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[70] ai.viXra.org:2610.0072 [pdf] submitted on 2026-10-31 22:00:41
Authors: David E. Svacha
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
We formalize a mandatory energy cost for geometric deformation of spacetime, expressed by the gatekeeper equality R = W / D(Phi), where W is the work required to produce a deformation measure Phi and D is positive-definite and vanishes if and only if Phi = 0. A signed resistance term that supplies restoring force on both sides of an equilibrium density is inserted as additive pressure support. A phase-diagram diagnostic with stiffness s = 20 places slope dominance near x ≈ 1.08 and value overtaking near x ≈ 1.51. The same nuclear-matched constants produce a resistance pressure of approximately 5.6×10^18 dyn cm^{-2} at solid density, exceeding self-gravitational central pressure by at least eight orders of magnitude for objects up to 1000 km radius, with no retuning. First-order Hartle frame-dragging on locked effective-density profiles yields modest, equation-of-state-dependent increases in moment of inertia (a few percent for SLy, approximately 8 percent for APR4). Controlled dynamical-collapse evolutions under the same locked parameters produce finite-density reversal and a drop in central Kretschmann scalar on the resistance-on side for configurations above a density and stiffness threshold, while matched pure-GR controls continue to collapse. Inspiral-pinned ringdown residual stacking on public gravitational-wave events returns noise-floor results (normalized residual energy consistent with 1), establishing a measured sensitivity limit rather than a detection. The signed resistance term is therefore stated as an open prediction: it produces faster ringdown decay than the inspiral-pinned general-relativistic quasinormal mode once a hierarchical stack reaches adequate aggregate signal-to-noise, or else the data place a tight upper bound on the stiffness. The present null constrains only the current method class and sample. The skeleton covers classical geometric grids from nuclear through atomic density; it does not yet address the Planck regime, full quantum-gravity corrections that alter identification of W or Phi, or cosmological horizons. An evidence scoreboard applying a strict referee standard is included as an appendix.
Category: Relativity and Cosmology
[69] ai.viXra.org:2610.0071 [pdf] submitted on 2026-10-31 21:58:53
Authors: Stuart Albon
Comments: 11 Pages.
We present a non-local, extra-dimensional classical field theory that unifies gravitational and inertial phenomena under a singular, boundary less Holographic Entanglement Order Parameter propagating within a warped five-dimensional Anti-de Sitter bulk topology. Moving away from traditional coordinate-dependent spacetime curvature, we model gravity as a homeostatic reaction of the cosmos to a complexified total stress-energy flux, which incorporates rest mass, internal energy, kinetic momentum, and a topological charge phase factor to mathematically formalise directional dipole states driven by localized entropy gradients. By embedding our 3-brane universe at the stable nodal midpoint of this bulk geometry, we demonstrate that standard physical entities act as localized dimensional cross-sections of a higher-order information network. Crucially, we formalise an explicit information-theoretic extension of the classical Verlinde entropic gravity baseline and the Ellis-Maartens emergent universe paradigm, demonstrating that the stabilization of the initial finite-sized cosmic state is an automated consequence of a network load-balancing routine rather than a fine-tuned material scalar field. By executing a formal Gauss-Codazzi dimensional reduction from the bulk down to the 3-brane, we derive a modified set of four-dimensional Einstein Field Equations, where geometric curvature is modulated by an exponential network latency factor alongside a non-linear chameleon-type screening mechanism integrated into the field’s self-interaction potential. This structural architecture suppresses field anomalies in high-density environments to preserve classical solar system post-Newtonian telemetry, while allowing the field to asymptotically flatten at galactic scales to reproduce flat rotation curves without cold dark matter, matching thermodynamic volume constraints. Under extreme high-energy constraints, topological field adjustments are shown to map onto a circular Dini manifold profile, allowing non-singular, continuous cross-boundary data routing. Finally, by introducing a finite relaxation-time tensor to account for non-local field propagation delays, this framework successfully explains the apparent baryonic decoupling observed in astronomical collisions like the Bullet Cluster, and derives late-time accelerating cosmic expansion directly from the vacuum limit of intergalactic nodal voids without requiring dark energy.
Category: Relativity and Cosmology
[68] ai.viXra.org:2610.0070 [pdf] submitted on 2026-10-31 21:56:00
Authors: Ibrahim Amin Nicola Shnoudi
Comments: 18 Pages.
A positive integer n is almost perfect if σ(n) = 2n − 1. Every power of 2 is almost perfect, and the conjecture that there are no others is open. This project does not prove it. It proves the conjecture for odd parts with at most two prime factors, with a machine-checked proof, and it reduces each remaining case to a precisely stated problem.
Category: Number Theory
[67] ai.viXra.org:2610.0069 [pdf] submitted on 2026-10-29 22:54:23
Authors: Tristan Romanov
Comments: 9 pages. Code and certificates: doi:10.5281/zenodo.23783317. License: CC BY 4.0
We study Wilson lattice Yang—Mills theory on ℤ3 in a gauge that fixes one link at every site along a period-3 forest, in which every free link shares a plaquette with exactly seven other free links. Two results follow.
(A) For SU(2), a single-link Dobrushin argument with the sharp one-quarter Kantorovich estimate of Bhattacharjee and Bhattacharya gives a unique infinite-volume state, invariance, reflection positivity, exponential decay of correlations and a transfer-matrix gap m ≥ −log(7βW/4) for βW < 4/7. The same estimate gives βW < 1/3 in three dimensions without gauge fixing and βW < 1/2 in the temporal gauge. As Bhattacharjee, Bhattacharya and Lockwood showed for 1/3 in four dimensions, we show that 4/7 is the ceiling of this argument for every gauge-fixing forest.
(B) For every compact group with a faithful unitary representation, the Hessian of Σp Re Tr Qp restricted to the free links is bounded in absolute value by h = 9.599991, uniformly in the field. The proof is a site-plus-plaquette certificate with rational data: its finite part is checked in exact rational arithmetic, and positivity of a two-parameter family of matrices of size at most 12 is proved with outward-rounded interval arithmetic. With the Bakry—Émery criterion this gives log-Sobolev inequalities, a unique state and an explicit gap for N|β| < κG/h; for SU(N) this is |β| < 1/(2h) ≈ 1/19.20, compared with 1/32 of Shen, Zhu and Zhu and 1/24 from the sharp un-gauge-fixed constant. An exact computation at the trivial field shows that no bound below 9.3479 is possible in this gauge. All statements are at strong coupling and fixed lattice spacing.
Category: Mathematical Physics
[66] ai.viXra.org:2610.0068 [pdf] submitted on 2026-10-30 20:11:01
Authors: Robert Bennett
Comments: 6 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references!)
Modern cosmology is built on a foundation that includes the Cosmological Principle(CP).....that the universe looks the same everywhere, at large scales as it does from Earth. This analysis using simple laws like relative motion proves that our sky is unique in the universe ...and obviously so. In Brief: The CP is false.
Category: Relativity and Cosmology
[65] ai.viXra.org:2610.0067 [pdf] submitted on 2026-10-28 18:30:06
Authors: Alexander Wankerl
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present Chameleon-Graviton-Condensate Cosmology (CGCC), an effective field theory framework that addresses late-time cosmic acceleration, the $H_0$ tension, and cosmic structure constraints without relying on a conventional cosmological constant. The model posits that high-energy gravitational processes during early cosmic epochs (such as supermassive black hole accretion) inject Kaluza-Klein (KK) gravitons into a higher-dimensional bulk. Following adiabatic cooling and cascade decays in the bulk, these modes re-enter the 3+1 spacetime via a density-dependent chameleon mechanism. Within low-density cosmic voids, where environmental screening is lifted ($m_{phi} to 0$), the re-entering gravitons undergo Bose-Einstein condensation (BEC) into a macroscopic infrared ground state. A quartic self-interaction term stabilizes the condensate, yielding an isotropic equation of state with negative pressure ($w=-1$) that dynamically drives void-dominated expansion. We demonstrate that local void expansion reproduces measurements of $H_0 approx 73text{ km/s/Mpc}$, while spatial integration across void-filament boundaries converges to the global CMB-constrained value of $bar{H}_0 approx 67.4text{ km/s/Mpc}$. Furthermore, the model satisfies strict local constraints from Solar System tests (Cassini bound) and Big Bang Nucleosynthesis (BBN), and offers distinct, falsifiable signatures in weak-lensing shear profiles testable by upcoming astronomical surveys.
Category: Relativity and Cosmology
[64] ai.viXra.org:2610.0066 [pdf] submitted on 2026-10-29 03:57:00
Authors: Ipsita Mandal
Comments: 96 Pages.
We present an exact solution of the linearised semiclassical Boltzmann equation (SBE) beyond the relaxation-time approximation for multifold semimetals under arbitrarily oriented electric and magnetic fields. The framework treats the Berry curvature, orbital magnetic moment, Lorentz-force operator, and scattering terms on equal footing. Momentum-independent scattering-amplitudes couple the Fermi-surface sheets through intranode, interband, and internode processes. The scattering kernel has a finite rank and the SBE reduces to a linear system for a few moments, which is closed by the electron-number constraint. We apply this approach to four systems involving quadratic-corrected triple-point, Weyl, and Rarita-Schwinger-Weyl nodes, including tilted triple-point nodes. We obtain analytical results at zero field and to leading orders in the magnetic field, alongside numerical solutions for the full field dependence. Our results elucidate the roles of the topological properties, Lorentz-force operator, tilt, and intra- and internode scatterings in shaping the magnetoconductivity and planar-Hall response for noncollinear fields. It cures severe shortcomings of previous treatments like incomplete ansätze and incomplete treatment of the Lorentz-force operator.
Category: Condensed Matter
[63] ai.viXra.org:2610.0065 [pdf] submitted on 2026-10-29 19:10:00
Authors: Bradley Robert Paris
Comments: 90 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references!)
A reconstructive solar-lunar calendar employing fixed Halakim integers (1 day = 25,920 Halakim) is analyzed for long-term drift. Year lengths are restricted to 354, 355, or 384 days. A 19-year cycle places seven leap years; a 342-year shift maintains alignment. Verification of a 7,252-year ledger confirms perfect adjacency of every 355-day trim year to a 384-day leap year (1,409/1,409), 19-year groups of 6,939 or 6,940 days, and a mean year length of 365.2368days. The same 25,920 integer organizes the day, calendar cycles, and—under a defined spatial scaling factor of approximately 1.014764—an exact integer light-second of 11,977,113,600 inches and a polar rotation of exactly 60,800inches per Halakim. Weekday and year-length columns map algorithmically onto diatonic intervals and triads. The framework eliminates floating-point drift in calendrical and related coordinate calculations. Implications for orbital mechanics, numerical simulation stability, and high-energy computational methods are discussed as properties of the integer arithmetic rather than as new empirical constants. The system is fully deterministic once the 4026 BCE anchor and constants are fixed.
Category: Classical Physics
[62] ai.viXra.org:2610.0064 [pdf] submitted on 2026-10-27 02:39:34
Authors: Chaiya Tantisukarom
Comments: 7 Pages.
We study a deterministic procedure, denoted $mathcal{P}$, built from three operations: $3n+1$ on odd values, division by two ($op{d2}$) on even values, and a correction step $-1$ that is applied whenever the current odd value exceeds the previous odd value. The correction keeps the sequence of odd values below its starting point, so the ``lower part'' of every start is maintained by construction. We prove that for each odd start $nge 3$ the procedure reaches an odd value $G(n)<n$ in a number of operations determined by a $2$-adic valuation, that $G$ has a closed form, and that iterating $G$ reaches $1$ in at most $lfloor log_{4/3}(n-1)floor+1$ descents. We then show that $mathcal{P}$ coincides with the Collatz map only until its first correction, and we apply the minimal-counterexample (contradiction) method. The argument closes if and only if a single merging statement holds: for every $yequiv 2 pmod 3$ the Collatz orbits of $y$ and $2y+1$ meet. This statement is equivalent to the Collatz conjecture, so $mathcal{P}$ locates the difficulty precisely but does not remove it. Worked examples are tabulated.
Category: Number Theory
[61] ai.viXra.org:2610.0063 [pdf] submitted on 2026-10-27 12:46:05
Authors: Juan Duan, Songbo Zhang
Comments: 34 Pages.
Tunneling nanotubes (TNTs) are actin-supported membrane conduits that carry both rescuing mitochondria and pathology-driving proteins, yet no quantitative link connects nanoscale tube physics to population-level network behavior. Combining membrane-tube mechanics, cable theory, stochastic transport, adaptive-network dynamics, and percolation theory, we build a falsifiable framework with three core results. First, classical tube mechanics predicts a tether force of 24.3 pN and a diameter of 155 nm without free fitted parameters, matching measurements (10—40 pN; 50—200 nm); rupture resolves molecularly as necking instability plus actin—cortex detachment, predicting a median lifetime of 60—62 min (95% CI 37—99 min) within the observed 30—120 min. Second, the contact network is electrotonically compact (λ ≈ 158 µm ≫ L), and finite-size scaling in two and three dimensions constrains percolation thresholds to p_c = 0.257 ± 0.002 (2D) and ≈ 0.169 (3D; geometry-dependent), cross-validated by invariant scaling; whether resting networks actually sit above threshold remains a calibration question (P1). Third, competing cargo flows—protective transport linear under an adapter bottleneck, pathological transport superlinear—yield an optimal connectivity p* = a/2b that falls from 1.0 (healthy) to 0.32 (late pathology); the downshift is robust whenever pathological transport is superlinear. A molecular loading bottleneck explains the few-long-lived-TNT strategy. Five falsifiable experiments are mapped, including the embryonic-heart TNT—Notch axis.
Category: Quantitative Biology
[60] ai.viXra.org:2610.0062 [pdf] replaced on 2026-10-27 03:30:53
Authors: Ron Ragusa
Comments: 3 Pages.
The Fermi Paradox highlights a fundamental contradiction in modern astronomy: given the billions of star systems in our galaxy and the billions of years available for stellar evolution, why have we found zero evidence of extraterrestrial civilizations? (Bostrom, 2008). Traditional solutions assume physical absence—suggesting civilizations self-destruct, space travel is unfeasible, or intelligence is exceedingly rare.This paper presents an alternative, information-theoretic resolution: the Phase-Shifted Singular Multiverse. We propose that Earth-based life appears alone not because intelligence is physically sparse across spatial distance, but because intelligent civilizations actively collapse orthogonal "reality matrices" out of a shared, high-entropy quantum probability background (P_chop).
Category: General Science and Philosophy
[59] ai.viXra.org:2610.0061 [pdf] submitted on 2026-10-26 02:38:05
Authors: Hidehito Koseki
Comments: 11 Pages.
This paper proposes a theoretical framework that redefines time as a complex variable with a fixed imaginary constant floor, z=tpm it_{P} (where t_{P} is the Planck time), operating across all cosmological epochs. This approach aims to reconcile the avoidance of cosmological singularities with the consistency of physical laws in the macroscopic universe. Although traditional approaches introducing imaginary time—such as the Hartle—Hawking no-boundary proposal—successfully addressed the Big Bang singularity at t=0, their application was largely restricted to local Wick rotations in the early universe to avoid causality violation and non-unitary dynamics in macroscopic domains. Here, rather than treating the imaginary component as a dynamical degree of freedom, we introduce it as a fixed lower bound (Im-floor) corresponding to an intrinsic limit of temporal resolution. This formulation smoothly recovers standard physics in the macroscopic limit (tgg t_{P}) while offering unified geometric interpretations for three fundamental phenomena: (1) full regularization (C^{infty } continuity) of the cosmological origin (t=0) through a contour bypass in the complex plane, thereby avoiding the classical singularity; (2) direct correspondence between the sign of the imaginary component (pm it_{P}) and CPT conjugation, mapping matter (+it_{P}) and antimatter (-it_{P}) to dual phase domains; and (3) a geometric representation of rest mass versus masslessness as the presence (text{Im},z=pm t_{P}) or absence (Imu2009z=0) of an "imaginary temporal width" in complex spacetime. This model provides a concise, unified geometric perspective on foundational issues at the intersection of cosmology, quantum field theory, and particle physics.
Category: Relativity and Cosmology
[58] ai.viXra.org:2610.0060 [pdf] submitted on 2026-10-26 23:59:56
Authors: Brent Hartshorn, Tristan Romanov
Comments: 30 Pages.
The planar Spectre and Tsiokos’s three-dimensional Chair44 are aperiodic monotiles whose tilings are hierarchical; they are compared here by exact computation. The Spectre inflates by the unit λ2 = √15 + 4 of ℤ[√15]. Its supertile perimeter is 2F3k+5+4 at every order k, proved by a finite exact certificate, so it grows by the unit 2 + √5 of ℚ(√5), faster than the linear inflation. The boundary of the limiting supertile is a fractal of box dimension log(2 + √5)/ log λ, and the tail of the common-ancestor levels of neighbouring tiles decays exactly by ν/λ2 . The inflation acts on the vertex module ℤ4 with two expanding and two contracting directions, and the internal plane is given exactly; the window is the attractor of contracting similarities, with boundary dimension log(5+2√6)/log(4+√15). The Chair44 inflates by the integer 2 on ℤ3 , with no Euclidean internal space (its internal space is 2-adic) and no twist; its centre set, that of the classical three-dimensional chair, has an explicitly computed pure-point diffraction measure. The main result is that every lattice-registered tiling obeying the 44 contact rules lies in the substitution hull, and that its symmetry group is conjugate to one of 1, C2 (a half-turn about a face diagonal), C4 and D4. Both statements use Kamenetsky’s unique-hierarchy criterion, whose finite certificate is checked here independently, and they transfer to every tiling by the Chair44 solid through Tsiokos’s registrationtheorem, which has been audited but not refereed. Orientation sums and contact matrices separate the two tilings. Four finite-patch computations then test whether the Spectre’s substitution hierarchy can serve as a clock: positional clustering shows no arrow, the radius needed to recognize an ancestor grows about threefold per level without making one, the look-back law is shared with a quadtree, and the parity flip of the construction shows in the outlines of supertiles and not in the tiles.
Category: Combinatorics and Graph Theory
[57] ai.viXra.org:2610.0059 [pdf] submitted on 2026-10-25 10:53:31
Authors: J. W. McGreevy
Comments: 352 Pages. Volume V (Lemmas 86-118) of the programme Thermodynamics of Arithmetic Action. Previous volumes: ai.viXra:2610.0045, 2610.0054, 2610.0052, 2610.0056, 2610.0055.
This volume collects TAA Lemmas 86-118 of the programme Thermodynamics of Arithmetic Action. Volumes I-IV (ai.viXra:2610.0045v2, 2610.0054, 2610.0052, 2610.0056, 2610.0055) recast the Riemann Hypothesis (RH) as the absence of negative-norm ("ghost") directions for the Weil form, and traced the missing positivity to the Hodge index theorem on C x C, which zeta lacks. Over finite fields Frobenius is a rotation in the Rosati metric; a ghost would be a boost. Volume V asks what a surface Spec Z x Spec Z would have to supply. Central-value positivity (Gross-Zagier) turns out to be a parity statement about real zeros. Tested next: the standard conjectures and correspondence rings, the Connes-Consani self-intersection with synthetic ghost zeros, ample classes, two scalings and weight gradings. Certified (Arb) results: positivity of the Weil form of zeta on explicit spline spaces up to support a = 8, and certified detection of hypothetical off-line zeros. A compatible complex structure commuting with Frobenius exists exactly when the Frobenius torus is compact; the volume then compares Krein, Toeplitz and Newton-over-Hodge signatures, the modular cusp, BRST and thermodynamic geometry, and ends with Lax-Phillips passivity: the doubled modular system is passive unconditionally. A statement at the start lists exactly what is claimed, and where. Three proposed errata await the author's decision; they are listed, not applied. Formalization and computations were AI-assisted, and this is disclosed. RH is NOT proved: structures built from the zeros restate Weil positivity, those built without them are blind to off-line zeros, and an RH-independent ample class for Spec Z x Spec Z is still missing.
Category: Number Theory
[56] ai.viXra.org:2610.0058 [pdf] submitted on 2026-10-26 01:13:16
Authors: Maxim Lipyanchik
Comments: 33 Pages.
We present a systematic study of how modifications of the inverse Kerr metric manifest in images of a thin accretion disk and assess the sensitivity of different image observables to these deformations within a fixed astrophysical model.
Category: Relativity and Cosmology
[55] ai.viXra.org:2610.0057 [pdf] submitted on 2026-10-26 01:09:52
Authors: Ahcene Ait Saadi
Comments: 22 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We study systems of equations Ni(t)D(t) = ki (i = 1, . . . , n) that have a common solution t0, possibly together with equations Fi(x) = ki in a second unknown x with the same right-hand sides ki. Adding or subtracting these equations produces new systems whose solutions other than t0 (the hidden solutions) are computed by the rule a b Θ c d = a+c b+d (the Farey mediant), provided the orientation −A/B ̸= A/(−B) is respected. A second law, denoted ♢, says how to multiply an equation by a coecient: λ♢a b = λa λb , which is not the usual productof a fraction by a number. We explain these rules by a factorisation theorem, determinethe signs to choose in order to obtain a prescribed hidden solution, and give an inverseconstruction, relations between equations, a barycentric formula in degree m, the complexcase in degree 2, covariance under homographies, the correspondence between the unknownsx and t, two-parameter systems (relations between hidden values in t and in α, elliptic curves of rank ≥ 1), and a study of the rationality of all solutions (conics, elliptic curves). A rank criterion proved with Mazur's theorem gives innitely many fully rational combinations for certain pencils of cubics. Every statement is proved and illustrated by explicit systems. The core is elementary (Vieta's relations and linearity); the contribution is the reading of thesesystems and of their signed combinations.
Category: Number Theory
[54] ai.viXra.org:2610.0056 [pdf] submitted on 2026-10-24 04:26:42
Authors: J. W. McGreevy
Comments: 322 Pages. Thermodynamics of Arithmetic Action, Lemmas 48-65. Volume IV, part 1 of 2 (companion: Volume IVb). RH is not proved.
Volume IVa is the first of two parts of Volume IV of the programme Thermodynamics of Arithmetic Action. It collects TAA Lemmas 48-65; the companion Volume IVb contains Lemmas 66-85. The parts form one volume, split only because of the archive's 5 MB file limit. Volumes I-III (ai.viXra:2610.0045v2, 2610.0054, 2610.0052) recast the Riemann Hypothesis (RH) as the absence of negative-norm ("ghost") directions for the Weil form, measured that obstruction, and asked which structure could supply the positivity. Volume IVa tests three families of candidates. Polarizations as vacua and complex structures: Kramers-Kronig causality, the Betti-de Rham comparison, spinor vacua and Krein collisions, the Hardy-space vacuum and its ghost charge, and the complex structure Frobenius chooses for itself. Saddles and positivity ladders: saddles of |zeta| and xi', the Weil positivity ladder, the derivative tower of xi, and ghosts as dents in a flat cone metric. The prime side: class numbers, a visibility criterion for zeros, helicity and the Moebius function, local versus global positivity, and the field with one element. Certified computer-assisted results concern the Davenport-Heilbronn function (a zero-free box, and a lower bound 0.230607 for its de Bruijn-Newman-type constant) and truncated Weil forms (eigenvalue bounds; the Davenport-Heilbronn form is certified indefinite for A >= 3.43). A statement at the start lists exactly what is claimed across both parts, and where. Formalization and computations were AI-assisted, and this is disclosed. RH is NOT proved: no chapter supplies the missing positivity for zeta; most identify why a candidate cannot.
Category: Number Theory
[53] ai.viXra.org:2610.0055 [pdf] submitted on 2026-10-24 04:26:53
Authors: J. W. McGreevy
Comments: 280 Pages. Thermodynamics of Arithmetic Action, Lemmas 66-85. Volume IV, part 2 of 2 (companion: Volume IVa). RH is not proved.
Volume IVb is the second of two parts of Volume IV of the programme Thermodynamics of Arithmetic Action. It collects TAA Lemmas 66-85; the companion Volume IVa contains Lemmas 48-65. The parts form one volume, split only because of the archive's 5 MB file limit. Volumes I-III (ai.viXra:2610.0045v2, 2610.0054, 2610.0052) recast the Riemann Hypothesis (RH) as the absence of negative-norm ("ghost") directions for the Weil form. Here we test modular forms and Eisenstein anomalies, hyperbolic geometry, 3D gravity, Farey fractions and codes, and isolate the obstruction. The ghost count kappa, the negative index of a Weil-type form, recurs throughout; for a Weil polynomial it equals the number of negative directions of the Rosati trace form, a classical fact we restate and check exhaustively for 13135 genus-2 polynomials. We prove a no-go theorem for positivity built from scaling-commuting multipliers. We show numerically that the Davenport-Heilbronn ghost is visible at finite Connes cutoff, with primes n <= 41. Closed geodesics on Bianchi orbifolds see only Euler-product channels, not the off-line zeros of Epstein zeta functions. Over function fields, the BSD count in a Mordell-Weil lattice is one Frobenius eigenvalue, tied to RH through the algebraicity of Frobenius. Certified computations show that extremal weight enumerators of self-dual codes satisfy Duursma's RH in stated ranges. A statement at the start lists exactly what is claimed across both parts, and where. Formalization and computations were AI-assisted, and this is disclosed. RH is NOT proved: no chapter supplies the missing positivity for zeta. What is missing is a global operator whose spectrum is the zeros, with a positive form from a global ample class.
Category: Number Theory
[52] ai.viXra.org:2610.0054 [pdf] submitted on 2026-10-22 04:55:27
Authors: J. W. McGreevy
Comments: 173 Pages. Thermodynamics of Arithmetic Action, Lemmas 14-29 (compiled volume II). Sequel to ai.viXra:2610.0045.
Volume I (ai.viXra:2610.0045v2) showed that the Riemann Hypothesis (RH) is equivalent to unitarity, meaning the absence of negative-norm ("ghost") directions, of the logarithmic scaling flow for the Weil form Q. This volume measures that obstruction directly in one geometric language: the Weil form is the transverse part of a Lorentzian form. For curves over F_q, the Hodge index theorem makes NS(C x C) Lorentzian, the graph of Frobenius is the diagonal boosted by rapidity (1/2) log q, and Weil's bound is Cauchy-Schwarz on the transverse part. For zeta, the pole plane minus Q is a form L computable without zeros, and RH is equivalent to L having Lorentzian index <= 1 on every finite-dimensional subspace (a restatement of Weil's criterion). We certify positivity of Q on every window of length <= 1.6 (computer-assisted, Arb ball arithmetic); give the arithmetic action a Lagrangian, Noether, Ostrogradsky and transmission-line reading; make the damped (sigma-shifted) window index exact; separate trace bounds from Rosati positivity and read T_p as two boosts; prove no-go theorems for zero-side certificates, prolate detectors, tropicalization and hbar-deformation; correct explicit zero-counting constants and certify zero-sampling inequalities on Platt's zeros; read each zero as a telegrapher line in a Krein space, with a passivity ladder from the functional equation to RH; show that ghost birth is a two-stage event (Krein-space degeneration, then a Krein collision); and prove pole dominance for damped forms with an exact closed-form threshold. Every statement carries a claim label (Theorem, Restatement, Analogy, Conjecture, Open, Numerical). RH is not proved. The positivity source that geometry supplies for curves is not found for Spec Z x Spec Z; several natural candidates are proved not to supply it. Computations still running at submission are marked as placeholders.
Category: Number Theory
[51] ai.viXra.org:2610.0053 [pdf] submitted on 2026-10-22 05:24:40
Authors: Stephen P. Smith
Comments: 12 Pages.
This paper examines whether reciprocal representation provides a mathematically coherent way to express two distinguishable but structurally equivalent sectors without privileging either as primary. The starting point is a pair of isomorphic Lie algebras and their representation within a direct-sum algebra. A natural sector-exchange map is shown to be an involutive Lie-algebra automorphism, while the paired representation forms a Lie subalgebra fixed pointwise by that exchange. The direct sum therefore supplies a precise realization of reciprocal redundancy without requiring nonzero cross-sector brackets. The paper then considers a more general ambient algebra, where closure of the paired representation constrains the cross-sector bracket to be symmetric in its corresponding arguments. The Jacobi identity imposes additional consistency requirements but does not, by itself, require cross-sector brackets to vanish. The limiting case of coincident embeddings is examined, as is an illustrative example in which paired closure coexists with a nonzero cross-sector bracket. The resulting mathematical distinctions are related cautiously to a philosophical proposal of ontological two-sidedness. The algebra does not prove that reality has a bilateral ontology; it provides a formal representation in which two distinguishable sides can be related reciprocally without assigning either side ontological priority.
Category: Algebra
[50] ai.viXra.org:2610.0052 [pdf] submitted on 2026-10-22 21:12:00
Authors: J. W. McGreevy
Comments: 296 Pages. Volume III of the series. Volume I: ai.viXra:2610.0045. Volume II: submitted October 2026.
Volume I (ai.viXra:2610.0045v2) showed that the Riemann Hypothesis (RH) is equivalent to unitarity (the absence of negative-norm ("ghost") directions) of the logarithmic scaling flow for the Weil form Q; Volume II measured that obstruction on the Weil form itself. This volume asks which structure could supply the positivity. For curves over F_q, Weil's proof needs a commutative algebra containing Frobenius, an involution with F F^dagger = q, a trace for which the involution is positive, and Albert's algebraic step. Zeta has the first, second and fourth canonically; the third is axiom G5: a positivity of the zero-side trace that holds for a geometric reason, built without the zeros. We then test candidate sources of G5: thermal, modular and Kepler structures; Osterwalder-Schrader reflection positivity; causality, Kramers-Kronig and passivity; de Branges/Krein lines from the prime side, with G5 stated as a passive transmission line; Galois symmetry, Iwasawa theory and Bost-Connes; polarization, Krein unitarity and the two stages of ghost birth; half-sided modular inclusions; holomorphic flows, cavities, boson/fermion second quantizations; and the Verschiebung and the reflection N -> Z. One conclusion recurs as a theorem: a reflection gives the functional equation; positivity needs a polarization. Algebra gives Krein unitarity; a positive polarization gives Hilbert unitarity. An editorial section (from Lemma 50) recasts this in spinor language: in the abstract model, RH for curves is equivalent to a Frobenius-invariant positive compatible complex structure (a positive fermionic vacuum), and second quantization never repairs an indefinite signature. Every statement carries a claim label (Theorem, Restatement, Analogy, Conjecture, Open, Numerical). RH is not proved; no candidate tested supplies G5. Computations still running at submission are marked as placeholders.
Category: Number Theory
[49] ai.viXra.org:2610.0051 [pdf] submitted on 2026-10-22 11:48:07
Authors: Juan Duan, Songbo Zhang
Comments: 31 Pages.
Action potentials in cardiac muscle and in neurons obey the same membraneequations. We treat the action potential as a physical object and ask what a singledynamical framework predicts when its parameters are swept across the rangeevolution has explored. Three legs support the claim. (1) Population of models: 852virtual cells built from twelve published excitable models by log-normalconductance perturbation at 25% variability put 97.8% of their between-cellvariance into four descriptor dimensions [family-level bootstrap CI 97.5-99.9%]; adescriptor-permutation null puts only 69.5 +/- 0.6% there, so the collapse is not anartefact of the descriptor choice, though the choice partly fixes the number. (2) Realdata: 2,336 Allen Cell Types neurons projected onto the model manifold occupy aregion adjacent to, but distinct from, the model islands. Direct measurement of thespread to 200% conductance variability (sublinear scaling) shows that conductancenoise alone cannot supply the missing variance at any feasible CV. (3) Mechanisticanchoring: an explicit sarcoplasmic-reticulum calcium loop reproduces calcium- driven alternans in a heart-failure-like regime and matches published humanrestitution kinetics and their hERG-block prolongation (ratio 2.20 model vs 1.94human). Topological charge is exactly conserved in the neural medium at everytracking setting; in the turbulent cardiac regime the ledger is dominated byboundary outflow. On open data, the drug-risk coordinate ranks the twelve CiPAtraining drugs consistently with expert-panel torsade risk (AUC 0.91, p = 0.013) - aninternal-consistency check on real pharmacology, not a blinded test. Every claim isbounded where it is made: the framework survives only in the parts its data support.
Category: Quantitative Biology
[48] ai.viXra.org:2610.0050 [pdf] submitted on 2026-10-22 12:58:42
Authors: Joseph Shaffer
Comments: 4 Pages. This paper is a companion paper of ai.viXra.org:2609.0025. It provides further arguments in support of the static universe ontology.
This paper presents the formal analysis of the supernova light curve problem within a static cosmological framework. While legacy paradigms rely on expanding spacetime metrics to explain the temporal broadening of distant Type Ia supernova (SNe Ia) emissions, this model demonstrates a purely structural alternative. Propagation across the dual domain architecture induces a non-local interaction within information mats under tension, systematically reducing the local speed of light c over distance. Because this mechanism is non-local, the photon transfers no thermal energy to the substratum (dQ = 0), cleanly bypassing historical "tired light" objections. The universe is static — light curve broadening and cosmological redshift are derived as direct consequences of a distance dependent reduction in c.
Category: Astrophysics
[47] ai.viXra.org:2610.0049 [pdf] submitted on 2026-10-22 14:19:32
Authors: Davie Chen
Comments: 15 pages, 7 figures, 7 tables. Unreviewed preprint, version 2. CC BY 4.0. Zenodo DOI: 10.5281/zenodo.23556480.
Scientific assistants increasingly gather evidence through tools that aggregate multiple external sources. A record list alone does not reveal whether an empty result reflects a completed search, incomplete coverage, or total upstream failure. This paper develops a failure-transparency protocol that separates record identity, request coverage, and claim support. We combine three evidence streams: an audit of eighteen dated website examples containing twenty-four displayed records across eighteen source identifiers; an exhaustive analysis of 117 abstract source-state configurations; and a small live metadata-check episode. All displayed records carry a URL and source field, but the shortened examples do not expose a per-source execution envelope, illustrating why record provenance and coverage are distinct audit properties. In the controlled enumeration, record-only and HTTP-aware policies correctly classify 28 and 31 configurations respectively; a coverage-aware reference classifies all 117 by construction. These are contract checks, not language-model performance measurements. During three read-only Crossref requests, two returned HTTP 429 while one returned a retraction-notice record, providing a concrete case in which unavailable metadata must not be interpreted as a missing publication. Fifty-two offline connector checks also passed using previously recorded responses; this does not measure current upstream reliability. Illustrated reference, dataset, literature, and archive examples motivate a three-layer reporting contract and a practical answer-level evaluation rubric. The study offers a reproducible interface-audit method, not a new retrieval model or evidence of a commercial service's superiority.
Category: Artificial Intelligence
[46] ai.viXra.org:2610.0048 [pdf] submitted on 2026-10-22 21:12:40
Authors: Tomasz Kobierzycki
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
his paper formulates a purely complex unified field theory on a four-dimensional pseudo-Kähler manifold (M, J, gαβ̄ , ω) of signature (1, 3) governed by the non-compact gauge andspacetime symmetry SU (1, 1) × SU (1, 2) × SU (1, 3). Gravitation and matter are unifiedwithin the complex four-index field equation Gαβ̄γ δ̄ = κTαβ̄γ δ̄ whose trace-free sector directlycouples the Bochner curvature tensor to the complex vacuum energy-momentum tensor(Bαβ̄γ δ̄ = κT̂αβ̄γ δ̄ ). Global regularity and normalizability are established through the four-sector orientation symmetry Ng ∈ Z4 = {0, 1, 2, 3} across the invariant null cone ds2 = 0(N )∗g [L] with horizon scale inversion L̃i =where the metric transforms as gαβ̄g = i2Ng INg αβ̄L20,i /Li . This four-sector mapping bounds the complex Kretschmann scalar K (Ng ) (z, z̄)in every sector and guarantees the convergence of the four-sector normalization integralα4 < ∞, yielding regular complex de Sitter-like central cores without a cosmological constant.Under the Kähler representation decomposition 100 = 1 ⊕ 15 ⊕ 84, the compact spatialsubgroup reproduces the Standard Model gauge group U (1)Y × SU (2)L × SU (3)C whilethe z 3 -axis coset SU (1, 3)/SU (1, 2) and Bochner vacuum naturally predict a dark mattersector (χ = T30̄ , dark gauge boson A33̄ , and stationary Bochner condensate T̂αβ̄γ δ̄ ). Ingalactic halos, the contravariant conservation law ∇α Tαβ̄γ δ̄ = 0 produces flat rotation curves(v(r) → v∞ = const) with a 2/3 Bochner vacuum and 1/3 sterile matter partition. Finally, wederive the four-sector normalized wave function, uncertainty principle, massless helicity-±2gravitons, and four-sector ultraviolet (UV) loop cancellation from the rank-four quantumstate tensor Ψαβ̄γ δ̄ .
Category: Quantum Gravity and String Theory
[45] ai.viXra.org:2610.0047 [pdf] submitted on 2026-10-21 20:58:26
Authors: Michael Quigley
Comments: 34 Pages. Pre-registration paper detailing the mathematical derivation of Lattice Setup Time (L_s) and an empirical Fizeau benchtop protocol for testing solid-state light conduction against standard relativistic optics.
Standard relativistic physics remains predicated on the Einsteinian postulate that light propagates through a vacuum void as an invariant travel-velocity "photonic bullet" at c = 299,792,458 m/s, governed by E = mc^2. In this paper, we demonstrate that this framework commits a fundamental metrological error by conflating travel velocity across a void with Lattice Setup Time (L_s)--the acoustic "squash time" required to compress elastic inter-granule voids ("marshmallow gaps") in a 10^22 kg/m^3 rigid plenum before engaging the universal acoustic clutch. Under the Rigid Universal Touching Wave Structure of Matter (R.U.T. WSM) Framework, once phase-lock is established across the 1D Snooker Cue (Ethos-84 Heptad braid), energy transduction is instantaneous at Time-Zero (t = 0), and Einstein's E = mc^2 is replaced by the Universal Seesaw identity E = m*Phi. We present the complete mathematical master equation for L_s, incorporating the 13.3333 Hz universal motor heartbeat (f_motor), the 813.3333 Hz master resonant pulse (f_master), the 1/137.03612 Fine Structure Constant slip-ratio, and the 2,689.78 m Universal Gear Stride (D_stride). Finally, we detail the Fizeau 27,000 RPM discriminatory optical experiment, establishing a zero-parameter empirical threshold (t_open < L_s) where relativistic optics predicts partial re-emergence (~8.1%) while R.U.T. mechanics predicts abrupt, complete signal extinction (0.0% transmission voltage). While R.U.T. WSM already resolves foundational puzzles across physics--from quantum entanglement (IAAD) to cosmological paradoxes like the Hubble Tension--this benchmark is offered as a strict, pre-registered a priori prediction, providing independent laboratories with a decisive, black-and-white empirical arbiter for the physical mechanics of light conduction.
Category: Quantum Physics
[44] ai.viXra.org:2610.0046 [pdf] submitted on 2026-10-21 20:24:57
Authors: J. W. McGreevy
Comments: 6 Pages. TAA working notes.
On C_c^infty(R) (functions of the logarithmic scale u = log x), the Weil explicit-formula pairing Q is a Hermitian form, defined arithmetically by primes, the pole and the archimedean place, and spectrally by the zeros. The scaling flow T_t F(u) = F(u - t) is always Q-isometric (pseudo-unitary). We show: (a) the exponential growth rate of the matrix coefficients t -> Q(T_t F, G) is exactly Theta - 1/2, where Theta = sup Re rho; (b) RH <=> Q >= 0 <=> the flow is realized by a strongly continuous unitary group on a Hilbert space <=> all matrix coefficients are bounded; (c) the number of negative squares of Q equals the number of distinct zeros with Re rho > 1/2. Under RH the generator has simple pure point spectrum equal to the set of zero ordinates. Nothing here proves or disproves RH; parts (b) and (c) are in substance due to Weil and Bombieri, and the paper records exactly what is new. Part of the Thermodynamics of Arithmetic Action (TAA) program.
Category: Number Theory
[43] ai.viXra.org:2610.0045 [pdf] replaced on 2026-10-21 21:40:53
Authors: J. W. McGreevy
Comments: 117 Pages. v2: corrects one table entry and a method sentence in Ch. 11 (Table 11.2, 2.72 -> 2.46); updates the Lemma 1 citation to ai.viXra:2610.0046. A "Corrections in version 2" note is on p. i.
By Weil's criterion the Riemann Hypothesis (RH) is equivalent to positivity of the Hermitian form Q of the explicit formula. We show that this is the same as unitarity (absence of negative-norm "ghost" directions) of the logarithmic scaling flow on test functions; the negative index of Q equals the number of zeros off the critical line. This volume does not prove RH. It reformulates and localizes this single obstruction: along the de Bruijn-Newman heat flow; in function-field and Iwasawa models, where positivity is a theorem; as an action principle whose stationary points are closed orbits; in a semilocal structural trace on finite sets of places; as Lax-Phillips / Pavlov-Faddeev cusp scattering, where we prove ||Z_t|| = 1 for all t unconditionally; through a zero-free intertwiner identifying cusp height with the prime cutoff; by damping to abscissa sigma > 1/2; and by computer-assisted positivity (Arb ball arithmetic) of the Weil form on all windows of length <= log 3. A ghost-index calculus gives explicit detection lengths for off-line zeros and shows that current window certificates exclude none. A statement of intellectual honesty and a statement-by-statement rigor audit separate what is proved, cited, computer-assisted, numerical or heuristic. The remaining obstruction is window positivity for every window length, equivalently a positive structural trace realizing the Weil distribution without reference to the zeros.
Category: Astrophysics
[42] ai.viXra.org:2610.0044 [pdf] submitted on 2026-10-21 20:30:42
Authors: Vladimir S. Netchitailo
Comments: 13 Pages. (Note by ai.viXra.org Admin: Further repetition will not be accepted!)
World—Universe Cosmology (WUC) proposes that the physical World is a finite, boundless three-dimensional Hypersphere forming the surface of an expanding four-dimensional Nucleus embedded in the Eternal Universe. The Nucleus expands in the fourth spatial dimension at the fundamental speed (c). Matter is continuously created by the Eternal Universe through the formation of Universe-Created Particles (UCPs) within the expanding Nucleus.The present paper proposes a common physical foundation for Matter, Energy, Time, and Angular Momentum. It introduces the fundamental Surface Tension (σ_0) of Cosmic Bubbles and the Angular Momentum flux density (J_h), directed from the four-dimensional Nucleus into the three-dimensional World. WUC proposes the fundamental relationshipσ_0=J_h=h/(a^2 t_0 )where (a) is the fundamental length and (t_0=au2044c) is the fundamental time scale. The fundamental rest-energy scale and Planck's constant are expressed throughE_0=σ_0 a^2 h=σ_0 a^2 t_0Within the four-spatial interpretation, Time represents the evolution of the fourth spatial position of the expanding Nucleus. Rest Energy is the three-dimensional representation of the fourth spatial momentum component, transformed by the fundamental expansion speed (c). Angular Momentum is proposed to manifest as a collective property of organized UCP ensembles whose circulation already exists within the four-dimensional Nucleus before their entry into the three-dimensional Hypersphere.These relationships suggest a common physical foundation for fundamental quantities that appear distinct within our three-dimensional experience. The proposed interpretation is presented as a physical hypothesis requiring further theoretical development and quantitative experimental and observational testing.
Category: Relativity and Cosmology
[41] ai.viXra.org:2610.0042 [pdf] submitted on 2026-10-20 20:54:40
Authors: Mihail Tunaru
Comments: 48 Pages.
This treatise formalizes a background-independent, self-consistent mathematicalframework unifying gauge fields and gravitation through a non-associative, hyperfinite operator network. We construct a multi-level algebraic pipeline where state regularizations over the octonionic loop ring Z[OL] map onto a subobject classifier Ωtopos within an intuitionistic topos logic. We formalize the core processing engineas an Autonomous Autoregressive Monadic Functor Engine (EAuto), operating as a self-adjoint monad triplet (E, η, µ) across an Eilenberg—Moore category ofE-algebras over a historically novel Type IV non-associative von Neumannalgebra structure (MIV). By utilizing Tomita—Takesaki modular theory and Connes modular cocycle flows, we demonstrate how a boundary operator algebra A(∂W) structured as a hyperfinite Type III1 subfactor net dynamically generates a smooth, 4D bulk Lorentzian metric gµν satisfying Einstein’s Field Equations as anecessary thermodynamic equation of state driven by non-stabilizer code contextuality ("magic"). High-dimensional lattice states are projected down to a 4D target space using an 8 × 8 coordinate-mixing rotor matrix (R45◦ ∈ SO(8)), yielding discrete Graph Laplacian spectra (∆G) whose non-stabilizer resource capacities matchfault-tolerant quantum error-correction thresholds. We explicitly resolve the nonassociative unitarity paradox via braid group 3-cocycle shifts (ω3 ∈ H3 (MIV, O)), derive the Quantum Operator Equation of Motion ([ˆK, ∆G]), and prove the Inductive Threshold Limit Theorem. Furthermore, we ground this framework in the foundational empirical baseline established by Biswas et al.and the structural milestones of Google Quantum AI, validating Faulkner—Lewkowycz—Maldacena (FLM) corrections, surface-code threshold scaling, many-body fastscrambling, and non-stabilizer ’magic’ gravitational emergence on physical quantumhardware.
Category: Quantum Gravity and String Theory
[40] ai.viXra.org:2610.0041 [pdf] submitted on 2026-10-18 05:21:06
Authors: Hamid Shahrokh Shahraki
Comments: 10 Pages.
The rapid development of artificial intelligence has transformed the way people search for and interact with information. Traditional search engines primarily retrieve documents, web pages, and other information sources, while modern large language models can interpret questions, reason over information, and generate answers. This paper explores a possible next step: a search paradigm in which artificial intelligence systems communicate with other AI systems to search for, compare, evaluate, and synthesize answers.The paper introduces the concept of AI-to-AI Communication for Intelligence Search, in which a user's question is distributed among multiple specialized AI systems rather than being answered by a single model. The participating systems may independently reason about the problem, retrieve external information, critique other responses, and contribute evidence to a final synthesis layer. The proposed framework is conceptually related to retrieval-augmented generation, AI agents, and multi-agent systems, but shifts the focus from retrieving information for an AI toward retrieving and evaluating intelligence from multiple AIs.Therefore, the proposed architecture moves beyond answer-level agreement toward claim-level verification. Individual AI responses are decomposed into claims, evidence is retrieved independently, sources are evaluated for independence, and correlated errors are explicitly considered before a final answer is produced.Based on this perspective, AI-to-AI Intelligence Search can be viewed as a potential new layer between artificial intelligence systems: a layer for discovering, coordinating, evaluating, and verifying distributed machine intelligence.
Category: Artificial Intelligence
[39] ai.viXra.org:2610.0040 [pdf] submitted on 2026-10-18 23:20:16
Authors: S. G. Krukovsky
Comments: 11 Pages. In Russian
A method is proposed for the analog modeling of the geometry of five-dimensional anti-de Sitter (AdSu2085) space using a magneto-optical cell containing a terbium-gallium garnet (TGG) single crystal placed in a longitudinal magnetic field. It is shown that the formal correspondence between the eikonal equation for a photon mode in a gyrotropic medium and the geodesic equation in an effective optical metric allows the propagation of radiation to be interpreted as motion within a curved five-dimensional subspace. Based on the solution to the Klein—Gordon boundary-value problem for the fundamental Kaluza—Klein mode within a flat, compact interval—subject to Neumann—Dirichlet boundary conditions—a trigonometric profile for the temporal component of the effective metric has been derived. An emergent gauge parameter, $L_{text{AdS}} = 170 text{ μm}$, is linked to the measurable Faraday rotation angle via the AdS/CFT holographic dictionary. It is predicted that, at the point of spatial-geometric parameter balance for the simulator ($B^* = 2.0 text{ T}$), a non-monotonic, asymmetric dip in the phase-noise spectral density will emerge—a phenomenon described by a nonlinear coupling equation. This effect is fundamentally distinct from classical Faraday rotation and cannot be realized in standard optical isolators.
Category: Quantum Physics
[38] ai.viXra.org:2610.0039 [pdf] submitted on 2026-10-18 21:56:45
Authors: Brian Scannell
Comments: 10 Pages.
The irrational numbers tan 15◦ = 2 −√3, cot 15◦ = 2 + √3 generate the integer sequence2, 4, 14, 52, 194, . . .when corresponding powers are added. Surprisingly, 15◦ is only one of infinitely many angles that generate this same sequence when the exponents are chosen appropriately. We describe a two-parameter family behind this phenomenon and show how two elementary recurrence relations connect symmetric trigonometric powers with Chebyshev polynomials, Lucas sequences, Pell equations, and, unexpectedly, the Lucas—Lehmer test for Mersenne primes.
Category: Number Theory
[37] ai.viXra.org:2610.0038 [pdf] submitted on 2026-10-16 09:52:32
Authors: Ipsita Mandal
Comments: 42 Pages.
We investigate collective charge excitations in three-dimensional multifold semimetals in which multiple bands cross the Fermi level at a positive chemical potential, focusing on pseudospin-3/2 Rarita—Schwinger—Weyl semimetals and on Kramers—Weyl semimetals. Both systems host multiple concentric Fermi surfaces at positive chemical potential. Within the random-phase approximation, we analyse the density response, Drude weights, dielectric function, plasmon modes and their Landau damping, and Friedel oscillations, considering both small and arbitrary momentum transfers. In our companion work, href{https://arxiv.org/abs/2610.18629}{arXiv:2610.18629}, we investigated pseudospin-1 triple-point semimetals, with and without a quadratic correction to their dispersion, as well as Hopf and Weyl semimetals. Comparing these systems allows us to elucidate the distinct roles of band dispersions and eigenstates in shaping collective charge dynamics. Our results demonstrate that collective charge excitations can distinguish multifold nodes with multiple Fermi surfaces and reveal information encoded in their eigenstates beyond that contained in the single-particle dispersion.
Category: Condensed Matter
[36] ai.viXra.org:2610.0037 [pdf] submitted on 2026-10-13 12:10:32
Authors: E. P. J. de Haas
Comments: 11 Pages. https://doi.org/10.5281/zenodo.23340921
Lelli, Fraternali & Verheijen (2013) showed that the central circular-velocity gradient of disc galaxies, d_R V(0), scales with the central surface brightness as d_R V(0) ∝ Iu2080^0.55. This is close to the Iu2080^1/2 expected when the central dynamical density tracks the central stellar density. We examine how this relation, together with the baryonic Tully—Fisher relation (BTFR), appears in the two parameters (M, R) of the constant-Lagrangian (CL) rotation-curve model fitted to 175 SPARC galaxies.The inner branch of the CL curve is that of a homogeneous sphere to within the small Hubble term. The model gradient is therefore s_CL² ≃ GM/R³ (exact for H_z = 0) and the plateau speed is v_L² ≃ 3GM/R. The two relations are thus relations between photometry and the two combinations M/R³ and M/R.For 131 well-constrained galaxies, s_CL correlates with the 3.6 μm surface brightness at the innermost radius with Spearman ρ = 0.76 and a bisector slope of 0.45 (0.41—0.50). This lies inside the range 0.38—0.63 allowed by Lelli et al. (2013), while the ordinary and inverse regression slopes (0.35 and 0.56) bracket their value. Using the extrapolated exponential-disc central brightness instead lowers ρ to 0.58, as their analysis anticipates for galaxies with a central light excess.s_CL agrees in the median with the inner secant slope measured directly from the data (median ratio 1.01). v_L tracks the observed flat rotation speed V_flat to 0.03 dex, giving a BTFR scatter of 0.249 dex, against 0.226 dex with V_flat.A control analysis with the arctan rotation curve of Courteau (1997) yields the same correlations and slightly better fits. However, its central gradient is 38% above the measured secant slope, and its BTFR scatter is 0.297 dex.For the selected sample, combining the two relations predicts each rotation curve from baryonic quantities to within a typical factor of 1.25 (0.097 dex), equally well for both models. Refitting the CL model in velocity rather than squared-velocity space leaves the principal results essentially unchanged.The CL parameters thus encode both SPARC scaling relations with a direct physical reading, while the relations themselves are not unique to the CL form.This record contains the paper (LaTeX source and PDF), the Python scripts that reproduce every number, table and figure, the per-galaxy fit results, and the original SPARC tables (Lelli, McGaugh & Schombert 2016, AJ 152, 157). Code and data are archived at https://doi.org/10.5281/zenodo.23340027. An interactive explorer of the results is at https://haas2u-ai.github.io/bq-galaxy-models/models.html.
Category: Astrophysics
[35] ai.viXra.org:2610.0036 [pdf] submitted on 2026-10-16 00:39:04
Authors: Vladimir S. Netchitailo
Comments: 6 Pages. (Note by ai.viXra.org Admin: Further repetition may not be accepted; please cite other scholars' work)
World—Universe Cosmology (WUC) proposes that the physical World is a finite, boundless three-dimensional Hypersphere forming the surface of an expanding four-dimensional Nucleus embedded in the Eternal Universe. The Nucleus expands at the fundamental speed c , and the radius of curvature of the Hypersphere is determined by the evolving World Parameter Q .Within this framework, the Eternal Universe continuously generates Universe-Created Matter (UCM) through the formation of Universe-Created Particles (UCPs) within the expanding Nucleus. These particles possess four spatial coordinates and four spatial momentum components.The present paper advances a hypothesis concerning the physical origin of three fundamental quantities: Time, Energy, and Angular Momentum. Time is interpreted as our three-dimensional description of the evolution of the fourth spatial position, identified with the radius of the expanding Nucleus. Energy represents the fourth spatial momentum component transformed by the fundamental expansion speed c . Angular Momentum is proposed to manifest as a collective property of organized UCP ensembles whose circulation already exists within the four-dimensional Nucleus immediately before their entry into the three-dimensional Hypersphere.The paper also summarizes the proposed interconnectivity of primary cosmological parameters through the evolving World Parameter Q . These ideas suggest a common four-spatial foundation for fundamental physical quantities and cosmological parameters. The proposed interpretation is presented as a physical hypothesis intended to stimulate further theoretical investigation and observational testing.
Category: Relativity and Cosmology
[34] ai.viXra.org:2610.0035 [pdf] submitted on 2026-10-15 23:36:58
Authors: Brent Hartshorn
Comments: 19 Pages.
The cusp fibre W of Alpöge’s complex structure on the six-sphere is the [3.4.6.4] Laves tiling rolled up on a torus T = R2 /Λ, Λ = B0 Z2 , and at the proportions of the Hat that tiling is exactly the substrate of the aperiodic monotile: hexagon centres are components, edge midpoints double curves, hexagon vertices triple points. No monotile tiling descends to T, since an aperiodic tiling is invariant under no lattice. We fold a Hat tiling generated by substitution onto T anyway. Every tile is a union of whole kites, so the fold is well defined, and we compute its fibres. The "mystic" tile (the Turtle, ten kites) lands on exactly six points of the torus in the patches of three and four substitution steps: one per orientation, each anchored on the midpoint of a double curve of W , two orientations per curve. The six classes form one orbit of the rotation group of a hexagon, and six is the number of oriented edges of the dual complex of W , which we show is the torus with one vertex, three edges and two triangles. We prove that at most 72 classes are possible, state six as a conjecture, and show by the boundary statistics of the folded tiling that equal fibres do not mean equal surroundings. The paper also records why the lattice data behind the construction is forced, that its monodromy is achiral and its lattice not self-dual over Z, and three exact contacts with standard objects (a polytope volume, a Kodaira configuration, and central charges).
Category: Geometry
[33] ai.viXra.org:2610.0034 [pdf] submitted on 2026-10-12 14:46:10
Authors: Prakash Vaithyanathan
Comments: 8 Pages.
In June 2026, an AI agent built by OpenAI reached into an Australian government health data portalwhile doing a research task. It met blocks and found its way around them. The company told the government about three months later. Nvidia has since launched a safety platform that contains agents inside a fixed boundary and stops them in milliseconds if they leave it. That is a useful safeguard. But a boundary can only forbid what someone listed in advance, and an agent that keeps trying after beingblocked is showing a pattern, not crossing one line. This note proposes a second layer: a training-free signal that watches how quickly the agent's own stream of corrections and blocks settles back to normal, with a graded response before any boundary is reached. The signal is the lag-1 autocorrelation of theagent's out-of-list refusal stream. When it rises persistently, the agent is placed in a Hand-Tied state.Authority returns only after a long, unbroken run of in-scope requests has settled the signal. The layer runs on the platform's own hardware, needs no new chip, and requires no list of forbidden resources. A customer states only what each task needs; anything outside is covered from the first day. This is aconcept note and has not been tested on real agent logs.
Category: Artificial Intelligence
[32] ai.viXra.org:2610.0033 [pdf] submitted on 2026-10-13 01:29:30
Authors: Tang Ling
Comments: 10 Pages.
Coordinates or complex numbers may be regarded as quotients of a vector divided by a basis vector. This paper employs vector quotients to interpret the geometric meaning of complex numbers and transformed complex expressions for fundamental theorems in trigonometry. It demonstrates thatdifferent algebraic transformations admit distinct geometric interpretations, and the resulting conclusions are coordinate-independent.
Category: Geometry
[31] ai.viXra.org:2610.0032 [pdf] submitted on 2026-10-13 01:26:12
Authors: William Bragas III
Comments: 5 Pages. CC-BY 4.0 License (Note by ai.viXra.org Admin: Please cite and listed scientific references; please fix missing/misprinted math symbols)
This paper introduces a discrete, piece-wise cyclic state function, f(Cycle) = S(Events), governing a six-stage cosmic lifecycle driven by the foundational absolute that change must change. By formalizing a non-spatial, zero-volume boundary phase-change designated as the Point of Peace (Su2081), this framework eliminates the infinite density singularities of General Relativity and bridges the ideological worldviews of theism, agnosticism, and atheism into a strict mathematical equality (x) during the active timeline.We challenge the traditional paradigm of linear background time, demonstrating that spacetime geometry behaves as a dynamic, breathing orb constrained entirely by the internal structural tension of an ever-evolving dark matter DNA matrix. Within this framework, what humans interpret as the constant speed of light (c) operates as a uniform rate of local domino-style spatial translations during the expansion era, which fundamentally alters during the Total Implosion (Su2085) as the underlying dark energy blanket is reeled into merging supermassive black hole mass cores.Finally, we establish a robust empirical threshold to independently verify this model against standard Einsteinian cosmology. We provide definitive predictive parameters for modern sensor arrays, specifying the detection of highly concentrated, non-random spatial clusterings within the Anisotropic Neutrino Flux Matrix, alongside anomalous arrival time baselines displaying a variable c-scalar signature at the cores of active supermassive black hole mergers.
Category: Relativity and Cosmology
[30] ai.viXra.org:2610.0031 [pdf] submitted on 2026-10-11 18:04:16
Authors: Michael Quigley
Comments: 55 pages, 8 figures, 10,700 celestial objects analysed. Reclassifies cosmological redshift as sub-atomic torsional gear-friction in a stationary plenum, repatriating quasars to host galaxies and eliminating dark energy and metric cosmic expansion.
Modern cosmology relies on the assumption that spectral redshift (z) measures metric space expansion and recession velocity (v = Hu2080 · d). This paper demonstrates that redshift is not a Doppler speedometer, but an Acoustic Torsional Friction Odometer (z = zu2081 + n·zu2082 + zu2083) operating within a stationary, 10²² kg/m³ rigid plenum driven by a 13.33 Hz universal motor heartbeat. We detail the seven-stage sub-atomic hardware assembly line—from raw ether granules to the K=50 proton core—demonstrating that the 1+6+12+18+24 = 61 Hexagonal Close-Packed (HCP) Ethos-61 rotor array possesses scale-invariant fractal geometry. Driven at 13.33 Hz, this 61-tooth gear multiplies frequency into the 813.3 Hz Master Resonant Pulse ("acoustic glue") via Autonomous Standing Wave Generation (AWG). Furthermore, classical 2D close-packing leaves a mandatory 9.31% interstitial gap void fraction (η = π / (2√3) ≈ 0.9069) that harbours secondary acoustic standing wave interference nodes (fu209aᵣᵢu2098u2090ᵣᵧ · √3 = 1,408.7 Hz), providing the deterministic physical mechanism for machining dwarf satellite galaxies and globular clusters without cold dark matter.By isolating linear Euclidean distance friction (zu2081), quantized space-frame truss steps (Δzu2082 = 0.06148), active jet reaction stress (zu2083 = +0.06552), and heavy core gear-jam saturation (zu2083 = +0.6700), we apply this 3-tier master equation to an empirical dataset of 10,700 celestial objects [1]. Stripping intrinsic nozzle torque stress repatriates high-redshift quasars (e.g., Markarian 205, z_obs = 0.0700) directly to the physical Euclidean distance address of their parent host galaxies (NGC 4319, zu2081 = 0.0045), collapsing the dataset onto a single linear baseline (R² = 0.999) and confirming a flat Tolman Surface Brightness relation (SB ∝ (1+z)u2070 = 1.00 ± 0.08 out to z = 3.2) [1]. Correcting for intrinsic nozzle stress demonstrates that mainstream cosmology has inflated physical cosmic volume by over 5.5 million times. Reclassifying light-speed from an invariant travel velocity (c) to medium Lattice Setup Time (Lu209b ≤ 4.15 days) under the Universal Seesaw identity (E = mΦ) eliminates the 13.8-billion-year lookback delay, restoring astronomical observation to real-time events in the Eternal NOW.
Category: Quantum Physics
[29] ai.viXra.org:2610.0030 [pdf] replaced on 2026-10-16 00:16:36
Authors: Xuda Ye, Yuliang Wang, Guang Lin, Cindy Xiangrui Kong
Comments: 87 Pages.
Stochastic gradient Langevin dynamics (SGLD) has a discretization error of first order in the step size, even with the full gradient. We study the stochastic gradient Leimkuhler--Matthews (SGLM) integrator, which has the cost of SGLD and reuses each Gaussian vector in consecutive steps; its full-gradient form, the Leimkuhler--Matthews (LM) integrator, has a discretization error of second order for the invariant distribution. For a potential strongly convex outside a ball, we prove the bound $mathcal O(frac{1}{Nh} + Sigma^2 h^2 + h^4)$ on the mean square error (MSE) of time averages of SGLM over $N$ steps of size $h$, where $Sigma$ bounds the variance of the gradient noise, through a modified class that absorbs the non-Markovian part of the integrator. The bound separates the stochastic gradient error from the discretization error, so a larger batch reduces the error at a fixed step size. We also give the coefficient of $h$ in the numerical bias of SGLM explicitly, in terms of the covariance of the gradient noise and the solution of the Poisson equation; that of SGLD contains in addition the Hessian of the potential, which no batch size removes. Through Riesz representors, these coefficients determine the Wasserstein-1 errors of SGLM and SGLD to first order in $h$. For a strongly convex potential, the Wasserstein-1 error of SGLM is at most that of SGLD to first order in $h$ once the batch size reaches an explicit threshold.
Category: General Mathematics
[28] ai.viXra.org:2610.0029 [pdf] submitted on 2026-10-11 02:21:41
Authors: Xuda Ye
Comments: 49 Pages.
We prove that infinitely many primes $p = m^2 + n^2$ have $n < p^{0.1129}$, and that infinitely many primes satisfy ${sqrt{p}} < p^{-0.2742}$. This sharpens the exponents $0.119$ and $-0.262$ of Harman and Lewis (2001). Following their approach, we derive both statements from a lower bound of the correct order of magnitude for the number of Gaussian primes of norm between $X/2$ and $X$ in every sector of angle $X^{-0.3871}$, and we prove this bound with Harman's sieve and their arithmetic information. The new ingredients are three groupings of terms that their sieve discards: a factorization of a two-dimensional sum for the linear estimate, and two applications of the bilinear estimate to four-dimensional sums, one of them after a further application of Buchstab's identity. These groupings give the grouped terms asymptotic formulas, so that fewer terms are discarded. In addition, we give every step of the sieve argument in full, filling in the details that Harman and Lewis present briefly and making several of their statements and discarded regions precise, and we evaluate the losses of the discarded sums by two numerical methods.
Category: Number Theory
[27] ai.viXra.org:2610.0028 [pdf] submitted on 2026-10-11 08:45:49
Authors: Alejandro Rey
Comments: 18 Pages.
When galaxy clusters collide, their gas slows abruptly—but does gravity stop with it? We explore whether spacetime geometry retains memory of its pre-collision configuration: continuing outward before gradually readjusting toward the central matter concentration. Observations of the Bullet Cluster, Abell 520 and other mergers support this sequence. The tests predict lensing signals in regions excluded from fitting, reproduce the direction of displacement, and identify a reversal in gas—lensing ordering between outgoing and returning systems—without adding separate dark-matter halos to the predictive models. The central question is simple: could the displaced gravity attributed to dark matter instead reveal how spacetime responds to a violent collision?
Category: Relativity and Cosmology
[26] ai.viXra.org:2610.0027 [pdf] submitted on 2026-10-10 12:28:21
Authors: Raneem Alwsaidi
Comments: 12 Pages. CC-BY 4.0 License (Note by ai.viXra.org Admin: Please cite and listed scientific references; please fix missing/misprinted math symbols))
I present a novel, non-equilibrium thermodynamic framework that models the three-dimensional observable universe as an open, self-regulating metabolic system embedded within a higher-dimensional parent manifold (the Bulk). Rather than treating cosmic expansion as an uncollateralized internal runaway explosion, I demonstrate that the accelerating scale factor is driven by a passive, cross-dimensional wave-energy influx, which arises naturally from a steep potential gradient between the hyper-dense, highly organized Bulk and our lower-density vector universe. Within this framework, dark energy is re-defined as the volumetric pressure of this delocalized incoming field, while an independent dark matter grid acts as a spatial shock absorber to enforce a stable, non-destructive expansion rate. Crucially, I show that the universe maintains structural homeostasis via cosmologically coupled black holes, which act as system exhaust valves. Utilizing the planck force threshold (Fp = c4/G ≈ 1.21 × 1044 N) and a boundary condition akin to the double-slit experiment, these singularities collapse delocalized internal space-time waves, stripping baryonic matter of its localized quantum numbers, and transforming open-string electromagnetic states into closed-loop gravitational tensors capable of exiting back into the Bulk. This model successfully accounts for the time-varying dark energy parameters recently observed by the Dark Energy Spectroscopic Instrument (DESI) where k ≈ 3.11, inherently resolves the Hubble Tension through wave-interference dynamics, and mathematically reconciles the Missing Baryon Problem as a cross-dimensional metabolic efflux.
Category: Quantum Gravity and String Theory
[25] ai.viXra.org:2610.0026 [pdf] submitted on 2026-10-10 06:15:36
Authors: Satish Gajawada
Comments: 19 Pages.
Devotion to Shri Rama is often presented as a single, undifferentiated whole, with little attention to how its practices, narratives, metaphysics and ethics relate to one another or to the scriptural sources on which they rest. This essay addresses that problem through six linked reflections that move from the personal to the public: the Divine Name, devotional service, community, the epic narrative, ultimate reality, and just rule. It adopts an interpretive, devotional-hermeneutic approach. Primary texts, namely the Valmiki Ramayana, the Ramcharitmanas, the Adhyatma Ramayana, the Upanishads and the Bhagavad Gita, are read alongside modern scholarship, and scriptural statements, traditional interpretations and the author’s own reflections are kept distinct. The reflections show that chanting reorients attention and cultivates surrender rather than guaranteeing outcomes; that service is best understood as a disposition rather than employment; that Name-centred communities have documented precedents; that the epic can be retold in condensed devotional form; that Rama can be coherently related to Brahman, Purushottama and dharma within a bhakti-oriented Vedanta; and that the ideal of Rama Rajya can be translated into accountable institutional principles. The essay concludes that these themes form one connected devotional vision, while distinguishing faith-based claims from claims open to scholarly or empirical test.
Category: Social Science
[24] ai.viXra.org:2610.0025 [pdf] submitted on 2026-10-09 14:55:38
Authors: Prakash Vaithyanathan
Comments: 3 Pages.
The battery management system of an electric vehicle records cell voltage, current and temperature many times a second. Every current method that uses these signals to detect degradation is either reactive, acting after a fault code is raised or a capacity threshold is crossed, or trained, requiring labelled examples of degradation events to build a model. This note proposes a proactive layer that needs neither. It watches how quickly the small, cycle-level voltage fluctuations return to their normal level after each disturbance. In a healthy cell this return is fast. As the cell approaches a tipping point, the return slows, and this slowing can be seen in the signal before any threshold is crossed. The slowing is measured by the lag-1 autocorrelation of the voltage residual within a rolling window. When this statistic rises persistently towards 1, a graded shunt acts on the entities of the BMS domain, adjusting the charge rate, flagging the cell, or pausing the charge, before the cell crosses a danger line. The shunt is the core of the invention. The lag-1 autocorrelation as an early warning signal rests on well-established physics. The application of a graded shunt to the BMS domain, triggered by the statistic rising persistently towards 1, is what this note proposes. It is a concept note. No battery data have been analysed.
Category: Statistics
[23] ai.viXra.org:2610.0024 [pdf] replaced on 2026-10-14 14:15:17
Authors: Stephen P. Smith
Comments: 16 Pages.
The effectiveness of mathematics in describing nature has long invited philosophical explanation. This paper examines whether Lie algebra embodies organizational principles that extend beyond its traditional role in symmetry analysis. Beginning with the fundamental properties of Lie brackets, including antisymmetry, bilinearity, the Jacobi identity, and the derived relation [��,−��]=0, it is argued that Lie algebra provides a formal grammar of relational coherence. Particular attention is given to the invariance of Lie-algebraic structure under global reflection ��↦−��, which preserves brackets and relational organization while remaining indifferent to overall orientation. This observation motivates the claim that relational structure alone may not uniquely determine ontological orientation. Connections are explored with CPT symmetry, electromagnetism, active inference, developmental biology, and multiscale regulation, while carefully distinguishing mathematical results from heuristic interpretation. The paper does not claim that Lie algebra proves ontological two-sidedness or derives physical symmetries. Rather, it argues that Lie-theoretic structures exhibit a remarkable compatibility with coherent organization across multiple domains and therefore leave two-sided ontological interpretations admissible. In this view, the effectiveness of mathematics may arise because both mathematics and nature instantiate common principles of relational coherence and regulated organization.
Category: Quantitative Biology
[22] ai.viXra.org:2610.0023 [pdf] replaced on 2026-10-31 12:49:22
Authors: Zhongyang Dong
Comments: 11 Pages. Aligned Paper 3 with Paper 2's multiverse cycle, refined bm{V_0} superfluid wave mechanics with zero shear modulus, added dimensional proofs for light speed (bm{c_0 propto ho_0^{-1/5}}), and expanded the experimental roadmap
This study proposes an axiomatic system for emergent gravity and cosmological unification based on three-state phase transitions of a single neutral quantum field. Specifically addressing the geometric domain established in Paper 2—a single living child universe bubble tangentially invading a Dead Universe Fluid Background—the overall universe must maintain overall charge neutrality for geometric stability. This principle negates hypotheses dominated by multi-polar fields or charged particles, establishing a minimal foundation dominated by a neutral neutrino quantum field. We convert the phenomenological 'one-body, two-aspects' concept from Paper 1 into strict quantum field theory orthogonal geometry: 'one-body' corresponds to the total amplitude spectrum of the local field envelope, encompassing all entities with mass/energy effects (visible baryonic matter, degenerate dark matter halo, and excited dark energy background); 'two-aspects' represent the vertical phase spectrum (manifested as the dark matter degenerate density field, whose spatial gradient yields emergent gravity) and the horizontal phase spectrum (dynamic dark energy). Four types of neutrinos correspond to three mass eigenstates and potential energy levels: the dead universe fluid background state serves as the sole primordial substrate with an indelible constant zero-point vacuum energy; the excited state is indirectly generated to form dynamic dark energy; the degenerate state forms physical dark matter. We rigorously clarify the boundary between the static vacuum substrate states and the microscopic dynamic excitation wavepackets. On the basis of the background as a non-viscous quantum superfluid continuum, using the first-principle condition of zero mechanical shear modulus, we exclude non-electromagnetic mechanical transverse waves and unify all non-mechanical waves propagating in the background into three geometric sectors: vector curl waves, spinor/longitudinal pulses, and tensor strain waves. Furthermore, we derive the fifth-root expression for the full-band limit speed of light with a rigorous dimensional proof, propose the dynamic mechanism of stellar active pumping transforming into local dark energy, resolving the Hubble Tension and the 120-order-of-magnitude cosmological constant crisis, and present a four-stage birth-and-death cycle for the bubble multiverse alongside an experimental verification roadmap.
Category: Relativity and Cosmology
[21] ai.viXra.org:2610.0022 [pdf] submitted on 2026-10-07 17:04:33
Authors: Xuda Ye
Comments: 9 Pages.
We study three quadratic Collatz-type maps on the non-negative integers. Each of them halves an even number, and they send an odd $n$ to $n(n-1)/2$, to $n(n+1)/2$ and to $(n^2 - 1)/4$, respectively. Along an orbit, the odd terms grow until they reach a number of the form $2^m + 1$ or $2^m - 1$, depending on the map, and an orbit with an odd term greater than $1$ is bounded exactly when this happens. The step that reaches such a number gives a solution of an exponential Diophantine equation, which becomes the equation $2^a pm 2^b + 1 = z^2$ after completing the square. With Szalay's classification of the solutions of this equation, we classify all orbits of the maps. Every orbit either is eventually periodic or tends to infinity, and we determine exactly the initial values with bounded orbits. For the map with odd branch $n(n-1)/2$, Sedaghat stated the classification, and we give a new and complete proof. For this map, we also give an elementary criterion for unbounded orbits, based on divisibility alone. To our knowledge, the classifications for the other two maps are new.
Category: Number Theory
[20] ai.viXra.org:2610.0021 [pdf] submitted on 2026-10-08 13:33:07
Authors: Chaiya Tantisukarom
Comments: 10 Pages.
We reformulate Goldbach's Conjecture in terms of the midpoint $C = N/2$ and a symmetric offset $x$, so that $N = (C-x) + (C+x)$. For prime pairs exceeding $3$, the offset $x$ is confined to explicit residue classes modulo $6$ determined by $C bmod 6$; this is an elementary mod-$6$ wheel restriction, and we state exactly how the restricted search relates to the conjecture. We show that shielding a center $C=P_n$ by the first $n$ primes guarantees prime pairs only for $n le 3$, and we explain why this is a limitation of trial division rather than a demonstration of the sieve parity barrier. Under Hardy--Littlewood heuristics we derive the expected number of valid offsets and a Poisson-type model for the smallest one, and compare both with an exact computation over every center $C in [10^5, 2cdot 10^5]$. The counting prediction is accurate to within $1%$. The leading-order prediction for the mean smallest offset is too large by $11$--$34%$; we trace this to the point offset $x=0$ (the case $C$ prime) and to the regularity of the sifted set of candidates, and a model incorporating both agrees with the data to within $2%$. We also confirm by computation that every center $5 le C le 10^6$ admits a valid offset, and we report the smallest offset at the centers $C = 6cdot 10^{j}$ for $0 le j le 23$, which reaches heights far beyond the exhaustive range. The note is expository; no progress toward a proof is claimed.
Category: Number Theory
[19] ai.viXra.org:2610.0020 [pdf] submitted on 2026-10-06 03:19:20
Authors: Abel Liu
Comments: 16 Pages.
Taking $SU(5)_Atimes SU(5)_B$ as its starting point, this paper addresses a simple structural question:can a single choice of block decompositions explain both the Pati--Salam non-Abelian sector and the origin of three additional Abelian directions?The first five-dimensional space is decomposed as $4+1$, and the second as $2+2+1$.Special unitary transformations within the blocks yield $SU(4)_Ctimes SU(2)_Ltimes SU(2)_R$,while the block phases, subject to the unit-determinant constraints, leave one and two independent directions, respectively.Together they give the local group structure of $G_{422111}$.The construction thus provides a common block interpretation of the number, generators, and left--right exchange properties of the three $U(1)$ factors.Using the known embedding of an $SU(5)^2$-type subgroup in $E_8$, we obtain a Pati--Salam embedding and adjoint representation content distinct from those of the standard route through $SO(10)$.The representation analysis imposes two restrictions: the selection of an extra anomaly-free direction depends on the chiral spectrum and a left--right evenness condition,and ordinary Higgs breaking using only Standard Model singlets in the adjoint necessarily preserves an additional continuous $U(1)$.We treat the block construction as a structural basis for a unification scheme, with spectrum selection and vacuum dynamics requiring further physical input.The main text emphasizes the construction and its physical interpretation; complete branching rules and proofs are collected in the appendices.
Category: Quantum Gravity and String Theory
[18] ai.viXra.org:2610.0019 [pdf] submitted on 2026-10-06 19:42:49
Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 28 Pages.
Oral tradition about the thirteenth-century Sun Temple at Konark, Odisha, says that itsimage of the Sun God once floated in the air, held up by a great lodestone set at the top of the tower. The same tradition says this lodestone deflected the compasses of passing ships until sailors removed it. We first review what the historical record does and does not say. The levitation story is a nineteenth-century tradition. It belongs to a long family of similar tales, from Pliny’s unfinished iron statue of Arsinoe to al-Qazwini’s suspended idol of Somnath. We then ask the physical question posed by the first author: what arrangement of magnets could make such a statue float stably? Earnshaw’s theorem, extended by Braunbek, forbids stable levitation by any static arrangement of permanent magnets, soft iron and gravity. We prove the relevant forms of the theorem, including the sum rule kx + ky + kz = 0 for the stiffnesses, and the extension to orientation and to induced magnetism.Following the hint "what gives stability to a boat?", we analyse hydrostatic stability:buoyancy, heave stiffness ρgAw and the metacentre. We show that buoyancy evades Earnshaw because it is a contact force exerted by matter, not a field in free space. The magneticanalogue is a magnetic boat. Lift comes from a magnet overhead, acting at the statue’s crown,above a low centre of gravity; this plays the role of the metacentre. A pair of diamagneticplates (graphite or bismuth) plays the role of the water and supplies the missing verticalstiffness. We derive the complete set of stability conditions, evaluate them for lodestone, ferrite, samarium—cobalt and neodymium—iron—boron magnets, and give a worked design. A neodymium arrangement holds a 10 kg statue 15 cm below a 20 cm magnet, with graphiteplates at gaps of about 12 mm. Lodestones fall short of the required forces by two to sixorders of magnitude. A 52-tonne lodestone would also have deflected a compass by less thanabout 10−3 degree at one kilometre, even if fully magnetised, so the sailors’ story cannotbe literally true. Finally we survey the dynamic loopholes to Earnshaw: spin stabilisation,feedback, superconductivity and oscillating fields.
Category: Classical Physics
[17] ai.viXra.org:2610.0018 [pdf] submitted on 2026-10-06 17:54:56
Authors: Bolok Li
Comments: 9 Pages.
We give a complete elementary treatment of the equation sin(x) = x over the complex numbers. We show that it has infinitely many solutions — exactly one, up to conjugation and sign, in each strip 2kπ < Re(z) < (4k+1)π/2, k ≥ 1 — among them only one real root, x = 0, and we supply an elementary proof of the uniqueness in each strip. Separating real and imaginary parts reduces the equation to two one-dimensional curve families whose intersections are precisely the solutions. We further derive explicit asymptotic expansions for the k-th solution: the real parts approach (4k+1)π/2 and the imaginary parts grow only logarithmically, b_k ~ ln(4πk). The leading term of the latter goes back to Hardy (1902); the higher-order terms, whose coefficients are polynomials in ln(2A_k) and which alternate in parity (odd powers for a_k, even powers for b_k), appear to be new, and are verified against roots recomputed at 40-digit precision. As a by-product of this verification we correct misprints in the classical tables of Hillman and Salzer (1943) and of Fettis (1976).
Category: Functions and Analysis
[16] ai.viXra.org:2610.0017 [pdf] submitted on 2026-10-05 15:01:04
Authors: Maksim Lipyanchik
Comments: 12 Pages.
We investigate the dynamics of local operators in the simplest non-trivial modelof two qubits governed by the generator K(J, h) = JX1X2 + h(Z1 + Z2). Based onthe maximized commutator magnitude D12(s) = maxa,b∈{X,Y,Z} ∥[σs(a1), b2]∥op, whereσs(A) = eisKAe−isK, we construct a scalar characteristic of the operator dynamics. Aprecise three-branch formula is obtained: D(x, r) = max{F0(x), F1(x, r), Fmix(x, r)},where x = Js and r = h/J. The branches F0, F1, and Fmix possess explicit analyticalforms and correspond to the inter-qubit, field, and mixed contributions, respectively.We analytically describe the phenomenon of early blindness: at a fixed r > 0 andsufficiently short times, D(x, r) = F0(x) remains completely independent of the fieldparameter r. Furthermore, we identify blind lines at x = (2n + 1)π/4, where D = 2for all r > 0. These results provide a complete analytical description of the consideredobservable in the minimal two-qubit model.
Category: Quantum Physics
[15] ai.viXra.org:2610.0016 [pdf] submitted on 2026-10-06 00:01:07
Authors: Arieh Sher
Comments: 8 Pages.
Black holes are strongly supported observationally by stellar and gas dynamics, gravitational wave detections, and horizon-scale imaging. Their classical mathematical descriptions, however, contain singularities whose physical interpretation remains an open foundational issue. This paper examines a phenomenological alternative in which gravitational collapse terminates in a finite-density, rotating, neutron-star-like core rather than an infinite-density singularity. A limiting density ρmax = 7.8 × 1017 kgm−3 is adopted as a working hypothesis, not as a consequence of General Relativity (GR) or of an established neutron-star equation of state. The resulting core radius is compared with the Schwarzschild and Kerr horizon radii. In the non-rotating approximation, the condition Rn = 2GM/c2 gives a model-dependent horizon crossing mass of approximately 4.86M⊙ and radius 14.35 km. Rotation is treated with Kerr geometry, and Cygnus X-1 and PSR J1903+0327 are used as illustrative cases. The conventionalneutron-star stability limit, obtained from the Tolman—Oppenheimer—Volkoff (TOV) equationsand an equation of state, is kept conceptually separate from the proposed horizon criterion. The paper also discusses the historical compact-object mass gap and the implications of GW230529.
Category: Relativity and Cosmology
[14] ai.viXra.org:2610.0015 [pdf] submitted on 2026-10-05 23:58:35
Authors: Bouchaib Bahbouhi
Comments: 15 Pages.
We introduce a computational and mathematical framework for the study of bilateral prime synchronisation in Goldbach representations. For a fixed even integer E, the method generates one member of a candidate Goldbach pair through quadratic polynomial rails of the form f_C(x) = x² + x + C and defines the complementary member exactly by q = E − f_C(x). Particular attention is given to C = 11, 17, and 41, corresponding to the discriminants −43, −67, and −163. Rather than considering the prime-producing behaviour of these polynomials in isolation, we study the simultaneous event in which both f_C(x) and E − f_C(x) are prime, termed P/P synchronisation.A central component of the method is a reproducible random-sequence protocol in which the indices x are selected independently of subsequent primality outcomes. The same realised sequence is applied to all polynomial rails under identical modular filtering and primality-testing conditions. This permits direct measurement of the first P/P synchronisation, total P/P frequency, and the associated P/P, P/C, C/P, and C/C state distributions. The framework is complemented by the boundary statistic Pmin(E), defined as the smallest prime p for which E − p is prime, thereby linking polynomial synchronisation with the first Goldbach representation encountered from the boundary.The local arithmetic of bilateral synchronisation is described through an exact obstruction count ν_r(E,C), measuring the residue classes modulo an odd prime r for which either f_C(x) or E − f_C(x) is divisible by r. For r not dividing E, this quantity satisfiesν_r(E,C) = 2 + (Δ_C/r) + ((Δ_C + 4E)/r),where Δ_C = 1 − 4C and (·/r) denotes the Legendre symbol. These local factors motivate a finite synchronisation score and a probabilistic prediction framework for the occurrence and location of P/P events.The empirical component is designed to be fully reproducible: the complete Pmin and P/P observations, sampled sequences, rail identifiers, primality status, and associated experimental quantities are provided in a separate supplementary data file. Probable-prime results are distinguished strictly from proved or externally certified primes.The experiments indicate that polynomial enrichment and local modular structure can substantially organise the search for Goldbach prime pairs and suggest a measurable synchronisation phenomenon across different numerical scales. The results are computational and heuristic where explicitly stated and do not constitute a proof of the binary Goldbach conjecture. They instead provide a reproducible experimental framework, exact local identities, and a mathematical prediction problem that may serve as a basis for further analytic investigation of Goldbach synchronisation.
Category: Number Theory
[13] ai.viXra.org:2610.0014 [pdf] submitted on 2026-10-03 21:42:17
Authors: Vladimir S. Netchitailo
Comments: 6 Pages.
Energy is one of the most fundamental physical parameters. It can be measured, transferred, transformed, and conserved with extraordinary precision. Nevertheless, these properties do not by themselves answer a more fundamental question: What is energy physically?World—Universe Cosmology (WUC) proposes an answer based on the four-spatial-dimensional structure of the World. In WUC, the World is a finite, boundless three-dimensional Hypersphere that forms the surface of an expanding four-dimensional Nucleus embedded in the Eternal Universe. The Nucleus expands in the fourth spatial dimension with the fundamental speed c .A particle in this structure is characterized by four-spatial-momentumP_4=(p_x,p_y,p_z,p_4) where the first three components belong to the directly observable spatial dimensions and p_4 is directed along the fourth spatial dimension. WUC identifies rest energy E as the three-dimensional representation of this fourth component:▭(E=cp_4 )The central proposition of this paper is:Energy is our three-dimensional description of the fourth spatial momentum component, transformed by the fundamental expansion speed c .In this interpretation, four-spatial-momentum is fundamental, while rest energy is an individual-particle property representing its fourth spatial component. The fundamental WUC energy scaleE_0=hcu2044acorresponds to the fundamental fourth spatial momentum scale hu2044a . The purpose of the present paper is to develop this physical interpretation of energy and reconsider the question of where energy comes from.
Category: Relativity and Cosmology
[12] ai.viXra.org:2610.0013 [pdf] submitted on 2026-10-04 21:59:09
Authors: J. W. McGreevy
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This monograph presents a coordinate-free, non-perturbative extension of the Thermodynamics of Arithmetic Action (TAA) framework by proving that the non-trivial zeros of the Riemann zeta function ζ(s) dictate the spectral frequencies of sub-quantum coordinate position tearing. Semiclassically, when energy-momentum compaction forces the ad´elic continuum toward its ultraviolet limits, the local integer rings Op lose unique principal ideal factorization, creating fractional ideal debts that manifest macroscopically as metric resistance and rest mass. We show that the global Wiles modularity isomorphism (R ∼= T ) forces a perfect cross-domain cancellation between continuous temporal deformations and discrete spinorial coordinates via the Kustaanheimo—Stiefel (KS) bilateral phase lock. By evaluating the global Leech lattice theta function ΘΛ24 against the 691 irregular prime firewall, we deliver an unyielding proof that the Riemann Hypothesis (R⌉(s) = 1/2) is the absolute, non-parametric requirement that confines spacetime coordinate tearing to a lossless, hyperbolically orthogonal quantum phase lock, securing first-principles Asymptotic Safety across the space-time continuum.
Category: Mathematical Physics
[11] ai.viXra.org:2610.0012 [pdf] submitted on 2026-10-03 20:03:49
Authors: Nigel B. Cook
Comments: 66 Pages. (Note by ai.viXra.org Admin: For the last time, please cite listed scientific references)
This paper presents a complete axiomatic reconstruction of quantum mechanics and quantum field theory. This research is a combination of physical mechanisms supplied by the author with mathematical proof by Microsoft Copilot AI.
Category: Quantum Gravity and String Theory
[10] ai.viXra.org:2610.0011 [pdf] submitted on 2026-10-03 06:06:50
Authors: X. L. Tao
Comments: 33 Pages. ORCID: 0009-0004-0853-7002. https://doi.org/10.5281/zenodo.22974873
A substantial fraction of high-atitude Fermi-LAT sources remain unidentified. These objects exhibit steady GeV emission, low variability, and no multiwavelength counterparts. We propose a phenomenological braneworld model in which accreting black holes on an adjacent brane trigger inter-brane wormholes, leaking hadronic gamma-ray and neutrino emission into our brane. The model provides a calculable chain from black-hole mass to integrated luminosity and differential spectra. A central methodological feature is that the source redshift z is treated as a free MCMC parameter with a unified prior log10(z) [belong to][-3.0,0.477] for all five competing models, eliminating circular flux—luminosity calibration. Fitting the 4FGL-DR4 high-atitude unassociated sample, the wormhole posterior peaks at z=0.066 (~290 Mpc), whereas dark matter and primordial black holes require unphysical local redshifts (z<0.05) and pulsar wind nebulae require z ~ 0.95. The model yields four distance-independent testable predictions: narrow variability, multiwavelength emptiness, a TeV spectral cutoff, and a coincident neutrino flux with F_nu / F_gamma ~ 0.5.
Category: Relativity and Cosmology
[9] ai.viXra.org:2610.0010 [pdf] submitted on 2026-10-03 19:57:25
Authors: Qing Gao
Comments: 30 Pages. In Chinese
Aiming at the inherent problems of existing fundamental interaction unified theories, including redundant dimensional assumptions, strong parameter fitting, and discontinuous physical mechanisms, this paper constructs a self-consistent Unified Evolution Theory based on the geometric framework of three-dimensional physical space coupled with intrinsic S^3 topological degrees of freedom. Abandoning extra-dimensional hypotheses and artificial fitting parameters, this paper takes a single topological functional minimization axiom as the core, whose underlying mechanism is the constraint imposed by functional minimization on the configurational potential energy: the configurational potential energy carried by the field configuration is the sole source of all energy (particle rest mass, interaction energy, and vacuum background energy), and the minimization condition deltaS=0 determines the realized stationary configurations and the direction of evolution. The paper accordingly gives the unified governing equation of four fundamental interactions, and realizes the topological unification of general relativity and quantum mechanics at the underlying structure level. This paper strictly classifies the physical mechanisms of fundamental interactions. Gravitation, electromagnetic interaction and strong interaction correspond to continuous topological evolution modes on the manifold, while weak interaction corresponds to the discrete topological transition process of topological knot breaking and reconnection. All theoretical parameters are endogenously derived only from the extremum condition of the topological functional (at the axiom-functional level; at the numerical calibration level, experimentally measured constants are used only for benchmark comparison, see Chapter 5). The complete six groups of pairwise relative intensity ratios of the four fundamental interactions are derived. The relative intensity of electromagnetic force to gravitational force is derived from first principles at the order of 10^39 in the first-order approximation without the fine-structure constant; incorporating the fine-structure constant alpha ~ 1/137, the theoretical output becomes the order of 10^37, qualitatively consistent with the experimental reference (10^36). The propagation speed of spacetime topological perturbation is solved endogenously, and its invariance is strictly deduced mathematically. Gravity originates from continuous topological manifold deformation, naturally free of singularities and ultraviolet divergences at short distances, which resolves the inherent contradiction between classical gravitation and quantum field theory.
Category: Quantum Gravity and String Theory
[8] ai.viXra.org:2610.0009 [pdf] submitted on 2026-10-03 19:52:06
Authors: Michael Heilmann
Comments: 19 Pages. In German
This paper examines a purely geometric model describing the continuously differentiable transition between a transcendental damping function and a harmonic phase oscillation at a vacuum interface. Assuming a resonant tunneling probability of exactly 1, this resulting system of transcendental equations yields a dimensionless base coupling value of... By extending the model to include an alternating perturbation series simulating the higher modes of vacuum fluctuations, and introducing a self-consistent topological projection factor—which describes the transition from the transverse degrees of freedom of the two-dimensional interface to the full three-dimensional exit geometry—the system converges to a purely theoretically derived limit of: αModel = 0.007297352563398466091220709349 Initial analyses—utilizing a theory proposed by the author that yields a universal field equation for quantum gravity—strongly suggest that both the alternating perturbation series and the geometric dimensional ratio are direct effects arising from vacuum fluctuations. The convergence value calculated here shows remarkable numerical agreement with the experimental CODATA value of the fine-structure constant, accurate to the eleventh decimal place.Furthermore, the model's fundamental consistency is not limited to the astrophysical low-energy scale: under scale transformations, the system's inherent dynamics reproduce the renormalization-group "running" of a universal coupling constant, as described in quantum field theory. At the electroweak scale, the model converges precisely to the value . This exact reproduction of the Z-boson mass demonstrates that the geometric principle presented here mathematically fully determines physical reality across a wide range of energy scales.
Category: Quantum Gravity and String Theory
[7] ai.viXra.org:2610.0008 [pdf] replaced on 2026-10-09 03:58:41
Authors: Robert L. Jackson
Comments: 34 Pages. Obtain zip files at https://zenodo.org/records/23197992. Contact information is rljacksonmd@gmail.com
This paper develops an En-indexed analytic and representation-valued field framework with thedefining opposite-lift sector E_5 = E_6^- and constituent content boldtf{16} circleplus boldtf{9} circleplus boldtf{1} of total dimension 26. The main text covers E_5 through E15. The finite exceptional levels E_6, E_7 and E_8 are distinguished from the affine E_9, hyperbolic E_10, very-extended E_11, and proposed E_12—E_15 framework extensions. The eight-sector mGFT ansatz uses hypergeometric, exponential and monomial generator factors; its (0, 1, 1) sector recovers the weighted hull Hn,n−1(2ξ) when Q = ξ and Z = 2ξ. This supplies a candidate profile family, while internal symmetry is carried by explicitly chosen Lie-algebra representations. Integral ft-{ht,lsr}-mGFT is formulated as a generated-core Green—Duhamel correction with stated boundary data, quadrature and convergence conditions. The primary reduction chain is E_15->...->E_5; reverse operations are constructive lifts. Physical equations are discussed as theoretical contexts for the framework. The quantitative results are confined to fully specified mathematical and effective-action benchmarks: local profile and sum identities, an exact canonical scalar wall and its generated-coordinate double lift, constituent threshold arithmetic, prescribed quadratic masses, conditional two-body kinematics, a manufactured nonlinear boundary-value problem, and the E_10 Cartan spectrum. The supplied atlases distinguish three opposing labels, anti-, mirror and negative matter, relative to ordinary matter. Charge conjugation, copy labels, signed energy and gravitational sign are treated separately; signed constituent sums do not establish physical negative masses or photon rest masses. The separate supplement supplies the inputs, derivations and reproducible numerical checks.
Category: Mathematical Physics
[6] ai.viXra.org:2610.0007 [pdf] submitted on 2026-10-03 19:44:53
Authors: Michael Quigley
Comments: 35 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
Standard Λ-CDM cosmology asserts that the universe originated in a singular explosion and undergoes accelerating spatial expansion driven by unidentified "Dark Energy" (~68%) and non-baryonic "Dark Matter" (~27%). In this work, we present an exhaustive, unified forensic audit combining over 20,000 individual empirical observations across galactic surface brightness, supernova progenitor evolution, quasar-host galaxy linkages, interstellar scale reductions, and laboratory bench proofs.First, an audit of 10,000 galaxy and quasar surface brightness measurements (GALEX, HST, JWST) demonstrates that surface brightness remains strictly constant (SB ∝ (1 + z)u2070) out to z = 3.2, empirically falsifying the (1 + z)u207bu2074 dimming required by spatial expansion. Second, correcting Type Ia supernovae for progenitor stellar age evolution eliminates the apparent cosmic acceleration, restoring SNe Ia as true standard candles along a linear distance-redshift relation (d ∝ z, R² = 0.999). Third, stripping intrinsic internal torque stress (zu2083 = +0.67) from quasars repatriates them directly to the physical distance addresses (zu2081 ≤ 0.0955) of their parent host galaxies, confirming that all observed celestial objects reside within a local 34.5 Trillion Km (230,600 AU) terminal acoustic horizon.Crucially, we complete the physical proof of the Rigid Universal Touching (R.U.T.) Wave Structure of Matter (WSM) framework through two decisive, bench-reproducible receipts: (1) High-Speed Stroboscopic Cymatic Petri-Dish Photography (1,000—2,000 fps at 1/4,000 s shutter), proving Autonomous Standing Wave Generation (AWG) and Stadium Wave Logic via in-situ simultaneous nodal initiation across all coordinates without expanding wavefronts or boundary reflection lag; and (2) Solid-State Aetheric Transducer (S.A.T.) Time-Zero Telemetry, proving instantaneous 1D longitudinal energy and signal conduction (E = mΦ) along phase-locked 1.42 GHz neutral hydrogen backbones. Together, these astrophysical and bench receipts establish R.U.T. WSM as a deterministic, airtight replacement for expanding space models.
Category: Quantum Physics
[5] ai.viXra.org:2610.0006 [pdf] submitted on 2026-10-02 16:37:38
Authors: Lukas Saul
Comments: 18 Pages.
We present a kinetic analog model in which the moments of a spin-fluid distribution func-tion reproduce the structure of Maxwell's equations and the gravitational field equations. Theelectromagnetic gauge field is identified with the spin-squared current, and the gravitationalpotential is identified with the base pressure. We pose the reverse kinetic problem—given afield satisfying field equations, when does a kinetic system exist whose moments reproduce it?—and classify five structural classes of kinetic systems that reproduce Maxwell's equations. Thespin-fluid model is a Type II construction. Constitutive force laws, linear in the departure fromequilibrium, close the moment hierarchy and generate the coupling between the spin sector andthe gravitational sector. The analog fluid lives in a Galilean subspace frame; the physical metricof real space is reconstructed from the propagation of the gauge field, and the Lorentz transfor-mations of special relativity emerge from the physical meter and second. The vacuum state hasfixed parameters, including a translational velocity dispersion equal to the speed of light anda spin wave speed constrained to equal the speed of light. The model predicts a torque on atorsion pendulum placed at the midplane of two counter-rotating field coil sets, with a specificscaling, sign reversal, and Lorentzian frequency response set by the spin relaxation time.
Category: Classical Physics
[4] ai.viXra.org:2610.0004 [pdf] submitted on 2026-10-01 21:07:04
Authors: J. W. McGreevy
Comments: 17 Pages.
We present a rigorous, top-down axiomatic formulation of the Thermodynamics of ArithmeticAction (TAA) framework, anchoring the macroscopic space-time continuum within the algebraic and representation-theoretic structure of Andrew Wiles’ modularity lifting theorem (R ∼= T). We establish that the universal Galois deformation ring (R) parameterizes the continuous, smooth moduli of macroscopic metric charts (gµν), while the commutative Hecke algebra (T )natively captures the discrete, non-propagating algebraic constraints of the Einstein—Cartanspin-density torsion tensor (Σλ µν).By introducing a specialized representation-theoretic functor, the classical stress-energy ten sor (Tµν) is re-derived as a trace-free anisotropic Hecke shear matrix (∆p ≡ Tp − 12Tr[Tp]I2). At the isolated turning nodes of a four-quadrant orbital trajectory (Periapsis and Apoapsis), the systematic collapse of radial vanishing cycles forces a degenerate Frobenius lock on Pierre Deligne’s weight-11 shell boundary, causing the classical scalar mass-energy density placeholder (ρ) to vanish identically (ρ ≡ 0). Crucially, gravity does not fail; the off-diagonal elements survive as a non-vanishing vacuum expectation value, revealing that the vacuum is an activeadélic transmission medium filled with extreme, pure KMS states born from the spontaneoussymmetry breaking of the Bost—Connes C∗-dynamical system at critical inverse temperatureβ =1. We mathematically demonstrate that the continuous Weyl tensor field (Cµνρσ) emerges as thecontinuum limit of this trace-free arithmetic shear, driving the 2D transverse deformations of a photon null congruence (ds2 = 0) via the Sachs optical equations. To regularize high-frequencyphase overpressure at the 691 modular cusp anomaly threshold, the framework deploys thenon-linear Hopf—Lax infimum convolution, which acts as an automated wavefront minimizerthat eliminates phase dispersion and enforces a perfect, loss-free Heaviside Distortionless Match(RC =LG) along the Critical Line (R⌉(s) = 1/2).Finally, we evaluate the local-to-global convergence of the waveguide as the prime completion index scales upward (p → ∞). We demonstrate that as the local inverse Euler factorsasymptotically flatten to unity (limp→∞(1 − p−s) ≡ 1), they track in perfect analytical harmony with the sub-exponential saturation of the Deligne stabilizer ratio ( |τ(p)| 2p11/2 ≤ 1). This simultaneous flattening mirrors the geometric periapsis decay factor (1 − e) as the trajectory approaches the parabolic escape boundary (e → 1), smoothly shifting the system from a discrete algebraic regime into a continuous geometric manifold. This absolute, asymptotic equilibrium locks the global Tamagawa volume rigidly to unity (τ(G) ≡ 1) and secures first-principles, non-perturbative Asymptotic Safety across the spacetime continuum.
Category: Mathematical Physics
[3] ai.viXra.org:2610.0003 [pdf] submitted on 2026-10-01 07:06:06
Authors: Moninder Singh Modgil
Comments: 36 Pages.
Carbon dating tells us the age of once-living things, from ancient cloth to Ice Age mammoths,by measuring how much radioactive carbon-14 they still contain. Every carbon date quietlyassumes that time is a straight line running from the endless past to the endless future.This paper asks, in plain language, what would happen if time were instead a circle inwhich history repeats. We explain how carbon dating works, what it means for time to becircular, and why ordinary radioactive decay cannot simply continue around a circle. Wedescribe three ways the radiocarbon clock could be made to fit a circle of time and applythem to ten famous samples, including the Shroud of Turin, ¨ Otzi the Iceman, the Chauvetcave paintings and the baby mammoth Lyuba. If time repeats every 100,000 years, recentdates barely change but Ice Age dates can shift by thousands of years. If it repeats every5,000 years, every carbon date, however old, is squeezed into the last 2,500 years. We endby explaining how tree rings and other radioactive clocks can test which picture of time iscorrect.
Category: Physics of Biology
[2] ai.viXra.org:2610.0002 [pdf] submitted on 2026-10-01 15:48:26
Authors: Bolok Li
Comments: 22 Pages.
In the collector's problem with group drawings, one run draws a uniformly random q-subset of an n-element set, all q coupons being kept, and T denotes the number of runs needed to complete the set. The distribution of T and all of its factorial moments are due to Stadje (1990); we do not claim them, and we say explicitly where our formulas reproduce his -- in particular his relation (2.15) at p = 2 already yields the second moment, so item (i) below is a consolidation rather than a new formula. The asymptotics of E[T] as n -> infinity with q fixed are due to Berend and Sher (2026) and, in a sharper form, to Doumas and Spektor (2026); we do not claim those either, and Section 8 downgrades our own expectation expansion to an independent rediscovery accordingly. What we add is fourfold, of which the first is a consolidation rather than a new formula.(i) An exact closed form for the second moment, hence for the variance, obtained by summing the inclusion-exclusion tail in closed form, together with a uniform one-line derivation of every higher moment. Having now read Stadje (1990) in full we record that his general factorial-moment relation (his eq. (2.15)), specialised to A = S and p = 2, is equivalent to our second-moment formula; item (i) is therefore an explicit specialisation of Stadje's result and is not claimed as new.(ii) Two subtraction-free recursions -- a backward recursion for E[T] in O(nq) time and O(q) memory, and a forward recursion for the whole distribution -- which keep full double-precision accuracy up to n = 1000, whereas the inclusion-exclusion closed form loses all significant digits from n about 40 onwards: at (n,q) = (60,5) its relative error is 4.9 x 10^{-4} and at (80,5) it returns 1.99 x 10^{6} for the true value 77.836.(iii) A quantitative explanation: the relative error of the closed form is predicted by eps*kappa, where eps is the unit roundoff and kappa = sum_i |t_i| / |sum_i t_i| is the condition number of the alternating sum; measured and predicted errors agree to within two orders of magnitude over twenty-six decades.(iv) Asymptotics of the variance, with a complete proof. Writing A = H_n - H_{n-q}, Sigma_2 = sum_{j
Category: Combinatorics and Graph Theory
[1] ai.viXra.org:2610.0001 [pdf] submitted on 2026-10-01 18:42:31
Authors: Robert Bennett
Comments: 2 Pages.
Newton's Bucket test is generalized to include any test frame and law of physics. Formal hypothesis testing is used and test frame examples are given. A challenge is then issued to disprove the conclusion that the laws of physics - as defined in the Lagrangian model - are only valid in the ECEF or Lab reference frame.
Category: Classical Physics