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The Prime Recycling ζ(s)

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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 pythonimportnumpyasnpfromscipyimportlinalgclassSU3(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),
])
defcomputeLocalAction(self):
pass@classmethoddefgetMeasure(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).

[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)))_.

integer partition

By parsering [π(1000)=168 primes](https://eq19.github.io/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://eq19.github.io/sitemap.xml):

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
-----
***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/maps/files/13722898/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
-----

Scheme13:9===========
(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

TheTruePrimePairs:
(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--|13variations48variations11variations

ThePrimeRecyclingζ(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¨ abstraction289|+-----+-----+-----+-----+-----+|||----› 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) «--3xΔ9 (2xMEC30) | {2®} |||||+-----+-----+-----+||---||---› 14:10|9|60|40|109 (28) -------------||||+-----+-----+-----+|||---› 15,18:11|1|30|40|71 (29,30,31,32) ----------13¨ inheritance329|+-----+-----+-----+|| ‹---------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¨ object168|+-----+||102-› 29:18|50|50(68) ---------> ∆27-∆9=Δ18|----------------------+-----+---

Final Theory

  1. Prime Identity

  2. Addition Zones (0-18)

  3. True Prime Pairs

  4. Primes Platform

  5. Pairwise Scenario

  6. Power of Magnitude

  7. The Pairwise Disjoint

  8. The Prime Recycling ζ(s)

  9. Implementation in Physics

  10. Multiplication Zones (18-30)

  11. Symmetrical Breaking (spin 8)

  12. The Angular Momentum (spin 9)

  13. Entrypoint of Momentum (spin 10)

  14. The Mapping of Spacetime (spin 11)

  15. Similar Order of Magnitude (spin 12)

  16. Searching for The Graviton (spin 13)

  17. Elementary Retracements (spin 14)

  18. Recycling of Momentum (spin 15)

  19. Exchange Entrypoint (spin 16)

  20. The Mapping Order (spin 17)

  21. Magnitude Order (spin 18)

  22. Exponentiation Zones (30-36)

  23. Electrodynamics (maps)

  24. Quantum Gravity (feed)

  25. Chromodynamics (lexer)

  26. Electroweak Theory (parser)

  27. Grand Unified Theory (syntax)

  28. Identition Zones (36-102)

  29. Theory of Everything (span 12)

  30. Everything is Connected (span 11)

  31. Truncated Perturbation (span 10)

  32. Quadratic Polynomials (span 9)

  33. Fundamental Forces (span 8)

  34. Elementary Particles (span 7)

  35. Basic Transformation (span 6)

  36. Hidden Dimensions (span 5)

  37. Parallel Universes (span 4)

  38. Vibrating Strings (span 3)

  39. Series Expansion (span 2)

  40. Wormhole Theory (span 1)

  41. (total pages)

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