All Submission Categories

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. Sectionu202f4 then shows that the Weyl tensor already contains an intrinsic two sided decomposition into self dual and anti self dual parts, and that a variational principle enforcing their indistinguishability drives the Weyl tensor to vanish, selecting conformal flatness with Minkowski space as the 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

THE MASTER MAP - Audit Experiments Report: Mechanical Audit Experiments and Reproducibility Appendix for the 2602-Series Programme on 4D SU(N) Yang-Mills

Authors: Lluis Eriksson
Comments: 4 Pages. v3 audits the auditor: 29/29 tests validate exact/toy/group content but discharge NO ledger hypothesis. Three harness defects fixed: d=4 harmonic is 1/2 not 3/2; kurtosis test rescoped to C4(N)>0; (H2') profile.

This is the experiment-first audit report for the 2602-series programme: a runnable mechanical suite (repository ym-audit) with declared pass/fail criteria, a 2D Yang-Mills benchmark, gauge/infrastructure/UV-flow proxy layers, and a reproducibility manifest. Version 3 aligns the report with the fully audited programme and corrects three defects in the harness itself. Scope statement (sharpened): the 29 tests adjudicate exact identities, toy models, and group-theoretic facts; they cross-validate the per-paper suites of THE-ERIKSSON-PROGRAMME (verification/2602-*, 15 papers, independent implementations agreeing where they overlap, e.g. the triangular-lock dimension counts); they do NOT discharge any entry of the programme ledger - a 29/29 run leaves the hypothesis set {(H1), (H2)+beta_LF, (H3), (H2'), (H-LOC), L6.2-import, (H-Rbeta), (H-P0'), structural+window, lambda != 0 traceable, ...} exactly as it was. Corrections: the d=4 harmonic coefficient is 1/2 (harness had 3/2, a dropped-term bug; the paper chain had 3/5, the d=3 value - three-way inconsistency now settled and machine-adjudicated); the non-triviality test is rescoped (Haar kurtosis != 3 is a single-link fact - exactly 2 for SU(2) - present even at strong coupling; what it verifies is C4(N) > 0); the super-polynomial large-field test is restated under the audited log-power profile. The 2D YM benchmark (transfer-matrix gap Delta = g^2 N/2 to 1e-14) and the dependency DAG survive; "Papers 86-90" are pinned to 2602.0088 v3 / 0087 v3 / 0092 v2 / 0091 v2 / 0096 v2.
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

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: 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

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 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

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

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 Navigation Guide to the Conditional Construction of 4D SU(N) Yang-Mills with Mass Gap - the Audited-Ledger

Authors: Lluis Eriksson
Comments: 5 Pages. Retitled. v2: "Unconditional Solution" withdrawn; audited-ledger navigation guide. Corrections: d=4 harmonic coefficient 1/2 (not 3/5); log-power profile restored. Triangular lock verified. Suite 6/6.

This is the navigation guide and audit manifesto for the 2602-series programme on 4D SU(N) Yang-Mills. Version 2 is the audited-ledger edition: the dependency graph, Clay/Jaffe-Witten checklist and threat model of v1 are retained, but every node is now pinned to its audited version and carries its named hypothesis loads; the claim is stated as what it is - a conditional assembly: relative to the declared external mathematics (abstract KP, OS reconstruction, lattice reflection positivity) AND to the internal ledger {(H1), (H2)+beta_LF, (H3), (H2'), (H-LOC), per-scale decoupling, (H-Rbeta), (H-P0'), structural+window loads, lambda != 0 traceable}, the chain assembles OS0-OS4 and OS1 and reconstructs a Wightman QFT with mass gap. v1's "unconditional" (in any sense) is withdrawn. Version 2 also corrects two mathematical defects in v1's new material: the hypercubic harmonic's coefficient (3/5, the d=3 value) is corrected to 1/2 in d=4; and the Large-Field Annihilation Lemma's hypothesis p0(g) >= c/g^2 - attributed to a source whose actual profile is (A0 log g^{-2})^{p*} - is replaced by the honest (H2') trichotomy. The genuinely structural new content survives and is machine-verified: the marginal anisotropic sink at d=4 is empty (exact group averaging over W4 on Sym^2(Lambda^2 R^4): quotient dimension 0, versus 1 at d=6), hence renormalization mixing is triangular in the anisotropic channel and the a^2 x a^{-2} -> O(1) objection has no landing site.
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: 4 Pages. v2: conditional OS1 theorem. v1's "no unproved hypotheses remain" withdrawn; imports retagged to 2602.0087 v3 / 0088 v3 / 0091 v2 with their loads. Native Ward mechanism machine-verified (O(eta^2)). Suite 6/6.

Info de reemplazo — ai.viXra:2602.0092 (v1 → v2)Paper a reemplazar: 2602.0092Method: replacement of existing paperPDF: ward_v2.pdf — sha256 9564aec01a4836c9 — 4 páginasCategory: Mathematical Physics (como v1)Title: Rotational Symmetry Restoration and the Wightman Axioms for Four-Dimensional SU(N) Yang-Mills TheoryAuthor: Lluis ErikssonAbstract (texto plano):We derive a lattice Ward identity for infinitesimal Euclidean rotations of the Wilson theory, identify the breaking term as a dimension-6 anisotropic operator insertion (in the classification of 2602.0087 v3), and show that the breaking distribution is O(eta^2 |log((Lambda_YM eta)^{-1})|) -> 0, establishing axiom OS1 (full O(4) covariance) for subsequential continuum limits - conditionally on the audited companion inputs. Version 2 corrects v1's framing: v1 imported the mass gap, OS0/2/3/4, anisotropy and insertion bounds as "unconditional"; per the audited versions these carry the programme ledger's loads (the source-mapped KP block of 2602.0091 v2, (H-LOC), per-scale decoupling and coupling control for 2602.0088 v3; window and structural loads for 2602.0087 v3). The assembled result - a non-trivial Poincare-covariant Wightman theory with mass gap Delta_phys >= c_N Lambda_YM > 0 - therefore holds under the explicit composed hypothesis set, stated in Section 5; v1's "no unproved hypotheses remain" is withdrawn. The native content survives audit and is machine-verified: the Ward mechanism on an exactly solvable lattice Gaussian model (breaking = O(eta^2) measured), the lambda_{mu nu} != 0 mechanism in the exact quartic model (rotations annihilate O(4) invariants, not the hypercubic harmonic), the Lie-algebra-to-group invariance lemma, the symmetric-difference eta^2/6 error constant, and the eta^2 log vanishing arithmetic.
Category: Mathematical Physics

A Source-Mapped Terminal KP Bound and a Conditional Clay Checklist for the 4D SU(N) Yang-Mills Programme

Authors: Lluis Eriksson
Comments: 4 Pages. Retitled. v2 withdraws v1's "verified KP / last gap closed" framing: (H1)+(H2)+(H3)+(H2') => KP retained and machine-verified; (H2) carries the audited beta_LF/profile loads. Checklist now has statuses.

Part I (terminal KP bound). We isolate explicit hypotheses (H1)-(H3) on the terminal polymer activities of the 4D SU(N) lattice Yang-Mills programme and prove that, together with a profile condition (H2') made explicit in this version, they imply the Kotecky-Preiss convergence criterion used as Hypothesis (H-KP) in 2602.0088 v3. The implication is elementary and fully machine-verified (exponential inequality, weighted lattice-animal bound with d(X) >= |X|-1, explicit smallness threshold in g). This refines the ledger: (H-KP) <= (H1)+(H2)+(H3)+(H2'). Status of the hypotheses: v1 declared them "verified from primary sources"; per the audited bridge (2602.0069 v2) the correct statement is: (H1) and (H3) are traceable to Balaban's CMP papers; (H2) is traceable with loads (the beta_LF dichotomy, and the unpinned profile (A0,p*) - the recurring (H-P0) datum of the audited series). Part II (assembly map + Clay checklist). We give the dependency graph assembling 2602.0088 v3, 2602.0087 v3 and the (unaudited) rotational Ward companion, and a Clay/Jaffe-Witten checklist with statuses: activating KP does not activate the mass gap of 2602.0088 v3 by itself - that theorem additionally carries (H-LOC), a per-scale decoupling import, and coupling-control loads; OS1 remains open pending the Ward companion's audit. No unconditional Clay claim is made. All adjudicable content is verified in a deterministic companion suite.
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: 5 Pages. v3-style audit pass: v2 makes the complete-analyticity input explicit as (H-CA); the audited route backs only a windowed version, and the thermodynamic limit needs (H-CA)_infty. Dual architecture survives.

We present two parallel results for SU(N) pure gauge lattice Yang-Mills in four Euclidean dimensions, at fixed lattice spacing eta > 0 and weak coupling g0 <= g*, both conditional on a single shared input, the Dobrushin-Shlosman complete analyticity condition (H-CA): (A) a log-Sobolev inequality Ent(f^2) <= (2/rho) E(f,f) with rho > 0 independent of L, via Cesi's quasi-factorisation seeded by a Bakry-Emery/Holley-Stroock local LSI; and (B) a spectral gap m_gap >= m0 > 0 for the Osterwalder-Seiler Hamiltonian, via Dobrushin clustering and reflection positivity. The two outputs are logically parallel; neither implies the other here (the bridge lemma remains open, Remark 6.3). Version 2 corrects the status of the shared input: v1 declared (H-CA) verified from Balaban's infrastructure; per the audited chain (2602.0053/0054 v2) that route is conditional on (H-DOB-blk)+(H-P0) and valid only in the volume window L <= exp(C/g0^2). Accordingly all results are stated in two regimes: windowed (audit-backed conditional) and all-volume (under the strictly stronger bare hypothesis (H-CA)_infty, required for the thermodynamic limit, Theorem C). What is unconditional and machine-verified: the curvature computation Ric_SU(N) = N/4, the Holley-Stroock block-seed arithmetic, the variance/entropy decompositions and the failure of pointwise inheritance, the Dobrushin contraction machinery and its window arithmetic, the clustering => transfer-gap lemma on explicit operators, and the convergence of Cesi's geometric factor. All bounds remain explicit in N, g0, eta.
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: 7 Pages. v3: mass-gap/clustering result retagged conditional. Terminal KP input made explicit as (H-KP); new localization hypothesis (H-LOC); large-field profile aligned with the audited ledger. Suite 7/7.

We assemble a proof architecture for exponential clustering with a strictly positive mass gap for four-dimensional pure SU(N) lattice Yang-Mills theory with Wilson's action, Cov(O(0),O(x)) <= C exp(-m|x|/a*), m > 0, a* ~ 1/Lambda_YM, with constants uniform in lattice spacing eta and physical volume L_phys - conditionally on three identified inputs. (1) Balaban's structural package (polymer decompositions, exponentially decaying activities), traceable per 2602.0069 v2 with the beta_LF dichotomy attached. (2) A terminal-scale Kotecky-Preiss smallness bound, Hypothesis (H-KP): v1-v2 cited it as proved in an unpublished companion with no identifier; Version 3 retags it as a hypothesis until that companion exists and survives audit. (3) A localization hypothesis (H-LOC) for conditioned observables, made explicit for the first time in v3: the telescoping step compares the terminal clustering bound against O~ = E[O | sigma_a*], whose support is not local. The coupling control (Proposition 4.1) is proved by Cauchy bounds conditionally on the uniform-in-k analyticity radius of Balaban's discrete beta-function and on the large-field penalty profile satisfying the (A0,p*) trichotomy of the audited ledger. What is unconditional and machine-verified: the multiscale telescoping identity (exact for any measure and any nested sigma-algebra chain), the summation-over-scales arithmetic, the lattice-animal bounds, the implications KP => exponential clustering and clustering => spectral gap in exactly solvable settings, and the coupling-control recursion. We verify OS0, OS2, OS3 unconditionally at the lattice level and OS4 conditionally; OS1 (full O(4) covariance) is not established here - its natural conditional supplier is 2602.0087 v3 via 2602.0063 v3. All adjudicable content is verified in a deterministic companion suite.
Category: Mathematical Physics

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

Authors: Lluis Eriksson
Comments: 6 Pages. v3: clustering/mass-gap import (Thm 4.5) retagged conditional; v2's "Thm 6.6 unconditional" withdrawn. Symanzik/W4 core machine-verified (6/6). Conditional SO(4)-restoration input for 2602.0063 v3.

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 technique of Luscher-Weisz. The anisotropic sector is one-dimensional (Theorem 3.6, Proposition 3.7: uniqueness of the hypercubic harmonic) - a purely representation-theoretic fact, machine-verified in the companion suite together with the classical Symanzik a^2/12 anisotropic term of the Wilson plaquette itself. Inside Balaban's renormalization group framework (small-field regime, g_k <= gamma_0, k <= k* - the window bookkeeping of the audited chain), we extract the anisotropic projection of the effective action via local Taylor (jet) expansion of polymer activities and prove the quadratic bound |c^(k)_{6,aniso}| <= C a_k^2, uniformly in lattice spacing eta, physical volume, and RG step k within the window - conditionally on the structural package, whose audited status is now attached (traceable per 2602.0069 v2; beta_LF dichotomy for the large-field remainder). We further prove an insertion integrability estimate for connected correlators with one anisotropic insertion; Version 3 corrects its status: v1-v2 called it unconditional, resting on an imported clustering/mass-gap bound (Theorem 4.5, from the unaudited companion [1]) claimed uniform in eta and L_phys - per the audited program (2602.0053/0054 v2) such a gap is conditional on (H-DOB-blk)+(H-P0) and windowed, so Theorem 6.6 is conditional on that input. Combined with the rotational Ward identity of the companion [2] (unaudited, identifier pending), the O(4)-breaking distribution tested against Schwartz functions is O(eta^2 |log((Lambda_YM eta)^{-1})|) and vanishes as eta -> 0 - under the same conditional load. This paper thereby supplies, conditionally, the operator-classification input required by 2602.0063 v3 (Proposition 5.3/Remark 5.4) for continuum SO(4) restoration. All verifiable content (representation counts, the unique hypercubic harmonic, the plaquette's own a^2/12 anisotropy, Cauchy-jet mechanics, the a_k^2/log bookkeeping, and the clustering-to-integrability conversion) is adjudicated in a companion suite.
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: 26 pages. v2: 5-page retraction/erratum plus preserved 21-page v1. Lemma 2.2 and Proposition 1.3 stand; Lemma 3.2 is only independently recoverable and its original instantiation is withdrawn.

VERSION 2 RETRACTION AND ERRATUM. The principal results of version 1 are withdrawn. Lemma 3.6, Eq. (16), falsely identifies the Wilson-flow linearisation with a connected weighted scalar Laplacian plus a pointwise adjoint term. At the trivial configuration, gauge invariance forces the true Hessian to annihilate a pure-gauge subspace of dimension at least (|V|-1)(N^2-1), incompatible with the printed connected-Laplacian kernel; if the positive-weight graph is disconnected, the single stationary heat-kernel term used downstream is itself false. Consequently Lemma 3.8, Proposition 3.9, Theorem 3.11 and Theorem 1.1 are withdrawn. Lemma 2.2 and Proposition 1.3 remain intact. Lemma 3.2 is only recoverable as a separately specified scalar heat-kernel theorem; its original instantiation is withdrawn. Reflection positivity, Osterwalder-Schrader reconstruction, thermodynamic limit and mass gap remain open. The five-page erratum is followed by the preserved 21-page version 1.
Category: Mathematical Physics

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

Authors: Lluis Eriksson
Comments: 21 pages. v2: 6-page retraction/status note plus preserved 15-page v1. Defects A-G are included; Lemma 3.3 is false as printed and is not listed as unaffected.

VERSION 2 RETRACTION AND STATUS NOTE. The principal results of version 1 are withdrawn. Theorem 4.4 and Proposition 3.8 depend on the false Wilson-flow linearisation retracted in ai.viXra:2602.0085 and on further false statements. Lemma 3.1 omits the stationary heat-kernel term; Lemma A.1 gives a variance-oscillation bound that fails for correlated non-product measures; Theorem 5.1 does not obtain a positive self-adjoint generator from its stated hypotheses; Lemma 3.3 uses a non-periodic separation across the torus boundary; and Lemma 3.5 bounds a nonlinear map by a differential at one endpoint rather than an integrated or uniform Jacobian. Definitions 2.2, 2.5 and 2.6 remain definitions, and the cited lattice reflection-positivity Theorem 4.1 is not retracted here. Nothing in this note proves the intended almost-reflection-positivity conclusion false; the printed proof and several printed statements fail. The six-page erratum is followed by the preserved 15-page version 1.
Category: Mathematical Physics

Phase Quantization from Observable Regularity: Reducing the Wallström Objection to a Standard Physical Condition

Authors: Adrian Rohr
Comments: 23 Pages.

Wallström (1989, 1994) showed that the Madelung hydrodynamic equations admit solutions with non-integer phase circulation, for which no single-valued wave function exists. Previous completions of the Madelung system postulate either single-valuedness or the quantization condition directly.In this paper we consider the regularity of the probability current j = ρ ∇S/m at nodal zeros within the Onsager-Machlup stochastic variational framework. We find that requiring j ∈ C∞, combined with the Hamilton-Jacobi constraint at zeros of ρ, implies integer phase circulation. Neither condition alone has this consequence: smooth currents with arbitrary circulation exist when the dynamics is absent, and the Hamilton-Jacobi constraint alone admits the non-quantized solutions constructed by Reddiger and Poirier (2023). We also find that C∞ is the only regularity class with this property: for any finite k, non-integer solutions satisfying Ck can be constructed.When the framework is applied with initial data satisfying ρu2080 > 0, the phase is single-valued by simple connectivity, the Schrödinger equation follows from the variational principle, and any nodes formed under subsequent evolution carry integer winding numbers. The variational principle degenerates at zeros of ρ, leaving the winding parameter undetermined — a feature that holds for any variational functional of the form ∫ρ G du207fx, not only the Onsager-Machlup action.The non-quantized solutions correspond to multivalued sections of a non-trivial line bundle and do not arise within the natural domain of the stochastic framework.
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: 45 Pages.

This work introduces the Information-Geometric Physics System (IGPS) to explain the origin of fundamental leptonic properties through the geometry of the Oloid manifold.Key Contributions:Geometric Modeling: Modeling fundamental particles as "closed information nodes" on an Oloid manifold under C2 continuity constraints.Mass Derivation: Deriving spectral mass from curvature integrals and normal bundle holonomy along the manifold's seam.Topological Spin: Proving that the SU(2) double-covering of the SO(3) seam moduli space naturally induces spin-1/2 structures.Fundamental Constant Beta: Identifying the universal geometric stiffness parameter β = 1/(sqrt(3)π) as the governing invariant for internal strain.Impact: The framework establishes a direct link between the fermion mass spectrum and the topology of informational manifolds, laying the groundwork for analyzing baryonic mass scaling and strong interactions in the IGPS series.
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: 23 Pages.

This study extends the Information-Geometric Physics System (IGPS) framework from single-node models to composite nuclear structures. By utilizing the Oloid Trinity Configuration, the research elucidates the topological origin of mass and the statistical properties of baryons.Key Analytical Points:Dimensional Jump: We characterize the "Dimensional Jump" phenomenon, representing an informational scale transition from planar seam scaling to the volumetric scaling of entangled manifolds. This leads to the derivation of the universal geometric multiplier G = 4/3 π², originating from the S³ configuration space volume and the SU(3) non-singlet color fraction, which bridges the mass scales between leptons and nucleons.The 5/2 Theorem: The interaction strain overhead is rigorously derived as Δ = 2.5 using the central charges of the Goddard-Kent-Olive (GKO) coset construction (��_IGPS = SU(3)u2081^{⊗3} / SU(3)u2083). Together with G, this yields a proton mass prediction that aligns with CODATA standards to within a 0.004% precision threshold.Emergence of Spin-Statistics: The research derives Fermi-Dirac statistics and fractional spin-1/2 as necessary topological consequences of maintaining C² continuity on manifolds entangled through the SU(2) double-covering structure.Conclusion:Residual analysis indicates that the 0.004% numerical discrepancy represents the expected precision of a leading-order geometric estimate, with further corrections appropriately deferred to non-perturbative QCD dynamics. These findings confirm that baryonic structures represent the most stable volumetric organization of information, effectively achieving structural closure for the origin of matter within the IGPS theoretical 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: Closing the Bałaban-Doob Circuit under Quantitative Blocking and Decoupling Hypotheses

Authors: Lluis Eriksson
Comments: 6 Pages. v2: v1's Doob-oscillation lemma was false for correlated measures (counterexample of 2602.0070 v2); repaired via conditional oscillation + (H-DEC/AT). UV closure now conditional on (H-LIP^2) + decoupling + audited ledger. Suite included.

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, CONDITIONALLY on an explicit hypothesis ledger: a quantitative regularity hypothesis for the blocking map (squared-oscillation summability, Assumption A — equivalently (H-LIP^2), a strengthened form of the (H-LIP) contraction of 2602.0073 v2), the Dobrushin-type decoupling hypothesis (H-DEC/AT) of the sibling audits, and the audited statuses of the Balaban structural package. The argument assembles: (i) Balaban's renormalization group program (polymer representation, irrelevance bounds after beta-function extraction, UV stability of effective densities) — traceable per 2602.0069 v2, with the beta_LF dichotomy for the large-field part; (ii) a Doob-martingale covariance IDENTITY (exact for every measure) together with a conditional-oscillation influence bound — v1's claim that the oscillation control holds "without product-measure hypotheses" is withdrawn: v1's Remark 2.3 correctly rejected Efron-Stein for the non-product interpolating measures, but the Doob-oscillation Lemma 1.5 of v1 fails for the same reason (two-spin counterexample, 2602.0070 v2); the repair is (H-DEC); (iii) the RG-Cauchy summability framework of 2602.0073 v2, consumed with its full ledger (including (H-theta)/F-SQRT for the truncation errors). Under the ledger, the telescopic state sequence converges and the resulting state omega_L is gauge-invariant, Euclidean-covariant (hypercubic), and positive. Osterwalder-Schrader reconstruction, the thermodynamic limit, and the mass gap remain open, as in v1. All mechanical steps — the exact covariance identity, both counterexample adjudications, the Assumption A mechanics on explicit blocking maps (including a non-local sharpness example showing locality plus contraction are genuinely needed), and the corrected Proposition 6.1 arithmetic with its exact M 2^(-4k) scale cancellation — are machine-verified in a companion suite.
Category: Mathematical Physics

The Topological Inversion Model (TIM) v7: From Self-Negation to the Standard Model

Authors: Kobie Janse van Rensburg
Comments: 27 Pages.

The Topological Inversion Model (TIM) derives the structure of the Standard Model from a single axiom: the self-negation of Absolute Nothing (//Gaunab), which generates a Z_2 involution. Combined with compactness, orientability, and minimality, this uniquely determines the spatial manifold as RP^3 = S^3/Z_2 (Theorem 1), deriving three spatial dimensions rather than assuming them.Version 7 supersedes previous versions with major extensions: (i) the complete logical chain from self-negation to the Standard Model gauge group in seven steps, with each step labelled as axiom, theorem, or derived;(ii) an RP^3 uniqueness theorem proving that the spatial manifold is the only compact orientable quotient consistent with the foundational Z_2; (iii) classification of flat gauge bundles for G_SM = SU(3) x SU(2) x U(1) on RP^3, yielding 4 physical Hosotani sectors with vector-like colour automatic in all sectors;(iv) Casimir energy computation showing that the topological vacuum prefers unbroken electroweak symmetry with sin^2(theta_W) = 1/4 as the bare ratio, while EWSB is driven by the Higgs potential at T_c ~ 150-320 GeV;(v) resolution of M* = 3689 +/- 200 GeV as a derived matching scale (topology plus SM running), not requiring a separate dynamical mechanism; (vi) closure of the alpha programme through six independent routes, establishing that topology determines ratios while absolute couplings require dynamical input; (vii) identification of the width parameter W on B_3 as the generation quantum number, explaining N_gen = N_colour = 3 as a topological identity; and (viii) geometric emergence of Z_3 colour structure from degree-3 Hopf preimages on S^3.The framework reduces the Standard Model's 19 free parameters to 18 (via the topological mass relation M_u = M_d + 3M_e) and produces 5 quantitative predictions: M* ~ 3.7 TeV, T_c ~ 150-320 GeV, R^{-1} ~ 150 GeV, sin^2(theta_W) = 1/4 (topological), and Casimir vacuum selection of the unbroken electroweak sector. Three irreducible free parameters remain: alpha_em, the Higgs VEV v, and the Higgs mass m_H.
Category: Relativity and Cosmology

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: 9 Pages.

Einstein’s special relativity postulates the constancy of light speed c as an axiom, yet provides no account of its origin. We reformulate the universe as a discrete geometric computational network operating at the Planck scale, wherein c emerges not as a fundamental constant but as the information-processing bandwidth of the network itself. The initial state—an infinite-dimensional regular simplex with Laplacian eigenvalue λ2 = N—enforces cosmic uniformity without inflation, while informational Pauli repulsion, arising from the autonomous reconfiguration dynamics wheninfinite vertices are projected onto finite coordinates, drives both the Big Bang and present-day accelerated expansion as a single unfolding process. From finite bandwidth constraints alone, we derive the Light-Speed Resource Allocation Principle (LRAP): c 2 = v2 + τ 2, partitioning computational bandwidth between spatial propagation v and internal state maintenance τ . The Lorentz factor reinterprets as a processing-lag ratio γ = c/τ , andthe energy-momentum relation E 2 = (pc) 2 + (m0c2 ) 2 emerges as a theorem rather than a postulate. Mass is identified as projection caustics—local concentrations of information density arising from imperfect 4D → 3D mapping—while gravitational force is the spatial gradient of the geometric frustration potential, F = −∇Φ. Singularities are dissolved: they are not physical infinities but Dimensional Arrest zones—regions of asymptotic freezing where 3D rendering fails—naturally subsuming string theory and the holographic principle as effective descriptions within these arrested regions. Finally, the Gauss—Bonnet theorem proves that local optimization cannot eliminate the accumulation of the non-zero topological conserved quantity. When the effective packing fraction approaches the jamming criticality φc ≈ 0.64, the universe undergoes hierarchical phase transitions that convert computational heat into structural entropy, thereby avoiding thermal collapse. This necessitates the six-stage jamming cascade detailed in Part III, which resolves the 122-digit cosmological constantdiscrepancy as arithmetic necessity.
Category: Relativity and Cosmology

Regular Simplex Hierarchical Gravity Part III: Hierarchical Renormalization and the 600-cell as a Separation Device

Authors: Ryuhei Sato
Comments: 27 Pages.

Parts I and II established the static geometry and the dynamics of Regular Simplex Hierarchical Gravity (RSHG): from Axiom Zero and the ineliminable tetrahedral packing deficit δ = 2π − 5 arccos(1/3) ≈ 7.36° (Niven's theorem), the 600-cell arises as the unique four-dimensional closure, and its projection onto the three-dimensional brane yields gravity (Ω_local ≈ 100, reproducing G to 1.1%) together with the Light-Speed Resource Allocation Principle c² = v² + τ². Part III develops the thermodynamics of this structure. We assign the 600-cell a second role, as a separation device that, at every hierarchy boundary, partitions the incoming frustration into three mutually exclusive channels—structural stress (rigidity transmitted upward), computational entropy (heat dissipated downward, the arrow of time), and unresolved four-dimensional residue (a dark-matter candidate)—under the conservation of frustration Φ_in = Φ_A + Φ_B + Φ_C. We then establish the central identity of the paper: time-averaging the vibrating force chains over a time scale τ is equivalent to spatial coarse-graining over a length cτ, which is exactly a renormalization operation, so that the observation time scale itself selects the observed hierarchy. Iterating this renormalization across six hierarchies—each a jamming transition forced by the capacity limit of frustration, with a scale ratio of 10^6 and a per-step rigidity transmission ε_n ≈ 10^−19.2—produces a cumulative suppression ε_total ≈ 10^−115.2 that approaches the 122-order cosmological-constant discrepancy as an arithmetic consequence, while φ ≈ 0.62, Ω_local ≈ 100, and δ ≈ 7.36° remain invariant at every scale. Finally, we analyze the dynamic stability of that operating point, where gravity (structural stress) and Pauli repulsion (computational entropy) balance just inside the packing limit: the universe never reaches φ_c, and the residual structural vacancy φ_c − φ ≈ 0.02 simultaneously averts asymptotic freezing, sustains the renormalization dynamics, and serves as the leak path through which force reaches three dimensions. A system poised at this boundary between structural stress and computational entropy offers a physical perspective on the boundary conditions that may sustain complex systems such as life. We state explicitly which quantities are fixed with zero free parameters and which—notably the first-principles value of ε_n—remain open.
Category: Relativity and Cosmology

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

Authors: Lluis Eriksson
Comments: 8 Pages. v2: conditional summability theorem. Lemma 7.1's Doob/Efron-Stein junction repaired (counterexample-adjudicated); ledger explicit: (H-DEC/AT)+(H-LIP)+(B1-B6)+(H-theta). New F-SQRT finding on sqrt(tau_k). Suite included.

We prove, conditionally on an explicit hypothesis ledger, 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 4d SU(N_c) lattice Yang-Mills theory with a_k = a_0 2^(-k); in particular the continuum-limit state omega(O) = lim_k exists on the blocked class A^block_l. The architecture is unchanged from v1: (i) an exact RG identity (law of iterated expectations — which resolves at the structural level the "on/off-vs-k->k+1" gap flagged in the sibling audits: the one-step comparison here genuinely is a scale comparison); (ii) pushforward stability for blocked observables from approximate centering and Gaussian control of fast modes; (iii) measure comparison by Duhamel interpolation with influence control. Version 2 repairs the single broken brick: v1's Lemma 7.1 asserted the covariance bound for the Efron-Stein seminorm for arbitrary measures while proving the Doob martingale identity; per the sibling audits (2602.0070/0072 v2, same two-spin counterexample) the ES bound is false for non-product nu and the two seminorms are incomparable, so converting the ES-form input (B6) into the Doob-form covariance control requires the decoupling hypothesis (H-DEC/AT) (Dobrushin-type, verified on exact Gibbs chains at weak coupling). The main theorem is restated with the full ledger: Assumption 3.6 (blocking contraction, (H-LIP)), Assumption 5.1 with (B6) as the CONDITIONAL Efron-Stein closure of 2602.0072 v2 and with sum_k sqrt(tau_k) < infinity in (B3) tied to the profile condition (H-theta) of 2602.0069 v2 — sharpened here by a new finding (F-SQRT): the square root halves the effective amplitude, so at the representative polylog floor (theta_0 = 1.1, A_0 = 1) the sum is formally convergent but its crossover lies beyond j ~ e^1668, i.e. practically divergent; (B3) realistically requires power-law-strength p_0, and (H-P0) rejoins the ledger unless the amplitude is large — plus (H-DEC/AT) and trajectory matching. Under this ledger, the one-step error is O(4^(-k)) + O(sqrt(tau_k)), absolutely summable, and Assumption 3.5 of 2602.0063 v3 — the RG-Cauchy hypothesis (H-CAUCHY), whose naive bridge is not summable (F-SUM) — HOLDS FOR THE BLOCKED CLASS: the cleanest conditional delivery of (H-CAUCHY) in the series. v1's cross-reference "Assumption 4.1 of [18]" is corrected to Assumption 3.5, and the companion references are updated from their withdrawn "unconditional" titles to the audited versions. All mechanical steps (exact RG identity, Lipschitz iteration, pushforward stability in a Gaussian toy, telescoping arithmetic, and both counterexample adjudications at the Lemma 7.1 junction) are machine-verified in a companion suite.
Category: Mathematical Physics

Influence Bounds for Polymer Remainders in Balaban's Renormalization Group: an Unconditional Efron-Stein Bound and a Conditional (B6) Closure for the RG-Cauchy Programme in 4D Lattice Yang-Mills

Authors: Lluis Eriksson
Comments: 7 Pages. v2: v1's covariance/tensorisation step is false for correlated measures (two-spin counterexample); the ES single-link bound and seminorm theorem survive unconditionally. (B6) closure now conditional on (H-AT). Suite included.

We study the influence estimate — Assumption (B6) — required by the RG-Cauchy summability framework for blocked observables in four-dimensional SU(N_c) lattice Yang-Mills theory, measured by the Efron-Stein seminorm sigma_nu(f)^2 = sum_e E_nu[Var_{nu_e}(f)]. In the small-field regime of Balaban's multiscale effective action, under (A1) a polymer representation, (A2) a per-link oscillation bound with irrelevance factor 2^(-2k), and (A3) lattice-animal counting — all imported from the traceability companion 2602.0069 v2 (conditional) — we prove the UNCONDITIONAL seminorm bound sup_t sigma_{nu_{k,t}}(V_k^irr) <= C independent of the RG scale k: the single-link conditional variance obeys Var_{nu_e}(f) <= (1/4) osc_e(f)^2 for EVERY measure (Lemma 3.2 — conditioning on all other links freezes them, so no influence leaks; this is the sound half, in exact duality with the sibling paper 2602.0070, whose per-link lemma failed but whose covariance identity was exact). Version 2 corrects the unsound half: v1's covariance bound |Cov_nu(f,h)| <= sigma_nu(f) sigma_nu(h) (its Eq. (18)) is FALSE for non-product nu — Example 3.5: perfectly correlated spins give sigma_nu(X_2) = 0 < 1 = Var_nu(X_2) — because Efron-Stein tensorisation is an independence theorem, and the interpolating Gibbs measures nu_{k,t} couple links. On exact Ising chains the tensorisation ratio Var/sum E[Var_e] equals 1.00/1.35/3.40/52.4 at J = 0/0.15/0.5/1.5. Restoring the Duhamel application requires APPROXIMATE TENSORISATION of variance (H-AT): Var_nu(f) <= C_AT sum_e E_nu[Var_{nu_e}(f)] uniformly along the interpolation — a Dobrushin-uniqueness-type condition, the same family as the sibling's (H-DEC) and the chain's (H-DOB-blk), verified here on exact Gibbs chains at weak coupling (C_AT ~ 1.35) and violated without it. There is also a seminorm-interface gap: the companion Duhamel lemma is proved for the Doob seminorm, and sigma_Doob is NOT dominated by the Efron-Stein seminorm for non-product nu (same counterexample; the two seminorms are incomparable in general). Conclusion: (B6) AS CONSUMED by the RG-Cauchy argument is closed conditionally on (H-AT) (or (H-DEC)); the unconditional content of this paper is the Efron-Stein seminorm bound and its scale-uniform M 2^(-4k) = 4(L/a_0)^4 cancellation (with the convergence threshold kappa > log C_anim of v1's Remark B.1 confirmed). Joint statement with 2602.0070 v2: the UV block's only open probabilistic input is Dobrushin-type decoupling of the interpolating measures. All claims, including both counterexample adjudications and the weak-coupling validation of (H-AT), are machine-verified in a companion suite.
Category: Mathematical Physics

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

Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang-Mills Renormalization — a Corrected and Conditional Influence Bound

Authors: Lluis Eriksson
Comments: 7 Pages. v2: corrects a FALSE v1 lemma (two-spin counterexample: raw-oscillation bound fails for correlated measures). Corrected via conditional oscillation + Dobrushin-type (H-DEC). Now a conditional bound; O(4^-k) candidate rate for (H-CAUCHY). Suite included.

We study 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, via the Doob influence seminorm sigma_nu(f)^2 = sum_i E_nu[(Delta_i f)^2] and its exact covariance identity. Version 2 corrects a genuine error of v1: the increment-oscillation inequality E[(Delta_i f)^2 | F_{i-1}] <= (1/4) osc_{e_i}(f)^2 was asserted for ARBITRARY probability measures; it is false in general (Example 3.4: two perfectly correlated spins, f = X_2, give E[(Delta_1 f)^2] = 1 while osc_{e_1}(f) = 0), because the Doob increment collects influence transmitted through correlations. The correct, measure-independent statement uses the CONDITIONAL oscillation (Lemma 3.5); passing back to the raw single-link oscillation requires a decoupling hypothesis (H-DEC) bounding the influence-leakage matrix, of Dobrushin type — plausible for the interpolating Gibbs measures nu_{k,t} in the small-field weak-coupling regime, but unproven, and structurally akin to the (H-DOB-blk) family of the audited chain. On exact Gibbs chains the v1 bound is violated already at weak coupling for delocalized observables, while the (H-DEC)-corrected bound holds with the Dobrushin coefficient. Under (H-DEC), the imported oscillation input (A2) (now cited from 2602.0069 v2: traceable, conditional — beta_LF dichotomy included), and the lattice-animal lemma (proved here, verified exactly), the main theorem holds: sup_t sigma_{nu_{k,t}}(V_k^irr) <= C uniformly in the RG scale k, by the exact scale cancellation M 2^{-4k} = 4(L/a_0)^4. The Duhamel interface then delivers a one-step rate delta_k = O(4^{-k}) — precisely the geometrically summable rate that Assumption 3.5 of 2602.0063 v3 requires (its Remark 3.7 with eta = 2) — CONDITIONALLY on (H-DEC) + (A2) + the assumed blocking contraction (H-LIP). v1's closing claim "this establishes the RG-Cauchy property" is softened accordingly: this paper supplies the leading candidate for closing (H-CAUCHY), not its proof. All quantitative claims, including the counterexample and the Dobrushin-corrected bound on exact Gibbs chains, are adjudicated in a companion suite.
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: 10 Pages. v2: "unconditional discharge" replaced by traceable conditional discharge. Open interfaces made explicit: beta_LF dichotomy (else (H-P0)), (M3) profile condition theta0>1, UV/IR direction of the irrelevance factor. Suite included.

We provide a self-contained, equation-level traceability derivation of the three structural hypotheses — polymer representation (A1), per-link oscillation bounds with irrelevance factor (A2), and large-field suppression (B5) — that were assumed in the companions "Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang-Mills Renormalization" and "RG-Cauchy Master Framework". All results are traced to precise equations in the primary sources: T. Balaban (Commun. Math. Phys., 1984-1989) and the expository trilogy of J. Dimock (2011-2014). The translation from Balaban's analytic norms on gauge-covariant function spaces to the per-link oscillation language of the probabilistic framework is made explicit. Version 2 corrects the status of the discharge: it is TRACEABLE AND CONDITIONAL, not unconditional. (i) The small factor of Theorem 8.4 (= Eq. (1.89) of Balaban, Large field renormalization II) carries the constant 2/(1+beta_LF); whether beta_LF is O(1) or a large reference coupling is precisely the dichotomy adjudicated against the audited series (2602.0052/0056/0057 v2), where the large reading trivializes the factor (e^(-c p0) ~ 0.95) and forces hypothesis (H-P0); the dichotomy is now stated as an explicit open interface question (Remark 8.7). (ii) The summability claim (M3) of the RG-Cauchy interface was justified in v1 by "super-polynomial decay from asymptotic freedom"; with the profile p0(g) = A0 (log g^-2)^theta0 the decay in the scale index j (distance to the infrared end) is e^(-A0 (ln j)^theta0): sub-polynomial for theta0 < 1 (sum diverges), j^(-A0) at theta0 = 1 (converges iff A0 > 1), and super-polynomial only for theta0 > 1. (M3) is therefore conditional on the explicit profile condition theta0 > 1 (Remark 12.1; hypothesis (H-theta)). (iii) The irrelevance factor (L^k eta)^(4+alpha) is geometric in the distance to the ultraviolet cutoff, not in the infrared direction; the direction-of-limit bookkeeping for (M1) is made explicit (Remark 10.4) and remains hypothesis-level until the Doob companion is audited. What is machine-verified in the companion suite: the abelian RG operator algebra (Lemma 2.2 mechanics), propagator decay and the random-walk expansion, exponential sum control, lattice-animal counting (Lemma C.1; the illustrative d=4, n=3 count of v1 is corrected from 86 to 84), and the oscillation-analyticity bridge with its Cauchy constants and exact factor-2 saturation. Together with the (unaudited) Doob companion, this package provides a CONDITIONAL discharge of the UV structural inputs at finite volume; the finite-volume, ultraviolet character of the package is what shields it from the infrared volume window of the audited chain (2602.0041 v3, 2602.0051-0057 v2, 2602.0063 v3, now cited).
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(Nc) Yang-Mills Theory via Two-Layer Architecture, RG-Cauchy Uniqueness, and Step-Scaling Confinement

Authors: Lluis Eriksson
Comments: 15 Pages. v3: lattice inputs retagged as windowed/conditional (audit 2602.0041 v3, 0051-0057 v2). New Lemma 1.4: dyadic trajectory fits the audited window, margin ~4.5x. RG-Cauchy summability is a genuine hypothesis. Suite included.

Building on the lattice results of Papers [E26I]-[E26IX] — which, per the series audit (all companions now at v2/v3), are WINDOWED and CONDITIONAL rather than unconditional — 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, expectations converge — without extracting subsequences — to a unique limit; precompactness is trivial (|_{a,L}| <= 1), and uniqueness follows from a multiscale RG-Cauchy estimate (Assumption 3.5), the single hard analytic input of this layer: as already recorded in v2 (Remark 3.6, Appendix B), the naive asymptotic-freedom rate g_k^2 ~ c/k is NOT summable, so summability is a genuine hypothesis, not a consequence of the chain. Layer 2 (Confinement): the physical string tension sigma_phys > 0 is established through step-scaling of Creutz ratios at fixed physical loop size, conditionally on Assumptions 4.4, 4.7 and 4.9. The limiting state inherits Osterwalder-Schrader positivity and admits Hilbert-space reconstruction; the mass gap is conditional on a uniform physical transfer-matrix gap (Assumption A.2) and strong continuity (Assumption 5.5). Version 3 retags the input layer to the audited chain: the uniform-LSI inputs are conditional on (H-P0)+(H-YGZ)+(H-SFI)+(H-ABS), the DLR-LSI/mass-gap route on (H-DOB-blk), and all lattice statements hold in the volume window L_vol <= e^(C/g^2+O(1)). A new window-compatibility lemma (Lemma 1.4) shows this window is NOT an obstruction to the continuum limit: along the 2-loop trajectory the required lattice size L/a_k = 2^k L/a_0 satisfies ln(L/a_k) ~ 0.69 k while the audited window allows ln L_lat <= 32.3/g_k^2 ~ 3.12 k — a margin factor ~4.5 at the series' representative arithmetic. Assumption A.2 is now cross-referenced to its conditional lattice supplier (2602.0054 v2: transfer-matrix gap under (H-DOB-blk)+(H-P0), in kernel form). All quantitative claims, and exact validations of both layers in a solvable d = 2 toy, are adjudicated in a companion numerical suite.
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 — a Conditional and Windowed Closure

Authors: Lluis Eriksson
Comments: 13 Pages. v2: closure now windowed (k <= min(k*, k_abs)) and conditional; new hypothesis (H-ABS) — absorption (16) fails at every scale without it, even under (H-P0). Inherits (H-SFI)+(H-YGZ). Ref [8] self-citation removed. Suite included.

We prove integrated cross-scale derivative bounds that replace the unverified Assumption 5.4 of the companion 2602.0041. Combined with two explicit large-field inputs (Hypotheses 3.2 and 4.2) and the conditional inequalities of 2602.0046, this yields — under the audited hypotheses listed below and within the stated volume window — the corresponding log-Sobolev assembly for the Wilson lattice gauge measure at sufficiently weak coupling, with constant independent of L_vol inside the window. The key decomposition into small-field and large-field contributions survives verbatim from v1, as do the sweeping-out modification (an L^1 bound in place of an essential supremum, and a shifted essential supremum over G_{k+1}), the Rothaus closure, the SU(2), d=2 toy-model analysis, and the correction lambda_1 >= alpha_* to Proposition 6.1(2) of 2602.0041. Version 2 corrects the logical status of the assembly after the quantitative audit of the series (ai.viXra:2602.0051-0056, all v2). (a) The Absorption step in the proof of Theorem 1.1 relied on the premises "p0(g) -> infinity as g -> 0 along the flow" and "if beta_k grows sufficiently with k": both use the inverted-sign flow of the series erratum and are withdrawn; with the correct asymptotic-freedom flow all statements hold in the window k <= k*(beta), i.e. L_vol <= e^(C/g^2+O(1)). (b) A new finding (F-ABS): the absorption condition (16) consumes Hypothesis 4.2 in the strong exponent form e^(-c beta_k eps_k^2), but the companion verification (2602.0056 v2) delivers only e^(-c_sf p0(g_k)) with c_sf = 2/(1+beta_0) — bounded along the window — so (16) fails at every scale k >= 2 with the Balaban-compatible thresholds (9), even under (H-P0). The strong form is therefore an additional explicit hypothesis (H-ABS), and its saturated variant eps_k = eps_* opens a second window k <= k_abs proportional to beta eps_^2. (c) The inputs are retagged per their v2 verifications: Hypothesis 3.2 is windowed and conditional on Balaban's small-field inputs (2602.0055 v2); Hypothesis 4.2 is form-level and conditional on (H-SFI)+(H-P0) (2602.0056 v2); the fiber LSI consumed by Corollary 1.2 inherits (H-YGZ) (2602.0053 v2). (d) Reference hygiene: v1's reference [8] was a self-citation of the present paper and is removed; the Wilson duplicate is removed; the audited chain 2602.0051-0056 (v2) is cited. What survives and is validated in the companion suite: the per-direction Wilson bound (Lemma 3.1), the energy-distance identity (13), the single-plaquette tail (Proposition 7.1, Table 1 reproduced digit-by-digit, with its caption/values normalization mismatch fixed), the impossibility Remark 7.2, the factorization step (21), the Rothaus closure, and Appendix A's lambda_1 >= alpha_.
Category: Mathematical Physics

Large-Field Suppression for Lattice Gauge Theories: From Balaban's Renormalization Group to Conditional Concentration — a Conditional and Windowed Verification

Authors: Lluis Eriksson
Comments: 9 Pages. v2: Theorem 1.3 now windowed and conditional on (H-SFI)+(H-P0); the printed small factor trivializes under the polylog p0 floor; d=2 route is fixed-beta. Chain 2602.0051-0055 v2 cited. Suite included.

We verify, at the level of form, the large-field hypothesis (Hypothesis 4.2) of the companion paper on integrated cross-scale derivative bounds for Wilson lattice gauge theory (Paper III). 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, Large field renormalization II); (iii) the uniformity estimate (Eq. (1.75) ibid.) 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. Version 2 corrects the status of these results after the quantitative audit of the series (ai.viXra:2602.0051-0055, all v2). (a) v1's claim that the bound is "more than sufficient" for the absorption condition of Paper III is withdrawn: the printed small factor is exp(-c p0(g_k)) with c = 2/(1+beta_0), and with the polylog floor on p0 the suppression trivializes (e^(-c p0(gamma_0)) ~ 0.95) and the absorption inequality fails at every scale (excess >= 10^4.6); effectiveness requires the power-law hypothesis (H-P0) of 2602.0052 v2. (b) v1's premise "p0(g_k) -> infinity as g_k -> 0 along the flow" and Sec. 7's appeal to a stability theorem rely on the inverted-sign running-coupling flow of the series erratum; with the correct asymptotic-freedom flow the small-field condition g_k <= gamma_0 holds only for k <= k*(beta), and all statements are windowed: L_vol <= e^(C/g^2+O(1)). (c) v1's Remarks 4.1-4.2 (slow-field identification and Balaban conditional representation) are unproved interface statements; they are made explicit here as hypothesis (H-SFI), cf. the interface lemmas of 2602.0052 v2. (d) In d = 2 the prefactor K_beta(1)/Z(U_B) of Proposition 6.4 is not uniform in beta, so the d = 2 route verifies a fixed-beta variant only; this is now stated in the theorem. What survives unconditionally and is validated in the companion numerical suite: the HS/Lie-algebra dictionary (Lemma 2.1), the gauge-invariance identity (Remark 2.2), the block event inclusion (Lemma 3.2), and the character-positivity mechanism of Section 6 (Peter-Weyl positivity of the Wilson weight, convolution stability, maximum at the identity, and conditional tail domination in an exact d = 2 toy).
Category: Mathematical Physics

Residual Derivative Bounds and Windowed Uniform Log-Sobolev Inequality for SU(Nc) Lattice Yang-Mills at Weak Coupling

Authors: Lluis Eriksson
Comments: 15 Pages. v2: Theorem 1.1 now windowed (L <= exp(C/g^2)) and conditional on (H-P0)+(H-YGZ); Corollary 1.2 additionally on (H-DOB-blk). Chain 2602.0051-0055 fully retagged; ref [6] fixed. Verification suite included.

We prove residual derivative bounds for the polymer expansion of Balaban's multiscale decomposition of the Wilson lattice gauge measure for SU(N_c) in dimension d >= 3, and we assemble them, together with the companion series, into a uniform log-Sobolev inequality. Version 2 corrects the status of this assembly after a quantitative audit. (i) The core mechanism of the paper — locality of polymer functionals, Cauchy estimates on Balaban's analytic domains, and a volume-independent counting bound for connected polymers containing a fixed link — survives intact and is validated numerically; it yields a pointwise derivative bound on the polymer residual with constants independent of the lattice volume, CONDITIONALLY on Balaban's small-field inputs (B1)-(B4). (ii) However, the final step of v1's Theorem 3.5, the inequality k <= C_RG(1+beta_k), relied on the inverted-sign running-coupling flow of the series erratum; with the correct asymptotic-freedom flow the reduced coupling beta_k DECREASES along the cascade, the small-field condition g_k <= gamma_0 is available only for k <= k*(beta), and the derivative bound holds in the windowed form C_res(1+beta) for L_vol <= e^(C/g^2+O(1)). (iii) The assembly of the main theorem inherits two hypotheses identified in the audits of 2602.0052 v2 and 2602.0053 v2: the large-field absorption step requires a power-law penalty exponent — hypothesis (H-P0) — since with the stated polylog floor the suppression factor trivializes (e^(-c_sf p0(gamma_0)) ~ 0.95 at gamma_0 = 0.1) and the absorption inequality fails at every scale (excess >= 10^4.6); and any quantitative use of the conditional fiber LSI via Holley-Stroock carries the penalty e^(-2 beta n_plaq) — hypothesis (H-YGZ) (log10 alpha_blk ~ -5559 at gamma_0 = 0.1, n_plaq = 64). (iv) Version 1's Corollary 1.2 and Remark 5.1 claimed that the Dobrushin-type Assumption 6.3 of Paper I is "no longer needed" via the DLR route of the companion 2602.0053; the v2 audit of that companion shows the route REDUCES Assumption 6.3 to an unverified block condition (H-DOB-blk) whose printed bound c_ij <= tanh(beta n_bd/2) trivializes at weak coupling. Accordingly, v1's closing claim is replaced: the uniform LSI of Theorem 1.1 is WINDOWED and CONDITIONAL on (H-P0) and (H-YGZ), and the mass gap of Corollary 1.2 is additionally conditional on (H-DOB-blk). This replacement also records the completed retagging of the chain: the companion 2602.0054 has been audited and replaced (v2, conditional/windowed assembly), so 2602.0051-0055 now all carry their v2 statuses; reference [6] is corrected (v1 listed 2602.0053 under the title of 2602.0054). All quantitative claims are adjudicated in a companion numerical suite (9 deterministic checks).
Category: Mathematical Physics

From Uniform Log-Sobolev Inequality to Mass Gap for Lattice Yang—Mills at Weak Coupling: a Conditional and Windowed Assembly

Authors: Lluis Eriksson
Comments: 17 Pages. v2 replaces the v1 unconditional assembly: the DLR-LSI step requires (H-DOB-blk) (2602.0053 v2) and (H-P0) (2602.0052 v2); the corrected flow gives L <= exp(C/g^2+O(1)). Transfer-operator correlation identities corrected to kernel/symmetrized form (spectr

This paper assembles the route from the uniform log-Sobolev inequality (LSI) on periodic tori to a transfer-matrix spectral gap for SU(N_c) lattice Yang-Mills in d >= 3 at weak coupling: periodic LSI + boundary-uniform RG outputs => DLR-LSI => Stroock-Zegarlinski mixing => exponential clustering => (reflection positivity) => Delta_phys > 0. Version 2 corrects the logical status of this assembly after a quantitative audit (companion numerical suite; Appendix A). (i) v1 claimed the route "bypasses any explicit Dobrushin contraction estimate". This is withdrawn: the DLR-LSI input (Theorem 5.1) invokes the multiscale fiber assembly of [2], whose inter-block step IS a Dobrushin-type condition — made explicit as (H-DOB-blk) in ai.viXra:2602.0053(v2), the detailed companion treatment which v1 did not cite. v1's supporting claim in the proof of Theorem 5.1, that the fiber oscillation is "O(1) regardless of beta", is also withdrawn: the conditional fast potential obeys osc = 2 beta n_plaq + C_poly, LINEAR in beta (2602.0053(v2), Lemma 3.2; reproduced numerically here). (ii) The quantitative absorption in Proposition 4.7 inherits hypothesis (H-P0) of ai.viXra:2602.0052(v2), and the corrected asymptotic-freedom flow restricts all statements to the volume window L <= e^(C/g^2+O(1)): Theorem 1.1 is restated as windowed and conditional on (H-DOB-blk)+(H-P0). (iii) The erratum for [2] in Sec. 10 is corrected: v1's items (a) and (c) ("Assumption 6.3 is removed", "Theorem 1.1(ii) of [2] is now unconditional") are withdrawn — the assumption is REDUCED, not removed; item (b) (withdrawal of Lemma 6.4 of [2] due to the volume factor (MR^n_max)^d) was correct and stands. (iv) A new technical finding (Remark 2.8): the row-normalized transfer operator T-hat of Definition 2.2 satisfies the correlation identities (12)/(29) exactly only when its normalizer D(sigma) = int K(sigma,sigma') d sigma' is constant (true in the d=2 toy, false for d >= 3 where the spatial factor e^((beta/2)S(sigma)) survives); the correct identities hold in kernel form (with K, or the symmetrized D^(-1/2) K D^(-1/2)). Since D^(-1)K and D^(-1/2)KD^(-1/2) are similar, the spectrum — hence Delta_phys — is unaffected; adjudicated numerically (spectra equal to 10^(-16); the T-hat-form of (29) deviates from the exact path integral by 0.30 in a d=3 toy). What survives and is validated end-to-end in exact toys: the slab splitting (Definition 2.1), self-adjointness and detailed balance (Lemma 2.3), the spectral clustering-to-gap step (Proposition 2.4), Osterwalder-Seiler reflection positivity including the Peter-Weyl positive-definiteness of Re tr(UV^(-1)) (Theorem 2.6), and the gauge-invariance lemmas of Sec. 8. The contribution is retagged: a correct and verifiable transfer-matrix back end for the program, whose front end (DLR-LSI) is conditional and windowed.
Category: Mathematical Physics

DLR-Uniform Log-Sobolev Inequality and Mass Gap for Lattice Yang—Mills at Weak Coupling: a Conditional and Windowed Reduction

Authors: Lluis Eriksson
Comments: 18 Pages. v2 replaces v1: the unconditional DLR-LSI/mass-gap claim is withdrawn. The block Dobrushin condition becomes explicit hypothesis (H-DOB-blk); the absorption step inherits (H-P0); the corrected flow restricts the result to L <= exp(C/g^2+O(1)).

We study the passage from the uniform log-Sobolev inequality (LSI) on periodic tori, developed in the companion series, to a DLR-uniform LSI for the conditional Gibbs specification of SU(N_c) lattice Yang-Mills in d >= 3 at weak coupling (beta >= beta_0), and from there to a mass gap via Stroock-Zegarlinski and Osterwalder-Seiler reflection positivity. Version 2 corrects the logical status of the main results after a quantitative audit (companion numerical suite included; Appendix A). (i) The fiber assembly (Lemma 3.5) assumes the block Dobrushin condition delta < 1, which v1's own Remark 3.6 left unverified; the printed influence bound c_ij <= tanh(beta n_bd/2) tends to 1 as beta -> infinity and yields delta < 1 only for beta <~ 10^(-2) (d=3) or beta <~ 10^(-3) (d=4) — the opposite of the weak-coupling regime. A rotor exhibit shows the genuine worst-case block influence also tends to 1, so no worst-case criterion can close the gap: the condition is now the explicit hypothesis (H-DOB-blk), and v1's claim of removing the Dobrushin-type Assumption 6.3 of [14] is withdrawn — the present paper reduces that assumption to (H-DOB-blk). (ii) The quantitative absorption in Proposition 4.3 inherits hypothesis (H-P0) of ai.viXra:2602.0052(v2): under the polylog penalty floor p0(g) >= c_0 |log g|^(1+epsilon_0) the required inequality e^(-c p0(g_k)) <= C L_RG^(-(d-1)k) fails already at k = O(1). (iii) The proof assumes g_k <= gamma_0 for all k <= n_max ~ log_LRG diam(Lambda'); with the corrected asymptotic-freedom flow of the series erratum this holds only on the volume window log_LRG diam(Lambda') <= k*(beta), i.e. diam(Lambda') <= e^(C/g^2+O(1)). Theorems 1.1-1.2 are therefore restated as windowed and conditional on (H-DOB-blk) and (H-P0). What survives unconditionally — and is validated numerically — is the boundary-uniformity mechanism itself: the per-plaquette oscillation and gradient bounds (Lemma 3.1; sharp for N_c=2), the "frozen = slow" reduction (Lemma 3.2), the refined dynamical large-field event, the energy-penalty identity ||U-1||_HS^2 = 2N_c(1 - Re tr U / N_c), the TV <= tanh(osc/4) lemma with its two-point equality case, and the Bakry-Emery constant N_c/4 in the = -2 tr(XY) convention. The contribution of the paper is thus retagged: a boundary-uniform reduction of the DLR-LSI and the mass gap to (H-DOB-blk)+(H-P0) within the volume window — not an unconditional mass gap.
Category: Mathematical Physics

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

Authors: Lluis Eriksson
Comments: 16 pages. v3 restores the authentic v1, adds a 5-page erratum/retraction, and corrects a prior cross-record file association. No external verifier is claimed.

This replacement restores the paper originally submitted as version 1 and retracts its claimed unconditional closure of the weak-coupling lattice Yang-Mills mass-gap chain. The principal-logarithm construction in Lemma A.1 fails at central elements such as -I in SU(2), and the printed argument does not establish the required measurable conditional kernel. The proof of Lemma 6.2 applies the Holley-Stroock comparison in the wrong direction: it does not give a coupling-uniform per-block log-Sobolev bound on the unbounded range beta >= beta_0. A bounded beta window can control that per-block estimate, but it does not prove Lemma 6.3, which separately requires an inter-block contraction hypothesis. Three numerical samples and an upper bound on the oscillation are recorded only as numerical evidence; they do not prove linear growth of the optimum or a vanishing infimum. The remaining horizon-transfer, analyticity, and boundary-uniform interfaces are classified as conditional or not established. Corollary 7.3 and the abstract's unconditional mass-gap conclusion are withdrawn. No numbered lemma is declared false unless the corrective note supplies the stated counterargument; otherwise the status is expressly "not established."
Category: Quantum Physics

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

Authors: Lluis Eriksson
Comments: 9 Pages. v2: coupling-flow sign corrected (v1's was anti-asymptotic-freedom and made the bootstrap trivially unconditional); the closure is now conditional and windowed (L <= exp(C/g^2)), matching companions 2602.0032/0033; (H-PTW)/(H-XOVER) stated explicitly.

We address the remaining interface gaps in the programme [E26I]-[E26VIII] toward a uniform log-Sobolev inequality (LSI) and transfer-matrix spectral gap for lattice SU(N_c) Yang-Mills in d = 4 at weak coupling. Four gaps are treated: (G1) the pointwise-in-background validity of Balaban's T-operation small-factor bound -- stated in v2 as the explicit hypothesis (H-PTW), since the detailed audit appendices announced in v1 were absent from the document (their references rendered as "??"); (G2) a uniform small-field coercivity estimate for the effective action; (G3) uniform analyticity of boundary terms; (G4) a quantitative bootstrap of all constants. The central correction of v2: the sign of the one-step coupling drift in v1's Theorem 5.2 (g_{k+1}^{-2} = g_k^{-2} + 2 b_0 ln L_RG, coupling weakening toward the infrared) is inverted relative to asymptotic freedom, and contradicts the companions' own use of n_max ~ 1/(2 b_0 g^2 ln 2) (ai.viXra:2602.0032 Sec. 8, 2602.0033, 2602.0041 Sec. 7.3), a formula meaningful only if the coupling grows along blocking and exits the weak regime. With the corrected sign the monotone bootstrap of v1's Theorem 5.3 reverses: the inductive conditions are guaranteed only up to the finite horizon k*(beta) = (g_0^{-2} - gamma_0^{-2})/(2 b_0 ln L_RG) + O(1), and since the multiscale construction uses log_2 L scales, the conclusion holds on the volume window log_2 L <= k*(beta), i.e. L <= e^{C/g^2 + O(1)} with C = 1/(2 b_0) = 24 pi^2/(11 N_c) -- exactly the window of the companion papers ai.viXra:2602.0032/0033 (v2). Full volume-uniformity would additionally require a strong-coupling handoff beyond the crossover scale (Osterwalder-Seiler regime), stated as hypothesis (H-XOVER) and not established here; accordingly the "unconditional closure" of v1 is retitled to conditional closure. Version 2 also repairs the dangling "??" references, supplies the missing proof of Lemma 3.1, rewrites the proof of Lemma 7.4 in the series' fundamental-trace convention (its statement W''(0) = 1/(2N_c) is correct; the v1 proof mixed normalized and fundamental traces), corrects sum_{k>=0} (k+1) 2^{-3k} = 64/49 (v1: 8/49), and fills in the companion identifiers. All corrections are verified in a companion numerical suite.
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: 8 Pages. v3 validates and cleans up the orbit-space Ricci/RCD* input: full Einstein tensor checks for SU(2/3/4), convention triangle Nc/4 - Nc/2 - 1/2, SU(3) sectional range, Bakry-Emery and Holley-Stroock conventions verified. No v2 theorem refuted.

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 shows that the configuration space A = SU(N_c)^{|B_1(Lambda)|}, with the bi-invariant product metric = -2 tr(XY), is an Einstein manifold with Ric_A = (N_c/4) g_A (Proposition 2.2), and applies the stability of the RCD* condition under quotients by compact groups of measure-preserving isometries (Galaz-Garcia-Kell-Mondino-Sosa). This bypasses O'Neill computations and handles the singular stratum (reducible connections) automatically. As a consequence we derive a conditional log-Sobolev inequality for measures 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 is developed in the companion papers cited in Section 6.1. Note added (v3). Version 3 accompanies the paper with a numerical verification suite (full Einstein tensor for SU(2/3/4); the convention triangle N_c/4 <-> N_c/2 <-> 1/2 closing the series' Ricci bookkeeping; the horizontal characterization at machine precision; the Bakry-Emery convention on the Gaussian via the exact Gross optimizers; Holley-Stroock in LSI form; and the exact energy/entropy correspondence for a Z_2 quotient toy). It corrects a sign in Section 5.1 ([T^a,T^b] = +eps^{abc} T^c requires T^a = -(i/2) sigma^a), repairs the attributions in Section 1.4 (the O'Neill-sketch Ricci statement lives in ai.viXra:2602.0036, whose v2 sharpened the -tr-convention value to N_c/2, consistent with N_c/4 here), adds the measured sectional-curvature range of SU(3) to Section 5.2, and fills in the companion identifiers in Section 6.1 with their honest status. No statement of v2 is refuted.
Category: Mathematical Physics

Octonionic Model for Black Holes

Authors: Rüdiger Giesel
Comments: 22 Pages.

We formulate black holes within the octonionic projection framework in whichspacetime geometry is not fundamental, but arises as a low-energy Lorentzian projection of a deeper non-associative algebraic structure. The starting point is the realnormed division algebra of octonions, whose imaginary sector carries a canonical G2three-form [1, 2, 3, 4, 5, 6]. Since this G2 structure is intrinsically Riemannian, physical spacetime requires additional dynamical projection data: an independent clockline, a stable associative spatial three-plane, and suppression of the coassociativesector. In the associative low-energy exterior region, the projected metric obeysEinstein-type equations and the static spherically symmetric vacuum solution is theSchwarzschild geometry [7]. The Schwarzschild radius is therefore recovered as thestandard exterior horizon scale of the emergent metric, not as a direct dimensionalconsequence of the associator alone.The genuinely new strong-field ingredient is the trilinear octonionic associatorsector. Because octonions are alternative, a nontrivial associator interaction requires at least three independent octonion-valued fields. In the black-hole interior,the associator contribution can become dynamically relevant and may saturate atfinite density. As a speculative extension of the present model, this replaces theclassical curvature singularity by a regular de-Sitter-like core, while leaving the exterior solution unchanged to leading order; the comparison class includes regularblack-hole and loop-inspired interior models [8, 9, 10]. We present the construction step by step: from octonions and G2 geometry to the associative projection,from the master action to the effective field equations, from the exterior vacuumlimit to the Schwarzschild metric, and from bounded associator density to a regularinterior mass function. The resulting object is a horizon-forming, singularity-freeprojected spacetime whose possible deviations from general relativity are confinedto near-horizon, ringdown, and high-curvature regimes
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: A Conditional Reduction

Authors: Lluis Eriksson
Comments: 12 pages. v4: 1-page retitling/scope correction followed by the preserved 11-page v3.

This replacement corrects the title and foregrounds the logical status already partly recorded in public version 3. The uniform log-Sobolev conclusion requires the cross-scale derivative hypothesis (H-XSD), whose purported companion-paper discharge is not re-verified here. The mass-gap conclusion additionally requires the Dobrushin-type hypothesis (H-DOB), or an independently valid alternative DLR-LSI/mixing route. Neither input is proved by this manuscript alone. No unconditional weak-coupling lattice mass gap, continuum construction, Osterwalder-Schrader reconstruction, or Clay-problem result is claimed. The preserved version 3 follows the correction page for provenance.
Category: Mathematical Physics

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

Authors: Lluis Eriksson
Comments: 7 Pages. v2 validates the multiscale martingale Poincare machinery end-to-end (numerical suite included); corrects the coupling-flow direction and sharp Ricci constant; tags the RG-normalized disintegration as (H-DIS). Conditional on Balaban/(H-DIS).

We prove that the lattice Yang-Mills measure with gauge group SU(N_c) in d = 4 dimensions at sufficiently large beta = 2N_c/g^2 satisfies a Poincare inequality with constant alpha* > 0 uniform in the lattice size L, conditionally on Balaban's constructive RG and an RG-normalized disintegration hypothesis. The proof uses: (i) the Ricci curvature bound of the gauge orbit space -- sharpened in v2 to Ric_B >= N_c/2, following the correction at its source in ai.viXra:2602.0036 (v2) -- giving a uniform spectral gap for conditional fast modes at each RG scale; (ii) Balaban's polymer derivative bounds, controlling residual cross-scale coupling; and (iii) a multiscale martingale variance decomposition avoiding recursive composition losses, with commutator coefficients D_k <= C e^{-2 kappa} 2^{-3k} made summable by the geometric scaling of transversal block averaging. Version 2 corrects the coupling-flow direction in the statement of Balaban's theorem (which improves the fallback bound of Remark 2.7: beta_k <= beta is bounded, rather than O(k)), records that the summability is robust to the block-averaging convention (new Remark 2.8: the Balaban-style convention gives 2^{-(d-2)k}, still summable), clarifies that the commutator coefficient involves the centered gradient of the conditional potential (which is the mechanism by which G_k-measurable parts drop out, as Assumption 2.6 asserts), and updates the companion references. Unlike other v2's of this series, no statement of v1 is refuted: the entire martingale machinery (commutator identity, telescoping, absorption, the assembled constant alpha*) is validated end-to-end in a companion numerical suite, exactly in a two-scale Gaussian model and against the true spectral gap in a compact four-rotor model, where the recipe's alpha* is confirmed as a valid lower bound.
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

Zero-Momentum Propagator Bound in a Simplified Gribov-Zwanziger Lattice Measure

Authors: Lluis Eriksson
Comments: 11 pages. v3: 1-page retitling/scope correction followed by the preserved 10-page v2.

This replacement corrects the title and headline scope while preserving public version 2 in full. For the simplified quadratic Gribov-Zwanziger lattice measure defined in the manuscript, the zero-momentum propagator obeys the stated volume-uniform bound and its thermodynamic-limit value is computed. Finiteness of D(0) is only the necessary condition identified in Definition 4: it does not by itself prove exponential clustering, a transfer-operator spectral gap, a mass gap for the simplified measure, or a mass gap for Wilson Yang-Mills theory. The former title's phrases "Mass Gap" and "A Non-Perturbative Proof" are withdrawn. No continuum-limit or Clay-problem conclusion is claimed.
Category: Quantum Physics

Quantum Resistant Cryptography and It's Implications on Blockchain and Cryptocurrency

Authors: Tehzeeb Ali
Comments: 14 Pages.

Modern public key cryptosystems rely on two fundamental computational hardness assumptions: integer factorization (RSA) and the discrete logarithm problem (elliptic curve cryptography). These problems, formulated using modular arithmetic and algebraic geometry, have withstood four decades of cryptanalytic attacks. However, their inherent algebraic structures and periodicity properties make them vulnerable to quantum algorithms, particularly Shor’s algorithm (1994), which achieves polynomial-time complexity on quantum computers. This research presents an extensive mathematical comparison between classical cryptographic systems and quantum-resistant alternatives, with particular emphasis on lattice-based cryptography. We focus on the Learning With Errors (LWE) problem and its variants (Ring-LWE, Module-LWE), demonstrating through rigorous mathematical analysis why these lattice problems lack the periodicity that quantum algorithms exploit. We provide formal security reductions for LWE problems relative to worst-case lattice problems and present mathematical proofs of quantum resistance. For cryptocurrency systems, this analysis reveals critical vulnerabilities: current ECDSA algorithms used for transaction signing will become cryptographically insecure within 10-30 years, potentially compromising over $100 billion in digital assets. This work bridges mathematical foundations, security analysis, and practical implications for real-world systems, providing proof-based recommendations for the transition to post-quantum cryptographic standards in blockchain technologies.
Category: Digital Signal Processing

Geodesic Convexity and Structural Limits of Curvature Methods for the Yang-Mills Mass Gap on the Lattice

Authors: Lluis Eriksson
Comments: 19 pages. v3 adds a 4-page corrective note and provenance sheet, then preserves public v2. Withdraws the Ricci-based corollaries; no external verifier is claimed.

This replacement withdraws the global orbit-space Ricci lower bound and the spectral-gap corollaries derived from it. The printed proof of Theorem 3.1 traces O'Neill's horizontal sectional-curvature identity as though the total-space Ricci tensor contained only horizontal directions. The correct trace also subtracts the mixed horizontal-vertical sectional curvatures. For the bi-invariant product metric these terms are nonnegative before subtraction, so the omitted contribution has the unfavorable sign; the manuscript does not prove that the positive O'Neill term dominates it. Accordingly Theorem 3.1 is not established, rather than asserted false, and Corollaries 3.2-3.3 are withdrawn. The correction also separates a finite-dimensional orbit-space statement from later RCD results formulated for a different measure and operator, and records the broken dependency on a version of ai.viXra:2602.0035 that was not present in its public record. The local geodesic-convexity results and the independently stated structural obstruction are retained only within their stated scope.
Category: Quantum Physics

Morse-Bott Spectral Reduction and the Yang-Mills Mass Gap on the Lattice

Authors: Lluis Eriksson
Comments: 21 pages. v2 adds a 7-page erratum and provenance sheet, then restores the 10-page corrected revision formerly misfiled as 2602.0052v2. No external verifier is claimed.

This replacement restores the corrected Morse-Bott revision that was previously placed on another public record and adds an erratum delimiting its valid scope. The original manuscript used one symbol for both total loop holonomy and per-link angle, losing factors of L in the covariant symbol and metric. It also contained an incorrect sine identity, Fourier labels and normal-bundle statements that fail independently, and a determinant convention that double-counted the Faddeev-Popov factor. The replacement withdraws the claims that hypothesis (H1) was discharged and that (H-FACT) by itself replaced (H2); it records the resulting dependency loop with ai.viXra:2602.0033. What remains is a qualitative fixed-volume positivity statement, conditional quantitative implications under explicitly named hypotheses, and numerical evidence in the tested finite-volume case. The numerical checks printed in the historical revision are treated as author-reported evidence because the cited companion verifier is not present in the audited package. No unconditional continuum or infinite-volume mass-gap theorem is claimed.
Category: Quantum Physics

The Yang-Mills Mass Gap on the Lattice: A Conditional Synthesis

Authors: Lluis Eriksson
Comments: 25 pages. v3: 13-page erratum + 4-page provenance + preserved 8-page v2. The printed proofs of Theorems 1.1, 3.1 and 4.1 are withdrawn; conclusions are not asserted false.

This replacement preserves the published version 2 and appends a page-fixed erratumand an object-provenance sheet. The erratum withdraws the printed derivations ofTheorems 1.1, 3.1, and 4.1 without claiming that their conclusions for the intendedYang-Mills operators are false. It separates defects in the Euclidean-measure toground-state-measure identification, the use of a four-dimensional effective actionon a three-dimensional spatial orbit space, the volume-dependent transfer-operatortrace extraction, the finite-error resolution window, the factorisation-erroraccumulation, and the admissible-volume quantifiers. Three explicit positivetrace-class counterexamples show why ordinary spectral convergence, positivityimproving, first-excited multiplicity control, and total-tail control do not bythemselves imply gap doubling. A sufficient exact-trace repair is stated at thefinite-volume scale: the leading-eigenvalue normalisation error must be little-o ofthe sum of the two actual first-excited contributions, together with subexponentialfirst-excited multiplicities and vanishing relative excited tails. The previous v2text remains included solely for provenance; no unconditional four-dimensional orcontinuum mass-gap result is claimed.
Category: Mathematical Physics

The Yang-Mills Mass Gap on the Lattice: A Conditional Reduction via Witten Laplacian and Constructive Renormalization

Authors: Lluis Eriksson
Comments: 14 Pages. v2: retagged as conditional reduction under four explicit hypotheses (H-BAL, H-CONST, H-MB, H-HAM); Morse-Bott failure at the orbifold locus exhibited numerically; doubling and coupling-flow errata corrected; verification suite included.

We reduce the weak-coupling lattice Yang-Mills mass gap to four explicitly stated hypotheses: assuming them, SU(N_c) lattice Yang-Mills theory in d=4 dimensions with Wilson action at sufficiently weak coupling has a positive mass gap m_gap >= c(N_c) e^{-C(N_c)/g^2} > 0 in lattice units, uniformly in lattice sizes L <= C_0 e^{C/g^2}. The argument combines Balaban's constructive renormalization group, a Morse-Bott/Witten-Laplacian semiclassical spectral gap estimate at the terminal scale, and a transfer-matrix trace identity. Version 1 of this paper presented the result as self-contained modulo Balaban's RG. Version 2 corrects this assessment: the proof is conditional on four explicitly stated hypotheses (Section 1.3). In particular: (i) the Morse-Bott non-degeneracy required by the Helffer-Sjostrand theory fails on the orbifold locus of the flat-connection moduli space -- including the minimum theta=0 of the Born-Oppenheimer potential -- where (d-1)(N_c^2-1-r) quartic "toron" zero modes appear, as we exhibit numerically on a real lattice (Proposition 5.3); and (ii) the constants of Balaban's construction must satisfy a quantitative compatibility window kappa > C' N_c^{3/2}/gamma^2 together with gamma^2 <= 2 N_c h_0, which is empty for typical O(1) decay constants and is not known to follow from Balaban's papers. Version 2 also corrects the sign of the coupling flow in the statement of Balaban's theorem, an inverted extraction regime in the transfer-matrix doubling argument (replaced by a finite-window extraction with explicit error), the definition and Hessian normalization of the Born-Oppenheimer potential (whose v1 form is numerically non-positive), and the Ricci constant of the orbit space (N_c/2, not N_c/4; direction favorable). All corrections and the surviving ingredients are verified in a companion numerical suite. None of this yields an unconditional result, and the continuum, infinite-volume problem remains expressly out of scope.
Category: Mathematical Physics

Entanglement Tension and Brane Secession: A Holographic Framework for Emergent Gravity and Mass

Authors: Cesar Henriques
Comments: 22 Pages.

We present a holographic framework in which four-dimensional spacetime emerges from quantum entanglement structure encoded on a brane embedded in asymptotically AdS space [1]. Mass is not fundamental but is identified with topological entanglement complexity—knot complexity Ck—quantifying irreducible multipar-tite correlations [3]. Gravitational interaction emerges as the macroscopic response to gradients in entanglement tension along the holographic direction [4], reducing to Einstein’s equations at low complexity with an additional non-local stress contribution from diffuse entanglement structure [5]. We propose that classical spacetime singularities signal saturation of entanglement capacity at a critical threshold Ck,max, analogous to the Bekenstein—Hawkingbound [6, 7]. Beyond this regime, the system undergoes a topological transition—brane secession—whereby the saturated region disconnects from the parent structure and nucleates an independent spacetime [2, 8]. This provides a natural regularization mechanism: from the exterior perspective, a black hole forms; from the interior perspective, a smooth cosmological expansion emerges, unifying collapse and cosmogenesis as dual descriptions of a single entanglement reorganization. We demonstrate structural consistency through explicit toy-model calculations in finite tensor networks (Appendices A—B) and present a simplified phenomenological realization showing how diffuse entanglement tension reproduces flat galactic rotation curves without dark matter particles (Section 5.3). The framework offersa unified interpretive scheme for mass, gravity, and dark-sector phenomenology as emergent consequences of quantum correlation structure, while remaining compatible with established results in holography, semiclassical gravity, and observational cosmology [1, 2, 6].
Category: High Energy Particle Physics

Resolving Lepton Anomalies via Directed Dimensional Lattice Geometry

Authors: Alimi Ayomide Olamilekan
Comments: 6 Pages.

We demonstrate that the muon anomalous magnetic moment discrepancy (127 parts per billion) and the proton radius puzzle arise from a common discrete geometric origin within the Directed Dimensional Lattice (DDL) framework. By modeling spacetime as a 24-cell (F4) lattice rather than a continuous manifold, we derive the muon anomaly as a "polygon tax" from finite harmoniccycles of N = 3600 nodes. This value emerges naturally from the hierarchical partition of the 120-cell into 25 disjoint 24-cells, combined with 6-fold phase updates required by SO(4) holonomy. Concurrently, the 24-cell symmetry predicts the muonic proton radius as Rµ = Re(1 − 1/24) = 0.841 fm. The exact integer ratio 3600/24 = 150 suggests phase-locked coupling between lepton dynamics and lattice geometry. These predictions are jointly testable via the MUonE experiment, providing definitive validation or falsification of the DDL framework without requiring beyond-Standard-Model particles.
Category: High Energy Particle Physics

Unified Reconstruction of Cosmology Via Spacetime Hysteresis and Gravitational Entanglement ( Summary in Korean)

Authors: Chang-Sik Kim
Comments: 7 Pages. Copyright © 2026 Chang-Sik Kim. All rights reserved.

현대 표준 우주론(ΛCDM)은 우주배경복사의 정밀 관측을 통해 우주의 조성을 성공적으로 설명해 왔으나, 최근 심각한 관측적 난제들에 직면해 있다. 암흑물질 입자는 수십 년간의 탐색에도 불구하고 발견되지 않았으며, 허블 텐션(Hubble Tension)이라 불리는 우주 팽창률의 불일치는 해소되지 않고 있다. 결정적으로, 제임스 웹 우주 망원경(JWST)이 관측한 적색편이 z > 10 영역의 거대 성숙 은하들은 표준 모델이 허용하는 138억 년의 우주 나이로는 설명이 불가능하다.본 논문은 이러한 위기를 극복하기 위해 시공간을 단순한 기하학적 매니폴드가 아닌, ‘기억(Memory)’과 ‘탄성(Elasticity)’을 가진 물리적 매질로 재정의하는 **‘시공간 탄성 이력 이론(Spacetime Elastic Hysteresis Theory)’**을 제안한다. 우리는 질량과 중력이 시공간 격자의 위상학적 엉킴 밀도(ψ)에서 기인한다는 구성 방정식인 **‘킴의 법칙(Kim’s Law, E = κψ)’**을 도입한다.우리는 엉킴 스칼라 필드(ψ)를 포함한 확장된 라그랑지안을 구성하고, 변분 원리를 통해 수정된 아인슈타인 장 방정식을 유도하였다. 여기서 도출된 **‘킴 텐서(Kim Tensor, K_μν)’**는 은하 규모에서 추가적인 중력 효과를 발생시켜 암흑물질 없이도 은하 회전 곡선의 평탄화를 완벽하게 설명한다. 또한, 시공간 매질의 점탄성(Viscoelasticity)에 의한 에너지 소산 효과인 ‘탄성 적색편이(Elastic Redshift)’를 고려하여 우주 팽창 역사를 재구성한 결과, 우주의 실제 나이는 **165.4억 년(16.54 Gyr)**으로 산출되었다. 이 새로운 타임라인은 JWST가 관측한 조기 거대 은하들의 형성과 진화에 필요한 시간을 자연스럽게 제공함으로써, 현대 우주론의 난제들을 통합적으로 해결한다.
Category: Astrophysics

Unified Reconstruction of Cosmology Via Spacetime Hysteresis and Gravitational Entanglement [ Updated 2]

Authors: Chang-Sik Kim
Comments: 7 Pages. Copyright © 2026 Chang-Sik Kim. All rights reserved.

Wepropose a scalar-tensor theory of gravity by redefining spacetime as a physical viscoelastic medium. Addressing the anomalies of the ΛCDMmodel—specifically the Hubble Tension and the early formation of massive galaxies observed by JWST—we introduce a constitutive relation, Kim’sLaw (E = κψ). This law postulates that the gravitational potential arises from the topological entanglement density (ψ) of the spacetime lattice. By constructing a Lagrangian density with an elastic potential term,we derive modified Einstein Field Equations. We explicitly demonstrate that the "missing mass" in galactic rotation curves is a manifestationof vacuum rigidity (Kµν) rather than non-baryonic Dark Matter. Furthermore, we incorporate an energy dissipation term (hysteresis) into the Friedmann equations, deriving a recalibrated cosmic age of 16.54 Gyr.This extended timeline resolves the conflict between standard cosmology and the existence of mature galaxies at z > 10.
Category: Quantum Gravity and String Theory

Golden Eigenvalues and the Tihany Conjecture for Mycielski Graphs

Authors: Vinicius F S Santos
Comments: 17 Pages. (Note by viXra Admin: Parts of the texts are cut off!)

The Erdős—Lovász Tihany Conjecture (1968) asserts that every graph G with χ(G) ≥ s + t − 1 > ω(G) admits a vertex partition into parts with chromatic numbers ≥ s and ≥ t, respectively. We prove the conjecture for the infinite family of pairs (3, k−2) on Mycielski graphs Mk for all k ≥ 5. Our approach is spectral, centred on the golden ratio φ = (1+√5)/2. The pentagon C5—the minimal graph with χ > ω—has adjacency eigenvalues {2, φ−1, φ−1,−φ,−φ}, and this golden spectral structure propagates through the Mycielski construction: the golden ratio’s defining equation μ2 − μ − 1 = 0 arises exactly from the Mycielski eigenvalue relation (Lemma 2.1). We prove the C5-Peeling Existence Theorem: for every Mk (k ≥ 4), a direction in the golden eigenspace peels off a C5 from Mk. The proof is constructive via spectral interferometry: two Mycielski lift paths span a four-dimensional subspace whose layer-control matrix has det = √5, enabling independent phase steering to select a diagonal lift C5—the reverse cycle through alternating address layers. Computationally, the Hoffman margin of this partition is F = φ−3 = √5 − 2 exactly, verified for all k ≤ 12. The key advance is the Golden Sub-Induction (Theorem 1.2): for k ≥ 6, the 1/φ shadow attenuation forces the peeled C5 into the original vertex block of Mk, so the remainder Mk Pk contains Mycielski(Mk−1 Pk−1) as a subgraph, where (Pk)k≥5 is a coherent family of peeled pentagons. Since χ(Mycielski(G)) = χ(G) + 1 for any graph with an edge, this yields the inductive bound χ(Mk Pk) ≥ k − 2. Combined with χ(C5) = 3, this settles the Tihany conjecture for the pair (3, k−2) on Mk for every k ≥ 5—an infinite family of previously open cases.
Category: Combinatorics and Graph Theory

Unified Reconstruction of Cosmology Via Spacetime Hysteresis and Gravitational Entanglement (In Korean)

Authors: Chang-Sik Kim
Comments: 21 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

Modern cosmology faces a "dual crisis": the failure to detect dark matter particles and the Hubble Tension. This research proposes a paradigm shift, redefining spacetime as an "Elastic Medium with Memory" (Hysteresis). Central to this is Kim’s Law (E = K*P (kappapsi)), which defines mass as the emergent manifestation of Spacetime Entanglement Density (P: psi). By correcting for Elastic Redshift (z_{elastic}), the model derives a true cosmic age of 16.5 billion years, resolving the paradox of mature early galaxies observed by the James Webb Space Telescope (JWST).2. Theoretical Framework: Kim-Einstein Equations2.1 The Unified LagrangianThe theory integrates a new elastic potential term, mathcal{L}_{entangle} (or mathcal{L}_{Knot}), into the standard Einstein-Hilbert action:
Category: Astrophysics

Gravitational Lensing and the Bullet Cluster via Spacetime Creep and Stress Relaxation

Authors: Chang-Sik Kim
Comments: 3 Pages.

The Bullet Cluster (1E 0657-56) is widely regarded as the most direct empirical evidence for particulate Dark Matter, due to the observed separation between the gravitational lensingcenter and the baryonic gas. In this third and final paper of the series, we demonstratethat this phenomenon can be explained within the Spacetime Elastic Hysteresis The ory without invoking non-baryonic particles. We introduce the mechanism of "Spacetime Creep," where the macroscopic entanglement strain (ψ) exhibits a delayed relaxation response to the rapid deceleration of baryonic matter. Our analysis shows that the viscoelastic stress relaxation time (τrelax) allows the gravitational potential peak to disassociate from the collisional gas, naturally reproducing the lensing anomalies observed in galaxy cluster collisions.
Category: Quantum Gravity and String Theory

Resolving the Hubble Tension and the Early Galaxy Problem via Viscoelastic Memory

Authors: Chang-Sik Kim
Comments: 3 Pages.

The "Hubble Tension"—the statistically significant discrepancy between the expansion rate of the universe measured from the early universe (CMB) and the late universe (SNIa)—remains one of the most challenging problems in modern cosmology. In this second paper of the series, we propose that this tension arises from neglecting the viscoelastic nature of spacetime.Building on Kim’s Law (V ∝ ψ2) established in Part 1, we introduce the concept of"Spacetime Hysteresis," where the release of stored elastic energy is delayed by a characteristic time scale τ. Our MCMC analysis shows that a delayed elastic response (τ ≈ 0.15)naturally boosts the late-time expansion rate to H0 ≈ 73 km/s/Mpc, resolving the tensionwithout breaking early-universe physics. Furthermore, this model implies a recalibrated cosmic age of 16.54 Gyr, providing a theoretical solution to the formation of mature galaxiesat z >10 observed by JWST.
Category: Astrophysics

Unified Reconstruction of Cosmology via Spacetime Hysteresis and Gravitational Entanglement [II in Korean]

Authors: Chang-Sik Kim
Comments: 25 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

Modern cosmology faces a "dual crisis": the failure to detect dark matter particles and the Hubble Tension. This research proposes a paradigm shift, redefining spacetime as an "Elastic Medium with Memory" (Hysteresis). Central to this is Kim’s Law (E = p*k ):(kappapsi), which defines mass as the emergent manifestation of Spacetime Entanglement Density (p: psi). By correcting for Elastic Redshift (z_{elastic}), the model derives a true cosmic age of 16.5 billion years, resolving the paradox of mature early galaxies observed by the James Webb Space Telescope (JWST).2. Theoretical Framework: Kim-Einstein Equations2.1 The Unified LagrangianThe theory integrates a new elastic potential term, mathcal{L}_{entangle} (or mathcal{L}_{Knot}), into the standard Einstein-Hilbert action:
Category: Astrophysics

Yang-Mills Existence and Mass Gap: A Framework via Anomaly Algebra, Gradient-Flow Spectral Methods, and Quantum Information

Authors: Lluis Eriksson
Comments: 13 Pages. v2 (all v1 numbered statements preserved; condensed edition): 1-form pair retagged as imported input with the Perron-Frobenius tension documented and demonstrated numerically; Result E renamed; citation repaired; Tables 3 and 5 replicated digit for digit

We present a rigorous framework for the Yang-Mills mass gap problem, combining three independent lines of argument that reinforce each other. Result A (Unconditional): a new MaxEnt Clustering-Recovery Bridge -- for lattice gauge states with finite correlation length xi, in the polymer/Kotecky-Preiss regime made precise in Section 5, the Petz recovery fidelity satisfies 1 - F <= C e^{-r/xi}, proved via maximum-entropy truncation on gauge-invariant algebras, a convergent polymer expansion, and the Fawzi-Renner theorem. Result B (unconditional on the lattice, conditional for all couplings): for SU(N) lattice gauge theory (T=0, theta=0, d=3+1, N >= 2), the algebraic phase exclusion, using the projective commutation relation of 1-form symmetry operators, excludes the trivially gapped symmetric phase (v2: given the imported lattice realization of the symmetry pair); combined with Perron-Frobenius non-degeneracy and Gauss-law constraints, this forces confinement at strong coupling; the extension to all couplings relies on Hypothesis 1.1 (absence of a bulk phase transition), supported but not proven. Under Hypothesis 1.1 the uniform lattice mass gap holds for all lattice spacings. Result C (Conditional): under the same hypothesis, the continuum limit exists as a Euclidean QFT satisfying all Osterwalder-Schrader axioms with mass gap. Result D: the gradient flow reduction (developed in the companion ai.viXra:2602.0020). v2 (no v1 numbered statement is changed): the exact lattice realization of the commuting projective 1-form pair is made an explicit imported input, and a new remark records the Perron-Frobenius tension that forces this framing -- at finite volume, PF uniqueness plus exact commutation of both generators would contradict the projective relation outright, so the magnetic operator commutes with H only up to defect terms (verified numerically: toric code, exact pair with 4-fold degenerate ground state; Z2 gauge theory with electric term, unique ground state with both string commutators nonzero); the Result-D naming collision is resolved (the d = 2+1 theorem is now Result E); an unresolved citation is repaired; the epsilon-powers in the MaxEnt bridge are harmonized; and a replication report is added: the 7-qubit Z2 table is reproduced digit for digit, the Z3 table is reproduced digit for digit after a documented g <-> 1/g erratum between the v1 script and table, and the torus finite-size-scaling table could not be reproduced from the printed conventions and is downgraded to archival status (no framework result depends on it). v2 is presented in condensed form: every v1 numbered statement is preserved with the same numbering; detailed proofs and the full computational listing remain in the v1 PDF as the archival source.
Category: Mathematical Physics

Gradient Flow Monotonicity and the Yang-Mills Mass Gap: A Conditional Reduction via Spectral Methods

Authors: Lluis Eriksson
Comments: 12 Pages. v2 (no v1 statement changed): spectral representation retagged as explicit hypothesis H0 for the interacting flow; broken citation repaired; Holley-Stroock volume-uniformity claim corrected; a_IR=0 classification retagged as physical input.

We establish a conditional reduction of the Yang-Mills mass gap problem to a concrete spectral inequality involving the gradient flow. Main result (informal): for pure SU(N) Yang-Mills theory, if the gradient flow beta-function satisfies a uniform strict asymptotic freedom condition |beta_GF(g)| >= delta g^3 for large g, and a Tauberian regularity condition holds for the spectral density, then: in d = 3 the theory has a mass gap Delta > 0; in d = 4 the infrared trace anomaly vanishes, a_IR = 0, ruling out a conformal infrared fixed point -- combined with the phase exclusion of the companion paper, this reduces the mass gap to explicit spectral conditions. However, the spectral argument is marginal in d = 4 and requires additional non-perturbative input. The proof uses a spectral representation of the gradient flow energy E(t) with the monotonicity identity R'(t) = -2 Var_t(lambda) <= 0, the Komargodski-Schwimmer a-theorem, and a gradient flow Poincare inequality connecting functional inequalities to exponential clustering. We verify all perturbative inputs: the free-field calibration gives R_free(t) = 2/t in d = 4 and the one-loop correction has the correct sign. We identify the indefiniteness of the Weitzenbock curvature term as the precise technical barrier in d = 4. v2 (no v1 numbered statement is changed): the fixed-measure spectral representation is retagged as an explicit hypothesis (H0) for the nonlinear interacting flow (equivalent to complete monotonicity of E(t), proven only for the linearized flow; the status table is retagged accordingly); an unresolved citation is repaired; the Holley-Stroock route claimed in v1 to give the Poincare inequality unconditionally at finite beta is corrected (its constant is exponential in the volume, so the L-uniform statement remains conditional outside the two controlled regimes); the a_IR = 0 phase classification behind the d = 3 mass-gap corollary is retagged as imported physical input; the Karamata attribution is replaced by the elementary direct bound actually used; and a verification suite adds numerical evidence: exact spectral machinery, lattice free-field calibration, the quantified d = 3 vs d = 4 dichotomy on synthetic spectral densities, and a first in-framework SU(2) Wilson-flow Monte Carlo diagnostic (8^4, beta = 2.4: c(t) = t^2 rises 42 percent across the measured window and R(t) < 2/t pointwise, i.e. beta_GF < 0 throughout -- numerical support for Hypothesis B' in a controlled lattice window, evidence not proof).
Category: Quantum Physics

Unified Reconstruction of Cosmology Via Spacetime Hysteresis and Gravitational Entanglement [summary]

Authors: Chang-Sik Kim
Comments: 7 Pages.

Contemporary cosmology is grappling with a fundamental crisis: the persistent failure to detect Dark Matter particles and the escalating "Hubble Tension." Recent high-redshift observations from the James Webb Space Telescope (JWST) have revealed massive, mature galaxies that defy the 13.8 billion-year timeline of the standard Lambda-CDM model.This dissertation proposes a revolutionary paradigm shift by redefining the vacuum of spacetime as an "Elastic Medium with Memory" (Spacetime Hysteresis). We introduce Kim’s Law (E = kappa * psi), which identifies the origin of mass-energy as the topological entanglement density (psi) of the spacetime lattice. By incorporating a new stress-energy tensor, the Kim Tensor, into Einstein’s Field Equations, we demonstrate that galactic rotation curves and gravitational lensing anomalies are manifestations of spacetime’s emergent rigidity, eliminating the need for hypothetical dark matter particles.Furthermore, we identify "Elastic Redshift"—energy dissipation within the strained spacetime medium—as a hidden variable in cosmic expansion. Correcting for this factor resolves the Hubble Tension and establishes a recalibrated cosmic age of 16.54 billion years. This theory provides the necessary temporal window for the evolution of early massive galaxies and offers a unified, dark-matter-free framework satisfying both quantum logic and general relativistic principles.
Category: Astrophysics

The Invisible War: Defending the Human Brain Against High-Engagement Psychological Warfare

Authors: Steven Hammon
Comments: 42 Pages.

The modern media ecosystem, driven primarily by profit-first engagement algorithms, has created significant issues in terms of information distribution. This paper argues that the public is subjected to pervasive psychological manipulation, primarily through the control of fear, hate, and polarization, with no simple choice to opt out while still being informed. This has cascading and concerning consequences, including measurable harm to the mental well-being of children, the fragmentation of social cohesion, and the systemic erosion of the democratic process. It also forces manipulative content and misinformation to be vilified as a problem. The paper examines the expectation that individuals should defend themselves against multi-billion-dollar manipulation engines. Censorship infringes on free speech and often fails to address the root cause. Instead, this paper proposes the implementation of an Ethical Journalism Standard (EJS), modeled on the MPAA film rating system, which has been shown to satisfactorily balance free speech with the need to protect children and society since 1968. The EJS would not ban or suppress default feed content. It would provide a label for journalism that adheres to the established Journalist Code of Ethics, and allow Ethical Journalism content to be selected, like how parents select a TV station of G-rated content. This empowers the public’s right to access factual information, to make informed choices about the information they consume and share, and to give informed consent about the future of their country. It also gives manipulation a place to be celebrated as a skill. By elevating credible, ethical content, society can foster a healthier information environment, safeguard children, and restore confidence in governments and media that is essential for a functioning democracy, while simultaneously embracing the right to free speech manipulation as a skill to be celebrated.
Category: Social Science

Entropy-Inertial Curvature: A Relational Hypothesis with Cosmological Consistency

Authors: Geza Kovacs
Comments: 2 Pages.

We propose a relational extension of General Relativity in which spacetime curvature is sourced nonlocally by retarded entropy gradients. Inertia emerges as macroscopic resistance to cosmic irreversibility. No new fundamental fields or free parameters are introduced; the sole scale is the cosmological horizon ($ell_n approx c/H_0$). Post-recombination entropy production yields a derived amplification factor $phi_0 approx 10^{10} pm 20%$, providing a thermodynamic explanation for galactic rotation curves (projected $chi^2/text{dof} approx 1.1$ from Gaia DR3 analogs and mocks for DR4) via retarded entropy gradients that induce effective inertial screening at low accelerations, and the $H_0$ tension via a dynamical, structure-dependent effective cosmological constant that boosts late-time expansion relative to early-universe CMB-calibrated values. The mechanism is naturally suppressed in the early universe ($sim 10^{-30}$ at BBN) consistent with the Weyl Curvature Hypothesis. We introduce a "Curvature Memory" effect to explain cluster lensing offsets and predict frequency-dependent GW phase skews ($sim 0.4$ ms) testable by LISA.
Category: Relativity and Cosmology

The Quantum Space Mechanism - The Origin of Forces

Authors: Joseph Koharski
Comments: 66 Pages. I added manuscript line numbers for easier reader reference and feedback. Corrected minor typographical errors and fixed intermediate arithmetic in the macroscopic dynamics calculations.

This document contains a compilation of five research papers detailing the Quantum SpaceMechanism (QSM). These papers propose a unified framework where Inertia, Gravity, and Timeemerge from the hydrodynamics of a viscous, dilatant vacuum substrate (the Higgs field). The seriescovers: (I) The Entropic Origin of Inertia and the Bridge Equation; (II) The Vacuum Yield Point andthe Origin of Gravity; (III) The Geometry of Mass and Particle Generations via Finslerian Anglesof Attack; (IV) Macroscopic Dynamics, Dark Matter as Metric Expansion, and Electromagnetism;and (V) The Origin of Time as Viscous Dissipation.
Category: Quantum Gravity and String Theory

On the Existence of Destiny: A Demonstration from Spacetime Physics

Authors: Manuel Alejandro Hernández Madan
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)

We demonstrate that the concept of destiny possesses rigorous mathematical foundation in spacetime physics. By analyzing the geometric structure of worldlines in Minkowski spacetime, we prove that destiny—defined as the endpoint of an observer’s worldline—exists with identical ontological status as the observer’s birth (the worldline’s starting point). This demonstration requires no metaphysical assumptions beyond those implicit in special relativity. The apparent paradox between destiny and free will is resolved by recognizing that both perspectives are simultaneously valid: complete determination in four dimensions coexists with genuine choice in sequential time. We remove "destiny" from the realm of mysticism and establish it as a geometric property of spacetime.
Category: History and Philosophy of Physics

A Scalar Product Approach to Strong Goldbach, Twin Primes, Polignac Conjectures And Geometric Unification of Regularized Prime Manifolds

Authors: Ezadiin Redwaan
Comments: 10 Pages.

We present a universal, non-constructive proof of the Strong Goldbach Conjecture and the Twin Prime Conjecture by shifting the problem from arithmetic density to Geometrical Mapping . By mapping the interaction between addition and multiplication onto a prime-based vector space, we prove that the identity 2n cos(θ) = a + b is a structural requirement of the space for every even integer 2n. This formulation resolves the parity problem through the Dot Product, demonstrating that a prime partition (a, b) is geometrically necessitated by the scalar projection of prime-based vectors. Furthermore, we show that the limiting behavior of the angular discrepancy θ necessitates the infinite existence of Twin Primes. This research establishes that prime distributionis a fundamental consequence of a deeper geometric necessity. This paper also proves Polignac’s Conjecture via Angular Singularity. Using the scalar product 2n cos(θ) = a+b, we map prime gaps to angular states θi ∈ (0, 90◦). We demonstrate that the loss of any gap triggers a Spectral Collapse, forcing the field into a 90◦ singularity where a + b = 0. To prevent this structural impossibility, all Polignac gaps must recur infinitely. This paper also introduces a novel geometric framework mapping the distribution of prime numbers onto an infinite-dimensional coordinate manifold. We establish a continuous functional relationship linking an independent compact scale operator n, a transfinite prime summation, at specific gaps, and a smooth angular coordinate θi strictly restricted to the open obtuse interval (90◦, 180◦)...
Category: Number Theory

Towards a Local Minimum Time Resolution in Curved Spacetime

Authors: Priyanshu Rauth
Comments: 5 Pages.

This paper explores the idea that spacetime may possess a minimal time interval that depends on gravitational redshift and curvature. Motivations from general relativity, quantum mechanics and approaches to quantum gravity suggest that both space and time may exhibit effective discreteness near the Planck scale. We review theoretical arguments for minimal intervals, including the generalized uncertainty principle and deformations of the Heisenberg algebra, and summarise recent experimental work with atomic clocks and proposals such as the Bose--Marletto--Vedral experiment. A phenomenological ansatz for a position--dependent minimal time increment is presented and we discuss how to improve its physical foundations. The aim is not to propose a theory of everything but to offer a conservative, focused framework that could guide future experiments.
Category: Relativity and Cosmology

Foundations of Physics: The Law of Quantized Reorganization Rate and the Theorie of Euclidean Quantum Reorganization

Authors: Christian B. Mueller
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper presents a novel framework for fundamental physics that replaces the geometriccurvature of spacetime with a resource-based conservation law. By treating reality as a discrete computational process, we derive the relationship between mass, energy, and the local rate of time. The model progresses from a 3D-accounting perspective (LQRR) to a 4D-Euclidean resonance framework (TEQR), providing a unified explanation for gravity, time dilation, and projection-based phenomena often attributed to Dark Matter.
Category: Relativity and Cosmology

Modular Cells for Quantification

Authors: Alaya Kouki
Comments: 44 Pages.

From Restraint Relativity it is possible to consider a corpuscle as a packet of strings. The variation of the length of this packet is equal to the phase speed of the corpuscle as a packet of waves times an universal constant. In a system of units where ℏ=c=a=1 the string vector becomes equal to the wave vector.From quantum mechanics we had deduce that a Planck oscillator can emit or absorb power only by quanta of power multiple integer of hν^2. This allows us to divide space-time in modular cells of action, momentum, energyu2026etc in the phase space geometry of the oscillator and resolve the problem of vacuum energy density. Planck system of units serves only for black holes topology.Space-time is a four open dimensions. More than four the dimension should be curled. Resolving gravitation field by computer machine with model using modular cells will be without singularities . Einstein equations of gravitational field are available only in a quasi static asymptotically flat Universe. Constants G & Λ of General Relativity are proportional to the inverse square of the Universe radius.
Category: Quantum Gravity and String Theory

Interconnected Infinities Giant Sphere Space - IIGSS

Authors: Mohammad Saeed Alnatour
Comments: 172 Pages. (Note by ai.viXra.org Admin: For the last time, author name is required in the article after article title and please cite listed scientific references)

Divergent series and singular integrals arise naturally in analysis, geometry, and theoretical physics, yet their standard treatment relies on analytic continuation or limit-based regularization. While these methods successfully assign finite values, they necessarily suppress information about how infinity is traversed. This work proposes a structural framework—Interconnected Infinities Giant Sphere Space (IIGSS), together with an intrinsic regulator, the Discrete Laplace Regulator (DLR), in which divergence is treated as a boundary phenomenon rather than a failure of summation.DLR operates directly on discrete sequences by introducing controlled exponential damping and expanding the resulting kernel at a well-defined infinite-traversal gate. Divergence appears explicitly as algebraic pole terms or logarithmic singularities in the gate expansion, encoding growth class and traversal density, while a pole-invariant constant—the Convergence Momentum (CM)—emerges as a finite structural quantity. Valuation is performed exclusively through gate expansion followed by pole removal, without index shifting, limit evaluation, or analytic continuation.Within this framework, classical zeta and Dirichlet regularizations are recovered as special projections under standard traversal, while traversal-sensitive features—such as zero insertion, spacing modulation, and phase structure—remain distinguishable. The framework accommodates finite-gate and oscillatory sequences and clarifies the limitations of reconstruction from regularized values alone. In physical applications, CM functions as a retained boundary invariant: when applied to spectral mode sums, such as those appearing in the Casimir effect, the regulator preserves observable finite quantities while rendering the underlying divergence structure explicit. DLR thus provides a higher-resolution language for infinity, preserving established results while exposing structural information necessarily omitted by classical methods.
Category: Functions and Analysis

Inverse Frequency Duality of Spacetime

Authors: Cameron Brogan-Higgins
Comments: 2 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

This conjecture proposes that spacetime can be understood as a distributed frequency field and that the cosmological singularity represents its reciprocal or inverse state. In this framework, the universe is not the aftermath of an energetic explosion but the expansion of a frequency inversion: the Fourier-dual expression of a compressed, information-complete origin. Curvature, expansion, and entropy are treated as emergent properties of a wave-domain oscillation in which spacetime and its singular inverse form conjugate aspects of a single cyclical process.
Category: Relativity and Cosmology

Emergent Quantum Mechanics, Special Relativity, Induced Gravity, Dirac Fermions and U(1) Gauge Interactions from Discrete Hypercubic SpacetimeLattice

Authors: Bertrand Jarry
Comments: 7 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0) (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present a complete bottom-up derivation of non-relativistic quantum me-chanics, special relativity, induced gravity (Sakharov mechanism), Dirac fermions, and U(1) gauge interactions from nearest-neighbor unitary evolution on a 4D hy-percubic lattice. The Schrödinger equation emerges exactly in the continuum limit, with higher-order Lorentz-violating corrections. We rigorously prove the Heisenberg uncertainty principle, quantum superposition, entanglement, and probability conser-vation as direct consequences of the discrete structure. Detailed calculations includeTaylor expansions to order 10, Fourier dispersion to k10, exact commutator[x, p], variance,norm conservation to order 8, 1016 GeV, is compatible with the latest LHAASO constraints on GRB 221009A(2025—2026). This work forms the foundation for emergent SU(2)×SU(3), Higgs,cosmology, and quantum gravity in subsequent papers.
Category: Quantum Gravity and String Theory

Rigidity-induced Scaling Laws in Unit Distance Graphs

Authors: Lucas Aloisio
Comments: 5 Pages.

We revisit the classical Unit Distance Problem posed by Erdős in 1946. While the upper bound of O(n4/3) established by Spencer, Szemerédi, and Trotter (1984) is tight for systems of pseudo-circles, it fails to account for the algebraic rigidity inherent to the Euclidean metric. By integrating structural rigidity decompositionwith the theory of Cayley-Menger varieties, we demonstrate that unit distance graphsexceeding a critical density must contain rigid bipartite subgraphs. We prove a "FlatnessLemma," supported by symbolic computation of the elimination ideal, showing that the configuration variety of a unit-distance K3,3 (and by extension K4,4) in R2 is algebraically singular and collapses to a lower-dimensional locus. This dimensional reduction precludes the existence of the amorphous, high-incidence structures required to sustain the n4/3 scaling, effectively improving the upper bound for non-degenerate Euclidean configurations.
Category: Combinatorics and Graph Theory

The Fractal Planck Voxel Model: A Geometric Unification of General Relativity, Quantum Mechanics, the Standard Model, and Consciousness

Authors: Benjamin R. Carignan
Comments: 59 Pages.

In 1899, Max Planck introduced the fundamental constants that now bear his name, combining the gravitational constant G, the speed of light c, and the reduced Planck's constant ħ to define natural units of length, time, and mass. The Planck length and Planck mass emerged as the scales at which quantum effects of gravity should become dominant — a transition zone where classical general relativity (GR) and quantum mechanics (QM) intersect. Planck himself viewed these units as theoretical curiosities, unaware that they hinted at a discrete structure underlying spacetime. We propose that spacetime at the Planck scale is composed of a grid — a lattice — of rhombic dodecahedral voxels with fractal boundaries. The unique properties of this shape impart it with the specific qualities and characteristics of the observed universe through emergent geometric rules. Through this single geometric structure, the Fractal Planck Voxel model (FPV) fully realizes the transition zone that Planck’s work hinted at over 125 years ago. The FPV model derives general relativity, quantum mechanics, the Standard Model gauge groups, three generations, particle masses, and mixing angles, all from voxel symmetry and triangular modes on rhombic faces, with the cosmological constant serving as the energy of fractal subdivision. The model also addresses numerous longstanding problems and questions in physics — from the collapse of the wave function to neutrino masses, dark matter, dark energy, the origin of the Higgs, and more. The fact that the FPV model does all of this while remaining consistent with all current observations — without additional fields, particles, dimensions, or fine-tuned parameters — lends strong credence to its validity as a unifying theory.
Category: Quantum Gravity and String Theory

Framework of a Unified Effective Field Theory for Gravity Based on Atomic-Scale Quantum Entanglement Networks

Authors: Yunsheng Shu, Shun Yao, Zhiyong Yao
Comments: 54 Pages.

This paper proposes a unified effective field theory (EFT) framework for gravity based on atomic-scale quantum entanglement networks. In this framework, the gravitational field of any object—universal gravitation—arises from the superposition of micro-gravity domains (ffGD) at the atomic level, with the strength of gravity precisely related to the total number of atoms, thereby unifying macroscopic phenomena with microscopic interpretations (the superposition of micro-gravity domains (ffGD) at the atomic level forms a gradient material field, and the gradient material field constitutes the geodesic of matter (planets)). Einstein’s theory of curved spacetime serves as an equivalent description at large scales, enabling the model to explain all classical gravitational effects while linking quantum origins to observable reality in an intuitive and engaging way: gravity can be imagined not as abstract curvature, but as the collective "pull" produced when atomic quantum threads are interwoven into the structure of space. The core of the framework is a topology-constrained effective field theory, which uses the emergent distance induced by mutual information and the Fisher information metric as the interface from discrete entanglement networks to continuous geometry, and has constrainable low-energy parameterization (e.g., ffff, ffff, cff, Λff). This paper emphasizes the paradigm of "falsifiability first", integrating strong-field endpoints (such as the effective reflection model of Planck entanglement nucleus boundary conditions) with weak-field, cosmological, and multi-messenger observations into a multi-channel decision matrix, systematically converting "non-detection" results into upper bounds on parameter space.
Category: Quantum Gravity and String Theory

Electromagnetic Field Energy as an Unaccounted Gravitational Source in Levitated Optomechanics Experiments

Authors: Joseph Wimsatt
Comments: 4 Pages. This paper identifies a potential systematic error in levitated optomechanics experiments attempting to measure quantum gravity effects. We show that electromagnetic field energy in optical traps gravitates through the stress-energy tensor

Recent advances in levitated optomechanics have enabled experiments probing gravitational interactions at unprecedented scales, with the goal of detecting quantum signatures of gravity. These experiments use high-intensity optical traps to levitate nanoparticles and measure gravitational forces between them. We demonstrate that the electromagnetic field energy density in these optical traps constitutes a gravitational source through the stress-energy tensor, yet this contribution is not accounted for in current experimental analyses. Using the linearized Einstein field equations, we calculate the gravitational potential and field arising from concentrated laser fields at experimentally relevant power densities (approximately 10^15 W/m^2). We find that the EM field gravitational contribution can be comparable to or exceed the gravitational effects being measured between particle masses, potentially constituting a systematic error of 1% to 100% in current experiments. We propose five calibration protocols to detect and characterize this effect, including power-scaling tests and field geometry variations that can discriminate EM field gravity from particle-particle gravitational interactions. If unaccounted for, this effect could compromise the interpretation of experiments seeking quantum signatures of gravity.
Category: Relativity and Cosmology

From Holographic Complexity to Emergent Spacetime: A Unified Framework for Early Universe Structure Formation via TSVF and Quantum Error Correction

Authors: Hassan Dawood Salman
Comments: 6 Pages. For numerical validation, see DOI 10.5281/zenodo.18382581

Recent observations by the James Webb Space Telescope (JWST) of massive galaxies at z > 10 reveal a profound tension with the standard ΛCDM structure formation paradigm. We propose a resolution rooted in Two-Boundary Quantum Cosmology (TBQC), where spacetime geometry emerges as a Holographic Quantum Error Correcting Code (HQECC). We formalize the selection of cosmic history using the Two-State Vector Formalism (TSVF), introducing a "Process Matrix" Weff that acts as a teleological filter, selecting histories that maximize computational efficiency (δAC = 0) without violating causality. This mechanism effectively lowers the critical density threshold for gravitational collapse, achieving spectacular agreement with JWST stellar mass and UV luminosity functions (χ²/dof ≈ 0.06). Our model exhibits surgical precision: active only at z > 10 while preserving all late-time constraints. We predict a unique, falsifiable 1500% enhancement in the 21cm power spectrum at k∗ ≈ 1 Mpcu207b¹, detectable by HERA Phase II (2025—2027) with > 100σ confidence.
Category: Astrophysics

Gravitational Rheology of a Unified Dark Sector Anisotropic Lensing and Stress-Driven Jets Near Black Hole Horizons

Authors: Eduardo Rodolfo Borrego Moreno
Comments: 22 Pages.

We extend an effective rheological description of a unified dark sector into the strong-field regime of rotating black holes within standard general relativity. Building on prior work where dark energy--like and dark matter--like phenomena emerge as distinct dynamical phases of a single residual medium, we examine the role of anisotropic stress and dissipation in gravitational optics and near-horizon dynamics. We show that stress gradients in the activated rheological phase contribute directly to the gravitational optical potential, yielding lensing without additional collisionless mass components. In the near-horizon region, convergent flows and stress amplification drive a phenomenological conversion regime that preserves total energy--momentum conservation and produces relativistic outflows. Toy estimates demonstrate that this mechanism can account for observed jet powers in low-accretion systems such as M87* ($sim 10^{42}-10^{44}$ erg s$^{-1}$), predicting lepton-dominated outflows with elevated linear polarization fractions ($Pi_{m lin} sim 15%-35%$), radial/poloidal morphology, and axis-aligned stability. These signatures are compatible with current EHT observations yet distinguishable from magnetically dominated models such as Blandford--Znajek. The framework provides a unified, testable description of dark phenomena across scales as phases of a single effective residual medium, without modifying Einstein gravity or introducing new degrees of freedom.
Category: Astrophysics