plan_is_right_for_you) licenses are beneficial for organizations that are expected to demonstrate a high level of governance of identities. That implies managing privileged access and automating access reviews and responses to potentially compromised accounts. + +[![Azure AD Premium P2](https://user-images.githubusercontent.com/8466209/229264239-2d34a7c4-0caf-4148-8c86-d4bc1a1e0ba9.png)](https://entra.microsoft.com/) + +AAD Premium P2 offers the following features: + +``` +All of the features listed for Azure AD Microsoft 365 apps +Leverage SSO for an unlimited number of pre-integrated SaaS applications +Configure self-service application assignment to enable users to self-discover and request access to applications +On-prem write-back for all password changes +Advanced usage reporting +HR-driven provisioning +Self-service group management and application management +Microsoft® Identity Management (MIM) CAL + MIM server for simplified lifecycle user management +Conditional access based on device state or location and group +Automate password rollover for group accounts +Join a Windows® Pro device to Azure AD to enable desktop SSO, and Administrator BitLocker recovery +Application proxy for on-premises, header-based, and Integrated Windows Authentication +MDM auto-enrollment, self-service BitLocker recovery, additional local admin tooling to Windows Pro devices via Azure AD Join +Role-based access control (RBAC) +Risk-based Identity Protection +Privileged identity management +Self-service entitlement management (My Access) +Access certifications and reviews +Entitlements management +Lifecycle Workflows (preview) +Privileged Identity Management (PIM), just-in-time access +Cloud app discovery (Windows Defender for cloud apps) +Identity Protection reporting: vulnerabilities and risky accounts +Identity Protection reporting: risk events investigation, SIEM connectivity +A service-level agreement +``` + +Azure AD Premium P2 is most commonly used for providing insight into user activity within Azure infrastructure, Microsoft 365, and web applications. + +[![Azure Active Directory Premium P1 vs. P2: Features comparison](https://user-images.githubusercontent.com/8466209/229262780-3143c0e6-ad52-4dd6-8351-12be563efc8c.png)](https://petri.com/azure-active-directory-premium-p1-vs-p2/#Azure_Active_Directory_Premium_P1_vs_P2_Features_comparison) + +### Storage + +![default](https://user-images.githubusercontent.com/8466209/229309763-6b4571aa-5373-4552-93a6-7028f75cf053.png) +[![default](https://user-images.githubusercontent.com/8466209/199137654-16103a10-3167-4a08-b128-dfdd5e169674.png)](https://user-images.githubusercontent.com/36441664/121343696-2bd55c80-c94d-11eb-9aff-76843fb799b6.png) + +[![default](https://user-images.githubusercontent.com/8466209/199134564-15e8f3f8-02b6-41f7-9d89-9a000faf04bf.png)](https://github.com/chetabahana/tensorflow/wiki/Tensor-Kit#updating) + diff --git a/identition/span4/gist07.html b/identition/span4/gist07.html new file mode 100644 index 00000000000..1bc86de97a5 --- /dev/null +++ b/identition/span4/gist07.html @@ -0,0 +1 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist07.md b/identition/span4/gist07.md new file mode 100644 index 00000000000..4cda1a801e4 --- /dev/null +++ b/identition/span4/gist07.md @@ -0,0 +1,3 @@ +[![default](https://user-images.githubusercontent.com/8466209/199138096-ab897288-10c7-4bd2-b0aa-cb7a2edac63d.png)](https://github.com/chetabahana/tensorflow/wiki/Java-SDK#skema) + +[![default](https://user-images.githubusercontent.com/8466209/199137158-5bbd47e0-d24d-428f-89d4-aa9d8820d5f9.png)](https://github.com/chetabahana/tensorflow/wiki/Java-SDK#pola) diff --git a/identition/span4/gist08.html b/identition/span4/gist08.html new file mode 100644 index 00000000000..056e2109480 --- /dev/null +++ b/identition/span4/gist08.html @@ -0,0 +1,39 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            FROM tensorflow/tensorflow:latest-gpu
+
+LABEL version="1.0.7"
+LABEL homepage="https://eq19.github.io/"
+LABEL maintainer="eq19 <admin@rq19.com>"
+LABEL repository="https://github.com/FeedMapping/deploy"
+
+ENV DEBIAN_FRONTEND noninteractive
+ENV DEBCONF_NOWARNINGS="yes"
+
+RUN apt-get update -qq < /dev/null
+RUN apt-get install -qq --no-install-recommends apt-utils < /dev/null
+
+ENV NVIDIA_VISIBLE_DEVICES all
+ENV NVIDIA_DRIVER_CAPABILITIES compute,utility
+ENV PATH="${PATH}:/root/.local/bin"
+
+RUN apt-get install -qq python3.8-venv < /dev/null
+RUN python3.8 -m venv nvidia < /dev/null
+RUN chown -R root nvidia && source nvidia/bin/activate
+RUN python -m pip install -U --force-reinstall pip < /dev/null
+RUN pip install tensorflow-gpu --root-user-action=ignore --quiet
+
+ENV NOKOGIRI_USE_SYSTEM_LIBRARIES=1
+ENV BUNDLE_SILENCE_ROOT_WARNING=1
+ENV RAILS_VERSION 5.0.1
+ENV RUBYOPT=W0
+
+RUN apt-get install -qq npm < /dev/null && npm install -qq yarn < /dev/null
+RUN apt-get install -qq ruby ruby-dev ruby-bundler build-essential < /dev/null
+RUN apt-get install -qq git < /dev/null && git config --global init.defaultBranch master
+
+RUN apt-get clean && rm -rf /var/lib/apt/lists/* /tmp/* /var/tmp/* < /dev/null
+RUN gem install rails --version "$RAILS_VERSION" < /dev/null
+
+COPY . .
+ENTRYPOINT ["/entrypoint.sh"]
+
+

            image

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist08.md b/identition/span4/gist08.md new file mode 100644 index 00000000000..3acaf07df7b --- /dev/null +++ b/identition/span4/gist08.md @@ -0,0 +1,49 @@ +``` +FROM tensorflow/tensorflow:latest-gpu + +LABEL version="1.0.7" +LABEL homepage="https://eq19.github.io/" +LABEL maintainer="eq19 " +LABEL repository="https://github.com/FeedMapping/deploy" + +ENV DEBIAN_FRONTEND noninteractive +ENV DEBCONF_NOWARNINGS="yes" + +RUN apt-get update -qq < /dev/null +RUN apt-get install -qq --no-install-recommends apt-utils < /dev/null + +ENV NVIDIA_VISIBLE_DEVICES all +ENV NVIDIA_DRIVER_CAPABILITIES compute,utility +ENV PATH="${PATH}:/root/.local/bin" + +RUN apt-get install -qq python3.8-venv < /dev/null +RUN python3.8 -m venv nvidia < /dev/null +RUN chown -R root nvidia && source nvidia/bin/activate +RUN python -m pip install -U --force-reinstall pip < /dev/null +RUN pip install tensorflow-gpu --root-user-action=ignore --quiet + +ENV NOKOGIRI_USE_SYSTEM_LIBRARIES=1 +ENV BUNDLE_SILENCE_ROOT_WARNING=1 +ENV RAILS_VERSION 5.0.1 +ENV RUBYOPT=W0 + +RUN apt-get install -qq npm < /dev/null && npm install -qq yarn < /dev/null +RUN apt-get install -qq ruby ruby-dev ruby-bundler build-essential < /dev/null +RUN apt-get install -qq git < /dev/null && git config --global init.defaultBranch master + +RUN apt-get clean && rm -rf /var/lib/apt/lists/* /tmp/* /var/tmp/* < /dev/null +RUN gem install rails --version "$RAILS_VERSION" < /dev/null + +COPY . . +ENTRYPOINT ["/entrypoint.sh"] + +``` + +[![image](https://user-images.githubusercontent.com/8466209/198936863-10e3e037-6665-49c3-b147-3accda4d133b.png)](https://hub.docker.com/r/tensorflow/tensorflow) + +[![default](https://user-images.githubusercontent.com/8466209/199148983-8c6e4c62-8503-4412-9a48-1b8cb54b7a94.png)](https://github.com/FeedMapping/mapping/releases/tag/v1.0.7) + +[![default](https://user-images.githubusercontent.com/8466209/198936548-967ca221-41b7-461b-9b4b-9ff30eedea50.png)](https://github.com/eq19/grammar/actions/runs/3357023441/jobs/5562550171) + +[![default](https://user-images.githubusercontent.com/8466209/225285187-916bee67-a633-4917-84da-7a3187caeb03.png)](https://console.cloud.google.com/billing/018F05-BD9DB7-0A1326/reports;grouping=GROUP_BY_SKU;products=services%2F6F81-5844-456A;credits=CREDIT_TYPE_UNSPECIFIED,PROMOTION,SUSTAINED_USAGE_DISCOUNT,SPENDING_BASED_DISCOUNT?authuser=1&cloudshell=false) + diff --git a/identition/span4/gist09.html b/identition/span4/gist09.html new file mode 100644 index 00000000000..ead2adeea61 --- /dev/null +++ b/identition/span4/gist09.html @@ -0,0 +1,32 @@ + gist09.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | {1} |{43}
+---+-----+-----
+ 2 | 44  |{57}
+---+-----+-----
+ 3 | 58  | 59
+---+-----+-----
+ 4 | 60  | 104
+---+-----+-----
+ 5 | 105 |{115}
+---+-----+-----
+ 6 |{116}| 134
+---+-----+-----
+ 7 | 135 | 162
+---+-----+-----
+ 8 | 163 | 175
+---+-----+-----
+ 9 | 176 |{176}
+---+-----+-----
+

            Let's say you have a defaut configuration of π(10)=2,3,5,7. How do you present your html page in order that all of the page elements are represented by the primes without any missing parts?

                  <html> → (29=10th prime) → next favicon
+        Δ     <head> ← (10)
+        |          <style>  - 5 ‹----
+        |                     Δ      |
+        3(29=10+19)‹------ favicon - 2,3,5=π(5)
+                   </style>          |
+             </head>               (89²)
+              <body> ← (19)          |
+                   <script> - 7 ‹----
+                   </script>
+             </body
+      </html>
+

            image

            default

            default

            default

            default

            Untitleddefault

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span4/gist09.md b/identition/span4/gist09.md new file mode 100644 index 00000000000..b35a2652b0b --- /dev/null +++ b/identition/span4/gist09.md @@ -0,0 +1,50 @@ +``` +---+-----+----- + 1 | {1} |{43} +---+-----+----- + 2 | 44 |{57} +---+-----+----- + 3 | 58 | 59 +---+-----+----- + 4 | 60 | 104 +---+-----+----- + 5 | 105 |{115} +---+-----+----- + 6 |{116}| 134 +---+-----+----- + 7 | 135 | 162 +---+-----+----- + 8 | 163 | 175 +---+-----+----- + 9 | 176 |{176} +---+-----+----- +``` + +Let's say you have a defaut configuration of π(10)=2,3,5,7. How do you present your html page in order that all of the page elements are represented by the primes without any missing parts? + +```html + → (29=10th prime) → next favicon + Δ ← (10) + | | + (89²) + ← (19) | + + +``` + +![image](https://user-images.githubusercontent.com/8466209/250567634-b46e7212-0bde-4934-9afa-4c02520f4bd4.png) + +[![default](https://user-images.githubusercontent.com/8466209/199243558-e974f2ff-55a7-4b4d-8958-d171deecb1d9.png)](https://github.com/jonico/awesome-runners) + +[![default](https://user-images.githubusercontent.com/8466209/199135210-06912985-b2b0-4495-94cb-9431935dc912.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-core-md) + +[![default](https://user-images.githubusercontent.com/8466209/199135743-79928119-2c84-4fa4-bd85-90d77ba3d8f8.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-core-md) + +![default](https://user-images.githubusercontent.com/8466209/227427522-5e34043d-17b7-4cc1-84e8-2194ca408597.png) + +![Untitled](https://user-images.githubusercontent.com/8466209/255234272-d951c8fc-1858-4f30-8497-b0202ed509bd.png)[![default](https://user-images.githubusercontent.com/36441664/83518550-c7dfb300-a504-11ea-9983-51c3eab2220d.jpg)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406) diff --git a/identition/span4/index.html b/identition/span4/index.html new file mode 100644 index 00000000000..bfff996048f --- /dev/null +++ b/identition/span4/index.html @@ -0,0 +1,19 @@ + Parallel Universes (span 4) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Parallel Universes (span 4)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-36 of orgs section-8 that is inherited from the spin section-4 by prime spin-56 and span-143 with the partitions as below.

            +
            +
            1. gist07.md
            2. gist08.md
            3. gist03.md
            4. Directory Structure
            5. Binary
            6. gist09.md
            7. The Classes
            8. License
            9. Lexer vs Parser

            When we come to a mapping of a Project, is critical to look for the future of Parts Unlimited otherwise the project will massively over budget and very late. So to deal with this we shall consider to move everything to the cloud…

            phoenix

            Since version 3.2 , a new Jekyll project bootstrapped with jekyll new uses gem-based themes to define the look of the site. This results in a lighter default directory structure: _layouts, _includes and _sass are stored in the theme-gem, by default.

            default

            +
            + + Note +
            +
            +

            In general relativity, gravity is a force that bends and warps space-time around supermassive bodies.

            • Even though gravity is one of the four fundamental forces in nature, it is very weak compared to the other three forces (electromagnetism, weak force and strong force). So it can’t be observed or identified on the scale of subatomic particles.
            • However, gravity is very dominant in long-distance scenarios. It controls the structure of the macro universe (galaxies, planets, stars, moons).
            • As far as quantum mechanics is concerned, gravity doesn’t have much effect. The probable nature of the quantum realm also poses a significant challenge for the induction of gravity in the quantum realm.
            • Generally, gravity does not act as a particle as its own. Even if a hypothetical model is introduced to explain the particle nature of a gravity particle, it violates fundamental energy laws.

            In the 1970s, theorists tried to discard the self-destructive idea of point-like gravity particles. Instead of point particles, strings were introduced. Even if strings collide, there will be no infinite energy problem. Strings can smoothly smash and rebound without implying any physically nonsense infinities.

            +
            +

            You can attach a persistent disk or create an instance with Local SSDs when using Container-Optimized OS. The disks can be mounted by creating a subdirectory under /mnt/disks directory (writable, executable, stateless, tmpfs) using startup-scripts.

            image

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            GitHub Actions workflow

            On the lagging strand template, a primase "reads" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            default

            You can run .NET applications in Linux containers, but only if they're written in .NET Core which can be deployed on Windows Server Containers. Applications running in Windows Server Containers can run in any language supported by Windows.

            kernel-6.1.21.1-microsoft-standard-WSL2.img

            Let's combine them all then we will get 168 which is the total primes out of 1000 numbers. This 168 we will get it also when we combine the 1's and 17's cell of (31+37)+(35+65)=68+100=168.

            zeta-vs-zero

            This can be remedied by re-mounting your Windows partition inside WSL with the metdata option. Edit the /etc/wsl.conf file (create it if it doesn't exist) and add the following:

            [automount]
+options = "metadata"
+

            Log out from WSL and log in again, and now the windows partition will be mounted with metadata and chmod will work against windows files. You can now chmod 600 ~/.ssh/id_rsa and everything will work correctly.

            default

            By this project we are going to use a library called Chevrotain. It can be used to build Lexers, Parsers and Interpreters for various use cases ranging from simple config files to full fledged programming languages.

            Lexers, Parsers and Interpreters with Chevrotain

            This Widows is an isolated container, lightweight package for running an application on the host operating system. Containers build on top of the host operating system's kernel (which can be thought of as the buried plumbing of the operating system).

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist01.html b/identition/span5/gist01.html new file mode 100644 index 00000000000..d4b61485d5a --- /dev/null +++ b/identition/span5/gist01.html @@ -0,0 +1 @@ + Triangular waves · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Triangular waves

            A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse) (Wikipedia).

            Making Triangular Waves

            Hamilton's program for proving the Poincaré conjecture involves first putting a Riemannian metric on the unknown simply connected closed 3-manifold. Such mechanism is discussed in detail by 16th prime identity.

            There are 243 prime pairs among the first 1000 primes that sum to 7920, where 243 x 7920 gives additive sum 1,924,560 (and we note that 7920 = 22 x 360 = 2(1092 − 892), which equates to 1,924,560/(2(1092 − 892) = 243.).

            default

            Consider these two (2) numbers are laid side by side as part of Fibonacci sequence on the Pascal Triangle. Thus the above is actually represesenting the pattern of true-prime-pairs via bilateral 9 sums.

            63 = 21 x 3 = 7 x 3 x 3

            Fibonacci Sequence Numbers

            Meanwhile the sum of 28 and 35, which is 63, has a digital root of 6+3 = 9 and is landed precisely on the 15's cell of the prime hexagon. So the interaction with the seven (7) objects is made through the object of 36 which has the same digital root of 9.

            la position du début de l'emplacement, dans les décimales du nombre e, de la séquence 0719425863, qui est la première occurrence d'une séquence de longueur 10 contenant chaque chiffre une et une seule fois (Wikipedia).

            This 1729 objects is passing the first cycle of True Prime Pairs so it will be located by the starting point of 286 objects of 2nd identity. This balancing will exchange 786 and 500 objects in pair.

            1729 = 786 + 157 + 786 = 500 + 286 + 157 + 286 + 500

            Euleur Gap

            The basic idea is to try to "improve" this metric; for example, if the metric can be improved enough so that it has constant positive curvature, then according to classical results in Riemannian geometry, it must be the 3-sphere.

            Hamilton prescribed the "Ricci flow equations" for improving the metric. Ricci flow expands the negative curvature part of the manifold and contracts the positive curvature part. In some cases, Hamilton was able to show that this works

            System Images

            Pass a startup script from Cloud Storage for the scripts greater than 256 KB.

            Startup script

            Artifact Registry expands on the capabilities of Container Registry and is the recommended container registry for Google Cloud.

            2023-03-01

            A Cloud Build trigger automatically starts a build whenever you make any changes to your source code. You can configure the trigger to build your code on any changes to the source repository or only changes that match certain criteria.

            8d0zCSMHxpgkFZTmXCGk

            Compute Engine supplies an up-to-date Container-Optimized OS (COS) image with Docker installed and launches your container when your VM starts. See below the access control for information about private registry permissions.

            DNA is read by DNA polymerase in the 3′ to 5′ direction, meaning the new strand is synthesized in the 5' to 3' direction. Since the leading and lagging strand templates are oriented in opposite directions at the replication fork, **a major issue** is how to achieve synthesis of new lagging strand DNA, whose direction of synthesis is opposite to the direction of the growing replication fork (Source: Wikipedia).

            default

            Means this field remains unthoucheable. Up to the previous topic of quantum we brought you AI. A touchable intelligence. By this project we would like to introduce a brand new intelligence called UI which is the abreviation of Untouched Inteligence

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist02.html b/identition/span5/gist02.html new file mode 100644 index 00000000000..b5ce681ef5f --- /dev/null +++ b/identition/span5/gist02.html @@ -0,0 +1,59 @@ + Where is the 5? · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Where is the 5?

            The four faces additively cascade 32 four-times triangular numbers (oeis.org/A046092). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of 1000th prime.

            encaptulatipn

            π(10) = 4
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+                                           ↓
+                                           |
+                                           ↓                                          
+                            114-89=139-114=25=5x5
+                                | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         ↓
+                                |                             |                         |
+                                 ------------ 10 -------------                          | 
+                                                                                        | 
+                                                                                        | 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+===== 
+  
+

            default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist02.md b/identition/span5/gist02.md new file mode 100644 index 00000000000..8d5e2a3805b --- /dev/null +++ b/identition/span5/gist02.md @@ -0,0 +1,69 @@ +## Where is the 5? + +The four faces additively cascade 32 four-times triangular numbers (oeis.org/A046092). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of 1000th prime. + +![encaptulatipn](https://user-images.githubusercontent.com/8466209/199354127-9e4d362a-933f-402b-a7a8-0010dc014747.png) + +``` +π(10) = 4 + + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + ↓ + | + ↓ + 114-89=139-114=25=5x5 + | + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ ↓ + | | | + ------------ 10 ------------- | + | + | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + + ``` + +![default](https://user-images.githubusercontent.com/8466209/199262407-7f8bee13-f240-4b1f-856e-ee93e97c5ddb.png) +![default](https://user-images.githubusercontent.com/8466209/199355377-8d93057a-769d-49ed-b401-722c0b33fdab.png) diff --git a/identition/span5/gist03.html b/identition/span5/gist03.html new file mode 100644 index 00000000000..8f3685df559 --- /dev/null +++ b/identition/span5/gist03.html @@ -0,0 +1,15 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 

              #8 |----------- 5® --------|------------ 7® --------------|
+     |  1  |---------------- 77 = 4² + 5² + 6² -------------|
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ user|  7  |  -  | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main|  -  |  9  | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+               Δ | Δ             |                       Δ  |   Δ
+              Φ17|Φ29            |                     96-99|  100 - 123 ({24})
+                 |--- A,T,G,C ---|                          |  └── 100 - 103 (4x) » 100
+                 Δ    2x2 = 4x   |-------  2x3 = 6x  -------|  └── 104 - 109 (6x) » 30
+                {98}                                        |  └── 110 - 123 (14x)» 70
+

            Key Difference between Python vs Ruby

            • Python support multiple inheritance, while Ruby support single inheritance.
            • Python is mainly used for academic, AI, machine learning, and scientific programming, while Ruby is used for web development and functional programming.
            • Python is not a fully object-oriented programming language. Whereas Ruby is a fully object-oriented programming language.
            • In Python, once a variable is set, you can't unset it back, while in Ruby, it will be present in the symbol table as long as the variable is in scope.
            • Python lambda functions are larger, while Ruby supports only a single-line lambda function.
            • Python is very explicit and elegant to read, while Ruby can be very hard to debug at times.
            • Python has methods, while Ruby has functions.

            default default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist03.md b/identition/span5/gist03.md new file mode 100644 index 00000000000..c8830a74dc6 --- /dev/null +++ b/identition/span5/gist03.md @@ -0,0 +1,31 @@ +![](https://user-images.githubusercontent.com/36441664/84945795-e43d3b80-b111-11ea-900a-f0b9236d7e69.png) + +``` + #8 |----------- 5® --------|------------ 7® --------------| + | 1 |---------------- 77 = 4² + 5² + 6² -------------| +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77 +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78 + main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + Δ | Δ | Δ | Δ + Φ17|Φ29 | 96-99| 100 - 123 ({24}) + |--- A,T,G,C ---| | └── 100 - 103 (4x) » 100 + Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 104 - 109 (6x) » 30 + {98} | └── 110 - 123 (14x)» 70 +``` + +> [Key Difference between Python vs Ruby](https://www.guru99.com/python-vs-ruby-difference.html) +- Python support multiple inheritance, while Ruby support single inheritance. +- Python is mainly used for academic, AI, machine learning, and scientific programming, while Ruby is used for web development and functional programming. +- Python is not a fully object-oriented programming language. Whereas **Ruby is a fully object-oriented programming language**. +- In Python, once a variable is set, you can’t unset it back, while in Ruby, it will be present in the symbol table as long as the variable is in scope. +- Python lambda functions are larger, while Ruby supports only a single-line lambda function. +- Python is very explicit and elegant to read, while Ruby can be very hard to debug at times. +- Python has methods, while Ruby has functions. + +![default](https://user-images.githubusercontent.com/8466209/199273134-783707cf-b29c-44b1-8cd9-c45ad79990f7.png) +![default](https://user-images.githubusercontent.com/8466209/199358225-8318b692-84c5-407a-a105-2498788948d5.png) +![default](https://user-images.githubusercontent.com/8466209/199359482-4793b2d0-c04a-4f45-8bcc-87a2f30ad511.png) diff --git a/identition/span5/gist04.html b/identition/span5/gist04.html new file mode 100644 index 00000000000..a0c80fa93cc --- /dev/null +++ b/identition/span5/gist04.html @@ -0,0 +1,45 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - |100 |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - |101 |  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   T
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |   H
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+   E
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   P
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |   O
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   W
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |   E
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   R
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   O
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |   F
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  |102 |   -|  - |  - |  - | ∑=168
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |   V
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+   S
+     |       Δ    Δ                |                     Φ12     |       Δ                   Δ |
+            113  150                                   ≜114-25          557                619 = 1+618
+

            default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist04.md b/identition/span5/gist04.md new file mode 100644 index 00000000000..59076c55466 --- /dev/null +++ b/identition/span5/gist04.md @@ -0,0 +1,51 @@ +[![default](https://user-images.githubusercontent.com/8466209/199272127-b1232a38-964f-49e5-83b5-ccff8da01e85.png)](https://github.com/chetabahana/chetabahana.github.io/wiki/Jekyll-Liquid#desain) +``` +| 1st (Form) | 2nd (Route) | 3rd (Channel) | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T + Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E + Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P + Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W + Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R + Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O + Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168 +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S + | Δ Δ | Φ12 | Δ Δ | + 113 150 ≜114-25 557 619 = 1+618 +``` + +![default](https://user-images.githubusercontent.com/8466209/199361092-349e5aef-fe53-4601-8c17-496d945b6ac3.png) +![default](https://user-images.githubusercontent.com/8466209/199361458-8414fe3d-c031-49ab-8167-78135c6c8cff.png) + diff --git a/identition/span5/gist05.html b/identition/span5/gist05.html new file mode 100644 index 00000000000..a7f75cebf9d --- /dev/null +++ b/identition/span5/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            ! default default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist05.md b/identition/span5/gist05.md new file mode 100644 index 00000000000..54e68add5c1 --- /dev/null +++ b/identition/span5/gist05.md @@ -0,0 +1,5 @@ + +![](https://user-images.githubusercontent.com/36441664/104337162-c1e49280-5527-11eb-9625-12b95f568aa4.png)! +![default](https://user-images.githubusercontent.com/8466209/199362826-1f59b53a-e036-4d6c-8528-832033cd1370.png) +![default](https://user-images.githubusercontent.com/8466209/199360397-0158fcf0-4378-4e86-93b4-9c8287c0273b.png) +![default](https://user-images.githubusercontent.com/8466209/199359982-229c7e19-9491-44fe-bc67-9c10b14609e9.png) diff --git a/identition/span5/gist06.html b/identition/span5/gist06.html new file mode 100644 index 00000000000..0f247193537 --- /dev/null +++ b/identition/span5/gist06.html @@ -0,0 +1,108 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            7 x 13 x 19 = 1729

            Centralizing

            7 + 11 + 13 + 17 + 19 = 67 = 19th prime

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+layer|  i  |   f
+-----+-----+---------
+     |  1  |   5
+  1  +-----+
+     |  2  |  {7}
+-----+-----+---    } 36
+     |  3  |  11
+ {2} +-----+
+     |  4  | {13}
+-----+-----+---------
+     |  5  |  17
+  3  +-----+       } 36
+     |  6  | {19}
+-----+-----+---------
+

            (12/2) th prime = 13

            default

            Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)

            101093483-6ac8d500-35ed-11eb-92d1-e264d22b341f

            So based on the difference between the numbers 25 to 29, we take the arrangement of the 25 repositories with the remaining four (4), namely 26 to 29 where we will get the vector arrangement (6,12,18) from True Prime Pairs.

            default

            114 + 2x11x13 = 114 + 286 = 400

            image

            109 - (168 - 100 + 1) = 109 - (68 + 1) = 109 - 69 = 40 = 400/10 ←← π(π(π(1000th prime)))+1

              --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+
              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
            -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+    2 -------------------+----+----+----+----+----+----+----+----+----+-----  ←-- bilateral 9 sums
+    3 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+

            12 - 10 = 2

            default

            (114/2)! = 57! = 1653 » 1653 / 57 = 29

            ∑(13:9) = ∑(29:43) = 11x13 + 5x40x50 = 10143

              -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+    2 -------------------+----+----+----+----+----+----+----+----+----+-----  ←-- bilateral 9 sums
+    3 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin                                          ↓
+                                           |
+                                           ↓                                          
+                            114-89=139-114=25=5x5
+                                | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         |    |
+                                |                             |                         |    |
+                                 ------------ 10 -------------                          |    |
+                                                                                        ↓    ↓ |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                |  2 | 60 | 40 | 1 | 30 | 30 | 5 |
+                                                                                +----+----+----+---+----+----+---+
+                                                                                        |    | |
+                                                                                     2+100 ◄- 
+  -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            Bonding Position

            default

            default

            default

            default

            default

            default default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist06.md b/identition/span5/gist06.md new file mode 100644 index 00000000000..31b0d31572c --- /dev/null +++ b/identition/span5/gist06.md @@ -0,0 +1,187 @@ +***7 x 13 x 19 = 1729*** + +[![Centralizing](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#prime-identity) + +***7 + 11 + 13 + 17 + 19 = 67 = 19th prime*** + +``` +True Prime Pairs: +(5,7), (11,13), (17,19) + +layer| i | f +-----+-----+--------- + | 1 | 5 + 1 +-----+ + | 2 | {7} +-----+-----+--- } 36 + | 3 | 11 + {2} +-----+ + | 4 | {13} +-----+-----+--------- + | 5 | 17 + 3 +-----+ } 36 + | 6 | {19} +-----+-----+--------- +``` + +![](https://user-images.githubusercontent.com/36441664/101619656-26529480-3a46-11eb-8498-3a7867c500a9.png) + +![](https://user-images.githubusercontent.com/36441664/75627425-9b18b880-5c02-11ea-97e5-7beb774079a7.png) + +***(12/2) th prime = 13*** + +[![default](https://user-images.githubusercontent.com/8466209/202855806-611c6a39-e40c-4aa9-ae28-e25aea82cb19.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f) + +***Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)*** + +![101093483-6ac8d500-35ed-11eb-92d1-e264d22b341f](https://user-images.githubusercontent.com/8466209/216657865-5b02d399-6e0a-49fe-a7ff-718ec7a7cb97.jpg) + +So based on the difference between the numbers 25 to 29, we take the arrangement of the 25 repositories with the remaining four (4), namely 26 to 29 where we will get the vector arrangement (6,12,18) from _[True Prime Pairs](https://www.eq19.com/addition/file02.html#true-prime-pairs)_. + +![](https://user-images.githubusercontent.com/36441664/73700083-28f2a800-4718-11ea-97b3-2e9a738dc09e.png) + +[![default](https://user-images.githubusercontent.com/36441664/75612568-4f5d0500-5b57-11ea-909d-856dcb7c139a.jpg)](https://blog.world-mysteries.com/science/vitruvian-man-by-leonardo-da-vinci/) + +![](https://user-images.githubusercontent.com/36441664/73604434-419d7980-45c3-11ea-8ad0-b62d8a27c5b0.png) + +***114 + 2x11x13 = 114 + 286 = 400*** + +![image](https://user-images.githubusercontent.com/8466209/216680164-43ed465c-1c6a-45a1-b3f8-3b6d8accf996.png) + +***109 - (168 - 100 + 1) = 109 - (68 + 1) = 109 - 69 = 40 = 400/10 ←← π(π(π(1000th prime)))+1*** + +``` + --------------------+-----+-----+-----+-----+-----+ | --- + 67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | | + | +-----+-----+-----+ | | + | 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism + | | +-----+-----+-----+ | | | + | | 86‹--- 13:9| 9 | 60 | 69 (27) «-- Δ19 (Rep Fork) | {2®} | | + | | | +-----+-----+-----+ | | --- + | | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | | + | | +-----+-----+-----+ | | + | ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance +329 | +-----+-----+-----+ | + | ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ | + -------------------+-----+-----+ --- +``` + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + Δ Δ + 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1 +``` + +``` +-----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10 + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + 2 -------------------+----+----+----+----+----+----+----+----+----+----- ←-- bilateral 9 sums + 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th +``` + +***12 - 10 = 2*** + +[![default](https://user-images.githubusercontent.com/36441664/128732737-81762604-0ae0-4a90-b5a8-30921cf46efb.png)](https://github.com/chetabahana/chetabahana.github.io/wiki/Mapping) + +![](https://user-images.githubusercontent.com/36441664/85206005-39af5d80-b349-11ea-851a-56309342b53f.png) + +***(114/2)! = 57! = 1653 » 1653 / 57 = 29*** + +![](https://user-images.githubusercontent.com/36441664/101807202-6d747e80-3b47-11eb-8a6b-9e2c6408b091.jpg) + +***∑(13:9) = ∑(29:43) = 11x13 + 5x40x50 = 10143*** + + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + 2 -------------------+----+----+----+----+----+----+----+----+----+----- ←-- bilateral 9 sums + 3 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin ↓ + | + ↓ + 114-89=139-114=25=5x5 + | + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ | | + | | | | + ------------ 10 ------------- | | + ↓ ↓ | + +----+----+----+---+----+----+---+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | + +----+----+----+---+----+----+---+ + | | | + 2+100 ◄- + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- +``` + +[![Bonding Position](https://user-images.githubusercontent.com/8466209/220001571-bddc7fee-5753-4ee3-b145-b3b1bb49a354.png)](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#bonding-position) + +![default](https://user-images.githubusercontent.com/8466209/198418951-a84a0f30-c5d7-4fff-8139-7806e3c22b3b.png) + +![default](https://user-images.githubusercontent.com/8466209/198419910-277fe92d-bb26-4b22-974f-bef1613d46c4.png) + +![default](https://user-images.githubusercontent.com/8466209/198421043-9c47aeb4-176f-44be-8bf9-3daffb19001e.png) + +![default](https://user-images.githubusercontent.com/8466209/198416547-0d9dbfb4-d78a-45b6-bd6c-e8846c928996.png) + +![default](https://user-images.githubusercontent.com/8466209/198769947-a514bf48-0da4-46ed-a25f-c35ab94da02d.png) + +![default](https://user-images.githubusercontent.com/8466209/198406080-2a29fe5f-e1c5-4c0e-aae2-78c3ce61f0c5.png) +![default](https://user-images.githubusercontent.com/8466209/199359804-73018ae2-b497-4118-97f1-ae3d7400b21e.png) + +![default](https://user-images.githubusercontent.com/8466209/199354838-c5735775-58e8-4a4a-b672-59997056036a.png) + +![default](https://user-images.githubusercontent.com/8466209/199355198-2342b2c0-c385-4ada-af51-2effb3152005.png) + +![default](https://user-images.githubusercontent.com/8466209/199363218-ef852193-d9ea-4d98-916e-6d79f492d86e.png) diff --git a/identition/span5/gist07.html b/identition/span5/gist07.html new file mode 100644 index 00000000000..a6be5934dd7 --- /dev/null +++ b/identition/span5/gist07.html @@ -0,0 +1,14 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | {1} |{11}
+---+-----+-----
+ 2 | 12  | 32
+---+-----+-----
+ 3 | 33  |{50}
+---+-----+-----
+ 4 | 51  |{86}
+---+-----+-----
+ 5 | 87  | 108
+---+-----+-----
+ 6 |{109}| 120
+---+-----+-----                                              ---
+

            default

            In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space (Wikipedia).

            default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span5/gist07.md b/identition/span5/gist07.md new file mode 100644 index 00000000000..247db90a973 --- /dev/null +++ b/identition/span5/gist07.md @@ -0,0 +1,24 @@ +``` +---+-----+----- + 1 | {1} |{11} +---+-----+----- + 2 | 12 | 32 +---+-----+----- + 3 | 33 |{50} +---+-----+----- + 4 | 51 |{86} +---+-----+----- + 5 | 87 | 108 +---+-----+----- + 6 |{109}| 120 +---+-----+----- --- +``` + +[![default](https://user-images.githubusercontent.com/36441664/76159498-b1b79600-6153-11ea-91e4-bc312f9456ac.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#scheme-139) +![](https://user-images.githubusercontent.com/36441664/99020210-96c5dd00-2590-11eb-8201-7590eb31ac59.jpg) + +>In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in ***four-dimensional space*** _([Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture))_. + +![](https://user-images.githubusercontent.com/36441664/82712407-12b22d00-9cb2-11ea-9cc2-3cf392b2d35c.png) +![default](https://user-images.githubusercontent.com/8466209/199263778-d09e3d86-c438-4447-8689-29178dbd367f.png) +[![default](https://user-images.githubusercontent.com/8466209/199364235-ce289eeb-27ee-4d2f-a36b-1b220831f922.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155) diff --git a/identition/span5/index.html b/identition/span5/index.html new file mode 100644 index 00000000000..944f571906a --- /dev/null +++ b/identition/span5/index.html @@ -0,0 +1,21 @@ + Hidden Dimensions (span 5) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Hidden Dimensions (span 5)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-35 of orgs section-7 that is inherited from the spin section-5 by prime spin-54 and span-144 with the partitions as below.

            +
            +
            1. gist04.md
            2. gist05.md
            3. Where is the 5?
            4. gist06.md
            5. gist03.md
            6. gist07.md
            7. Triangular waves

            A lexer is the part of an interpreter that turns a sequence of characters (plain text) into a sequence of tokens. The Parser which takes the tokens from the lexer and returns a syntax tree based on a grammar. The grammar is often expressed in a meta language.

            BusyBox v1.34.1 (2022-07-19 20:11:24 UTC) multi-call binary.
+
+Usage: mv [-finT] SOURCE DEST
+or: mv [-fin] SOURCE... { -t DIRECTORY | DIRECTORY }
+
+Rename SOURCE to DEST, or move SOURCEs to DIRECTORY
+
+	-f	Don't prompt before overwriting
+	-i	Interactive, prompt before overwrite
+	-n	Don't overwrite an existing file
+	-T	Refuse to move if DEST is a directory
+	-t DIR	Move all SOURCEs into DIR
+

            default

            By this modification we are going to build the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence. So follow to the scheme then it would get 50 nodes out of the total nodes of 66.

            default

            The next step we will explore to find out if this configuration is relevant in the programming process. The following will explain how the formations are arranged so that we can simulate an instance based on their respective characters.

            image

            By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist01.html b/identition/span6/gist01.html new file mode 100644 index 00000000000..718b1721ed5 --- /dev/null +++ b/identition/span6/gist01.html @@ -0,0 +1 @@ + The Prime hexagon · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Prime hexagon

            Cranks of prime

            Turbulent Combustion

            default

            [Navier–Stokes Equation

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist02.html b/identition/span6/gist02.html new file mode 100644 index 00000000000..dd006de35ba --- /dev/null +++ b/identition/span6/gist02.html @@ -0,0 +1 @@ + Why was 6 afraid of 7? · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Why was 6 afraid of 7?

            default

            default

            default

            default

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist02.md b/identition/span6/gist02.md new file mode 100644 index 00000000000..2693b6cd0fa --- /dev/null +++ b/identition/span6/gist02.md @@ -0,0 +1,17 @@ +## Why was 6 afraid of 7? + +[![default](https://user-images.githubusercontent.com/8466209/199381132-1c2beef1-d8a1-4bdf-8e11-37c71c5aaa39.png)](https://github.com/chetabahana/chetabahana.github.io/wiki/26#Skema) + +[![default](https://user-images.githubusercontent.com/8466209/199381827-514ef150-0ca2-4a61-8554-b69946ad2afd.png)](https://www.google.com/search?q=minor+hexagon&tbm=isch) + +[![default](https://user-images.githubusercontent.com/8466209/199380441-f5d66d42-3bf4-4442-afb8-3c23347dd8f1.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md) + +[![default](https://user-images.githubusercontent.com/8466209/199380298-8f5e14a4-453a-46a9-8cfe-46859414d300.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-2_assigning-md) + +[![default](https://user-images.githubusercontent.com/8466209/199380073-a9657bf5-e4da-468d-9e32-d910f48de2ce.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-grammar-md) + +[![default](https://user-images.githubusercontent.com/8466209/199375180-51cbbd05-1884-400d-a747-3f1eb3d4057b.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-base-md) + +[![default](https://user-images.githubusercontent.com/8466209/199376315-60f50c75-257f-4f81-89ae-b0a05b2eb1ea.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde#file-hexagon-md) + +[![default](https://user-images.githubusercontent.com/8466209/199383689-383d4092-1310-4ffa-b246-d1ee5461f96c.png)](https://github.com/FeedMapping/prime-hexagon/tree/9d46dc7d05f5af89dac3abee000a0666d291e7ab/numberGenerator/python/prime_lists) diff --git a/identition/span6/gist03.html b/identition/span6/gist03.html new file mode 100644 index 00000000000..1b229145214 --- /dev/null +++ b/identition/span6/gist03.html @@ -0,0 +1 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            If you clearly know what kind of neural networks architecture you want, you may need to dive directly into TensorFlow. Whereas Keras is preferred forfast prototyping, where you want to experiment with your ideas and see the results quickly.

            default

            default

            default default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist03.md b/identition/span6/gist03.md new file mode 100644 index 00000000000..58a2e0be400 --- /dev/null +++ b/identition/span6/gist03.md @@ -0,0 +1,12 @@ +[![default](https://user-images.githubusercontent.com/8466209/199389773-2950d6e1-9bf8-488b-9192-53f8356188f0.png)](https://github.com/spacetimeengineer/spacetimeengine/tree/48924e3cf7f163d7016e2bde7518baa1bbf5e7dd/spacetimeengine) + +[![default](https://user-images.githubusercontent.com/8466209/199374989-188e57d5-a21e-4523-97b1-27d996223e8e.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-base-md) + +If you clearly know what kind of neural networks architecture you want, you may need to dive directly into TensorFlow. Whereas Keras is preferred forfast prototyping, where you want to experiment with your ideas and see the results quickly. + +[![default](https://user-images.githubusercontent.com/8466209/199374038-d20dd4f9-a851-4258-a397-a3c7eac597ca.png)](https://github.com/chetabahana/tensorflow/tree/623216733f8902b0dfab1cb7e318441537dce855/tensorflow/python/keras) + +[![default](https://user-images.githubusercontent.com/8466209/199371855-fe818d94-f6bf-4f3d-94d0-2d18002f3888.png)](https://github.com/chetabahana/tensorflow/wiki/Trend-Analysis#template) + +[![default](https://user-images.githubusercontent.com/8466209/199390946-f6bc9455-2500-40e6-b8cf-30cd1aa09963.png)](https://github.com/chetabahana/tensorflow/wiki/Tensor-Kit#branching) +[![default](https://user-images.githubusercontent.com/8466209/199371755-103f98fc-3735-42dd-81e7-089d2faf8e37.png)]() diff --git a/identition/span6/gist04.html b/identition/span6/gist04.html new file mode 100644 index 00000000000..f9ad1d32041 --- /dev/null +++ b/identition/span6/gist04.html @@ -0,0 +1,8 @@ + Fonts Test · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Fonts Test

            {:.font-mono}

            ABCDEFGHIJKLMNOPQRSTUVWXYZ
+abcdefghijklmnopqrstuvwxyz
+1234567890
+一二三四五六七八九十百千萬上中下左右大小春夏秋冬東南西北金木水火土
+‘?'"!"(%)[#]{@}/&\<-+÷×=>®©$€£¥¢:;,.*
+

            {:.font-body}

            ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 一二三四五六七八九十百千萬上中下左右大小春夏秋冬東南西北金木水火土 ‘?'"!"(%)[#]{@}/&<-+÷×=>®©$€£¥¢:;,.*

            {:.font-head}

            ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 一二三四五六七八九十百千萬上中下左右大小春夏秋冬東南西北金木水火土 ‘?'"!"(%)[#]{@}/&<-+÷×=>®©$€£¥¢:;,.*

            font-awesome

            <i class="fa fa-check-circle text-green">checked</i>
+<i class="fa fa-battery-quarter text-red">battery</i>
+

            checked battery

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist05.html b/identition/span6/gist05.html new file mode 100644 index 00000000000..79986752c61 --- /dev/null +++ b/identition/span6/gist05.html @@ -0,0 +1,84 @@ + Markdown Elements · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Markdown Elements

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            There should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs.

            There should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs. There should be whitespace between paragraphs.

            There should be no margin above this first sentence.

            Blockquotes should be a lighter gray with a gray border along the left side.

            There should be no margin below this final sentence.

            Header 1

            This is a normal paragraph following a header. Bacon ipsum dolor sit amet t-bone doner shank drumstick, pork belly porchetta chuck sausage brisket ham hock rump pig. Chuck kielbasa leberkas, pork bresaola ham hock filet mignon cow shoulder short ribs biltong.

            Header 2

            This is a blockquote following a header. Bacon ipsum dolor sit amet t-bone doner shank drumstick, pork belly porchetta chuck sausage brisket ham hock rump pig. Chuck kielbasa leberkas, pork bresaola ham hock filet mignon cow shoulder short ribs biltong.

            Header 3

            +
            + + Note +
            +
            +

            This is a note

            Markdown is supported, Text can be bold, italic, or strikethrough. Links should be blue with no underlines

            inline code

            inline code inside link

            +
            +

            Header 4

            • This is an unordered list following a header.
            • This is an unordered list following a header.
            • This is an unordered list following a header.
            Header 5
            1. This is an ordered list following a header.
            2. This is an ordered list following a header.
            3. This is an ordered list following a header.
            Header 6
            What Follows
            A table A header
            A table A header
            A table A header

            There's a horizontal rule above and below this.

            Here is an unordered list:

            • Salt-n-Pepa
            • Bel Biv DeVoe
            • Kid ‘N Play

            And an ordered list:

            1. Michael Jackson
            2. Michael Bolton
            3. Michael Bublé

            And an unordered task list:

            • Create a sample markdown document
            • Add task lists to it
            • Take a vacation

            And a "mixed" task list:

            • Steal underpants
            • ?
            • Profit!

            And a nested list:

            • Jackson 5
              • Michael
              • Tito
              • Jackie
              • Marlon
              • Jermaine
            • TMNT
              • Leonardo
              • Michelangelo
              • Donatello
              • Raphael

            Definition lists can be used with HTML syntax. Definition terms are bold and italic.

            Name
            Godzilla
            Born
            1952
            Birthplace
            Japan
            Color
            Green

            Tables should have bold headings and alternating shaded rows.

            Artist Album Year
            Michael Jackson Thriller 1982
            Prince Purple Rain 1984
            Beastie Boys License to Ill 1986

            If a table is too wide, it should condense down and/or scroll horizontally.

            Artist Album Year Label Awards Songs
            Michael Jackson Thriller 1982 Epic Records Grammy Award for Album of the Year, American Music Award for Favorite Pop/Rock Album, American Music Award for Favorite Soul/R&B Album, Brit Award for Best Selling Album, Grammy Award for Best Engineered Album, Non-Classical Wanna Be Startin' Somethin', Baby Be Mine, The Girl Is Mine, Thriller, Beat It, Billie Jean, Human Nature, P.Y.T. (Pretty Young Thing), The Lady in My Life
            Prince Purple Rain 1984 Warner Brothers Records Grammy Award for Best Score Soundtrack for Visual Media, American Music Award for Favorite Pop/Rock Album, American Music Award for Favorite Soul/R&B Album, Brit Award for Best Soundtrack/Cast Recording, Grammy Award for Best Rock Performance by a Duo or Group with Vocal Let's Go Crazy, Take Me With U, The Beautiful Ones, Computer Blue, Darling Nikki, When Doves Cry, I Would Die 4 U, Baby I'm a Star, Purple Rain
            Beastie Boys License to Ill 1986 Mercury Records noawardsbutthistablecelliswide Rhymin & Stealin, The New Style, She's Crafty, Posse in Effect, Slow Ride, Girls, (You Gotta) Fight for Your Right, No Sleep Till Brooklyn, Paul Revere, Hold It Now, Hit It, Brass Monkey, Slow and Low, Time to Get Ill

            Code snippets like var foo = "bar"; can be shown inline.

            Also, this should vertically align with this and this.

            Code can also be shown in a block element.

            var foo = "bar";
+

            Code can also use syntax highlighting.

            var foo = "bar";
+
            Long, single-line code blocks should not wrap. They should horizontally scroll if they are too long. This line should be long enough to demonstrate this.
+
            var foo =
+  "The same thing is true for code with syntax highlighting. A single line of code should horizontally scroll if it is really long.";
+

            Inline code inside table cells should still be distinguishable.

            Language Code
            Javascript var foo = "bar";
            Ruby foo = "bar"

            Small images should be shown at their actual size.

            Octocat

            Mathjax Test

            \[\begin{aligned} & \phi(x,y) = \phi \left(\sum_{i=1}^n x_ie_i, \sum_{j=1}^n y_je_j \right) = \sum_{i=1}^n \sum_{j=1}^n x_i y_j \phi(e_i, e_j) = \\ & (x_1, \ldots, x_n) \left( \begin{array}{ccc} \phi(e_1, e_1) & \cdots & \phi(e_1, e_n) \\ \vdots & \ddots & \vdots \\ \phi(e_n, e_1) & \cdots & \phi(e_n, e_n) \end{array} \right) \left( \begin{array}{c} y_1 \\ \vdots \\ y_n \end{array} \right) \end{aligned}\]
            +
            + + Note +
            +
            +

            For documentation, see: https://kramdown.gettalong.org/syntax.html#math-blocks

            +
            +

            Mermaid Test

            ```mermaid
+graph TB
+    c1-->a2
+    subgraph one
+    a1-->a2
+    end
+    subgraph two
+    b1-->b2
+    end
+    subgraph three
+    c1-->c2
+    end
+```
+
            +
            graph TB + c1-->a2 + subgraph one + a1-->a2 + end + subgraph two + b1-->b2 + end + subgraph three + c1-->c2 + end +
            +
            +
            +
            graph TD; + A-->B; + A-->C; + B-->D; + C-->D; +
            +
            +
            +
            classDiagram +classA <|-- classB +classC *-- classD +classE o-- classF +classG <-- classH +classI -- classJ +classK <.. classL +classM <|.. classN +classO .. classP +
            +
            +
            +
            erDiagram + CUSTOMER ||--o{ ORDER : places + ORDER ||--|{ LINE-ITEM : contains + CUSTOMER }|..|{ DELIVERY-ADDRESS : uses +
            +
            +

            Primer Utilities Test

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            Text can be bold, italic, or strikethrough. Links should be blue with no underlines (unless hovered over).

            +
            + + Tip +
            +
            +

            Edit this page to see how to add this to your docs, theme can use @primer/css utilities

            +
            +
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist06.html b/identition/span6/gist06.html new file mode 100644 index 00000000000..5113369cc6a --- /dev/null +++ b/identition/span6/gist06.html @@ -0,0 +1,20 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist06.md b/identition/span6/gist06.md new file mode 100644 index 00000000000..529cd640a36 --- /dev/null +++ b/identition/span6/gist06.md @@ -0,0 +1,24 @@ +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + Δ Δ + 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1 +``` + +[![default](https://user-images.githubusercontent.com/8466209/199502657-1ba96c92-29f9-41ec-90a9-cbc5adec9464.png)](https://gist.github.com/eq19/8cab5e72d52ecb338a2f2187082a1699#file-runner-md) + diff --git a/identition/span6/gist07.html b/identition/span6/gist07.html new file mode 100644 index 00000000000..eaf70dd9c0e --- /dev/null +++ b/identition/span6/gist07.html @@ -0,0 +1 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist07.md b/identition/span6/gist07.md new file mode 100644 index 00000000000..9900728d821 --- /dev/null +++ b/identition/span6/gist07.md @@ -0,0 +1,9 @@ + + +[![default](https://user-images.githubusercontent.com/8466209/199505430-103ea007-46c1-462d-a508-4cb2f952533f.png)](https://github.com/MarketLeader/marketleader.github.io/tree/bb03da9405c488db8999a56d56b31081dd13ebe5) + +[![default](https://user-images.githubusercontent.com/8466209/199506031-040881cb-5ba0-4b9c-b217-19c6f70db625.png)](https://gist.github.com/eq19/b32915925d9d365e2e9351f0c4ed786e#file-runner-md) + +[![default](https://user-images.githubusercontent.com/8466209/199531841-702f40e4-c1b6-434b-b0de-7cd3c721bc7f.png)](https://stackoverflow.com/a/74291357/4058484) + +[![default](https://user-images.githubusercontent.com/8466209/199534966-02f7e806-6cba-4c3c-829c-8886774a6b4a.png)](https://stackoverflow.com/questions/52395202/pushing-changes-in-the-git-submodule) diff --git a/identition/span6/gist08.html b/identition/span6/gist08.html new file mode 100644 index 00000000000..013a593f266 --- /dev/null +++ b/identition/span6/gist08.html @@ -0,0 +1,30 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
              =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+                                           ↓
+                                           |
+                                           ↓                                          
+                            114-89=139-114=25=5x5
+                                | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         ↓
+                                |                             |                         |
+                                 ------------ 10 -------------                          | 
+                                                                                        | 
+                                                                                        | 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist08.md b/identition/span6/gist08.md new file mode 100644 index 00000000000..b0ed1c6db77 --- /dev/null +++ b/identition/span6/gist08.md @@ -0,0 +1,35 @@ +``` + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + ↓ + | + ↓ + 114-89=139-114=25=5x5 + | + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ ↓ + | | | + ------------ 10 ------------- | + | + | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- + ``` + +[![default](https://user-images.githubusercontent.com/8466209/199508386-69859804-9ccb-4f5d-8314-8ca0be0af235.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-pairing-md) + +[![default](https://user-images.githubusercontent.com/8466209/199510678-abc4b002-b54a-4a80-9e12-1ef6527ca511.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-mirror-md) diff --git a/identition/span6/gist09.html b/identition/span6/gist09.html new file mode 100644 index 00000000000..a0bcd9ad46d --- /dev/null +++ b/identition/span6/gist09.html @@ -0,0 +1,15 @@ + gist09.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist09.md b/identition/span6/gist09.md new file mode 100644 index 00000000000..4b3d47e96bb --- /dev/null +++ b/identition/span6/gist09.md @@ -0,0 +1,20 @@ +``` +1st layer: +It has a total of 1000 numbers +Total primes = π(1000) = 168 primes + +2nd layer: +It will start by π(168)+1 as the 40th prime +It has 100x100 numbers or π(π(10000)) = 201 primes +Total cum primes = 168 + (201-40) = 168+161 = 329 primes + +3rd layer: +Behave the same as 2nd layer which has a total of 329 primes +The primes will start by π(π(π(1000th prime)))+1 as the 40th prime +This 1000 primes will become 1000 numbers by 1st layer of the next level +Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 +``` + +[![default](https://user-images.githubusercontent.com/8466209/199512064-fe149c63-1c7b-4d67-b700-fb61c52382de.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406) + +[![default](https://user-images.githubusercontent.com/8466209/199510889-f6bca686-74cf-4fed-a7c1-bd1269058e63.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md) diff --git a/identition/span6/gist10.html b/identition/span6/gist10.html new file mode 100644 index 00000000000..340c34e7e93 --- /dev/null +++ b/identition/span6/gist10.html @@ -0,0 +1,16 @@ + gist10.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | 1   |{73}
+---+-----+-----
+ 2 |{74} | 94
+---+-----+-----
+ 3 | 95  | 113
+---+-----+-----
+ 4 |{114}| 121
+---+-----+-----
+ 5 | 122 | 135
+---+-----+-----
+ 6 | 136 | 156
+---+-----+-----
+ 7 |{157}|{165}
+---+-----+-----
+

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span6/gist10.md b/identition/span6/gist10.md new file mode 100644 index 00000000000..f0e25fbab85 --- /dev/null +++ b/identition/span6/gist10.md @@ -0,0 +1,25 @@ +``` +---+-----+----- + 1 | 1 |{73} +---+-----+----- + 2 |{74} | 94 +---+-----+----- + 3 | 95 | 113 +---+-----+----- + 4 |{114}| 121 +---+-----+----- + 5 | 122 | 135 +---+-----+----- + 6 | 136 | 156 +---+-----+----- + 7 |{157}|{165} +---+-----+----- +``` + +[![default](https://user-images.githubusercontent.com/8466209/199369598-357b1b6f-378b-4a56-8c7b-519316418edb.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-implementation) + +[![default](https://user-images.githubusercontent.com/8466209/199392998-1322a3f1-182f-4f69-9af9-f9691bcb617b.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md) + +[![default](https://user-images.githubusercontent.com/8466209/199392725-b5483087-9b7f-4381-b73d-21849a88d295.png)](https://github.com/chetabahana/tensorflow/wiki#manuscript) + +[![default](https://user-images.githubusercontent.com/8466209/199392468-a2738235-b65f-47da-848d-ffa0340cd51b.png)](https://github.com/chetabahana/tensorflow/wiki#delivery) \ No newline at end of file diff --git a/identition/span6/index.html b/identition/span6/index.html new file mode 100644 index 00000000000..2881de36d9c --- /dev/null +++ b/identition/span6/index.html @@ -0,0 +1,40 @@ + Basic Transformation (span 6) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Basic Transformation (span 6)

            +
            +
            + + Tip +
            +
            +

            This section is referring to wiki page-34 of orgs section-6 that is inherited from the spin section-6 by prime spin-50 and span-145 with the partitions as below.

            +
            +
            +
            1. gist08.md
            2. gist03.md
            3. Why was 6 afraid of 7?
            4. gist06.md
            5. gist10.md
            6. gist07.md
            7. gist09.md
            8. Fonts Test
            9. The Prime hexagon
            10. Markdown Elements

            For some Enneagram theorists the lines connecting the points add further meaning to the information provided by the descriptions of the types. Sometimes called the "security" and "stress" points, or points of "integration" and "disintegration".

            From this perspective, there are twenty-seven (27) distinct personality patterns, because people of each of the nine (9) types also express themselves as one of the three (3) subtypes (Wikipedia).

            This is managed within twelve (12) flows (A: to W:). Each flows is representing a certain period which is converting the three (3) layers of 19 cells with a cumulative sum of 1, 7 and 19 in sequence as explained before.

            default

            default

            default

            image

            It turns out it's actually pretty straight forward to set WSL to use your Windows home directory. First, within WSL edit the /etc/passwd file (eg with sudo nano /etc/passwd).

            +
            eq19:x:1000:1000:eQ19:/home/eq19:/bin/bash
+eq19:x:1000:1000:eQ19:/mnt/c/users/Admin:/bin/bash
+

            image

            default

            +
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist01.html b/identition/span7/gist01.html new file mode 100644 index 00000000000..9e24686c583 --- /dev/null +++ b/identition/span7/gist01.html @@ -0,0 +1,76 @@ + Double strands · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Double strands

            The bilateral way of 329 vs 289 of 286 objects of 2nd prime identity will be taken as the basis that is involving 26-9=17 of other identities where the square of 17 which is 17x17=329 acts as the central of syntax algorithm.

            id: 26
+
+---+-----+-----+-----+-----+
+ 1 |   5 |   1 |  6  |   7 |----------------------------
+---+-----+-----+-----+-----+                            |
+ 2 |   2 |   7 |  9  |  16 |----------------------      |
+---+-----+-----+-----+-----+                      |     |
+ 3 |  58 |  10 |  68 |  78 |----------------      |     |
+---+-----+-----+-----+-----+                |     |     |
+ 4 |  35 |  69 | 104 | 173 |----------      |     |     |
+---+-----+-----+-----+-----+          |     |     |     |
+ 5 | {17}| 105 | 122 |{227}|          |     |     |     |
+---+-----+-----+-----+-----+- Cross  {17}Δ26|43Δ30|13Δ17|30
+ 6 | {17}|{123}| 140 | 263 |          |     |     |     |
+---+-----+-----+-----+-----+          |     |     |     |
+ 7 |  18 | 141 | 159 | 300 |----------      |     |     |
+---+-----+-----+-----+-----+                |     |     |
+ 8 |  15 | 160 | 175 | 335 |----------------      |     |
+---+-----+-----+-----+-----+                      |     |
+ 9 |  15 | 176 | 191 | 367 |----------------------      |
+---+-----+-----+-----+-----+                            |
+10 |  35 |{192}|{227}| 419 |----------------------------   
+---+-----+-----+-----+-----+
+

            By taking the 200 residual objects we will get their recycing scenario which is similar to the leading and lagging strands of DNA Replication where the result is obtained on the lagging stage by initiating a DNA synthesis called RNA Primer.

            RNA primers are used by living organisms in initiation of synthesizing a strand of DNA. A class of enzymes called primases add a complementary RNA primer to the reading template on both the leading and lagging strands (Wikipedia).

            image

            There are situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics. Finally, there exist scenarios in which there could actually be more than 4D of spacetime.

            default

            Note that 1/109's decimal expansion is period 108 (making it a ‘long period prime' in that 1/p has the maximal period of p−1 digits). This period consists of 54 bilateral 9 sums = 486, which is the number of primes in the 243 pairs summing to 7920.

            36 + 72 = 108

            This behaviour would come to the feature of golden ratio. However it is not stand as a basic rule but as an impact of 329's vs 289's layers. That is also the reason why we could only see the three (3) digits of 618 out of the Fibonaci constant.

            φ = 1.618 = Fibonaci = Golden Ratio

            The 200 objects that goes from the 2nd to 3rd prime identity would take position as multiplication zone by given of 100x2=200 which is then be used in turn to 100+2=102 (addition zone) and 100^2=10000 (exponentiation zone)

            2 + 60 + 40 = 102

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            So it is converting all residual objects out of the prime recycling of Riemann Zeta in to those three (3) basic arithmetic operations of Euler's identity as well the Fibonacy constant (φ) to Euler's number (e). Thus none of residual is neglected by an assumption.

            DNA polymerase (responsible for DNA replication) enzymes are only capable of adding nucleotides to the 3'-end of an existing nucleic acid, requiring a primer be bound to the template before DNA polymerase can begin a complementary strand.

            DNA polymerase adds nucleotides after binding to RNA primer and synthesizes the whole strand. Later, the RNA strands must be removed accurately and replace them with DNA nucleotides forming a gap region known as a nick that is filled in using an enzyme called ligase (Wikipedia).

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity with DNA Replication as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ

            layer | node | sub |  i      |   f
+------+------+-----+---------+------                                             ---
+      |      |     |  1,2:1 √|  71 (2,3) -------------                            |
+      |      |  1  +---------+                        |                           |
+      |  1   |     |      2  |                        |                          (5) 
+      |      |-----+---------+                        |                           |
+      |      |     |      3  |                        |                           |
+  1   +------+  2  +---------+----                    |                          ---
+      |      |     |      4  |                        |                           |
+      |      +-----+---------+                        |                           |
+      |  2   |     |      5  |                        |                          (7) 
+289 √ |      |  3  +---------+                        |                           |
+|     |      |     |      6  |                        | {6®}                      |
+------+------+-----+---------+------      } (36)      | ↓                        ---
+      |      |     |      7  |                        | 29=MEC30 - Δ1             |
+      |      |  4  +---------+                        | ↓                         |
+      |  3   |     |      8  | 109 (26) √ --          | 9+60+40 from 329-40 √    (11) 
+      |      +-----+---------+              |         | ↓ lagging √               |
+      |      |     |      9  |  69 (27) √   | {2®}    | 9+60=40+29 from 168 √     |
+  2   +------|  5  +---------+-----         |         | ↓ leading √              ---
+      |      |     |      10 | 109 (28) √ --          | 9+60+40 goes to 329 √     |
+      |      |-----+---------+                        | ↓                         |
+      |  4   |     |      11 | 71 (29,30,31,32) ------  ↓                        (13)
+329 √ |      |  6  +---------+                          9+9+9=27 (Triangular) √   |
+|     |      |     |      12 | {70} (36)                                          |
+------+------+-----+---------+------------------                                 ---
+      |      |     |   20:13 |                                                    |
+      |      |  7  +---------+                                                    |
+      |  5   |     |      14 |                                                  (17) 
+      |      |-----+---------+                                                    |
+      |      |     |      15 |                                                    |
+  3   +------+  8  +---------+-----                                              ---
+      |      |     |      16 |                                                    |
+      |      |-----+---------+                                                    |
+      |  6   |     |      17 | 100(50)                                          (19) 
+168   |      |  9  +---------+                                                    |
+|     |      |     |      18 | 50(68)                                             |
+------|------|-----+---------+------                                             ---
+
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist02.html b/identition/span7/gist02.html new file mode 100644 index 00000000000..71e522e5790 --- /dev/null +++ b/identition/span7/gist02.html @@ -0,0 +1 @@ + gist02.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist02.md b/identition/span7/gist02.md new file mode 100644 index 00000000000..d48743a7968 --- /dev/null +++ b/identition/span7/gist02.md @@ -0,0 +1,8 @@ +![default](https://user-images.githubusercontent.com/8466209/200012043-620aa039-3b72-4165-83ad-e35d3d972a1b.png) + +[![default](https://user-images.githubusercontent.com/8466209/200002482-af3ef796-e71b-426c-b71d-1bd732ba5c6e.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-6_pattern-md) + +[![default](https://user-images.githubusercontent.com/8466209/200007203-bdea0db7-7825-4f34-b8c2-a1b5baf99b87.png)](https://eq19.github.io/) + +[![default](https://user-images.githubusercontent.com/8466209/200003416-da978633-24fb-4e8d-aa12-5c18fee76667.png)](https://github.com/eq19) + diff --git a/identition/span7/gist03.html b/identition/span7/gist03.html new file mode 100644 index 00000000000..824ee74cf86 --- /dev/null +++ b/identition/span7/gist03.html @@ -0,0 +1,105 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            By prime hexagon we can see that seven (7), hold the power to make the prime spin remain on the track. This power is then transfered to twelve (12) spins.

            image

            So basically there is a power transformation between an addition of 3 and 4 to 7 in to their multiplication in to 12 where this 7 will be treated as one of their member.

              #8 |----------- 5® --------|------------ 7® --------------|
+     |  1  |---------------- 77 = 4² + 5² + 6² -------------|
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ user|  7  |  -  | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main|  -  |  9  | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+               Δ | Δ             |                       Δ  |   Δ
+              Φ17|Φ29            |                     96-99|  200
+                 |--- A,T,G,C ---|                          |  └── 30
+                 Δ    2x2 = 4x   |-------  2x3 = 6x  -------|  └── 70
+                {98}                                        |  └── 100
+

            Therefore the 12 will consist of 11 groups runner and 1 profile of the transformation result. Follow to the prime hexagon we collect them in 19 gists as below.

            $ gh api -H "${HEADER}" /users/eq19/gists --jq 'sort_by(.created_at)|.[].url'
+
+https://api.github.com/gists/c9bdc2bbe55f2d162535023c8d321831 19 grammar 36
+https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 syntax
+https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 parser
+https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 lexer
+https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 feed
+https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 maps
+https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 io 30
+                                                           --------
+https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
+https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
+https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
+https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
+https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
+https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
+https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
+https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
+https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
+https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
+https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
+https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37
+

            Since 19 is thouching the first node then the workflow will be proceeded as bilateral way

            https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
+https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
+https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
+https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
+https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
+https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
+https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
+https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
+https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
+https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
+https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
+https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37
+12 months (moon)
+-------- bilateral 9 sums
+7 days (sun)
+https://api.github.com/gists/c9bdc2bbe55f2d162535023c8d321831 19 grammar 36
+https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 syntax
+https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 parser
+https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 lexer
+https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 feed
+https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 maps
+https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 io 30
+

            Here we can see that the transformation from 7 to 12 is actualy started from the prime 13. So the power of 7 is transfered to 77 by the prime pair 11 and 13.

            image

            The nodes is from converted from 7 to 77 whivh is 7 times 11. By the prime pair 11 and 13, the total nodes is involving 1 + 7 + 29 + 77 = 37 + 77 = 114 nodes

              Δ1 + Δ7 + Δ29  →  | Δ37 + Δ77 = Δ114 = Δ113 + Δ1 → 
+
+     |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - | 100|  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - | 101|  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  | 102|   -|  - |  - |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+     |       Δ    Δ    Δ           |                     Φ12     |       Δ                   Δ |
+           -113 +150 = +37                                             +102 = +139    -113 -114
+

            As conclution the behaviour of this 7 is happen between the sequence of 30 and 36 while the 12 is happen between the sequence of 36 and 102.

            default

            By observing more detail we spread the power of 7.

            **168 + 329 + 289 - 619 - 30 - 30 - 5 = 786 - 619 - 65 = 102 = (2,60,40)**

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist03.md b/identition/span7/gist03.md new file mode 100644 index 00000000000..1c88e86718f --- /dev/null +++ b/identition/span7/gist03.md @@ -0,0 +1,139 @@ +By prime hexagon we can see that seven (7), hold the power to make the prime spin remain on the track. This power is then transfered to twelve (12) spins. + +![image](https://user-images.githubusercontent.com/8466209/253148724-8dffc1e4-e2a9-478e-ae13-7bb1c0303406.png) + +So basically there is a power transformation between an addition of 3 and 4 to 7 in to their multiplication in to 12 where this 7 will be treated as one of their member. + +``` + #8 |----------- 5® --------|------------ 7® --------------| + | 1 |---------------- 77 = 4² + 5² + 6² -------------| +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77 +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + user| 7 | - | - | - | - | 7 | 8 | - | - | 8 | 8 | 3 | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78 + main| - | 9 | 7 | 9 | 6 | - | - | 8 | 5 | - | - | - | +-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ + Δ | Δ | Δ | Δ + Φ17|Φ29 | 96-99| 200 + |--- A,T,G,C ---| | └── 30 + Δ 2x2 = 4x |------- 2x3 = 6x -------| └── 70 + {98} | └── 100 +``` + +Therefore the 12 will consist of 11 groups runner and 1 profile of the transformation result. Follow to the prime hexagon we collect them in [19 gists](https://gist.github.com/mine) as below. + +``` +$ gh api -H "${HEADER}" /users/eq19/gists --jq 'sort_by(.created_at)|.[].url' + +https://api.github.com/gists/c9bdc2bbe55f2d162535023c8d321831 19 grammar 36 +https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 syntax +https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 parser +https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 lexer +https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 feed +https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 maps +https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 io 30 + -------- +https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77 +https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10 +https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9 +https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8 +https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7 +https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6 +https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5 +https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4 +https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3 +https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2 +https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1 +https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37 +``` + +Since 19 is thouching the first node then the workflow will be proceeded as bilateral way + +``` +https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77 +https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10 +https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9 +https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8 +https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7 +https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6 +https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5 +https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4 +https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3 +https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2 +https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1 +https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37 +12 months (moon) +-------- bilateral 9 sums +7 days (sun) +https://api.github.com/gists/c9bdc2bbe55f2d162535023c8d321831 19 grammar 36 +https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 syntax +https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 parser +https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 lexer +https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 feed +https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 maps +https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 io 30 +``` + +Here we can see that the transformation from 7 to 12 is actualy started from the prime 13. So the power of 7 is transfered to 77 by the prime pair 11 and 13. + +![image](https://user-images.githubusercontent.com/8466209/253148763-4a982982-4f70-4d7d-b524-51b72c6f17e9.png) + +The nodes is from converted from 7 to 77 whivh is 7 times 11. By the prime pair 11 and 13, the total nodes is involving 1 + 7 + 29 + 77 = 37 + 77 = 114 nodes + +``` + Δ1 + Δ7 + Δ29 → | Δ37 + Δ77 = Δ114 = Δ113 + Δ1 → + + | 1st (Form) | 2nd (Route) | 3rd (Channel) | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - | 100| - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - | 101| - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114| +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | + +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - | 102| -| - | - | - | +=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ + 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | +-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ + | Δ Δ Δ | Φ12 | Δ Δ | + -113 +150 = +37 +102 = +139 -113 -114 +``` + +As conclution the behaviour of this 7 is happen between the sequence of 30 and 36 while the 12 is happen between the sequence of 36 and 102. + +![default](https://user-images.githubusercontent.com/8466209/200024664-afc433a0-5f7f-4ec1-9bfc-77d672817fed.png) + +By observing more detail we spread the power of 7. + +*****168 + 329 + 289 - 619 - 30 - 30 - 5 = 786 - 619 - 65 = 102 = (2,60,40)***** diff --git a/identition/span7/gist04.html b/identition/span7/gist04.html new file mode 100644 index 00000000000..a478699d88a --- /dev/null +++ b/identition/span7/gist04.html @@ -0,0 +1,12 @@ + Why is 7 the most feared number? · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Why is 7 the most feared number?

            default

                     3               4                       6                              6
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                                    ↓                              ↓
+                                                 4 pairs                        4 pairs
+

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist04.md b/identition/span7/gist04.md new file mode 100644 index 00000000000..2fe4dd52054 --- /dev/null +++ b/identition/span7/gist04.md @@ -0,0 +1,23 @@ +## Why is 7 the most feared number? + +[![default](https://user-images.githubusercontent.com/8466209/199844359-3f898aad-0661-4ccb-9d90-1e2aadbdf662.png)](https://gist.github.com/eq19/88d09204b2e5986237bd66d062406fde#file-feeding-md) + +``` + 3 4 6 6 + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↓ + 4 pairs 4 pairs +``` + +[![default](https://user-images.githubusercontent.com/8466209/199874512-8d89c3b9-832c-48b7-91f3-e422bb2cc8bb.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-dockerfile-md) + +![default](https://user-images.githubusercontent.com/8466209/200098839-e77950cb-a21d-4103-acb6-02349fd7fdd8.png) + +[![default](https://user-images.githubusercontent.com/8466209/200098936-de751345-d67a-4783-b3a7-e0326ed56051.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md) diff --git a/identition/span7/gist05.html b/identition/span7/gist05.html new file mode 100644 index 00000000000..d3fcccb3c5a --- /dev/null +++ b/identition/span7/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist05.md b/identition/span7/gist05.md new file mode 100644 index 00000000000..378ea23b20f --- /dev/null +++ b/identition/span7/gist05.md @@ -0,0 +1,4 @@ +![default](https://user-images.githubusercontent.com/8466209/200098879-84208edb-d66b-4d46-bcfb-3889cf23801b.png) + +[![default](https://user-images.githubusercontent.com/8466209/200098961-f051223d-ea39-4f8a-a7ea-a26496da988b.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-logic-md) + diff --git a/identition/span7/gist06.html b/identition/span7/gist06.html new file mode 100644 index 00000000000..78264c3d930 --- /dev/null +++ b/identition/span7/gist06.html @@ -0,0 +1,20 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root         1 → 4 (5)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin         2 → 8 (10)
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin         5 → 7 (12)
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            default

            default

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist06.md b/identition/span7/gist06.md new file mode 100644 index 00000000000..f9cc6650e56 --- /dev/null +++ b/identition/span7/gist06.md @@ -0,0 +1,35 @@ +![default](https://user-images.githubusercontent.com/8466209/200699492-2ceabad2-17e9-4f8c-a87f-518a15119700.png) + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root 1 → 4 (5) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin 2 → 8 (10) + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin 5 → 7 (12) + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + Δ Δ + 12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1 +``` + +[![default](https://user-images.githubusercontent.com/8466209/200107646-e12803d2-f71d-46d4-a408-a3de05ecd627.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-opposite-md) + +![default](https://user-images.githubusercontent.com/8466209/200103953-a6ea55a1-bb07-48d8-9d92-40050acca532.png) + +![default](https://user-images.githubusercontent.com/8466209/200103981-7a0d9e10-8523-4dc6-89e0-5a340b70acbe.png) + +![default](https://user-images.githubusercontent.com/8466209/200100113-9642fff1-8cbf-4fac-8aab-d11f7dc43f4f.png) + +![default](https://user-images.githubusercontent.com/8466209/200100230-92467b4d-a88f-4cee-ac81-cd32e6e5099b.png) + +![default](https://user-images.githubusercontent.com/8466209/200102363-1b1cc49a-1320-454b-a857-9c25956acdcf.png) diff --git a/identition/span7/gist07.html b/identition/span7/gist07.html new file mode 100644 index 00000000000..544efd916f4 --- /dev/null +++ b/identition/span7/gist07.html @@ -0,0 +1 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist07.md b/identition/span7/gist07.md new file mode 100644 index 00000000000..0b88d60977f --- /dev/null +++ b/identition/span7/gist07.md @@ -0,0 +1,5 @@ +[![default](https://user-images.githubusercontent.com/8466209/200121103-538c687c-0748-4e81-b40b-2de82fa3a305.png)](https://stackoverflow.com/a/59952803/4058484) + +[![default](https://user-images.githubusercontent.com/8466209/200120900-ad4b3617-3f7f-465c-a741-2c95dbaa8ca7.png)](https://www.tensorflow.org/install/source_windows) + +[![default](https://user-images.githubusercontent.com/8466209/200121011-d320bf1f-93b7-42b5-9894-f6939e5948e5.png)](https://developer.nvidia.com/cuda-10.1-download-archive-base) diff --git a/identition/span7/gist08.html b/identition/span7/gist08.html new file mode 100644 index 00000000000..3a206b72640 --- /dev/null +++ b/identition/span7/gist08.html @@ -0,0 +1,46 @@ + gist08.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 | {1} |{56}
+---+-----+-----
+ 2 | 57  |{71}
+---+-----+-----
+ 3 | 72  | 85
+---+-----+-----
+ 4 |{86} |{89}
+---+-----+-----
+ 5 | 90  | 94
+---+-----+-----
+ 6 | 95  | 102
+---+-----+-----
+ 7 | 103 |{171}
+---+-----+-----
+ 8 | 172 | 206
+---+-----+-----
+
            import pandas as pd
+import numpy as np
+
+# Make numpy values easier to read.
+np.set_printoptions(precision=3, suppress=True)
+
+import tensorflow as tf
+from tensorflow.keras import layers
+
+abalone_train = pd.read_csv(
+    "https://storage.googleapis.com/download.tensorflow.org/data/abalone_train.csv",
+    names=["Length", "Diameter", "Height", "Whole weight", "Shucked weight",
+           "Viscera weight", "Shell weight", "Age"])
+
+abalone_train.head()
+abalone_features = abalone_train.copy()
+abalone_labels = abalone_features.pop('Age')
+abalone_features = np.array(abalone_features)
+abalone_features
+
+abalone_model = tf.keras.Sequential([
+  layers.Dense(64),
+  layers.Dense(1)
+])
+
+abalone_model.compile(loss = tf.keras.losses.MeanSquaredError(),
+                      optimizer = tf.keras.optimizers.Adam())
+abalone_model.fit(abalone_features, abalone_labels, epochs=10)
+

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span7/gist08.md b/identition/span7/gist08.md new file mode 100644 index 00000000000..2dab6f6182b --- /dev/null +++ b/identition/span7/gist08.md @@ -0,0 +1,54 @@ +``` +---+-----+----- + 1 | {1} |{56} +---+-----+----- + 2 | 57 |{71} +---+-----+----- + 3 | 72 | 85 +---+-----+----- + 4 |{86} |{89} +---+-----+----- + 5 | 90 | 94 +---+-----+----- + 6 | 95 | 102 +---+-----+----- + 7 | 103 |{171} +---+-----+----- + 8 | 172 | 206 +---+-----+----- +``` + +``` +import pandas as pd +import numpy as np + +# Make numpy values easier to read. +np.set_printoptions(precision=3, suppress=True) + +import tensorflow as tf +from tensorflow.keras import layers + +abalone_train = pd.read_csv( + "https://storage.googleapis.com/download.tensorflow.org/data/abalone_train.csv", + names=["Length", "Diameter", "Height", "Whole weight", "Shucked weight", + "Viscera weight", "Shell weight", "Age"]) + +abalone_train.head() +abalone_features = abalone_train.copy() +abalone_labels = abalone_features.pop('Age') +abalone_features = np.array(abalone_features) +abalone_features + +abalone_model = tf.keras.Sequential([ + layers.Dense(64), + layers.Dense(1) +]) + +abalone_model.compile(loss = tf.keras.losses.MeanSquaredError(), + optimizer = tf.keras.optimizers.Adam()) +abalone_model.fit(abalone_features, abalone_labels, epochs=10) +``` + +[![default](https://user-images.githubusercontent.com/8466209/200127121-3ead6276-c908-495d-9ddf-9c858258f8f8.png)](https://colab.research.google.com/github/tensorflow/docs/blob/master/site/en/tutorials/load_data/csv.ipynb#scrollTo=uZdpCD92SN3Z) + +[![default](https://user-images.githubusercontent.com/8466209/200127760-db1529e5-d019-46c3-a283-1fe8119d2fc8.png)](https://archive.ics.uci.edu/ml/datasets/abalone) diff --git a/identition/span7/index.html b/identition/span7/index.html new file mode 100644 index 00000000000..6855b251123 --- /dev/null +++ b/identition/span7/index.html @@ -0,0 +1,37 @@ + Elementary Particles (span 7) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Elementary Particles (span 7)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-33 of orgs section-5 that is inherited from the spin section-7 by prime spin-48 and span-147 with the partitions as below.

            +
            +
            1. gist02.md
            2. gist06.md
            3. gist05.md
            4. Why is 7 the most feared number?
            5. gist07.md
            6. gist03.md
            7. gist08.md
            8. Double strands

            1155 / 5 = 286 - 55 = 200 + 31 = 231

            layer|  i    |   f
+-----+-------+------
+     | 1,2:1 | (2,3)
+  1  +-------+
+     | 3:2   | (7)
+-----+-------+------
+     | 4,6:3 | (10,11,12)  <--- 231 (3x)
+  2  +-------+
+     |{7}:4  |({13})
+-----+-------+------
+     | 8,9:5 | (14,{15})   <--- 231 (2x)
+  3  +-------+
+     | 10:6  | (19)
+-----+-------+------
+

            We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N/n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape (arXiv:2010.16383v4).

            Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series

            Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as Montgomery conjecture of the nontrivial zeros of the zeta function. Means it also depends on Riemann hypotesis which is still in a major issue. Similar case left science today many unsolved problems that associated with.

            Eigenvectors_of_a_linear_operator

            In order to propagate through space and interact we shall attemp it using string theory One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become irrational partitions.

            In turns out that quantum string theory always destroys the symmetries of the classical string theory, except in one special case: when the number of dimensions is 10. That's why string theory works only in 10 dimensions (Physicsforums).

            default

            True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|------------------------- Skema-12 ------------------------|
+|------------ 6¤ -------------|------------- 6¤ ------------|
+|--------------------------- 192 ---------------------------|
+|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
++----+----+----+----+----+----+----+----+----+----+----+----+
+|---------  5¤  ---------|---- {48} ----|----- {48} ---|{43}|
+|---------  5¤  ---------|------------ {96} -----------|{43}|
+|--------- {53} ---------|-------------- {139} -------------|
+|------- Skema-23 -------|------------- Skema-34 -----------|    
+

            default

            This 23 units will form Scheme-23 as two (2) long strands which is known as doble helix Here we call them as Scheme-23 (71) and Scheme-23 (68). These strands are originated by the three (3) layers of True Prime Pairs.

            Scheme-139

            default

            default

            default

            Since the arithmetic mean of those primes yields 157 then the existence of 114 will remain to let this 18+19=37th prime number stands as the balanced prime.

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist01.html b/identition/span8/gist01.html new file mode 100644 index 00000000000..a99e5ed8f87 --- /dev/null +++ b/identition/span8/gist01.html @@ -0,0 +1 @@ + Seven Ate Nine (7, ‘8’, 9) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Seven Ate Nine (7, ‘8', 9)

            default

            This is a polar plot of the first 20 non-trivial Riemann zeta function zeros (including Gram points along the critical line {\displaystyle \zeta (1/2+it)}{\displaystyle \zeta (1/2+it)} for real values of {\displaystyle t}t running from 0 to 50. The consecutive zeros have 50 red plot points between each with zeros identified by magenta concentric rings (scaled to show the relative distance between their values of t) Source: Wikipedia

            default

            The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems. Source: Wikipedia

            default

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist02.html b/identition/span8/gist02.html new file mode 100644 index 00000000000..ae53e8a8d3a --- /dev/null +++ b/identition/span8/gist02.html @@ -0,0 +1 @@ + gist02.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist02.md b/identition/span8/gist02.md new file mode 100644 index 00000000000..fa59e1667f3 --- /dev/null +++ b/identition/span8/gist02.md @@ -0,0 +1,3 @@ +[![default](https://user-images.githubusercontent.com/8466209/200241752-e70d2eeb-5885-4f99-9362-4a05aeeb4435.png)](https://dev.to/thomasaudo/get-started-with-github-grapql-api--1g8b) + +![default](https://user-images.githubusercontent.com/8466209/200250136-7fe7a768-08a5-4bfb-ad19-c2a93cda363b.png) diff --git a/identition/span8/gist03.html b/identition/span8/gist03.html new file mode 100644 index 00000000000..2987d8c3c8e --- /dev/null +++ b/identition/span8/gist03.html @@ -0,0 +1,18 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            FROM tensorflow/tensorflow:latest-gpu
+
+LABEL version=v1.0.9
+
+ENV DEBCONF_NOWARNINGS="yes"
+ARG DEBIAN_FRONTEND=noninteractive
+
+ENV NVIDIA_VISIBLE_DEVICES all
+ENV NVIDIA_DRIVER_CAPABILITIES compute,utility
+
+RUN apt-get update &>/dev/null
+RUN apt-get install python3.8-venv &>/dev/null
+RUN /usr/bin/python3.8 -m venv /maps &>/dev/null
+
+ADD . /maps
+ENTRYPOINT ["/maps/entrypoint.sh"]
+
+

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist03.md b/identition/span8/gist03.md new file mode 100644 index 00000000000..3d74fec5e8f --- /dev/null +++ b/identition/span8/gist03.md @@ -0,0 +1,24 @@ +``` +FROM tensorflow/tensorflow:latest-gpu + +LABEL version=v1.0.9 + +ENV DEBCONF_NOWARNINGS="yes" +ARG DEBIAN_FRONTEND=noninteractive + +ENV NVIDIA_VISIBLE_DEVICES all +ENV NVIDIA_DRIVER_CAPABILITIES compute,utility + +RUN apt-get update &>/dev/null +RUN apt-get install python3.8-venv &>/dev/null +RUN /usr/bin/python3.8 -m venv /maps &>/dev/null + +ADD . /maps +ENTRYPOINT ["/maps/entrypoint.sh"] + +``` + +[![default](https://user-images.githubusercontent.com/8466209/200241238-23d238be-9006-4ac8-b9e8-1daa48ab8d8f.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-6_pattern-md) + +[![default](https://user-images.githubusercontent.com/8466209/200240844-1e76f817-775a-4cc1-9998-20e71efcc4ee.png)](https://github.com/eq19/grammar/actions/runs/3405771627/jobs/5663983028) + diff --git a/identition/span8/gist04.html b/identition/span8/gist04.html new file mode 100644 index 00000000000..704dbf5abb1 --- /dev/null +++ b/identition/span8/gist04.html @@ -0,0 +1,30 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+=======================+====+====+====+====+====+====+====+====+====+=====
+                                           ↓
+                                           |
+                                           ↓                                          
+                            114-89=139-114=25=5x5
+                                | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         ↓
+                                |                             |                         |
+                                 ------------ 10 -------------                          | 
+                                                                                        | 
+                                                                                        | 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist04.md b/identition/span8/gist04.md new file mode 100644 index 00000000000..dd3c6f62af5 --- /dev/null +++ b/identition/span8/gist04.md @@ -0,0 +1,36 @@ +[![default](https://user-images.githubusercontent.com/8466209/200248298-9c3979fa-9aa2-4283-839d-6ab4e76a667f.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-5-replicate-md) + +``` +=======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th +=======================+====+====+====+====+====+====+====+====+====+===== + ↓ + | + ↓ + 114-89=139-114=25=5x5 + | + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ ↓ + | | | + ------------ 10 ------------- | + | + | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) + -----------------------+----+----+----+----+----+----+----+----+----+----- +``` + +[![default](https://user-images.githubusercontent.com/8466209/200247726-5fddd4ad-210b-436b-9f22-0b93be6d01b4.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-regenerate-md) + diff --git a/identition/span8/gist05.html b/identition/span8/gist05.html new file mode 100644 index 00000000000..27b2dda20e5 --- /dev/null +++ b/identition/span8/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist05.md b/identition/span8/gist05.md new file mode 100644 index 00000000000..beee923e92b --- /dev/null +++ b/identition/span8/gist05.md @@ -0,0 +1,3 @@ +[![default](https://user-images.githubusercontent.com/8466209/200239492-515b374f-6180-4df0-840c-2f10ab5ef07b.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-grammar-md) + +[![default](https://user-images.githubusercontent.com/8466209/200244306-f5e5a428-83b9-46bb-a4b1-c96367e278b2.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-grammar-md) diff --git a/identition/span8/gist06.html b/identition/span8/gist06.html new file mode 100644 index 00000000000..93439a6d23b --- /dev/null +++ b/identition/span8/gist06.html @@ -0,0 +1 @@ + How to select repos? · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            How to select repos?

            default

            default

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist06.md b/identition/span8/gist06.md new file mode 100644 index 00000000000..0db22a8de9f --- /dev/null +++ b/identition/span8/gist06.md @@ -0,0 +1,12 @@ +## How to select repos? +[![default](https://user-images.githubusercontent.com/8466209/200460413-0ff244c9-04b2-49f1-86cc-cd6955d5dc6a.png)](https://github.com/eq19/grammar) + +[![default](https://user-images.githubusercontent.com/8466209/200459104-d508754e-cbae-4d07-b0c9-3c339ea6e917.png)](https://www.eq19.com/grammar/) + +[![default](https://user-images.githubusercontent.com/8466209/200458239-51004392-df2f-4e29-8cf6-04a462068331.png)](https://github.com/eq19/grammar/actions) + +[![default](https://user-images.githubusercontent.com/8466209/200469800-6c46fee3-5ce8-4999-b414-0a771e3fc93c.png)](https://www.eq19.com/grammar/) + +[![default](https://user-images.githubusercontent.com/8466209/200475393-f3e42f0b-d291-4f17-93c4-9bec6e6943de.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#primes-platform) + +[![default](https://user-images.githubusercontent.com/8466209/200472044-dab44257-7c9a-4a91-82bb-c90cb7143e91.png)](https://gist.github.com/eq19/6e2fcc2138be6fb68839a3ede32f0525) diff --git a/identition/span8/gist07.html b/identition/span8/gist07.html new file mode 100644 index 00000000000..7228ac26d79 --- /dev/null +++ b/identition/span8/gist07.html @@ -0,0 +1,18 @@ + gist07.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 |  1  |  4
+---+-----+-----
+ 2 |  5  | 14
+---+-----+-----
+ 3 | 15  | 26
+---+-----+-----
+ 4 | 27  | 40
+---+-----+-----
+ 5 | 41  |{47}
+---+-----+-----
+ 6 | 48  | 54
+---+-----+-----
+ 7 | 55  |{71}
+---+-----+-----
+ 8 | 72  | 75
+---+-----+-----
+

            default

            default

            The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the ‘non-obvious' zeros of the zeta function are complex numbers with real part 1/2 (Clay Institute).

            Riemann Hypothesis

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span8/gist07.md b/identition/span8/gist07.md new file mode 100644 index 00000000000..41f8c0c8247 --- /dev/null +++ b/identition/span8/gist07.md @@ -0,0 +1,27 @@ +``` +---+-----+----- + 1 | 1 | 4 +---+-----+----- + 2 | 5 | 14 +---+-----+----- + 3 | 15 | 26 +---+-----+----- + 4 | 27 | 40 +---+-----+----- + 5 | 41 |{47} +---+-----+----- + 6 | 48 | 54 +---+-----+----- + 7 | 55 |{71} +---+-----+----- + 8 | 72 | 75 +---+-----+----- +``` + +[![default](https://user-images.githubusercontent.com/8466209/200224482-708a56dc-196e-4f13-865b-07585322a6b8.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-8_spinning-md) + +[![default](https://user-images.githubusercontent.com/8466209/200468834-b2000e6d-0447-4948-b24d-086747d9b905.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-tensor-md) + +>The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2 _([Clay Institute](https://www.claymath.org/millennium-problems))_. + +[![Riemann Hypothesis](https://user-images.githubusercontent.com/8466209/218374273-729fee09-5480-4fb3-a3a6-0dc050bdbe26.png)](https://www.claymath.org/millennium-problems/riemann-hypothesis) \ No newline at end of file diff --git a/identition/span8/index.html b/identition/span8/index.html new file mode 100644 index 00000000000..9761a690b86 --- /dev/null +++ b/identition/span8/index.html @@ -0,0 +1,82 @@ + Fundamental Forces (span 8) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Fundamental Forces (span 8)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-32 of orgs section-4 that is inherited from the spin section-8 by prime spin-44 and span-147 with the partitions as below.

            +
            +
            1. gist03.md
            2. gist07.md
            3. How to select repos?
            4. gist02.md
            5. gist05.md
            6. gist04.md
            7. Seven Ate Nine (7, ‘8', 9)

            In many ways, a black hole acts like an ideal black body, as it reflects no light. Here is an animated simulation of a Schwarzschild black hole with a galaxy passing behind. Around the time of alignment, extreme gravitational lensing of the galaxy is observed.

            black hole

                            largest part=21 → 11+13+12=36 →  MEC30
+                        ↓                      |
+---+-----+-----+-----+-----+                   ↓
+ 1 | 19  | 1   | 20  | 21  |-------------------|-----
+---+-----+-----+-----+-----+                   ↓     |
+ 2 | 18  | 21  | 39  | 60  |-------------------      |
+---+-----+-----+-----+-----+                   |     |
+ 3 |{63} | 40  | 103 | 143 |-------------      |     |
+---+-----+-----+-----+-----+             |     |     |
+ 4 | 37  | 104 | 141 | 245 |-------      |     |     |
+---+-----+-----+-----+-----+       |     |     |     |
+ 5 | 10* | 142 | 152 | 294 |- 11** | 13  | 12  | 12  | 18
+---+-----+-----+-----+-----+       |     |     |     |
+ 6 | 24  | 153 | 177 | 332 |-------      |     |     |
+---+-----+-----+-----+-----+             |     |     |
+ 7 | 75  | 178 | 253 | 431 |-------------      |     |
+---+-----+-----+-----+-----+                   |     |
+ 8 | 30  | 254 | 284 | 538 |-------------------      |
+---+-----+-----+-----+-----+                   ↓     |
+ 9 | 1   | 285 | 286 | 571 |-------------------|-----
+===+=====+=====+=====+=====+                   ↓
+45 | 277 |                      ← 11+13+12=36 ←  MEC30
+---+-----+                                     |
+ ↑
+Note:
+10* stands as the central rank
+11** stands as the central parts
+

            According to the observations made by NASA, Astronomers have uncovered TON 618 as the record breaking supermassive black hole, weighing 66 trillion and brilliantly as 140 trillion times that of the Sun, making it one of the brightest object in the Universe.

            default

            If the statement that it is indeed located at the center of our universe then the said black hole would behave as the exchange position between twin (2) universes. This would for sure strengthen the syntax algorithm of our implementation.

            7 x 11 = 77 = 99 - 22 = 11 x (9 -2)

              #8  |------- 5® --------|------------ 7® --------------|
+      | 1 |-------------- 77 = 4² + 5² + 6² -------------|
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ repo |{1}|{2}| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+ user | 7 | - | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+------+---|---+---+---+---+---+---+---+---+----+----+----+ 7,78
+ main | - | 9 | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+------+---|---+---+---+---+---+---+---+---+----+----+----+
+        Δ | Δ             |                      Δ  |   Δ
+       Φ17|Φ29            |                    96-99|  100 - 123 ({24})
+          |--- A,T,G,C ---|                         |  └── 100 - 103 (4x) » 100
+          Δ    2x2 = 4x   |-------  2x3 = 6x -------|  └── 104 - 109 (6x) » 30
+         {98}                                       |  └── 110 - 123 (14x)» 70
+
+
            Direction:
+- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.
+- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.
+- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.
+ 
+Conclution:
+- All of the other primes than 2 is 1 less than the number n times the number of 2. 
+- Those Mersenne primes is generated as 1 less than the power n of the number of 2. 
+- Thus they will conseqently be carried out by the same scheme of this number of 2.
+

            Perceptually, everything is separate and finite. But actually, everything is connected and infinite. It is this infinite connection, despite our limited finite perceptions, that makes us one with the cosmos.

            Primes Platform

            +
            + + Note +
            +
            +

            This progression 41,43,47,53,61,71,83,97,113,131 whose general term is 41+x+xx, is as much remarkable since the 40 first terms are all prime numbers (Euler’s letter to Bernoulli).

            +
            + 
            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave the same as 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

            default

            I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.

            That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated.

            Truncate to Determine Integer Values

            default

            runner

            Everything is linked

            The ζ(s) will behave as the other universe (not the twin) which was initiated paralelly by a big bang. While this parts are relativity young. it will continue to grow as a four-vector. So it will need a gap between each identities to proceed the thing.

            Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed (Wikipedia)

            Infinite number

            By our universe it could be represented by the central black hole which is very strong to throw away every objects but it has no resistance against any exchange from the other universe.

            In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle (Wikipedia).

            the central black hole_

            So by the ζ(s) then our multiverse is belong to a group of multiple universes inside the lightest particle of a mass gap out of one of the like of them somewhere in an infinite number of another parallel universes.

            Prof Stephen Hawking's final research paper suggests that our Universe may be one of many similar (BBC News).

            everything is linked

            Another suggestion which has just yet been in a topic of the science is that the similar behaviour also happen by particles such as hydrogen which is throwing all of the waves out of the central. So hypothetically it suppose to have a populated infinite number of its own parallel universes because whatever a smallest thing is arised, they could only exist by the same law of physics,

            Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron (Wikipedia).

            the electron in a hydrogen

            Consider that this law of physics would exist everywhere. So it is also one of their law when the 1st sequence of the ten (10) digits of 0719425863 in Euler's number is zero (0). Thus theoretically it speaks if an existence of everything arose from nothingness.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist01.html b/identition/span9/gist01.html new file mode 100644 index 00000000000..fe148aee2b1 --- /dev/null +++ b/identition/span9/gist01.html @@ -0,0 +1,41 @@ + Lexer vs Parser · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Lexer vs Parser

            enneatruth_anim

            image

            Notice how the 3, 9, and 6 is in red and does not connect at the base. That is because it is a vector. The 1,2,4,8,7,5 is the third dimension while the oscillation between the 3 and 6 demonstrates the fourth dimension, which is the higher dimensional magnetic field of an electrical coil.

            image

            The 3, 9, and 6 always occur together with the 9 as the control. In fact, the Yin/Yang is not a duality but rather a trinary. This is because the 3 and 6 represent each side of the Yin/Yang and the 9 is the "S" curve between them. Everything is based on thirds. We think that the universe is based on dualities because we see the effects not the cause.

            Four (4) Vector

            !

            Φ(11,13) = (114 - 10²) + 13 = 27

            1729 = 7 x 13 x 19
+1729 / 7 = 13 x 19 = 247
+
+1729 = 7 x 13 x 19
+       7 + 13 = 20 = d(2)
+                     └──  2 x 19 = 38
+
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+| {1}|  2 |  3 |  4 |  5 | {6}| {7}|  8 |  9 | 10 | 11 | 12 | 13 | 14 |
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+| {3}| {4}|  3 |  4 |  5 |  2 |  3 |  2 |  2 |  1 |  2 |  5 |  1 |  1 |{38}
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285
+|  3 |  8 |  9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|-- 38 ---|              |-- 33 ---|                        |-- {27}--|
+

            Four Spacetime Dimensions

            ------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            RiemannZeta_Zeros

            Riemann Zeta

            With the above description then the instance configuration is via matrix integration from tensorflow which is placed at the end position to the turning point 100 vs 50 to the format (2,3) i.e. at id: 68.

            π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66

            default

            30 + (5+13) + (7+11) + (17+19) = 30 + 18 + 18 + 36 = 30 + 36 + 36 = 102 = 2 + 100

            default

            With the above description, of course, you can guess where the next direction will be. That is from one (1) unit of DNA to one (1) unit of whole unity. That's why we need a solution of the remaining six (6) other cases to be placed with id: 11, 12, 14, 15, 26 and 28 so that id: 68 is congrued to the number two (2).

            docker-github-runner

            Therefore the five (5) identities of (10, 11,12,14,15) are twisted prior joining the two (2) identities of (26,28). Since each of these seven (7) identities is linked by the eleven (11) objects then they turn to a strong seven (77). Lets's discuss them one by one.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist02.html b/identition/span9/gist02.html new file mode 100644 index 00000000000..6cd4ff0f8d4 --- /dev/null +++ b/identition/span9/gist02.html @@ -0,0 +1,84 @@ + The Bilateral 9 Sums · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Bilateral 9 Sums

            Root 4x
+29
+ └── 30
+      └── 31
+           └── 32
+    
+Rewrite Root 4x → Twin 4x
+
+Root 4x
+29
+ └── 30
+      └── 31
+           └── 32
+    
+Twin 4x
+33
+ └── 34
+      └── 35
+           └── 36
+
+  -----------------------+----+----+----+----+
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 | 
+  =======================+====+====+====+====+
+   19 → π(10)            |  2 |  3 |  5 |  7 | 4 x Root
+  -----------------------+----+----+----+----+
+   17 → π(20)            | 11 | 13 | 17 | 19 | 4 x Twin
+  -----------------------+----+----+----+----+
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - | ← Rewrite here
+  =======================+====+====+====+====+
+
            # Sample workflow for building and deploying a Jekyll site to GitHub Pages
+name: Build and deploy Jekyll site to GitHub Pages
+
+on:
+  # 💎 Runs on pushes targeting the default branch
+  push:
+    branches:
+      - eQ19
+      - Chetabahana
+
+  # Allows you to run this workflow manually from the Actions tab
+  workflow_dispatch:
+
+# Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages
+permissions: write-all
+
              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ←------------ Rewrite here
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+

            Recombimation

            default

              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+=====  ←-- Rewrite here (bilateral 9 sums)
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+
            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist02.md b/identition/span9/gist02.md new file mode 100644 index 00000000000..a2979516cc0 --- /dev/null +++ b/identition/span9/gist02.md @@ -0,0 +1,100 @@ +## The Bilateral 9 Sums + + +``` +Root 4x +29 + └── 30 + └── 31 + └── 32 + +Rewrite Root 4x → Twin 4x + +Root 4x +29 + └── 30 + └── 31 + └── 32 + +Twin 4x +33 + └── 34 + └── 35 + └── 36 + + -----------------------+----+----+----+----+ + True Prime Pairs Δ | 1 | 2 | 3 | 4 | + =======================+====+====+====+====+ + 19 → π(10) | 2 | 3 | 5 | 7 | 4 x Root + -----------------------+----+----+----+----+ + 17 → π(20) | 11 | 13 | 17 | 19 | 4 x Twin + -----------------------+----+----+----+----+ + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | ← Rewrite here + =======================+====+====+====+====+ +``` + +``` +# Sample workflow for building and deploying a Jekyll site to GitHub Pages +name: Build and deploy Jekyll site to GitHub Pages + +on: + # 💎 Runs on pushes targeting the default branch + push: + branches: + - eQ19 + - Chetabahana + + # Allows you to run this workflow manually from the Actions tab + workflow_dispatch: + +# Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages +permissions: write-all +``` + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10 + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ←------------ Rewrite here + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin +``` +## Recombimation +[![default](https://user-images.githubusercontent.com/8466209/200229388-03811f48-2492-4845-b15f-85259cd93717.png)](https://www.primesdemystified.com/#primingthesquares) + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th ←------------ 10 + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + =======================+====+====+====+====+====+====+====+====+====+===== ←-- Rewrite here (bilateral 9 sums) + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30 + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th ←------------ 20 + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th +``` + diff --git a/identition/span9/gist03.html b/identition/span9/gist03.html new file mode 100644 index 00000000000..60489e462e9 --- /dev/null +++ b/identition/span9/gist03.html @@ -0,0 +1,48 @@ + gist03.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Because "Ate Nine" (89)

            default

            11_89_109_7919_8128

            =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+                                           ↓
+                                           |
+                                           ↓                                          
+                            114-89=139-114=25=5x5
+                                | 
+                                |                              ----------- 5 -----------
+                                |                             |                         |  
+                                ↓                             ↑                         ↓
+ |   mapping    |     feeding     |  lexering    |  parsering   |   syntaxing   |  grammaring  |
+ |------------- 36' --------------|----------------------------36' ----------------------------|
+ |     19'      |        17'      |      13'     |      11'     |       7'      |       5'     |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+ |  2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
+ +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+                                ↓                             ↑                         ↓
+                                |                             |                         |
+                                 ------------ 10 -------------                          | 
+                                                                                        | 
+                                                                                        | 
+   -----------------------+----+----+----+----+----+----+----+----+----+-----           |
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum             |
+  =======================+====+====+====+====+====+====+====+====+====+=====            ↓
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  ◄- 4 =  π(10)
+
              -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root         1 → 4 (5)
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin         2 → 8 (10)
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin         5 → 7 (12)
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+                                           |
+                                           ↓                
+

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist03.md b/identition/span9/gist03.md new file mode 100644 index 00000000000..742f60f57b9 --- /dev/null +++ b/identition/span9/gist03.md @@ -0,0 +1,65 @@ +Because "Ate Nine" (89) + +[![default](https://user-images.githubusercontent.com/8466209/200234332-efce4c04-5f83-4cae-893f-f895eae27647.png)](https://ell.stackexchange.com/questions/115903/why-is-7-the-most-feared-number) + +[![11_89_109_7919_8128](https://user-images.githubusercontent.com/8466209/200228344-9f344f49-3e5d-480f-b11c-6e30a20a8f44.jpg)](https://www.primesdemystified.com/First1000Primes.html) + +``` +=======================+====+====+====+====+====+====+====+====+====+===== 4th Twin + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + ↓ + | + ↓ + 114-89=139-114=25=5x5 + | + | ----------- 5 ----------- + | | | + ↓ ↑ ↓ + | mapping | feeding | lexering | parsering | syntaxing | grammaring | + |------------- 36' --------------|----------------------------36' ----------------------------| + | 19' | 17' | 13' | 11' | 7' | 5' | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + | 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 | + +----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+ + ↓ ↑ ↓ + | | | + ------------ 10 ------------- | + | + | + -----------------------+----+----+----+----+----+----+----+----+----+----- | + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum | + =======================+====+====+====+====+====+====+====+====+====+===== ↓ + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10) +``` + +``` + -----------------------+----+----+----+----+----+----+----+----+----+----- + True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum + =======================+====+====+====+====+====+====+====+====+====+===== + 19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root 1 → 4 (5) + -----------------------+----+----+----+----+----+----+----+----+----+----- + 17 → π(20) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin + -----------------------+----+----+----+----+----+----+----+----+----+----- + 13 → π(30) → 12 (Δ1) | 23 | 29 | - | - | - | - | - | - | - |10th + =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin 2 → 8 (10) + 11 → π(42) | 31 | 37 | 41 | - | - | - | - | - | - |13th + -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin + 7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th + -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin + 5 → π(72) → 18 (Δ13) | 61 | 67 | 71 | - | - | - | - | - | - |20th + =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin 5 → 7 (12) + 3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th + =======================+====+====+====+====+====+====+====+====+====+===== + | + ↓ +``` + +[![default](https://user-images.githubusercontent.com/8466209/200474984-d0d05783-787c-460b-a80f-3f26debc0c0d.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-feeding-md) + +[![default](https://user-images.githubusercontent.com/8466209/200225487-5e40102b-e8f9-4aa7-8a64-7529dfc14c7c.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-8_spinning-md) + +[![default](https://user-images.githubusercontent.com/8466209/200244306-f5e5a428-83b9-46bb-a4b1-c96367e278b2.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-feeding-md) + diff --git a/identition/span9/gist04.html b/identition/span9/gist04.html new file mode 100644 index 00000000000..d5c053e41b9 --- /dev/null +++ b/identition/span9/gist04.html @@ -0,0 +1 @@ + gist04.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist04.md b/identition/span9/gist04.md new file mode 100644 index 00000000000..889237d8224 --- /dev/null +++ b/identition/span9/gist04.md @@ -0,0 +1,9 @@ +[![default](https://user-images.githubusercontent.com/8466209/201015369-c6ba5c75-c2c7-415b-b424-debaa5c7f64a.png)](https://gist.github.com/eq19/6c89c3b0f109e0ead561a452720d1ebf#file-feeding-md) + +![default](https://user-images.githubusercontent.com/8466209/201012946-c1b10170-a14b-46aa-8c13-4646cf7cadb4.png) + +![default](https://user-images.githubusercontent.com/8466209/201013443-232335d2-af81-47eb-b93e-8005cb5fed56.png) + +![default](https://user-images.githubusercontent.com/8466209/201014411-83fc0bd6-96dc-40ad-9eca-0a56695df151.png) + +![default](https://user-images.githubusercontent.com/8466209/201014604-fd2d3b83-f243-4fc5-8032-ed984cb28002.png) diff --git a/identition/span9/gist05.html b/identition/span9/gist05.html new file mode 100644 index 00000000000..93071b36a3b --- /dev/null +++ b/identition/span9/gist05.html @@ -0,0 +1 @@ + gist05.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist05.md b/identition/span9/gist05.md new file mode 100644 index 00000000000..a95342f399b --- /dev/null +++ b/identition/span9/gist05.md @@ -0,0 +1,7 @@ +![default](https://user-images.githubusercontent.com/8466209/201009382-ca13eae0-6ae9-4512-aa40-8b8c4f2f276b.png) + +![default](https://user-images.githubusercontent.com/8466209/201010402-205363e4-af41-4b07-b501-22f6533a0210.png) + +![default](https://user-images.githubusercontent.com/8466209/201017831-469513ee-0e92-4b27-9b3d-cb00add66966.png) + +![default](https://user-images.githubusercontent.com/8466209/201019936-a8a19fe8-6a8a-4909-ae8d-063fafed564b.png) diff --git a/identition/span9/gist06.html b/identition/span9/gist06.html new file mode 100644 index 00000000000..9c887c4fab1 --- /dev/null +++ b/identition/span9/gist06.html @@ -0,0 +1,12 @@ + gist06.md · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum 
            ---+-----+-----
+ 1 |  1  |  28
+---+-----+-----
+ 2 |  29 |  37
+---+-----+-----
+ 3 | {38}| {48}
+---+-----+-----
+ 4 |  49 | 127
+---+-----+-----
+ 5 | 128 | 129
+---+-----+-----
+

            default

            default

            default

            default

            default

            default

            default

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist06.md b/identition/span9/gist06.md new file mode 100644 index 00000000000..30d5c1c8ca7 --- /dev/null +++ b/identition/span9/gist06.md @@ -0,0 +1,33 @@ +``` +---+-----+----- + 1 | 1 | 28 +---+-----+----- + 2 | 29 | 37 +---+-----+----- + 3 | {38}| {48} +---+-----+----- + 4 | 49 | 127 +---+-----+----- + 5 | 128 | 129 +---+-----+----- +``` + +![default](https://user-images.githubusercontent.com/8466209/201078012-9b1b1575-a598-4876-aeb4-aef6e8f6d957.png) + +![default](https://user-images.githubusercontent.com/8466209/201077251-993d5ce3-a131-41a9-9f7e-36cb6e5f3b14.png) + +![default](https://user-images.githubusercontent.com/8466209/201078741-00eab47a-7346-4403-a6b8-c0d52956891a.png) + +![default](https://user-images.githubusercontent.com/8466209/201080070-a8895143-3188-4372-ba40-6b0452f432dd.png) + +![default](https://user-images.githubusercontent.com/8466209/201080731-3b71a429-5ab0-4786-a965-4813d47a19ee.png) + +![default](https://user-images.githubusercontent.com/8466209/201081540-f39e3e47-fd2c-4199-ad54-8d65bd9423d9.png) + +![default](https://user-images.githubusercontent.com/8466209/201084190-f171aeb3-0464-427c-bb04-772fd7c01223.png) + +![default](https://user-images.githubusercontent.com/8466209/201085311-e840b515-1764-4d26-8b2d-794016969784.png) + +![default](https://user-images.githubusercontent.com/8466209/201086588-c03cd0e6-fae5-4a18-b491-a34a82b28bf6.png) + +![default](https://user-images.githubusercontent.com/8466209/200228973-fd99095b-aad2-4824-b3dc-d6b21fae38ea.png) diff --git a/identition/span9/gist07.html b/identition/span9/gist07.html new file mode 100644 index 00000000000..495d565a429 --- /dev/null +++ b/identition/span9/gist07.html @@ -0,0 +1,35 @@ + How to deal with cicular destination of 36? · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            How to deal with cicular destination of 36?

            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            default

                  |      |-----+-----+-----+                         |
+      |  4   |     |  11 |15,18|  29,30,31,32 ←---4x----    ←--- 35,34,33 are missing?
+      |      |  6  +-----+-----+
+      |      |     |  12 |  19 |  36  --------------------------------------
+------+------+-----+-----+-----+-------                                     |
+      |      |     |  13 |  20 | {38}                                       |
+      |      |  7  +-----+-----+                                            | 
+      |  5   |     |  14 |21,22| {40,41} = (19-17)x ----                    |
+      |      |-----+-----+-----+                         |                  |
+      |      |     |  15 |  23 | {42}                   6x + 13x = 19x      |
+  3   +------+  8  +-----+-----+                         |                  |
+      |      |     |  16 |24,27| {43,44,45,46} ←- 4x --                     |
+      |      |-----+-----+-----+                                            |
+      |  6   |     |  17 |  28 | {50} = 46 + 4                              |
+      |      |  9  +-----+-----+                                            |
+      |      |     |  18 |  29 | {68} = 32 + 36  ←- they meet here ---------
+------|------|-----+-----+------
+

            default

            default

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/identition/span9/gist07.md b/identition/span9/gist07.md new file mode 100644 index 00000000000..e9d60d01ef3 --- /dev/null +++ b/identition/span9/gist07.md @@ -0,0 +1,48 @@ +## How to deal with cicular destination of 36? + +``` +$True Prime Pairs: + (5,7), (11,13), (17,19) + + layer| i | f + -----+-----+--------- + | 1 | 5 + 1 +-----+ + | 2 | 7 + -----+-----+--- } 36 » 6® + | 3 | 11 + 2 +-----+ + | 4 | 13 + -----+-----+--------- + | 5 | 17 + 3 +-----+ } 36 » 6® + | 6 | 19 + -----+-----+--------- +``` +![default](https://user-images.githubusercontent.com/8466209/201023835-b641450d-827b-4362-8a63-8520edb50ece.png) + +``` + | |-----+-----+-----+ | + | 4 | | 11 |15,18| 29,30,31,32 ←---4x---- ←--- 35,34,33 are missing? + | | 6 +-----+-----+ + | | | 12 | 19 | 36 -------------------------------------- +------+------+-----+-----+-----+------- | + | | | 13 | 20 | {38} | + | | 7 +-----+-----+ | + | 5 | | 14 |21,22| {40,41} = (19-17)x ---- | + | |-----+-----+-----+ | | + | | | 15 | 23 | {42} 6x + 13x = 19x | + 3 +------+ 8 +-----+-----+ | | + | | | 16 |24,27| {43,44,45,46} ←- 4x -- | + | |-----+-----+-----+ | + | 6 | | 17 | 28 | {50} = 46 + 4 | + | | 9 +-----+-----+ | + | | | 18 | 29 | {68} = 32 + 36 ←- they meet here --------- +------|------|-----+-----+------ +``` + +[![default](https://user-images.githubusercontent.com/8466209/201008595-9917fb26-bfea-46e6-b0e1-32db79a12e98.png)](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-runner-md) + +![default](https://user-images.githubusercontent.com/8466209/201008977-b10573d2-b295-440d-82fe-c707474694ce.png) + +![default](https://user-images.githubusercontent.com/8466209/201009190-a8d4dac6-5331-46c5-a704-1e02113f6e6d.png) diff --git a/identition/span9/index.html b/identition/span9/index.html new file mode 100644 index 00000000000..bc25cd03e77 --- /dev/null +++ b/identition/span9/index.html @@ -0,0 +1,9 @@ + Quadratic Polynomials (span 9) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Quadratic Polynomials (span 9)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-31 of orgs section-3 that is inherited from the spin section-9 by prime spin-42 and span-148 with the partitions as below.

            +
            +
            1. How to deal with cicular destination of 36?
            2. gist04.md
            3. gist05.md
            4. The Bilateral 9 Sums
            5. gist03.md
            6. gist06.md
            7. Lexer vs Parser

            default

            default

            default

            default

            default

            default

            default

            default

            default

            default

            default

            The exchange interaction is a quantum mechanical process that only happens between identical particles in chemistry and physics. The energy produced when two or more electrons with the same spin swap locations in a subshell's degenerate orbitals .

            default

            On the instinctual level, people may internally stress and externally express the need to protect themselves (self-preservation), to connect with important others or partners (sexual), or to get along or succeed in groups (social).

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 00000000000..d8c14e805e5 --- /dev/null +++ b/index.html @@ -0,0 +1,155 @@ + eQuantum · Mapping the quantum way across prime identity
            eQuantum
            Mapping the quantum way
            eQuantum

            Prime Identity

            We are going to assign prime identity as a standard model that attempts to stimulate a quantum field model called eQuantum for the four (4) known fundamental forces.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-0 of zone section-0 that is inherited from the zone section-0 by prime spin- and span- with the partitions as below.

            +
            +
            1. Addition Zones (0-18)
            2. Multiplication Zones (18-30)
            3. Exponentiation Zones (30-36)
              1. Electrodynamics (maps)
              2. Quantum Gravity (feed)
              3. Chromodynamics (lexer)
              4. Electroweak Theory (parser)
              5. Grand Unified Theory (syntax)
            4. Identition Zones (36-102)
              1. Theory of Everything (span 12)
              2. Everything is Connected (span 11)
              3. Truncated Perturbation (span 10)
              4. Quadratic Polynomials (span 9)
              5. Fundamental Forces (span 8)
              6. Elementary Particles (span 7)
              7. Basic Transformation (span 6)
              8. Hidden Dimensions (span 5)
              9. Parallel Universes (span 4)
              10. Vibrating Strings (span 3)
              11. Series Expansion (span 2)
              12. Wormhole Theory (span 1)

            This presentation was inspired by theoretical works from Hideki Yukawa who in 1935 had predicted the existence of mesons as the carrier particles of strong nuclear force.

            Addition Zones

            Here we would like to recompile the way we take on getting the arithmetic expresion of an individual unit expression (identity) such as a taxicab number below.

            +
            + + Note +
            +
            +

            It is a taxicab number, and is variously known as Ramanujan’s number and the Ramanujan-Hardy number, after an anecdote of the British mathematician GH Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital (Wikipedia).

            +
            +

            Ramanujan-Hardy number

            These three (3) number are twin primes. We called the pairs as True Prime Pairs. Our scenario is mapping the distribution out of these pairs by taking the symmetrical behaviour of 36 as the smallest power (greater than 1) which is not a prime power.

            +
            + + Tip +
            +
            +

            The smallest square number expressible as the sum of four (4) consecutive primes in two ways (5 + 7 + 11 + 13 and 17 + 19) which are also two (2) couples of prime twins! (Prime Curios!).

            +
            + 
            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

            Thus in short this is all about the method that we called as the 19 vs 18 Scenario of mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

            Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f
+------+------+-----+----------
+      |      |     |  1  | 
+      |      |  1  +-----+          
+      |  1   |     |  2  | (5)
+      |      |-----+-----+
+      |      |     |  3  |
+  1   +------+  2  +-----+----
+      |      |     |  4  |
+      |      +-----+-----+
+      |  2   |     |  5  | (7)
+      |      |  3  +-----+
+      |      |     |  6  |
+------+------+-----+-----+------      } (36)
+      |      |     |  7  |
+      |      |  4  +-----+
+      |  3   |     |  8  | (11)
+      |      +-----+-----+
+      |      |     |  9  |
+  2   +------|  5  +-----+-----
+      |      |     |  10 |
+      |      |-----+-----+
+      |  4   |     |  11 | (13)
+      |      |  6  +-----+
+      |      |     |  12 |
+------+------+-----+-----+------------------
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17)
+      |      |-----+-----+
+      |      |     |  15 |
+  3   +------+  8  +-----+-----       } (36)
+      |      |     |  16 |
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+      |      |     |  18 |
+------|------|-----+-----+------
+

            The main background is that, as you may aware, the prime number theorem describes the asymptotic distribution of prime numbers which is still a major problem in mathematic.

            Multiplication Zones

            Instead of a proved formula we came to a unique expression called zeta function. This expression first appeared in a paper in 1737 entitled Variae observationes circa series infinitas.

            +
            + + Tip +
            +
            +

            This expression states that the sum of the zeta function is equal to the product of the reciprocal of one minus the reciprocal of primes to the powers. But what has this got to do with the primes? The answer is in the following product taken over the primes p (discovered by Leonhard Euler):

            +
            +

            zeta function

            This issue is actually come from Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is considered to be the most important of unsolved problems in pure mathematics.

            +
            + + Note +
            +
            +

            In addition to the trivial roots, there also exist complex roots for real t. We find that the he first ten (10) non-trivial roots of the Riemann zeta function is occured when the values of t below 50. A plot of the values of ζ(1/2 + it) for t ranging from –50 to +50 is shown below. The roots occur each time the locus passes through the origin. (mathpages).

            +
            +

            trivial roots

            Meanwhile obtaining the non complex numbers it is easier to look at a graph like the one below which shows Li(x) (blue), R(x) (black), π(x) (red) and x/ln x (green); and then proclaim "R(x) is the best estimate of π(x)." Indeed it is for that range, but as we mentioned above, Li(x)-π(x) changes sign infinitely often, and near where it does, Li(x) would be the best value.

            non complex numbers

            And we can see in the same way that the function Li(x)-(1/2)Li(x1/2) is ‘on the average' a better approximation than Li(x) to π(x); but no importance can be attached to the latter terms in Riemann's formula even by repeated averaging.

            Exponentiation Zones

            The problem is that the contributions from the non-trivial zeros at times swamps that of any but the main terms in these expansions.

            +
            + + Warning +
            +
            +

            A. E. Ingham says it this way: Considerable importance was attached formerly to a function suggested by Riemann as an approximation to π(x)… This function represents π(x) with astonishing accuracy for all values of x for which π(x) has been calculated, but we now see that its superiority over Li(x) is illusory… and for special values of x (as large as we please) the one approximation will deviate as widely as the other from the true value (primes.utm.edu).

            +
            +

            howmany primes

            Moreover in it was verified numerically, in a rigorous way using interval arithmetic, that The Riemann hypothesis is true up to 3 · 10^12. That is, all zeroes β+iγ of the Riemann zeta-function with 0<γ≤3⋅1012 have β=1/2.

            +
            + + Danger +
            +
            +

            We have Λ ≤ 0.2. The next entry is conditional on taking H a little higher than 10*13, which of course, is not achieved by Theorem 1. This would enable one to prove Λ < 0.19. Given that our value of H falls between the entries in this table, it is possible that some extra decimals could be wrought out of the calculation. We have not pursued this (arXiv:2004.09765).

            +
            +

            functional equation

            This Euler formula represents the distribution of a group of numbers that are positioned at regular intervals on a straight line to each other. Riemann later extended the definition of zeta(s) to all complex numbers (except the simple pole at s=1 with residue one). Euler's product still holds if the real part of s is greater than one. Riemann derived the functional equation of zeta function.

            +
            + + Danger +
            +
            +

            The Riemann zeta function has the trivial zeros at -2, -4, -6, … (the poles of gamma(s/2)). Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 < Re(s) < 1, and that they are symmetric about the critical line Re(s)=1/2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line (primes.utm.edu).

            +
            +

            zeta function

            If both of the above statements are true then mathematically this Riemann Hypothesis is proven to be incorrect because it only applies to certain cases or limitations. So first of all the basis of the Riemann Hypothesis has to be considered.

            +
            + + Warning +
            +
            +

            The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the functional equations. (Riemann Zeta - pdf)

            +
            +

            Riemann hypothesis

            On the other hand, the possibility of obtaining the function of the distribution of prime numbers shall go backwards since it needs significant studies to be traced.

            Or may be start again from the Euleur Function.

            Identition Zones

            Freeman Dyson discovered an intriguing connection between quantum physics and Montgomery's pair correlation conjecture about the zeros of the zeta function which dealts with the distribution of primes.

            +
            + + Note +
            +
            +

            The Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. (Google Patent DE102011101032A9)

            +
            +

            The Mathematical Elementary Cell 30

            The path plan assume that a symmetric distribution of prime numbers with equal axial lengths from a middle zero axis = 15 is able to determine the distribution of primes in a given number space. This assumption finally bring us to the equation of Euler's identity.

            +
            + + Note +
            +
            +

            Euler’s identity is considered to be an exemplar of deep mathematical beauty as it shows a profound connection between the most fundamental numbers. Three (3) of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation (Wikipedia).

            +
            +

            Euler's identity

            The finiteness position of Euler's identity by the said MEC30 opens up the possibility of accurately representing the self-similarity based on the distribution of True Prime Pairs so that all number would belongs together with their own identitities.

            +
            + + Tip +
            +
            +

            See that there are multiple repetition from addition to multiplication which may lead up to the concept of 11th-dimension. This path is being applied as you can find on the left sidebar. (Please change the view to desktop mode if you are on mobile browser).

            +
            +

            DE102011101032A9.pdf

            Nothing is going to be easly about the nature of prime numbers but they demonstrably congruent to something organized. Let's discuss starting with the addition zones.

            eQuantum Project
            Copyright © 2023-2024

            Reference:

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/10.html b/multiplication/10.html new file mode 100644 index 00000000000..54f06638e35 --- /dev/null +++ b/multiplication/10.html @@ -0,0 +1,174 @@ + Symmetrical Breaking (spin 1) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Symmetrical Breaking (spin 1)

            In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-10 of gist section-6 that is inherited from the gist section-23 by prime spin- and span- with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

            Perfect Symmetry

            Rodin Coil

            images (3)

            $True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+
            +
            + + Note +
            +
            +

            124875 is a doubling circuit . By addition, all numbers reduce to the root number. The numbers all spiral around O, this spiral makes the 124875 doubling circuit and also correlates 369. 124875 is also a halving circuit. By addition every number will reduce to its own root number. (Vortex Math)

            +
            +

            Vortex Math

            vortex-space-background_445983-2550

            Spontaneous Symmetry breaking

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
++----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 |
++----+----+----+----+----+----+
+|------------ {72} -----------|
+|------------- 6¤ ------------|
+
+The Fermion Fields
+(19,17,i12), (11,19,i18), (18,12,i13)
+
++----+----+----+----+----+----+----+----+----+
+| 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+
+|---- {48} ----|---- {48} ----|---- {43} ----|
+|------------ {96} -----------|----- 3¤ -----|
+
            +
            + + Note +
            +
            +

            The pseudoscalar meson nonet. Members of the original meson “octet (8)” are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet (9), the Eightfold Way name derives from the patterns of eight for the mesons and baryons in the original classification scheme. (Wikipedia)

            +
            +

            8foldway svg

            For some Enneagram theorists the lines connecting the points add further meaning to the information provided by the descriptions of the types. Some times called the "security" and "stress" points, or points of "integration" and "disintegration".

            +
            + + Note +
            +
            +

            In geometry, an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon.[1]

            The word ‘enneagram’ combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆ (grammē) meaning a line.

            • A regular enneagram is a 9-sided star polygon. It is constructed using the same points as the regular enneagon, but the points are connected in fixed steps.
            • Two forms of regular enneagram exist:
              • One form connects every second point and is represented by the Schläfli symbol {9/2}.
              • The other form connects every fourth point and is represented by the Schläfli symbol {9/4}.
            • There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles.[3][4] (If the triangles are alternately interlaced, this results in a Brunnian link.)
            • From this perspective, there are twenty-seven (27) distinct personality patterns, because people of each of the nine (9) types also express themselves as one of the three (3) subtypes.

            This star figure is sometimes known as the star of Goliath, after {6/2} or 2{3}, the star of David.[5] (Wikipedia)

            +
            +

            The Seventh Enneagram

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+                         |---- {48} ----|---- {48} ----|---- {43} ----|
+                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|
+
            +
            + + Note +
            +
            +

            Vortex Based Mathematics transcends our myopic quantitative understanding for the way Number operates in our holographic universe. Numbers are not just mere quantities. Each has its own unique quality, archetype, and behavior. Vortex Based Math (VBM) is the study of Number in and of itself. Numeronomy as opposed to Numerology. The bedrock of the Quadrivium, Number structures our conceptual waking reality. As Pythagoras once so aptly put it, “All is Number”. (JoeDubs)

            +
            +

            Vortex Based Mathematics

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|--------------- 7¤ ---------------|👈
+|-------------- {89} --------------|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+                         |---- {48} ----|---- {48} ----|---- {43} ----|
+                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|👈
+
            +
            + + Note +
            +
            +

            The pattern of weak isospin T3, weak hypercharge YW, and color charge of all known elementary particles, rotated by the weak mixing angle to show electric charge Q, roughly along the vertical. The neutral Higgs field (gray square) breaks the electroweak symmetry and interacts with other particles to give them mass. (Wikipedia)

            +
            +

            SO(10)

            Rooting the biggest problems in physics

            +
            + + Note +
            +
            +

            Explanatory diagram showing how symmetry breaking works. At a high enough energy level, a ball settled in the center (lowest point), and the result has symmetry. At lower energy levels, the center becomes unstable, the ball rolls to a lower point - but in doing so, it settles on an (arbitrary) position and the result is that symmetry is broken - the resulting position is not symmetrical (Wikipedia)

            +
            +

            Spontaneous_symmetry_breaking_(explanatory_diagram)

            Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×10³⁴ years.

            Vortex vs String

            vortex-vs-spinor

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|👈
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+                         |---- {48} ----|---- {48} ----|---- {43} ----|👈
+                         |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|
+
            +
            + + Note +
            +
            +

            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

            +
            +

            SO(10)

            SU(5)_representation_of_fermions

            This eleven (11) will continue to be discussed on identition zone.

            2×96 = 192 = 5 + 7 + 11 + 13 + 17 + 19 +23 + 29 + 31 + 37 (10 consecutive primes)

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|-------------------------------- 2x96 -------------------------------|
+|--------------- 7¤ ---------------|------------ 7¤ ------------------|
+|-------------- {89} --------------|{12}|-- {30} -|-- {36} -|-- {25} -|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----|
+|---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|
+|-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
+      13 variations               48 variations          11 variations 
+
            +
            + + Note +
            +
            +

            Researchers at the U.S. Department of Energy’s Ames Laboratory have discovered a new type of Weyl semimetal, a material that opens the way for further study of Weyl fermions, a type of massless elementary particle hypothesized by high-energy particle theory and potentially useful for creating high-speed electronic circuits and quantum computers.

            • Researchers created a crystal of molybdenum and tellurium, one of only a few compounds that had been predicted to host a new and recently postulated type of Weyl state, where the hole and electron bands normally separated by an indirect gap touch at a few Weyl points. Those points are equivalent to magnetic monopoles in the momentum space and are connected by Fermi arcs.
            • A combination of angle resolved photoemission spectroscopy (ARPES), modelling, density functional theory and careful calculations were used to confirm the existence of this new type of Weyl semimetal. This material provides an exciting new platform to study the properties of Weyl fermions, and may lead the way to more new materials with unusual transport properties.

            “This an important, interdisciplinary discovery because it allows us to study many aspects of these exotic particles predicted by high energy physics theory in solid state, without need for extremely expensive particle accelerators,” said Adam Kaminsky, Ames Laboratory scientist and professor in the Department of Physics and Astronomy at Iowa State University. “From my perspective as solid state physicist it is absolutely extraordinary to observe two bands touching each other at certain points and being connected by Fermi arcs – objects that are prohibited to exist in “ordinary” materials.” (rdworldonline.com)

            +
            +

            rd1608_fermion

            7 + 11 + 13 = 31

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+    |-------------------------------- 2x96 -------------------------------|
+❓  |--------------- 7¤ ---------------|------------ 7¤ ------------------|
+〰️43👉------------- {89} --------------|{12}|-- {30} -|-- {36} -|-- {25} -|
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉89〰️
+    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|   ❓
+    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
+          13 variations               48 variations          11 variations 
+
            +
            + + Note +
            +
            +

            This proposition was first demonstrated by Edwin Hubble (1889-1953). The American astronomer discovered in 1929 that every galaxy is pulling away from us, and that the most distant galaxies are moving the most quickly. This suggests that there was a time in the past when all the galaxies were located at the same spot, a time that can only correspond to the Big Bang. (Hubble bubble)

            +
            +

            HD-wallpaper-black-hole-black-hole-candle-cosmos-earth-edge-light-space-vortex

            A deeper understanding requires a unification of the aspects discussed above in terms of an underlying principle.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/11.html b/multiplication/11.html new file mode 100644 index 00000000000..1f4c6c8db7d --- /dev/null +++ b/multiplication/11.html @@ -0,0 +1,99 @@ + The Angular Momentum (spin 2) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Angular Momentum (spin 2)

            Under certain conditions, energy could not take on any indiscriminate value, the energy must be some multiple of a very small quantity (later to be known as a quantum).

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-13 of gist section-9 that is inherited from the gist section-20 by prime spin-112 and span-10 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            This is also consistent with the fact that the quadratic residues for modulo 30 (making them congruent with perfect squares) are 1 and 19.

            Perfect Squares

            multilateral sum simmetry

            (17+13) + (11+19) = (7+11) + (19+23) = 60

            image

            Examples_Dyad_Sets_Congruent_1_and_71_Mod_90

            Reversal behaviour

            329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ

            default

            2 + 60 + 40 = 102

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave reversal to 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.

            +
            + + Note +
            +
            +

            Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler’s prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau’s problems (Wikipedia).

            +
            +

            prime Sacks_spiral

            Reversal Behaviour

            Fibonacci Retracement

            +
            + + Note +
            +
            +

            The weak mixing angle or Weinberg angle[2] is a parameter in the Weinberg–Salam theory of the electroweak interaction, part of the Standard Model of particle physics, and is usually denoted as θW. It is the angle by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon.[3]. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for (Wikipedia)

            +
            +

            Weinberg_angle_(relation_between_coupling_constants

            More interesting is that, like the Prime Hexagon it self, they are newly discovered. See how these layers will behave there:

            +
            + + Note +
            +
            +

            This progression 41,43,47,53,61,71,83,97,113,131 whose general term is 41+x+xx, is as much remarkable since the 40 first terms are all prime numbers (Euler’s letter to Bernoulli).

            +
            +

            So here we are going to discuss about this number particularly with the said recombination which resulting the above Δ1 with 619.

            There are many other prime curiousity has been stated for this number 619 but almost none about 619-1 which is 618.

            (786/1000)² = 618/1000

            (786) 618-FEED

            There are set of sequence known as Fibonacci retracement. For unknown reasons, these Fibonacci ratios seem to play a role in the stock market, just as they do in nature.

            +
            + + Note +
            +
            +

            The mathematically significant Fibonacci sequence defines a set of ratios known as Fibonacci retracements which can be used to determine probable entry and exit points for the equities when paired with additional momentum. The Fibonacci retracement levels are 0.236, 0.382, 0.618, and 0.786.

            • The key Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it. For example, 21 divided by 34 equals 0.6176, and 55 divided by 89 equals about 0.61798.
            • The 38.2% ratio is discovered by dividing a number in the series by the number located two spots to the right. For instance, 55 divided by 144 equals approximately 0.38194.
            • The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example, 8 divided by 34 equals about 0.23529.
            • The 78.6% level is given by the square root of 61.8%, while not officially a Fibonacci ratio, 0.5 is also commonly referenced (50% is derived not from the Fibonacci sequence but rather from the idea that on average stocks retrace half their earlier movements). (Golden Ratio - Articles)
            +
            +

            (√0.618 - 0.618) x 1000 = (0.786 - 0.618) x 1000 = 0.168 x 1000 = 168 = π(1000)

            Fibonacci retracement

            They are used to determine critical points where an asset's momentum is likely to reverse. This study cascade culminating in the Fibonacci digital root sequence (also period-24).

            Truncated Perturbation

            image

            +
            + + Note +
            +
            +

            I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.

            +
            + 
            That is what I found.  Phi and its members have a pisano period if the resulting fractional numbers are truncated.
+

            Truncate to Determine Integer Values

            Direction:
+- The initial of 168 & 329 brings the 102 as 100+2 to π(π(10000))-1=200 or 100 x 2.
+- Then the 289 lets this 100x2 to 100² so it brings 100 to 10000 by the power of 2.
+- At the last it will be separated by the scheme of 168 to 102 goes back 100 and 2.
+ 
+Conclusion:
+- All of the other primes than 2 is 1 less than the number n times the number of 2. 
+- Those Mersenne primes is generated as 1 less than the power n of the number of 2. 
+- Thus they will conseqently be carried out by the same scheme of this number of 2.
+
            +
            + + Note +
            +
            +

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            +
            +

            11's additive sums

            103 - 43 = 60

                |-------------------------------- 2x96 -------------------------------|
+❓  |--------------- 7¤ ---------------|------------ 7¤ ------------------|
+〰️43👉------------- {89} --------------|-------------- {103} -------------|
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉89〰️
+    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|   ❓
+    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
+          13 variations               48 variations          11 variations 
+
            +
            + + Note +
            +
            +

            To date, I have found only one number sequence that visibly produces non-random results: pi and its powers, shown as truncated for display purposes. I believe these data suggest prime numbers are linked in some way to pi. (Hexspin)

            +
            +

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/12.html b/multiplication/12.html new file mode 100644 index 00000000000..d01a2a0b48f --- /dev/null +++ b/multiplication/12.html @@ -0,0 +1,148 @@ + Entrypoint of Momentum (spin 3) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Entrypoint of Momentum (spin 3)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-14 of gist section-10 that is inherited from the gist section-21 by prime spin-111 and span-9 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Coupling Behaviour

            Parameters of the Standard Model
+Symbol	Description	Renormalization
+scheme (point)	Value	Experimental
+uncertainty
+1. me | Electron mass |   | 510.9989461 keV | ±3.1 meV
+2. mμ | Muon mass |   | 105.6583745 MeV | ±2.4 eV
+3. mτ | Tau mass |   | 1.77686 GeV | ±0.12 MeV
+4. mu | Up quark mass | μMS = 2 GeV | 2.16 MeV | +0.49 −0.26 MeV
+5. md | Down quark mass | μMS = 2 GeV | 4.67 MeV | +0.48 −0.17 MeV
+6. ms | Strange quark mass | μMS = 2 GeV | 93.4 MeV | +8.6 −3.4 MeV
+7. mc | Charm quark mass | μMS = mc | 1.27 GeV | ±0.02 GeV
+8. mb | Bottom quark mass | μMS = mb | 4.18 GeV | +0.03 −0.02 GeV
+9. mt | Top quark mass | On-shell scheme | 172.69 GeV | ±0.30 GeV
+10. θ12 | CKM 12-mixing angle |   | 13.1° |  
+11. θ23 | CKM 23-mixing angle |   | 2.4° |  
+12. θ13 | CKM 13-mixing angle |   | 0.2° |  
+13. δ | CKM CP-violating Phase |   | 0.995 |  
+14. g1 or g' | U(1) gauge coupling | μMS = mZ | 0.357 |  
+15. g2 or g | SU(2) gauge coupling | μMS = mZ | 0.652 |  
+16. g3 or gs | SU(3) gauge coupling | μMS = mZ | 1.221 |  
+17. θQCD | QCD vacuum angle |   | ~0 |  
+18. v | Higgs vacuum expectation value |   | 246.2196 GeV | ±0.2 MeV
+19. mH | Higgs mass |   | 125.18 GeV | ±0.16 GeV
+
            +
            + + Note +
            +
            +

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            +
            +

            11's additive sums

            π(10) = 2,3,5,7

            IMG_20240105_140622

            +
            + + Note +
            +
            +

            image

            +
            +

            IMG_20240105_141215

            IMG_20240105_133751

            IMG_20240105_135516

            Within a cycle this scheme would generate the prime platform which is performing the rank of 10 shapes starting with the primes 2,3,5,7.

            +
            + + Tip +
            +
            +

            That is, if the powers of 10 all returned with blue spin, or as a series of rainbows, or evenly alternating colors or other non-random results, then I’d say prime numbers appear to have a linkage to 10. I may not know what the the linkage is, just that it appears to exist (HexSpin).

            +
            +

            SO(10)

            IMG_20240109_004026

            Via the 11 partitions as the lexer and 13 frames as the parser we do a recombination to build the grammar in 6 periods.

            +
            + + Note +
            +
            +

            Twisted strip model for one wavelength of a photon with circular polarisation in at space. A similar photon in a closed path in curved space with periodic boundary conditions of length C.

            • The B-fi eld is in the plane of the strip and the E-field is perpendicular to it (a).
            • The E-fi eld vector is radial and directed inwards, and the B-fi eld is vertical (b).

            The magnetic moment ~, angular momentum L~, and direction of propagation with velocity c are also indicated. (Is the electron a photon with toroidal topology? - pdf)

            +
            +

            a-Twisted-strip-model-for-one-wavelength-of-a-photon-with-circular-polarisation-in-at

            Twisted Patterns

                |-------------------------------- 2x96 -------------------------------|
+❓  |--------------- 7¤ ---------------|------------ 7¤ ------------------|
+〰️43👉------------- {89} --------------|-------------- {103} -------------|
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89
+    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|  ✔️
+    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
+          13 variations               48 variations          11 variations 
+
            +
            + + Note +
            +
            +

            F11 (89): The decimal expansion of 89’s reciprocal (1/89) is period-44 (see graphic below) composed of 22 bi-lateral 9 sums = 198, while 89 + 109 = 198, 7920/198 = 40 and 8,363,520/198 = 20 x 2112 (7919’s index number as a member of this domain). And, curiously, 198’s inverse (891) + 109 = 1000, while the sum of 89 and 109’s inverses, 98 + 901, = 999. Then consider that, while it’s obvious 997 of the first 1000 primes are not divisible by 2, 3, or 5, one might miss the fact that 997 minus its reverasl, 799, = 198 = 89 + 109. And for the record we note that 1/109’s decimal expansion is period 108 (making it a ‘long period prime’ in that 1/p has the maximal period of p−1 digits). This period consists of 54 bilateral 9 sums = 486, which (coincidentally?) is the number of primes in the 243 pairs summing to 7920 (more about these, below). (PrimesDemystified)

            +
            +

            43 + 1 = 44 periods

            The decimal expansion of 89's reciprocal (1/89)

            +
            + + Note +
            +
            +

            1092 − 892 = 3960 and 3960 x 2 = 7920; which equates to 8,363,520/(1092 − 892) = 2112, and when you plug 7919 into the formula for triangular numbers you generate 31,359,240 = 7919 x (1092 − 892). And here’s another grouping that relates to these ratios: (672 − 232) = (1092 − 892) and (672 + 1092) − (232 + 892) = 7920 = 2(1092 − 892). And here we correlate 11’s additive sums with 3960, 7920 and the first 1000 prime numbers. (PrimesDemystified)

            +
            +

            11_3960_1st_1000_primes

            +
            + + Note +
            +
            +

            The symmetry of this supergravity theory is given by the supergroup OSp(1❕32) which gives the subgroups O(1) for the bosonic symmetry and Sp(32) for the fermion symmetry. This is because spinors need 32 components in 11 dimensions. 11D supergravity can be compactified down to 4 dimensions which then has OSp(8❕4) symmetry. (We still have 8 × 4 = 32 so there are still the same number of components.) Spinors need 4 components in 4 dimensions. This gives O(8) for the gauge group which is too small to contain the Standard Model gauge group U(1) × SU(2) × SU(3) which would need at least O(10).(Wikipedia) 👈 π(10)

            +
            +

            M-Theory

                |-------------------------------- 2x96 -------------------------------|
+✔️  |--------------- 7¤ ---------------|------------ 7¤ ------------------|
+〰️Osp(8|4) 👉------ {89} --------------|-------------- {103} -------------|
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89
+    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|
+    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
+          13 variations               48 variations          11 variations 
+

            Shock wave

            Many physicists suspect that the fact that the observable universe contains more matter than antimatter is caused by a chiral anomaly

            +
            + + Note +
            +
            +

            The pion is one of the particles that mediate the residual strong interaction between a pair of nucleons. This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the Yukawa potential.

            Pions are pseudoscalars under a parity transformation. Pion currents thus couple to the axial vector current and so participate in the chiral anomaly. (Wikipedia)

            +
            +

            residual strong force

            In phenomenology, Yukawa coupling can be observed in phenomenology from 6 quark masses and 4 CKM mixing parameters.

            +
            + + Note +
            +
            +

            Since the range of the nuclear force was known, Yukawa used his equation to predict the mass of the mediating particle as about two hundreds (200) times the mass of the electron. Physicists called this particle the “meson,” as its mass was in the middle of the proton and electron. Yukawa’s meson was found in 1947, and came to be known as the pion. (Wikipedia)

            +
            +

            The_Minimal_Flavor_Structure_of_Quarks_and_Leptons

            +
            + + Note +
            +
            +

            It is widely accepted that audible thunder is generated by the lightning channel and the subsequent shock wave that travels extremely rapidly (~3000 m/s) a few provides a experimentally-proved thunder generation mechanism. (Wikipedia)

            +
            +

            two main types of lightning discharges

            The parity is associated to the shock wave (3km/s) produced after a lightning discharge (300,000km/s) propagated in 3 periods of travels to the normal speed of 1km/s.

            +
            + + Note +
            +
            +

            Depending on the conditions surrounding the lightning rod such as the air composition, atmospheric pressure, the thunder will travel at a unique velocity, pitch, frequency band and duration depending on the characteristics of the lightning rod. Indeed, as shown in the study by Blanco et al. (2009) the geometry plays a vital role in the perceived resulting sound.(Wikipedia)

            +
            +

            Thunder_diagram

            +
            + + Note +
            +
            +

            This is typical for processes in which the so-called initial state radiation takes place. It is well known that emission of real or virtual photons from the initial colliding electrons essentially modify the shapes of the narrow resonance curves [39]: the curves become wider, a suppression of the resonance maximum is observed and the main distinctive feature – the radiation tail – appears to the right of the resonance pole. (Glashow resonance in neutrino–photon scattering)

            +
            +

            1The Glashow resonance in neutrino–photon scattering

            This OSp(8❕4) will be assigned to 4xMEC30 and let the 4x30=120 numbers of 32 prime positions minus 5 types of bosons gives 27 variations of decay objects.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/13.html b/multiplication/13.html new file mode 100644 index 00000000000..fffceaf8bd8 --- /dev/null +++ b/multiplication/13.html @@ -0,0 +1,273 @@ + The Mapping of Spacetime (spin 4) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Mapping of Spacetime (spin 4)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-15 of gist section-11 that is inherited from the gist section-22 by prime spin-110 and span-8 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Decay Frames

            +
            + + Note +
            +
            +

            As we’ve already alluded, to lay the foundation for a bijection with numbers not divisible by 2, 3, or 5, each of the pyramid’s four lateral faces is constructed from a 32-step triangular number progression (oeis.org/A000217: a(n) = n(n+1)/2 …).

            +
            +

            image

            7 = 4th prime

             Osp(1) |  1 |  2 |  3 |  4 
+--------+----+----+----+----
+ π(10)  |  2 |  3 |  5 |  7 ✔️
+

            19 = 8th prime

             Osp(2) |  1 |  2 |  3 |  4 | th
+========+====+====+====+====+====
+ π(10)  |  2 |  3 |  5 |  7 | 4th
+--------+----+----+----+----+----
+ π(19)  | 11 | 13 | 17 | 19 | 8th ✔️
+

            29 = 10th prime

             Osp(3) |  1 |  2 |  3 |  4 | th
+========+====+====+====+====+====
+ π(10)  |  2 |  3 |  5 |  7 | 4th
+--------+----+----+----+----+----
+ π(19)  | 11 | 13 | 17 | 19 | 8th
+--------+----+----+----+----+----
+ π(29)  | 23 | 29 |  - |  - | 10th ✔️
+

            109 = 29th prime

             Osp(8|4) |  1 |  2 |  3 |   4 | th
+==========+====+====+====+=====+====
+ π(10)    |  2 |  3 |  5 |   7 | 4th
+----------+----+----+----+-----+----
+ π(19)    | 11 | 13 | 17 |  19 | 8th
+----------+----+----+----+-----+----
+ π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10) ✔️ 
+==========+====+====+====+=====+====
+ π(❓)    | .. | .. | .. |  .. | ❓th
+----------+----+----+----+-----+----
+ π(❓)    | .. | .. | .. |  .. | ❓th
+----------+----+----+----+-----+----
+ π(❓)    | .. | .. | .. |  .. | ❓th 👈 π(19) ❓
+==========+====+====+====+=====+====
+ π(❓)    | .. | .. | .. |  .. | ❓th
+----------+----+----+----+-----+----
+ π(❓)    | .. | .. | .. |  .. | ❓th
+----------+----+----+----+-----+----
+ π(109)   | .. | .. | .. | 109 | 29th 👈 π(29) ✔️
+

            12 + 18 + 13 = 43

             Osp(8|4) |  1 |  2 |  3 |   4 | th
+==========+====+====+====+=====+====
+ π(10)    |  2 |  3 |  5 |   7 | 4th
+----------+----+----+----+-----+----
+ π(19)    | 11 | 13 | 17 |  19 | 8th
+----------+----+----+----+-----+----
+ π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10)
+==========+====+====+====+=====+====
+ π(29+12) | 31 | 37 | 41 |   - | 13th ✔️
+----------+----+----+----+-----+----
+ π(41+18) | 43 | 47 | 53 |  59 | 17th ✔️
+----------+----+----+----+-----+----
+ π(59+13) | 61 | 67 | 71 |   - | 20th 👈 π(19+1) ✔️
+==========+====+====+====+=====+====
+ π(❓)    | .. | .. | .. |  .. | ❓th
+----------+----+----+----+-----+----
+ π(❓)    | .. | .. | .. |  .. | ❓th
+----------+----+----+----+-----+----
+ π(109)   | .. | .. | .. | 109 | 29th 👈 π(29)
+

            109 - 72 = 37

             Osp(8|4) |  1 |  2 |  3 |   4 | th
+==========+====+====+====+=====+====
+ π(10)    |  2 |  3 |  5 |   7 | 4th
+----------+----+----+----+-----+----
+ π(19)    | 11 | 13 | 17 |  19 | 8th
+----------+----+----+----+-----+----
+ π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10)
+==========+====+====+====+=====+====
+ π(41)    | 31 | 37 | 41 |   - | 13th
+----------+----+----+----+-----+----
+ π(59)    | 43 | 47 | 53 |  59 | 17th 
+----------+----+----+----+-----+- ---
+ π(72)    | 61 | 67 | 71 |   - | 20th 👈 π(19+1)
+==========+====+====+====+=====+====
+ π(72+11) | 73 | 79 | 83 |   - | 23th ✔️
+----------+----+----+----+-----+----
+ π(83+18) | 89 | 97 |101 |   - | 26th ✔️
+----------+----+----+----+-----+----
+ π(101+8) |103 |107 |109 |   - | 29th 👈 π(29+1) ✔️
+

            Decay Objects

            +
            + + Note +
            +
            +

            “Eliason’s work has been both praised and criticized within the academic community. Some scholars have praised his innovative approach to the study of the Torah and the insights that it has yielded. Others have criticized his methods as being overly subjective and lacking in scientific rigor. (Torah Geometry)

            +
            +

            dreidel-letters-3

            +
            + + Note +
            +
            +

            Despite the controversy surrounding his work, Eric Eliason’s Torah geometry and gematria remain a fascinating subject of study for those interested in the mysteries of religious texts and the ways in which they can be interpreted and understood.

            +
            +

            a-tree-maze-7

            +
            + + Note +
            +
            +

            Mathematically, this type of system requires 27 letters (1-9, 10–90, 100–900). In practice, the last letter, tav (which has the value 400), is used in combination with itself or other letters from qof (100) onwards to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit (final) forms of the Hebrew letters. (Wikipedia)

            +
            +

            Hebrew numerals

            The first object symboled by "star" above is taken from one of the Higgs particles called neutral CP-odd (A) and behave as the base unit.

            +
            + + Note +
            +
            +

            The Higgs mechanism breaks electroweak symmetry in the Standard Model, giving mass to particles through its couplings.

            • Current data from electroweak precision measurements points to a light Higgs {Mmggs < 199 GeV @ 95% CL [1]). However, the Higgs has never been definitively observed (MHiggs > 114 GeV at 95% CL [2]).
            • A Standard Model Higgs suffers from the so called hierarchy problem. The theory needs fine-tuned parameters to accomodate a light Higgs mass. Supersymmetry offers a solution to this problem, through a symmetry between fermions and bosons.
            • The Minimal Supersymmetric Standard Model contains two Higgs doublets, leading to five physical Higgs bosons: Two neutral CP-even states (h and H), one neutral CP-odd (A), and two charged states (H+ and H~).
            • At tree-level, the masses are governed by two parameters, often taken to be mA and tan/3 [3]. When tan/3 > > 1 , A is nearly degenerate with one of the CP-even states (denoted φ). Where mA < 130 GeV (mA > 130), mA = mh (mA = mH).
            • In this same large tan/3 region, the cross sections for some production mechanisms such as pp -» Α(φ) and pp -» A($i)bb are enhanced by factors of tan /32(sec/32). For example, with Λ/S = 2 TeV, tan/3 = 30 and mA = 100 GeV, the cross sections for pp —>· A and pp —> φ are each of or-der 10 pb[4].
            • The cross section for pp -> Α/φΜ) is smaller, but within the same order of magnitude. In the same region, the branching ratios to Α/φ ->· bb and rr dominate, at ~ 90% and ~ 10% respectively, independent of mass.
            • Due to their similar masses, cross-sections and branching ratios in the high tan/3 region, we search for *both A and φ simultaneously$.
            • At the Tevatron, we search for pp —>> Α/φ —► rr (the bb final state is expected to be overwhelmed by dijet background) and pp ->· Α/φΰ) -» bbbb.
            • This search for pp -> Α/φ -> r+r~ is underway at CDF. The dominant issues for this analysis are: tau identification, ditau mass reconstruction, irreducible background from Z —► rr, and event loss at the trigger level.

            Wherever not specified, we use the benchmark case of mA = 95 GeV and tan ß = 40 to quote efficiencies and cross-sections. (Search for MSSM Higgses at the Tevatron)

            +
            +

            π(10) = 2,3,5,7

            SO(10) 

            Sub  | i  |  β  | f   
+=======+====+=====+=======  ===   ===   ===   ===   ===   ===
+ 1:1:0 | 1  |   1 | 2 {71}   1     1     |     |     |     |
+-------+----+-----+-------  ---   ---    |     |     |     |
+ 1:2:1 | 2  |   2 | 3 {71}         |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:2:2 | 3  |   3 |                |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:3:3 | 4  |   4 |                |     |     |     |     |  
+-------+----+-----+----            |     |     |     |     |
+ 1:3:4 | 5  |   5 |                |     |     |     |     |
+-------+----+-----+----            9     1‘    |    Δ100   |
+*1:3:5 | 6  |   6 |                |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:6 | 7  |   7 |                |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+ 1:4:7 | 8  |   8 |                |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:8 |{9} |   9 | 15 = 9 + 6 √   |     |     |     |     | ← 15 ✓
+=======+====+=====+====           ===   ===    1"   ===    |
+*1:4:9 |{10}|  10 | 19 = 9 + 10 √  |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+ 2:1:0 | 11 |  20 | 20 = 19 + log 10 √   |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:2:1 | 12 |  30 |                      |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:2:2 | 13 |  40 |                      |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:3:3 | 14 |  50 |                      |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:3:4 | 15 |  60 |                      9‘    |   Δ200  Δ600
+-------+----+-----+----                  |     |     |     |
+*2:3:5 | 16 |  70 |                      |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:4:6 | 17 |  80 |                      |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:4:7 |{18}|  90 | 32 = 26 + 6 √        |     |     |     |← 32 = 31 + ∆1✓
+=======+====+=====+====                 ===   ===   ===    |
+*2:4:8 |{19}| 100 | 36 = 26 + 10 √       |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:4:9 | 20 | 200 | 38 = 36 + log 100 √        |     |     |
+-------+----+-----+----                        |     |     |
+ 3:1:0 | 21 | 300 |                            |     |     |
+-------+----+-----+----                        |     |     |
+ 3:2:1 | 22 | 400 |                            |     |     |
+-------+----+-----+----                        |     |     |
+*3:2:2 | 23 | 500 |                            |     |     |
+-------+----+-----+----                        |     |     |
+*3:3:3 | 24 | 600 |                            9"  Δ300    |
+-------+----+-----+----                        |     |     |
+ 3:3:4 | 25 | 700 |                            |     |     |
+-------+----+-----+----                        |     |     |
+*3:3:5 | 26 | 800 |                            |     |     |
+-------+----+-----+----                        |     |     |
+*3:4:6 | 27 | 900 | 46 = 40 + 6 √              |     |     |← 46 = 45 + ∆1 ✓
+=======+====+=====+====                       ===   ===   ===
+ 3:4:7 |{28}|1000 | 50 = 40 + 10 = 68 - 18 √
+
            +
            + + Note +
            +
            +

            Valise adinkras, although an important subclass, do not encode all information present when a 4D supermultiplet is reduced to 1D. We extend this to non-valise adinkras providing a complete eigenvalue classification via Python code.

            +
            +

            IMG_20231228_185122

            In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become the irrational partitions.

            Flavour and Colors

            image

            image

            +
            + + Note +
            +
            +

            You might imagine, right away, that there are nine gluons that are possible: one for each of the color-anticolor combinations possible. Indeed, this is what almost everyone expects, following some very straightforward logic.

            • There are three possible colors, three possible anticolors, and each possible color-anticolor combination represents one of the gluons. If you visualized what was happening inside the proton as follows:
              • a quark emits a gluon, changing its color,
              • and that gluon is then absorbed by another quark, changing its color,

            you’d get an excellent picture for what was happening with six of the possible gluons. (Why are there only 8 gluons)

            +
            +

            Why are there only 8 gluons?

            There is also another explanation to the above color charge based on gluons transform in the adjoint representation of SU(3), which is 8-dimensional.

            Triangular Wave

            One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so one of solution would be truncated approach.

            +
            + + Note +
            +
            +

            The first 3 triplets are prime and form the first triangle on top. Then we do the next two and the last one on the bottom because we will sandwich the other 3 in.

            • These all match perfectly or one letter off on the bottom triangle, by sliding. The BGY slides, the YBG matches the YBR except one letter.
            • Notice that the first 3 are prime. Then the next 4 are quite factorable. The 29 (RBR) is prime and there is no 29th letter, ending the pattern. 26 and 27 lead to 28 letters. Incidentally, the first 3 primes add to 99 and the primes add to 128. The last three to cover (RYY,YBY and RBR) match up with the top triangle’s bottom (except one letter) with RYY in reverse and make a matching triangle together. RYY has the most factors. The last 3 end in 29, suggesting an end to the pattern as there is no 29th letter.
            • The final letter is B and it matches the middle letter, the two letters at the top and the two letters at the bottom if we do the BGY slide in one way.

            Only B.

            +
            +

            a-triangle-sandwich-3

            +
            + + Note +
            +
            +

            Speculating beyond the pyramidal model just described, the ratios seem to suggest that this geometry can be conceived sinusoidally as a Fourier series forming continuous triangular waves that reverse polarity in quarter cycles. For example, the 9th harmonic of the fundamental frequency 440 Hz = 3960 Hz (and keep in mind that 3960 = 1092 − 892, their relationship to the first 1000 primes covered in detail earlier in this section). Then consider that 8,363,520 (additive sum of the pyramid)/(1092 − 892) = 2112 (index # of the 1000th prime); 8/3/6/3/5/20 x (1092 − 892) x 360 = 2112; and that 443,520 (additive sum of the pyramidion)/(1092 − 892) = 112 (index # of 419, the 81st prime [as in 92, interestingly], and in turn 7919 x 28/528 = [419]; whole number part taken). (PrimesDemystified)

            +
            +

            Here's a draft of what the proposed triangular wave might look like:

            Triangular Wave

            Base on the above discussions we conclude that the decay frames should behave as 4 times Triangular Waves as well, let have it done by The True Primer Pairs.

            +
            + + Note +
            +
            +

            Surprisingly, the 24-cell hexagon confines all natural numbers. The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon’s outer boundary, other than 2 and 3, the initial primes that forced the number line into this complex coil. Without a prime number in the outer set of triangles, the number line does not change to an outward course and remains forever contained in the 24 cells shown above. (HexSpin)

            +
            + 
            The True Prime Pairs
+(5,7), (11,13), (17,19)
+
+Tabulate Prime by Power of 10
+loop(10) = π(10)-π(1) = 4-0 = 4
+loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+--------------------------+----+----+----+----+----+----+----+----+----+-----
+ True Prime Pairs → Δ→π  |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+==========================+====+====+====+====+====+====+====+====+====+=====
+ 19 → π(∆10) → π(10)     |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+--------------------------+----+----+----+----+----+----+----+----+----+-----
+ 17 → π(10+∆9) → π(19)   | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+ 13 → π(19+∆10) → π(29)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+--------------------------+----+----+----+----+----+----+----+----+----+-----
+ 11 → π(29+∆12) → π(41)  | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+  7 → π(41+∆18) → π(59)  | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+--------------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+  5 → π(59+∆13) → π(72)  | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+==========================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+  3,2 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+==========================+====+====+====+====+====+====+====+====+====+=====
+         Δ                                                            Δ
+12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-
+
            +
            + + Note +
            +
            +

            Speaking of iterative digital division–a powerful tool for exposing structure–we get this astonishing equation: iteratively dividing the digital roots of the first 12 Fibonacci numbers times the divisively iterated 1000th prime, 7919, times 3604 gives us 1000.

            • Keep in mind that the first two and last two digits of the Fibo sequence below, 11 and 89, sum to 100; that 89 is the 11th Fibo number; that there are 1000 primes between 1 and 892; and that 89 has the Fibonacci sequence embedded in its decimal expansion:
            +
            +

            1/1/2/3/5/8/4/3/7/1/8/9 x 7/9/1/9 x 3604 = 1000

            One Grand Pyramid

                |-------------------------------- 2x96 -------------------------------|
+    |--------------- 7¤ ---------------|---------------- 7¤ --------------|👈❓
+〰️Osp(8|4) 👉------ {89} --------------|-------------- {103} -------------|
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+    +----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89
+    |---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|
+    |-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
+          13 variations               48 variations          11 variations 
+

            image

                |-------------------------------- 2x96 ---------------------|
+    |--------------- 7¤ ---------------|---------- 5¤ ----------| ✔️
+〰️Osp(8|4) 👉------ {89} --------------|-------- {103} ---------|
+    +----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
+    +----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---👉109²-89²=11×360 ✔️
+    |---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+    |-------- Bosons --------|---------- Fermions ---------|-- Graviton
+          13 variations               48 variations           11 variations
+

            image

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/14.html b/multiplication/14.html new file mode 100644 index 00000000000..d6645a361af --- /dev/null +++ b/multiplication/14.html @@ -0,0 +1,276 @@ + Similar Order of Magnitude (spin 5) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Similar Order of Magnitude (spin 5)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-16 of gist section-12 that is inherited from the gist section-23 by prime spin-109 and span-7 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Double Beta Decay

            Every second, trillions upon trillions of the tiny particles shoot down to Earth from space almost completely unaffected by any matter they come across.

            image

            +
            + + Note +
            +
            +

            Feynman diagram of neutrinoless double beta decay, with two neutrons decaying to two protons.

            • The only emitted products in this process are two electrons, which can occur if the neutrino and antineutrino are the same particle (i.e. Majorana neutrinos) so the same neutrino can be emitted and absorbed within the nucleus.
            • In conventional double beta decay, two antineutrinos — one arising from each W vertex — are emitted from the nucleus, in addition to the two electrons.

            The detection of neutrinoless double beta decay is thus a sensitive test of whether neutrinos are Majorana particles. (Wikipedia)

            +
            +

            Quantum Field Theory

            +
            + + Note +
            +
            +

            We analyze a simple extension of the Standard Model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group.

            • Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sectorand the SM particles, and generate masses for the active neutrinos via the seesawmechanism.
            • We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario.

            We also study the constraints from direct Dark Matter searches and the prospects for indirect detectionvia sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV. (Sterile Neutrino portal to Dark Matter II - pdf)

            +
            +

            Sterile Neutrino portal to Dark Matter II

            +
            + + Note +
            +
            +

            The current status of the nucleon decay experiments is as follows: the partial lifetimelimit on p → π0e+ is τ (p → π0e+) > 1.67 × 1034 years, and the bound on the partial lifetime for p → K+ν is τ (p → K+ν) > 6.6 × 1033 years [42, 43]. It is expected that a future experiment, the Hyper-Kamiokande, may achieve a sensitivity of 5-10 times the present bound. (Proton Decay - pdf)

            +
            +

            image

            p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry
+7 11 4 1 0 11 ◄--- #19 👈 30
+8 13 5 1 0 13 ◄--- #17 ◄--∆32-- #49 👈 30 ✔️
+9 17 0 1 1 17 ◄--- 7th prime 👈 f(#36) ◄--- antisymmetric state ✔️
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

            Exact Dark Symmetry

            image

            lightning speed ÷ shockwave speed = 300000km/s ÷ 3km/s = 100000 ÷ 1

              Sub  | i  |     β | f   
+=======+====+=======+=======  ===   ===   ===   ===   ===   ===
+ 1:1:0 | 1  |     1 | 2 {71}   1     1     |     |     |     |
+-------+----+-------+-------  ---   ---    |     |     |     |
+ 1:2:1 | 2  |     2 | 3 {71}         |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:2:2 | 3  |     3 | 7 = 1 + 2x3    |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:3:3 | 4  |     4 | 10 = 9 + 1     |     |     |     |     |  
+-------+----+-------+----            |     |     |     |     |
+ 1:3:4 | 5  |     5 | 11 = 9 + 2     |     |     |     |     |
+-------+----+-------+----            9     1‘    |    Δ100   |
+*1:3:5 | 6  |     6 | 12 = 9 + 3     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:4:6 | 7  |     7 | 13 = 9 + 4     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+ 1:4:7 | 8  |     8 | 14 = 9 + 5     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:4:8 |{9} |     9 | 15 = 9 + 6     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:4:9 |{10}|    10 | 19 = 9 + 10    |     |     |     |     |
+=======+====+=======+====           ===   ---    1"   ---    |
+ 2:1:0 | 11 |    20 | 20 = 19 + log 10¹    |     |     |     |
+-------+----+-------+----                  |     |     |     |
+ 2:2:1 | 12 |    30 | 26 = 20 + 2x3        |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:2:2 | 13 |    40 | 27 = 26 + 1          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:3:3 | 14 |    50 | 28 = 26 + 2          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+ 2:3:4 | 15 |    60 | 29 = 26 + 3          9‘    |   Δ200    |
+-------+----+-------+----                  |     |     |     |
+*2:3:5 | 16 |    70 | 30 = 26 + 4          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:4:6 | 17 |    80 | 31 = 26 + 5          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+ 2:4:7 |{18}|    90 | 32 = 26 + 6          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:4:8 |{19}|   100 | 36 = 26 + 10         |     |     |     |
+=======+====+=======+====                 ===   ---   ---  ∆1000
+*2:4:9 | 20 |   200 | 38 = 36 + log 10²          |     |     |
+-------+----+-------+----                        |     |     |
+ 3:1:0 | 21 |   300 | 40 = 36 + 2 x log 10²      |     |     |
+-------+----+-------+----                        |     |     |
+ 3:2:1 | 22 |   400 | 41 = 40 + 1                |     |     |
+-------+----+-------+----                        |     |     |
+*3:2:2 | 23 |   500 | 42 = 40 + 2                |     |     |
+-------+----+-------+----                        |     |     |
+*3:3:3 | 24 |   600 | 43 = 40 + 3                9"  Δ300    |
+-------+----+-------+----                        |     |     |
+ 3:3:4 | 25 |   700 | 44 = 40 + 4                |     |     |
+-------+----+-------+----                        |     |     |
+*3:3:5 | 26 |   800 | 45 = 40 + 5                |     |     |
+-------+----+-------+----                        |     |     |
+*3:4:6 | 27 |   900 | 46 = 40 + 6                |     |     |
+-------+----+-------+----                        |     |     |
+ 3:4:7 |{28}|  1000 | 50 = 40 + 10               |     |     |
+=======+====+=======+====                       ===  ====    |
+*3:4:8 |{29}|  2000 | 68 = 50 + 3 x (2x3)      {10³}   |     |
+-------+----+-------+----                        Δ     |     |
+ 3:4:9 |{30}|  3000 |{71}= 68 + log 10³                |     |   
+-------+----+-------+----                              |     |
+ 3:2:1 | 31 |  4000 | 72 = 71 + 1                      |     |
+-------+----+-------+----                              |     |
+*3:2:2 | 32 |  5000 | 73 = 71 + 2                      |     |
+-------+----+-------+----                              |     |
+*3:3:3 | 33 |  6000 | 74 = 71 + 3                    Δ400    |
+-------+----+-------+----                              |     |
+ 3:3:4 | 34 |  7000 | 75 = 71 + 4                      |     |
+-------+----+-------+----                              |     |
+*3:3:5 | 35 |  8000 | 76 = 71 + 5                      |     |
+-------+----+-------+----                              |     |
+*3:4:6 | 36 |  9000 |{77}= 71 + 6                      |     |
+-------+----+-------+----                              |     |
+ 3:4:7 |{37}| 10000 | 81 = 71 + 10 = 100 - 19          |     |
+=======+====+=======+====                             ====  ----
+

            32-5 = 27 = 9x3

            +
            + + Note +
            +
            +

            The four faces of our pyramid additively cascade 32 four-times triangular numbers (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of 32^2 = 1024 = 2^10). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of the 1000th prime within our domain, and equals the total number of ‘elements’ used to construct the pyramid. (PrimesDemystified)

            +
            +

            109 = 29th prime = ((10th)th prime)

                |-------------------------------- 2x96 ---------------------|
+    |--------------- 7¤ ---------------|---------- 5¤ ----------|
+✔️👉|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
+    +----+----+----+----+----+----+----+----+----+----+----+----+
+    |  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
+    +----+----+----+----+----+----+----+----+----+----+----+----+
+    |--------- {53} ---------|---- {48} ----|---- {48} ----|---👉109²-89² ✔️
+    |---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+    |-------- Bosons --------|---------- Fermions ---------|-- Graviton
+          13 variations               48 variations           11 variations
+

            Parity Order

            symmetry-09-00097-ag-550

            +
            + + Note +
            +
            +

            The origin of multiple generations of fermions, and the particular count of 3, is an unsolved problem of physics.

            In standard quantum field theory, under certain assumptions, a single fermion field can give rise to multiple fermion poles with mass ratios of around eπ≈23 and e2π≈535 potentially explaining the large ratios of fermion masses between successive generations and their origin. (Wikipedia)

            +
            + 
            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                       MEC 30 / 2
+------+------+-----+-----+------      ‹------------------------------ 0 {-1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)               ∆9 ✔️  |
+      |      +-----+-----+                    👆     |          Double
+      |      |     |  9  | ∆9+∆(89-71)=∆27= { ∆9 ✔️  |‹--109² { Beta
+  2   +------|  5* +-----+-----               👇     |          Decay
+      |      |     |  10 |                    ∆9 ✔️  |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- 
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7 x 24 = 168 √
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- 
+------|------|-----+-----+-----  ‹----------------------------------- 30 {+1/2}
+

            matrix-folding

            Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+Sequence:
+ By the next layer the 89² will become 89 and 5 become 5² or 25.
+ This 89 and 25 are in the same layer with total of 114 or prime 619
+ So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+
            +
            + + Note +
            +
            +

            Using Euler’s method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler (Wikipedia).

            +
            +

            π(π(π(1000th prime))) + 1 = 40

            image

            Distribution Order

            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave reversal to 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            96 perfect squares

            Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycling .

            89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️
+

            223622800-4602ad28-1622-4742-821e-d702c0fc8303

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/15.html b/multiplication/15.html new file mode 100644 index 00000000000..6a647ef8e85 --- /dev/null +++ b/multiplication/15.html @@ -0,0 +1,362 @@ + The Search for The Graviton (spin 6) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Search for The Graviton (spin 6)

            Most theories containing gravitons suffer from severe problems. This has led theorists to make choices subjectively (as always) on what is the most elegant theory.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-17 of gist section-13 that is inherited from the gist section-24 by prime spin-108 and span-6 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way.

            Boson Decay

            Higgs boson decay process into two Z bosons, each decaying in to two leptons. When a particle decays, it transforms into other particles (called decay products).

            +
            + + Note +
            +
            +

            Attempts to extend the Standard Model or other quantum field theories by adding gravitons run into serious theoretical difficulties at energies close to or above the Planck scale.

            • This is because of infinities arising due to quantum effects; technically, gravitation is not renormalizable.
            • Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view, this situation is not tenable.

            One possible solution is to replace particles with strings. String theories are quantum theories of gravity in the sense that they reduce to classical general relativity plus field theory at low energies, but are fully quantum mechanical, contain a graviton, and are thought to be mathematically consistent. (Wikipedia)

            +
            +

            Search for The Graviton

            There are 5 different string theories, each requiring 10 dimensions. On the other hand, string theory is supposed to be fundamental theory.

            +
            + + Warning +
            +
            +

            Introduced earlier in GUTS: The Unification of Forces Superstring theory is an attempt to unify gravity with the other three forces and, thus, must contain quantum gravity.

            • The main tenet of Superstring theory is that fundamental particles, including the graviton that carries the gravitational force, act like one-dimensional vibrating strings.
            • Since gravity affects the time and space in which all else exists, Superstring theory is an attempt at a Theory of Everything (TOE).
            • Each independent quantum number is thought of as a separate dimension in some super space (analogous to the fact that the familiar dimensions of space are independent of one another) and is represented by a different type of Superstring.
            • As the universe evolved after the Big Bang and forces became distinct (spontaneous symmetry breaking), some of the dimensions of superspace are imagined to have curled up and become unnoticed.
            • Forces are expected to be unified only at extremely high energies and at particle separations on the order of 10^-35m. This could mean that Superstrings must have dimensions or wavelengths of this size or smaller.
            • Just as quantum gravity may imply that there are no time intervals shorter than some finite value, it also implies that there may be no sizes smaller than some tiny but finite value. That may be about 10^-35m.
            • If so, and if Superstring theory can explain all it strives to, then the structures of Superstrings are at the lower limit of the smallest possible size and can have no further substructure.
            • This would be the ultimate answer to the question the ancient Greeks considered: There is a finite lower limit to space. Not only is Superstring theory in its infancy, it deals with dimensions about 17 orders of 10^-18m magnitude smaller than the details that we have been able to observe directly.
            • It is thus relatively unconstrained by experiment, and there are a host of theoretical possibilities to choose from. This has led theorists to make choices subjectively (as always) on what is the most elegant theory, with less hope than usual that experiment will guide them.
            • It has also led to speculation of alternate universes, with their Big Bangs creating each new universe with a random set of rules. These speculations may not be tested even in principle, since an alternate universe is by definition unattainable. It is something like exploring a self-consistent field of mathematics, with its axioms and rules of logic that are not consistent with nature.

            Such endeavors have often given insight to mathematicians and scientists alike and occasionally have been directly related to the description of new discoveries. (College Physics 2e - pdf page 1518)

            +
            +

            +
            + + Note +
            +
            +

            With William Thomson’s idea of vortex atoms coming of age in the shape of string and superstring theories, in recent years hopes for a $nite theory of quantum gravity have centered on the quantum superstring (QSS).

            • Although the perturbation expansion yields finite terms, the summations do involve infinities [ 2481. However, that would still be true in quantum electrodynamics (QED) ; in perturbative treatments in quantum field theory these infinities are assumed to arise because of non-perturbative solutions and are regarded as an indication of the latter’s existence. Should we then consider the search for a theory of quantum gravity as having reached its goal and should we therefore cross it out as a motivation for the study of non-Riemannian gravitational theories?
            • The basic assumption in the post- 1984 treatment of the quantum superstring [ 2381 “theory of everything” (TOE), an on-mass-shell S-matrix type theory, is that its truncation below Planck mass should go over smoothly into an off-mass-shell relativistic quantum (point) local field theory * (including a version of ten-dimensional supergravity, in one sector of the “heterotic string” [ 2471, for instance) thus, even if the search were over, the same geometrical-gravitational question then relates to that truncated “low-energy” field theory and its gravitational sector.

            Moreover, it has been pointed out [ 1051 that consistency would then require the low-energy $eid theory to be fmite by itseIf! This then implies the existence of a finite or renormalizable relativistic quantum field theory of gravity. (Gauge theory of gravity - pdf)

            +
            +

            476931_1_En_1

            The symmetry of this supergravity theory is given by the supergroup OSp(1\32) which gives the subgroups O(1) for the bosonic and Sp(32) for the fermion.

            +
            + + Note +
            +
            +

            In general relativity, gravity is a force that bends and warps space-time around supermassive bodies.

            • Even though gravity is one of the four fundamental forces in nature, it is very weak compared to the other three forces (electromagnetism, weak force and strong force). So it can’t be observed or identified on the scale of subatomic particles.
            • However, gravity is very dominant in long-distance scenarios. It controls the structure of the macro universe (galaxies, planets, stars, moons).
            • As far as quantum mechanics is concerned, gravity doesn’t have much effect. The probable nature of the quantum realm also poses a significant challenge for the induction of gravity in the quantum realm.
            • Generally, gravity does not act as a particle as its own. Even if a hypothetical model is introduced to explain the particle nature of a gravity particle, it violates fundamental energy laws.

            In the 1970s, theorists tried to discard the self-destructive idea of point-like gravity particles. Instead of point particles, strings were introduced. Even if strings collide, there will be no infinite energy problem. Strings can smoothly smash and rebound without implying any physically nonsense infinities.

            +
            +

            An-adinkra-for-the-chiral-multiplet

            This standard model is missing the Gravitational interaction and it is postulated that there exists a particle called the Graviton that leads to supergravity theory.

            +
            + + Note +
            +
            +

            Supergravity is an extension of supersymmetry, designed to include the principles of General Relativity. In order to make this possible, supersymmetry has to become local, with a spacetime-dependent spinor ǫ(x) parametrising the infinitesimal SUSY transformation.

            • The key ingredient of supergravity is the graviton hµν , a massless spin-2 elementary particle which couples to the stress-energy tensor, thus mediating gravitational interactions.
            • Its fermionic, spin-3/2 partner, the gravitino ψαµ, equipped both with a spinor index α and a spacetime index µ, is the gauge field of local supersymmetry and becomes massive when SUSY is broken, by absorbing the emerging goldstino in the so-called super-Higgs mechanism.
            • There are two ways in which the graviton can be related to the metric gµν, either through an infinitesimal expansion gµν = ηµν + hµν around the flat metric ηµν , or through the vielbein formalism.

            As is well-known from General Relativity, the metric (and implicitly the graviton) has tosatisfy the Einstein’s field equations (Holomorphic_Yukawa_Couplings - pdf)

            +
            +

            NLFIW

            +
            + + Note +
            +
            +

            Think of it this way, all gravitating bodies in the universe would be surrounded at all times by a cloud of tunneling electrons. We cannot see these particles since they’re so small and since they permeate all of space. They would also tunnel to a different location about once every Planck time (about 10^-43 seconds) whenever they interact with another particle.

            • These interactions between particles amount to the exchanges of bosons between electrons and other electrons or other fermions. At each point where the electron absorbs another boson, we say that the wave function of the electron collapses, and it tunnels to a new location whereupon it interacts with yet another particle.
            • The cloud of electron surrounding gravitating objects would diminish in inverse proportion to the square of the distance; hence, if you recede from an objects’ surface, you’re less likely to find an electron tunneling from that object.
            • Electrons also make an excellent candidate for a particle of gravity since they absorb and emit photons readily, and we know from Einstein’s theory of general relativity that light interacts readily with gravitational fields, and that gravitational fields are thought to emit photons spontaneously.
            • This spontaneous emission of photons is what we refer to as the cosmological constant or dark energy, and in our current thinking on the topic we imagine that particles of antimatter are created and annihilate with particles of matter leading, occasionally, to the emission of a photon. I suspect that this is incorrect and that no such thing as antimatter really exists. I suspect that positrons are really tunneling W particles and that this Dirac Sea, or background of tunneling electrons, is really giving rise to this phenomenon of the cosmological constant, or vacuum energy, we observe inn nature.
            • As a consequence, we would need to adumbrate our standard model of particle physics by about half. This ought to be seen as a positive thing in physics. No longer do we have untestable assumptions (such as the creation and annihilation of particles) in our models, and we have a far easier means of now beginning to probe the quantum nature of gravity.

            The other fascinating consequence of this way of thinking is that gravity would no longer be a fundamental force; instead it would be a secondary effect of electromagnetism. This should have been what we anticipated all along; and now, we might have a quantum theory focusing on only three forces and a theory of gravitation that is truly particle-based. (Medium - Article)

            +
            +

            Cut the Standard Model

            +
            + + Note +
            +
            +

            There are two groups of scientists (called collaborations) looking for evidence of gravitons in proton-proton collision experiments at the Large Hadron Collider at CERN. Once a graviton has been created, it’s expected to decay in one of a few possible ways - and it’s evidence of these decays that the collaborations are looking for. ATLAS search for evidence that the gravitons decays into two photons, and the CMS search for evidence that the graviton decays into two jets (bursts) of hadrons (a particular class of particle). (ThingsWeDontKnow.com)

            +
            +

            fully-expanded-incl-matrices

            Prime Assessments

            p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry
+7 11 4 1 0 11 ◄--- #19 ◄--- #43 ◄--- 24s 👈 30 ✔️
+8 13 5 1 0 13 ◄--- #17 ◄--- #49 ◄--- 32s 👈 30 ✔️
+9 17 0 1 1 17 ◄--- 7th prime 👈 5 ◄--- antisymmetric state ✔️
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

            image

            Lightning speed ÷ Shockwave speed = 300000km/s ÷ 3km/s = 100000 ÷ 1

              Sub  | i  |     β | f   
+=======+====+=======+=======  ===   ===   ===   ===   ===   ===
+ 1:1:0 | 1  |     1 | 2 {71}   1     1     |     |     |     |
+-------+----+-------+-------  ---   ---    |     |     |     |
+ 1:2:1 | 2  |     2 | 3 {71}         |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:2:2 | 3  |     3 | 7 = 1 + 2x3    |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:3:3 | 4  |     4 | 10 = 9 + 1     |     |     |     |     |  
+-------+----+-------+----            |     |     |     |     |
+ 1:3:4 | 5  |     5 | 11 = 9 + 2     |     |     |     |     |
+-------+----+-------+----            9     1‘    |    Δ100   |
+*1:3:5 | 6  |     6 | 12 = 9 + 3     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:4:6 | 7  |     7 | 13 = 9 + 4     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+ 1:4:7 | 8  |     8 | 14 = 9 + 5     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:4:8 |{9} |     9 | 15 = 9 + 6     |     |     |     |     |
+-------+----+-------+----            |     |     |     |     |
+*1:4:9 |{10}|    10 | 19 = 9 + 10    |     |     |     |     |
+=======+====+=======+====           ===   ---    1"   ---    |
+ 2:1:0 | 11 |    20 | 20 = 19 + log 10¹    |     |     |     |
+-------+----+-------+----                  |     |     |     |
+ 2:2:1 | 12 |    30 | 26 = 20 + 2x3        |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:2:2 | 13 |    40 | 27 = 26 + 1          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:3:3 | 14 |    50 | 28 = 26 + 2          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+ 2:3:4 | 15 |    60 | 29 = 26 + 3          9‘    |   Δ200    |
+-------+----+-------+----                  |     |     |     |
+*2:3:5 | 16 |    70 | 30 = 26 + 4          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:4:6 | 17 |    80 | 31 = 26 + 5          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+ 2:4:7 |{18}|    90 | 32 = 26 + 6          |     |     |     |
+-------+----+-------+----                  |     |     |     |
+*2:4:8 |{19}|   100 | 36 = 26 + 10         |     |     |     |
+=======+====+=======+====                 ===   ---   ---  ∆1000
+*2:4:9 | 20 |   200 | 38 = 36 + log 10²          |     |     |
+-------+----+-------+----                        |     |     |
+ 3:1:0 | 21 |   300 | 40 = 36 + 2 x log 10²      |     |     |
+-------+----+-------+----                        |     |     |
+ 3:2:1 | 22 |   400 | 41 = 40 + 1                |     |     |
+-------+----+-------+----                        |     |     |
+*3:2:2 | 23 |   500 | 42 = 40 + 2                |     |     |
+-------+----+-------+----                        |     |     |
+*3:3:3 | 24 |   600 | 43 = 40 + 3                9"  Δ300    |
+-------+----+-------+----                        |     |     |
+ 3:3:4 | 25 |   700 | 44 = 40 + 4                |     |     |
+-------+----+-------+----                        |     |     |
+*3:3:5 | 26 |   800 | 45 = 40 + 5                |     |     |
+-------+----+-------+----                        |     |     |
+*3:4:6 | 27 |   900 | 46 = 40 + 6                |     |     |
+-------+----+-------+----                        |     |     |
+ 3:4:7 |{28}|  1000 | 50 = 40 + 10               |     |     |
+=======+====+=======+====                       ===  ====    |
+*3:4:8 |{29}|  2000 | 68 = 50 + 3 x (2x3)      {10³}   |     |
+-------+----+-------+----                        Δ     |     |
+ 3:4:9 |{30}|  3000 |{71}= 68 + log 10³                |     |   
+-------+----+-------+----                              |     |
+ 3:2:1 | 31 |  4000 | 72 = 71 + 1                      |     |
+-------+----+-------+----                              |     |
+*3:2:2 | 32 |  5000 | 73 = 71 + 2                      |     |
+-------+----+-------+----                              |     |
+*3:3:3 | 33 |  6000 | 74 = 71 + 3                    Δ400    |
+-------+----+-------+----                              |     |
+ 3:3:4 | 34 |  7000 | 75 = 71 + 4                      |     |
+-------+----+-------+----                              |     |
+*3:3:5 | 35 |  8000 | 76 = 71 + 5                      |     |
+-------+----+-------+----                              |     |
+*3:4:6 | 36 |  9000 |{77}= 71 + 6                      |     |
+-------+----+-------+----                              |     |
+ 3:4:7 |{37}| 10000 | 81 = 71 + 10 = 100 - 19          |     |
+=======+====+=======+====                             ====  ----
+

            32-5 = 27 = 9x3

            +
            + + Note +
            +
            +

            The four faces of our pyramid additively cascade 32 four-times triangular numbers (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of 32^2 = 1024 = 2^10). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of the 1000th prime within our domain, and equals the total number of ‘elements’ used to construct the pyramid. (PrimesDemystified)

            +
            +

            +
            + + Note +
            +
            +

            While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles.

            • It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton.
            • Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons.
            • The graviton’s Compton wavelength is at least 1.6×10^16 m, or about 1.6 light-years, corresponding to a graviton mass of no more than 7.7×10−23 eV/c2.[22]
            • This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation, the same formula that relates electromagnetic wavelength to photon energy.
            • However, if gravitons are the quanta of gravitational waves, then the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.
            • Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the GW170104 event, which was ~ 1,700 km. The report[22] did not elaborate on the source of this ratio.

            It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way. (Wikipedia)

            +
            +

            Double decay generations = 2^π(11 dimensions) = 2⁵ = 32

            E = mc²
+m = E/c²
+
+c = 1 light-second
+  = 1000 years x L / t
+  = 12,000 months x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+1 year = 12 months
+1000 years = 12,000 months
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+
+Conclusion:
+π(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (5th level) ✔️
+   👇
+π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown ✔️
+   👇
+π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe ✔️
+   👇
+π(π(32(109²-89²))) Moon vs Sun vs Galaxies ✔️
+   👇
+|--👇---------------------------- 2x96 ---------------------|
+|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
+|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown ✔️
+|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+|-------- Bosons --------|---------- Fermions ---------|-- Graviton
+       13 variations               48 variations           11 variations
+

            BBC News: Prof Stephen Hawking's final research paper suggests that our Universe may be one of many similar. This paper is the fruit of 20 years' work.

            Parity Order

            +
            + + Note +
            +
            +

            In the second opposing term, the position 13 gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the 11th prime number is now forced as a new axis-symmetrical zero position. (Google Patent DE102011101032A9)

            +
            +

            s(18) = 1 + 49 = 68 - 18 = 50

            ∆9 (local) + 2×∆9 (decay) = ∆27

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} | ✔️   |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown ✔️       |
+----------------------+-----+                                                ---
+

            Tabulate Prime by Power of 10:
+
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+
+Sequence:
+ By the next layer the 89² will become 89 and 5 become 5² or 25.
+ This 89 and 25 are in the same layer with total of 114 or prime 619
+ So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+
            +
            + + Note +
            +
            +

            Using Euler’s method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler (Wikipedia).

            +
            +

            π(π(π(1000th prime))) + 1 = 40

            image

            Distribution Order

            169 - 1 cycle of 360° = 169 - ∆1 = 168 = π(1000)

            96 perfect squares

            +
            + + Note +
            +
            +

            The primary reason that the electron is considered to be elementary is that experimentally it appears to be point-like and hence structureless.

            • At the same time we are confronted with the fact that it has a rich set of properties which are fundamental to its nature.
            • It has an elementary charge, a half-integral spin, a de nite mass, a well de ned dipole moment, an anomalous spin factor g-2 and of course a wave-particle nature.

            It seems inappropriate to think about such things as the elementary charge as a separate building block from the elementary particle which carries it. (Is the electron a photon with toroidal topology? - pdf)

            +
            + 
              Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
+   Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
+===========+=========+=========+===========+===========+============+===========
+bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
+-----------+---------+---------+-----------+-----------+------------+-- 17
+bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️
+===========+=========+=========+===========+===========+============+===========
+bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
+-----------+---------+---------+-----------+-----------+------------+-- 19
+bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
+===========+=========+=========+===========+===========+============+===========
+majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️
+-----------+---------+---------+-----------+-----------+------------+-----------
+majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
+===========+=========+=========+===========+===========+============+===========
+  SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
+===========+=========+=========+===========+===========+============+===========
+     Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️
+
            +
            + + Note +
            +
            +

            Folio math is similar to modular math, but instead of the numbers wrapping around or spinning around a unit circle, they turn back at different positions on both the X and Y axis. In other words, they never make full cycles.

            • The Y-Axis splits at the top, and the X-Axis splits on the left. The colors help this stand out. Let’s start with the top of the Y-Axis. All digits at the top of the Y-Axis reduce down to 1,7,4 or 5,2,8.
            • This is important. Using this Prime Number Folio Coordinate System, it’s easier to think of prime numbers in separate sequences across from each other and right or left-handed rather than next to each other on a number line. I see them as Chiral.
            • All digits in on the right-hand side of the Y-Axis reduce down to 5, 2 or 8. (For example 179 has 3 digits, what matters is that the numbers 1 +7+9 sum to the number 8.) So this would be considered a right-handed prime number. Or a number on the right side of the Y-Axis.

            The image stands on its own. The patterns should jump off the page. Especially with the color. Right-handed numbers have different properties than the left-handed numbers. These observations are in no way mathematically rigorous.

            • The numbers on the right side (5,2,8)| of the Y-Axis include not only prime numbers, but the products of the prime numbers combined from both sides of the Y-axis.
            • Every product on the right-hand side of the Y-Axis is created from two primes (or semi-primes or combination of semi-primes) from both sides of the Y-axis (one from each side), which ALWAYS sum to an exact multiple of 6. These are plotted on the right side of the X-Axis. (For example 7×11=77. While 7+11=18.)

            Using this Folio Coordinate System, it’s easy to see how the products and sums and their distribution are directly related to each other. You might want to start thinking about the Goldbach Conjecture.

            • All products and sums on the right side are indigo/purple to show how they combine with the red and blue prime numbers.
            • It looks like we are simply adding 6 to each Axis/number line, when in fact we are adding the number 1 to each consecutive number but positioning it at different points while moving around both the X and Y Axis.
            • The colors should help your eye follow the numbers. Follow the colors of the rainbow/number combination to help you move around the system. (R-1,O-2,Y-3,G-4,B-5,I-6).

            The number 35 is an important number. It’s the first number on the right-hand side that’s a product of two prime factors of 5 x 7 = 35.

            • The sum of 5 + 7 = 12. Since the right-handed numbers are distributed evenly by 6, we can add 7 x 6 = 42 to 35 and land on the number 77.
            • So now we know that starting with the number 35 if we add 42 continuously we will NEVER land on a prime number. We can also add 5 x 6 = 42 to 35 and land on 65.
            • We also know that 7 + 11 = 18. The next number that introduces a product of two primes is 5 x 13 = 65 and 5 + 13 = 18. So we can take 6 x 13 = 78 and add this to 65 and land on 143. Which is the product of 11 x 13 = 143.
            • Starting with 65 we can add 78 continuously and NEVER land on a prime number.
            • In the meantime 77 (The product of 7 and 11 now introduces the prime number 11 into the mix. So 77 + (6x11) = 143.
            • Starting with 77 we can add 66 continuously and NEVER land on a prime number.

            You can’t add multiples of 6 until that multiple is introduced into the sequence. The primes on the left behave differently. You can still move around using multiples of 6, but there is no common starting point like the number 35.

            • You have to start with the squares of 5 at 25 (in blue) for one sequence of numbers and the square of 7 at 49 (in red) for the other sequence of numbers.
            • The sums of these products are also not exact multiples of 6. They sum to 10 and 14 and are matched to the split X Axis on the left-hand side of the graph.

            The Prime Number Folio Coordinate System and it’s natural numbers are all you need to find a prime number or a composite number and it’s factors. No need for complex numbers or the Reimann Hypothesis. (Medium)

            +
            +

            Being brought forth you will also begin to uncover the irrelevant role that the Riemann hypothesis plays 7 ate 9 in understanding this elegant distribution.

            The Prime Number Folio Coordinate System

            +
            + + Note +
            +
            +

            This curve is a polar plot of the first 20 non-trivial Riemann zeta function zeros including Gram points along the critical line ζ(1/2+t) for real values of t running from 0 to 50. The consecutive zeros have 50 red plot points between each with zeros identified by magenta concentric rings (scaled to show the relative distance between their values of t). (Wikipedia)

            +
            +

            20x10+ ½(16×6) + ¼(12×18) + ⅛(16×16) = 200 + 48 + 32 + 6 = 286 = 2 x 11 x 13

            RiemannZeta Zeros

            Despite there are many studies and papers it is still an important open problem today.

            +
            + + Warning +
            +
            +

            The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the functional equations. (Riemann Zeta - pdf)

            +
            +

            Riemann hypothesis

            Sehr leider Herr Riemann. Bis jetzt Leute können den Fall immer noch nicht lösen.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/16.html b/multiplication/16.html new file mode 100644 index 00000000000..242d36d9271 --- /dev/null +++ b/multiplication/16.html @@ -0,0 +1,175 @@ + Elementary Retracements (spin 7) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Elementary Retracements (spin 7)

            With the MEC 30 as a folding rule, we describe an application that is familiar and simple. And thus use the identical property of energy and number distribution.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-18 of gist section-14 that is inherited from the gist section-25 by prime spin-107 and span-5 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Thus, we get an unmistakable motion plan of energy, based on the number distribution on the MEC 30 as a folding rule.

            Spin Networks

            In fact spin networks constitute a basis that minimize the degree of over-completeness of the loop basis, and for trivalent intersections eliminate it entirely.

            Vertex-with-m-outgoing-and-n-ingoing-lines_Q320

            The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations.

            images (10)

            The-action-of-the-area-operator-on-a-node-with-intertwiner-C-j-1-j-2-k-a-1-a-2-b-C-j-3-j_Q320

            maxwell-interaction

            41114_2016_3_Equ98

            Constant Area

            The five (5) of integer number partitions profound connection between the most fundamental as it also links the five (5) fundamental mathematical constants:

            (1) The number 1, the multiplicative identity,
            (2) The number i, the imaginary unit of the complex numbers.
            image
            (3) The number π = 3.1415…, the fundamental circle constant, and

            Pi-unrolled-720

            (4) The number e = 2.718…, also known as Euler's number, which occurs widely in mathematical analysis.

            image

            (5) Furthermore, the equation is given in the form of an expression set equal to zero, the number 0, as the additive identity which is common practice in several areas of mathematics.

            Euler's identity is a special case of Euler's formula eix = cos x + i sin x when evaluated for x = π, In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia)

            Euler's identity

            It is stated by DE102011101032A9 that using Euler's identity, the MEC30 standard is more accurately than a measurement.

            +
            + + Note +
            +
            +

            In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix

            +
            +

            ang5

            The distribution of prime numbers is a central point of study in number theory. So let's start from there.

            +
            + + Note +
            +
            +

            The Lorentz group consists, unsurprisingly, of the Lorentz transformations, which are the linear transformations preserving the Minkowski dot product. Equivalently, they are the linear transformations fixing that hyperboloid of two sheets. If we discard one of the sheets, we obtain the orthochronous (time-preserving) subgroup.

            • From the perspective of the centre of the cone, the hyperboloid looks like an open disc. The orthochronous Lorentz transformations precisely correspond to distance-preserving transformations of the hyperbolic plane. These are themselves determined uniquely by a conformal (or anticonformal) transformation of the ‘circle at infinity’.
            • Adding an extra dimension, the orthochronous Lorentz group O^{+}(3,1) is isomorphic to the group of distance-preserving transformations of hyperbolic 3-space, which is again isomorphic to the group of (anti-)conformal transformations of the ‘sphere at infinity’, namely our index-2 supergroup of the Möbius group.

            Moreover, this nicely generalises: the group generated by geometric inversions on the n-sphere is abstractly isomorphic to the orthochronous Lorentz group O^{+}(n+1,1). And when n = 24, we get a very beautiful discrete subgroup, namely the automorphism group of the II(25,1) lattice intimately related to the Leech lattice. (Complex Projective 4-Space)

            +
            +

            spacetime

            Bispinor Structure

            +
            + + Note +
            +
            +

            The Lie group structure of the Lorentz group is explored. Its generators and its Lie algebra are exhibited, via the study of infinitesimal Lorentz transformations.

            • The exponential map is introduced and it is shown that the study of the Lorentz group can be reduced to that of its Lie algebra.
            • Finally, the link between the restricted Lorentz group and the special linear group is established via the spinor map.

            The Lie algebras of these two groups are shown to be identical (up to some isomorphism).

            +
            +

            270355_1_En_7_Fig1_HTML

            +
            + + Note +
            +
            +

            The four pairwise disjoint and non-compact connected components of the Lorentzgroup L = O(1, 3) and corresponding subgroups:

            • the proper Lorentz group L+ = SO(1, 3),
            • the orthochronous Lorentz group L↑,
            • the orthochronous Lorentz group Lo = L↑ + ∪ TL↑+ (see below) and
            • the proper orthochronous Lorentz group L↑+ = SO+(1, 3), which contains the identity element.

            Of course, the sets L↓−, L↑− and L↓+ do not represent groups due to the missing identity element. ([The-four-pairwise-disjoint)

            +
            +

            The-four-pairwise-disjoint-and-non-compact-connected-components-of-the-Lorentz-group-L

            +
            + + Note +
            +
            +

            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

            +
            +

            SO(10)

            SU(5)_representation_of_fermions

            Spin-½ objects are all fermions (a fact explained by the spin–statistics theorem) and satisfy the Pauli exclusion principle where Euler's Identity satisfy Pauli Matrices

            Spin_half_angular_momentum

            5-Table1-1

            The edges are labelled by spins together with `intertwiners' at the vertices which are prescription for how to sum over different ways the spins are rerouted.

            Euclidean-space

            Bispinor Fashion

            +
            + + Note +
            +
            +

            The color strong force is the strong interaction between the three quarks that a proton or neutron is made of.

            • It is called the color strong force because, like the electromagnetic force, the strong force has charges.
            • The electromagnetic force has only one type of charge, which can be either positive or negative (magnetic charges are just slow-moving electric charges), but the strong force has three types.
            • These three types of charges are named after colors: red, green, and blue. They also have anti-colors: anti-red, anti-green and anti-blue. Like the electromagnetic force’s positive and negative charges, different colors attract, and the same colors repel. Some particles that have color charge are quarks and antiquarks.
            • The type of quark is not related to that quark’s color charge at all. Quarks are one of the smallest particles currently known. They take up no space because they are points, and they are the only particles that we have not been able to break apart from other particles yet. This is because the nature of the strong force between particles is that it becomes stronger the further away the particles are.

            The force carrier of the strong force is called the gluon. Gluons also have color charge. Both quarks and gluons have properties that make them unique from other particles, as described in the Standard Model. (Wikipedia).

            +
            +

            Nuclear_Force_anim

            +
            + + Note +
            +
            +

            Shortly after the existence of quarks was proposed by Murray Gell-Mann and George Zweig in 1964, Moo-Young Han and Yoichiro Nambu introduced a hidden internal degree of freedom in which quark wave functions were antisymmetric, thus solving the spin-statistics problem of the Gell Mann-Zweig quark model.

            • Han and Nambu initially designated this degree of freedom by the group SU(3)’, but it was referred to in later papers as “the three triplet model.” One feature of the model (which was originally preferred by Han and Nambu) was that it permitted integrally charged quarks, as well as the fractionally charged quarks initially proposed by Zweig and Gell-Mann.
            • Somewhat later, in the early 1970s, Gell-Mann, in several conference talks, coined the name “Color” to describe the internal degree of freedom of the three triplet model, and advocated a new field theory, designated as “Quantum Chromodynamics” (QCD) to describe the interaction of quarks and gluons within hadrons. In Gell-Mann’s QCD, each quark and gluon had fractional electric charge, and carried what came to be called “Color Charge” in the space of the Color degree of freedom.In quantum chromodynamics (QCD), a quark’s color can take one of three values or charges: red, green, and blue. An antiquark can take one of three anticolors: called antired, antigreen, and antiblue (represented as cyan, magenta, and yellow, respectively). Gluons are mixtures of two colors, such as red and antigreen, which constitutes their color charge. QCD considers eight gluons of the possible nine color–anticolor combinations to be unique; see eight gluon colors for an explanation.
            • All three colors mixed together, or any one of these colors and its complement (or negative), is “colorless” or “white” and has a net color charge of zero. Due to a property of the strong interaction called color confinement, free particles must have a color charge of zero.
            • A baryon is composed of three quarks, which must be one each of red, green, and blue colors; likewise an antibaryon is composed of three antiquarks, one each of antired, antigreen and antiblue. A meson is made from one quark and one antiquark; the quark can be any color, and the antiquark has the matching anticolor.

            The following illustrates the coupling constants for color-charged particles. In a quantum field theory, a coupling constant and a charge are different but related notions. The coupling constant sets the magnitude of the force of interaction; for example, in quantum electrodynamics, the fine-structure constant is a coupling constant. (Wikipedia)

            +
            +

            Neutron_QCD_Animation

            IMG_20240111_062522

            SO(10)

            This diagram is representing groupings (leptons, quarks, weak-force bosons) with 6 quarks in a way that par allels the 6 leptons.

            +
            + + Note +
            +
            +

            In physics, and specifically in quantum field theory, a bispinor is a mathematical construction that is used to describe some of the fundamental particles of nature, including quarks and electrons.

            • It is a specific embodiment of a spinor, specifically constructed so that it is consistent with the requirements of special relativity.
            • Bispinors transform in a certain “spinorial” fashion under the action of the Lorentz group, which describes the symmetries of Minkowski spacetime.
            • They occur in the relativistic spin-1/2 wave function solutions to the Dirac equation.
            • Bispinors are so called because they are constructed out of two simpler component spinors, the Weyl spinors. Each of the two component spinors transform differently under the two distinct complex-conjugate spin-1/2 representations of the Lorentz group.
            • This pairing is of fundamental importance, as it allows the represented particle to have a mass, carry a charge, and represent the flow of charge as a current, and perhaps most importantly, to carry angular momentum.ang5
            • More precisely, the mass is a Casimir invariant of the Lorentz group (an eigenstate of the energy), while the vector combination carries momentum and current, being covariant under the action of the Lorentz group.
            • The angular momentum is carried by the Poynting vector, suitably constructed for the spin field.[1]
            • A bispinor is more or less “the same thing” as a Dirac spinor. The convention used here is that the article on the Dirac spinor presents plane-wave solutions to the Dirac equation using the Dirac convention for the gamma matrices. That is, the Dirac spinor is a bispinor in the Dirac convention.
            • Bispinors are elements of a 4-dimensional complex vector space (1/2, 0) ⊕ (0, 1/2) representation of the Lorentz group.

            Dirac bispinor 6D shows eight (8) quantum spin eigenstates in six (6) dimensions of complex spacetime: 0 (the Higgs field), ±½ (fermions), ±1 (bosons), ±⅔ (anti-fermions), 2 (graviton). Top-left Minkowski diagram displays 6D spacetime curvature. Bottom-right projection displays the 2 orthogonal sinusoids of the Dirac harmonic oscillator, and their phase offsets.

            +
            +

            Dirac_bispinor_6D

            Mass vs Gap (Δ)

            FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.

            +
            + + Note +
            +
            +

            They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a perturbative approach is usually implemented, this being equivalent to summing over Feynman diagrams. (Wikiwand)

            +
            +

            default

              Tabulate Prime by Power of 10
+  loop(10) = π(10)-π(1) = 4-0 = 4
+  loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
+  loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
+
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
+  -----------------------+----+----+----+----+----+----+----+----+----+-----
+   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
+  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
+   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
+    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
+  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
+    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
+  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
+    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th 
+  =======================+====+====+====+====+====+====+====+====+====+=====
+           Δ                                                            Δ
+  12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-1
+

            So when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming bilateral 9 sum which facilitate them to finaly generate 1000 primes.

            image

            These waves have phase offsets, meaning they peak at different times. This all relates to Zitterbewegung, a term describing the jittery motion of particles in quantum mechanics.

            +
            + + Note +
            +
            +

            In this work, we propose a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates.

            • We take gaphene/SiC heterostructure as a role model and demonstrate experimentally the substrate modulation leads to Dirac fermion cloning and consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space.
            • Our theoretical modeling captures the cloning mechanism of Dirac states and indicates that flat bands can emerge at certain magic lattice constants of substrate when the period of modulation becomes nearly commensurate with the (√3 ×√3)R30◦ supercell of graphene.

            The results show that the epitaxial monolayer graphene is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons. (Dirac Fermion Cloning - pdf)

            +
            +

            Dirac Fermion Cloning

            +
            + + Note +
            +
            +

            The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the “mass gap”: the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. (Clay Institute)

            +
            + 
            E = mc²
+m = E/c²
+
+c = 1 light-second
+  = 1000 years x L / t
+  = 12,000 months x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+1 year = 12 months
+1000 years = 12,000 months
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+
+Conclusion:
+π(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (mass of matter) ✔️
+   👇
+π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown (gap in 2nd-level)✔️
+   👇
+π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level) ✔️
+   👇
+π(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st gap via dark matter) ✔️
+   👇
+|--👇---------------------------- 2x96 ---------------------|
+|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
+|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown
+|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+|-------- Bosons --------|---------- Fermions ---------|-- Graviton
+       13 variations               48 variations           11 variations
+

            When recombination is occur then the prime 13 is forced to → 12 where the impact (Δ1) goes to 18+13+12=43 on the last 7th row forming the Primes Platform. Thus we got 109 objects including for the 7 rows back to the original stage.

            origin

            To conclude, we believe we have the first firm evidence of Majorana fermion, after 80 years of this whole saga of trying to find it.

            +
            + + Note +
            +
            +

            And we believe this discovery will have important implications in the knowledge and lives of human beings. For example, we live in a universe full of matter now, but the Big Bang created both matter and antimatter. (Quantized signature of majorana)

            +
            +

            majorana

            So what happened to all the antimatter? Where did it go? Perhaps the Majorana fermion can go some ways towards explaining that.

            IMG_20240109_004026

            The above is observed following the W0 (assumptions of relativistic quantum mechanics) for the Existence and Mass Gap which transform under the homogeneous group as a four-vector and has a mass gap Δ > 0.

            image

            +
            + + Note +
            +
            +

            Yang–Mills Existence and Mass Gap: Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R^4 and has a mass gap Δ > 0. (In quantum field theory, the mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle.) (Wikipedia)

            +
            +

            Yang–Mills and Mass Gap

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/17.html b/multiplication/17.html new file mode 100644 index 00000000000..7cd674df3a6 --- /dev/null +++ b/multiplication/17.html @@ -0,0 +1,456 @@ + The Recycling Momentum (spin 8) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Recycling Momentum (spin 8)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-19 of gist section-15 that is inherited from the gist section-26 by prime spin-106 and span-4 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            The Extra Dimensions

            By this image you would see how the earth movements should actually work based on spacetime curved by mass and energy on our solar system. But it is still not enough.

            +
            + + Note +
            +
            +

            Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990 that they were all different limiting cases of a single theory in 11 dimensions known as M-theory (Wikipedia).

            +
            +

            Solar Ststem

            Nowadays there are many scientists come in to the conclusion that there should be extra dimensions involved and typically it would take a very complicated form.

            +
            + + Note +
            +
            +
            1. Line/length
            2. Plane/shapes
            3. Depth, representing a stretching and shearing of the plane
            4. Time, stands as starting point to attemp the Theory Of Everything (TOE).
            5. Alternate world (we could measure similarities and differences of what might have been). Some theories state that light is nothing but ripples of vibrations in the fifth dimension
            6. A plane of possible worlds that start with the same conditions (example: the Big Bang). Theoretically, if you were to master the sixth and seventh dimensions, you could travel through time.
            7. Access to different worlds with different initial conditions. Here, everything would have happened differently, including the beginning conditions (one universe started with the Big Bang, another with the Oscillating Universe theory).
            8. This dimension is similar to the seventh. There are multiple universes that all started differently and histories that branch out infinitely.
            9. Here, we can compare all the could-have-been universes, each with a possibly different set of laws of physics.
            10. Kinda like an extra room to accommodate ALL the theories. In additions, some physicists believe that at the instant of the Big Bang, the universe(s) was fully 10 dimensional.
            +
            +

            extra dimensions

            The coupling dynamics of dimension d ⩾ 4 reflects to matter–antimatter annihilation that tied in with addition, multiplication and exponentiation function of Euler Indentity.

            +
            + + Note +
            +
            +

            In 1922, Hermann Weyl claimed that Maxwell’s theory of electromagnetism can be expressed in terms of an action only for a four-dimensional manifold. Finally, Tangherlini showed in 1963 that when there are more than three spatial dimensions, electron orbitals around nuclei cannot be stable; electrons would either fall into the nucleus or disperse. (Wikipedia)

            +
            +

            pairing from nothingness

            By the exponentiation zones these annihilation relates to the fundamental circle constant π = 3.1415…. So how does it go with imajinari constant?

            +
            + + Note +
            +
            +

            Euler’s identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler’s formula e^ix = cos x + i sin x when evaluated for x = π. (Wikipedia).

            +
            +

            Euler's identity of Matter and Antimatter

            Rotation vs Revolution

            85060684-db12a400-b1cf-11ea-8f37-6b9b3bcab2f2

            +
            + + Note +
            +
            +

            The full Lagrangian of the SM is rather cumbersome and can be found in The Physics of the Standard Model and Beyond - pdf. A graphical representation of elementary particle interactions is shown on Fig. 1.1

            • Three major groups of true elementary particles are distinguished in the framework of the SM: fermions, in particular quarks and leptons, gauge bosons, which are interaction carriers and the Higgs boson, responsible for the masses of elementary particles.
            • Fermions have spin equal to n/2, n = 1, 2, 3 . . . and obey Fermi-Dirac statistics. Quarks, charged leptons and neutrinos belong to the SM fermions. Bosons have an integer spin and are described by Bose-Einstein statistics. The SM interaction carriers are the gauge bosons γ, Z, W± (vectors) and the Higgs boson H (scalar).

            All the particles of the Standard Model have been experimentally observed, including the Higgs boson in 2012.[2][3] Many other hypothetical elementary particles, such as the graviton, have been proposed, but not observed experimentally. (Wikipedia)

            +
            +

            The Standard Model - Measurement_of_the_e_c_1S_production_cross-section.pdf

            In order to propagate this annihilation and how they interact with each other we shall attemp it using string theory that bring the concept of eleven (11) dimensions.

            +
            + + Note +
            +
            +

            The Milky Way is a barred spiral galaxy with a D25 isophotal diameter estimated at 26.8 ± 1.1 kiloparsecs (87,400 ± 3,600 light-years),[10] but only about 1,000 light-years thick at the spiral arms (more at the bulge).

            • Recent simulations suggest that a dark matter area, also containing some visible stars, may extend up to a diameter of almost 2 million light-years (613 kpc).
            • The Milky Way has several satellite galaxies and is part of the Local Group of galaxies, which form part of the Virgo Supercluster, which is itself a component of the Laniakea Supercluster.
            • It is estimated to contain 100–400 billion stars and at least that number of planets. The Solar System is located at a radius of about 27,000 light-years (8.3 kpc) from the Galactic Center, on the inner edge of the Orion Arm, one of the spiral-shaped concentrations of gas and dust. The stars in the innermost 10,000 light-years form a bulge and one or more bars that radiate from the bulge.
            • The Galactic Center is an intense radio source known as Sagittarius A, a supermassive black hole of 4.100 (± 0.034) million solar masses.[39][40] Stars and gases at a wide range of distances from the Galactic Center orbit at approximately 220 kilometers per second (136 miles per second).
            • The constant rotational speed appears to contradict the laws of Keplerian dynamics and suggests that much (about 90%) of the mass of the Milky Way is invisible to telescopes, neither emitting nor absorbing electromagnetic radiation. This conjectural mass has been termed “dark matter”. The rotational period is about 212 million years at the radius of the Sun.[16]

            The Milky Way as a whole is moving at a velocity of approximately 600 km per second (372 miles per second) with respect to extragalactic frames of reference. The oldest stars in the Milky Way are nearly as old as the Universe itself and thus probably formed shortly after the Dark Ages of the Big Bang.[42] (Wikipedia)

            +
            + 
            E = mc²
+m = E/c²
+
+c = 1 light-second
+  = 1000 years x L / t
+  = 12,000 months x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+1 year = 12 months
+1000 years = 12,000 months
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+
+Conclusion:
+π(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (mass of matter)
+   👇
+π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown (gap in 2nd-level)
+   👇
+π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level)
+   👇
+π(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter) 
+   👇
+|--👇---------------------------- 2x96 ---------------------|
+|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
+|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉
+|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+|-------- Bosons --------|---------- Fermions ---------|-- Graviton
+|----- (Sun Orbit) ------|-------- (Moon Orbit) -------| (11 Galaxies) ✔️
+|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way ✔️
+

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------  ✔️   |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+

            1st Fermion Fields = 96 / 12 Moon Orbit = 8 (1st-gap)

            8 (1st-gap)

            Truncated Perturbation

            +
            + + Note +
            +
            +

            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

            +
            +

            SO(10)

            SU(5)_representation_of_fermions

            10th prime = 29 = 28+1

                        3 x 3rd-gap
+           ∆     ∆     ∆
+           |     |     |
+-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap
+  1' |  1  | {2} |  3  |  4  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  2' |  5  |  6  |  7  |  8  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  3' |  9  |{10} |  2¤ (M dan F)
+     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      
+  4' | 11  | 12  | 13  | 3¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  5' | 14  | 15  | 16  | 17  | 4¤    
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  6' | 18  | 19  |{20} | 3¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap
+  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap
+           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆
+           |     |     |     |     |     |     |     | P(7)=142857
+               8 x 3rd-gap inside the 2nd-gap          (Truncated)
+
            +
            + + Note +
            +
            +

            In 2016, using 20 years of images from the Hubble space telescope, it was estimated that there were in total two trillion (2×10<sup>12</sup>) or more galaxies in the observable universe, and as many as an estimated 1×10<sup>24</sup> stars (more stars than all the grains of sand on all beaches of the planet Earth) (Wikipedia)

            +
            +

            image

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨  encapsulation
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨  abstraction
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ---------- ✔️      13¨  inheritance
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨  class
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨  object
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) ---------> Δ18                           |
+----------------------+-----+                                                ---
+
            +
            + + Note +
            +
            +

            The matter representations come in three copies (generations) of the 16 representation. The Yukawa coupling is 10H 16f 16f. *This includes a right-handed neutrino”. One may either include three copies of singlet representations φ and a Yukawa coupling (the “double seesaw mechanism”); or else, add the Yukawa interaction or add the nonrenormalizable coupling. (Wikipedia)

            +
            +

            SO(10)

            SO(10)_-_16_Weight_Diagram svg

            Each result goes to the 9th object of prime 67 which is 19th prime. This mass gap of (Δ > 0) is actually the quantum way of our eQ19-algorithm.

            +
            + + Note +
            +
            +

            In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.

            • A critical feature of the technique is a middle step that breaks the problem into “solvable” and “perturbative” parts.
            • In perturbation theory, the solution is expressed as a power series in a small parameter.
            • The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller. An approximate ‘perturbation solution’ is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the ‘first order’ perturbation correction.

            Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in general remains actively and heavily researched across multiple disciplines.(Wikipedia)

            +
            + 

                        3 x 3rd-gap
+           ∆     ∆     ∆
+           |     |     |
+-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap
+  19 |  1  | {2} |  3  |  4  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  17 |  5  |  6  |  7  |  8  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  ❓ |  9  |{10} |  2¤ (M dan F)
+     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      
+  ❓ | 11  | 12  | 13  | 3¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  ❓ | 14  | 15  | 16  | 17  | 4¤    
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  ❓ | 18  | 19  |{20} | 3¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap
+  ❓ | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap
+           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆
+           |     |     |     |     |     |     |     | P(7)=142857
+               8 x 3rd-gap inside the 2nd-gap          (Truncated)
+

            96 perfect squares

            These waves have phase offsets, meaning they peak at different times. This all relates to Zitterbewegung, a term describing the jittery motion of particles in quantum mechanics.

            Expanded Structure

            This diagram is representing groupings (leptons, quarks, weak-force bosons) with 6 quarks in a way that parallels the 6 leptons.

            +
            + + Note +
            +
            +

            There are 8 different types of tiny particles, or ‘states’, that we can find in a special kind of space that has 6 dimensions and involves both real and imaginary numbers. These particles include:

            • The Higgs field, which doesn’t spin and is represented by 0.
            • Fermions, which are particles like electrons, having a spin of plus or minus a half.
            • Bosons, like photons, which have a spin of plus or minus 1.
            • Anti-fermions, which are like fermions but have a spin of plus or minus two-thirds.
            • The graviton, believed to be responsible for gravity, with a spin of 2.

            In a diagram at the top left, this 6-dimensional space is shown to be curved. In another diagram at the bottom right, we see two waves that are perpendicular to each other, representing the motion of a particle in a ‘Dirac harmonic oscillator’ – a concept in quantum mechanics. (Physics In History)

            +
            +

            Dirac_bispinor_6D

            Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The corresponding eigenvalue is often represented as the multiplying factor.

            +
            + + Note +
            +
            +

            The red vectors are not parallel to either eigenvector, so, their directions are changed by the transformation. The lengths of the purple vectors are unchanged after the transformation (due to their eigenvalue of 1), while blue vectors are three times the length of the original (due to their eigenvalue of 3). See also: An extended version, showing all four quadrants.

            +
            +

            Therefore this 12's treatment will involve at least 11 groups of runner and one (1) profile of the 7's transformation. We collect them in 11 + 7 = 18 gists as below.

            +
            + + Note +
            +
            +

            Gists provide a simple way to share code snippets with others. Every gist is a Git repository, which means that it can be forked and cloned. If you are signed in to GitHub when you create a gist, the gist will be associated with your account and you will see it in your list of gists when you navigate to your gist home page. (GitHub)

            +
            + 
            $ gh api -H "${HEADER}" /users/eq19/gists --jq '.[].url'
+
+https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar 36
+https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax
+https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser
+https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer
+https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed
+https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 30
+                                                           --------
+https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
+https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
+https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
+https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
+https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
+https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
+https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
+https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
+https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
+https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
+https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
+https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37
+

            By the prime hexagon the 19th spin is touching back to the first node. So the workflow will be proceeded as bilateral way and twisted them by such a kind of double strands.

            +
            + + Tip +
            +
            +

            Since the higher primes is more than 71 then the most logical position will be in the 11s somewhere in the third of minor hexagon. By the MEC30 we can see that they will be pushed to and ended up on the prime 13.

            +
            + 
            https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
+https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
+https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
+https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
+https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
+https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
+https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
+https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
+https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
+https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
+https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
+https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 1
+-------- bilateral
+https://github.com/eq19/eq19.github.io/wiki                   19 identity 37
+https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar
+https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax
+https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser
+https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer
+https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed
+https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 30
+

            We concluded later on that this bilateral would not come to be possible if only one (1) profile is assigned. Therefore we add another profile so they would be 11 + 2 = 13's.

            These are the ones that bring 11 + 13 = 24 cell hexagons.

            Orbital structure

            The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.

            +
            + + Note +
            +
            +

            The points that lie on the line through the origin, parallel to an eigenvector, remain on the line after the transformation. These lines are represented as faint blue and violet lines, matching the associated eigenvectors. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. Notice that all blue vectors are scaled by a factor of 3. This is their associated eigenvalue. The violet vectors are not scaled, so their eigenvalue is 1.

            +
            +

            streching

            By our project the scheme will be treated as the sun and the moon orbit where this 31 is the maximum days of a month:

            +
            + + Tip +
            +
            +

            By the exponentiation zones and identition zones they will end up as 7 days (sun) and 12 months (moon) while the 11 will represent the ones outside the orbit (stars or galaxies). This 7 vs 12 is the point of view from the earth which making its position is just in the right location (not too far nor to close) with the sun within the universe.

            +
            + 
            https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 1
+https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed
+https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer
+https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser
+https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax
+https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar
+https://github.com/eq19/eq19.github.io.wiki                   19 identity 37
+7 days (sun)
+-------- bilateral 9 sums
+12 months (moon)
+https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 1
+https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
+https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
+https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
+https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
+https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
+https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
+https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
+https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
+https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
+https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
+https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
+

            We are going to manage the relation of all the involved things in the scheme above using wiki and gist. The main different with gist is that wiki is allowing folder. So we can sort the files regardless where the folder that contained the file is located.

            +
            + + Note +
            +
            +

            Gists and Wiki are actually Git repositories, which means that you can fork or clone any gist, even if you aren’t the original author. (GitHub)

            +
            + 
            #!/usr/bin/env bash
+
+WIKI=https://github.com/$2/$1.wiki.git
+BASE=https://github.com/eq19/eq19.github.io.wiki.git
+rm -rf /tmp/workdir /tmp/gistdir && mkdir /tmp/gistdir
+
+git ls-remote ${WIKI} > /dev/null 2>&1
+git clone $([ $? == 0 ] && echo $WIKI || echo $BASE) /tmp/workdir
+gh gist clone 0ce5848f7ad62dc46dedfaa430069857 /tmp/gistdir/addition
+
+gh gist clone b32915925d9d365e2e9351f0c4ed786e /tmp/gistdir/identition/folder1
+gh gist clone 88d09204b2e5986237bd66d062406fde /tmp/gistdir/identition/folder2
+gh gist clone 8cab5e72d52ecb338a2f2187082a1699 /tmp/gistdir/identition/folder3
+gh gist clone 54600a56d20163c2da8910dd804ec406 /tmp/gistdir/identition/folder4
+gh gist clone f1af4317b619154719546e615aaa2155 /tmp/gistdir/identition/folder5
+gh gist clone 6c89c3b0f109e0ead561a452720d1ebf /tmp/gistdir/identition/folder6
+gh gist clone f21abd90f8d471390aad23d6ecc90d6d /tmp/gistdir/identition/folder7
+gh gist clone 6e2fcc2138be6fb68839a3ede32f0525 /tmp/gistdir/identition/folder8
+gh gist clone b541275ab7deda356feef32d600e44d8 /tmp/gistdir/identition/folder9
+gh gist clone 80c8098f16f3e6ca06893b17a02d910e /tmp/gistdir/identition/folder10
+gh gist clone 4ffc4d02579d5cfd336a553c6da2f267 /tmp/gistdir/identition/folder11
+
+gh gist clone f78d4470250720fb18111165564d555f /tmp/gistdir/exponentiation/folder13
+gh gist clone 765ddc69e339079a5a64b56c1d46e00f /tmp/gistdir/exponentiation/folder14
+gh gist clone b9f901cda16e8a11dd24ee6b677ca288 /tmp/gistdir/exponentiation/folder15
+gh gist clone dc30497160f3389546d177da901537d9 /tmp/gistdir/exponentiation/folder16
+gh gist clone e84a0961dc7636c01d5953d19d65e30a /tmp/gistdir/exponentiation/folder17
+gh gist clone e9832026b5b78f694e4ad22c3eb6c3ef /tmp/gistdir/exponentiation/folder18
+
+find /tmp/workdir -type f -name "Home.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
+find /tmp/workdir -type f -name "*zone.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
+find /tmp/workdir/identition -type f -name "*.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
+find /tmp/workdir/exponentiation -type f -name "*.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
+find /tmp/gistdir -type d -name .git -prune -exec rm -rf {} \; && find /tmp/gistdir -type f -name "README.md" -exec rm -rf {} \;
+

            The implementation from addition folder 1 will be exposed by the exponentiation folder 7 meanwhile the folder 12 of multiplication goes to identition zone of 11 folders.

            So they are 4 folders (1, 7, 11, 12) remain inviolable by the gist.

            Section Layers

            The above scheme is also applied in to our project sections which is consists of four (4) zones, the 1st- layer covers addition and multiplication zones, the rest are single zones.

            Section layers

            Dayson introduced the idea of rank of a partition to accomplish the task he set for himself. He made the following conjectures which were proved in 1954 by Peter Swinnerton-Dyer an English mathematician specialising in number theory.

            +
            + + Note +
            +
            +

            Dayson’s friend the neurologist and author Oliver Sacks said: “A favourite word of Freeman’s about doing science and being creative is the word subversive (tending or intending to subvert or overthrow, destroy, or undermine an established or existing system, especially a legally constituted or a set of beliefs), and he’s done that all his life (Wikipedia).

            +
            + 
            N(0, 5, 5n + 4) = N(1, 5, 5n + 4) = N(2, 5, 5n + 4) = N(3, 5, 5n + 4) = N(4, 5, 5n + 4)
+N(0, 7, 7n + 5) = N(1, 7, 7n + 5) = N(2, 7, 7n + 5) = . . . = N(6, 7, 7n + 5)
+

            The concepts of rank and crank can both be used to classify partitions of certain integers into subclasses of equal size. The two concepts produce different subclasses of partitions. This is illustrated in the following two tables.

            +
            + + Note +
            +
            +

            Although not in the form that Dayson have defined, it was found that the last problem on which Ramanujan worked on before his death was cranks. Berndt and his coauthors have given substantial evidence that Ramanujan knew about the function (Wikipedia).

            +
            +

            default

            The subclasses of partitions develops characters similar to the distribution of prime numbers. This results in a fundamental causal relation to the primes, systemically the products are entered into the position system.

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  current discussion               |
+-----+-----+-----+-----+-----+                                              |
+ 17¨ | {5¨}| {3¨}|  2¨ |  7¨ | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  6¨ |  6¨ |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    17¤
+ 11¨ |  3¨ | {3¨}| {5¨}| 3¤        ----->  assigned to "id:33"              |
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  4¨ |  4¨ |  5¨ |  6¨ | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                             ---
+{18¨}|  5¨ |  5¨ |  8¨ | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+                12¤
+ 43¨ | {3¨}| {5¨}|  5¨ | {5¨}| {3¨}|  7¨ | {5¨}| {3¨}|  7¨ | 9¤ (C1 & C2)   |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |-----  13¨  -----|------ 15¨ ------|------ 15¨ ------|
+     |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            A seemingly unrelated construction is the j-function of number theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern.

            +
            + + Note +
            +
            +

            Although this function appears in a branch of mathematics that seems very different from the theory of finite groups, the two subjects turn out to be intimately related (Wikipedia).

            +
            +

            Monstrous moonshine

            We propose a new higher dimensional version of the McKay correspondence which enables us to understand the Hodge theory assigned to singular Gorenstein varieties by physicists, and so-called Higgs bundles.

            +
            + + Note +
            +
            +

            Hodge theory can be extended to cohomology with coefficients in nonabelian groups between flat vector bundles which, by the Riemann-Hilbert correspondence, are the same as local systems (Hodge Theory in String Theory)

            +
            +

            Hodge conjecture

            Our results lead to the conjecture that string theory indicates the existence of some new cohomology theory for algebraic varieties with Gorenstein singularities.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/18.html b/multiplication/18.html new file mode 100644 index 00000000000..c8b72b8300b --- /dev/null +++ b/multiplication/18.html @@ -0,0 +1,558 @@ + Exchange Entrypoint (spin 9) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Exchange Entrypoint (spin 9)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-20 of gist section-16 that is inherited from the gist section-27 by prime spin-105 and span-3 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Spinors vs Antispinor

            One consequence of this is that, in 4 dimensions, we cannot talk about rotation about a line the only non-trivial rotation fixes a plane.

            Configuration-of-asymmetric-and-symmetric-laminates

            image

            Thus, these cubic monomials with one free vector index have 32 × 11 − 32 = 320 degrees of freedom and are in the {320} representation.

            +
            + + Note +
            +
            +

            In physics, and specifically in quantum field theory, a bispinor is a mathematical construction that is used to describe some of the fundamental particles of nature, including quarks and electrons.

            • It is a specific embodiment of a spinor, specifically constructed so that it is consistent with the requirements of special relativity.
            • Bispinors transform in a certain “spinorial” fashion under the action of the Lorentz group, which describes the symmetries of Minkowski spacetime.
            • They occur in the relativistic spin-1/2 wave function solutions to the Dirac equation.
            • Bispinors are so called because they are constructed out of two simpler component spinors, the Weyl spinors.
            • Each of the two component spinors transform differently under the two distinct complex-conjugate spin-1/2 representations of the Lorentz group.
            • This pairing is of fundamental importance, as it allows the represented particle to have a mass, carry a charge, and represent the flow of charge as a current, and perhaps most importantly, to carry angular momentum.
            • More precisely, the mass is a Casimir invariant of the Lorentz group (an eigenstate of the energy), while the vector combination carries momentum and current, being covariant under the action of the Lorentz group.
            • The angular momentum is carried by the Poynting vector, suitably constructed for the spin field.[1]
            • A bispinor is more or less “the same thing” as a Dirac spinor. The convention used here is that the article on the Dirac spinor presents plane-wave solutions to the Dirac equation using the Dirac convention for the gamma matrices. That is, the Dirac spinor is a bispinor in the Dirac convention.

            By contrast, the article below concentrates primarily on the Weyl, or chiral representation, is less focused on the Dirac equation, and more focused on the geometric structure, including the geometry of the Lorentz group. Thus, much of what is said below can be applied to the Majorana equation. (Wikipedia)

            +
            +

            The-electric-dipole-bispinor-as-source-of-fields-of-Matter-and-Antimatter

            Matter vs Antimatter

            +
            + + Note +
            +
            +

            Giving a specific example of a result obtained with data from the ATLAS experiment, Priscilla Pani, ATLAS experiment co-convener of the LHC Dark Matter Working Group, highlights how the collaboration has recently searched the full LHC dataset from the machine’s second run (Run 2), collected between 2015 and 2018, *to look for instances in which the Higgs boson might decay into dark-matter particles. “We found no instances of this decay but we were able to set the strongest limits to date on the likelihood that it occurs,”” says Pani. (CERN)

            +
            +

            Map-1_Plan de travail 1

            +
            + + Note +
            +
            +

            In order to be four-spinors like the electron and other lepton components, there must be one quark component for every combination of flavour and colour, bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four component bispinor, for a total of 96 complex-valued components for the fermion field. (Wikipedia)

            +
            +

            24 x π(7) = 32 x π(π(11)) = 96

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+ 
+layer | node | sub |  i  |  f.                                      MEC 30 / 2
+------+------+-----+-----+------      ‹--------------------------- 30 {+1/2}
+      |      |     |  1  | --------------------------
+      |      |  1  +-----+                           |    
+      |  1   |     |  2  | (5)                       |
+      |      |-----+-----+                           |
+      |      |     |  3  |                           |
+  1   +------+  2  +-----+----                       |
+      |      |     |  4  |                           |
+      |      +-----+-----+                           |
+      |  2   |     |  5  | (7)                       |
+      |      |  3  +-----+                           |
+      |      |     |  6  |                          11s ‹-- ∆28 = (71-43)
+------+------+-----+-----+------      } (36)         |
+      |      |     |  7  |                           |
+      |      |  4  +-----+                           |
+      |  3   |     |  8  | (11)                      |
+      |      +-----+-----+                           |
+      |      |     |  9  | ‹-- ∆18 = (89-71)         |
+  2   +------|  5* +-----+-----                      |
+      |      |     |  10 |                           |
+      |      |-----+-----+                           |
+      |  4   |     |  11 | (13) --------------------- ∆32 ✔️
+      |      |  6  +-----+            ‹------------------------------ 15 {0}
+      |      |     |  12 |---------------------------
+------+------+-----+-----+------------               |
+      |      |     |  13 |                           |
+      |      |  7  +-----+                           |
+      |  5   |     |  14 | (17)                      |
+      |      |-----+-----+                           |
+      |      |     |  15 |                           7s ‹-- ∆24 = (43-19)
+  3*  +------+  8  +-----+-----       } (36)         |
+      |      |     |  16 |                           |
+      |      |-----+-----+                           |
+      |  6   |     |  17 | (19)                      |
+      |      |  9  +-----+                           |
+      |      |     |  18 | -------------------------- ∆68 ✔️
+------|------|-----+-----+-----                            ‹------  0 {-1/2}
+

            IMG_20240111_062522

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |  169-1🌀  |  329+289  | ✔️
+-----+-----+-----+-----+-----+ ----------------------------------> 1st-gap
+  1' |  1  | {2} |  3  |  4  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  2' |  5  |  6  |  7  |  8  | 4¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  3' |  9  |{10} |  2¤ (M dan F)
+     +-----+-----+-----+ ---------------> 2nd-gap inside the 1st-gap      
+  4' | 11  | 12  | 13  | 3¤
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  5' | 14  | 15  | 16  | 17  | 4¤    
+     +-----+-----+-----+-----+ ---------> 2nd-gap inside the 1st-gap
+  6' | 18  | 19  |{20} | 3¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 2nd-gap
+  ∑  | 21  | 22  | 23  | 24  |{25} | 26  | 27  | 28  | 29  | 9¤
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ----> 1st-gap
+           ∆     ∆     ∆     ∆     ∆     ∆     ∆     ∆  👆
+           |     |     |     |     |     |     |     | P(7)=142857
+               8 x 3rd-gap inside the 2nd-gap          (Truncated)
+

            Rate to Infinity

            +
            + + Note +
            +
            +

            This is because spinors need 32 components in 11 dimensions. 11D supergravity can be compactified down to 4 dimensions which then has OSp(8\4) symmetry. (We still have 8 × 4 = 32 so there are still the same number of components.) Spinors need 4 components in 4 dimensions. This gives O(8) for the gauge group which is too small to contain the Standard Model gauge group U(1) × SU(2) × SU(3) which would need at least O(10). (Wikipedia)

            +
            +

            32 = 8 x 4 = 2³ x 2² = 2⁵

            Global Properties

            +
            + + Note +
            +
            +

            Eigenvalue curves (right) showing a triple eigenvalue at zero for τ = 1 and double eigenvalues at 1 ± √2i for τ = 4/√3. On the left the graph of 1/Q(λ) with the same eigenvalue curves plotted in the ground plane. Green stars indicate the eigenvalues of A, blue stars the roots of puv(λ) and triangles the zeroes of Q(λ) (Global properties of eigenvalues - pdf)

            +
            +

            Digital Root (32) = triple (3) + double (2) = 5 eigenvalues

            Eigenvalue-curves-right-showing-a-triple-eigenvalue-at-zero-for

            100 + 68 + 32 = 168 + 32 = π(1000) + 32 = 200

            +
            + + Note +
            +
            +

            The plot shows the eigenvalues of A + tuu > J for 0 ≤ t ≤ 125000 in red, and the eigenvalues of A − tuu>J for the same range of t in cyan

            • Then, one checks easily that A is J-Hamiltonian, and that u >JAu = 0, while u >JA3u = −4 6= 0.
            • The polynomial puv(λ) for v = −Ju is constant, equal to −4.
            • Hence all the four eigenvalues † of A + tuu >J **are going to infinity””, as is shown in thefollowing figure.

            Note also that the rate of convergence to infinity in this example should be as the fourth root of t, which is confirmed by the graph (the fourth root of 125000 is about 19). (Global properties of eigenvalues)

            +
            +

            4 x 8 = 32 = 2⁵

            Four eigenvalues going to infinity

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} ✔️     |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} ✔️
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} ✔️     |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} ✔️
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |
+----------------------+-----+                                                ---
+

            Elementary Structure

            You may refer to the structure of minor hexagon it shows that this reversal behaviour is linked to the nature of the prime numbers.

            +
            + + Note +
            +
            +

            Aside from 2 and 3, primes come in two flavors, 1 modulo 6 and 5 modulo 6, or the dark and light blue triangles in figure 2(a). The program determines where primes land in the hexagon by moving between the 6 possible positions where primes may land, figure 2(b) . The 1-type primes land in python cells 1, 3, and 5. The 5-type primes land in 0, 2, and 4 cells. Finally, it can print output in the form of figure 2(c). (HexSpin)

            +
            +

            Finding a Number in the Hexagon

            Here we are using the inverse function to exponentiation by 3 x 6 = 18 spins. This is what we mean by the multiplication zones that is applied to each of addition zones.

            +
            + + Tip +
            +
            +

            The three (3) minor hexagons are surrounded by the primes (19, 43, 71) which is close to the multiplication of six (6) with 3, 7, 12 to 18, 42, 72. One of a mysterious thing is that 19 × 6 = 43 + 71 where ∆1 is balancing and keep them to remain stay on the 18s scheme. Therefore we use the primes 43 and 71 as corresponding eigenvalues which is the factor by which the eigenvector is scaled.

            +
            +

            19 x 6 = 43 + 71 = 114

            f(30) = 66 - 30 - 30 - 5 = 1

            p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
+3 2 0 1 0 2 👉 2
+4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
+5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40 
+          6 👉 11s Composite Partition ◄--- 102 👈 4th spin
+6 7 3 1 0 7 ◄--- #23 👈 1 ◄--- break MEC30 symmetry ✔️
+7 11 4 1 0 11 ◄--- #19 ◄--- #43 ◄--- 24s 👈 30
+8 13 5 1 0 13 ◄--- #17 ◄--- #49 ◄--- 32s 👈 30
+9 17 0 1 1 17 ◄--- 7th prime 👈 5 ◄--- antisymmetric state ✔️
+           18 👉 7s Composite Partition ◄--- 168 👈 7th spin
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
+..
+..
+40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+..
+..
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36  👉 7s
+-----
+

            These features are the solution to arrange 30 files located in in four (4) of zone folders as the lexer to cope with the Prime Spin and MEC30 Structure.

            +
            + + Note +
            +
            +

            Now such interaction between the elementary particles can be described by means of a field of force, just as the interaction between the charged particles is described by the electromagnetic field. The above considerations show that the interaction of heavy particles with this field is much larger than that of light particles with it.

            • Now the binding energy of the proton in C12, which is estimated from the difference of masses of C12 and B11, is. This corresponds to a binding energy 0,0152 in mass unit, being thirty (30) times the electron mass. (page 53)
            • Assuming λ=5×10-¹²cm, we.obtain for me a value 2×10² times as large as the electron mass. As such a quantum with large mass and positive or negative charge has never been found by the experiment, the above theory seems to be on a wrong line. We can show, however, that, in the ordinary nuclear transformation, such a quantum can not be emitted into outer space. (page 54)

            The interaction of such a quantum with the heavy particle should be far greater than that with the light particle in order to account for the large interaction of the neutron and the proton as well as the small probability of β-disintegration. (Yukawa - pdf)

            +
            + 
            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|--- ✔️    |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------› ✔️    |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |
+----------------------+-----+                                                ---
+

            Speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve.

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹---------------------- ✔️   17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|---- ✔️    |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |
+----------------------+-----+                                                ---
+

            Higgs Mechanism

            360_F_60364421_ehBG4nFhe9uM5sAfvGO8uFl852OvBgmg

            Elementary-particles-of-standard-model-2

            hq720

            109 + 30 + 30 = 139 + 30 = 169

            the 4 couplings

            +
            + + Note +
            +
            +

            In a quantum system, a physical state is described by a state vector:

            • A pair of distinct state vectors are physically equivalent if they differ only by an overall phase factor, ignoring other interactions.
            • A pair of indistinguishable particles such as this have only one state.
            • This means that if the positions of the particles are exchanged (i.e., they undergo a permutation), this does not identify a new physical state, but rather one matching the original physical state.

            In fact, one cannot tell which particle is in which position. (Wikipedia)

            +
            + 
            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} | ✔️   |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown ✔️       |
+----------------------+-----+                                                ---
+

            download (2)

            Sun vs Moon

            1

            Thus a characteristic constant of this system depending on uniformperiods of the month and the year.

            +
            + + Note +
            +
            +

            Since the presence of the sun changes the geometrical properties of space and time , we must screen out its gravitational effect on the earth moon system according to the validity condition of the second postulate of special relativity, i.e. we must only consider the lunar geocentric motion without the heliocentric motion of the earth-moon system. Thus a velocity component VO=V cosO representing the net orbital velocity of the moon as shown in fig. (1) is introduced for calculating the net length L of the lunar orbit assuming a stationary earth. (Determination Of The Greatest Speed C)

            +
            + 
            E = mc²
+m = E/c²
+
+c = 1 light-second
+  = 1000 years x L / t
+  = 12,000 months x 2152612.336257 km / 86164.0906 sec
+  = 299,792.4998 km / sec
+
+Note:
+1 year = 12 months
+1000 years = 12,000 months
+Te = earth revolution = 365,25636 days
+R = radius of moon rotation to earth = 384,264 km
+V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
+Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
+Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
+t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
+L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km
+
+Conclusion:
+π(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (mass of matter)
+   👇
+π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown (gap in 2nd-level)
+   👇
+π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe (2nd gap in 1st-level)
+   👇
+π(π(32(109²-89²))) Moon vs Sun vs Galaxies (1st-gap via dark matter) 
+   👇
+|--👇---------------------------- 2x96 ---------------------|
+|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
+|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
++----+----+----+----+----+----+----+----+----+----+----+----+
+|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉
+|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
+|-------- Bosons --------|---------- Fermions ---------|-- Graviton
+|-- Sun Orbit (7 days) --|--- Moon Orbit (12 months) --| (11 Galaxies) ✔️
+|------------ Part of 1 Galaxy (Milky Way) ------------| Non Milky Way
+

            image

            The seven (7) groups

            +
            + + Tip +
            +
            +

            The number of primes less than or equal to a thousand π(1000) = 168 equals the number of hours in a week 24 × 7 = 168. The tessellating field of equilateral triangles fills with numbers, with spin orientation flipping with each prime number encountered, creating three (3) minor hexagons.

            +
            +

            ∆28 - ∆27 = 1000 - 900 + π(27/9) = 100 + 2 = 102 (Recycled to original state)

            $True Prime Pairs:
+(5,7),(11,13),(17,19)
+
+|------------ 7'----------------|--------------------------- 12' ----------------------------|
+|      3'     |        4'       |              6'             |              6'              |
++---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+| 1 |  2 |  3 | 4 |  5 |  6 | 7 | 8 |  9 |  10 | 11 | 12 | 13 | 14 | 15 |  16 | 17 | 18 | 19 |
++---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+| 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 |  8 | 40 | 50 |  1 | 30 | 200 |  8 | 10 | 40 |
++---+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
+| Z | W± |  γ | A   H+   H-  hH | u    c    t     g    γ  eμτ |  d    s    b     g   ν¤    γ |  
+
+|---- 102  ---|-----  66  ------|-------- 329 = 7 x 47 -------|- 289 = (8+9)² = 2 & (2³+9²) -|
+|--2x3x(8+9)--|--- 2x3x(2+9) ---|---- (1+2) & (2x9)+(2+9) ----|------ 2 & (8x9)+(8+9) -------|
+|-------- 168 = π(1000) --------|------ 1229 = π(10000) ------|------ π(89²) = 1000 ---------|
+|-------- 168 = π(618xΦ) -------|----- 618 = 1000/Φ = 1000x1000/1618 = 10^6/(2x8)&(2x9) -----|
+
            +
            + + Note +
            +
            +

            In particle physics, a lepton is an elementary particle of half-integer spin (spin 1⁄2) that does not undergo strong interactions.[1]

            • Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutral leptons (better known as neutrinos).
            • Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed.
            • The best known of all leptons is the electron.

            There are six types of leptons, known as flavours, grouped in three generations.[2]

            Electrodynamics

            For every lepton flavor, there is a corresponding type of antiparticle, known as an antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. According to certain theories, neutrinos may be their own antiparticle. It is not currently known whether this is the case. (Wikipedia)

            +
            +

            universe review

            It is stated that if vector of the composite system is mathematically equivalent then the entangled states of the two particles are different (otherwise the antisymmetric state vector would vanish).

            +
            + + Note +
            +
            +

            The aim of this paper is to offer a conceptual analysis of Weinberg’s proof of the spin-statistics theorem by comparing it with Pauli’s original proof and with the subsequent textbook tradition, which typically resorts to the dichotomy positive energy for half-integral spin particles/micro causality for integral-spin particles.

            • In contrast to this tradition, Weinberg’s proof does not directly invoke the positivity of the energy, but derives the theorem from the single relativistic requirement of micro causality. This seemingly innocuous difference marks an important change in the conceptual basis of quantum physics.
            • Its historical, theoretical, and conceptual roots are here reconstructed. The link between Weinberg’s proof and Pauli’s original is highlighted: Weinberg’s proof turns out to do justice to Pauli’s anti-Dirac lines of thought.

            The work of Furry and Oppenheimer is also surveyed as a “third way” between the textbook tradition established by Pauli and Weinberg’s approach - pdf

            +
            +

            Increasing_disorder svg

            This is nothing but Pauli's Exclusion Principle forbidding the possibility of any two indistinguishable particles being in the same dynamic state (Pauli, 1925).

            Irrational Partitions

            By this exponentiation zones we will get multiple layers of primes density. So we need to get in to the patterns of the above hexagonal forms through deep learning.

            +
            + + Note +
            +
            +

            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

            +
            +

            SO(10)

            SU(5)_representation_of_fermions

            [(6 + 6) x 6] + [6 + (6 x 6)] = 72 + 42 = 71 + 42 + 1 = 114 objects

            layer | node | sub |  i  |  f                               
+------+------+-----+---------- 
+      |      |     |  1  | -----------------------  71 = 72-1
+      |      |  1  +-----+                        |
+      |  1   |     |  2  | (5)                    |
+      |      |-----+-----+                        |
+      |      |     |  3  | ---------              |
+  1   +------+  2  +-----+----      |             |
+      |      |     |  4  |          5x ---        |
+      |      +-----+-----+          |     |       |
+      |  2   |     |  5  | (7) -----      |       |
+      |      |  3  +-----+                |       |
+289+11=300   |     |  6  |                |       |
+------+------+-----+-----+----- 72 x 6   7x --- 11x = 77 (rational)
+      |      |     |  7  |                |       |
+      |      |  4  +-----+                |       |
+      |  3   |     |  8  | (11)  ---      |       |
+      |      +-----+-----+          |     |       |
+      |      |     |  9  |          2x ---        |
+  2   +------|  5  +-----+-----     |             |
+      |      |     |  10 | ---------              |
+      |      |-----+-----+                        |
+      |  4   |     |  11 | (13) ------------------  71 = 72-1
+      |      |  6  +-----+
+329+71=400   |     |  12 |------------------------  70 = 72-2
+------+------+-----+-----+
+      |      |     |  13 |
+      |      |  7  +-----+
+      |  5   |     |  14 | (17) ◄---------------------------
+      |      |-----+-----+
+      |      |     |  15 | ◄-- 42 x 6 partitions of 13 (irrational)
+  3   +------+  8  +-----+----- 
+      |      |     |  16 |      ◄---------------------------
+      |      |-----+-----+
+      |  6   |     |  17 | (19)
+      |      |  9  +-----+
+168+32=200   |  |  |  18 |------------------------  68 = 72-4
+------|------|--|--+-----+
+       900 -----
+

            The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum mechanics. It is a key result in quantum-mechanical system, and its discovery was a significant landmark in the development of the subject.

            +
            + + Note +
            +
            +

            Complex plot of a wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space (Wikipedia).

            +
            +

            Wavepacket-a2k4-en

            The Prime Recycling ζ(s):
+(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
+
+----------------------+-----+-----+-----+                                    ---
+     7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----  ✔️    |
+     |                +-----+-----+-----+-----+                        |      |
+     |  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
+     |  |             +-----+-----+-----+-----+             |          |      |
+     |  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
+     |  |  |          +-----+-----+-----+-----+             |   |      |     ---
+      --|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
+        |  |          +-----+-----+-----+-----+                 |      |      |
+         --|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
+289        |          +-----+-----+-----+-----+-----+                  |      |
+ |          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
+  --------------------+-----+-----+-----+-----+-----+                  |     ---
+     67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
+     |                +-----+-----+-----+                              |      |
+     |  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
+     |  |             +-----+-----+-----+                       |      |      |
+     |  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} |      |
+     |  |  |          +-----+-----+-----+                       |      |     ---
+     |  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
+     |  |             +-----+-----+-----+                              |      |
+     |   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ------------ ✔️   13¨
+329  |                +-----+-----+-----+                                     |
+  |   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
+   -------------------+-----+-----+                                          ---
+    786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
+     |                +-----+-----+                                           |
+     | 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
+     |  |             +-----+-----+-----+-----+-----+                  |      |
+     |  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
+     |  |  |          +-----+-----+-----+-----+-----+             |    |     ---
+      --|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
+        |  |          +-----+-----+                               |           |
+         --|---› 28:17| 100 | {100} (50) ------------------------»           19¨
+168        |          +-----+                                                 |
+|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown          |
+----------------------+-----+                                                ---
+

            A set of conceptual problems has to be solved, including a superposition principle which requires a linear vector field and quantisation of space-time itself.

            +
            + + Note +
            +
            +

            The approach taken is to think of the solutions of an equation as a geometric object. For example, an equation in two variables defines a curve in the plane. More generally, an equation, or system of equations, in two or more variables defines a curve, a surface or some other such object in n-dimensional space (Wikipedia).

            +
            +

            Consider this could only be solved by prime theory. An experimental observation of the graviton, the gravitational force carrier, is extremely hard due to small coupling.

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤ ✔️ --->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ |  .. |  .. | ..  |  .. | 4¤  ----->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            This idea was taken as the earliest in 1960s Swinnerton-Dyer by using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

            +
            + + Note +
            +
            +

            In the early 1960s Peter Swinnerton-Dyer used the EDSAC computer to calculate the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

            • Based on these numerical results, Birch & Swinnerton-Dyer (1965) conjectured that Np for a curve E with rank r obeys an asymptotic law.
            • The conjecture predicts that the data should form a line of slope equal to the rank of the curve, which is 1 in this case drawn in red in red on the graph

            The Birch and Swinnerton-Dyer conjecture, considered one of the top unsolved problems in mathematics as of 2022. (Wikipedia).

            +
            +

            The Birch and Swinnerton-Dyer conjecture

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/19.html b/multiplication/19.html new file mode 100644 index 00000000000..3f5288c00d0 --- /dev/null +++ b/multiplication/19.html @@ -0,0 +1,346 @@ + The Mapping Order (spin 10) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            The Mapping Order (spin 10)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-21 of gist section-17 that is inherited from the gist section-28 by prime spin-104 and span-2 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Rational Objects

            In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).

            +
            + + Note +
            +
            +

            The central problem is to determine when a Diophantine equation has solutions, and if it does, how many. Two examples of an elliptic curve, that is, a curve of genus 1 having at least one rational point. Either graph can be seen as a slice of a torus in four-dimensional space (Wikipedia).

            +
            +

            Number theory

            One of the main reason is that one does not yet have a mathematically complete example of a quantum gauge theory in four-dimensional space-time. It is even a sign that Einstein's equations on the energy of empty space are somehow incomplete.

            +
            + + Note +
            +
            +

            Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein’s papers, comprising more than 30,000 unique documents (Wikipedia).

            +
            +

            default

            Speculation is that the unfinished book of Ramanujan's partition, series of Dyson's solutions and hugh of Einstein's papers tend to solve it.

            Dyson introduced the concept in the context of a study of certain congruence properties of the partition function discovered by the mathematician Srinivasa Ramanujan who the one that found the interesting behaviour of the taxicab number 1729.

            +
            + + Note +
            +
            +

            The concept was introduced by Freeman Dysonin a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. (Wikipedia)

            +
            +

            Rank_of_a_partition

            Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University, in 1900. They were then applied to the study of the symmetric group. Their theory was further developed by many mathematicians, including W. V. D. Hodge

            +
            + + Note +
            +
            +

            In number theory and combinatorics, rank of a partition of a positive integer is a certain integer associated with the partition meanwhile the crank of a partition of an integer is a certain integer associated with that partition (Wikipedia).

            +
            +

            Supersymmetry

            In mathematics, the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition.

            +
            + + Note +
            +
            +

            On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! (Clay Institute’s - Official problem description).

            +
            +

            image

            25 + 19 + 13 + 7 = 64 = 8 × 8 = 8²

            The True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+|--------------- 7¤ ---------------|
+|-------------- {89} --------------|👈
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
++----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+        ∆         ∆      |---- {48} ----|---- {48} ----|---- {43} ----|👈
+        7        13      |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|
+                         |-------------------- 9¤ --------------------|
+                            ∆                               |-- 25 ---|
+                           19                                    ∆
+                                                               5 x 5
+
            +
            + + Note +
            +
            +

            SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

            +
            +

            SO(10)

            SU(5)_representation_of_fermions 

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ |  5¨ |  3¨ | ..  |  .. | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+
            +
            + + Note +
            +
            +

            Family Number Group +3, +6, +9 being activated by the Aetheron Flux Monopole Emanations, creating Negative Draft Counterspace, Motion and Nested Vortices.) (RodinAerodynamics)

            +
            +

            guest7

            This idea was taken as the earliest in 1960s Swinnerton-Dyer by using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

            +
            + + Note +
            +
            +

            From these numerical results the conjecture predicts that the data should form a line of slope equal to the rank of the curve, which is 1 in this case drawn in red in red on the graph (Wikipedia).

            +
            +

            Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as _[Mo Unfortunately the rotation of this eigenvalues deals with four-dimensional space-time which was already a big issue.

            Geometry of 4D rotations

            In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture.

            +
            + + Note +
            +
            +

            Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries (ClayMath Institute).

            +
            +

            Poincaré Conjecture

            More generally, the central problem is to determine when an equation in n-dimensional space has solutions. However at this point, we finaly found that the prime distribution has something to do with the subclasses of rank and crank partitions.

            Ricci Flow

            guest5

            p r i m e s
+1 0 0 0 0 0
+2 1 0 0 0 1
+3 2 0 1 0 2
+4 3 1 1 0 3
+5 5 2 1 0 5
+6 7 3 1 0 7
+7 11 4 1 0 11
+8 13 5 1 0 13
+9 17 0 1 1 17 ◄--- has a total of 18-7 = 11 composite √
+10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
+-----
+11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19
+12 29 2 -1 1 ∆3 ◄--- 2nd ∆prime ◄--- Fibonacci Index #20
+13 31 1 -1 1 ∆4
+14 37 1 1 1 ∆5 ◄--- 3th ∆prime ◄--- Fibonacci Index #21
+15 41 2 1 1 ∆6
+16 43 3 1 1 ∆7 ◄--- 4th ∆prime ◄--- Fibonacci Index #22
+17 47 4 1 1 ∆8
+18 53 4 -1 1 ∆9
+19 59 4 1 1 ∆10
+20 61 5 1 1 ∆11 ◄--- 5th ∆prime ◄--- Fibonacci Index #23
+21 67 5 -1 1 ∆12
+22 71 4 -1 1 ∆13 ◄--- 6th ∆prime ◄--- Fibonacci Index #24
+23 73 3 -1 1 ∆14
+24 79 3 1 1 ∆15
+25 83 4 1 1 ∆16
+26 89 4 -1 1 ∆17 ◄--- 7th ∆prime ◄--- Fibonacci Index #25
+27 97 3 -1 1 ∆18
+28 101 2 -1 1 ∆19 ◄--- 8th ∆prime ◄--- Fibonacci Index #26
+29 103 1 -1 1 ∆20
+30 107 0 -1 1 ∆21
+31 109 5 -1 0 ∆22
+32 113 4 -1 0 ∆23 ◄--- 9th ∆prime ◄--- Fibonacci Index #27
+33 127 3 -1 0 ∆24
+34 131 2 -1 0 ∆25
+35 137 2 1 0 ∆26
+36 139 3 1 0 ∆27
+37 149 4 1 0 ∆28
+38 151 5 1 0 ∆29 ◄--- 10th ∆prime  ◄--- Fibonacci Index #28
+39 157 5 -1 0 ∆30
+40 163 5 1 0 ∆31 ◄--- 11th ∆prime ◄--- Fibonacci Index #29
+-----
+41 167 0 1 1 ∆0
+42 173 0 -1 1 ∆1
+43 179 0 1 1 ∆2 ◄--- ∆∆1
+44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
+45 191 2 1 1 ∆4
+46 193 3 1 1 ∆5 ◄--- ∆∆3 ◄--- 2nd ∆∆prime ◄--- Fibonacci Index #31
+47 197 4 1 1 ∆6
+48 199 5 1 1 ∆7 ◄--- ∆∆4
+49 211 5 -1 1 ∆8
+50 223 5 1 1 ∆9
+51 227 0 1 2 ∆10
+52 229 1 1 2 ∆11 ◄--- ∆∆5 ◄--- 3rd ∆∆prime ◄--- Fibonacci Index #32
+53 233 2 1 2 ∆12
+54 239 2 -1 2 ∆13 ◄--- ∆∆6
+55 241 1 -1 2 ∆14
+56 251 0 -1 2 ∆15
+57 257 0 1 2 ∆16
+58 263 0 -1 2 ∆17 ◄--- ∆∆7 ◄--- 4th ∆∆prime ◄--- Fibonacci Index #33
+59 269 0 1 2 ∆18
+60 271 1 1 2 ∆19 ◄--- ∆∆8
+61 277 1 -1 2 ∆20
+62 281 0 -1 2 ∆21
+63 283 5 -1 1 ∆22
+64 293 4 -1 1 ∆23 ◄--- ∆∆9
+65 307 3 -1 1 ∆24
+66 311 2 -1 1 ∆25
+67 313 1 -1 1 ∆26
+68 317 0 -1 1 ∆27
+69 331 5 -1 0 ∆28
+70 337 5 1 0 ∆29 ◄--- ∆∆10
+71 347 0 1 1 ∆30
+72 349 1 1 1 ∆31 ◄--- ∆∆11 ◄--- 5th ∆∆prime ◄--- Fibonacci Index #34
+73 353 2 1 1 ∆32
+74 359 2 -1 1 ∆33
+75 367 1 -1 1 ∆34
+76 373 1 1 1 ∆35
+77 379 1 -1 1 ∆36
+78 383 0 -1 1 ∆37 ◄--- ∆∆12
+79 389 0 1 1 ∆38
+80 397 1 1 1 ∆39
+81 401 2 1 1 ∆40
+82 409 3 1 1 ∆41 ◄--- ∆∆13 ◄--- 6th ∆∆prime ◄--- Fibonacci Index #35
+83 419 4 1 1 ∆42
+84 421 5 1 1 ∆43 ◄--- ∆∆14
+85 431 0 1 2 ∆44
+86 433 1 1 2 ∆45
+87 439 1 -1 2 ∆46
+88 443 0 -1 2 ∆47 ◄--- ∆∆15
+89 449 0 1 2 ∆48
+90 457 1 1 2 ∆49
+91 461 2 1 2 ∆50
+92 463 3 1 2 ∆51
+93 467 4 1 2 ∆52
+94 479 4 -1 2 ∆53 ◄--- ∆∆16
+95 487 3 -1 2 ∆54
+96 491 2 -1 2 ∆55
+97 499 1 -1 2 ∆56
+98 503 0 -1 2 ∆57
+99 509 0 1 2 ∆58
+100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36
+-----
+101 523 5 -1 1 ∆2 ◄--- ∆∆18 ◄--- 1st ∆∆∆prime ◄--- Fibonacci Index #37 √
+102 541 5 1 1 ∆3 ◄--- ∆∆∆1 ◄--- 1st ÷÷÷composite ◄--- Index #(37+2)=#39 √
+103 547 5 -1 1 ∆4
+104 557 4 -1 1 ∆5 ◄--- ∆∆∆2 ◄---2nd ∆∆∆prime √
+105 563 4 1 1 ∆6
+106 569 4 -1 1 ∆7 ◄--- ∆∆∆3 ◄--- 3rd ∆∆∆prime √
+107 571 3 -1 1 ∆8
+108 577 3 1 1 ∆9
+109 587 4 1 1 ∆10
+110 593 4 -1 1 ∆11 ◄--- ∆∆∆4 ◄--- 2nd ÷÷÷composite ◄--- Index #(37+3)=#40 √
+111 599 4 1 1 ∆12
+112 601 5 1 1 ∆13 ◄--- ∆∆∆5 ◄--- 4th ∆∆∆prime √
+113 607 5 -1 1 ∆14
+114 613 5 1 1 ∆15
+115 617 0 1 2 ∆16
+116 619 1 1 2 ∆17 ◄--- ∆∆∆6 ◄--- 3rd ÷÷÷composite ◄--- Index #(37+5)=#42 √
+117 631 1 -1 2 ∆18
+118 641 0 -1 2 ∆19 ◄--- ∆∆∆7 ◄--- 5th ∆∆∆prime √
+119 643 5 -1 1 ∆20
+120 647 4 -1 1 ∆21
+121 653 4 1 1 ∆22
+122 659 4 -1 1 ∆23 ◄--- ∆∆∆8 ◄--- 4th ÷÷÷composite ◄--- Index #(37+7)=#44 √
+123 661 3 -1 1 ∆24
+124 673 3 1 1 ∆25
+125 677 4 1 1 ∆26
+126 683 4 -1 1 ∆27
+127 691 3 -1 1 ∆28
+128 701 2 -1 1 ∆29 ◄--- ∆∆∆9 ◄--- 5th ÷÷÷composite ◄--- Index #(37+11)=#48 √
+129 709 1 -1 1 ∆30
+130 719 0 -1 1 ∆31 ◄--- ∆∆∆10 ◄--- 6th ÷÷÷composite ◄--- Index #(37+13)=#50 √
+131 727 5 -1 0 ∆32
+132 733 5 1 0 ∆33
+133 739 5 -1 0 ∆34
+134 743 4 -1 0 ∆35
+135 751 3 -1 0 ∆36
+136 757 3 1 0 ∆37 ◄--- ∆∆∆11 ◄--- 6th ∆∆∆prime √
+137 761 4 1 0 ∆38
+138 769 5 1 0 ∆39
+139 773 0 1 1 ∆40
+140 787 1 1 1 ∆41 ◄--- ∆∆∆12 ◄--- 7th ÷÷÷composite ◄--- Index #(37+17)=#54 √
+141 797 2 1 1 ∆42
+142 809 2 -1 1 ∆43 ◄--- ∆∆∆13 ◄--- 7th ∆∆∆prime √
+143 811 1 -1 1 ∆44
+144 821 0 -1 1 ∆45
+145 823 5 -1 0 ∆46
+146 827 4 -1 0 ∆47 ◄--- ∆∆∆14 ◄--- 8th ÷÷÷composite ◄--- Index #(37+19)=#56 √
+147 829 3 -1 0 ∆48
+148 839 2 -1 0 ∆49
+149 853 1 -1 0 ∆50
+150 857 0 -1 0 ∆51
+151 859 5 -1 -1 ∆52
+152 863 4 -1 -1 ∆53 ◄--- ∆∆∆15 ◄--- 9th ÷÷÷composite ◄--- Index #(37+23)=#60 √
+153 877 3 -1 -1 ∆54
+154 881 2 -1 -1 ∆55
+155 883 1 -1 -1 ∆56
+156 887 0 -1 -1 ∆57
+157 907 5 -1 -2 ∆58
+158 911 4 -1 -2 ∆59 ◄--- ∆∆∆16 ◄--- 10th ÷÷÷composite ◄--- Index #(37+29)=#66 √
+159 919 3 -1 -2 ∆60
+169 929 2 -1 -2 ∆61 ◄--- ∆∆∆17 ◄--- 8th ∆∆∆prime √
+161 937 1 -1 -2 ∆62
+162 941 0 -1 -2 ∆63
+163 947 0 1 -2 ∆64
+164 953 0 -1 -2 ∆65
+165 967 5 -1 -3 ∆66
+166 971 4 -1 -3 ∆67 ◄--- ∆∆∆18 ◄--- 11th ÷÷÷composite ◄--- Index #(37+31)=#68 √
+167 977 4 1 -3 ∆68
+168 983 4 -1 -3 ∆69
+169 991 3 -1 -3 ∆70
+170 997 3 1 -32 ∆71 ◄--- ∆∆∆19 ◄--- 9th ∆∆∆prime √
+

            Scot_Number_Map_Diag

            The Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it rounder, in the hope that one may draw topological conclusions from the existence of such "round" metrics.

            +
            + + Note +
            +
            +

            Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere (Wikipedia)

            +
            +

            default

            The Ricci Flow method has now been developed not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI (Artificial intelligence). No wonder now all the science leads to it.

            So what we've discussed on this wiki is entirely nothing but an embodiment of this solved Poincare Conjecture. This is the one placed with id: 10 (ten) which stands as the basic algorithm of π(10)=(2,3,5,7).

            +
            + + Note +
            +
            +

            Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence. AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence (Human vs AI).

            +
            +

            Poincaré Conjecture

            Finite collections of objects are considered 0-dimensional. Objects that are "dragged" versions of zero-dimensional objects are then called one-dimensional. Similarly, objects which are dragged one-dimensional objects are two-dimensional, and so on.

            +
            + + Note +
            +
            +

            The basic ideas leading up to this result (including the dimension invariance theorem, domain invariance theorem, and Lebesgue covering dimension) were developed by Poincaré, Brouwer, Lebesgue, Urysohn, and Menger (MathWorld).

            +
            +

            default

            Spacetime Patterns

            toroid_color

            In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.

            +
            + + Note +
            +
            +

            It’s possible to build a Hessian matrix for a Newton’s method step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector. (Tensorflow)

            +
            +

            Tensorflow - Batch Jacobian

            When the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent.

            +
            + + Note +
            +
            +

            When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant ad often referred to simply as the Jacobian in literature. (Wikipedia)

            +
            +

            Hessian matrix for Newton Method

            Double Strands

            Here we adopt an analysis of variance called N/P-Integration that was applied to find the best set of environmental variables that describe the density out of distance matrices.

            +
            + + Note +
            +
            +

            With collaborators, we regularly work on projects where we want to understand the taxonomic and functional diversity of microbial community in the context of metadata often recorded under specific hypotheses. Integrating (N-/P- integration; see figure below) these datasets require a fair deal of multivariate statistical analysis for which I have shared the code on this website. (Umer.Ijaz)

            +
            +

            N-/P- integration

            It can be used to build parsers/compilers/interpreters for various use cases ranging from simple config files to full fledged programming languages.

            +
            + + Note +
            +
            +

            With theoretical foundations in Information Engineering (Discrete Mathematics, Control Theory, System Theory, Information Theory, and Statistics), my research has delivered a suite of systems and products that has allowed me to carve out a niche within an extensive collaborative network (>200 academics). (Umer.Ijaz)

            +
            +

            information engineering

            Since such interactions result in a change in momentum, they can give rise to classical Newtonian forces of rotation and revolution by means of orbital structure.

            torus

            As you can see on the left sidebar (dekstop mode) a total of 102 items will be reached by the end of Id: 35.

            So when they transfered to Id: 36 it will cover 11 x 6 = 66 items thus the total will be 102 + 66 = 168

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/20.html b/multiplication/20.html new file mode 100644 index 00000000000..c30dbb64414 --- /dev/null +++ b/multiplication/20.html @@ -0,0 +1,177 @@ + Magnitude Order (spin 11) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Magnitude Order (spin 11)

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-22 of gist section-18 that is inherited from the gist section-29 by prime spin-103 and span-1 with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            Assigning The Lexer

            image

            Φ = 2,10
+Δ = 5,7,17
+3': 13,18,25,42
+2' » 13 to 77, Δ = 64
+2' and 3' » 13 to 45, Δ = 32
+
+2" + 5" = 7" = 77
+2"=22, 3"=33, 2" + 3" = 5" = 55
+
+13, 16, 18, 21, 23, 25, 28, 30, 32, 34, 
+36, 38, 40, 42, 
+45, 47, 49, 51, 53, 
+55, 57, 59, 61, 
+63, 65, 67, 69, 71, 73, 75, 77
+

            image

            Next we will discuss how to form these numbers on each screens. As explained earlier, there are all three (3) layers. The instance is going to simulate DNA polymerase with proofreading ability.

            Proofreading Ability

            +
            + + Note +
            +
            +

            Proofreading removes the mismatched nucleotide and extension continues. If a mismatch is accidentally incorporated, the polymerase is inhibited from further extension (Wikipedia).

            +
            +

            DNA polymerases

            +
            + + Note +
            +
            +

            A current model of meiotic recombination, initiated by a double-strand break or gap, followed by pairing with an homologous chromosome and strand invasion to initiate the recombinational repair process (Wikipedia).

            +
            +

            image

            π(96) = 96/4 = 24

            $True Prime Pairs:
+(5,7), (11,13), (17,19)
+
+     |    168    |    618    |
+-----+-----+-----+-----+-----+                                             ---
+ 19¨ |  3¨ |  4¨ |  6¨ |  6¨ | 4¤  ----->  assigned to "id:30"             19¨
+-----+-----+-----+-----+-----+                                             ---
+ 17¨ |  5¨ |  3¨ |  ❓ |  ❓ | 4¤ ✔️ --->  assigned to "id:31"              |
+     +-----+-----+-----+-----+                                              |
+{12¨}|  .. |  .. |  2¤ (M & F)     ----->  assigned to "id:32"              |
+     +-----+-----+-----+                                                    |
+ 11¨ |  .. |  .. |  .. | 3¤ ---->  Np(33)  assigned to "id:33"  ----->  👉 77¨
+-----+-----+-----+-----+-----+                                              |
+ 19¨ |  .. |  .. |  .. |  .. | 4¤  ----->  assigned to "id:34"              |
+     +-----+-----+-----+-----+                                              |
+{18¨}|  .. |  .. |  .. | 3¤        ----->  assigned to "id:35"              |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+ 43¨ |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. |  .. | 9¤ (C1 & C2)  43¨
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+               ---
+139¨ |  1     2     3  |  4     5     6  |  7     8     9  |
+                    Δ                 Δ                 Δ       
+

            Strand Partition

            169-over-109-blood-pressure

            Fidelity is very important in DNA replication. Mismatches in DNA base pairing can potentially result in dysfunctional proteins and could lead to cancer. Hydrogen bonds play a key role in base pair binding and interaction.

            +
            + + Note +
            +
            +

            The function of DNA polymerase is not quite perfect, with the enzyme making about one mistake for every billion base pairs copied. Error correction is a property of some, but not all DNA polymerases. This process corrects mistakes in newly synthesized DNA (Wikipedia).

            +
            +

            dna-genetics-biochemistry

            ezgif com-optimize

            Symmetry Breaking

            1 instance + 7 blocks + 29 flats + 77 rooms = 114 objects

            Prime Loops:
+π(10) = 4 (node)
+π(100) = 25 (partition)
+π(1000) - 29 = 139 (section)
+π(10000) - 29th - 29 = 1091 (segment)
+π(100000) - 109th - 109 = 8884 (texture)
+Sum: 4 + 25 + 139 + 1091 + 8884 = 10143 (object)
+
+Sequence Layers:
+- By the next layer the 89² will become 89 and 5 become 5² or 25.
+- This 89 and 25 are in the same layer with total of 114 or prime 619
+- So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
+
+-----+-----+-----+-----+-----+     -----------------------------------------------
+{786}| 1,2 |  2  | 2,3 | 3,4 | {19}                                          |
+-----+-----+-----+-----+-----+                                               |
+ {86}|  4  | 4,5 | 5,6 |{6,7}| 17                                        Base Zone
+     +-----+-----+-----+-----+                                               |
+ {78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ                                      |
+     +-----+-----+-----+                                               -----------
+ {67}| 9,11|11,12|12,14| 11 <----------- Mid Zone                            |
+ ----+-----+-----+-----+-----+                                               |
+  {6}|15,16|17,18|18,20|21,22| 19                                      Mirror Zone
+     +-----+-----+-----+-----+                                               |
+  {8}|23,25|25,27|27,29| 18                                                  |
+     +-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+  {7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+         -----------
+     |  1     2     3  |   4     5     6 |   7     8      9  |
+     |------ 29' ------|--------------- 139' ----------------|
+     |------ 102¨ -----|---------------  66¨ ----------------|
+

            Four-vector configuration

            If you are using Docker-for-Windows, you can run now both Windows and Linux containers simultaneously: Running Docker Windows and Linux Containers Simultaneously, not only the Linux container itself, but also an orchestrator like Kubernetes: Kubernetes is Now Available In Docker Desktop Stable Channel

            image

            On the lagging strand template, a primase "reads" the template DNA and initiates synthesis of a short complementary RNA primer. This is assigned to Windows container.

            GitHub Actions workflow

            The leading strand is the strand of new DNA which is synthesized in the same direction as the growing replication fork. This sort of DNA replication is continuous. This workflow is assigned to Linux container (Ubuntu).

            +
            + + Note +
            +
            +

            DNA polymerase extends primed segments, forming Okazaki fragments. The RNA primers are then removed and replaced with DNA, and the fragments of DNA are joined by DNA ligase and are bound to the helicase heximer (Wikipedia).

            +
            +

            DNA ligase

            In eukaryotes the helicase wraps around the leading strand, and in prokaryotes it wraps around the lagging strand. As helicase unwinds DNA at the replication fork, the DNA ahead is forced to rotate resulting a build-up of twists in the DNA ahead.

            +
            + + Note +
            +
            +

            Because of its orientation, replication of the lagging strand is more complicated as compared to that of the leading strand. As a consequence, the DNA polymerase on this strand is seen to “lag behind”.

            +
            +

            container-diagram

            layer | node | sub |    i     |   f
+------+------+-----+----------+-----+-----+-----+                                    ---
+      |      |     |    1,2:1 |   1 |  30 |  40 | 71 (2,3) ‹-------------------       |
+      |      |  1  +----------+-----+-----+-----+                              |      |
+      |  1   |     |        2 |                                                |      5¨  encapsulation
+      |      |-----+----------+            -----------------------------       |      |
+      |      |     |        3 |           |                             |      |      |
+  1   +------+  2  +----------+----       |       LAGGING SCHEME        |      |     ---
+      |      |     |        4 |           |    (Exponentiation Zone)    |      |      |
+      |      +-----+----------+           |                             |      |      |
+      |  2   |     |        5 |           ------------------------------       |      7¨  abstraction
+289   |      |  3  +----------+                                                |      |
+|     |      |     |        6 |  ‹---------------------------- Φ               | {6®} |
+------+------+-----+----------+-----+-----                                     |     ---
+      |      |     |     11:7 |   5 |   9 |  14 (20) --------› ¤               |      |
+      |      |  4  +----------+-----+-----+-----+                              |      |
+      |  3   |     |     12:8 |   9 |  60 |  40 | 109 (26) «------------       |     11¨  polymorphism
+      |      +-----+----------+-----+-----+-----+                       |      |      |
+      |      |     |     13:9 |   9 |  60 |  69 (27) «-- Δ19 (Rep Fork) | {2®} |      |
+  2   +------|  5  +----------+-----+-----+-----+                       |      |     ---
+      |      |     |    14:19 |   9 |  60 |  40 | 109 (28) -------------       |      |
+      |      |-----+----------+-----+-----+-----+                              |      |
+      |  4   |     | 15,18:11 |   1 |  30 |  40 | 71 (29,30,31,32) ------------      13¨  inheritance
+329   |      |  6  +----------+-----+-----+-----+                                     |
+|     |      |     |    19:12 |  10 |  60 | {70} (36) -------› Φ                      |
+------+------+-----+----------+-----+-----+                                          ---
+      |      |     |    20:13 |  90 |  90 (38) ‹-------------- ¤                      |
+      |      |  7  +----------+-----+                                                 |
+      |  5   |     |       14 |            -----------------------------             17¨  class
+      |      |-----+----------+           |                             |             |
+      |      |     |       15 |           |       LEADING SCHEME        |             |
+  3   +------+  8  +----------+-----      |    (Multiplication Zone)    |            ---
+      |      |     |       16 |           |                             |             |
+      |      |-----+----------+-----+      -----------------------------              |
+      |  6   |     |    28:17 | 100 |                                                19¨  object
+168   |      |  9  +----------+-----+                                                 |
+|     |      |     |    29:18 | 50  | 50(68) ---------> Δ18                           |
+------|------|-----+----------+-----+                                                ---
+

            This distribution of fermion parameters are shown by [13,17], [11,19] in the coupling of MEC30. So we shall find the rest of [7,23], [1,29] in the boson field.

            +
            + + Note +
            +
            +

            In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction.

            • Originally, the coupling constant related the force acting between two static bodies to the “charges” of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r².
            • The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter
            • The solution to both these problems comes from the Higgs mechanism, which involves scalar fields (the number of which depend on the exact form of Higgs mechanism) which (to give the briefest possible description) are “absorbed” by the massive bosons as degrees of freedom, and which couple to the fermions via Yukawa coupling to create what looks like mass terms.

            The next step is to couple the gauge fields to the fermions, allowing for interactions. (Wikipedia)

            +
            +

            Euler's identity

            By The GitHub Runner you can connect to the Google COS Instance. For self-hosted runners defined at the organization level, configure runs-on.group in your workflow file to target a runner groups or combine groups and labels.

            Build Coupling Runner

            The runner is the application that runs a job from a GitHub Actions workflow. It is used by GitHub Actions in the hosted virtual environments, or you can self-host the runner in your own environment. We use both of them to create group as a four-vector.

            choosing-the-runner

            On the other hand, with larger systems we are able to transfer the behavior of the energy from the subatomic space into the haptic space with the scale described here (thought experiment Schröninger's cat). Thus, we are still able to apply the Schröninger wave equation in the haptic space, and replace the Hamiltonian with our measurements. default

            The problems would arise when the Windows Container in Github deliver the RNA Primer to Google instance as Windows Image because it shall read the image while the COS is run under Linux. So it will need to proof and solve without actually having to try.

            +
            + + Note +
            +
            +

            If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem given N cities to visit, how can one do this without visiting a city twice? (Clay Institute).

            +
            +

            P vs NP Problem

            Getting the proofreading ability of DNA polymerase to quickly solve problem for about one mistake for every billion base pairs copied is somehow that required by one of a major unsolved problem in theoretical computer science called P vs NP.

            +
            + + Note +
            +
            +

            P vs. NP deals with the gap between computers being able to quickly solve problems vs. just being able to test proposed solutions for correctness. As such, the P vs. NP problem is the search for a way to solve problems that require the trying of millions, billions, or trillions of combinations without actually having to try each one (P vs. NP Explained).

            +
            +

            P_versus_NP_problem

            It is stated that Np for a curve E with rank r obeys an asymptotic law and is still remain unsolved. Thus it would mean that using Euler's identity to get a definite pattern of prime distribution is still a long way to go.

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/multiplication/index.html b/multiplication/index.html new file mode 100644 index 00000000000..a13ec24fcaa --- /dev/null +++ b/multiplication/index.html @@ -0,0 +1,87 @@ + Multiplication Zones (18-30) · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Multiplication Zones (18-30)

            Multiplication is the form of expression set equal to the inverse function of symmetrical exponentation which stand as multiplicative identity reflects a point across the origin.

            +
            + + Tip +
            +
            +

            This section is referring to wiki page-9 of gist section-5 that is inherited from the gist section-19 by prime spin- and span- with the partitions as below.

            +
            +
            1. Symmetrical Breaking (spin 1)
            2. The Angular Momentum (spin 2)
            3. Entrypoint of Momentum (spin 3)
            4. The Mapping of Spacetime (spin 4)
            5. Similar Order of Magnitude (spin 5)
            6. The Search for The Graviton (spin 6)
            7. Elementary Retracements (spin 7)
            8. The Recycling Momentum (spin 8)
            9. Exchange Entrypoint (spin 9)
            10. The Mapping Order (spin 10)
            11. Magnitude Order (spin 11)

            The multiplication zones is a symmetric matrix representing the multilinear relationship of a stretching and shearing within the plane of the base unit.

            In our approach a 3-form is not an object that exist in addition to the metric, it is the only object that exist and in particular the 4D metric, is defined by the 3-form.

            +
            + + Note +
            +
            +

            We would like to say that our present use of G2 structures (3-forms in 7D) is different from whatone can find in the literature on Kaluza–Klein compactifications of supergravity.

            • We show that the resulting 4D theory is (Riemannian) General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian.
            • Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of . Realistic values of Λ correspond to of Planck size.

            Also, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. (General relativity from three-forms in seven dimensions - pdf)

            +
            +

            3-forms in 7D

            +
            + + Note +
            +
            +

            When the digital root of perfect squares is sequenced within a modulo 30 x 3 = modulo 90 horizon, beautiful symmetries in the form of period-24 palindromes are revealed, which the author has documented on the On-Line Encyclopedia of Integer Sequences as Digital root of squares of numbers not divisible by 2, 3 or 5 (A24092):

            1, 4, 4, 7, 1, 1, 7, 4, 7, 1, 7, 4, 4, 7, 1, 7, 4, 7, 1, 1, 7, 4, 4, 1

            In the matrix pictured below, we list the first 24 elements of our domain, take their squares, calculate the modulo 90 congruence and digital roots of each square, and display the digital root factorization dyad for each square (and map their collective bilateral 9 sum symmetry). (PrimesDemystified)

            +
            +

            Distribution of Perfect Squares

            Square of Nine

            The last "Superstring revolution" was impressive but it was close to 30 years ago now and we still don't seem to be adopting it as The Truth.

            +
            + + Note +
            +
            +

            The vortex theory of the atom was a 19th-century attempt by William Thomson (later Lord Kelvin) to explain why the atoms recently discovered by chemists came in only relatively few varieties but in very great numbers of each kind. Based on the idea of stable, knotted vortices in the ether or aether, it contributed an important mathematical legacy.

            • The vortex theory of the atom was based on the observation that a stable vortex can be created in a fluid by making it into a ring with no ends. Such vortices could be sustained in the luminiferous aether, a hypothetical fluid thought at the time to pervade all of space. In the vortex theory of the atom, a chemical atom is modelled by such a vortex in the aether.
            • Knots can be tied in the core of such a vortex, leading to the hypothesis that each chemical element corresponds to a different kind of knot. The simple toroidal vortex, represented by the circular “unknot” 01, was thought to represent hydrogen. Many elements had yet to be discovered, so the next knot, the trefoil knot 31, was thought to represent carbon.

            However, as more elements were discovered and the periodicity of their characteristics established in the periodic table of the elements, it became clear that this could not be explained by any rational classification of knots. This, together with the discovery of subatomic particles such as the electron, led to the theory being abandoned. (Wikipedia)

            +
            +

            We found also a useful method called Square of Nine which was developed by WD Gann to analyze stock market behaviour base on astrological pattern.

            +
            + + Note +
            +
            +

            He designed a new approach to predicting market behavior using several disciplines, including geometry, astrology, astronomy, and ancient mathematics. They say that not long before his death, Gann developed a unique trading system. However, he preferred not to make his invention public or share it with anyone. (PipBear)

            +
            +

            The Square of 9

            By parsering 168 primes of 1000 id's across π(π(100 x 100)) - 1 = 200 then the (Δ1) would be initiated. As you may guess they will slightly forms the hexagonal patterns.

            +
            + + Note +
            +
            +

            The Hexagon chart begins with a 0 in the center, surrounded by the numbers 1 through 6. Each additional layer adds 6 more numbers as we move out, and these numbers are arranged into a Hexagon formation. This is pretty much as far as Gann went in his descriptions. He basically said, “This works, but you have to figure out how.”One method that I’ve found that works well on all these kinds of charts is plotting planetary longitude values on them, and looking for patterns. On the chart above, each dot represents the location of a particular planet. The red one at the bottom is the Sun, and up from it is Mars. These are marked on the chart. Notice that the Sun and Mars are connected along a pink line running through the center of the chart. The idea is that when two planets line up along a similar line, we have a signal event similar to a conjunction in the sky. Any market vibrating to the Hexagon arrangement should show some kind of response to this situation. (Wave59)

            +
            +

            Patterns of planetary longitude

            We are focusing to MEC30 so we end up this exponentiation by the famous quote from WD Gann himself stating an important changes by certain repetition of 30.

            +
            + + Tip +
            +
            +

            W.D. Gann: “Stocks make important changes in trend every 30, 60, 120, 150, 210, 240, 300, 330, 360 days or degrees from any important top or bottom.”

            +
            +

            WD Gann - Hexagonal Chart

            In line with 168 there is 330 located of 10th layer. Since the base unit of 30 repeats it self on the center then this 11 x 30 = 330 is pushed to the 10 + 1 = 11th layer.

            During this interchange, the two 16-plets will be crossing over and farther apart but they are more likely to "stick together" and not switch places.

            +
            + + Note +
            +
            +

            The terminating digits of the prime root angles (24,264,868; see illustration of Prime Spiral Sieve) when added to their reversal (86,846,242) = 111,111,110, not to mention this sequence possesses symmetries that dovetail perfectly with the prime root and Fibo sequences.

            • And when you combine the terminating digit symmetries described above, capturing three rotations around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry:Prime-Numbers-Demystified-by-8-Dimensional-Algorithms.pdf
            • The pattern of 9’s created by decomposing and summing either the digits of Fibonacci numbers indexed to the first two rotations of the spiral (a palindromic pattern {1393717997173931} that repeats every 16 Fibo index numbers) or, similarly, decomposing and summing the prime root angles.
            • The decomposition works as follows (in digit sum arithmetic this would be termed summing to the digital root) of F17 (the 17th Fibonacci number) = 1597 = 1 + 5 + 9 + 7 = 22 = 2 + 2 = 4:image

            Parsing the squares by their mod 90 congruence reveals that there are 96 perfect squares generated with each 4 * 90 = 360 degree cycle, which distribute 16 squares to each of 6 mod 90 congruence sub-sets defined as n congruent to {1, 19, 31, 49, 61, 79} forming 4 bilateral 80 sums. (PrimesDemystified)

            +
            +

            16 squares

            Each of the 6 columns has 8 bilateral 360 sums, tor a total of 48 * 360 = 40 * 432. This number 432 plays significant roles on the Series Expansion.

            The Interchange Layers

            By the six (6) matrices above it is clearly shows that there is a fascinating connection between prime numbers and the Golden ratio.

            +
            + + Note +
            +
            +

            The first 1000 prime numbers are silently screaming: “Pay attention to us, for we hold the secret to the distribution of all primes!” We heard the call, and with ‘strange coincidences’ leading the way have discovered compelling evidence that the 1000th prime number, 7919, is the perfectly positioned cornerstone of a mathematical object with highly organized substructures and stunning reflectional symmetries. (PrimesDemystified)

            +
            + 
            1st layer:
+It has a total of 1000 numbers
+Total primes = π(1000) = 168 primes
+
+2nd layer:
+It will start by π(168)+1 as the 40th prime
+It has 100x100 numbers or π(π(10000)) = 201 primes
+Total cum primes = 168 + (201-40) = 168+161 = 329 primes
+
+3rd layer:
+Behave reversal to 2nd layer which has a total of 329 primes
+The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
+This 1000 primes will become 1000 numbers by 1st layer of the next level
+Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1 
+

            π(1000) = π(Φ x 618) = 168

            default

            eQuantum
            profiles
            GitHub
            Homepage
            Repository
            Gist
            This Software is under the terms of The Unlicense.
            \ No newline at end of file diff --git a/robots.txt b/robots.txt new file mode 100644 index 00000000000..b08aee560f5 --- /dev/null +++ b/robots.txt @@ -0,0 +1,4 @@ +User-agent: * +Allow: / + +Sitemap: /sitemap.xml diff --git a/search.html b/search.html new file mode 100644 index 00000000000..ba3e542a3b1 --- /dev/null +++ b/search.html @@ -0,0 +1 @@ + Search · eQuantum
            eQuantum
            Mapping the quantum way
            eQuantum

            Searching

              eQuantum
              profiles
              GitHub
              Homepage
              Repository
              Gist
              This Software is under the terms of The Unlicense.
              \ No newline at end of file diff --git a/sitemap.xml b/sitemap.xml new file mode 100644 index 00000000000..5382b2137dc --- /dev/null +++ b/sitemap.xml @@ -0,0 +1 @@ + /identition/span4/gist07.html 0.2 2024-03-13T10:30:28-05:00 /identition/span4/gist08.html 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist08.html 1.0 2024-03-13T10:30:28-05:00 /identition/span5/gist04.html 1.0 2024-03-13T10:30:28-05:00 /identition/span3/gist05.html 1.0 2024-03-13T10:30:28-05:00 /identition/span2/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span7/gist02.html 0.3 2024-03-13T10:30:28-05:00 /identition/span4/gist03.html 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist03.html 0.7 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist02.html 0.4 2024-03-13T10:30:28-05:00 /identition/span2/gist09.html 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist02.html 0.8 2024-03-13T10:30:28-05:00 /identition/span5/gist05.html 0.3 2024-03-13T10:30:28-05:00 /identition/span4/gist04.html 1.0 2024-03-13T10:30:28-05:00 /identition/span5/gist02.html 1.0 2024-03-13T10:30:28-05:00 /identition/span4/gist02.html 1.0 2024-03-13T10:30:28-05:00 /identition/span5/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span3/gist07.html 1.0 2024-03-13T10:30:28-05:00 /identition/span9/gist07.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist05.html 0.5 2024-03-13T10:30:28-05:00 /identition/span8/gist03.html 0.4 2024-03-13T10:30:28-05:00 /identition/span3/gist03.html 0.6 2024-03-13T10:30:28-05:00 /identition/span2/gist02.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist03.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist04.html 0.2 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist05.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist06.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist07.html 0.9 2024-03-13T10:30:28-05:00 /exponentiation/span15/gist02.html 0.9 2024-03-13T10:30:28-05:00 /exponentiation/span15/gist03.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist04.html 0.4 2024-03-13T10:30:28-05:00 /identition/span9/gist04.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span15/gist04.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span15/gist05.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist03.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist01.html 0.1 2024-03-13T10:30:28-05:00 /identition/span7/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span4/gist09.html 1.0 2024-03-13T10:30:28-05:00 /identition/span2/gist03.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist06.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist07.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist08.html 0.3 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist09.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist10.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/gist12.html 0.6 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist03.html 0.5 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist04.html 1.0 2024-03-13T10:30:28-05:00 /identition/span8/gist07.html 0.6 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist05.html 0.5 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist07.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist08.html 0.5 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist09.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span17/gist10.html 0.4 2024-03-13T10:30:28-05:00 /identition/span7/gist05.html 0.2 2024-03-13T10:30:28-05:00 /identition/span4/gist05.html 1.0 2024-03-13T10:30:28-05:00 /identition/span5/gist03.html 1.0 2024-03-13T10:30:28-05:00 /identition/span3/gist02.html 0.9 2024-03-13T10:30:28-05:00 /identition/span3/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span2/gist07.html 1.0 2024-03-13T10:30:28-05:00 /identition/span5/gist07.html 0.7 2024-03-13T10:30:28-05:00 /identition/span6/gist06.html 0.9 2024-03-13T10:30:28-05:00 /identition/span4/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span2/gist08.html 1.0 2024-03-13T10:30:28-05:00 /identition/span7/gist04.html 0.9 2024-03-13T10:30:28-05:00 /identition/span2/gist04.html 1.0 2024-03-13T10:30:28-05:00 /identition/span11/gist09.html 0.7 2024-03-13T10:30:28-05:00 /identition/span10/gist10.html 1.0 2024-03-13T10:30:28-05:00 /identition/span8/gist06.html 0.5 2024-03-13T10:30:28-05:00 /identition/span10/gist04.html 0.2 2024-03-13T10:30:28-05:00 /identition/span7/gist07.html 0.3 2024-03-13T10:30:28-05:00 /identition/span10/gist03.html 0.3 2024-03-13T10:30:28-05:00 /identition/span10/gist02.html 0.4 2024-03-13T10:30:28-05:00 /identition/span7/gist03.html 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist10.html 0.5 2024-03-13T10:30:28-05:00 /identition/span10/gist05.html 0.3 2024-03-13T10:30:28-05:00 /identition/span10/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span10/gist07.html 0.5 2024-03-13T10:30:28-05:00 /identition/span10/gist08.html 0.5 2024-03-13T10:30:28-05:00 /identition/span10/gist09.html 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist07.html 0.4 2024-03-13T10:30:28-05:00 /identition/span11/gist02.html 0.6 2024-03-13T10:30:28-05:00 /identition/span11/gist04.html 0.6 2024-03-13T10:30:28-05:00 /identition/span11/gist08.html 0.8 2024-03-13T10:30:28-05:00 /identition/span11/gist03.html 0.7 2024-03-13T10:30:28-05:00 /identition/span6/gist09.html 0.5 2024-03-13T10:30:28-05:00 /identition/span11/gist05.html 1.0 2024-03-13T10:30:28-05:00 /identition/span11/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span11/gist07.html 0.3 2024-03-13T10:30:28-05:00 /identition/span6/gist04.html 1.0 2024-03-13T10:30:28-05:00 /identition/span7/gist08.html 0.8 2024-03-13T10:30:28-05:00 /identition/span9/gist05.html 0.3 2024-03-13T10:30:28-05:00 /identition/span9/gist02.html 1.0 2024-03-13T10:30:28-05:00 /identition/span9/gist03.html 1.0 2024-03-13T10:30:28-05:00 /identition/span9/gist06.html 0.7 2024-03-13T10:30:28-05:00 /identition/span8/gist02.html 0.2 2024-03-13T10:30:28-05:00 /identition/span8/gist05.html 0.2 2024-03-13T10:30:28-05:00 /identition/span8/gist04.html 1.0 2024-03-13T10:30:28-05:00 / 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist01.html 1.0 2024-03-13T10:30:28-05:00 /addition/ 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist02.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist02.html 0.3 2024-03-13T10:30:28-05:00 /addition/2.html 1.0 2024-03-13T10:30:28-05:00 /identition/span2/gist05.html 1.0 2024-03-13T10:30:28-05:00 /identition/span2/gist01.html 1.0 2024-03-13T10:30:28-05:00 /identition/span3/gist01.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist03.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist03.html 1.0 2024-03-13T10:30:28-05:00 /addition/3.html 1.0 2024-03-13T10:30:28-05:00 /identition/span3/gist04.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist04.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist04.html 0.3 2024-03-13T10:30:28-05:00 /identition/span4/gist01.html 1.0 2024-03-13T10:30:28-05:00 /addition/4.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist05.html 1.0 2024-03-13T10:30:28-05:00 /identition/span5/gist01.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist05.html 0.5 2024-03-13T10:30:28-05:00 /addition/5.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist06.html 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist01.html 0.4 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist06.html 0.2 2024-03-13T10:30:28-05:00 /addition/6.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist07.html 1.0 2024-03-13T10:30:28-05:00 /identition/span7/gist01.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist07.html 0.5 2024-03-13T10:30:28-05:00 /addition/7.html 1.0 2024-03-13T10:30:28-05:00 /identition/span8/gist01.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist08.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist08.html 1.0 2024-03-13T10:30:28-05:00 /addition/8.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/ 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist09.html 1.0 2024-03-13T10:30:28-05:00 /identition/span9/gist01.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/gist09.html 0.5 2024-03-13T10:30:28-05:00 /multiplication/10.html 1.0 2024-03-13T10:30:28-05:00 /identition/span10/gist01.html 0.5 2024-03-13T10:30:28-05:00 /identition/span1/gist10.html 1.0 2024-03-13T10:30:28-05:00 /identition/span11/gist01.html 0.8 2024-03-13T10:30:28-05:00 /identition/span1/gist11.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist12.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist13.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/11.html 1.0 2024-03-13T10:30:28-05:00 /identition/span1/gist14.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/12.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span14/gist01.html 0.9 2024-03-13T10:30:28-05:00 /identition/span1/gist15.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/13.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span15/gist01.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/14.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/15.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/16.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/17.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/18.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/19.html 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist01.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist02.html 1.0 2024-03-13T10:30:28-05:00 /multiplication/20.html 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist03.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span17/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist04.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span16/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist05.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span15/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist06.html 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span14/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist07.html 1.0 2024-03-13T10:30:28-05:00 /identition/ 1.0 2024-03-13T10:30:28-05:00 /exponentiation/span13/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/ 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist08.html 1.0 2024-03-13T10:30:28-05:00 /identition/span12/gist09.html 1.0 2024-03-13T10:30:28-05:00 /identition/span11/ 1.0 2024-03-13T10:30:28-05:00 /identition/span10/ 1.0 2024-03-13T10:30:28-05:00 /identition/span9/ 1.0 2024-03-13T10:30:28-05:00 /identition/span8/ 1.0 2024-03-13T10:30:28-05:00 /identition/span7/ 1.0 2024-03-13T10:30:28-05:00 /identition/span6/ 1.0 2024-03-13T10:30:28-05:00 /identition/span5/ 1.0 2024-03-13T10:30:28-05:00 /identition/span4/ 1.0 2024-03-13T10:30:28-05:00 /identition/span3/ 1.0 2024-03-13T10:30:28-05:00 /identition/span2/ 1.0 2024-03-13T10:30:28-05:00 /identition/span1/ 1.0 2024-03-13T10:30:28-05:00 /identition/span6/gist05.html 1.0 2024-03-13T10:30:28-05:00 \ No newline at end of file diff --git a/sw.caches.js b/sw.caches.js new file mode 100644 index 00000000000..4eb8d22b7be --- /dev/null +++ b/sw.caches.js @@ -0,0 +1 @@ +self.addEventListener("activate", function (event) { const current = ["rundocs/jekyll-rtd-theme@2.0.10"]; event.waitUntil( caches.keys().then(function (keyList) { return Promise.all( keyList.map(function (key) { if (current.indexOf(key) === -1) { return caches.delete(key); } }) ); }) ); }); self.addEventListener("fetch", function (e) { if (e.request.url.match("rundocs/jekyll-rtd-theme@2.0.10")) { e.respondWith( caches.match(e.request).then(function (resp) { if (resp !== undefined) { return resp; } else { return fetch(e.request, { cache: "no-store", }) .then(function (resp) { let clone = resp.clone(); caches.open("rundocs/jekyll-rtd-theme@2.0.10").then(function (cache) { cache.put(e.request, clone); }); return resp; }) .catch(console.log); } }) ); } }); \ No newline at end of file