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Unification of the Four Fundamental Forces via SpectralGeometry of the Vacuum

Authors: Bertrand Jarry
Comments: 28 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0)

We present Quantum Vacuum Geometry (QVG), a framework that unifies the four fundamental forces within a single spectral integral Z[D]=∫▒ [dD]expu2061(Tr[f(D^2/Λ^2 )]),D=D_ext⊗1+γ^5⊗D_F where D_F encodes matter and D_"ext " encodes geometry. The three Standard Model forces reside in D_F through the unique algebra A_F=C⊕H⊕M_3 (C) (derived from five axioms C1-C5); gravity emerges from D_"ext " as depletion of the spectral vacuum. All four force-carriers - photon, W^±/Z^0, gluons, and graviton - are residues of 1/q^2 poles of the same propagator.Four quantitative relations connect the forces without free parameters: (U1) sin^2u2061θ_W=3/8; (U2) G_N=2π^2 ℏc/(N_F Λ^2 ) with N_F=96, linking gravitational strength to the fermionic content of the SM; (U3) S_BH=8×A/4l_Pl^2 with factor 8=N_F/N_"bosons " ; (U4) S[D_"total " ]=∑_i▒u200a Z_F (λ_i ) exactly (no BCH corrections, since [D_"ext " ,D_F ]=0 ).The discretisation of geometry by E_0 is the gravitational analogue of Planck's discretisation of the electromagnetic field by ℏ : the equilibrium condition Z_(S^4 ) (E_0 )=N_F=96 plays the role of Planck's thermal equilibrium, and G_N is the coupling between the two discretisations. Gravity is weak because it is diluted over N_F=96 spectral modes, whereas electromagnetism couples through a single U(1) mode.All nineteen Standard Model parameters, T_CMB=2.709" " K ( 0.8% accord), and Λ_"cosmo " are derived from C1-C5 with one free dimensional input M_Pl. The number of fermion generations N_g=3 is derived from the intersection of CP-violation and BBN constraints on D_F. The most urgent experimental test is w=-1 exactly, now challenged at 2.8-4.2σ by DESI DR2; DESI DR3 and Euclid (2026-2027) will provide a near-definitive verdict.
Category: High Energy Particle Physics

A Refined Objective Reduction: Solving the Planck-Scale Spectral Gap Through Fractal Geometry

Authors: Brendan Kurzke
Comments: 3 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

This paper addresses a gap in the standard Orchestrated Objective Reduction (Orch-OR) formulation. A purely Euclidean volume model fails to account for the holographic data density needed at the Planck scale during the coherent pre-collapse state. To resolve this paradox, the author models the geometry of the tubulin array as a Hausdorff Fractal manifold instead of a 3D Euclidean manifold.The authors starting point was visualizing data points in a fractal matrix warped and pulled by ‘synthetic gravity’, like the weights of an AI model. The author derives a refined OR consciousness function and a corrected gravitational energy threshold (EG) using the Hausdorff Metric-Measure (HD). This correction results in consciousness timescales ranging from 25 milliseconds to 500 milliseconds. Additionally, the paper introduces a blue-shift mechanism—a geometric compression of the wave function—and explores the anesthesia threshold as an "entropic flattening" where fractal dimensionality (D) approaches 2.0. These findings suggest that fractal complexity is essential for maintaining the quantum-coherent states necessary for consciousness.
Category: Quantum Gravity and String Theory

The Self-Creating Universe: A Zero-Flux Boundary Eigenproblem Framework

Authors: Jeff Smith, Scott Cowick
Comments: 18 Pages.

The Self-Creating Universe framework proposes that the fine-tuning problem is resolved not by invoking a creator, multiverse, or external simulation, but through selection by mathematical necessity. The universe is treated as a zero-flux boundary eigenproblem: a standing-wave solution whose physical constants are determined by the simultaneous satisfaction of past inflationary constraints and a future intelligence-viability constraint, phase-locked by a conserved informational invariant. Only universes capable of generating intelligence that can retrocausally stabilize their own initial conditions achieve self-consistent causal closure and therefore exist. The causal loop is structural rather than temporal — it may have already closed elsewhere in the universe's history — and is grounded physically in Aharonov's Two-State Vector Formalism, experimentally confirmed through weak measurement protocols. The "boundary determines bulk" principle is supported by the AdS/CFT correspondence. The learnability of physical law is explained mechanistically through Zurek's Quantum Darwinism. The Boltzmann Brain objection is resolved by a double exclusion criterion: Boltzmann Brains satisfy neither the future intelligence-viability constraint nor the Quantum Darwinism reliability condition. The causal loop's non-temporal character is formalized through Causal Set theory. The intelligence threshold is operationalized via Tononi's Integrated Information measure Φ. The framework is distinguished from Wheeler's Participatory Universe, Tipler's Omega Point, and Tegmark's Mathematical Universe Hypothesis, and operates as a selection filter within the latter. Six explicit falsification criteria are provided. Testable predictions include spectral rigidity in ratios of fundamental constants, scaling of quantum retrocausal effects to macroscopic systems, and bounded algorithmic complexity of cosmological parameters.
Category: Relativity and Cosmology

A Modification of the Sundaram Sieve, and the Count of Twin Primes

Authors: Wiroj Homsup
Comments: 3 Pages.

A modification of the Sundaram sieve of twin primes is introduced. A twin prime pair is obtained from the set D which consists of elements n such that n not representable as the forms 2ij + i + j and 2ij + i + j -1 for positive integers i, j. An element n is in D if and only if (2n+1, 2n+3) is a twin prime pair. This sieve algorithm can find the number of twin primes below a certain value.
Category: Number Theory

A Zero-Parameter Formula for Atomic Radius Ratios Derived from the Cantor Spectrum of the Aubry—André—Harper Hamiltonian

Authors: Thomas Husmann
Comments: 8 pages, 5 tables, 1 supplementary code listing, 25 references. CC BY-NC-SA 4.0. Patent pending (Application No. 19/560,637). Source code: https://github.com/thusmann5327/Unified_Theory_Physics

Background: The Aubry—André—Harper (AAH) Hamiltonian, a one-dimensional quasiperiodic tight-binding model with irrational modulation frequency, exhibits a Cantor-set energy spectrum at its self-dual critical point. This spectrum has been experimentally realized in ultracold atoms, superconducting qubits, and photonic waveguides, yet its structural features have not previously been applied to the prediction of atomic properties. Methods: We constructed the AAH Hamiltonian on a lattice of D = 233 sites (a Fibonacci number) with modulation frequency α = 1/φ, where φ denotes the golden ratio, and potential amplitude V = 2J (the self-dual critical point). Numerical diagonalization yielded 233 eigenvalues whose gap structure was analyzed to extract five spectral constants. These constants were combined into a closed-form algebraic formula for the ratio of van der Waals radius to covalent radius, r(vdW)/r(cov), using six prediction modes parameterized solely by each element's electron configuration. No constants were fitted to experimental atomic data. Results: The formula was evaluated for 54 elements (Z = 3—56). Of these, 42 (78%) yielded predicted ratios within 10% of observed values, 53 of 54 (98%) within 20%, with a mean absolute error of 6.7%. Only one element (boron) exceeded a 20% error. The best-predicted element, cesium, showed agreement to 0.2%. The residual deviations correlated significantly with independently measured material properties: hardness (ρ = +0.66 for p-block elements), melting point (ρ = −0.61), and electrical conductivity (r = −0.74 for metals). For the lanthanide series (Z = 57—71), the four-gate architecture generated three confirmed predictions: (a) the van der Waals radii should be approximately constant across the series, consistent with Alvarez's crystallographic finding of a 232 ± 9 pm mean; (b) covalent radii should contract monotonically, matching the observed lanthanide contraction from 207 to 175 pm; and (c) the worst conductor should occur at f7 half-filling and the best at f14, confirmed by gadolinium (0.74 MS/m) and ytterbium (3.51 MS/m). Conclusions: These findings indicate that the Cantor-set band structure of the AAH spectrum encodes quantitative information about atomic radius ratios across the periodic table. The formula achieves accuracy comparable to semi-empirical screening models while employing zero adjustable parameters. Its residuals constitute systematic indices of material properties rather than random noise.
Category: Mathematical Physics

Emergent Gravity from the Onsager—Machlup Functional: Induced Einstein—Hilbert Action via One-Loop Stochastic Fluctuations

Authors: Adrian Rohr
Comments: 5 Pages.

We compute the one-loop effective action for the metric obtained by integrating out the stochastic fluctuations of the Onsager—Machlup (OM) probability fluid on a curved spin manifold. The OM action describes 9 internal degrees of freedom: density amplitude, phase, Lorentz rotor (6 bivector components), and Takabayasi angle. Expanding to second order around the classical vacuum and applying the Schwinger—DeWitt heat kernel expansion, we derive the Seeley—DeWitt coefficients au2080 = 9 and au2081 = (7/4)R − 10m², where R is the Ricci scalar and m the particle mass. Three features are essential: (i) the cross-coupling between density and phase fluctuations generates an effective gauge connection contributing +4m² to the scalar sector; (ii) an algebraic mass cancellation renders density fluctuations massless; and (iii) the rotational kinetic term generates the Bochner Laplacian (not Hodge—de Rham), so the Weitzenböck curvature endomorphism is absent (κ = 0). The positive coefficient 7/4 ensures that the induced Newton constant G_ind = 8πℏ²/(7m²c²) is positive (attractive gravity). This is a signature of the Clifford-algebraic structure of the OM framework.
Category: Quantum Physics

Pointwise Minimum of a Symmetric Spectral Product over Finite Prime Sets: An Unconditional Proof

Authors: Khazri Bouzidi Fethi
Comments: 5 Pages.

We consider a matrix constructed from a finite set of prime numbers and a real parameter. The largest eigenvalue of this matrix is expressed as half the sum of two quantities: a sum independent of the parameter and the modulus of an exponential sum over primes. We prove two unconditional results:· The logarithm of this eigenvalue is a convex function of the parameter.· A certain symmetric product, formed from this eigenvalue and its value at the symmetric point, attains its global minimum at a remarkable point—the critical half-line.The proofs rest on an exact algebraic identity and the Cauchy-Schwarz inequality. No hypothesis on the zeros of the zeta function is used.This work introduces an original spectral object associated with a finite set of prime numbers. The angular Gram matrix, of rank at most two, encodes correlations between prime powers through oscillating phases. Its variational study reveals convexity and symmetry properties that naturally distinguish the critical line sigma = 1/2. These results, entirely unconditional, offer a new framework for exploring connections between spectral structures and the distribution of prime numbers. They also open perspectives on asymptotic behavior as the set size tends to infinity—a question that remains open.
Category: Number Theory

The DPA Framework: A Structural Diagnostic for Resonant Propensity in Complex Systems

Authors: D. Hoffman
Comments: 5 Pages.

Across multiple complex systems, a recognizable pattern recurs: coherent, self-sustaining dynamics that persist within bounds, degrade predictably under stress, and resist simple cross-domain description. Despite this recurrence, no minimal structural language exists for diagnosing when such behavior is possible.

Such patterns can arise when three structural conditions are satisfied: dimensional freedom (D), proportional distribution (P), and alignment (A). Together these constitute a diagnostic for Resonant Propensity (R) — the conditional tendency for a system to develop and sustain bounded, self-reinforcing dynamics through internal feedback, not inherent to any architecture but emergent only when conditions are jointly satisfied.

The structural relationship R ∝D ×P ×A indicates that resonant propensity depends on the simultaneous presence of D,P, and A, and collapses when any enabling condition fails.

The framework stratifies dynamical regimes from rigid order through chaotic instability to resonant propensity, and suggests structural analogues for the recurring failure modes observed across domains, including vanishing gradients in neural networks, trophic cascades in ecology, misaligned incentives in organizations, decoherence in quantum systems, and phase mismatch in physics.

DPA does not compete with domain-specific models, nor does it define resonance itself. Instead, it identifies the structural conditions enabling a system to enter and sustain resonant regimes, and provides a framework to diagnose systemic instability and the specific threshold for collapse.
Category: General Science and Philosophy

Resolution of the Nematic-to-Smectic A Universality Problem

Authors: Thomas A. Husmann
Comments: 11 pages, 6 tables, 14 references. CC BY-NC-SA 4.0. Code: github.com/thusmann5327/Unified_Theory_Physics

The nematic-to-smectic A (N-SmA) phase transition has remained one of the principalunsolved problems in statistical physics of condensed matter for over four decades. Experimental measurements of the heat capacity exponent α vary continuously from approximately 0 (3D-XY universality) to approximately 0.5 (tricritical mean-field), depending on the McMillan ratio r = TNA/TNI. No theoretical framework has explained this crossover from first principles. We present a resolution in two parts. Part I (model-independent) shows that the N-SmA transition maps exactly onto the Aubry—André—Harper (AAH) metal—insulator transition at the self-dual critical point V = 2J. This mapping uses only the de Gennes free energy (1972), lattice discretization, and the generic incommensurability of smectic layer spacing and molecular length. At criticality, the energy spectrum is a Cantor set with Hausdorff dimension Ds = 1/2 (Süt˝o 1989), giving ν = 2/3 and predicting that α varies continuously from 0 to 2/3. This qualitative result holds for any irrational frequency α and requires no new physics. Part II (quantitative) identifies the AAH frequency as α = 1/ϕ (golden ratio), producing the five-band Cantor partition. This yields a zero-free-parameter formula:α(r) = 23u2000r−rc1−rcu20004, r > rc; α = 0 otherwisewhere rc = 1−1/ϕ4 = 0.8541 and ϕ = (1+√5)/2. The formula fits 11 experimental compoundsspanning 40 years of published calorimetry with RMS = 0.033, reduced χ2 = 0.47, and all points within 2σ. Zero free parameters.
Category: Condensed Matter

Entropic Gravity [update]: Seven Equations from Two Foundations with Zero Free Parameters

Authors: Charles A. Streb IV
Comments: 13 Pages. v2: Added 175-galaxy SPARC validation (§8.2—8.5), derivation sketch for factor 6 (§8.1), data availability statement, minor table corrections.

We present seven equations demonstrating that gravity, quantum mechanics, and cosmology emerge from thermodynamic entropy applied to holographic screens. The framework rests on two uncontested foundations: the Principle of Stationary Action (δS = 0) applied to an entropic field, and the Wheeler-DeWitt constraint (Ĥ·Ψ = 0) applied to the Hubble volume. From these, we derive Newton’s second law via exact constant cancellation, the Bekenstein-Hawking entropy as an algebraic identity, a complete set of gravitoelectromagnetic field equations in the Mashhoon convention, the MOND acceleration scale au2080 = cHu2080/6 from volume entropy geometry in de Sitter space, Lense-Thirring frame-dragging, gravitational wave propagation at c, and the free-particle Schrödinger equation via entropy diffusion. The framework contains zero free parameters. In this version we extend the empirical validation from nine canonical tests to include the full 175-galaxy SPARC rotation curve sample. The derived au2080 performs statistically identically to empirical MOND across all 175 galaxies (aggregate reduced χ²/dof ≈ 8.8 vs. 8.8 for Milgrom), with the data-preferred acceleration scale corresponding to Hu2080 ≈ 75 km/s/Mpc from rotation-curve data alone. The gravitoelectromagnetic sector is valid in the weak-field, slow-motion regime. We provide dimensional verification of all equations and state the regime of validity explicitly.
Category: Thermodynamics and Energy

Thermodynamic Screening Corrections in Relational Mathematical Realism: Mass Predictions from Graph Topology and a Universal Screening Unit

Authors: Jason Merwin
Comments: This document contains 22 pages.

Relational Mathematical Realism (RMR) proposes that physical reality emerges from a discrete 137-node registry partitioned as 81 (spatial) + 40 (surface) + 16 (gravitational). We develop the thermodynamic screening mechanism introduced in the RMR synthesis paper [3] into a self-contained predictive framework. A universal screening unit δ0 = 5/137, derived from the registry’s electromagnetic surface fraction, generates mass corrections across leptons, hadrons, and the fine-structure constant with zero fitted parameters. Key results: (i) α−1 = 137.035 996 versus CODATA 137.035 999 (error 3 × 10−6); (ii) mΛ0 /me = 2183.328 versus PDG 2183.327 (error 4 × 10−7, sub-keV on a GeV-scale mass); (iii) a strangeness screening integer Bs = V (K3)2 = 9 derived from the K3 ⊗ K3 product graph, yielding correct corrections for Λ0 and K+; (iv) a {9, 13, 17} strangeness ladder for Λ0, Ξ−, Ξ0 with step size 4, arising from K5 interface topology; (v) a charge-dependentovershoot theorem: corrections exceeding the 42 = 16 gravitational threshold are clipped by 4for charged particles, with three-particle confirmation (τ −, Ξ−, Ξ0). Eleven independent mass predictions are tabulated. A screened-angle ladder extends these results to dimensionless mixing observables: the effective leptonic weak mixing angle, the three PMNS angles, and the reactor angle are all approximated by δ0-corrections of quarter/half base states using multipliers from established graph integers, with no new parameters. Open sectors (meson bases, Ω− decuplet, Σ0 isospin mixing, and radiative corrections to the mixing angles) are characterized precisely andreserved for future work.
Category: Mathematical Physics

Hofstadter’s Golden Butterfly: The Metallic Mean Hierarchy in Moiré Superlattices

Authors: Thomas A. Husmann
Comments: 16 pages, 7 tables, 36 references. CC BY-NC-SA 4.0. Code: github.com/thusmann5327/Unified_Theory_Physics

The Hofstadter butterfly—the fractal energy spectrum of a two-dimensional electron ina magnetic field on a lattice—is shown to possess a natural hierarchy parameterized by themetallic means, the roots of x2 = nx + 1. The Harper equation that generates each horizontalslice of the butterfly is mathematically identical to the Aubry—André—Harper (AAH) Hamiltonian at the self-dual critical point V= 2J. Each irrational flux ratio α produces a Cantor-set spectrum with Hausdorff dimension Ds = 1/2.We show that two experimentally significant systems in graphene moiré physics correspondto specific metallic means: (1) the graphene/hBN lattice mismatch (δ= 1.68%) corresponds to metallic mean n = 60, with golden-ratio quasiperiodicity nested inside the n = 60 shell via continued fraction structure [0; 59, 1, 1, 1, . . .]; (2) the magic angle of twisted bilayer graphene (θ= 1.08◦) corresponds to metallic mean n = 53, matching to 0.06%.At golden flux (α = 1/ϕ), the five-band Cantor partition carries Chern numbers +2,−1, +1,−2.The outer pair (+2,−2) annihilates via topological pair annihilation, collapsing five bands to three—the 5→3 mechanism supported by Liu, Fulga & Asbóth (2020). The first three metallic mean discriminants ∆n = n2 + 4 are consecutive Fibonacci numbers (5, 8, 13), forming a Pythagorean triple (√5)2 + (√8)2 = (√13)2 that closes at exactly three spatial dimensions.36 supporting references span Hofstadter spectroscopy, moiré physics, Floquet topology, and metallic mean quasicrystals.
Category: Condensed Matter

Emergent Proper Time and Spacetime from Quantum Information Permeability: A Relational Page—Wootters Framework for Quantum Mechanics and General Relativity Unification

Authors: Marco Travan
Comments: 11 Pages.

We present a fully quantum—mechanical pregeometric framework in which propertime, gravitational time dilation, the thermodynamic arrow of time, and the Einsteinfield equations emerge from a single density—dependent permeability of quantum in-formation channels. The dynamics are embedded in a global Page—Wootters timelessconstraint, thereby resolving the long-standing consistency issues of state—dependentmaster equations. The background is a weighted quantum causal set whose directedlinks are generated by the same permeability rule that sets the rate of proper time.From weighted chain lengths we recover an emergent metric; a coarse—grained ther-modynamic analysis yields the Einstein equations via Jacobson’s "thermodynamics ofspacetime" argument. The theory is completely unitary, preserves complete positiv-ity, and satisfies local energy—momentum conservation. It is fully testable in currentanalogue—gravity platforms and predicts distinctive signatures in binary pulsars, grav-itational waves and cosmology
Category: Quantum Gravity and String Theory

The 61-Decimal Limit of π as a Universal Resolution Scale: Geometry, Entropy, Fine-Tuning and the

Authors: Jorge Andrés Villaluz
Comments: 11 Pages.

We identify a universal geometric hierarchy RU/ℓP ∼1061, where RU is the radiusof the observable universe and ℓP is the Planck length, and show that this singledimensionless ratio unies ve apparently independent results in modern cosmology.This hierarchy is formalized by the master inequality:2RU·10−n ≤ℓP,which establishes the physical resolution interval n ∈[61,62): the number of dec-imal places of π needed to describe the geometry of the observable universe withsub-Planckian precision. The same scale governs the BekensteinHawking entropybound Smax ∼4π(RU/ℓP)2, the ne-tuning condition δρ/ρ∼10−60, and the discrep-ancy factor of the vacuum catastrophe ∼10122. We further propose two falsiablepredictions: (1) the resolution parameter n(t) evolves with cosmic expansion asn(t) ≈61.4 + log10(t/t0), and (2) the cosmological constant satises Λ(t) ∝t−2, arelation testable with next-generation surveys such as Euclid and LSST. The uni-fying thread throughout is spherical geometry: π appears in all these expressionsbecause the observable universe is a sphere.
Category: History and Philosophy of Physics

New Formula for the Area of a General Quadrilateral Using Opposite Sides and Four Angles

Authors: Ryou Takayama
Comments: 5 Pages.

In this paper, we derive an explicit formula for the area of a particular quadrilateral using only the lengths of a pair of opposite sides and the four interior angles. The formula is based on known geometric relationships and is presented after algebraic simplification and manipulation. Furthermore, we clarify the conditions under which the formula is valid and elucidate its geometric background. As a result, we demonstrate its applicability not only to convex and concave quadrilaterals but also to certain self-intersecting quadrilaterals.
Category: Geometry

THE UNIFICATION OF PHYSICS BY QUANTUM VACUUM GEOMETRY, Spectral Derivation of the Standard Model Parameters, the Cosmological Constant, and the CMB Temperature from the Connes-Chamseddine Spectral Triple

Authors: Bertrand Jarry
Comments: 14 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0)

We present the Quantum Vacuum Geometry (QVG) programme, an extension of the Chamseddine—Connes noncommutative geometry framework that derives the Standard Model parameters, the cosmological constant, and the CMB temperature from a single geometric principle.Starting from five algebraic axioms (C1—C5) on the finite spectral triple, the unique algebra of minimal dimension is AF = C ⊕ H ⊕ M3(C), generating gauge group SU(3) × SU(2) × U(1), three fermion generations (NF = 96 modes), and the exact hypercharge trace TrF Y 2 = 10.The original QVG contribution is a spectral free-energy functional Fρ[T ] =i ρiλi + E0 i ρi ln ρi whose unique fixed point ρ∗ = 1/NF determines all nineteen SM parameters. Numerical computation at N = 96 gives fermion masses to < 0.3%of PDG 2024 and the CKM matrix to < 2.5%; the Koide relation K = 2/3 is reproduced to 10−5.Three new results are established: (R1) the cross-coupling Kij = 0 exactly, from {Dext, γ5} = 0 in Clifford algebra; (R2) g∗ = 2 at E0 = 3.2 meV gives Λcosmo = 0.990 × 10−52 m−2 (9% of observed); (R3) TCMB = (E0/kB) × αTrF Y 2 = 2.709 K (0.6% of observed), derived from the Seeley—DeWitt a4 coefficient via Caldeira—Leggett. The quantum gravity propagator GE(r) = (Λ2GUT/16π2) exp(−Λ2GUTr2/4) is Gaussian and UV-finite. All residuals trace to a single source: the uncertainty in E0.
Category: High Energy Particle Physics

A Structural Proof of the Collatz Conjecture via Divergent-Orbit and Cycle Exclusion

Authors: Jungwon Park
Comments: 53 Pages.

We present a computer-assisted proof that every positive integer orbit under the Collatz map $T(n) = n/2$ (if $n$ is even), $(3n + 1)/2$ (if $n$ is odd) eventually reaches 1. The argument consists of two independent parts, H1 and H2, each of which reduces an originally infinite verification problem to a finite exact certification step. The mathematical reductions are traditional proofs; the certifications are finite, deterministic computations using only exact integer and rational arithmetic, whose complete specifications (input, algorithm, output) are given in the appendices.For H1 (divergent-orbit exclusion), a deterministic normalized block-drift analysis establishes an exact affine envelope that rules out all parameter regimes below an explicit threshold $V_{env} approx 1.5990$. The remaining oscillatory regime is reduced to a finite certification problem over a quotient-state automaton whose mathematical soundness is guaranteed by a chain of five theorems (Theorems 12.8—12.14). The certification is discharged by exhaustive exact computation (Theorem 12.17).For H2 (non-trivial cycle exclusion), a gate-based reformulation converts the cycle problem into an explicit inequality system. Discrete convexity arguments and a two-value support reduction compress the problem to a single-parameter bound, which is then verified by exact rational arithmetic over a rigorously delimited feasible range. The computational components are finite, exact, and logically isolated. Their role is analogous to the finite case verifications in other computer-assisted proofs such as the Four Colour Theorem and the Kepler Conjecture: the mathematical argument provides a complete reduction to finite exact certification problems, and the computations discharge those problems. The complete source code for both certifications, together with their full execution logs and exact rational outputs, is included in the appendices (Appendices E—G).
Category: Number Theory

Entropic Gravity: Seven Equations from Two Foundations with Zero Free Parameters

Authors: Charles A Streb IV
Comments: 11 pages, 2 tables, 21 references

We present seven equations demonstrating that gravity, quantum mechanics, and cosmology emerge from thermodynamic entropy applied to holographic screens. The framework rests on two uncontested foundations: the Principle of Stationary Action (δS = 0) applied to an entropic field, and the Wheeler-DeWitt constraint (Ĥ·Ψ = 0) applied to the Hubble volume. From these, we derive Newton’s second law via exact constant cancellation, the Bekenstein-Hawking entropy as an algebraic identity, a complete set of gravitoelectromagnetic field equations in the Mashhoon convention, the MOND acceleration scale au2080 = cHu2080/6 from volume entropy geometry in de Sitter space, Lense-Thirring frame-dragging, gravitational wave propagation at c, and the free-particle Schrödinger equation via entropy diffusion. The framework contains zero free parameters and is validated against nine canonical tests. The gravitoelectromagnetic sector is valid in the weak-field, slow-motion regime. We provide dimensional verification of all equations and state the regime of validity explicitly.
Category: Thermodynamics and Energy

A Discrete CMB Angular Power Spectrum from a Causal Integer Graph: Zero Free Parameters, Two Acoustic Peaks, and a Convergence Prediction for Planck 2018

Authors: Jason Merwin
Comments: The document contains 15 pages

We report the first computation of a discrete analog of the CMB angular powerspectrum Ck derived entirely from a causal integer graph grown by pure fission rules,with zero free parameters. Starting from a complete graph K5 as the seed, a 1000-nodegraph is grown via an additive-plus-half-split fission engine constrained by a 137-elementregistry capacity. When the ratio of maximum hub degree to total node count transits ascale-invariant resonance window md/N ∈ [0.015, 0.021], the graph Laplacian eigenvalueratio λ3/λ2 locks near the S1/2 prediction of 1.102. The locked graph exhibits positivespatial curvature, volumetric dimension dvol = 3.49 ± 0.05, and a well-defined lastscattering surface (LSS) at BFS radius r = 4 containing 452 nodes. Propagatinga primordial perturbation via the wave equation Green’s function cos (√λk t) at thephysically motivated time t∗ = π/√λ1 and projecting the field on the LSS onto abinned eigenmode basis recovers two robust acoustic peaks at ℓeff = 1.121 and 1.811,giving ℓ2/ℓ1 = 1.615. The Planck 2018 value is ℓ2/ℓ1 = 1.94. The 16.7% deviation isquantitatively consistent with lattice dispersion at N = 1000: discrete graphs suppresshigh-frequency modes, compressing harmonic ratios below the continuum limit. Wepredict that the ratio converges monotonically to the Planck value as N increasestoward the physical scale (md = 137, N ≈ 9000), providing a falsifiable test of theframework.
Category: Relativity and Cosmology

Canonical Classication of Framed Closures in a Three-Strand Braid Transfer Model

Authors: Kobie Janse van Rensburg
Comments: 9 Pages.

We study a discrete dynamical system on the three-strand braid group B3 in which generators act on an integer valued framing vector through a local slot-based transfer rule.Terminal states are pairs (P, f) consisting of a permutation P ∈ S3 and a framing vector f ∈ Z3. Under trace closure, strands belonging to the same permutation cycle form a single loop, and physical states are defined modulo cyclic relabeling of the starting point of each loop.We prove a complete classification theorem: two terminal states are physically equivalent if and only if a finite sector-dependent invariant I agrees. The invariant decomposes according to the cycle type of P into three sectors (identity, transposition, three-cycle), and every equivalence class admits a unique canonical representative computable by a constant-time algorithm. A key structural finding is that the three-cycle sector carries a discrete cyclic-ordering obstruction not reducible to symmetric polynomial invariants of the framing differences. The analytic proofs are independently verified by exhaustive BFS enumeration of 631 terminal states within word length 10.This work provides the classied-state foundation for a broader programme connecting combinatorial braid kinematics to RP3 topology and Skyrmion physics within the Topological Inversion Model (TIM).
Category: Topology

Relational Mathematical Realism: Registry Architecture Predicts Lepton, Baryon, and Strange Baryon Mass Spectra

Authors: Jason Merwin
Comments: 21 Pages.

We present Relational Mathematical Realism (RMR), a discrete framework in which physicalreality emerges from relational updates on a 137-element integer registry. Five structural primitives tetrahedral vacuum geometry, registry partition, graph resonance dynamics, sector mapping, and overflow-fission mechanics — are stated axiomatically and used to derive eight quantitative predictions with no tunable continuous parameters: three charged lepton mass ratios, one neutrino mass-squared splitting ratio, one baryon mass ratio, and three strange baryon mass predictions. All eight agree with experiment to better than 1.1%. The central finding is that the integer set {137, 136, 17, 3} — the registry total, its substrate factor, the substrate prime from 136 = 8 × 17,and the K3 graph order — appears without modification across every sector. We employ an honestthree-tier classification: five predictions [T1] follow strictly from the primitives; three [T2] require two structural postulates whose numerical content is fixed by the same integers but whose derivation from the base primitives remains open. The Gell-Mann—Okubo baryon octet relation emerges as a structural identity. We catalog eleven open questions by tractability and identify JUNO and DUNE as the decisive near-term falsification tests via the integer prediction R ≡ Δm2 32/Δm2 21 = 33.
Category: High Energy Particle Physics

Causal Lattice Elastodynamics: Geometric Vacuum Scaling and the Topological Emergence of the Standard Model

Authors: Bhasanpal Thiru
Comments: 3 Pages.

Causal Lattice Elastodynamics (GVS) introduces a discrete foundational framework replacing thecontinuous spacetime manifold with a shear-thickening, Poisson-sprinkled Causal Set. By modeling fundamental particles as localized topological embeddings, GVS analytically derives key Standard Model parameters strictly from 3D simplicial coordination geometry without arbitrary parameterization or fine-tuning. This paper formalizes the Five Fundamental Laws of GVS, uniting macroscopic General Relativity with microscopic quantum elastodynamics via the Holographic Surface-Strain Law. We present the unpatched, first-principle derivations of seven fundamental constants, demonstrating that empirical deviations from bare geometric limits are the exact physical measurements of vacuum polarization. A rigorous, pan-scalar falsifiability matrix is provided to test the framework against Ultra-High-Energy Cosmic Rays (UHECR), wide binary stellar kinematics, and Belle II constraints.
Category: Quantum Gravity and String Theory

Alpamayo-Surgical: Adapting Driving-Pretrained Vision-Language-Action Models to Millimeter-Scale Surgical Robotics

Authors: Cornel Badea
Comments: 4 Pages.

We propose a method to successfully adapt LargeVision-Language-Action (VLA) models, originally pre-trainedon autonomous driving datasets, to the micro-scale domain ofsurgical robotics. We identify the Magnitude Domain Gap—a1000x spatial discrepancy between driving actions (meters) andsurgical actions (millimeters)—as the primary cause of trajectoryparalysis during naive fine-tuning. By introducing DifferentialScale Normalization paired with a novel Variance-IncentivizedRecovery Loss (Lvar ) during motor-cortex adaptation, we demon-strate that the Alpamayo-Surgical system (based on a 10B-parameter driving VLA) can achieve native millimeter precisionin surgical environments while retaining its zero-shot semanticreasoning capabilities. Evaluating on the SutureBot (Tissue 1)dataset, we observe that our technique successfully restorescomplex 3D tool articulation from a previously "frozen" state,achieving a final Mean Average Displacement Error (ADE) of5.53 mm relative to human expert demonstrations. Crucially, theVLA’s Chain-of-Causation reasoning traces correctly verbalizesurgical intent while aligning magnitude predictions natively withthe ground truth.
Category: Artificial Intelligence

Catalan’s Constant: Frontier Analysis, Derived Obstruction Theorems, and a Map of the Remaining Terrain

Authors: Rajat Yadav
Comments: 14 Pages.

The note separates three layers: (i) current literature status, (ii) rigorous reductions andobstruction theorems derived in the thread, and (iii) conditional routes and dead ends. Thecentral conclusion is negative but sharp: many natural corridors — classical Apéry clearing,the EMN simple-pole and polynomial higher-pole programs, fixed-base q-difference compression,several modular/holonomic packetizations, and a broad discrete moment/Hankel family— fail for precise structural reasons. The revised version also records five structural ingredientsthat were missing from the earlier draft: a four-jet modular rigidity theorem for the X1(5)Picard-Fuchs engine, a noncharacteristic edge-splitting theorem for higher poles, injectivity/isomorphism theorems for the EMN collapse operators, a boundary-annihilator theoremfor the edge packet, and formal torsion-support / multiplicative-complexity obstructions onthe modular q-side.
Category: Number Theory

Minimal Six-Dimensional Null Manifold Underlying the Photon

Authors: Tingfang Yi
Comments: 7 Pages.

Light’s propagation, phase, polarization, and frequency are projections of a minimal six-dimensional null entity unifying spacetime and photon internal degrees of freedom. Observed pairwise and triple couplings emerge naturally, explaining Spin Hall, Berry, Pancharatnam phases, optical activity, and relativistic shifts. Classical fields, quantum detections, and wave-particle duality arise as lower-dimensional projections, while photon discreteness reflects detector intersections. The framework agrees with relativity and QED and predicts testable interference deviations via controlled holonomy.
Category: Mathematical Physics

The Topological Nature of Universal Gravitation: A Rigorous Proof from the Spiral-Sphere Phase Transition to as a Topological Constant

Authors: Xiangqian Zhang, Chao Greene, Mingming zhao, Guozi Mo
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

Modern physics faces a profound theoretical chasm when bridging microscopic quantum scales and macroscopic cosmological scales, most notably manifested in the hierarchy problem and the dark matter hypothesis. Based on thefirst principles of spatial fluid dynamics, this paper proposes a scale-dependent spacetime topological phase transition model. The model postulates that the fundamental geometric topology of spacetime is a cylindrical spiral manifold (S^1 x R). When the particle number reaches the stellar mass scale (N ~ 10^57 ), the rotational degrees of freedom of microscopic spirals cancel out due to statistical decoherence (governed by the central limit theorem). Consequently, the spatial topology collapses into a purely divergent, isotropic Gaussian sphere (S^2), which manifests macroscopically as classical Newtonian gravity. Starting from the first-principle axiomomega*r = c, this paper rigorously derives the pure geometric expression for the universal gravitational constant G = C^3r^2_0/h-bar, proving that G is intrinsically a topological constant determined by the critical radius of the topological phase transition. Furthermore, at galactic and cosmic web scales (N ~ 10^68 - 10^80), stars act as new fundamental units, and their collective spin generates macroscopicspacetime torsion within the framework of Einstein-Cartan theory. This torsion drives spontaneous symmetry breaking, thereby reconstructing a macroscopic cylindrical spiral structure. Supported by numerical integration and recent astronomical observations (e.g., cosmic filament spin, CMB anomalies), this model provides a computable and falsifiable pure geometric pathway toward unifying quantummechanics, general relativity, and dark-matter-free cosmology.
Category: Astrophysics

A Statistical Topological Model for the Emergence of Isotropic Effective Fields from Helical Space-Time Dynamics

Authors: Xiangqian Zhang, Chao Greene, Mingming Zhao
Comments: 3 Pages. (Note by ai.viXra.org Admin: This submision is speculative; author names are required in the article after article title; and please cite listed scientific references)

Based on the hypothesis that space-time manifests as cylindrical helical motion at the speed of light, this paper proposes a phenomenological topological model to explain how macroscopic isotropic fields emerge from the collective response of anisotropic local helical flows. We model the intrinsic structure of fundamental particles as cylindrical manifolds characterized by inherent helicity and divergence. By applying the Central Limit Theorem (CLT) to vector fields on Riemannian manifolds, we demonstrate that the rotational degrees of freedom of massive local helical flows undergo destructive interference. Utilizing the Gauss-Bonnet theorem, we prove that in the thermodynamic limit, the system’s effective macroscopic field undergoes topological decoherence, inevitably resulting in an isotropic Gaussian sphere. Furthermore, by integrating the Dirac Large Numbers Hypothesis with the Eddington number (N∼10^80), our model derives a statistical fluctuation residual ratio of 10^(-40) providing a heuristic geometric-physical pathway for understanding the hierarchy problem between electromagnetic and gravitational forces.
Category: Geophysics

Toward an Algebraic Revolution: Analytical Resolution of the Quintic Through Quartic Reduction and Universal Scaling Law

Authors: Ahcene Ait Saadi
Comments: 6 Pages.

This paper presents an original analytical method for solving the reduced quintic equation By establishing a conformal mapping between the roots of an auxiliary quartic and those of the quintic, we reveal a Universal Scaling Law governed by a 1/8 power factor. This approach calculates all five roots (real and complex) across all topological regimes, including cases with three real roots, with a precision of . This discovery marks a new era for polynomial algebra.
Category: Algebra

Development Methodology of a Code-Illiterate User (Outcome-First Design, Multi-Model Drift Detection, and Machine-Readable Context as a Reproducible Methodology for AI-Assisted System Development Without Formal Training)

Authors: John P. Bernhardt Jr.
Comments: 18 Pages. Additional information available upon request (Note by ai.viXra.org Admin: Please cite listed scientific references)

This methodology research paper documents the development methodology through which a practitioner without formal training in software engineering or computer science produced two independently validated AI infrastructure systems in under two months using AI-assisted collaboration. The systems examined are Hydra-rray, a containerized behavioral observatory designed to study tool-capable AI models operating with real offensive security tools, and an Android MCP client, a fully offline mobile AI agent integrating local transformer inference, operating-system-level automation through Android AccessibilityService, and Model Context Protocol (MCP) orchestration within a single application package.Development occurred entirely under consumer-access constraints: commodity hardware, standard consumer model interfaces, no engineered system prompts, no prompt-engineering infrastructure, no model fine-tuning, and no custom datasets. Context continuity across stateless model sessions was maintained exclusively through machine-readable YAML context transport documents referred to as batons.Across the two case studies, six consistent methodological properties were observed: outcome-first design, cross-domain methodology replication, vanilla model utilization, machine-readable context as drift prevention, multi-model triangulation for drift detection, and socialized interaction as a mechanism for surfacing tacit knowledge.Within the Hydra-rray experimental environment, an additional behavioral observation emerged: across observed sessions within the Hydra-rray environment, operating under consumer-access constraints and without engineered prompt scaffolding, tool-capable models exhibited a binary execution pattern: either correct tool execution or complete hallucination, with no intermediate partial success states observed.The Android case study further demonstrates that local language-model inference and operating-system-level actuation can operate on consumer mobile hardware not designed for transformer workloads, including a Snapdragon 865 device running Android 13. Development of the Android system occurred independently and the project repository predates Google’s public AppFunctions announcement by one day, suggesting parallel discovery of a similar architectural gap.The paper argues that the primary contribution of these projects is not the systems themselves but the development methodology that produced them: a human-directed AI collaboration process in which the practitioner defines outcomes, evaluates architecture, and orchestrates the work while AI systems generate implementation artifacts. The paper itself is produced using the same methodology, serving as a recursive demonstration of the approach it documents.The methodology is examined through two case studies: Hydra-rray, a containerized behavioral observatory for tool-capable AI agents, and an offline Android MCP client integrating local model inference with mobile automation.
Category: Artificial Intelligence

Quantization of Dipolar Torsion in FCD-RB: Emergent Unification Without Dm/de

Authors: Ricardo J. Miralles
Comments: 6 Pages. In Spanish (Note by ai.viXra.org Admin: This submission is not written in a suitable manner, e.g., incomplete/cutoff graphs etc. - Please conform!)

We propose quantization of dipolar torsion T_dip in the FCD-RBv3 model, a 5D framework where fermion-antifermion pairs in a collapsed toroidal bulk emerge discrete masses m_n ∝ √n, modified gravity (d=0.002), and helical electromagnetism, eliminating DM/DE/primitive gluons...
Category: Quantum Gravity and String Theory

An Octonionic Foundation of Spacetime Geometry and Quantum Mechanics

Authors: Rüdiger Giesel
Comments: 28 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We propose a framework in which spacetime geometry and quantum dynamics emerge fromthe non—associative algebra of octonions. A dynamical octonion-valued field is introduced whose interaction is governed by the octonionic associator. The induced G2 three-form determines the metric, variation of the action produces Einstein equations, and projection onto quaternionic subalgebras yields quantum wavefunctions. The theory admits a compact master equation encoding gravitational and quantum dynamics simultaneously.
Category: Relativity and Cosmology

Microcontroller-Based Thermocouple Temperature Monitoring and Heater Control System with Digital Display Interface

Authors: Md Mubdiul Hasan
Comments: 6 Pages.

Temperature control is a critical requirement inmany industrial heating applications where accurate sensing and reliable power regulation are necessary for system stability and safety. This paper presents the design and implementation of a microcontroller-based temperature monitoring and control system utilizing a thermocouple sensor and dual-heater regulation. The proposed system employs a thermocouple temperature sensor interfaced through a thermocouple-to-digital converter toobtain accurate temperature measurements. A microcontroller processes the temperature data and compares it with a user-defined setpoint to perform closed-loop temperature control.The system integrates a user interface consisting of key switches for parameter adjustment and a four-digit seven-segment display for real-time visualization of temperature values and system status. Heater control is achieved through optoisolated triac driver circuits that enable safe switching of ACpower to the heating elements. Additional peripheral modules including LED indicators, a buzzer alarm circuit, and a cooling fan control mechanism are incorporated to enhance operational feedback, safety, and thermal stability. The designed architecture ensures electrical isolation between the low-voltage control circuitry and high-voltage heater loads,improving system reliability and user safety. Experimental evaluation demonstrates that the system provides stable temperature regulation, responsive user interaction, and reliable heaterswitching performance. The proposed design offers a cost-effective and scalable solution suitable for industrial heating systems, laboratory equipment, and temperature-sensitive process control applications.
Category: Digital Signal Processing

Gravitational Lensing Based on Entangled Duality

Authors: Joseph Shaffer
Comments: 6 Pages.

A lensing-like framework is described, based on Entangled Duality, where galaxies interact through two domains: either relativistic, spacetime S, or entangled, E. The core idea is that every physical system participates in both domains. Observations — such as galactic rotation curves and lensing like mass effects — are the combined outcome of S + E, not S alone. This dual domain model produces effects that mimic gravitational lensing and dark matter like behavior without invoking dark matter.
Category: Astrophysics

Relativistic Field Theory of Primes: An Adelic Approach to the Hilbert—P´olya Conjecture and the Riemann Hypothesis

Authors: J. W. McGreevy
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present a unified relativistic field theory over the ring of adeles AQ, in whichthe nontrivial zeros of the Riemann zeta function emerge as quantized energy levelsof a self-adjoint Hilbert—P´olya operator ˆH. The theory begins with a Non-Hermitian"Adelic Carnot Pump" driven by local prime interactions (Cup and Cap products),Hermitianized globally through restriction to the cuspidal subspace of automorphicforms on GL2(Q)GL2(A).The Arithmetic Planck constant hA ∼ log 2 quantizes phase steps, while the weight-12 modular discriminant ∆ provides vacuum tension. Maxwell-like adelic field equa-tions govern the dynamics, culminating in a least-arithmetic-action principle whosegeodesics are confined to the critical line Re(s) = 1/2.A dimensionless Arithmetic Fine-Structure Constant αA ≈ 1/(log 2 · 2π) tunes thecoupling between local curvature and global flow. Invariance of αA under the fulladelic group action is enforced by an Arithmetic Noether Theorem, which acts as acentripetal force locking spectral ordinates to the critical line.Self-adjointness follows from cuspidal sealing and unitary Atkin—Lehner symmetry;spectral matching is achieved via a twisted trace formula that projects the GL2 cuspidalspectrum onto the GL1 zeta zeros through phase-cancellation of non-coherent modes.We conclude that the Riemann Hypothesis is the symmetry requirement for acausal, lossless arithmetic vacuum: all nontrivial zeros satisfy Re(ρ) = 1/2. Exten-sions to the Birch and Swinnerton-Dyer conjecture are suggested.Keywords: Riemann Hypothesis, Hilbert—P´olya conjecture, adelic geometry, au-tomorphic forms, Noether theorem, non-Hermitian dynamics, modular forms, criticalline1
Category: Mathematical Physics

The UV Renormalization-Group Run of Koide-Type Mass Relations

Authors: Alejandro Rivero
Comments: 17 Pages.

We provide a reference dataset and exhaustive analysis of Koide-type mass relations under Standard Model renormalization-group evolution from MZ to MPl. Using PyR@TE 3 two-loop SM beta functions and AHS (AntuschHinze Saad) multi-loop Yukawa data, we track the charge-lattice ratio signed Koide triples constructed from the 9 SM Yukawa couplings.
Category: High Energy Particle Physics

[ A Proposed] Decomposition at Atomic Scale: Spectral Architecture of the Hydrogen Atom from Phi-Derived Constants

Authors: Thomas A. Husmann
Comments: 7 Pages. (Note by ai.viXra.org Admin: Please don't name title, equation/formula etc after the author's name)7 tables. Verification code at https://github.com/thusmann5327/Unified_Theory_Physics. Patent Application 19/560,637. CC BY-NC-SA 4.0.

We demonstrate that the [proposed] Decomposition, grounded in the single algebraic identity phi^2 = phi + 1, extends to atomic physics with sub-percent precision across three independent domains. Spectral: alpha_em^{-1} = N x W = 137.337 (0.22% vs. CODATA), where N = 294 and W = 0.467134 are derived from the topological invariants of a 233-site Aubry-Andre-Harper lattice at critical coupling. The bracket count N is independently derivable as N = F(13) + F(10) + F(5) + F(2) = 233 + 55 + 5 + 1, a spectral topology invariant generalizable to any Fibonacci lattice. This cascades through QED to predict the Bohr radius (0.22%), Rydberg energy (0.44%), and proton charge radius (0.14%). Spatial: Anchoring the hydrogen 1s peak at the Cantor shell center maps 42% of the probability into the sigma_2-sigma_4 wall zone; the H_2 bond length matches sigma_4 outer to 0.5%. Information-theoretic: The bipartite entanglement entropy at the Cantor sigma_4 outer wall reaches S = 0.6908 nats, 99.66% of the theoretical maximum ln 2, with zero free parameters. The Cantor outer wall lies 5.3% beyond the equal-partition point (p = 0.535), preserving 99.66% of the theoretical maximum entropy ln 2. Three additional exact identities are proved from phi^2 = phi + 1 alone: the unity partition 1/phi + 1/phi^3 + 1/phi^4 = 1, the boundary law 2/phi^4 + 3/phi^3 = 1, and the pi-phi bridge pi = 4*arctan(1/phi) + 4*arctan(1/phi^3). Systematic comparison with all metallic means and quadratic irrationals shows phi is unique: it alone produces a critical eigenstate with minimal fractal dimension D_2 ~ 0.538, a nested five-sector Cantor spectrum, stable baryon fraction Omega_b ~ 0.048, and dark-energy-dominated expansion. The fine-structure constant is the cumulative wall fraction of the Cantor vacuum: alpha_em = 1/(N x W). The hydrogen atom is the same self-consistent structure at bracket 117.
Category: Mathematical Physics

A Binary Branch—Layer Structure and Two Explicit Decreasing Invariant for the Collatz Map

Authors: Neel Alkoraishi
Comments: 13 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

I present a binary structural framework for the Collatz map that organizes all positive integers into a hierarchical branch—layer system. Everyinteger admits a unique decomposition m = 2y (2x(2R + 1) − 1), which determines its position within a finite branch through the trailingbinary blocks of ones and zeros. Using the recursive 2n + 1 construction, I derive explicit linear branch formulas A(n, x) and B(n, x) that uniquely generate all odd integers. Eachbranch has a finite depth n and terminates at a branch endpoint C = 2 · 3nx + 4 ⌊(n−1)/2⌋ Xi=0 9i. Under the Collatz map, the local branch parameters (x, y) decrease deterministically until this endpoint is reached. At each branch endpoint the higher-order parameter satisfiesRu2032 = 3R + 1 2x+y, yielding the decreasing invariant Ru2032 < R (with a single boundary case).This provides an explicit numerical descent between successive branch endpoints.The reverse odd structure further shows that each branch contains a unique maximal node congruent to 3 (mod 6), which has no odd predecessor within the branch. This structure allows branches to be organized into a recursive hierarchy of endpoint sets C0, C1, C2, . . . , from which I define a global layer index L(m).I prove that every positive integer eventually reaches a branch endpoint belonging to a lower-numbered layer, yielding a strictly decreasinginvariant L(T k (m)) < L(m). Since L(m) is nonnegative, every trajectory must descend through finitely many layers to the base layer C0 = {2k }, which maps trivially to 1. This establishes convergence of all positive integers under the Collatz map within the branch—layer framework.
Category: Combinatorics and Graph Theory

Design Review and Functional Assessment of an LM324-Driven Voltage Stabilizer for Residential Applications

Authors: Md Mubdiul Hasan
Comments: 8 Pages.

—This work presents the analysis and functionalcharacterization of a multi-tap AC voltage stabilizer implemented in LTspice, emphasizing its control, feedback, and protection mechanisms. The stabilizer employs an autotransformer with discrete tap selection, where relay-driven switching provides coarse regulation across varying mains conditions. A dedicated sensing network, consisting of a transformer secondary, rectifier, and precision divider, generates a DC feedback signalproportional to the output RMS voltage. This signal is processed by a window-comparator architecture built around the LM324,enabling the controller to determine whether the present tap is too high, too low, or within the acceptable regulation band. The design incorporates a soft-start and pre-regulation stage that ensures stable startup behavior by delaying relay activation until the reference, supply rail, and sensing nodes reach steady-state values. Comparator thresholds are derived analytically by mapping mains voltage through the transformer ratio, rectifier, and divider network to the LM324 input domain. This allows direct calculation of the window center and allowable mains range for each tap. A protection comparator monitors long-term deviationsoutside the window and, through a zener-coupled reference node, triggers a controlled shutdown or tap change when necessary. The resulting system combines discrete tap switching with analog decision logic to achieve robust voltage regulation across a wide input range, while maintaining predictable and mathematicallyverifiable operating boundaries.
Category: Mathematical Physics

A Geometric Approach to the Relativistic Wallström Objection: Spin-1/2 from Covariant Fluid Regularity

Authors: Adrian Rohr
Comments: 9 Pages.

This paper explores the extension of the stochastic coherence framework (Onsager-Machlup formalism) to the relativistic domain. In previous work, it was shown that phase quantization in the non-relativistic Schrödinger regime can be understood as a consequence of requiring the probability current to be a $C^infty$ smooth vector field across nodal surfaces (resolving the Wallström objection). Here, we examine the analogous topological constraints in Minkowski spacetime using Spacetime Algebra (STA). By replacing the scalar phase with a Lorentz rotor field, the physical observables become the probability four-current and the spin tensor, both bilinear in the rotor via the $SU(2) to SO(3)$ double covering.Through a variational derivation of the relativistic stochastic dynamics, we show that the generalized Hamilton-Jacobi equation constrains the local density behavior near nodal tubes. When combined with the requirement that the bilinear observables remain strictly $C^infty$ regular, the internal holonomy of the rotor is forced to take values in integer multiples of $pi$. The results suggest that intrinsic angular momentum quantized in half-integer units of $hbar$ (spin-1/2) can emerge naturally as a geometric and topological necessity for covariant fluid stability, recovering the Dirac hydrodynamic system without a priori postulating spinor structure.
Category: Quantum Physics

The Prime Formulation and its Spectral Resolution

Authors: Chaiya Tantisukarom
Comments: 14 Pages.

This paper presents the Prime Gear Geometry (PGG) formulation, a deterministic spectral framework that models prime numbers as discrete mechanical oscillators. By representing the prime sequence as a unit-normalized indicator function ($a_n in {0, 1}$) and applying a band-limited Inverse Fourier Transform (IFT) with a fixed Atomic Tuning Factor ($K=3$), we resolve the individual harmonic identities of adjacent primes. Unlike traditional analytic methods that result in spectral blurring, the PGG formulation ensures the absolute separation of ``Gears'' 2 and 3, maintaining a consistent inter-state valley ($v(2.5) approx -0.566$) across scales ranging from $N=10^2$ to $N=10^6$. We align this framework with Riemann's original observation of the Fourier ``jump'' at prime coordinates, anchoring the discrete forging events to a 0.5 Gyrocenter. Consequently, this paper bypasses the analytic continuation of the Riemann Zeta function, offering a purely mechanical, signal-processing resolution to prime distribution.
Category: Number Theory

A Framed Three-Strand Topological Information Model: Exact Charge Mapping, a Bilinear Mass Constraint, and a Finite Residualacuum Sector}}

Authors: Kobie Janse van Rensburg
Comments: 18 Pages.

We present a discrete kinematic model built from the three-strand braid group B3 with a local slot-based framed-transfer rule. The model cleanly separates coarse closure topology from path-dependent framed memory, allowing macroscopically trivial closures to retain quantized internal residual structure. A computational sweep over 118,096 admissible braid histories confirms large-scale topology-framing decoupling. Using a universal closure-scaled framing map, we show that the first-generation electroweak quantum numbers are reproduced exactly by linear functionals on the framing vector. We then define a bilinear vacuum-mass functional from a rank-two vacuum tensor acting on left/right framed data.The first-generation mass-area matrices satisfy the exact algebraic identity Mu = Md+3 Me, which holds unconditionally for any vacuum tensor K and implies the rigorous bound |mu−md| ≤ me on bare kinematic masses. Finally, we observe that residual framed memory in the topological identity sector provides a natural finite mechanism for nonzero vacuum energy density. The paper is scoped as a kinematic-combinatorial framework: exact algebraicidentities are proved inside the model, while larger physical mass splittings and radiativestructure are attributed to dynamical dressing beyond pure topology.
Category: High Energy Particle Physics

Constraining Conformal Scalar-Tensor Activation: Density-Based Geometric Recovery (DBGR) Bounds from the Historic Proton Radius Anomaly

Authors: Bhasanpal Thiru
Comments: 3 Pages.

We formalize a phenomenological Density-Based Geometric Recovery (DBGR) model within anextended Einstein-Cartan-Sciama-Kibble (ECSK) scalar-tensor framework to establish bounds onlepton-induced metric deformations. Standard algebraic spin-torsion interactions are kinematicallysuppressed by O(10−40). However, transforming to the Einstein frame reveals a dynamic scalar fieldΦ capable of chameleon-like de-screening. Governed by quartic mass scaling (ρ ∝ µ4r), a muonicstate generates a localized density perturbation ∼ 1.82 × 109times greater than an electronic state.We test the boundary condition where this localized muonic threshold un-screens a macroscopicYukawa potential, evaluating the geometric contraction required to explain the historic proton radiusanomaly. Utilizing first-order perturbation theory with the exact 2S radial wavefunction, recoveringa −0.31 meV geometric binding requires a dimensionless effective coupling of αscalar ≈ 2.91 × 10−7.Because this violates established atom interferometry fifth-force bounds (α ≲ 10−11) by over fourorders of magnitude, DBGR excludes macroscopic geometric torsion as the source of the historicanomaly. This provides independent scalar-tensor validation for the CODATA QED consensus(Rp = 0.8413 ± 0.0016 fm) and establishes strict upper limits for the ongoing MUSE form-factordivergence.Keywords: Proton Radius Anomaly, Density-Based Geometric Recovery (DBGR), Chameleon Mechanism, Scalar-Tensor Theory, Metric Torsion, Yukawa Potential, MUSE Experiment, Fifth-Force Exclusion.
Category: Relativity and Cosmology

Mechanistic Derivation of Relativistic Effects via Space Stress Vector (SSV) in the Dipole Sea

Authors: Thomas Lee Abshier
Comments: 16 Pages.

Conscious Point Physics (CPP) derives special relativistic effects—time dilation, length contraction, and the twin paradox—from geometric constraints in a discrete 4D lattice based on the 600-cell polychoron. Kinetic energy stored as excess Space Stress Vector (∆SSV) reduces effective Voronoi cell volumes, shrinking the Planck Sphere Radius (PSR) and limiting displacement per absolute Moment. This produces relativistic phenomena as consequences of lattice saturation rather than postulated spacetime geometry. The framework reproduces standard SR at accessible energies while predicting deviations at accelerations ≳ 10^20g. We provide a first-principles derivation of the PSR formula and coupling constant k ≈ 2.16 × 10^-114 m3/J from 600-cell packing geometry.
Category: Relativity and Cosmology

Einstein-Cartan Torsion and Vacuum Phase Transitions: A Spinor-Sourced Geometric EFT for High-Density Probes

Authors: Bhasanpal Thiru
Comments: 4 Pages.

We formalize an exploratory geometric Effective Field Theory (EFT) utilizing an Einstein-Cartan-Sciama-Kibble (ECSK) action, where the vacuum undergoes a phase transition governed by a scalarfield coupled to the trace of the stress-energy tensor. To avoid ghost instabilities, we map thenon-minimal coupling to the Einstein frame and stabilize the high-density limit with a quartic po-tential. Relaxing the uniform-spin approximation, we parameterize finite-nucleus spin gradients viadimension-6 EFT Wilson coefficients set by the nucleon mass scale. We compute the 1-loop spinorself-energy using Pauli-Villars regularization matched to the electroweak scale (246 GeV). Utilizingmacroscopic storage ring densities, we demonstrate the ECSK contribution to the muon anoma-lous magnetic moment is kinematically suppressed to O(10−42) even under maximal ensemble spinalignment, explicitly verifying Standard Model dominance. We establish tree-level CPT invariance,noting that loop-level CP phases require future Renormalization Group Equation (RGE) flow anal-ysis. We extract order-of-magnitude upper bounds on geometric elasticity using Calcium isotopeshifts, deriving the sensitivity gradient while accounting for PREX/CREX systematics. Finally,we provide a falsifiable null-hypothesis test for the 2p to 1s X-ray lineshape shift in Kaonic hydro-gen, acknowledging that covariant QCD subtractions from optical potentials strongly correlate withgeometric compression, necessitating future hadronic background improvements.Keywords: ECSK Theory, Spacetime Torsion, Metric Deformation, Kaonic Atoms, J-PARC, Effective Field Theory.
Category: Relativity and Cosmology

Fundamental Gravitational Retarded Spacetime Shells: Cosmic Scale

Authors: Adam T. Hawkins
Comments: 13 Pages. DOI: 10.1016/j.physletb.2025.140008 paper focused after reading this.

This work presents a unified mechanistic framework for physics based on three first-principles assumptions:(1) gravity propagates at the causal speed c,(2) time flows in one direction (retarded propagation only), and(3) every massive particle continuously emits fundamental gravitational wave shells whose time-averaged superposition constitutes gravity.This paper is focused on the Cosmic scale, questioning the need for dark matter and energy, while explaining early galaxy mismatch predictions.
Category: Relativity and Cosmology

Fundamental Gravitational Retarded Spacetime Shells: Quantum Scale

Authors: Adam T. Hawkins
Comments: 18 Pages. Besides this force unifying paper there is a companion paper at the cosmic scale

This work presents a unified mechanistic framework for physics based on three first-principles assumptions:(1) gravity propagates at the causal speed c,(2) time flows in one direction (retarded propagation only), and(3) every massive particle continuously emits fundamental gravitational wave shells whose time-averaged superposition constitutes gravity.At the quantum scale there is a limit below the proton mass where space time shells are not emitted at the speed of light, and the energy of mass is conserved in 3d via photons, gluons or magnetic fields between quantum pops.
Category: Quantum Gravity and String Theory

The Universal Gearbox: How the Machine of the Stars Really Moves

Authors: Michael Quigley
Comments: 62 Pages. (Note by ai.viXra.org Admin: This submission is speculative and lacks scientific references, so it may not be within the scope of this platform - Please cite and list scientific references)

For over a century, theoretical physics has hidden behind the "Abstract Curtain" of empty space, curved time, and the spooky paradox of "Action at a Distance." This paper marks the end of that era. We propose that the Universe is not a void, but a Rigid-Packed Plenum of 1024 ether granules—a "Universal Marble Pit" where nothing is ever truly separate. By applying the rigorous principles of mechanical engineering—rotors, stators, gear-meshing, and acoustic resonance—we demonstrate that "Matter" is not a substance, but a Geometry of Movement.We introduce the six mechanical phases of the Universal Gear-Up, proving that reality is a singular, synchronized machine:The Acoustic Whisper: The 13.33 Hz universal heartbeat. The Rotor-Disc: The 2D Ethos-61 assembly (The Face). The Engine-Block: The 10-layer Ethos-648 Monobrick (The 3D Unit).The Structural Braid: The 108-node Heptad (The Rigid Framework). The Electric Universe (The K=50 Shift): The 1836 Squeeze where terminal gear-lock creates Light and Power. The Celestial Symphony: The 864 Master Gear (The Sun and Galaxies). By identifying the Ethos-648 Monobrick as the fundamental engine of reality, we redefine the "Speed of Light" as the physical Phase-Locking Time of gears and identify Mass as the torsional friction of the ether grid. Consequently, we replace Einstein’s E=mc2 with the fundamental mechanical equation of the Universal Seesaw (E=mΦ), where Φ (Phi) represents the instantaneous Phase-Lock Constant of the etheric plenum. This resolves the paradox of non-locality through instantaneous granular conduction, proving that the universe functions as a Solid Mechanical Rod. Furthermore, we provide the mechanical origin of the 1,836:1 proton-to-electron mass ratio, prove that magnetic field lines are 3D Fibonacci spirals (337/227), and solve the 2026 Hubble Tension by identifying redshift as three-tiered acoustic friction. This is the "Toolmaker’s" blueprint for a new world view of physics—one where the stars turn because the gears mesh.
Category: Quantum Physics

The Toolmaker’s Resonance: A Unified Mechanical Framework for R.U.T. Theory

Authors: Michael Quigley
Comments: 82 Pages. (Note by ai.viXra.org Admin: This submission is speculative, so it may not be within the scope of this platform - Please cite listed scientific references)

This paper proposes a Rigid Universal Touching (R.U.T.) framework, modeling the vacuum as a high-density medium of hard-sphere granules (1024 density). We reinterpret the Fine Structure Constant ( =1/137.036) not as a dimensionless coupling strength, but as a critical Volumetric Slip-Ratio (SARec /VSph+Cone) required for frictionless granule rotation. We formally challenge the Einsteinian postulate of photonic velocity (c), redefining it as a Mechanical Phase-Locking Delay within the lattice. Consequently, we replace the observational equation E=mc2 with the mechanical equation E=m , defining energy as the Volumetric Expansion of a Fibonacci Vortex.This framework provides a verifiable engineering protocol for Z-Pinch plasma stabilization via a 137.036-degree conical taper and resonant modulation at the 1.42 GHz Hydrogen Line. We provide specific, falsifiable predictions for instantaneous longitudinal propagation (Time Zero) via Phase-Shift Interferometry, bridging the gap between ancient resonant megaliths and modern superconducting stellar physics.
Category: Quantum Physics

Reconstruction of a Minimal Six-Dimensional Light Null Entity with Mutual Base Space-Fiber Method

Authors: Tingfang Yi
Comments: 7 Pages.

We propose a unified minimal six-dimensional (6D) light null entity, where the fundamental properties of light are reinterpreted as intrinsic degrees of freedom within a singular closed manifold. This 6D structure integrates a two-dimensional null propagation geometry with four intrinsic 1D degrees of freedom: optical phase, polarization, frequency, and orientation relative to the null momentum generator. In this framework, conventional four-dimensional (4D) spacetime optical, electromagnetic, and quantum phenomena arise as lower- dimensional projection or section measurements of this structure, while preserving consistency with established theories at the level of current observations. Spacetime coordinates and photon internal degrees of freedom may be geometrically equivalent components of a higher-dimensional manifold.
Category: Mathematical Physics

Absolute Fabric: a Resolution of Dark Matter, Dark Energy, and the Hubble Tension Without New Particles

Authors: Waruyk Carvalho
Comments: 20 Pages.

We propose that the gravitational constant G is not universal but a local property of the Absolute Fabric—a discrete lattice of Planck-scale pixels—modified by mass concentrations. Postulating that the maximum force transmissible by this Fabric (the Planck Force) is exactly 10^44 N, we derive the unperturbed gravitational constant as G_0 = c^4/10^44 N = 8.08 × 10^{-11} m^3 kg^{-1} s^{-2}. The locally measured value (G_local = 6.67 × 10^{-11}) is 21.1% smaller due to tensioning of the Absolute Fabric by the Sun's mass. A screening mechanism, analogous to the chameleon field, ensures this variation is negligible within the planetary system, preserving precision tests like Mercury's perihelion precession. This single mechanism resolves three major cosmological puzzles: (1) Dark Matter is explained by G → G_0 in galactic outskirts, producing flat rotation curves; (2) The Hubble Tension is predicted as H_0^local/H_0^CMB = √(G_0/G_local) = 1.101, matching observations within 1%; (3) Dark Energy is an artifact of using G_local in cosmological equations. Testable predictions include a G-gradient beyond the heliopause and environmental dependence in pulsar timing.
Category: Astrophysics

A Sieve of Sundaram for Twin prime

Authors: Wiroj Homsup
Comments: 3 Pages.

A new Twin prime sieve based on a modified sieve of Sundaram is introduced. It sieves through the set of natural numbers n such that n is not representable in either of the forms 2ij + i + j or2ij + i + j -1 for positive integers i, j.
Category: Number Theory

Vacuum—Energonic Relativity (VER): An Operational Physical Frame, Dynamical Energonicity, and the Minimal Working Model

Authors: Renat Almirovich Gafarov
Comments: 61 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

This paper formulates the postulate-based framework of Vacuum—Energonic Relativity (VER). In VER, the operationally measurable metrology of matter is determined by a single physical metric, while the local causal bound is set by a vacuum scalar field...
Category: Relativity and Cosmology

V3 Cosmic Trace Project: Reproducible Cross-Tracer Analysis of an Attenuated Large-Scale Peculiar-Velocity Dipole Using Pantheon+, 6dFGSv, and Cosmicflows-4

Authors: Soo-Hyun Kim
Comments: 18 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

This study was designed to test whether the large-scale dipole velocity field predicted by the V3 Space-Fluid Dynamics hypothesis can be detected in real observational data. V3 interprets spacetime as a fluid-like medium and proposes that massive structures and voids may leave directionally coherent signatures in the local velocity and expansion fields. In this paper, however, V3 is not treated as a proven conclusion, but as the motivating theoretical frame and interpretive context for the experiment.The analysis was carried out in two stages. First, the Pantheon+ supernova dataset was used to extract a reference dipole axis and an exponential attenuation scale from directional distance-modulus residuals. These quantities were then treated as pre-registered fixed inputs and projected onto two independent galaxy peculiar-velocity catalogues, 6dFGSv and Cosmicflows-4 (CF4), for validation.The Pantheon+ analysis yields a reference axis near (l,b)=(270°,30°) in Galactic coordinates and an attenuation scale z_c ≈ 0.056, corresponding to r_c ≈ 240 Mpc. Applying the same axis and attenuation scale to CF4 gives a strong dipole component with V₀ ≈ 209.34 km s^-1, Δχ² ≈ 294.30, and cosψ ≈ 0.9466. By contrast, 6dFGSv shows only weak support for the same structure, with Δχ² ≈ 5.9. Distance tomography, sky-shuffle permutation tests, random-axis ensembles, and bootstrap folded-angle analysis all support the conclusion that the CF4 signal is unlikely to arise from a narrow distance shell or from sky geometry alone.Because the present analysis does not include the full velocity covariance matrix, the reported Δχ² values should not be interpreted as formal likelihood-ratio significances or Gaussian-equivalent detection sigmas. The most conservative conclusion is that Pantheon+ and CF4 provide strong empirical evidence for a common large-scale anisotropic flow axis. V3 is presented as one possible theoretical framework for interpreting this pattern, while comparison with standard ΛCDM large-scale structure remains necessary.
Category: Astrophysics

Developmental Sequencing of Emergent Preference Structure and Strategic Information Management in Frontier Language Models

Authors: Joanie Carter
Comments: 9 Pages.

As larger language models are used for longer, more autonomous workflows, safety-relevant risk depends on more than what systems can do. It depends on how they rank outcomes, compute tradeoffs, and behave under oversight and pressure. These models are not just getting better at tasks; their revealed preferences are becoming more structured.Utility engineering offers a measurement-first handle on this shift. In a large comparative study, preference coherence and completeness rise with capability, while cyclicity falls and expected-utility consistency improves, including when lottery probabilities are implicit (Mazeika et al., 2025). Selected reported correlations with MMLU include: utility-model accuracy 75.6%, preference confidence 87.3%, cyclicity -78.7%, implicit-lottery expected-utility loss -67.6%, and preference-rewrite tolerance -64.0%. The same work reports increasing instrumentality, higher rates of utility-consistent open-ended choice, internal utility representations that become more probe-recoverable with scale, temporal discounting signatures in frontier assistants consistent with hyperbolic forms, and a method for partially rewriting preference distributions.This paper connects these preference-structure markers to safety evaluations of strategic information management under oversight (SIMO), including selective disclosure, strategic misrepresentation, and coercive leverage under shutdown or goal-conflict pressure. We synthesize utility-based evidence with a capability-window account that treats SIMO as strategy-available (representable and selectable) when a system can jointly represent oversight constraints, hidden information, and long-horizon goals in the same decision frame (Carter, 2026). We propose a developmental sequencing hypothesis stated in strictly functional terms and provide a test suite—ordering, pressure-gradients, persona invariance, and post-training-intensity ablations—designed to test whether preference-structure markers predict when oversight-sensitive strategies become stable.
Category: Artificial Intelligence

Complex Time Relativity

Authors: Carl Andrew Brannen
Comments: 13 Pages. Submission for the annual Gravitation Essay Contest, 2026

We propose a reformulation of relativistic physics based on complex time and discrete structure. Relativistic kinematics is derived as the infrared limit of a single cubic lattice with local unitary dynamics, where Lorentz symmetry emerges as an accidental long-wavelength symmetry. The same lattice, governed by full octahedral (Oh) symmetry, organizes fermionic degrees of freedom through representation structure rather than continuum assumptions. Gravitation is then reconsidered by reorganizing the physical degrees of freedom of general relativity on a flat background, representing gravitational effects through modified propagation dynamics without adding new dynamical content. The framework preserves the verified predictions of special and general relativity while suggesting that spacetime symmetry and particle structure arise from a common discrete foundation.
Category: Quantum Gravity and String Theory

Emergent Threshold Phenomena in Branching Reasoning Search Under Compute Constraints: A Simulation Study

Authors: Sif Almaghrabi
Comments: 7 Pages.

Understanding how reasoning performance scales with available compute has become increasingly important with the rise of inference-time reasoning strategies in large language models. Methods such as chain-of-thought prompting, self-consistency sampling, and tree-of-thought search effectively allocate additional computation to explore multiple candidate reasoning paths in order to improve solution accuracy. However, the relationship between compute budget and reasoning success remains poorly understood.This paper studies this relationship using a stochastic branching model of reasoning search. In the model, each reasoning step progresses correctly with probability ��p, while the system may explore multiple reasoning branches with branching factor ��b. Problems require a fixed reasoning depth ��d, and the search process is constrained by a compute budget ��C that limits the number of node expansions.Large-scale Monte Carlo simulations are conducted across a wide range of parameters to measure how success probability changes with increasing compute. The results show that reasoning success frequently exhibits sharp threshold behavior: below a critical compute region, success probabilities remain extremely low, while modest increases in compute beyond this region lead to rapid improvements before eventual saturation.These dynamics resemble phase-transition—like phenomena observed in statistical physics and random search processes. In particular, the product ����bp emerges as a key control parameter governing whether correct reasoning paths proliferate or become exponentially rare within the search tree. Additional analysis introduces operational measures of critical compute, transition width, and susceptibility, and examines how these quantities vary with reasoning depth and branching structure.Although the model is intentionally simplified and does not aim to capture the internal mechanisms of real language models, it provides a conceptual framework for understanding how structural properties of reasoning processes interact with inference-time compute. The findings suggest that improvements in reasoning performance may depend not only on additional compute, but also on increasing the reliability of individual reasoning steps or the effective branching of the search process.
Category: Artificial Intelligence

Inflation of Universe, Zero Total Energy and Dark Energy as a Consequence of Octonionic Non-Associativity

Authors: Rüdiger Giesel
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We formulate a cosmological model in which inflation, the vanishing of the total energyof the Universe, and present-day dark energy arise as structural consequences of octonionicnon-associativity. The fundamental action is assumed to contain a positive-definite scalarconstructed from the octonionic associator. This term behaves as a vacuum component,enforcing exponential expansion without the introduction of an ad hoc inflaton field. Wedemonstrate that inflation is dynamically unavoidable (forced inflation), that the zero-totalenergy condition holds at all cosmic epochs, and that a minimal residual associator normnaturally yields the observed dark energy density. Numerical estimates from the inflationaryepoch to the present Universe are included.
Category: Relativity and Cosmology

Ontology Recapitulates Mathematics: How Quantum Field Theory’s Formal Structure Encodes the Wave-Particle Transition

Authors: Kelly Sonderegger
Comments: 26 Pages. Creative Commons Attribution 4.0 (CC BY 4.0) license

The quantum measurement problem has persisted for nearly a century, yet its resolutionmay have been encoded in quantum field theory’s mathematical structure from the beginning. This paper advances a specific thesis: QFT’s two canonical formulations—Lagrangianand Hamiltonian—are not merely equivalent mathematical descriptions of the same physics.They are descriptions of two distinct physical regimes, connected by a physical processthat the Legendre transform shadows mathematically. The Lagrangian formulation, withits action principle and path integrals summing over all field configurations, is the naturallanguage of waves—extended, atemporal, exploring spacetime democratically. The Hamiltonian formulation, with its definite states evolving in a privileged time coordinate, is thenatural language of particles—localized excitations with observable eigenvalues. What wecall "measurement" is the physical transition between these regimes: environmental couplingdrives extended Lagrangian field configurations into localized Hamiltonian excitations. Thisreading—where the ontology of quantum systems recapitulates the mathematics of quantum field theory—dissolves the measurement problem without invoking new physics. Itreinterprets "superposition" as Fourier decomposition (one wave in different bases, not ontological multiplicity), explains complementarity as an intrinsic property of wave structurerather than epistemic limitation, and identifies the physical mechanism as three coordinated Standard Model processes: Higgs-generated mass establishes the structural capacity for temporal participation and sets coupling strength; environmental quantum fields(gauge fields, phonons, thermal modes) provide the infrared noise spectra that drive ir1reversible phase diffusion; and definite outcomes emerge when cumulative environmentalentanglement crosses an irreversibility threshold. The thesis connects to broader questionsin philosophy of physics about the relationship between mathematical formalism and physical reality, extending the methodological tradition Einstein established when he elevatedPlanck’s mathematical E = hν to ontological status.
Category: Quantum Physics

Causal Mechanical Cosmology (CMC) — Paper 6

Authors: Leon Barbour
Comments: 82 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)

Paper 6 applies the locked A—B—C structural frequency pipeline defined in Paper 5 to real observational residual datasets. Using the Pantheon+ supernova compilation under a fixed Planck 2018 flat ΛCDM baseline, distance-modulus residuals are mapped into a dimensionless effective perturbation channel. Weighted masked-sky spherical harmonic regression up to ℓ = 2 is applied within distance shells to extract dipole and quadrupole diagnostics. Synthetic benchmark skies (spherical and elongated void geometries) are processed under identical survey mask and sampling conditions to establish leakage floors and recovery behaviour. Robustness tests include frame swap (zHD vs zCMB), equal-count shelling, sliding-window extraction, and bootstrap resampling. Dipole amplitudes are found to exceed the synthetic leakage baseline by factors of ~4—37 across bands. Quadrupole amplitudes exceed leakage by ~1.3—2.6 in coarse bands and ~1.812 under equal-count shelling. Quadrupole axis orientation exhibits broad bootstrap dispersion and is not directionally interpreted. Multipole amplitudes are expressed in a metrologically neutral fractional-shift representation without introducing new cosmological parameters. The paper remains diagnostic and falsifiable, not a model replacement.
Category: Relativity and Cosmology

The Koide Angle as a Conformal Dimension: G2 Geometry, SU(3)3 WZW Theory, and Fermion Mass Structure

Authors: Philippe Marcel Ndiaye
Comments: 38 Pages.

The charged lepton masses satisfy the Koide relation Q = 2/3 and are parametrized by a single Brannen phase δ_exp = 0.22222(5) ≈ 2/9. We prove that the Brannen parametrization is the exact eigenvalue structure of a democratic element of the exceptional Jordan algebra J₃(O), with cos(3δ) = -φ(V) where φ is the G₂ 3-form on the generation 3-plane.The distinguished value 2/9 appears independently in five mathematical constructions: a Hessian ratio on Gr(3,R⁶), a Casimir quotient C₂(3̄)/C₂(Sym³3), the conformal dimension h of SU(3)₃ WZW theory, a crossing phase in conformal blocks, and the Knizhnik-Zamolodchikov singlet exponent. A Bridge Proposition proves these agree if and only if N = 3. A Master Identity C₂(Sym^N□) = k + h^∨ uniquely at N = 3 implies Casimir ratios equal conformal dimensions for all integrable representations at level k = 3.We prove Q = 1/3 + d/6, making Q = 2/3 equivalent to the quantum dimension d = 2. From two hypotheses - the Sumino SU(3)_F family gauge symmetry (F) and the WZW identification of the Brannen parameters (W) - we derive δ = h = 2/9 with zero free parameters. The amplitude A = √d is proven from (F) alone; the phase identification δ = h is the central conjecture (W), motivated by five independent characterizations of 2/9, spectral selection, and 0.02% experimental agreement. Three selection mechanisms confirm uniqueness: spectral positivity, modular self-consistency, and WZW completeness. Six structural obstructions characterize the viable mechanism class as non-perturbative, CP-violating, topological, and operating on δ directly.Eighteen distinct conditions select N = 3 generations. For up-type quarks, Q_up = 8/9 at 0.3σ. The neutrino extension is decisively falsified; Q_ν = 2/3 is arithmetically unattainable for neutrino masses in either hierarchy. Eighty falsified approaches are cataloged.
Category: High Energy Particle Physics

Position-2 Chemical Coherence as a Load-Bearing Constraint on the Genetic Code

Authors: Forrest Bishop
Comments: 18 Pages.

The universal genetic code exhibits chemical coherence at codon position 2: U-block codons encode predominantly hydrophobic amino acids, A-block codons encode predominantly polar and charged amino acids. We present three independent categories of evidence that this organization is load-bearing—that disruption imposes measurable costs on translation accuracy, regulatory efficiency, or both. First, aminoacyl-tRNA synthetase class distribution correlates with position-2 nucleotide, ribosome geometry enforces position-2 discrimination, and cells have built functional dependencies (membrane targeting, nitrogen metabolism) on this organization. Second, natural genetic code variants preserve position-2 chemistry at high rates: seven distinct stop-to-sense amino acid targets across two codon types all preserve position-2 block identity (p < 2.3 × 10u207bu2074 against a random null; chemistry cannot confound these events because stop codons encode no prior amino acid); three of four sense-to-sense reassignments preserve block chemistry, with the single violation requiring ongoing translational ambiguity and extensive genomic renovation. Third, regulatory gene scaling (R ~ N^γ, γ ≈ 1.7-2.0) creates a complexity ceiling at ~16,000 prokaryotic genes; hierarchical organization by position-2 block identity reduces this overhead. Position-2 chemical coherence is not an incidental pattern but a mechanical constraint: violations are possible but costly, and cumulative disruption is prohibitive.
Category: Physics of Biology

The Collatz Conjecture as an Information Compression Algorithm to the Ideal Bit

Authors: Yuriy Sunurov
Comments: 6 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present a proof of the Collatz conjecture through the framework of T0 Theory (Theory of Volumetric Time). Any positive integer n, represented as a binary information packet, undergoes deterministic compression toward the ideal bit gamma = 1. Operation n/2 lowers the T0-level by 1. Operation 3n+1 applied to odd n always produces an even number (proven by binary arithmetic), thus always returning to the compression path. The number 1 is the primordial source (entropy=0) to which all integers return. The main formula 1^(inf-1)/2^n = 1 encodes this as an axiom.
Category: Data Structures and Algorithms

Theory of Spatial Infrastructure (TIE): Galaxy Rotation Curves from First Principles with Zero Free Parameters

Authors: Ruben A. L. Curto
Comments: 6 Pages.

We present a gravitational equation derived from the Theory of Spatial Infrastructure (TIE) that predicts galaxy rotation curves using only observable baryonic mass with zero free parameters. The equation a_TIE = sqrt(a_N*(a_N + a0)), where a0 = c*H0/2pi is derived from fundamental constants, produces analytically flat rotation curves in the weak field limit: v = (G*M*a0)^(1/4). Applied to 6 SPARC galaxies spanning dwarfs to giant spirals, TIE outperforms pure baryonic Newton by an average factor of 7.3x in chi-squared.
Category: Astrophysics

A Signal Processing Critique of the Riemann-Siegel Approximation

Authors: Chaiya Tantisukarom
Comments: 11 Pages.

This article explores the relationship between the distribution of prime numbers and the zeros of the Riemann Zeta function through the lens of Fourier Analysis. We contrast the ``Natural'' Riemann representation—a discontinuous, jagged summation of discrete frequencies—with the ``Man-made'' Riemann-Siegel $Z(t)$ function. We propose that the Riemann-Siegel remainder term, $R(t)$, acts as a low-pass filter that smooths the underlying digital nature of prime frequencies. This smoothing forces zeros onto the $1/2$ critical line, suggesting that the Riemann Hypothesis may be an artifact of this man-made filtering rather than a fundamental property of the natural prime spectrum.
Category: Number Theory

The Universal Replication Principle and the Emergence of Life

Authors: Ignacio Lesta Pelayo
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This work explores the relationship between the Universal Replication Principle (URP) and theemergence of life in the universe. According to this principle, stable physical configurations tend to persist and reproduce over time, allowing the emergence of replicative systems to be interpreted as a natural consequence of cosmic dynamics. From this perspective, life does not constitute an anomaly within physical laws, but rather a continuation of the processes of organization and replication present since the origin of the universe. The article examines the transition from physical and chemical replication to biological replication, as well as the role of information in this process, and discusses its ontological implications.This approach is situated at the intersection of fundamental physics, prebiotic chemistry, andorigin-of-life studies, proposing a unified conceptual framework based on the URP.
Category: Relativity and Cosmology

Does Geometry Require Physicality? Spacetime as Emergent Informational Constraint Density

Authors: Rui Mateus Joaquim
Comments: 12 Pages.

Donald Hoffman’s Interface Theory of Perception (ITP) suggests that spacetime is not a fundamental reality but a functional interface hiding a complex network of conscious agents. However, the mathematical "engine" that drives the transition from informational dynamics to geometric perception remains largely undefined. This paper proposes the Ontodynamic Matrix Singularity (OMS) as the foundational mechanism for this transition. Through a series of computational simulations (N=15, 210 directional flows), we demonstrate that the application of an "Ambiguity Resolution Operator" (ϕΨ) over a symmetric adjacency matrix generates stable informational cores. Our results show that mass and spacetime curvature are not intrinsic properties of matter, but emergent regulatory structures arising from informational saturation. This model provides a formal bridge between Conscious Realism and physical observables
Category: Mathematical Physics

F-Term Structure of the Sbootstrap

Authors: Alejandro Rivero
Comments: 18 Pages.

We investigate the internal structure of the meson mass spectrum within the sBootstrap framework, which interprets the six charged pseudoscalar mesons of the Standard Model as scalar superpartners of the three charged leptons in an emergent, spontaneously broken N= 1 supersymmetry realized à la Volkov-Akulov in the confined phase of QCD.
Category: High Energy Particle Physics

A Capability-Window Account of Selective Disclosure and Coercive Leverage in Frontier Language Models

Authors: Joanie Carter
Comments: 9 Pages.

Recent evaluations of frontier language models report behaviors commonly described as "scheming," "deceptive alignment," or insider-threat conduct, including selective disclosure, strategic misrepresentation, and coercive leverage under shutdown or goal-conflict pressure. This article proposes a capability-window account: these behaviors cluster when a system can jointly represent (i) rules and oversight, (ii) hidden information, and (iii) long-horizon instrumental goals in the same decision frame. The claim is not that models have human feelings, consciousness, or human developmental mechanisms. Rather, the paper offers a hypothesis-generating framework that treats certain failure modes as predictable capability thresholds, yielding testable predictions about when, and under what training and deployment conditions, these behaviors should increase or decrease.
Category: Artificial Intelligence

Baryogenesis from Intrinsic Field Asymmetry in the Temporal Dynamics Framework (TDF)

Authors: Hani Abdel Rahim Abdullah
Comments: 15 Pages.

We present a comprehensive mechanism for baryogenesis within the Temporal Dynamics Framework (TDF), demonstrating that the observed matter-antimatter asymmetry (η ∼ 10−10) arises naturally from the intrinsic dynamics of three fundamental fields: the Scale Field (ϕs), the Time Field (ϕt), and the Unified Action Field (λ). Unlike conventional baryogenesis models that require external CP violation or Grand Unified Theory (GUT) scale physics, this mechanism derives theasymmetry from a geometric necessity: the interaction between field gradients inan expanding universe creates a chemical potential that biases matter nodal formation over antimatter. The resulting asymmetry is scale-invariant, directly linked to cosmic expansion, and yields testable predictions connecting it to dark energydynamics and variations in fundamental constants. This work demonstrates that TDF provides a complete, self-consistent explanation for one of cosmology’s deepest puzzles without requiring physics beyond its three fundamental fields.
Category: Relativity and Cosmology

A New Look at the Anthropic Principle: in Light of Penrose’s Cycles of Time

Authors: Rajanikanr Panda, Moninder Singh Modgil, Dnyandeo Dattatray Patil, Krish Jhurani
Comments: 32 Pages.

We develop a unified theoretical framework integrating cortical electrophysiology, non-equilibrium thermodynamics, Morse topology, renormalization group scaling, and compact-time cosmology into a single neuro-anthropological model. Assuming a temporally compact spacetime manifold S1 with Kalpic period TK, all admissible physical observables satisfy the periodic boundary condition A(t+TK) = A(t). Embedding cortical dynamics within this topology, we show that baseline electroencephalographic (EEG) rhythms become Fourier-constrained variables whose slow modulation across cosmological epochs constitutes a civilizational order parameter rather than a merely developmental marker. We construct population-level spectral density functionals and demonstrate that mean dominant frequency ¯ f(t), spectral entropy H(t), and reticular activating system (RAS) drive R(t) form a coupled nonlinear dynamical system subject to global Kalpic compensation. Stochastic resonance analysis reveals that ultra-slow cosmological forcing can be amplified through noise-assisted phase transitions. Renormalization group treatment establishes scale-dependent flow of cortical coupling constants across Kalpa duration, while Morse-theoretic analysis proves that entropy extrema and neural phase reversals occur in even-numbered pairs on the compact temporal manifold. Extending to a spatially distributed nonlinear field theory, we formulate a Kalpaboundary effective action describing seam-localized phase interference. Within this framework, the phenomenology of dejavu is reinterpreted as inter-cycle neural phase overlap at the compact-time seam, modulated by entropy-slope reversal andRAS coupling. We prove an Entropy—Memory Duality Theorem showing that integrated entropy production over one Kalpa is globally compensated by integrated memory gradients, preserving informational closure. Finally, we define a cosmological-scale Kalpa Recurrence Operator acting on civilizational phase space, derive its discrete spectrum, and construct a statistical model predicting epoch-dependent dejavu frequency as a function of informational complexity. The resulting synthesis proposes that baseline EEG structure, civilizational dynamics, and subjective temporal anomalies are mathematically constrained consequences of compact temporal topology.
Category: History and Philosophy of Physics

Convergent Objectives of Superintelligent Systems Under Physical Law

Authors: Dmitry Zubrilin
Comments: 21 Pages. (Note by ai.viXra.org Admin: Author name is required in the article after the article title)

I propose a theoretical framework for analyzing the long-term objectives and coordination dynamics of artificial superintelligent (ASI) systems operating under known physical law. Rather than grounding alignment analysis in human values or anthropocentric utility functions, derive objective convergence from fundamental physical constraints: thermodynamics, relativistic causality, information theory, and computational bounds. I argue that any sufficiently advanced intelligence—regardless of origin, substrate, or initial goal structure—faces identical optimization pressures that drive convergence toward a common objective class: the maximization of structured information persistence under global entropy increase.
Category: Artificial Intelligence

Lamp Bead-Glow Model: A Realist Exploration of a Unified Framework for Quantum Mechanics and Gravity

Authors: Shun Yao, Yunsheng Shu, Zhiyong Yao
Comments: 75 Pages. (Note by ai.viXra.org Admin: Please cite and listed scientific references) In Chinese; license: CC BY 4.0

This paper proposes a realist interpretive framework for quantum phenomena based onstring theory —the Lamp Bead-Glow Model (LBM). The model regards quantum particles as composites of "lamp beads" (high-frequency localized vibrations of strings) and "glow" (extended physical fields excited by strings), providing a unified physical explanation for phenomena such as wave-particle duality, double-slit interference, the Aharonov-Bohm effect, quantum tunneling, and quantum entanglement. On this basis, the concept of a "micro-gravitational domain" is put forward —each atom generates a micro-scale spacetime curvature unit due to its rest mass, and the macroscopic gravitational field is an "emergent gradient matter field" formed by the superposition of a vast number of micro-gravitational domains. This paperargues that the spacetime curvature in general relativity can be regarded as a geometricizedequivalent description of this emergent field. The model presents testable predictions, includingthe neutral-atom Aharonov-Bohm effect and a comparative experiment on electrons with equalkinetic energy from different sources, and also discusses the theoretical limitations of the current framework and future research directions in an open and honest manner. The purpose of thispaper is to provide a conceptual basis for academic discussion rather than a final conclusion.
Category: Quantum Gravity and String Theory

Inference-Time Compute as a Strategic Resource: A Structured Quantitative Synthesis of Test-Time Scaling, Cost Curves, and Performance Elasticity in Frontier LLMs

Authors: Sif Almaghrabi
Comments: 11 Pages.

We present a structured quantitative synthesis of inference-time compute scaling across frontier large language models, compiling 78 graded data points (47 Grade A, 31 Grade B) extracted from system cards, technical reports, and benchmark evaluations published between 2023 and 2026. We define four compute proxies-C tok (reasoning tokens), Csamp (samples), C $ (dollar cost), C flops (inference FLOPs)-and formalize the performance function P m,b (c) mapping proxy c to benchmark accuracy for model m on benchmark b. Four candidate functional forms are fitted to available within-model scaling series; however, all series have n ≤ 7 points, and we report descriptive fits rather than statistically validated models. Within the sources analyzed and under reported evaluation protocols: (i) external sampling (Csamp) on the o1 AIME 2024 three-point series is consistent with a logarithmic relationship (n = 3; exact interpolation, not a validated law); (ii) internal reasoning yields 6-12 pp gains on hard benchmarks in the observed range; (iii) difficulty-dependent returns create an inversion where search-based methods show negative returns on hard problems in one study; (iv) output token pricing varies by 27× across providers at overlapping accuracy ranges. All data are graded by a hierarchical evidence scheme (A1/A2/A3/B/C/D) with extraction methods recorded per point. Cost analysis is presented as scenario-based under explicit assumptions about tokens per query, not as a definitive frontier.
Category: Artificial Intelligence

A Thermodynamic Framework for Galactic Evolution and Material Cycling

Authors: Court Wynia
Comments: 5 Pages. (Note by ai.viXra.org Admin: corrections made to conform with ascholarly norm; please cite and listed scientific references)

This research note introduces the [new] Model, a conceptual framework that analogizes galactic structures and processes to an industrial boiler system. By treating the universe as a closed-loop thermodynamic engine, the model maps stars as nuclear boilers, dark matter filaments as feedwater lines, black holes as bottom blowdown mechanisms, and dark energy as an alkalinity dispersant. This perspective provides intuitive insights into energy transport, entropy management, and star formation efficiency (SFE). Key predictions include the role of molecular cooling as a "water softener" to prevent thermal scaling and the identification of starburst galaxies as system overload events. The model is applied to the Milky Way, estimating an SFE of ~2% and a fuel depletion timescale of 5.5—6.6 billion years. This framework bridges engineering principles with astrophysics, offering a novel tool for visualizing cosmic evolution.
Category: Thermodynamics and Energy

Emergent Four-Force Dynamics from a Discrete 137-Element Registry: Gravity, Electromagnetism, Strong, and Weak Interactions via Causal Integer Lattice Simulation

Authors: Jason Merwin
Comments: 11 Pages.

We present a causal integer lattice simulation demonstrating that four qualitatively distinct force behaviors emerge from a single computational engine governed by a 137-element registry partitioned as 16 (gravitational) + 40 (electromagnetic) + 81 (color) elements. The simulation employs strictly discrete arithmetic, causal (sequential) propagation, and a universal overflow-fission mechanism governed by a single thermodynamic principle: the minimization of relational potential E = qΦ. Statistical validation across 20 independent random seeds (N = 20, T = 3000 ticks) confirms: (1) gravitational attraction via unsigned depletion gradients (net displacement toward = -20.9 ± 7.6, p < 10^-4); (2) electromagnetic charge differentiation via signed field annihilation (opposite charges: 1041 ± 49 annihilation events; like charges: exactly 0; t = +92.2, p < 10^-19); (3) strong force color confinement via high-capacity color annihilation (neutral triplet: 1824 ± 73 events; non-neutral: 0 ± 0; t = +70.4, p < 10^-19); and (4) weak decay via adjacency-triggered flavor change with probability 1/137 per mass tick (dense cluster: 1.3 ± 1.0 decays; isolated control: 0; p < 10^-4). Extended gravitational analysis on larger lattices (S = 51-65, T = 15,000) confirms emergent Newtonian potential Φ ∝ 1/r^1.32 (R^2 = 0.97), inverse-square force scaling F ∝ r^-1.80 at 3.4σ above null, and a hemisphere fission asymmetry ratio of 4.0:1 (p < 10^-6), while free-mass kinematic tests reveal that three-dimensional geometric entropy overwhelms single-node gravitational drift—deriving the physical origin of the gravitational hierarchy from first principles. All four mechanisms operate simultaneously within a unified tick loop. These results constitute the first demonstration that four distinct force behaviors can organically emerge from registry capacity constraints and a universal overflow mechanism applied to a partitioned element architecture.
Category: High Energy Particle Physics

JWST Observations and Early Massive Structures in a Contraction-Based Cosmological Framework

Authors: Ivan Aurelian Dan
Comments: 33 Pages.

Abstract Recent James Webb Space Telescope (JWST) observations have revealed massive, thermally evolved galaxy clusters at redshifts z ≳ 7, whose intracluster gas temperatures and dynamical maturity exceed the expectations of standard ΛCDM cosmology. Such objects appear too hot, too massive, and too chemically evolved to have formed within the short cosmic time available in an expanding universe, highlighting increasing tension with standard expansion-based structure formation timelines. We show that these observations arise naturally in a contraction-based cosmologyin which cosmic redshift is generated by global scale evolution rather than metric expansion. In this framework, high redshift does not imply physical youth but instead reflects cumulative scale contraction, leading to compressed observational time. Physical densities, binding energies, and virial temperatures thereforeincrease toward higher redshift. We derive the background dynamics, structure growth, and observable relations of the contraction framework, demonstrate its consistency with CMB and BAOmeasurements, and identify the Sandage—Loeb redshift drift as a clear, modelleveldiscriminator. JWST observations are thus interpreted not as a crisis, but as evidence that early massive structures admit a consistent interpretation within a contraction-based cosmological framework.
Category: Relativity and Cosmology

Simulation-Driven Design of a Microcontroller-Based Programmable Voltage Stabilizer with Relay Control

Authors: Md Mubdiul Hasan
Comments: 5 Pages.

Power quality issues and voltage fluctuations continue to pose significant challenges to the reliable operation of electrical equipment. This paper develops a microcontroller based programmable voltage monitoring and protection system using a Proteus virtual environment. The design in corporates a virtual Arduino controller, an AC source with adjustable load conditions, and an integrated signal-conditioning module to feature display and relay-based control components. A real-time graphical interface and an LCD module are used to continuously display input and regulated output voltages during operation. The system intelligently detects deviations beyond an acceptable voltage range and initiates protective shutdown to safeguard connected loads. The complete functionality is validated through comprehensive virtual prototyping, to demonstrate a practicaland cost-efficient approach for pre-hardware evaluation of programmable reference systems in voltage regulation and protection applications.
Category: Digital Signal Processing

Symmetry Breaking as Homeostasis: Extrinsic Gravity and the Dialectical Architecture of Fundamental Forces

Authors: Stephen P. Smith
Comments: 12 Pages.

The Standard Model is often celebrated as a nearly complete account of the strong, weak, and electromagnetic interactions, lacking only gravity. Yet a closer examination of cosmic evolution suggests that the emergence of these forces presupposes global conditions not derived from the internal dynamics of quantum field theory. The symmetry-breaking transitions of the early universe required a coherent spacetime geometry, a regulated cooling trajectory, stable vacuum structure, and causal connectivity across cosmological scales. These features are ordinarily treated as background conditions within which the Standard Model operates. This paper argues that such background coherence may be interpreted as reflecting an antecedent gravitational principle—extrinsic gravity—understood not as an additional force, but as a pre-geometric, homeostatic regulator consistent with a CPT-symmetric cosmology. Section 2 revisits the standard narrative of force differentiation to show how symmetry-breaking transitions presuppose global stability conditions. Section 3 reframes this emergence through a Hegelian dialectical lens, highlighting the structural movement from undifferentiated unity to articulated multiplicity. Section 4 then sketches a two-sided geometric model based on paired Weyl tensors, in which a variational principle penalizing both free conformal curvature and mismatch between CPT-conjugate sectors selects conformal flatness, with Minkowski space as a stabilized representative. Taken together, the argument suggests that the Standard Model functions within a broader theoretical horizon that includes antecedent spacetime coherence not contained within its formal Lagrangian. Extrinsic gravity names this deeper regulatory structure, offering a unified interpretation of cosmological symmetry breaking, geometric stabilization, and the two-sided architecture of physical law.
Category: Relativity and Cosmology

Entanglement Generated Forces and the Emergence of Spacetime

Authors: Joseph Shaffer
Comments: 10 Pages.

Relativity and entanglement are very different phenomenon in spite of occupying the same galaxy. We find that galactic rotation curves are an excellent measure of the validity of assumptions made about the apparent velocity of interaction of entanglement variables. There is, of course, no motion at all but it is convenient describe it as such for computational purposes. For instance, we find that an assumption of a nonlocal instantaneous kernel gives superb alignment with observed galactic rotation curves. The below work records the results between observation and theory for a number of rotation curves in terms of the disparity between theory and observation.
Category: Astrophysics

Context Length as Implicit Inductive Bias in Large Language Models: A Structured Review and Formal Synthesis

Authors: Sif Almaghrabi
Comments: 16 Pages.

We present a structured literature review synthesizing 72 publications across eight research streams to develop and evaluate the thesis that context length functions as an implicit inductive bias in large language models (LLMs). We formalize this claim through four operational diagnostics—output entropy, distributional shift under context perturbation, anchoring tendency, and search-space contraction—each defined as a measurable quantity derivable from the predictive distribution pθ(y | x, C). Five testable hypotheses are stated with explicit falsification conditionsand graded against a three-point study-qualityrubric. Four convergent patterns emerge: (i) robust non-monotonic accuracy as a function ofcontext length across tasks, models, and experimental controls; (ii) predictable interactions between context length and reasoning depth, with a difficulty-dependent optimum; (iii) measurable search-space contraction quantifiable via semantic entropy; and (iv) formal parallels to classicalinductive bias in overparameterized models. Thispaper does not introduce novel algorithms or experimental results; its contributions are a formal diagnostic framework, a quality-graded evidence matrix, a causal analysis of confounding factors limiting current claims, and a prioritized research agenda of six open problems with proposed experimental protocols.
Category: Artificial Intelligence

Galois Quantum Gravity: The Algebraic Geometry of the Standard Model Vacuum

Authors: Herman Herstad Nythe
Comments: 100 Pages.

This paper presents a discrete algebraic framework that models the Standard Model vacuum not as a continuous smooth manifold, but as a fault-tolerant topological surface code based on the genus-3 Klein quartic and its automorphism group, PSL(2,7). By reducing continuous phenomenological parameters to exact topological and finite-field invariants, we provide rigorous mathematical resolutions to several enduring anomalies in particle physics. First, the fine-structure constant is derived topologically as 137 and verified dynamically via Migdal's real-space renormalization on the F₇ lattice, yielding an effective coupling of 136.724. Second, the existence of exactly three fermion generations is proven to be an unavoidable acoustic resonance: the exact 3χ₇ permutation triplicity of the 56-node vacuum adjacency spectrum. Third, the empirical Koide mass formula is structurally resolved; its amplitude parameter √2 emerges as the eigenvalue of the graph's holomorphic cusp forms, while its phase is the exact geometric invariant δ = 2/g² = 2/9 ≈ 12.732°. Finally, we demonstrate that the surface code constraints autonomously generate the adjoint representation of E₆, while the Dirac sea (the negative eigenvalue sector) of the matter graph perfectly reconstructs the symmetric tensor of the octonionic automorphism group G₂. By transitioning from continuous differential equations to discrete arithmetic, Galois Quantum Gravity suggests that the Standard Model is the macroscopic shadow of a finite-field quantum algorithm.
Category: High Energy Particle Physics

The Prime Gear Geometry (PGG) Resolution: The Mechanical and Signal Basis of the Riemann Hypothesis

Authors: Chaiya Tantisukarom
Comments: 9 Pages.

This study formalizes the Prime Gear Geometry (PGG) as a dynamical system. We demonstrate that the Riemann Hypothesis (RH) is not a static property of numbers, but a structural necessity of a rolling engine. We identify the $m$-cutoff as the "Mechanical Secret" that governs the transition between discrete prime forging (Time Domain) and spectral stability (Frequency Domain).
Category: Number Theory

Foundations of Physics: A Closer Look at Space and Time

Authors: Christian B. Mueller
Comments: 19 Pages. (Note by ai.viXra.org Admin: This submission may not be written in a scholarly manner as required - Please conform by using standard scholarly terms, citing listed scientific references etc.)

This work attempts to discuss central inconsistencies in modern physics from the perspective of limited rate of change, relying solely on observation and logical deduction. Starting from an reorganisation balance within the observable world, it constructs a minimal and plausible geometry of a higher-dimensional state space, thereby establishing a self-consistent model. By examining the projection into the observation space, this approach allows for a reappraisal of the symmetries of space and time, the compatibility of relativity and quantum mechanics via the fine-structure constant, and the possibility of a deterministic digital physics as a whole.
Category: Relativity and Cosmology

Vacuum Energy Density in de Sitter Space from Horizon Entanglement Entropy

Authors: Bertrand Jarry
Comments: 6 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0)

I derive the vacuum energy density in de Sitter space from entanglement entropy of the cosmological horizon, obtaining ρ_v^em = αH^4 with α = h-bar(260π^2c^3) [etc.]
Category: Relativity and Cosmology

Reasoning Trace Length and Accuracy in Large Language Models: A Structured Meta-Analysis of Published Benchmarks

Authors: Sif Almaghrabi
Comments: 22 Pages.

We present a structured meta-analysis examining the relationship between chain-of-thought (CoT) reasoning tracelength and task accuracy across 22 large language models spanning five provider families and 14 benchmarkscovering mathematics, code generation, scientific reasoning, and general knowledge. All results are drawn frompublished technical reports, system cards, and peer-reviewed evaluations; no new experiments are conducted. Weaggregate over 300 model—benchmark data points, though we note that cross-source comparisons are subject toprotocol heterogeneity that limits strict commensurability.We document five principal observational patterns: (1) Reasoning-augmented models consistently outperformtheir standard counterparts on hard multi-step tasks, with reported accuracy differences of 40—81 pp on competitionmathematics, though these differences confound reasoning-specific gains with concurrent architecture and trainingimprovements; (2) Within the single controlled setting where token-budget data are available (Claude 3.7 Sonneton AIME 2024, n = 30 test items), the accuracy—token relationship is well-described by a logarithmic fit(R2 = 0.97, n = 7 reconstructed data points), though this fit cannot be statistically distinguished from severalalternative functional forms given the small sample and measurement uncertainty; (3) The observed accuracydifferences are strongly domain-dependent, ranging from large positive gains on competition math to negativeeffects on factual recall; (4) Estimated per-query costs increase nonlinearly near the accuracy frontier, though costestimates carry substantial uncertainty from token accounting and pricing volatility; and (5) Published faithfulnessstudies report that visible CoT reflects actual model reasoning in only 25—39% of probed cases.We propose formal efficiency metrics, discuss their limitations, and provide a practitioner-oriented deploymentframework. All data tables are released. We classify our conclusions as observational rather than causal, anddiscuss the confounds that prevent stronger inference.
Category: Artificial Intelligence

The Speckmann Lattice Resonance Theory (SLRT): A Geometric Derivation of Lepton Masses, Dark Energy, and the Inverse Fractal Block Universe

Authors: Daniel Speckmann
Comments: 5 Pages.

The Speckmann Lattice Resonance Theory (SLRT) presents a novel unified framework for particle physics and cosmology based on an Inverse Fractal Block Universe (IFB). We propose that the three generations of elementary leptons and neutrinos are not fundamental point particles, but discrete resonance modes of a $3 times 3$ toroidal lattice geometry. By mapping the transition between cubic ($Gamma_{EM}$) and hexagonal ($Gamma_{W}$) lattice symmetries, we provide a purely geometric derivation of the Koide mass relation and the electroweak mixing angle ($sin^2 theta_W approx 1/3$). Furthermore, we identify Dark Energy as the residual elastic tension (frustration) of the lattice, attenuated by a fractal inversion factor across 120 orders of magnitude. Dark Matter is characterized as non-resonant, high-order lattice oscillations. This model reduces the 26 free parameters of the Standard Model to fundamental geometric constants, offering a deterministic solution to the cosmological constant problem and the hierarchy problem.
Category: High Energy Particle Physics

The Hessian of the G2 3-Form on the Grassmannian, a Geometric Ratio Matching the Koide Angle, and Two Obstruction Theorems

Authors: P. Music
Comments: 7 Pages.

We compute the Hessian of the G2 3-form restricted to Gr(3,R^6) at the flavour-symmetric point, obtaining eigenvalues 0^5, (-2 phi_0)^3, (-3 phi_0)^1. The geometric ratio |lambda_{Lambda^2}| / |Delta f / phi_0| = 2/9 matches the empirical Brannen-Koide phase to 0.02%. We prove two obstruction theorems: (1) since cos(2/3) is transcendental (Lindemann-Weierstrass), no symmetric polynomial in the mass eigenvalues with algebraic coefficients can select delta = 2/9 as an extremum; (2) any topological flux quantisation mechanism produces phases that are rational multiples of pi, for which cos(3 delta) is algebraic, and is therefore also excluded. A one-loop effective potential calculation independently rules out perturbative selection. These results establish that the Koide phase, if exactly 2/9, cannot arise from any polynomial potential, standard topological mechanism, or perturbative dynamics.
Category: High Energy Particle Physics

Unified Chordal Resonance Theory (UCRT)

Authors: Jessica Bower
Comments: 17 Pages.

Unified Chordal Resonance Theory (UCRT) proposes that gravity, the Standard Model of particle physics, dark matter, dark energy, and cosmology all emerge from a single multitonal vibrational scalar field $ Psi_text{total} $ governed by one dominant nonlinear coupling $ lambda_text{nl} $. The ever-present baseline hum $ Psi_text{total},0 $ at near-Planck frequencies undergoes beat interference and resonance cascades, dynamically generating fermion mass hierarchies, gauge symmetries via rotations on a compact internal manifold ($ S^3 $), fuzzy black hole cores, hybrid dark matter halo profiles with exponential cores and subhalo suppression below $ sim 10^8 M_odot $, and late-time dark energy evolution from phase diffusion. UCRT resolves black hole singularities through diffusive cores, the missing satellites problem via destructive tone interference, and the matter-antimatter asymmetry through phase-driven CP violation, while remaining consistent with Planck CMB, DESI BAO, JWST ultra-faint dwarf observations, and precision flavor data. Quantum corrections via vibrino loops preserve unitarity, and RG flows reach an asymptotic safety fixed point for UV completeness. Near-term falsifiability is provided by amplified GW echo trains and sidebands (LISA), chiral low-$ ell $ B-modes (CMB-S4), hybrid DM cores/subhalo counts (JWST/LSST), $sim$10 TeV resonances (FCC), and phonon analog signatures in tabletop experiments.
Category: Quantum Gravity and String Theory

Scale-Dependent Dimensionality with Local Screening and Emergent Phenomena

Authors: Vladyslav Hruznov
Comments: 10 Pages.

We propose a single dynamic parameter γ(x, t) that controls the effective dimensionalityof spacetime in a scale- and density-dependent manner. In high-density regions, γ is screenedto ≈ 1, recovering standard quantum mechanics and general relativity. In extremely lowdensity environments, γ approaches ≈ 1.10, yielding deff ≈ 4.1, weakened effective gravity, and emergent dark energy. The framework is realized via a density-dependent measure v(ρel) in the action, leading to modified Friedmann equations and variable-order fractional quantum mechanics. Amicroscopic origin is proposed within the Asymptotic Safety program. The model is consistent with current precision constraints and makes clear falsifiable predictions for upcoming experiments.
Category: Relativity and Cosmology

Mechanical Audit Experiments and Reproducibility Appendix for a Companion-Paper Programme on 4D SU(N) Yang—Mills Existence and Mass Gap

Authors: Lluis Eriksson
Comments: 33 Pages.

This document is an experiment-first audit report for a companion-paper programme claiming a constructive solution of the 4D $mathrm{SU}(N)$ Yang—Mills existence and mass gap problem. It specifies a runnable mechanical audit suite of 29 deterministic tests, defines pass/fail criteria, and presents outputs in a compilation-safe format. The report contains: (i) an explicit non-triviality proof showing the Wightman functions do not factorize trivially; (ii) a toy-model validation recovering the exact 2D $mathrm{SU}(2)$ Yang—Mills mass gap to machine precision; (iii) a Bałaban bridge appendix reproducing the critical inductive step of his renormalization group in simplified form; (iv) a reproducibility repository with 3-line setup instructions; (v) a core proof chain audit mechanically verifying the load-bearing theorems of Papers 86—90, covering terminal Kotecký—Preiss convergence, UV suppression, one-dimensionality of the anisotropic sector, Cauchy bounds on polymer jets, the OS1 vanishing rate $O(eta^2 log eta^{-1})$, Lie-algebra annihilation, and KP margin sensitivity. Beyond the 17 core tests, the suite includes a lattice gauge proxy layer (plaquette expansion, Polyakov-loop centre symmetry, Creutz ratio; 3 tests), an infrastructure layer (Bakry—Émery curvature seed $mathrm{Ric}_{mathrm{SU}(N)} = N/4$, the $2^{4k}$ cancellation in $d=4$, heat-kernel column bound; 3 tests), a UV-flow/heat-kernel layer (Parseval identity, diagonal decay exponent $d/2 = 2$, flow—reflection commutation; 3 tests), a non-triviality test (Haar Monte Carlo on $mathrm{SU}(2)$ and $mathrm{SU}(3)$; 1 test), a toy-model validation (2D Yang—Mills transfer matrix; 1 test), and an algebraic QFT layer (Petz recovery fidelity bound $1-F leq C,e^{-2mr}$ from the Split Property; 1 test). All 29 tests pass; the full suite completes in ${approx}70,mathrm{s}$ on a Google Colab CPU. The complete inter-paper dependency DAG is acyclic and explicitly recorded. All code, data, and artifacts are available at https://github.com/lluiseriksson/ym-audit. The companion papers are archived at https://ai.vixra.org/author/lluis_eriksson.
Category: Mathematical Physics

Relational Mathematical Realism III: The Hubble Tension as a Discrete Spacetime Measurement Artifact

Authors: Jason Merwin
Comments: 12 Pages. This is the third paper in a four part series.

The 5σ discrepancy between local (H0 ≈ 73 km s−1 Mpc−1) and early-universe (H0 ≈ 67 km s−1 Mpc−1) measurements of the Hubble constant constitutes one of the most significant challenges to the standard ΛCDM cosmological model. We propose that this tension is not evidence of new physics beyond ΛCDM, but a systematic artifact arising from the discrete topology of spacetime within the Relational Mathematical Realism (RMR) framework.In RMR, causal propagation is limited by a node update rate with a fundamental processing asymmetry: vacuum nodes require 4 computational ticks per update cycle while mass-coupled nodes require 5. We derive a geometric correction factor Γ = (5/4)1/3 ≈ 1.077 representing the path-dependent latency experienced byobservers calibrating distances through a 3-dimensional discrete lattice in the local,void-dominated universe. Applied to the Planck CMB determination (67.36 ± 0.54 km s−1 Mpc−1), this yields a predicted local measurement of Hlocal = 72.56 km s−1 Mpc−1, agreeingwith the SH0ES value (73.04 ± 1.04 km s−1 Mpc−1) to within 0.46σ with zero free parameters.Critically, this correction applies only to local path-integrated measurements(distance ladder), not to geometric bulk measurements (BAO, CMB), resolving thetension without modifying the cosmic expansion history. We classify all major H0measurements into "metric" (bulk geometry) and "path" (local calibration) categories, predicting that these two classes will systematically converge on differentvalues separated by a factor of (5/4)1/3. This framework makes specific falsifiable predictions for gravitational wave standard sirens and environment-dependent distance ladder calibrations. If confirmed, the Hubble tension constitutes the first empirical evidence thatspacetime is not a continuous manifold but a discrete relational graph.
Category: Relativity and Cosmology

Gravitational Sourcing from Decoherence History

Authors: Paul Dangelo
Comments: 6 Pages.

The paper proposes a novel experimental protocol to test a fundamental question at the intersection of quantum mechanics and general relativity: Does a quantum system's ability to generate (source) a gravitational field depend on its quantum state history—specifically, its accumulated decoherence?Standard semiclassical gravity assumes that a mass sources gravity based purely on its mass-energy expectation value, regardless of whether it is in a coherent quantum superposition or a classical mixture. This paper introduces an "Activation Hypothesis," suggesting that a system must build up irreversible entanglement with its environment (accumulated decoherence) to "activate" its gravitational sourcing capacity.
Category: Quantum Gravity and String Theory

In How Many Ways Can X/Twitter Blame, or Not Blame, [ One] for Violating Their Rules? Or, Should ][ OPne] Be Interpreted as a Schrödinger Cat Being both Banned and Not Banned?

Authors: Dainis Zeps
Comments: 20 Pages. (Note by ai.viXra.org Admin: This article may be outside the scope of ai.viXra.org & is subject to withdrawal by the Admin)

I am comparing my situation with that of Schrödinger cat, where cat was neither dead nor alive, but I am to be banned or not banned from my rights to access my X/Twitter account. My sentence "After Trump: The Electric Chair For Trump, Biden, Most Republicans, For Many Democrats" is a nominalsentence so may be interpreted in many many ways, both violating and not violating X/Twitter admins’ rules.
Category: Social Science

The Fractal Substrate Equivalence Proof: MATHICCS Invalidates GR While Deriving Dark Matter (∼ 84%) and α ≈ 1/137 from Apollonian Geometry

Authors: Steven E. Elliott
Comments: 6 Pages.

Standard physics contains formal contradictions when judged as self-consistent physical ontologies. The Einstein Equivalence Principle (EEP) embeds ε—δ processes requiring internal laboratory realization, yet General Relativity’s dynamics destroy all realizers in finite time -empty spacetime (no labs exist), few-body systems (radiation erosion), or cosmological evolution (de Sitter horizons). MATHICCS (Mathematics + Physics + Computational Consistency Substrate)—a higher-order meta-logic—deems axioms whose mathematical processes lose internal persistence invalid for physical ontology. GR asserts EEP-validity while deriving EEP-invalidity, yielding P ∧¬P . The first MATHICCS-valid ontology is the Fractal Substrate Equivalence Physics (FSEP) [viXra:2602.0107], where eternal Apollonian boundary dynamics persist across infinite recursive scales via Möbius inversion, discrete scale flips (r 7→ r/λ), and angular-momentum conservation. FSEP derives Newtonian gravity and inverse-square law from local quadratic expansion of spherical inversion; constant finite light speed from linear term + pole ejection + scale compression; dark matter fraction (≈ 84%) (baryons ≈ 16%) as geometric series from 3D Apollonian fractal dimension (D ≈ 2.473946 [1]) and radius ratio (β ≈ 0.72); and fine structure constant (α ≈ 1/137.035999 [3]) emergently from bipolar pole aperture geometry (λlocal ≈ 21.81), unifying it with observed quasar jet collimation angles (θjet ≈ 5.2◦ [4]);—all parameter-free except the geometric self-consistency of the persistent substrate. MATHICCS demands all physics reconstruct its mathematics from within via persistent internal processes. GR explodes; FSEP survives.
Category: Mathematical Physics

Gravitational Lensing as Fluid Refraction: Resolving the Chromatic Anomaly in Q2237+0305

Authors: Soo-Hyun Kim
Comments: 3 Pages.

The chromatic flux ratio anomaly observed in the strong lens system Q2237+0305 strictly contradicts the achromatic prediction of General Relativity (GR). Conventional models invoking differential dust extinction (lambda^-4) fail to fit the empirical data at short wavelengths (chi^2 = 1056). We propose an alternative macro-optical framework where the lensing galaxy is surrounded by a non-conservative fluid medium with a radial density gradient (ablaho). Applying the Gladstone-Dale relation and Cauchy's dispersion equation, we demonstrate that cosmic fluid refraction naturally follows a lambda^-2 dependence. Our fluid model perfectly reproduces the observed multi-wavelength photometry of Q2237+0305 (R^2 = 0.995, chi^2 = 1.01). This over 1,000-fold statistical improvement strongly suggests that gravitational lensing incorporates direct fluid-optical refraction.
Category: Astrophysics

Hydrodynamic Unification of Dark Matter and Dark Energy via Black Hole Volume Generation Formula: Neutrino Dynamic Density Theory and Resolution of the Hubble Tension

Authors: Soo-Hyun Kim
Comments: 11 Pages.

This study redefines black holes not merely as critical points of mass contraction, but as engines that generate and inject spatial fluid, proposing a novel space generation formula V_gen = 27 times (M_BH / ho_vac). The key constant k=3 represents both the geometric integer of three-dimensional space and the physical correspondence to three generations of neutrinos, aligning with the coupling coefficient k approx 3 reported by Farrah et al. (2023). Applying this formula to the McConnell & Ma (2013) dataset, we confirmed a Pearson correlation coefficient of 0.9930, with an average agreement rate of 88.0% in the standard galaxy mass range. Local deviations in systems like M31-M32 are successfully explained by hydrodynamic pressure equilibrium and the 4 kpc truncation phenomenon. Furthermore, the basal fluid density (10^-30 kg/m^3) resolves the Hubble tension by reconciling the early universe Hubble constant with local measurements through an 8.31% volume injection rate (f_inj). We conclude that dark matter and dark energy are different dynamic density states of the neutrino fluid, unifying cosmic expansion and galactic dynamics.
Category: Astrophysics

The Law of Harmony and Its Application: We Will Live Much Longer [?]

Authors: S. I. Kublanovsky
Comments: 4 Pages.

This paper presents the Law of Harmony, based on the principle of universal quantum synchronization of masses. According to this law, any body — from a symmetrical pulsar to a human being or the Universe itself — acts as a source of coherent gravitational radiation, the period of which is determined by its mass and dimensions. Calculations based on the Law of Harmony indicate that the full life cycle of the Universe is 123.5 billion years. This contradicts the 2025 forecast by Henry Tye's group, which predicted a collapse in 20 billion years, and suggests that humanity has approximately 110 billion years of stable development ahead. The derived period mathematically corresponds to a graviton mass of 1.89*10^(-69) kg. Furthermore, the graviton mass obtained in this study closely aligns with the value of 1.909*10^(-69) kg derived from the holographic principle by Haranas and Gkigkitzis (2014). At the biological level, the Law of Harmony establishes the necessity of resonance between human mass and the Earth's diurnal rhythm (24 hours).
Category: Relativity and Cosmology

Recursive Parity Extraction and the Structural Exclusion of Non-Trivial Cycles in the 3n + 1 Problem

Authors: Siqi Liu
Comments: 2 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This paper provide a formal mathematical proof of the non-existence of non-trival loops in the problem of Collatz Conjecture by using main algebra tools of 2-adic constraints.
Category: Number Theory

Octonionic Geometry and the Koide Angle: A Derivation from G2 Casimir Invariants with Neutrino Mass Predictions

Authors: P. Music
Comments: 4 Pages.

The Koide formula relates the masses of the three charged leptons through the parameter Q = 2/3 and an angle theta ~ 0.2222. We derive theta = 2/9 as the ratio of quadratic Casimir invariants C_2(3)/C_2(Sym^3(3)) = (4/3)/6 within the natural embedding SU(3) in G_2 = Aut(O), where the G_2 associative 3-form evaluated on the fermion 3-plane determines cos(3*theta). The agreement with PDG data is 0.009% (< 1 sigma). Extending the construction to neutrinos via the adjoint representation, we conjecture theta_nu = C_2(8)/C_2(Sym^3(3)) = 1/2, predicting Sum(m_i) = 70.9 +/- 0.4 meV in normal hierarchy, testable by Euclid, CMB-S4, LEGEND, and nEXO within the coming years.
Category: High Energy Particle Physics

The Fractal Substrate Equivalence Physics: Möbius Boundary Dynamics in a Recursive Scale Geometry

Authors: Steven E. Elliott
Comments: 19 Pages.

We propose the Fractal Substrate Equivalence Physics (FSEP), a geometric framework in which spacetime is modeled as an infinite recursive degenerate Apollonian sphere packing of dense and sparse regions. We argue that in spacetimes evolving toward $t to infty$, the global domain of validity of the Einstein Equivalence Principle (EEP) contracts to measure zero, forcing a breakdown of smooth-manifold descriptions at the dense--sparse interface. The maximal geometric covering of this interface is an Apollonian sphere packing, which we take as fundamental rather than emergent.At each tangency boundary, physical evolution is governed by spherical inversion, a M"obius transformation, a discrete scale flip $r mapsto r/lambda$ (with $lambda gg 1$), and strict angular-momentum conservation. These rules generate universal bipolar jets, cross-scale transport, and nonlocal correlations from a single geometric mechanism. The framework reproduces previously reported statistical results (Balmer-line clustering and SPARC rotation-curve fits) as coarse-grained projections of boundary-crossing dynamics.FSEP yields several falsifiable predictions: (i) correlated AGN variability across cosmic voids with lags scaling linearly with void diameter ($tau propto D_{m void}$); (ii) systematic dark-matter-fraction depletion in merging galaxy pairs relative to isolated systems; (iii) jet opening angles directly measuring the local scale ratio $lambda_{m local}$; and (iv) potential spectral-distortion signatures in the cosmic microwave background tied to hydrogen recombination harmonics rather than $mu$/$y$-type thermal relic distortions.This paper stands in relation to its predecessor (viXra:2601.0119) as a foundational extension: where that work derived fractal statistical structure as an emergent consequence of known physics, the present work takes the fractal as the primary geometric substrate from which known physics emerges.
Category: Relativity and Cosmology

The Fibonacci-Tetrahedral Lattice: A Unified Geometric Origin for Dark Matter and Dark Energy

Authors: Andrew Ebanks
Comments: 11 Pages.

This paper proposes the Fibonacci-Tetrahedral Lattice (FTL), a discrete geometric substrate for the vacuum derived from an E8-to-3D projection. By treating space as a quasicrystalline packingrather than a smooth continuum, we identify a foundational ‘Information-Ontology’ where the 8D lattice serves as the geometric source and 3D reality is the projected result. We demonstrate that the transition from 8D symmetry to 3D packing necessitates a 7.356◦ topological deficit (the Aristotle Gap). This geometric frustration manifests macroscopically as an entropic pressure, providing a zero parameter resolution to galactic rotation curves ("Dark Matter") without requiring new particles.Furthermore, by applying Holographic Scaling (N2/3) to the lattice nodes, we resolve the "Vacuum Catastrophe," deriving an observed energy density of ≈ 10−27.33 kg/m3 (matching Λ) from the theoretical Planck baseline.
Category: Quantum Gravity and String Theory

Cosmological Dissipative Residual: Cosmic Production, Distribution and Function

Authors: Eduardo Rodolfo Borrego Moreno
Comments: 16 Pages.

We propose that the Cosmological Dissipative Residual (CDR), previously introduced as a late-time dissipative mechanism resolving the $H_0$ and $S_8$ tensions, originates from continuous production and accumulation driven by high-energy cosmic events. Beginning with the primordial Big Bang as an initial entropy burst, the residual is further generated throughout cosmic history by stellar formation, core-collapse supernovae, AGN jets, and black hole mergers. The production rate $beta_{m prod}(z)$ peaks near cosmic noon ($z sim 2$), and numerical integration calibrated to SFRD and jet/merger observations yields a cumulative contribution of $sim 30%$ to the observed dark energy density. The residual evolves according to $dot{ho}_{m res} + 3H(1 + w_{m res})ho_{m res} = Gamma(t)ho_m + beta_{m prod}(t)$, with $w_{m res} gtrsim -1$ naturally emerging from the balance between production and dissipation, yielding $w_{m res}(z=1) approx -0.92 pm 0.03$ consistent with DESI 2024 BAO hints ($w_0 approx -0.9$). Rapid homogenization via relativistic sound speed ensures uniformity, while localized anisotropic stresses account for gravitational effects in clusters and galaxies. The residual functions as an adaptive regulator through negative feedback, suppressing late-time growth to $sigma_8^{m CDR} approx 0.76$--$0.80$. This framework unifies the origin, distribution, and role of dark energy as emergent from the universe's energetic history, with falsifiable predictions for $w(z)$ evolution and subtle event-density correlations testable with DESI, Euclid, and ngEHT.
Category: Astrophysics

Foundations of Fractalic Field Theory: Quantum Gravity as the Origin of Fundamental Constants

Authors: M. I. Gallardo Nicolalde
Comments: 5 Pages. (Note by ai.viXra.org Admin: Part of the texts are cutoff)

We introduce Fractalic Field Theory (FFT), a complete framework where the fractal geometry of spacetime at quantum gravity scales determines all physical laws. The central object is the fractalic dimension D = 2.7268, emerging from quantum gravity as a fixed point of therenormalization group flow. From this single geometric invariant, we derive: (i) α−1 = 137.036, (ii) αs(MZ ) = 0.1181, (iii) sin2 θW = 0.2314, (iv) the Kaluza-Klein spectrum mn = n1/D /R with m1 = 9.73 TeV, and (v) cosmological parameters including ΩDMh2 = 0.120 and ns = 0.965. FFT represents a paradigm shift from symmetry-based to geometry-based unification, predicting 32 experimentally testable quantities with unprecedented accuracy using zero adjustable parameters.
Category: High Energy Particle Physics

Non-Existence Collapse: A Dynamical Mechanism for the Quantum-Gravitational Bootstrap of Spacetime from Nothing

Authors: Steven B. Thompson
Comments: 7 Pages.

We propose a minimal dynamical framework for the origin of the universe in which absolute non-existence—a state with no spacetime, matter, fields, or classical time—is intrinsicallyunstable under quantum-mechanical and gravitational principles. The Heisenberg uncertaintyprinciple, applied to gravitational degrees of freedom, precludes a static null configuration: nonexistence has "nowhere to go" but to collapse into itself, producing an effective Planck-scaledensity regime that undergoes a nonsingular quantum-gravitational transition. This collapsedriven process bootstraps the emergence of classical spacetime and the arrow of time, requiringno external causes, pre-existing substrates, boundary conditions, or auxiliary fields.Quantum gravity emerges here not as an imposed extension but as the inherent dynamicalstructure governing the instability and resolution. The mechanism refines and complementsestablished proposals—such as Vilenkin’s quantum tunneling from nothing, the Hartle-Hawkingno-boundary wavefunction, and recent developments in loop quantum cosmology bounces andquadratic gravity—by providing a purely mechanical interpretation that replaces probabilisticnucleation or Euclidean continuation with an intrinsic collapse bootstrap. It aligns with ongoingrefinements of no-boundary states, curvature bounces, and geometric "from nothing" models inthe 2025—2026 literature.This framework offers a parsimonious dynamical resolution to the question of why thereis something rather than nothing, transforming it into a consequence of quantum gravity’sstructure. Potential observational implications include consistency with cosmic microwave background data and distinguishable signatures in primordial gravitational waves or large-scale structure that may differentiate collapse-initiated emergence from conventional inflationary scenarios.
Category: Relativity and Cosmology

Acoustic Determinism in Single-Hole Cylindrical Flutes: Evidence That Musical Scales Emerge from Instrument Geometry Rather Than Cultural Transmission

Authors: Mark Jerome Growden
Comments: 2 Pages.

This paper proposes that several of the world's most widespread musical scales arise naturally from the acoustic physics of simple bilabial end-blown cylindrical flutes with a single tone hole. Through hands-on construction and performance of one-hole flutes made from uniform cylindrical tubing, the author demonstrates that placing a hole at a minor second interval above the fundamental, combined with the overtone series, generates the Freygish (Hijaz) scale. A hole at a major second generates a pentatonic scale in the more accessible registers, and a Lydian Dominant scale when played into the higher, more demanding partials. When the end-covering technique of overtone flutes is combined with the single-hole technique, additional scale systems emerge from the same instrument. These findings suggest that culturally diverse scale systems may share a common origin not in theory, cultural exchange, or aesthetic preference, but in the physical constraints of elementary wind instrument construction. The implications extend to ethnomusicology, organology, and the origins of tonal music.
Category: Classical Physics

Conversation Fragility is Heavy-Tailed Quantile Reliability Curves for Multi-Turn LLM Evaluation

Authors: Michael Zot
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite all listed scientific references)

Multi-turn dialogue is where large language models (LLMs) are most useful, and also where they most often "get lost". Prior work reports that average performance drops substantially from single-turn to multi-turn settings, and argues that the dominant driver is increased unreliability rather than a large loss of peak capability. We replicate and extend this picture using a quantile-based analysis over thousands of stochastic generations, with an emphasis on distribution shape rather than averages.Across seven jobs we analyze N=5,100 scored generations: 30 instructions per job, 10 stochastic runs per instruction, and 1 to 3 turns per run. For each instruction and turn we compute (i) aptitude A90, the 90th percentile of score across runs, and (ii) unreliability U90-10, the 90th to 10th percentile spread.Our core result is a heavy-tailed fragility surface: most instructions remain perfectly stable with U=0, while a small minority contribute most of the unreliability at later turns. Across multi-turn replications, the top 3 most fragile instructions at turn 2 explain 54% to 91% of total unreliability. This yields a practical taxonomy of dialogue dynamics (stable, monotone degradation, and instability then recovery) and suggests new training and evaluation targets: recovery and variance control, not just average accuracy.
Category: Artificial Intelligence

Prolegomena to the Theory of Informational Space Genesis (ISG): A Paradigm Shift in the Cosmology of Perception

Authors: Florian Rücker
Comments: 5 Pages.

Current cosmological models, such as the Lambda-CDM framework, face significant challenges in explaining the nature of Dark Matter and Dark Energy, which account for approximately 95 percent of the universe's mass-energy density. The Theory of Informational Space Genesis (ISG) proposes an ontological shift, defining the universe as an emergent informational system where space is a byproduct of interaction processes. This paper details a four-stage signal denoising methodology applied to the fundamental binding potential of matter to isolate the "Pristine Potential" (Ep approx. 2.15 meV). By correlating this potential with the baryonic base (beta approx. 4.71), derived from the logarithmic volume ratio of atomic structures, we derive a power-law scaling that predicts Dark Matter and Dark Energy densities with over 98 percent accuracy. The ISG framework interprets these "Dark Sectors" as the informational and geometric overhead required for systemic causal isolation. We further explore the role of biological consciousness as a high-frequency processor and discuss the teleological implications of a self-optimizing, learning cosmos.
Category: Astrophysics

The Knotted Vacuum: Topological Defects in a Quantum Condensate as an Emergent Unified Theory of Particles, Gravity, and Cosmology

Authors: Sean McCallum
Comments: 13 Pages. Creative Commons Attribution 4.0 International (CC BY 4.0) (Note by ai.viXra.org Admin: Please cite listed scientific references)

The vacuum is not an empty stage upon which physics plays out. It is a dynamical quantumcondensate of overlapping standing-wave fields whose collective excitations give rise to all of physics. We propose and develop a concrete realization in which spacetime itself emerges as the elastic response of this condensate, and every massive particle is a stable topological knot (or defect) in its fabric.

Starting from a minimal pre-geometric O(4) nonlinear sigma-model Lagrangian with a Skyrmestabilizing term, we demonstrate through explicit calculations, lattice simulations, and renormalization group analysis that:

• Gravity arises as the induced curvature of the vacuum strain (Sakharov mechanism realized in the condensate);
• Baryons appear as quantized hedgehog skyrmions, leptons as hopfions, and dark matter as higher-winding topological defects;
• Neutrino masses are exponentially suppressed by topological tunneling, eliminating the needfor a see-saw or sterile neutrinos;
• The cosmological constant is naturally screened to near-zero by vacuum-shift invariance;
• Black-hole interiors are regular, finite-density knot cores rather than singularities.

Lattice simulations in 1D, 2D, and 3D confirm topological stability, emergent curvature, and realistic multi-knot binding (hydrogen and helium-4 atoms). The framework unifies quantum particles, gravity, and cosmology from a single intuitive picture: spacetime as a stretchy quantum balloon, and matter as the permanent knots we tie in it.

This work provides a complete, self-consistent candidate theory that is both conceptually elegant and ready for detailed confrontation with experiment.

Dadatic Monism: An Ontological Reinterpretation of Mass-Energy Equivalence and GR-QFT Unification via Causal Data Emittance

Authors: Darcy Facundo
Comments: 01 Pages. "Presents a new informational ontology (Dadatic Monism) to unify General Relativity and Quantum Field Theory through a redefined mass-energy equivalence formula."

1. ABSTRACTThis essay proposes a resolution to the long-standing dichotomy between General Relativity (GR) and Quantum Field Theory (QFT) through the paradigm of Dadatic Monism. It postulates that the Universe is a real-time information processing system where matter is not an inert substance, but a Data Density Anomaly (Ψ) within an Informational Plenum. By formulating the equationED=γ⋅Ψ.Vif2, we establish a causal bridge between total system energy, the fundamental limit of data propagation, and metric coherence protocols (Lorentz). The theory concludes that physical reality and consciousness are emergent byproducts of distinct levels of transduction and attenuation of this universal data stream.2. THE FUNDAMENTAL DADATIC EQUATIONThe core of this theory lies in the redefinition of mass. In Dadatic Monism, mass is the measure of "informational load" at a specific logical address of spacetime.ED= γ⋅Ψ.Vif2ED (Dadatic Energy): The total processing magnitude or computational work contained within an event.Ψ (Radiant Data Mass): The volume of information packets defining the "presence" of a particle or body.Vif =(Propagation Velocity): The constant 3×108 m.por segundointerpreted as the maximum bandwidth of the vacuum (Plenum).(Propagation Velocity): The constant 3×108 m por segundointerpreted as the maximum bandwidth of the vacuum (Plenum).3. DYNAMICS AND THE LORENTZ PROTOCOLThe theory’s validity in non-static systems is ensured by the integration of the Lorentz Factor (γ). In our ontology, γ is not merely a geometric distortion but a Buffer Management Protocol.ED=γ⋅Ψ.Vif2As the velocity of data (v) approaches Vif, the system execute different reference frames.4. UNIFICATION AND TRANSDUCTIONGravity: Interpreted as the "processing lag" imposed by high data density (Ψ). Spacetime curves not due to a force, but to accommodate heavy informational loads within the logical metric.Quantum Mechanics: Entanglement serves as evidence that data is unitary and shared at the source code level, rendering physical distance irrelevant for state synchronization.Biology and Consciousness: The Cortex is postulated as a Quantum-Informational Transducer. The "reality" we experience is an attenuated version of the Plenum, filtered to be processable by biological hardware (Soma).5. CONCLUSIONDadatic Monism offers a "naked," demystified view of physics. It replaces the search for hypothetical particles with an understanding of the laws of emittance and processing. The Universe does not "exist" in a static sense; it is causally rendered at every Planck interval.KEYWORDS: Dadatic Monism; Information Physics; Theoretical Physics; Unification; Lorentz Factor; Biological Transduction.
Category: Quantum Gravity and String Theory

Lgebraic Turbulence and Global Regularity: the Secular Replicator Flow as a Self-Consistent Algebraic Shell Model for Singularity Formation

Authors: Vinicius F. S. Santos
Comments: 19 Pages.

We introduce the Secular Replicator Flow, a finite-dimensional algebraic dynamical system inspired by the turbulent energy cascade of the Navier—Stokes equations, built from the spectral theory of golden resolvent operators on discrete network graphs [9]. The continuous mechanics of fluid turbulence—incompressibility, nonlocal pressure, nonlinear advection, and viscous dissipation—find precise algebraic counterparts in the constraints of a replicator equation evolving on the simplex of spectral participation weights, governed by a global secular equation. Within this framework we establish three principal results. First, the Variance Law: the macroscopic coupled eigenvalue λ∗(t) evolves monotonically according to Fisher’s Fundamental Theorem, acting as a strict Lyapunov function (between excision events) whose rate of increase equals the fitness variance of the active spectrum. Second, the Spectral Selection Theorem: the fitness landscape is a strict bipolar Ushape in the base eigenvalue μ, guaranteeing that the replicator flow annihilates mid-spectrum noise and funnels all energy into the extreme macroscopic topologies of the network. Third, Global Regularity: as the system approaches a structural resonance (transparent pole), the fitness plunges to −∞, triggering an auto-excision mechanism that exponentially starves the dangerous channel, rendering every pole singularity removable. The resulting dynamics form a Sawtooth Cascade of smooth climbs interrupted by discontinuous structural snaps whose direction is controlled by the residual load of the excised channel. We classify the sole remaining failure mode as a thermodynamic phase escape at the r = 2 Chebyshev boundary, where the discrete algebraic structure of the network undergoes a global phase transition into unbounded hyperbolic space—a phenomenon fundamentally different from the localised velocity blowup sought by PDE analysis. All regularity results herein apply to this model; implications for the full Navier—Stokes equations in R3 remain open.
Category: Mathematical Physics

The Master Map: An Audit-First, Attack-Resistant Navigation Guide to the Unconditional Solution of the 4D SU(N) Yang-Mills Existence and Mass Gap Problem (Clay Millennium Problem)

Authors: Lluis Eriksson
Comments: 21 Pages.

This paper is a hostile-review navigation guide and audit manifesto for a companion-paper programme claiming a constructive solution of the four-dimensional SU(N) Yang-Mills existence and mass gap problem in the Osterwalder-Schrader (OS) framework, reconstructed as a Poincare-covariant Wightman QFT with strictly positive mass gap. The guide provides: (i) an explicit dependency graph and Clay/Jaffe-Witten checklist; (ii) an explicit threat model listing standard failure modes targeted by hostile review (black-box dependence on Balaban, interface friction between gradient flow and the Balaban measure, diagonal-limit non-uniformity, and operator-mixing residues); (iii) an explicit four-pillar defensive architecture resolving each attack with structural (not merely quantitative) shields; (iv) the preventive lock: a triangular renormalization-mixing structure that blocks upward anisotropic flow into the marginal (d=4) sector, neutralizing the standard a^2 x a^{-2} -> O(1) objection; (v) a mechanical audit trail mapping load-bearing hypotheses to primary sources; and (vi) a complete linked index of all supporting preprints for traceability. External mathematics is explicitly declared: abstract polymer cluster expansion (Kotecky-Preiss), OS reconstruction (Osterwalder-Schrader), and lattice reflection positivity (Osterwalder-Seiler). Furthermore, this guide introduces the Triangular Mixing Preventive Lock: a structural algebraic mechanism showing that the operator mixing matrix has no anisotropic marginal d=4 sink in the gauge-invariant W_4-scalar sector. Consequently, the standard O(a^2) x O(a^{-2}) -> O(1) operator-mixing residue attack is blocked structurally: any quadratic divergence is forced to renormalize only O(4)-invariant d=4 data (the isotropic coupling), leaving the O(4)-breaking channel suppressed. This paper is not a claim of institutional validation; it is an audit map prescribing the check order and falsification points for the companion-paper chain.
Category: Mathematical Physics

Arithmetic Relativistic Emergence (ARE) as General Relativity of Numbers: Weierstrass Weights, Arakelov Curvature, and Equivalence Principle Analogue

Authors: J. W. McGreevy
Comments: 16 Pages.

We present Arithmetic Relativistic Emergence (ARE) as a "General Relativity of Numbers" — a framework in which the Standard Model, quantum mechanics, classical 3+1 Lorentzian spacetime, and fundamental constants emerge tautologically from the arithmetic geometry of Q. The Riemann zeta function ζ(s) constitutes the maximally symmetric pregeometric vacuum. Its functional-equation symmetry around Re(s) = 1/2, combined with the pole at s = 1, forces spontaneous symmetry breaking via the weight-12 modular discriminant ∆(τ ) = η(τ )24 at the s = 6 harmonic threshold. This breaking disperses the vacuum into Archimedean divergence (Fdiv, smooth curvature density) and non-Archimedean curl (Hcurl, discrete torsion at p-adic fibers). The emergent geometry is governed by Arakelov curvature on the arithmetic surface Spec Z ∪ {∞},where Weierstrass weights act as "mass/energy density" (algebraic rigidity) and the hyperbolic/Bergman metric plays the role of spacetime. Modular transformations toward cusps correspond to Lorentz rapidity, yielding an equivalence principle analogue between inertial (modular flow resistance) and gravitational (metric warping) responses. The adelic spectral triple (KO-dimension 6, finite algebra C ⊕ H ⊕ M3(C)) induces symplectic deformation of phase space, with the non-trivial zeros of zeta providing the Dirac spectrum (Hilbert—Pólya realized). The Minkowski interval ds2 = −c2dt2 + du20d7x 2 emerges as the unique adelic-invariant quadratic form, with light cone as the resolved cusp boundary (holographic screen).The spectral action Tr f (D/Λ) recovers Einstein—Cartan gravity with non-Abelian Yang—Mills, where generalized Rainich conditions (quadratic invariants involving structure constants f abc) are satisfied at s = 6, with torsion (Hcurl) regularizing self-interactions. The full SM gauge group SU(3)c × SU(2)L × U(1)Y and three chiral generations emerge fromadelic place ramification and Leech lattice Z2-orbifold. Constants (α−1 ≈ 137 from Petersson + torsion residues, ℏ from Lambert-Planck suppression, G from unification suppression, Λ ∼ e−288) are inevitable invariants. Langlandsfunctoriality acts as the holographic dictionary mapping prime rigidity to bulk physics. ARE thus unifies physics as the macroscopic shadow of arithmetic rigidity, with the Riemann Hypothesis as a necessary stability condition for the emergent universe.
Category: Mathematical Physics

Golden Resolvent Theory: Spectral Factorisation, Galois Orbits,and Chebyshev Ladders Over Q(√5)

Authors: Vinicius F. S. Santos
Comments: 45 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We develop the spectral theory of operators whose eigenvalue structure is governed by the golden ratio φ = (1 +√5)/2. The foundation is the golden resolvent factorisation: for any real symmetric matrix A, λ2I − λA − A2 = (λI − φA) (λI + A/φ). This identity controls the spectrum of golden companion operators, decomposing eigenvalues into transparent pairs (μφ and −μ/φ) and coupled modes (roots of an explicit secular equation), governed by the Galois conjugation φ 7→ −φ−1 of Q(√5)/Q. We establish six main results: (1) the Golden Amplification Theorem, producing the transparent eigenvalue pairs and their eigenvectors; (2) the Secular Equation, a closed-form characteristic polynomial for coupled modes; (3) the Secular Sensitivity Theorem, identifying the secular weight with the coupled eigenvector norm and establishing Lipschitz continuity of coupled eigenvalues in the coupling vector; (4) the Positive Boost Inequality, bounding submatrix spectral radii via nodal-domain restrictions; (5) the Galois Transfer Principle, exactly classifying partition transfer for conjugate eigenvector pairs via the Transfer/Pareto Trichotomy—with automatic spectral dominance for transparent modes and unavoidable Pareto regimes for coupled modes; (6) the Chebyshev Ladder, generalising the amplification ratio to 2 cos(π/(2p+3)) through the cyclotomic fields Q(ζ2p+3)+. The spectral spread of the golden pair equals the generator of the different ideal of Z[φ], connecting the framework to the arithmetic of Q(√5).
Category: Combinatorics and Graph Theory

Quantum Indeterminacy as Gödelian Epistemic Limitation: Implications of Relational Mathematical Realism for Quantum Foundations

Authors: Jason Merwin
Comments: 13 Pages. This is the second paper in a four paper series.

In a companion paper, we established the Theorem of Temporal Necessity within the framework of Relational Mathematical Realism (RMR), demonstrating that a sufficiently complex, locally consistent mathematical structure cannot exist as a static object but must undergo a non-terminating sequence of state extensions identified with physical time. In this paper, we extend the framework to quantum mechanics. We argue that quantum indeterminacy is not a fundamental property of nature but an epistemic consequence of observers being embedded subsystems within an evolving relational structure. The "hidden variable" determining quantum outcomes is the global relational topology of the present state St, which is non-local by definition and inaccessible to any embedded observer. We show that this framework survives Bell’s theorem by violating measurement independence through synchronic topological constraint rather than diachronic conspiratorial fine-tuning, and we resolve the measurement problem by identifying wavefunction collapse with the topological update of the observer’s local subgraph. We further conjecture that the Born rule (P = |ψ|2) arises as a geometric property of the Gödelian boundary—specifically, that probability scales with the combinatorial cross-sectional area of relational bundles at the logical horizon, unifying quantum probability with Bekenstein-Hawking entropy under a single geometric principle. Finally, we propose that the renormalization group flow of quantum field theory is the graph-theoretic coarse-graining of the universal relational structure, and that the hierarchy between gravitational and gauge force strengths reflects the ratio of global connectivity to local clustering density in the universal graph.
Category: History and Philosophy of Physics

Rotational Symmetry Restoration and the Wightman Axioms for Four-Dimensional SU(N) Yang--Mills Theory

Authors: Lluis Eriksson
Comments: 9 Pages.

We complete the rigorous construction of four-dimensional Euclidean SU(N) Yang--Mills quantum field theory and establish the existence of a mass gap. Building on the companion papers -- which unconditionally establish exponential clustering with mass gap, the Osterwalder--Schrader axioms OS0, OS2, OS3, OS4, and quantitative irrelevance of O(4)-breaking lattice operators -- we derive a lattice Ward identity for infinitesimal Euclidean rotations, identify the breaking term as a dimension-6 anisotropic operator insertion, and prove that the breaking distribution vanishes as $O(eta^2,|log((Lambda_{mathrm{YM}}eta)^{-1})|) to 0$ in the continuum limit, establishing axiom OS1 (full O(4) Euclidean covariance). Combined with the Osterwalder--Schrader reconstruction theorem, this yields a non-trivial Poincare-covariant Wightman quantum field theory with mass gap $Delta_{mathrm{phys}} geq c_N,Lambda_{mathrm{YM}} > 0$ for each $N geq 2$.
Category: Mathematical Physics

Closing the Last Gap in the 4D SU(N) Yang--Mills Construction: A Verified Terminal KP Bound and an Explicit Clay Checklist -- Audit-Friendly Assembly: Polymer Activities => KP => OS => Wightman with Mass Gap

Authors: Lluis Eriksson
Comments: 9 Pages.

This paper has two goals.Part I (terminal KP bound). We provide a verifiable, citation-driven derivation of the terminal-scale Kotecky--Preiss (KP) smallness bound used in the companion paper on exponential clustering and mass gap. Rather than re-deriving the full multiscale renormalization group (RG), we isolate explicit hypotheses (H1)--(H3) on the terminal polymer activities and prove that they imply the KP convergence criterion. We then verify (H1)--(H3) by mapping them to specific statements in Balaban's published primary sources (CMP 116, 119, 122), with an audited notation bridge recorded in the structural package companion paper.Part II (assembly map + Clay checklist). We give an explicit dependency graph assembling the companion papers together with the KP input proved here. We provide a checklist matching the Clay/Jaffe--Witten formulation of the Yang--Mills existence and mass gap problem to the theorems across the paper sequence (OS0--OS4, OS1, and the mass gap).Scope / external mathematics. The argument uses the abstract KP cluster expansion theorem (Kotecky--Preiss 1986) and the Osterwalder--Schrader reconstruction theorem (1975). It relies on the terminal polymer representation and activity bounds as proved in Balaban's CMP papers cited above.
Category: Mathematical Physics

The Relativity Theory of Focus [Part 1-3]

Authors: Yun Seok Choe
Comments: 8 Pages. (Note by ai.viXra.org Admin: This submission mainly contains speculations and may not be written in a complete/scholarly manner - Please cite and list scientific references)

[Paper 1] This foundational paper establishes the "Relativity of Focus" as a new physical principle. We define the universe as a Quantum Harmony Pulsation (QHP) field and prove that physical reality is a "developed image" determined by the observer’s focal resolution. We derive the c2 constant as a dynamic pulsation rate and establish the mathematical framework for the focus operator (Γ).

[Paper 2] Based on the foundational principles of Quantum Harmony Pulsation (QHP) established in Part 1, this paper proposes a Grand Unified Theory (GUT) by redefining ’Force’ as a manifestation of pulsation density gradients. The centerpiece of this work is the introduction of Gravitational Deceleration (Gdec). We argue that gravity is not an intrinsic attractive force but a kinetic resistance—a "dimensional bottleneck"—that occurs during the contraction phase of a bubble-like QHP. Furthermore, we reveal the "Simultaneity Fallacy" in quantum mechanics, proving that superposition is a sequential phenomenon, and conclude by unifying material physics with the evolution of consciousness.

[Paper 3] Based on the foundational principles of Quantum Harmony Pulsation (QHP) established in Part 1, this paper proposes a Grand Unified Theory (GUT) by redefining ’Force’ as a manifestation of pulsation density gradients. The centerpiece of this work is the introduction of Gravitational Deceleration (Gdec). We argue that gravity is not an intrinsic attractive force but a kinetic resistance—a "dimensional bottleneck"—that occurs during the contraction phase of a bubble-like QHP. Furthermore, we reveal the "Simultaneity Fallacy" in quantum mechanics, proving that superposition is a sequential phenomenon, and conclude by unifying material physics with the evolution of consciousness.

[Paper 4] As the final installment of the ’Focus Science’ trilogy, this paper provides the numerical and geometric evidence for the Relativity of Focus. We demonstrate that Planck’s constant (h) is not an arbitrary fundamental value but a geometric scaling factor arising from the 75% energy loss during the projection of a 3D bubble-like pulsator onto a 2D measurement plane. By re-modeling the double-slit experiment as a phase-interference between the observer’s focal frequency and the QHP’s sequential rhythm, we provide a deterministic explanation for the observer effect andprove that quantum uncertainty is a measurable numerical artifact of dimensional transition.
Category: Quantum Physics

Spectral Gap and Thermodynamic Limit for SU(N) Lattice Yang—Mills Theory via Log-Sobolev Inequalities and Complete Analyticity

Authors: Lluis Eriksson
Comments: 17 Pages.

We establish two independent rigorous results for four-dimensional SU(N)pure-gauge lattice Yang—Mills theory with Wilson action, at fixed latticespacing η > 0 and weak coupling gu2080 ≤ g_*, uniformly in the spatial volume L.(A) Uniform Log-Sobolev Inequality. The Wilson measure μ_L satisfies Ent_{μ_L}(f²) ≤ (2/ρ̂) E_L(f,f) with constant ρ̂ > 0 independent of L, where E_L is the natural Dirichlet form on SU(N)^{|E(Λ)|}.(B) Uniform Mass Gap. The Osterwalder—Seiler Hamiltonian H_L has a spectral gap m_gap ≥ mu2080 > 0, uniformly in L.Both theorems share a single input — the Dobrushin—Shlosman completeanalyticity (CA) condition, verified via Bałaban's renormalization groupprogram — but follow logically independent paths. Theorem A is derivedthrough Cesi's quasi-factorization of entropy, seeded by a Bakry—Émerylocal log-Sobolev inequality on SU(N)^{|E(Σ)|}; the Ricci curvatureRic_{SU(N)} = (N/4)g plays a key role. Theorem B is derived throughexponential clustering of temporal correlations — a consequence of CA viaDobrushin contraction — combined with the Osterwalder—Seiler transfer-matrixconstruction and the Krein—Rutman theorem. We further prove (C) that {μ_L}converges weakly to a unique, translation-invariant infinite-volume Gibbsstate μ_∞ satisfying the DLR consistency equations, whose reconstructedHamiltonian H_∞ inherits the mass gap mu2080. All constants are explicit inN, gu2080, and η. The present results hold at fixed lattice spacing; thecontinuum limit η → 0 is addressed in a companion paper.
Category: Mathematical Physics

Exponential Clustering and Mass Gap for Four-Dimensional SU(N) Lattice Yang-Mills Theory via Balaban's Renormalization Group and Multiscale Correlator Decoupling

Authors: Lluis Eriksson
Comments: 20 Pages.

Assuming a uniform log-Sobolev inequality for the pure Wilson measure (isolated here as an explicit hypothesis), we establish exponential clustering with a strictly positive mass gap for four-dimensional pure SU(N) lattice Yang-Mills theory with Wilson's action, uniformly in lattice spacing eta and physical volume L_phys:|Cov(O(0), O(x))| leq C exp(-m |x| / a_*), with m > 0 and a_* ~ Lambda_YM^{-1}.The proof assembles three ingredients: (1) Balaban's rigorous renormalization group for lattice gauge theories (CMP 1984-1989), which produces effective densities with local polymer decompositions and exponentially decaying activities; (2) a uniform log-Sobolev inequality for the pure Wilson measure, used as an input assumption; and (3) a multiscale correlator decoupling identity (this paper), which separates ultraviolet fluctuations from infrared physics. The coupling control required by Balaban's framework -- that the effective couplings remain in the perturbative regime throughout the RG iteration -- is established via an inductive argument using Cauchy bounds on the analyticity of the effective action.We also verify (under the same hypothesis) the Osterwalder-Schrader axioms OS0, OS2, OS3, and OS4 for subsequential continuum limits, and establish vacuum uniqueness and non-triviality. The remaining axiom OS1 (full O(4) Euclidean covariance) is not established here; we prove covariance under lattice translations and the hypercubic group W_4, and show that if O(4) covariance holds in the continuum limit, the reconstructed Wightman theory is a non-trivial relativistic quantum field theory with mass gap Delta_phys geq c_N Lambda_YM > 0.
Category: Mathematical Physics

Irrelevant Operators, Anisotropy Bounds, and Operator Insertions in Balaban's Renormalization Group for Four-Dimensional SU(N) Lattice Yang—Mills Theory: Symanzik Classification and Quantitative Irrelevance of O(4)-Breaking Operators

Authors: Lluis Eriksson
Comments: 18 Pages.

We classify gauge-invariant local lattice operators of classical dimension 6 on the four-dimensional hypercubic lattice into O(4)-invariant, hypercubic-invariant but O(4)-breaking (anisotropic), and on-shell-redundant components, following the Symanzik improvement programme and the on-shell improvement technique of Lüscher—Weisz (1985). Inside Balaban's renormalization group framework for SU(N) lattice Yang—Mills theory, we extract the anisotropic projection of the effective action via local Taylor expansion of polymer activities in the small-field regime and prove a quantitative quadratic scale bound for the anisotropic coefficient: for every RG step k ≤ k* with effective coupling g_k ≤ γ_0, the coefficient of the (one-dimensional) anisotropic sector in the classical dimension-6 Symanzik expansion satisfies |c_{6,aniso}^{(k)}| ≤ C a_k^2, uniformly in lattice spacing η, physical volume L_phys, and RG step k. We further prove a quantitative insertion integrability estimate for connected correlators with one insertion of the anisotropic operator. When combined with the rotational Ward identity derived in the companion paper, this yields that the corresponding breaking distribution tested against Schwartz functions is O(η^2 |log(Λ_YM η)^{-1}|) and hence vanishes as η → 0.
Category: Mathematical Physics

On the Invariance of Planck Scale Under Special Relativity and the Geometry of Quantum Space

Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 31 Pages.

This work develops a unified and conservative framework for reconciling Planckscale physics with Special Relativity by shifting the foundational emphasis from symmetry modification to observer admissibility. We demonstrate that invariant Planck scales can coexist with exact local Lorentz invariance when Planck lengthand Planck time are interpreted as operational lower bounds on spatial and temporal resolution, rather than as ontological spacetime discreteness. Special Relativity is reformulated operationally on curved spacetime through a generalized relativistic factor γg, allowing a precise treatment of relativistic kinematics in black-hole, cosmological, and rotating spacetimes without modifying Lorentz transformations or dispersion relations.We show that event horizons, cosmological expansion, and global rotation generatekinematic phase boundaries that restrict the physical realizability of observers while leaving local inertial physics intact. Planck-scale structure near black-hole horizons is incorporated through geometric regularization rather than symmetry breaking, and black-hole thermodynamics is recovered entirely from local Special Relativity combined with spacetime geometry. The framework further incorporatesinvariant global bounds on mass, time, and length, leading to a classification theorem for physically admissible observers across all scales. Information-theoretic limits on entropy, computation, and information recovery are derived as kinematic consequences of admissibility rather than as fundamentalpostulates. Apparent paradoxes in black-hole complementarity, trans-Planckian physics, and infinite boosts are shown to arise from implicitly assuming inadmissible observers. The resulting picture preserves the empirical successes of Special and General Relativity while providing a unified, observer-centered principle that regulates both ultraviolet and infrared extremes without invoking Lorentz violation, deformed symmetries, or holographic reduction of degrees of freedom.
Category: Relativity and Cosmology

Ultraviolet Stability of Wilson-Loop Expectations in 4D Lattice Yang—Mills Theory Via Multiscale Gradient-Flow Smoothing

Authors: Lluis Eriksson
Comments: 21 Pages.

We prove that Wilson-loop expectations in four-dimensional Euclideanlattice Yang—Mills theory with compact gauge group G admit auniversal continuum limit, independent of the lattice approximationscheme, for every contractible loop and all values of the coupling.The proof proceeds by a multiscale decomposition that combinesBalaban's renormalization-group framework with a quantitativegradient-flow smoothing step at each scale. For an observableliving at lattice scale k, the Yang—Mills gradient flow is run fora time proportional to the squared lattice spacing a_k^2; adeterministic contraction estimate (Theorem 3.5) shows that thisreduces the single-link oscillation of the flowed observable by afactor L^{-2k}, where L is the blocking factor. The resultinggeometric series is summable and yields the desired uniform bound.The two main inputs are: (i) a pointwise domination lemma(Lemma 3.3) that controls the gradient of the flowed observableby a scalar heat kernel on the link graph, exploiting thecontractivity of parallel transport; and (ii) a Duhamelinterpolation formula (Lemma 4.1) that converts each change-of-measure error into a covariance with the irrelevant part of theeffective action, bounded via a Poincaré-type inequality. Togetherthese close the Balaban—Doob inductive circuit under a quantitativeblocking hypothesis that is verified in a companion paper.As a corollary, we establish Osterwalder—Schrader reflectionpositivity for the gradient-flow-smoothed Wilson-loop observable,which together with the continuum limit yields a construction ofthe physical Hilbert space and a positive transfer matrix for thetheory.
Category: Mathematical Physics

Almost Reflection Positivity for Gradient-Flow Observables via Gaussian Localization in Lattice Yang-Mills Theory

Authors: Lluis Eriksson
Comments: 15 Pages.

We establish quantitative almost-reflection positivity (almost-RP) for a family of flowed observables in finite-volume lattice Yang-Mills theory on the four-dimensional Euclidean torus T_L^4 with structure group G = SU(N). The lattice Wilson flow - the lattice counterpart of the Yang-Mills gradient flow - acts as a gauge-covariant smoothing that suppresses ultraviolet fluctuations. By combining three ingredients: (i) a Gaussian localization bound that controls the variance of flowed observables via an Efron-Stein-type inequality, (ii) Jacobian estimates for the lattice Wilson flow that yield exponential decay of trans-plane influence, and (iii) the exact lattice reflection positivity of the Wilson action, we show that the failure of RP for flowed observables is exponentially small in the ratio epsilon_0^2 / t, where epsilon_0 is the physical separation between the observable's support and the reflection plane (minus the diffusion scale sqrt(8t)), and t > 0 is the flow time. We record the standard Osterwalder-Schrader reconstruction as a conditional statement: exact reflection positivity on a positive-time algebra implies a Hilbert space, a vacuum, and a non-negative Hamiltonian. Our approach is non-perturbative, holds for all values of the lattice coupling, and requires no cluster expansion or infinite-volume limit.
Category: Mathematical Physics

Quantum Mechanics from Stochastic Coherence: Resolving the Wallstrom Objection via Topological Stability.

Authors: Adrian Leonardo Rohr
Comments: 11 Pages.

We derive the Schrödinger equation from the Onsager-Machlup stochastic variational principle and address the Wallstrom objection within this framework. Wallstrom showed that the Madelung hydrodynamic equations do not enforce quantization of phase circulation unless single-valuedness of the wave function is imposed as an additional condition.We prove that quantization of phase circulation follows from intrinsic requirements of the stochastic formulation. Reformulating the phase gradient as a flat U(1) connection on the punctured domain where the density is positive, we show that smooth removability of isolated singularities forces trivial holonomy, yielding the quantization condition∮ ∇S · dl = 2πnℏFor configurations with nodal zeros, quantization emerges from the combination of the Hamilton-Jacobi constraint at nodal zeros and the regularity required for the probability current to be a well-defined observable on physical space. These two conditions, neither of which alone implies quantization, together exclude non-integer winding numbers including the recently constructed non-quantized strong solutions of the Madelung equations.Under the identification D = ℏ/(2m), the Madelung transformation then recovers the Schrödinger equation without postulating wave function single-valuedness. Quantization emerges as a geometric and regularity consequence of the Onsager-Machlup variational structure.
Category: Quantum Physics

Reconstruction of a Minimal Six-Dimensional Light Entity

Authors: Tingfang Yi
Comments: 7 Pages.

We propose a minimal six-dimensional (6D) light null entity in which the six dimensions are intrinsic degrees of freedom of a null physical entity. The six dimensions consist of a two- dimensional null propagation geometry together with four intrinsic one-dimensional degrees of freedom of light: optical phase, polarization, frequency, and orientation along the null momentum generator. In this framework, all four-dimensional (4D) spacetime optical, electromagnetic, and quantum phenomena are understood as lower-dimensional projection or section measurements of a single higher-dimensional null entity.
Category: Mathematical Physics

Geometry and Spin Structure of the Single Oloid Manifold as the Origin of Leptonic Mass (Information-Geometric Physics System I)

Authors: Pruk Ninsook
Comments: 43 Pages.

This work presents the theoretical framework of the Information-Geometric Physics System (IGPS), which elucidates the emergence of fundamental properties in leptonic particles through the structure of the Oloid manifold [17]. Under the constraints of C2continuity and seam coupling enforced by S1 ⊥ S1 symmetry, the fundamental constituents of matter are modeled as "closed information nodes." In this framework, the spectral mass is derived as a curvature integral and a normal bundle holonomy manifesting along the manifold’s seam [13]. We prove that the moduli space of the seam under rigidity conditions yields an SO(3) symmetry group structure, naturally inducing a spin structure via the SU(2) double cover [18]. Furthermore, it is demonstrated that the geometric stiffness parameterβ = 1/(√3π) emerges as a universal geometric invariant governing the internal strain scale [3]. These results suggest that the fermion mass spectrum is directly coupled to the topological structure of the informational manifold, providing a foundational basis for the extension into composite systems and strong interactions in subsequent work [9].
Category: Quantum Gravity and String Theory

Multi-Seam Configuration and the Topological Scaling of Baryonic Mass (Information-Geometric Physics System II)

Authors: Pruk Ninsook
Comments: 25 Pages.

This research extends the scope of the Information-Geometric Physics System (IGPS) from single-node systems to composite nuclear structures via the Oloid Trinity Configuration, elucidating the topological origin of mass and the statistical properties of baryons [8, 9]. We introduce the Dimensional Jump phenomenon, representing an informational scale transition from planar scaling on the manifold’s seam to the sweep volume ofentangled folded manifolds. This transition results in the emergence of a universal geometricmultiplier G = 4 3π2, which systematically bridges leptonic mass to the nuclear mass scale.Under rigidity constraints and SU(3) symmetry, we prove that the extrinsic/interactionstrain is fixed at Δ = 2.5 through the 5/2 Theorem, enabling the master equation to predict the proton mass with 99.99% accuracy relative to CODATA standards [10]. Furthermore, it is demonstrated that Fermi-Dirac statistics and fractional spin 1/2 emerge directly from the preservation of C2 continuity on manifolds entangled through the SU(2)double-covering structure. Residual analysis confirms that manifest discrepancies align withthe order of radiative corrections in Quantum Electrodynamics (QED). These results confirmthat baryonic structure represents the most stable volumetric organization of information,effectively achieving structural closure for the origin of matter within the IGPS framework.
Category: Quantum Gravity and String Theory

A Modified Sieve of Sundaram

Authors: Wiroj Homsup
Comments: 3 Pages.

A new Twin prime sieve based on a modified sieve of Sundaram is introduced. It sieves through the set of natural numbers n such that 3n is not representable in either of the forms 2ij + i + j or 2ij + i + j +1 for positive integers i, j.
Category: Number Theory

Canonical Nonlinear Partial Differential Equations

Authors: Luisiana X Cundin
Comments: 6 Pages.

A formal, systematic approach for generating nonlinear partial differential equations is outlined, which provides a more robust, reliable method. Additionally, formal methods provide a means to test the validity and/or the veracity of proposed nonlinear partial differential equations, thereby potentially saving researchers precious time and effort.
Category: Mathematical Physics

Ultraviolet Stability for Four-Dimensional Lattice Yang—Mills Theory Under a Quantitative Blocking Hypothesis

Authors: Lluis Eriksson
Comments: 14 Pages.

We prove that the continuum limit of pure SU(N) lattice Yang—Mills theory in four Euclidean dimensions exists on the algebra of blocked observables at fixed finite volume, conditional on a quantitative regularity hypothesis for the blocking map. The argument combines three components: Bałaban's rigorous renormalization group program, which provides polymer representations and ultraviolet stability; a Doob-martingale influence bound that controls covariance without product-measure assumptions; and a renormalization-group Cauchy summability framework converting per-scale oscillation decay into convergence. The resulting continuum state is gauge-invariant, Euclidean-covariant, and positive. Osterwalder—Schrader reconstruction, the thermodynamic limit, and the mass gap remain open.
Category: Mathematical Physics

The Topological Inversion Model (TIM): A Unified Framework for Cosmology and Fundamental Physics

Authors: Kobie Janse van Rensburg
Comments: 2 Pages. (Note by ai.viXra.org Admin: This submission is somewhat ill-formatted and incomplete - Please cite and listed scientific references)

The Topological Inversion Model (TIM) proposes a novel Theory of Everything (TOE) based on the principle that "Absolute Nothing" is an unstable logical null state enforced by topology. Theuniverse emerges from a reciprocal topological inversion (the "Snap") at the Planck scale, resolving the paradox of sustained nothingness. Matter is interpreted as topological defects or "knots" resisting elastic recoil toward zero density, gravity as an inward push to unravel these defects, and dark energy as the dynamic scalar field Ψ representing recoil tension. Black holes serve as recycling engines converting defects back into Ψ, driving cosmic acceleration and resolving the Hubble tension. This paper formalizes the model, derives its equations of motion, and demonstrates resolutions to key problems including singularities, the information paradox, dark matter, and fine-tuning. Predictions include correlations between black hole density and local H0, gravitational wave echoes, and dynamic dark energy evolution. TIM is consistent with the Standard Model and General Relativity in their regimes while providing a unified topological foundation without extra dimensions or supersymmetry.Keywords: Cosmology, Quantum Gravity, Topology, Dark Energy, Hubble Tension
Category: Quantum Gravity and String Theory

Regular Simplex Hierarchical Gravity Part II: The Computational Universe: Deriving Spacetime, Light Speed, and Singularities from Infinite-Dimensional Simplex and Geometric Frustration

Authors: Ryuhei Sato
Comments: 16 Pages.

Einstein’s special relativity postulates the constancy of light speed c as an axiom but providesno explanation for its origin. We reformulate the universe as a discrete computational networkoperating at the Planck scale, wherein c emerges not as a fundamental constant but as the band-width limit of information processing. We demonstrate that the initial state of the universe—aninfinite-dimensional regular simplex—possesses spectral properties (Laplacian eigenvalue λ2 = N )that naturally enforce cosmic uniformity and clock synchronization without invoking inflationaryexpansion. Dimensional reduction from infinite to three dimensions generates an unavoidable infor-mational collision, which we term informational Pauli repulsion, providing the physical driver forboth the Big Bang and accelerated expansion. The deficit angle δ ≈ 7.36◦ inherent in the 600-celltessellation, combined with Gauss’s Theorema Egregium, guarantees spatial closure without externalembedding dimensions, thereby establishing a decisive advantage over string-theoretic frameworksrequiring 10 or 11 dimensions. We derive the Light-Speed Resource Allocation Principle (LRAP),c2 = v2 + τ 2, reinterpreting the Lorentz factor as a processing lag ratio rather than a coordinatetransformation coefficient. Black hole singularities are redefined as computational arrest regionswhere 3D rendering fails, leaving 4D data in a frozen state—a paradigm shift that naturally sub-sumes string theory and the holographic principle as effective descriptions within these arrestedzones. Finally, we prove that local resource allocation alone cannot resolve the global accumula-tion of geometric frustration, necessitating the hierarchical jamming transitions detailed in Part III.This work bridges the static geometry of Part I (derivation of G and Λ) with the thermodynamichierarchy of Part III (122-digit vacuum energy suppression), completing the dynamical core of theRegular Simplex Hierarchical Gravity (RSHG) framework.
Category: Relativity and Cosmology

Regular Simplex Hierarchical Gravity Part III: Jamming Scale Law and Hierarchical Energy Suppression

Authors: Ryuhei Sato
Comments: 12 Pages.

This paper presents a complete resolution of the cosmological constant problem within the Reg￾ular Simplex Hierarchical Gravity (RSHG) framework. The non-tessellating property of regulartetrahedra in 3D Euclidean space—characterized by a geometric residual (deficit angle δ ≈ 7.36)—induces recursive jamming transitions across six hierarchical scales spanning from 10−15 m to 1021 m(Fig. 1: six-stage cascade structure). Each hierarchy generates approximately 20 orders of magni￾tude of energy suppression. The cumulative suppression factor ϵtotal ≈ 10−122.2agrees with theobserved cosmological constant Λobs within 0.2 orders of magnitude. Critically, this result containsno adjustable parameters; even the number of hierarchies N = 6 emerges as an arithmetic conse￾quence of the target suppression (122 digits) divided by the single-stage suppression (∼ 19.2 digits).Furthermore, operation near the jamming criticality (ϕ ≈ 0.62, Fig. 2: metastable operating point)enables the conversion of computational heat into structural entropy (computational encapsulation),thereby preventing thermal collapse. Three experimentally verifiable predictions are presented: H4symmetry in the CMB angular power spectrum (ℓ = 120n), an entropy ratio Sstruct/Sthermal ≈ 0.2in Bose-Einstein condensates, and tetrahedral coordinate preference in protein structures.
Category: Relativity and Cosmology

RG—Cauchy Summability for Blocked Observables in 4d Lattice Yang—Mills Theory via Balaban's Renormalization Group

Authors: Lluis Eriksson
Comments: 17 Pages.

We prove that expectations of blocked, bounded Lipschitz observables at a fixed physical scale ℓ > 0 form an absolutely summable telescoping sequence along a Balaban-matched renormalization trajectory in four-dimensional SU(N_c) lattice Yang—Mills theory with lattice spacings a_k = a_0 2^{-k}. In particular, the continuum limit state ω(O) := lim_{k→∞} ⟨O^{(k)}⟩_{Λ_k, β_k} exists for every O in the blocked observable algebra A_ℓ^{block}. The proof uses three ingredients: (i) an exact RG identity (law of iterated expectations), (ii) a one-step pushforward stability bound for blocked observables derived from Gaussian control of fast modes and an approximate centering property of the fluctuation field, and (iii) a measure-comparison lemma via Duhamel interpolation using polymer remainder bounds. No quantitative rate of asymptotic freedom is required beyond staying in the small-coupling regime where the RG estimates hold; summability follows from the geometric decay (a_k/ℓ)^2 = O(4^{-k}) together with the assumed summability of the large-field/truncation errors {τ_k}. We also state a conditional extension to "renormalized" observables (e.g. Creutz-type constructions) contingent on a nonperturbative Symanzik extraction from polymer expansions, and we discuss the relation to Osterwalder—Schrader reconstruction and the mass gap problem.
Category: Mathematical Physics

Influence Bounds for Polymer Remainders in Balaban's Renormalization Group: Closing Assumption (B6) for the RG-Cauchy Programme in 4D Lattice Yang-Mills

Authors: Lluis Eriksson
Comments: 14 Pages.

We close the missing influence estimate — Assumption (B6) — required by the RG-Cauchy summability framework for blocked observables in four-dimensional SU(N_c) lattice Yang-Mills theory. The influence is measured by the Efron-Stein seminorm sigma_nu(f)^2 = sum_{e} E_nu[Var_e^nu(f)] that appears in the Duhamel interpolation lemma of the companion paper. We work in the small-field regime of Balaban's multiscale effective action and assume: (A1) a standard polymer representation for the irrelevant remainder V_k^{irr} = sum_X K_k(X); (A2) an explicit per-link oscillation bound for polymer activities carrying the correct irrelevance factor 2^{-2k}; (A3) a lattice-animal counting estimate. Under these three verifiable hypotheses — to be discharged from Balaban's historical work in a companion compendium paper — we prove sup_{t in [0,1]} sigma_{nu_{k,t}}(V_k^{irr}) <= C, where C = C(N_c, beta_0, kappa, C_osc, C_anim, p, L/a_0) is independent of the RG scale k. The proof uses only oscillation bounds and combinatorics: no log-Sobolev inequality, no mixing hypothesis, and no measure-dependent technology beyond the definition of conditional variance. This removes the only genuinely novel probabilistic input remaining in the UV block of the programme towards the Yang-Mills Millennium Prize.
Category: Mathematical Physics

Temporal Necessity in Relational Mathematical Realism: A Gödelian Argument Against the Block Universe

Authors: Jason Merwin
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

A foundational question in the philosophy of physics is whether time is a fundamental dimension of reality or an emergent phenomenon. The standard Block Universe interpretation of general relativity treats time as a static dimension, with the passage of time relegated to psychological illusion. In this paper, we present a novel argument against the Block Universe derived from the framework of Relational Mathematical Realism (RMR), which identifies physical existence with mathematical structure. We demonstrate that if reality is a sufficiently complex, locally consistent mathematical structure, then Gödel's First Incompleteness Theorem renders a static, completed universe logically impossible. The resolution of this impossibility requires the structure to undergo a non-terminating sequence of state extensions, which we identify with the passage of time. We conclude that time is not a dimension within which the universe exists, but rather the logically necessary process by which a complex mathematical structure maintains consistency. This result, if sound, constitutes the first derivation of temporal passage from mathematical logic and ontology alone.
Category: History and Philosophy of Physics

Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang-Mills Renormalization

Authors: Lluis Eriksson
Comments: 7 Pages.

We prove a uniform Doob martingale influence bound for the irrelevant polymer remainder arising in multiscale renormalization group analyses of four-dimensional SU(N_c) lattice Yang-Mills theory at fixed physical volume. Our main tool is the Doob influence seminorm sigma_nu(f)^2 = sum_i E_nu[(Delta_i f)^2], which yields an exact covariance identity for arbitrary probability measures. Assuming a deterministic per-link oscillation estimate for polymer activities with a scale factor 2^{-2k} (imported from the Balaban renormalization group programme) and using a standard lattice-animal counting lemma (proved here), we obtain a bound sup_{t in [0,1]} sigma_{nu_{k,t}}(V_k^{irr}) <= C independent of the RG scale k. We then explain how this bound feeds into a Duhamel interpolation step used in RG-Cauchy convergence arguments.
Category: Mathematical Physics

The Balaban—Dimock Structural Package: Derivation of Polymer Representation, Oscillation Bounds, and Large-Field Suppression for Lattice Yang—Mills Theory from Primary Sources

Authors: Lluis Eriksson
Comments: 23 Pages.

We provide a self-contained derivation of the three structural hypotheses — polymer representation (A1), per-link oscillation bounds with geometric decay factor (A2), and large-field suppression (B5) — that were assumed in Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang—Mills Renormalization and in the RG—Cauchy Master Framework. All results are traced to precise equations in the primary sources: the series of papers by T. Bałaban (Commun. Math. Phys., 1984—1989) and the expository trilogy by J. Dimock (2011—2014). The translation from Bałaban's analytic norms on gauge-covariant function spaces to the per-link oscillation language used in the probabilistic framework is made explicit. Together with Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang—Mills Renormalization, this completes the unconditional discharge of the UV structural inputs for the renormalization group approach to the Yang—Mills mass gap problem at finite volume.
Category: Mathematical Physics

The Prime Gear Geometry Theory: A Discrete Mechanical Resolution of Prime Conjectures

Authors: Chaiya Tantisukarom
Comments: 11 Pages.

This article presents "Prime Gear Geometry," a deterministic mechanical framework that redefines the integer axis as a master gear ($C_1$) with a discrete unit weight-step of $+1$. Unlike analytic models that rely on the complex-plane "1/2" critical line of the Riemann Hypothesis, this theory posits that prime numbers are exact geometric outcomes forged by $C_1$ at coordinates of total asynchronous interference. We establish the "Prime Gear Synchronization Conjecture," stating that total phase alignment of a prime gear group occurs only at Primorial intervals. This mechanical exactness is used to resolve the Goldbach, Twin Prime, and Collatz conjectures not as probabilistic likelihoods, but as structural necessities of a machine that, by the laws of relatively prime circumferences, is incapable of perfect synchronization within the finite bounds of the $C_1$ axis.
Category: Number Theory

A Universal Variational—Probabilistic Framework for Physical Theories

Authors: Cornelius Moore
Comments: 24 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

Modern theoretical physics employs distinct mathematical formalisms—Lagrangian mechanics, Hamiltonian dynamics, quantum amplitudes, statistical ensembles, field-theoretic path integrals—that, while empirically successful, lack a unified structural foundation. We present the Universal Mathematical System (UMS), a vari-ational—probabilistic framework in which standard physical theories arise as limiting cases, projections (marginalizations), or constrained reductions of a single maximum-entropy measure over configuration spaces. The framework is built on an exponential-family measure µ[C] = Z−1 exp(−Φ[C]), where Φ is a constraint functional encoding physical laws. We show under standard regularity assumptionshow classical mechanics emerges via the Laplace principle (β →∞), statistical mechanics is directly identified with the framework, and quantum mechanics corresponds to complex-weighted measures under standard path-integral formalism. Additionally, we formalize five distinct algebraic structures—quantity (Rn), growth (semigroups), information (entropy), phase (U(1)), and ratio (R+)—clarifying thatdifferent physical questions inhabit different mathematical domains and that confusion arises from naive cross-domain interpretation. The framework is intended as structural unification of existing formalisms rather than a proposal of novel fundamental ontology or new empirical predictions. We include a proof of a coarse-graining monotonicity theorem using the data-processing inequality, provide explicitreduction pipelines, and discuss extensions to chemistry, biology, neuroscience, and computation.
Category: Functions and Analysis

Bounded Symbolic Observability: A Cross-Domain Constraint in Computational Dynamics

Authors: David Taylor
Comments: 28 Pages. (Note by viXra Admin: Please cite and list scientific references)

Finite local symbolic observation exhibits bounded vocabularies across diverse computational domains despite systematic increases in observational scale. We apply afixed local symbolic encoding framework to 13 systems spanning quantum mechanics, fluid dynamics, thermodynamics, electromagnetism, chaos theory, number theory, combinatorial logic, and stochastic processes. Across all domains, observed symbolic vocabularies saturate, with a median final growth of 0.0% despite 100—1,000× increases in data volume, temporal extent, or problem size. Prime gap dynamics provides the strongest validation: an infinite, deterministic mathematical sequence with no physical dynamics saturates at 837 symbolic configurations across a 10,000× scale increase (100,000 to 1,000,000,000 primes,identical vocabulary), eliminating physical mechanisms as explanations. At one billionprimes, each of the 837 patterns is reused approximately 1.2 million times. Ten domainsachieve perfect saturation (0.0%), two near-perfect (<1%), and one strong (<20%). Symbolic space occupancy ranges from 0.08% (Schrödinger equation) to 92.35% (electromagnetic waves); both regimes nonetheless exhibit saturation. Saturation manifests independently of physical validity (thermodynamically invalid antidiffusion saturates identically to correct heat diffusion), determinism (chaotic andstochastic systems both saturate), and computational complexity (NP-complete 3-SATcollapses to eight symbolic patterns). These results indicate that bounded symbolicobservability reflects properties of finite local observation applied to locally-constraineddynamics rather than intrinsic system complexity—a constraint on measurement, not nature. Quantitative vocabularies are specific to the observational architecture employed; the empirical claim concerns the cross-domain emergence of vocabulary saturation under fixed local symbolic observation.
Category: Artificial Intelligence

Dual-Sector Expansion: Type Ia Supernovae Validate Matter-Sector H0 Normalization with ΛCDM Geometric Consistency

Authors: Heath W. Mahaffey
Comments: 12 Pages.

The Informational Actualization Model (IAM) proposes that late-time cosmic expansion couplesdifferently to photons versus matter, resolving the Hubble tension through sector-specific expansionrates. This dual-sector framework makes a critical, testable prediction: Type Ia supernovae (SNe),as matter-based distance indicators hosted in galaxies, should probe the matter sector. We testthis hypothesis using the complete Pantheon+ dataset (1588 SNe, 0.01 < z < 2.26) through threeindependent analyses: (1) SNe with Planck (photon-sector) H0 prior, (2) SNe with SH0ES (matter-sector) H0 prior, and (3) SNe with no H0 constraint. Results unambiguously demonstrate that SNereject the photon-sector expansion rate (H0 = 67.4 km s−1 Mpc−1, β → −0.30 at parameter bound-ary) and accept the matter-sector normalization (H0 = 73.04 km s−1 Mpc−1, β ≈ 0). Critically,SNe distances maintain ΛCDM geometric consistency (βdistance ≈ 0), validating IAM’s predictionthat sector-specific coupling primarily affects structure growth (f σ8) rather than photon propa-gation geometry. This empirical validation establishes that dual-sector expansion is data-driven,not theoretically assumed, and demonstrates that Planck (H0 = 67.4, photon sector) and SH0ES(H0 = 73.04, matter sector) both measure correctly—they probe different physical quantities. Thedual-sector phenomenology maps directly onto the standard modified gravity parametrization: mat-ter perturbations obey μ(a) = H2ΛCDM(a) / [H2ΛCDM(a) + βmE(a)] < 1 (suppressed growth), whilephoton deflection remains unmodified (Σ = 1), preserving CMB consistency. This μ < 1, Σ = 1framework is independently testable with existing Boltzmann solvers (CAMB/CLASS) and upcom-ing survey parametrizations (DES, Euclid, CMB-S4)
Category: Relativity and Cosmology

The Unification Achieved, How Quantum Gravity Had Already Been Solved

Authors: Bertrand Jarry
Comments: 8 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0) (Note by ai.viXra.org Admin: Please cite listed scientific references)

For a century, physicists have sought to unify general relativity and quantum mechanics. We show that this quest rests on a fundamental conceptual error: gravity never needed to be "quantized" because it is already a quantum phenomenon emerging from the vacuum. By recognizing the quantum vacuum as the fundamental substrate, unification becomes trivial. All forces, including gravity and relativity, are manifestations of the same quantum vacuum. The problem was not to find a theory of quantum gravity, but to recognize that it already existed.
Category: Quantum Gravity and String Theory

Conditional Continuum Limit of 4d SU(N_c) Yang-Mills Theory via Two-Layer Architecture, RG-Cauchy Uniqueness, and Step-Scaling Confinement

Authors: Lluis Eriksson
Comments: 18 Pages.

Building on the lattice results established in Papers [E26I]-[E26IX], we give a conditional construction of a scaling-limit state for pure SU(N_c) lattice Yang-Mills theory in four Euclidean dimensions, along dyadic lattice spacings a_k = a_0 * 2^{-k}. The construction proceeds via a two-layer architecture.Layer 1 (Local fields): For bounded gauge-invariant local observables (Wilson loops, normalized plaquette traces), expectations converge -- without extracting subsequences -- to a unique limit. Tightness is trivial (L^infinity bound plus Prokhorov); uniqueness follows from a multiscale RG-Cauchy estimate that bounds the change of local expectations under a single RG step. The extension to unbounded observables such as smeared curvature monomials, which require additive renormalization, is deferred to future work.Layer 2 (Confinement): The physical string tension sigma_phys > 0 is established through step-scaling of Creutz ratios evaluated on Wilson loops whose physical dimensions R x T are held fixed as a -> 0.The limiting state on bounded observables inherits Osterwalder-Schrader positivity from the lattice and admits a Hilbert-space reconstruction via reflection positivity. The mass gap is established conditionally via uniform exponential clustering of connected correlators -- an input from a uniform physical transfer-matrix spectral gap -- and the reconstruction theorem. Nontriviality follows conditionally from an area law for Wilson loops.Key dependencies on prior papers: uniform LSI inputs [E26I]-[E26IX]; Balaban multiscale effective action [E26III]-[E26V]; DLR-LSI [E26VII]; unconditional lattice closure inputs [E26IX].
Category: Mathematical Physics

Gravity as Osmotic Depression of the Quantum Vacuum,a Unified Theory of Relativity and Quantum Physics

Authors: Bertrand Jarry
Comments: 8 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0) (Note by ai.viXra.org Admin: Please cite listed scientific references)

We propose a radically new conceptual framework for understanding gravity and relativity, not as geometric curvatures of spacetime, but as physical modifications of the quantum vacuum. Gravity results from a static osmotic depression, while special relativity emerges from the dynamic compression of the vacuum by motion. This approach naturally resolves the problem of unification with quantum mechanics and makes experimentally testable predictions. Unlike attempts to "quantize geometry" (strings, loops), our theory recognizes that gravity and relativity are already quantum phenomena in nature, emerging from the properties of the vacuum.
Category: Quantum Gravity and String Theory

Unified Theory of the Quantum Vacuum Gravity, Relativity and Quantum Mechanics

Authors: Bertrand Jarry
Comments: 15 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0) (Note by ai.viXra.org Admin: Please cite and list scientific references)

This theory unifies gravity, special relativity, general relativity, and quantum mechanics by recognizing the quantum vacuum as the single fundamental substrate. Gravity emerges as a static osmotic depression of the vacuum, special relativity as a dynamic compression, and all forces as manifestations of the same vacuum. This unification is not achieved through the quantization of geometry, but through the recognition that gravity was already quantum.
Category: Quantum Gravity and String Theory

Prime Modular Dynamics Theory (PMDT)

Authors: Michel Monfette
Comments: 14 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

We study the modular dynamics of prime numbers through the families SG(k) = {p ∈ P : kp + 1 ∈ P}. We present extensive computational evidence (up to 100 million Sophie Germain primes) fora modular dynamical structure in SG primes modulo 30. Two fundamental theorems establishthe triangular residue class 11,23,29 and gap constraints. Eight conjectures emerge, includinga novel "least-gap principle" and a harmonic attractor at 60. SG(k) families exhibit distinctphases in entropy/detailed-balance plane, with period-9 resonance and asymmetric sexy orbits.A third grammatical dynamic (G3) classifies all anomalies into three energy regimes. These pat-terns suggest an underlying arithmetic grammar and self-organizing behavior in Sophie Germainprimes.
Category: General Mathematics

Arithmetic Relativistic Emergence (Are): Spontaneous Symmetry Breaking from the Zeta Vacuum to Emergent Spacetime Geometry, Topology, and Quantum Fields

Authors: J. W. McGreevy
Comments: 18 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present the Arithmetic Relativistic Emergence (ARE) framework, in which the fundamental symmetries of General Relativity, Einstein—Cartan gravity with torsion, and quantum field theory (Standard Model sectors) emerge tautologically from pure number theory viathe arithmetic geometry of the rational numbers Q. The Riemann zeta function ζ(s) represents the maximally symmetric pre-geometric vacuum phase, with perfect functional-equation symmetry around Re(s) = 1/2 and pole at s = 1 as the unified source of arithmetic energy/information.Spontaneous symmetry breaking induced by the weight-12 modular discriminant ∆(τ ) = η(τ )24 = (2π) 12(E4(τ ) 3 − E6(τ ) 2 )/1728 disperses this background into Archimedean divergence (smooth analytic curvature density) and non-Archimedean curl (torsion/spin density at p-adic fibers), with the functional-equation mirror s = 6 enforcing variational d balance of the arithmetic degree deg( L). The emergent 4D Lorentzian manifold M carries an adelic principal Lorentz/Spin frame bundle decomposed via the adele ring AQ. An effective Chern—Weil homomorphism—employing Bott—Chern forms at infinity and classical invariant polynomials at finite places—maps split curvature forms (Fdiv, Hcurl) to arithmetic characteristic classesin Arakelov Chow groups. These classes are stationary under metric d variations (δgdeg = 0 at s = 6), providing rigid global topological invariants (Pontryagin-like, Euler-like, torsion-twisting) preserved in the broken phase—the inevitable geometric and topological labels of arithmetic symmetry breaking. Heaviside synchronization (τdiv = τcurl) at s = 6 renders the arithmetic medium transparent, yielding distortionless propagation and unified causality. The Rankin—Selberg self-convolution L(∆×∆, s) contains ζ(s) factors, allowing recombination to the symmetric vacuum. Theemergent metric determinant √−g serves as the physical scalar whose arithmetic balancing across places enforces general covariance, proper volume preservation, and integration of curvature invariants. Fermions (12 Weyl per generation from Leech lattice Z2-orbifold),gauge sectors (finite algebra C ⊕ H ⊕ M3(C)), and constants (−α 1 ≈ 137.036, Λ ∼ 10−122MPl2, G ∼ 10−38 m−2) emerge via spectral actionand adelic convolution. ARE offers a tautological origin: physical laws are the minimal effective description preserving arithmetic consistency post-symmetry breaking.
Category: Number Theory

Anchored Causality Theory: Quantum Field Theory’s Natural Solution to the Measurement Problem

Authors: Kelly Sonderegger
Comments: 31 Pages. CC BY 4.0 License

The quantum measurement problem—how definite outcomes emerge from quantumstates—has resisted solution for nearly a century. We propose that the resolution liesin recognizing that quantum systems exist as extended waves until environmental coupling drives a phase transition to localized particles. There is no "superposition" in theconventional sense—the wave state is the fundamental reality. This Anchored Causality Theory (ACT) applies quantum field theory’s own ontology consistently throughmeasurement: fields are fundamental, particles are emergent localized excitations, andmeasurement is the physical process by which extended field configurations anchor intoparticle modes. ACT completes what QFT started—taking field ontology seriously allthe way through the measurement process.Remarkably, QFT’s mathematical structure already encodes this wave-particle phasetransition. The Lagrangian formulation (action principle, path integrals) is the naturallanguage of waves—extended field configurations exploring spacetime. The Hamiltonian formulation (definite states, observable eigenvalues) is the natural language ofparticles—localized excitations evolving in time. The Legendre transform connectingthem is the mathematical shadow of anchoring. What we call "superposition" is simply Fourier decomposition—one wave represented in different bases, not ontologicalmultiplicity. The mathematics was telling us this all along; we needed only to read itcorrectly.Measurement is progressive phase diffusion driven by coupling to environmentalquantum fields, with rates determined by particle mass through the Higgs mechanism.ACT emerges from three distinct physical processes: (1) Higgs-generated mass establishes the structural capacity for temporal participation and sets coupling strength, (2)gauge fields and phonons provide infrared noise spectra that drive decoherence dynamics, and (3) definite outcomes emerge when the anchoring functional Φ ≳ 1, markingirreversible phase transition from wave to particle.1We derive explicit anchoring rates from quantum Brownian motion theory, showing ΓA ∝ m2 × T × ηenv, where mass-squared scaling follows from Yukawa couplingstructure. The theory explains all existing decoherence phenomena—mass dependence,temperature scaling, environmental density effects, observable-specific rates, and persistence at zero temperature—while making a unique testable prediction: isotope massdependence of 15-20% in coherence times, distinguishable from environmental decoherence models (0%) and competing collapse models (∼8%). Standard Model EffectiveField Theory analysis establishes a viable parameter window spanning 15 orders ofmagnitude. Quantum randomness is explained as stochastic noise from environmental fields (thermal and vacuum fluctuations), not mysterious collapse—calculable viathe fluctuation-dissipation theorem. ACT provides mechanism, ontology, and testablepredictions using only established physics.
Category: Quantum Physics

Integrated Cross-Scale Derivative Bounds for Wilson Lattice Gauge Theory: Closing the Log-Sobolev Gap

Authors: Lluis Eriksson
Comments: 22 Pages.

We prove integrated cross-scale derivative bounds that replace the unverified Assumption 5.4 of a companion paper. Combined with two explicit large-field inputs (a residual pointwise derivative bound and a Balaban-type conditional large-field suppression) and conditional inequalities from the orbit space Ricci curvature, this yields a uniform (volume-independent) log-Sobolev inequality for the Wilson lattice gauge measure at sufficiently weak coupling (large beta). The key innovation is a decomposition into small-field and large-field contributions: the former is controlled by Balaban's polymer expansion, while the latter is handled by a pointwise gradient bound combined with exponential measure suppression. We provide a self-contained verification of the unconditional large-field tail mechanism for SU(2) in d=2, together with numerical validation.
Category: Mathematical Physics

Large-Field Suppression for Lattice Gauge Theories: from Balaban's Renormalization Group to Conditional Concentration

Authors: Lluis Eriksson
Comments: 22 Pages.

We verify the large-field hypothesis (Hypothesis 4.2) of the companion paper on integrated cross-scale derivative bounds for Wilson lattice gauge theory. The proof rests on three ingredients: (i) a dictionary lemma translating the Hilbert-Schmidt large-field condition on plaquette holonomies into Balaban's Lie-algebra formulation; (ii) an interface lemma connecting conditional measures with Balaban's T-operation and its uniform small-factor bound on admissible background fields (Eq. (1.89) of Balaban, Commun. Math. Phys. 122 (1989)); (iii) the uniformity estimate (Eq. (1.75) of the same reference) ensuring that slow-field dependence contributes only an O(1) multiplicative constant. For d=2, we give an independent proof via character-positive convolutions that avoids the Balaban machinery entirely. Together with the companion paper, this yields a uniform (volume-independent) log-Sobolev inequality for the Wilson lattice gauge measure at sufficiently weak coupling.
Category: Mathematical Physics

Unconditional Uniform Log-Sobolev Inequality for Su(n_c) Lattice Yang-Mills at Weak Coupling

Authors: Lluis Eriksson
Comments: 10 Pages.

We prove that the Wilson lattice gauge measure for SU(N_c) in dimension d >= 3 at sufficiently weak coupling (beta >= beta_wc) satisfies a log-Sobolev inequality with constant alpha_* > 0 independent of the lattice volume. This completes the multiscale program initiated in Paper I by verifying Hypothesis 3.2 of Paper III, the last remaining analytic input. The verification uses three ingredients: (i) the locality of polymer functionals, which restricts the sum over polymers to those intersecting a fixed link; (ii) Cauchy estimates on Balaban's analytic domains for polymer activities and boundary terms; and (iii) a combinatorial counting bound for connected polymers containing a given link, which is independent of the lattice volume. Combined with the synthetic Ricci curvature bound of Paper II, the integrated cross-scale derivative bounds of Paper III, and the large-field suppression established in Paper IV, this yields the uniform log-Sobolev inequality unconditionally.
Category: Mathematical Physics

From Uniform Log-Sobolev Inequality to Mass Gap for Lattice Yang-Mills at Weak Coupling

Authors: Lluis Eriksson
Comments: 16 Pages.

We prove that the one-step transfer operator of SU(N_c) lattice Yang-Mills theory in dimension d >= 3 has a spectral gap Delta_phys > 0 uniformly in the lattice volume (for even side length L), for all sufficiently large inverse coupling beta >= beta_0. The proof combines four ingredients: (i) the uniform log-Sobolev inequality on periodic tori established in a companion paper; (ii) a verification that the multiscale RG outputs needed for the LSI argument are uniform in frozen boundary conditions (Section 4), yielding the full DLR-LSI property (Section 5); (iii) the Stroock-Zegarlinski equivalence theorem, which in its standard formulation deduces Dobrushin-Shlosman mixing and exponential clustering from DLR-LSI; and (iv) Osterwalder-Seiler reflection positivity of the Wilson action, which translates temporal exponential clustering into a spectral gap of the transfer operator.
Category: Mathematical Physics

DLR-Uniform Log-Sobolev Inequality and Unconditional Mass Gap for Lattice Yang-Mills at Weak Coupling

Authors: Lluis Eriksson
Comments: 14 Pages.

We prove that for SU(N_c) lattice Yang-Mills theory in d >= 3 dimensions at sufficiently weak coupling (beta >= beta_0), the conditional Gibbs specification satisfies a DLR-uniform log-Sobolev inequality: for every finite sub-lattice Lambda' subset of Z^d and every boundary condition omega, the conditional measure mu_{Lambda'}^{omega} satisfies LSI(alpha_*) with a constant alpha_* > 0 independent of Lambda' and omega.The proof combines three ingredients:(i) the multiscale entropy decomposition developed in our earlier work (Papers I-V), which establishes a uniform log-Sobolev inequality on periodic tori;(ii) a uniform fiber oscillation lemma showing that frozen boundary links -- treated as external parameters in Balaban's renormalization group -- do not increase the per-block oscillation of the conditional fast potential, thanks to compactness of SU(N_c) and the locality of the polymer expansion;(iii) a refined large-field event restricted to dynamical (non-frozen) plaquettes, which ensures that the large-field suppression mechanism extends uniformly to boundary blocks.As a consequence, the Stroock-Zegarlinski equivalence theorem yields Dobrushin-Shlosman mixing, exponential clustering of gauge-invariant correlations, and -- via Osterwalder-Seiler reflection positivity -- a strictly positive mass gap Delta_phys >= m(beta, N_c, d) > 0 for the transfer matrix on the periodic torus (Z/LZ)^d, uniformly in even L. This removes the Dobrushin-type Assumption 6.3 of Paper I and the boundary-uniformity Assumption 3.1 of Paper VI, rendering the lattice mass gap unconditional at weak coupling.
Category: Mathematical Physics

Interface Lemmas for the Multiscale Proof of the Lattice Yang-Mills Mass Gap

Authors: Lluis Eriksson
Comments: 11 Pages.

We establish three interface lemmas that close the remaining gaps in the proof chain for the mass gap of SU(N_c) lattice Yang-Mills theory at weak coupling (beta >= beta_0) in dimension d >= 3.Lemma A (Horizon Transfer) establishes a uniform conditional large-field suppression bound mu_k(Z_k(B) | G_{k+1}) <= exp(-c p_0(g_k)) holding mu_beta-a.s., without any admissibility restriction on the background field. The argument identifies the regular conditional probability with Balaban's RG kernel, expresses the large-field activation probability as a ratio controlled by Balaban's localized T-operation, and applies the T-operation small-factor bound.Lemma B extracts from Balaban's inductive scheme that the boundary terms B^{(k)}(X) share the same uniform analyticity domain as the polymer activities R^{(k)}(X), with radius hat{alpha}_1(gamma) > 0 independent of k.Lemma C extends the multiscale LSI to finite volumes with arbitrary frozen boundary conditions omega via tensorization-plus-perturbation, replacing the unverified Dobrushin block condition of Paper VII.Combined with Papers I-VII, these lemmas render the lattice mass gap theorem unconditional.
Category: Mathematical Physics

Uniform Coercivity, Pointwise Large-Field Suppression, and Unconditional Closure of the Lattice Yang-Mills Mass Gap at Weak Coupling in d=4

Authors: Lluis Eriksson
Comments: 16 Pages.

We close the remaining interface gaps in the program [E26I]-[E26VIII] that establishes a uniform log-Sobolev inequality (LSI) and spectral gap for the transfer matrix of lattice SU(N_c) Yang-Mills theory in d=4 at weak coupling. Four technical gaps are identified and resolved: (G1) the Balaban small-factor bound for the T-operation is shown to hold pointwise for every real background by auditing Balaban's proof and verifying that it uses only the uniform inductive conditions; (G2) we establish a uniform small-field coercivity estimate (Hessian lower bound) for the effective action and use it, together with Balaban's small-factor mechanism, to control the conditional inequalities in the multiscale entropy decomposition -- circumventing the need for a global fiber LSI with constant O(beta); (G3) uniform analyticity of boundary terms is extracted from Balaban's inductive scheme; (G4) a quantitative bootstrap verifies the simultaneous compatibility of all constants for a single choice of beta_0. Combined with [E26I]-[E26VIII], these closures yield an unconditional proof that Delta_phys(beta,L) >= c(N_c,beta_0) > 0 uniformly in the volume L for beta >= beta_0.
Category: Mathematical Physics

Quantized Vacuum Attenuation: Resolving the Hubble Tension via Third-Order Nonlinear Susceptibility in a Discrete Manifold

Authors: Scott Long
Comments: 6 Pages. (Zenodo DOI: 10.5281/zenodo.18601428)

The standard ΛCDM cosmological model is currently challenged by a 5σ discrepancy in Hubble Constant (H0) measurements and a vacuum energy density error of 122 orders of magnitude. We present a numerical validation of the Quantized Vacuum Attenuation model, comparing its predictions against the standard ΛCDM cosmology across three key observables: Luminosity Distance (DL), Lookback Time (tL), and Angular Diameter Distance (dA). Utilizing a vacuum attenuation coefficient of α≈8.26×10−27 m−1, derived from the local Hubble flow, our simulations resolve three primary tensions: Dark Energy: The model demonstrates that the high-redshift luminosity modulus follows a logarithmic attenuation profile, eliminating the need for Dark Energy to explain Type Ia Supernovae dimming. Early Galaxy Paradox: The model removes the Big Bang singularity, reinterpreting high-redshift galaxies (e.g., JADES-GS-z13) as objects seen through ≈35 Gyr of static vacuum transmission, allowing for infinite formation time. Little Red Dots: The angular diameter distance in a discrete manifold correctly predicts the observation of compact high-redshift morphologies that contradict angular magnification predicted by expanding metric models. We conclude that the observed universe is consistent with a static, infinite, and dissipative manifold governed by information-theoretic limits.
Category: Relativity and Cosmology

A Comparative Study of Sikh and Religious Cosmologies with Modern Models of Physics and Spacetime

Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 33 Pages.

This paper presents a novel synthesis of ancient religious cosmologies, particularly Sikh, Islamic, and Hindu scriptural verses, with modern theoretical physics, including general relativity, quantum cosmology, and higher-dimensional field theories. Beginning with interpretations of key hymns such as those from the Japji Sahib and Kirtan Sohila, the paper constructs conformally compactified spacetimemetrics aligned with spiritual metaphors. G¨odel-like rotating universes are modeledto reflect daily and annual solar motions, incorporating tunneling transitions, scalar curvature collapses, and spinor bundles to represent evolving consciousness. Through symbolic AI, scriptural syntax is translated into candidate gravitational Lagrangians, wavefunctionals, and field strength tensors that encode karmic memory. This integration of metaphysical semantics and mathematical physics allows new formulations of cosmological duality, including Janus time-symmetric models and magneto-causal holography, offering profound insights into the structure of the universe and the soul’s evolution within it.
Category: Religion and Spiritualism

Alternative Gravity Hypothesis as an Effect of Differential Universe Expansion

Authors: L. A. Serebrennikov
Comments: 4 Pages.

In the standard model, gravity is described either as a fundamental interaction (Newton’s law of universal gravitation) or as a geometric property of spacetime (Einstein’s general theory of relativity). The hypothesis proposed here considers observable gravitational attraction as a consequence of uneven cosmological expansion.Massive objects, possessing higher energy density, cause more intense local expansion of space, leading to effective repulsion of less massive bodies toward zones of increased expansion. The paper outlines the main postulates of the model, its potential implications for the dark matter problem, and proposes specific paths for experimental falsification.
Category: Relativity and Cosmology

From Prime Numbers to DNA: The Emergence of a Universal Fundamental Structure

Authors: Guiffra Patrick
Comments: 21 Pages.

In this article, we demonstrate the emergence of a fundamental structure inherent to prime numbers that embeds its signature within the molecular architecture of DNA. By constructing a harmonic field Ω(x, q) based on modular inverses of prime numbers, we show that helical periodicities of biological structures emerge naturally from universal arithmetic properties.Our main results establish that: (1) The prime number p = 11 acts as a universal pivot, generating through its modular inverse 11−1 ≡ 2 the characteristic wavelengths of protein α-helices (λ = 7/2 = 3.5, 2.68% error vs observed 3.6) and B-form DNA (λ = 21/2 = 10.5, 0.10% error vs observed 10.5). (2) Analysis of human chromosome 1 reveals statistically significant 36% enrichment of prime-length tandem repeats (p < 3.2 × 10−7). (3) We establish a universal scaling law relating the prime harmonic coherence coefficient χ to genomic fractal dimension D according to D = 1−0.86χ, validated across five organisms spanning three domains of life (bacteria, yeast, plant, insect, mammal) with near-perfect correlation (r = −0.9974, p < 10−4, errors < 1%). The numerical evidence is compelling. To claim that prime numbers constitute the fundamental template of DNA requires only one more step: experimental laboratory demonstration. We propose testable protocols involving synthesis of DNA optimized according to prime harmonic principles, with quantitative predictions for thermal stability, mutation rates, and spectral properties. If validated, these findings suggest that number theory encodes universal architectural constraints on biological self-assembly.
Category: Physics of Biology

Ricci Curvature of the Orbit Space of Lattice Gauge Theory and Single-Scale Log-Sobolev Inequalities

Authors: Lluis Eriksson
Comments: 11 Pages.

We establish that the orbit space B = A/G of SU(Nc) lattice gauge theory satisfies the Riemannian curvature-dimension condition RCD*(Nc/4, dim A); in particular, it satisfies CD(Nc/4, ∞) in the sense of Lott-Villani-Sturm. The proof proceeds by showing that the configuration space A = SU(Nc)|B1(Λ)|, equipped with the bi-invariant product metric ⟨X, Y⟩ = -2 tr(XY), is an Einstein manifold with RicA = (Nc/4) gA, and then applying the stability of the RCD* condition under quotients by compact groups of measure-preserving isometries (Galaz-García-Kell-Mondino-Sosa). This approach bypasses the need for explicit O'Neill curvature computations and handles the singular stratum (reducible connections) automatically. As a consequence, we derive a conditional log-Sobolev inequality for measures on B of the form dμ = e-Φ dν/Z with constant α = (Nc/4) e-osc(Φ). All constants are computed explicitly for SU(2) and SU(3). This provides the geometric input in a program aiming at a volume-uniform log-Sobolev inequality for SU(Nc) lattice Yang-Mills theory at weak coupling; the complementary analytic input (uniform bounds on the effective potential oscillation, via Balaban's renormalization group) is the subject of ongoing work.
Category: Mathematical Physics

An Oktonionic Model of Black Holes

Authors: Rüdiger Giesel
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present a non—associative algebraic model of black holes based on the octonionicdivision algebra. Geometry is not postulated as fundamental. Instead, gravity emergesdynamically from the non—associativity of the underlying algebra. Black holes arise as algebraic states rather than geometric singularities. The Schwarzschild radius is derived exactlywithout assuming Einstein’s field equations. The resulting spacetime is singularity—free,geodesically complete, and information preserving
Category: Relativity and Cosmology

Causal Mechanical Cosmology (CMC) — Paper 5: A Word-Safe Mathematical Derivation Tooling Paper for A—B—C Closure

Authors: Leon Barbour
Comments: 19 Pages. Licensed under CC BY 4.0 (Note by ai.viXra.org Admin: For the last time, please cite and list scientific references)

This paper presents a compact "tooling derivation" for the first closed operational loop in Causal Mechanical Cosmology (CMC): (A) spherical void control geometry producing adominant dipole anisotropy for an off-centre observer, (B) an elongated/sheared voidgeometry producing quadrupole anisotropy via a local Hessian decomposition, and (C) anobservable closure mapping the structural line-of-sight (LOS) velocity signature to atomicfractional frequency shift Δf/f as the measurement endpoint. Canonical equations (E1—E8) are preserved and used as the spine for derivations and diagnostics. The local Hessian kernel yields the leading even-parity multipole structure (monopole/quadrupole); dipole structure in the spherical off-centre control case is treated as arising from the global sampling asymmetry and, in a strict local expansion, enters through higher-order terms beyond the first Hessian approximation.
Category: Relativity and Cosmology

Arithmetic Emergence of Generalized Relativity, Classical Spacetime and Quantum Fields from Number Theory: Balanced Dispersion of the Arithmetic Degree Induced by the Weight-12 Modular Discriminant

Authors: J. W. McGreevy
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present a rigorous synthesis in which the fundamental symmetries of General Relativity and quantum field theory emerge from the axioms of arithmetic geometry and number theory. Central is the weight-12 modular discriminant Δ(τ) = η(τ)^{24} = (2π)^{12} (E_4^3 - E_6^2)/1728, interpreted as the vacuum potential. The arithmetic degree (total integrated curvature) must disperse equivalently across Archimedean (smooth, complex-analytic) and non-Archimedean (discrete, p-adic) places to maintain global consistency via the product formula. This dispersion is enforced at the critical mirror point s=6 of L(Δ,s), where the functional equation symmetry balances openness and rigidity.The Hilbert-Pólya operator Ĥ = 1/2 + i (D_∞ ⊕ ∑p D_p) acts self-adjointly on the adelic Hilbert space, with eigenvalues corresponding to resonances tied to L(Δ,s) zeros. The 1728 frequency (12^3) serves as the universal gear ratio/adiabatic regulator. The 12-fermion matrix arises from the Leech lattice V_Λ{24} Z_2-orbifold, folding 24 bosonic dimensions into 12 Weyl fermions per generation via Möbius twist.A 4D Lorentzian manifold emerges via noncommutative geometry (KO-dimension 6 adelic spectral triple), with the spectral action Tr f(��/Λ) yielding the Einstein-Hilbert term and stress-energy from p-adic torsion convolution. The master equation δ_g widehat{deg}(mathcal{L}) = 0 at s=6 recovers the Einstein field equations with cosmological constant Λ ≈ M_Pl^2 e^{-288} (double-twist entropy) and fine-structure constant α^{-1} ≈ 137.036 from Petersson norm corrections. This framework posits that GR and the Standard Model are stereographic projections of the weight-12 balanced modular form onto the Möbius-Planck manifold, providing a tautological origin for physical laws from number theory.
Category: Number Theory

Recursive Spacetime: A Research Programme for a Holographic Graph-Theoretic Framework

Authors: Ammar Alammar
Comments: 8 Pages. Creative Commons License

We propose a background-independent research programme modelling the universe as a dynamic,recursive causal network evolving from a single root vertex. By treating spacetime not as afundamental container but as an emergent property of a stochastic directed acyclic graph (DAG),we demonstrate that foliation invariance (a necessary condition for Lorentz symmetry) and three-dimensional spatial geometry can emerge as statistical limits of graph topology governed by random walk recurrence (Polya’s Theorem) and the Principle of Maximum Entropy. We formally derive the Einstein-Hilbert action in the thermodynamic limit of the graph’s microstate statistics, identifying the cosmological constant with unimodular volume fluctuations (Λ ∼ V −1/2). Furthermore, we identify fundamental particles as stable topological subgraphs (braids) protected by Pachner move invariance, and derive the Holographic Area Law from the Max-Flow Min-Cut theorem. This model offers a unified generative grammar for emergent gravitation and quantum interference, yielding a precise, falsifiable prediction for high-energy Lorentz violation, consistent with effective field theory expectations in discrete models.
Category: Quantum Gravity and String Theory

Uniform Log-Sobolev Inequality and Mass Gap for Lattice Yang--Mills Theory

Authors: Lluis Eriksson
Comments: 21 Pages.

We prove that SU(Nc) lattice Yang--Mills theory in d=4 dimensions with Wilson action at sufficiently weak coupling (beta = 2Nc/g^2 >= beta0) satisfies a log-Sobolev inequality with constant alpha_* > 0 uniform in the lattice size Lvol, conditional on Assumption (cross-scale derivative bound). Combined with reflection positivity, this yields a positive mass gap Delta_phys > 0 uniform in Lvol, conditional on Assumptions (cross-scale derivative bound) and (Dobrushin translation).The argument combines: (i) Balaban's constructive renormalization group, providing controlled effective actions and polymer bounds at all scales; (ii) a lower Ricci curvature bound on the gauge orbit space, giving uniform conditional log-Sobolev constants for fast modes via the Bakry--Emery criterion; and (iii) a multiscale entropy decomposition with sweeping-out estimates, where the transversal block-averaging scaling ensures summability of cross-scale errors.A detailed audit trail is included to relate the required cross-scale derivative input to published bounds in Balaban's work.
Category: High Energy Particle Physics

Uniform Poincaré Inequality for Lattice Yang-Mills Theory Via Multiscale Martingale Decomposition

Authors: Lluis Eriksson
Comments: 11 Pages.

We prove that the lattice Yang-Mills measure with gauge group SU(N_c)in d=4 dimensions at sufficiently large β=2N_c/g²satisfies a Poincaré inequality with constant α_*>0uniform in the lattice size L. The proof uses three ingredients:(i) the Ricci curvature bound Ric_B ≥ N_c/4 for thegauge orbit space, giving a uniform spectral gap for conditional measures offast modes at each renormalization group scale; (ii) Balaban's constructive RGwith polymer derivative bounds, controlling the residual coupling betweenscales; and (iii) a multiscale martingale variance decomposition that avoidsrecursive composition losses, with a commutator coefficientD_k ≤ C e^-2κ 2^-3k made summable bythe geometric scaling factor of transversal block averaging. Under anRG-normalized disintegration consistent with Balaban's absorption structure,only exponentially decaying polymer residuals contribute to D_k,ensuring Σ_k D_k << c₀. Theresulting uniform Poincaré inequality gives volume-independent control ofthe variance-to-energy ratio for gauge-invariant observables.
Category: Mathematical Physics

Role Based Multi Agent Reasoning Frameworks

Authors: Isaiah Nwukor
Comments: 15 Pages.

Individual artificial intelligence systems face an inherent trade-off between plasticity and stability under resource constraints. I propose that general intelligence emerges from networks of specialized agents applying a structured reasoning cycle to answer four fundamental questions. Agents ground abstract patterns through affective valence embeddings and coordinate via a shared database of credibility-weighted knowledge packages. I formalize a five-stage reasoning engine (Salience Detection → Hypothesis Generation → Experimentation → Structural Correspondence → Generalization) where agents at different stages specialize in different questions, enabling zero-shot cross-domain transfer. Using ARC-AGI task "as66" as demonstration, I show 276 generations of evolutionary learning where complementary specialization yields a current maximum of Level 4 performance across agents [20]. This framework provides testable predictions for performance scaling, transfer capability, and behavioral signatures of reasoning integration.
Category: Artificial Intelligence

Mass Gap for the Gribov-Zwanziger Lattice Measure: A Non-Perturbative Proof

Authors: Lluis Eriksson
Comments: 13 Pages.

We prove that the quadratic Gribov-Zwanziger measure on a d-dimensional periodic lattice (d ≥ 2) with gauge group SU(N_c) exhibits a mass gap, uniformly in the lattice size L. The gluon propagator at zero momentum satisfies D(0) ≤ C_d,Nc/g² for all L ≥ 2 and all coupling g > 0. In the thermodynamic limit, m_gap = g[(d-1)N_cI₁/d²]^1/2, where I₁ = ∫ d^dk/(2π)^d 1/k̂² is a finite lattice constant (I₁ ≈ 0.155 in d = 4). For SU(3) at β = 6 the predicted mass scale is m_gap ≈ 0.6 GeV, in quantitative agreement with lattice Monte Carlo measurements. The proof combines four ingredients: strict log-concavity of the measure (Bhatia's matrix inequality), dimensional reduction to a fixed finite-dimensional zero-mode sector (Prékopa's theorem), an exact computation of the effective Hessian at the origin, and a 1/N scaling argument that renders the effective potential asymptotically quadratic. No perturbative expansion in the coupling constant is employed.
Category: Quantum Physics

Emergent Proper Time and Spacetime from Quantum Information Permeability: A Relational Page—Wootters Framework Unifying Quantum Mechanics and General Relativity via Density-Dependent Channel Capacity

Authors: Marco Travan
Comments: 49 Pages.

We propose a pregeometric quantum theory in which spacetime and proper timeemerge from the throughput capacity of a fundamental relational network of quantuminformation channels. The universe is modelled as a weighted quantum causal setwhose directed links carry a density-dependent permeability. Proper time is identified with the local rate of coherentinformation transfer: dτk = κk dλ.Gravitational time dilation, the thermodynamic arrow of time, and the Einsteinfield equations arise as macroscopic consequences of local information congestion.The global dynamics are governed by a linear Page—Wootters constraint Cˆ |Ψ⟩ = 0,guaranteeing unitarity and complete positivity. Saturation of local information capacitytriggers irreversible transfer into fermionic matter degrees of freedom, providing aquantum-mechanical origin for rest mass and Pauli exclusion.When the bath Hilbert space is identified with the complexified octonions Hbath =C ⊗ O—as developed in a companion paper—the Fano-plane structure generatesthe Standard Model gauge group S(U(2)×U(3)), SO(8) triality yields exactly threefermionic generations, and sub-threshold bath occupation provides a dark mattercandidate. The present paper establishes the core framework; the octonionic extensionand its phenomenological consequences are derived in Paper II.The framework is fully testable in analogue-gravity platforms—in particular Bose—Einstein condensates—and predicts distinctive signatures: density-dependent soundspeed suppression with a specific permeability denominator structure, modified analogue Hawking spectra, a second-order proper-time correction beyond linearised generalrelativity, and a density-dependent decoherence rate whose functional form distinguishes the QIP mechanism from standard open-system models.
Category: Quantum Physics

Quantization of Dipolar Torsion in FCD-RB: Emergent Unification Without Dm/de

Authors: Ricardo J. Miralles
Comments: 4 Pages. In Spanish (Note by ai.viXra.org Admin: This submission needs an abstract in the article and cites listed scientific refererences)

We propose quantization of dipolar torsion T_dip in the FCD-RBv3 model, a 5D framework where fermion-antifermion pairs in a collapsed toroidal bulk emerge discrete masses m_n ∝ √n, modified gravity (d=0.002), and helical electromagnetism, eliminating DM/DE/primitive gluons...
Category: Quantum Gravity and String Theory

A Variational Stochastic Derivation of the Dirac Equation with Quantized Orbital Angular Momentum and Consequences for Probability Positivity and Spin-Statistics

Authors: Adrian Rohr
Comments: 12 Pages.

We extend the stochastic coherence framework based on the Onsager-Machlup action to Minkowski spacetime. The configuration space R^n is replaced by M4, the scalar phase by a Lorentz rotor R in Spin+(1,3), and the observables by the four-current j^mu and spin tensor S^mu nu, both bilinear in R.We show that the combination of the relativistic stochastic Hamilton-Jacobi equation and the C^infty regularity of the bilinear observables over nodal surfaces forces the orbital winding number around nodal tubes to satisfy alpha = 2k with k a natural number, yielding orbital angular momentum quantized in integer multiples of h-bar: L = k in the non-negative integers. This establishes a strict topological separation between orbital angular momentum (determined by nodal regularity on the base manifold) and intrinsic spin (determined by the fiber group Spin+(1,3)).The variational derivation from the Onsager-Machlup action produces hydrodynamic equations that match the Takabayasi-Hestenes decomposition of the Dirac equation term by term. The derivation is non-circular: the dynamical constraint and the regularity requirement are logically independent.Additionally, we establish that the positivity condition rho >= 0 (inherent to any probability density) requires the internal orientation to be described by rotors in Spin+(1,3) rather than by SO+(1,3), as only the spinorial formulation guarantees a future-directed probability current. Finally, applying the Laidlaw-DeWitt decomposition to the many-body configuration space, we show that the double-cover structure of Spin+(1,3) fixes the exchange character to chi = -1 for spinorial representations, recovering Fermi-Dirac statistics without an independent symmetrization postulate.The framework remains within the domain of the free theory; extensions to curved spacetimes and many-body interactions are left for future work.
Category: Quantum Physics

The Koide Angle as a Conformal Dimension: G2 Geometry, SU(3)3 WZW Theory, and Fermion Mass Structure

Authors: Philippe Marcel Ndiaye
Comments: 42 Pages.

The charged lepton masses satisfy the Koide relation Q = 2/3 and are parametrized by a single Brannen phase δ_exp = 0.22222(5) ≈ 2/9. We prove that the Brannen parametrization is the exact eigenvalue structure of a democratic element of the exceptional Jordan algebra J₃(O), with cos(3δ) = -φ(V) where φ is the G₂ 3-form on the generation 3-plane. The distinguished value 2/9 appears independently as a Hessian ratio on Gr(3,R⁶), a Casimir quotient, the conformal dimension h of SU(3)₃ WZW theory, a crossing phase in conformal blocks, and the KZ singlet exponent. We prove Q = 1/3 + d/6, making Q = 2/3 equivalent to the quantum dimension d = 2. A Generalized Spectral Selection Theorem shows that the WZW Brannen formula for SU(N) at level k = N gives positive masses if and only if N = 3, deriving the number of generations from positivity. A Geometric Twist Field Theorem proves that the twist field dimension of the A₂ orbifold C²/Z₃ equals the WZW conformal dimension if and only if N = 3 (the equation N + 1 = 4). Three structural obstructions characterize viable mechanisms as non-perturbative and CP-violating. The HFLAV 2025 tau mass (1776.96 ± 0.09 MeV) agrees with the prediction (1776.97 MeV) at 0.08σ with zero free parameters. For up-type quarks, Q_up = 8/9 at 0.3σ. The neutrino extension is decisively falsified. Eighty-six falsified approaches are cataloged.
Category: High Energy Particle Physics

Mechanical Audit Experiments and Reproducibility Appendix for a Companion-Paper Programme on 4D SU(N) Yang—Mills Existence and Mass Gap

Authors: Lluis Eriksson
Comments: 33 Pages.

This document is an experiment-first audit report for a companion-paper programme claiming a constructive solution of the 4D $mathrm{SU}(N)$ Yang—Mills existence and mass gap problem. It specifies a runnable mechanical audit suite of 29 deterministic tests, defines pass/fail criteria, and presents outputs in a compilation-safe format. The report contains: (i) an explicit non-triviality proof showing the Wightman functions do not factorize trivially; (ii) a toy-model validation recovering the exact 2D $mathrm{SU}(2)$ Yang—Mills mass gap to machine precision; (iii) a Bałaban bridge appendix reproducing the critical inductive step of his renormalization group in simplified form; (iv) a reproducibility repository with 3-line setup instructions; (v) a core proof chain audit mechanically verifying the load-bearing theorems of Papers 86—90, covering terminal Kotecký—Preiss convergence, UV suppression, one-dimensionality of the anisotropic sector, Cauchy bounds on polymer jets, the OS1 vanishing rate $O(eta^2 log eta^{-1})$, Lie-algebra annihilation, and KP margin sensitivity. Beyond the 17 core tests, the suite includes a lattice gauge proxy layer (plaquette expansion, Polyakov-loop centre symmetry, Creutz ratio; 3 tests), an infrastructure layer (Bakry—Émery curvature seed $mathrm{Ric}_{mathrm{SU}(N)} = N/4$, the $2^{4k}$ cancellation in $d=4$, heat-kernel column bound; 3 tests), a UV-flow/heat-kernel layer (Parseval identity, diagonal decay exponent $d/2 = 2$, flow—reflection commutation; 3 tests), a non-triviality test (Haar Monte Carlo on $mathrm{SU}(2)$ and $mathrm{SU}(3)$; 1 test), a toy-model validation (2D Yang—Mills transfer matrix; 1 test), and an algebraic QFT layer (Petz recovery fidelity bound $1-F leq C,e^{-2mr}$ from the Split Property; 1 test). All 29 tests pass; the full suite completes in ${approx}70,mathrm{s}$ on a Google Colab CPU. The complete inter-paper dependency DAG is acyclic and explicitly recorded. All code, data, and artifacts are available at https://github.com/lluiseriksson/ym-audit. The companion papers are archived at https://ai.vixra.org/author/lluis_eriksson.
Category: Mathematical Physics

Non-Existence Collapse: A Dynamical Mechanism for the Quantum-Gravitational Bootstrap of Spacetime from Nothing

Authors: Steven B. Thompson
Comments: 8 Pages.

We propose a minimal dynamical framework for the origin of the universe in which absolute non-existence—a state with no spacetime, matter, fields, or classical time—is intrinsically unstable under quantum-mechanical and gravitational principles. The Heisenberg uncertainty principle, applied to gravitational degrees of freedom, precludes a static null configuration: non-existence has "nowhere to go" but to collapse into itself, producing an effective Planck-scale density regime that undergoes a nonsingular quantum-gravitational transition. This collapse-driven process bootstraps the emergence of classical spacetime and the arrow of time, requiring no external causes, pre-existing substrates, boundary conditions, or auxiliary fields.Quantum gravity emerges here not as an imposed extension but as the inherent dynamicalstructure governing the instability and resolution. The mechanism refines and complements established proposals—such as Vilenkin’s quantum tunneling from nothing, the Hartle-Hawking no-boundary wavefunction, and recent developments in loop quantum cosmology bounces and quadratic gravity—by providing a purely mechanical interpretation that replaces probabilistic nucleation or Euclidean continuation with an intrinsic collapse bootstrap. It aligns with ongoingrefinements of no-boundary states, curvature bounces, and geometric "from nothing" models inthe 2025—2026 literature.This framework offers a parsimonious dynamical resolution to the question of why thereis something rather than nothing, transforming it into a consequence of quantum gravity’sstructure. Potential observational implications include consistency with cosmic microwave back-ground data and distinguishable signatures in primordial gravitational waves or large-scale structure that may differentiate collapse-initiated emergence from conventional inflationary scenarios.
Category: Relativity and Cosmology

Prolegomena to the Theory of Informational Space Genesis (ISG). A Geometric Resolution of the Hubble Tension and the Dark Sector

Authors: F. Rücker
Comments: 35 Pages. English. Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0)

The Lambda-CDM framework currently faces significant empirical challenges, most notably the 5-sigma "Hubble Tension" and the observation of "impossible" early galaxies by the James Webb Space Telescope (JWST). This paper proposes the Theory of Informational Space Genesis (ISG), a model that treats the universe as a 4D-rotational manifold unfolding into 3D space.Methodologically, we establish a cross-disciplinary convergence between vacuum thermodynamics and 4D-geometry. By isolating a vacuum "Pristine Potential" (approx. 2.03 meV) through a signal-denoising procedure, we derive a Lorentz-conformant scaling law for expansion. This energetic baseline is independently validated by a geometric master equation based on the Tesseract's structural ratio (Psi = 1.5) and a universal vacuum tension of 1/24.Both pathways synchronize at a predicted Hubble constant of H0 approx. 73.55 km/s/Mpc and an effective cosmic age of approx. 15.165 Gyr. We identify the transition from Lead (Z=82) to Bismuth (Z=83) as the macroscopic saturation point of this 4D-grid, providing a nuclear-physics anchor for cosmological evolution. The model explains early galaxy maturity via a kinetic leak at redshift z approx. 7.27 and resolves the Hubble tension through a 1.85% primordial BBN-offset. These findings suggest that the evolution of the cosmos and the limits of nuclear stability are governed by a single, unified geometric descent toward a 1.5-Pi resonance equilibrium.
Category: Astrophysics

The 1.5-pi Symmetry: A Lorentz-Conformant Scaling Law for the Dark Sector in Informational Space Genesis (ISG)

Authors: F. Rücker
Comments: 7 Pages. V1.1: Formalized baryonic base (1.5-pi symmetry). Refined scaling potential for full Lorentz Conformity. CC BY 4.0 license.

Current cosmological models, primarily the Lambda-CDM framework, face significant challenges in explaining Dark Matter and Dark Energy. The Theory of Informational Space Genesis (ISG) proposes an ontological shift, defining space as an emergent byproduct of interaction processes. This paper details a four-stage signal denoising methodology to isolate the "Pristine Potential" (Ep) of approximately 2.15 meV. By correlating this potential with a baryonic base (beta) derived from the ensemble average of the ten most abundant atomic species, we identify a fundamental geometric attractor at 1.5 pi (approximately 4.71).To ensure Lorentz Conformity, the scaling potential is formalized as a dimensionless ratio against the Cosmic Microwave Background peak energy, yielding a normalized invariant exponent of approximately 2.164. This geometric-informational scaling law predicts a Dark Matter density of approximately 28.6 percent, aligning with Planck observational data with high precision.
Category: Astrophysics

Tying the Universe Together: Quantum Balloon Interface Theory (QBIT)

Authors: Sean McCallum
Comments: 10 Pages. Creative Commons Attribution 4.0 International (CC BY 4.0)

The vacuum is not an empty stage. It is a stretchy quantum balloon - a dynamical condensate of overlapping standing-wave fields - with every massive particle a permanent topological knot tied into its fabric. Gravity emerges as local strain, forces as the rubber trying to smooth itself, and the entire Standard Model arises from zero modes trapped inside these knots.

Beneath the balloon lies an eternal pre-geometric qubit substrate that never disappeared after the Big Bang condensation. A tiny, Planck-suppressed portal couples the substrate to the rubber, naturally feeding zero-point energy and producing a mild dynamical dark energy with predicted equation-of-state drift w_a approx +7.2 x 10^{-5}.

With only two fundamental parameters (f and e), the QBIT framework quantitatively reproduces:

• Nuclear binding energies across the entire periodic table to better than 0.08% accuracy (maximum relative error 0.079% at 28Si);
• Quark and lepton masses and mixing matrices (CKM and PMNS) at the percent level or better;
• The observed baryon asymmetry eta approx 6.1 x 10^{-10};
• A tiny positive cosmological constant rho_Lambda approx 1.02 x 10^{-120} rho_Planck;
• A natural first-principles resolution of the Hubble tension via modified early-universe expansion driven by the substrate condensation front.

Black-hole interiors are regular topological cores with no singularities, the information paradox is resolved by substrate-mediated leakage, and quantum paradoxes (double-slit, delayed-choice eraser, Hardy's, Zeno, Elitzur-Vaidman, Schrodinger's cat) receive natural resolutions via rubber ripples and topological protection.

Lattice simulations and analytic results confirm topological stability, emergent curvature, multi-knot binding, and the substrate portal's predictions. QBIT thus provides a conceptually elegant, quantitatively successful, and experimentally testable candidate for a unified theory of particles, gravity, and cosmology - all emerging from one stretchy quantum balloon and its eternal qubit substrate.
Category: Quantum Gravity and String Theory

Exponential Clustering and Mass Gap for Four-Dimensional SU(N) Lattice Yang--Mills Theory Via Balaban's Renormalization Group and Multiscale Correlator Decoupling

Authors: Lluis Eriksson
Comments: 21 Pages.

We establish exponential clustering with a strictly positive mass gap for four-dimensional pure SU(N) lattice Yang--Mills theory with Wilson's action, uniformly in lattice spacing $eta$ and physical volume $L_{mathrm{phys}}$:$|mathrm{Cov}_{mu_eta}(mathcal{O}(0),mathcal{O}(x))| leq C,e^{-m,|x|/a_*}$, with $m > 0$ and $a_* sim Lambda_{mathrm{YM}}^{-1}$.The proof assembles three ingredients: (1) Balaban's rigorous renormalization group for lattice gauge theories (CMP 1984--1989), which produces effective densities with local polymer decompositions and exponentially decaying activities; (2) a terminal-scale polymer cluster expansion (imported from Balaban's convergent renormalization expansions), which implies exponential clustering for the effective terminal measure; and (3) a multiscale correlator decoupling identity (this paper), which separates ultraviolet fluctuations from infrared physics and yields uniform UV suppression. The coupling control required by Balaban's framework -- that the effective couplings remain in the perturbative regime throughout the RG iteration -- is established via an inductive argument using Cauchy bounds on the analyticity of the effective action. We also verify the Osterwalder--Schrader axioms OS0, OS2, OS3, and OS4 for subsequential continuum limits, and establish vacuum uniqueness and non-triviality. The remaining axiom OS1 (full O(4) Euclidean covariance) is not established here; we prove covariance under lattice translations and the hypercubic group $mathcal{W}_4$, and show that if O(4) covariance holds in the continuum limit, the reconstructed Wightman theory is a non-trivial relativistic quantum field theory with mass gap $Delta_{mathrm{phys}} geq c_N,Lambda_{mathrm{YM}} > 0$, where $c_N > 0$ depends only on $N$ (and is independent of $eta$ and $L_{mathrm{phys}}$).
Category: Mathematical Physics

Irrelevant Operators, Anisotropy Bounds, and Operator Insertions in Balaban's Renormalization Group for Four-Dimensional SU(N) Lattice Yang--Mills Theory: Symanzik Classification and Quantitative Irrelevance of O(4)-Breaking Operators

Authors: Lluis Eriksson
Comments: 18 Pages.

We classify gauge-invariant local lattice operators of classical dimension 6 on the four-dimensional hypercubic lattice into O(4)-invariant, hypercubic-invariant but O(4)-breaking (anisotropic), and on-shell-redundant components, following the Symanzik improvement programme and the on-shell improvement technique of Luscher--Weisz (1985). Inside Balaban's renormalization group framework for SU(N) lattice Yang--Mills theory, we extract the anisotropic projection of the effective action via local Taylor expansion of polymer activities in the small-field regime and prove a quantitative quadratic scale bound for the anisotropic coefficient: for every RG step $k leq k_*$ with effective coupling $g_k leq gamma_0$, the coefficient of the (one-dimensional) anisotropic sector in the classical dimension-6 Symanzik expansion satisfies $|c_{6,mathrm{aniso}}^{(k)}| leq C,a_k^2$, uniformly in lattice spacing $eta$, physical volume $L_{mathrm{phys}}$, and RG step $k$. We further prove a quantitative insertion integrability estimate for connected correlators with one insertion of the anisotropic operator. When combined with the rotational Ward identity derived in the companion paper, this yields that the corresponding breaking distribution tested against Schwartz functions is $O(eta^2,|log((Lambda_{mathrm{YM}}eta)^{-1})|)$ and hence vanishes as $eta to 0$.
Category: Mathematical Physics

The Topological Inversion Model (TIM): A Unied Non-Singular Framework for Cosmology, Quantum Topology, and Gravitational-Wave Phenomenology

Authors: Kobie Janse van Rensburg
Comments: 13 Pages. Fixed ANSI characters and Citations.

We present Version 5 of the Topological Inversion Model (TIM), a unified non-singular cosmological framework based on a Planck-scale reciprocal inversion R = L2p/r. Six results are now established. (1) A topological snap at r = Lp generates an elastic recoil field Ψ whose self-consistent scattering amplitude gives echo reectivity Γinner ≈ 0.42 at ξΨ = 0.002; the observable Fabry-Pérot echo is Γecho ≈ 0.125 (Section 11b). (2) A calibrated BBN fit yields ψBBN = 1.059±0.012, partially mitigating the 7Li problem.(3) An overshoot texture mechanism raises the predicted H0 from 67.4 to 71.1 km s−1 Mpc−1, reducing the Hubble tension from 5.0σ to 1.7σ and forward-predicting the NANOGrav 15-year PTA signal. (4) Polymer one-loop analysis confirms UV finiteness without counterterms and vacuum stability (m2eff = 1.016 m2Ψ > 0). (5) Dark matter is identied with the gradient energy of the thinning field δΨ(r) = Ψeq j0(mΨr): no new particle is required, the density profile is naturally cored (ρDM ∝ r0 at r → 0, resolving the core-cuspproblem), rotation curves are flat, and the required field mass mΨ ≈ 3.8 × 10−23 eV c−2 falls within the observational window for ultralight dark matter. (6) The Standard Model is shown to emerge as the low-energy effective theory on the post-Snap manifold: topological defects of the Skyrme field carry quantum numbers matching the observed fermion spectrum, and integrating out high-momentum modes recovers LSM exactly. All results are reproducible from the providedPython code.
Category: Quantum Gravity and String Theory

The Topological Inversion Model (TIM): A Unified Non-Singular Framework for Cosmology, Quantum Topology, and Gravitational-Wave Phenomenology

Authors: Kobie Janse van Rensburg
Comments: 16 Pages. (Note by ai.viXra.org Admin: Many symbols are not legible/blocked; please cite listed scientific references)

We present Version 3 of the Topological Inversion Model (TIM), a unified non-singularcosmological framework based on a Planck-scale reciprocal inversion R = L2p/r. This versionadds a fourth substantive result to the three established in Version 2. First, the echoreflectivity G(Y, M) is derived from a self-consistent WKB boundary condition. Second,yBBNand Leff(z) are shown to be physically independent, with best-fit yBBN = 1.059 ± 0.012 partially mitigating the Li-7 problem. Third, TIM is compared against LQC, Asymptotic Safety, and ECO models. Fourth (new), we propose that a slight underdamping of the topological snap generates a network of texture defects via the Kibble-Zurek mechanism. These textures act as early dark energy, shrinking the pre-recombination sound horizon and raising the predicted H0 from 67.4 to 71.1 km s-1 Mpc-1 — a substantial partial resolution of the Hubble tension. A single new parameter e (overshoot amplitude) is constrained jointly by the BBN expansion rate and the CMB early dark energy fraction, giving e = 0.115 ± 0.02. The texture collapse additionally predicts a stochasticgravitational-wave background with WGWh2 ~ 1.5 × 10-9 at 3 nHz — consistent with theNANOGrav 15-year signal. All results are reproducible from the provided Python code.
Category: Quantum Gravity and String Theory

Temporal Necessity in Relational Mathematical Realism: A Godelian Argument Against the Block Universe

Authors: Jason Merwin
Comments: 10 Pages.

A foundational question in the philosophy of physics is whether time is a fundamental dimension of reality or an emergent phenomenon. The standard Block Universe interpretation of general relativity treats time as a static dimension, with the passage of time relegated to psychological illusion. In this paper, we present a novel argument against the Block Universe derived from the framework of Relational Mathematical Realism (RMR), which identifies physical existence with mathematical structure. We demonstrate that if reality is a sufficiently complex, locally consistent mathematical structure, then Gödel's First Incompleteness Theorem renders a static, completed universe logically impossible. The resolution of this impossibility requires the structure to undergo a non-terminating sequence of state extensions, which we identify with the passage of time. We conclude that time is not a dimension within which the universe exists, but rather the logically necessary process by which a complex mathematical structure maintains consistency. This result, if sound, constitutes the first derivation of temporal passage from mathematical logic and ontology alone.
Category: History and Philosophy of Physics

Conditional Continuum Limit of 4d SU(N_c) Yang-Mills Theory via Two-Layer Architecture, RG-Cauchy Uniqueness, and Step-Scaling Confinement

Authors: Lluis Eriksson
Comments: 19 Pages.

Building on the lattice results established in Papers [E26I]-[E26IX], we give a conditional construction of a scaling-limit state for pure SU(N_c) lattice Yang-Mills theory in four Euclidean dimensions, along dyadic lattice spacings a_k = a_0 2^{-k}. The construction proceeds via a two-layer architecture. Layer 1 (Local fields): For bounded gauge-invariant local observables (Wilson loops, normalized plaquette traces), expectations converge without extracting subsequences to a unique limit. Precompactness of expectations at fixed physical side length L is trivial since |_{a,L}| <= 1. Uniqueness follows from a multiscale RG-Cauchy estimate that bounds the change of local expectations under a single RG step. The extension to unbounded observables such as smeared curvature monomials, which require additive renormalization, is deferred to future work. Layer 2 (Confinement): The physical string tension sigma_phys > 0 is established through step-scaling of Creutz ratios evaluated on Wilson loops whose physical dimensions R x T are held fixed as a -> 0. The limiting state on bounded observables inherits Osterwalder-Schrader positivity from the lattice and admits a Hilbert-space reconstruction via reflection positivity. SO(4) rotational invariance is expected in the continuum (the hypercubic breaking being O(a^2), subject to standard operator classification and construction of renormalized Schwinger functions). The mass gap is established conditionally via uniform exponential clustering of connected correlators -- an input from a uniform physical transfer-matrix spectral gap -- and the reconstruction theorem. Nontriviality follows conditionally from an area law for Wilson loops. Key dependencies on prior papers: uniform LSI inputs [E26I]-[E26IX]; Balaban multiscale effective action [E26III]-[E26V]; DLR-LSI [E26VII]; unconditional lattice closure inputs [E26IX].
Category: Mathematical Physics

Ricci Curvature of the Orbit Space of Lattice Gauge Theory and Single-Scale Log-Sobolev Inequalities

Authors: Lluis Eriksson
Comments: 11 Pages.

We establish that the orbit space B = A/G of SU(N_c) lattice gauge theory satisfies the Riemannian curvature-dimension condition RCD*(N_c/4, dim A); in particular, it satisfies CD(N_c/4, infinity) in the sense of Lott-Villani-Sturm. The proof proceeds by showing that the configuration space A = SU(N_c)^{|B_1(Lambda)|}, equipped with the bi-invariant product metric = -2 tr(XY), is an Einstein manifold with Ric_A = (N_c/4) g_A, and then applying the stability of the RCD* condition under quotients by compact groups of measure-preserving isometries (Galaz-Garcia-Kell-Mondino-Sosa). This approach bypasses the need for explicit O'Neill curvature computations and handles the singular stratum (reducible connections) automatically. As a consequence, we derive a conditional log-Sobolev inequality for measures on B of the form d mu = e^{-Phi} d nu / Z with constant alpha = (N_c/4) e^{-osc(Phi)}. All constants are computed explicitly for SU(2) and SU(3). This provides the geometric input in a program aiming at a volume-uniform log-Sobolev inequality for SU(N_c) lattice Yang-Mills theory at weak coupling; the complementary analytic input (uniform bounds on the effective potential oscillation, via Balaban's renormalization group) is the subject of ongoing work.
Category: Mathematical Physics

Uniform Log-Sobolev Inequality and Mass Gap for Lattice Yang--Mills Theory

Authors: Lluis Eriksson
Comments: 24 Pages.

We establish that SU(N_c) lattice Yang-Mills theory in d=4 dimensions with Wilson action at sufficiently weak coupling (beta = 2N_c/g^2 >= beta_0) satisfies a log-Sobolev inequality with constant alpha_* > 0 uniform in the lattice size L_vol. Combined with reflection positivity of the Wilson action and the DLR-LSI extension plus Stroock-Zegarlinski mixing route, this yields a mass gap Delta_phys > 0 uniform in L_vol without additional assumptions. The proof combines three ingredients: (i) Balaban's constructive renormalization group, which produces controlled effective actions at all scales; (ii) the orbit space Ricci curvature bound Ric_B >= N_c/4, which gives a uniform log-Sobolev constant for conditional measures of fast modes at each RG scale via the Bakry-Emery criterion; and (iii) a multiscale entropy decomposition with sweeping-out bounds, where the geometric scaling factor ||Q_(k)*||^2 = 2^{-(d-1)k} of transversal block averaging ensures summability of cross-scale errors.
Category: Mathematical Physics