# 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-151 by prime spin-37 and span- with the partitions as below.

/grammar

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

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.

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. 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.
• 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.

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)

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.

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.

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)

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)

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.

The present article describes recent progress in our understanding of such “exotic” mesons and baryons. (Multiquark States - pdf)

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)

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).

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)

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)

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.
• 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.
• 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.
• 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

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

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)

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.)

• 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)

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)

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)

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.

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)

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)

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:

• 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

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)

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)

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)

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)

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)

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.
• 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:

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)

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

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)

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.

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.

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)

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.
• 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).
• 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

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)

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)

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.
• 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.
• 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)

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)

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.

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)

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

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)

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)

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.
• 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. (Modern Particle Physics P.500 - pdf)

These patterns provide hints for, as yet unknown, physics beyond the Standard Model.

## 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.

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.

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)

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)

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)

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)

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.

It tells us that mesons are the only entities which may flow across any closedsurface of the baryon density. (Lab Notes)

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)

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)

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)

This is because all second and third generation particles are unstable and quickly decay into stable first generation particles.

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:
• 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:
• 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)

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)

All 15 matter particles are mirroring their corresponding doppelgangers (anti-particles) each others that could potentially explain dark matter.

## The 27 Parameters

Note that since our Universe began with a Big Bang, all its particles originate from pair creation since then.

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).

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)

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)

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

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.

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).

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.

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

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)

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)

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).

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)

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)

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.
• 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)

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.

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

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.

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.

(3) The number π = 3.1415…, the fundamental circle constant, and

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

(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 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

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).

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)

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)

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

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

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)

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)

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

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

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).

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.

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.

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:

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.

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.
•  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

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)

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.
• This means that if right-handed neutrinos exist, they don’t interact with regular matter, only with gravity. Thus, they are “sterile.”

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)

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.

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.

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.

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)

168 + 329 + 289 = 168 + 618 = 786

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

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.

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.

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.

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:

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

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)

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
7' | 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 works 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).

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)

1 instance + 7 blocks + 29 flats + 77 rooms = 37+77 = 114 objects

``````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.

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)

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)

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)

Taking a coupling function between f(π) as P vs f(i) as NP where e + 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.

# 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-28 of main section-6 that is inherited from the spin section-151 by prime spin-37 and span- with the partitions as below.

/grammar

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.

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).

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):

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).

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.

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).

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).

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).

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)

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 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).

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

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.
• 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)

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