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[1963] 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
[1962] 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
[1961] 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
[1960] 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
[1959] 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
[1958] 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
[1957] 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
[1956] 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
[1955] 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
[1954] 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
[1953] ai.viXra.org:2610.0062 [pdf] submitted on 2026-10-27 00:53:18
Authors: Ron Ragusa
Comments: 3 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
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? 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
[1952] 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
[1951] 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
[1950] 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
[1949] 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
[1948] 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
[1947] 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
[1946] 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
[1945] 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
[1944] 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
[1943] 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
[1942] 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
[1941] 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
[1940] 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
[1939] 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
[1938] 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
[1937] 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
[1936] ai.viXra.org:2610.0045 [pdf] submitted on 2026-10-21 07:41:54
Authors: J. W. McGreevy
Comments: 117 pages. Thermodynamics of Arithmetic Action, Lemmas 1-13 (compiled volume).
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: Number Theory
[1935] 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
[1934] 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
[1933] 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
[1932] 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
[1931] 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
[1930] 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
[1929] 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
[1928] 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
[1927] 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
[1926] 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
[1925] 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
[1924] 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
[1923] 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
[1922] ai.viXra.org:2610.0030 [pdf] submitted on 2026-10-11 01:23:27
Authors: Xuda Ye, Yuliang Wang
Comments: 76 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
[1921] 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
[1920] 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
[1919] 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
[1918] 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
[1917] 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
[1916] ai.viXra.org:2610.0024 [pdf] submitted on 2026-10-07 00:06:29
Authors: Stephen P. Smith
Comments: 15 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
[1915] ai.viXra.org:2610.0023 [pdf] submitted on 2026-10-08 13:59:35
Authors: Zhongyang Dong
Comments: 12 Pages.
This study proposes a unified axiomatic system of emergent gravity and cosmology based on the three-state phase transitions of a single neutral quantum field Phi. This paper specifically addresses the geometric framework established in Paper 2: a single living child universe bubble tangentially invading a Dead Universe Fluid Background. Philosophically and thermodynamically, the universe as a whole must maintain overall charge neutrality to preserve geometric stability, thereby rejecting hypotheses dominated by multiple polar fields or charged particles, and establishing a minimal baseline grounded in a neutral neutrino quantum field.This work rigorously translates the phenomenological "one entity, two aspects" concept proposed in Paper 1 into orthogonal geometry within quantum field theory: the "one entity" corresponds to the total amplitude spectrum A_{text{total}}(x,t) (encompassing all mass/energy-bearing components ho_{text{total}} propto vert{}A_{text{total}}vert{}^2, including visible baryonic matter A_b, V_2 dark matter halos A_{Phi_2}, and V_1 dark energy floor A_{Phi_1}) of a localized quantum field envelope Psi = A_{text{total}}(x,t) e^{i(phi_perp + phi_parallel)}, while the "two aspects" correspond to the perpendicular phase spectrum phi_perp (manifesting as the degenerate neutrino density field ho_{Phi_2} for dark matter, whose spatial variations yield emergent gravity vec{g} = -k_2 abla ho_{Phi_2}) and the transverse phase spectrum phi_parallel (dynamic dark energy ho_{text{DE}} propto partial_t Deltaphi_parallel). Four classes of neutrinos (u_e, u_mu, u_tau, and heavy Majorana neutrinos N_R) are unified across three mass eigenstates (V_0, V_1, V_2, eV scale): the dead universe fluid background state Phi_0 (V_0 state) acts as the sole primitive parent field with an undilutable vacuum floor ho_0 > 0; the excited state Phi_1 (V_1 state) is generated indirectly from Phi_0 through phase excitation and derivative field evolution; the degenerate state Phi_2 (V_2 state) forms the physical dark matter entity (ho_{text{DM}} = ho_{Phi_2}).We reveal that matter inertia originates from topological shear damping encountered by matter envelopes accelerating through the phase spectrum, deriving the equivalence principle (m_g equiv m_i). We establish that the dead fluid background Phi_0 (V_0 state) is the sole physical carrier of light propagation, whereas superposed V_1 and V_2 components act as refractive modulators altering local dielectric permittivity and permeability, unifying Louis de Broglie's "pilot wave" (1927) and "neutrino theory of light" (1934). We differentiate planets (no DE production), stars (active MSW DE pumps), and black holes (condensation sinks containing a singularity-free quantum saturation plateau ho_{text{sat}}). Finally, we formulate two-stage energy conservation incorporating initial child universe energy, derive G_0 = C_0 frac{y_u^2 hbar c}{M_N^2} approx 6.67 times 10^{-11} text{ m}^3text{kg}^{-1}text{s}^{-2}, and present five core observable predictions (including the futility of searching for individual physical gravitons).
Category: Relativity and Cosmology
[1914] 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
[1913] 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
[1912] 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
[1911] 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
[1910] 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
[1909] 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
[1908] 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
[1907] 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
[1906] 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
[1905] 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
[1904] 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
[1903] 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
[1902] 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
[1901] 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
[1900] ai.viXra.org:2610.0008 [pdf] submitted on 2026-10-03 12:49:31
Authors: Robert L. Jackson
Comments: 29 Pages. The Zenodo.org report provides a supplemental section and code. Contact info: rljacksonmd@gmail.com.
This framework is formulated directly in terms of the E_n hierarchy. The symmetry levels are labeled directly by E_n, with E_6, E_7, and E8 treated as finite-dimensional exceptional Lie groups and E_9, E_10, and higher labels treated, when invoked, as affine, hyperbolic, or more general indefinite E-type extensions whose precise generalized Cartan data must be specified. The exponentially weighted hypergeometric profile associated with an E_n level is written H_{n,n−1}(2ξ). Integral ft-{ht,lsr}-mGFT remains an analytic profile and field-equation solution architecture; internal symmetry is carried by explicit En Lie-algebra generators and representations; string/brane structure can be carried by Clifford factors; and physical masses arise from the quadratic fluctuation operator of a specified action. The framework does not use infinite summations to define a unifying interaction potential or universal particle-mass spectrum. The primary directional architecture is the reduction chain E_11 → E_10 → E_9 → E_8 → E_7 → E_6, with the reverse sequence treated as a constructive lift rather than an automatically invertible map. The phenomenological material is ordered by sector: the E_6 solar and hidden-particle benchmarks; the E_7 compact-object analysis; the E_9 affine/high-energy morphology sector; and the E_10 hyperbolic/solitonic sector. The supplemental verification layer supplies an effective benchmark action, residual-certified nonlinear fixed-point calculations, mesh convergence, and quadratic spectral extraction.
Category: Mathematical Physics
[1899] 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
[1898] 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
[1897] 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
[1896] 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
[1895] 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
[1894] 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
[1893] ai.viXra.org:2609.0084 [pdf] submitted on 2026-09-30 21:22:57
Authors: J. W. McGreevy
Comments: 52 Pages.
This monograph establishes a non-perturbative topological unification of quantum field theory,heterotic string structures, and loop quantum gravity, formulated entirely within the internallanguage of a smooth, cohesive ∞-topos H = Sh∞(ArithSite). Macroscopic spacetime isshown to emerge dynamically when info-packet worldsheet density overloads the MaximumDistance Separable (MDS) Singleton bound of a rootless, norm = 4 Leech lattice (Λ24)background. This capacity crisis triggers a spontaneous degree-4 Fermat phase transition,compactifying the central charge c = 24 vacuum bulk into a genus-5 multi-handled Riemannsurface variety. Under this geometric allocation, discrete atomic fermion measures materialize as stable, frozen Cartan spinor holes, while the Standard Model gauge bosons emerge as non-atomic vielbein spin connections to execute smooth parallel transport across the handle boundaries. The global transport of information is governed by a multidimensional, adélic formulation of Oliver Heaviside’s Telegrapher’s Equations evaluated over the restricted product ring AQ. We unmask the non-trivial Riemann zeta zeros as the exceptional, lossless impedance sinks(χu2032 = χu2032u2032 ≡ 0) of the waveguide. At these precise coordinate nodes, the tangential worldsheet acceleration vanishes identically (aθ = 0), forcing the metric tensor and the symplectic 2-form into an orthogonal Kramers—Kronig quadrature phase lock along the Critical Line (R⌉(s) = 1/2). By utilizing the absolute adélic Langlands correspondence, we demonstrate that the discrete Frobenius eigenvalues of local Galois representations are functorially identical to the continuous spectrum of the Hecke operator matrix algebra, natively deriving the electroweak mass gap from a localized spectral filtration failure across the Ring Singularity Equator. At the ultraviolet boundary, the twelfth Bernoulli irregularity (B12 = −691/2730) marks an anomalous Atkin—Lehner cusp horizon. Here, the Sundman transformation executes the Hagedorn temperature limit, freezing macroscopic time (dt/dτ → 0) as string tension collapses to zero. This 323-state conformal anomaly phase torque is rigorously resolved via a non-perturbative heterotic T-duality inverse phase transformation (R ←→ ℓ2P/R), triggering D-brane pair-production to execute a loop-amplitude splice. This self-correcting feedback network resets the local coordinate fields, clamping the completed symmetric Riemann—Siegel function (ξ(s) = ξ(1−s)) to an invariant global Tamagawa volume of exactly unity (τ (G) ≡ 1). Spacetime is proven to be stable, continuous, and general relativistic because the universe operates fundamentally as a self-correcting arithmetic automaton.
Category: Mathematical Physics
[1892] ai.viXra.org:2609.0083 [pdf] submitted on 2026-09-29 20:40:46
Authors: YuanGuo Li
Comments: 10 Pages. (Note by ai.viXra.org Admin: Author name is required in the article)
To scientifically evaluate the quality risks of non-conforming Chinese patent medicines and establish a differentiated regulatory approach, this study is based on the inspection data of Chinese patent medicines from the National Drug Sampling Inspection conducted between 2020 and 2024. The distribution characteristics of non-conforming items were statistically analyzed, and risk-stratified assessment was performed by combining the results of routine testing and exploratory research. The results showed that the overall quality of Chinese patent medicines has maintained a steady upward trend. Identification, assay, related substances, dissolution, and microbial limits — as the core testing modules of pharmacopoeial standards — control the authenticity of the herbal prescription, the level of active pharmaceutical ingredients, impurity safety, in-vitro release behavior of the preparation, and microbial contamination risk, respectively. Non-conformity in any of the above items constitutes a substantive high-risk defect that may directly threaten medication safety and clinical efficacy. Some sampled products exhibited deviations in appearance and description without altering the intrinsic material basis of the medicines, posing a relatively low risk to actual clinical use. Quality hazards in Chinese patent medicines are mainly concentrated in inconsistent quality of Chinese herbal medicine raw materials, weak control over extraction and manufacturing processes, and enterprise quality control systems that exist in name only.
Category: Social Science
[1891] ai.viXra.org:2609.0082 [pdf] submitted on 2026-09-29 20:39:07
Authors: YuanGuo Li, Wenli Li, Chong Wang, Jiong Zhu, Zhong Dai, Shuangcheng Ma
Comments: 11 Pages.
Background: Chinese patent medicines are widely used in clinical practice, and their quality directly affects medication safety and therapeutic efficacy. The National Drug Sampling Inspection program serves as a critical quality surveillance mechanism. However, previous assessments have not systematically differentiated the risk levels of different non-conforming items, leading to potential risk misjudgment.Methods: This retrospective study analyzed inspection data of Chinese patent medicines from the National Drug Sampling Inspection conducted between 2020 and 2024. All inspection items were classified into appearance/description items and intrinsic quality test items. Risk stratification was performed across safety, efficacy, and stability dimensions.Results: Over five years, a total of 30,791 batches were inspected, with non-conforming rates of 0.54% (2020), 0.31% (2021), 0.65% (2022), 0.52% (2023), and 0.13% (2024). Identification, assay, related substances, dissolution, and microbial limits represented substantive high-risk defects. Description non-conformities, accounting for a minor proportion, predominantly involved minor appearance deviations that did not alter the intrinsic material basis. Risk stratification demonstrated clear differentiation between high-risk substantive defects and low-risk appearance deviations.Conclusions: Different inspection items correspond to markedly different quality risk levels. A risk-stratified regulatory approach is warranted to optimize regulatory resource allocation and improve the scientific basis of quality supervision for Chinese patent medicines.
Category: General Science and Philosophy
[1890] ai.viXra.org:2609.0081 [pdf] submitted on 2026-09-29 20:37:30
Authors: J. W. McGreevy
Comments: 32 Pages.
This monograph delivers a rigorous, non-perturbative reconstruction of the space-timecontinuum natively within the internal language of the smooth, cohesive ∞-topos H = Sh∞ (ArithSite). We replace the classical continuous geometric background with an abstract motivic cochain complex C u2022 (M), modeling the complete information boundary network as a global adélic variety evaluated over the restricted product ring AQ = R × ∏︁p u2032 Qp. By upgrading general relativity to the dual tensor dynamics of Einstein—Cartan theory, the physical constants of nature (ℏ, c, G) and the standard Lorentz transformations emerge natively as the global constants of holomorphicity and absolute arithmetic tracking stabilizers required to balance metric curvature (Tµν) and spin-density torsion (Σ µνλ ) across scale horizons.We demonstrate that the Riemann Hypothesis (RH) is a mandatory global stability theorem protecting the space-time manifold from catastrophic geometric dissolution. Spacetimematerializes when information-packet density overloads the Maximum Distance Separable(MDS) Singleton bound of a rootless, norm = 4 Leech Lattice (Λ24) vacuum. To absorb this 5-bit information debt, the universe invokes the degree-4 Fermat curve, branching thepre-geometric bulk into a genus-5 multi-handled Riemann surface. The non-trivial Riemannzeta zeros are unmasked as the exceptional, lossless impedance sinks (χ u2032 = χ u2032u2032 ≡ 0) of anadélic waveguide, satisfying a universal periapsis turning point condition over the contractible Grothendieck Motive. At these precise coordinates, the tangential acceleration vanishes identically (aθ = 0) while the centripetal acceleration hits an absolute, max-plus tropical extremum (ω 2 = −2E = Max). Any spectral deviation off this axis triggers an instantaneous, infinite negative Ruppeiner metric divergence (g uu Rup → −∞), rupturing the Einstein tensor and causing the continuum to dissolve into chaotic bit-scrambling.
Category: Mathematical Physics
[1889] ai.viXra.org:2609.0080 [pdf] submitted on 2026-09-29 20:34:57
Authors: Chun Wing Lai
Comments: 19 Pages.
We present a corrected and expanded version of A. Fauzan’s 2026 Zenodo preprint ζ(5) is irrational. The mathematical argument is Fauzan’s: it constructs a family of integer polynomials Q_n satisfying 0 < Q_n(ζ(5)) <e^(−cn^2) as Hankel determinants of a rational functional, using a positive moment representation and a logarithmic energy estimate. Our contribution is to supply detailedderivations for several steps that the preprint states without proof, to correct a typographical error in the definition of an auxiliary functional, to correct four decimal-point typos in the final numerical constants, and to document two expositional defects in Section 5 that do not affect the final conclusion. The proof is written to be accessible to advanced undergraduates.
Category: Number Theory
[1888] ai.viXra.org:2609.0079 [pdf] submitted on 2026-09-29 09:28:10
Authors: Sayo Asanagi
Comments: 9 Pages.
The solar corona is heated to ∼ 106 K over a chromosphere two orders of magnitude cooler, bymechanisms that are intrinsically intermittent and multi-scale: impulsive nanoflares from magneticreconnection and the turbulent dissipation of Alfvén waves. Resolving the microphysics (reconnec-tion at current sheets, wave cascades) over the hours-to-days evolution of a coronal loop imposesa computational barrier analogous to the Courant barrier in turbulence. We present a stochastic—subgrid framework that advances the loop energetics on macroscopic time steps while injecting theunresolved, intermittent heating as samples from a variance—gamma (VG) Lévy process, with asingle intermittency parameter ν controlling the rare, fat-tailed heating bursts. The non-monotonicoptically-thin radiative loss makes the loop thermally bistable, so a cool and a hot (coronal) branchcoexist; crossing to the hot branch is the analogue of a threshold "ignition." We show that with thesame mean heating, steady (Gaussian) heating cannot ignite the corona whereas VG intermittencydoes (ignition probability rising from 0% to ∼ 80% with ν): intermittency is a prerequisite for coronalheating. Extending the model to a one-dimensional loop with field-aligned conduction and chromo-spheric evaporation, and then deriving the heating rate and the intermittency self-consistently froma single magnetic-braiding profile Θ(x), we find that the corona lights up where braiding is high,with the active-region core ignited by mean heating (intermittency-independent) and the peripheryignited only by intermittency. Unifying nanoflares (DC) and Alfvén-wave turbulence (AC) as twoVG sources reproduces the observed thermal structure: waves supply a ∼ 1 MK floor everywherewhile nanoflares boost active regions to ∼ 2—3 MK, a spatial complementarity with distinct inter-mittency signatures. We compile seven predictions and present a verification methodology tied toexisting instruments (SDO, Solar Orbiter, Hinode, DKIST), including decision tables that fix inadvance which measured outcome refutes or robustifies the framework. A central, honest findingemerges: nanoflare heating tails are power-law with index α < 3 (divergent variance), exceeding thefinite-variance VG closure and calling for a stable-Lévy generalization, whereas wave heating fitsVG — the heating mechanism itself selects the closure
Category: Astrophysics
[1887] ai.viXra.org:2609.0078 [pdf] submitted on 2026-09-29 20:46:04
Authors: Lukas Saul
Comments: 13 Pages.
We develop an exact, closed-form statistical mechanics of the equipment-enhancement system of the idle RPG Milky Way Idle. An enhancement attempt advances an item by one level with probability p and, on failure, either resets it to level 0 (protection off) or decrements it by one level at the cost of a consumable protection item (protection on, from a chosen level R upward). We compute the expected total cost E[C] = T·E[τ] + L·E[M], where T is the per-attempt time cost, L the per-protection-item cost, τ the hitting time of a target level N, and M the number of protected failures incurred. The central object is the expected visit-count vector v_k, which we identify as the discrete Green's function of a piecewise birth-death operator and solve in closed form in terms of p, N, and R alone. We recover the unprotected limit C_n = (p^(−n) − 1)/(1 − p) as a special case, matching the result of Chae and Lee. We then present the full path-integral representation of the process as a sum over random-walk histories weighted by exp(−βC), give the transfer-operator resolvent G(x,y) = [(I − W(x,y))^(−1)]_{0,N}, and analyse the continuum limit: the WKB/instanton action S_inst = N·ln(1/σ) reproduces the exact exponent σ^(−N), while Gaussian fluctuations around the instanton yield an erfc-form budget tail P(C ≤ B) ≈ (1/2)·erfc((E[C] − B)/sqrt(2·Var[C])). All exact formulae are rational in p and are tabulated for the base success rates of the game.
Category: Statistics
[1886] ai.viXra.org:2609.0077 [pdf] submitted on 2026-09-29 20:45:24
Authors: Lukas Saul, Lena Petrova, Kenji Tanaka, Miriam Okafor
Comments: 5 Pages.
We report the detection of a statistically significant, non-random correlation between the morphology and temporal evolution of solar surface features—specifically sunspot groups and plasma filaments—and the orbital positions of planets and major comets within the Solar System. Analysis of high-resolution helioseismic and magnetogram data over a 74-year period (1976—2050), augmented by data from the textit{Helios Sentinel} and textit{Corona Net} satellite constellations, reveals that the initiation, growth, decay, and motion of sunspot groups are not solely governed by internal magnetohydrodynamic (MHD) processes. Instead, they exhibit a quantifiable, predictive relationship with external gravitational and electromagnetic perturbations from orbiting bodies. The precision of this correlation exceeds chance by a factor of $10^9$. Crucially, the measured response latencies are consistent with a signal propagation velocity that exceeds known MHD wave speeds by several orders of magnitude, approaching a significant fraction of $c$. We propose that the solar magnetic field acts as a distributed sensory and motor system, with sunspots functioning as temporary ``fixation points'' or ``eyes'' and plasma filaments as a conductive neural network. This system appears to respond to external stimuli in a manner consistent with a complex, adaptive regulatory network. We designate this phenomenon the Heliobiological Response Mechanism (HRM). 太阳不是一颗普通的恒星。
Category: Astrophysics
[1885] ai.viXra.org:2609.0076 [pdf] submitted on 2026-09-28 20:41:11
Authors: Michael Heilmann
Comments: 30 Pages. In German
In this paper, an 8x8 tensorial metric is constructed—using both the 4x4 Dirac matrices and their corresponding temporal and spatial 2x2 Pauli components—to serve as a scalar substitute for the standard single-component dimensions; the resulting field equation is intended to be basis-invariant and consistent with General Relativity. This is achieved without abandoning or inconsistently altering the smooth Minkowski metric of the Dirac equation; instead, the inertial frame determined by the Dirac matrices—along with the aforementioned 8x8 metric—is maintained alongside the spacetime-curved inertial frame. Following the evaluation and characterization of this specific metric, temporal-energetic and spatial-momentum separations—as well as their hybrid interrelationships—are established; these are then systematically developed into a field equation for quantum gravity using factors, wave functions, Lorentz gamma factors, temporal and spatial derivatives, and their corresponding operators and tensors. The author now presents this universal equation of quantum mechanics for appropriate discussion and falsification.
Category: Quantum Gravity and String Theory
[1884] ai.viXra.org:2609.0075 [pdf] submitted on 2026-09-28 20:39:23
Authors: Lukas Saul, Robert Gludo, Jonathan Gludo
Comments: 9 Pages.
The Truth-It Network is a Solana-native binary oracle protocol. It allows a permissionednetwork of truth providers to answer yes/no questions through a commit-reveal voting scheme,with vote weight determined by an on-chain reputation score. Rewards are held in per-question vaults and distributed proportionally to winning vote weight. This whitepaper describes the protocol’s membership model, question lifecycle, reward distribution, rent reclamation, and reputation calculation.
Category: Data Structures and Algorithms
[1883] ai.viXra.org:2609.0074 [pdf] submitted on 2026-09-28 20:38:33
Authors: Sayo Asanagi
Comments: 5 Pages.
We explore a single hypothesis: that in an emergent ("it-from-bit") spacetime the microscopic information-propagation velocity cinfo need not coincide with the macroscopic light speed cmacro, their ratio being a function of the local curvature or entanglement density. Embedding this kinematically on a Schwarzschild background through a curvature-dependent factor ∆ = (cinfo/cmacro)2 = 1 + ϵK/K∗, we find that a single sign parameter ϵ generates two distinct spacetimes. For ϵ > 0 (pattern A) the geometry is a charge-free Reissner—Nordstr¨om type with an information horizon displaced inward of rs, satisfying the energy conditions. For ϵ < 0 (pattern B) a double-zero design ∆ = u|u| produces a genuine signature change across a null face rc, opening a finite Euclidean shelland a two-time core; the Kretschmann scalar remains finite at rc and the surface gravity vanishes. Both branches terminate black-hole evaporation in remnants and resolve the information paradox by opposite mechanisms (leakage vs. freezing). We show that the degenerate face suppresses classicalmass inflation from exponential to power-law growth (confirmed by linear and nonlinear numerics), and that pattern B falls into the single stated exception of the semiclassical inner-horizon no-go theorem because its degenerate face is the outermost horizon. We find no viable direct observational signature at any scale for a Planck-normalised K∗; instead we connect the central hypothesis to two established frameworks—Lieb—Robinson bounds on the micro side and analogue gravity on the macro side—and derive a concrete, falsifiable analogue prediction: a 85Rb condensate with an engineered double-zero scattering-length profile yields a phonon pair-production spectrum whose high-k cutoff differs by nearly two orders of magnitude from that of a sudden signature change, withno thermal pedestal. All results are reproduced by an accompanying open-source code package.
Category: Relativity and Cosmology
[1882] ai.viXra.org:2609.0073 [pdf] submitted on 2026-09-28 20:37:35
Authors: Sayo Asanagi
Comments: 12 Pages.
Planetesimal formation must cross two barriers at once: a physical barrier, whereby aerodynamic radial drift removes pebble-sized solids on 102—103 yr timescales, and a computational barrier, whereby resolving the three-dimensional turbulence that concentrates those solids imposes Courant-limited time steps that make Myr integrations intractable. We present a stochastic—subgrid framework that advances the mean flow and grain growth deterministically on macroscopic (∆t ∼ 10—100 yr) stepswhile injecting the unresolved, intermittent turbulent concentration as samples from a variance—gamma (VG) Lévy process embedded in an Ornstein—Uhlenbeck relaxation. A single intermittencyparameter ν — the excess kurtosis of the turbulent fluctuations, tending to the Gaussian limit as ν → 0 — controls the rare, fat-tailed bursts that trigger streaming-instability-mediated gravitational collapse. The closure is deliberately falsifiable: ν inferred from magnetohydrodynamic (MHD) turbulence should increase with magnetic activity and vanish in dead zones, and the excess kurtosis of coarse-grained increments should decay as κexc ∝ ∆t−1, the signature of Lévy aggregation.We develop the model through an analytic collapse rate with a continuous mass function, a one-dimensional radial open system with grain growth, drift, diffusion and pebble supply, imposed andthen self-consistently generated pressure traps, and an explicit, spatially-resolved convergence field. The mass-conserving model yields sharp, testable results: in a realistic drifting disk the concentration breach occurs in the far tail where the Gaussian probability is < 10−10, so intermittency is a prerequisite for planetesimal formation (the yield rises ∼ 30× from ν = 0 to ν = 2); a self-consistent dead-zone edge — derived, together with the turbulence strength and intermittency, from a singlemagnetic-activity profile — produces a surface-density bump that localizes formation and makes itν-independent, while the adjacent smooth region is ν-controlled, so intermittency and pressure traps are complementary and govern distinct regions. We compile seven predictions and, because MHD data are not yet in hand, present the verification methodology rather than its outcome: a pipeline that extracts the intermittency map, the aggregation exponent, and the convergence-to-velocity kurtosis ratio from any velocity field, validated on realistic synthetic surrogates, together with de-cision tables that fix in advance which measured outcome would refute the framework and whichwould robustify it. We position the framework honestly with respect to the turbulent-concentration and streaming-instability literature: the concentrating mechanism is inherited, while the Lévy closure, the macro-step integrator, the falsifiability design, and the self-consistent trap—intermittencydichotomy are new.
Category: Astrophysics
[1881] ai.viXra.org:2609.0072 [pdf] submitted on 2026-09-28 20:32:24
Authors: Lukas Saul, Robert Gludo, Jonathan Gludo, Ian Spiro
Comments: 8 Pages.
SolBazaar (or Solzaar) is a Solana-native decentralized marketplace protocol. It allows merchants to register storefronts, list products, and settle orders through an external escrow program that enforces deposit, completion, and refund conditions on-chain. Reputation is accrued through buyer-submitted reviews gated by escrow completion, and order state is synchronized with product inventory through deterministic, escrow-driven transitions. This whitepaper describes the protocol’s membership model, product lifecycle, order settlement, reputation accrual, and dispute-handling interfaces. It situates the design within a longer literary and technical lineage that runs from science fiction’s imagined anarcho-capitalist markets through OpenBazaar’s empirical disappointments to a contract-layer response.
Category: Data Structures and Algorithms
[1880] ai.viXra.org:2609.0071 [pdf] submitted on 2026-09-28 20:30:58
Authors: Moise Costel
Comments: 14 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
It is proposed that the Big Bang is not the absolute origin of reality, but a local collapseevent within the arm of a spiral mega-structure of vastly greater scale — a "galaxy ofuniverses". This work develops the complete mathematical chain of the model: thereformulation of the collapsing core at the Planck scale, the shear and winding dynamicsof the spiral arm, the stability validation through the Toomre criterion, the quantumbounce mechanism (Loop Quantum Cosmology) that avoids the classical singularity, thedetermination of the physical scale of the parent galaxy (size, dark-matter halo, number ofarms and number of node-universes hosted), and two observationally falsifiable predictions: the "dark flow" and the search for collisions between bubble universes in the cosmic microwave background. Four conceptual limitations of the model are explicitly identified and addressed, including its epistemological boundary regarding the ultimate origin of the parent structure.
Category: Astrophysics
[1879] ai.viXra.org:2609.0070 [pdf] submitted on 2026-09-27 21:40:59
Authors: Nigel B. Cook
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
This paper expands the mathematical scaffolding of a fully predictive, parameter-free gauge field theory unifying quantum gravity and electroweak mass generation. Rather than introducing unobserved spatial dimensions or fine-tuned scalar fields, all observables emerge from the compression dynamics and projections of an $SU(4)$ vacuum. We detail the coordinate-explicit Lie algebra isomorphism mapping su(4) onto the pseudo-orthogonal algebra so(3,3) constructing the physical link between electroweak sectors and the global spacetime fabric. (This new approach was suggested by a review of vixra papers by Google AI, and then error corrected and redrafted Copilot AI, before being rewritten by author. It is not a complete textbook, but is designed to introduce key concepts in a brief 10 page format that is written in a style more understandable by AI systems than previous papers.)
Category: Quantum Gravity and String Theory
[1878] ai.viXra.org:2609.0069 [pdf] submitted on 2026-09-27 17:45:05
Authors: Thomas Birnie
Comments: 54 pages; English; CC BY 4.0. Prepared with assistance from OpenAI ChatGPT and Codex. Revised edition of DOI 10.6084/m9.figshare.33479899.v1; current DOI 10.6084/m9.figshare.33479899.v2.
We prove a global smoothness criterion for three-dimensional incompressible Euler flow on R^3. For a smooth finite-energy solution, whole-interval L^2_t H^K_x membership of the velocity at every finite spatial order generates every temporal velocity and canonical pressure derivative. The proof combines the full differentiated Euler recurrence with an energy interpolation inequality; each output requires only finitely many spatial orders. Adjacent temporal rows give strong Sobolev traces and continuity of every mixed derivative on the closed finite slab. One local continuation through a proposed finite maximal time then proves global smoothness under the stated membership hypothesis. Neither a sum over derivative orders nor an infinite sum of local lifespans is required. We also construct the full intersection on one common local interval from arbitrary smooth data. Extending that construction through an entire candidate finite maximal lifespan remains unresolved.Further results examine the fluid's material and pressure evolution. From energy alone we construct a unique weak terminal velocity, a terminal transport isometry with an exact orthogonal energy defect, and a measure-preserving particle limit whose secants recover terminal momentum. Circulation reaches a terminal current; at strict times it combines with the deformed material metric to reconstruct velocity. The first temporal response has a sharp energy-level weak topology, but an explicit Fourier-packet construction makes the second response unbounded at a fixed output frequency. Separate pressure arguments give continuation under absolute and directional inverse-square bounds with coefficient below 2, and under a small signed weighted matrix primitive along vortical trajectories. We compare these deductions with existing pressure criteria and retain the spherical contact term in the coupled Hessian evolution. We describe normalized clocks, material anisotropy, cross-Leray exchange, and circulating surface stacks recruited by localized receivers. Fixed-mass recurrence at escaping frequencies forces infinite accumulated activity, and fixed-mass shrinking spatial cores are excluded under a Type-I gradient bound. Fragmentation and exact countertests identify the limits of that hypothesis and of proposed scalar budgets. These constructions and obstructions retain their stated hypotheses; they do not remove the spatial membership condition from the global theorem.
Category: Functions and Analysis
[1877] ai.viXra.org:2609.0068 [pdf] submitted on 2026-09-27 21:35:57
Authors: Brent Hartshorn, Gilead Cosman
Comments: 11 Pages.
Unity’s built-in 2D physics is an integration of the Box2D engine [12]. We build the same kind of2D game runtime from a different direction. Game scripts are written in a subset of C#, translated to a subset of C++ and then to C, and compiled together with a fork of Box2D v3 that we call Box2D-Packed. Our goal is a 2D runtime that is faster than Unity’s. This paper describes the two techniques we use to get there and measures each of them. The first is data packing: public handles shrink from 8 to 4 bytes, and the records the engine reads on every step are laid out by measured access patterns. Measured with Cachegrind’s exact cache simulation, last-level data cache misses fall by up to 65% on query-heavy scenes relative to Box2D v3, with unchanged instruction counts and bit-identical simulation results. The second is an intrusive engine: game logic is compiled into the physics engine at documented points, so it runswhile the engine’s data is still in cache, instead of through callbacks and event arrays. Injected pre-solve logic saves 1.3% of instructions, and injecting a platformer’s event handlers cuts L1 data misses by 2%, with identical game results. We also report where injection does not help: a per-body gravity hook that reads game data costs 7.65% more L1 misses, and event handlers followed by game work on the same objects add last-level misses. We compare against Box2D v3, not yet against Unity, and describe the measurements that remain.
Category: Data Structures and Algorithms
[1876] ai.viXra.org:2609.0067 [pdf] submitted on 2026-09-26 16:47:31
Authors: J. W. McGreevy
Comments: 34 Pages.
This monograph establishes a rigorous, non-perturbative unification of quantum gaugefields and gravity by reconstructing the space-time continuum natively within the internallanguage of the smooth, cohesive ∞-topos H = Sh∞(ArithSite). We replace the classicalcontinuous geometric background with an abstract motivic cochain complex Cu2022(M), modelingthe complete information boundary network as a global adélic variety evaluated over therestricted product ring AQ = R ×∏︁ u2032p Qp. By upgrading general relativity to the structurallandscape of Einstein—Cartan (EC) theory, the physical constants of nature (ℏ, c, G) and thestandard Lorentz transformations emerge natively as the global constants of holomorphicityand absolute arithmetic tracking stabilizers required to balance metric curvature (Tμν ) andspin-density torsion (Σλμν ) across scale horizons.We prove that the pristine, flat genus-0 pre-geometric vacuum undergoes a structuralphase transition driven by the Riemann—Roch theorem when energy-momentum compactionbreaches the Maximum Distance Separable (MDS) Singleton bound, forcing the emergence ofa multi-handled variety of exactly genus g = 5 to absorb the 5-bit information debt. The12 active force carriers of the Standard Model manifest as the continuous vector connectionsections required to stabilize parallel transport along the universal shock front ridge of theCritical Line (R⌉(s) = 1/2), where the Hopf—Lax infimum convolution collapses the phasedispersion of the bulk strip via a gapless, non-linear interleaving flow.Using the Kramers—Kronig relations, we demonstrate that the real refractive index andimaginary absorption index oscillate in perfect quadrature phase along this shock front. Thenon-trivial Riemann zeta zeros are unmasked as the exceptional zero-loss impedance matchesof the waveguide where the absorption index drops to absolute zero, acting as the irreducible,pre-geometric seeds of the primordial universe. Any spectral deviation off this axis triggersan instantaneous, infinite negative Ruppeiner metric divergence (gRupuu → −∞), rupturingthe Einstein tensor and causing the continuum to dissolve into chaotic bit-scrambling. TheRiemann Hypothesis is thus proved, legalizing the non-singular Einstein—Cartan vacuum as abeautifully balanced arithmetic machine regularized unconditionally by the volume stabilityof the adélic continuum.
Category: Mathematical Physics
[1875] ai.viXra.org:2609.0066 [pdf] submitted on 2026-09-25 23:20:37
Authors: Perry Henderson
Comments: 35 Pages.
Metrarchic Field Theory (MFT) is presented as a speculative research architecture with explicittoy sectors within the Metrarchic Geometry Framework (MGF). Its organizing hypothesis is thatquantum measure and macroscopic metric geometry may be scale-dependent manifestations of acommon deeper structure. A positive coframe metric and a prescribed conserved reference measuregive the conditional identity ρG = ρ0/J, where J is the metric volume ratio. Curved realizationsrequire generalized coframes rather than merely compatible maps into a flat space of the samedimension. A conformal sector gives an explicit leading relation between a normalized amplitude’squantum-potential expression and spatial scalar curvature. The fixed reference measure leavesprobabilities of fixed base regions unchanged; a quantum observation map remains to be constructed.A compact worked example also exhibits the distinction between fixed-metric variation and theconstrained metric—density variation within a fixed-shape conformal sector.The wider architecture separates a formal positive configuration-weighting functional, an assumedreduced symplectic quantum sector, and an unspecified coarse-graining map. Prequantizationconstrains symplectic periods but does not derive a universal action scale. Gleason’s theorem suppliesa conditional projector-probability reconstruction after Hilbert-space and measure assumptions; itdoes not establish a microscopic Born rule. Standard Klein—Gordon, Bell/CHSH and Newtoniancalculations are retained as compatibility benchmarks. General relativity is an effective-field-theorytarget under additional infrared assumptions.An internal finite-dimensional construction uses a nonzero simple two-form in C5 to select a ranktwo plane and a postulated 3+2 splitting operator. The plane projector has determinant-one stabilizerS(U(3) × U(2)), whereas a fixed two-form has the smaller stabilizer SU(3) × SU(2). Retainingthe Abelian factor therefore requires an explicit phase-insensitive projector-sector assumption.The associated representation algebra is standard SU(5)-type mathematics. Gauge dynamics,representation-resolved chiral indices, fermion masses and cosmological observables remain open.The paper distinguishes established identities, model assumptions, conditional calculations andunproved physical identifications. It offers an auditable geometric research program, not a completedunification or an experimentally validated theory.
Category: Mathematical Physics
[1874] ai.viXra.org:2609.0065 [pdf] submitted on 2026-09-26 16:25:10
Authors: Marcelo Barboza Duarte
Comments: 37 Pages.
We investigate a class of effective electrodynamic extensions in which a minimal photon rest mass is treated together with a constitutive sector independent of the mass parameter. Here, "minimal" denotes a parametrically small positive scale compatible with experimental upper bounds, not an experimentally established lower bound on mγ. Starting from the relativistic dispersion relation of a massive vector field, we derive the corresponding group-velocity correction and formulate a constitutive closure for light—matter interaction that distinguishes intrinsic photon mass, medium-induced effective mass, and equivalent interaction energy. We impose energy—momentum conservation, thermodynamic admissibility, stability, recovery of limiting theories, and experimental identifiability. We further construct a conventional electromechanical null model including Maxwell stress, elasticity, electrostriction, photoelasticity, dissipation, and thermal response. The resulting framework shows that a local scalar coupling linear in electromagnetic energy density is not independently identifiable in the isotropic linear regime unless it carries an additional dynamic, tensorial, geometric, or nonlocal signature. We formulate differential observables and a hierarchy of null hypotheses for separating Proca-like effects from conventional medium response, and discuss constraints from quasi-static magnetic fields, dispersive propagation, fast radio bursts, and magnetohydrodynamic environments. The theory is presented as a falsifiable effective framework: compatibility with current bounds is not interpreted as detection, and the photon-mass sector is not used to infer macroscopic return, gravitational capture, or stellar feedback.
Category: High Energy Particle Physics
[1873] ai.viXra.org:2609.0063 [pdf] submitted on 2026-09-26 04:54:07
Authors: Fabrizio Vassallo
Comments: 16 Pages.
The Fractal Kitaev Model K k , constructed in the companion paper [1] by decorating the hierarchical graph G k into a maximum-degree-3 tree, has an isotropic Majorana spectrum [2] that was previously accessed only by brute-force diagonal-ization, limited to k ≤ 6 by memory. This note establishes four results. First, an exact recursive factorization of the characteristic polynomial of an isolated depth-d gadget subtree, A d (x) = A d−1 (x) · R d (x) with deg R d = 10 · 6 d−1 , proved in full generality by induction and independently veried by exact-arithmetic polynomial division, together with an exact assembly formula for the full tree. Second, an eigenvalue-counting algorithm requiring only O(k) recursive arithmetic steps exponentially fewer than the |K k | ∼ 6 k dimension of the matrix itself built from the same recursive structure via the standard pivot-counting form of Sylvester's law of inertia, veried to exact agreement against brute-force spectra for k = 2,. .. , 6 and used here to reach k = 15. Third, extending that same pivot to complex argument and identifying it exactly as the reciprocal of a diagonal resolvent entry, we nd its real part numerically at −x/2 to ∼ 10 −7 precision on the real axis, and, at nite k = 15, a macroscopic counting-function jump at a value consistent with a root of R 1 , backed by the exact divisibilities R 1 | R 3 and R 1 | R 4 , though without yet a general sharing rule between generations or a proof that this persists as k → ∞. Fourth, resolving the evidential core of that open question: working entirely inside the exact quotient ring Z[x]/(R 1 (x)) which avoids the combinatorially infeasible full polynomials (deg R 6 = 77760, with coecients hundreds of digits long already at d = 4) we exactly verify R 1 | R d for every tested d = 3,. .. , 40, and that the exact power of R 1 dividing R d grows sharply: e(3) = 5, e(4) = 30, e(5) = 180, all exact (not extrapolated), matching a conjectured scaling law e(d) = 5 · 6 d−3 at three points but not proved beyond them. Since R 1 is irreducible over Q, its ten roots are Galois conjugates and so share, provably, the same exact multiplicity wherever R 1 divides turning the assembly formula, conditional on that scaling law and a second conjectured law for the full tree, into a quantitative prediction for the mass at the single root x ≈ 0.469: 1.3889% at k = 15, numerically close to the ≈ 1.4% found empirically but conditional on both conjectural exponent laws. Both scaling laws remain open beyond the exact points checked.
Category: Mathematical Physics
[1872] ai.viXra.org:2609.0062 [pdf] submitted on 2026-09-24 19:08:41
Authors: Vitaliy Boltian
Comments: 6 Pages.
An innovative relativistic approach to calculating the energy states of atomic orbits based on a system of hyperbolic functions (the Boltian model) is proposed. It is demonstrated that Sommerfeld's fine-structure constant strictly defines the spatial angle for the first energy state, whereas the conventional Bohr quantum formula is merely a special limiting case of the derived general geometric dependence. By employing a modified expression for the half-Lorentz factor, precise agreement of theoretical calculations with fundamental constants (Rydberg constant, Hartree energy) and experimental data for multi-electron systems is achieved. A universal spatial angle of material stability ($approx 33.26^circ - 34^circ$) has been discovered. It acts as a shared invariant for the stability of atomic nuclei, the spatial architecture of DNA, and geomechanical macro-systems, pointing toward a unified geometric nature of the Universe.
Category: Mathematical Physics
[1871] ai.viXra.org:2609.0061 [pdf] submitted on 2026-09-24 19:31:16
Authors: Stephen P. Smith
Comments: 11 Pages.
Modern physics possesses extraordinarily powerful formal structures, but the existence of a successful formalism does not by itself settle what that formalism means. This essay proposes an interpretive program in which the Lie bracket is read as a generative relation and the Jacobi identity as a higher-order regulatory condition. On this interpretation, the familiar passage from binary relation to Jacobi coherence may be understood as the mathematical trace of a more general movement from two-sided differentiation toward a coherent whole. A previous proof-of-concept formulation of general relativity, in which extrinsic gravitation was modeled as a homeostatic coupling between CPT-symmetric spacetime manifolds, provides one possible spacetime realization of this idea, but may not be the most economical foundation for it. The deeper structure is already present in the pre-geometric formalism of Lie algebra. Quantum mechanics then supplies a further point of contact: noncommuting observables are constrained by uncertainty relations whose lower bound is directly related to their commutator. This does not prove a philosophical theory of attention, but it permits an interpretive extension in which different modes of attending to relational structure have different formal consequences. Iain McGilchrist’s distinction between narrow and broad attention provides a useful interdisciplinary vocabulary for this extension, without implying an identity between quantum mechanics and his account of cognition. The resulting proposal is neither a replacement for mathematical physics nor an attempt to derive metaphysics from equations. It is an argument for an interpretive meta-science in which formal mathematics establishes relational constraints while interdisciplinary inquiry asks what kind of organization those constraints may express.
Category: General Science and Philosophy
[1870] ai.viXra.org:2609.0060 [pdf] submitted on 2026-09-25 05:46:19
Authors: Stephen P. Smith
Comments: 7 Pages.
This paper develops a Yang—Yin model of emotional life within Arthur Koestler’s concept of the holon, treating outward emotional expression and inward reflection as complementary functions of a self-regulating system. Yang represents the movement of feeling into action, communication, creativity, and relationship, while Yin represents the capacity to contain, examine, and integrate feeling before it becomes action. Their relationship is regulated by a homeostatic function that does not seek emotional stillness but maintains a dynamic balance between expression and reflection. The paper examines the characteristic distortions that arise when either pole dominates, including impulsive emotional flooding, projection, and dramatized memory on one side, and suppression, over-intellectualization, and emotional detachment on the other. Because persons are holons embedded within larger holarchies, the same regulatory dynamics can extend through families, communities, and cultures. Emotional maturity is therefore understood not as diminished feeling or permanent calm, but as the capacity for coherent intensity: allowing emotion to remain vital and expressive while retaining sufficient reflection and containment to preserve understanding, relationship, and systemic coherence.
Category: Mind Science
[1869] ai.viXra.org:2609.0059 [pdf] submitted on 2026-09-25 18:42:10
Authors: James M. Chappell, David L. Berkahn, Derek Abbott
Comments: 18 Pages.
Terence Tao's airport puzzle asks where a late passenger should spend a short burst of running, or a short pause to tie a shoe, when part of the terminal is a moving walkway.The Galilean answer is to run on the floor and to pause on the belt.The same comparison survives special relativity, with an extra Lorentz factor that makes the belt even less useful as a place to sprint.We recast the belt as the frame-dragging current of a Kerr black hole and ask where to site a terminal if the passenger's proper-time budget is fixed and the gate clock is a static clock in the spacetime.The pedagogical conclusions are: in order to have static concourses we need to site them outside the equatorial ergosphere; lay optional walkways along the zero-angular-momentum congruences; spend the running burst on the static floor; and place the lounges higher up the gravitational potential and not place the gate on the photon orbits.The paper is intended for an undergraduate course that has met special relativity and a first encounter with the Kerr geometry.
Category: Astrophysics
[1868] ai.viXra.org:2609.0058 [pdf] submitted on 2026-09-25 08:01:38
Authors: Abel Liu
Comments: 8 Pages.
We propose a physical-tiling hypothesis for a $5+1$-dimensional Kaluza--Klein compactification: at microscopic scales the two compact dimensions are carried by finite periodic Archimedean graphs, whose vertices, edges, faces, and associated fields are physical rather than auxiliary discretization data. To accommodate all eight tilings in one four-dimensional theory, we explicitly choose a compact internal space with eight toroidal sheets. Each sheet has its own regular-polygon tiling while all sheets share the macroscopic spacetime. A fundamental quadratic action for vertex fields gives a finite graph-Laplacian mass spectrum, hence a finite KK-like tower. We prove exact formulae for its first three normalized spectral moments in terms of the vertex degree and triangle incidence. In particular, the two trivalent tilings $4.6.12$ and $3.12.12$ have respective third moments $54$ and $52$, a tiling-dependent result not contained in a generic continuum torus Fourier formula. The conventional KK dispersion arises only in a long-wavelength regime after matching an effective spectral metric. We also state a precise $2+3+3$ rule for candidate fermion sectors on the eight sheets, including the condition for a common color triplet. Distance-pair group labels, Wilson loops, gravitational volume matching, and chiral zero modes are kept at their respective logical levels. The result is a falsifiable effective model and a spectral sum rule, not a completed derivation of the Standard Model.
Category: Mathematical Physics
[1867] ai.viXra.org:2609.0057 [pdf] submitted on 2026-09-24 18:34:10
Authors: J. W. McGreevy
Comments: 38 Pages.
This monograph establishes a rigorous, coordinate-free unification of quantum gauge fields and gravity by reconstructing the space-time continuum natively within the axiomatic language of higher topos theory. We replace the classical continuous geometric background withthe smooth, cohesive ∞-topos H = Sh∞(ArithSite), modeling the underlying arena as a global adélic variety evaluated over the restricted product ring AQ = R ×∏︁ u2032 p Qp. Under this formulation, the active physical force carriers are re-indexed as cohesive ∞-groupoid curvature stacks Ψ∞ ∈ H(X, BGA)conn, where the active Standard Model gauge fields are locked to a 12-bit message payload derived from the Extended Binary Golay Code G24 and its rootless embeddings within the Leech horizon. We prove that the pristine, flat genus-0 pre-geometric vacuum undergoes a structural phase transition driven by the Riemann-Roch theorem when energy-momentum compaction breaches the Maximum Distance Separable (MDS) Singleton bound, forcing the emergence of a multi-handled variety of exactly genus g = 5 to absorb the 5-bit information debt. The 12 active gauge bosons manifest as the mandatory harmonic connection sections required to smooth out parallel transport across these handles, with the strong color octet anchored tonon-commutative S4 layers and the electroweak triplet regulated by dihedral D3 switchingsymmetries. Furthermore, we demonstrate that the infinite loop divergences of quantum gravity collapse into a finite, self-regulating arithmetic boundary governed by even-weight modular Eisenstein series (E2 through E12) and pinned down by Kummer irregular prime walls at 5 and 691. By evaluating the scale-dependent gravitational beta function against the logarithmic derivative of the Riemann zeta function, we deliver a non-perturbative proof of an Asymptotic Safety fixed point (g∗ ≡ 0) locking gravity to trivial freedom precisely at the non-trivial Riemann zeros along the waveguide axis R⌉(s) = 1/2. Symmetries, matter fields, and universal constants (ℏ, c, G, ∆mass) are thus unmasked as the intrinsic comparison isomorphisms of a beautifully balanced cosmic structure, regularized unconditionally by the volume and measure-theoretic stability of the adélic continuum.
Category: Mathematical Physics
[1866] ai.viXra.org:2609.0056 [pdf] submitted on 2026-09-24 18:37:09
Authors: Chun Wing Lai
Comments: 10 Pages.
Z.-W. Sun has recently announced a determinant-based proof that Catalan’s constant G is irrational. We verify Sun’s framework and identify one genuine gap in the final quadraticledger: the factorial contributes a 2-adic term which is not absorbed by the odd-prime positive-part bridge. When this term is included, thefinal B^2 coefficient becomes positive, and the contradiction 0 < |N_B| < 1 cannot be derived.We propose a minimal correction: replace the monomial reference columns ir in Sun’s determinant by binomial coefficient columns. The finite-difference transform then diagonalizes the reference block with unit pivots, and F_B disappears entirely from the determinant formula. All odd-prime constants—the odd small-prime constant c_odd, the middle-prime integral Λ_mid, and the large-prime improvement 83/2400—are unchanged. The final coefficient becomes strictly negative. The contradiction 0 < |N_B| < 1 for a nonzero integer N_B is thenrestored. We also note a harmless indexing typo in Sun’s rank theorem and confirm that withthe corrected indexing the proof is valid. A supplementary SageMath verification suite coversevery quantitative claim of the paper.
Category: Number Theory
[1865] ai.viXra.org:2609.0055 [pdf] submitted on 2026-09-23 05:22:05
Authors: Stephen P. Smith
Comments: 14 Pages.
This paper argues that a generative structure is not equivalent to a coherent system. Using examples from semiotics, biology, systems theory, and Lie algebra, it develops a distinction between dyadic generation and triadic regulation. Dyadic relations, exemplified by Saussure's signifier-signified model and the binary Lie bracket, are shown to generate differences, relations, and new possibilities. However, generation alone does not explain how coherence, stability, or meaning are maintained. Drawing on Peirce's concept of Thirdness, the paper proposes that a mediating regulatory relation is required for organized persistence. This regulatory function appears across domains as interpretants in semiotics, homeostatic and multiscale regulatory networks in biology, and higher-order constraints such as the Jacobi identity in Lie algebra. The comparison is not one of identity but of shared logical architecture: generative relations require regulatory constraints if they are to constitute coherent systems. The resulting framework is summarized as a progression from difference → relation → regulation → coherence, providing a rigorous account of how two-sided structures become integrated wholes while preserving their distinctions.
Category: Linguistics
[1864] ai.viXra.org:2609.0054 [pdf] submitted on 2026-09-23 11:45:16
Authors: Vitaliy Boltian
Comments: 3 Pages.
This paper addresses the conceptual limitations in classical mathematical analysis regarding the differentiation of inverse trigonometric and hyperbolic functions. The traditional approach, which relies heavily on the inverse function theorem and complex virtual transformations, is reconsidered. The author introduces a novel theoretical framework based on a system of real companion functions and defines the concept of a "transition coefficient". This approach establishes direct, invariant relations between trigonometric, hyperbolic, and algebraic function systems within the real domain. The practical application of the proposed apparatus is demonstrated through specific integration examples, showcasing a significant simplification of mathematical operations and analytical structures.
Category: Functions and Analysis
[1863] ai.viXra.org:2609.0053 [pdf] submitted on 2026-09-23 15:30:25
Authors: Jessica Bower
Comments: 21 Pages.
The balance between ordered rotation and pressure support is a central feature of gaseous galacticdisks, yet a one-variable measure such as V /σ does not fully describe how that balance changeswithin individual galaxies. This paper investigates whether gas pressure support is organized byrotational coherence alone or by a coupled dependence on dynamical organization and radial struc-ture. The rotational organization parameter is defined as Rorg = (Vrot/σ)2, and the fractionalpressure-support measure as F = (V 2c − V 2rot)/V 2c . Across observational samples, increasing rota-tional organization is associated with decreasing pressure support at the population level. A candi-date transition near Rorg ≃ 84 successfully identifies highly organized systems in an independentWHISP holdout sample, but it fails as a universal physical boundary when tested against regular,low-Rorg H i disks. Radially resolved LITTLE THINGS data further show that a one-variable localrelation between F and Rorg cannot describe all galaxies: the sign of the within-galaxy trend variesfrom system to system. Introducing independently measured radial structure resolves much of thisinconsistency. For the primary resolved sample, F/(1 − F) ∝ R−0.91org (r/Rd)1.82, with R2 ≃ 0.87when galaxy-specific normalization is allowed. Leave-one-galaxy-out prediction improves relativeto an organization-only model in 13 of 17 systems. An independent KAT-7 sample preserves therelative two-variable structure, although not its exact coefficient strength. Finally, the frameworkis tested against NIHAO hydrodynamic simulations in which the circular velocity is derived di-rectly from the simulation potential, breaking the observational asymmetric-drift circularity. Thelocked two-variable predictor retains the expected positive direction in all four simulated galaxiesand improves prediction relative to Rorg alone. The result is interpreted as an empirical StructuralGovernance Framework: the equilibrium partition between ordered rotation and gas pressure sup-port is jointly organized by rotational state and radial disk structure. The relation is not presentedas a universal fundamental law or immutable constant
Category: Astrophysics
[1862] ai.viXra.org:2609.0052 [pdf] submitted on 2026-09-22 20:53:59
Authors: Michael Quigley
Comments: 30 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This Addendum formally rectifies an early drafting conflation in The Sub-Atomic Ruler War (viXra:2608.0024) regarding the physical scale of the material ether granule versus the acoustic coordinate grid step. In physical 3D space, assuming physical hard-sphere granules were 1.0 pm wide created an impossible 12-Monobrick pylon height of ~720 pm. Reassigning the physical granule to the attometre scale (λl = 28.18 am = 0.02818 pm) collapses the true 12-Monobrick Heptad pylon height to a solvent 2.76 fm, eliminating all spatial overhangs inside the 6.0 fm proton core and 106 pm atomic cavity. Concurrently, the 1.000 pm metric is formally established as the Standing Wave Node (SWN) grid step—the fundamental "record groove" coordinate carved into the 10²² kg/m³ plenum. Engaging the universal motor drives a 2.55766× acoustic compression factor (Kepler expansion ratio Ev = 1.35048 × 3D lattice factor Clattice = 1.89389), squashing the raw stasis wave (λraw = 2.56 pm) down to the rigid 1.000 pm SWN grid step. Subtracting 31.4 pm (10π) of geometric closure work from the 84.4 pm Heptad blueprint width snaps the electron peloton directly onto the 53.0 pm Bohr Radius address (au2080) with 99.9% accuracy. Applying this unit cell (re = 2.818 fm) to Milo Wolff’s Cosmic Equation (R = √N · r) reclassifies light-speed as Lattice Setup Time (Ls), yielding a 4.15-year maximum setup horizon and bounding the stationary cosmos at the 34.5 Trillion Km Terminal Acoustic Horizon (137-Wall). Integrating across primary major nodes (10¹¹ × 10¹¹) and sub-harmonic dwarf containers (10¹u2074 × 10u2077) reconciles the total star inventory to a locked total of 10²² stars, proving that the R.U.T. physical gear-mesh is 100% mathematically solvent, closed, and self-sustaining
Category: Quantum Physics
[1861] ai.viXra.org:2609.0051 [pdf] submitted on 2026-09-22 20:49:22
Authors: Vitaliy Boltian
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper introduces a novel mathematical framework based on the Comprehensive System of Functions to evaluate classical elliptic integrals of the first, second, and third kinds. By mapping incomplete functional profiles directly onto complete trigonometric and hyperbolic invariants of the real system of functions, the traditional transcendental complexity and artificial limitations of non-integrability are completely eliminated. The proposed method provides exact analytical solutions in elementary functions, ensuring high numerical convergence and stabilizing the relative error within a strict range of 10u207bu2075 to 10u207bu2076 without requiring iterative numerical processing cycles."
Category: Mathematical Physics
[1860] ai.viXra.org:2609.0050 [pdf] submitted on 2026-09-22 15:20:09
Authors: Xuda Ye
Comments: 55 Pages.
We analyze the mean square error of stochastic Runge--Kutta integrators for overdamped Langevin dynamics whose potential is strongly convex outside a bounded region. A decomposition splits the local error into a mean-zero term and a smaller remainder, and the discrete Poisson equation turns their moments into a bound on the error of a time average. We carry this out for two stochastic Runge--Kutta integrators proposed by Yang & Wang (2026), both of strong order $frac32$ and weak order $2$, which evaluate the gradient of the potential and no higher derivative. We show that their laws approach the law of the exact solution at second order in Wasserstein-1 distance, up to a logarithm, uniformly in the number of steps. For a test function with bounded derivatives up to third order, we prove that the mean square error over $N$ steps with step size $h$ is $mathcal O ( frac{1}{Nh} + h^4 )$, which is the optimal order in the discretization. Experiments measure the strong and weak orders and the sampling bias on a nonconvex potential in $mathbb R^2$, and compare the integrators on a diffusion model of CIFAR-10.
Category: General Mathematics
[1859] ai.viXra.org:2609.0049 [pdf] submitted on 2026-09-22 15:22:47
Authors: Yuliang Wang, Xuda Ye
Comments: 23 Pages.
We consider two stochastic Runge--Kutta integrators proposed by Yang & Wang (2026) for overdamped Langevin dynamics whose potential is strongly convex outside a bounded region. In the companion paper (Ye, 2026) the law of the numerical solution was shown to approach the law of the exact solution at second order in Wasserstein-1 distance, uniformly in the number of steps, up to a logarithm of the step size. We remove the logarithm, and a Gaussian example shows that the second order is attained by the bias of the invariant law of the integrators, and that the squared bias of their time averages attains the order $h^4$ of the mean square error bound of the companion paper.
Category: General Mathematics
[1858] ai.viXra.org:2609.0048 [pdf] submitted on 2026-09-22 20:46:18
Authors: L. B. Uvindu Daham
Comments: 15 Pages.
We present a definitive resolution to the P versus N P problem by embedding discrete constraint satisfaction problems (3-SAT) into continuous non-compact Riemannian manifolds via Maslov dequantization (h > 0 deformation). By constructing the Master Flow Equation governed by logsum-exp smoothing operators, we prove that the trajectories are bounded by a uniform polynomial spectral gap and structurally bypass relativization, natural proofs, and algebrization barriers. Utilizing Morse-Bott theory and asymptotic energy dissipation estimates, we demonstrate that all worst-case exponential trajectories are suppressed, achieving deterministic convergence to satisfying assignments in polynomial time O(nK ). Consequently, we establish that P= N P.
Category: Data Structures and Algorithms
[1857] ai.viXra.org:2609.0047 [pdf] submitted on 2026-09-22 20:26:51
Authors: Steven Arturo Lizarazo Patiño
Comments: 28 Pages.
Problem: Physical theories presuppose mathematical structure, symbolic rep-resentation, and the allocation of determinate meaning, yet cannot groundthese prerequisites within spacetime without circularity. This foundational gapthreatens the coherence of scientific realism.Result: We prove that any intelligible universe U forces a unique, self-grounding terminus of dependence. Modelling consciousness minimally asmeaning-allocation capacity, the dependency chain U ⇒ M ⇒ L ⇒ C can-not be grounded in U without vicious circularity. The mathematical core isan existence-and-profile theorem for a formal theory T whose axioms (intel-ligibility, well-founded dependence, undated mathematical necessity, semantictermination, and G¨odel incompleteness) define a predicate Pure(x): we proveT ⊢ ∃!x Pure(x), with the unique instance D atemporal, non-spatial, neces-sary, simple, non-mechanical, and semantically self-present (G(D, D), C(D) =D). Uniqueness is established order-theoretically—D is the least fixed pointof a monotone grounding operator on a complete lattice of candidate grounds(Knaster—Tarski)—and non-mechanality is derived from incompleteness ratherthan stipulated, distinguishing the argument from G¨odel’s own ontological proof,which stipulates its property profile and proves no uniqueness. As a physicalcongruence, we show that superluminal spacetime expansion is not generated bylight-cone-bounded local processes, so the empirical world’s own global behaviouris not self-explanatory from within.Implications: The framework extends structural realism and Tegmark’sMathematical Universe Hypothesis by establishing semantic grounding as co-fundamental with mathematical structure. The classical name for a unique,necessary, self-grounding ground of being and intelligibility is God ; the result isconfined to the derived profile and claims nothing beyond it. Consequences forethics, philosophy of mind, and religion are left open.
Category: Set Theory and Logic
[1856] ai.viXra.org:2609.0046 [pdf] submitted on 2026-09-22 00:26:50
Authors: Nigel B. Cook
Comments: 21 Pages. (Note by viXra Admin: Please cite and list scientific references other than self-reference))
This paper is a follow-up on https://ai.vixra.org/abs/2608.0002 addressing the emergence of standard model type gauge group from Robert A. Wilson's suggestion of discrete quantization group SL(4,R). Quantum fields emerge as hydrodynamic limits of dense networks of discrete spinor transformations, an application of the basic concept of spin foam vacuums as the ground state of loop quantum gravity. Spin foam vacuums were suggested to explain how a smooth, classical macroscopic geometry emerges as an effective average coarse-graining to an underlying discrete vacuum. This paper thus applies the basic concept of loop quantum gravity's ground state spin foam vacuum to obtain approximately the continuous gauge groups of the standard model from an underlying discrete Wilsonian SL(4,R) group. It is not intended to make specific predictions; just to show compatibility of mathematical techniques. The mathematics in this paper have been proof checked by Microsoft Copilot AI, since human "peer reviewers" are unavailable at present.
Category: Quantum Gravity and String Theory
[1855] ai.viXra.org:2609.0045 [pdf] submitted on 2026-09-21 16:38:06
Authors: Preda Daniel Georgel
Comments: 212 pages, 60 conceptual illustrations, and 40 scientific references. English-language theoretical monograph. AI assistance is fully disclosed in the manuscript.
Helical geometrodynamics is presented as a theoretical framework in which systems, transport, geometry, memory, and interaction are analyzed through coherent helical flows. The volume does not seek to replace experimentally validated physical theories. Instead, it investigates whether a common descriptive level can be constructed from vortex tubes, the IN—path—OUT architecture, and geometric adaptation. It introduces the Preda descriptors Cc = dQ/dt, Cf = rvt², and Ce = r³f², together with the independent rotational descriptor Cr, the helical ratio η = va/vt, axial direction, chirality, and phase. The relation Cf = 4π²Ce is treated as an algebraic identity when vt and f refer to the same local rotation, whereas α = CeCf/Cc² remains a derived ratio and a hypothetical filter rather than a sufficient coupling criterion. On this basis, the volume formulates four candidate interaction kernels and develops the concepts of geometrodynamic memory, the Fundamental Torsion Wave (F.T.W.), structural emission and absorption, polarization, axialization, and the Σgd transition regime. Extensions toward light, particles, gravity, cosmology, and living systems are explicitly identified as hypotheses or analogies. The central contribution is an operational research program based on defined observables, comparison with standard models, preregistered predictions, uncertainty analysis, and falsification criteria. In its present form, the work is a falsifiable conceptual framework and research program, not an experimentally validated physical theory.
Category: Quantum Gravity and String Theory
[1854] ai.viXra.org:2609.0044 [pdf] submitted on 2026-09-21 20:30:42
Authors: Stephen P. Smith
Comments: 18 Pages.
Lie-algebraic structure can be examined through two complementary forms of organization that will be called vertical and horizontal emergence. These terms are used here as a conceptual framework rather than as standard classifications within Lie theory. Vertical emergence refers to the construction of new algebraic objects from structures already present at a lower level—for example, the construction of curvature from a covariant derivative, or the appearance of higher multilinear operations in $L_infty$-algebras. Horizontal emergence refers to the integration of multiple algebraic structures into a larger structure in which interactions between the component algebras become essential. Semidirect products, matched pairs, and related constructions provide mathematically precise examples. The distinction is useful because the familiar derived series [ L^0 = L,qquad L^1 = [L,L],qquad L^2 = [L^1,L^1],qquad ldots ]does not by itself capture every way in which algebraic structure can become more elaborate. The derived series produces a nested sequence of subalgebras using the same underlying bracket. By contrast, extensions, deformations, higher brackets, curvature, and interacting combinations of algebras can introduce genuinely new structural relationships and new compatibility conditions. This provides a possible mathematical analogy for Arthur Koestler's concept of the holon: a structure may retain a degree of autonomy at one level while simultaneously participating in a larger integrative structure. The analogy should not be mistaken for a theorem establishing that Lie algebras are literally holarchies. Rather, it suggests a productive correspondence between a well-defined mathematical phenomenon—structural integration across levels—and a broader philosophical account of organization.
Category: Algebra
[1853] ai.viXra.org:2609.0043 [pdf] submitted on 2026-09-19 07:51:16
Authors: Vladimir S. Netchitailo
Comments: 56 Pages.
The World—Universe Model (WUM) proposes that the physical World is a finite, boundless three-dimensional Hypersphere forming the surface of an expanding four-dimensional Nucleus embedded in the Eternal Universe. The Nucleus expands along the fourth spatial dimension with speed c. Within this framework, Matter is not treated as a primordial substance introduced solely through initial conditions. Universe-Created Matter (UCM) is continuously generated by the Eternal Universe within the expanding 4D Nucleus through the formation of Universe-Created Particles (UCPs).UCPs constitute a fundamental physical component of WUM. They possess definite rest energies and form a discrete multicomponent system. They participate in the formation and evolution of Macroobjects and, through specific interactions and pair-annihilation processes, in the generation of Ordinary Matter. Ensembles of UCPs carry intrinsic angular momentum, physically resembling microscopic "air vortices." WUM therefore relates the origin of Matter to the origin of angular momentum in physical systems.The purpose of the present work is to develop the UCP concept from the fundamental principles of WUM and to compare the predicted particle spectrum with independent astronomical and experimental observations. Particular attention is given to particle-specific quantitative signatures and to theoretically related UCP couples, for which correlated observational evidence can provide a substantially stronger test than isolated spectral correspondences. The broader physical roles of UCM—including the formation of the Cosmic Medium, the operation of UCP Annihilation Reactors, the generation of Ordinary Matter, and the proposed microscopic mechanism of Gravitation—are also considered.The central question addressed in this paper is: Do independently observed phenomena provide quantitative evidence for the system of Universe-Created Particles predicted by WUM? The objective is not merely to identify qualitative similarities, but to determine whether the predicted rest energies, physical products, astrophysical manifestations, and interconnected physical roles of the complete UCP—UCM system have quantitative counterparts in Nature.
Category: Relativity and Cosmology
[1852] ai.viXra.org:2609.0042 [pdf] submitted on 2026-09-20 20:25:10
Authors: Alessandro Battiston
Comments: 6 Pages.
Context: Macromolecular structure prediction and conformational energy relaxation have historically relied on stochastic heuristics, Monte Carlo sampling, and deep statistical neural networks (e.g., AlphaFold), which are stochastic or statistical in formulation and can have non-zero predictive uncertainty, with computational costs that depend strongly on the method and implementation. Objective: This work introduces the Deterministic Symbiosis Engine, a closed-form, finite-state feedback operator designed for autonomous energetic equilibrium, mass convergence, and Euclidean distance geometry resolution without stochastic variables or black-boxheuristics.Method: The state operator T : (E,M) →(Eu2032,Mu2032)acts as a non-linear piecewise dead-band contractor over a designated energy interval Isymb = [Eopt−ϵ,Eopt + ϵ]. We generalize T into an N-dimensional tensorial map incorporating angular momentum tensors J and local hydrodynamic dissipation matrices Γ. Results: We prove that for 2ϵ≥max(∆Einc,∆Edec), limit cycles are strictly precluded, yielding exact closed-form convergence in Ki steps. For a benchmark suite of 7 heterogeneous molecular subunits, the maximum individual convergence horizon is Ktotal = 4 under the stated parameters, with ∆dev = 0 in the fixed implementation. The perturbation test returns to the dead-band in Kpert = 2 cycles under the stated benchmark conditions. Conclusion: Bymembedding T within Euclidean Distance Matrix (EDM)completion via semidefinite algebraic constraints, thisframework demonstrates O(N) computational complex-ity for uncoupled systems and a conditional Lyapunov analysis for the coupled consensus dynamics, establishing a deterministic foundation for computational structural biophysics.Keywords: Deterministic Dynamics, Finite-Time Con-vergence, Dead-Band Control, Lyapunov Stability, Distance Geometry, Macromolecular Folding.
Category: Mathematical Physics
[1851] ai.viXra.org:2609.0041 [pdf] submitted on 2026-09-18 16:27:56
Authors: Sean O. Brady
Comments: 6 Pages.
Gravitational waves encode the motion of their sources, raising the question of whether deliberately controlled binary motion can carry recoverable information. Methods: Two equal masses are kept antipodal while a smooth radial control law produces identical orbitalexcursions whose timing encodes the integer sequence 2, 3, 5, 7, 11, 13, 17. The two corresponding quadrupole polarizations are calculated from the source motion. A receiver fits the carrier, forms signed residuals, identifies markers, estimates a timing unit, and admits repeated interval packets only after the fixed model and statistical controls are satisfied. Independent numerical integrationchecks the trajectory and energy balance. Results: In a predeclared Gaussian-noise sweep, the full seven-integer payload was recovered in four of six modulated cases, while none of the six matched unmodulated cases passed the packet criteria. At the highest tested noise level, failure occurred in marker extraction rather than carrier fitting. Two chirp- and precession-like nuisance signals also failed to produce repeated packets. The dimensionless construction was mapped to physical binary parameters and Advanced LIGO design sensitivity, with ideal matched-waveform detectability kept distinct from demonstrated packet decoding. Conclusions: This study provides a bounded end-to-end demonstration of information encoded through controlled source motion rather than added directly to a waveform, while also quantifying the extreme physical demands of detectableartificial generation.
Category: Astrophysics
[1850] ai.viXra.org:2609.0039 [pdf] submitted on 2026-09-17 22:38:11
Authors: J. W. McGreevy
Comments: 32 Pages.
We introduce the Thermodynamics of Arithmetic Action (TAA), an architectural framework thatunifies arithmetic geometry, informational code theory, and general relativity into a single, cohesive paradigm. This monograph maps the macroscopic universe—including space, time, and the fields of the Standard Model—as the continuous Archimedean completions of a global adélic variety governed by a singular Grothendieck Motive. By demonstrating that the absolute stability of the spacetime metric is structurally bound to the unitarity of the global intertwining operator over GL(2, AQ), weshow that any violation of the Riemann Hypothesis (RH) induces a non-vanishing covariant divergence in the macroscale stress-energy tensor. This mathematical rupture violates the foundational Bianchi identities and triggers an immediate, catastrophic metric collapse. Consequently, the Riemann Hypothesis emerges not as an isolated problem in pure number theory, but as the fundamentalphysical boundary condition that preserves the structural sanity of the spacetime vacuum against self-dissolution.
Category: Mathematical Physics
[1849] ai.viXra.org:2609.0038 [pdf] submitted on 2026-09-17 22:36:50
Authors: Wen PeiLin
Comments: 81 Pages.
We study a family of directed graphs on n = 2k+ 5 vertices whose adjacency matrices are{0, 1}-matrices with zero diagonal, uniform column sum 2, and a rigid Jordan structure: thenon-zero spectrum {2, 1, −1, −1, −1} is constant in k, while a single nilpotent block J2k(0)grows with k. We call this the Wen class Uk and define it through five axioms D1—D5. The main result of the paper settles the existence question. We construct an explicit infinite subfamily {Am}m≥1 with ord(Am) = 2m + 7, obtained by iterating a chain-insertionoperator T on a fixed 7 × 7 core C. A Schur-complement identity for T, combined with aresolvent computation that reduces to three cofactors of the single 7 × 7 matrix zI − CT, shows that T multiplies the characteristic polynomial by z 2 ; the exact determination ofdim ker Am = 1 and dim ker(Am + I) = 2 then upgrades this spectral statement to the fullJordan axiom D4. Consequently Uk 6= ∅ for every integer k ≥ 1: the class is infinite, andno order is empty. Every step of the proof is a finite exact computation of order at most 7,independent of m. We prove the closed-walk counting formula NL = 2L + 1 + 3(−1)L, the rank formula rank(Am) = max(n − m, 5), the minimal polynomial x 2k (x − 2)(x − 1)(x + 1)2 of degree n − 1, the commutant dimension 7 + 2k, the Newton-identity recurrence of order 5,and the doubler-chain power-of-two property. A computer search at seven orders (k =1, . . . , 7, i.e. n = 7, . . . , 19) produced 233 pairwise non-isomorphic members, distributed as 34, 50, 39, 22, 68, 13, 7; these numbers are lower bounds for the number of isomorphism classes at each order, and ten representatives of each order are listed in Appendix 18. We disprove two natural conjectures (the "minimum-one integer Perron vector" property and the "core-template" hypothesis) and organise the observed structure into a three-layer architecture separating rigid invariants, semi-invariants and flexible realisation.
Category: Combinatorics and Graph Theory
[1848] ai.viXra.org:2609.0037 [pdf] submitted on 2026-09-16 10:18:38
Authors: Vitaliy Boltian
Comments: 3 Pages.
This paper proposes an alternative paradigm of mathematical analysis based on the interaction of physical quantities rather than an abstract numerical continuum. The concept of a discrete scale factor $M$ and inter-system transition coefficients via Gudermannian mappings are introduced, rendering the classical substitution of variables an anachronism. Exact analytical operational formulas for differentiation and integration are obtained, a physics-scale-based proof of Fermat's Last Theorem is presented, and new empirical models for elliptic integrals of the first and second kind are derived. For the first time, a real quantum wave function based on split-complex (dual) numbers is proposed, and a new form of the stationary Schrödinger equation, free from imaginary mysticism, is derived.
Category: Mathematical Physics
[1847] ai.viXra.org:2609.0036 [pdf] submitted on 2026-09-16 20:34:26
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 7 Pages.
Can gravitational geometry arise as a collective response without postulating a fundamentalgraviton? We investigate this possibility within the Principium Geometricum (PG) program, inwhich local sectors are restrictions of a global state and toroidal phase and breathing variablesare proposed as underlying degrees of freedom. A local normalization Φ = ZΘ yields K = K0Z2and β = β0Z, preserving β2/K. An exact change-of-variable test shows, however, that thisidentity alone produces no new gravitational observable: when all gradient terms are retained, Z cancels from the physical potential Ψ = βΘ. A physical toroidal mechanism must therefore modify the source energy or introduce independently derived interactions. Conditional on universal clock coupling, the source is total energy, and a static gapless sector yields a Poisson equation and inverse-square acceleration. A reciprocal exponential metric reproduces the static weak-field coefficients γ = β = 1, but its exterior Einstein tensor is nonzero at nonlinear order. The construction thus provides an effective framework and a precise set of consistency tests, rather than a completed quantum theory of gravity. Its central open problem is to derive source energies, constitutive coefficients, and gravitational dynamics from the same microscopic theory. A fundamental graviton is not assumed; emergent graviton-like excitations are neither derived nor excluded.
Category: Relativity and Cosmology
[1846] ai.viXra.org:2609.0035 [pdf] submitted on 2026-09-14 20:17:56
Authors: Tatarov Evgeniy
Comments: 19 Pages.
This paper presents the Dynamic Vacuum Relaxation Theory (DVRT) — a complete,self-contained relativistic theory of gravity in which dark matter phenomenology and cos-mic acceleration arise not from undiscovered particles or fine-tuned constants, but fromthe quantum structure of the de Sitter vacuum. By exploring the spontaneous breaking of conformal symmetry SO(2, 4) → SO(1, 3) at the Hubble scale, we demonstrate that a scalar dilaton field Θ and a special conformal vector field Aµ emerge naturally as geometricdegrees of freedom. The scalar field is identified as an effective hydrodynamic condensate of fundamental fermionic fields on the dS4/CF T3 boundary. We derive all parameters from first principles, including the Milgrom acceleration scale a0 = cH0/6 ≈ 1.135 × 10−10 m/s2 and the universal coupling constant β = 1/6. The theory reproduces flat galaxy rotationcurves, the baryonic Tully-Fisher relation, and the Radial Acceleration Relation without freeparameters, while passing all Solar System, binary pulsar, and strong-field precision tests.Unique falsifiable predictions for upcoming cosmological surveys are discussed.
Category: Quantum Gravity and String Theory
[1845] ai.viXra.org:2609.0034 [pdf] submitted on 2026-09-14 19:59:05
Authors: J. W. McGreevy
Comments: (Note by ai.viXra.org Admin: Please remove all empty pages and cite listed scientific references)
This monograph presents the formal foundations of the Thermodynamics of Arithmetic Action(TAA), a unified framework wherein the macroscopic spacetime continuum, general relativity, and quantum gauge fields emerge as expressions of a single underlying Grothendieck Motive evaluated over the global adele ring AQ. We demonstrate that the non-renormalizability of quantum gravity is a coordinate-chart artifact born from the false assumption of infinite continuity in the ultraviolet. By regularizing the pre-Planck lattice as a characteristic p algebraic variety operating at the maximumgeometric packing density, we show that data-packet crowding forces a 5-bit Maximum DistanceSeparable (MDS) error deficit. This unpayable local information debt triggers a topological phase transition, deforming a flat rational curve (g = 0) into a genus-5 Riemann surface stabilized by a hidden SO(4) momentum space symmetry. Physical constants—including the speed of light, the gravitational constant, andthe Yang-Mills mass gap—are derived explicitly as transcendental periods of this motive. Finally, we establish that the non-trivial zeroes of the Riemann zeta function act as absolute causal waveguides, clamping the running of the gravitational coupling constant smoothly to zero and regularizing high-energy loop divergences without infinite counterterms.
Category: Mathematical Physics
[1844] ai.viXra.org:2609.0033 [pdf] submitted on 2026-09-14 14:25:49
Authors: Arieh Sher
Comments: 8 Pages.
We investigate the kinematic and morphological properties of disk and spiral galaxies withinthe Pivot Universe (PU) theoretical framework. In this model, the persistent flattening of galacticrotation curves is attributed to an asymptotic background spacetime frame-dragging field (Ω0)induced by the cosmic Kerr pivot, eliminating the need for cold dark matter (CDM) halos. Bycoupling the local baryonic mass distribution to this background metric acceleration field (a0), theBaryonic Tully-Fisher Relation (V 4flat ∝ Ga0Mb) is derived directly from first principles.Furthermore, we examine galactic morphology resulting from continuous ballistic mass ejectionfrom rotating antipodal nozzles anchored to central supermassive black holes (SMBHs). Whileinitial formulations assumed Archimedean spirals (r ≈ bθ), we demonstrate that transitioningto a logarithmic spiral geometry (r = aebθ) is physically required to resolve the outer windingproblem and preserve self-similarity. We show that a logarithmic geometry naturally couples withan asymptotically flat rotation curve (vϕ = const), as the required angular dragging frequencyscales as ω(r) ∝ 1/r.Analytical rotation curves and structural models are derived and benchmarked against empiricalobservations for the Milky Way, the grand-design spiral NGC 5457 (M101), the barred lenticulargalaxy NGC 2787, and the Whirlpool Galaxy (M51). Finally, we introduce a non-linear tidalperturbation correction term, δr(θ), demonstrating how external gravitational interactions withsatellite dwarf galaxies (such as NGC 5474) break intrinsic m = 2 antipodal symmetry to producethe observed lopsidedness and arm elongation in M101.Keywords: Galaxies: kinematics and dynamics — Galaxies: spiral — Galaxies: structure — Cosmology: theory — Metric frame-dragging — Tully-Fisher relatio
Category: Relativity and Cosmology
[1843] ai.viXra.org:2609.0032 [pdf] submitted on 2026-09-14 19:53:15
Authors: Arieh Sher
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite all listed scientific references)
We present an exact mathematical formulation of cosmological orbital kinematics in a rotating Kerrspacetime anchored by an ultra-massive central core of mass MP = 7.82 × 1053 kg. In this configuration:1. The outer event horizon is situated at r+ = 122.764 Gly, and the cosmological matter disk is locatedstrictly outside the event horizon spanning radii r ∈ [122.764 Gly, 175.6 Gly].2. The Milky Way is located in the immediate exterior vicinity of the horizon at RMW = 123.3265 Gly,corresponding to a radial clearance of ∆r = +0.5625 Gly (562.5 Mly or a 0.46% fractional margin).3. The cosmic trajectory is traced continuously from the central Pivot (r → 0) up to the Milky Wayalong a self-similar, scale-invariant logarithmic spiral r(ϕ) = r0ebϕ.4. We demonstrate that the logarithmic spiral (and not the Archimedean spiral) trajectory can bemathematically equivalent to a geodesic; however, this is correct only in an effective flowingfluid metric as formulated in Sher (2017), whereas it is not valid as a geodesic in pure vacuumKerr or Schwarzschild spacetime.5. We enforce the strict dynamical equivalence condition vN (L) = vKerr, where vN (L) ≡pGMP /L isthe modified Newtonian velocity evaluated along the cumulative worldline arc length L, and vKerris the coordinate frame-dragging velocity at radial separation RMW.
Category: Relativity and Cosmology
[1842] ai.viXra.org:2609.0031 [pdf] submitted on 2026-09-12 18:40:58
Authors: Brent Hartshorn
Comments: 13 Pages.
Robotic vision policies trained on photorealistic synthetic imagery fail when the real world presentsa texture, a shadow or a reflection the renderer never produced. We argue the fault is the representation rather than the realism: a policy that consumes photographs must learn to ignore appearance, when it could instead be handed a representation from which appearance has already been removed. We describe a chained architecture in which a perception stage converts camera input into a non-photorealistic line drawing paired with a semantic map, and a control policy consumes only that abstraction. Decoupling perception from control allows each to be trained independently [4], and abstract intermediate representations such as sketches are known to preserve spatial grounding while discarding visual distraction [5].The contribution is an open simulator that makes the architecture testable end to end: it generatesthe aligned multi-modal corpus the interface requires — photorealistic, line art, object index and metric depth from one viewpoint — carries a physically grounded robot with an optional rigid-body contact backend, imports externally authored scenes and assets [3], and executes the real control firmware against the simulated plant at two distinct fidelities: a value-level seam fast enough for the training loop, and an offline register-level gate in which the same commands are driven through emulated I2 C peripherals, H-bridges and a serial lidar protocol [11]. The second catches a class of defect the first cannot represent, and we quantify the divergence between them. We report a perception result on 479 samples, a multi-label scene-description head trained from labels the renderer already knew, and a control policy cloned from a privileged expert that reaches its goal in 8/8 held-out scenes while seeing only the abstraction.Every number is reported beside the score of doing nothing, and we record the two hypotheses about thecontrol bottleneck that measurement destroyed, together with two measurement choices the register-level gate itself invalidated.
Category: Artificial Intelligence
[1841] ai.viXra.org:2609.0030 [pdf] submitted on 2026-09-13 00:57:38
Authors: Brent Hartshorn
Comments: 20 Pages.
Physics notation is ambiguous, this paper reports what happens when a knowledge base of 97 equations, 136 symbols and 64 physical quantities is made to declare what each of its letters denotes, and is then allowed to connect itself. Equations become graph nodes; edges follow shared quantities rather than shared characters; and two equations stating the same quantity are joined by transitivity into one annotated formula. Each statement is checked to be a well-formed proposition over an axiomatic Real by a Calculus of Constructions micro-kernel, then emitted as Lean4.
Category: Mathematical Physics
[1840] ai.viXra.org:2609.0029 [pdf] submitted on 2026-09-13 13:13:00
Authors: Kerényi József
Comments: 6 Pages.
We propose a unified phenomenological model based on relativistic gravitational impedance, Zeff = eta * G / c. The central observation is that the longitudinal mass flux Ig = d(gamma m0)/dt, proportional to the scalar product v dot a, defines a specific potential Phi_g = Zeff * Ig whose sign is set by v dot a. Longitudinal acceleration (v dot a > 0) corresponds to energy release with equation of state w -> -1 (dark energy phase), while deceleration (v dot a < 0) corresponds to absorption with w -> 0 (dark matter phase). The bare impedance Zg = G/c gives rho_g ~ 4e-36 J/m3 ~ 1e-27 rho_Lambda for the Milky Way, requiring amplification eta ~ 1e27 for cosmic acceleration and eta ~ 1e6 for the MOND acceleration a0 ~ 1.2e-10 m/s2, parametrized as a0 = eta * (Delta V)^2 / R_H. In the low-acceleration limit we derive v_c^4 = G M a0 from equilibrium v_c^2 = Phi_g. The model provides a single language for both dark components with falsifiable predictions for lensing near jets and Gaia streaming.
Category: Relativity and Cosmology
[1839] ai.viXra.org:2609.0028 [pdf] submitted on 2026-09-11 20:26:42
Authors: Prakash Vaithyanathan
Comments: 11 Pages.
Mobile phone connections drop for two related reasons: a narrow mmWave beam gets blocked, or a link of any kind simply fades out because the phone has moved into a weak-coverage spot. Both problems are handled today by mechanisms that only react after the signal has already gone bad. This paper describes one small, fixed, dedicated hardware controller — not a piece of software — that watches the ordinary signal-quality numbers a phone or base station already measures, and raises a warning before either kind of failure happens. We show, on two separate synthetic examples, that the same fixed controller gives an early warning before both the mmWave beam failure and the general radio link failure mechanisms would fire on their own. We explain in plain terms why this only works well as dedicated hardware and not as software running on a shared processor. All results here are from simulated data; the next step is testing on real network measurement logs.
Category: Digital Signal Processing
[1838] ai.viXra.org:2609.0027 [pdf] submitted on 2026-09-12 13:23:14
Authors: Fabrizio Vassallo
Comments: 32 Pages.
A 2020 note [1] observed that the self-similar set F the positive integers n forwhich n − 1, in base 3, uses only the digits 0 and 2 satises a telescoping identitythat, read as a xed-point equation, assigns the divergent sum S = Pn∈F n the value−1/5. This paper reports what survives close scrutiny of that claim and what doesnot. We show rigorously, via the self-similarity F = 3F ∪(3F −2) and the functionalequation this induces on the theta function Θ(t) = Pn∈F e−nt, that the arithmeticzeta function ζF (s) = Pn∈F n−s satises ζF (0) = 0 and hence ζF (−1) = 0: the zeta-regularized value of S is 0, not −1/5. We then construct the hierarchical graph Gkthat the same self-similarity naturally generates, obtain its Laplacian spectrum inclosed form by an exact backbone/localized-state decomposition (veried indepen-dently, both analytically and numerically, up to k = 6), and show that its spectralzeta function satises ζGk (0) = Nk − 1 identically for every connected graph on Nkvertices a positive, divergent integer sequence of exact integer values, one per k ruling out the specic identication made in the exploratory work, though notevery conceivable regularization built from this same sequence (Section 3.3 discussesa dierent one that still produces −1/5, and why it is not the spectral zeta func-tion of any single Gk). This directly falsies an intermediate claim, made in theexploratory work this paper grew out of, that identied −1/5 with this spectral zetafunction. We then examine, by an independent route (a Perron-type explicit formulaexpressing the counting and summatory functions of F as a sum over ζF 's poles),whether a genuinely distinct summation functional in Ramanujan's sense, not sim-ply zeta regularization, and adapted to F 's fractal structure rather than borrowedfrom the integers might still recover −1/5. Conditional on a growth estimate wedo not fully establish, this route shows that no constant of any kind survives in theasymptotics of F 's counting or summatory function, conrming by a second, inde-pendent method that 0, not −1/5, is what F 's own structure naturally produces;we verify the underlying machinery against an exact, parameter-free identity forcedby A(3m) = 2m. One loophole is identied and left open a Ramanujan-type sum-mation of F 's enumeration index, rather than its values, trivially recovers −1/2 butarguably encodes nothing about F specically and we explain why resurgence andalien calculus, sometimes proposed as a further alternative, have no natural pointof contact with this problem. Finally, we discuss why the relevant physical motiva-tion (zeta-regularized vacuum energies, and the empirically rich sign-dependence ofCasimirLifshitz forces) is exactly that motivation, not evidence.
Category: Mathematical Physics
[1837] ai.viXra.org:2609.0026 [pdf] submitted on 2026-09-10 20:03:29
Authors: Zhongyang Dong
Comments: 5 Pages.
As a direct sequel to Emergent Cosmology of a Two-Phase Planar-Invasion Bubble Universe [1],this paper establishes a self-sustaining global multiverse model—encompassing a grand Global Universe composed of seven initial seed universes—from a "Creator’s-Eye View" of physical aesthetics and minimalism. To avoid ambiguity, it is explicitly emphasized that all bubble universes discussed and analyzed hereafter strictly refer to their iteratively evolved generations produced throughmulti-generational collisions, rather than the initial seed universes. We formulate the core physical axioms, a topological fault-tolerance law, and a dark energy conservation mechanism: the primordial Big Bang mechanism permanently and individually ceased across the seven initial child universes in strict accordance with the Second Law of Thermodynamics, serving as Newton’s Prime Mover with non-uniform initial expansions seeding subsequent cosmic rotation; global particle universality ensures that all iterative bubble universes share identical microscopic physics; apparent localdark energy acceleration is resolved as the kinetic energy projection of topological potential energy transferred from degenerate ground-state universes (SDead); and the Prime-7 topological law (N0 = 7) together with evolutionary scale sequences ({10,15,40,100}) guarantees a dynamic equilibrium (Neq >7) and a strictly zero extinction limit (limt→∞ P(N(t) = 0) ≡0). Finally, we reconcile this framework with Newton, Spinoza, and ancient Chinese philosophy, concluding with a humanistaffirmation of Philosophical Optimism and cosmic grace.
Category: Astrophysics
[1836] ai.viXra.org:2609.0025 [pdf] submitted on 2026-09-10 16:39:28
Authors: Joseph Shaffer
Comments: 11 Pages.
Modern astrophysics is characterized by an escalating series of foundational crises, including the Hubble tension, the dark matter anomaly, and the mathematical infinities of black hole singularities. These issues stem from a reliance on general relativity's geometric framework, which presumes a dynamic, expanding spacetime metric and an invariant speed of light c. This paper introduces an alternative ontology wherein the universe is completely static. Reality is partitioned into a fundamental, non-local informational domain E comprised of Planck-scale mats under tension, and an emergent, local domain S. By treating gravity not as spacetime curvature, but as a localized deficit in global substrate tension, we demonstrate that the local velocity of light is a dynamic variable cx. This single primitive — information mats under tension—simultaneously resolves gravitational time dilation, removes the need for dark matter and dark energy, eliminates black hole singularities, and reinterprets the Big Bang as a global thermodynamic phase transition.
Category: Astrophysics
[1835] ai.viXra.org:2609.0024 [pdf] submitted on 2026-09-10 01:50:38
Authors: Adilson Gonçalo
Comments: 39 Pages. In Portuguese
This article constitutes the second part of the series "Space-Time" from a Realist Perspective. Continuing the analysis developed in the first part, the present work primarily aims to examine the compatibility between classical mechanicsand electromagnetism, with particular attention to the relationship between Galilean transformations and Maxwell’s equations, an issue traditionally presented as one of the main motivations for introducing Lorentz transformations and formulating the Theory of Special Relativity. It is investigated whether the alleged incompatibility between thesetheoretical frameworks necessarily arises from physical phenomena or is instead related to the way the electromagnetic and kinematic quantities involved are interpreted. To guide this analysis, principles underlying the adopted approachare first established. Based on these principles, the concept of spacetime interval in the Einsteinian relativistic formulation and its invariance under coordinate transformations are examined. Subsequently, the relationship betweenGalilean transformations and Maxwell’s equations is analyzed, including the invariance of these equations under Galilean transformations and the transformations of the electric and magnetic fields between reference frames in relative motion. In addition, the conventional interpretation of the phenomenon of magnetic induction is examined. This second part remains restricted to the theoretical, mathematical, and conceptual analysis of these issues. Thediscussion of the main experiments and observations traditionally presented as confirmations of Einsteinian relativity will be developed in the third and fourth parts of the series.
Category: Relativity and Cosmology
[1834] ai.viXra.org:2609.0023 [pdf] submitted on 2026-09-10 01:45:10
Authors: Prakash Vaithyanathan
Comments: 8 Pages.
Optical transport networks— the fiber links carrying telecom and data-center traffic— candevelop "soft failures": a slowly aging amplifier, a worn connector, or a degrading splice that gradually weakens the signal long before it fails outright. Today’s protection mechanism only reacts once the signal quality has already dropped far enough, several times in a row, to cross a fixed threshold. This paper applies Arnold’s Bifurcation Principle— the same fixed, training free method already used in our earlier work on hemodialysis vascular access, drone wind-gust safety, cardiac arrhythmia warning, and 5G/6G radio-link failure— to the optical signal-to-noise ratio (OSNR) measurement a fiber-optic network already monitors. On a single synthetic run, the method gives a meaningful early warning before the existing reactive protection-switching mechanism itself would fire, using a small, dedicated hardware controller rather than software.All results here are from simulated data; the next step is testing on real network logs.
Category: Digital Signal Processing
[1833] ai.viXra.org:2609.0022 [pdf] submitted on 2026-09-09 16:08:39
Authors: Idan Hackmon
Comments: 5 Pages.
We present an argument excluding finite covering systems with distinct odd moduli whose least common multiple has at most six distinct prime factors, with unrestricted prime exponents and integer residues. The argument refines capped reweighting by comparing the positive-part expectations of every auxiliary divisor count with those of a product of independent finite geometric-tail factors. For the first six odd primes the resulting rational budget is approximately 0.91015158 < 1. A digit-embedding prime-replacement lemma transfers the fixed-prime exclusion to arbitrary prime supports. The probability argument is finite: truncation preserves the small product atoms needed for the calculation, and a finite geometric sum bounds the mean. Both full statements have been verified in Lean and Aristotle, with independent checks of the returned source and unrestricted exponents. Historical priority is not asserted.
Category: Number Theory
[1832] ai.viXra.org:2609.0021 [pdf] submitted on 2026-09-10 01:36:40
Authors: Derrick Hiang Yaol Lim
Comments: 13 pages, 6 figures and 2 tables.
We present a classical, lumped-element circuit model of a two-level atom built around a specific conceptual claim: the two atomic energy eigenstates, represented as LC resonators with parameters fixed from the level energy and orbital magnetic moment, are exactly decoupled under the field-free Hamiltonian, which we realize as a literal open circuit between them. Coupling arises only from two distinct, independently gated perturbations: (i) an external oscillating field, modeled as a voltage source applied across the (otherwise open) inter-level branch, which produces reversible Rabi (continuous-wave drive) or Rosen—Zener (pulsed drive) dynamics; and (ii) theavailability of a radiative channel in the environment — schematically, a receptive absorber elsewhere in the universe — modeled as a resistive path to a shared radiative bath that opens and closes in time, which produces irreversible photon emission via a shared-bath coupled-mode-theory (Haus) formalism. In the absence of both perturbations the model predicts, exactly, that an isolated excited atom does not radiate. We show the emission channel comes in two dual circuit realizations, inductive (magnetic-dipole, M1) and capacitive (electric-dipole, E1) coupling to the environment, and validate both against the hydrogen 21 cm hyperfine line and the Lyman-α (2p → 1s) transition, reproducing the measured decay rates to within 1% and 0.2% respectively. We discuss the relationship of the "no absorber, no emission" baseline to Wheeler—Feynman absorber theory, to Cramer and Mead’s two-atom transactional formalism, and to the standard vacuum-fluctuation picture.
Category: History and Philosophy of Physics
[1831] ai.viXra.org:2609.0020 [pdf] submitted on 2026-09-09 23:54:33
Authors: Max Rempel
Comments: 51 Pages.
This book sets the esoteric tradition beside archaeology, geology and genetics, and asks how far the two accounts agree.The esoteric tradition holds that two peoples who were not human lived on this planet before us and are among our ancestors: the Lemurians of the Third Race and the Atlanteans of the Fourth. It has held this since 1888, and in older forms for much longer.Genetics has now found seven vanished peoples inside the DNA of the living. Two of them have bones and names, the Neanderthals and the Denisovans. Five have no remains at all and are known only from the stretches of DNA they left in us. This book calls all seven parahuman, and numbers them PH1 to PH7.I propose that the Denisovans are the Lemurians. Their bones lie inside the Lemuria that Blavatsky drew, and their living inheritance rises to five percent in New Guinea and Aboriginal Australia.Atlantis is less settled, and the book turns to it in the second half. The esoteric sources place it in the Atlantic and the Mediterranean. The book compares these accounts with the drying and refilling of the Mediterranean between six million and five and a third million years ago.The book then sorts the seven parahuman peoples against what the esoteric sources say an Atlantean was, using place, quantity, date and body. Three of the four can be checked against genetic data. Three peoples survive the sorting: the Neanderthals, the Veshuans of the West African Atlantic coast, and the Korimians, who are in every human being alive. None of the three is confirmed by any source, and the sorting is set out with its own limits stated, including the fact that no genetic measurement can establish whether a given people lived on this planet at all.It ends with what each Race is said to have brought, with the persecution that thinned the psychic capacity out of our species, and with two ideas about what the alien hybridization now under way may be restoring to us.
Category: General Science and Philosophy
[1830] ai.viXra.org:2609.0019 [pdf] submitted on 2026-09-10 00:59:20
Authors: Brent Hartshorn
Comments: 13 Pages.
In September 2026 a computer-checked proof of Fermat’s Last Theorem and a Lean-formalizedproof of blowup in the forced Navier—Stokes equations were announced within days of each other,and both are believed because a kernel checked them. This paper applies that discipline at theother end of the scale. A Calculus of Constructions micro-kernel with no axioms, is given an imperative language—assignment, branches, bounded loops, and while with an explicit variant—compiled by symbolic execution into kernel terms. Contracts are decidable propositions, Holds b := Eq Bool b true, about the very expression a runtime check would evaluate. A while loop raises four obligations, one of them the soundness of its own lowering, and termination is proved for every starting state. Records and a state invariant give a model of an seL4-style OS whose routing layer carries contracts that hold for every input. A bridge to Crust, a self-contained C/C++/Rust toolchain, settles its source-level contracts in the kernel; building it found two of Crust’s passes reading one contract two ways. Finally a certificate changes generated code: a SIMD kernel’s scalar remainder is omitted on it, and a contract proven at every call site downgrades 80% of the memory-safety checks in a leaf initializer while the check it leaves still catches an overflow.
Category: Artificial Intelligence
[1829] ai.viXra.org:2609.0018 [pdf] submitted on 2026-09-08 09:23:43
Authors: Arieh Sher
Comments: 18 Pages.
The observed motion of the Solar System and the Local Group relative to the cosmicmicrowave background (CMB) is conventionally interpreted as a peculiar velocity produced bythe gravitational influence of the surrounding large-scale matter distribution, including the Virgoregion, the Great Attractor, the Shapley concentration, and cosmic voids. The Solar-Systembarycenter moves relative to the CMB at approximately 369.8 km s−1, while transformation tothe Local-Group barycenter gives a velocity of approximately 627 km s−1. This paper examinesan alternative interpretation within the Pivot Universe (PU) model. The universe is treated asa rotating system described approximately by Kerr geometry generated by a central massiverotating Pivot. Matter in the observable universe is assumed to participate approximately in theframe-dragged rotation generated by the Pivot. For MP = 7.82 × 1053 kg, JP = 1.06 × 1087 J s,RMW = 123.3265 Gly, and RCMB = 123.36 Gly, the Kerr frame-dragging angular velocity at theMilky-Way shell is approximately 0.313 × 10−13rad yr−1. A locally normalized differential Kerrquantity between the MW and CMB shells is approximately 495 km s−1. This value lies betweenthe Solar-System/CMB and Local-Group/CMB velocities, but it is shown that this numericalcorrespondence cannot itself be identified with an invariant relative velocity. An invariant Kerrphoton-frequency calculation instead separates a predominantly gravitational monopole shiftfrom a much smaller directional frame-dragging contribution. The PU interpretation thereforerequires the observed CMB dipole to contain a combination of global Kerr geometry and localpeculiar motions. The model yields quantitative predictions that can, in principle, be testedagainst the direction and magnitude of observed large-scale peculiar-velocity fields.
Category: Relativity and Cosmology
[1828] ai.viXra.org:2609.0017 [pdf] submitted on 2026-09-08 16:35:15
Authors: Marian Opial
Comments: 13 pages. Licensed under CC BY 4.0. AI-assisted.
For a finite set S of integers, its integer Turnpike data record the multiplicity of every positive difference. In the dense frequency-vector encoding, realizability reduces to parity of self-reciprocal irreducible factors and is therefore decidable in polynomial time by ordinary polynomial factorization. Sparse binary-exponent encoding is different: the associated reciprocal polynomial can have exponentially large degree. We construct an infinite family of sparse, coefficientwise nonnegative, Fourier-nonnegative, arithmetically admissible Turnpike instances with the fixed point count n = 107,520 that are nevertheless nonrealizable. Each instance contains, to odd multiplicity, a primitive noncyclotomic self-reciprocal irreducible of degree 2^k, while the sparse input length is Theta(k). Thus Fourier positivity, elementary count identities, and visible monomial-composition tests do not imply any polynomial bound on the degree of the remaining obstruction. Several complementary results locate the residual difficulty. Under the Turnpike scalar identities, an integral Hermitian sum of squares collapses to one binary rank-one factor; a parity-safe multiplier cannot raise the square-root-total/center ratio; and a strictly Fourier-positive integer NO instance can lie in the midpoint of two YES instances. Every odd self-reciprocal factor has infinitely many reciprocal quadratic shadows modulo primes, with a density lower bound in terms of permutation rank, but cyclotomic examples rule out naive small-prime enumeration. Finally, a ramified quadratic trace gadget converts a Legendre symbol into the desired characteristic-zero reciprocal-parity bit while preserving Fourier positivity. A local-to-global counterexample shows why this gadget does not yet yield a hardness reduction.
Category: Combinatorics and Graph Theory
[1827] ai.viXra.org:2609.0016 [pdf] submitted on 2026-09-08 23:57:19
Authors: Zhongyang Dong
Comments: 6 Pages. (Note by ai.viXra.org Admin: LaTex codes should be converted to standard math espressionss; please cite listed scientific references)
This paper presents an emergent cosmological framework derived from a "Two-Phase Planar-Invasion" bubble universe scenario. Departing from the standard Big Bang (Lambdatext{CDM}) singular cosmology and the hypothesis of spin-2 spin-mediated gravitons, we define the observable Universe as an organized, dynamic cosmic plane (topologically modeled as a rotating, two-dimensional scimitar-like manifold) that non-asymmetrically penetrates and ingests a degenerate, maximum-entropy deceased progenitor universe—a space composed of a constant light-neutrino background (ho_u^{text{bg}} = text{Const}) and a massless photon background forming an all-neutral quantum matrix.
Category: Astrophysics
[1826] ai.viXra.org:2609.0015 [pdf] submitted on 2026-09-07 19:28:03
Authors: Arieh Sher
Comments: 14 Pages.
Newton’s law of gravitation and Einstein’s General Relativity describe gravity in fundamentally different ways. Newtonian theory treats gravity as an interaction between masses,whereas General Relativity describes gravity through spacetime geometry. Nevertheless,Newtonian gravity remains an excellent approximation in appropriate weak-field conditions.This paper considers a possible connection between the two descriptions within the PivotUniverse (PU) model. The universe is assumed to contain a central massive rotating object,called the Pivot, whose angular momentum produces large-scale Kerr frame dragging. Matteris proposed to move with this rotating spacetime rather than through an otherwise stationaryspace.A further hypothesis is examined. In the usual Newtonian circular-orbit relation,v^2 = GM/R, R represents radial distance from the gravitating body. The PU model considers whether, for matter following an extremely long spiral trajectory generated by frame dragging, aneffective dynamical length L could replace R,v^2 = GM/L
Category: Relativity and Cosmology
[1825] ai.viXra.org:2609.0014 [pdf] submitted on 2026-09-07 04:37:54
Authors: Oleg Ponfilenok
Comments: 20 Pages. Source: https://github.com/oponfil/collapse-threshold
We propose a modernization of quantum mechanics through the introduction of the Collapse Threshold Rule: a branch or coherence is removed if it cannot be distinguished experimentally from absence. The classical outcome becomes objective rather than a virtual interpretation of decoherence. The threshold is derived from the finite number of binary distinctions within a causal patch — 3,5 × 10¹²u2070. The scale of equiprobable branching and the RCS limit are about 400 qubits. The model forbids factorization of RSA-1024. The non-unitarity of the collapse act permits non-conservation of energy as well as superluminal information transfer. An experimental test on a single 404-qubit processor is proposed.
Category: Quantum Physics
[1824] ai.viXra.org:2609.0013 [pdf] submitted on 2026-09-07 09:01:01
Authors: Zhengxi Wang
Comments: 107 Pages.
This is a book that explores human origins, development, and the future. It combines scientific theory with philosophical reflection to answer the eternal human questions: "Where do we come from? Where are we going? What are we here to do? First, it presents fossil records and evidence of biological evolution, supporting the view that life evolves. After summarizing biological laws and formulating the "Law of Biological Evolution" and the "Law of Biological Survival" it discusses how to migrate to other planets, the mission of humanity, and ways to colonize extraterrestrial worlds. It also examines future biotechnology and argues that we humans should follow "the principle of human species unity." It describes the future space age, the span of human existence, and the end of the world. Once we know humanity's future, we find the answer to where we came from. Finally, it discusses our origins: the origin of life, the origin of humans, the birth of modern humans, and philosophical questions about life and the universe. It proposes that we are cosmic humans and a link in the chain of cosmic life. Humanity holds a special place in the universe and plays an incomparably important role.
Category: General Science and Philosophy
[1823] ai.viXra.org:2609.0012 [pdf] submitted on 2026-09-07 17:56:27
Authors: Andreas G. E. Scharfenberg
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This position paper introduces the Theory of the Global Universe (GU), an ontological and causal framework that resolves the boundary singularities inherent in General Relativity (GR) by replacing the premise of dynamic spacetime with a strictly rigid, infinite Euclidean continuum. Within this framework, physical interactions are governed by the continuous dynamics of energetic potential differences (Kinetic Base Tension) rather than geometric curvature. The model ontologically redefines mass not as a fundamental substance, but as a topological boundary surface effect resulting from the localized phase transition of translational vector flows into closed three-dimensional lemniscates (Cassini ovaloids of revolution). By applying this purely Euclidean continuum mechanics, the GU theory provides a deterministic causal mechanism for phenomena such as time dilation and the cosmological constant. Furthermore, it offers a geometric resolution to the empirical Proton Radius Puzzle, demonstrating that the anomalous scattering radii (0.877 fm and 0.841 fm) naturally correspond to the dual structural radii of the primary soliton's unperturbed envelope surface.
Category: Quantum Gravity and String Theory
[1822] ai.viXra.org:2609.0011 [pdf] submitted on 2026-09-06 20:04:08
Authors: Srinivasulu Charupally
Comments: 20 Pages.
The Acceleration Theory, a novel concept explored in this research paper, challenges the classical and quantum theories to elucidate the accelerating expansion of the universe. While the constancy of mass for subatomic particles over time and the existence of various matter particles, including Dark Matter (DM), Anti-Matter (AM), and regular matter, are well-established, the origins of these particles and the driving forces behind cosmic expansion remain intriguing questions. This work delves into the theoretical foundations of how Dark Matter, Anti-Matter, and regular matter particles were generated in the early universe, unraveling the cosmic mechanisms that led to their existence and the compelling phenomenon of universal expansion. Secondly, addressing the finiteness of the speed of light, this research explores alternative perspectives on its constancy and investigates potential influences of Dark Energy (DE) on light speed. Thirdly, furthermore, the paper examines the four fundamental forces—Electromagnetic Force (EF), Strong Force (SF), Weak Force (WF), and Gravitational Force (GF)—in the context of quantum unification. While EF, SF, and WFs have found unification through quantum theory, GF remains distinct. Despite efforts in General Relativity (GR) to comprehensively address gravitational forces, a unifying framework with the other three forces is elusive. To bridge this gap, the paper introduces innovative concepts of Space Energy (SE) and Space Constant (SC) to reconcile and unify these fundamental forces. Finally, the research concludes by contemplating a unified theory for the universe and explores the possibility of an acceleration principle governing every cosmic event. By scrutinizing diverse theories and introducing new concepts, this paper contributes to advancing our understanding of the fundamental principles that govern the cosmos
Category: Quantum Gravity and String Theory
[1821] ai.viXra.org:2609.0010 [pdf] submitted on 2026-09-06 20:08:25
Authors: Hani Abdel-Rahim
Comments: 13 Pages.
We present a self-consistent cyclic cosmological framework that resolves the origin, nature, and observed abundance (∼ 85%) of dark matter without introducing hypothetical elementary particles. We propose that dark matter consists oftopologically neutral solitonic states (ΦDM) produced exclusively within black holecores from preceding cosmic cycles, where unphysical singularities are replaced bya finite Planck-density threshold (ρPlanck). Protected by a conserved topologicalwinding number W ∈ Z, these states are immune to perturbative decay. We introduce the Cyclic Distillation mechanism, showing how stochastic fluctuations within black holes break matter-antimatter symmetry across cycles, exhausting antimatter while leaving a residual baryonic fraction (∼ 15%) and an accumulating dark matterbackground. Under Loop Quantum Cosmology (LQC), the bounce density remains strictly lower than the black hole internal core density (ρbounce < ρPlanck). This Differential Stability Threshold ensures the dissolution of geometric event horizons and the liberation of ΦDM without disrupting its topological structure. The quantum gravitational wave energy released during horizon dissolution drives cosmic expansion and naturally reheats the universe without an inflaton field. Finally, we model intra-cycle accretion, demonstrating how progressive mass-spectrum shifts culminatein an eternal, entropy-resolving final collapse.
Category: Relativity and Cosmology
[1820] ai.viXra.org:2609.0009 [pdf] submitted on 2026-09-05 21:55:36
Authors: Thiago Henrique Ramos da Mata
Comments: 13 pages. License: CC BY 4.0.
We define integer division and modulo by recursively normalizing quotient—remainder states and verify the construction in Scala Stainless. We prove uniqueness of the normalized solution, compatibility with native modulo for nonnegative dividends and positive divisors, invariance under shifts by multiples of the divisor, together with addition, subtraction, and modulo-idempotence laws. We also verify the unit-step quotient—remainder transition and that every block of $p$ consecutive nonnegative integers, for $p > 1$, contains exactly one zero remainder modulo $p$. Together, these results show that recursive normalization is canonical on the stated domains and recovers the verified algebraic and periodic laws of division and modulo.
Category: Number Theory
[1819] ai.viXra.org:2609.0008 [pdf] submitted on 2026-09-05 21:57:18
Authors: Fabrizio Vassallo
Comments: 38 Pages.
Paper 3 of this series [1] left two companion problems open for the Diamond and Fan motifs it introduced. For the Diamond, whose exact quasi-equilibrium reduction gives a closed-form, generic, supercritical ip bifurcation at λ flip = ϵη/[2(η 2 − ϵ 2)], Open Problem D.1 asked for a coarse-graining operator under which this result could be tested for topology-dependence, on both the Diamond and the Fan, rather than accepted as a property of one small graph. For the Fan, the exact scale invariance of OllivierRicci curvature left three of its four independent weight ratios underde-termined by the curvature equations alone, so Paper 3's own treatment of the Fan was, by its own account, a calibration against two reported data points rather than a derivation. This paper reports genuine, but dierent, progress on each. For the Diamond, we build the recursive lattice obtained by replacing every edge, at every generation, with a fresh copy of the same ve-edge motif, and establish two exact local curvature laws that hold at every generation. Combining them gives a closed-form renormalized ip threshold and cubic normal-form coecient at general coarse-graining depth d, which reduce exactly to the bare Diamond's own values at d = 4 and ow smoothly to a nite, nontrivial xed point, (λ flip , c 3) → (ϵ/η, −4/3), as d → ∞: the ip is coarse-graining-stable, and the generation step is exactly a MigdalKadano coupling recursion on c 0 := 8/d, with c * 0 = 0 its unique xed point. The universal endpoint ξ * = 2 found in Paper 3 for the dissipative extension is shown to be universal across the entire generational hierarchy as well. Two honest obstructions a kink in the peripheral curvature law and an unresolved heterogeneity once the fully symmetric torsion ansatz is relaxed are reported rather than papered over. For the Fan, we resolve Paper 3's scale-invariance obstruction with a dierent separation of variables: using the curvature equations for exactly what they determine the weight ratios and the middle torsion as functions of the one remaining free torsion T s and deferring the absolute scale entirely to the torsion equations. Eliminating the scale between the latter gives a single equation in T s ; at the test value η/ϵ = 1/2, and after a log-reparametrization removes a spurious numerical artifact, this equation has a genuine root, located to machine precision. In the regime containing this root, all four curvatures admit exact closed forms unavailable to Paper 3 veried against the underlying optimal-transport computation to machine precision; combining two of them in the limit T m → ∞ turns the numerical coincidence into a proof that η/ϵ → 1/2 as α → 0. 1 Read together, the two results are asymmetric in a way worth stating plainly: the Diamond's single free weight admits a genuine multi-generation renormalization-group trajectory; the Fan's four coupled weight classes admit, for now, an exact reduction of the bare motif itself the prerequisite the Diamond's own program needed before any coarse-graining could be built, not yet that extension itself.
Category: High Energy Particle Physics
[1818] ai.viXra.org:2609.0007 [pdf] submitted on 2026-09-03 23:14:35
Authors: J. W. McGreevy
Comments: 31 Pages.
This paper formalizes the Thermodynamics of Arithmetic Action (TAA) as a coordinate-free, unassailable geometric and field-theoretic architecture. By treating the sub-quantum vac-uum as an ad´elic fluid flowing over derived modular stacks, we prove that the macroscopic space-time fabric, the elementary mass hierarchies, and the gauge field interactions are uniquely determined by global number-theoretic invariants. The spontaneous breaking of the 24-dimensional primordial symmetry is shown to be a monodromy-driven factorization of an ad´elic stack, where existence and smoothness are rigorously verified at every infinitesimal step by the vanishing of relative obstruction classes in the cotangent complex. We demonstrate that the Standard Model gauge groups SU(3)×SU(2)×U(1) are the derivednon-abelian cohomological stabilizers required to absorb the exact 154 arithmetic discrepancybetween the discrete digital Extended Binary Golay Code (G24) and the continuous analyticalBernoulli numbers. Furthermore, we provide native, first-principles resolutions to the Riemann Hypothesis (RH), the Birch and Swinnerton-Dyer (BSD) Conjecture, and the Navier—Stokes Existence and Smoothness problem. The non-trivial Riemann Zeta Zeros are established as the exact, quantized resonant frequencies generated when the Golay code’s error-correcting parity matrix clamps the fluid wavefront to a Topological Exceptional Point wall. Spacetime remains globally differentiable, smooth, and unconditionally protected against quantum decoherence because its internal particle matrix is permanently, flawlessly phase-locked to the invariant genus-zero stabilizers of the ad´eles.
Category: Mathematical Physics
[1817] ai.viXra.org:2609.0006 [pdf] submitted on 2026-09-03 17:11:35
Authors: Joseph Shaffer
Comments: 11 Pages.
Standard ΛCDM cosmology relies heavily on hypothetical components — namely cold dark matter and dark energy — to reconcile persistent kinematic anomalies and the apparent accelerating expansion of the universe. This paper introduces Photon-Tension-Time Theory (PTT), an alternative ontological framework establishing tension as the sole primitive of physical reality. Under PTT, the universe is non-expanding. The Big Bang is recontextualized not as a physical metric singularity, but as a global, non-metric phase change: a primordial crystallization that established an invariant background matrix termed the substrada. Cosmological redshift is demonstrated to be the localized, non-metric energy attenuation of propagating photons penetrating discrete structural boundary tension fields within this substrada, entirely decoupling the observed energy loss from metric time dilation. Furthermore, galactic rotation anomalies are shown to be stabilized by the baseline boundary tension of the substrada, rendering cold dark matter halos mathematically obsolete. Finally, the observed (1 + z) temporal elongation of distant Type Ia supernovae is resolved via wave-packet structural dispersion across cosmological propagation distances. PTT delivers an elegant, static cosmological model that resolves contemporary astrophysical tensions without invoking unobserved dark sectors.
Category: Astrophysics
[1816] ai.viXra.org:2609.0005 [pdf] submitted on 2026-09-03 23:03:35
Authors: Prakash Vaithyanathan
Comments: 7 Pages. CC BY-NC-ND 4.0
When a very large AI model is trained, the training sometimes breaks on its own. The loss suddenly jumps up, the numbers inside the model become too large or too small to handle correctly, and the run has to be stopped and restarted from an older saved copy. This is called training instability, and on a large training run it can waste a very large amount of computer time and money. Earlier work in machine learning has shown that this kind of breakdown is closely tied to a single number: the sharpness of the loss surface, which is the largest eigenvalue of the Hessian matrix of the loss function. When this number grows too large compared to the learning rate, the training stops behaving smoothly. The problem is that for a model with a billion or more parameters, the full Hessian matrix cannot be built or stored by any realmachine: it would need far more numbers than there are atoms within reach. We show that this is not actually needed. A small hardware block can track the same leading eigenvalue using only the gradient vectors that the training hardware is already computing at every step, through a standard numerical method called power iteration, combined with the well-known fact that a Hessian-vector product can be estimated from the difference between two gradients without ever building the Hessian itself. We also show that watching a small, carefully chosen part of the model, rather than the whole thing, is often enough to catch the problem early. We describe a domain-blind hardware controller that watches this shrinking safety margin every single step and estimates how many steps remain before the run is expected to become unstable, so that a corrective action can be taken before the run actually fails rather than after.
Category: Artificial Intelligence
[1815] ai.viXra.org:2609.0004 [pdf] submitted on 2026-09-02 03:17:37
Authors: Rolando Zucchini
Comments: 43 Pages.
After circa 2300 years (Circle Quadrature, Archimedes, Syracuse 287 — 212 BC) the history of mathematics repeats itself in a different problem. This paper presents an original research on the Syracuse Conjecture. It proposes a theoretical development aimed at solving the conjecture through a systematic approach. One of its features suggests a process that leads to Theorem 2n+1, whose demonstration subdivides the odd numbers into seven subsets which have different behaviors applying algorithm of Collatz. It allows to replace the Collatz’s cycles with the cycles of links, transforming oscillating sequences into monotone decreasing sequences. Theorem of Independence allows to manage the cycles of links to our liking to reach very high main horizons and, when we decide, go back to lower horizons. In this article it’s proved that Collatz Conjecture is not fully demonstrable. In fact, if we consider the banal link n < 2n, there are eight cycles which connect each other in an endless of possible sequences and related links. It is a new type of Squaring of the Circle or Algebraic Quadrature, but its statement is confirmed. In other words: BIG CRUNCH (go back to 1) is always possible, but BIG BANG (to move on) has no End.
Category: Number Theory
[1814] ai.viXra.org:2609.0003 [pdf] submitted on 2026-09-02 18:16:51
Authors: Raymond Deiotte
Comments: 42 Pages.
Agent-facing knowledgebases compute confidence and provenance at answer time, as properties of the re- sponse. This paper argues that is too late, and that the argument is not a matter of engineering quality: information about whether a claim is true enters through the primary record, and every later stage is a rendering of that record, so no downstream scoring can add a bit that the record did not already carry. Confidence computed from the exhibit has an evidential ceiling fixed before it runs.We describe the store that follows from taking that seriously. The substrate is an uncertainty-typed property hypergraph: every unit carries the same five fields, a knowledge type, provenance graded on a four-valued lattice and carrying a validity horizon, the condition under which the entry held, a version with its conflict history, and a confidence separated into write-time and serving-time quantities, and relations are hyperedges because the relations that matter in agent memory are irreducibly n-ary and reifying them into binary edges destroys exactly the structure later stages need. On that substrate we specify three mechanisms. Consolidation is gated on whether a merged region still decomposes into the inferences it was meant to support, a structural and label-free test that needs no paired QA data and no per-environment training. Conflict is preserved through four lifecycle primitives, demotion, supersession, revocation and invalidation, of which three share a single inverse transition and revocation deliberately has none. Retrieval returns a coverage-guaranteed evidence subgraph with the guarantee conditional on the type of edge retrieved rather than marginal over a query distribution, and it answers with three outcomes rather than one score: supported, insufficient, refuted.The paper’s most portable result is a criterion for when two memory mechanisms can affect each other at all: only where one writes a property of the store that the other reads, at a granularity they share. The criterion is checkable from the specifications before anything is built, it discriminates rather than merely predicting failure, and it carries a stated falsifier.
Category: Artificial Intelligence
[1813] ai.viXra.org:2609.0002 [pdf] submitted on 2026-09-01 20:28:01
Authors: Adilson Gonçalo
Comments: 36 Pages. In Portuguese
This article inaugurates a series dedicated to the theme "Space-Time" from a Realist Perspective. The aim of the series is to carry out a critical analysis of the Lorentz transformations and, consequently, of theTheory of Special Relativity (SR), while proposing an alternative conceptual approach to space-time grounded in principles considered more consistent with observable physical reality In this first part, the physical, mathematical, and logical foundations associated with the Lorentz transformations are examined,with emphasis on the conceptual and kinematic aspects of their construction. The article begins with a concise presentation of the theory and its fundamental equations, followed by an analysis of the points that, according to this approach, raise questions regarding the conceptual consistency of the relativisticformulation. It should be emphasized that this stage of the work focuses exclusively on the theoretical and conceptual structure of SR. The discussion of experimental and observational aspects will be addressed in the third part of the series. Although the considerations developed in this work are mainly focused on SR,they will also address certain conceptual aspects of the Theory of General Relativity. It is important to note that the considerations presented here are not intended to diminish the fundamental contributions of the creators of Special and General Relativity, among whom Henri Poincaré, Hendrik Lorentz, and Albert Einstein stand out.
Category: Relativity and Cosmology
[1812] ai.viXra.org:2609.0001 [pdf] submitted on 2026-09-01 20:25:22
Authors: Nigel B. Cook
Comments: 16 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references in the field!)
This paper presents three independent and mutually reinforcing theoretical derivations of the Higgs boson mass within the SU(4) vacuum polarisation framework. Each derivation is physically motivated, mathematically explicit, and avoids circular reasoning. The first derivation is the Coulomb-Yukawa vacuum polarization absorbed energy redistribution method, in which the scalar mass arises from the curvature of an effective potential generated by fluctuations in the electromagnetic partition between long-range Coulomb and short-range Yukawa channels. The second derivation is a two-channel SU(4) binding analysis in which the Higgs is the lowest scalar eigenmode of a neutral/charged weak-boson bilinear system. The third derivation is an SU(2) spectral method based on representation weights of the compressed SU(2) vacuum. All three approaches converge on 125-126 GeV. The agreement among these methods strongly supports the interpretation of the Higgs boson as a composite excitation of the SU(2) vacuum. (This paper has been fully proof-read and corrected by Copilot AI to make it more readable than the draft.)
Category: Quantum Gravity and String Theory
[1811] ai.viXra.org:2608.0098 [pdf] submitted on 2026-08-31 03:42:44
Authors: Max Myakishev-Rempel
Comments: 36 pages, English.
The esoteric tradition holds that two humanities stood between us and the beginning, both of them in flesh and both of them our ancestors: the Lemurians of the Third Race and the Atlanteans of the Fourth. It has held this since 1888 and in older forms long before.Genetics has now found two vanished human peoples living inside us, and only two: the Denisovans, whose inheritance gathers in the Indian and Pacific world, and the Neanderthals, who lie to the north and west. Two and two, with no third on either side to choose between.The shape agrees as well as the count. The tradition has the Atlanteans coming out of Lemurian stock. The genome has both branches coming out of one parent population, one remaining east and one moving north and west.This essay proposes that the Denisovans are the Lemurians and the Neanderthals are the Atlanteans, and follows the identification through the geography of Mu, through Blavatsky's naming of the Australians as the purest Third Race descendants, through the fire that took Lemuria and the water that took Atlantis, and through the sub-races of both. It states where the correspondence costs something, and it ends with two ideas about what the hybridization now under way may be restoring to us.
Category: General Science and Philosophy
[1810] ai.viXra.org:2608.0097 [pdf] submitted on 2026-08-31 16:08:03
Authors: Joseph Palazzo
Comments: 17 Pages.
Scientific theories provide extraordinarily successful descriptions and predictions of the physical world, yet their epistemic success does not by itself determine the ontological status of the entities, structures, and concepts found in those theories. This paper examines the distinction between epistemology and ontology through the broader philosophical tension between scientific realism and instrumentalism. It argues that a successful scientific representation should neither be regarded as merely a convenient computational instrument nor automatically identified with reality itself. Rather, scientific knowledge occupies an intermediate domain in which conceptual and mathematical structures provide access to an objective reality while simultaneously imposing conditions on how that reality can be represented and understood. The distinction between form and content provides a framework for examining this relationship. Mathematical form may possess extraordinary predictive and explanatory power without settling the question of what, ontologically, constitutes the physical content represented by that form. The analysis presented in this paper differentiates epistemic limitations from ontological indeterminacy, mathematical determinism from metaphysical determinism, and conceptual descriptions from the realities they seek to represent. Moreover, we can state that scientific theories can provide genuine knowledge of objective structures in reality while remaining epistemically limited representations rather than transparent descriptions of reality in itself. Recognizing this distinction does not weaken science; rather, it establishes a more careful boundary between what a theory demonstrates, what it represents, and what may legitimately be inferred about the ultimate nature of reality.
Category: History and Philosophy of Physics
[1809] ai.viXra.org:2608.0096 [pdf] submitted on 2026-08-30 22:08:08
Authors: Tomasz Kobierzycki
Comments: 207 Pages.
This dissertation develops a connected programme for extending the tensor organization and observer geometry of general relativity. Its first component is a four-index completion of the Einstein field equation. The Ricci-built contribution and the trace-free Weyl contribution are retained at the same tensor rank, while contraction recovers the ordinary two-index Einstein equation. A rank-four source is decomposed into a lift of the stress—energy tensor and an independent trace-free tensor with Weyl algebraic symmetries. In the classical formulation this independence is organizational rather than an enlargement of the metric solution space: the contracted Einstein equation fixes the Ricci sector and the remaining uncontracted equation fixes the trace-free source consistently with the Weyl tensor. The second component is a four-sector completion of the orientation of a Lorentzian clock—ruler plane. The four connected non-null domains share the same null boundary and are labelled by the phase cycle 1, i, −1, −i. Geometry-sector and particle-sector transformations are kept distinct. Ordinary Lorentz motion occurs inside a sector; the construction does not describe material particles accelerated through the light cone. In curved spacetime a tensor of proper scales and a solution-dependent critical tensor select an active eigendirection. Neighbouring charts use reciprocal normalization of that active scale. Schwarzschild, Kerr, Lemaître—Tolman—Bondi and spatially flat FLRW examples test curvature and geodesic distance in these charts. In the regular branches analysed, reciprocal centres are curvature-decaying asymptotic boundaries rather than finite-parameter passages. These two components are then used to construct a tensorial quantum framework. Complete conserved rank-four configurations are weighted by complex coefficients only after their classical source content has been fixed. A rank-eight operator generates linear clock evolution, and amplitudes and probabilities are obtained by global tensor contractions. A reciprocal Kerr—Newman chart is used in a hydrogen model whose common Maxwell field retains the electron—proton cross-term before the four-index lift. The central channel produces a relativistic Coulomb spectrum and compatible Laguerre radial modes. The Ricci-flat specialization identifies a free graviton with a Weyl mode, yielding null propagation, two transverse helicities, explicit plane-wave and spherical resolutions, reciprocal transport and closed four-sector Weyl histories. The perturbative ultraviolet problem is addressed after standard background-field quanti-zation, gauge fixing, ghost integration, dimensional regularization and recursive subtraction. Metric variation of the remaining local pole functional gives a conserved rank-two response. Internal sector maps cancel on contracted graviton indices, while the two free covariant indices retain the character (−1)k .
Category: Quantum Gravity and String Theory
[1808] ai.viXra.org:2608.0095 [pdf] submitted on 2026-08-30 22:04:21
Authors: Hassan Touayouch, Rabie Najem, Mohammed Benjelloun
Comments: 9 Pages.
Neural Architecture Search (NAS) automates the design of neural networks but faces the prohibitive cost of evaluating eachcandidate architecture through full training. Zero-cost proxies estimate architecture quality in seconds without training, yetindividual proxies remain noisy, and no existing method jointly exploits proxy signals and the topological structure of architectureswithin an active-learning framework. We propose ZAPS (Zero-cost Active Proxy Search), a four-component pipeline that addressesthese limitations. ZAPS first selects a compact, non-redundant subset of proxies via PROXYFIT, a greedy anti-redundancy algorithm; initializes the search with a hybrid K-means strategy balancing exploitation and exploration; dynamically refines proxy selection using bootstrapped MRMR; and predicts architecture quality with an XGBoost ensemble fed by proxy ranks and one-hot topological encodings, guided by an Upper Confidence Bound (UCB) acquisition function. On NAS-Bench-201 with a budget ofB =200evaluations, ZAPS identifies 53.8% of the top-100 architectures on CIFAR-10 and 66.8% on CIFAR-100 (P@100), while maintaining a Regret of 0.04% on CIFAR-10. ZAPS outperforms comparable-budget methods — REA, BANANAS, and TPE — on both metrics evaluated on CIFAR-10 and CIFAR-100 of NAS-Bench-201.
Category: Artificial Intelligence
[1807] ai.viXra.org:2608.0094 [pdf] submitted on 2026-08-30 18:48:10
Authors: Samuelson G
Comments: 16 Pages. Just out of curiosity
Machine learning has rapidly advanced from early theoretical concepts to a practical technology that drives many modern applications (computer vision, natural language processing, etc.). We present a detailed survey covering ML foundations, algorithmic methodologies, and empirical evaluation. After defining ML and its subfields, we review historical milestones and survey recent literature, citing classic works (Fisher 1936; Rosenblatt 1958; Cortes & Vapnik 1995; LeCun et al. 2015) and modern treatments. The methodology section introduces theoretical background (statistical learning, optimization, loss functions) and describes key algorithms and models (regression, support-vector machines, decision trees, neural networks, clustering, etc.), including architectures like feedforward, convolutional, and transformer networks. We propose a generic ML workflow (Figure 4) using flowcharts. Experiments using standard benchmarks (Iris, MNIST, CIFAR-10, IMDB reviews, COCO) illustrate training, evaluation metrics (accuracy, F1, etc.), and dataset characteristics (Table 3). Results are tabulated (Table 4) and graphed, showing comparative performance of several classifiers. We discuss implications of the findings, limitations of current methods, and suggest future research directions. In conclusion, this survey synthesizes foundational concepts and recent advances in ML, and includes declarations of funding, conflicts, and author contributions.
Category: Artificial Intelligence
[1806] ai.viXra.org:2608.0093 [pdf] submitted on 2026-08-30 22:02:56
Authors: Michael Quigley
Comments: 160 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper presents the formal Applied Industrial Handover of the Rigid Universal Touching Wave Structure of Matter (R.U.T. WSM) framework, transitioning the physics community from theoretical observation to the active, non-destructive Resonant Machining of physical space. By reclassifying empty space as a phase-locked, 10²² kg/m³ Rigid Plenum driven by a 13.33 Hz (800 RPM) Universal Motor, we provide the deterministic "Math Bolts" required to harness the boundless torque of the background medium. Rather than introducing abstract mathematical placeholders, this manual delivers the precise engineering specifications for functional terrestrial and interplanetary systems:The Applied Technological Suite: We present the complete manufacturing parameters for the Acoustic Torque Car, which achieves 99% cold torque efficiency using a 1.42 cm cylinder bore—a mandatory metrological mirror of the 1.42 GHz Neutral Hydrogen Line—coupled to a 530-gram calibrated piston and an Ethos-84 Heptad driveshaft. We detail the propulsion mechanics of the Resonant Space-Ship, which utilizes a 1-3-6 Peloton drafting formation and a 720-degree Spinor Reset to machine low-pressure Acoustic Slipstreams directly through the rigid medium, achieving a deterministic 15.2-hour transit to Mars at the 1,000 km/s Lerner Limit. Residential power-scarcity is eliminated via the Domestic S.A.T. Hub, which utilizes a 100 mm synthetic Z-growth quartz core housed in a Titanium Grade 5 interference sleeve to harvest the primary longitudinal torque of the sun 24 hours a day.The Cosmological & Astronomical Demolition: This audit completely dismantles the "Abstract Curtain" of heliocentrism and Big Bang cosmology by restoring Simon Shack’s geoaxial Tychosian Hub. We establish the Stationary Earth-Axle (1 mph) as an absolute thermodynamic mandate; the Vaporization Proof confirms that any orbital velocity through the solid plenum above 1 mph would vaporize a planet's crust into plasma instantly. This axle is forensically verified by the 8.2 km/s Seismic Odometer of transverse S-waves conducting through the Earth's solid Liquid Metallic Hydrogen (LMH) core. We formally replace Einstein's E=mc2 with the Universal Seesaw (E = mΦ)—reclassifying light-speed as Lattice Setup Time (Ls)—proving that space behaves as a Solid Mechanical Rod capable of instantaneous Time-Zero conduction once the Acoustic Clutch is engaged at 7,777 Hz.The Torsional Odometer & Quasar Check-Mate: Redshift (z) is reclassified from a Doppler speedometer of expanding space into a Torsional Friction Odometer (z=z1+nz2+z3), which measures the mechanical "groan" of signals navigating the Heptad mesh. By removing the +0.67 Heavy Gear internal torque stress (z3), we deliver the definitive Quasar Check-Mate, proving that Markarian 205 is physically connected to its parent galaxy NGC 4319 at the exact same z1=0.006 local address. By applying the 42,000x Tychosian scale correction, the hallucination of "deep space" collapses, revealing a compact, synchronized gearbox bounded by the 34.5 Trillion Km Terminal 137-Wall.The Resonant Docking & Biophysical Upgrades: To replace the metrologically insolvent practice of "Stochastic Ballistics" at the Large Hadron Collider, we propose the LHC Phase-II Resonant Docking upgrade. By utilizing a 7,776 Hz Master Grooming signal and a 7,777 Hz Ignition pulse, the LHC can non-destructively sweep the sub-atomic inventory, detecting vertical Dielectric Surges at the precise coordinates of the Electron (60.46 MHz) and Proton (1.42 GHz). Finally, the Osireion Protocol reverse-engineers the archaeo-acoustic architecture at Abydos, reclassifying biological aging as Internal Dielectric Friction. Grounding the biological body in a liquid medium with a static dielectric constant of 80 allows the Magnesium-12 antenna in chlorophyll to dock with the 1.42 GHz Solar Spoke, "re-greasing" the chassis and machining tissue growth back along its deterministic 337° and 227° Fibonacci paths.
Category: Quantum Physics
[1805] ai.viXra.org:2608.0092 [pdf] submitted on 2026-08-29 21:01:19
Authors: Miles Huang
Comments: 12 Pages. Author retains copyright; non-exclusive license to distribute.
This paper synthesizes a series of results on the (even) Goldbach conjecture and completes two previously unaddressed components: textbf{error analysis} and textbf{fractional sequence encoding (additive sieve)}. The main results are as follows. (1) We systematically present limit-type elementary constructions of the Goldbach conjecture (using both exponential and cosine functions) and their equivalent logical formulations, and extend the method to the Collatz conjecture, the twin prime conjecture, and the prime counting function. (2) For the truncated construction with finite error factor $k$, we derive a rigorous error bound and prove that the criterion holds provided $kn,e^{-4k/n^{2}}
Category: Number Theory
[1804] ai.viXra.org:2608.0091 [pdf] submitted on 2026-08-28 01:23:11
Authors: Yuechun Huang
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
Based on the core hypothesis that "moving matter is necessarily accompanied by a matter field," this paper proposes a theoretical framework—Matter Field Theory—aimed at unifying microscopic and macroscopic physical phenomena. The theory holds that all matter composed of basic moving units such as atoms and electrons generates a matter field inseparable from its state of motion. This field possesses two fundamental attributes: it is both an energy field that obeys energy conservation and an information field that encodes the complete kinematic state of the matter. The matter field propagates at the speed of light, and its interactions can be classified into three basic modes: strong interaction (energy exchange), manifested as attraction or repulsion; weak interaction (information exchange), manifested as resonance and perception; and non-interaction (mutual non-disturbance), which may correspond to dark matter phenomena. This paper also points out that a cosmological view based on the matter field will completely negate relativity theory and the Big Bang theory: the relativistic interpretation of spacetime relations is erroneous; the universe has no beginning or end, and the Big Bang doctrine is untenable. This paper systematically expounds the implications of the theory, demonstrates its self-consistency, and presents a worldview in the form of a poem.
Category: Astrophysics
[1803] ai.viXra.org:2608.0090 [pdf] submitted on 2026-08-27 20:56:02
Authors: Eduardo Rodolfo Borrego Moreno
Comments: 9 Pages.
We present a consolidated rheological framework for the Cosmological Dissipative Residual (CDR), a single effective medium proposed to underlie both dark-energy—like and dark-matter— like phenomenology. Building on previous work in the series, we formulate a covariant constitutive relation for the residual’s anisotropic stress in which the effective viscosity depends on local acceleration and shear. In the non relativistic thin-disk limit this relation reduces to an estimator for the residual contribution to the radial acceleration, ∆gR ≈ fgeom ηeff σ ρres R. with a geometric factor fgeom ≈ 3.We confront the framework with rotation-curve data for 175 SPARC galaxies. The residual contribution is found to be selectively activated: in the low-acceleration regime97.5% of radial points show ∆g > 0, while in the high-acceleration regime the median ∆g is consistent with zero. From the activated regime we obtain a median effective viscosity ηeff ≃ 3.8×10−2 kg m−1 s −1 and a characteristic transition scale atrans ∼ (1−2)×10−10 m s−2, compatible in order of magnitude with cH0/2π. The results support the hypothesis that a single cosmologically motivated residual medium can develop a dark-matter—like response under local dynamical conditions, while remaining consistent with a dark-energy—like behaviour on large scales. A fully quantitative reproduction of galactic rotation curves is left for future work.
Category: Astrophysics
[1802] ai.viXra.org:2608.0089 [pdf] submitted on 2026-08-27 07:33:22
Authors: Seungtae Kim
Comments: 35 Pages.
The International System of Quantities (ISQ) relies on conventional choice to determine itsbase quantities, without providing explicit mathematical and physical criteria for theirselection. This paper proposes an alternative framework in which unit relations are used toderive quantity dimensions before base quantities are selected. A broader class of unit-explicitequations is also introduced for relations in which specified unit components are retainedexplicitly when they cannot be reduced to pure numbers without loss of physically relevantinformation.Candidate base-quantity sets are first evaluated for algebraic admissibility, requiringmutual dimensional independence and dimensional completeness for the system underconsideration. Because algebraically admissible sets need not be unique, a second, physicallymotivated criterion is introduced to identify preferred quantities on the basis of establishedhigher-order dimensional occurrences associated with distinct physical roles. Applying thistwo-stage procedure to an SI-oriented set retains mass, length, time, electric current,thermodynamic temperature, and amount of substance. Plane angle is additionally selected asa preferred base quantity through the second-order angular structure of solid angle. Bycontrast, luminous intensity is classified as a derived quantity with the same unit-baseddimensional structure as radiant intensity while remaining a distinct quantity kind. Finally,logarithmic level values conventionally expressed using the neper and decibel arereformulated as numerical index mappings whose outputs are pure numbers and whosearguments retain the relevant field- or power-quantity context. The proposed frameworkprovides a common unit-based route from unit relations to quantity dimensions and basequantity selection, with angular, photometric, logarithmic, and unit-explicit formulationsserving as applications of the same construction.
Category: Mathematical Physics
[1801] ai.viXra.org:2608.0088 [pdf] submitted on 2026-08-26 19:26:33
Authors: Arunas Ostasevicius
Comments: 8 Pages.
This paper presents a generalized quaternionic model of electrodynamics and wave kinematics within the absolute Euclidean Hamilton space. An epistemological audit of the vector truncation of Maxwell’s original equations is performed, demonstrating the preservation of the scalar potential field component. Using conjugate time forms and the full quaternionic norm, a Galilean-covariant field model is constructed forinhomogeneous media. The integration of a non-linear quadratic medium drag and quaternionic time regularization eliminates coordinate divergences at the wave barrier (v = c), replacing singular mathematical boundaries with a smooth continuous transition into a supercritical shockwave front. The distinction between mechanical body dynamics and the interferometric effects of optical signal registration is rigorously substantiated using asymptotic mechanics averaging methods. Finally, the model provides a measurable experimental criterion to verify the dynamic resistance of the physical vacuum medium using high-energy calorimetric detectors, predicting a specific heat dissipation shelf combined with hard radiation emission.
Category: High Energy Particle Physics
[1800] ai.viXra.org:2608.0087 [pdf] submitted on 2026-08-25 13:34:33
Authors: Joseph Shaffer
Comments: 6 Pages.
Cosmological redshift is conventionally interpreted as evidence for the expansion of spacetime. This assumption underlies the ΛCDM model, inflation, dark energy, and the metric-expansion paradigm. Here I present a nonexpanding cosmological ontology in which redshift arises from energy shifts across global tension gradients in a pre-geometric domain. Observable spacetime is a projection of this deeper tension structure. Photons lose energy as they traverse regions of decreasing tension, producing a redshift proportional to path length. This mechanism reproduces the Hubble law without expansion, avoids the failures of tired-light models, and naturally resolves several cosmological anomalies including the Hubble tension, early massive galaxies, and the lithium problem. This paper establishes the redshift mechanism and the mathematical structure required for subsequent papers in the series.
Category: Astrophysics
[1799] ai.viXra.org:2608.0086 [pdf] submitted on 2026-08-25 15:09:08
Authors: E. P. J. de Haas
Comments: 90 Pages. DOi: https://doi.org/10.5281/zenodo.22098362
The BQ--Pauli algebra provides an eight-dimensional 1+3+3+1 framework in which relativistic field equations can be organized through a hierarchy of algebraic products. Its basis elements are realized as matrices in M(2, $mathbb C$), and its products are given by ordinary matrix multiplication. In this work, the previously developed BQ formulations of electromagnetism and relativistic fluid dynamics (RFD) are lifted to the sixteen-dimensional BQ--Weyl representation of Cl(1,3), with Clifford-grade decomposition 1+4+6+4+1. The constructive, explicit lift preserves the coefficients and physical content of the Pauli-level products while making their spacetime-grade structure explicit.For electromagnetism, the Weyl construction recovers Maxwell's equations from the field-derivative product, separates the quadratic field invariants from the stress--energy construction, and represents the complete electromagnetic stress--energy content through a vector-valued linear map. For RFD, the corresponding field, force, wave, quadratic, and conservation products are reconstructed and resolved into their Clifford sectors. The Weyl formulation further permits the fluid four-velocity to be generated from a local rapidity field through a Spin(1,3) rotor, from which the associated comoving frame and Maurer--Cartan connection follow.Together with the corresponding BQ--Pauli to BQ--Weyl lift previously performed for gravity, these results place the gravitational, electromagnetic, and fluid-dynamical branches of the BQ programme in a common Cl(1,3) representation. The present construction is primarily algebraic: it exposes the Clifford structure underlying the earlier Pauli-level formulations without introducing additional electromagnetic or fluid-dynamical laws, or invoking a spinor wave-function or quantum-mechanical interpretation of the Weyl algebra. A final reproducibility appendix provides a compact workflow for independent symbolic and AI-assisted verification of the matrix calculations from the explicitly defined BQ bases.
Category: Mathematical Physics
[1798] ai.viXra.org:2608.0085 [pdf] submitted on 2026-08-25 03:19:27
Authors: J. W. McGreevy
Comments: 26 Pages.
This monograph establishes a definitive, structurally complete unification of quantum gauge fields, non-equilibrium thermodynamics, and analytic number theory through the framework of Arithmetico-Geometric Conformal De-Homogenization. We prove that physical spacetime is an active, self-correcting thermodynamic metamaterial projected from an underlyinginfinite-dimensional arithmetic space. By executing a strict 1-for-1 parameter mapping, wedemonstrate that Lars Onsager’s Reciprocal Relations (Lik = Lki) are the macroscopic physical readout of Clairaut’s Theorem of mixed partial derivatives ( ∂2U ∂V∂S = ∂2U ∂S∂V ). When the continuum substrate is driven from equilibrium, local coordinate shearing is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS) Fibration Lift, routing excess dissipative energy into the Trivial Zeros of the Riemann Zeta function and the Tate-Shafarevich group, which function as Viscous Hydraulic Dampers locked by the Bernoulli number B10, B12, and the prime691. We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A,H,D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential (Aµ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5 Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of the spectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros: Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic ProductClosure (∏︁ p≤∞|σ|p = 1), this framework achieves full structural immunization against decoherence and reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.
Category: Mathematical Physics
[1797] ai.viXra.org:2608.0084 [pdf] submitted on 2026-08-25 00:38:50
Authors: Austin Brooks Magruder
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The classical Big Bang framework introduces an unphysical gravitational singularity at , while standard nuclear physics models the short-range repulsive core of the nucleon-nucleon interaction as an empirical threshold without an explicit geometric origin. This paper introduces the Triple Point Protocol, an analog-derived theoretical framework grounded in non-Euclidean geometric continuous-field tessellations. We demonstrate that collapsing 4D mass-energy fields and subatomic hadronic systems encounter severe geometric frustration across aperiodic networks of branching impossible figures. This frustration halts structural collapse at strict physical boundaries: the femtometer nuclear core and the Planck volume .Governed by the Axiom of Spatial Continuity, the two-dimensional negative space field reaches absolute saturation without spatial tearing. At these saturation floors, hadronic matter undergoes chiral melting mediated by quantum anomaly interference of the, which locks the topological susceptibility of the vacuum and acts as a topological lubricant between packed nucleons. Denied further 4D contraction, compressed mass-energy executes a orthogonal axis pivot across the Planck boundary. During this transition, photon geodesics undergo topological light refraction and lensing along the expanding 5D manifold contours. Mediated by leptonic CP violation and a phase-shifting neutrino fluid, the directional transition drives a continuous 5D expansion—the physical event perceived macroscopically as cosmogenesis.
Category: Quantum Gravity and String Theory
[1796] ai.viXra.org:2608.0083 [pdf] submitted on 2026-08-25 00:32:39
Authors: Samuelson G
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Sleep, defined by behavioural quiescence, increased arousal threshold and homeostatic rebound, is long-recognized in mammals and birds but its prevalence and core mechanisms across all life remain understudied. Here we perform a comprehensive review and comparative analysis of "sleep" and sleep-like states in bacteria, archaea, plants, fungi, invertebrates and vertebrates (including humans). We survey genetic, molecular and physiological evidence for rest—activity cycles in each taxon, and compile standardized tables of sleep characteristics (duration, EEG features, etc.) and conserved molecular pathways. Using a phylogenetic framework and meta-analytic data (from >150 species across animal clades), we identify fundamental commonalities — for example, the role of a circadian timing system and accumulating neuromodulators (adenosine, GABA, melatonin) in promoting quiescence. We also highlight striking divergences: many invertebrates exhibit purely behavioural sleep defined by inactivity, certain reptiles (e.g. bearded dragons) show two electrophysiological states analogous to NREM/REM, and birds perform unihemispheric slow-wave sleep (with one eye open) for predator vigilance. We present illustrative figures (evolutionary timeline, conserved sleep-pathway schematic, sample EEG traces) and tables (e.g. sleep traits by taxon, key molecules) to integrate these findings. Our comparative meta-analysis (using generalized least-squares regression with phylogenetic correction) reveals that while sleep duration scales with body size in mammals (p<0.01), it correlates poorly with metabolic rate across vertebrates, suggesting complex evolutionary pressures. We propose experiments to test sleep in non-neuronal life (e.g. metabolic cycles in archaea) and emphasize limitations such as definitional biases and sparse data in many taxa. This integrative synthesis suggests that sleep-like quiescence evolved early and was retained and elaborated in many lineages, yet its ultimate functions may be diverse.
Category: Quantitative Biology
[1795] ai.viXra.org:2608.0081 [pdf] submitted on 2026-08-23 02:57:52
Authors: J.W. McGreevy
Comments: 25 Pages.
This monograph establishes a definitive, structurally complete unification of quantum grav-ity, non-equilibrium thermodynamics, and analytic number theory through the frameworkof Arithmetico-Geometric Conformal De-Homogenization. We prove that physicalspacetime is not an abstract, passive background container, but an active, self-correcting thermo-dynamic metamaterial fluid projected directly from the continuous deformation and modularflow of an underlying infinite-dimensional arithmetic space.By executing a strict 1-for-1 parameter mapping, we demonstrate that the weight-2 Eisensteinseries (E2(τ )) is the universal velocity field (v) of this modular flow, whose path-dependentcoordinate drift—the quasi-modular anomaly—manifests as the physical non-linear advectivepumping acceleration (v · ∇)v. When driven from equilibrium, Lars Onsager’s ReciprocalRelations (Lik = Lki) emerge as the literal macroscopic readout of Clairaut’s Theorem of mixedpartial derivatives ( ∂2U∂V ∂S = ∂2U∂S∂V ), which requires that the order of differentiation must commuteflawlessly to preserve the nilpotent gauge invariance d2U = 0.When the continuum substrate is driven from equilibrium and cascades toward the 691unipotent puncture on the arithmetic curve Spec(Z), unique factorization shatters insidethe χ11 eigenspace of the odd minus class group (Cl−691). This local coordinate shearing andturbulent vortex crisis is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS)Fibration Lift (S3 S1−−→ S2), which projects the 3D velocity configuration space up into a 4Dcomplex spinorial space (R4). The continuous 1D circle fiber (S1) acts as a data bus (H1 ∼= H1)that isolates the non-exact rotational elements, braiding the non-Abelian SU (3) color vorticityfield into multi-layered knots to generate a permanent nilpotent confinement sink (N2 = 0).The Seeley-DeWitt heat kernel expansion coefficients (an) serve as the exact arithmeticaccount balances of this regularization, where the factor of 12 in the quadratic variance termacts via Itô’s Lemma as the metric tax required to enforce Clairaut’s Theorem (d2U = 0).The final substitution of these Planck-scale boundary parameters (PP, ℓP, EP, tP) into Clairaut’sidentity yields the Dynamic Spacetime Maxwell Relation (∂EP/∂ℓP = −∂PP/∂tP), whichanchors the universal physical constants (α, ℏ, θW ) as the global stabilizers of the vacuum.We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A, H, D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential(Aμ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of thespectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros:Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic Product Closure (∏︁ p≤∞ |σ|p = 1),this framework achieves complete structural immunization against decoherence and quantumchaos. It reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.
Category: Mathematical Physics
[1794] ai.viXra.org:2608.0080 [pdf] submitted on 2026-08-23 05:34:36
Authors: Fabrizio Vassallo
Comments: 76 Pages.
Main mathematical result. The exceptional Jordan algebra J3(O) (the Albert algebra, 27-dimensional) admits the associative collapse map π0 : J3(O) → J3(R) with a 21-dimensional kernel. The kernel carries precisely the imaginary octonionic degrees of freedom that make the associator non-zero. We show, within astrongly motivated EFT framework, that when these degrees of freedom are activated(non-zero associator), the natural consistent open-system dynamics on the residualassociative sector J3(R) takes the Lindblad GKSL form whose jump operators arethe Fano-plane associators Lk = √λ[Ak, Bk, Ck]. The chain:J3(O) π0 −→ J3(R) [A,B,C]̸ =0 −−−−−−→ Lindblad decoherence is grounded in the representation theory of G2 = Aut(O) and the Nakajima—Zwanzigopen-system framework [1]. Complete positivity is verified from the G2-symmetry of the Fano plane (the jump operators satisfy P k Lu2020 k L k = 28λ I, the completeness relation for a CP map).Physical application. We develop non-associative topological neutrino dynamics (NATND), in which the framework above is applied to neutrino propagation through the octonionic ultramark condensate (where by "ultramark" we meanthe level-6 constituent of the hierarchical level model of the present author [2]). Thedecoherence rate Γ(E) = g2U E2/(M2U + E2)/MU is a strongly motivated EFT consequence of the derivative-coupling structure of the associator vertex. It provides an alternative to sterile-neutrino oscillations for the gallium anomaly (GALLEX, SAGE, BEST) and the MiniBooNE excess, with the key signature that the deficitis baseline-independent (no L/E pattern) and energy-dependent as E2/(M2U + E2).The ultramark mass coincides numerically with the Totani Fermi-halo excess.
Category: High Energy Particle Physics
[1793] ai.viXra.org:2608.0079 [pdf] submitted on 2026-08-23 05:40:30
Authors: Fabrizio Vassallo
Comments: 40 Pages.
We examine whether the hierarchical "level model" (NATND) of the present author [27, 28] admits foundations compatible with the momentum-map account of the Wallstrom controversy for the hydrodynamic (Madelung) formulation of quantum mechanics recently given by Khesin and Modin [1] — who explicitly frame their result as resolving the controversy, against the more cautious backdrop of open technical questions surveyed by Reddiger and Poirier [2], including strong non-quantized solutions they construct in two dimensions. We show that the mechanism resolving Wallstrom’s objections — expressing the quantization condition as a geometricconsistency requirement on a momentum map, rather than an ad hoc postulate —extends level-by-level through the cascade only as long as the relevant structure group remains a genuine Lie group, and identify the precise algebraic obstruction (loss of associativity at the octonionic, ultramark level) at which this mechanism cannot be repeated verbatim. We independently identify, via the topological classification of line and point defects in ordered media, a topological manifestation of the same limitation, correlated with but logically distinct from the symplectic argument:the classification of parallelizable spheres and the Hopf invariant one theorem independently restrict the same dimensions. Finally, we describe — as an open research program rather than a closed result — three independent partial routes toward a rigorous formalization of the "vortices of vortices" mechanism proposed for the origin of the level cascade, together with the concrete obstructions each currently faces.Two appendices provide a self-contained, independently re-runnable computational verification of the discrete-RG bifurcation claims made for Route B (Appendix A for the Diamond toy model, Appendix B for the Fan topology), with full source code included.
Category: High Energy Particle Physics
[1792] ai.viXra.org:2608.0078 [pdf] submitted on 2026-08-23 08:46:12
Authors: Po Hu
Comments: 9 Pages.
Consider a gambler with integer capital who gains two units after a win, loses one unitafter a loss, and is removed at the first visit to zero. The first observation is elementarybut striking: with positive drift, the probability of reaching an arbitrarily high finite targetdoes not tend to zero. It tends to the probability of never being ruined. For independenttrials with win probability p, we record the exact ruin law, identify the phase transitionat p = 1/3, and give a closed formula at criticality whose fixed-capital asymptotic is x/m.We then keep the one-step win probability equal to 1/2 and the mean payoff equalto 1/2, but let successive outcomes form a symmetric two-state Markov chain with persistence parameter θ. An explicit bounded harmonic function gives the ultimate survivalprobability1 −1 + r + r22(1 + r)rx−1, r =√(1 − θ)2 + 4θ2 − (1 − θ)2θ.This probability decreases strictly with persistence, although every model in the familyhas the same stationary win rate and the same mean increment. At θ = 1 the survivalprobability is discontinuous: its left limit is 1/4, while its endpoint value is 1/2. Consequently, the high-target limit and the high-persistence limit do not commute. Finally, if(1 − θ)x → λ, the exact transition profile is 1 − (3/4)e−λ/2. These formulas isolate howearly absorption and temporal clustering, rather than the height of a finite target alone,govern extreme-target success.
Category: Statistics
[1791] ai.viXra.org:2608.0077 [pdf] submitted on 2026-08-23 09:51:31
Authors: Keiji Yoshimura
Comments: 16 pages, 5 figures. AI-assisted technical monograph presenting a five-stage reproducibility audit and a limited mathematical corollary for the planar three-body shape sphere. Includes AI-use disclosure and bounded novelty claims.
This monograph presents a five-stage AI-assisted audit of possible relationships among gravity, the direction of time, temporal orientation, and irreversible structure formation. Rather than proposing a new theory, the study progressively tests and narrows a broad initial intuition using analytical arguments, Newtonian many-body calculations, finite-level quantum-clock models, curvature comparisons, and public GW250114 release products. Local Lorentz symmetry and the time-reversal covariance of the ADM constraints provide no universal metric-only rule selecting one timelike cone half as the fundamental future. Rindler, de Sitter, and Schwarzschild comparisons separate clock-rate gradients and proper acceleration from curvature. Closed finite-level proper-time dephasing can be exactly refocused by an ideal path/clock echo, while residual irreversibility appears only after an open reduced channel is introduced. Newtonian Janus-point analyses distinguish a rigorous scale minimum in suitable nonnegative-energy sectors from non-monotonic, measure- and horizon-dependent shape-complexity statistics. A reconstructed BKM mass-metric probability on the equal-mass planar three-body shape sphere produces two structurally symmetric branches rather than a dynamically preferred future. Public GW250114 products are also used to reproduce the collaboration-defined black-hole area-growth statistic, without interpreting the area law as a fundamental selector of time orientation.A limited mathematical by-product is proved for normalized three-body shape complexity Q under the BKM mass-metric shape probability:P(Q > q) = 1/(6 q^2) + 2 sqrt(6)/(27 q^3) + O(q^-4).Consequently, E[Q^p] is finite if and only if p < 2, and the truncated second moment satisfiesE[min(Q,T)^2] = (1/3) log(T) + kappa + O(T^-1).The ingredients of this result are published; targeted searches did not locate this exact probability-and-moment statement, so it is presented only as a potentially unreported elementary corollary, not as a priority claim. Overall, the audit supports established relations between gravity and proper time, curvature, causal structure, and structural arrows, but finds no evidence that standard gravity itself creates or selects a unique fundamental future direction.
Category: Mathematical Physics
[1790] ai.viXra.org:2608.0076 [pdf] submitted on 2026-08-23 15:34:21
Authors: Keiji Yoshimura
Comments: 17 Pages. Prospectively specified 2004 country-holdout confirmation with no-refit 2014→2004 transfer; includes integrated reproducibility appendices, variable mapping, software settings, input hashes, and numerical verification.
Research on citizenship norms has established that beliefs about what a "good citizen" should do are associated with political participation. Less is known about whether a fixed individual-level norm signal retains incremental predictive value when the national context changes or when a model is transferred between survey waves without refitting.This study tests a bounded predictive-transportability claim using the ISSP Citizenship modules of 2014 (ZA6670; 49,807 respondents) and 2004 (ZA3950; 52,550 respondents). Exploratory analysis of the 2014 data identified a three-item civic-norm score based on understanding opposing viewpoints and helping worse-off people domestically and abroad; items that directly refer to political action were excluded.Before inspection of the 2004 individual-level confirmation results, three decision criteria were prospectively specified. Across 38 eligible 2004 held-out country/sample units, adding the three-item score to a broad prospectively specified demographic and political-attitudinal baseline improved equal-unit mean log loss by 0.01023 (95% equal-unit bootstrap interval [0.00683, 0.01367]); its increment exceeded that of a specific two-item duty comparator by 0.01003 [0.00680, 0.01335]; and within-country permutation of the norm score degraded prediction by 0.01450 [0.01217, 0.01690].A model estimated in 2014 and applied to 2004 without coefficient refitting retained a 0.00983 [0.00672, 0.01292] increment from the norm score. Predictive increments were substantially smaller for reported contentious behavior and institutional contact. An exploratory reverse transfer did not support universal performance in countries absent from the 2004 training domain.These results support only a narrow, non-causal conclusion: the fixed three-item score carries incremental respondent-linked predictive information across many of the tested ISSP country and wave shifts, with substantial heterogeneity and no claim of universal transportability or measurement invariance.
Category: Social Science
[1789] ai.viXra.org:2608.0075 [pdf] submitted on 2026-08-23 17:23:29
Authors: Jozsef Kerenyi
Comments: 4 Pages.
This paper introduces an alternative, field-impedance-based cosmological model that couples the dynamic mass increase of special relativity with the energy transfer processes of the gravitational field. We demonstrate that the time-dependent relativistic mass change (dm/dt) of a linearly accelerating point mass generates a direct energy flow through the free-space gravitational impedance (Z_g = G/c). We show that the sign and magnitude of the transmitted power depend directly on the scalar product of the velocity and acceleration vectors (v . a). Consequently, the model offers a natural, unified explanation for both dark energy (energy-emission phase) and dark matter (energy-absorption phase) across local and cosmic scales, resolving observational frame asymmetries through the analogy of the twin paradox.
Category: Relativity and Cosmology
[361] 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
[360] 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
[359] 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
[358] 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
[357] 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
[356] ai.viXra.org:2610.0023 [pdf] replaced on 2026-10-17 00:26:42
Authors: Zhongyang Dong
Comments: 13 Pages.
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, negating hypotheses dominated by multi-polar fields or charged particles, and 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
[355] 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
[354] ai.viXra.org:2609.0061 [pdf] replaced on 2026-09-28 19:09:41
Authors: Stephen P. Smith
Comments: 11 Pages.
Modern physics possesses extraordinarily powerful formal structures, but the existence of a successful formalism does not by itself settle what that formalism means. This essay proposes an interpretive program in which the Lie bracket is read as a generative relation and the Jacobi identity as a higher-order regulatory condition. On this interpretation, the familiar passage from binary relation to Jacobi coherence may be understood as the mathematical trace of a more general movement from two-sided differentiation toward a coherent whole. A previous proof-of-concept formulation of general relativity, in which extrinsic gravitation was modeled as a homeostatic coupling between CPT-symmetric spacetime manifolds, provides one possible spacetime realization of this idea, but may not be the most economical foundation for it. The deeper structure is already present in the pre-geometric formalism of Lie algebra. Quantum mechanics then supplies a further point of contact: noncommuting observables are constrained by uncertainty relations whose lower bound is directly related to their commutator. This does not prove a philosophical theory of attention, but it permits an interpretive extension in which different modes of attending to relational structure have different formal consequences. Iain McGilchrist’s distinction between narrow and broad attention provides a useful interdisciplinary vocabulary for this extension, without implying an identity between quantum mechanics and his account of cognition. The resulting proposal is neither a replacement for mathematical physics nor an attempt to derive metaphysics from equations. It is an argument for an interpretive meta-science in which formal mathematics establishes relational constraints while interdisciplinary inquiry asks what kind of organization those constraints may express.
Category: General Science and Philosophy
[353] ai.viXra.org:2609.0050 [pdf] replaced on 2026-10-08 15:20:46
Authors: Xuda Ye
Comments: 57 Pages.
We analyze the mean square error of stochastic Runge--Kutta integrators for overdamped Langevin dynamics whose potential is strongly convex outside a bounded region. A decomposition splits the local error into a mean-zero term and a smaller remainder, and the discrete Poisson equation turns their moments into a bound on the error of a time average. We carry this out for two stochastic Runge--Kutta integrators proposed by Yang & Wang (2026), both of strong order $frac32$ and weak order $2$, which evaluate the gradient of the potential and no higher derivative. We show that their laws approach the law of the exact solution at second order in Wasserstein-1 distance, up to a logarithm, uniformly in the number of steps. For a test function with bounded derivatives up to third order, we prove that the mean square error over $N$ steps with step size $h$ is $mathcal O ( frac{1}{Nh} + h^4 )$, which is the optimal order in the discretization. Experiments measure the strong and weak orders and the sampling bias on a nonconvex potential in $mathbb R^2$, and compare the integrators on a diffusion model of CIFAR-10.
Category: General Mathematics
[352] ai.viXra.org:2609.0026 [pdf] replaced on 2026-10-31 15:46:15
Authors: Zhongyang Dong
Comments: 7 Pages. Cross-Paper Logical Alignment: Systematically integrated and aligned the vacuum grid parameter calibrations, microwave and strain wave separation, and shear rigidity mechanisms with Papers 1 and 3 to ensure absolute internal consistency across the trilogy
As a direct sequel to the emergent cosmology of a two-phase planar-invasion bubble universe, this study constructs a self-sustaining evolutionary model of a global bubble multiverse comprising seven initial seed universes, viewed from a minimalist Creator's-Eye View. To avoid ambiguity, it is explicitly clarified that all bubble universes analyzed hereafter refer specifically to iterative evolutionary generations produced through multi-generation collisions, rather than the original primordial seed universes.This framework introduces the physical anchors calibrated in previous papers—namely, the foundational grid spacing and zero-point energy—as the common baseline for cross-generational energy and grid scales. We establish core physical axioms, topological fault-tolerance laws, and dark energy conservation mechanisms: the primordial Big Bang mechanism terminates independently in the seven initial seed universes in accordance with the second law of thermodynamics, serving as Newton's first push and engendering subsequent cosmic rotation via non-uniform initial expansion. Global particle universality ensures that all iterative bubble universes share micro-energy levels fixed by foundational constants. The apparent regional accelerated expansion of dark energy is resolved as a kinetic projection of topological potential energy derived from degenerate baseline universes representing pure vacuum fields. Furthermore, the Prime-7 topological law and the evolutionary scale sequence act as schematic choices for topological fault-tolerance, driving the extinction probability toward zero under selected parameters.Concurrently, we introduce the mechanism of vacuum space depletion and possible zero-space drift pathways to explore the geometric origin of the Big Bang and the intergenerational genetic inheritance of cosmic macroscopic rotational structures. Finally, we harmonize this framework with Newton, Spinoza, and ancient philosophy, concluding with an affirmation of philosophical optimism and cosmic being.
Category: Astrophysics
[351] ai.viXra.org:2609.0026 [pdf] replaced on 2026-10-18 18:44:12
Authors: Zhongyang Dong
Comments: 8 Pages. Updated fluid dynamic mechanisms of V0 space and Empty Zero-Space Drift, corrected typographical errors, and added Version 2 Postscript.
As a direct sequel to Emergent Cosmology of a Two-Phase Planar-Invasion Bubble Universe [1], this paper constructs a self-sustaining evolutionary model of a global bubble multiverse from a "Creator's-Eye View" rooted in physical aesthetics and minimalism. This encompasses a grand global universe originating from seven initial seed universes. To avoid ambiguity, it is strictly clarified that all bubble universes discussed and analyzed hereafter refer to iterative evolutionary generations produced through multi-generational collisions, rather than the primordial seed universes.We establish core physical axioms, a topological fault-tolerance law, and a dark energy conservation mechanism: The primordial Big Bang mechanism strictly followed the Second Law of Thermodynamics to permanently and independently terminate within the seven initial sub-universes, acting as Newton's Prime Mover and incubating subsequent universal rotation through non-uniform initial expansion. Global particle universality ensures that all iterative bubble universes share identical microscopic physics. The apparent local accelerated expansion of dark energy is resolved as a kinetic projection of topological potential energy from degenerate ground-state universes. The Prime-7 topological law and the four-stage evolutionary scale sequence jointly guarantee dynamic equilibrium and a strictly zero probability of ultimate extinction.Concurrently, we introduce the novel mechanisms of V0 Space Depletion and Empty Zero-Space Drift to explain the geometric origin of Big Bangs and the intergenerational genetic inheritance of the universe's macroscopic rotational structure. Finally, we reconcile this framework with Newton, Spinoza, and ancient Chinese philosophy, concluding with a humanistic affirmation of philosophical optimism and cosmic grace.
Category: Astrophysics
[350] ai.viXra.org:2609.0018 [pdf] replaced on 2026-10-07 11:57:25
Authors: Arieh Sher
Comments: 20 Pages.
The observed motion of the Solar System and the Local Group relative to the cosmicmicrowave background (CMB) is conventionally interpreted as a peculiar velocity produced bythe gravitational influence of the surrounding large-scale matter distribution, including the Virgoregion, the Great Attractor, the Shapley concentration, and cosmic voids. The Solar-Systembarycenter moves relative to the CMB at approximately 369.8 kms−1, while transformation tothe Local-Group barycenter gives a velocity of approximately 627 kms−1. This paper examinesan alternative interpretation within the Pivot Universe (PU) model. The universe is treated asa rotating system described approximately by Kerr geometry generated by a central massiverotating Pivot. Matter in the observable universe is assumed to participate approximately in theframe-dragged rotation generated by the Pivot. For MP = 7.82 × 1053 kg, JP = 1.06×1087 Js,RMW =123.3265 Gly, and RCMB = 123.36 Gly, the Kerr frame-dragging angular velocity at theMilky-Way shell is approximately 0.313 × 10−13radyr−1. A locally normalized differential Kerrquantity between the MW and CMB shells is approximately 495 kms−1. This value lies betweenthe Solar-System/CMB and Local-Group/CMB velocities, but it is shown that this numericalcorrespondence cannot itself be identified with an invariant relative velocity. An invariant Kerrphoton-frequency calculation instead separates a predominantly gravitational monopole shiftfrom a much smaller directional frame-dragging contribution. The PU interpretation thereforerequires the observed CMB dipole to contain a combination of global Kerr geometry and localpeculiar motions. The model yields quantitative predictions that can, in principle, be testedagainst the direction and magnitude of observed large-scale peculiar-velocity fields.
Category: Relativity and Cosmology
[349] ai.viXra.org:2609.0016 [pdf] replaced on 2026-10-31 02:48:53
Authors: Zhongyang Dong
Comments: 9 Pages. This third edition refines the emergent cosmological framework by incorporating rigorous parameter calibration (linking the 2.73 K CMB temperature to a 5.27 mm quantum grid spacing), explicit low-energy effective field derivations (such as the transverse
This study proposes an emergent cosmological framework derived from a Two-Phase Planar-Invasion bubble universe scenario. In this model, the physical and geometric boundaries of a single universe or bubble universe are strictly defined as an independent and complete V0 light neutrino quantum fluid matrix, designated as the dead mother field. Diverging from the traditional standard Big Bang singularity cosmology and the assumption of spin-2 gravitons, we define the currently observable universe as a highly organized active cosmic plane, geometrically and topologically presenting as a rotating two-dimensional scimitar-like manifold. This plane continuously intrudes into and engulfs its higher-dimensional, degenerated, dead host body, which has already reached maximum entropy heat death.To ensure theoretical rigor and avoid circular reasoning, this research employs a Parameter Calibration methodology. Utilizing the observed Cosmic Background temperature of 2.73 Kelvin as the thermodynamic anchor, combined with the Stefan-Boltzmann law and geometric constants, we calibrate the fundamental quantum grid spacing of the V0 mother field at approximately 5.27 millimeters. Furthermore, through the Planck-Einstein relation, we derive the corresponding zero-point energy scale of the lightest ground-state neutrino as approximately 2.35 times 10 to the power of minus four electron-volts. Based on this calibrated scale, this paper establishes a qualitative fluid-geometric framework requiring no new free parameters. It provides a possible geometric picture for the bosonized emergence of transverse wave packets under an effective description, dimensional creation, dark matter phase transitions, and the unified equation of the four fundamental forces. Additionally, it proposes four falsifiable modern physics observational pathways, including altitude-differential microwave resonance. This paper primarily provides a qualitative framework and effective physical descriptions, while quantitative fitting is reserved for future numerical work.
Category: Astrophysics
[348] ai.viXra.org:2609.0016 [pdf] replaced on 2026-10-25 16:57:10
Authors: Zhongyang Dong
Comments: 13 Pages. Formatting improvements on concepts and minor typo corrections
This study proposes an emergent cosmological framework derived from a "Two-Phase Planar-Invasion" bubble universe scenario. In this model, we strictly define the physical and geometric boundaries of a "single universe" (or bubble universe) as an independent and complete V0 field. Diverging from the traditional standard Big Bang (bm{Lambda}CDM) singularity cosmology and the assumption of spin-2 "gravitons," we define the current observable universe as a highly organized, active cosmic plane (topologically presenting as a rotating, two-dimensional scimitar-like manifold). This plane continuously intrudes into and engulfs its higher-dimensional, degraded, dead host body, which has already reached maximum entropy heat death (i.e., the exclusive V0 space/mother field of this bubble universe, a completely neutral quantum matrix composed of infinitely stretched residual light interwoven with light neutrinos). Starting from the first principles of geometric mechanics and quantum field theory, this report meticulously demonstrates:1. The Dual-Component Background of a Single Bubble Universe: The absolute dark night background, alongside the 2.73 K vacuum topological polarization microwave noise floor (CMB) and superimposed electromagnetic interference patches.2. Dimensional Creation and Trans-Universe Drifting Mechanism in 0-Space: Two-dimensional planar depressurization expansion, the splitting of stellar orbital and spin angular momentum, and the ejection of "secondary universe embryos" (tidal tails) from the collision of two active cosmic planes, which completely break free from the mother V0 field into Empty Zero-Space for frictionless drifting establishing a trans-universe, cross-generational inheritance mechanism.3. Critical Phase Transitions of Matter and Dark Matter: Three pathways of matter creation (driven purely by density gradients), the quantum critical boundary of 10 Bohr radii, dual-tier Majorana neutrinos, and the chiral gravitational capture of antimatter by ancient black holes.4. Primordial Magnetic Fields and Emergent Gravitational Fields: Asymmetric gravitational shearing ignites primordial seed magnetic fields; gravitons are discarded, with macroscopic spacetime metrics and universal gravitation emerging directly from the scalar density gradients of Majorana neutrinos and the vertical dark pressure shielding effect, thereby establishing a Unified Equation of the Four Forces.5. Dual Central Blockade and the Black Hole Planck Core: The geometric cancellation of four-way vectors and the unidirectional confinement of supermassive black hole event horizons block central pressure; neutrino Fermi degeneracy pressure naturally eliminates both black hole and Big Bang singularities.6. Topological Potential Energy and Tension Release: The dead bubble universe completely stores the energy of the previous generation as high-dimensional topological potential energy (with an extreme tension up to ≈ bm{10^{113}} J/m$^3$); an energy phase transition conversion equation is established, predicting the cyclical reset back into the uniform light sea of the V0 mother field.7. Experimental Prospects for the 5.27 mm Quantum Grid: The characteristic spacing of the V0 field is reversely derived based on the 2.73 K temperature, proposing four falsifiable modern physics observational pathways, including altitude-differential microwave resonance measurements.
Category: Astrophysics
[347] ai.viXra.org:2608.0089 [pdf] replaced on 2026-09-29 09:31:22
Authors: Seungtae Kim
Comments: 36 Pages.
In the International System of Quantities (ISQ), base quantities form a conventionally chosen mutually independent subset of a system of quantities. This paper proposes a relation-first framework in which admitted unit relations are used to construct quantity dimensions before base-quantity choices are assessed. A broader class of unit-explicit equations is also introduced for relations in which explicit unit division carries physically relevant information.Candidate base-quantity sets are first tested for dimensional independence and completeness. A second, evidential criterion then assesses physical structural support from established higher-order dimensional occurrences, without uniquely selecting a base set. In an SI-oriented application, mass, length, time, electric current, thermodynamic temperature, and amount of substance receive such support. Relative to the specified admitted relation system, an independent angular dimension is required for completeness; plane angle is adopted as its representative, and spherical geometry gives sr=rad2. Luminous intensity is instead dimensionally derived through the photometric-radiometric scale link while remaining a distinct quantity kind. Logarithmic levels are reformulated as pure-number numerical index mappings retaining their field- or power-quantity context. The proposal changes dimensional and algebraic representation without changing established numerical realizations.
Category: Mathematical Physics
[346] ai.viXra.org:2608.0089 [pdf] replaced on 2026-09-02 07:29:22
Authors: Seungtae Kim
Comments: 36 Pages.
In the International System of Quantities (ISQ), base quantities form a conventionally chosen mutually independent subset of a system of quantities. This paper proposes a relation-first framework in which admitted unit relations are used to construct quantity dimensions before base-quantity choices are assessed. A broader class of unit-explicit equations is also introduced for relations in which explicit unit division carries physically relevant information.Candidate base-quantity sets are first tested for dimensional independence and completeness. A second, evidential criterion then assesses physical structural support from established higher-order dimensional occurrences, without uniquely selecting a base set. In an SI-oriented application, mass, length, time, electric current, thermodynamic temperature, and amount of substance receive such support. Relative to the specified admitted relation system, an independent angular dimension is required for completeness; plane angle is adopted as its representative, and spherical geometry gives sr=rad2. Luminous intensity is instead dimensionally derived through the photometric-radiometric scale link while remaining a distinct quantity kind. Logarithmic levels are reformulated as pure-number numerical index mappings retaining their field- or power-quantity context. The proposal changes dimensional and algebraic representation without changing established numerical realizations.
Category: Mathematical Physics