Physical Sciences

Abstract: We establish the unique topological setting of any unified gauge theory with quantized charge, and derive its physical consequences. A gauge field is a principal bundle equipped with a gauge symmetry and connection potential. We prove that (1) given electromagnetism as a U(1) gauge theory with quantized charge, and (2) the existence of a unified single-field theory, a unified theory must be formulated, up to homotopy equivalence of the base and isomorphism of bundles, on the universal complex Hopf fibration bundle S¹ → S^∞ → CP^∞ and its finite approximations S¹ → S²ⁿ⁺¹ → CPⁿ. Completeness and indecomposability are derived consequences, not additional axioms. The Standard Model gauge groups arise as natural reductions along the nested shell hierarchy: U(1) from the circular S¹ fiber, SU(2) from the S³ shell and SU(3) from the S⁵ shell. The classifying spaces BU(1), BSU(2), and BSU(3) are all internal to this single hierarchy; each is obtained by changing the quotient on the same universal total space S^∞, not by independent construction. The unified structure group G_total = (SU(3) × SU(2) × U(1) × SO(4))/Γ is intrinsically non-factorable due to the generating role of the universal first Chern class in H^∗(CP^∞;Z) ≅ Z[c₁]. The unique universal action on the Hopf bundle is derived from SO(4)-equivariance, the Killing form, and degree classification; the torsion action is the unique admissible positive-definite quadratic form. The Einstein, Maxwell, and Yang–Mills field equations all follow from this single action. The Beltrami operator B = ⋆d|ξ on the contact distribution is doubly forced as both the action Hessian and the unique equivariant first-order operator. The result is a topologically enhanced Standard Model: every term of the conventional SM Lagrangian appears with identical structure, with no free parameters, and with gravity via Chern–Simons theory on S³, the Beltrami mass operator, and the resolution of the strong CP problem as enhancements. Gravity emerges on the S³ = SU(2) shell, sharing exactly one generator—the Cartan U(1)—with the gauge sector; gauge–gravity unification is the fibration U(1) → SU(2) itself. On each Hopf shell, the Beltrami operator is elliptic, essentially self-adjoint, and possesses a discrete spectrum stable under torsion perturbations by the Kato–Rellich theorem. Fiber winding decomposition yields independent topological sectors whose Gaussian functional determinants, regularized via spectral zeta functions, generate intrinsic mass scales. Fermion mixing (CKM, PMNS) arises from intersection-form overlaps of admissible cycles in H^∗(CP⁴), with CP violation induced by fiber holonomy phases. The electroweak vacuum expectation value v serves as the unit conversion factor between geometric and laboratory scales; given this single identification, the fine-structure constant and all shell-specific mass scales, spectral coefficients, and interaction strengths entering the particle spectrum are fixed by the spectral geometry of the complex Hopf fibration. The framework predicts the complete particle mass spectrum and anomalous magnetic moments, with suggested independent experimental tests (torsion-induced phase wobble, absolute neutrino mass scale, and the electron, µ and τ g − 2) providing falsifiability. Fundamental constants arise from topological normalization. Further results include anomaly cancellation, dark sector effects from bundle torsion and holonomy, and the elimination of singularities. The mathematical results stand independently as contributions to the topology of classifying spaces, reductions along nested Hopf shells, and contact spectral geometry.

Abstract: A current interest in lunar exploration led by Artemis program pushes scientists to search for lunar water deposits directly on the surface of the Moon with small robotic rovers. The Institute of Experimental and Applied Physics, Czech Technical University in Prague (IEAP CTU) is developing a miniature Timepix3-based detector Neutron HardPix capable of mapping the water deposits using non-invasive detection of neutrons created underground by cosmic rays and thermalized by hydrogen. This neutron spectrometer measures count rate variations of thermal, epithermal and fast neutrons attributed to the hydrogen abundance in lunar subsurface, while monitoring cosmic radiation as a natural source of neutrons. Neutron HardPix is based on the miniature (< 0.1 U, 130 g) radiation monitor HardPix with multiple space heritage.

Abstract: We investigate a minimal deterministic hypothesis: that the internal symmetries and Lorentzian kinematics of low-energy physics arise as emergent geometric-phase (Berry / Wilczek–Zee) holonomy of a single elastic substrate—a static four-dimensional cubic brane lattice in a 4D Euclidean ambient, whose only nonlinearity is the Pythagorean link length. With explicit, reproducible computations we show that (i) the Lorentzian signature (3,1) of the effective metric is the sign pattern of the directional prestress, not an imposed structure; (ii) the fluctuation operator about a finite-amplitude periodic carrier has an isolated rank-3 complex eigenbundle whose gauge-invariant Wilczek–Zee curvature generates the full Lie algebra su(3) (Lie-closure rank 8, not merely so(3)), with the abelian trace as a candidate electromagnetic U(1); (iii) emergent gauge invariance, locality, and power counting force the leading dynamics of both sectors to Maxwell and Yang–Mills form, with substrate-induced positive couplings and no mass term; and (iv) the rank selection U(3)-not-U(4) and the U(1)/SU(3) split are set by the prestress parameters. We are deliberate about scope: the color-carrying background is a stable but higher-energy texture, not the ground state, and the emergent Lorentz invariance is only approximate—the residual anisotropy being itself the escape from the Weinberg–Witten no-go; matter and confinement are not treated. The result is a constructive proof of concept that one deterministic elastic substrate can carry a U(1)×SU(3) gauge structure and a Lorentzian light cone as emergent symmetries.

Abstract: Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by coordinate and momentum spinors. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Dirac equation the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors. In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In the presence of a potential the momentum components cease to commute with each other. To neutralize this effect, the Schrödinger equation is supplemented by several equations with mixed partial derivatives on coordinates. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant. This novel equation permitted the construction of an actually invariant procedure for the second quantization of the fermion field in spinor coordinate space. Furthermore, it is demonstrated that the field operators are a combination of plane waves in spinor or vector space, with the coefficients of which being pseudospinors or pseudovectors. Each of these pseudovectors or pseudospinors corresponds to one of the particles presented in the theory of electrodynamics. Furthermore, each plane wave possesses an additional coefficient in the form of a creation or annihilation operator. In vector space, these operators commute, whereas in spinor space they anticommutate. The paper presents the spinor and vector representations of the field operators in explicit form, comprising sets of 16 pseudospinors or 4 pseudovectors corresponding to particles represented in electrodynamics. An explicit form of the symmetric traceless tensor with spin two, zero mass and two polarizations is presented, which can serve as a model of the graviton. The results obtained may prompt changes in some aspects of the construction of Feynman diagrams. Among other things, it presents a purely mathematical derivation of Maxwell's inhomogeneous equations without reference to empirical data on the action of electric current, which is usually referred to when deriving equations. Section 4 presents Einstein's inhomogeneous equation, which features the Riemann tensor rather than the Ricci tensor, with the energy-momentum tensor of a charged particle having four indices rather than two. In the case where a particle of matter has a charge, another Riemann tensor is added to Einstein’s equation, in addition to the usual Riemann curvature tensor, which describes the additional curvature created for a charged particle by an electromagnetic field.

Abstract: Neutron stars observed as pulsars are among the most versatile natural laboratories in physics. Their clock- like rotational stability, strong surface gravity, supranuclear interior densities, broadband pulsed emission, and distribution across the sky allow a single class of object to probe questions that range from the behaviour of matter at extreme density, through the strong-field and radiative regimes of general relativity (GR), to the most ambitious target of all—residual, Planck-scale imprints of a quantum theory of gravity. This survey reviews, at the level of a working researcher, the principal ways in which pulsars test physics beyond the established classical-GR+quantum-field-theory description, organized into five complementary pillars: (i) tests of Lorentz invariance through energy-dependent photon time-of-flight; (ii) the nanohertz gravitational-wave background detected by pulsar timing arrays, with its astrophysical and cosmological interpretations; (iii) strong-field tests of GR with relativistic binary pulsars; (iv) the dense-matter equation of state inferred from neutron-star masses and radii; and (v) searches for stochastic spacetime “foam” through the decoherence and blurring of astrophysical signals. For each pillar we give the governing relations, summarize current best constraints, and state plainly what the method can and cannot deliver. The resulting picture is asymmetric but coherent: pulsars now furnish some of the most precise tests of strong-field gravity and the tightest astrophysical handles on the dense-matter equation of state, whereas in the quantum-gravity sector they chiefly bound and falsify candidate theories—frequently as a complement to gamma-ray and cosmological probes—rather than isolating a unique microscopic completion.

Abstract: The light hadron spectrum is reconstructed over a finite relational arithmetic substrate, on a single Ω-hard scale. A baryon is the colour-neutral invariant of the triality frame, the determinant residue Λ³ = 1 (baryon number), forced by the gluon residue 0 and completing the Carrier-residue series photon 2, gluon 0, hadron 1. Its constituents are the wrapped composites of confinement, so each mass is M_B = √σ [ f_fl + κ_hf g_spin ] + ∆^EM, the confinement scale √σ ∼ Λ_QCD times dimensionless structure, and the scale cancels in every flavour and spin relation. We derive the Gell-Mann–Okubo octet relation (0.57%) and the decuplet equal spacing (9.2%, closed to 0.4% at second order); the decuplet–octet hyperfine pattern as the colour-magnetic character invariant (colour factor −8, spin 1/2 S(S + 1) − 9/8 ); the Coleman–Glashow isospin identity (0.79%); heavy-quark symmetry (2.4%); and the vector-meson nonet equal spacing 2M_K∗ = M_ρ + M_ϕ (0.42%). The absolute octet and decuplet follow from one scale and three sub-horizon eigenvalues, anchored to N, Λ, ∆, to within 1.1%; the baryon scale is itself the computed finite eigenvalue E₀ ≃ 2.232, M_N = E₀√σ predicting the nucleon to 4.6%. The sector introduces no new Ω-hard residue; every predicate resolves to a sub-horizon residue, a closed-form framed-rational or a profinite eigenvalue, or to the single confinement scale. Every exact claim is verified in finite-field or cyclotomic arithmetic, the continuum entering only as a labelled degenerate idealisation.

Abstract:

The flavour sector of the Standard Model is reconstructed over a finite relational arithmetic substrate. The substrate fixes the structural half, one fermion generation as the spinor 16, the Higgs mass bridge m = yv, and the three-generation count. The paper derives the masses, the mixings, as well as quantitative residue. We furthermore show that the unresolved residue is organised by the substrate’s two structural numbers, the four-fold (4 | Ω − 1, the quarter-turn) and the cubic (3 | Ω + 1, the triality centre), the pair that fixes Ω ≡ 5 (mod 12). The charged-lepton Koide relation is derived exactly, Q = 2/3: generation universality forces the Yukawa amplitude matrix to a C₃-circulant, the quarter-turn fixes the amplitude √2, and the lightest generation at the quarter-turn boundary fixes the leading phase π/12, leaving the electron massless at leading order. The three generative roles supply the Froggatt–Nielsen charges (0, 1, 2), giving the λ-texture and the Cabibbo angle V_us = √(m_d/m_s); the Georgi–Jarlskog factor is the colour rank N_c = 3; the up-quark Koide value is Q_u = 5/6. The mixing split is the lopsided M_e = M_d^T. For the neutrinos colourlessness fixes the signed (Takagi) amplitude invariant Q_ν = 2/3; with the drive-invariant quarter-turn boundary branch this selects normal ordering and ∑ m_ν ≃ 59 meV, and the cube-root phase makes leptonic CP near-maximal, δ_CP ≃ −130◦. Beyond the overall mass scale, the sector reduces to one carrier-scale phase δ₀ ≃ 2/9, with everything else derived or predicted; the matter sector thus rests on two Ω-hard residues, one scale and one phase. Every exact claim is verified in finite-field or cyclotomic arithmetic, the continuum entering only as a labelled degenerate idealisation.

Abstract: The electromagnetic, weak, and strong interactions, together with one Standard-Model generation of matter, arise on a finite relational arithmetic substrate \(\mathbb F_\Omega\) as the gauging of its relational frame data: a cell-local change of frame is a gauge symmetry and the compensating connection is the field. The three interactions are the substrate's three internal frame data: the multiplicative phase, the spinorial extension, and the colour frame. A finite-window correspondence ties the finite gauge groups so produced to the observable compact theory: a cyclotomic representation reproduces the gauge invariants, the Yang-Mills kinetic operator, and the chiral matter within a bounded horizon \(H\ll\Omega\) at residue \(O(H/\Omega)\), proven on the resolvable class, the cross-scale extension a finite Carrier-scale residue. Concretely, electric charge is a quantised winding index and the bare coupling the phase-channel capacity \(1/4\pi\); electroweak breaking gives the massless photon, custodial \(\rho=1\), and sin² θ_W=3/8; colour SU(3) is the special unitary group of a Hermitian three-form; and one generation is the anomaly-free SO(10) spinor 16 with a right-handed neutrino. The four interactions and three generations are organised by one closed role ladder (the count/generate split), forbidding a fifth force and a fourth generation and forcing SO(10) unification. Every exact claim is verified in finite-field or cyclotomic arithmetic, the continuum entering only as a labelled degenerate idealisation.

Abstract: This paper develops a neutral-parent closure theory of the lowest baryonic mass read-outs. In this framework, particles are interpreted as persistent carrier defects whose observable identities arise only after internal return closure, carrier embedding, and Lorentz-covariant read-out. A key structural requirement is that such defects have a codimension-two carrier-facing form, so that a transverse linking loop can support phase holonomy and stable particle identity. Before read-out, the defect-internal space is treated as premetric and is described by finite Zn return closures rather than continuous gauge groups; after read-out, the effective descriptions are compatible with the usual SU(2) and SU(3) language of the Standard Model. The common scale used in the calculation is the first-resolution scale structurally fixed in the companion charged-lepton analysis, with the electron mass used only as the dimensional unit. The neutron is modeled as the lowest closed neutral read-out of the neutral-parent closure, while the proton is modeled as the lowest charged-boundary opening of the same closure. The resulting parameter-free formulas reproduce the neutron–electron and proton–electron mass ratios within about minus 0.92 and plus 0.35 standard deviations of the CODATA values, and imply a neutron–proton splitting within about 0.36 eV of observation. The paper also explains the Lorentz rest-mass read-out and the information-state meaning of chamber counting, while leaving a theorem-level derivation of the complete closure complex as an open task.

Abstract: This preprint has been withdrawn at the request of the author due to serious scientific errors that cannot be corrected by updating the paper.

Abstract: In the linear approximation of general relativity, the field and force equations are transformed into vector equations with forms identical to covariant Maxwell and Lorentz force equations and are benchmarked to known strong-field solutions. The transformed equations can be used to: Apply aspects of electromagnetism theory and electrodynamics to weak-field gravitation; design laboratory tests of general relativity at high speeds; and characterize more accurately the coalescence of compact binaries. If linearized gravitation is treated as a vector field, one consequence is that ordinary quadrupole radiation from a rotating binary is found to be a linear superposition of Doppler-modulated dipole gravitational waves from each mass. Dipole waves at the orbit frequency may be observable in the merger event GW150914 at about 0.5 percent of the power and 7 percent of the strain amplitude. Another consequence is a cosmic gravitational background (CGB) much like the cosmic microwave background. The CGB relates the Hubble constant to Planck’s constant at an equilibrium temperature of about 20 to 22 K. An exact solution of Einstein’s equation for a static universe with a CGB accounts for the Hubble redshift, mature galaxies at high redshifts, and the appearance of cosmic acceleration in SN-Ia supernova light curves.

Abstract: We present a spectral-action framework for connecting Generalized Trace Dynamics (GTD) to the structural form of the low-energy action of the observed universe. The fundamental single-STM-atom Lagrangian is decomposed exactly into a purely bosonic sector, boson–fermion cross terms, and bifermionic terms. This sectorwise decomposition furnishes a dictionary to almost-commutative spectral geometry: the bosonic sector supplies a quadratic GTD Dirac functional built from the six split-biquaternionic differential directions together with octonionic vector/gauge fluctuations; the cross sector supplies, under an explicit localization hypothesis, a sesquilinear fermionic pairing; and the bifermionic sector supplies the scalar/internal channel that is bosonized into the Higgs bridge field. We also record the principal-symbol link between the SO(3,3) BF variables and the four-dimensional leafwise Dirac operator. Under stated assumptions — spontaneous localization, Euclidean continuation, six- to four-dimensional BF reduction, and a candidate observed-leaf finite geometry compatible with the E₆/J₃(O_C) inputs — the bosonic heat-kernel expansion yields the structural low-energy classes of terms: Einstein–Hilbert gravity, Yang–Mills kinetic terms, and scalar kinetic and potential terms. In addition, we provide a candidate finite spectral triple with explicit finite trace invariants, verify that the localization map respects the one-generation lepton/quark representation split, identify visible color-singlet scalar channels with electroweak quantum numbers (1,2, ±1/2), and exhibit a smooth regulator family with explicit cutoff moments (f₀,f₂,f₄). Conversely, the assembled low-energy spectral action admits a natural inverse bilinear lift back to split bioctonionic trace dynamics. The result is a structural framework with conditional consistency checks and reductions, not a complete first-principles derivation.

Abstract: Rare charm decays offer a clean arena for visible massive dark photon searches through narrow dielectron resonances. In the process D⁰→γA^′→γe⁺e⁻, the observable signal rate is controlled simultaneously by the flavor changing charm transition, the radiative D⁰→γ hadronic matrix element, the visible decay probability of A′, and the experimental response of the reconstructed mass spectrum. We introduce a visible coupling formulation that combines these ingredients into a single search parameter while keeping the form factor and the A′→e⁺e⁻ branching fraction as explicit external inputs. This provides a direct bridge between branching fraction sensitivity and coupling reach, without assuming a specific experimental background model. The central novelty of this approach is that it separates the particle physics information entering the signal rate from the analysis dependent ingredients that determine the observable mass spectrum. We apply this construction to the D⁰→γe⁺e⁻ spectrum, including effective exposure, reconstruction efficiency, mass resolution, and the treatment of the ρ/ω and ϕ regions. The ρ/ω and ϕ dominated intervals are kept outside the coupling definition and left to experiment specific resonance treatment. This formulation gives a practical and reusable basis for comparing visible massive dark photon sensitivity across current and future charm data sets.

Abstract: Over the last few years, we have attempted to develop an \( E_8 \times E_8 \) theory of unification to combine the standard model with general relativity. In the present new work, we give a self-contained construction in which the two extra \( SU(3) \) factors that appear in the maximal subgroup chain \( E_8\supset E_6\times SU(3) \) on each side of \( E_8\times \omega E_8 \) generate: (i) a six-dimensional base \( (M_6,g) \) of signature \( (3,3) \); (ii) two embedded Lorentzian 4D spacetimes; and (iii) per side, a canonical real 4-dimensional internal fibre naturally identified with the tangent of \( \mathbb{C}P^2=SU(3)/S(U(2)\times U(1)) \). The key algebraic ingredient is the octonionic split \( O=H\oplus H\varepsilon \) with \( \varepsilon\perp H \), by which the branch AdjSU(3) →\( \mathbf{3}_0\oplus \mathbf{2}_{+1}\oplus\overline{\mathbf{2}}_{-1}\oplus \mathbf{1}_0 \) is realised as ℑ\( H\oplus (H\varepsilon)_{\mathbb{R}}\oplus R \). The two \( U(1) \) factors play the role of Spin\( ^c \) connections on the \( \mathbb{C}P^2 \) fibres.The dynamical localisation that selects the two Lorentzian leaves—reproducing 4D gravity in Plebanski form—is developed in a companion work [1].

Abstract: The Standard Model describes particle phenomena through continuous gauge structures, chiral assignments, color, generations, and Yukawa masses, but it does not derive these labels from a deeper structural principle. This paper proposes a carrier-resolution interpretation in which particle species are not separate primitive objects, but different carrier-readable manifestations of one loop-detectable codimension-two archetype defect. The carrier supplies Lorentzian propagation and globally available \(U(1)\) phase closure, while particle labels arise through holonomy, embedding, closure, and saturation conditions. The framework argues that local \(U(1)\) closure favors a neutral-parent starting point, whose persistent asymmetric resolution is modeled as \[P_0\longrightarrow Z_2\oplus (Z_2\!\rightarrow\!Z_3).\] The \(Z_2\) branch is interpreted as lepton-like after Lorentz embedding, whereas the \(Z_2\!\rightarrow\!Z_3\) branch supports a nested confined \(Z_3\) monodromy interpreted as hadronic structure. Incomplete \(Z_3\) sectors are not carrier-readable as isolated hadrons; the usual \(SU(3)_C\) QCD description is retained as the effective high-energy continuum envelope of temporarily resolved \(Z_3\) sectorality. The paper further gives a conditional interpretation of the three observed generations as leading saturation modes of the dominant \(U(1)/Z_2/Z_3\) closure backbone, while higher \(Z_n\) refinements appear as suppressed response corrections rather than ordinary additional generations. As a concrete test, the neutron--proton magnetic-moment ratio is derived from an ideal \(Z_3\)-complete baseline and a rule-generated interface sequence through \(Z_7\). The successive predictions improve from the \(10^{-4}\) level to the few-ppm level and then to below one ppm of observation, without introducing new particles, new fundamental interactions, or fitted coefficients.

Abstract: The charged-lepton mass hierarchy remains unexplained in the Standard Model: the Higgs mechanism relates \(m_e\), \(m_\mu\), and \(m_\tau\) to three Yukawa couplings, but does not determine their ratios. This paper applies a minimal effective subset of a previously developed reconstruction framework, including carrier embedding, finite-action phase behavior, and codimension-two defect structure, to the charged-lepton mass problem. Charged leptons are modeled as carrier-embedded defect channels arising from a common neutral parent, and their masses are interpreted as quadratic residual responses. The natural variables are therefore root residuals rather than masses themselves. The main algebraic result is that Koide's relation is equivalent to equality between the democratic parent component and the orthogonal channel-splitting component of the charged-lepton root vector. This reduces the hierarchy to a one-angle problem on the Koide cone. The remaining angle is fixed by an effective weak-closure selector involving the neutron--proton mass difference, the democratic electron projection, the beta-continuum scale, the fine-structure constant as a \(U(1)\) carrier-dressing factor, and a finite positive-end recoil term. No continuous parameter is fitted. Using only \(m_e\), \(m_p\), \(m_n\), and \(\alpha\) as physical boundary inputs, the weak-closure selector gives \[m_\mu^{\rm pred}\simeq 105.6565~{\rm MeV}, \qquad m_\tau^{\rm pred}\simeq 1776.94~{\rm MeV}, \] with relative errors of approximately \(-0.0017\%\) and \(+0.0045\%\), respectively. The Koide-cone reduction is algebraic, while the weak-closure selector is presented as an effective boundary condition requiring future microscopic derivation. The result provides a falsifiable route by which the charged-lepton hierarchy may arise from neutral-parent root balance and weak closure rather than from three independent Yukawa parameters.

Abstract: The charged-lepton Koide relation Q = (∑m_ℓ)/(∑√m_ℓ)2 = 2/3 has held to one part in 10⁵ for over four decades without an accepted derivation. The same rational value 2/3 is forced by C₃ phase cancellation identities in three-beam interference, where three coherent sources at 120^◦ separation produce hexagonal patterns with a fixed quadratic intensity ratio. Whether the shared 2/3 is a surface coincidence or reflects deeper structural overlap between interference geometry and the fermion mass spectrum is the question this paper investigates. We show that a companion identity (the F identity) reduces to the classical Descartes circle theorem at Q = 2/3, and that integer-wavelength resonance conditions at sinθ = 2/(3N) provide a geometric counterpart to Shulga’s compact-cycle offset δ = 2/9. A geometric-mean cascade motivated by hierarchies previously noted in the quark mass literature suggests fixed closed-form targets for three light-quark masses (ms, md, mu) from a single input µ_⋆ = ∑m_ℓ = 1883.1 MeV, with internal self-consistency at 0.06% and deviations from PDG/FLAGreference values within current uncertainties. The algebraic overlap is not limited to the shared numerical value 2/3: the C₃ phase-cancellation algebra that forces Q = 2/3 in interference also fixes the companion identity and the Descartes connection, while the associated integer-wavelength resonance conditions place δ = 2/9 in the same geometric framework. The construction does not propose a mechanism for fermion masses; we present these correspondences as empirical constraints on whatever dynamics produces the fermion spectrum, not as a theory of those dynamics. This work appears within the same month as three independent publications on the Koide relation (Sec. 10), suggesting the tools for understanding it may be maturing.

Abstract: Machine learning capabilities are expanding into scientific domains at an accelerating pace. When applied to high energy physics pattern discovery, they will generate candidates faster than traditional evaluation can absorb. ML finds patterns in past data. It is inherently post hoc. Whether those patterns reflect structure or coincidence is unknowable at discovery time. This limitation applies equally to human and computational pattern finding. What differs is scale. ML candidate generation is effectively unbounded, while human evaluation capacity remains fixed. When generation rate exceeds evaluation bandwidth, binary accept or reject degenerates to random sampling. Information theoretically, the only response that preserves ranking under a finite evaluation budget is stratification. By focusing on stratification rather than binary filtering, rule adjustments can be made retroactively, thresholds tuned as results accumulate, and evaluation bandwidth focused on top ranked candidates. This paper attempts to codify those criteria, proposing seven computationally evaluable standards for stratifying ML generated patterns. The goal is not to deliver verdicts but to prioritize which candidates merit preregistration and longitudinal tracking. The framework preserves the essential paradigm: pattern plus theory equals potentially real physics. Patterns alone, however striking, remain candidates until theoretical understanding arrives. Making these criteria explicit enables prefiltering at scale while creating a collaborative resource rather than a competitive one. ML capabilities extend what physicists can search while preserving how physicists evaluate. We offer this provisional framework for community calibration, with the goal of developing validation infrastructure before the capability fully arrives.

Abstract:

The Koide relation \( Q = (\sum m_\ell)/(\sum \sqrt{m_\ell})^2 = 2/3 \) for the charged leptons has held to one part in \( 10^5 \) for over forty years without an accepted derivation and is widely regarded as numerology. This paper takes the relation as a clue rather than an endpoint. Treating lepton mass square roots as Descartes-circle curvatures, the outer root of the Descartes quadratic equals the closed form \( \mathcal{F} = e_1 - \sqrt{p_2} \) when Koide holds exactly (Proposition 1); equivalently, \( \mathcal{F}^2 = \alpha_K^2\,\mu_\star \) with \( \alpha_K^2 = 5/2 - \sqrt{6} \) and \( \mu_\star = \sum_\ell m_\ell \) the lepton-sum scale. The three-input symmetric-polynomial identity thus collapses to one dimensionless Koide-determined constant times the lepton-sum scale. Kocik [10] first observed a Descartes-like reading of Koide; our mutually-tangent variant is mathematically distinct but follows the same geometric spirit. The four-curvature completion carries a testable consequence absent from the bare three-mass relation: evaluating the squared fourth curvature numerically, \( \mathcal{F}^2 = 95.113 \) MeV, and comparing against the strange-quark \( \bar{MS} \) mass at \( \mu_\star \) within current lattice precision yields a residual of \( +0.04 \) MeV against \( \pm 0.69 \) MeV, about \( +0.06\sigma \). The lepton-side quantity is fixed to better than \( 0.01\% \); future lattice improvements will sharpen or refute the present numerical agreement. To our knowledge this paper implements the first Monte Carlo null test of the Koide relation under a random-spectrum prior; a Koide-conditioned null-model calibration across four prior shapes pre-registered for the analysis gives hit fractions at the sub-percent level — model-conditional frequencies, not \( p \)-values. Scale, input, prior, and filter sensitivities, together with the error budget, are reported; full Monte Carlo protocols, numerical output, and pre-registration are in a companion methods note [15].

Abstract: This article is a review of developed in 2007-2025 years Planck scale informational physical model that is based on 3 main points. First of all on the 2007 “The Information as Absolute” conception, where the fundamental phenomena/notions “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, which are fundamentally transcendent in conventional philosophy and sciences, are rigorously scientifically defined. The conception completely rigorously scientifically legitimates the outstanding C. F. von Weizsäcker “Ur hypothesis”, and E. Fredkin “Digital Philosophy/Physics”, which posit that Matter is constructed from some binary reversible logical elements; and on all reliable experimental data. Correspondingly in the model it is postulated that Matter’s ultimate base is the [4+4+1]4D dense lattice of primary [4+4+1]4D binary reversible fundamental logical elements [FLE], which is placed in the corresponding Matter’s fundamentally absolute “Cartesian” [4+4+1]4D spacetime with metrics (cτ,X,Y,Z, g,w,e,s,ct), while everything in Matter is/are some specific disturbances in the lattice. Basing on the above in the model a number of physical problems are either solved or essentially clarified, e.g. of what is real Matter’s spacetime above, what are the physical sense of Lorentz transformations; uncertainty and wave-particle duality in QM; particles and antiparticles, etc. Besides initial Planck scale models of fundamental Gravity, Electric, and Nuclear/Strong Forces are developed, where it is shown that these Forces strengths ratio is in accordance with experimental values only if the FLE size and FLE flip time are Planck length and Planck time; the model rather probably really scientifically clarifies some cosmological problems, including the “matter-antimatter asymmetry: one. Etc. more of the problems see in the article.