Exponentiation Zones (30-36)

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

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

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)

Hyperopt in algorithmic trading involves tuning multiple interacting components such as buy/sell logic, ROI models, risk protections, and meta-settings. To manage this complexity and define a meaningful sequence, we draw an analogy from the layered architecture of physics: from weak nuclear interactions to the theory of everything.

1. Weak Nuclear – [buy¹, custom-entry²]: The buy logic initiates trades and responds to localized, short-lived signals — akin to the weak nuclear force, which governs subatomic transformations. Custom entry logic represents nuanced early decision-making.
2. Electromagnetic (QED) – [sell³, custom-exit⁴]: The sell logic reacts to opposing conditions and manages exits through symmetric, responsive forces. Like electromagnetism, this governs interactions and balance through custom-exit dynamics.
3. Electroweak (QED + Weak + QM) – [custom-entry², custom-exit⁴, roi⁵]: This layer unifies buying and selling into a cohesive interactive force. Here, quantum mechanics is conceptually embedded: representing probabilistic filters, confidence thresholds, and dynamic decision-making within custom-entry and custom-exit. ROI emerges here as a modulated outcome of quantum-level signal interaction.
4. Strong Nuclear (QCD) – [trailing⁶, protection⁷, timeframe⁸]: Trailing stops, protection logic, and timeframe define the internal trade architecture. This layer offers resilience and cohesion, much like the strong nuclear force binds particles under high tension.
5. Grand Unified Theory (GUT) – [trades⁹, roi⁵]: Abstracting above local behaviors, this layer analyzes trade performance and profit structure. It combines earlier logic into a unifying profit mechanism and long-term strategy shaping.
6. Quantum Gravity (Meta-Layer) – [default¹⁰, leverage¹¹, global-overrides¹²]: This meta-layer defines the curvature of the environment. Default settings, leverage, and global overrides determine the system’s flexibility and risk profile — mirroring how gravity shapes the space-time structure of the trading universe.
7. Theory of Everything (TOE) – [all¹³]: The final layer integrates all previous dimensions. It represents full-system optimization, where all logic, protections, and meta-controls are harmonized into a complete strategic model.

By mapping the 13 available optimization spaces to this seven-layered structure — with quantum mechanics embedded rather than added — this framework maintains coherence with both physics and practical hyperoptimization architecture.

This thesis constitutes a first attempt to derive aspects of standard model particle physics from little more than an algebra.

• Here, we argue that physical concepts such as particles, causality, and irreversible time may result from the algebra acting on itself.
• We then focus on a special case by considering the algebra R ⊗ C ⊗ H ⊗ O, the tensor product of the only four normed division algebras over the real numbers.
• Using nothing more than R ⊗ C ⊗ H ⊗ O acting on itself, we set out to find standard model particle representations: a task which occupies the remainder of this text.
• From the C ⊗ H portion, we find generalized ideals, and show that they describe concisely all of the Lorentz representations of the standard model.
• From the C ⊗ O portion, we find minimal left ideals, and show that they mirror the behaviour of a generation of quarks and leptons under su(3)c and u(1)em.
• These unbroken symmetries, su(3)c and u(1)em, appear uniquely in this model as particular symmetries of the algebra’s ladder operators. Electric charge, here, is seen to be simply a number operator for the system.
• We then combine the C ⊗ H and C ⊗ O portions of R ⊗ C ⊗ H ⊗ O, and focus on a leptonic subspace, so as to demonstrate a rudimentary electroweak model. Here, the underlying ladder operators are found to have a symmetry generated uniquely by su(2)L and u(1)Y.
• Furthermore, we find that this model yields a straight forward explanation as to why SU(2)L acts only on left-handed states.
• We then make progress towards a three-generation model. The action of C ⊗ O on itself can be seen to generate a 64-complex-dimensional algebra, wherein we are able to identify two sets of generators for SU(3)c.
• We apply these generators to the rest of the space, and find that it breaks down into the SU(3)c representations of exactly three generations of quarks and leptons.

Furthermore, we show that these three-generation results can be extended, so as to include all 48 fermionic U(1)em charges. (Standard Model from an algebra - pdf)

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

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

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

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

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)

Bispinors are so called because they are constructed out of two (2) simpler component spinors, the Weyl spinors. Each of the two (2) component spinors transform differently under the two (2) distinct complex-conjugate spin-1/2 representations of the Lorentz group. This pairing is of fundamental importance, as it allows the represented particle to have a mass, carry a charge, and represent the flow of charge as a current, and perhaps most importantly, to carry angular momentum. (Wikipedia)

The most general Lagrangian with massless neutrinos, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment.

• The 19 certain parameters are summarized below:
• The neutrino parameter values are still uncertain.
• The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter.

The renormalization scale may be identified with the Planck scale or fine-tuned to match the observed cosmological constant. However, both options are problematic. (Wikipedia)

In principle, there is one further parameter in the Standard Model; the Lagrangianof QCD can contain a phase that would lead to CP violation in the strong interac-tion.

• Experimentally, this strong CP phase is known to be extremely small, θCP ≃ 0, and is usually taken to be zero.
• If θCP is counted, then the Standard Model has 26 free parameters.
• The relatively large number of free parameters is symptomatic of the StandardModel being just that; a model where the parameters are chosen to match the observations, rather than coming from a higher theoretical principle.
• Putting aside θCP, of the 25 SM parameters, 14 are associated with the Higgs field, eight with theflavour sector and only three with the gauge interactions.

Likewise, the coupling constants of the three gauge interactions are of a similar order of magnitude, hinting that they might be different low-energy manifestations of a Grand Unified Theory (GUT) of the forces. These patterns provide hints for, as yet unknown, physics beyond the Standard Model. (Modern Particle Physics - pdf)

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 contribution to the fermion mass (Scale symmetry breaking - pdf)

Now we show the interplay of the finite system of prime positions with the 15 finite even positions in the cyclic convolution. Consequently, we only need to fold a 30’s cycle as so that we can identify the opposite prime positions that form their specific pairs in a specific convolution.

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)

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)

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)

Straight forward 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)

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)

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 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)

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)

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)

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)

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.

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:

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)

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)

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).

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)

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)

The electroweak force is believed to have separated into the electromagnetic and weak forces during the quark epoch of the early universe.

• In physical cosmology, the quark epoch was the period in the evolution of the early universe when the fundamental interactions of gravitation, electromagnetism, the strong interaction and the weak interaction had taken their present forms, but the temperature of the universe was still too high to allow quarks to bind together to form hadrons.
• The quark epoch began approximately 10−¹² seconds after the Big Bang, when the preceding electroweak epoch ended as the electroweak interaction separated into the weak interaction and electromagnetism.
• During the quark epoch, the universe was filled with a dense, hot quark–gluon plasma, containing quarks, leptons and their antiparticles.
• Collisions between particles were too energetic to allow quarks to combine into mesons or baryons.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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.

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)

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)

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)

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. These patterns provide hints for, as yet unknown, physics beyond the Standard Model. (Modern Particle Physics P.500 - pdf)

Moreover this model represents Quark-Gluon Plasma, with all of the fundamental forces in the early stage after Big Bang. (Youtube)

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)

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)

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 Lie group structure of the Lorentz group is explored. Its generators and its Lie algebra are exhibited, via the study of infinitesimal Lorentz transformations.

• The exponential map is introduced and it is shown that the study of the Lorentz group can be reduced to that of its Lie algebra.
• Finally, the link between the restricted Lorentz group and the special linear group is established via the spinor map.

The Lie algebras of these two groups are shown to be identical (up to some isomorphism).

The four pairwise disjoint and non-compact connected components of the Lorentzgroup L = O(1, 3) and corresponding subgroups:

• the proper Lorentz group L+ = SO(1, 3),
• the orthochronous Lorentz group L↑,
• the orthochronous Lorentz group Lo = L↑ + ∪ TL↑+ (see below) and
• the proper orthochronous Lorentz group L↑+ = SO+(1, 3), which contains the identity element.

Of course, the sets L↓−, L↑− and L↓+ do not represent groups due to the missing identity element. (The-four-pairwise-disjoint)

Fermion particles are described by Fermi–Dirac statistics and have quantum numbers described by the Pauli exclusion principle. They include the quarks and leptons, as well as any composite particles consisting of an odd number of these, such as all baryons and many atoms and nuclei. Fermions have half-integer spin; for all known elementary fermions this is 1⁄2. In the Standard Model, there are 12 types of elementary fermions: six quarks and six leptons.

• Leptons do not interact via the strong interaction. Their respective antiparticles are the antileptons, which are identical, except that they carry the opposite electric charge and lepton number. The antiparticle of an electron is an antielectron, which is almost always called a “positron” for historical reasons.
  • There are six leptons in total; the three charged leptons are called “electron-like leptons”, while the neutral leptons are called “neutrinos”.
  • Neutrinos are known to oscillate, so that neutrinos of definite flavor do not have definite mass, rather they exist in a superposition of mass eigenstates.
  • The hypothetical heavy right-handed neutrino, called a sterile neutrino, has been omitted.
• Quarks are the fundamental constituents of hadrons and interact via the strong force. Quarks are the only known carriers of fractional charge, but because they combine in groups of three quarks (baryons) or in pairs of one quark and one antiquark (mesons), only integer charge is observed in nature.
  • Their respective antiparticles are the antiquarks, which are identical except that they carry the opposite electric charge (for example the up quark carries charge +2⁄3, while the up antiquark carries charge −2⁄3), color charge, and baryon number.
  • There are six flavors of quarks; the three positively charged quarks are called up-type quarks while the three negatively charged quarks are called down-type quarks.

All known fermions except neutrinos, are also Dirac fermions; that is, each known fermion has its own distinct antiparticle. It is not known whether the neutrino is a Dirac fermion or a Majorana fermion.[4] Fermions are the basic building blocks of all matter. They are classified according to whether they interact via the strong interaction or not.

In physics, a subatomic particle is a particle smaller than an atom.[1]

• According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a baryon, like a proton or a neutron, composed of three quarks; or a meson, composed of two quarks), or an elementary particle, which is not composed of other particles (for example, quarks; or electrons, muons, and tau particles, which are called leptons).[2]
• Particle physics and nuclear physics study these particles and how they interact.[3]
• Most force carrying particles like photons or gluons are called bosons and, although they have discrete quanta of energy, do not have rest mass or discrete diameters (other than pure energy wavelength) and are unlike the former particles that have rest mass and cannot overlap or combine which are called fermions.

Experiments show that light could behave like a stream of particles (called photons) as well as exhibiting wave-like properties. This led to the concept of wave–particle duality to reflect that quantum-scale particles behave both like particles and like waves; they are sometimes called wavicles to reflect this. (Wikipedia)

There are 3 primary concepts in the diagram. We will start with an intro to lexers (tokenization), parsers, grammars and much more. Then build a simple calculator that uses all these concepts.

• The lexer which takes input as a string and converts the input into a set of tokens.
• The Parser which takes the tokens from the lexer and returns a syntax tree based on a grammar. The grammar is often expressed in a meta language such as Backus-Naur Form (BNF). The grammar is the language of languages and provides the rules and syntax.
• The interpreter which takes in the syntax tree and evaluates the result. In this case we return the result of calculator input.

Other than building a simple calculator using chevrotain the concepts that we will learn here are those that are used to build programming languages like javascript, .net, SQL and much more. Perhaps one day you will make your own language. Chevrotain

In this example, the content from a Markdown document document.md that specifies layout: docs gets pushed into the {{ content }} tag of the layout file docs.html. Because the docs layout itself specifies layout: page, the content from docs.html gets pushed into the {{ content }} tag in the layout file page.html. Finally because the page layout specifies layout: default, the content from page.html gets pushed into the {{ content }} tag of the layout file default.html. (JekyllRb)

This is the partial of the whole scheme from our Quantum Project based on the algorithm of DNA Recombination: M+F to C1+C2:

The M+F symbols will stand as: Project Maps (M) + Project Feed (F) while<br>C1+C2 as implementations, see sample: Project Base (C1) + Project Core (C2).

The final result of this Q(19,10) would form π(10)=(2,3,5,7) as the 1st row of 19.

Still far from production but at least it has a minimum error. You may check the running code starting with Sequence Diagram shown below which is developed as the initial step on building the 10143 Grammars.

This sample was developed by converting eQuantum to eCommerce using the cyclic algorithm of 168 vs 618 that act as Lexer and Parser.

Although the code is already running but however it is not yet user friendly as it could run only in GitHub API Platform.

Mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17) (₠Quantum).

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)

Why collaborating with physicists?

• Contribute to the understanding of the Universe.
• Open methodological challenges.
• Test bed for developing ambitious ML/AI methods, as enabled by the precise mechanistic understanding of physical processes.
• Core problems in particle physics transfer to other fields of science (likelihood-free inference, domain adaptation, optimization, etc).
• A high-level summary of various aspects of machine learning in LHC data reconstruction, mostly based on CMS examples. A short summary of a particular use case: ML for combining signals across detector subsystems with particle flow. This talk is in personal capacity (not representing CMS or CERN), representing my biased views.

You can find a great and fairly complete overview of ML papers in HEP. (Pata Slides)

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)

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

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

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

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