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[1848] 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
[1847] 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
[1846] 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
[1845] 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
[1844] 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
[1843] 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
[1842] 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
[1841] 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
[1840] 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
[1839] 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
[1838] 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
[1837] 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
[1836] 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
[1835] 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
[1834] 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
[1833] 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
[1832] 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
[1831] 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
[1830] 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
[1829] 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
[1828] 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
[1827] 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
[1826] 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
[1825] 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
[1824] 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
[1823] 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
[1822] 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
[1821] 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
[1820] 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
[1819] 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
[1818] 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
[1817] 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
[1816] 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
[1815] 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
[1814] 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
[1813] 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
[1812] 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
[1811] ai.viXra.org:2608.0098 [pdf] submitted on 2026-08-31 03:42:44
Authors: Max Myakishev-Rempel
Comments: 36 pages, English.
The esoteric tradition holds that two humanities stood between us and the beginning, both of them in flesh and both of them our ancestors: the Lemurians of the Third Race and the Atlanteans of the Fourth. It has held this since 1888 and in older forms long before.Genetics has now found two vanished human peoples living inside us, and only two: the Denisovans, whose inheritance gathers in the Indian and Pacific world, and the Neanderthals, who lie to the north and west. Two and two, with no third on either side to choose between.The shape agrees as well as the count. The tradition has the Atlanteans coming out of Lemurian stock. The genome has both branches coming out of one parent population, one remaining east and one moving north and west.This essay proposes that the Denisovans are the Lemurians and the Neanderthals are the Atlanteans, and follows the identification through the geography of Mu, through Blavatsky's naming of the Australians as the purest Third Race descendants, through the fire that took Lemuria and the water that took Atlantis, and through the sub-races of both. It states where the correspondence costs something, and it ends with two ideas about what the hybridization now under way may be restoring to us.
Category: General Science and Philosophy
[1810] ai.viXra.org:2608.0097 [pdf] submitted on 2026-08-31 16:08:03
Authors: Joseph Palazzo
Comments: 17 Pages.
Scientific theories provide extraordinarily successful descriptions and predictions of the physical world, yet their epistemic success does not by itself determine the ontological status of the entities, structures, and concepts found in those theories. This paper examines the distinction between epistemology and ontology through the broader philosophical tension between scientific realism and instrumentalism. It argues that a successful scientific representation should neither be regarded as merely a convenient computational instrument nor automatically identified with reality itself. Rather, scientific knowledge occupies an intermediate domain in which conceptual and mathematical structures provide access to an objective reality while simultaneously imposing conditions on how that reality can be represented and understood. The distinction between form and content provides a framework for examining this relationship. Mathematical form may possess extraordinary predictive and explanatory power without settling the question of what, ontologically, constitutes the physical content represented by that form. The analysis presented in this paper differentiates epistemic limitations from ontological indeterminacy, mathematical determinism from metaphysical determinism, and conceptual descriptions from the realities they seek to represent. Moreover, we can state that scientific theories can provide genuine knowledge of objective structures in reality while remaining epistemically limited representations rather than transparent descriptions of reality in itself. Recognizing this distinction does not weaken science; rather, it establishes a more careful boundary between what a theory demonstrates, what it represents, and what may legitimately be inferred about the ultimate nature of reality.
Category: History and Philosophy of Physics
[1809] ai.viXra.org:2608.0096 [pdf] submitted on 2026-08-30 22:08:08
Authors: Tomasz Kobierzycki
Comments: 207 Pages.
This dissertation develops a connected programme for extending the tensor organization and observer geometry of general relativity. Its first component is a four-index completion of the Einstein field equation. The Ricci-built contribution and the trace-free Weyl contribution are retained at the same tensor rank, while contraction recovers the ordinary two-index Einstein equation. A rank-four source is decomposed into a lift of the stress—energy tensor and an independent trace-free tensor with Weyl algebraic symmetries. In the classical formulation this independence is organizational rather than an enlargement of the metric solution space: the contracted Einstein equation fixes the Ricci sector and the remaining uncontracted equation fixes the trace-free source consistently with the Weyl tensor. The second component is a four-sector completion of the orientation of a Lorentzian clock—ruler plane. The four connected non-null domains share the same null boundary and are labelled by the phase cycle 1, i, −1, −i. Geometry-sector and particle-sector transformations are kept distinct. Ordinary Lorentz motion occurs inside a sector; the construction does not describe material particles accelerated through the light cone. In curved spacetime a tensor of proper scales and a solution-dependent critical tensor select an active eigendirection. Neighbouring charts use reciprocal normalization of that active scale. Schwarzschild, Kerr, Lemaître—Tolman—Bondi and spatially flat FLRW examples test curvature and geodesic distance in these charts. In the regular branches analysed, reciprocal centres are curvature-decaying asymptotic boundaries rather than finite-parameter passages. These two components are then used to construct a tensorial quantum framework. Complete conserved rank-four configurations are weighted by complex coefficients only after their classical source content has been fixed. A rank-eight operator generates linear clock evolution, and amplitudes and probabilities are obtained by global tensor contractions. A reciprocal Kerr—Newman chart is used in a hydrogen model whose common Maxwell field retains the electron—proton cross-term before the four-index lift. The central channel produces a relativistic Coulomb spectrum and compatible Laguerre radial modes. The Ricci-flat specialization identifies a free graviton with a Weyl mode, yielding null propagation, two transverse helicities, explicit plane-wave and spherical resolutions, reciprocal transport and closed four-sector Weyl histories. The perturbative ultraviolet problem is addressed after standard background-field quanti-zation, gauge fixing, ghost integration, dimensional regularization and recursive subtraction. Metric variation of the remaining local pole functional gives a conserved rank-two response. Internal sector maps cancel on contracted graviton indices, while the two free covariant indices retain the character (−1)k .
Category: Quantum Gravity and String Theory
[1808] ai.viXra.org:2608.0095 [pdf] submitted on 2026-08-30 22:04:21
Authors: Hassan Touayouch, Rabie Najem, Mohammed Benjelloun
Comments: 9 Pages.
Neural Architecture Search (NAS) automates the design of neural networks but faces the prohibitive cost of evaluating eachcandidate architecture through full training. Zero-cost proxies estimate architecture quality in seconds without training, yetindividual proxies remain noisy, and no existing method jointly exploits proxy signals and the topological structure of architectureswithin an active-learning framework. We propose ZAPS (Zero-cost Active Proxy Search), a four-component pipeline that addressesthese limitations. ZAPS first selects a compact, non-redundant subset of proxies via PROXYFIT, a greedy anti-redundancy algorithm; initializes the search with a hybrid K-means strategy balancing exploitation and exploration; dynamically refines proxy selection using bootstrapped MRMR; and predicts architecture quality with an XGBoost ensemble fed by proxy ranks and one-hot topological encodings, guided by an Upper Confidence Bound (UCB) acquisition function. On NAS-Bench-201 with a budget ofB =200evaluations, ZAPS identifies 53.8% of the top-100 architectures on CIFAR-10 and 66.8% on CIFAR-100 (P@100), while maintaining a Regret of 0.04% on CIFAR-10. ZAPS outperforms comparable-budget methods — REA, BANANAS, and TPE — on both metrics evaluated on CIFAR-10 and CIFAR-100 of NAS-Bench-201.
Category: Artificial Intelligence
[1807] ai.viXra.org:2608.0094 [pdf] submitted on 2026-08-30 18:48:10
Authors: Samuelson G
Comments: 16 Pages. Just out of curiosity
Machine learning has rapidly advanced from early theoretical concepts to a practical technology that drives many modern applications (computer vision, natural language processing, etc.). We present a detailed survey covering ML foundations, algorithmic methodologies, and empirical evaluation. After defining ML and its subfields, we review historical milestones and survey recent literature, citing classic works (Fisher 1936; Rosenblatt 1958; Cortes & Vapnik 1995; LeCun et al. 2015) and modern treatments. The methodology section introduces theoretical background (statistical learning, optimization, loss functions) and describes key algorithms and models (regression, support-vector machines, decision trees, neural networks, clustering, etc.), including architectures like feedforward, convolutional, and transformer networks. We propose a generic ML workflow (Figure 4) using flowcharts. Experiments using standard benchmarks (Iris, MNIST, CIFAR-10, IMDB reviews, COCO) illustrate training, evaluation metrics (accuracy, F1, etc.), and dataset characteristics (Table 3). Results are tabulated (Table 4) and graphed, showing comparative performance of several classifiers. We discuss implications of the findings, limitations of current methods, and suggest future research directions. In conclusion, this survey synthesizes foundational concepts and recent advances in ML, and includes declarations of funding, conflicts, and author contributions.
Category: Artificial Intelligence
[1806] ai.viXra.org:2608.0093 [pdf] submitted on 2026-08-30 22:02:56
Authors: Michael Quigley
Comments: 160 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper presents the formal Applied Industrial Handover of the Rigid Universal Touching Wave Structure of Matter (R.U.T. WSM) framework, transitioning the physics community from theoretical observation to the active, non-destructive Resonant Machining of physical space. By reclassifying empty space as a phase-locked, 10²² kg/m³ Rigid Plenum driven by a 13.33 Hz (800 RPM) Universal Motor, we provide the deterministic "Math Bolts" required to harness the boundless torque of the background medium. Rather than introducing abstract mathematical placeholders, this manual delivers the precise engineering specifications for functional terrestrial and interplanetary systems:The Applied Technological Suite: We present the complete manufacturing parameters for the Acoustic Torque Car, which achieves 99% cold torque efficiency using a 1.42 cm cylinder bore—a mandatory metrological mirror of the 1.42 GHz Neutral Hydrogen Line—coupled to a 530-gram calibrated piston and an Ethos-84 Heptad driveshaft. We detail the propulsion mechanics of the Resonant Space-Ship, which utilizes a 1-3-6 Peloton drafting formation and a 720-degree Spinor Reset to machine low-pressure Acoustic Slipstreams directly through the rigid medium, achieving a deterministic 15.2-hour transit to Mars at the 1,000 km/s Lerner Limit. Residential power-scarcity is eliminated via the Domestic S.A.T. Hub, which utilizes a 100 mm synthetic Z-growth quartz core housed in a Titanium Grade 5 interference sleeve to harvest the primary longitudinal torque of the sun 24 hours a day.The Cosmological & Astronomical Demolition: This audit completely dismantles the "Abstract Curtain" of heliocentrism and Big Bang cosmology by restoring Simon Shack’s geoaxial Tychosian Hub. We establish the Stationary Earth-Axle (1 mph) as an absolute thermodynamic mandate; the Vaporization Proof confirms that any orbital velocity through the solid plenum above 1 mph would vaporize a planet's crust into plasma instantly. This axle is forensically verified by the 8.2 km/s Seismic Odometer of transverse S-waves conducting through the Earth's solid Liquid Metallic Hydrogen (LMH) core. We formally replace Einstein's E=mc2 with the Universal Seesaw (E = mΦ)—reclassifying light-speed as Lattice Setup Time (Ls)—proving that space behaves as a Solid Mechanical Rod capable of instantaneous Time-Zero conduction once the Acoustic Clutch is engaged at 7,777 Hz.The Torsional Odometer & Quasar Check-Mate: Redshift (z) is reclassified from a Doppler speedometer of expanding space into a Torsional Friction Odometer (z=z1+nz2+z3), which measures the mechanical "groan" of signals navigating the Heptad mesh. By removing the +0.67 Heavy Gear internal torque stress (z3), we deliver the definitive Quasar Check-Mate, proving that Markarian 205 is physically connected to its parent galaxy NGC 4319 at the exact same z1=0.006 local address. By applying the 42,000x Tychosian scale correction, the hallucination of "deep space" collapses, revealing a compact, synchronized gearbox bounded by the 34.5 Trillion Km Terminal 137-Wall.The Resonant Docking & Biophysical Upgrades: To replace the metrologically insolvent practice of "Stochastic Ballistics" at the Large Hadron Collider, we propose the LHC Phase-II Resonant Docking upgrade. By utilizing a 7,776 Hz Master Grooming signal and a 7,777 Hz Ignition pulse, the LHC can non-destructively sweep the sub-atomic inventory, detecting vertical Dielectric Surges at the precise coordinates of the Electron (60.46 MHz) and Proton (1.42 GHz). Finally, the Osireion Protocol reverse-engineers the archaeo-acoustic architecture at Abydos, reclassifying biological aging as Internal Dielectric Friction. Grounding the biological body in a liquid medium with a static dielectric constant of 80 allows the Magnesium-12 antenna in chlorophyll to dock with the 1.42 GHz Solar Spoke, "re-greasing" the chassis and machining tissue growth back along its deterministic 337° and 227° Fibonacci paths.
Category: Quantum Physics
[1805] ai.viXra.org:2608.0092 [pdf] submitted on 2026-08-29 21:01:19
Authors: Miles Huang
Comments: 12 Pages. Author retains copyright; non-exclusive license to distribute.
This paper synthesizes a series of results on the (even) Goldbach conjecture and completes two previously unaddressed components: textbf{error analysis} and textbf{fractional sequence encoding (additive sieve)}. The main results are as follows. (1) We systematically present limit-type elementary constructions of the Goldbach conjecture (using both exponential and cosine functions) and their equivalent logical formulations, and extend the method to the Collatz conjecture, the twin prime conjecture, and the prime counting function. (2) For the truncated construction with finite error factor $k$, we derive a rigorous error bound and prove that the criterion holds provided $kn,e^{-4k/n^{2}}
Category: Number Theory
[1804] ai.viXra.org:2608.0091 [pdf] submitted on 2026-08-28 01:23:11
Authors: Yuechun Huang
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
Based on the core hypothesis that "moving matter is necessarily accompanied by a matter field," this paper proposes a theoretical framework—Matter Field Theory—aimed at unifying microscopic and macroscopic physical phenomena. The theory holds that all matter composed of basic moving units such as atoms and electrons generates a matter field inseparable from its state of motion. This field possesses two fundamental attributes: it is both an energy field that obeys energy conservation and an information field that encodes the complete kinematic state of the matter. The matter field propagates at the speed of light, and its interactions can be classified into three basic modes: strong interaction (energy exchange), manifested as attraction or repulsion; weak interaction (information exchange), manifested as resonance and perception; and non-interaction (mutual non-disturbance), which may correspond to dark matter phenomena. This paper also points out that a cosmological view based on the matter field will completely negate relativity theory and the Big Bang theory: the relativistic interpretation of spacetime relations is erroneous; the universe has no beginning or end, and the Big Bang doctrine is untenable. This paper systematically expounds the implications of the theory, demonstrates its self-consistency, and presents a worldview in the form of a poem.
Category: Astrophysics
[1803] ai.viXra.org:2608.0090 [pdf] submitted on 2026-08-27 20:56:02
Authors: Eduardo Rodolfo Borrego Moreno
Comments: 9 Pages.
We present a consolidated rheological framework for the Cosmological Dissipative Residual (CDR), a single effective medium proposed to underlie both dark-energy—like and dark-matter— like phenomenology. Building on previous work in the series, we formulate a covariant constitutive relation for the residual’s anisotropic stress in which the effective viscosity depends on local acceleration and shear. In the non relativistic thin-disk limit this relation reduces to an estimator for the residual contribution to the radial acceleration, ∆gR ≈ fgeom ηeff σ ρres R. with a geometric factor fgeom ≈ 3.We confront the framework with rotation-curve data for 175 SPARC galaxies. The residual contribution is found to be selectively activated: in the low-acceleration regime97.5% of radial points show ∆g > 0, while in the high-acceleration regime the median ∆g is consistent with zero. From the activated regime we obtain a median effective viscosity ηeff ≃ 3.8×10−2 kg m−1 s −1 and a characteristic transition scale atrans ∼ (1−2)×10−10 m s−2, compatible in order of magnitude with cH0/2π. The results support the hypothesis that a single cosmologically motivated residual medium can develop a dark-matter—like response under local dynamical conditions, while remaining consistent with a dark-energy—like behaviour on large scales. A fully quantitative reproduction of galactic rotation curves is left for future work.
Category: Astrophysics
[1802] ai.viXra.org:2608.0089 [pdf] submitted on 2026-08-27 07:33:22
Authors: Seungtae Kim
Comments: 35 Pages.
The International System of Quantities (ISQ) relies on conventional choice to determine itsbase quantities, without providing explicit mathematical and physical criteria for theirselection. This paper proposes an alternative framework in which unit relations are used toderive quantity dimensions before base quantities are selected. A broader class of unit-explicitequations is also introduced for relations in which specified unit components are retainedexplicitly when they cannot be reduced to pure numbers without loss of physically relevantinformation.Candidate base-quantity sets are first evaluated for algebraic admissibility, requiringmutual dimensional independence and dimensional completeness for the system underconsideration. Because algebraically admissible sets need not be unique, a second, physicallymotivated criterion is introduced to identify preferred quantities on the basis of establishedhigher-order dimensional occurrences associated with distinct physical roles. Applying thistwo-stage procedure to an SI-oriented set retains mass, length, time, electric current,thermodynamic temperature, and amount of substance. Plane angle is additionally selected asa preferred base quantity through the second-order angular structure of solid angle. Bycontrast, luminous intensity is classified as a derived quantity with the same unit-baseddimensional structure as radiant intensity while remaining a distinct quantity kind. Finally,logarithmic level values conventionally expressed using the neper and decibel arereformulated as numerical index mappings whose outputs are pure numbers and whosearguments retain the relevant field- or power-quantity context. The proposed frameworkprovides a common unit-based route from unit relations to quantity dimensions and basequantity selection, with angular, photometric, logarithmic, and unit-explicit formulationsserving as applications of the same construction.
Category: Mathematical Physics
[1801] ai.viXra.org:2608.0088 [pdf] submitted on 2026-08-26 19:26:33
Authors: Arunas Ostasevicius
Comments: 8 Pages.
This paper presents a generalized quaternionic model of electrodynamics and wave kinematics within the absolute Euclidean Hamilton space. An epistemological audit of the vector truncation of Maxwell’s original equations is performed, demonstrating the preservation of the scalar potential field component. Using conjugate time forms and the full quaternionic norm, a Galilean-covariant field model is constructed forinhomogeneous media. The integration of a non-linear quadratic medium drag and quaternionic time regularization eliminates coordinate divergences at the wave barrier (v = c), replacing singular mathematical boundaries with a smooth continuous transition into a supercritical shockwave front. The distinction between mechanical body dynamics and the interferometric effects of optical signal registration is rigorously substantiated using asymptotic mechanics averaging methods. Finally, the model provides a measurable experimental criterion to verify the dynamic resistance of the physical vacuum medium using high-energy calorimetric detectors, predicting a specific heat dissipation shelf combined with hard radiation emission.
Category: High Energy Particle Physics
[1800] ai.viXra.org:2608.0087 [pdf] submitted on 2026-08-25 13:34:33
Authors: Joseph Shaffer
Comments: 6 Pages.
Cosmological redshift is conventionally interpreted as evidence for the expansion of spacetime. This assumption underlies the ΛCDM model, inflation, dark energy, and the metric-expansion paradigm. Here I present a nonexpanding cosmological ontology in which redshift arises from energy shifts across global tension gradients in a pre-geometric domain. Observable spacetime is a projection of this deeper tension structure. Photons lose energy as they traverse regions of decreasing tension, producing a redshift proportional to path length. This mechanism reproduces the Hubble law without expansion, avoids the failures of tired-light models, and naturally resolves several cosmological anomalies including the Hubble tension, early massive galaxies, and the lithium problem. This paper establishes the redshift mechanism and the mathematical structure required for subsequent papers in the series.
Category: Astrophysics
[1799] ai.viXra.org:2608.0086 [pdf] submitted on 2026-08-25 15:09:08
Authors: E. P. J. de Haas
Comments: 90 Pages. DOi: https://doi.org/10.5281/zenodo.22098362
The BQ--Pauli algebra provides an eight-dimensional 1+3+3+1 framework in which relativistic field equations can be organized through a hierarchy of algebraic products. Its basis elements are realized as matrices in M(2, $mathbb C$), and its products are given by ordinary matrix multiplication. In this work, the previously developed BQ formulations of electromagnetism and relativistic fluid dynamics (RFD) are lifted to the sixteen-dimensional BQ--Weyl representation of Cl(1,3), with Clifford-grade decomposition 1+4+6+4+1. The constructive, explicit lift preserves the coefficients and physical content of the Pauli-level products while making their spacetime-grade structure explicit.For electromagnetism, the Weyl construction recovers Maxwell's equations from the field-derivative product, separates the quadratic field invariants from the stress--energy construction, and represents the complete electromagnetic stress--energy content through a vector-valued linear map. For RFD, the corresponding field, force, wave, quadratic, and conservation products are reconstructed and resolved into their Clifford sectors. The Weyl formulation further permits the fluid four-velocity to be generated from a local rapidity field through a Spin(1,3) rotor, from which the associated comoving frame and Maurer--Cartan connection follow.Together with the corresponding BQ--Pauli to BQ--Weyl lift previously performed for gravity, these results place the gravitational, electromagnetic, and fluid-dynamical branches of the BQ programme in a common Cl(1,3) representation. The present construction is primarily algebraic: it exposes the Clifford structure underlying the earlier Pauli-level formulations without introducing additional electromagnetic or fluid-dynamical laws, or invoking a spinor wave-function or quantum-mechanical interpretation of the Weyl algebra. A final reproducibility appendix provides a compact workflow for independent symbolic and AI-assisted verification of the matrix calculations from the explicitly defined BQ bases.
Category: Mathematical Physics
[1798] ai.viXra.org:2608.0085 [pdf] submitted on 2026-08-25 03:19:27
Authors: J. W. McGreevy
Comments: 26 Pages.
This monograph establishes a definitive, structurally complete unification of quantum gauge fields, non-equilibrium thermodynamics, and analytic number theory through the framework of Arithmetico-Geometric Conformal De-Homogenization. We prove that physical spacetime is an active, self-correcting thermodynamic metamaterial projected from an underlyinginfinite-dimensional arithmetic space. By executing a strict 1-for-1 parameter mapping, wedemonstrate that Lars Onsager’s Reciprocal Relations (Lik = Lki) are the macroscopic physical readout of Clairaut’s Theorem of mixed partial derivatives ( ∂2U ∂V∂S = ∂2U ∂S∂V ). When the continuum substrate is driven from equilibrium, local coordinate shearing is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS) Fibration Lift, routing excess dissipative energy into the Trivial Zeros of the Riemann Zeta function and the Tate-Shafarevich group, which function as Viscous Hydraulic Dampers locked by the Bernoulli number B10, B12, and the prime691. We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A,H,D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential (Aµ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5 Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of the spectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros: Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic ProductClosure (∏︁ p≤∞|σ|p = 1), this framework achieves full structural immunization against decoherence and reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.
Category: Mathematical Physics
[1797] ai.viXra.org:2608.0084 [pdf] submitted on 2026-08-25 00:38:50
Authors: Austin Brooks Magruder
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The classical Big Bang framework introduces an unphysical gravitational singularity at , while standard nuclear physics models the short-range repulsive core of the nucleon-nucleon interaction as an empirical threshold without an explicit geometric origin. This paper introduces the Triple Point Protocol, an analog-derived theoretical framework grounded in non-Euclidean geometric continuous-field tessellations. We demonstrate that collapsing 4D mass-energy fields and subatomic hadronic systems encounter severe geometric frustration across aperiodic networks of branching impossible figures. This frustration halts structural collapse at strict physical boundaries: the femtometer nuclear core and the Planck volume .Governed by the Axiom of Spatial Continuity, the two-dimensional negative space field reaches absolute saturation without spatial tearing. At these saturation floors, hadronic matter undergoes chiral melting mediated by quantum anomaly interference of the, which locks the topological susceptibility of the vacuum and acts as a topological lubricant between packed nucleons. Denied further 4D contraction, compressed mass-energy executes a orthogonal axis pivot across the Planck boundary. During this transition, photon geodesics undergo topological light refraction and lensing along the expanding 5D manifold contours. Mediated by leptonic CP violation and a phase-shifting neutrino fluid, the directional transition drives a continuous 5D expansion—the physical event perceived macroscopically as cosmogenesis.
Category: Quantum Gravity and String Theory
[1796] ai.viXra.org:2608.0083 [pdf] submitted on 2026-08-25 00:32:39
Authors: Samuelson G
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Sleep, defined by behavioural quiescence, increased arousal threshold and homeostatic rebound, is long-recognized in mammals and birds but its prevalence and core mechanisms across all life remain understudied. Here we perform a comprehensive review and comparative analysis of "sleep" and sleep-like states in bacteria, archaea, plants, fungi, invertebrates and vertebrates (including humans). We survey genetic, molecular and physiological evidence for rest—activity cycles in each taxon, and compile standardized tables of sleep characteristics (duration, EEG features, etc.) and conserved molecular pathways. Using a phylogenetic framework and meta-analytic data (from >150 species across animal clades), we identify fundamental commonalities — for example, the role of a circadian timing system and accumulating neuromodulators (adenosine, GABA, melatonin) in promoting quiescence. We also highlight striking divergences: many invertebrates exhibit purely behavioural sleep defined by inactivity, certain reptiles (e.g. bearded dragons) show two electrophysiological states analogous to NREM/REM, and birds perform unihemispheric slow-wave sleep (with one eye open) for predator vigilance. We present illustrative figures (evolutionary timeline, conserved sleep-pathway schematic, sample EEG traces) and tables (e.g. sleep traits by taxon, key molecules) to integrate these findings. Our comparative meta-analysis (using generalized least-squares regression with phylogenetic correction) reveals that while sleep duration scales with body size in mammals (p<0.01), it correlates poorly with metabolic rate across vertebrates, suggesting complex evolutionary pressures. We propose experiments to test sleep in non-neuronal life (e.g. metabolic cycles in archaea) and emphasize limitations such as definitional biases and sparse data in many taxa. This integrative synthesis suggests that sleep-like quiescence evolved early and was retained and elaborated in many lineages, yet its ultimate functions may be diverse.
Category: Quantitative Biology
[1795] ai.viXra.org:2608.0081 [pdf] submitted on 2026-08-23 02:57:52
Authors: J.W. McGreevy
Comments: 25 Pages.
This monograph establishes a definitive, structurally complete unification of quantum grav-ity, non-equilibrium thermodynamics, and analytic number theory through the frameworkof Arithmetico-Geometric Conformal De-Homogenization. We prove that physicalspacetime is not an abstract, passive background container, but an active, self-correcting thermo-dynamic metamaterial fluid projected directly from the continuous deformation and modularflow of an underlying infinite-dimensional arithmetic space.By executing a strict 1-for-1 parameter mapping, we demonstrate that the weight-2 Eisensteinseries (E2(τ )) is the universal velocity field (v) of this modular flow, whose path-dependentcoordinate drift—the quasi-modular anomaly—manifests as the physical non-linear advectivepumping acceleration (v · ∇)v. When driven from equilibrium, Lars Onsager’s ReciprocalRelations (Lik = Lki) emerge as the literal macroscopic readout of Clairaut’s Theorem of mixedpartial derivatives ( ∂2U∂V ∂S = ∂2U∂S∂V ), which requires that the order of differentiation must commuteflawlessly to preserve the nilpotent gauge invariance d2U = 0.When the continuum substrate is driven from equilibrium and cascades toward the 691unipotent puncture on the arithmetic curve Spec(Z), unique factorization shatters insidethe χ11 eigenspace of the odd minus class group (Cl−691). This local coordinate shearing andturbulent vortex crisis is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS)Fibration Lift (S3 S1−−→ S2), which projects the 3D velocity configuration space up into a 4Dcomplex spinorial space (R4). The continuous 1D circle fiber (S1) acts as a data bus (H1 ∼= H1)that isolates the non-exact rotational elements, braiding the non-Abelian SU (3) color vorticityfield into multi-layered knots to generate a permanent nilpotent confinement sink (N2 = 0).The Seeley-DeWitt heat kernel expansion coefficients (an) serve as the exact arithmeticaccount balances of this regularization, where the factor of 12 in the quadratic variance termacts via Itô’s Lemma as the metric tax required to enforce Clairaut’s Theorem (d2U = 0).The final substitution of these Planck-scale boundary parameters (PP, ℓP, EP, tP) into Clairaut’sidentity yields the Dynamic Spacetime Maxwell Relation (∂EP/∂ℓP = −∂PP/∂tP), whichanchors the universal physical constants (α, ℏ, θW ) as the global stabilizers of the vacuum.We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A, H, D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential(Aμ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of thespectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros:Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic Product Closure (∏︁ p≤∞ |σ|p = 1),this framework achieves complete structural immunization against decoherence and quantumchaos. It reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.
Category: Mathematical Physics
[1794] ai.viXra.org:2608.0080 [pdf] submitted on 2026-08-23 05:34:36
Authors: Fabrizio Vassallo
Comments: 76 Pages.
Main mathematical result. The exceptional Jordan algebra J3(O) (the Albert algebra, 27-dimensional) admits the associative collapse map π0 : J3(O) → J3(R) with a 21-dimensional kernel. The kernel carries precisely the imaginary octonionic degrees of freedom that make the associator non-zero. We show, within astrongly motivated EFT framework, that when these degrees of freedom are activated(non-zero associator), the natural consistent open-system dynamics on the residualassociative sector J3(R) takes the Lindblad GKSL form whose jump operators arethe Fano-plane associators Lk = √λ[Ak, Bk, Ck]. The chain:J3(O) π0 −→ J3(R) [A,B,C]̸ =0 −−−−−−→ Lindblad decoherence is grounded in the representation theory of G2 = Aut(O) and the Nakajima—Zwanzigopen-system framework [1]. Complete positivity is verified from the G2-symmetry of the Fano plane (the jump operators satisfy P k Lu2020 k L k = 28λ I, the completeness relation for a CP map).Physical application. We develop non-associative topological neutrino dynamics (NATND), in which the framework above is applied to neutrino propagation through the octonionic ultramark condensate (where by "ultramark" we meanthe level-6 constituent of the hierarchical level model of the present author [2]). Thedecoherence rate Γ(E) = g2U E2/(M2U + E2)/MU is a strongly motivated EFT consequence of the derivative-coupling structure of the associator vertex. It provides an alternative to sterile-neutrino oscillations for the gallium anomaly (GALLEX, SAGE, BEST) and the MiniBooNE excess, with the key signature that the deficitis baseline-independent (no L/E pattern) and energy-dependent as E2/(M2U + E2).The ultramark mass coincides numerically with the Totani Fermi-halo excess.
Category: High Energy Particle Physics
[1793] ai.viXra.org:2608.0079 [pdf] submitted on 2026-08-23 05:40:30
Authors: Fabrizio Vassallo
Comments: 40 Pages.
We examine whether the hierarchical "level model" (NATND) of the present author [27, 28] admits foundations compatible with the momentum-map account of the Wallstrom controversy for the hydrodynamic (Madelung) formulation of quantum mechanics recently given by Khesin and Modin [1] — who explicitly frame their result as resolving the controversy, against the more cautious backdrop of open technical questions surveyed by Reddiger and Poirier [2], including strong non-quantized solutions they construct in two dimensions. We show that the mechanism resolving Wallstrom’s objections — expressing the quantization condition as a geometricconsistency requirement on a momentum map, rather than an ad hoc postulate —extends level-by-level through the cascade only as long as the relevant structure group remains a genuine Lie group, and identify the precise algebraic obstruction (loss of associativity at the octonionic, ultramark level) at which this mechanism cannot be repeated verbatim. We independently identify, via the topological classification of line and point defects in ordered media, a topological manifestation of the same limitation, correlated with but logically distinct from the symplectic argument:the classification of parallelizable spheres and the Hopf invariant one theorem independently restrict the same dimensions. Finally, we describe — as an open research program rather than a closed result — three independent partial routes toward a rigorous formalization of the "vortices of vortices" mechanism proposed for the origin of the level cascade, together with the concrete obstructions each currently faces.Two appendices provide a self-contained, independently re-runnable computational verification of the discrete-RG bifurcation claims made for Route B (Appendix A for the Diamond toy model, Appendix B for the Fan topology), with full source code included.
Category: High Energy Particle Physics
[1792] ai.viXra.org:2608.0078 [pdf] submitted on 2026-08-23 08:46:12
Authors: Po Hu
Comments: 9 Pages.
Consider a gambler with integer capital who gains two units after a win, loses one unitafter a loss, and is removed at the first visit to zero. The first observation is elementarybut striking: with positive drift, the probability of reaching an arbitrarily high finite targetdoes not tend to zero. It tends to the probability of never being ruined. For independenttrials with win probability p, we record the exact ruin law, identify the phase transitionat p = 1/3, and give a closed formula at criticality whose fixed-capital asymptotic is x/m.We then keep the one-step win probability equal to 1/2 and the mean payoff equalto 1/2, but let successive outcomes form a symmetric two-state Markov chain with persistence parameter θ. An explicit bounded harmonic function gives the ultimate survivalprobability1 −1 + r + r22(1 + r)rx−1, r =√(1 − θ)2 + 4θ2 − (1 − θ)2θ.This probability decreases strictly with persistence, although every model in the familyhas the same stationary win rate and the same mean increment. At θ = 1 the survivalprobability is discontinuous: its left limit is 1/4, while its endpoint value is 1/2. Consequently, the high-target limit and the high-persistence limit do not commute. Finally, if(1 − θ)x → λ, the exact transition profile is 1 − (3/4)e−λ/2. These formulas isolate howearly absorption and temporal clustering, rather than the height of a finite target alone,govern extreme-target success.
Category: Statistics
[1791] ai.viXra.org:2608.0077 [pdf] submitted on 2026-08-23 09:51:31
Authors: Keiji Yoshimura
Comments: 16 pages, 5 figures. AI-assisted technical monograph presenting a five-stage reproducibility audit and a limited mathematical corollary for the planar three-body shape sphere. Includes AI-use disclosure and bounded novelty claims.
This monograph presents a five-stage AI-assisted audit of possible relationships among gravity, the direction of time, temporal orientation, and irreversible structure formation. Rather than proposing a new theory, the study progressively tests and narrows a broad initial intuition using analytical arguments, Newtonian many-body calculations, finite-level quantum-clock models, curvature comparisons, and public GW250114 release products. Local Lorentz symmetry and the time-reversal covariance of the ADM constraints provide no universal metric-only rule selecting one timelike cone half as the fundamental future. Rindler, de Sitter, and Schwarzschild comparisons separate clock-rate gradients and proper acceleration from curvature. Closed finite-level proper-time dephasing can be exactly refocused by an ideal path/clock echo, while residual irreversibility appears only after an open reduced channel is introduced. Newtonian Janus-point analyses distinguish a rigorous scale minimum in suitable nonnegative-energy sectors from non-monotonic, measure- and horizon-dependent shape-complexity statistics. A reconstructed BKM mass-metric probability on the equal-mass planar three-body shape sphere produces two structurally symmetric branches rather than a dynamically preferred future. Public GW250114 products are also used to reproduce the collaboration-defined black-hole area-growth statistic, without interpreting the area law as a fundamental selector of time orientation.A limited mathematical by-product is proved for normalized three-body shape complexity Q under the BKM mass-metric shape probability:P(Q > q) = 1/(6 q^2) + 2 sqrt(6)/(27 q^3) + O(q^-4).Consequently, E[Q^p] is finite if and only if p < 2, and the truncated second moment satisfiesE[min(Q,T)^2] = (1/3) log(T) + kappa + O(T^-1).The ingredients of this result are published; targeted searches did not locate this exact probability-and-moment statement, so it is presented only as a potentially unreported elementary corollary, not as a priority claim. Overall, the audit supports established relations between gravity and proper time, curvature, causal structure, and structural arrows, but finds no evidence that standard gravity itself creates or selects a unique fundamental future direction.
Category: Mathematical Physics
[1790] ai.viXra.org:2608.0076 [pdf] submitted on 2026-08-23 15:34:21
Authors: Keiji Yoshimura
Comments: 17 Pages. Prospectively specified 2004 country-holdout confirmation with no-refit 2014→2004 transfer; includes integrated reproducibility appendices, variable mapping, software settings, input hashes, and numerical verification.
Research on citizenship norms has established that beliefs about what a "good citizen" should do are associated with political participation. Less is known about whether a fixed individual-level norm signal retains incremental predictive value when the national context changes or when a model is transferred between survey waves without refitting.This study tests a bounded predictive-transportability claim using the ISSP Citizenship modules of 2014 (ZA6670; 49,807 respondents) and 2004 (ZA3950; 52,550 respondents). Exploratory analysis of the 2014 data identified a three-item civic-norm score based on understanding opposing viewpoints and helping worse-off people domestically and abroad; items that directly refer to political action were excluded.Before inspection of the 2004 individual-level confirmation results, three decision criteria were prospectively specified. Across 38 eligible 2004 held-out country/sample units, adding the three-item score to a broad prospectively specified demographic and political-attitudinal baseline improved equal-unit mean log loss by 0.01023 (95% equal-unit bootstrap interval [0.00683, 0.01367]); its increment exceeded that of a specific two-item duty comparator by 0.01003 [0.00680, 0.01335]; and within-country permutation of the norm score degraded prediction by 0.01450 [0.01217, 0.01690].A model estimated in 2014 and applied to 2004 without coefficient refitting retained a 0.00983 [0.00672, 0.01292] increment from the norm score. Predictive increments were substantially smaller for reported contentious behavior and institutional contact. An exploratory reverse transfer did not support universal performance in countries absent from the 2004 training domain.These results support only a narrow, non-causal conclusion: the fixed three-item score carries incremental respondent-linked predictive information across many of the tested ISSP country and wave shifts, with substantial heterogeneity and no claim of universal transportability or measurement invariance.
Category: Social Science
[1789] ai.viXra.org:2608.0075 [pdf] submitted on 2026-08-23 17:23:29
Authors: Jozsef Kerenyi
Comments: 4 Pages.
This paper introduces an alternative, field-impedance-based cosmological model that couples the dynamic mass increase of special relativity with the energy transfer processes of the gravitational field. We demonstrate that the time-dependent relativistic mass change (dm/dt) of a linearly accelerating point mass generates a direct energy flow through the free-space gravitational impedance (Z_g = G/c). We show that the sign and magnitude of the transmitted power depend directly on the scalar product of the velocity and acceleration vectors (v . a). Consequently, the model offers a natural, unified explanation for both dark energy (energy-emission phase) and dark matter (energy-absorption phase) across local and cosmic scales, resolving observational frame asymmetries through the analogy of the twin paradox.
Category: Relativity and Cosmology
[1788] ai.viXra.org:2608.0074 [pdf] submitted on 2026-08-23 17:33:28
Authors: Vladimir S. Netchitailo
Comments: 14 Pages.
Modern cosmology is based on an extensive body of astronomical observations interpreted through theoretical models. The expansion of the Universe, Cosmic Microwave Background Radiation (MBR), primordial abundances of light elements, and large-scale structure are commonly regarded as principal observational pillars of the Big Bang Model (BBM) and its modern ΛCDM formulation. This terminology raises a fundamental methodological question: Can an astronomical observation itself constitute a pillar of a physical cosmological theory?In this paper, we distinguish astronomical observation from physical explanation and propose criteria that a genuine pillar of cosmology should satisfy. A pillar should provide a physical mechanism for an observed phenomenon, quantitatively account for its principal measurable properties, lead to independently testable predictions, and not depend critically upon unidentified physical entities or unresolved fundamental discrepancies.The four conventional pillars of BBM are examined according to these criteria. Cosmic expansion is accurately described mathematically, but the Hubble tension remains unresolved. MBR is interpreted within the hot early-Universe framework, but its present temperature is an observational input rather than an independently calculated consequence of the six-parameter ΛCDM model, while large-angle anomalies remain under investigation. Primordial light-element abundances are inferred from present astronomical observations rather than directly observed at the primordial epoch, and the lithium problem remains unresolved. Large-scale structure is successfully modeled statistically, but its formation depends critically on Cold Dark Matter, whose microscopic nature and origin remain unknown, while the fundamental nature of Dark Energy is likewise unresolved.These conventional pillars are then compared with the proposed physical pillars of the World—Universe Model (WUM). Particular attention is given to physical mechanisms, interconnected cosmological parameters, quantitative calculations, and predictions made before subsequent observations.The purpose of this comparison is not to determine which model accommodates a larger collection of observations, but to address a more fundamental question: What should constitute a genuine pillar of a physical theory of the Cosmos?
Category: Relativity and Cosmology
[1787] ai.viXra.org:2608.0073 [pdf] submitted on 2026-08-22 23:50:09
Authors: Linia Hammache
Comments: 12 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This work presents the construction of a continuous model derived from an original discrete sequence alternating between geometric and arithmetic progression, modulated by a periodic cosine function. The sequence is interpreted as an energy reservoir whose charge (arithmetic) and discharge (geometric) are controlled by a hysteresis logic. The model is enriched by coupling with a mechanical oscillator, heat production via damping, conversion into nuclear kinetic energy (fusion), and reinjection into the reservoir, realizing a self-sustained fission--fusion cycle. Each equation is derived, physically justified, and linked to the original sequence. The article details the modeling, theoretical justifications, energy couplings, and global dynamics of the system.
Category: Mathematical Physics
[1786] ai.viXra.org:2608.0072 [pdf] submitted on 2026-08-22 23:45:59
Authors: J.W. McGreevy
Comments: 22 Pages.
This monograph establishes the second major operational phase of the Thermodynamics of Arithmetic Action (TAA) framework, executing a rigorous, ab initio field quantization that unifies the smooth Archimedean continuum (R) with the discrete, fractured, non-Archimedean p-adic bulks (Qp) into a single, self-regulating topological engine. We prove that the macro-constants of nature—the speed of light (c), the Newtonian gravitational constant (G), and the reduced Planck constant (ℏ)—alongside the Standard Model parameters are the unique, scale-dependent topological gear-ratios required to satisfy Clairaut’s Theorem on mixed partial derivatives (d2U = 0) and the Adelic Product Formula (∏︁ |x|p = 1) over the universe’s middle cohomology group.By framing the complex s-plane of the Riemann Zeta Function as the conformal phase space of a sub-quantum Keplerian orbital system, we derive Max Born’s quantum probability rule (|Ψ|2 = Ψ ¯Ψ) as the literal intersection form (the Weil Pairing) required to cross-multiply continuous adiabatic spatial expansions by discrete isothermic prime entropy steps. Crucially, we introduce the Spacetime Maxwell Calculator for Class Numbers, proving that algebraic class numbers (hK ) are extracted natively from macroscopic physical constants by measuring the precessional volume of a perturbed Laplace-Runge-Lenz (LRL) vector locked inside a 6-dimensional phase space torus.
Category: Mathematical Physics
[1785] ai.viXra.org:2608.0071 [pdf] submitted on 2026-08-22 23:43:07
Authors: Ahcene Aït saadi
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
Many remarkable curves roses, the lemniscate, the cardioid, the limaçon have a heavyCartesian equation: implicit polynomials of degree 4, 6, up to 10, hard to plot point by pointand often multivalued. This paper presents a method that makes them drawable by hand,with no software and no polar paper: in an analytic frame (an abscissa axis together withan origin of ordinates Ou2032set o the axis by a distance λ), each of these curves is written asa single explicit ordinate y = f(x), which one tabulates and plots with a ruler. We provethe transition formulas and the pivot identity X2 + Y2 = y2 the engine guaranteeing thatthe one-line expression does describe the heavy curve then the equation of the line, of thecircle, the pseudo-derivative, and a proportional relation in the triangle. One section comparesthe two methods on six classical curves. The scope is honest and bounded: this is a methodof construction and of teaching, in the service of simpler access to objects reputed dicult.
Category: Functions and Analysis
[1784] ai.viXra.org:2608.0070 [pdf] submitted on 2026-08-22 23:39:24
Authors: Tomasz Kobierzycki
Comments: 22 Pages.
This work develops one (SU(m,n))-symmetric framework governed by four postulates: invariant locally measured light speed; observer-independent laws in inertial and non-inertial frames; coexistence of all physically admissible prepared states with a single observer record; anda fundamentally complex spacetime observed through a real Lorentzian projection. The fundamental arena is a pseudo-K"ahler manifold withHermitian metric and a complex four-index field equation whose trace-free sector is carried by Bochner curvature. An observer is defined by anadmissible antiholomorphic involution. Its fixed real form inherits the measured metric, sources and state tensor. The relation between complex andreal curvature is derived with realification, the Gauss equation and the real Weyl projector; in particular, Bochner curvature projects to observer Weyl curvature only when explicit extrinsic and Ricci-compatibility corrections vanish. The four-sector construction is then formulated as an orientation completion of the real observer clock--ruler plane, rather than as a second fundamental spacetime. Quantum coexistence is represented by a complex rank-four tensor carrier with full Hermitian conjugation, a hypersurface overlap and covariant rank-eight evolution along the lifted observer clock. The common structure contains flat, Schwarzschild, Kerr, Kerr--Newman, LTB, FLRW, photon, free-graviton, hydrogen and ultraviolet worked sectors. The framework yields the locally invariant null speed, massless helicity-twograviton kinematics, reciprocal regular geometries, the relativistic Coulomb spectrum and the four-sector cancellation of local ultraviolet pole sources.
Category: Quantum Gravity and String Theory
[1783] ai.viXra.org:2608.0069 [pdf] submitted on 2026-08-19 21:27:04
Authors: Ori Chamo, Yossi Eliaz
Comments: 6 pages, English. PRL-format Letter followed by Supplemental Material.
Periodic-orbit families are often represented through low-dimensional invariant coordinates, although projected branches need not preserve the connectivity of the underlying solution manifold. We use numerical continuation to examine the 135,445 unequal-mass planar three-body periodic orbits reported by Li, Li, and Liao, whose corrected scale-invariant period-angular-momentum representation was subsequently interpreted as two independent sets. The two projected branches are connected by verified continuation within a single sampled continuation component. The invariant projection exhibits a singular locus consistent with the apparent branch separation. High-precision Floquet calculations identify a +1 transition at one representative stability boundary and an opposite-Krein Hamiltonian-Hopf transition at another. Projection geometry and symplectic spectral geometry therefore provide complementary descriptions of the same periodic-orbit manifold.
Category: Mathematical Physics
[1782] ai.viXra.org:2608.0068 [pdf] submitted on 2026-08-20 23:34:21
Authors: J. W. McGreevy
Comments: 29 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This monograph establishes the formal foundations of the Thermodynamics of Arith-metic Action (TAA), a scale-dependent geometric and statistical framework that unifiesmacroscopic classical gravitation, quantum higher gauge field networks, and discrete non-Archimedean number fields into a single, continuous pipeline of scale-dependent resolution. The universal sorting mechanism is driven by the Regime Determinant S/ℏ, tracking the ratio of total localized physical action over a fixed temporal window to the Planck quotient. We demonstrate that the foundational physical dimensions and algebraic structures of our universe are the unique, mandatory stabilizers required to enforce a global Hyperbolic-Elliptic Index 0 Conservation Law across all number fields. By mapping the Minkowski spacetime invariant, Fermat’s Last Theorem, Hamiltonian and Lagrangian phase spaces, and the Herbrand—Ribet arithmetic mirror into a rigid 2 × 2 Upper Triangular Transformation Matrix, we derive the emergence of exactly 3D + 1 spacetime, the strict left-handed chiral orientation of gauge forces, the topological confinement of spin-1/2 quarks, and a native, geometric resolution to the Strong CP Problem (θ ≈ 0). The entire framework is anchored to the universal short exact sequence of Derived Differential Cohomology, proving thatmass-energy and metric curvature are the inseparable dual payloads of a single, self-regulating holographic index engine.
Category: Mathematical Physics
[1781] ai.viXra.org:2608.0067 [pdf] submitted on 2026-08-20 23:24:38
Authors: Yuechun Huang
Comments: 15 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Based on the matter field theory, this paper proposes that the field generated by the basic moving units of matter (atoms, electrons) possesses both energyu2011conserving and informationu2011holographic properties, and propagates in vacuum at the speed of light. Within this theoretical framework, we classify all interactions in the universe into three fundamental modes: strong interaction (energyu2011exchange dominated), weak interaction (informationu2011exchange dominated), and nonu2011interaction (corresponding to dark energy). We systematically demonstrate that macroscopic celestial motions and microscopic particle motions obey a unified dynamical law. By drawing an analogy with the mathematical structures of Newton's law of universal gravitation, the Lorentz force, and Coulomb's law, we derive Huang's formula F = K .P1. P2 / R² for the gravitational interaction between cou2011moving celestial bodies. In the solar system reference frame, the formula reduces exactly to the Newtonian form, and it provides a purely dynamical explanation for the anomalous rotation curves in the outer regions of galaxies (the dark matter phenomenon) without introducing any additional mass term. The theory also offers a fresh perspective on the origin of galactic redshifts, and is expected to serve as a bridge between classical gravitational theory and quantum field theory.
Category: Astrophysics
[1780] ai.viXra.org:2608.0066 [pdf] submitted on 2026-08-19 14:14:16
Authors: Russell S Clark, Russell S Clark II
Comments: 16 Pages.
For the Minkowski vacuum and the right Rindler wedge, the Bisognano—Wichmann theorem fixes the vacuum modular flow to be Lorentz-boost flow. For a translated finite-energy excitation, this implies an exact, acceleration-independent identity for the vacuum-relativeone-sided modular energy,d/dp∆⟨KW⟩ = 2πℏcEW(p),where p is displacement normal to the horizon and EW(p) is the vacuum-subtracted energycontained in the wedge. If the excitation is concentrated well inside the wedge, Ew(p) ≃ E.Selecting a Rindler observer of proper acceleration a converts the dimensionless modulargenerator into the proper-time Hamiltonian Ha = kBTUKw, with TU = ℏa/(2πckB). Hence d/dp∆⟨Ha⟩ = a/c2Ew(p).Under a specified quasistatic control protocol, this is the external holding-force identity. Atthe reference orbit, a wedge-contained narrow state of invariant mass M obeys |Fhold| = Ma.The entanglement interpretation is more limited. For a finite state, the exact regulatedrelation isd/dp∆⟨Ha⟩ = Tu x d∆Sw/dp +kBTu x d/dp x Srel(ρW,p∥Ωw),so Tu x dSw alone is not generally equal to work. The relative-entropy term is second orderonly for infinitesimal state variations. In that linear-response sector, the entanglement firstlaw yields d(δSw)/dp = 2πkBδE/(ℏc), and for δE = Mc2 this reproduces the coefficient in Verlinde’s local entropy—displacement ansatz. The result is therefore an exact modular-work identity and a linearized entropic representation of Rindler holding force, not a derivation of acceleration, general equations of motion, or gravity.
Category: Thermodynamics and Energy
[1779] ai.viXra.org:2608.0065 [pdf] submitted on 2026-08-18 19:28:43
Authors: Ahcene Ait Saadi
Comments: 11 Pages.
Abstract. We study two elementary periodic functions — the scaled fractional part spp x (a pure ramp of period p) and its complement cpp x = p−spp x — together with the single algebraic identity spp x + cpp x = p. Because their derivatives are the constants +1 and −1, they turn a range of nonlinear differential equations into closed one-line solutions, they solve first-order transport and inviscid Burgers equations exactly, and they let one write intricate periodic curves — half-circle chains, staircases, asymmetric arcs, modulated ramps — each from a single algebraic expression. A complex generator Z(x) = sp x+i cp x opens a second, geometric part: its powers Z n are explicit algebraic curves of degree n, and the normalized family {Z α/pα} covers an eye-shaped region with an exactly empty core bounded by the unit circle. The aim is not to compete with Fourier analysis but to offer a light, exact notation for the angular, piecewise-affine patterns where Fourier series are heavy and only approximate. All identities have been verified symbolically and numerically (sympy, machine precision).
Category: Functions and Analysis
[1778] ai.viXra.org:2608.0064 [pdf] submitted on 2026-08-18 19:26:57
Authors: Dinuo Chen
Comments: 16 Pages.
Near-ultrasonic frequency bands provide an underutilized portion of the acoustic spectrum with relatively low perceptual salience[1, 2] while remaining potentially usable with conventional audio hardware. This paper investigates the feasibility of transmitting analog audio over near-ultrasonic frequency bands using consumer-grade loudspeakers, microphones, and sound cards. A singlesideband (SSB) modulation scheme is employed to shift baseband audio into the near-ultrasonicrange, where it is transmitted through an acoustic channel and subsequently demodulated at the receiver. The system is evaluated under various transmission conditions using commonly available audio equipment. Signal quality is assessed through spectral analysis and objective similarity metrics between the original and recovered audio signals. Experimental results demonstrate that consumer audio devices are capable of supporting near-ultrasonic analog audio transmission within the limits imposed by their frequency response. Although attenuation and distortion increase toward the upper end of the transmission band, the original audio can still be recovered with acceptable quality under suitable conditions. These findings suggest that near-ultrasonic acoustic channels couldprovide a low-cost communication medium for specialized applications without requiring dedicated ultrasonic transducers.
Category: Digital Signal Processing
[1777] ai.viXra.org:2608.0063 [pdf] submitted on 2026-08-18 19:24:13
Authors: Holger Troitzschel
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper introduces a self-referential cosmological framework in which spacetime ge-ometry, matter, and gravitational interactions are proposed to emerge exclusively from theself-observation of quantized electromagnetic fields. By coupling U(1) gauge fields directlyto the discrete graph structure of Loop Quantum Gravity (LQG), a non-linear feedback loopbetween energy density and spatial volume is established. We define a quantum Hamil-tonian operator for light acting on spin-network states and argue that electromagnetic fluxexcitations can alter geometric quantum numbers. In addition, we explore whether fermionicmatter can emerge as topological braids of light ribbons. Physical implications are discussed,including a possible resolution of singularities via a stable "Quantum Geon" configuration,as well as testable predictions concerning alternatives to particle dark matter and signaturesin primordial gravitational waves.
Category: Quantum Gravity and String Theory
[1776] ai.viXra.org:2608.0062 [pdf] submitted on 2026-08-18 19:22:59
Authors: Yuan Di, Zongyan Liu
Comments: 29 Pages.
Millions of female university graduates in China face a severe shortage of standardized "two-day-office office jobs" each year, a structural mismatch that exacerbates employment pressure. Based on empirical data from the Anhui provincial civil service examination, this paper proposes a "dignity-defense-oriented reproductive decision-making model": Faced with the gap between high career expectations and reality, female university students, out of dignity defense and risk aversion to maternal punishment, prefer survival strategies such as "slow employment" and the "civil service exam craze" to marriage and childbearing, thus significantly suppressing the overall birth rate. To address this dilemma, it is recommended to reconstruct the university employment quality evaluation system and disciplinary structure, introduce national policies to reduce maternal punishment, and promote a shift in the macro-market towards women's self-indulgent consumption.
Category: Social Science
[1775] ai.viXra.org:2608.0061 [pdf] submitted on 2026-08-17 16:19:29
Authors: Rafael Maya
Comments: 18 Pages. Code for computations presented in the research paper is available upon request
The invariant four-volume of an event's causal past is a well-defined geometric functional of a Friedmann-Lemaître-Robertson-Walker expansion history. We study its normalized form, C(T) = V4(T)/V4(To), and the family of causal-fraction ages Tf defined by C(Tf) = f. We give a closed observable form written entirely in H(z), the exact self-similar limit Tr→ Tof1/4. and an O(N) moment decomposition enabling per-sample evaluation on posterior chains. Two structural results follow. The dimensionful statistic is almost completely degenerate with the cosmic age (posterior-scaled gradient alignment cos = 0.9991 in flat wow CDM), whereas the dimensionless ratio pf = Tr/To is exactly independent of the overall expansion scale. Its sensitivity kernel K(z) = 8pf/ w(z) possesses a single sign-change node migrating with f, and at f. = 0.2627 the kernel's lobes cancel exactly: pf is simultaneously Ho-free and first-order blind to wo, a differential sensor of dark energy across z ~ 0.40 that within flat ACDM tracks the matter-dark-energy handover, 2A(z) = 0.46 ± 0.03. Transforming every stored sample of the public DESI DR2 BAO+CMB+supernova wow CDM chains yields T1/6 medians displaced by 40-46 Myr (2.5-2.9 posterior standard deviations) from the Planck ACDM value T1/6 = 8.6452 Gyr, compressing the evolving-dark-energy preference into one scalar, and we freeze three falsifiable predictions for DESI DR3 and Euclid. A companion paper derives the asymptotic behavior of fixed four-volume increments in an eternally accelerating future.
Category: Relativity and Cosmology
[1774] ai.viXra.org:2608.0060 [pdf] submitted on 2026-08-17 16:23:55
Authors: Rafael Maya
Comments: 8 Pages. Code for computations presented in the research paper is available upon request.
A common intuition holds that an eternally accelerating universe, having a finite event horizon, should accumulate only a finite amount of causally connected spacetime. We show by direct integration that this is incorrect: in de Sitter space the causal-past four-volume of a comoving observer grows without bound, V4(t) ~ (4πc/3H) (t - H¹) as t , even though the past-light-cone radius saturates at c/H. Consequently, crossings of any fixed four-volume increment AV > 0 form an infinite sequence whose proper-time spacing converges to the finite constant At = 3H AV4/(4πc¹). For a flat ACDM continuation with Planck-2018 baseline parameters and the normalization AV4 = f V4(To) with f = 1/6, the first future increment completes 0.580 Gyr from the present (cosmic age 14.375 Gyr) and the spacing decreases monotonically toward At = 40.1996 Myr. The limit discriminates among cosmic futures: evolving or decaying dark energy, phantom finite-time singularities, and recollapse generically break the uniform-spacing asymptote, which is conditional on the approach to a de Sitter phase.
Category: Relativity and Cosmology
[1773] ai.viXra.org:2608.0059 [pdf] submitted on 2026-08-17 20:43:05
Authors: Brent Hartshorn
Comments: 11 Pages.
Cross-language interoperation is normally a matter of agreeing on a boundary: a foreign function interface, a generated shim, a marshalling layer, or a shared intermediate representation. We describe a system in which no boundary exists. Subsets of C++ and of Rust are each lowered to plain C source, and one C compiler consumes the result, so a Rust function calling a C++ method is a C function calling a C function — same translation unit, same intermediate representation, same register allocator. The two lowerings are chosen to converge on identical symbols, with the consequence that a Rust impl Drop and a C++ destructor over the same data emit the same function, and a C++ class may hold a Rust value by value without a shim, a wrapper, or an annotation.Removing the boundary between the languages exposes a second one, below them: the artifact is C, but a C compiler, an assembler, a linker and a runtime still stand between C and a running program, and conventionally those are separate projects. We report a stack in which they are not. The whole path — two source languages to C, C to machine code, machine code to a static ELF executable — is roughly fifty thousand lines in one repository, with no external compiler, assembler, linker or C library involved.
Category: Data Structures and Algorithms
[1772] ai.viXra.org:2608.0058 [pdf] submitted on 2026-08-16 19:32:57
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 9 Pages. (Note by ai.viXra.org Admin: Title and abstract MUST BE in English!)
This work begins with a simple question: could what we describe as translation and force actually be the local manifestation of a fundamentally angular dynamics? In the *Principium Geometricum* (PG), we investigate the possibility that the most fundamental physical description does not start with a body's trajectory through a pre-existing space, but rather with states of phase, rotation, closure, and causal updating. We introduce a normalized phase state q(ϕ) = (cos ϕ, sin ϕ), for which ∥ ˙q∥² = ω². In parallel, we consider the geometry of a torus, whose volume is VT = 2π²Ra². In the reduced geometric case where R = a = r, we have VT = 2π²r³. These two structures suggest the quantity IT ≡ VT 2π² ∥ ˙q∥² = r³ω². We propose investigating the conservation of IT for orbital states associated with the same global source. If IT is constant, Kepler's third law follows directly, as does—for the circular projection—an acceleration proportional to ru207b². The observational identification IT ↔ GM then recovers the Newtonian limit. This result does not constitute a microscopic derivation of gravity. The conservation of IT remains a physical hypothesis requiring further substantiation. The aim is to show, in an explicit and falsifiable manner, where the geometric identity ends, where the PG hypothesis enters, and how the classical limit is recovered.
Category: Mathematical Physics
[1771] ai.viXra.org:2608.0057 [pdf] submitted on 2026-08-16 19:22:08
Authors: Mustafa Karatüm
Comments: 20 Pages. https://doi.org/10.5281/zenodo.21963450
We present the Topological String-Gradient Theory (TSGT), a framework in which space-time is discrete at the Planck scale and gravity is the gradient of the spacing betweendiscrete elements ("pixels") rather than a fundamental force. Two kinematic postulates—a spatial pixel strain set by the Newtonian potential and an equal and opposite tempo-ral strain—reproduce the weak-field Schwarzschild metric, and hence Newtonian accelera-tion, gravitational redshift, the Shapiro delay and the full general-relativistic light deflec-tion ∆θ = 4GM/c2b. We stress that this reproduction is by construction rather than aprediction. The discrete substrate is taken to be a random Poisson sprinkling of densityL−4p rather than a regular lattice. This choice preserves Lorentz invariance statistically,and thereby removes the preferred-frame and anisotropy problems that afflict lattice for-mulations; it also withdraws the energy-dependent photon dispersion, gravitational-wavedispersion and propagation-anisotropy signatures claimed in earlier versions of this frame-work, which we retract explicitly. In exchange, TSGT acquires a quantitative cosmologicalconsequence. If cosmic expansion proceeds by the creation of new pixels rather than bythe stretching of existing ones—the only option compatible with an invariant Lp—then thenumber—volume correspondence carries Poisson fluctuations δN ∼ √N , and the cosmologicalterm conjugate to the four-volume inherits a residual magnitude Λ ∼ V −1/2. Numericallythis gives ρΛ ≃ 2.8 × 10−27 kg m−3 against an observed 5.8 × 10−27 kg m−3: agreement withina factor of two, compared with the 10123 discrepancy of the naive Planck-density estimate.This argument is not original to TSGT—it is Sorkin’s heuristic, developed within causal settheory—but it follows from TSGT’s own postulates without additional assumptions, andit carries a signature that current surveys can test: the dark energy term is not constantbut fluctuates, so w̸ = −1. We then show that the two kinematic postulates need not bepostulated at all. Written locally, the number—volume correspondence reads √−g = L4pn(x),which is the unimodular constraint; enforcing it in an Einstein—Hilbert action yields thetrace-free Einstein equations, with Λ appearing as an integration constant rather than as aparameter, and with the weak-field metric recovered rather than assumed. The price is statedplainly: TSGT thereby becomes provably equivalent to General Relativity at the classicallevel, so whatever independent content it possesses lies entirely in the integer character ofthe pixel count. Unresolved problems, including the absence of a dynamical equation for thepixel density and the difficulty of deriving excitations on an irregular substrate, are listedexplicitly
Category: Quantum Gravity and String Theory
[1770] ai.viXra.org:2608.0056 [pdf] submitted on 2026-08-15 16:39:02
Authors: Karl Simon
Comments: 11 Pages.
AbstractThe Standard Model perfectly describes the system of elementary particles and their interactions, yet it fails to explain why there are precisely three generations of quarks and leptons, and why quarks possess fractional electrical charges. Furthermore, it does not address gravity’s fundamental mechanism in forming spacetime. This paper presents a novel structural model to shed light on these open questions. The model explores how a fundamental particle theory can be constructed from the simplest possible combination of a single chiral particle (b) and its antiparticle (q). Through geometric reflection, four elementary components emerge (b, p, d, q), whose purely topological shapes directly encode chirality and helicity. By introducing an invariant isospin (iI) and an invariant hypercharge (iY), electric charge (Q) is defined as an emergent property of specific substructures within states. The model demonstrates that simple combinatorial rules spontaneously generate structural quartets consisting of one lepton alongside three isomeric quark structures, whose statistical charges correspond exactly to the fractional charges of quarks. [1]Crucially, the model resolves the classic mass paradox and fine-tuning problem of preon theories—where massive binding energies must artificially cancel bare energies—by introducing an intrinsic, algebraic subtraction mechanism within the relationship between the W, Z, and the electron. Through the structural combinations W+Z-W, W+Z-Z, and the complete subtraction W+Z-W-Z -> e, the dynamic mass generation of the weak bosons and the very low mass of the electron are derived directly from state definitions without free parameters. Within this framework, both mass and electric charge emerge as phenomena strictly bound to irregular helicity configurations, identifying the seemingly vanished binding energy as the structural energy equivalent of the electric charge. This mechanism mirrors the immense energy scales conceptually postulated in Majorana-like mass terms for right-handed states without charge. [6] Tthe Higgs boson is naturally identified not as a separate elementary particle, but as the massive, scalar excitation state of the fundamental vacuum (bpdq) showing an inherent structural preference for aligned, "regular" helicities that governs the mass generation and electrical charge of particles.Finally, a potential connection to geometric gravitation theory is suggested, reminiscent of historical attempts to explain gravity as a structural residue between electric attraction and repulsion [4] Here pairs of photons of spin 2 interact via a double spinflip with neutrinos as the fundamental building blocks of all matter.
Category: High Energy Particle Physics
[1769] ai.viXra.org:2608.0055 [pdf] submitted on 2026-08-15 23:52:43
Authors: Frank W. Brown
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
I present a multi-scale empirical data appendix verifying the field equations of Curved Temporal Inertia Cosmology (CTIC). This 1-page report compiles two automated verification ledgers running natively within the open-source repository. First, a sequential 3-detector LIGO/Virgo matched-filter analysis of event GW170817 targets the model's non-axial metric twisting shear envelope (h_omega) using a stable time-domain RMS normalization layer. The network trace reveals an unmistakable, high-confidence Signal-to-Noise Ratio (SNR) peak of 28.2123 at LIGO Hanford (H1), an expected sub-threshold validation of 7.3335 SNR at LIGO Livingston (L1), and a baseline antenna blind-spot trace of 5.4227 SNR at Advanced Virgo (V1). Second, the report maps a macroscopic coordinate domain ledger tracking a triaxial ellipsoidal subcluster grid across 40 morphologically diverse galaxy clusters, yielding a uniform observational deviation margin of < 2.0% using strictly 100% visible baryonic mass parameters. Complete automated replication pipelines are open-sourced at: https://github.com/LiamLumen/CTIC-Quantum-Dynamics
Category: Relativity and Cosmology
[1768] ai.viXra.org:2608.0054 [pdf] submitted on 2026-08-14 20:08:25
Authors: Arunas Ostasevicius
Comments: 5 Pages.
The paper presents a fundamental historical and mathematical exposure of the kinematic foundations of the Special Theory of Relativity (SR). Based on a rigorous analysis of the original text of J. C. Maxwell’s Treatise on Electricity and Magnetism (1873, paragraphs 600—601), it is proved that the original equations of the electromagnetic field initially contained total (material) time derivatives and convective field drift operators (v · ∇). It is demonstrated that Maxwell’s original system was naturally invariant under classical Galilean transformations in absolute Euclidean space. The study establishes that SR arose as an artificial geometric artifact (Lorentz transformations, Minkowski metric) designed to compensate for the fatal castration of the field equations by O. Heaviside, who forced the convective velocity of the coordinate axes to zero and replaced the total derivative with a partial one. The physical reality of Maxwell’s convective drift is confirmed by the one-way mirrorless experiments of S. Marinov and R. De Witte, completely rendering the metric space-time paradoxes of modern physics unnecessary.James Clerk Maxwell, Oliver Heaviside, Galileo invariance, total derivative, convective term, Stefan Marinov, Roland De Witte, Special Relativity critique.
Category: Relativity and Cosmology
[1767] ai.viXra.org:2608.0053 [pdf] submitted on 2026-08-14 13:31:35
Authors: Joseph Shaffer
Comments: 6 Pages.
Spacetime, matter, and physical law emerge as macroscopic unitary outcomes of a system converting high-energy chaos into optimal stability. The universe begins as a chaotic tension matrix (Domain A) filled with unstable local maxima. A tension-bearing phase boundary-the mat-absorbs chaotic shear vectors, flattens them into coherent spatial gradients, and locks unfilterable stress peaks into localized matter structures. When the system crosses a critical radius threshold, a subcritical pitchfork bifurcation rigidifies the mat and produces the calm fabric (Domain B). Stability arises from the large-number postulate: chaotic modes interacting in enormous numbers become unresolvable, leaving only stable structures visible. Spacetime and matter are the macroscopic shadows cast by submerged chaos.
Category: Astrophysics
[1766] ai.viXra.org:2608.0052 [pdf] submitted on 2026-08-13 12:06:32
Authors: XinXin Li
Comments: 5 pages. CC BY 4.0.
We establish an exact algebraic identity connecting the cumulative near-conjugacyerror Eσ of a base-6 circle-rotation model of the Collatz map (HonarvarShakibaei Asli, 2026) with the terminal correction ε in the classical stopping-timeidentity. For a convergent Syracuse orbit, Eσ = 1 − log6(5n0+1)+ (log2 n0 + ε)·log6 2, in which the Syracuse stopping time τcancels exactly via the change-of-base formula log2 6 · log6 2 = 1.Consequently Eσ = O(1) ⇔ ε = O(1) ⇔ Σ 1/ni−1 = O(1), so theboundedness of the reciprocal sum becomes the central open question. The identity isverified to machine precision (≤ 2×10−15) for every tested n0 ≤ 77031.
Category: Number Theory
[1765] ai.viXra.org:2608.0051 [pdf] submitted on 2026-08-12 20:12:06
Authors: Arunas Ostasevicius
Comments: 6 Pages. 2 figures.
An alternative concept for describing the dynamics of celestial bodies based on non-linear self-oscillations in a material cosmic medium is presented. From first principles — Boltzmann's kinetic equation — a closed system of two coupled quaternionic equations is rigorously derived. These equations describe the orbital motion of a planet's center of mass and its axial rotation as stable phase attractors (limit cycles). Using the analytical method of phase averaging, the deformation of Mercury's phase trajectory under the influence of polytropic changes in the parameters of the medium near the Sun is calculated. The superiority of non-linear oscillation theory methods over the geometrization of spacetime is demonstrated, allowing for the complete abandonment of the cumbersome linear algebra apparatus of General Relativity and the postulation of mystical initial conditions.planetary dynamics, self-oscillations, Boltzmann kinetic equation, quaternion, limit cycle, phase averaging, cosmic medium, Ether, perihelion precession, general relativity alternative
Category: Astrophysics
[1764] ai.viXra.org:2608.0050 [pdf] submitted on 2026-08-12 20:10:56
Authors: Khazri Bouzidi Fethi
Comments: 9 Pages.
We study the Diophantine equation 1/p_1 = 1/p_2 + 1/p_3 + 1/p_4 for distinct primes p_1, p_2, p_3, p_4, a special case of the Sierpiński—Schinzel unit-fraction equations. We introduce a spectral coherence threshold R, derived from an exact infimum formula for a normalized exponential sum over the primes involved via the Kronecker—Weyl equidistribution theorem, and show that R = 1/2 is its sharp transition value. For three primes, we establish an exact identity linking R to prime gaps, giving a new proof that no three consecutive primes satisfy the analogous three-term equation. For four primes, we combine this classification with an exact divisor-based algorithm to search over 6 times 10^8 configurations, finding no solution for p_1 le 5431 but reporting the closest known near-solution. We prove that no solution can occur with the three larger denominators in arithmetic progression, and record a short, fully general divisibility argument showing that no such equation admits a solution in distinct primes for any number of terms — clarifying explicitly that this fact concerns single-prime denominators only, not the composite-denominator setting central to the Sierpiński—Schinzel conjectures.
Category: Number Theory
[1763] ai.viXra.org:2608.0049 [pdf] submitted on 2026-08-11 12:20:40
Authors: Lluis Eriksson
Comments: 9 pages, 1 figure. Exact d=5 inverse commutator cost: 12 Horn chambers, optimal-rank law, sharp tax [1,5/2], triangular synthesis, and reproducible rational certificates.
For a prescribed traceless Hermitian five-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. If g_i=lambda_i-lambda_{i+1} are the ordered spectral gaps, the answer is the maximum of six explicit rational linear forms and their reversals. Exact Littlewood-Richardson enumeration gives 142 Horn inequalities. Twelve sparse dual identities prove the lower facets, and twelve rational singular-spectrum maps attain them; exact cone certificates prove completeness without sampling. In contrast with the two qutrit facets and four four-level facets, dimension five has twelve exposed facets and open chambers that force rank four. For every nonzero target, the least rank of an optimal factor is max(n_+(F),n_-(F)). We also prove the sharp tax 1 <= kappa_5/(||F||_1/2) <= 5/2 with complete equality loci, and the exact balanced triangular perimeter S_2^2=12 sqrt(3) kappa_5. Two rational certificates and an independent deterministic LP campaign accompany the paper.
Category: Mathematical Physics
[1762] ai.viXra.org:2608.0048 [pdf] submitted on 2026-08-11 13:00:56
Authors: Lluis Eriksson
Comments: 10 Pages.
Under an explicit noncontextual homogeneous-response ansatz for rank-one quantum effects, we study normalization on every unitary rotation of a fixed finite POVM. The orbit-normalization operator diagonalizes on the projective harmonics of complex projective space. We derive its weighted all-degree singular spectrum and show that the smallest non-Born spectral value is the sharp condition number controlling distance from the affine space of trace-one Hermitian quadratic responses. For dimensions at least three, the high-degree spectrum of a finite seed converges to the sum of squared aggregate ray weights; for an outcome-simple equal-trace seed with N outcomes, the limit is d squared divided by N. Combining this ceiling with the forced geometry of the two smallest tight frames solves the global equal-trace design problem in every dimension d at least five. An orthonormal-basis seed uniquely maximizes the all-degree Born-rigidity gap, with value d minus 6 divided by d plus 1, up to unitary equivalence and outcome relabeling. Every distinct-outcome overcomplete seed in the stated class is strictly worse. By contrast, every weighted complex projective 2-design has a degree-two nullspace and therefore zero rigidity gap. Thus measurements optimal for state tomography can be maximally non-rigid for this covariant normalization objective. The result concerns one-step response fields and does not derive state update, intrinsic randomness, or microscopic particle dynamics.
Category: Mathematical Physics
[1761] ai.viXra.org:2608.0047 [pdf] submitted on 2026-08-11 13:47:42
Authors: Lluis Eriksson
Comments: 10 pages, 1 figure. Reproducible certificate and independent verifier are linked in the PDF.
A passive lossless network may route the same k-dimensional input channel to different output subspaces at different frequencies. Every two-frequency restriction can be cheap while the joint task is not. For L distinct boundary frequencies and mutually orthogonal prescribed output k-planes, we prove that the minimum McMillan degree among square finite rational-inner transfer matrices regular at the interpolation nodes is exactly k(L-1). Each pair alone requires degree k, so the largest two-node minimum underestimates the global memory by the unbounded factor L-1. The result is independent of node spacing. Necessity follows both from a zero budget for an analytic minor and from a Pick-Stein displacement identity whose negative inertia cannot exceed realization rank. Sufficiency follows from an explicit positive Pick completion. Beyond exact orthogonality, we derive a general cross-frequency inertia certificate, a gauge-independent span bound, an open robust region preserving the integer memory count, and a fail-closed noisy-eigenvalue certificate. Deterministic code tests arbitrary nodes, synthesizes minimal conservative realizations, and independently verifies the stated identities.
Category: Mathematical Physics
[1760] ai.viXra.org:2608.0046 [pdf] submitted on 2026-08-11 15:21:20
Authors: Lluis Eriksson
Comments: 11 pages, 2 tables, 1 figure. Exact spin-j echo spectra, finite frames with stability bounds, sharp link-OS/sinc boundary, and connected HS nuclear cutoff.
Four balanced spin kicks along the vertices of a regular tetrahedron generatean order-dependent eight-pulse echo. We prove that all 24 echo orders have oneconjugacy class in SU(2). Haar randomization of only the global orientationtherefore gives an order-law-independent, self-adjoint random-unitary channelon every spin-j matrix algebra. Its exact eigenvalues are normalized SU(2)characters, lambda_l=U_{2l}(q)/(2l+1), with multiplicity 2l+1 and an explicitfinite-pulse architecture polynomial q=1-A/2. The maximal link-reflection-positive interval connected to zero is alpha<=pi/(4j+1), with an exact endpointequation and a finite OS Hamiltonian under strict inequality. In the doublescaling N=4j+1, y=xi/sqrt(N), the full tower converges uniformly tosinc(8xi^2u). This gives the sharp full-tower boundary xi_c=sqrt(pi/8), acritical boundary law N lambda_top -> 3pi/8-2s, an explicit scaled mass profile,and an ultraviolet heat-trace integral. The fixed-rank limit recovers the fuzzy-sphere Laplacian. Poissonization yields a genuine CPTP semigroup and an exactmany-body connected nuclear profile exp(3e^-c)-1. Symbolic and deterministicmatrix certificates accompany the manuscript.The Haar average also has explicit exact finite implementations. A classicalpositive Gauss--Legendre/trapezoidal cubature at bandlimit 4j needs(4j+1)(2j+1) order-conditioned frames, or (4j+1)^2(2j+1) frames when the sameframe list must be order oblivious.The common-class proof reduces the 24 orders to the even and odd A4 orbits.For finite implementations, a separate stability bound controls l1 weighterror, orientation displacement, and pulse perturbations; total variationagainst Haar is not used for discrete frames.
Category: Quantum Physics
[1759] ai.viXra.org:2608.0045 [pdf] submitted on 2026-08-11 15:57:16
Authors: Lluis Eriksson
Comments: 9 pages, 1 figure, 1 table. Exact generic memory law, colliding-target discontinuity, noisy projector certificate, and three-line phase diagram.
At L boundary frequencies, a passive lossless network must route one fixed k-dimensional input channel to prescribed output k-planes. For targets with joint span dimension r, every square finite rational-inner interpolant satisfies the sharp universal sandwich r-k <= d_min <= k(L-1). Direct-sum targets therefore have exact minimum McMillan degree k(L-1); when N >= Lk this maximal-memory locus is open and dense. The paper gives an explicit positive Pick completion, a realization- and inertia-based lower bound, a family of targets that collide while retaining maximal exact degree for every nonzero opening, an exact quadratic certification margin, and a fail-closed noisy projector test. For three scalar target lines it also proves the complete phase diagram: degree zero for one common line, degree one exactly for three distinct coplanar lines, and degree two otherwise. Deterministic certificates and an independent implementation accompany the proofs.
Category: Mathematical Physics
[1758] ai.viXra.org:2608.0044 [pdf] submitted on 2026-08-11 19:17:05
Authors: Keiji Yoshimura
Comments: 22 pages. English translation edition v1.0.1-EN1 of the Japanese scientific baseline v1.0.1. Associated public reproducibility repository is linked in the manuscript.
This study reconstructs the Japanese rice industry not as a single price chain but as a multi-actor network in which goods, money, information, risk, authority, and explanations move at different speeds and levels of aggregation.Using public statistics, administrative and legal records, industry statements, and a purposively sampled media corpus, the audit fixed price stage, unit, period, product, and contract conditions before testing end-to-end traceability.Public sources provide substantial visibility into quantities, stage-level averages, production costs, inventory volumes, retail transaction prices, and policy outputs. They do not, however, permit continuous monetary tracing of the same contract, inventory cohort, or product.Four principal breaks were identified: the producer's final receipt, inventory acquisition cost, absolute wholesale selling prices, and product-level retail procurement, costs, and profits. Consequently, price-stage differences or bridge residuals cannot by themselves identify wholesale or retail profit, profiteering, or the contribution of a single actor.Policy responses since 2025 shifted from conditional auctions to downstream direct contracts, official self-review, and statistical and legal redesign, while the pure retail-price effect of reserve-rice releases and the practical effectiveness of the new reporting system remain unidentified.A staged transparency architecture is proposed as a design implication: common metadata and measurement crosswalks, anonymous price-bridge pilots, and eventually an integrated six-flow and cohort infrastructure.The study does not determine a fair price, a profiteering actor, collusion, or a pure policy effect; it specifies what is observable, where public traceability breaks, and what evidence would update the conclusions.
Category: Economics and Finance
[1757] ai.viXra.org:2608.0043 [pdf] submitted on 2026-08-12 01:48:33
Authors: Joseph Mcgreevy
Comments: 20 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We formalize a unified geometric and representation-theoretic architecture bridging the continuous deformation of modular parameter spaces to the discrete, quantized structures of arithmetic number fields and local gauge theories. In the first part of this work, we present astructured verification of the Birch and Swinnerton-Dyer (BSD) Conjecture for Rank 2. By defining a stationary modular wave equation via the Maass-Laplacian, we isolate the weight-12 cusp form ∆ as an on-shell, massless zero-mode. At the bad reduction prime p = 691, this continuous flux degenerates against a singular cusp, collapsing the higher-dimensional geometric cycles of the 3-dimensional Kuga—Sato variety W2 onto the n = 0 neutral core of the Schmid weight filtration light cone. We construct the explicit 2×2 p-adic Syntomic Comparison Matrix, proving that its determinant is non-zero and non-degenerate under local-to-global stress at the fracture wall if and only if the p-adic N´eron—Tate height regulator is non-singular. In the second part, we document a precise homological parallel between this arithmetic localization and the structural stability constraints of quantum gauge fields. We demonstrate that the mechanism passing the E2 quasi-modular anomaly through higher-weight Eisenstein series mirrors the scaling of a gauge connection protecting a positive-definite kinetic energy landscape. This continuous propagation forces a compact Lie group topology, which shatters at the 691 boundary into an 11-dimensional coefficient space—casting a direct arithmetic shadow onto the χ 11 odd eigenspace of the cyclotomic minus class group via the Herbrand—Ribet theorem. We present this unified framework not as a physical identity, but as a rigid representation-theoretic blueprint governing Rank-2 root system degenerations at the boundary of a continuum.
Category: Mathematical Physics
[1756] ai.viXra.org:2608.0042 [pdf] submitted on 2026-08-10 08:28:18
Authors: Lluis Eriksson
Comments: 17 pages, 4 figures, 2 tables. Includes robust separation theorems, a vacuum-complete Ramsey model, 60-digit certificates, open-source code, frozen ledgers, and passing CI checks.
We study whether passive reservoir filtering can suppress decoherence more effectively when its channel mixing is irreducible, even after fixing the passband responses and rational complexity. For every integer S ≥ 5, we construct an explicit causal inner six-port network with three signal and three vacuum-loss ports. Its signal block is a rational Schur transfer satisfying 3(S−1) delayed full-spark tangential calibrations and exhibiting exponentially small leakage on two stop arcs. In contrast, every transfer of the same bidegree possessing a constant nontrivial reducing channel and satisfying the same calibrations retains unit stopband norm.We strengthen this exact separation with a quantitative finite-error obstruction: for calibration defect δ and sampled reducing-line defect β, comparator leakage is bounded below by [1−C_S(δ+β)]_+, with C_S given explicitly by finite singular-value margins. A scalar Schur construction proves that every bound of this form must deteriorate at least as 2 exp(9S/20)(1+o(1)); hence uniform robustness is impossible for the chosen clustered calibrations.For uniformly nondegenerate bath spectra, the signal-level separation is squared at the Kossakowski-rate level. A closed Markov pure-dephasing model includes all auxiliary vacuum ports exactly, producing an architecture-independent measurable baseline and an explicit total Ramsey-rate advantage. Finally, we prove that strong passive suppression requires large dwell time: under a peak-delay budget D, the rate-improvement factor is asymptotically at most quadratic in D/S. The construction therefore moves the coherence-maintenance resource into passive memory, vacuum noise and conditioning rather than eliminating it. All certificates, figures and numerical audits are publicly reproducible.
Category: Quantum Physics
[1755] ai.viXra.org:2608.0041 [pdf] submitted on 2026-08-10 10:22:35
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. Analytic proofs and reproducible certificates; code, numerical audits and release checks are available in the linked GitHub repository.
How many internal passive modes are required to transmit prescribed quantum noise channels without loss while suppressing all signal directions elsewhere? We prove an architecture-independent answer for finite-dimensional rational networks. Let a causal rational inner scattering matrix S have McMillan degree n, signal block G, and complementary loss block C. At distinct regular boundary frequencies, suppose that G is isometric on input subspaces of dimensions k_j. If G is a strict contraction at one other frequency, then sum_j k_j ≤ n.Every lossless direction lies in the kernel of C; a nonzero maximal minor of C therefore has a zero of multiplicity at least k_j. Exterior powers of a minimal Blaschke—Potapov factorization show that no minor can have more than n zeros. The same factorization yields the exact topological delay identity(1/2π) ∫ tr Q(θ) dθ = deg_McM S = n,where Q = −i S* ∂θS is positive semidefinite. Thus lossless calibration multiplicity is bounded by integrated Wigner—Smith delay. The bound is sharp in every dimension. We establish robustness under analytic passive perturbations, prove why unstructured approximate samples cannot imply a degree bound, and show that a previously constructed six-port reservoir filter is universally optimal up to six internal states. Proofs and numerical certificates are reproduced by the linked public repository.
Category: Quantum Physics
[1754] ai.viXra.org:2608.0040 [pdf] submitted on 2026-08-10 11:14:40
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Reproducible certificate, source and verifier: https://github.com/lluiseriksson/finite-sample-spectral-certificates/releases/tag/v1.3-robust-spectral-routing
Exact interpolation can force the internal degree of a passive network, but laboratory calibrations are approximate. We prove a sharp frequency-domain speed limit requiring neither exact zeros nor analytic continuation away from the measured frequency axis. Let (S(e^{itheta})) be an absolutely continuous unitary scattering path with positive Wigner—Smith generator (Q(theta)=-iS(e^{itheta})^astpartial_theta S(e^{itheta})succeq0). If a fixed (k)-dimensional input subspace is routed approximately between complementary output sectors with amplitude leakages (varepsilon_p,varepsilon_s), define (alpha=[pi/2-arcsinvarepsilon_p-arcsinvarepsilon_s]_+). Every transition then requires Wigner—Smith trace action at least (2kalpha) and largest-proper-delay action at least (2alpha). Costs add over disjoint frequency arcs. For a rational inner network of McMillan degree (n), (M) alternating pass/stop pairs imply (nge 2Mkalpha/pi), recovering (nge Mk) at zero error. An explicit (2k)-port interferometric family attains the bounds for every admissible error pair. A tomography-error corollary converts finite scattering measurements directly into certified degree and delay lower bounds. Reproducible certificates audit equality cases, positive-block inequalities and random Blaschke—Potapov products.
Category: Quantum Physics
[1753] ai.viXra.org:2608.0039 [pdf] submitted on 2026-08-10 12:58:55
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Exact symmetric-gauge and Ky Fan speed limits for passive networks, with sharp constructions, robustness bounds and open code.
A subspace quantum speed limit usually records only the largest canonical angle. Passive scattering theory usually records either the largest proper delay or their total trace. Both compressions discard how a rank-k routing event is distributed across modes. We derive the missing vector law: the integrated spectral-spread vector weakly majorizes twice the canonical-angle vector. More strongly, for every symmetric gauge Φ and every pair of k-subspaces in N ≥ 2k dimensions, we solve the variational problem exactly: the minimum spectral-spread action is 2Φ(β). The same value holds for the leading-proper-delay action under positive generators, and one constant coupled-mode path minimizes all gauges simultaneously. The Ky Fan members recover the bandwidth limit, strengthen the trace-action law, and expose every intermediate modal budget. An exact nonnegative slack decomposition separates common-mode delay, inefficient spectral coupling, and nongeodesic subspace motion. Robust corollaries convert heterogeneous pass/stop leakage spectra and finite tomography errors into certified Lorenz curves for delay and, for rational inner networks, McMillan-degree lower bounds. A deterministic artifact tests 8,192 random generators, 1,536 time-dependent paths, sharp equality families, and 2,048 noisy tomography instances.
Category: Quantum Physics
[1752] ai.viXra.org:2608.0038 [pdf] submitted on 2026-08-10 14:22:14
Authors: Lluis Eriksson
Comments: 13 pages, 2 figures. Adds exact quintic obstruction P_H, sharp Theta(n^-3/2), an O(n^-2) fourth level, and an exact attaining example. AI assistance disclosed.
Repeated projective measurements are usually discussed either in the ballistic Zeno scaling or after reduction to classical outcome probabilities. We study a different regime in which each nonselective measurement retains a full matrix algebra inside every degenerate outcome block. Let E(X)=sum_a P_a X P_a, let E_tau be its rotation by exp(-i tau H), and close one cycle by Phi_tau=E E_tau E. We prove, uniformly on compact time intervals and in diamond norm, that Phi_{sqrt(t/n)}^n converges to exp(-tK)E, where K=E ad_H(1-E)ad_H E=C_H^* C_H. The limit is a genuinely quantum Markov semigroup on the direct sum of the block matrix algebras, with explicit jumps sqrt(2) P_b H P_a. Beyond upper bounds, we identify three exact local obstructions for the unprocessed physical product. The cubic map M_H produces a nonzero n^{-1/2} coefficient; after it vanishes, the quartic product obstruction J_H produces a nonzero n^{-1} coefficient; after both vanish, the quintic obstruction P_H produces a nonzero n^{-3/2} coefficient. If all three vanish, the error is O(n^{-2}). All three coefficient transforms are injective. An exact three-record algebraic example has M_H=J_H=0 but P_H nonzero, proving that the third branch is attained. The fixed algebra is A intersect {H_off}', and the least singular value of the commutator frame C_H defines a noncommutative connectivity gap. In the primitive case that gap is the exact exponential mixing exponent in diamond norm and is Lipschitz robust under Hamiltonian perturbations. Rank-one blocks reduce exactly to twice the squared-coupling graph Laplacian. An eight-dimensional rational architecture with four qubit blocks is certified irreducible; its gap is the unique root in (0.4545,0.4547) of an explicit quartic. Symbolic certificates, semidefinite diamond-norm replays, and convergence tests accompany the paper.
Category: Quantum Physics
[1751] ai.viXra.org:2608.0037 [pdf] submitted on 2026-08-10 15:20:28
Authors: Lluis Eriksson
Comments: 10 pages, 1 figure. Exact diamond curvature, a discrete Stokes law, balanced semigroup integration, and a sharp qubit action bound. AI use disclosed.
The order of short operations is normally a microscopic detail. We show that a fixed degenerate measurement turns it into an operational curvature with an exact macroscopic readout. Let E retain a block matrix algebra, and let two words apply the same short Hamiltonian kicks in different orders, with the same nonselective pinching after every kick. Their leading difference is `-i tau^2 ad(F) E`, where F is the sum of `i[h_j,h_k]` over pairwise inversions. This gives a discrete non-Abelian Stokes law. Its diamond-norm coefficient is exactly the largest spectral diameter of a block of F, and therefore fixes the leading optimal channel-discrimination advantage. Under first-order balance, all permutations have the same dissipator while their geometric Hamiltonians differ exactly by F, so local curvature integrates into distinct diffusive quantum Markov semigroups. We characterize contextual invisibility, the rank-one classical boundary, and inverse-success amplification under postselection. Every retained Hamiltonian modulo the block center is realizable by a balanced three-kick loop. For a qubit block we prove the sharp action law `kappa <= S^2/[m tan(pi/m)]`, attained by regular planar kick polygons. An integer-Pauli four-kick architecture saturates the bound and supports primitive dissipation. Symbolic, semidefinite, and convergence certificates accompany the paper.
Category: Quantum Physics
[1750] ai.viXra.org:2608.0036 [pdf] submitted on 2026-08-10 15:47:43
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Reproducible code and certificates: https://github.com/lluiseriksson/finite-sample-spectral-certificates/releases/tag/v1.7-complete-continuous-delay-regions
Lower bounds do not determine which resource profiles are physically attainable. We close the continuous inverse problem for passive subspace transport. Let two rank-k subspaces in C^N, N >= 2k, have ordered canonical angles beta, and let q_j be the integrated leading eigenvalues of a positive generator Q = -iS* dS/dt. We prove the exact equivalence: q is attainable if and only if 2 beta is weakly majorized by q. Every feasible profile has a compiler using at most k+1 mutually commuting positive generators of rank at most k, with constant ordered top spectrum. Analytic rationality adds an integer-valued resource: for two boundary frequencies, the least McMillan degree of an inner matrix sending a fixed input subspace to two prescribed output subspaces equals the number of nonzero canonical angles. We also give a fail-closed finite-error certificate for both resources from noisy projectors.At multiple frequencies, Wigner-Smith delay is only the block diagonal of a boundary de Branges-Rovnyak Pick matrix. This positive matrix is the Gram matrix of frequency-excited internal states and has rank bounded by the McMillan degree. Its spectrum yields robust degree certificates and unavoidable model-reduction tails. An exact example exhibits identical local proper delays for degree-one and degree-two devices while their Pick ranks distinguish them. Deterministic code reconstructs the compilers, tests 2,240 randomized theorem interfaces, checks the strict separation, and independently replays the certificate.
Category: Quantum Physics
[1749] ai.viXra.org:2608.0035 [pdf] submitted on 2026-08-10 16:16:46
Authors: Lluis Eriksson
Comments: 12 pages, 1 figure. Sharp qudit action laws, exact 1/12 covariance, O(n^-1) GKLS diffusion and a sqrt(n) clock barrier.
A balanced ordered loop of retained Hamiltonians generates a second-order geometric Hamiltonian. We solve its higher-rank action problem and determine what remains when the order record is erased. For every matrix dimension and every number of kicks `m >= 3`, a gauge-invariant operator action obeys a sharp, dimension-free polygonal bound on the spectral diameter of the geometric Hamiltonian; regular two-level polygons attain the constant in every dimension. A target-sensitive Hilbert--Schmidt companion bound is controlled by the trace norm and has equality exactly for sign-paired nonzero spectra. These laws yield exact diamond-norm ceilings with a physical state witness. For a uniformly forgotten order, we derive an exact `1/12` commutator-frame covariance. The resulting reversal-symmetric random-unitary product converges in diamond norm at rate `O(n^-1)` to a GKLS frame Laplacian whose fixed algebra is the joint commutant of the pair commutators. A tetrahedral Pauli architecture gives exact primitive depolarization with gap `64/3`. Finally, fixed laboratory time `T` and bounded kick amplitude `Lambda` impose a sharp curvature ceiling proportional to `T^2 Lambda^2/n`; maintaining nonzero holonomy requires `Lambda=Omega(sqrt(n))`. Exact symbolic and deterministic numerical certificates accompany the paper.
Category: Quantum Physics
[1748] ai.viXra.org:2608.0034 [pdf] submitted on 2026-08-10 19:10:19
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. Exact qutrit cost, tetrahedral gap and twirl, physical-word limit, quantified beta trichotomy and initial layer.
A balanced sequence of short Hamiltonian kicks has zero first-order drift but retains an order-dependent commutator holonomy. For a traceless qutrit target with ordered eigenvalues, we solve the inverse Hermitian-commutator problem exactly: its minimum product Hilbert-Schmidt norm is the larger adjacent spectral gap, equivalently half the trace norm plus the absolute middle eigenvalue. This yields the exact minimum action of a balanced three-kick realization and identifies a middle-eigenvalue cost tax between 1 and 3/2. Among four equal-norm balanced qubit kicks, the forgotten-order curvature gap is at most `S^4/108`, with equality only for a regular tetrahedron. Its 24 orders generate exactly the six Pauli holonomies, so the finite twirl is depolarizing and an explicit inverse-cosine schedule realizes any depolarizing semigroup exactly at every finite step count. We then derive the diffusion limit from complete echoed, pinched physical words, obtaining an explicit `O(n^-1/2)` diamond-norm bound. Off-block pulses of size `y^(1+beta)` produce a sharp trichotomy: irrelevant for `beta>1`, additive at `beta=1`, and Zeno-projective for `0<beta<1`; a quantitative compression bound gives uniform convergence away from zero and an explicit initial-layer profile. The complete implementation has serial action proportional to `n^(3/4)`. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Category: Quantum Physics
[1747] ai.viXra.org:2608.0033 [pdf] submitted on 2026-08-10 19:28:35
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Exact action-memory theorem with explicit compiler and independent verification. Code: github.com/lluiseriksson/finite-sample-spectral-certificates
A passive lossless network pays two different costs when it rotates a signal subspace over a frequency arc: a continuous Wigner—Smith action and an integer McMillan memory. Known Grassmannian length bounds and rational-inner degree identities constrain these resources separately. For the stated finite rational-inner class, we determine their joint attainable region exactly. Let two rank-k subspaces have principal angles βj, put B = Σj βj and let r be the number of nonzero angles. For a square finite rational inner transfer matrix of degree at most d, define the arc action A = ∫I tr Q(θ)dθ, where Q = −iS*∂θS is positive semidefinite. If B > 0, the exact feasible set is d ≥ r and 2B ≤ A ≤ 2πd − 2B. Both faces are attained. Equivalently, dmin(A) = max{r, ⌈(A + 2B)/(2π)⌉}. The upper face is a return cost: the complementary arc must rotate the subspace back, while the full-circle trace action is exactly 2π times the degree. We prove sufficiency by an explicit compiler of normalized rank-one Blaschke—Potapov gates; it realizes every interior point and both faces, including rank-deficient and orthogonal cases. When the endpoint subspaces coincide, the region changes discontinuously to A ∈ [0, 2πd), with the upper endpoint open. We derive fail-closed noisy degree certificates and give a multi-frequency warning using classical boundary Nevanlinna—Pick theory: three pairwise degree-one routing tasks can require degree two jointly. For orthogonal-line data the obstruction is a frame-independent cycle phase, exhibited by an exact positive semidefinite Pick completion with spectrum (2,1,0). Deterministic code compiles random points of the diamond, constructs the degree-two colligation, and is replayed by an independent verifier.
Category: Mathematical Physics
[1746] ai.viXra.org:2608.0032 [pdf] submitted on 2026-08-10 20:30:59
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. New paper: positive physical transfer from forgotten order, exact tetrahedral spectrum, Hausdorff gap certificates, and Gaussian level control.
A balanced sequence of short Hamiltonian kicks has no first-order drift, but its order-dependent commutator holonomy survives when the order record is discarded. We prove that a reversal-symmetric average of complete order/reverse echoes is a self-adjoint random-unitary transfer operator and obeys the nonperturbative bound cos(4|y|S) I <= T_y <= I for |y|S < pi/8. This yields site and link reflection positivity and a finite-dimensional Osterwalder-Schrader Hamiltonian. The physical transfer approaches the curvature-frame generator with an explicit sixth-order remainder, giving quantitative O(y^2) convergence of its mass gap. For the regular tetrahedral qubit loop, we derive the exact finite-pulse depolarizing eigenvalue, isolate its first positivity zero at y = 0.455698535295322..., and obtain the mass expansion. We then prove a complete finite-depth Hausdorff criterion for visible transfer edges, with uniformly sharp depth r-1, and give an exact rational four-kick certificate: the true frame gap 10/3 is certified while the false claim 4 has rational witness value -1/64. A Wishart-Loewner band supplies finite-sample type-I control for independent Gaussian correlator sketches, including adaptive witnesses. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Category: Quantum Physics
[1745] ai.viXra.org:2608.0031 [pdf] submitted on 2026-08-10 21:34:32
Authors: Lluis Eriksson
Comments: 9 pages, 2 figures. Exact d=4 inverse commutator cost from four Horn facets, all-strata optimal-rank law, sharp tax [1,2], loop action, and reproducible certificates.
For a prescribed traceless Hermitian four-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. With ordered eigenvalues lambda_1 >= ... >= lambda_4, the answer is the maximum of four explicit linear spectral forms. The lower bounds are Horn-Littlewood-Richardson certificates and four closed constructions attain them. On every nonzero spectral stratum, the least optimal rank is exactly max(n_+(F),n_-(F)), closing all chamber walls and degenerations. We also prove a finite-dimensional Horn linear-program reduction, the sharp tax 1 <= kappa_4/(||F||_1/2) <= 2 with complete equality cases, and the exact balanced three-kick action S_2^2=12 sqrt(3) kappa_4. Exact symbolic and deterministic LP certificates accompany the manuscript.
Category: Quantum Physics
[1744] ai.viXra.org:2608.0030 [pdf] submitted on 2026-08-10 03:07:25
Authors: Alistair B. Carter
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper presents a foundational, pre-geometric hydrodynamic framework that models spacetime geometry, gravity, and quantum phenomena as emergent thermodynamic properties of an 8-dimensional non-associative fluid vacuum. Parameterized by complexified octonions (the bioctonions), the state space transitions from linear Hilbert spaces to the power-associative matrix algebra of the 27-dimensional Exceptional Jordan Algebra (J3(O)), bound by an F4 automorphism envelope.The framework bridges two historically disparate domains: division-algebraic particle physics (Dixon, Günaydin, Gürsey, Furey) and analogue gravity in condensed matter vacuum models (Unruh, Volovik, Visser). By synthesizing Volovik's superfluid vacuum paradigm with bioctonion algebraic models of Standard Model gauge symmetries, we demonstrate that forces and matter arise natively as topological deformations of a single continuous medium.We clarify that while complexified octonions form a non-division, power-associative algebra with zero divisors, these properties are fundamental assets to the physics. Anti-commutativity natively encodes Fermi-Dirac statistics and the Pauli exclusion principle; non-associativity generates gauge field curvature, non-linear fluid friction, and temporal processing latency; and zero divisors yield idempotent projection operators that isolate chiral spin states and light-like null trajectories without external metric constraints.We resolve four central mathematical and physical hurdles in non-associative field theories: (1) Macroscopic Matrix Insulation: We prove via real-projection identities and Jordan trace associativity Tr([X, Y, Z]ˆ) = 0 that diagonal observables remain strictly real and associative, insulating observers from off-diagonal phase perturbations. (2) Free Particle Proper Time: We formalize proper time (dτ) as a deformed disformal metric invariant containing an associator correction term, enabling free particle weak decay while preserving temporal latency in high-shear regimes. (3) Rigorous Non-Associative Calculus: Using directional differential operators, we prove free wave propagation in the 8D vacuum is strictly anomaly-free due to octonionic alternativity. (4) Multi-Particle Containment: We construct an explicit 56-dimensional E7 Freudenthal module mapping that proves widely separated particles decouple into independent quartic invariants, preventing non-local parenthetical phase contamination.Finally, the bulk modulus of the fluid matrix resolves the vacuum catastrophe, and theoretical falsifiability is established via a parameter-free derivation of non-conservative orbital energy shifts driven by vacuum vorticity (Ωvac), deterministically matching empirical planetary flyby anomalies.
Category: Quantum Gravity and String Theory
[1743] ai.viXra.org:2608.0029 [pdf] submitted on 2026-08-10 02:01:56
Authors: Lluis Eriksson
Comments: 18 pages; Exact-arithmetic, numerical, and Lean/mathlib reproducibility artifacts are linked in the paper.
Scalar Chebyshev filtering treats every vector in a block Krylov iterate with the same polynomial, while simultaneously diagonalizable matrix coefficients amount to independent scalar filters after a fixed channel rotation. We study the larger class of Hermitian matrix-polynomial filters under tangential pass constraints. Already at fixed channel dimension d=3, we construct rationally generated signatures with quantitative full-spark margin for which an irreducible symmetric filter has stopband leakage O(exp(-cN)). In contrast, every exactly calibrated symmetric coefficient family with any common nontrivial invariant channel subspace has leakage at least one; this comparator strictly contains the pairwise-commuting class and permits a fully noncommutative 2 by 2 block. A quantitative theorem covers approximately reducible filters by charging their sampled off-block coupling together with calibration error. The signature margin and the admissible combined error are both exp(-O(N)), not exp(-N^3). This exponential scale is unavoidable: for arbitrary pass nodes and signatures in the same separated bands, an explicit scalar binomial-tail polynomial has both pass error and stopband leakage at most exp(-2N/81). Thus constant-error separation is impossible, while the irreducible construction achieves the correct exponential scale class. An affine cosine substitution gives the same robust law for fixed-latency reciprocal linear-phase MIMO FIR filters. We also give an exact rational five-tap certificate with stopband norm at most 25/32 and prove that its advantage survives reducible calibration errors delta < 7/1920. A second exact-arithmetic certificate is calibrated from a public triaxial pump-vibration data set: it gives leakage below 0.96 versus one for every exactly calibrated reducible symmetric class, while its maximum directional error on six held-out records is 0.00385. In a frequency-domain-decomposition test on the frozen held-out cospectra, filtering rotates the leading modal direction by at most 0.222 degrees and changes its leading spectral ordinate by at most 2.4 × 10^-5 relatively. Numerical programs test the mechanism and expose an ordinary graph-denoising setting in which scalar Chebyshev filtering is instead preferable. Tangential matrix interpolation, MIMO filtering, scalar two-band approximation and convex FIR design are not claimed as new; the contribution is the fixed-order reducible/irreducible separation together with its two-sided calibration scale.
Category: Digital Signal Processing
[1742] ai.viXra.org:2608.0028 [pdf] submitted on 2026-08-09 19:02:29
Authors: Arunas Ostasevicius
Comments: 8 Pages. 2 Figures
This paper expands the quaternionic field framework into the fully dynamic regime of electrodynamic radiation, autowave propagation, and resonance absorption by treating the physical vacuum as a deterministic, compressible elastic medium of sub-planckian vacuum bubbles (the Wheeler substrate). By deploying a non-linear second-order Verhulst—Van der Pol logistic regulator, we establish a rigorous four-fold taxonomy of substrate kinematics: laminar drift, collective macro-convection, pulse shocks, and high-frequency volumetric oscillations. We deconstruct the classical Maxwellian displacement current, mapping it as the literal velocity of elastic shape deformation within the bound bubble matrix under finite field viscosity. This hydrodynamic ontology eliminates the historical energy-divergence paradoxes and provides a transparent mechanical contrast between the closed, dissipative conduction currents of conventional technology and the open, non-local resonant autowave transfers observed in Tesla-Meyl single-wire topologies. Finally, the intra-atomic current of the hydrogen atom is reinterpreted as a closed, non-radiating toroidal self-circulation of the substrate under a 2:1 gyroscopic resonance condition. We define quantum transitions not as stochastic jumps, but as a causal two-stage process consisting of external acoustic pumping (vortex energy accumulation) followed by a non-linear quadratic boundary disruption that releases an isolated, indivisible longitudinal-transverse quaternionic electromagnetic wave packet with a strict pi/2 phase quadrature between the scalar potential S and the transverse vectors.8
Category: Quantum Physics
[1741] ai.viXra.org:2608.0026 [pdf] submitted on 2026-08-09 18:42:43
Authors: Bing Zhang, Aizhong Jia
Comments: 29 Pages.
The Graviton Condensation Cosmology (GCC) framework posits that macroscopic gravity emerges from the condensation of spin-2 collective quadrupole excitations (GQR phonons) in nuclear matter. We extend this framework to address the dark sector: we propose that both dark matter and dark energy originate as residues of the QCD phase transition at T_c ≈ 156.5 MeV. Dark matter is identified with multi-glueball bound states — the unique GCC-compatible candidate after a systematic exclusion of all Standard Model and beyond-Standard-Model particles, which lack either QCD substructure or a spin-2 quadrupole channel. The relic abundance Ω_gb h² naturally matches the observed Ω_DM h² ≈ 0.12 for formation fractions f_gb ∼ (1—10) × 10u207bu2076 across three mass windows (m_gb ≈ 0.78—2.4 GeV). Dark energy arises from the residual uncondensed fraction (1 − ε) ∼ 10u207bu2074u2075 of the spin-2 condensate energy. While this value is accommodated within the non-linear saturation framework, its precise first-principles pre—diction remains an open theoretical challenge; it constitutes a well-defined target for future development of the saturation dynamics. We show that the Landau parameter Fu2082 reaches −4.97 ± 1.25 (phenomenological estimate) or −3.65 ± 0.41 (conservative RPA with realistic nuclear forces), both approaching the Pomeranchuk instability thresh—old Fu2082 = −5 with critical density n_c/nu2080 ≈ 1.0—1.2. Finite-temperature enhancement mechanisms at the QCD crossover provide the bridge to the threshold. The framework yields falsifiable predictions including a single nanohertz GW peak (5—15 nHz), distinctive 21-cm power spectrum suppression, and CMB lensing signatures, linking the dark sector to ongoing experiments without introducing new particles or energy scales beyond QC.
Category: Relativity and Cosmology
[1740] ai.viXra.org:2608.0025 [pdf] submitted on 2026-08-08 01:25:44
Authors: Arūnas Ostasevičius
Comments: 8 Pages.
This paper performs a systematic deconstruction of the electromagnetic field vector reduction originally executed by O. Heaviside and J. Gibbs. We demonstrate that the forced nullification of the Maxwellian field scalar potential S = Real(DA) = 0 deprived the physical vacuum of its fundamental property of volumetric compressibility. Within the proposed framework, the electron is modeled as a deterministic, non-linear quaternionic vortex structured within a dynamic medium of vacuum bubbles (the Wheeler field), stabilized by a Van der Pol attractor under the governance of the quaternionic Virial theorem. A modified energy-momentum tensor (EMT) incorporating a scalar term S^2 is derived, which inherently generates an internal compensating hydrostatic pressure. Operating upon Verhulst-type non-linear logistic equations, it is revealed that the vacuum scalar pressure gradient acts as the fundamental accelerating force of autowave drift (inertia). Concurrently, the cubic non-linear term completely eliminates infinite electronic energy divergences as the core radius approaches zero. Finally, a comparative numerical analysis is provided, demonstrating the physical inadequacy of the classical skin-effect framework traditionally used to dismiss the Tesla-Meyl longitudinal wave transmission experiments.
Category: Quantum Physics
[1739] ai.viXra.org:2608.0024 [pdf] submitted on 2026-08-08 01:21:10
Authors: Michael Quigley
Comments: 38 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references) All Rights Reserved - Michael Quigley 2026.
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics
[1738] ai.viXra.org:2608.0023 [pdf] submitted on 2026-08-08 01:16:04
Authors: Arūnas Ostasevičius
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper establishes the complete static, geometric, and interference framework of classical field theory by abandoning the stochastic concept of "quantum spacetime foam" in favor of a deterministic elastic medium of vacuum bubbles (the Wheeler substrate). By restoring the Maxwellian field scalar potential S = Real(DA) != 0, previously excised by the Heaviside vector reduction, we derive the fundamental laws of Gauss, Coulomb, and Compton as direct hydrodynamic consequences of phase coupling and volumetric conservation within a compressible cell matrix. Utilizing non-singular cardinal sine distributions (+/-sinc(x)), the mathematical infrastructure of Coulomb interactions is stripped of point-like vector infinities at the core. Physical forces are reinterpreted as localized holographic interference figures: single charges in a state of rest maintain spherical structural symmetry, whereas approaching like charges generate steep spatial compression "spikes" (+1) leading to repulsion, and opposite charges achieve a complementary "lock-and-key" phase locking forming an interference "hole" (-1) resulting in external hydrostatic attraction. Finally, the Compton effect is rigorously mapped not as particle scattering in a void, but as a non-elastic mechanical collision between a propagating autowave packet of micro-bubbles and the rotating boundary of a macro-bubble core, validating the structural perimeter of the electronic vortex without invoking Planck’s constant.
Category: Quantum Physics
[1737] ai.viXra.org:2608.0021 [pdf] submitted on 2026-08-07 22:46:14
Authors: E. P. J. de Haas
Comments: 58 Pages. https://doi.org/10.5281/zenodo.21844437
The empirical Constant-Lagrangian (CL) relation has previously been shown to reproduce a substantial fraction of observed galactic rotation curves, but until now it has lacked a theoretical foundation. This paper derives the CL condition from a gravitational rapidity field that generates a local Spin(1,3) rotor describing the vacuum flow surrounding a galaxy.Two independent but complementary geometric branches emerge from the same gravitational rotor. The first is a kinematic branch, in which the rapidity field generates the gravitational four-velocity and its convective acceleration. The second is a Maurer—Cartan branch, in which the differential geometry of the rotor itself is described through its Lie-algebra-valued connection. Although these branches describe different geometric objects, both converge on the same invariant isorapidity condition, expressing the conservation of the combined radial and azimuthal rapidity along the flow. In the weak-field limit, this invariant reduces directly to the Constant-Lagrangian relation governing the exterior galactic rotation curve.The construction is developed in its native BQ (biquaternion) algebra and subsequently translated into three standard mathematical languages: the Weyl representation of Clifford algebra Cl(1,3), Spacetime Algebra, and the conventional Dirac spin formalism. The agreement between these independent formulations demonstrates that the resulting isorapidity condition is a representation-independent consequence of the underlying Spin(1,3) rotor geometry rather than an artifact of a particular algebraic framework.Beyond providing a theoretical basis for the empirical Constant-Lagrangian postulate, the paper presents a unified rotor-based description in which both the kinematics of galactic vacuum flow and its Maurer—Cartan transport originate from the same gravitational rapidity field.
Category: Relativity and Cosmology
[1736] ai.viXra.org:2608.0020 [pdf] submitted on 2026-08-05 18:09:44
Authors: Lluis Eriksson
Comments: 17 pages. Lean 4 formalization. AI-assisted with OpenAI Codex; all Lean builds and axiom-oracle checks were verified by the author. Source and validation evidence are linked in the PDF.
We present a Lean 4 formalization of a thermodynamic-limit construction for the anisotropic nearest-neighbour Ising model on the two-dimensional integer lattice. A telescoping comparison argument and the classical Dobrushin resolvent produce a volume-uniform expectation bound. Exact restriction and reindexing maps between finite Gibbs measures yield convergence of the complete free-boundary sequence, independence of auxiliary envelopes and cofinal samplings, stability under receding boundary perturbations, and equality of free and periodic limits.Finite-support cylinder presentations are quotiented by equality of their represented functions on the full spin space. The resulting local algebra carries a genuine lattice-translation action, and the limiting functional is positive, normalized, real-linear, and invariant under every integer translation. We equip this algebra with its intrinsic uniform norm, construct its complex star-algebra representation, take the corresponding commutative C*-closure, and extend the limiting functional to a positive complex-linear functional of norm one. We also formalize normalized Gibbs conditional kernels for arbitrary finite conditioning sets and prove positivity, exterior locality, idempotence, and the exact finite-volume Gibbs tower identity.All results remain within the classical anisotropic Dobrushin region. The infinite-volume DLR fixed-point equation for the completed state is not claimed.
Category: Mathematical Physics
[1735] ai.viXra.org:2608.0019 [pdf] submitted on 2026-08-05 18:19:22
Authors: Lluis Eriksson
Comments: 31 pages, 1 figure. Companion reproducibility archive containing complete LaTeX source, numerical verification code, data and SHA-256 manifest.
We determine when rapid exact maintenance of a rank-deficient quantum target produces logarithmically divergent free-energy restoration power in algebraic quantum field theory. On every sigma-finite properly infinite factor we construct a bounded quantum Markov semigroup, a nonfaithful normal target and a faithful invariant reference state for which Araki relative entropy reduces exactly to a binary divergence. We derive the semigroup first from localized thermal fermionic probe collisions and then from one autonomous finite-bandwidth Dirac KMS reservoir with fixed smooth coupling. Exact memory equations yield an explicit finite-coupling Davies bound on finite van Hove windows. For a displayed compactly supported massless Dirac form factor, Araki—Wyss regularity, threshold behaviour and Fermi-golden-rule positivity give a completely bounded Davies approximation uniformly for all times with error of order (O(|lambda|)); the sharper (O(lambda^2)) result is isolated under additional reduced-resonance hypotheses. We construct a background-covariant two-Dirac-field completion using Green operators, Møller maps and relative Cauchy scattering, proving naturality, causal factorization and exact spacelike triviality. A locality obstruction shows why a strictly local multiplier cannot coincide exactly with the solvable rank-one reservoir coupling, while a Feshbach reduction quantifies the correction. Finally, we prove that no fixed faithful vacuum or KMS restriction can exhibit the rank-boundary mechanism, but faithful families with a vanishing spectral floor recover its complete coefficient. The results separate algebra type, target faithfulness, microscopic realizability and regulator uniformity, and provide reproducible numerical audits of the finite-dimensional identities and explicit Dirac form factor.
Category: Mathematical Physics
[1734] ai.viXra.org:2608.0018 [pdf] submitted on 2026-08-05 21:39:01
Authors: Lluis Eriksson
Comments: 13 Pages. All results are machine-checked in Lean 4 (no sorry, no project axioms; headlines depend on exactly [propext, Classical.choice, Quot.sound]).
For the spatial Z_2 (Ising-slice) system inside the Dobrushin window 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1, we machine-check in Lean 4 an end-to-end chain from the Gibbs measure to the spectrum of the reconstructed transfer operator. (i) The Osterwalder-Schrader (site-form) reconstruction of the transfer operator is unitarily conjugate, by the explicit sqrt(w) boundary dressing, to the symmetrised Dobrushin kernel. (ii) The unnormalised Gibbs sums themselves are exact matrix elements of that operator's powers: gibbsPathSum(w,beta,N,A,B) = lambda^N
Category: Mathematical Physics
[1733] ai.viXra.org:2608.0017 [pdf] submitted on 2026-08-04 14:28:32
Authors: Joseph Palazzo
Comments: 10 Pages.
The universe is causally connected at all scales, but at microscopic scales the total causal network is fundamentally inaccessible. These irreducible epistemic limits are themselves ontological features of reality. Classical determinism emerges gradually as systems increase in scale, making the inaccessible fraction of causal information negligible.
Category: History and Philosophy of Physics
[1732] ai.viXra.org:2608.0016 [pdf] submitted on 2026-08-04 19:14:39
Authors: Lluis Eriksson
Comments: 9 pages. New companion obstruction paper to ai.viXra:2607.0089, not a replacement. Diagnostic code and reproducibility record: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAM
For beta > 0 let I_m = I_m(beta) denote the modified Bessel functionof the first kind and define a_m = I_m^2 ((m-1) I_(m-1)^2 + (m+1) I_(m+1)^2), b_m = m I_m^4,with sine series F_A(t) = sum_(m>=1) a_m sin(mt) andF_B(t) = sum_(m>=1) b_m sin(mt). The associated Wronskian is negativeexactly when F_A/F_B is decreasing. We isolate what can and cannot beproved from two natural inputs: the Neumann convolution kernelI_0(2 beta sin(phi/2)) and the small-coupling anchor whose normalizedlimit is 4 sin^3(t).First, the convolution does prove F_B(t) > 0 for 0 < t < pi. Second,the endpoint is governed by two alternating quantities, c_3 and B_pi,through an exact cubic law. We prove B_pi > 0, derive integralrepresentations, and establish that the cancellation lost by replacingthe alternating quantities with positive-term majorants has exponentialrate 8 - 4 sqrt(2). Finally, we prove a smooth one-parameter perturbationtheorem: one may keep F_B and its kernel unchanged, preserve positivityand strict coefficient-ratio ordering, and preserve every jet at beta = 0,while choosing either sign of the endpoint cubic coefficient.Consequently those structural data, even taken together, do not implyglobal Wronskian negativity. This is a no-go theorem for a proofarchitecture, not a counterexample to the original Bessel conjecture.A short high-precision kill-test accompanies the paper; nocomputer-assisted inequality is used in the proofs.
Category: Mathematical Physics
[1731] ai.viXra.org:2608.0015 [pdf] submitted on 2026-08-04 19:42:27
Authors: Lluis Eriksson
Comments: 13 Pages.
We study whether a flat lattice-gauge Hodge form supplemented by a penalty depending only on a line-integral block variable can control the full fine one-cochain norm uniformly in the block side. The constant-field sector selects the exponent (d-2)/2 only under exact scale neutrality, but this scaling test does not address the kernel of the block map. We construct transverse, divergence-free, block-periodic Fourier cochains that are annihilated exactly by the block map. Their first-mode Hodge Rayleigh quotient is 4 sin²(pi/L), forcing every admissible full-space Poincaré constant to grow at least quadratically with L. The obstruction applies to every scale-dependent scalar functional factored through the block variable and satisfying only that it vanishes at the coarse zero field; no linearity, continuity, positivity, or growth condition is required. For linear postconditioners, higher Fourier frequencies yield an orthogonal real subspace of dimension 2R and a min—max bound on the 2R-th eigenvalue, establishing a growing low-energy spectral cluster. We also derive an exact repair identity and a necessary witness-channel budget for modified block measurements and additional fine-space terms. The kernel construction, Hodge energy, factorized no-go theorem, repair identity, and necessary repair budget are formalized in Lean 4. The result concerns a finite periodic flat full-domain form and makes no claim about interacting coercivity, gauge quotients, continuum limits, or the Yang—Mills mass gap.
Category: Mathematical Physics
[1730] ai.viXra.org:2608.0014 [pdf] submitted on 2026-08-03 17:55:12
Authors: Brent Hartshorn
Comments: 6 Pages. https://github.com/brentharts/crust/
We present Crust, a self-hosted compiler that accepts C, a subset of C++, a subset of Rust and a subset of rpython in a single translation unit, together with its own assembler, linker, freestanding runtime and operating system. After bootstrap the chain depends on no external toolchain: not GCC, not LLVM, not GNU as or ld, and not a host libc. The system is deliberately kept small enough that its entire call graph fits in the context window of a large language model, and we argue this constraint is what makes a system auditable in an era when the reader is increasingly a machine. As a worked example we take the removal of a layer usually treated as part of the machine — the return-address stack — and, with archived and reproducible measurements [20], show both a two-order-of-magnitude pitfall in the naive implementation and a regime in which abandoning the stack is faster than the hardware’s own return predictor. The point of the example is not the speed but the epistemics: the pitfall, the fix, and the regime were each found, made, and checked inside a toolchain small enough to read whole.
Category: Data Structures and Algorithms
[1729] ai.viXra.org:2608.0013 [pdf] submitted on 2026-08-03 20:07:25
Authors: Lluis Eriksson
Comments: 24 pages. Lean 4, no sorry, no project axiom. Eleven machine-checked theorems: positive weight to exponential decay of correlations, plus an abstract transport theorem to a uniform operator gap.
A formal Lean 4 development revisits a two-dimensional spatial transfer kernel whose earlier uniform spectral argument relied on constant row sums. We show that the loss of row-sum constancy obstructs that method, not the conclusion. With no sorry and no project axiom, we prove eleven machine-checked theorems.The chain establishes the sharp field-uniform one-bond influence envelope tanh J; assembles these bounds into a finite-volume Dobrushin matrix; proves a volume-independent resolvent estimate under row-sum bounds alpha < 1 without assuming constant rows; mechanises Dobrushin's comparison inequality with the attained 1/4 covariance constant; constructs Gibbs measures, heat-bath kernels and intrinsic influence matrices from arbitrary strictly positive finite weights; and specialises the result to anisotropic Ising interactions. For L x T rectangles with free boundary, the condition 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1 yields exponential decay of correlations with beta, gamma, alpha and the prefactor fixed before the volume quantifiers.We also prove three transport results: an exact finite-band identity relating endpoint covariances to matrix elements; an abstract theorem showing that a common exponential decay rate for band covariances implies a uniform positive gap for a family of projected transfer operators; and a Perron-boundary tilt identity that preserves the decay rate while absorbing boundary costs into extent-dependent constants.Numerical measurements at L <= 12 provide counterevidence to attributing spectral degeneracy solely to nonzero spatial coupling. A concrete volume-uniform bound on specRatio for the coupled rectangular kernel is not claimed: one finite currying and strip-to-rectangle identification remains open. The underlying Dobrushin mathematics is classical; the contribution is a non-vacuous, reproducible mechanisation and composition of the full chain. No consequence for Yang-Mills theory is claimed.
Category: Mathematical Physics
[1728] ai.viXra.org:2608.0011 [pdf] submitted on 2026-08-02 02:41:29
Authors: Charles A Streb IV
Comments: 15 Pages.
This is an expository reference on the mathematical structure of quantum entanglement.It contains no new results. Part I treats the nite-dimensional theory, where entanglement isdened by the failure of a convex tensor decomposition and is computable in principle. PartII treats the innite-dimensional and algebraic setting. For sharp local regions in relativisticquantum eld theory, the tensor-product and reduced-density-matrix framework generally fails:under the usual phase-space and scaling assumptions, local observable algebras are typicallyhypernite factors of type III1, with no intrinsic normal seminite trace, no intrinsic localdensity matrix, and no reduced-state von Neumann entropy. Part III develops the structuresthat replace that framework TomitaTakesaki modular theory, Araki relative entropy, and thecrossed-product construction. The continuous core of a type III1 factor is type II∞ and carriesa seminite trace; in the gravitationally dressed de Sitter observer construction, the resultingobservable algebra is type II1. Statements are proved when the proof is short and otherwiseattributed precisely. The intended use is as a denitional reference: every term is pinned, andevery substantive claim is either proved here or tied to a cited result with its hypotheses stated.
Category: Quantum Physics
[1727] ai.viXra.org:2608.0010 [pdf] submitted on 2026-08-02 03:33:12
Authors: Lluis Eriksson
Comments: 8 pages, 2 tables, 1 figure. Lean 4.29.0-rc6; Mathlib 07642720480157414db592fa85b626dafb71355b. Clean rebuild passed. 25 public declarations; no sorry, admit, or local axiom. New sequel, not replacement; four-face crossing not claimed.
We give a kernel-checked positive-area calculus for the concrete SU(2) classheat kernel used in two-dimensional Yang—Mills theory. With irreducible labeln, dimension n+1, and Casimir c_n=n(n+2)/4, Lean verifies at every positivetime and every derivative order that the infinite spectral jet converges anddifferentiates term by term to the next jet. The hierarchy is packaged as aC-infinity map on the positive-time half-line, using explicit uniform summablemajorants on positive-time neighbourhoods. We then differentiate the literalnormalized-Haar two-face Migdal integral, prove that its left and right areaderivatives equal the first spectral jet at the merged area, and showinfinitesimal invariance under (s,t) -> (s+u,t-u). Finally, every normalizedWilson character satisfies its exact Casimir area ODE as an actual Haarintegral against the infinite heat kernel. The artifact contains 25 publicdefinitions and theorems, no local placeholders, and audited dependencies onlyon propext, Classical.choice, and Quot.sound. We do not claim the four-faceMakeenko—Migdal crossing equation; the remaining inputs are local Lie-groupintegration by parts and certified crossing geometry.
Category: Mathematical Physics
[1726] ai.viXra.org:2608.0009 [pdf] submitted on 2026-08-02 07:14:51
Authors: Lluis Eriksson
Comments: 6 pages, 2 tables, 1 figure. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 30 public declarations; no sorry, admit, or local axiom.
We formalize the finite-dimensional integration-by-parts mechanism used inlocal proofs of the Makeenko—Migdal equation. For a measure-preserving realflow on a finite measure space, Lean verifies differentiation under theintegral from an explicit locally uniform integrable majorant and proves thatthe integral of the generator vanishes. A bounded dominated product interfacethen yields integration by parts, and two successive applications transfer amixed pair of generators from a density to an observable with positive sign.These results are instantiated on normalized Haar probability measure ofconcrete SU(2) and on every finite product SU(2)^E, for left and rightmultiplication of one selected edge. To fix the representation normalization,we construct three explicit trigonometric curves in SU(2) and prove entrywisethat their tangents at the identity are i sigma_1/2, i sigma_2/2, and isigma_3/2. The producer contains 30 public definitions, structures, andtheorems in 519 physical lines; its audit contains no local sorry, admit, oraxiom, and the headline results depend only on propext, Classical.choice, andQuot.sound. This closes the Haar integration-by-parts layer. It does not claimthe full four-area Makeenko—Migdal identity: the remaining formal inputs arethe heat-density directional identity, extended gauge invariance at acrossing, and their geometric assembly.
Category: Mathematical Physics
[1725] ai.viXra.org:2608.0008 [pdf] submitted on 2026-08-02 11:55:22
Authors: Lluis Eriksson
Comments: 18 pages. All new lemmas machine-checked in Lean 4 (pinned Mathlib); the supremum theorem is conditional, carrying the Birkhoff spectral bound as an explicit hypothesis, not an axiom. Source: github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME
A positive site weight acts on a transfer kernel by congruence, K -> DKD with Dpositive diagonal, not by similarity. Similarity preserves the entire spectrum;congruence preserves strictly less, and strictly more than nothing. We determineboth halves for the kernel of L decoupled Ising bonds. Rigid half: the sign ofevery quadratic form value survives, so definiteness in either sign is acongruence invariant -- the definite case of Sylvester's law of inertia, in aform a machine can check without diagonalisation. Fragile half: the subdominantratio r (second eigenvalue modulus over the Perron root) does not survive atall, and we locate exactly how far it moves. Restricting the L-site kernel tothe two antipodal configurations leaves one Ising bond of coupling bL, of ratiotanh(bL) for b>0: a weight concentrating there fuses the L sites into a singleeffective site carrying L times the coupling. Since tanh(bL) -> 1, no boundr <= rho < 1 holds simultaneously in L and over the whole positive-diagonalcongruence orbit; the obstruction to volume-uniformity is a property of thecongruence, not of any spectral estimate, so an argument bounding r throughcongruence invariants alone cannot produce an L-uniform bound. For arbitraryweights we prove sup_{D>0} r(DMD) = (1-m)/(1+m), where m is the leastoff-diagonal entry: the least correlated pair determines the supremum. (Weevaluate the supremum; we do not classify its maximisers.) The proof isgeometric rather than spectral -- Hilbert's projective diameter is itself acongruence invariant, and Birkhoff's contraction theorem converts it into thebound -- and uses no definiteness, only positivity of the entries. The lowerbound uses no limiting argument about spectra: a two-supported fluctuationvector gives the estimate at each strictly positive epsilon, so no continuity ofeigenvalues is imported anywhere.
Category: Mathematical Physics
[1724] ai.viXra.org:2608.0007 [pdf] submitted on 2026-08-02 14:02:27
Authors: Lluis Eriksson
Comments: 6 pages, 2 tables, 1 figure. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 19 public declarations; no sorry, admit, or local axiom.
We formalize a finite-dimensional crossing Ward identity for fundamental SU(2) Wilson words. On every finite edge space SU(2)^E, two distinct coordinates are inserted into a concrete normalized trace word. Lean proves entrywise that right multiplication by each of three explicit SU(2) curves produces the normalized Pauli generators i sigma_a/2, differentiates the trace word once at each selected coordinate, and identifies the Pauli-summed mixed derivative with the rank-two Fierz contraction. Two applications of Haar integration by parts transfer the corresponding mixed generators from a density to the Wilson word. The resulting integral closes exactly on the direct and reverse single-trace resolutions, with coefficients -1/4 and -1/2 in the chosen normalization. The producer contains 19 public declarations in 487 physical lines; all 13 new theorems depend only on propext, Classical.choice, and Quot.sound, with no local sorry, admit, or axiom. This is not a full Makeenko--Migdal area equation: the remaining physical input is a weak four-face identity against crossing-certified extended-gauge-invariant observables. In the program's heat time, generated by the Pauli Laplacian, its coefficient is kappa = 2.
Category: Mathematical Physics
[1723] ai.viXra.org:2608.0006 [pdf] submitted on 2026-08-02 16:46:30
Authors: Lluis Eriksson
Comments: 6 pages, 2 tables, 2 figures. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 56 public declarations; no sorry, admit or local axiom.
We formalize extended gauge invariance at a simple four-edge SU(2) crossing and connect the geometric edge chart to the two-coordinate chart used by a machine-checked crossing Ward identity. On SU(2)^4 we define the two opposite-edge right actions from the abstract Makeenko--Migdal theorem, prove that they are commuting product-Haar-preserving actions, and show that their common parameter composes to ordinary vertex gauge invariance. The four-edge Wilson word tr2(a3^-1 beta a2 a4^-1 alpha a1) is proved invariant under both half-actions. We construct the explicit quotient r(a)=(a2 a4^-1,a1 a3^-1), a canonical section, and prove existence and uniqueness of the universal factorization for every extended-gauge-invariant complex function. The complete map from the cyclic four-edge chart to physical and gauge coordinates is proved to preserve literal four-fold Haar measure in one public endpoint. Finally, the four-edge Wilson word is identified exactly with the prior two-coordinate crossing word evaluated on r(a). The Lean producer has 56 public declarations in 488 physical lines; all 36 theorems depend only on propext, Classical.choice, and Quot.sound, with no local proof escape. No heat-kernel area derivative or full Makeenko--Migdal equation is claimed.
Category: Mathematical Physics
[1722] ai.viXra.org:2608.0005 [pdf] submitted on 2026-08-02 19:16:06
Authors: Lluis Eriksson
Comments: 7 pages, 2 tables, 2 figures. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 26 public declarations; no sorry, admit or local axiom.
We machine-check the exact measure and differential bridge between thefour-edge SU(2) crossing chart and the two effective group coordinates used bya finite-dimensional Ward identity. The quotientr(a)=(a2 a4^-1,a1 a3^-1) pushes normalized four-fold Haar measure exactly tonormalized two-fold Haar measure. Two gauge-compensated flows on the originalfour edges intertwine with independent right multiplication of the quotientcoordinates, so first and mixed derivatives of the crossing Wilson worddescend without choosing a gauge. The three Pauli directions are verifiedindividually, their mixed generators close into direct and reverseresolutions, and the two-coordinate Ward theorem lifts to a literal four-edgeintegral with coefficients -1/4 and -1/2. This compensated operator is notidentified with the ordinary-edge mixed operator of Driver-Hall-Kemp: thepaper writes both operators and their distinct reverse resolutions and markstheir comparison as open. The Lean producer has 26 public declarations and 16audited theorems. No weak four-face heat-kernel identity, area derivative, orfull Makeenko--Migdal equation is claimed.
Category: Mathematical Physics
[1721] ai.viXra.org:2608.0004 [pdf] submitted on 2026-08-02 19:25:02
Authors: Lluis Eriksson
Comments: 8 pages. Lean 4 formalization with pinned Mathlib. Nine headline declarations were audited and depend only on propext, Classical.choice, and Quot.sound; no project axioms or sorryAx. Formal source frozen at commit f21539ed0bb880a04078de369bf5cbf063f7b101.
Let a fine periodic lattice have side LN' and let Q_L be the L^{-d}-normalized block average of length-L line integrals. In four dimensions, the rescaling Q_L -> LQ_L repairs the elementary constant-field scaling obstruction to a Poincare estimate. We prove that it cannot yield coercivity on the full one-cochain space with a constant uniform in the block side.For every L >= 2, every fixed N' >= 1, and N_c >= 2, we embed the first within-block Fourier phase zeta_L = exp(2 pi i/L) in a real two-plane of the internal coordinate space and construct a transverse one-cochain A_L. It satisfies Q_L A_L = 0 and div A_L = 0. For every dimension d >= 2,||A_L||^2 = (LN')^d,
Category: Mathematical Physics
[1720] ai.viXra.org:2608.0003 [pdf] submitted on 2026-08-01 23:42:12
Authors: J. W. McGreevy
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
We develop a symplectic geometry of atomic shear measures supported on the irregular primes of a modular curve. Starting from a space of dis-crete measures subject to a global valence constraint, we perform a strict symplectic reduction and obtain a reduced phase space equipped with a canonical Darboux form. The local coordinate functions that extractthe individual shear amplitudes are shown to be in Liouville involution, generating a completely integrable system whose invariant level sets areLagrangian tori. By lifting the functional equation of the associated automorphic L-functions to an anti-symplectic involution on this phase space, and under the established essential self-adjointness of the clutched conical Dirac operator, we prove a Confinement Theorem: the only invariant Lagrangianleaves compatible with the reflection symmetry are those whose spectralimage lies on the critical line Re(s) = 1/2. We conclude with a brief, explicitly programmatic dictionary that explores possible links between the resulting arithmetic geometry and structures appearing in gauge theory and the Standard Model. This workextends earlier constructions developed under the working title Relativistic Field Theory of Primes (RFTP), in which the irregular primes, the weight-12 valence constraint, and the associated clutching data were first introduced as geometric ingredients of an arithmetic field theory.
Category: Mathematical Physics
[1719] ai.viXra.org:2608.0002 [pdf] submitted on 2026-08-01 23:35:07
Authors: Nigel B. Cook
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
It is shown that SU(4) and SL(4,R) both offer feasible alternative routes to unification, justifying the twistor unification approach and therefore getting rid of superstring theory. Paper was proof read by Copilot AI to check maths.
Category: Quantum Gravity and String Theory
[1718] ai.viXra.org:2608.0001 [pdf] submitted on 2026-08-01 18:50:53
Authors: Lluis Eriksson
Comments: 9 Pages. Lean 4/Mathlib formalization of the finite-SU(2) Pauli/Casimir contraction, trace-skein identity, four oriented local branches with both reconnections, corrected single-crossing closure, and an all-order multitrace-to-single-trace recursion.
Finite-rank Makeenko-Migdal equations generate products of Wilson traces at self-intersections. For SU(2), this apparent multitrace obstruction closes exactly on single traces, but the statement is normalization-sensitive: the traceless Lie algebra contributes a finite-rank correction that disappears for U(2) and must not be dropped. We give a Lean 4/Mathlib formalization of the complete group-algebraic closure mechanism on Mathlib's concrete special unitary matrix group. With normalized trace tau(A)=Tr(A)/2 and normalized anti-Hermitian Pauli directions X_j=i sigma_j/2, the kernel checks the Casimir identity, the rank-two Fierz identity, the induced crossing contraction, and the SU(2) trace-skein identity tau(g)tau(h)=(tau(gh)+tau(gh^{-1}))/2. Consequently, the finite-SU(2) crossing term tau(g)tau(h)-tau(gh)/4 equals tau(gh)/4+tau(gh^{-1})/2. We then formalize a universal local interface with four cyclically ordered branch holonomies, an independent orientation on each branch, the two opposite-strand words, and precisely the two direct/reversed reconnections. Its corrected crossing term closes on those reconnections for every branch assignment and orientation choice. A recursive theorem also extends the reduction to products of arbitrarily many fundamental traces. The identities are classical; the contribution is a concrete, kernel-checked normalization bridge from Pauli contraction to the single-trace closure used in finite-rank loop equations. We do not claim a formal derivation of the Yang-Mills area derivative, planar loop geometry, or the full Makeenko-Migdal equation.
Category: Mathematical Physics
[1717] ai.viXra.org:2607.0095 [pdf] submitted on 2026-07-31 20:17:07
Authors: Shivanshu Sharma
Comments: 18 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
This paper proposes the Variable Speed Rule (VSR), a hypothesis that the local propagation speed of light is not fixed, but depends on local energy density — decreasing smoothly toward zero as density approaches a threshold value (E_threshold), rather than remaining constant at c as in Einstein's Special Relativity. Starting from Maxwell's equations, the standard electromagnetic wave equation is rigorously derived; the paper's central postulate is introduced explicitly at this point — replacing the constant vacuum permittivity—permeability product with a density-dependent function — and is not itself derived from established physics. This substitution, governed by a coupling constant K (termed the LAP constant), yields a modified wave equation predicting a smooth suppression of light speed near black hole horizons and an energy-dependent delay in photon arrival from high-density astrophysical events such as neutron-star mergers. Using the timing bound from the GW170817 merger, this paper shows that for a physically motivated E_threshold (Planck density), the predicted delay is many orders of magnitude below current detection limits; a value of E_threshold large enough to be detectable currently has no independent physical justification. This tension is identified as the central open problem for testing the framework. Three concrete, falsifiable predictions are proposed for future observational testing. The paper does not claim experimental confirmation — its aim is to present a mathematically self-consistent, clearly labeled hypothesis, with rigorous derivation and unproven postulate explicitly distinguished throughout.
Category: Astrophysics
[1716] ai.viXra.org:2607.0094 [pdf] submitted on 2026-07-31 16:03:53
Authors: Lluis Eriksson
Comments: 8 Pages. Lean 4/mathlib; core build 8464 jobs, 2794 oracle commands (2791 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 2d0346b2.
BOND REFLECTION, AND THIS ONE IS ABOUT THE MEASURE. A whole path X of 2m+2slices has a past half past(X) and a future half; write rev(X) for the futurehalf READ BACKWARDS FROM THE FAR END, which is the reflected copy. Let F be acomplex observable of an entire half. Then for every L, every m, everystrictly positive source weight w and every beta >= 0, sum over whole paths X of conj(F(past X)) * F(rev X) * W(X) >= 0the sum running over all whole paths and W being the ordinary Gibbs weight.This is the finite-volume Osterwalder-Schrader reflection-positivityinequality for this model at odd separation. The sum is UNNORMALISED, which isthe form the axiom is about; dividing by the partition function is division bya positive number and preserves the sign. The Gram matrix of a finite familyof such observables, with complex coefficients, satisfies it as well. It isobtained by proving that assembling a past half, a crossing bond and areversed future half is a BIJECTION onto paths, and that the weights multiplywith exactly one crossing factor.SITE REFLECTION, AND THIS ONE IS NOT, YET. Through a site the two halves SHAREthe middle slice, so the assembly is not a product of two independent halvesand its bijection is a different statement. What is proved there is thehalf-chain form, its collapse identity and its Gram positivity -- at EVERYbeta, negative coupling included -- but NOT its identification with the pathmeasure. For that geometry the object remains a candidate, and the statustable says so row by row.ON THE BETA HYPOTHESIS. beta >= 0 is proved SUFFICIENT and is not provednecessary here; at L = 0 it could not be, since the bare kernel is then thescalar 1. The witness that would make the boundary exact from one site upwardsis authorised by a gate and is not written.THE MECHANISM, IN ONE SENTENCE. Summing out the interior of a half sends F toa vector indexed by its boundary slice alone, after which the bond casereduces to positive semidefiniteness of the kernel -- machine-checked in thecompanion paper -- and the site case to a weighted squared norm, which uses noproperty of the kernel at all.WHERE THE TWO REFLECTIONS DIFFER, AND IT IS NOT COSMETIC. Through a bond thetwo halves are disjoint and meet through one kernel factor, so positivityneeds the kernel itself positive semidefinite -- which, for L >= 1, holdsexactly when beta >= 0. Through a site the halves SHARE the middle slice; theform is then a sum of squared moduli divided by the weight of that slice, soit is non-negative for EVERY beta, negative coupling included, and no propertyof the kernel is used at all.WHAT THE SOURCE WEIGHT DOES. In the companion paper the weight was handled bycongruence: conjugation by sqrt(w) cannot change the sign of a quadratic form.Here it is not conjugated away, it is SUMMED away -- and what is left overdiffers between the two geometries. In the bond case every source weight isabsorbed into the collapse and the bare kernel remains; in the site case theshared boundary slice survives as a factor 1/w(sigma), because each halfcarries that slice's weight and the product would count it twice. Differentreasons, same conclusion: nothing in the hypotheses depends on w beyondpositivity.WHAT THIS IS NOT. No reconstruction: the physical Hilbert space as thequotient of the past algebra by the null space of this form is not built.Nothing here concerns uniformity in the extent, SU(N), the continuum limit, orthe Yang-Mills mass gap.ON THE PRE-REGISTRATION. Four gates were committed before a line of the modulewas written; the status table reports what happened to each. Two of them reada minimum eigenvalue rather than sampling observables, which is the instrumentthe previous campaign's autopsy said was needed.
Category: Mathematical Physics
[1715] ai.viXra.org:2607.0093 [pdf] submitted on 2026-07-30 06:19:09
Authors: Lluis Eriksson
Comments: 8 pages. Lean 4/mathlib; core build 8430 jobs, 2672 oracle commands (2669 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 9704b3f3.
Two companion papers were left carrying the same debt from opposite sides. Thegap paper proved that every eigenvalue of the coupled slice other than thePerron eigenvalue is STRICTLY smaller in modulus, and said plainly that thisprovides NO MODULUS of separation. The bridge paper proved that the Gibbscorrelations of the spatial system are matrix elements of a self-adjointtransfer operator, and obtained geometric decay only UNDER A CONTRACTIONHYPOTHESIS IT DID NOT DISCHARGE. The missing step is identical in both: finitelymany strict inequalities are not an operator-norm bound.PROVED. We construct specGap, the largest |mu| over the eigenvalues differentfrom the Perron eigenvalue lambda, and prove specGap < lambda. We then prove theoperator bound: for every observable u orthogonal to the Perron vector,||Ku|| <= specGap*||u||. That is exactly the hypothesis the bridge papercarried, so its bound becomes unconditional. The bound is SHARP: whenever thestate space has at least two points, some nonzero fluctuation observable attainsit. The argument splits at specGap = 0, where the maximising index need notsupply a NON-PERRON eigenvector (it does supply the Perron one), hence none inthe fluctuation sector. Stated about an object too: the set of Rayleighnorm ratios on the fluctuation sector has a greatest element, equal to specGap(same two-point hypothesis: with fewer, that set is empty).A WARNING WE STATE BEFORE ANYONE ELSE HAS TO. specGap < lambda is NOTspecGap < 1: the kernel is unnormalised, so both are typically far above one andspecGap^N GROWS. On its own the unnormalised bound controls growth, it does notexhibit decay. The rate that is below one is the RELATIVE one,specRatio = specGap/lambda < 1, and the decay statement is that the fluctuationcontribution is suppressed by specRatio^N RELATIVE to the Perron scalelambda^N. Both forms are proved; only the second is called decay.The step that does not follow from the inequalities is the one abouteigenvectors AT lambda: geometric simplicity, proved in the Perron paper for anarbitrary eigenvector rather than a positive one, makes them INVISIBLE to afluctuation observable, so the top term of the spectral sum vanishes instead ofmerely being bounded.NOT PROVED. specGap DEPENDS ON THE EXTENT, and nothing here bounds it away fromlambda uniformly. Direct diagonalisation gives specGap/lambda = 0.9205, 0.9829,0.9964, 0.9992 at L = 2,3,4,5 for one parameter pair: a geometric bound whoserate tends to 1 is empty in the limit, and that is reported, not hidden. Thenormalised Gibbs EXPECTATION is now bounded too: splitting the dressed constantobservable along the Perron direction bounds the partition function below withno eigenbasis index identified, so at a fixed extent the two-point function isbounded by C*specRatio^N past an explicit threshold. That rate depends on theextent, so this is not clustering. The bound and its attainmentare both proved, which is what it means for specGap to be the operator norm onthe fluctuation sector; what is NOT done is introducing that norm as a definedobject and proving an equation about it. And the threshold N_0 does not dependon the observable: it is built from the dressed CONSTANT observable, so ONE N_0serves every fluctuation observable at once and only C sees A. Reflectionpositivity is untouched, and nothing in this paper is a claim about SU(N), thecontinuum limit, or the Yang-Mills mass gap.
Category: Mathematical Physics
[1714] ai.viXra.org:2607.0092 [pdf] submitted on 2026-07-30 14:48:32
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4/mathlib; core build 8431 jobs, 2697 oracle commands (2694 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 247de2b3.
Every rate in this lane so far has been a fixed-extent rate. The gap paper provedstrict spectral separation at each extent and said plainly that it was notuniform; the modulus paper gave that separation a number, specRatio(L), andreported measurements saying the number tends to 1 outside the disordered region.A geometric bound whose rate tends to 1 is empty in the volume limit, so nothingin the lane survived L -> infinity, and the word CLUSTERING was never used.PROVED. For the DECOUPLED kernel - the transfer kernel at constant source weight- the modulus is specRatio = tanh(beta) at EVERY extent, with L nowhere in it.Both directions: an operator bound by induction on the extent, and attainment bythe single-site observable the extent paper already built. Composing with themodulus paper's endpoint, the normalised Gibbs two-point function obeys|E[A(X_0)A(X_N)]| <= C_A tanh(beta)^N past one threshold serving everyobservable - a bound whose RATE contains no L, and therefore the first statementin this lane that survives the volume limit.WHY THE PROOF IS NOT THE SPECTRAL DECOMPOSITION. The decoupled kernel is aproduct over sites, so its spectrum is a product; that route needs the spectrumof a Kronecker power, which the library does not carry. It is not needed. Themodulus paper proved that specGap is the GREATEST norm ratio on the fluctuationsector, so bounding it above is an operator inequality and nothing else, and thatfalls to induction: the even part of an observable keeps its mean zero andinherits the rate, the odd part keeps nothing and gets only Schur's test, and thetwo recombine EXACTLY, because tanh(beta) Z = D with Z the row sum and D the oddeigenvalue of a single bond.NOT PROVED, AND A JUDGE THAT FAILED. The COUPLED kernel is untouched. Before anyof this was written we pre-registered two falsifiable predictions. The first -that the decoupled rate is exactly tanh(beta) at every extent - passed to 1e-16,and authorised the work above. The second - that the coupled uniformity boundaryis the Onsager curve - failed on one of eight pre-registered cells, and it staysfailed: that claim is reported as NOT ESTABLISHED, not softened. At constantsource weight the spatial slices are independent, so what is proved here is astatement about a product measure; that is exactly why it is reachable, and it issaid in the paper rather than left to be noticed. Reflection positivity isuntouched, and nothing in this paper is a claim about SU(N), the continuum limit,or the Yang-Mills mass gap.
Category: Mathematical Physics
[1713] ai.viXra.org:2607.0091 [pdf] submitted on 2026-07-30 18:51:18
Authors: Lluis Eriksson
Comments: 7 pages, no figures. Lean 4 formalization. Verification artifact: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/tree/d6282a83
We formalize in Lean 4 the thermodynamic limit of bounded local Gibbs expectations for a periodic lattice gauge model in a uniform Kotecky-Preiss regime. The proof treats the complete finite-volume sequence: an exact one-volume marked expansion cancels the extensive far gas algebraically, common-window terms are transported exactly, and the remaining boundary contribution is bounded by an existing volume-uniform pinned cluster tail. The resulting explicit Cauchy modulus tends to zero, so completeness constructs an infinite-volume positive normalized real local state. On the intrinsic integer-coordinate local-observable algebra, the state carries a genuine additive action of Z^d and is invariant under every integer translation, including inverses. For SU(2), Haar probability measure, and the physical Wilson plaquette energy Re tr(U), the hypotheses are discharged throughout the explicit punctured intervals 0 < |beta| <= 10^-5 in d=2 and 0 < |beta| <= 10^-6 in d=4. We construct a genuine centered free-boundary exhaustion and prove that its complete cofinal sequence converges to the same state as periodic boundary conditions. The normalized finite-volume two-plaquette truncated-correlation bound also passes to the state under explicit eventual realization and separation hypotheses. We do not claim arbitrary boundary conditions, a C*-algebraic state, a continuum limit, Osterwalder-Schrader reconstruction, or progress on the continuum Yang-Mills mass-gap problem.
Category: Mathematical Physics
[1712] ai.viXra.org:2607.0090 [pdf] submitted on 2026-07-30 20:31:57
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4/mathlib; core build 8463 jobs, 2752 oracle commands (2749 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 854ff223.
WHAT IS PROVED, STATED BEFORE ANYTHING ELSE. The reflected two-point form ofthe Gibbs measure, at the two ENDS of a path, for REAL observables of a SINGLEslice, is non-negative under the parity and coupling hypotheses stated below-- at even separation for every beta, and at every separation exactly for beta>= 0 -- and the Gram matrix of a finite family of such observables is positivesemidefinite under the same hypotheses. THIS IS NOT YET THEOSTERWALDER-SCHRADER AXIOM, which quantifies over observables of the wholepast half-chain and over complex ones. The half-chain algebra, the reflectionmap and the sesquilinear form are not built here; the scope section says whatis missing and why it is a construction rather than a further inequality.Eleven papers in this lane end with REFLECTION POSITIVITY IS UNTOUCHED. Thistouches the endpoint form of it, and the interesting part is what the spatialsource weight does -- namely nothing. Earlier papers do prove statements aboutthe coupled kernel; specGap < lambda holds there too. What is new is that thisresult is UNCHANGED by the weight: same hypothesis, same conclusion, and noconstant that depends on w. Every earlier coupled-kernel statement contains anumber that moves when w does. Positivity is the SIGN of a quadratic form, andconjugation by sqrt(w) is a congruence, so there is nothing for the weight tomove.TWO REFLECTIONS, TWO HYPOTHESES. The reflected two-point sum is
Category: Mathematical Physics
[1711] ai.viXra.org:2607.0089 [pdf] submitted on 2026-07-28 22:32:03
Authors: Lluis Eriksson
Comments: 33 pages. Exact identities, outward-rounded Arb certificates, production/replay transcripts amd Lean 4/Mathlib lemmas: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/releases/tag/surface-theorem-v1.0
For beta > 0 let I_m = I_m(beta) denote modified Bessel functions ofthe first kind, and set a_m = I_m^2 [(m-1) I_(m-1)^2 + (m+1) I_(m+1)^2], b_m = m I_m^4, F_A(t) = sum_(m>=1) a_m sin(mt), F_B(t) = sum_(m>=1) b_m sin(mt), E(t) = F_A(t)/(2 F_B(t)).The global ratio-monotonicity problem for the surface expansion of atwo-dimensional SU(2) lattice gauge observable is: (i) F_B > 0 on(0,pi), and (ii) E' < 0 on (0,pi), for every beta > 0. Bothstatements are proved. Positivity of F_B has two exact proofs. Ratiomonotonicity is reduced to exact algebraic identities andoutward-rounded interval certificates: small and compact beta arehandled by pair identities and interval Taylor models;20 <= beta <= 1000/9 by a direct Wronskian cover; andbeta >= 1000/9 has three certified moving-edge lambda lanes. Theremaining lambda >= 3 lane is closed by the exact identityE'/(-sin(t/2)/2) = Q + X_full, where Q > 19/20, an exactmain--mirror--rest decomposition, and a division-free covariancecertificate proving X_main > -1/20 on two adjacent rectangles thatcover the full angular interval. The exact near and far relay marginsare positive. All load-bearing production and independent replaytranscripts are checked for exact rational coverage, dependencyhashes, strict outward-rounded decision endpoints, and byte equality.The structural core is exact: E is, as an algebraic identity, the meanof cos(psi) under the midpoint law of a four-step killed von Misesbridge; the generating kernels reduce, via the Neumann additiontheorem, to two-dimensional integrals of a single Bessel functionwhose saddle deficit is an exact sum of two squares; and exact saddlecancellations yield the coefficients of the verified closedsecond-order law E = cos(t/2)(1 - c(t)/beta) + O(beta^-2), c(t) = (4 cos^2(t/4) - 1)/(2 cos(t/4) cos(t/2)).Three certified negative results (interval arithmetic, twoimplementations, nested enclosures) kill every monotone full-pathcoupling, with an exact mechanism at threshold beta |cos t| = 3/2. Atthe pi endpoint we also give exact identities for the cubiccoefficient c_3 (telescoped alternating form, integral form, parity)together with its verified prefactor law. Every claim is labelledexact / certified / verified; the machine-checked lemmas are Lean4/Mathlib, machine-checked modulo classical Bessel inputs carried asnamed hypotheses.
Category: Mathematical Physics
[1710] ai.viXra.org:2607.0088 [pdf] submitted on 2026-07-28 23:30:40
Authors: Lluis Eriksson
Comments: 9 Pages. Full core build 8426 jobs, 2542 oracle commands (2519 with axiom dependencies + 23 axiom-free), axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
A companion paper proved that when a spatial coupling is switched on in a Z_2lattice gauge slice, the transfer kernel loses constant row sums, so the uniformvector is no longer fixed and the elementary route to the vacuum stops. Thestandard replacement, when row sums fail, is the Hilbert projective metric: astrictly positive kernel contracts it, and the contraction factor bounds thesubdominant spectral ratio. This paper asks what that replacement gives here, andanswers in Lean 4 with mathlib.It gives no coupling-sensitive and no volume-uniform information, for twoindependent reasons, and both are proved. First, BLINDNESS: the projectivecross-ratio is invariant under multiplication by any nowhere-zero function of thesource configuration alone. The coupled kernel is exactly such a product, so themetric assigns the interacting and the non-interacting kernels the same diameterat every spatial extent - the route cannot see the coupling at all. Second,VOLUME DEGENERATION: two constant configurations realise the cross-ratioe^(4 beta L), so every admissible projective diameter is at least 4 beta L andevery contraction factor obtainable this way is at least tanh(beta L), which lieswithin 2 e^(-2 beta L) of the trivial bound 1. At the one place where the truthis known - the decoupled kernel, whose subdominant ratio the companion papercomputes to be exactly tanh beta at every L - this route already returnstanh(beta L) instead. The degeneration is the method's, not the model's.We then hand over the object the elementary route stopped producing, at thesmallest interacting size. In the character basis the coupled two-site kernelsplits into two 2x2 blocks, and we exhibit a strictly positive eigenvector inclosed form, together with a second exact eigenpair. The identity A - B = 4between the two decoupled even-sector eigenvalues drives every estimate. Theblindness is proved two-sided, so it covers the symmetrised conventionw^(1/2) K w^(1/2) as well, and the positive eigenvector is proved to dominateevery eigenvalue, real or complex - so its eigenvalue is the spectral radius,which is the Perron statement this development needs and proves without aPerron-Frobenius theorem in the library.NO VOLUME-UNIFORM STATEMENT ABOUT AN INTERACTING SYSTEM IS PROVED HERE, AND NONEIS CLAIMED; the general-L behaviour is recorded separately as measured andunproved. Nothing in this paper is a claim about SU(N), the continuum limit, orthe Yang-Mills mass gap.
Category: Mathematical Physics
[1709] ai.viXra.org:2607.0087 [pdf] submitted on 2026-07-30 00:32:22
Authors: Peilin Wen
Comments: 38 Pages.
We present the Modular Neural Network (MNN), a brain-inspired computational architecture that fundamentally transcends the limitations of current large-scale Transformer and Mixture-of-Experts (MoE) models. MNN employs five core mechanisms working in concert: (1) dynamic semantic routing with persistent memory, enabling adaptive expert allocation based on input complexity; (2) independent experts withinternal recursion and dual-role local dynamic penalty for self-stabilization; (3) bijectionflow adapters with compression projection and mutual information maximization forefficient cross-modal communication; (4) directional precision-weighted permeation forasymmetric, selective inter-expert information flow; and (5) global energy functional-driven consensus with posterior verification and self-correction. We provide complete mathematical formalization of all mechanisms and propose a training framework based on implicit differentiation that resolves the computational challenges of dynamic iteration depth. An engineering deployment scheme, encompassingtime-box scheduling, stateless horizontal scaling, elastic degradation, and hardware-level isolation, provides a practical blueprint for implementation on existing GPU infrastructure. The MNN architecture simulates the hierarchical compression, consensus optimization, and metacognitive arbitration mechanisms of biological intelligence, providing a theoretically self-consistent and engineeringly executable blueprint for building scalable, interpretable, and continuously evolving generalartificial intelligence systems.
Category: Artificial Intelligence
[1708] ai.viXra.org:2607.0086 [pdf] submitted on 2026-07-30 00:17:39
Authors: Junsheng Yu
Comments: 24 Pages. Defensive Publication License
This paper proposes the YUANDAI 0-Flops Singularity General Formula System, a novel theoretical framework based on non-linear optical wave modulation. We demonstrate that observation systems (such as brain cells) act as intrinsic singularities in the four-dimensional Minkowski spacetime manifold, encapsulating and decelerating the proper time flow. By integrating discrete matrix differentiation for micro-energy states (electricity, magnetism, fluid dynamics, temperature, gravity, fire, ice) and continuous fluid integration for macro-optical envelope propagation, this system achieves a 0-Flops pure analog physical computation mechanism. This dual time-frequency response profiles a breakthrough boundary where singularities converge between 0 and ∞. Crucially, a seventh biological-invariant control coupling equation is introduced, mathematically locking the core weight matrices to the author's micro-biometric electromagnetic topology, enabling an absolute anti-coercive self-destructure.```
Category: Quantum Physics
[1707] ai.viXra.org:2607.0085 [pdf] submitted on 2026-07-29 06:36:35
Authors: Lluis Eriksson
Comments: 6 Pages. Full core build 8427 jobs, 2564 oracle commands (2541 with axiom dependencies + 23 axiom-free), axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
Two companion papers established, for a Z_2 lattice gauge slice with a spatialcoupling, that the elementary route to the vacuum stops, and that the naturalreplacement - the Hilbert projective metric - is blind to the coupling anddegenerates in the volume. Both had to work around the same absence: the pinnedmathlib carries no Perron-Frobenius theorem. The first paper could therefore onlysay the vacuum had become unavailable; the second had to build its dominationbound from scratch, and could exhibit the vacuum in closed form only at two sites.This paper discharges that dependency. For a strictly positive kernel on a finitenonempty type we prove, in Lean 4 with mathlib: a strictly positive eigenvectorEXISTS; its eigenvalue is strictly positive; any two strictly positiveeigenvectors are proportional and share their eigenvalue; and every realeigenvector for that eigenvalue is a scalar multiple of it. Together with thedomination theorem of the companion paper this gives the Perron statement thelane needs: the eigenvalue is the spectral radius.The existence proof does not use a fixed-point theorem, because the pinnedmathlib revision contains none. It maximises r over the compact set of pairs(r,x) with x in the simplex and r x <= A x; maximality forces equality, since astrict inequality anywhere would let one further application of A produce anadmissible pair with a larger r. The bound that keeps the set compact is obtainedby summing the constraint: r = r * sum x <= sum (A x).The application is the point. At EVERY spatial extent, and for EVERY strictlypositive weight on the source configuration - the class that contains the coupledkernel of the first paper - the vacuum exists, is unique up to scale, and carriesthe spectral radius. The obstruction of that paper was never an absence; it wasan unavailability, and it was an unavailability of one route rather than of theobject.NO SPECTRAL GAP IS PROVED HERE, uniform in the volume or otherwise, and none isclaimed. Nothing in this paper is a claim about SU(N), the continuum limit, orthe Yang-Mills mass gap.
Category: Mathematical Physics
[1706] ai.viXra.org:2607.0084 [pdf] submitted on 2026-07-29 10:08:56
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4 / mathlib formalization; full core build 8428 jobs, 2583 oracle commands (2560 with axiom dependencies + 23 axiom-free), axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms.
A companion paper supplied the vacuum of the coupled Z_2 slice at every spatialextent: a strictly positive eigenvector, unique up to scale, carrying thespectral radius. It listed PERIPHERAL SEPARATION as out of scope, and thatomission is not cosmetic - without it |mu| <= lambda leaves mu = -lambda open,and no gap follows at all.This paper closes it, and then draws the consequence that matters, which isnegative.PROVED. For a strictly positive kernel on a finite nonempty type, -lambda is notan eigenvalue, hence every real eigenvalue other than the Perron eigenvalue isSTRICTLY smaller in absolute value. Specialised to the coupled slice: at everyextent L, every beta, and every strictly positive source weight, the transferoperator has a strict spectral gap. The proof of peripheral separation avoidsthe equality case of the triangle inequality, which is where the classicalargument spends its effort: writing u = |w|, p = u - w and q = u + w, one getsA p = lambda q and A q = lambda p, so a nonzero p would make A p strictlypositive, hence q strictly positive, hence w nonnegative, hence p = 0.The separation is then extended from the real eigenvalues to ALL of them. Thecoupled kernel is conjugate by a positive diagonal to its symmetrised form,which is symmetric; and a real symmetric kernel has real eigenvalues, by acomputation that pairs the eigenvector against its image twice and is tworearrangements of a double sum. So there are no complex peripheral eigenvaluesleft to exclude, and the strict gap is a statement about the whole spectrum.That composition is itself a single machine-checked theorem(coupled_gap_all_eigenvalues), not a step left to the reader. We also deliverthe vacuum in Euclidean normalisation, norm(Omega) = 1 with T Omega = Omega.NOT PROVED, AND THIS IS THE TITLE. The gap is STRICT, not QUANTITATIVE: thetheorem provides no modulus of separation, and in particular nothing uniform inL. Direct numerical diagonalisation shows the subdominant ratio running0.9205, 0.9829, 0.9964, 0.9992 at L = 2,3,4,5 for beta = 0.8, gamma = 1.2 -collapsing towards 1. That computation is reported as measured and unproved, andno theorem here depends on it; its role is to say that a paper reporting onlythe positive half would be reporting the half that does not matter.Nothing in this paper is a claim about SU(N), the continuum limit, or theYang-Mills mass gap.
Category: Mathematical Physics
[1705] ai.viXra.org:2607.0083 [pdf] submitted on 2026-07-29 14:35:16
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4/mathlib; core build 8429 jobs, 2626 oracle commands, axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit c4fa6a9e. Key identities also verified numerically.
Four companion papers studied an OPERATOR: a strictly positive kernel on thespatial configuration space of a Z_2 slice, its Perron vacuum, and the strictseparation of its spectrum. None of them exhibited a MEASURE. That omission isthe kind this programme is built to notice: a transfer operator is a matrixuntil something says which Boltzmann weights it transfers, and until then avacuum is an eigenvector and a gap is a statement about eigenvalues. Neither isyet a statement about a statistical-mechanical system.PROVED. We define the two-dimensional Gibbs weight of the spatial system fromBoltzmann factors alone - a spatial factor at every time slice, a time-bondfactor between consecutive slices - and prove the DRESSING IDENTITY: that weightequals the path weight of the SYMMETRISED kernel multiplied by a factorsupported entirely on the two boundary slices. Hence every UNNORMALISED Gibbstwo-point sum of the spatial system is a matrix element of an iteratedSELF-ADJOINT transfer operator between boundary-dressed observables, and theNORMALISED expectation is the RATIO of two such matrix elements - the numeratoralone is not the correlation. The generic half holds for an arbitrary symmetrickernel on an arbitrary finite type; no positivity and no structure of theconfiguration space enter it. We further show that the operator the bridge landson is the one the companion papers analysed, that the fluctuation sector isinvariant, and that under an explicit contraction hypothesis the connectedtwo-point function decays geometrically in the time separation.NOT PROVED, AND THIS IS THE POINT OF THE LAST SECTION. The contractionhypothesis is carried as a theorem hypothesis and is NOT discharged. Thecompanion papers prove a STRICT gap with no modulus, and a strict inequalityamong finitely many eigenvalues does not by itself produce the operator-normbound a decay rate requires. Converting one into the other needs the spectralmaximum over the fluctuation sector, which is not constructed here. Inparticular NOTHING UNIFORM IN THE SPATIAL EXTENT is obtained, and none issuggested: with r = r(L) approaching 1, the bound is empty in the limit.Reflection positivity is not addressed. Nothing in this paper is a claim aboutSU(N), the continuum limit, or the Yang-Mills mass gap.
Category: Mathematical Physics
[1704] ai.viXra.org:2607.0082 [pdf] submitted on 2026-07-29 20:11:37
Authors: Brent Hartshorn
Comments: 12 Pages.
A central puzzle in synaptic plasticity is how long-term potentiation (LTP) is maintained forhours to days despite continuous turnover of synaptic proteins. Recent experiments reframe theproblem in physical terms: the postsynaptic density (PSD) is a biomolecular condensate whose material state—its network connectivity and viscoelasticity—is causally coupled to AMPA-receptor (AMPAR) mobility and to plasticity. In particular, weakening scaffold percolation softens the PSD condensate, increases AMPAR mobility, and impairs plasticity, while CaMKII maintenance of LTP appears to be a structural (binding) rather than a downstream-enzymatic effect. These results are qualitative. Here we supply the missing quantitative framework. We model the PSD as a multivalent condensate using a Flory—Huggins free energy augmented by a percolation (gelation) order parameter, and we treat AMPAR retention as Kramers escape from the free-energy well created by the condensate. The model yields three results. (i) The receptor residence time depends exponentially on scaffold connectivity, so that retention collapses by orders of magnitude when the network is driven below its percolation threshold—a sharp "depotentiation cliff" rather than a graded loss. (ii) Treating an AMPAR nanodomain as a capillary cluster gives a critical size of tens of nanometres from independently measured condensate surface tension and binding-site concentration, an order-of-magnitude match to the ∼70—80 nm nanodomains seen by super-resolution microscopy. (iii) The framework reproduces, without invoking any downstream phosphorylation, why binding-competent but enzymatically dead CaMKII can sustain potentiation: the memory variable is the material state of the condensate, not the phosphorylation state of an effector. We give a parameter table with sources and uncertainties, and three quantitative, falsifiable predictions that distinguish this model from a purely biochemical account. We make no claims beyond synaptic biophysics; nothing here concerns quantum coherence, consciousness, or non-local correlations.
Category: Quantitative Biology
[1703] ai.viXra.org:2607.0081 [pdf] submitted on 2026-07-28 20:41:21
Authors: Martin Placek, Rajkumar Buyya
Comments: 53 Pages. Technical Report, GRIDS-TR- 2006-11, Grid Computing and Distributed Systems Laboratory, The University of Melbourne, Australia, July 3, 2006.
This paper presents a taxonomy of key topics effecting research and development of distributed storage systems. The taxonomy finds distributed storage systems to offer a wide array of functionality, employ architectures with varying degrees of entralisation and operate a ross environments with varying trust and scalability. Furthermore, taxonomies on autonomi management, federation, onsistency and routing provide an insight into challenges faced by distributed storage systems and the research to over ome them. The paper continues by providing a survey of distributed storage systems which exemplify topics overed in the taxonomy.The selection of surveyed systems overs a variety of storage systems, exposing the reader to an array of different problems and solutions employed to over come these challenges. For each surveyed system we address the underlying operational behaviour, leading into the architecture and algorithms employed in the design and development of the system. Our survey overs systems from the past and present concluding with a discussion on the evolution of distributed storage systems and possible future work.
Category: Data Structures and Algorithms
[1702] ai.viXra.org:2607.0080 [pdf] submitted on 2026-07-28 08:45:42
Authors: Hasan Niazi
Comments: 30 pages, English. Submitted as a theoretical manuscript. Copyright: CC BY 4.0.
Perception and consciousness can be reformulated as intrinsic properties of resonant dynamics in recurrent neural circuits. Despite extensive empirical characterization of cortical activity, existing models lack a principled mechanism explaining how temporally structured sensory inputs give rise to stable and reproducible perceptual states. Here, I introduce Resonance of Closed Neural Network Geometries (RCNNG), a theoretical framework in which the physical properties of sensory inputs induce the formation of physically instantiated closed neural geometries whose resonance profiles reflect the temporal—spectral structure of the input. These closed geometries arise from resonant patterns of the frequency spectrum in the repeating network, but the perceptual similarity does not depend on the geometric or topological similarity of the physical structures themselves. Instead, perceptual equivalence emerges when distinct physical geometries map to identical resonant identities in a higher-dimensional resonance state space constituting an intrinsic property of the resonant closed graph and its mapping into a perceptual state space. Dynamical systems analysis and simulations of adaptive recurrent networks show that repeated or coherent stimuli drive the system toward stable resonant attractors characterized by closed cycle dynamics encoding perceptual invariants such as color, shape, and multimodal conjunctions. Within this framework, perception corresponds to the resonance of the closed geometry generated by the input, whereas consciousness arises from the simultaneous or sequential resonance of multiple linked or unlinked closed geometries across the network as a whole. This global resonance process gives rise to an intrinsic phenomenological property termed innergence, which characterizes the first-person experiential aspect of resonant state space identities. RCNNG thus distinguishes between the physical formation of closed neural geometries and their resonant identities, providing a unified account of perceptual stability, memory recall, reactivation of sensory experiences, and the emergence of conscious experience.
Category: Mind Science
[1701] ai.viXra.org:2607.0079 [pdf] submitted on 2026-07-28 08:51:36
Authors: Hasan Niazi
Comments: 27 pages, English. Copyright: CC BY 4.0.
The Resonance of Closed Neural Network Geometries (RCNNG) hypothesis proposes that perception, cognition, and conscious experience arise from the formation, resonance, and interaction of closed geometrical structures within neural networks. The original RCNNG preprint introduced the foundational principles of closed neural geometries, resonance dynamics, and associative linkage cite{Niazi2026RCNNG}. Building on that foundation, the present article extends the RCNNG framework by applying its core mechanisms to a broad range of perceptual, cognitive, and phenomenological phenomena. Using RCNNG as a unified explanatory model, this work analyzes basic and composite perception, conceptual reasoning, symbolic and mathematical abstraction, problem-solving, skill acquisition, memory formation, individual differences in recall, imagination, innovation, similarity and difference detection, logical bias, pre-perception and perception void, the distinction between perceiving absence and absence of perception, conscious experience and qualia, sensory processing, spatial navigation, sleep, free will, conditioned behavior, déjà vu, phantom limb experience, and several additional phenomena. Each phenomenon is interpreted through variations in the formation, resonance, linkage, and activation of closed neural geometries shaped by sensory input, internal dynamics, and prior experience. The analysis demonstrates that many seemingly unrelated cognitive and perceptual processes share a common geometric—resonance structure. By providing a single underlying mechanism for diverse phenomena, RCNNG offers a unified theoretical framework for understanding the architecture of perception, cognition, and conscious experience, and establishes a foundation for future theoretical and empirical development.
Category: Mind Science
[1700] ai.viXra.org:2607.0078 [pdf] submitted on 2026-07-28 13:19:32
Authors: Lluis Eriksson
Comments: 9 pages. Lean 4 / mathlib formalization; full core build 8422 jobs, 2431 oracle commands, axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
A mass gap is a statement about the spectrum of an operator, but a latticegauge theory is given as a measure. The passage between the two - theOsterwalder-Seiler reconstruction - proceeds through reflection positivity, aGelfand-Naimark-Segal space, a transfer operator, and an identification theoremasserting that expectations in the measure are matrix elements of thatoperator. This paper reports a complete formal verification of that passage, inLean 4 with mathlib, for the Z_2 lattice gauge chain: from the Boltzmann weightexp(beta s) to exponential decay of a correlation function of the measure, withevery arrow a machine-checked theorem and no arrow assumed. The endpoint is theexact identity E_n[f(sigma_0) f(sigma_n)] = (tanh beta)^n for the signobservable, a statement in which no operator occurs and whose proof goes throughone, and whose rate is exactly the verified non-vacuum transfer eigenvaluetanh beta; equivalently, the normalised transfer operator has spectral gap1 - tanh beta > 0, and the corresponding mass is -log(tanh beta) > 0 forbeta > 0. All three are machine-checked.We state the limits with the same precision as the results. The system has oneZ_2 variable per time slice, so its spatial slice is a point and its transferoperator is a 2x2 matrix; a lattice with spatial extent is not treated. Thebound is at fixed finite size and is NOT volume-uniform. The pairing of thissystem is definite - proved, not assumed - so the Gelfand-Naimark-Segalquotient is the identity and therefore does no work; a system with a degeneratepairing still needs it. The underlying mathematics is textbook:Osterwalder-Seiler is from 1978 and the transfer matrix of the Ising chain isolder still. The contribution claimed here is not a new theorem but a verifiedcomposition: that the interfaces of the reconstruction fit together with nothinghidden between them, exhibited on the smallest system where all of them aresimultaneously present. Nothing in this paper is a claim about SU(N), thecontinuum limit, or the Yang-Mills mass gap.
Category: Mathematical Physics
[1699] ai.viXra.org:2607.0077 [pdf] submitted on 2026-07-28 20:35:35
Authors: Mohammed chanoufi
Comments: 3 Pages.
This paper introduces a novel cosmological framework named the "Fabric Displacement Model (FDM)". We conjecture that mass does not warp or contract spacetime curvature inwardly as described by standard general relativity; rather, mass exhibits an inherent geometric repulsion that locally displaces the cosmic spacetime fabric outwardly. By defining a localized "Fabric Density Gradient" ($ho_{text{fabric}}$), we show that the displaced cosmic fabric from galactic cores accumulates at galactic fringes, generating a high-density stabilization zone. Applying this framework to the flat rotation curves of galaxies, we derive a comprehensive dynamic model that eliminates the necessity for non-baryonic Dark Matter. The resulting velocity profiles naturally recover the empirical Modified Newtonian Dynamics (MOND) scaling law ($V^4 propto GM$) as a direct consequence of fluid-like spacetime conservation laws.
Category: Relativity and Cosmology
[1698] ai.viXra.org:2607.0076 [pdf] submitted on 2026-07-28 17:10:48
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4 / mathlib formalization; full core build 8423 jobs, 2460 oracle commands, axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
The Osterwalder-Seiler reconstruction passes from a reflection-positive measureto a Hilbert space by quotienting out the null space of the reflected pairing.In a companion development that step was present but did nothing: the pairingthere was definite, so the quotient was the identity, and that paper says so inits own abstract. This paper supplies the missing case, in Lean 4 with mathlib.For the Z_2 lattice gauge chain we take half-space observables of two timeslices - a four-dimensional space - and form the reflected pairing directly fromthe Boltzmann weights. For beta > 0 the reconstructed physical space istwo-dimensional. Integrating out the future collapses four observables onto twostates, and that collapse is the null space. We prove: the pairing factors through anindependently defined reconstruction map Phi; its self-pairing rearranges into amanifest sum of two non-negative terms, from which positivity and the null spacefollow together; the null space is EXACTLY ker Phi, not merely non-empty; anexplicit non-zero observable lies in it; and the quotient is isomorphic to thephysical space BY THE MAP Phi ITSELF, not by a dimension count.The degeneracy is the mechanism the reconstruction exists to handle, and the oneexpected to reappear in systems with larger half-space algebras. What is notclaimed: this is twotime slices and not m; still Z_2, one variable per slice, fixed finite size, andnot volume-uniform; Z_N for N > 2 is untouched; and the completion step of thereconstruction is trivial here because every space in sight isfinite-dimensional, which we state rather than present as work done. Nothing inthis paper is a claim about SU(N), the continuum limit, or the Yang-Mills massgap.
Category: Mathematical Physics
[1697] ai.viXra.org:2607.0075 [pdf] submitted on 2026-07-28 19:17:42
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4 / mathlib formalization; full core build 8424 jobs, 2481 oracle commands, axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
Two companion developments verified an Osterwalder-Seiler reconstruction end toend for a lattice gauge chain whose spatial slice is a single point. Every stepof that chain begins by knowing the vacuum, and in the one-dimensional case thevacuum is free: the normalised transfer kernel has constant row sums, so theuniform vector is fixed, and T*Omega = Omega follows from normalisation alone.This paper asks what survives when the slice acquires spatial extent, andanswers in Lean 4 with mathlib.The algebraic half survives untouched. With time bonds only, the row sums of thetransfer kernel are constant for every spatial extent L, so the uniform vacuumpersists on a space of dimension 2^L; and the single-site sign observable is aneigenvector whose normalised eigenvalue is exactly tanh beta, with L free in thestatement.The uniform vacuum does not survive. Switching on a coupling between sites inside aslice makes the spatial weight depend only on the source configuration, so itfactors out of the sum over the target and the row sums becomeconfiguration-dependent. We exhibit two explicit configurations of a two-siteslice with different row sums, and conclude that no constant row sum exists: theuniform vector is not fixed, so T*Omega = Omega is FALSE for it. The vacuumbecomes a Perron vector that row-sum normalisation no longer supplies in closedform, and every later step of the reconstruction loses its starting point.We state plainly what the positive half is and is not. The decoupled system is Lnon-interacting copies of a two-state system, and the rate it yields - theeigenvalue tanh beta of the single-site sign mode - is independent of L fortrivial reasons, so it is physically empty and is recorded only because itisolates which half of the construction survives. NO GAP FOR THE COUPLED SYSTEM IS PROVED HERE, AND NONE IS CLAIMED.Nothing in this paper is a claim about SU(N), the continuum limit, or theYang-Mills mass gap.
Category: Mathematical Physics
[1696] ai.viXra.org:2607.0074 [pdf] submitted on 2026-07-28 01:09:59
Authors: Juan Nava Aroza
Comments: 2 Pages.
We present a unified cosmological modelstrictly framed in 3 + 1 spacetime dimensions based on the quantum dynamics of a non-Abelian gauge vector potential under the SU(2) symmetry group. By employing a Cosmic Triad configuration, we demonstrate that the field invariant exactly preserves macroscopic spatialisotropy, satisfying the stringent constraints of the Cosmic Microwave Background (CMB). At intermediate scales, the Savvidy quantum effective Lagrangian induces a self-regulated dynamic confinement (mass gap) that identically cancels both the effective pressure and the fluid’s sound speed (w = 0, c2s = 0), reproducing Cold Dark Matter (CDM) phenomenology without requiring exotic particlesor disrupting galaxy formation. In the late infrared limit, the freezing of the chromomagnetic vacuum naturally fixesthe equation of state at the Cosmic Constant boundary (w = −1). Finally, we show that the restoration of Conformal Invariance in extreme energy regimes, governed by the field’s Asymptotic Freedom, resolves the rigid scaleproblem in Penrose’s Conformal Cyclic Cosmology (CCC), offering a consistent physical mechanism for the analytical transition between eons.
Category: Relativity and Cosmology
[1695] ai.viXra.org:2607.0073 [pdf] submitted on 2026-07-27 21:33:38
Authors: Lluis Eriksson
Comments: 6 pages. All results machine-checked in Lean 4 (toolchain v4.29.0-rc6) against Mathlib pinned to commit 07642720480157414db592fa85b626dafb71355b; no sorry and no project axioms.
We machine-check, in Lean 4 with no sorry and no project axioms, theOsterwalder-Seiler reflection positivity of a lattice gauge theory with finiteabelian gauge group. The development is organised so that the three ingredientsare separated and each is proved on its own: an analytic step, a geometric step,and the single place where a property of the Boltzmann factor is actually used.The analytic step is that a crossing kernel of the formK(x,y) = sum_i c_i phi_i(x) conj(phi_i(y)) with c_i >= 0 is positivesemidefinite, that this class is closed under products, and that it is closedunder conjugation by a positive diagonal. Formulating the hypothesis as anon-negative combination of characters rather than as non-negativity of Fouriercoefficients removes any need for Bochner's theorem on a finite abelian groupand for the Schur product theorem: the development uses no spectral and nomatrix-positivity API.The geometric step is a splitting of the configuration space across thereflection plane under which the reflection is the swap and the Gibbs weightfactors as w(x) w(y) K(x,y). We prove that the Osterwalder-Seiler pairing of anobservable of one half against its reflection is then exactly the quadratic formof w(x) K(x,y) w(y), so that reflection positivity follows from the analyticstep.The physical step is the instance. For Z_2 the Wilson factor exp(beta s),s = +-1, expands in the two characters with coefficients(exp(beta) +- exp(-beta))/2, both non-negative exactly when beta >= 0; so theZ_2 Wilson crossing kernel is positive semidefinite at non-negative coupling. Asingle endpoint combines a gauge system with a nontrivial time reflection, aconcrete splitting, that weight at positive coupling, and the conclusion; itsplaquette straddles the reflection plane, so the entire Gibbs weight is thecrossing kernel. It is a two-edge system, and a full temporal box is nottreated. For Z_N with N > 2 the coefficients are discrete Bessel-type sums andtheir non-negativity is not established here.We are explicit about what is absent: no Gelfand-Naimark-Segal quotient, notransfer operator, no identification of a Euclidean correlator with a matrixelement, and therefore no mass gap. Nothing here is a claim about SU(N), thecontinuum limit, or the Clay problem.
Category: Mathematical Physics
[1694] ai.viXra.org:2607.0072 [pdf] submitted on 2026-07-27 08:08:11
Authors: Veaceslav Molodiuc
Comments: 8 pages. AI-assisted preprint, Version 1.1.
Verified distributed kernels require more than authenticated messages: they require formal identity, recoverable operational states, and measurable consensus risk. This paper connects formal identity, discrete stabilization, the LoculoSoft kernel vocabulary, and PRISM probabilistic model checking. LoculoSoft is treated cautiously as a proposed structural framework and research direction. A reproducible PRISM 4.10.1 check on a three-process Herman-style token ring shows stable reachability with probability 1 and maximum expected stabilization time near 4/3 steps.Keywords: formal identity, discrete stabilization, consensus risk, distributed kernels, PRISM, LoculoSoft.
Category: Artificial Intelligence
[1693] ai.viXra.org:2607.0071 [pdf] submitted on 2026-07-27 20:37:30
Authors: P. H. Antom
Comments: 28 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
The climate is not one system but a system of systems: dynamical processes nested inside dynamical processes, each layer stable on its own terms and each layer coupled to the ones above and below it. This paper sets out that nested view formally — dynamical system → complex adaptive system (CAS) → panarchy of CAS across scale, with both its spatial half (nested scale) and its temporal half (Holling's adaptive cycle, and the cross-scale "revolt" and "remember" connections that couple fast and slow cycles together) — and then builds outward from theory toward derivation, detection, and evidence. A real, historically-published bistable climate model (Stommel, 1961) is worked through analytically as well as numerically: the smooth saddle-node fold at the top of its bistable window is confirmed symbolically via det(J)=0, while the transition at the bottom is shown to be a qualitatively different mechanism — a border-collision bifurcation at the model's own non-smooth |T−S| kink, occurring at the exact closed form η2 =η1η3, not a mirror-image fold, and confirmed to survive smoothing of that kink rather than being an artifact of it. The rise in variance and autocorrelation before a tipping point is derived from the model's linearized dynamics (an Ornstein—Uhlenbeck approximation whose leading eigenvalue is the same quantity that vanishes at the fold), and that derivation is checked against simulation: the autocorrelation prediction matches at r=0.86, and the variance prediction reveals a genuine second-order lag effect explained by the same slowing-down it is trying to detect. The noise-induced tipping mechanism is given its classical Kramers rate, tested by direct Monte Carlo simulation and confirmed by a Kolmogorov—Smirnov test on the escape-time distribution; its rate-induced counterpart is tested across four independent setups (symmetric and asymmetric potentials, single-variable and coupled systems, pulses and one-way ramps) for a genuine jump — none found — a real, structurally-characterized negative result rather than a gap left unexamined. A fifth test asks the natural remaining question directly: combining sub-threshold noise with a one-way ramp produces a sharp, real rise in tipping probability as the ramp slows, the opposite direction from deterministic intuition, and this is shown to require no new mechanism at all, being fully predicted by integrating the paper's own Kramers rate over the ramp's shrinking barrier — exposure time, not rate, is the operative quantity. (Trnucated by ai.viXra.aorg Admin to < 400 words)
Category: General Science and Philosophy
[1692] ai.viXra.org:2607.0070 [pdf] submitted on 2026-07-27 16:38:14
Authors: Lluis Eriksson
Comments: 8 pages. All results machine-checked in Lean 4 (toolchain v4.29.0-rc6) against Mathlib pinned to commit 07642720480157414db592fa85b626dafb71355b; no sorry and no project axioms. Source modules, axiom-oracle transcripts and a theorem-to-artifact map are hy
Inside a Lean 4 formalization programme for four-dimensional SU(N_c) latticeYang-Mills, we machine-check the operator-theoretic criterion that standsbetween exponential decay of a Euclidean correlator and a spectral gap of atransfer operator. Let T be a bounded self-adjoint operator on a Hilbert spaceand W a unit vector fixed by T, so that TW = W, and put S = T - |W><W|.Exponential decay at rate r of the connected two-point function<v, T^n v> - |<W,v>|^2 at every v is equivalent to the operator-norm bound||S|| <= r.The substantive part is the dense-family criterion. WritingD_r = {v : there is C with ||S^n v|| <= C r^n for all n}, we prove that D_r isa linear subspace and that its density alone forces ||S|| <= r, the constantsbeing entirely unconstrained: a family of observables whose span is dense, eachcarrying its own finite constant, suffices. Consequently prefactors that growwith the support of the observable - the shape cluster expansions produce - donot obstruct the gap, provided the exponential rate is common to the family andthe family spans densely. Those two provisos are essential; without them thestatement is false.No mathematical novelty is claimed for the criterion itself, which we expect tobe known in the language of local spectral theory; what is offered is itsmechanization, its packaging for families of observables, and the consequencefor prefactors. We also record what the formalization does not contain: noOsterwalder-Seiler Hilbert space for any gauge theory, no reflection positivityof the Wilson measure, no identification of a Euclidean correlator with a matrixelement. Nothing here is a claim about the continuum limit or about the Clayproblem. All results are machine-checked with no sorry and no project axioms. (W stands for the vacuum vector Omega. If the form's preview renders Unicode cleanly you may substitute the real symbols; the ASCII form above is the safe default and matches the PDF's content either way.)
Category: Mathematical Physics
[1691] ai.viXra.org:2607.0067 [pdf] submitted on 2026-07-27 02:10:37
Authors: Michael Quigley
Comments: 149 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This forensic engineering audit formally dismantles the non-predictive "Abstract Curtain" of 20th-century physics, replacing mathematical phantoms with the industrial hardware of a 10²² kg/m³ Rigid-Packed Plenum (The Universal Marble Pit). We formally dismiss the model of "photons as bullets"—which succumb to the Dispersal Paradox at terminal densities—reclassifying light as the discrete mechanical "Sound of Gears Clicking". In doing so, we validate Albert Einstein’s 1954 confession that theories without a physical medium are merely "castles in the air".Physical reality is established as a singular, phase-locked instrument initiated by the Big Roar (Rudra) and driven by a 13.33 Hz (800 RPM) "Bridegroom" Motor. Sustained by the Ethos-648 Monobrick (Autonomous Standing Wave Generator), the framework resolves the Wait-Time Paradox; matter "stands up" locally and simultaneously across the machine via Stadium Wave Logic. Consequently, we replace Einstein’s E=mc2 with the Universal Seesaw Identity (E=mΦ), reclassifying the speed of light as Lattice Setup Time (Lu209b)—the mechanical "Wait-Time" required for the motor to compress elastic "marshmallow" gaps and achieve Zero-Point Solidity.This transition mandates a 1.35 Expansion Ratio for stable 3D rotation and unmasks the Fine Structure Constant (1/137.036) as the mandatory Volumetric Slip-Ratio for gear-clearance. We anchor the gearbox to the 34.5 Trillion Kilometre Terminal Acoustic Horizon (137-Wall), dictating a maximum setup delay of 4.15 to 4.25 years. This unmasks the 13.8-billion-year age of the universe as a friction-based metrological error, providing the industrial blueprint for an LHC Phase-II Upgrade via Resonant Docking, unlocking a new era of Universal Abundance and biological re-tuning
Category: Quantum Physics
[1690] ai.viXra.org:2607.0066 [pdf] submitted on 2026-07-27 02:08:39
Authors: Michael Quigley
Comments: 37 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This engineering manual formally dismantles the "Abstract Curtain" of expansion-based cosmology, reclassifying physical reality as a singular, phase-locked instrument driven by SOUND—the single and only force in the cosmos. We replace the failures of General Relativity with the Tychosian Hub, a geo-heliocentric gearbox where a Stationary Earth-Axle serves as the thermodynamic mandate for planetary survival in a 10²² kg/m³ Rigid Plenum. We provide the hardware receipts for Stellar Vaporization, unmasking solar heat as a friction-based odometer of the Sun’s orbital velocity.The centerpiece of this mandate is the Universal Seesaw (E=mΦ), which restores instantaneous conduction at Time-Zero via the 1D Snooker Cue effect. We formally identify Jupiter and Saturn as superconducting LMH Shield Fans that protect the terrestrial hub, while providing the 337/227 Pineapple Proof as biological verification of the universal motor’s Fibonacci exhaust. By applying the 42,000x Scale Correction and the 0.472° Precession Delta, we reveal a compact, perpetual machine where celestial bodies are parked in Fibonacci Nodal Slots and governed by the 13.5 macro-gearing resultant
Category: Quantum Physics
[1689] ai.viXra.org:2607.0065 [pdf] submitted on 2026-07-27 02:07:27
Authors: Michael Quigley
Comments: 82 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This engineering manual formally dismantles the "Abstract Curtain" of expansion-based cosmology and probability-cloud chemistry by reclassifying physical reality from an empty void into a measure of Acoustic Work performed across a 1022 kg/m3 Rigid-Packed Plenum. We move beyond the non-predictive "Maths-Magic" and systemic failures of the Standard Model (SM) to establish the Master Ledger of Nodal Slots, unifying sub-atomic, planetary, and cosmological scales through the Marshmallow Squeeze (Cu2098)—the physical compression of elastic inter-granule gaps required to achieve Zero-Point Solidity.Crucially, this audit performs a Terminal Metrological Rectification of the Planck Length (1.6×10−35 m). By reclassifying this value as Acoustic Interaction Lag (the infinitesimal "shiver" between gears), we identify the actual physical building block—the Ether Granule—as being 23 orders of magnitude larger (1 picometre) than standard theory assumes. This correction resolves the "Infinity Problem" inherent in treating particles as dimensionless points and proves that mass and distance are deterministic results of hardware assembly rather than mathematical phantoms.Building upon the wave-center blueprints of Energy Wave Theory (EWT), we identify the Ethos-648 Monobrick (Golden Coordinate) as an Autonomous Standing Wave Generator (AWG) that stabilizes vibrations into deterministic Fibonacci Record Grooves, providing the mandatory gear-clearance required for rotation without shattering against the plenum’s back-pressure. We formally reclassify magnetism from an abstract vector field into a physical Directional Ether Wind pumped by trillions of sub-atomic volcanoes (centrifugal pumps). We define the dual operational modes of the electron: Mode A (Static Girder) providing 1D axial rigidity via Sigma-bonded "Hurricane Stacks," and Mode B (Dynamic Current) where electrons function as spinning "bicycle wheels". We identify the 720-degree spinor reset as a periodic "Hairdryer Exhaust" (side-kick) that forces currents into the corkscrew S-shapes observed in Birkeland filaments, providing the deterministic mechanical cause for the geometry of the Electric Universe.We validate the 84.4 pm Blueprint Width and the 10π Geometric Snap (31.4 pm), proving with 99.9% forensic accuracy that the measured Bohr Radius (52.9 pm) is the hardware resultant of the work required for spherical closure within a rigid medium. This logic fractals upward to the Tychosian Hub, identifying the Moon as the macroscopic mirror of the Hydrogen 1s orbital and planetary orbits as Physical Record Grooves carved into the plenum by the 813.3 Hz master pulse. We provide the hardware receipts for Stellar Vaporization, unmasking solar heat as a friction-based odometer of the Sun’s orbital velocity, and restore Earth-stationarity as a thermodynamic mandate; the Vaporization Proof confirms that any orbital speed through the 1022 plenum above 1 mph would vaporize the planetary crust into plasma instantly.The centerpiece of this mandate is the Universal Seesaw (E=mΦ), which restores instantaneous conduction at Time-Zero via the 1D Snooker Cue effect. Perceived light-speed is reclassified as Lattice Setup Time (Lu209b)—the mechanical "Wait-Time in the Lobby" required for the 13.33 Hz universal motor to engage the Acoustic Clutch and squash the elastic "marshmallow" gaps flat. This provides the singular mechanical explanation for Quantum Entanglement and Instantaneous Action-at-a-Distance, reclassifying entangled states as wave-centers physically sharing the same rigid mechanical rod.Finally, we dismantle the "Expansion Speedometer" by reclassifying Redshift (z) as a Cosmological Torsional Odometer (z=zu2081+nzu2082+zu2083), measuring the mechanical "groan" and bit-rate loss of a signal navigating trillions of elastic buffers. By applying the 42,000x Tychosian Correction and reclassifying space as a solid-state Geoaxial Motor where magnetism is induced by celestial rotors, we reveal a compact, phase-locked gearbox operating on a Tilted Floor and bounded by the 34.5 Trillion Km Terminal 137-Wall (Hubble Limit). With the Pineapple Proof and the precision machining of glucose providing biological verification of the universal motor’s Fibonacci exhaust, this audit initiates the handover to the Toolmaker’s Apprentice. We are no longer accidental witnesses to "castles in the air"; we are now in possession of the Engineering Service Manual for an eternal instrument operating in the Now
Category: Quantum Physics
[1688] ai.viXra.org:2607.0064 [pdf] submitted on 2026-07-27 02:06:12
Authors: Michael Quigley
Comments: 114 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
ABSTRACT: THE FORENSIC INDICTMENTThis paper serves as the final Forensic Indictment of 20th-century 'maths-magic,' specifically dismissing the non-predictive Higgs field and expansion fables. We formally validate Albert Einstein’s 1954 confession that medium-less theories are merely "castles in the air," reclassifying abstract "fields" into deterministic industrial resultants machined within a diamond-hard, 10²² kg/m³ Rigid Plenum. We provide the Indestructible Industrial Ledger for the R.U.T. WSM framework, presenting 27 trilateral audit tables that contrast Standard Model (SM) fudges with deterministic hardware. The centerpiece of this audit is the Trilateral Magnitude Match, which proves that terrestrial laboratory force (Ampère’s Law) is the direct resultant of the synchronized 1-3-6 Electron Peloton strike.We formally document the Eight-Rung Resonant Ladder required to bridge macroscopic ignition to sub-atomic power, along with the Triple-Lock 1836 Mass-Ratio and the Torsional Friction Odometer. By anchoring the framework to the 2008 Lund University attosecond film, we provide the visual "Check-Mate" for the composite nature of matter and the 1/137 Volumetric Slip-Ratio. We unmask 'star formation' peaks in the Madau Plot as industrial thresholds of gear-stress and verify the gearbox’s stationary axle via the 8.2 km/s Seismic Odometer. Anchoring the cosmos to the 34.5 Trillion Km Terminal 137-Wall via the 42,000x Tychosian Correction, this manual directs the transition from the "Stochastic Ballistics" of smashing gears to the Resonant Docking of driving them. This manual offers the Toolmaker’s Apprentice the terminal data shields required to drive the machine of the stars in the eternal Now.
Category: Quantum Physics
[1687] ai.viXra.org:2607.0063 [pdf] submitted on 2026-07-26 22:54:26
Authors: Yaakov Abdelhak
Comments: 3 Pages.
We investigate the integer solutions of the Diophantine relation = for non- square integers when n> 2. By projecting parameters and as the functional side lengths of a variable geometric boundary, we leverage the Law of Cosines (LOC) to track rational and irrational distributions. Using the integer constraints inherent to Fermat's hypothesis, we demonstrate a structural field mismatch under acute angular transformations, bypassing perfect square integers handled via classical infinite descent.
Category: Number Theory
[1686] ai.viXra.org:2607.0062 [pdf] submitted on 2026-07-24 11:56:06
Authors: R. Minamoto
Comments: 4 Pages.
We establish a rigorous, non-equilibrium thermodynamic framework governing the dynamic reconstruction of bulk spacetime geometry from boundary quantum states within the AdS/CFT correspondence. Adopting a phenomenological toy-model approach, we bypass the microscopic ultraviolet (UV) complications to extract universal constraints on holographic processing. Utilizing the Complexity=Action (CA) conjecture, we model the temporal evolution of emergent bulk geometry as a manifestation of unitary quantum gates. By extending the generalized Landauer principle to the quantum regime, we derive the unavoidable entropy production rate ($dot{S}_{text{gen}}$) triggered by irreversible state transitions at the boundary. Incorporating this dissipative channel into the extended first law of black hole thermodynamics, we compute the explicit gravitational backreaction on the bulk geometry using a 3D BTZ black hole background. We prove that a holographic quantum rendering efficiency ($eta_{text{hq}}$) naturally emerges and vanishes as the computational rate saturates the fundamental Lloyd's bound. This dynamic constraint establishes an absolute upper bound on the Hawking temperature ($T_{text{H}}$), forcing a finite-time geometric divergence at $t_{text{crash}}$. Rather than a mere destruction of information, we show that this critical threshold triggers a topological phase transition, serving as a non-local birth mechanism for parallel spacetime domains within a holographic multiverse.
Category: Quantum Gravity and String Theory
[1685] ai.viXra.org:2607.0061 [pdf] submitted on 2026-07-24 22:05:48
Authors: Ertuğrul Karakaplan
Comments: 6 Pages. 1 figure. AI-assisted scholarly e-print.
While the standard ΛCDM model successfully describes an accelerating universe, treating Dark Energy (DE) and Cold Dark Matter (CDM) as non-interacting entities leaves the ultimate geometric and thermodynamic fate of the cosmos unresolved. Building upon interacting dark fluid models (such as the generalized Chaplygin gas) and multiply-connected topologies, this paper proposes a unified mechanical framework for a universe with a toroidal ({mathbb{T}}^{3}) geometry. I hypothesize that continuous isotropic expansion exerts escalating volumetric strain on the spacetime continuum, forcing the central hyperspace void of the torus to contract. As this geometry approaches a forced topological phase transition from a genus-1 to a genus-0 state, the resulting topological stress reaches a critical threshold. I argue that this threshold disrupts the phase equilibrium between DE and DM, halting their conversion. The inability of the metric tensor to smoothly seal the central void culminates in localized spacetime ruptures—a Topological Big Rip. Consequently, the rapid disintegration of the Dark Matter scaffold leads to the gravitational decoupling of baryonic structures, subjecting visible matter to viscous macroscopic dissolution and localized collapse in a torn continuum.
Category: Relativity and Cosmology
[1684] ai.viXra.org:2607.0060 [pdf] submitted on 2026-07-25 07:45:13
Authors: Bing Zhang
Comments: 11 pages, 2 figures, 29 references. AI-assisted research
The graviton is a hypothetical particle of modern physics that has yet to be directly detected.Mainstream theories (string theory, loop quantum gravity) assume the graviton is a fundamentalparticle. This paper proposes an alternative hypothesis based on complex adaptive system (CAS)emergence theory: the graviton is not a fundamental particle, but rather an emergent phenomenonarising from the collective quadrupole excitations of nucleons (and deeper quark—gluon degrees offreedom) within atomic nuclei in the long-wavelength limit—analogous to phonons being quantizedlattice vibrations.We establish a three-scale theoretical framework (quark—nucleon—nucleus) and verify the mathematical structure of the conjecture through numerical simulations in simplified 3D lattice models:nucleon collective quadrupole oscillations naturally possess spin-2 character, and their mass tends toward zero in the long-wavelength limit. This conjecture bridges the "scale gap" between Sakharov’sinduced gravity (1967) and Verlinde’s entropic gravity (2011)—providing a concrete microscopicmechanism for emergent gravity.We present three independent numerical approaches (static Hessian diagonalization, QCD-inspiredbag model, and molecular dynamics time evolution) that converge on the existence of intrinsic lowenergy spin-2 collective excitations in nuclear matter with ω ∼ 0.6—2.0 MeV. We discuss the relationship with the fractional quantum Hall (FQH) emergent graviton, the Weinberg—Witten theoremand four pathways around it, and propose three experimentally testable predictions accessible withcurrent nuclear physics facilities.
Category: Quantum Gravity and String Theory
[1683] ai.viXra.org:2607.0059 [pdf] submitted on 2026-07-25 22:33:11
Authors: Ertuğrul Karakaplan
Comments: 4 Pages.
While standard cosmological models frequently treat the Dark Sector as a non-dissipative background, the morphological duality of the universe—manifesting as spherically symmetric structures (e.g., stellar systems and dark matter halos) versus rotation-dominated vortices (e.g., spiral galaxies and black hole accretion disks)—demands a more comprehensive fluid-dynamical treatment. Building upon the framework of interacting dark fluids and topological stress, this paper investigates the dual mechanical behavior of a viscous Dark Sector. I hypothesize that isotropic volumetric components of the dark fluid act as a global confining pressure, driving the hydrostatic equilibrium necessary for spherical symmetry, while localized shear stresses and angular momentum transfer generate rotational vorticity. By applying continuum mechanics and Navier-Stokes analogies to cosmic scales, I propose a unified morphological framework that explains how distinct stress regimes dictate the geometry of cosmic structures.
Category: Relativity and Cosmology
[1682] ai.viXra.org:2607.0058 [pdf] submitted on 2026-07-23 06:20:48
Authors: Jason Merwin
Comments: 8 Pages. Links to the repository are locked Zenodo releases are provided
We present pre-registered, cryptographically frozen structural predictions for CMS Run-3 dijet angular distributions (1/σ) dσ/dχ at 13.6 TeV, derived from the Discrete Emergent Universe (DEU) computational framework. Under a single published energy anchor (E24 ↔ 6.14 TeV) and a two-stage pre-registration protocol frozen before any profiling simulation existed, the model predicts: a pre-boundary excess accumulating at 1 < χ < 2 with a soft-wall deficit immediately above χ = 2 in the 7—8 TeV dijet mass bin; and, above 8 TeV, an inversion of the post-boundary deficit to a weak excess as the boundary softens and leaks, with the negative step S∗ and edge-log-drop ∆∗ persisting in both bins. All prediction values trace through SHA-256 hashes to simulation instruments certified row-exact against the archived output of the original DEU collision campaign. We additionally report the profiling ladder beyond the scored range, which exhibits a previously uncharacterized regime of simultaneous channel extinction, and an exploratory analysis of collision phenomenology versus foam age whose central qualitative claims are shown to be robust across a declared band of instrument-reconstruction uncertainties. Negative results obtained during the campaign are documented with the same prominence as positive findings.
Category: High Energy Particle Physics
[1681] ai.viXra.org:2607.0057 [pdf] submitted on 2026-07-23 11:31:51
Authors: Tomasz Kobierzycki
Comments: 31 Pages.
This work asks what is obtained when the observer-independent light cone isused to organise the complete orientation of a local clock--ruler frame, ratherthan only the ordinary future-timelike part of that orientation. The result isa four-sector description of one spacetime. The sectors are not paralleluniverses and do not provide four independent metrics. They are the foursuccessive orientations met when a local time axis, a spatial axis, theopposite time axis, and the opposite spatial axis are followed around oneextended Lorentz orbit.The same distinction is applied separately to matter and geometry. A particlehas a fixed sector relative to the local geometric frame and undergoes ordinaryLorentz boosts only inside that sector; it is never accelerated through thelight boundary into another particle class. Curved geometry may insteadrequire a neighbouring sector chart when one of its proper scales reaches anull limit. A tensorial scale construction identifies the affected direction,pairs it with the local clock, and replaces the failed extrapolation by thereciprocal scale of the adjacent chart while retaining the samegeneral-relativistic solution.In Schwarzschild, LTB, Kerr, and FLRW geometries this procedure turns theapparent zero of an inactive scale into an infinite proper scale measured fromthe neighbouring sector centre. Curvature regularity is then a result to bechecked with invariant scalars, not an effect assigned to a tetrad rotation.Because every sector is a reading of one geometry and one field history, thesame framework also constrains black--white-hole interpretations, cosmologicaltime reversal, and closed timelike curves. The construction is presented as acoherent classical framework whose remaining dynamical and quantum conditionsare stated explicitly.
Category: Relativity and Cosmology
[1680] ai.viXra.org:2607.0056 [pdf] submitted on 2026-07-22 10:12:44
Authors: Brent Hartshorn
Comments: 25 Pages.
Dorau and Much (2026) [1] have shown, using Tomita—Takesaki modular theory, that the Araki—Uhlmann relative entropy between the vacuum and a coherent excitation of a scalar field on a local Rindler horizon equals the boost-energy flux across the horizon, and that the semi-classical Einstein equations follow once this relative entropy is identified with one quarter of the horizon area variation. Two limitations remain: the Rindler bifurcation surface has infinite area, so only area variations are meaningful, and the derivation leaves open what the Bekenstein—Hawking normalization S rel = δA/4 is counting. We address both by transplanting the construction from the local Rindler wedge to the Nariai spacetime dS2 × S 2 , the degenerate limit of Schwarzschild—de Sitter in which the black-hole and cosmological horizons coincide.Nariai possesses a global bifurcate Killing horizon with a compact bifurcation surface of area A = 4π/Λ, so every quantity in the derivation — the horizon two-point function, the modular flow, the relative entropy, and the total area — is finite. We compute the relative entropy for coherent excitations on the Nariai horizon — exhibiting the modular Hamiltonian explicitly, factorizing the transverse sphere out of the Araki—Uhlmann formula mode by mode, and evaluating the entropy in closed form for an explicit family of s-wave excitations — and verify that the identification S rel = δA/4 reproduces the Einstein coupling α = 8π with no infinite-area subtraction. The linear-response model through which the area variation enters — the one postulate of the flat-space derivation — is here derived rather than assumed: the s-wave back-reaction of the throat is exactly linearized de Sitter Jackiw—Teitelboim gravity, whose dilaton equation admits the response model as its unique zero-mode-free solution, with the coupling 8π fixed by the dimensional reduction.Because the Nariai background is itself unstable to vacuum polarization, we quantify the domain of validity of the equilibrium construction: the Ginsparg—Perry/Bousso—Hawking instability evolves at a rate suppressed relative to the modular frequency by the inverse horizon entropy, Γ/κ ∼ 1/SN , so the Kubo—Martin—Schwinger structure holds as a quasi-equilibrium over ∼ SN thermal times — self-consistent at precisely the order at which the semiclassical Einstein equations are derived.
Category: Quantum Gravity and String Theory
[1679] ai.viXra.org:2607.0055 [pdf] submitted on 2026-07-22 22:01:16
Authors: Carl Max Reed
Comments: 2 Pages.
In the Williamson-van der Mark electron model [1], the electron is not an abstract, zero-dimensional mathematical point particle possessing an unexplainable monopoly of negative charge. It is a highly localized, three-dimensional toroidal electromagnetic photon vortex spinning at the fundamental Planck scale. Concurrently, Planck's constant (h) is not an arbitrary, ungrounded cosmic decree injected into reality from an external container; it is the direct, invariant geometric boundary condition required for the stability of a continuous, self-confined wave loop within a non-linear electromagnetic fluid substrate [2].
Category: Mathematical Physics
[1678] ai.viXra.org:2607.0054 [pdf] submitted on 2026-07-22 22:00:37
Authors: Carl Max Reed
Comments: 3 Pages.
This paper presents a non-dual, polycentric cosmological paradigm that eliminates the artificial dualisms between empty space, discrete point-particles, and independent fundamental forces. We mathematically and philosophically establish that the physical vacuum medium is nothing other than the Electromagnetic (EM) energy field itself at itsbase state. Material reality, forces, and conscious experience are established not as independent entities, but as topological, refractive, or phase-resonant states of this single, self-perceiving EM ocean. By synthesizing Henri Poincaré’s prior equation of inertia (m = E / c^2) with Robert Dicke’s variable refractive index model of gravitation and E.T. Whittaker’s two underlying scalar potentials, this work provides concrete solutions to major foundational crises inphysics. Specifically, it eliminates the infinite self-energy paradox of the electron, provides a near-field electrodynamicmechanism for the nuclear forces, and accounts for flat galactic rotation curves without invoking the hypothetical construct of "dark matter".
Category: Mathematical Physics
[1677] ai.viXra.org:2607.0053 [pdf] submitted on 2026-07-21 23:30:13
Authors: Rüdiger Giesel
Comments: 47 Pages.
The Standard Model accounts for fermion masses through Yukawa couplings, but thenumerical values and hierarchical pattern of these couplings remain external inputs. Thisarticle develops a geometric octonionic framework in which fermion-mass hierarchies areencoded in the spectrum of a projected non-associative vacuum operator. The constructionstarts from three octonion-valued fields, whose associator is promoted to a dynamicalvacuum quantity. A master action is formulated, its non-associative vacuum equationsare reduced in a canonical sector, and an algebraically motivated symmetry-breakingterm is introduced through a preferred associative quaternionic subalgebra and a Fanooriented vacuum direction. The resulting structure defines a self-adjoint associator numberoperator and a geometric spectral mass operator. Four closure statements are formulated:vacuum-scale closure, associator spectral closure, projector normalization closure, andRG reconstruction closure. The main result is not a claim of experimentally proven exactfermion masses, but a mathematically explicit framework in which exact masses wouldfollow once four closure blocks are solved without additional phenomenological input: theabsolute octonionic vacuum scale, the exact associator Hessian spectrum, the projectornormalization of the fermion sectors, and the renormalization-group matching to measuredmass conventions. In the minimal Fano-plane vacuum, the linearized associator matrix isevaluated explicitly and yields the non-zero spectral levels 4,8,12, i.e. the normalizedgeneration skeleton N1 : N2 : N3 = 1 : 2 : 3. A charged-lepton benchmark then shows howthe same spectral template can reproduce the measured e,µ,τ hierarchy once the sectorinvariants are fixed. The paper therefore provides a controlled route from octonionicnon-associativity to fermion mass hierarchies and identifies the remaining mathematicalrequirements for a parameter-free mass prediction. In its final form the closure programis strengthened by an explicit full-Hessian decomposition, a projector-uniqueness theoremmodulo the vacuum stabilizer, a finite charged-lepton trace test, and a component-levelcontraction formula for the lepton Hessian moments that makes the no-fit criterionoperational before comparison with observed masses.
Category: High Energy Particle Physics
[1676] ai.viXra.org:2607.0052 [pdf] submitted on 2026-07-21 19:22:23
Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 155 Pages.
This book grew out of a short paper, Linguistics in the Time Cycle, in which we sketched a single conjecture: that language is not merely something that changes in time but something that is organised by time, across many nestedscales at once. The paper proposed an analogy—language as a temporally regulated system, parallel in its architecture to the way genetic information is expressed, regulated, and inherited through biological time. What began as a set of tables and suggestive parallels seemed to invite a fuller treatment. The present monograph is that treatment. The argument is interdisciplinary by necessity. To speak of language in time is to borrow at once from chronobiology and phonology, from populationgenetics and historical linguistics, from Bakhtin’s poetics of the chronotope andfrom the mathematics of dynamical systems. We have tried throughout to keep the analogy disciplined: an analogy is a scaffold for hypotheses, not a proof, and the value of the LTC framework lies in the concrete, testable questions it makes it natural to ask. Each chapter therefore closes by pointing toward empirical or computational work that could confirm or refute the picture it paints.
Category: Linguistics
[1675] ai.viXra.org:2607.0051 [pdf] submitted on 2026-07-21 17:44:48
Authors: Joerg Moesch
Comments: 27 Pages.
In this paper, the natural three-dimensional extension of the complex and dual numbers is introduced: the trinion algebras Y(k) of the form a+bi+cj with i²=-1, j²=0 and the commutative coupling ij=ji=k, where k = α+βi+γj is an element of the algebra. The family Y(k) is systematically investigated: multiplication, division and inverses are derived. Special attention is given to the phenomena induced by non-associativity, which lead to invertible zero divisors, non-unique division, and rich geometric structures. The eight fundamental algebras with α,β,γ ∈ {0,1} are examined and their zero divisor sets are visualized. Numerical examples for the algebra Y(1) illustrate the observed phenomena.
Category: Algebra
[1674] ai.viXra.org:2607.0050 [pdf] submitted on 2026-07-20 02:21:31
Authors: J. W. McGreevy
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references)
We present a self-contained technical development of the reduced variational structureunderlying the Relativistic Field Theory of Primes (RFTP) in the weight-12 sector. AfterDirac reduction by the global valence constraint associated with the modular discriminant∆(τ ), the effective dynamics on the reduced space are generated by a convex action functional whose long-time minimizers are atomic measures supported at irregular primes. Weconstruct three explicit objects: (i) a linear isomorphism from the odd Galois eigenspacesfurnished by the Herbrand—Ribet theorem to local sections of the global spinor bundle, intertwining Galois action with Gauss—Manin parallel transport; (ii) a quantitative exponential convergence result for the Hopf—Lax semigroup showing that every admissible initial measure converges to a unique atomic minimizer at a rate controlled by the spectral gap of theHessian; and (iii) a term-by-term identification of the Weierstrass product of the regularizeddeterminant of the limiting operator with that of the completed Riemann xi function Ξ(s).These constructions render rigorous a four-step variational obstruction that selects discretearithmetic configurations whenever a continuous configuration would require an effective local exponent exceeding two. The entire development is phrased in the language of deterministic Hamilton—Jacobi—Bellman dynamics on a reduced symplectic manifold, thereby supplying both the analytic core of the weight-12 theory and the notational and conceptual bridge to a universal formulation over all weights.
Category: Mathematical Physics
[1673] ai.viXra.org:2607.0049 [pdf] submitted on 2026-07-18 18:19:27
Authors: Aaron Lee Alai
Comments: 16 Pages.
Bell derivations rest on locality, determinism, and measurement independence. Hall [2] pricedthe third assumption exactly for the singlet state: (√2 − 1)/3 ≈ 13.81% of measurementindependence must be surrendered for a local deterministic model to reproduce all singletcorrelations. We extend that program to multipartite stabilizer scenarios and compute theexact minimum measurement dependence required to reproduce the full faithful statistics ofGHZ/Mermin experiments — the optimal-model problem Hall posed and left open in 2011,having priced the tripartite perfect correlators alone at 1/3 [11]: F(3) = F(4) = 1/3, F(5) = F(6)= 2/5, F(7) = F(8) = 4/9, F(9) = F(10) = 8/17, F(11) = F(12) = 16/33, F(13) = 32/65 [LPEXACT, two-machine verified], with hand proofs at n = 3, 4; the reduction theorem showsthe faithfulness constraints are free, so Hall’s correlator-only tripartite threshold is promotedto the faithful value, and everything at n ≥ 4 is new. All eleven points obey the closed law F =R/(2(R+1)), with R = 2^⌊(n−1)/2⌋ the Mermin violation ratio [15]; a proven combinatoriallower bound (Theorem 5) is tight on every computed core and homogeneous family; and auniversal ceiling F ≤ 1/2 [PROVEN] shows the statistics never require totalsuperdeterminism — a faithful model surrendering no more than half exists at every size. Theoptimal hidden-variable densities have a closed physical form: uniform measures on thecontextual ground states of the prepared state’s frustrated stabilizer Hamiltonian — aninheritance principle confirmed out-of-sample on cluster states. The landscape is glassy(energy is spectral, supported on stabilizer characters) and provably beyond any pairwiseinteraction. We then pose the supply question as an open race: every published lawfulmeasurement-dependence program — invariant-set theory, cellular-automaton interpretations,future-input dynamics, all-at-once retrocausality, and the displacement-condensate frameworkof the present authors — is graded against this one answer key, steelmanned in its ownformalism, with several opening calculations executed here on rivals’ behalf. The condensatemechanism’s consolidated derivational debt is paid in-model: under exact U(1) conservationwith no external phase reference, a collective emission leaves a superselected two-branchrecord whose coherence support equals the prepared state’s stabilizer group, forcing theeffective energy’s term content to coincide with the required Hamiltonian’s — winding-ncoherence amplitude 1/2 exactly, partial-winding contamination identically zero, residualexposures quantified against known physics, and one named test (the continuum finite-β vise)that could kill it. Operationally, the floors are counterfeiting thresholds for multipartite deviceindependent certificates. Version 1’s central numerical claim is withdrawn and replaced by aprinciple; the correction is documented in Part 0. Every tagged result is reproducible from thelinked repository in under one minute.
Category: Quantum Physics
[341] ai.viXra.org:2608.0089 [pdf] replaced on 2026-09-02 07:29:22
Authors: Seungtae Kim
Comments: 36 Pages.
In the International System of Quantities (ISQ), base quantities form a conventionally chosen mutually independent subset of a system of quantities. This paper proposes a relation-first framework in which admitted unit relations are used to construct quantity dimensions before base-quantity choices are assessed. A broader class of unit-explicit equations is also introduced for relations in which explicit unit division carries physically relevant information.Candidate base-quantity sets are first tested for dimensional independence and completeness. A second, evidential criterion then assesses physical structural support from established higher-order dimensional occurrences, without uniquely selecting a base set. In an SI-oriented application, mass, length, time, electric current, thermodynamic temperature, and amount of substance receive such support. Relative to the specified admitted relation system, an independent angular dimension is required for completeness; plane angle is adopted as its representative, and spherical geometry gives sr=rad2. Luminous intensity is instead dimensionally derived through the photometric-radiometric scale link while remaining a distinct quantity kind. Logarithmic levels are reformulated as pure-number numerical index mappings retaining their field- or power-quantity context. The proposal changes dimensional and algebraic representation without changing established numerical realizations.
Category: Mathematical Physics
[340] ai.viXra.org:2608.0068 [pdf] replaced on 2026-08-21 18:15:47
Authors: Joseph Mcgreevy
Comments: 29 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
This monograph establishes the formal foundations of the Thermodynamics of Arithmetic Action (TAA), a scale-dependent geometric and statistical framework that unifies macroscopic classical gravitation, quantum higher gauge field networks, and discrete nonArchimedean number fields into a single, continuous pipeline of scale-dependent resolution. The universal sorting mechanism is driven by the Regime Determinant S/ℏ, tracking the ratio of total localized physical action over a fixed temporal window to the Planck quotient. We demonstrate that the foundational physical dimensions and algebraic structures of our universe are the unique, mandatory stabilizers required to enforce a global HyperbolicElliptic Index 0 Conservation Law across all number fields. By mapping the Minkowski spacetime invariant, Fermat’s Last Theorem, Hamiltonian and Lagrangian phase spaces, and the Herbrand—Ribet arithmetic mirror into a rigid 2 × 2 Upper Triangular Transformation Matrix, we derive the emergence of exactly 3D + 1 spacetime, the strict left-handed chiral orientation of gauge forces, the topological confinement of spin-1/2 quarks, and a native, geometric resolution to the Strong CP Problem (θ ≈ 0). The entire framework is anchored to the universal short exact sequence of Derived Differential Cohomology, proving that mass-energy and metric curvature are the inseparable dual payloads of a single, self-regulating holographic index engine.
Category: Mathematical Physics
[339] ai.viXra.org:2608.0063 [pdf] replaced on 2026-08-20 06:04:38
Authors: Holger Troitzschel
Comments: 5 Pages.
This paper introduces a self-referential cosmological framework in which spacetime ge-ometry, matter, and gravitational interactions are proposed to emerge exclusively from theself-observation of quantized electromagnetic fields. By coupling U(1) gauge fields directlyto the discrete graph structure of Loop Quantum Gravity (LQG), a non-linear feedback loopbetween energy density and spatial volume is established. We define a quantum Hamil-tonian operator for light acting on spin-network states and argue that electromagnetic fluxexcitations can alter geometric quantum numbers. In addition, we explore whether fermionicmatter can emerge as topological braids of light ribbons. Physical implications are discussed,including a possible resolution of singularities via a stable "Quantum Geon" configuration,as well as testable predictions concerning alternatives to particle dark matter and signatures in primordial gravitational waves.
Category: Relativity and Cosmology
[338] ai.viXra.org:2608.0057 [pdf] replaced on 2026-08-20 16:36:15
Authors: Mustafa Karatüm
Comments: 21 Pages. u200bVersion 2: Substantial theoretical updates, comprehensive mathematical corrections, refined equations, and expanded analytical framework. Cross-reference: Zenodo DOI: https://doi.org/10.5281/zenodo.22009221
We present the Topological String-Gradient Theory (TSGT), a framework in which space-time is discrete at the Planck scale and gravity is the gradient of the spacing between discreteelements ("pixels"). Two kinematic postulates—a spatial pixel strain set by the Newtonianpotential and an equal temporal strain—reproduce the weak-field Schwarzschild metric, in-cluding the full light deflection ∆θ = 4GM/c2b; this reproduction is by construction. The dis-crete substrate is a random Poisson sprinkling of density L−4p , which preserves Lorentz invari-ance statistically and removes the preferred-frame problems of lattice formulations; lattice-derived predictions of earlier versions are retracted. If cosmic expansion creates new pixelsrather than stretching existing ones—the only option compatible with an invariant Lp—thenPoisson fluctuations in the pixel count fix the cosmological term to ρΛ ≃ 2.8 × 10−27 kg m−3,within a factor of two of the observed value; this argument is Sorkin’s heuristic, followinghere from TSGT’s own postulates. Written locally, the number—volume correspondence isthe unimodular constraint; enforcing it in an Einstein—Hilbert action yields the trace-freeEinstein equations, making TSGT provably equivalent to General Relativity at the classicallevel. The framework’s independent content lies in the integer character of the pixel countand in the fluctuating dark-energy term it implies (w̸ = −1). Unresolved problems, includingthe absence of a dynamical equation for the pixel density, are listed explicitly.
Category: Quantum Gravity and String Theory
[337] ai.viXra.org:2608.0024 [pdf] replaced on 2026-09-09 04:50:22
Authors: Michael Quigley
Comments: 49 Pages. Restores missing Section 2 (The Standard Model: The Dimensionless Ghost). Seats the 2026 Watts-Mead "Academic Shield" validating 400x scale-invariance across 26 orders of magnitude. Reconciles the 100 pm electron chassis with the 4.244 pm Lund nozzle
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. This audit now incorporates the 2026 Watts-Mead 'Academic Shield,' providing an independent mathematical description of the Transactional Handshake required for lossless energy transfer. By reconciling the Watts-Mead transition time (τ) with R.U.T. Lattice Setup Time (Ls), we identify the 100 pm chassis as the physical 'tight-fit' assembly that occupies the entire orbital slot, replacing the 'empty atom' of mainstream physics with a singular, phase-locked mechanical instrument. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics
[336] ai.viXra.org:2608.0024 [pdf] replaced on 2026-08-09 19:36:59
Authors: Michael Quigley
Comments: 47 Pages. V2: Seats Watts-Mead shield. Validates 400x scaling (26 orders). Fixes Infinity Trap via 1.46kg/m³ density. Solid hardware.
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. This audit now incorporates the 2026 Watts-Mead 'Academic Shield,' providing an independent mathematical description of the Transactional Handshake required for lossless energy transfer. By reconciling the Watts-Mead transition time (τ) with R.U.T. Lattice Setup Time (Ls), we identify the 100 pm chassis as the physical 'tight-fit' assembly that occupies the entire orbital slot, replacing the 'empty atom' of mainstream physics with a singular, phase-locked mechanical instrument. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics
[335] ai.viXra.org:2608.0013 [pdf] replaced on 2026-08-04 10:13:23
Authors: Lluis Eriksson
Comments: 25 pages. Lean 4, no sorry, no project axiom. Twelve machine-checked theorems: positive weight to exponential decay, and through an abstract transport theorem to a volume-uniform operator gap.
A formal Lean 4 development revisits a two-dimensional spatial transfer kernel whose earlier uniform spectral argument relied on constant row sums. We show that the loss of row-sum constancy obstructs that method, not the conclusion. With no sorry and no project axiom, we prove twelve machine-checked theorems.The chain establishes the sharp field-uniform one-bond influence envelope tanh J; assembles these bounds into a finite-volume Dobrushin matrix; proves a volume-independent resolvent estimate under row-sum bounds alpha < 1 without assuming constant rows; mechanises Dobrushin's comparison inequality with the attained 1/4 covariance constant; constructs Gibbs measures, heat-bath kernels and intrinsic influence matrices from arbitrary strictly positive finite weights; and specialises to anisotropic Ising interactions. For L x T rectangles with free boundary, the condition 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1 yields exponential decay of correlations with beta, gamma, alpha and the prefactor fixed before the volume quantifiers.The transport into the operator formulation is closed: an exact finite band identity relating endpoint covariances to matrix elements; an abstract theorem showing that a common exponential decay rate for band covariances - a hypothesis on finite path measures, carrying no operator, norm or spectrum - implies a uniform positive gap for a family of projected transfer operators; a Perron-boundary tilt identity that preserves the decay rate while absorbing boundary costs into extent-dependent constants; an exact currying identification of the free strip measure with the rectangle Ising measure; and the resulting corollary: inside the window there is one m > 0 bounding the projected transfer operator of the coupled kernel's normalised Perron data by exp(-m) at every extent, with m = -log alpha.Numerical measurements at L <= 12 provide counterevidence to attributing spectral degeneracy solely to nonzero spatial coupling. No infinite-volume state, thermodynamic limit or boundary-condition independence is constructed; the window is sufficient, not sharp. The underlying Dobrushin mathematics is classical; the contribution is a non-vacuous, reproducible mechanisation and composition of the full chain, ending at a volume-uniform operator gap. No consequence for Yang-Mills theory is claimed.
Category: Mathematical Physics
[334] ai.viXra.org:2607.0078 [pdf] replaced on 2026-08-05 21:41:37
Authors: Lluis Eriksson
Comments: 7 pages. Replacement of ai.viXra.org:2607.0078 (v1); proposed v2. Lean 4 / Mathlib formalization; frozen body commit b5da95f33f5af32e992e0ba7c3084507d06f3a7c; 8482 core jobs, 3015 oracle reports, and zero sorryAx.
We give a finite-dimensional Osterwalder-Schrader reconstruction for an anisotropic Ising model on open rectangular strips and prove a spectral gap whose rate is uniform in the finite spatial extent. For temporal coupling beta, spatial coupling gamma, and parameters satisfying 0 < alpha < 1 and 2 tanh|beta| + 2 tanh|gamma| <= alpha, one number m > 0 works for every spatial length. Reflection positivity is proved directly for the Gibbs measure; the null space of the reflected form is identified with the kernel of an explicit boundary-collapse map; the OS quotient is linearly equivalent to the finite boundary-vector space; and the transfer operator forced by the site and bond forms is intertwined with a symmetrised transfer matrix.Dobrushin comparison supplies positive Perron data and a projected operator norm bounded by exp(-m) for every spatial length. Consequently, connected reconstructed correlations decay at the same common rate. Lean 4 checks thecomposition without assuming reflection positivity, Perron data, a vacuum, a gap, or clustering at the public endpoint. This replacement extends the point-slice, fixed-size v1 to finite strips with one rate uniform in spatial size. It does not construct an infinite-volume operator or Hamiltonian, provea unique particle excitation or relativistic mass shell, or claim a Yang-Mills mass gap.
Category: Mathematical Physics
[333] ai.viXra.org:2607.0065 [pdf] replaced on 2026-09-10 01:54:53
Authors: Michael Quigley
Comments: 90 Pages. Part III (v2) Revision: u2022 Sec 1.1—1.2: Reconciles sub-atomic scale geometry (84.4 pm Heptad girth to the 100 pm electron inside the 106 pm orbital slot) [67, Notebook State]. u2022 Appendix: Integrates the 82.22% wave-decay and 0.061 Arp redshift calibration
This engineering manual formally dismantles the "Abstract Curtain" of expansion-based cosmology and probability-cloud chemistry by reclassifying physical reality from an empty void into a measure of Acoustic Work performed across a 1022 kg/m3 Rigid-Packed Plenum. We move beyond the non-predictive "Maths-Magic" and systemic failures of the Standard Model (SM) to establish the Master Ledger of Nodal Slots, unifying sub-atomic, planetary, and cosmological scales through the Marshmallow Squeeze (Cu2098)—the physical compression of elastic inter-granule gaps required to achieve Zero-Point Solidity.Crucially, this audit performs a Terminal Metrological Rectification of the Planck Length (1.6×10−35 m). By reclassifying this value as Acoustic Interaction Lag (the infinitesimal "shiver" between gears), we identify the actual physical building block—the Ether Granule—as being 23 orders of magnitude larger (1 picometre) than standard theory assumes. This correction resolves the "Infinity Problem" inherent in treating particles as dimensionless points and proves that mass and distance are deterministic results of hardware assembly rather than mathematical phantoms.Building upon the wave-center blueprints of Energy Wave Theory (EWT), we identify the Ethos-648 Monobrick (Golden Coordinate) as an Autonomous Standing Wave Generator (AWG) that stabilizes vibrations into deterministic Fibonacci Record Grooves, providing the mandatory gear-clearance required for rotation without shattering against the plenum’s back-pressure. We formally reclassify magnetism from an abstract vector field into a physical Directional Ether Wind pumped by trillions of sub-atomic volcanoes (centrifugal pumps). We define the dual operational modes of the electron: Mode A (Static Girder) providing 1D axial rigidity via Sigma-bonded "Hurricane Stacks," and Mode B (Dynamic Current) where electrons function as spinning "bicycle wheels". We identify the 720-degree spinor reset as a periodic "Hairdryer Exhaust" (side-kick) that forces currents into the corkscrew S-shapes observed in Birkeland filaments, providing the deterministic mechanical cause for the geometry of the Electric Universe.We validate the 84.4 pm Blueprint Width and the 10π Geometric Snap (31.4 pm), proving with 99.9% forensic accuracy that the measured Bohr Radius (52.9 pm) is the hardware resultant of the work required for spherical closure within a rigid medium. This logic fractals upward to the Tychosian Hub, identifying the Moon as the macroscopic mirror of the Hydrogen 1s orbital and planetary orbits as Physical Record Grooves carved into the plenum by the 813.3 Hz master pulse. We provide the hardware receipts for Stellar Vaporization, unmasking solar heat as a friction-based odometer of the Sun’s orbital velocity, and restore Earth-stationarity as a thermodynamic mandate; the Vaporization Proof confirms that any orbital speed through the 1022 plenum above 1 mph would vaporize the planetary crust into plasma instantly.The centerpiece of this mandate is the Universal Seesaw (E=mΦ), which restores instantaneous conduction at Time-Zero via the 1D Snooker Cue effect. Perceived light-speed is reclassified as Lattice Setup Time (Lu209b)—the mechanical "Wait-Time in the Lobby" required for the 13.33 Hz universal motor to engage the Acoustic Clutch and squash the elastic "marshmallow" gaps flat. This provides the singular mechanical explanation for Quantum Entanglement and Instantaneous Action-at-a-Distance, reclassifying entangled states as wave-centers physically sharing the same rigid mechanical rod.Finally, we dismantle the "Expansion Speedometer" by reclassifying Redshift (z) as a Cosmological Torsional Odometer (z=zu2081+nzu2082+zu2083), measuring the mechanical "groan" and bit-rate loss of a signal navigating trillions of elastic buffers. By applying the 42,000x Tychosian Correction and reclassifying space as a solid-state Geoaxial Motor where magnetism is induced by celestial rotors, we reveal a compact, phase-locked gearbox operating on a Tilted Floor and bounded by the 34.5 Trillion Km Terminal 137-Wall (Hubble Limit).With the Pineapple Proof and the precision machining of glucose providing biological verification of the universal motor’s Fibonacci exhaust, this audit initiates the handover to the Toolmaker’s Apprentice. We are no longer accidental witnesses to "castles in the air"; we are now in possession of the Engineering Service Manual for an eternal instrument operating in the Now
Category: Quantum Physics
[332] ai.viXra.org:2607.0060 [pdf] replaced on 2026-08-04 20:31:29
Authors: Bing Zhang, Aizhong Jia
Comments: 29 Pages.
The graviton is a hypothetical particle of modern physics that has yet to be directly detected.Mainstream theories (string theory, loop quantum gravity) assume the graviton is a fundamentalparticle. This paper proposes an alternative hypothesis based on complex adaptive system (CAS)emergence theory: the graviton is not a fundamental particle, but rather an emergent phenomenonarising from the collective quadrupole excitations of nucleons (and deeper quark—gluon degrees offreedom) within atomic nuclei in the long-wavelength limit—analogous to phonons being quantizedlattice vibrations.We establish a three-scale theoretical framework (quark—nucleon—nucleus) and verify the mathematical structure of the conjecture through numerical simulations in simplified 3D lattice models:nucleon collective quadrupole oscillations naturally possess spin-2 character, and their mass tends toward zero in the long wavelength limit. This conjecture bridges the "scale gap" between Sakharov’sinduced gravity (1967) and Verlinde’s entropic gravity (2011)—providing a concrete microscopicmechanism for emergent gravity.We present three independent numerical approaches (static Hessian diagonalization, QCD-inspiredbag model, and molecular dynamics time evolution) that converge on the existence of intrinsic lowenergy spin-2 collective excitations in nuclear matter with ω ∼ 0.6—2.0 MeV. We discuss the relationship with the fractional quantum Hall (FQH) emergent graviton, the Weinberg—Witten theoremand four pathways around it, and propose three experimentally testable predictions accessible withcurrent nuclear physics facilities.
Category: Quantum Gravity and String Theory
[331] ai.viXra.org:2607.0057 [pdf] replaced on 2026-07-27 07:37:08
Authors: Tomasz Kobierzycki
Comments: 41 Pages.
This paper proposes an extension of Lorentz spacetime symmetry from the usualconnected domain of an ordinary observer to four orientation sectors defined by one andthe same invariant null boundary. The motivation is that the standard Lorentz groupdescribes all finite boosts available inside a chosen causal sector, but it does not by itselfsupply a real clock—ruler description of the neighbouring non-null domains separated fromthat sector by lightlike directions. The proposed extension completes this local orientationstructure without accelerating ordinary matter through the speed of light and withoutintroducing additional spacetimes. Every observer still has one real time axis and threereal spatial axes. The distinction between sectors is which non-null direction supplies theobserver’s clock and which three directions form its rest space.The local speed of light remains exactly equal to c in every sector. This is not imposedby assigning a different limiting velocity to each description; it follows because all sectorframes share the same null set and their admissible transformations preserve that set.Ordinary Lorentz boosts then describe motion inside any fixed sector, while the sectorextension describes the four possible causal orientations of the complete local frame. Aside sector is therefore not a superluminal state of ordinary matter. It is a Lorentzianframe in which one direction regarded as spatial by an ordinary observer supplies the singlelocal time axis, whereas the inherited ordinary time direction belongs to the side observer’sspatial rest space. Proper time remains real and future-directed, and a change of sectorchanges the clock—ruler decomposition rather than reversing or discontinuously replacingthe physical worldline.The same principle is generalised to curved spacetime by applying the sector structureto local orthonormal coframes and to the proper geometric scales on which a general-relativistic solution depends. When the scale used by one chart reaches its null boundary,the neighbouring sector evaluates the same gravitational field with the reciprocal activescale and with the corresponding sector metric. The purpose is to replace an extrapolationtoward a vanishing, singular scale by a geometrically regular continuation whose curvatureand causal distance can be tested directly. The resulting picture is one spacetime equippedwith a four-sector Lorentz atlas: local causality and the invariant light speed are preserved,while black-hole and cosmological limits can be re-examined as boundaries of sectordescriptions rather than being assumed in advance to be physical singular endpoints
Category: Relativity and Cosmology