Chromodynamics (lexer)
Quantum Chromodynamics (QCD) is the theory of the strong interactions that glue together quarks inside protons and neutrons, the constituents of ordinary matter.
This section is referring to wiki page-24 of main section-2 that is from the spin section-131 by prime spin-33 and span- with the partitions as below.
/lexer
- Addition Zones (0-18)
- Multiplication Zones (18-30)
- Symmetrical Breaking (spin 8)
- The Angular Momentum (spin 9)
- Entrypoint of Momentum (spin 10)
- The Mapping of Spacetime (spin 11)
- Similar Order of Magnitude (spin 12)
- Searching for The Graviton (spin 13)
- Elementary Retracements (spin 14)
- Recycling of Momentum (spin 15)
- Exchange Entrypoint (spin 16)
- The Mapping Order (spin 17)
- Magnitude Order (spin 18)
- Exponentiation Zones (30-36)
- Identition Zones (36-102)
- Theory of Everything (span 12)
- Everything is Connected (span 11)
- Truncated Perturbation (span 10)
- Quadratic Polynomials (span 9)
- Fundamental Forces (span 8)
- Elementary Particles (span 7)
- Basic Transformation (span 6)
- Hidden Dimensions (span 5)
- Parallel Universes (span 4)
- Vibrating Strings (span 3)
- Series Expansion (span 2)
- Wormhole Theory (span 1)
Is QCD a confining theory ? This is one of the fundamental questions and constitutes one of the famous Millennium Prize problems.
Feynman diagram
This section serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks in quantum chromodynamics of colours of the gluon.
In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).
Like electromagnetism (QED), it is a gauge theory, where the force between charged particles originates in the exchange of intermediate massless vector bosons: one photon in the case of QED and eight gluons in the case of QCD.
QCD is extremely predictive:
- One gauge coupling constant, six quark masses and the so-called theta vacuum angle are the only free parameters from which a plethora of phenomena can in principle be predicted, such as the spectrum of hadrons and their interactions.
- The famous theta vacuum angle is the only source of CP violation (asymmetry between matter and antimatter) of the strong interactions, but has been constrained from the measurement of the neutron electric dipole moment to be unnaturally small.
The fact that this parameter is so small is the so-called strong CP problem.
The gauge symmetry of QCD is based on the special unitary group, SU(3), and the associated charge is called color. Quarks carry three basic charges or colors: red, blue and green.
In spite of the simplicity of the QCD Lagrangian, quantitative predictions are highly non trivial.
- Indeed the colored quarks or gluons have not been observed in isolation.
- This fact is referred to as confinement, an essential property of QCD which implies that only states that carry no color charge can propagate freely.
The neutral composites that we observe in nature are the hadrons: mesons composed of a quark and an antiquark, or baryons composed of three quarks.
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.
One of the more mature applications of LQCD simulations is precisely the study of confinement and asymptotic freedom. Simulations have demonstrated that the energy between a quark and antiquark pair increases linearly with their separation.
- The running of the QCD gauge coupling has been also studied beyond perturbation theory confirming the property of asymptotic freedom and providing the most accurate determination of the QCD coupling strength, as can be seen from the upper-right figure.
- Nevertheless, there are still important limitations in lattice simulations. One of the major difficulties has to do with the treatment of the quark degrees of freedom. It is very difficult to maintain the chiral properties of the continuum action, which is mandatory to simulate the light quarks. Very important progress has been made in the last decade on this problem. Fermion discretizations that can maintain chiral properties have been found (domain wall fermions and overlap fermions), and variants of the most cost-effective Wilson fermions with improved chiral behaviour, the so-called twisted-mass Wilson fermions, have made the simulation of the chiral regime feasible.
- Furthermore important algorithmic improvements (like Schwarz preconditioning, deflation acceleration, trivializing maps and the Wilson flow and open boundary conditions and twisted-mass reweighting) have been necessary to incorporate efficiently the contribution of quarks to the path integral, which represents the quantum effects of virtual quark-antiquark pairs. State-of-the-art simulations nowadays include the most relevant quark effects: those of the two lightest u and d quarks (Nf=2 simulations), those plus the strange quark (Nf=2+1 simulations) and more recently also the charm quark (Nf=2+1+1 simulations) has been included.
- The lattice approach is not universally applicable but has been used to compute from first principles many physical quantities beyond the QCD coupling constant, including the hadron mass spectrum, the quark condensate, quark masses, decay constants and form factors for leptonic and semileptonic decays.
- Also the lattice approach is mandatory in computing weak matrix elements, such as the K or B-parameters of meson-antimeson oscillations that are very important for the precise determination of the elements of the CKM mixing matrix, and for performing consistency checks of unitarity and searching possible physics beyond the SM.
- Another important contribution of lattice QCD is the computation of the moments of parton and gluon distribution functions, essential for the calculation of cross sections in the LHC and Tevatron, as well as the isosinglet and strange sigma terms that play a role in the direct searches for dark matter.
The lattice is also the method to study QCD in extreme conditions (high temperature and density) such as those that would be found in the early Universe or in astrophysical objects such as neutron stars (IFIC).
Matrix Scheme
Quarks have three colors. Color is to the strong interaction as electric charge is to the electromagnetic interaction.
red anti-red, red anti-blue, red anti-green,
blue anti-red, blue anti-blue, blue anti-green,
green anti-red, green anti-blue, green anti-green.
This exponentiation takes important roles since by the multiplication zones the MEC30 forms a matrix of 8 x 8 = 64 = 8² where the power of 2 stands as exponent
During the last few years of the 12th century, Fibonacci undertook a series of travels around the Mediterranean. At this time, the world’s most prominent mathematicians were Arabs, and he spent much time studying with them. His work, whose title translates as the Book of Calculation, was extremely influential in that it popularized the use of the Arabic numerals in Europe, thereby revolutionizing arithmetic and allowing scientific experiment and discovery to progress more quickly. (Famous Mathematicians)
Since the first member is 30 then the form is initiated by a matrix of 5 x 6 = 30 which has to be transformed first to 6 x 6 = 36 = 6² prior to the above MEC30's square.
A square system of coupled nonlinear equations can be solved iteratively by Newton’s method. This method uses the Jacobian matrix of the system of equations. (Wikipedia)
Fermions and bosons—fermions have quantum spin = 1/2.
- The elementary fermions are leptons and quarks.
- There are three generations of leptons: electron, muon, and tau, with electric charge −1, and their neutrinos with no electric charge.
- There are three generations of quarks: (u, d); (c, s); and (t, b).
The (u, c, t) quarks have electric charge 2/3 while the (d, s, b) quarks have electric charge −1/3. (IntechOpen)
Interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used.
Bosons have quantum spin = 1: photon, quantum of the electromagnetic field; gluon, quantum of the strong field; and W and Z, weak field quanta, which we do not need.
An animation of color confinement, a property of the strong interaction. If energy is supplied to the quarks as shown, the gluon tube connecting quarks elongates until it reaches a point where it “snaps” and the energy added to the system results in the formation of a quark–antiquark pair. Thus single quarks are never seen in isolation. (Wikipedia)
Fermion | spinors | charged | neutrinos | quark | components | parameter
Field | (s) | (c) | (n) | (q=s.c.n) | Σ(c+n+q | (complex)
===========+=========+=========+===========+===========+============+===========
bispinor-1 | 2 | 3 | 3 | 18 | 24 | 19+i5
-----------+---------+---------+-----------+-----------+------------+-----------
bispinor-2 | 2 | 3 | 3 | 18 | 24 | 17+i7 👈
===========+=========+=========+===========+===========+============+===========
bispinor-3 | 2 | 3 | 3 | 18 | 24 | 11+i13
-----------+---------+---------+-----------+-----------+------------+-----------
bispinor-4 | 2 | 3 | 3 | 18 | 24 | 19+i5
===========+=========+=========+===========+===========+============+===========
Total | 8 | 12 | 12 | 72 | 96 | 66+i30
Interactions
The subclasses of partitions systemically develops characters similar to the distribution of prime numbers.
Unlike the strong force, the residual strong force diminishes with distance, and does so rapidly. The decrease is approximately as a negative exponential power of distance, though there is no simple expression known for this; see Yukawa potential. The rapid decrease with distance of the attractive residual force and the less rapid decrease of the repulsive electromagnetic force acting between protons within a nucleus, causes the instability of larger atomic nuclei, such as all those with atomic numbers larger than 82 (the element lead). (Wikipedia)
Feynman diagram for the same process as in the animation, with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion “in-flight”, are not shown. The π⁰ pion contains an anti-quark, shown to travel in the opposite direction, as per the Feynman–Stueckelberg interpretation. (Wikipedia)
The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.
- These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation (so they can generate unitary matrix group elements of SU(3) through exponentiation[1]). These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann’s quark model.[2] Gell-Mann’s generalization further extends to general SU(n). For their connection to the standard basis of Lie algebras, see the Weyl–Cartan basis.
- Since the eight matrices and the identity are a complete trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that satisfied by the Pauli matrices. Namely, using the dot to sum over the eight matrices and using Greek indices for their row/column indices
- A particular choice of matrices is called a group representation, because any element of SU(3) can be written in the form using the Einstein notation, where the eight are real numbers and a sum over the index j is implied. Given one representation, an equivalent one may be obtained by an arbitrary unitary similarity transformation, since that leaves the commutator unchanged.
- The matrices can be realized as a representation of the infinitesimal generators of the special unitary group called SU(3). The Lie algebra of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight linearly independent generators, which can be written as g_{i}, with i taking values from 1 to 8
These matrices serve to study the internal (color) rotations of the gluon fields associated with the coloured quarks of quantum chromodynamics (cf. colours of the gluon). A gauge colour rotation is a spacetime-dependent SU(3) group element where summation over the eight indices (8) is implied. Wikipedia)
$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-----+-----+ ---
17¨ | 5¨ | 3¨ | ❓ | ❓ | 4¤ ✔️ ---> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| .. | .. | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | .. | .. | .. | 3¤ ----> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+-----+-----+ |
19¨ | .. | .. | .. | .. | 4¤ -----> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ
From the 50 we gonna split the 15 by bilateral 9 sums resulting 2 times 15+9=24 which is 48. So the total of involved objects is 50+48=98.
Consider the evidence: scattering experiments strongly suggest a meson to be composed of a quark anti-quark pair and a baryon to be composed of three quarks. The famous 3R experiment also suggests that whatever force binds the quarks together has 3 types of charge (called the 3 colors).
- Now, into the realm of theory: we are looking for an internal symmetry having a 3-dimensional representation which can give rise to a neutral combination of 3 particles (otherwise no color-neutral baryons).
- The simplest such statement is that a linear combination of each type of charge (red + green + blue) must be neutral, and following William of Occam we believe that the simplest theory describing all the facts must be the correct one.
- We now postulate that the particles carrying this force, called gluons, must occur in color anti-color units (i.e. nine of them).
- BUT, red + blue + green is neutral, which means that the linear combination red anti-red + blue anti-blue + green anti-green must be non-interacting, since otherwise the colorless baryons would be able to emit these gluons and interact with each other via the strong force—contrary to the evidence. So, there can only be EIGHT gluons.
This is just Occam’s razor again: a hypothetical particle that can’t interact with anything, and therefore can’t be detected, doesn’t exist. The simplest theory describing the above is the SU(3) one with the gluons as the basis states of the Lie algebra. That is, gluons transform in the adjoint representation of SU(3), which is 8-dimensional. (Physics FAQ)
Please note that we are not talking about the number of 19 which is the 8th prime. Here we are talking about 19th as sequence follow backward position of 19 as per the scheme below where the 19th prime which is 67 goes 15 from 66 to 51.
- In quantum field theory, the theta vacuum is the semi-classical vacuum state of non-abelian Yang–Mills theories specified by the vacuum angle θ that arises when the state is written as a superposition of an infinite set of topologically distinct vacuum states.
- The dynamical effects of the vacuum are captured in the Lagrangian formalism through the presence of a θ-term which in quantum chromodynamics leads to the fine tuning problem known as the strong CP problem.
- It was discovered in 1976 by Curtis Callan, Roger Dashen, and David Gross,[1] and independently by Roman Jackiw and Claudio Rebbi (Wikipedia).
π(1000) = π(Φ x 618) = 168 = 100 + 68 = (50x2) + (66+2) = 102 + 66
$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-----+-👇--+ ---
17¨ | 5¨ | 3¨ | ❓ | 7¨ | 4¤ ✔️ ---> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| .. | .. | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | .. | .. | .. | 3¤ ----> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+-----+-----+ |
19¨ | .. | .. | .. | .. | 4¤ -----> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ
In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).
Young diagrams associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia).
In mathematics, orthonormality typically implies a norm which has a value of unity (1). Gell-Mann matrices, however, are normalized to a value of 2.
- Thus, the trace of the pairwise product results in the ortho-normalization condition where delta is the Kronecker delta.
- This is so the embedded Pauli matrices corresponding to the three embedded subalgebras of SU(2) are conventionally normalized.
- In this three-dimensional matrix representation, the Cartan subalgebra is the set of linear combinations (with real coefficients) of the two matrices which commute with each other.
The SU(2) Casimirs of these subalgebras mutually commute. However, any unitary similarity transformation of these subalgebras will yield SU(2) subalgebras. There is an uncountable number of such transformations. (Wikipedia)
$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-👇--+-----+ ---
17¨ | {5¨}| {3¨}| 2¨ | 7¨ | 4¤ ✔️ ---> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| .. | .. | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | .. | .. | .. | 3¤ ----> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+-----+-----+ |
19¨ | .. | .. | .. | .. | 4¤ -----> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ
So basically there is a basic transformation between addition of 3 + 4 = 7 in to their multiplication of 3 x 4 = 12 while the 7 vs 12 will be treated as exponentiation.
Power of Magnitude
For any model, squared amplitudes and Wilson coefficients can be calculated at the tree level or the one-loop level.
A key question related to the consistency of Standard Model is the Yang–Mills existence and mass gap problem.
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.
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.
Analytical expressions, squared amplitudes or Wilson coefficients are converted into C++ code in a self-contained library compiled independently.
Phenomenological Analysis
This code can therefore be used for numerical evaluation in different scenarios to perform a phenomenological analysis.
The number 120 = MEC30 x 4 has 32 prime positions minus 5 prime number products = 27 prime numbers. The information of the prime number products translates our theory into a checkerboard-like pattern using the finite 8 prime positions from the MEC 30, we call it Ikon. 8 × 8 primary positions = 64 primary positions of the checkerboard icon.
Note that the hexagon in the middle has 37 circles and the total figure, a star of David has 73. For this one you go around one point of the pattern in a circle until you go past a letter that you have already covered. For instance in B-R-A-Sh you will have to switch the position for the Sh because it moves more than through the alphabet. S-I-T does the same with the T.
Composite Contribution
The above seven (7) primes will act then as extended branes. This is what we mean by addition zones and it happens whenever a cycle is restarted.
$True Prime Pairs:
(5,7), (11,13), (17,19)
layer | node | sub | i | f. MEC 30 / 2
------+------+-----+-----+------ ‹------------------------------ 0 {-1/2}
| | | 1 | --------------------------
| | 1 +-----+ |
| 1 | | 2 | (5) |
| |-----+-----+ |
| | | 3 | |
1 +------+ 2 +-----+---- |
| | | 4 | |
| +-----+-----+ |
| 2 | | 5 | (7) |
| | 3 +-----+ |
| | | 6 | 11s ‹-- ∆28 = (71-43)
------+------+-----+-----+------ } (36) |
| | | 7 | |
| | 4 +-----+ |
| 3 | | 8 | (11) |
| +-----+-----+ |
| | | 9 |‹-- ∆9 = (89-71) / 2 |
2 +------| 5* +-----+----- |
| | | 10 | |
| |-----+-----+ |
| 4 | | 11 | (13) ---------------------
| | 6 +-----+ ‹------------------------------ 15 {0}
| | | 12 |---------------------------
------+------+-----+-----+------------ |
| | | 13 | |
| | 7 +-----+ |
| 5 | | 14 | (17) |
| |-----+-----+ |
| | | 15 | 7 x 24 = 168 ✔️
3* +------+ 8 +-----+----- } (36) |
| | | 16 | |
| |-----+-----+ |
| 6 | | 17 | (19) |
| | 9 +-----+ |
| | | 18 | --------------------------
------|------|-----+-----+----- ‹----------------------------------- 30 {+1/2}
This scheme goes to the unification of 11s with 7s to 18s meanwhile the 11th it self behave as residual by the 5th minor hexagon between the 30 to 36' cells.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18
---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----+----
19| 20| 21| 22| 23| 24| 25|
---+---+---+---+---+---+---+
- | - | - | 28| 29|
By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.
You likely noticed I began with 2 rather than 1 or 0 when I first constructed the hexagon. Why? Because they do not fit inside — they stick off the hexagon like a tail. Perhaps that’s where they belong. However, if one makes a significant and interesting assumption, then 1 and 0 fall in their logical locations – in the 1 and 0 cells, respectively. _(HexSpin)
0 + 30 + 36 + 102 = 168 = π(1000)
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17
---+---+---+---+---+---+---+---+---+---+----+----+----+----+----+----+----+----
- | - | 20| 21| 22| 23| 24| 25|
---+---+---+---+---+---+---+
- | - | - | - | 28| 29|
---+---+---+---+---+---+
30| 31|
---+---+
36|
This behaviour finaly brings us to a suggestion that the dimension in string theory are linked with the prime distribution level as indicated by the self repetition on MEC30.
7th spin - 4th spin = (168 - 102)s = 66s = 6 x 11s = 30s + 36s
p r i m e s
1 0 0 0 0 0
2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin ✔️
3 2 0 1 0 2 👉 2
4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40
6 👉 11s Composite Partition ◄--- 102 👈 4th spin ✔️
6 7 3 1 0 7 ◄--- #23
7 11 4 1 0 11 ◄--- #19
8 13 5 1 0 13 ◄--- # 17 ◄--- #49
9 17 0 1 1 17 ◄--- 7th prime
18 👉 7s Composite Partition ◄--- 168 👈 7th spin ✔️
10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
-----
11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
..
..
40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
-----
41 167 0 1 1 ∆0
42 173 0 -1 1 ∆1
43 179 0 1 1 ∆2 ◄--- ∆∆1
44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
..
..
100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 👉 7s
-----
It will be forced back to Δ19 making a cycle that bring back the 12 to → 13 of 9 collumns and replicate The Scheme 13:9 through (i=9,k=13)=9x3=27 with entry form of (100/50=2,60,40) as below:
The 10 ranks will coordinate with the 18 to raise up the symmetrical behaviour of 12+24=36 which is prime pair 17+19=36 and let the 2 and 3 out of 2,3,5,7 to begin a new cycle while the 5,7 will pair the 11,13 and 17,19 as True Prime Pairs.
I like that 0 can occupy a center point. Incidentally, this circular shape minus all my numbers and colors s has been called Seed of Life / Flower of Life by certain New Age groups who claim it has a sacred geometry. Please don’t see this as an endorsement of any spiritual group or religion. (Prime Hexagon - Circulat Form)
