# Recycling of Momentum (spin 15)

This section is referring to *wiki page-17* of *gist section-13* that is *inherited * from *the gist section-97* by *prime spin-26* and *span-* with *the partitions* as below.

/parser

## 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.

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)*.

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.

*Line/length**Plane/shapes*, representing a stretching and shearing of the plane*Depth*, stands as starting point to*Time**attemp*the.*Theory Of Everything (TOE)*(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*Alternate world*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.*A plane of possible 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).*Access to different worlds*- This dimension is similar to the seventh. There are
that all started differently and histories that branch out infinitely.*multiple universes* - Here, we can compare
, each with a possibly different set of laws of physics.*all the could-have-been universes* - Kinda like
. In additions, some physicists believe that at the instant of the Big Bang, the universe(s) was fully 10 dimensional.*an extra room to accommodate ALL the theories*

The coupling dynamics of dimension d ⩾ 4 reflects to ** matter–antimatter annihilation** that tied in with

**of**

*addition, multiplication and exponentiation function**Euler Indentity*.

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)*

By the *exponentiation zones* these annihilation relates to the fundamental *circle constant*`π = 3.1415…`

. So how does it go with ** imajinari constant**?

** 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)*.

## Rotation vs Revolution

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)*

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**.

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
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.*satellite galaxies* - It is estimated to contain 100–400 billion stars and at least that number of planets.
. The stars in the innermost 10,000 light-years form a bulge and one or more bars that radiate from the bulge.*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 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.
. The rotational period is about 212 million years at the radius of the Sun.[16]*This conjectural mass has been termed “dark matter”*

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)*

## Truncated Perturbation

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

*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)
```

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)*

```
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 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)*

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.

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)
```

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.

** 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:

, which doesn’t spin and is represented by 0.*The Higgs field*, which are particles like electrons, having a spin of plus or minus a half.*Fermions*, like photons, which have a spin of plus or minus 1.*Bosons*, which are like fermions but have a spin of plus or minus two-thirds.*Anti-fermions*, believed to be responsible for gravity, with a spin of 2.*The graviton*

** 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)*

Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The corresponding eigenvalue is often represented as the ** multiplying factor**.

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.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*.

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.

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.

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:

By the *exponentiation zones* and *identition zones* they will end up as 7 days (** sun**) and 12 months (

**) while the 11 will represent the ones outside the orbit (**

*moon***or**

*stars***). 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.**

*galaxies*```
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.

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.

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)*.

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.

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)*.

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)*

Our results lead to the conjecture that string theory indicates the existence of some new cohomology theory for algebraic varieties with Gorenstein singularities.