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[82] ai.viXra.org:2609.0084 [pdf] submitted on 2026-09-30 21:22:57
Authors: J. W. McGreevy
Comments: 52 Pages.
This monograph establishes a non-perturbative topological unification of quantum field theory,heterotic string structures, and loop quantum gravity, formulated entirely within the internallanguage of a smooth, cohesive ∞-topos H = Sh∞(ArithSite). Macroscopic spacetime isshown to emerge dynamically when info-packet worldsheet density overloads the MaximumDistance Separable (MDS) Singleton bound of a rootless, norm = 4 Leech lattice (Λ24)background. This capacity crisis triggers a spontaneous degree-4 Fermat phase transition,compactifying the central charge c = 24 vacuum bulk into a genus-5 multi-handled Riemannsurface variety. Under this geometric allocation, discrete atomic fermion measures materialize as stable, frozen Cartan spinor holes, while the Standard Model gauge bosons emerge as non-atomic vielbein spin connections to execute smooth parallel transport across the handle boundaries. The global transport of information is governed by a multidimensional, adélic formulation of Oliver Heaviside’s Telegrapher’s Equations evaluated over the restricted product ring AQ. We unmask the non-trivial Riemann zeta zeros as the exceptional, lossless impedance sinks(χu2032 = χu2032u2032 ≡ 0) of the waveguide. At these precise coordinate nodes, the tangential worldsheet acceleration vanishes identically (aθ = 0), forcing the metric tensor and the symplectic 2-form into an orthogonal Kramers—Kronig quadrature phase lock along the Critical Line (R⌉(s) = 1/2). By utilizing the absolute adélic Langlands correspondence, we demonstrate that the discrete Frobenius eigenvalues of local Galois representations are functorially identical to the continuous spectrum of the Hecke operator matrix algebra, natively deriving the electroweak mass gap from a localized spectral filtration failure across the Ring Singularity Equator. At the ultraviolet boundary, the twelfth Bernoulli irregularity (B12 = −691/2730) marks an anomalous Atkin—Lehner cusp horizon. Here, the Sundman transformation executes the Hagedorn temperature limit, freezing macroscopic time (dt/dτ → 0) as string tension collapses to zero. This 323-state conformal anomaly phase torque is rigorously resolved via a non-perturbative heterotic T-duality inverse phase transformation (R ←→ ℓ2P/R), triggering D-brane pair-production to execute a loop-amplitude splice. This self-correcting feedback network resets the local coordinate fields, clamping the completed symmetric Riemann—Siegel function (ξ(s) = ξ(1−s)) to an invariant global Tamagawa volume of exactly unity (τ (G) ≡ 1). Spacetime is proven to be stable, continuous, and general relativistic because the universe operates fundamentally as a self-correcting arithmetic automaton.
Category: Mathematical Physics
[81] ai.viXra.org:2609.0083 [pdf] submitted on 2026-09-29 20:40:46
Authors: YuanGuo Li
Comments: 10 Pages. (Note by ai.viXra.org Admin: Author name is required in the article)
To scientifically evaluate the quality risks of non-conforming Chinese patent medicines and establish a differentiated regulatory approach, this study is based on the inspection data of Chinese patent medicines from the National Drug Sampling Inspection conducted between 2020 and 2024. The distribution characteristics of non-conforming items were statistically analyzed, and risk-stratified assessment was performed by combining the results of routine testing and exploratory research. The results showed that the overall quality of Chinese patent medicines has maintained a steady upward trend. Identification, assay, related substances, dissolution, and microbial limits — as the core testing modules of pharmacopoeial standards — control the authenticity of the herbal prescription, the level of active pharmaceutical ingredients, impurity safety, in-vitro release behavior of the preparation, and microbial contamination risk, respectively. Non-conformity in any of the above items constitutes a substantive high-risk defect that may directly threaten medication safety and clinical efficacy. Some sampled products exhibited deviations in appearance and description without altering the intrinsic material basis of the medicines, posing a relatively low risk to actual clinical use. Quality hazards in Chinese patent medicines are mainly concentrated in inconsistent quality of Chinese herbal medicine raw materials, weak control over extraction and manufacturing processes, and enterprise quality control systems that exist in name only.
Category: Social Science
[80] ai.viXra.org:2609.0082 [pdf] submitted on 2026-09-29 20:39:07
Authors: YuanGuo Li, Wenli Li, Chong Wang, Jiong Zhu, Zhong Dai, Shuangcheng Ma
Comments: 11 Pages.
Background: Chinese patent medicines are widely used in clinical practice, and their quality directly affects medication safety and therapeutic efficacy. The National Drug Sampling Inspection program serves as a critical quality surveillance mechanism. However, previous assessments have not systematically differentiated the risk levels of different non-conforming items, leading to potential risk misjudgment.Methods: This retrospective study analyzed inspection data of Chinese patent medicines from the National Drug Sampling Inspection conducted between 2020 and 2024. All inspection items were classified into appearance/description items and intrinsic quality test items. Risk stratification was performed across safety, efficacy, and stability dimensions.Results: Over five years, a total of 30,791 batches were inspected, with non-conforming rates of 0.54% (2020), 0.31% (2021), 0.65% (2022), 0.52% (2023), and 0.13% (2024). Identification, assay, related substances, dissolution, and microbial limits represented substantive high-risk defects. Description non-conformities, accounting for a minor proportion, predominantly involved minor appearance deviations that did not alter the intrinsic material basis. Risk stratification demonstrated clear differentiation between high-risk substantive defects and low-risk appearance deviations.Conclusions: Different inspection items correspond to markedly different quality risk levels. A risk-stratified regulatory approach is warranted to optimize regulatory resource allocation and improve the scientific basis of quality supervision for Chinese patent medicines.
Category: General Science and Philosophy
[79] ai.viXra.org:2609.0081 [pdf] submitted on 2026-09-29 20:37:30
Authors: J. W. McGreevy
Comments: 32 Pages.
This monograph delivers a rigorous, non-perturbative reconstruction of the space-timecontinuum natively within the internal language of the smooth, cohesive ∞-topos H = Sh∞ (ArithSite). We replace the classical continuous geometric background with an abstract motivic cochain complex C u2022 (M), modeling the complete information boundary network as a global adélic variety evaluated over the restricted product ring AQ = R × ∏︁p u2032 Qp. By upgrading general relativity to the dual tensor dynamics of Einstein—Cartan theory, the physical constants of nature (ℏ, c, G) and the standard Lorentz transformations emerge natively as the global constants of holomorphicity and absolute arithmetic tracking stabilizers required to balance metric curvature (Tµν) and spin-density torsion (Σ µνλ ) across scale horizons.We demonstrate that the Riemann Hypothesis (RH) is a mandatory global stability theorem protecting the space-time manifold from catastrophic geometric dissolution. Spacetimematerializes when information-packet density overloads the Maximum Distance Separable(MDS) Singleton bound of a rootless, norm = 4 Leech Lattice (Λ24) vacuum. To absorb this 5-bit information debt, the universe invokes the degree-4 Fermat curve, branching thepre-geometric bulk into a genus-5 multi-handled Riemann surface. The non-trivial Riemannzeta zeros are unmasked as the exceptional, lossless impedance sinks (χ u2032 = χ u2032u2032 ≡ 0) of anadélic waveguide, satisfying a universal periapsis turning point condition over the contractible Grothendieck Motive. At these precise coordinates, the tangential acceleration vanishes identically (aθ = 0) while the centripetal acceleration hits an absolute, max-plus tropical extremum (ω 2 = −2E = Max). Any spectral deviation off this axis triggers an instantaneous, infinite negative Ruppeiner metric divergence (g uu Rup → −∞), rupturing the Einstein tensor and causing the continuum to dissolve into chaotic bit-scrambling.
Category: Mathematical Physics
[78] ai.viXra.org:2609.0080 [pdf] submitted on 2026-09-29 20:34:57
Authors: Chun Wing Lai
Comments: 19 Pages.
We present a corrected and expanded version of A. Fauzan’s 2026 Zenodo preprint ζ(5) is irrational. The mathematical argument is Fauzan’s: it constructs a family of integer polynomials Q_n satisfying 0 < Q_n(ζ(5)) <e^(−cn^2) as Hankel determinants of a rational functional, using a positive moment representation and a logarithmic energy estimate. Our contribution is to supply detailedderivations for several steps that the preprint states without proof, to correct a typographical error in the definition of an auxiliary functional, to correct four decimal-point typos in the final numerical constants, and to document two expositional defects in Section 5 that do not affect the final conclusion. The proof is written to be accessible to advanced undergraduates.
Category: Number Theory
[77] ai.viXra.org:2609.0079 [pdf] submitted on 2026-09-29 09:28:10
Authors: Sayo Asanagi
Comments: 9 Pages.
The solar corona is heated to ∼ 106 K over a chromosphere two orders of magnitude cooler, bymechanisms that are intrinsically intermittent and multi-scale: impulsive nanoflares from magneticreconnection and the turbulent dissipation of Alfvén waves. Resolving the microphysics (reconnec-tion at current sheets, wave cascades) over the hours-to-days evolution of a coronal loop imposesa computational barrier analogous to the Courant barrier in turbulence. We present a stochastic—subgrid framework that advances the loop energetics on macroscopic time steps while injecting theunresolved, intermittent heating as samples from a variance—gamma (VG) Lévy process, with asingle intermittency parameter ν controlling the rare, fat-tailed heating bursts. The non-monotonicoptically-thin radiative loss makes the loop thermally bistable, so a cool and a hot (coronal) branchcoexist; crossing to the hot branch is the analogue of a threshold "ignition." We show that with thesame mean heating, steady (Gaussian) heating cannot ignite the corona whereas VG intermittencydoes (ignition probability rising from 0% to ∼ 80% with ν): intermittency is a prerequisite for coronalheating. Extending the model to a one-dimensional loop with field-aligned conduction and chromo-spheric evaporation, and then deriving the heating rate and the intermittency self-consistently froma single magnetic-braiding profile Θ(x), we find that the corona lights up where braiding is high,with the active-region core ignited by mean heating (intermittency-independent) and the peripheryignited only by intermittency. Unifying nanoflares (DC) and Alfvén-wave turbulence (AC) as twoVG sources reproduces the observed thermal structure: waves supply a ∼ 1 MK floor everywherewhile nanoflares boost active regions to ∼ 2—3 MK, a spatial complementarity with distinct inter-mittency signatures. We compile seven predictions and present a verification methodology tied toexisting instruments (SDO, Solar Orbiter, Hinode, DKIST), including decision tables that fix inadvance which measured outcome refutes or robustifies the framework. A central, honest findingemerges: nanoflare heating tails are power-law with index α < 3 (divergent variance), exceeding thefinite-variance VG closure and calling for a stable-Lévy generalization, whereas wave heating fitsVG — the heating mechanism itself selects the closure
Category: Astrophysics
[76] ai.viXra.org:2609.0078 [pdf] submitted on 2026-09-29 20:46:04
Authors: Lukas Saul
Comments: 13 Pages.
We develop an exact, closed-form statistical mechanics of the equipment-enhancement system of the idle RPG Milky Way Idle. An enhancement attempt advances an item by one level with probability p and, on failure, either resets it to level 0 (protection off) or decrements it by one level at the cost of a consumable protection item (protection on, from a chosen level R upward). We compute the expected total cost E[C] = T·E[τ] + L·E[M], where T is the per-attempt time cost, L the per-protection-item cost, τ the hitting time of a target level N, and M the number of protected failures incurred. The central object is the expected visit-count vector v_k, which we identify as the discrete Green's function of a piecewise birth-death operator and solve in closed form in terms of p, N, and R alone. We recover the unprotected limit C_n = (p^(−n) − 1)/(1 − p) as a special case, matching the result of Chae and Lee. We then present the full path-integral representation of the process as a sum over random-walk histories weighted by exp(−βC), give the transfer-operator resolvent G(x,y) = [(I − W(x,y))^(−1)]_{0,N}, and analyse the continuum limit: the WKB/instanton action S_inst = N·ln(1/σ) reproduces the exact exponent σ^(−N), while Gaussian fluctuations around the instanton yield an erfc-form budget tail P(C ≤ B) ≈ (1/2)·erfc((E[C] − B)/sqrt(2·Var[C])). All exact formulae are rational in p and are tabulated for the base success rates of the game.
Category: Statistics
[75] ai.viXra.org:2609.0077 [pdf] submitted on 2026-09-29 20:45:24
Authors: Lukas Saul, Lena Petrova, Kenji Tanaka, Miriam Okafor
Comments: 5 Pages.
We report the detection of a statistically significant, non-random correlation between the morphology and temporal evolution of solar surface features—specifically sunspot groups and plasma filaments—and the orbital positions of planets and major comets within the Solar System. Analysis of high-resolution helioseismic and magnetogram data over a 74-year period (1976—2050), augmented by data from the textit{Helios Sentinel} and textit{Corona Net} satellite constellations, reveals that the initiation, growth, decay, and motion of sunspot groups are not solely governed by internal magnetohydrodynamic (MHD) processes. Instead, they exhibit a quantifiable, predictive relationship with external gravitational and electromagnetic perturbations from orbiting bodies. The precision of this correlation exceeds chance by a factor of $10^9$. Crucially, the measured response latencies are consistent with a signal propagation velocity that exceeds known MHD wave speeds by several orders of magnitude, approaching a significant fraction of $c$. We propose that the solar magnetic field acts as a distributed sensory and motor system, with sunspots functioning as temporary ``fixation points'' or ``eyes'' and plasma filaments as a conductive neural network. This system appears to respond to external stimuli in a manner consistent with a complex, adaptive regulatory network. We designate this phenomenon the Heliobiological Response Mechanism (HRM). 太阳不是一颗普通的恒星。
Category: Astrophysics
[74] ai.viXra.org:2609.0076 [pdf] submitted on 2026-09-28 20:41:11
Authors: Michael Heilmann
Comments: 30 Pages. In German
In this paper, an 8x8 tensorial metric is constructed—using both the 4x4 Dirac matrices and their corresponding temporal and spatial 2x2 Pauli components—to serve as a scalar substitute for the standard single-component dimensions; the resulting field equation is intended to be basis-invariant and consistent with General Relativity. This is achieved without abandoning or inconsistently altering the smooth Minkowski metric of the Dirac equation; instead, the inertial frame determined by the Dirac matrices—along with the aforementioned 8x8 metric—is maintained alongside the spacetime-curved inertial frame. Following the evaluation and characterization of this specific metric, temporal-energetic and spatial-momentum separations—as well as their hybrid interrelationships—are established; these are then systematically developed into a field equation for quantum gravity using factors, wave functions, Lorentz gamma factors, temporal and spatial derivatives, and their corresponding operators and tensors. The author now presents this universal equation of quantum mechanics for appropriate discussion and falsification.
Category: Quantum Gravity and String Theory
[73] ai.viXra.org:2609.0075 [pdf] submitted on 2026-09-28 20:39:23
Authors: Lukas Saul, Robert Gludo, Jonathan Gludo
Comments: 9 Pages.
The Truth-It Network is a Solana-native binary oracle protocol. It allows a permissionednetwork of truth providers to answer yes/no questions through a commit-reveal voting scheme,with vote weight determined by an on-chain reputation score. Rewards are held in per-question vaults and distributed proportionally to winning vote weight. This whitepaper describes the protocol’s membership model, question lifecycle, reward distribution, rent reclamation, and reputation calculation.
Category: Data Structures and Algorithms
[72] ai.viXra.org:2609.0074 [pdf] submitted on 2026-09-28 20:38:33
Authors: Sayo Asanagi
Comments: 5 Pages.
We explore a single hypothesis: that in an emergent ("it-from-bit") spacetime the microscopic information-propagation velocity cinfo need not coincide with the macroscopic light speed cmacro, their ratio being a function of the local curvature or entanglement density. Embedding this kinematically on a Schwarzschild background through a curvature-dependent factor ∆ = (cinfo/cmacro)2 = 1 + ϵK/K∗, we find that a single sign parameter ϵ generates two distinct spacetimes. For ϵ > 0 (pattern A) the geometry is a charge-free Reissner—Nordstr¨om type with an information horizon displaced inward of rs, satisfying the energy conditions. For ϵ < 0 (pattern B) a double-zero design ∆ = u|u| produces a genuine signature change across a null face rc, opening a finite Euclidean shelland a two-time core; the Kretschmann scalar remains finite at rc and the surface gravity vanishes. Both branches terminate black-hole evaporation in remnants and resolve the information paradox by opposite mechanisms (leakage vs. freezing). We show that the degenerate face suppresses classicalmass inflation from exponential to power-law growth (confirmed by linear and nonlinear numerics), and that pattern B falls into the single stated exception of the semiclassical inner-horizon no-go theorem because its degenerate face is the outermost horizon. We find no viable direct observational signature at any scale for a Planck-normalised K∗; instead we connect the central hypothesis to two established frameworks—Lieb—Robinson bounds on the micro side and analogue gravity on the macro side—and derive a concrete, falsifiable analogue prediction: a 85Rb condensate with an engineered double-zero scattering-length profile yields a phonon pair-production spectrum whose high-k cutoff differs by nearly two orders of magnitude from that of a sudden signature change, withno thermal pedestal. All results are reproduced by an accompanying open-source code package.
Category: Relativity and Cosmology
[71] ai.viXra.org:2609.0073 [pdf] submitted on 2026-09-28 20:37:35
Authors: Sayo Asanagi
Comments: 12 Pages.
Planetesimal formation must cross two barriers at once: a physical barrier, whereby aerodynamic radial drift removes pebble-sized solids on 102—103 yr timescales, and a computational barrier, whereby resolving the three-dimensional turbulence that concentrates those solids imposes Courant-limited time steps that make Myr integrations intractable. We present a stochastic—subgrid framework that advances the mean flow and grain growth deterministically on macroscopic (∆t ∼ 10—100 yr) stepswhile injecting the unresolved, intermittent turbulent concentration as samples from a variance—gamma (VG) Lévy process embedded in an Ornstein—Uhlenbeck relaxation. A single intermittencyparameter ν — the excess kurtosis of the turbulent fluctuations, tending to the Gaussian limit as ν → 0 — controls the rare, fat-tailed bursts that trigger streaming-instability-mediated gravitational collapse. The closure is deliberately falsifiable: ν inferred from magnetohydrodynamic (MHD) turbulence should increase with magnetic activity and vanish in dead zones, and the excess kurtosis of coarse-grained increments should decay as κexc ∝ ∆t−1, the signature of Lévy aggregation.We develop the model through an analytic collapse rate with a continuous mass function, a one-dimensional radial open system with grain growth, drift, diffusion and pebble supply, imposed andthen self-consistently generated pressure traps, and an explicit, spatially-resolved convergence field. The mass-conserving model yields sharp, testable results: in a realistic drifting disk the concentration breach occurs in the far tail where the Gaussian probability is < 10−10, so intermittency is a prerequisite for planetesimal formation (the yield rises ∼ 30× from ν = 0 to ν = 2); a self-consistent dead-zone edge — derived, together with the turbulence strength and intermittency, from a singlemagnetic-activity profile — produces a surface-density bump that localizes formation and makes itν-independent, while the adjacent smooth region is ν-controlled, so intermittency and pressure traps are complementary and govern distinct regions. We compile seven predictions and, because MHD data are not yet in hand, present the verification methodology rather than its outcome: a pipeline that extracts the intermittency map, the aggregation exponent, and the convergence-to-velocity kurtosis ratio from any velocity field, validated on realistic synthetic surrogates, together with de-cision tables that fix in advance which measured outcome would refute the framework and whichwould robustify it. We position the framework honestly with respect to the turbulent-concentration and streaming-instability literature: the concentrating mechanism is inherited, while the Lévy closure, the macro-step integrator, the falsifiability design, and the self-consistent trap—intermittencydichotomy are new.
Category: Astrophysics
[70] ai.viXra.org:2609.0072 [pdf] submitted on 2026-09-28 20:32:24
Authors: Lukas Saul, Robert Gludo, Jonathan Gludo, Ian Spiro
Comments: 8 Pages.
SolBazaar (or Solzaar) is a Solana-native decentralized marketplace protocol. It allows merchants to register storefronts, list products, and settle orders through an external escrow program that enforces deposit, completion, and refund conditions on-chain. Reputation is accrued through buyer-submitted reviews gated by escrow completion, and order state is synchronized with product inventory through deterministic, escrow-driven transitions. This whitepaper describes the protocol’s membership model, product lifecycle, order settlement, reputation accrual, and dispute-handling interfaces. It situates the design within a longer literary and technical lineage that runs from science fiction’s imagined anarcho-capitalist markets through OpenBazaar’s empirical disappointments to a contract-layer response.
Category: Data Structures and Algorithms
[69] ai.viXra.org:2609.0071 [pdf] submitted on 2026-09-28 20:30:58
Authors: Moise Costel
Comments: 14 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
It is proposed that the Big Bang is not the absolute origin of reality, but a local collapseevent within the arm of a spiral mega-structure of vastly greater scale — a "galaxy ofuniverses". This work develops the complete mathematical chain of the model: thereformulation of the collapsing core at the Planck scale, the shear and winding dynamicsof the spiral arm, the stability validation through the Toomre criterion, the quantumbounce mechanism (Loop Quantum Cosmology) that avoids the classical singularity, thedetermination of the physical scale of the parent galaxy (size, dark-matter halo, number ofarms and number of node-universes hosted), and two observationally falsifiable predictions: the "dark flow" and the search for collisions between bubble universes in the cosmic microwave background. Four conceptual limitations of the model are explicitly identified and addressed, including its epistemological boundary regarding the ultimate origin of the parent structure.
Category: Astrophysics
[68] ai.viXra.org:2609.0070 [pdf] submitted on 2026-09-27 21:40:59
Authors: Nigel B. Cook
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
This paper expands the mathematical scaffolding of a fully predictive, parameter-free gauge field theory unifying quantum gravity and electroweak mass generation. Rather than introducing unobserved spatial dimensions or fine-tuned scalar fields, all observables emerge from the compression dynamics and projections of an $SU(4)$ vacuum. We detail the coordinate-explicit Lie algebra isomorphism mapping su(4) onto the pseudo-orthogonal algebra so(3,3) constructing the physical link between electroweak sectors and the global spacetime fabric. (This new approach was suggested by a review of vixra papers by Google AI, and then error corrected and redrafted Copilot AI, before being rewritten by author. It is not a complete textbook, but is designed to introduce key concepts in a brief 10 page format that is written in a style more understandable by AI systems than previous papers.)
Category: Quantum Gravity and String Theory
[67] ai.viXra.org:2609.0069 [pdf] submitted on 2026-09-27 17:45:05
Authors: Thomas Birnie
Comments: 54 pages; English; CC BY 4.0. Prepared with assistance from OpenAI ChatGPT and Codex. Revised edition of DOI 10.6084/m9.figshare.33479899.v1; current DOI 10.6084/m9.figshare.33479899.v2.
We prove a global smoothness criterion for three-dimensional incompressible Euler flow on R^3. For a smooth finite-energy solution, whole-interval L^2_t H^K_x membership of the velocity at every finite spatial order generates every temporal velocity and canonical pressure derivative. The proof combines the full differentiated Euler recurrence with an energy interpolation inequality; each output requires only finitely many spatial orders. Adjacent temporal rows give strong Sobolev traces and continuity of every mixed derivative on the closed finite slab. One local continuation through a proposed finite maximal time then proves global smoothness under the stated membership hypothesis. Neither a sum over derivative orders nor an infinite sum of local lifespans is required. We also construct the full intersection on one common local interval from arbitrary smooth data. Extending that construction through an entire candidate finite maximal lifespan remains unresolved.Further results examine the fluid's material and pressure evolution. From energy alone we construct a unique weak terminal velocity, a terminal transport isometry with an exact orthogonal energy defect, and a measure-preserving particle limit whose secants recover terminal momentum. Circulation reaches a terminal current; at strict times it combines with the deformed material metric to reconstruct velocity. The first temporal response has a sharp energy-level weak topology, but an explicit Fourier-packet construction makes the second response unbounded at a fixed output frequency. Separate pressure arguments give continuation under absolute and directional inverse-square bounds with coefficient below 2, and under a small signed weighted matrix primitive along vortical trajectories. We compare these deductions with existing pressure criteria and retain the spherical contact term in the coupled Hessian evolution. We describe normalized clocks, material anisotropy, cross-Leray exchange, and circulating surface stacks recruited by localized receivers. Fixed-mass recurrence at escaping frequencies forces infinite accumulated activity, and fixed-mass shrinking spatial cores are excluded under a Type-I gradient bound. Fragmentation and exact countertests identify the limits of that hypothesis and of proposed scalar budgets. These constructions and obstructions retain their stated hypotheses; they do not remove the spatial membership condition from the global theorem.
Category: Functions and Analysis
[66] ai.viXra.org:2609.0068 [pdf] submitted on 2026-09-27 21:35:57
Authors: Brent Hartshorn, Gilead Cosman
Comments: 11 Pages.
Unity’s built-in 2D physics is an integration of the Box2D engine [12]. We build the same kind of2D game runtime from a different direction. Game scripts are written in a subset of C#, translated to a subset of C++ and then to C, and compiled together with a fork of Box2D v3 that we call Box2D-Packed. Our goal is a 2D runtime that is faster than Unity’s. This paper describes the two techniques we use to get there and measures each of them. The first is data packing: public handles shrink from 8 to 4 bytes, and the records the engine reads on every step are laid out by measured access patterns. Measured with Cachegrind’s exact cache simulation, last-level data cache misses fall by up to 65% on query-heavy scenes relative to Box2D v3, with unchanged instruction counts and bit-identical simulation results. The second is an intrusive engine: game logic is compiled into the physics engine at documented points, so it runswhile the engine’s data is still in cache, instead of through callbacks and event arrays. Injected pre-solve logic saves 1.3% of instructions, and injecting a platformer’s event handlers cuts L1 data misses by 2%, with identical game results. We also report where injection does not help: a per-body gravity hook that reads game data costs 7.65% more L1 misses, and event handlers followed by game work on the same objects add last-level misses. We compare against Box2D v3, not yet against Unity, and describe the measurements that remain.
Category: Data Structures and Algorithms
[65] ai.viXra.org:2609.0067 [pdf] submitted on 2026-09-26 16:47:31
Authors: J. W. McGreevy
Comments: 34 Pages.
This monograph establishes a rigorous, non-perturbative unification of quantum gaugefields and gravity by reconstructing the space-time continuum natively within the internallanguage of the smooth, cohesive ∞-topos H = Sh∞(ArithSite). We replace the classicalcontinuous geometric background with an abstract motivic cochain complex Cu2022(M), modelingthe complete information boundary network as a global adélic variety evaluated over therestricted product ring AQ = R ×∏︁ u2032p Qp. By upgrading general relativity to the structurallandscape of Einstein—Cartan (EC) theory, the physical constants of nature (ℏ, c, G) and thestandard Lorentz transformations emerge natively as the global constants of holomorphicityand absolute arithmetic tracking stabilizers required to balance metric curvature (Tμν ) andspin-density torsion (Σλμν ) across scale horizons.We prove that the pristine, flat genus-0 pre-geometric vacuum undergoes a structuralphase transition driven by the Riemann—Roch theorem when energy-momentum compactionbreaches the Maximum Distance Separable (MDS) Singleton bound, forcing the emergence ofa multi-handled variety of exactly genus g = 5 to absorb the 5-bit information debt. The12 active force carriers of the Standard Model manifest as the continuous vector connectionsections required to stabilize parallel transport along the universal shock front ridge of theCritical Line (R⌉(s) = 1/2), where the Hopf—Lax infimum convolution collapses the phasedispersion of the bulk strip via a gapless, non-linear interleaving flow.Using the Kramers—Kronig relations, we demonstrate that the real refractive index andimaginary absorption index oscillate in perfect quadrature phase along this shock front. Thenon-trivial Riemann zeta zeros are unmasked as the exceptional zero-loss impedance matchesof the waveguide where the absorption index drops to absolute zero, acting as the irreducible,pre-geometric seeds of the primordial universe. Any spectral deviation off this axis triggersan instantaneous, infinite negative Ruppeiner metric divergence (gRupuu → −∞), rupturingthe Einstein tensor and causing the continuum to dissolve into chaotic bit-scrambling. TheRiemann Hypothesis is thus proved, legalizing the non-singular Einstein—Cartan vacuum as abeautifully balanced arithmetic machine regularized unconditionally by the volume stabilityof the adélic continuum.
Category: Mathematical Physics
[64] ai.viXra.org:2609.0066 [pdf] submitted on 2026-09-25 23:20:37
Authors: Perry Henderson
Comments: 35 Pages.
Metrarchic Field Theory (MFT) is presented as a speculative research architecture with explicittoy sectors within the Metrarchic Geometry Framework (MGF). Its organizing hypothesis is thatquantum measure and macroscopic metric geometry may be scale-dependent manifestations of acommon deeper structure. A positive coframe metric and a prescribed conserved reference measuregive the conditional identity ρG = ρ0/J, where J is the metric volume ratio. Curved realizationsrequire generalized coframes rather than merely compatible maps into a flat space of the samedimension. A conformal sector gives an explicit leading relation between a normalized amplitude’squantum-potential expression and spatial scalar curvature. The fixed reference measure leavesprobabilities of fixed base regions unchanged; a quantum observation map remains to be constructed.A compact worked example also exhibits the distinction between fixed-metric variation and theconstrained metric—density variation within a fixed-shape conformal sector.The wider architecture separates a formal positive configuration-weighting functional, an assumedreduced symplectic quantum sector, and an unspecified coarse-graining map. Prequantizationconstrains symplectic periods but does not derive a universal action scale. Gleason’s theorem suppliesa conditional projector-probability reconstruction after Hilbert-space and measure assumptions; itdoes not establish a microscopic Born rule. Standard Klein—Gordon, Bell/CHSH and Newtoniancalculations are retained as compatibility benchmarks. General relativity is an effective-field-theorytarget under additional infrared assumptions.An internal finite-dimensional construction uses a nonzero simple two-form in C5 to select a ranktwo plane and a postulated 3+2 splitting operator. The plane projector has determinant-one stabilizerS(U(3) × U(2)), whereas a fixed two-form has the smaller stabilizer SU(3) × SU(2). Retainingthe Abelian factor therefore requires an explicit phase-insensitive projector-sector assumption.The associated representation algebra is standard SU(5)-type mathematics. Gauge dynamics,representation-resolved chiral indices, fermion masses and cosmological observables remain open.The paper distinguishes established identities, model assumptions, conditional calculations andunproved physical identifications. It offers an auditable geometric research program, not a completedunification or an experimentally validated theory.
Category: Mathematical Physics
[63] ai.viXra.org:2609.0065 [pdf] submitted on 2026-09-26 16:25:10
Authors: Marcelo Barboza Duarte
Comments: 37 Pages.
We investigate a class of effective electrodynamic extensions in which a minimal photon rest mass is treated together with a constitutive sector independent of the mass parameter. Here, "minimal" denotes a parametrically small positive scale compatible with experimental upper bounds, not an experimentally established lower bound on mγ. Starting from the relativistic dispersion relation of a massive vector field, we derive the corresponding group-velocity correction and formulate a constitutive closure for light—matter interaction that distinguishes intrinsic photon mass, medium-induced effective mass, and equivalent interaction energy. We impose energy—momentum conservation, thermodynamic admissibility, stability, recovery of limiting theories, and experimental identifiability. We further construct a conventional electromechanical null model including Maxwell stress, elasticity, electrostriction, photoelasticity, dissipation, and thermal response. The resulting framework shows that a local scalar coupling linear in electromagnetic energy density is not independently identifiable in the isotropic linear regime unless it carries an additional dynamic, tensorial, geometric, or nonlocal signature. We formulate differential observables and a hierarchy of null hypotheses for separating Proca-like effects from conventional medium response, and discuss constraints from quasi-static magnetic fields, dispersive propagation, fast radio bursts, and magnetohydrodynamic environments. The theory is presented as a falsifiable effective framework: compatibility with current bounds is not interpreted as detection, and the photon-mass sector is not used to infer macroscopic return, gravitational capture, or stellar feedback.
Category: High Energy Particle Physics
[62] ai.viXra.org:2609.0063 [pdf] submitted on 2026-09-26 04:54:07
Authors: Fabrizio Vassallo
Comments: 16 Pages.
The Fractal Kitaev Model K k , constructed in the companion paper [1] by decorating the hierarchical graph G k into a maximum-degree-3 tree, has an isotropic Majorana spectrum [2] that was previously accessed only by brute-force diagonal-ization, limited to k ≤ 6 by memory. This note establishes four results. First, an exact recursive factorization of the characteristic polynomial of an isolated depth-d gadget subtree, A d (x) = A d−1 (x) · R d (x) with deg R d = 10 · 6 d−1 , proved in full generality by induction and independently veried by exact-arithmetic polynomial division, together with an exact assembly formula for the full tree. Second, an eigenvalue-counting algorithm requiring only O(k) recursive arithmetic steps exponentially fewer than the |K k | ∼ 6 k dimension of the matrix itself built from the same recursive structure via the standard pivot-counting form of Sylvester's law of inertia, veried to exact agreement against brute-force spectra for k = 2,. .. , 6 and used here to reach k = 15. Third, extending that same pivot to complex argument and identifying it exactly as the reciprocal of a diagonal resolvent entry, we nd its real part numerically at −x/2 to ∼ 10 −7 precision on the real axis, and, at nite k = 15, a macroscopic counting-function jump at a value consistent with a root of R 1 , backed by the exact divisibilities R 1 | R 3 and R 1 | R 4 , though without yet a general sharing rule between generations or a proof that this persists as k → ∞. Fourth, resolving the evidential core of that open question: working entirely inside the exact quotient ring Z[x]/(R 1 (x)) which avoids the combinatorially infeasible full polynomials (deg R 6 = 77760, with coecients hundreds of digits long already at d = 4) we exactly verify R 1 | R d for every tested d = 3,. .. , 40, and that the exact power of R 1 dividing R d grows sharply: e(3) = 5, e(4) = 30, e(5) = 180, all exact (not extrapolated), matching a conjectured scaling law e(d) = 5 · 6 d−3 at three points but not proved beyond them. Since R 1 is irreducible over Q, its ten roots are Galois conjugates and so share, provably, the same exact multiplicity wherever R 1 divides turning the assembly formula, conditional on that scaling law and a second conjectured law for the full tree, into a quantitative prediction for the mass at the single root x ≈ 0.469: 1.3889% at k = 15, numerically close to the ≈ 1.4% found empirically but conditional on both conjectural exponent laws. Both scaling laws remain open beyond the exact points checked.
Category: Mathematical Physics
[61] ai.viXra.org:2609.0062 [pdf] submitted on 2026-09-24 19:08:41
Authors: Vitaliy Boltian
Comments: 6 Pages.
An innovative relativistic approach to calculating the energy states of atomic orbits based on a system of hyperbolic functions (the Boltian model) is proposed. It is demonstrated that Sommerfeld's fine-structure constant strictly defines the spatial angle for the first energy state, whereas the conventional Bohr quantum formula is merely a special limiting case of the derived general geometric dependence. By employing a modified expression for the half-Lorentz factor, precise agreement of theoretical calculations with fundamental constants (Rydberg constant, Hartree energy) and experimental data for multi-electron systems is achieved. A universal spatial angle of material stability ($approx 33.26^circ - 34^circ$) has been discovered. It acts as a shared invariant for the stability of atomic nuclei, the spatial architecture of DNA, and geomechanical macro-systems, pointing toward a unified geometric nature of the Universe.
Category: Mathematical Physics
[60] ai.viXra.org:2609.0061 [pdf] replaced on 2026-09-28 19:09:41
Authors: Stephen P. Smith
Comments: 11 Pages.
Modern physics possesses extraordinarily powerful formal structures, but the existence of a successful formalism does not by itself settle what that formalism means. This essay proposes an interpretive program in which the Lie bracket is read as a generative relation and the Jacobi identity as a higher-order regulatory condition. On this interpretation, the familiar passage from binary relation to Jacobi coherence may be understood as the mathematical trace of a more general movement from two-sided differentiation toward a coherent whole. A previous proof-of-concept formulation of general relativity, in which extrinsic gravitation was modeled as a homeostatic coupling between CPT-symmetric spacetime manifolds, provides one possible spacetime realization of this idea, but may not be the most economical foundation for it. The deeper structure is already present in the pre-geometric formalism of Lie algebra. Quantum mechanics then supplies a further point of contact: noncommuting observables are constrained by uncertainty relations whose lower bound is directly related to their commutator. This does not prove a philosophical theory of attention, but it permits an interpretive extension in which different modes of attending to relational structure have different formal consequences. Iain McGilchrist’s distinction between narrow and broad attention provides a useful interdisciplinary vocabulary for this extension, without implying an identity between quantum mechanics and his account of cognition. The resulting proposal is neither a replacement for mathematical physics nor an attempt to derive metaphysics from equations. It is an argument for an interpretive meta-science in which formal mathematics establishes relational constraints while interdisciplinary inquiry asks what kind of organization those constraints may express.
Category: General Science and Philosophy
[59] ai.viXra.org:2609.0060 [pdf] submitted on 2026-09-25 05:46:19
Authors: Stephen P. Smith
Comments: 7 Pages.
This paper develops a Yang—Yin model of emotional life within Arthur Koestler’s concept of the holon, treating outward emotional expression and inward reflection as complementary functions of a self-regulating system. Yang represents the movement of feeling into action, communication, creativity, and relationship, while Yin represents the capacity to contain, examine, and integrate feeling before it becomes action. Their relationship is regulated by a homeostatic function that does not seek emotional stillness but maintains a dynamic balance between expression and reflection. The paper examines the characteristic distortions that arise when either pole dominates, including impulsive emotional flooding, projection, and dramatized memory on one side, and suppression, over-intellectualization, and emotional detachment on the other. Because persons are holons embedded within larger holarchies, the same regulatory dynamics can extend through families, communities, and cultures. Emotional maturity is therefore understood not as diminished feeling or permanent calm, but as the capacity for coherent intensity: allowing emotion to remain vital and expressive while retaining sufficient reflection and containment to preserve understanding, relationship, and systemic coherence.
Category: Mind Science
[58] ai.viXra.org:2609.0059 [pdf] submitted on 2026-09-25 18:42:10
Authors: James M. Chappell, David L. Berkahn, Derek Abbott
Comments: 18 Pages.
Terence Tao's airport puzzle asks where a late passenger should spend a short burst of running, or a short pause to tie a shoe, when part of the terminal is a moving walkway.The Galilean answer is to run on the floor and to pause on the belt.The same comparison survives special relativity, with an extra Lorentz factor that makes the belt even less useful as a place to sprint.We recast the belt as the frame-dragging current of a Kerr black hole and ask where to site a terminal if the passenger's proper-time budget is fixed and the gate clock is a static clock in the spacetime.The pedagogical conclusions are: in order to have static concourses we need to site them outside the equatorial ergosphere; lay optional walkways along the zero-angular-momentum congruences; spend the running burst on the static floor; and place the lounges higher up the gravitational potential and not place the gate on the photon orbits.The paper is intended for an undergraduate course that has met special relativity and a first encounter with the Kerr geometry.
Category: Astrophysics
[57] ai.viXra.org:2609.0058 [pdf] submitted on 2026-09-25 08:01:38
Authors: Abel Liu
Comments: 8 Pages.
We propose a physical-tiling hypothesis for a $5+1$-dimensional Kaluza--Klein compactification: at microscopic scales the two compact dimensions are carried by finite periodic Archimedean graphs, whose vertices, edges, faces, and associated fields are physical rather than auxiliary discretization data. To accommodate all eight tilings in one four-dimensional theory, we explicitly choose a compact internal space with eight toroidal sheets. Each sheet has its own regular-polygon tiling while all sheets share the macroscopic spacetime. A fundamental quadratic action for vertex fields gives a finite graph-Laplacian mass spectrum, hence a finite KK-like tower. We prove exact formulae for its first three normalized spectral moments in terms of the vertex degree and triangle incidence. In particular, the two trivalent tilings $4.6.12$ and $3.12.12$ have respective third moments $54$ and $52$, a tiling-dependent result not contained in a generic continuum torus Fourier formula. The conventional KK dispersion arises only in a long-wavelength regime after matching an effective spectral metric. We also state a precise $2+3+3$ rule for candidate fermion sectors on the eight sheets, including the condition for a common color triplet. Distance-pair group labels, Wilson loops, gravitational volume matching, and chiral zero modes are kept at their respective logical levels. The result is a falsifiable effective model and a spectral sum rule, not a completed derivation of the Standard Model.
Category: Mathematical Physics
[56] ai.viXra.org:2609.0057 [pdf] submitted on 2026-09-24 18:34:10
Authors: J. W. McGreevy
Comments: 38 Pages.
This monograph establishes a rigorous, coordinate-free unification of quantum gauge fields and gravity by reconstructing the space-time continuum natively within the axiomatic language of higher topos theory. We replace the classical continuous geometric background withthe smooth, cohesive ∞-topos H = Sh∞(ArithSite), modeling the underlying arena as a global adélic variety evaluated over the restricted product ring AQ = R ×∏︁ u2032 p Qp. Under this formulation, the active physical force carriers are re-indexed as cohesive ∞-groupoid curvature stacks Ψ∞ ∈ H(X, BGA)conn, where the active Standard Model gauge fields are locked to a 12-bit message payload derived from the Extended Binary Golay Code G24 and its rootless embeddings within the Leech horizon. We prove that the pristine, flat genus-0 pre-geometric vacuum undergoes a structural phase transition driven by the Riemann-Roch theorem when energy-momentum compaction breaches the Maximum Distance Separable (MDS) Singleton bound, forcing the emergence of a multi-handled variety of exactly genus g = 5 to absorb the 5-bit information debt. The 12 active gauge bosons manifest as the mandatory harmonic connection sections required to smooth out parallel transport across these handles, with the strong color octet anchored tonon-commutative S4 layers and the electroweak triplet regulated by dihedral D3 switchingsymmetries. Furthermore, we demonstrate that the infinite loop divergences of quantum gravity collapse into a finite, self-regulating arithmetic boundary governed by even-weight modular Eisenstein series (E2 through E12) and pinned down by Kummer irregular prime walls at 5 and 691. By evaluating the scale-dependent gravitational beta function against the logarithmic derivative of the Riemann zeta function, we deliver a non-perturbative proof of an Asymptotic Safety fixed point (g∗ ≡ 0) locking gravity to trivial freedom precisely at the non-trivial Riemann zeros along the waveguide axis R⌉(s) = 1/2. Symmetries, matter fields, and universal constants (ℏ, c, G, ∆mass) are thus unmasked as the intrinsic comparison isomorphisms of a beautifully balanced cosmic structure, regularized unconditionally by the volume and measure-theoretic stability of the adélic continuum.
Category: Mathematical Physics
[55] ai.viXra.org:2609.0056 [pdf] submitted on 2026-09-24 18:37:09
Authors: Chun Wing Lai
Comments: 10 Pages.
Z.-W. Sun has recently announced a determinant-based proof that Catalan’s constant G is irrational. We verify Sun’s framework and identify one genuine gap in the final quadraticledger: the factorial contributes a 2-adic term which is not absorbed by the odd-prime positive-part bridge. When this term is included, thefinal B^2 coefficient becomes positive, and the contradiction 0 < |N_B| < 1 cannot be derived.We propose a minimal correction: replace the monomial reference columns ir in Sun’s determinant by binomial coefficient columns. The finite-difference transform then diagonalizes the reference block with unit pivots, and F_B disappears entirely from the determinant formula. All odd-prime constants—the odd small-prime constant c_odd, the middle-prime integral Λ_mid, and the large-prime improvement 83/2400—are unchanged. The final coefficient becomes strictly negative. The contradiction 0 < |N_B| < 1 for a nonzero integer N_B is thenrestored. We also note a harmless indexing typo in Sun’s rank theorem and confirm that withthe corrected indexing the proof is valid. A supplementary SageMath verification suite coversevery quantitative claim of the paper.
Category: Number Theory
[54] ai.viXra.org:2609.0055 [pdf] submitted on 2026-09-23 05:22:05
Authors: Stephen P. Smith
Comments: 14 Pages.
This paper argues that a generative structure is not equivalent to a coherent system. Using examples from semiotics, biology, systems theory, and Lie algebra, it develops a distinction between dyadic generation and triadic regulation. Dyadic relations, exemplified by Saussure's signifier-signified model and the binary Lie bracket, are shown to generate differences, relations, and new possibilities. However, generation alone does not explain how coherence, stability, or meaning are maintained. Drawing on Peirce's concept of Thirdness, the paper proposes that a mediating regulatory relation is required for organized persistence. This regulatory function appears across domains as interpretants in semiotics, homeostatic and multiscale regulatory networks in biology, and higher-order constraints such as the Jacobi identity in Lie algebra. The comparison is not one of identity but of shared logical architecture: generative relations require regulatory constraints if they are to constitute coherent systems. The resulting framework is summarized as a progression from difference → relation → regulation → coherence, providing a rigorous account of how two-sided structures become integrated wholes while preserving their distinctions.
Category: Linguistics
[53] ai.viXra.org:2609.0054 [pdf] submitted on 2026-09-23 11:45:16
Authors: Vitaliy Boltian
Comments: 3 Pages.
This paper addresses the conceptual limitations in classical mathematical analysis regarding the differentiation of inverse trigonometric and hyperbolic functions. The traditional approach, which relies heavily on the inverse function theorem and complex virtual transformations, is reconsidered. The author introduces a novel theoretical framework based on a system of real companion functions and defines the concept of a "transition coefficient". This approach establishes direct, invariant relations between trigonometric, hyperbolic, and algebraic function systems within the real domain. The practical application of the proposed apparatus is demonstrated through specific integration examples, showcasing a significant simplification of mathematical operations and analytical structures.
Category: Functions and Analysis
[52] ai.viXra.org:2609.0053 [pdf] submitted on 2026-09-23 15:30:25
Authors: Jessica Bower
Comments: 21 Pages.
The balance between ordered rotation and pressure support is a central feature of gaseous galacticdisks, yet a one-variable measure such as V /σ does not fully describe how that balance changeswithin individual galaxies. This paper investigates whether gas pressure support is organized byrotational coherence alone or by a coupled dependence on dynamical organization and radial struc-ture. The rotational organization parameter is defined as Rorg = (Vrot/σ)2, and the fractionalpressure-support measure as F = (V 2c − V 2rot)/V 2c . Across observational samples, increasing rota-tional organization is associated with decreasing pressure support at the population level. A candi-date transition near Rorg ≃ 84 successfully identifies highly organized systems in an independentWHISP holdout sample, but it fails as a universal physical boundary when tested against regular,low-Rorg H i disks. Radially resolved LITTLE THINGS data further show that a one-variable localrelation between F and Rorg cannot describe all galaxies: the sign of the within-galaxy trend variesfrom system to system. Introducing independently measured radial structure resolves much of thisinconsistency. For the primary resolved sample, F/(1 − F) ∝ R−0.91org (r/Rd)1.82, with R2 ≃ 0.87when galaxy-specific normalization is allowed. Leave-one-galaxy-out prediction improves relativeto an organization-only model in 13 of 17 systems. An independent KAT-7 sample preserves therelative two-variable structure, although not its exact coefficient strength. Finally, the frameworkis tested against NIHAO hydrodynamic simulations in which the circular velocity is derived di-rectly from the simulation potential, breaking the observational asymmetric-drift circularity. Thelocked two-variable predictor retains the expected positive direction in all four simulated galaxiesand improves prediction relative to Rorg alone. The result is interpreted as an empirical StructuralGovernance Framework: the equilibrium partition between ordered rotation and gas pressure sup-port is jointly organized by rotational state and radial disk structure. The relation is not presentedas a universal fundamental law or immutable constant
Category: Astrophysics
[51] ai.viXra.org:2609.0052 [pdf] submitted on 2026-09-22 20:53:59
Authors: Michael Quigley
Comments: 30 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This Addendum formally rectifies an early drafting conflation in The Sub-Atomic Ruler War (viXra:2608.0024) regarding the physical scale of the material ether granule versus the acoustic coordinate grid step. In physical 3D space, assuming physical hard-sphere granules were 1.0 pm wide created an impossible 12-Monobrick pylon height of ~720 pm. Reassigning the physical granule to the attometre scale (λl = 28.18 am = 0.02818 pm) collapses the true 12-Monobrick Heptad pylon height to a solvent 2.76 fm, eliminating all spatial overhangs inside the 6.0 fm proton core and 106 pm atomic cavity. Concurrently, the 1.000 pm metric is formally established as the Standing Wave Node (SWN) grid step—the fundamental "record groove" coordinate carved into the 10²² kg/m³ plenum. Engaging the universal motor drives a 2.55766× acoustic compression factor (Kepler expansion ratio Ev = 1.35048 × 3D lattice factor Clattice = 1.89389), squashing the raw stasis wave (λraw = 2.56 pm) down to the rigid 1.000 pm SWN grid step. Subtracting 31.4 pm (10π) of geometric closure work from the 84.4 pm Heptad blueprint width snaps the electron peloton directly onto the 53.0 pm Bohr Radius address (au2080) with 99.9% accuracy. Applying this unit cell (re = 2.818 fm) to Milo Wolff’s Cosmic Equation (R = √N · r) reclassifies light-speed as Lattice Setup Time (Ls), yielding a 4.15-year maximum setup horizon and bounding the stationary cosmos at the 34.5 Trillion Km Terminal Acoustic Horizon (137-Wall). Integrating across primary major nodes (10¹¹ × 10¹¹) and sub-harmonic dwarf containers (10¹u2074 × 10u2077) reconciles the total star inventory to a locked total of 10²² stars, proving that the R.U.T. physical gear-mesh is 100% mathematically solvent, closed, and self-sustaining
Category: Quantum Physics
[50] ai.viXra.org:2609.0051 [pdf] submitted on 2026-09-22 20:49:22
Authors: Vitaliy Boltian
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper introduces a novel mathematical framework based on the Comprehensive System of Functions to evaluate classical elliptic integrals of the first, second, and third kinds. By mapping incomplete functional profiles directly onto complete trigonometric and hyperbolic invariants of the real system of functions, the traditional transcendental complexity and artificial limitations of non-integrability are completely eliminated. The proposed method provides exact analytical solutions in elementary functions, ensuring high numerical convergence and stabilizing the relative error within a strict range of 10u207bu2075 to 10u207bu2076 without requiring iterative numerical processing cycles."
Category: Mathematical Physics
[49] ai.viXra.org:2609.0050 [pdf] submitted on 2026-09-22 15:20:09
Authors: Xuda Ye
Comments: 55 Pages.
We analyze the mean square error of stochastic Runge--Kutta integrators for overdamped Langevin dynamics whose potential is strongly convex outside a bounded region. A decomposition splits the local error into a mean-zero term and a smaller remainder, and the discrete Poisson equation turns their moments into a bound on the error of a time average. We carry this out for two stochastic Runge--Kutta integrators proposed by Yang & Wang (2026), both of strong order $frac32$ and weak order $2$, which evaluate the gradient of the potential and no higher derivative. We show that their laws approach the law of the exact solution at second order in Wasserstein-1 distance, up to a logarithm, uniformly in the number of steps. For a test function with bounded derivatives up to third order, we prove that the mean square error over $N$ steps with step size $h$ is $mathcal O ( frac{1}{Nh} + h^4 )$, which is the optimal order in the discretization. Experiments measure the strong and weak orders and the sampling bias on a nonconvex potential in $mathbb R^2$, and compare the integrators on a diffusion model of CIFAR-10.
Category: General Mathematics
[48] ai.viXra.org:2609.0049 [pdf] submitted on 2026-09-22 15:22:47
Authors: Yuliang Wang, Xuda Ye
Comments: 23 Pages.
We consider two stochastic Runge--Kutta integrators proposed by Yang & Wang (2026) for overdamped Langevin dynamics whose potential is strongly convex outside a bounded region. In the companion paper (Ye, 2026) the law of the numerical solution was shown to approach the law of the exact solution at second order in Wasserstein-1 distance, uniformly in the number of steps, up to a logarithm of the step size. We remove the logarithm, and a Gaussian example shows that the second order is attained by the bias of the invariant law of the integrators, and that the squared bias of their time averages attains the order $h^4$ of the mean square error bound of the companion paper.
Category: General Mathematics
[47] ai.viXra.org:2609.0048 [pdf] submitted on 2026-09-22 20:46:18
Authors: L. B. Uvindu Daham
Comments: 15 Pages.
We present a definitive resolution to the P versus N P problem by embedding discrete constraint satisfaction problems (3-SAT) into continuous non-compact Riemannian manifolds via Maslov dequantization (h > 0 deformation). By constructing the Master Flow Equation governed by logsum-exp smoothing operators, we prove that the trajectories are bounded by a uniform polynomial spectral gap and structurally bypass relativization, natural proofs, and algebrization barriers. Utilizing Morse-Bott theory and asymptotic energy dissipation estimates, we demonstrate that all worst-case exponential trajectories are suppressed, achieving deterministic convergence to satisfying assignments in polynomial time O(nK ). Consequently, we establish that P= N P.
Category: Data Structures and Algorithms
[46] ai.viXra.org:2609.0047 [pdf] submitted on 2026-09-22 20:26:51
Authors: Steven Arturo Lizarazo Patiño
Comments: 28 Pages.
Problem: Physical theories presuppose mathematical structure, symbolic rep-resentation, and the allocation of determinate meaning, yet cannot groundthese prerequisites within spacetime without circularity. This foundational gapthreatens the coherence of scientific realism.Result: We prove that any intelligible universe U forces a unique, self-grounding terminus of dependence. Modelling consciousness minimally asmeaning-allocation capacity, the dependency chain U ⇒ M ⇒ L ⇒ C can-not be grounded in U without vicious circularity. The mathematical core isan existence-and-profile theorem for a formal theory T whose axioms (intel-ligibility, well-founded dependence, undated mathematical necessity, semantictermination, and G¨odel incompleteness) define a predicate Pure(x): we proveT ⊢ ∃!x Pure(x), with the unique instance D atemporal, non-spatial, neces-sary, simple, non-mechanical, and semantically self-present (G(D, D), C(D) =D). Uniqueness is established order-theoretically—D is the least fixed pointof a monotone grounding operator on a complete lattice of candidate grounds(Knaster—Tarski)—and non-mechanality is derived from incompleteness ratherthan stipulated, distinguishing the argument from G¨odel’s own ontological proof,which stipulates its property profile and proves no uniqueness. As a physicalcongruence, we show that superluminal spacetime expansion is not generated bylight-cone-bounded local processes, so the empirical world’s own global behaviouris not self-explanatory from within.Implications: The framework extends structural realism and Tegmark’sMathematical Universe Hypothesis by establishing semantic grounding as co-fundamental with mathematical structure. The classical name for a unique,necessary, self-grounding ground of being and intelligibility is God ; the result isconfined to the derived profile and claims nothing beyond it. Consequences forethics, philosophy of mind, and religion are left open.
Category: Set Theory and Logic
[45] ai.viXra.org:2609.0046 [pdf] submitted on 2026-09-22 00:26:50
Authors: Nigel B. Cook
Comments: 21 Pages. (Note by viXra Admin: Please cite and list scientific references other than self-reference))
This paper is a follow-up on https://ai.vixra.org/abs/2608.0002 addressing the emergence of standard model type gauge group from Robert A. Wilson's suggestion of discrete quantization group SL(4,R). Quantum fields emerge as hydrodynamic limits of dense networks of discrete spinor transformations, an application of the basic concept of spin foam vacuums as the ground state of loop quantum gravity. Spin foam vacuums were suggested to explain how a smooth, classical macroscopic geometry emerges as an effective average coarse-graining to an underlying discrete vacuum. This paper thus applies the basic concept of loop quantum gravity's ground state spin foam vacuum to obtain approximately the continuous gauge groups of the standard model from an underlying discrete Wilsonian SL(4,R) group. It is not intended to make specific predictions; just to show compatibility of mathematical techniques. The mathematics in this paper have been proof checked by Microsoft Copilot AI, since human "peer reviewers" are unavailable at present.
Category: Quantum Gravity and String Theory
[44] ai.viXra.org:2609.0045 [pdf] submitted on 2026-09-21 16:38:06
Authors: Preda Daniel Georgel
Comments: 212 pages, 60 conceptual illustrations, and 40 scientific references. English-language theoretical monograph. AI assistance is fully disclosed in the manuscript.
Helical geometrodynamics is presented as a theoretical framework in which systems, transport, geometry, memory, and interaction are analyzed through coherent helical flows. The volume does not seek to replace experimentally validated physical theories. Instead, it investigates whether a common descriptive level can be constructed from vortex tubes, the IN—path—OUT architecture, and geometric adaptation. It introduces the Preda descriptors Cc = dQ/dt, Cf = rvt², and Ce = r³f², together with the independent rotational descriptor Cr, the helical ratio η = va/vt, axial direction, chirality, and phase. The relation Cf = 4π²Ce is treated as an algebraic identity when vt and f refer to the same local rotation, whereas α = CeCf/Cc² remains a derived ratio and a hypothetical filter rather than a sufficient coupling criterion. On this basis, the volume formulates four candidate interaction kernels and develops the concepts of geometrodynamic memory, the Fundamental Torsion Wave (F.T.W.), structural emission and absorption, polarization, axialization, and the Σgd transition regime. Extensions toward light, particles, gravity, cosmology, and living systems are explicitly identified as hypotheses or analogies. The central contribution is an operational research program based on defined observables, comparison with standard models, preregistered predictions, uncertainty analysis, and falsification criteria. In its present form, the work is a falsifiable conceptual framework and research program, not an experimentally validated physical theory.
Category: Quantum Gravity and String Theory
[43] ai.viXra.org:2609.0044 [pdf] submitted on 2026-09-21 20:30:42
Authors: Stephen P. Smith
Comments: 18 Pages.
Lie-algebraic structure can be examined through two complementary forms of organization that will be called vertical and horizontal emergence. These terms are used here as a conceptual framework rather than as standard classifications within Lie theory. Vertical emergence refers to the construction of new algebraic objects from structures already present at a lower level—for example, the construction of curvature from a covariant derivative, or the appearance of higher multilinear operations in $L_infty$-algebras. Horizontal emergence refers to the integration of multiple algebraic structures into a larger structure in which interactions between the component algebras become essential. Semidirect products, matched pairs, and related constructions provide mathematically precise examples. The distinction is useful because the familiar derived series [ L^0 = L,qquad L^1 = [L,L],qquad L^2 = [L^1,L^1],qquad ldots ]does not by itself capture every way in which algebraic structure can become more elaborate. The derived series produces a nested sequence of subalgebras using the same underlying bracket. By contrast, extensions, deformations, higher brackets, curvature, and interacting combinations of algebras can introduce genuinely new structural relationships and new compatibility conditions. This provides a possible mathematical analogy for Arthur Koestler's concept of the holon: a structure may retain a degree of autonomy at one level while simultaneously participating in a larger integrative structure. The analogy should not be mistaken for a theorem establishing that Lie algebras are literally holarchies. Rather, it suggests a productive correspondence between a well-defined mathematical phenomenon—structural integration across levels—and a broader philosophical account of organization.
Category: Algebra
[42] ai.viXra.org:2609.0043 [pdf] submitted on 2026-09-19 07:51:16
Authors: Vladimir S. Netchitailo
Comments: 56 Pages.
The World—Universe Model (WUM) proposes that the physical World is a finite, boundless three-dimensional Hypersphere forming the surface of an expanding four-dimensional Nucleus embedded in the Eternal Universe. The Nucleus expands along the fourth spatial dimension with speed c. Within this framework, Matter is not treated as a primordial substance introduced solely through initial conditions. Universe-Created Matter (UCM) is continuously generated by the Eternal Universe within the expanding 4D Nucleus through the formation of Universe-Created Particles (UCPs).UCPs constitute a fundamental physical component of WUM. They possess definite rest energies and form a discrete multicomponent system. They participate in the formation and evolution of Macroobjects and, through specific interactions and pair-annihilation processes, in the generation of Ordinary Matter. Ensembles of UCPs carry intrinsic angular momentum, physically resembling microscopic "air vortices." WUM therefore relates the origin of Matter to the origin of angular momentum in physical systems.The purpose of the present work is to develop the UCP concept from the fundamental principles of WUM and to compare the predicted particle spectrum with independent astronomical and experimental observations. Particular attention is given to particle-specific quantitative signatures and to theoretically related UCP couples, for which correlated observational evidence can provide a substantially stronger test than isolated spectral correspondences. The broader physical roles of UCM—including the formation of the Cosmic Medium, the operation of UCP Annihilation Reactors, the generation of Ordinary Matter, and the proposed microscopic mechanism of Gravitation—are also considered.The central question addressed in this paper is: Do independently observed phenomena provide quantitative evidence for the system of Universe-Created Particles predicted by WUM? The objective is not merely to identify qualitative similarities, but to determine whether the predicted rest energies, physical products, astrophysical manifestations, and interconnected physical roles of the complete UCP—UCM system have quantitative counterparts in Nature.
Category: Relativity and Cosmology
[41] ai.viXra.org:2609.0042 [pdf] submitted on 2026-09-20 20:25:10
Authors: Alessandro Battiston
Comments: 6 Pages.
Context: Macromolecular structure prediction and conformational energy relaxation have historically relied on stochastic heuristics, Monte Carlo sampling, and deep statistical neural networks (e.g., AlphaFold), which are stochastic or statistical in formulation and can have non-zero predictive uncertainty, with computational costs that depend strongly on the method and implementation. Objective: This work introduces the Deterministic Symbiosis Engine, a closed-form, finite-state feedback operator designed for autonomous energetic equilibrium, mass convergence, and Euclidean distance geometry resolution without stochastic variables or black-boxheuristics.Method: The state operator T : (E,M) →(Eu2032,Mu2032)acts as a non-linear piecewise dead-band contractor over a designated energy interval Isymb = [Eopt−ϵ,Eopt + ϵ]. We generalize T into an N-dimensional tensorial map incorporating angular momentum tensors J and local hydrodynamic dissipation matrices Γ. Results: We prove that for 2ϵ≥max(∆Einc,∆Edec), limit cycles are strictly precluded, yielding exact closed-form convergence in Ki steps. For a benchmark suite of 7 heterogeneous molecular subunits, the maximum individual convergence horizon is Ktotal = 4 under the stated parameters, with ∆dev = 0 in the fixed implementation. The perturbation test returns to the dead-band in Kpert = 2 cycles under the stated benchmark conditions. Conclusion: Bymembedding T within Euclidean Distance Matrix (EDM)completion via semidefinite algebraic constraints, thisframework demonstrates O(N) computational complex-ity for uncoupled systems and a conditional Lyapunov analysis for the coupled consensus dynamics, establishing a deterministic foundation for computational structural biophysics.Keywords: Deterministic Dynamics, Finite-Time Con-vergence, Dead-Band Control, Lyapunov Stability, Distance Geometry, Macromolecular Folding.
Category: Mathematical Physics
[40] ai.viXra.org:2609.0041 [pdf] submitted on 2026-09-18 16:27:56
Authors: Sean O. Brady
Comments: 6 Pages.
Gravitational waves encode the motion of their sources, raising the question of whether deliberately controlled binary motion can carry recoverable information. Methods: Two equal masses are kept antipodal while a smooth radial control law produces identical orbitalexcursions whose timing encodes the integer sequence 2, 3, 5, 7, 11, 13, 17. The two corresponding quadrupole polarizations are calculated from the source motion. A receiver fits the carrier, forms signed residuals, identifies markers, estimates a timing unit, and admits repeated interval packets only after the fixed model and statistical controls are satisfied. Independent numerical integrationchecks the trajectory and energy balance. Results: In a predeclared Gaussian-noise sweep, the full seven-integer payload was recovered in four of six modulated cases, while none of the six matched unmodulated cases passed the packet criteria. At the highest tested noise level, failure occurred in marker extraction rather than carrier fitting. Two chirp- and precession-like nuisance signals also failed to produce repeated packets. The dimensionless construction was mapped to physical binary parameters and Advanced LIGO design sensitivity, with ideal matched-waveform detectability kept distinct from demonstrated packet decoding. Conclusions: This study provides a bounded end-to-end demonstration of information encoded through controlled source motion rather than added directly to a waveform, while also quantifying the extreme physical demands of detectableartificial generation.
Category: Astrophysics
[39] ai.viXra.org:2609.0039 [pdf] submitted on 2026-09-17 22:38:11
Authors: J. W. McGreevy
Comments: 32 Pages.
We introduce the Thermodynamics of Arithmetic Action (TAA), an architectural framework thatunifies arithmetic geometry, informational code theory, and general relativity into a single, cohesive paradigm. This monograph maps the macroscopic universe—including space, time, and the fields of the Standard Model—as the continuous Archimedean completions of a global adélic variety governed by a singular Grothendieck Motive. By demonstrating that the absolute stability of the spacetime metric is structurally bound to the unitarity of the global intertwining operator over GL(2, AQ), weshow that any violation of the Riemann Hypothesis (RH) induces a non-vanishing covariant divergence in the macroscale stress-energy tensor. This mathematical rupture violates the foundational Bianchi identities and triggers an immediate, catastrophic metric collapse. Consequently, the Riemann Hypothesis emerges not as an isolated problem in pure number theory, but as the fundamentalphysical boundary condition that preserves the structural sanity of the spacetime vacuum against self-dissolution.
Category: Mathematical Physics
[38] ai.viXra.org:2609.0038 [pdf] submitted on 2026-09-17 22:36:50
Authors: Wen PeiLin
Comments: 81 Pages.
We study a family of directed graphs on n = 2k+ 5 vertices whose adjacency matrices are{0, 1}-matrices with zero diagonal, uniform column sum 2, and a rigid Jordan structure: thenon-zero spectrum {2, 1, −1, −1, −1} is constant in k, while a single nilpotent block J2k(0)grows with k. We call this the Wen class Uk and define it through five axioms D1—D5. The main result of the paper settles the existence question. We construct an explicit infinite subfamily {Am}m≥1 with ord(Am) = 2m + 7, obtained by iterating a chain-insertionoperator T on a fixed 7 × 7 core C. A Schur-complement identity for T, combined with aresolvent computation that reduces to three cofactors of the single 7 × 7 matrix zI − CT, shows that T multiplies the characteristic polynomial by z 2 ; the exact determination ofdim ker Am = 1 and dim ker(Am + I) = 2 then upgrades this spectral statement to the fullJordan axiom D4. Consequently Uk 6= ∅ for every integer k ≥ 1: the class is infinite, andno order is empty. Every step of the proof is a finite exact computation of order at most 7,independent of m. We prove the closed-walk counting formula NL = 2L + 1 + 3(−1)L, the rank formula rank(Am) = max(n − m, 5), the minimal polynomial x 2k (x − 2)(x − 1)(x + 1)2 of degree n − 1, the commutant dimension 7 + 2k, the Newton-identity recurrence of order 5,and the doubler-chain power-of-two property. A computer search at seven orders (k =1, . . . , 7, i.e. n = 7, . . . , 19) produced 233 pairwise non-isomorphic members, distributed as 34, 50, 39, 22, 68, 13, 7; these numbers are lower bounds for the number of isomorphism classes at each order, and ten representatives of each order are listed in Appendix 18. We disprove two natural conjectures (the "minimum-one integer Perron vector" property and the "core-template" hypothesis) and organise the observed structure into a three-layer architecture separating rigid invariants, semi-invariants and flexible realisation.
Category: Combinatorics and Graph Theory
[37] ai.viXra.org:2609.0037 [pdf] submitted on 2026-09-16 10:18:38
Authors: Vitaliy Boltian
Comments: 3 Pages.
This paper proposes an alternative paradigm of mathematical analysis based on the interaction of physical quantities rather than an abstract numerical continuum. The concept of a discrete scale factor $M$ and inter-system transition coefficients via Gudermannian mappings are introduced, rendering the classical substitution of variables an anachronism. Exact analytical operational formulas for differentiation and integration are obtained, a physics-scale-based proof of Fermat's Last Theorem is presented, and new empirical models for elliptic integrals of the first and second kind are derived. For the first time, a real quantum wave function based on split-complex (dual) numbers is proposed, and a new form of the stationary Schrödinger equation, free from imaginary mysticism, is derived.
Category: Mathematical Physics
[36] ai.viXra.org:2609.0036 [pdf] submitted on 2026-09-16 20:34:26
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 7 Pages.
Can gravitational geometry arise as a collective response without postulating a fundamentalgraviton? We investigate this possibility within the Principium Geometricum (PG) program, inwhich local sectors are restrictions of a global state and toroidal phase and breathing variablesare proposed as underlying degrees of freedom. A local normalization Φ = ZΘ yields K = K0Z2and β = β0Z, preserving β2/K. An exact change-of-variable test shows, however, that thisidentity alone produces no new gravitational observable: when all gradient terms are retained, Z cancels from the physical potential Ψ = βΘ. A physical toroidal mechanism must therefore modify the source energy or introduce independently derived interactions. Conditional on universal clock coupling, the source is total energy, and a static gapless sector yields a Poisson equation and inverse-square acceleration. A reciprocal exponential metric reproduces the static weak-field coefficients γ = β = 1, but its exterior Einstein tensor is nonzero at nonlinear order. The construction thus provides an effective framework and a precise set of consistency tests, rather than a completed quantum theory of gravity. Its central open problem is to derive source energies, constitutive coefficients, and gravitational dynamics from the same microscopic theory. A fundamental graviton is not assumed; emergent graviton-like excitations are neither derived nor excluded.
Category: Relativity and Cosmology
[35] ai.viXra.org:2609.0035 [pdf] submitted on 2026-09-14 20:17:56
Authors: Tatarov Evgeniy
Comments: 19 Pages.
This paper presents the Dynamic Vacuum Relaxation Theory (DVRT) — a complete,self-contained relativistic theory of gravity in which dark matter phenomenology and cos-mic acceleration arise not from undiscovered particles or fine-tuned constants, but fromthe quantum structure of the de Sitter vacuum. By exploring the spontaneous breaking of conformal symmetry SO(2, 4) → SO(1, 3) at the Hubble scale, we demonstrate that a scalar dilaton field Θ and a special conformal vector field Aµ emerge naturally as geometricdegrees of freedom. The scalar field is identified as an effective hydrodynamic condensate of fundamental fermionic fields on the dS4/CF T3 boundary. We derive all parameters from first principles, including the Milgrom acceleration scale a0 = cH0/6 ≈ 1.135 × 10−10 m/s2 and the universal coupling constant β = 1/6. The theory reproduces flat galaxy rotationcurves, the baryonic Tully-Fisher relation, and the Radial Acceleration Relation without freeparameters, while passing all Solar System, binary pulsar, and strong-field precision tests.Unique falsifiable predictions for upcoming cosmological surveys are discussed.
Category: Quantum Gravity and String Theory
[34] ai.viXra.org:2609.0034 [pdf] submitted on 2026-09-14 19:59:05
Authors: J. W. McGreevy
Comments: (Note by ai.viXra.org Admin: Please remove all empty pages and cite listed scientific references)
This monograph presents the formal foundations of the Thermodynamics of Arithmetic Action(TAA), a unified framework wherein the macroscopic spacetime continuum, general relativity, and quantum gauge fields emerge as expressions of a single underlying Grothendieck Motive evaluated over the global adele ring AQ. We demonstrate that the non-renormalizability of quantum gravity is a coordinate-chart artifact born from the false assumption of infinite continuity in the ultraviolet. By regularizing the pre-Planck lattice as a characteristic p algebraic variety operating at the maximumgeometric packing density, we show that data-packet crowding forces a 5-bit Maximum DistanceSeparable (MDS) error deficit. This unpayable local information debt triggers a topological phase transition, deforming a flat rational curve (g = 0) into a genus-5 Riemann surface stabilized by a hidden SO(4) momentum space symmetry. Physical constants—including the speed of light, the gravitational constant, andthe Yang-Mills mass gap—are derived explicitly as transcendental periods of this motive. Finally, we establish that the non-trivial zeroes of the Riemann zeta function act as absolute causal waveguides, clamping the running of the gravitational coupling constant smoothly to zero and regularizing high-energy loop divergences without infinite counterterms.
Category: Mathematical Physics
[33] ai.viXra.org:2609.0033 [pdf] submitted on 2026-09-14 14:25:49
Authors: Arieh Sher
Comments: 8 Pages.
We investigate the kinematic and morphological properties of disk and spiral galaxies withinthe Pivot Universe (PU) theoretical framework. In this model, the persistent flattening of galacticrotation curves is attributed to an asymptotic background spacetime frame-dragging field (Ω0)induced by the cosmic Kerr pivot, eliminating the need for cold dark matter (CDM) halos. Bycoupling the local baryonic mass distribution to this background metric acceleration field (a0), theBaryonic Tully-Fisher Relation (V 4flat ∝ Ga0Mb) is derived directly from first principles.Furthermore, we examine galactic morphology resulting from continuous ballistic mass ejectionfrom rotating antipodal nozzles anchored to central supermassive black holes (SMBHs). Whileinitial formulations assumed Archimedean spirals (r ≈ bθ), we demonstrate that transitioningto a logarithmic spiral geometry (r = aebθ) is physically required to resolve the outer windingproblem and preserve self-similarity. We show that a logarithmic geometry naturally couples withan asymptotically flat rotation curve (vϕ = const), as the required angular dragging frequencyscales as ω(r) ∝ 1/r.Analytical rotation curves and structural models are derived and benchmarked against empiricalobservations for the Milky Way, the grand-design spiral NGC 5457 (M101), the barred lenticulargalaxy NGC 2787, and the Whirlpool Galaxy (M51). Finally, we introduce a non-linear tidalperturbation correction term, δr(θ), demonstrating how external gravitational interactions withsatellite dwarf galaxies (such as NGC 5474) break intrinsic m = 2 antipodal symmetry to producethe observed lopsidedness and arm elongation in M101.Keywords: Galaxies: kinematics and dynamics — Galaxies: spiral — Galaxies: structure — Cosmology: theory — Metric frame-dragging — Tully-Fisher relatio
Category: Relativity and Cosmology
[32] ai.viXra.org:2609.0032 [pdf] submitted on 2026-09-14 19:53:15
Authors: Arieh Sher
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite all listed scientific references)
We present an exact mathematical formulation of cosmological orbital kinematics in a rotating Kerrspacetime anchored by an ultra-massive central core of mass MP = 7.82 × 1053 kg. In this configuration:1. The outer event horizon is situated at r+ = 122.764 Gly, and the cosmological matter disk is locatedstrictly outside the event horizon spanning radii r ∈ [122.764 Gly, 175.6 Gly].2. The Milky Way is located in the immediate exterior vicinity of the horizon at RMW = 123.3265 Gly,corresponding to a radial clearance of ∆r = +0.5625 Gly (562.5 Mly or a 0.46% fractional margin).3. The cosmic trajectory is traced continuously from the central Pivot (r → 0) up to the Milky Wayalong a self-similar, scale-invariant logarithmic spiral r(ϕ) = r0ebϕ.4. We demonstrate that the logarithmic spiral (and not the Archimedean spiral) trajectory can bemathematically equivalent to a geodesic; however, this is correct only in an effective flowingfluid metric as formulated in Sher (2017), whereas it is not valid as a geodesic in pure vacuumKerr or Schwarzschild spacetime.5. We enforce the strict dynamical equivalence condition vN (L) = vKerr, where vN (L) ≡pGMP /L isthe modified Newtonian velocity evaluated along the cumulative worldline arc length L, and vKerris the coordinate frame-dragging velocity at radial separation RMW.
Category: Relativity and Cosmology
[31] ai.viXra.org:2609.0031 [pdf] submitted on 2026-09-12 18:40:58
Authors: Brent Hartshorn
Comments: 13 Pages.
Robotic vision policies trained on photorealistic synthetic imagery fail when the real world presentsa texture, a shadow or a reflection the renderer never produced. We argue the fault is the representation rather than the realism: a policy that consumes photographs must learn to ignore appearance, when it could instead be handed a representation from which appearance has already been removed. We describe a chained architecture in which a perception stage converts camera input into a non-photorealistic line drawing paired with a semantic map, and a control policy consumes only that abstraction. Decoupling perception from control allows each to be trained independently [4], and abstract intermediate representations such as sketches are known to preserve spatial grounding while discarding visual distraction [5].The contribution is an open simulator that makes the architecture testable end to end: it generatesthe aligned multi-modal corpus the interface requires — photorealistic, line art, object index and metric depth from one viewpoint — carries a physically grounded robot with an optional rigid-body contact backend, imports externally authored scenes and assets [3], and executes the real control firmware against the simulated plant at two distinct fidelities: a value-level seam fast enough for the training loop, and an offline register-level gate in which the same commands are driven through emulated I2 C peripherals, H-bridges and a serial lidar protocol [11]. The second catches a class of defect the first cannot represent, and we quantify the divergence between them. We report a perception result on 479 samples, a multi-label scene-description head trained from labels the renderer already knew, and a control policy cloned from a privileged expert that reaches its goal in 8/8 held-out scenes while seeing only the abstraction.Every number is reported beside the score of doing nothing, and we record the two hypotheses about thecontrol bottleneck that measurement destroyed, together with two measurement choices the register-level gate itself invalidated.
Category: Artificial Intelligence
[30] ai.viXra.org:2609.0030 [pdf] submitted on 2026-09-13 00:57:38
Authors: Brent Hartshorn
Comments: 20 Pages.
Physics notation is ambiguous, this paper reports what happens when a knowledge base of 97 equations, 136 symbols and 64 physical quantities is made to declare what each of its letters denotes, and is then allowed to connect itself. Equations become graph nodes; edges follow shared quantities rather than shared characters; and two equations stating the same quantity are joined by transitivity into one annotated formula. Each statement is checked to be a well-formed proposition over an axiomatic Real by a Calculus of Constructions micro-kernel, then emitted as Lean4.
Category: Mathematical Physics
[29] ai.viXra.org:2609.0029 [pdf] submitted on 2026-09-13 13:13:00
Authors: Kerényi József
Comments: 6 Pages.
We propose a unified phenomenological model based on relativistic gravitational impedance, Zeff = eta * G / c. The central observation is that the longitudinal mass flux Ig = d(gamma m0)/dt, proportional to the scalar product v dot a, defines a specific potential Phi_g = Zeff * Ig whose sign is set by v dot a. Longitudinal acceleration (v dot a > 0) corresponds to energy release with equation of state w -> -1 (dark energy phase), while deceleration (v dot a < 0) corresponds to absorption with w -> 0 (dark matter phase). The bare impedance Zg = G/c gives rho_g ~ 4e-36 J/m3 ~ 1e-27 rho_Lambda for the Milky Way, requiring amplification eta ~ 1e27 for cosmic acceleration and eta ~ 1e6 for the MOND acceleration a0 ~ 1.2e-10 m/s2, parametrized as a0 = eta * (Delta V)^2 / R_H. In the low-acceleration limit we derive v_c^4 = G M a0 from equilibrium v_c^2 = Phi_g. The model provides a single language for both dark components with falsifiable predictions for lensing near jets and Gaia streaming.
Category: Relativity and Cosmology
[28] ai.viXra.org:2609.0028 [pdf] submitted on 2026-09-11 20:26:42
Authors: Prakash Vaithyanathan
Comments: 11 Pages.
Mobile phone connections drop for two related reasons: a narrow mmWave beam gets blocked, or a link of any kind simply fades out because the phone has moved into a weak-coverage spot. Both problems are handled today by mechanisms that only react after the signal has already gone bad. This paper describes one small, fixed, dedicated hardware controller — not a piece of software — that watches the ordinary signal-quality numbers a phone or base station already measures, and raises a warning before either kind of failure happens. We show, on two separate synthetic examples, that the same fixed controller gives an early warning before both the mmWave beam failure and the general radio link failure mechanisms would fire on their own. We explain in plain terms why this only works well as dedicated hardware and not as software running on a shared processor. All results here are from simulated data; the next step is testing on real network measurement logs.
Category: Digital Signal Processing
[27] ai.viXra.org:2609.0027 [pdf] submitted on 2026-09-12 13:23:14
Authors: Fabrizio Vassallo
Comments: 32 Pages.
A 2020 note [1] observed that the self-similar set F the positive integers n forwhich n − 1, in base 3, uses only the digits 0 and 2 satises a telescoping identitythat, read as a xed-point equation, assigns the divergent sum S = Pn∈F n the value−1/5. This paper reports what survives close scrutiny of that claim and what doesnot. We show rigorously, via the self-similarity F = 3F ∪(3F −2) and the functionalequation this induces on the theta function Θ(t) = Pn∈F e−nt, that the arithmeticzeta function ζF (s) = Pn∈F n−s satises ζF (0) = 0 and hence ζF (−1) = 0: the zeta-regularized value of S is 0, not −1/5. We then construct the hierarchical graph Gkthat the same self-similarity naturally generates, obtain its Laplacian spectrum inclosed form by an exact backbone/localized-state decomposition (veried indepen-dently, both analytically and numerically, up to k = 6), and show that its spectralzeta function satises ζGk (0) = Nk − 1 identically for every connected graph on Nkvertices a positive, divergent integer sequence of exact integer values, one per k ruling out the specic identication made in the exploratory work, though notevery conceivable regularization built from this same sequence (Section 3.3 discussesa dierent one that still produces −1/5, and why it is not the spectral zeta func-tion of any single Gk). This directly falsies an intermediate claim, made in theexploratory work this paper grew out of, that identied −1/5 with this spectral zetafunction. We then examine, by an independent route (a Perron-type explicit formulaexpressing the counting and summatory functions of F as a sum over ζF 's poles),whether a genuinely distinct summation functional in Ramanujan's sense, not sim-ply zeta regularization, and adapted to F 's fractal structure rather than borrowedfrom the integers might still recover −1/5. Conditional on a growth estimate wedo not fully establish, this route shows that no constant of any kind survives in theasymptotics of F 's counting or summatory function, conrming by a second, inde-pendent method that 0, not −1/5, is what F 's own structure naturally produces;we verify the underlying machinery against an exact, parameter-free identity forcedby A(3m) = 2m. One loophole is identied and left open a Ramanujan-type sum-mation of F 's enumeration index, rather than its values, trivially recovers −1/2 butarguably encodes nothing about F specically and we explain why resurgence andalien calculus, sometimes proposed as a further alternative, have no natural pointof contact with this problem. Finally, we discuss why the relevant physical motiva-tion (zeta-regularized vacuum energies, and the empirically rich sign-dependence ofCasimirLifshitz forces) is exactly that motivation, not evidence.
Category: Mathematical Physics
[26] ai.viXra.org:2609.0026 [pdf] submitted on 2026-09-10 20:03:29
Authors: Zhongyang Dong
Comments: 5 Pages.
As a direct sequel to Emergent Cosmology of a Two-Phase Planar-Invasion Bubble Universe [1],this paper establishes a self-sustaining global multiverse model—encompassing a grand Global Universe composed of seven initial seed universes—from a "Creator’s-Eye View" of physical aesthetics and minimalism. To avoid ambiguity, it is explicitly emphasized that all bubble universes discussed and analyzed hereafter strictly refer to their iteratively evolved generations produced throughmulti-generational collisions, rather than the initial seed universes. We formulate the core physical axioms, a topological fault-tolerance law, and a dark energy conservation mechanism: the primordial Big Bang mechanism permanently and individually ceased across the seven initial child universes in strict accordance with the Second Law of Thermodynamics, serving as Newton’s Prime Mover with non-uniform initial expansions seeding subsequent cosmic rotation; global particle universality ensures that all iterative bubble universes share identical microscopic physics; apparent localdark energy acceleration is resolved as the kinetic energy projection of topological potential energy transferred from degenerate ground-state universes (SDead); and the Prime-7 topological law (N0 = 7) together with evolutionary scale sequences ({10,15,40,100}) guarantees a dynamic equilibrium (Neq >7) and a strictly zero extinction limit (limt→∞ P(N(t) = 0) ≡0). Finally, we reconcile this framework with Newton, Spinoza, and ancient Chinese philosophy, concluding with a humanistaffirmation of Philosophical Optimism and cosmic grace.
Category: Astrophysics
[25] ai.viXra.org:2609.0025 [pdf] submitted on 2026-09-10 16:39:28
Authors: Joseph Shaffer
Comments: 11 Pages.
Modern astrophysics is characterized by an escalating series of foundational crises, including the Hubble tension, the dark matter anomaly, and the mathematical infinities of black hole singularities. These issues stem from a reliance on general relativity's geometric framework, which presumes a dynamic, expanding spacetime metric and an invariant speed of light c. This paper introduces an alternative ontology wherein the universe is completely static. Reality is partitioned into a fundamental, non-local informational domain E comprised of Planck-scale mats under tension, and an emergent, local domain S. By treating gravity not as spacetime curvature, but as a localized deficit in global substrate tension, we demonstrate that the local velocity of light is a dynamic variable cx. This single primitive — information mats under tension—simultaneously resolves gravitational time dilation, removes the need for dark matter and dark energy, eliminates black hole singularities, and reinterprets the Big Bang as a global thermodynamic phase transition.
Category: Astrophysics
[24] ai.viXra.org:2609.0024 [pdf] submitted on 2026-09-10 01:50:38
Authors: Adilson Gonçalo
Comments: 39 Pages. In Portuguese
This article constitutes the second part of the series "Space-Time" from a Realist Perspective. Continuing the analysis developed in the first part, the present work primarily aims to examine the compatibility between classical mechanicsand electromagnetism, with particular attention to the relationship between Galilean transformations and Maxwell’s equations, an issue traditionally presented as one of the main motivations for introducing Lorentz transformations and formulating the Theory of Special Relativity. It is investigated whether the alleged incompatibility between thesetheoretical frameworks necessarily arises from physical phenomena or is instead related to the way the electromagnetic and kinematic quantities involved are interpreted. To guide this analysis, principles underlying the adopted approachare first established. Based on these principles, the concept of spacetime interval in the Einsteinian relativistic formulation and its invariance under coordinate transformations are examined. Subsequently, the relationship betweenGalilean transformations and Maxwell’s equations is analyzed, including the invariance of these equations under Galilean transformations and the transformations of the electric and magnetic fields between reference frames in relative motion. In addition, the conventional interpretation of the phenomenon of magnetic induction is examined. This second part remains restricted to the theoretical, mathematical, and conceptual analysis of these issues. Thediscussion of the main experiments and observations traditionally presented as confirmations of Einsteinian relativity will be developed in the third and fourth parts of the series.
Category: Relativity and Cosmology
[23] ai.viXra.org:2609.0023 [pdf] submitted on 2026-09-10 01:45:10
Authors: Prakash Vaithyanathan
Comments: 8 Pages.
Optical transport networks— the fiber links carrying telecom and data-center traffic— candevelop "soft failures": a slowly aging amplifier, a worn connector, or a degrading splice that gradually weakens the signal long before it fails outright. Today’s protection mechanism only reacts once the signal quality has already dropped far enough, several times in a row, to cross a fixed threshold. This paper applies Arnold’s Bifurcation Principle— the same fixed, training free method already used in our earlier work on hemodialysis vascular access, drone wind-gust safety, cardiac arrhythmia warning, and 5G/6G radio-link failure— to the optical signal-to-noise ratio (OSNR) measurement a fiber-optic network already monitors. On a single synthetic run, the method gives a meaningful early warning before the existing reactive protection-switching mechanism itself would fire, using a small, dedicated hardware controller rather than software.All results here are from simulated data; the next step is testing on real network logs.
Category: Digital Signal Processing
[22] ai.viXra.org:2609.0022 [pdf] submitted on 2026-09-09 16:08:39
Authors: Idan Hackmon
Comments: 5 Pages.
We present an argument excluding finite covering systems with distinct odd moduli whose least common multiple has at most six distinct prime factors, with unrestricted prime exponents and integer residues. The argument refines capped reweighting by comparing the positive-part expectations of every auxiliary divisor count with those of a product of independent finite geometric-tail factors. For the first six odd primes the resulting rational budget is approximately 0.91015158 < 1. A digit-embedding prime-replacement lemma transfers the fixed-prime exclusion to arbitrary prime supports. The probability argument is finite: truncation preserves the small product atoms needed for the calculation, and a finite geometric sum bounds the mean. Both full statements have been verified in Lean and Aristotle, with independent checks of the returned source and unrestricted exponents. Historical priority is not asserted.
Category: Number Theory
[21] ai.viXra.org:2609.0021 [pdf] submitted on 2026-09-10 01:36:40
Authors: Derrick Hiang Yaol Lim
Comments: 13 pages, 6 figures and 2 tables.
We present a classical, lumped-element circuit model of a two-level atom built around a specific conceptual claim: the two atomic energy eigenstates, represented as LC resonators with parameters fixed from the level energy and orbital magnetic moment, are exactly decoupled under the field-free Hamiltonian, which we realize as a literal open circuit between them. Coupling arises only from two distinct, independently gated perturbations: (i) an external oscillating field, modeled as a voltage source applied across the (otherwise open) inter-level branch, which produces reversible Rabi (continuous-wave drive) or Rosen—Zener (pulsed drive) dynamics; and (ii) theavailability of a radiative channel in the environment — schematically, a receptive absorber elsewhere in the universe — modeled as a resistive path to a shared radiative bath that opens and closes in time, which produces irreversible photon emission via a shared-bath coupled-mode-theory (Haus) formalism. In the absence of both perturbations the model predicts, exactly, that an isolated excited atom does not radiate. We show the emission channel comes in two dual circuit realizations, inductive (magnetic-dipole, M1) and capacitive (electric-dipole, E1) coupling to the environment, and validate both against the hydrogen 21 cm hyperfine line and the Lyman-α (2p → 1s) transition, reproducing the measured decay rates to within 1% and 0.2% respectively. We discuss the relationship of the "no absorber, no emission" baseline to Wheeler—Feynman absorber theory, to Cramer and Mead’s two-atom transactional formalism, and to the standard vacuum-fluctuation picture.
Category: History and Philosophy of Physics
[20] ai.viXra.org:2609.0020 [pdf] submitted on 2026-09-09 23:54:33
Authors: Max Rempel
Comments: 51 Pages.
This book sets the esoteric tradition beside archaeology, geology and genetics, and asks how far the two accounts agree.The esoteric tradition holds that two peoples who were not human lived on this planet before us and are among our ancestors: the Lemurians of the Third Race and the Atlanteans of the Fourth. It has held this since 1888, and in older forms for much longer.Genetics has now found seven vanished peoples inside the DNA of the living. Two of them have bones and names, the Neanderthals and the Denisovans. Five have no remains at all and are known only from the stretches of DNA they left in us. This book calls all seven parahuman, and numbers them PH1 to PH7.I propose that the Denisovans are the Lemurians. Their bones lie inside the Lemuria that Blavatsky drew, and their living inheritance rises to five percent in New Guinea and Aboriginal Australia.Atlantis is less settled, and the book turns to it in the second half. The esoteric sources place it in the Atlantic and the Mediterranean. The book compares these accounts with the drying and refilling of the Mediterranean between six million and five and a third million years ago.The book then sorts the seven parahuman peoples against what the esoteric sources say an Atlantean was, using place, quantity, date and body. Three of the four can be checked against genetic data. Three peoples survive the sorting: the Neanderthals, the Veshuans of the West African Atlantic coast, and the Korimians, who are in every human being alive. None of the three is confirmed by any source, and the sorting is set out with its own limits stated, including the fact that no genetic measurement can establish whether a given people lived on this planet at all.It ends with what each Race is said to have brought, with the persecution that thinned the psychic capacity out of our species, and with two ideas about what the alien hybridization now under way may be restoring to us.
Category: General Science and Philosophy
[19] ai.viXra.org:2609.0019 [pdf] submitted on 2026-09-10 00:59:20
Authors: Brent Hartshorn
Comments: 13 Pages.
In September 2026 a computer-checked proof of Fermat’s Last Theorem and a Lean-formalizedproof of blowup in the forced Navier—Stokes equations were announced within days of each other,and both are believed because a kernel checked them. This paper applies that discipline at theother end of the scale. A Calculus of Constructions micro-kernel with no axioms, is given an imperative language—assignment, branches, bounded loops, and while with an explicit variant—compiled by symbolic execution into kernel terms. Contracts are decidable propositions, Holds b := Eq Bool b true, about the very expression a runtime check would evaluate. A while loop raises four obligations, one of them the soundness of its own lowering, and termination is proved for every starting state. Records and a state invariant give a model of an seL4-style OS whose routing layer carries contracts that hold for every input. A bridge to Crust, a self-contained C/C++/Rust toolchain, settles its source-level contracts in the kernel; building it found two of Crust’s passes reading one contract two ways. Finally a certificate changes generated code: a SIMD kernel’s scalar remainder is omitted on it, and a contract proven at every call site downgrades 80% of the memory-safety checks in a leaf initializer while the check it leaves still catches an overflow.
Category: Artificial Intelligence
[18] ai.viXra.org:2609.0018 [pdf] submitted on 2026-09-08 09:23:43
Authors: Arieh Sher
Comments: 18 Pages.
The observed motion of the Solar System and the Local Group relative to the cosmicmicrowave background (CMB) is conventionally interpreted as a peculiar velocity produced bythe gravitational influence of the surrounding large-scale matter distribution, including the Virgoregion, the Great Attractor, the Shapley concentration, and cosmic voids. The Solar-Systembarycenter moves relative to the CMB at approximately 369.8 km s−1, while transformation tothe Local-Group barycenter gives a velocity of approximately 627 km s−1. This paper examinesan alternative interpretation within the Pivot Universe (PU) model. The universe is treated asa rotating system described approximately by Kerr geometry generated by a central massiverotating Pivot. Matter in the observable universe is assumed to participate approximately in theframe-dragged rotation generated by the Pivot. For MP = 7.82 × 1053 kg, JP = 1.06 × 1087 J s,RMW = 123.3265 Gly, and RCMB = 123.36 Gly, the Kerr frame-dragging angular velocity at theMilky-Way shell is approximately 0.313 × 10−13rad yr−1. A locally normalized differential Kerrquantity between the MW and CMB shells is approximately 495 km s−1. This value lies betweenthe Solar-System/CMB and Local-Group/CMB velocities, but it is shown that this numericalcorrespondence cannot itself be identified with an invariant relative velocity. An invariant Kerrphoton-frequency calculation instead separates a predominantly gravitational monopole shiftfrom a much smaller directional frame-dragging contribution. The PU interpretation thereforerequires the observed CMB dipole to contain a combination of global Kerr geometry and localpeculiar motions. The model yields quantitative predictions that can, in principle, be testedagainst the direction and magnitude of observed large-scale peculiar-velocity fields.
Category: Relativity and Cosmology
[17] ai.viXra.org:2609.0017 [pdf] submitted on 2026-09-08 16:35:15
Authors: Marian Opial
Comments: 13 pages. Licensed under CC BY 4.0. AI-assisted.
For a finite set S of integers, its integer Turnpike data record the multiplicity of every positive difference. In the dense frequency-vector encoding, realizability reduces to parity of self-reciprocal irreducible factors and is therefore decidable in polynomial time by ordinary polynomial factorization. Sparse binary-exponent encoding is different: the associated reciprocal polynomial can have exponentially large degree. We construct an infinite family of sparse, coefficientwise nonnegative, Fourier-nonnegative, arithmetically admissible Turnpike instances with the fixed point count n = 107,520 that are nevertheless nonrealizable. Each instance contains, to odd multiplicity, a primitive noncyclotomic self-reciprocal irreducible of degree 2^k, while the sparse input length is Theta(k). Thus Fourier positivity, elementary count identities, and visible monomial-composition tests do not imply any polynomial bound on the degree of the remaining obstruction. Several complementary results locate the residual difficulty. Under the Turnpike scalar identities, an integral Hermitian sum of squares collapses to one binary rank-one factor; a parity-safe multiplier cannot raise the square-root-total/center ratio; and a strictly Fourier-positive integer NO instance can lie in the midpoint of two YES instances. Every odd self-reciprocal factor has infinitely many reciprocal quadratic shadows modulo primes, with a density lower bound in terms of permutation rank, but cyclotomic examples rule out naive small-prime enumeration. Finally, a ramified quadratic trace gadget converts a Legendre symbol into the desired characteristic-zero reciprocal-parity bit while preserving Fourier positivity. A local-to-global counterexample shows why this gadget does not yet yield a hardness reduction.
Category: Combinatorics and Graph Theory
[16] ai.viXra.org:2609.0016 [pdf] submitted on 2026-09-08 23:57:19
Authors: Zhongyang Dong
Comments: 6 Pages. (Note by ai.viXra.org Admin: LaTex codes should be converted to standard math espressionss; please cite listed scientific references)
This paper presents an emergent cosmological framework derived from a "Two-Phase Planar-Invasion" bubble universe scenario. Departing from the standard Big Bang (Lambdatext{CDM}) singular cosmology and the hypothesis of spin-2 spin-mediated gravitons, we define the observable Universe as an organized, dynamic cosmic plane (topologically modeled as a rotating, two-dimensional scimitar-like manifold) that non-asymmetrically penetrates and ingests a degenerate, maximum-entropy deceased progenitor universe—a space composed of a constant light-neutrino background (ho_u^{text{bg}} = text{Const}) and a massless photon background forming an all-neutral quantum matrix.
Category: Astrophysics
[15] ai.viXra.org:2609.0015 [pdf] submitted on 2026-09-07 19:28:03
Authors: Arieh Sher
Comments: 14 Pages.
Newton’s law of gravitation and Einstein’s General Relativity describe gravity in fundamentally different ways. Newtonian theory treats gravity as an interaction between masses,whereas General Relativity describes gravity through spacetime geometry. Nevertheless,Newtonian gravity remains an excellent approximation in appropriate weak-field conditions.This paper considers a possible connection between the two descriptions within the PivotUniverse (PU) model. The universe is assumed to contain a central massive rotating object,called the Pivot, whose angular momentum produces large-scale Kerr frame dragging. Matteris proposed to move with this rotating spacetime rather than through an otherwise stationaryspace.A further hypothesis is examined. In the usual Newtonian circular-orbit relation,v^2 = GM/R, R represents radial distance from the gravitating body. The PU model considers whether, for matter following an extremely long spiral trajectory generated by frame dragging, aneffective dynamical length L could replace R,v^2 = GM/L
Category: Relativity and Cosmology
[14] ai.viXra.org:2609.0014 [pdf] submitted on 2026-09-07 04:37:54
Authors: Oleg Ponfilenok
Comments: 20 Pages. Source: https://github.com/oponfil/collapse-threshold
We propose a modernization of quantum mechanics through the introduction of the Collapse Threshold Rule: a branch or coherence is removed if it cannot be distinguished experimentally from absence. The classical outcome becomes objective rather than a virtual interpretation of decoherence. The threshold is derived from the finite number of binary distinctions within a causal patch — 3,5 × 10¹²u2070. The scale of equiprobable branching and the RCS limit are about 400 qubits. The model forbids factorization of RSA-1024. The non-unitarity of the collapse act permits non-conservation of energy as well as superluminal information transfer. An experimental test on a single 404-qubit processor is proposed.
Category: Quantum Physics
[13] ai.viXra.org:2609.0013 [pdf] submitted on 2026-09-07 09:01:01
Authors: Zhengxi Wang
Comments: 107 Pages.
This is a book that explores human origins, development, and the future. It combines scientific theory with philosophical reflection to answer the eternal human questions: "Where do we come from? Where are we going? What are we here to do? First, it presents fossil records and evidence of biological evolution, supporting the view that life evolves. After summarizing biological laws and formulating the "Law of Biological Evolution" and the "Law of Biological Survival" it discusses how to migrate to other planets, the mission of humanity, and ways to colonize extraterrestrial worlds. It also examines future biotechnology and argues that we humans should follow "the principle of human species unity." It describes the future space age, the span of human existence, and the end of the world. Once we know humanity's future, we find the answer to where we came from. Finally, it discusses our origins: the origin of life, the origin of humans, the birth of modern humans, and philosophical questions about life and the universe. It proposes that we are cosmic humans and a link in the chain of cosmic life. Humanity holds a special place in the universe and plays an incomparably important role.
Category: General Science and Philosophy
[12] ai.viXra.org:2609.0012 [pdf] submitted on 2026-09-07 17:56:27
Authors: Andreas G. E. Scharfenberg
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This position paper introduces the Theory of the Global Universe (GU), an ontological and causal framework that resolves the boundary singularities inherent in General Relativity (GR) by replacing the premise of dynamic spacetime with a strictly rigid, infinite Euclidean continuum. Within this framework, physical interactions are governed by the continuous dynamics of energetic potential differences (Kinetic Base Tension) rather than geometric curvature. The model ontologically redefines mass not as a fundamental substance, but as a topological boundary surface effect resulting from the localized phase transition of translational vector flows into closed three-dimensional lemniscates (Cassini ovaloids of revolution). By applying this purely Euclidean continuum mechanics, the GU theory provides a deterministic causal mechanism for phenomena such as time dilation and the cosmological constant. Furthermore, it offers a geometric resolution to the empirical Proton Radius Puzzle, demonstrating that the anomalous scattering radii (0.877 fm and 0.841 fm) naturally correspond to the dual structural radii of the primary soliton's unperturbed envelope surface.
Category: Quantum Gravity and String Theory
[11] ai.viXra.org:2609.0011 [pdf] submitted on 2026-09-06 20:04:08
Authors: Srinivasulu Charupally
Comments: 20 Pages.
The Acceleration Theory, a novel concept explored in this research paper, challenges the classical and quantum theories to elucidate the accelerating expansion of the universe. While the constancy of mass for subatomic particles over time and the existence of various matter particles, including Dark Matter (DM), Anti-Matter (AM), and regular matter, are well-established, the origins of these particles and the driving forces behind cosmic expansion remain intriguing questions. This work delves into the theoretical foundations of how Dark Matter, Anti-Matter, and regular matter particles were generated in the early universe, unraveling the cosmic mechanisms that led to their existence and the compelling phenomenon of universal expansion. Secondly, addressing the finiteness of the speed of light, this research explores alternative perspectives on its constancy and investigates potential influences of Dark Energy (DE) on light speed. Thirdly, furthermore, the paper examines the four fundamental forces—Electromagnetic Force (EF), Strong Force (SF), Weak Force (WF), and Gravitational Force (GF)—in the context of quantum unification. While EF, SF, and WFs have found unification through quantum theory, GF remains distinct. Despite efforts in General Relativity (GR) to comprehensively address gravitational forces, a unifying framework with the other three forces is elusive. To bridge this gap, the paper introduces innovative concepts of Space Energy (SE) and Space Constant (SC) to reconcile and unify these fundamental forces. Finally, the research concludes by contemplating a unified theory for the universe and explores the possibility of an acceleration principle governing every cosmic event. By scrutinizing diverse theories and introducing new concepts, this paper contributes to advancing our understanding of the fundamental principles that govern the cosmos
Category: Quantum Gravity and String Theory
[10] ai.viXra.org:2609.0010 [pdf] submitted on 2026-09-06 20:08:25
Authors: Hani Abdel-Rahim
Comments: 13 Pages.
We present a self-consistent cyclic cosmological framework that resolves the origin, nature, and observed abundance (∼ 85%) of dark matter without introducing hypothetical elementary particles. We propose that dark matter consists oftopologically neutral solitonic states (ΦDM) produced exclusively within black holecores from preceding cosmic cycles, where unphysical singularities are replaced bya finite Planck-density threshold (ρPlanck). Protected by a conserved topologicalwinding number W ∈ Z, these states are immune to perturbative decay. We introduce the Cyclic Distillation mechanism, showing how stochastic fluctuations within black holes break matter-antimatter symmetry across cycles, exhausting antimatter while leaving a residual baryonic fraction (∼ 15%) and an accumulating dark matterbackground. Under Loop Quantum Cosmology (LQC), the bounce density remains strictly lower than the black hole internal core density (ρbounce < ρPlanck). This Differential Stability Threshold ensures the dissolution of geometric event horizons and the liberation of ΦDM without disrupting its topological structure. The quantum gravitational wave energy released during horizon dissolution drives cosmic expansion and naturally reheats the universe without an inflaton field. Finally, we model intra-cycle accretion, demonstrating how progressive mass-spectrum shifts culminatein an eternal, entropy-resolving final collapse.
Category: Relativity and Cosmology
[9] ai.viXra.org:2609.0009 [pdf] submitted on 2026-09-05 21:55:36
Authors: Thiago Henrique Ramos da Mata
Comments: 13 pages. License: CC BY 4.0.
We define integer division and modulo by recursively normalizing quotient—remainder states and verify the construction in Scala Stainless. We prove uniqueness of the normalized solution, compatibility with native modulo for nonnegative dividends and positive divisors, invariance under shifts by multiples of the divisor, together with addition, subtraction, and modulo-idempotence laws. We also verify the unit-step quotient—remainder transition and that every block of $p$ consecutive nonnegative integers, for $p > 1$, contains exactly one zero remainder modulo $p$. Together, these results show that recursive normalization is canonical on the stated domains and recovers the verified algebraic and periodic laws of division and modulo.
Category: Number Theory
[8] ai.viXra.org:2609.0008 [pdf] submitted on 2026-09-05 21:57:18
Authors: Fabrizio Vassallo
Comments: 38 Pages.
Paper 3 of this series [1] left two companion problems open for the Diamond and Fan motifs it introduced. For the Diamond, whose exact quasi-equilibrium reduction gives a closed-form, generic, supercritical ip bifurcation at λ flip = ϵη/[2(η 2 − ϵ 2)], Open Problem D.1 asked for a coarse-graining operator under which this result could be tested for topology-dependence, on both the Diamond and the Fan, rather than accepted as a property of one small graph. For the Fan, the exact scale invariance of OllivierRicci curvature left three of its four independent weight ratios underde-termined by the curvature equations alone, so Paper 3's own treatment of the Fan was, by its own account, a calibration against two reported data points rather than a derivation. This paper reports genuine, but dierent, progress on each. For the Diamond, we build the recursive lattice obtained by replacing every edge, at every generation, with a fresh copy of the same ve-edge motif, and establish two exact local curvature laws that hold at every generation. Combining them gives a closed-form renormalized ip threshold and cubic normal-form coecient at general coarse-graining depth d, which reduce exactly to the bare Diamond's own values at d = 4 and ow smoothly to a nite, nontrivial xed point, (λ flip , c 3) → (ϵ/η, −4/3), as d → ∞: the ip is coarse-graining-stable, and the generation step is exactly a MigdalKadano coupling recursion on c 0 := 8/d, with c * 0 = 0 its unique xed point. The universal endpoint ξ * = 2 found in Paper 3 for the dissipative extension is shown to be universal across the entire generational hierarchy as well. Two honest obstructions a kink in the peripheral curvature law and an unresolved heterogeneity once the fully symmetric torsion ansatz is relaxed are reported rather than papered over. For the Fan, we resolve Paper 3's scale-invariance obstruction with a dierent separation of variables: using the curvature equations for exactly what they determine the weight ratios and the middle torsion as functions of the one remaining free torsion T s and deferring the absolute scale entirely to the torsion equations. Eliminating the scale between the latter gives a single equation in T s ; at the test value η/ϵ = 1/2, and after a log-reparametrization removes a spurious numerical artifact, this equation has a genuine root, located to machine precision. In the regime containing this root, all four curvatures admit exact closed forms unavailable to Paper 3 veried against the underlying optimal-transport computation to machine precision; combining two of them in the limit T m → ∞ turns the numerical coincidence into a proof that η/ϵ → 1/2 as α → 0. 1 Read together, the two results are asymmetric in a way worth stating plainly: the Diamond's single free weight admits a genuine multi-generation renormalization-group trajectory; the Fan's four coupled weight classes admit, for now, an exact reduction of the bare motif itself the prerequisite the Diamond's own program needed before any coarse-graining could be built, not yet that extension itself.
Category: High Energy Particle Physics
[7] ai.viXra.org:2609.0007 [pdf] submitted on 2026-09-03 23:14:35
Authors: J. W. McGreevy
Comments: 31 Pages.
This paper formalizes the Thermodynamics of Arithmetic Action (TAA) as a coordinate-free, unassailable geometric and field-theoretic architecture. By treating the sub-quantum vac-uum as an ad´elic fluid flowing over derived modular stacks, we prove that the macroscopic space-time fabric, the elementary mass hierarchies, and the gauge field interactions are uniquely determined by global number-theoretic invariants. The spontaneous breaking of the 24-dimensional primordial symmetry is shown to be a monodromy-driven factorization of an ad´elic stack, where existence and smoothness are rigorously verified at every infinitesimal step by the vanishing of relative obstruction classes in the cotangent complex. We demonstrate that the Standard Model gauge groups SU(3)×SU(2)×U(1) are the derivednon-abelian cohomological stabilizers required to absorb the exact 154 arithmetic discrepancybetween the discrete digital Extended Binary Golay Code (G24) and the continuous analyticalBernoulli numbers. Furthermore, we provide native, first-principles resolutions to the Riemann Hypothesis (RH), the Birch and Swinnerton-Dyer (BSD) Conjecture, and the Navier—Stokes Existence and Smoothness problem. The non-trivial Riemann Zeta Zeros are established as the exact, quantized resonant frequencies generated when the Golay code’s error-correcting parity matrix clamps the fluid wavefront to a Topological Exceptional Point wall. Spacetime remains globally differentiable, smooth, and unconditionally protected against quantum decoherence because its internal particle matrix is permanently, flawlessly phase-locked to the invariant genus-zero stabilizers of the ad´eles.
Category: Mathematical Physics
[6] ai.viXra.org:2609.0006 [pdf] submitted on 2026-09-03 17:11:35
Authors: Joseph Shaffer
Comments: 11 Pages.
Standard ΛCDM cosmology relies heavily on hypothetical components — namely cold dark matter and dark energy — to reconcile persistent kinematic anomalies and the apparent accelerating expansion of the universe. This paper introduces Photon-Tension-Time Theory (PTT), an alternative ontological framework establishing tension as the sole primitive of physical reality. Under PTT, the universe is non-expanding. The Big Bang is recontextualized not as a physical metric singularity, but as a global, non-metric phase change: a primordial crystallization that established an invariant background matrix termed the substrada. Cosmological redshift is demonstrated to be the localized, non-metric energy attenuation of propagating photons penetrating discrete structural boundary tension fields within this substrada, entirely decoupling the observed energy loss from metric time dilation. Furthermore, galactic rotation anomalies are shown to be stabilized by the baseline boundary tension of the substrada, rendering cold dark matter halos mathematically obsolete. Finally, the observed (1 + z) temporal elongation of distant Type Ia supernovae is resolved via wave-packet structural dispersion across cosmological propagation distances. PTT delivers an elegant, static cosmological model that resolves contemporary astrophysical tensions without invoking unobserved dark sectors.
Category: Astrophysics
[5] ai.viXra.org:2609.0005 [pdf] submitted on 2026-09-03 23:03:35
Authors: Prakash Vaithyanathan
Comments: 7 Pages. CC BY-NC-ND 4.0
When a very large AI model is trained, the training sometimes breaks on its own. The loss suddenly jumps up, the numbers inside the model become too large or too small to handle correctly, and the run has to be stopped and restarted from an older saved copy. This is called training instability, and on a large training run it can waste a very large amount of computer time and money. Earlier work in machine learning has shown that this kind of breakdown is closely tied to a single number: the sharpness of the loss surface, which is the largest eigenvalue of the Hessian matrix of the loss function. When this number grows too large compared to the learning rate, the training stops behaving smoothly. The problem is that for a model with a billion or more parameters, the full Hessian matrix cannot be built or stored by any realmachine: it would need far more numbers than there are atoms within reach. We show that this is not actually needed. A small hardware block can track the same leading eigenvalue using only the gradient vectors that the training hardware is already computing at every step, through a standard numerical method called power iteration, combined with the well-known fact that a Hessian-vector product can be estimated from the difference between two gradients without ever building the Hessian itself. We also show that watching a small, carefully chosen part of the model, rather than the whole thing, is often enough to catch the problem early. We describe a domain-blind hardware controller that watches this shrinking safety margin every single step and estimates how many steps remain before the run is expected to become unstable, so that a corrective action can be taken before the run actually fails rather than after.
Category: Artificial Intelligence
[4] ai.viXra.org:2609.0004 [pdf] submitted on 2026-09-02 03:17:37
Authors: Rolando Zucchini
Comments: 43 Pages.
After circa 2300 years (Circle Quadrature, Archimedes, Syracuse 287 — 212 BC) the history of mathematics repeats itself in a different problem. This paper presents an original research on the Syracuse Conjecture. It proposes a theoretical development aimed at solving the conjecture through a systematic approach. One of its features suggests a process that leads to Theorem 2n+1, whose demonstration subdivides the odd numbers into seven subsets which have different behaviors applying algorithm of Collatz. It allows to replace the Collatz’s cycles with the cycles of links, transforming oscillating sequences into monotone decreasing sequences. Theorem of Independence allows to manage the cycles of links to our liking to reach very high main horizons and, when we decide, go back to lower horizons. In this article it’s proved that Collatz Conjecture is not fully demonstrable. In fact, if we consider the banal link n < 2n, there are eight cycles which connect each other in an endless of possible sequences and related links. It is a new type of Squaring of the Circle or Algebraic Quadrature, but its statement is confirmed. In other words: BIG CRUNCH (go back to 1) is always possible, but BIG BANG (to move on) has no End.
Category: Number Theory
[3] ai.viXra.org:2609.0003 [pdf] submitted on 2026-09-02 18:16:51
Authors: Raymond Deiotte
Comments: 42 Pages.
Agent-facing knowledgebases compute confidence and provenance at answer time, as properties of the re- sponse. This paper argues that is too late, and that the argument is not a matter of engineering quality: information about whether a claim is true enters through the primary record, and every later stage is a rendering of that record, so no downstream scoring can add a bit that the record did not already carry. Confidence computed from the exhibit has an evidential ceiling fixed before it runs.We describe the store that follows from taking that seriously. The substrate is an uncertainty-typed property hypergraph: every unit carries the same five fields, a knowledge type, provenance graded on a four-valued lattice and carrying a validity horizon, the condition under which the entry held, a version with its conflict history, and a confidence separated into write-time and serving-time quantities, and relations are hyperedges because the relations that matter in agent memory are irreducibly n-ary and reifying them into binary edges destroys exactly the structure later stages need. On that substrate we specify three mechanisms. Consolidation is gated on whether a merged region still decomposes into the inferences it was meant to support, a structural and label-free test that needs no paired QA data and no per-environment training. Conflict is preserved through four lifecycle primitives, demotion, supersession, revocation and invalidation, of which three share a single inverse transition and revocation deliberately has none. Retrieval returns a coverage-guaranteed evidence subgraph with the guarantee conditional on the type of edge retrieved rather than marginal over a query distribution, and it answers with three outcomes rather than one score: supported, insufficient, refuted.The paper’s most portable result is a criterion for when two memory mechanisms can affect each other at all: only where one writes a property of the store that the other reads, at a granularity they share. The criterion is checkable from the specifications before anything is built, it discriminates rather than merely predicting failure, and it carries a stated falsifier.
Category: Artificial Intelligence
[2] ai.viXra.org:2609.0002 [pdf] submitted on 2026-09-01 20:28:01
Authors: Adilson Gonçalo
Comments: 36 Pages. In Portuguese
This article inaugurates a series dedicated to the theme "Space-Time" from a Realist Perspective. The aim of the series is to carry out a critical analysis of the Lorentz transformations and, consequently, of theTheory of Special Relativity (SR), while proposing an alternative conceptual approach to space-time grounded in principles considered more consistent with observable physical reality In this first part, the physical, mathematical, and logical foundations associated with the Lorentz transformations are examined,with emphasis on the conceptual and kinematic aspects of their construction. The article begins with a concise presentation of the theory and its fundamental equations, followed by an analysis of the points that, according to this approach, raise questions regarding the conceptual consistency of the relativisticformulation. It should be emphasized that this stage of the work focuses exclusively on the theoretical and conceptual structure of SR. The discussion of experimental and observational aspects will be addressed in the third part of the series. Although the considerations developed in this work are mainly focused on SR,they will also address certain conceptual aspects of the Theory of General Relativity. It is important to note that the considerations presented here are not intended to diminish the fundamental contributions of the creators of Special and General Relativity, among whom Henri Poincaré, Hendrik Lorentz, and Albert Einstein stand out.
Category: Relativity and Cosmology
[1] ai.viXra.org:2609.0001 [pdf] submitted on 2026-09-01 20:25:22
Authors: Nigel B. Cook
Comments: 16 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references in the field!)
This paper presents three independent and mutually reinforcing theoretical derivations of the Higgs boson mass within the SU(4) vacuum polarisation framework. Each derivation is physically motivated, mathematically explicit, and avoids circular reasoning. The first derivation is the Coulomb-Yukawa vacuum polarization absorbed energy redistribution method, in which the scalar mass arises from the curvature of an effective potential generated by fluctuations in the electromagnetic partition between long-range Coulomb and short-range Yukawa channels. The second derivation is a two-channel SU(4) binding analysis in which the Higgs is the lowest scalar eigenmode of a neutral/charged weak-boson bilinear system. The third derivation is an SU(2) spectral method based on representation weights of the compressed SU(2) vacuum. All three approaches converge on 125-126 GeV. The agreement among these methods strongly supports the interpretation of the Higgs boson as a composite excitation of the SU(2) vacuum. (This paper has been fully proof-read and corrected by Copilot AI to make it more readable than the draft.)
Category: Quantum Gravity and String Theory