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[1913] 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
[1912] 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
[1911] 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
[1910] 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
[1909] 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
[1908] 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
[1907] 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
[1906] 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
[1905] 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
[1904] 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
[1903] 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
[1902] 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
[1901] 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
[1900] 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
[1899] 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
[1898] ai.viXra.org:2610.0005 [pdf] submitted on 2026-10-02 16:40:22
Authors: Lukas Saul
Comments: 18 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We extend the spin-fluid kinetic analog gravity model of Paper I to massive charged particles.We show that the collision term in the spin-squared sector generates the quantum potential of the Madelung equations, reproducing the Schrödinger equation and yielding a formula for ħ in terms of the model's collision parameters. We then introduce the helical vortex as the soliton structure for the electron. The helical vortex has both poloidal circulation, which gives the spin, and azimuthal circulation, which gives the magnetic moment. The pitch of the helix determines the translational velocity and is always negative in the plasma reference frame. The vortex is stabilized by the Meno mechanism—orientation-dependent collisions that create an inward recoil pressure—and by the virial balance, which includes the Coulomb self-energy. We derive formulas for the electron charge, mass, and ħ in terms of the analog parameters. We show that the helical vortex reproduces the far-field electric (Coulomb), magnetic (dipole), and gravitational (Newtonian) fields, with a Yukawa correction at intermediate distances. We show that the model reproduces the full Lorentz force, Stern-Gerlach splitting, Aharonov-Bohm phase, and Larmor precession. We discuss the g − 2 anomaly and the electron electric dipole moment as targets for future quantitative work. We predict that the electron has negative active gravitational mass while the positron has positive, and we show that this is consistent with the Eöt-Wash null results because the neutron's mass is dominated by QCD binding energy, not valence quark masses. We close with a brief mention of the three families and quarks as speculative extensions.
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
[1788] ai.viXra.org:2608.0074 [pdf] submitted on 2026-08-23 17:33:28
Authors: Vladimir S. Netchitailo
Comments: 14 Pages.
Modern cosmology is based on an extensive body of astronomical observations interpreted through theoretical models. The expansion of the Universe, Cosmic Microwave Background Radiation (MBR), primordial abundances of light elements, and large-scale structure are commonly regarded as principal observational pillars of the Big Bang Model (BBM) and its modern ΛCDM formulation. This terminology raises a fundamental methodological question: Can an astronomical observation itself constitute a pillar of a physical cosmological theory?In this paper, we distinguish astronomical observation from physical explanation and propose criteria that a genuine pillar of cosmology should satisfy. A pillar should provide a physical mechanism for an observed phenomenon, quantitatively account for its principal measurable properties, lead to independently testable predictions, and not depend critically upon unidentified physical entities or unresolved fundamental discrepancies.The four conventional pillars of BBM are examined according to these criteria. Cosmic expansion is accurately described mathematically, but the Hubble tension remains unresolved. MBR is interpreted within the hot early-Universe framework, but its present temperature is an observational input rather than an independently calculated consequence of the six-parameter ΛCDM model, while large-angle anomalies remain under investigation. Primordial light-element abundances are inferred from present astronomical observations rather than directly observed at the primordial epoch, and the lithium problem remains unresolved. Large-scale structure is successfully modeled statistically, but its formation depends critically on Cold Dark Matter, whose microscopic nature and origin remain unknown, while the fundamental nature of Dark Energy is likewise unresolved.These conventional pillars are then compared with the proposed physical pillars of the World—Universe Model (WUM). Particular attention is given to physical mechanisms, interconnected cosmological parameters, quantitative calculations, and predictions made before subsequent observations.The purpose of this comparison is not to determine which model accommodates a larger collection of observations, but to address a more fundamental question: What should constitute a genuine pillar of a physical theory of the Cosmos?
Category: Relativity and Cosmology
[1787] ai.viXra.org:2608.0073 [pdf] submitted on 2026-08-22 23:50:09
Authors: Linia Hammache
Comments: 12 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This work presents the construction of a continuous model derived from an original discrete sequence alternating between geometric and arithmetic progression, modulated by a periodic cosine function. The sequence is interpreted as an energy reservoir whose charge (arithmetic) and discharge (geometric) are controlled by a hysteresis logic. The model is enriched by coupling with a mechanical oscillator, heat production via damping, conversion into nuclear kinetic energy (fusion), and reinjection into the reservoir, realizing a self-sustained fission--fusion cycle. Each equation is derived, physically justified, and linked to the original sequence. The article details the modeling, theoretical justifications, energy couplings, and global dynamics of the system.
Category: Mathematical Physics
[1786] ai.viXra.org:2608.0072 [pdf] submitted on 2026-08-22 23:45:59
Authors: J.W. McGreevy
Comments: 22 Pages.
This monograph establishes the second major operational phase of the Thermodynamics of Arithmetic Action (TAA) framework, executing a rigorous, ab initio field quantization that unifies the smooth Archimedean continuum (R) with the discrete, fractured, non-Archimedean p-adic bulks (Qp) into a single, self-regulating topological engine. We prove that the macro-constants of nature—the speed of light (c), the Newtonian gravitational constant (G), and the reduced Planck constant (ℏ)—alongside the Standard Model parameters are the unique, scale-dependent topological gear-ratios required to satisfy Clairaut’s Theorem on mixed partial derivatives (d2U = 0) and the Adelic Product Formula (∏︁ |x|p = 1) over the universe’s middle cohomology group.By framing the complex s-plane of the Riemann Zeta Function as the conformal phase space of a sub-quantum Keplerian orbital system, we derive Max Born’s quantum probability rule (|Ψ|2 = Ψ ¯Ψ) as the literal intersection form (the Weil Pairing) required to cross-multiply continuous adiabatic spatial expansions by discrete isothermic prime entropy steps. Crucially, we introduce the Spacetime Maxwell Calculator for Class Numbers, proving that algebraic class numbers (hK ) are extracted natively from macroscopic physical constants by measuring the precessional volume of a perturbed Laplace-Runge-Lenz (LRL) vector locked inside a 6-dimensional phase space torus.
Category: Mathematical Physics
[1785] ai.viXra.org:2608.0071 [pdf] submitted on 2026-08-22 23:43:07
Authors: Ahcene Aït saadi
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
Many remarkable curves roses, the lemniscate, the cardioid, the limaçon have a heavyCartesian equation: implicit polynomials of degree 4, 6, up to 10, hard to plot point by pointand often multivalued. This paper presents a method that makes them drawable by hand,with no software and no polar paper: in an analytic frame (an abscissa axis together withan origin of ordinates Ou2032set o the axis by a distance λ), each of these curves is written asa single explicit ordinate y = f(x), which one tabulates and plots with a ruler. We provethe transition formulas and the pivot identity X2 + Y2 = y2 the engine guaranteeing thatthe one-line expression does describe the heavy curve then the equation of the line, of thecircle, the pseudo-derivative, and a proportional relation in the triangle. One section comparesthe two methods on six classical curves. The scope is honest and bounded: this is a methodof construction and of teaching, in the service of simpler access to objects reputed dicult.
Category: Functions and Analysis
[1784] ai.viXra.org:2608.0070 [pdf] submitted on 2026-08-22 23:39:24
Authors: Tomasz Kobierzycki
Comments: 22 Pages.
This work develops one (SU(m,n))-symmetric framework governed by four postulates: invariant locally measured light speed; observer-independent laws in inertial and non-inertial frames; coexistence of all physically admissible prepared states with a single observer record; anda fundamentally complex spacetime observed through a real Lorentzian projection. The fundamental arena is a pseudo-K"ahler manifold withHermitian metric and a complex four-index field equation whose trace-free sector is carried by Bochner curvature. An observer is defined by anadmissible antiholomorphic involution. Its fixed real form inherits the measured metric, sources and state tensor. The relation between complex andreal curvature is derived with realification, the Gauss equation and the real Weyl projector; in particular, Bochner curvature projects to observer Weyl curvature only when explicit extrinsic and Ricci-compatibility corrections vanish. The four-sector construction is then formulated as an orientation completion of the real observer clock--ruler plane, rather than as a second fundamental spacetime. Quantum coexistence is represented by a complex rank-four tensor carrier with full Hermitian conjugation, a hypersurface overlap and covariant rank-eight evolution along the lifted observer clock. The common structure contains flat, Schwarzschild, Kerr, Kerr--Newman, LTB, FLRW, photon, free-graviton, hydrogen and ultraviolet worked sectors. The framework yields the locally invariant null speed, massless helicity-twograviton kinematics, reciprocal regular geometries, the relativistic Coulomb spectrum and the four-sector cancellation of local ultraviolet pole sources.
Category: Quantum Gravity and String Theory
[1783] ai.viXra.org:2608.0069 [pdf] submitted on 2026-08-19 21:27:04
Authors: Ori Chamo, Yossi Eliaz
Comments: 6 pages, English. PRL-format Letter followed by Supplemental Material.
Periodic-orbit families are often represented through low-dimensional invariant coordinates, although projected branches need not preserve the connectivity of the underlying solution manifold. We use numerical continuation to examine the 135,445 unequal-mass planar three-body periodic orbits reported by Li, Li, and Liao, whose corrected scale-invariant period-angular-momentum representation was subsequently interpreted as two independent sets. The two projected branches are connected by verified continuation within a single sampled continuation component. The invariant projection exhibits a singular locus consistent with the apparent branch separation. High-precision Floquet calculations identify a +1 transition at one representative stability boundary and an opposite-Krein Hamiltonian-Hopf transition at another. Projection geometry and symplectic spectral geometry therefore provide complementary descriptions of the same periodic-orbit manifold.
Category: Mathematical Physics
[1782] ai.viXra.org:2608.0068 [pdf] submitted on 2026-08-20 23:34:21
Authors: J. W. McGreevy
Comments: 29 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This monograph establishes the formal foundations of the Thermodynamics of Arith-metic Action (TAA), a scale-dependent geometric and statistical framework that unifiesmacroscopic classical gravitation, quantum higher gauge field networks, and discrete non-Archimedean number fields into a single, continuous pipeline of scale-dependent resolution. The universal sorting mechanism is driven by the Regime Determinant S/ℏ, tracking the ratio of total localized physical action over a fixed temporal window to the Planck quotient. We demonstrate that the foundational physical dimensions and algebraic structures of our universe are the unique, mandatory stabilizers required to enforce a global Hyperbolic-Elliptic Index 0 Conservation Law across all number fields. By mapping the Minkowski spacetime invariant, Fermat’s Last Theorem, Hamiltonian and Lagrangian phase spaces, and the Herbrand—Ribet arithmetic mirror into a rigid 2 × 2 Upper Triangular Transformation Matrix, we derive the emergence of exactly 3D + 1 spacetime, the strict left-handed chiral orientation of gauge forces, the topological confinement of spin-1/2 quarks, and a native, geometric resolution to the Strong CP Problem (θ ≈ 0). The entire framework is anchored to the universal short exact sequence of Derived Differential Cohomology, proving thatmass-energy and metric curvature are the inseparable dual payloads of a single, self-regulating holographic index engine.
Category: Mathematical Physics
[1781] ai.viXra.org:2608.0067 [pdf] submitted on 2026-08-20 23:24:38
Authors: Yuechun Huang
Comments: 15 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Based on the matter field theory, this paper proposes that the field generated by the basic moving units of matter (atoms, electrons) possesses both energyu2011conserving and informationu2011holographic properties, and propagates in vacuum at the speed of light. Within this theoretical framework, we classify all interactions in the universe into three fundamental modes: strong interaction (energyu2011exchange dominated), weak interaction (informationu2011exchange dominated), and nonu2011interaction (corresponding to dark energy). We systematically demonstrate that macroscopic celestial motions and microscopic particle motions obey a unified dynamical law. By drawing an analogy with the mathematical structures of Newton's law of universal gravitation, the Lorentz force, and Coulomb's law, we derive Huang's formula F = K .P1. P2 / R² for the gravitational interaction between cou2011moving celestial bodies. In the solar system reference frame, the formula reduces exactly to the Newtonian form, and it provides a purely dynamical explanation for the anomalous rotation curves in the outer regions of galaxies (the dark matter phenomenon) without introducing any additional mass term. The theory also offers a fresh perspective on the origin of galactic redshifts, and is expected to serve as a bridge between classical gravitational theory and quantum field theory.
Category: Astrophysics
[1780] ai.viXra.org:2608.0066 [pdf] submitted on 2026-08-19 14:14:16
Authors: Russell S Clark, Russell S Clark II
Comments: 16 Pages.
For the Minkowski vacuum and the right Rindler wedge, the Bisognano—Wichmann theorem fixes the vacuum modular flow to be Lorentz-boost flow. For a translated finite-energy excitation, this implies an exact, acceleration-independent identity for the vacuum-relativeone-sided modular energy,d/dp∆⟨KW⟩ = 2πℏcEW(p),where p is displacement normal to the horizon and EW(p) is the vacuum-subtracted energycontained in the wedge. If the excitation is concentrated well inside the wedge, Ew(p) ≃ E.Selecting a Rindler observer of proper acceleration a converts the dimensionless modulargenerator into the proper-time Hamiltonian Ha = kBTUKw, with TU = ℏa/(2πckB). Hence d/dp∆⟨Ha⟩ = a/c2Ew(p).Under a specified quasistatic control protocol, this is the external holding-force identity. Atthe reference orbit, a wedge-contained narrow state of invariant mass M obeys |Fhold| = Ma.The entanglement interpretation is more limited. For a finite state, the exact regulatedrelation isd/dp∆⟨Ha⟩ = Tu x d∆Sw/dp +kBTu x d/dp x Srel(ρW,p∥Ωw),so Tu x dSw alone is not generally equal to work. The relative-entropy term is second orderonly for infinitesimal state variations. In that linear-response sector, the entanglement firstlaw yields d(δSw)/dp = 2πkBδE/(ℏc), and for δE = Mc2 this reproduces the coefficient in Verlinde’s local entropy—displacement ansatz. The result is therefore an exact modular-work identity and a linearized entropic representation of Rindler holding force, not a derivation of acceleration, general equations of motion, or gravity.
Category: Thermodynamics and Energy
[1779] ai.viXra.org:2608.0065 [pdf] submitted on 2026-08-18 19:28:43
Authors: Ahcene Ait Saadi
Comments: 11 Pages.
Abstract. We study two elementary periodic functions — the scaled fractional part spp x (a pure ramp of period p) and its complement cpp x = p−spp x — together with the single algebraic identity spp x + cpp x = p. Because their derivatives are the constants +1 and −1, they turn a range of nonlinear differential equations into closed one-line solutions, they solve first-order transport and inviscid Burgers equations exactly, and they let one write intricate periodic curves — half-circle chains, staircases, asymmetric arcs, modulated ramps — each from a single algebraic expression. A complex generator Z(x) = sp x+i cp x opens a second, geometric part: its powers Z n are explicit algebraic curves of degree n, and the normalized family {Z α/pα} covers an eye-shaped region with an exactly empty core bounded by the unit circle. The aim is not to compete with Fourier analysis but to offer a light, exact notation for the angular, piecewise-affine patterns where Fourier series are heavy and only approximate. All identities have been verified symbolically and numerically (sympy, machine precision).
Category: Functions and Analysis
[1778] ai.viXra.org:2608.0064 [pdf] submitted on 2026-08-18 19:26:57
Authors: Dinuo Chen
Comments: 16 Pages.
Near-ultrasonic frequency bands provide an underutilized portion of the acoustic spectrum with relatively low perceptual salience[1, 2] while remaining potentially usable with conventional audio hardware. This paper investigates the feasibility of transmitting analog audio over near-ultrasonic frequency bands using consumer-grade loudspeakers, microphones, and sound cards. A singlesideband (SSB) modulation scheme is employed to shift baseband audio into the near-ultrasonicrange, where it is transmitted through an acoustic channel and subsequently demodulated at the receiver. The system is evaluated under various transmission conditions using commonly available audio equipment. Signal quality is assessed through spectral analysis and objective similarity metrics between the original and recovered audio signals. Experimental results demonstrate that consumer audio devices are capable of supporting near-ultrasonic analog audio transmission within the limits imposed by their frequency response. Although attenuation and distortion increase toward the upper end of the transmission band, the original audio can still be recovered with acceptable quality under suitable conditions. These findings suggest that near-ultrasonic acoustic channels couldprovide a low-cost communication medium for specialized applications without requiring dedicated ultrasonic transducers.
Category: Digital Signal Processing
[1777] ai.viXra.org:2608.0063 [pdf] submitted on 2026-08-18 19:24:13
Authors: Holger Troitzschel
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper introduces a self-referential cosmological framework in which spacetime ge-ometry, matter, and gravitational interactions are proposed to emerge exclusively from theself-observation of quantized electromagnetic fields. By coupling U(1) gauge fields directlyto the discrete graph structure of Loop Quantum Gravity (LQG), a non-linear feedback loopbetween energy density and spatial volume is established. We define a quantum Hamil-tonian operator for light acting on spin-network states and argue that electromagnetic fluxexcitations can alter geometric quantum numbers. In addition, we explore whether fermionicmatter can emerge as topological braids of light ribbons. Physical implications are discussed,including a possible resolution of singularities via a stable "Quantum Geon" configuration,as well as testable predictions concerning alternatives to particle dark matter and signaturesin primordial gravitational waves.
Category: Quantum Gravity and String Theory
[1776] ai.viXra.org:2608.0062 [pdf] submitted on 2026-08-18 19:22:59
Authors: Yuan Di, Zongyan Liu
Comments: 29 Pages.
Millions of female university graduates in China face a severe shortage of standardized "two-day-office office jobs" each year, a structural mismatch that exacerbates employment pressure. Based on empirical data from the Anhui provincial civil service examination, this paper proposes a "dignity-defense-oriented reproductive decision-making model": Faced with the gap between high career expectations and reality, female university students, out of dignity defense and risk aversion to maternal punishment, prefer survival strategies such as "slow employment" and the "civil service exam craze" to marriage and childbearing, thus significantly suppressing the overall birth rate. To address this dilemma, it is recommended to reconstruct the university employment quality evaluation system and disciplinary structure, introduce national policies to reduce maternal punishment, and promote a shift in the macro-market towards women's self-indulgent consumption.
Category: Social Science
[1775] ai.viXra.org:2608.0061 [pdf] submitted on 2026-08-17 16:19:29
Authors: Rafael Maya
Comments: 18 Pages. Code for computations presented in the research paper is available upon request
The invariant four-volume of an event's causal past is a well-defined geometric functional of a Friedmann-Lemaître-Robertson-Walker expansion history. We study its normalized form, C(T) = V4(T)/V4(To), and the family of causal-fraction ages Tf defined by C(Tf) = f. We give a closed observable form written entirely in H(z), the exact self-similar limit Tr→ Tof1/4. and an O(N) moment decomposition enabling per-sample evaluation on posterior chains. Two structural results follow. The dimensionful statistic is almost completely degenerate with the cosmic age (posterior-scaled gradient alignment cos = 0.9991 in flat wow CDM), whereas the dimensionless ratio pf = Tr/To is exactly independent of the overall expansion scale. Its sensitivity kernel K(z) = 8pf/ w(z) possesses a single sign-change node migrating with f, and at f. = 0.2627 the kernel's lobes cancel exactly: pf is simultaneously Ho-free and first-order blind to wo, a differential sensor of dark energy across z ~ 0.40 that within flat ACDM tracks the matter-dark-energy handover, 2A(z) = 0.46 ± 0.03. Transforming every stored sample of the public DESI DR2 BAO+CMB+supernova wow CDM chains yields T1/6 medians displaced by 40-46 Myr (2.5-2.9 posterior standard deviations) from the Planck ACDM value T1/6 = 8.6452 Gyr, compressing the evolving-dark-energy preference into one scalar, and we freeze three falsifiable predictions for DESI DR3 and Euclid. A companion paper derives the asymptotic behavior of fixed four-volume increments in an eternally accelerating future.
Category: Relativity and Cosmology
[1774] ai.viXra.org:2608.0060 [pdf] submitted on 2026-08-17 16:23:55
Authors: Rafael Maya
Comments: 8 Pages. Code for computations presented in the research paper is available upon request.
A common intuition holds that an eternally accelerating universe, having a finite event horizon, should accumulate only a finite amount of causally connected spacetime. We show by direct integration that this is incorrect: in de Sitter space the causal-past four-volume of a comoving observer grows without bound, V4(t) ~ (4πc/3H) (t - H¹) as t , even though the past-light-cone radius saturates at c/H. Consequently, crossings of any fixed four-volume increment AV > 0 form an infinite sequence whose proper-time spacing converges to the finite constant At = 3H AV4/(4πc¹). For a flat ACDM continuation with Planck-2018 baseline parameters and the normalization AV4 = f V4(To) with f = 1/6, the first future increment completes 0.580 Gyr from the present (cosmic age 14.375 Gyr) and the spacing decreases monotonically toward At = 40.1996 Myr. The limit discriminates among cosmic futures: evolving or decaying dark energy, phantom finite-time singularities, and recollapse generically break the uniform-spacing asymptote, which is conditional on the approach to a de Sitter phase.
Category: Relativity and Cosmology
[1773] ai.viXra.org:2608.0059 [pdf] submitted on 2026-08-17 20:43:05
Authors: Brent Hartshorn
Comments: 11 Pages.
Cross-language interoperation is normally a matter of agreeing on a boundary: a foreign function interface, a generated shim, a marshalling layer, or a shared intermediate representation. We describe a system in which no boundary exists. Subsets of C++ and of Rust are each lowered to plain C source, and one C compiler consumes the result, so a Rust function calling a C++ method is a C function calling a C function — same translation unit, same intermediate representation, same register allocator. The two lowerings are chosen to converge on identical symbols, with the consequence that a Rust impl Drop and a C++ destructor over the same data emit the same function, and a C++ class may hold a Rust value by value without a shim, a wrapper, or an annotation.Removing the boundary between the languages exposes a second one, below them: the artifact is C, but a C compiler, an assembler, a linker and a runtime still stand between C and a running program, and conventionally those are separate projects. We report a stack in which they are not. The whole path — two source languages to C, C to machine code, machine code to a static ELF executable — is roughly fifty thousand lines in one repository, with no external compiler, assembler, linker or C library involved.
Category: Data Structures and Algorithms
[1772] ai.viXra.org:2608.0058 [pdf] submitted on 2026-08-16 19:32:57
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 9 Pages. (Note by ai.viXra.org Admin: Title and abstract MUST BE in English!)
This work begins with a simple question: could what we describe as translation and force actually be the local manifestation of a fundamentally angular dynamics? In the *Principium Geometricum* (PG), we investigate the possibility that the most fundamental physical description does not start with a body's trajectory through a pre-existing space, but rather with states of phase, rotation, closure, and causal updating. We introduce a normalized phase state q(ϕ) = (cos ϕ, sin ϕ), for which ∥ ˙q∥² = ω². In parallel, we consider the geometry of a torus, whose volume is VT = 2π²Ra². In the reduced geometric case where R = a = r, we have VT = 2π²r³. These two structures suggest the quantity IT ≡ VT 2π² ∥ ˙q∥² = r³ω². We propose investigating the conservation of IT for orbital states associated with the same global source. If IT is constant, Kepler's third law follows directly, as does—for the circular projection—an acceleration proportional to ru207b². The observational identification IT ↔ GM then recovers the Newtonian limit. This result does not constitute a microscopic derivation of gravity. The conservation of IT remains a physical hypothesis requiring further substantiation. The aim is to show, in an explicit and falsifiable manner, where the geometric identity ends, where the PG hypothesis enters, and how the classical limit is recovered.
Category: Mathematical Physics
[1771] ai.viXra.org:2608.0057 [pdf] submitted on 2026-08-16 19:22:08
Authors: Mustafa Karatüm
Comments: 20 Pages. https://doi.org/10.5281/zenodo.21963450
We present the Topological String-Gradient Theory (TSGT), a framework in which space-time is discrete at the Planck scale and gravity is the gradient of the spacing betweendiscrete elements ("pixels") rather than a fundamental force. Two kinematic postulates—a spatial pixel strain set by the Newtonian potential and an equal and opposite tempo-ral strain—reproduce the weak-field Schwarzschild metric, and hence Newtonian accelera-tion, gravitational redshift, the Shapiro delay and the full general-relativistic light deflec-tion ∆θ = 4GM/c2b. We stress that this reproduction is by construction rather than aprediction. The discrete substrate is taken to be a random Poisson sprinkling of densityL−4p rather than a regular lattice. This choice preserves Lorentz invariance statistically,and thereby removes the preferred-frame and anisotropy problems that afflict lattice for-mulations; it also withdraws the energy-dependent photon dispersion, gravitational-wavedispersion and propagation-anisotropy signatures claimed in earlier versions of this frame-work, which we retract explicitly. In exchange, TSGT acquires a quantitative cosmologicalconsequence. If cosmic expansion proceeds by the creation of new pixels rather than bythe stretching of existing ones—the only option compatible with an invariant Lp—then thenumber—volume correspondence carries Poisson fluctuations δN ∼ √N , and the cosmologicalterm conjugate to the four-volume inherits a residual magnitude Λ ∼ V −1/2. Numericallythis gives ρΛ ≃ 2.8 × 10−27 kg m−3 against an observed 5.8 × 10−27 kg m−3: agreement withina factor of two, compared with the 10123 discrepancy of the naive Planck-density estimate.This argument is not original to TSGT—it is Sorkin’s heuristic, developed within causal settheory—but it follows from TSGT’s own postulates without additional assumptions, andit carries a signature that current surveys can test: the dark energy term is not constantbut fluctuates, so w̸ = −1. We then show that the two kinematic postulates need not bepostulated at all. Written locally, the number—volume correspondence reads √−g = L4pn(x),which is the unimodular constraint; enforcing it in an Einstein—Hilbert action yields thetrace-free Einstein equations, with Λ appearing as an integration constant rather than as aparameter, and with the weak-field metric recovered rather than assumed. The price is statedplainly: TSGT thereby becomes provably equivalent to General Relativity at the classicallevel, so whatever independent content it possesses lies entirely in the integer character ofthe pixel count. Unresolved problems, including the absence of a dynamical equation for thepixel density and the difficulty of deriving excitations on an irregular substrate, are listedexplicitly
Category: Quantum Gravity and String Theory
[1770] ai.viXra.org:2608.0056 [pdf] submitted on 2026-08-15 16:39:02
Authors: Karl Simon
Comments: 11 Pages.
AbstractThe Standard Model perfectly describes the system of elementary particles and their interactions, yet it fails to explain why there are precisely three generations of quarks and leptons, and why quarks possess fractional electrical charges. Furthermore, it does not address gravity’s fundamental mechanism in forming spacetime. This paper presents a novel structural model to shed light on these open questions. The model explores how a fundamental particle theory can be constructed from the simplest possible combination of a single chiral particle (b) and its antiparticle (q). Through geometric reflection, four elementary components emerge (b, p, d, q), whose purely topological shapes directly encode chirality and helicity. By introducing an invariant isospin (iI) and an invariant hypercharge (iY), electric charge (Q) is defined as an emergent property of specific substructures within states. The model demonstrates that simple combinatorial rules spontaneously generate structural quartets consisting of one lepton alongside three isomeric quark structures, whose statistical charges correspond exactly to the fractional charges of quarks. [1]Crucially, the model resolves the classic mass paradox and fine-tuning problem of preon theories—where massive binding energies must artificially cancel bare energies—by introducing an intrinsic, algebraic subtraction mechanism within the relationship between the W, Z, and the electron. Through the structural combinations W+Z-W, W+Z-Z, and the complete subtraction W+Z-W-Z -> e, the dynamic mass generation of the weak bosons and the very low mass of the electron are derived directly from state definitions without free parameters. Within this framework, both mass and electric charge emerge as phenomena strictly bound to irregular helicity configurations, identifying the seemingly vanished binding energy as the structural energy equivalent of the electric charge. This mechanism mirrors the immense energy scales conceptually postulated in Majorana-like mass terms for right-handed states without charge. [6] Tthe Higgs boson is naturally identified not as a separate elementary particle, but as the massive, scalar excitation state of the fundamental vacuum (bpdq) showing an inherent structural preference for aligned, "regular" helicities that governs the mass generation and electrical charge of particles.Finally, a potential connection to geometric gravitation theory is suggested, reminiscent of historical attempts to explain gravity as a structural residue between electric attraction and repulsion [4] Here pairs of photons of spin 2 interact via a double spinflip with neutrinos as the fundamental building blocks of all matter.
Category: High Energy Particle Physics
[1769] ai.viXra.org:2608.0055 [pdf] submitted on 2026-08-15 23:52:43
Authors: Frank W. Brown
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
I present a multi-scale empirical data appendix verifying the field equations of Curved Temporal Inertia Cosmology (CTIC). This 1-page report compiles two automated verification ledgers running natively within the open-source repository. First, a sequential 3-detector LIGO/Virgo matched-filter analysis of event GW170817 targets the model's non-axial metric twisting shear envelope (h_omega) using a stable time-domain RMS normalization layer. The network trace reveals an unmistakable, high-confidence Signal-to-Noise Ratio (SNR) peak of 28.2123 at LIGO Hanford (H1), an expected sub-threshold validation of 7.3335 SNR at LIGO Livingston (L1), and a baseline antenna blind-spot trace of 5.4227 SNR at Advanced Virgo (V1). Second, the report maps a macroscopic coordinate domain ledger tracking a triaxial ellipsoidal subcluster grid across 40 morphologically diverse galaxy clusters, yielding a uniform observational deviation margin of < 2.0% using strictly 100% visible baryonic mass parameters. Complete automated replication pipelines are open-sourced at: https://github.com/LiamLumen/CTIC-Quantum-Dynamics
Category: Relativity and Cosmology
[1768] ai.viXra.org:2608.0054 [pdf] submitted on 2026-08-14 20:08:25
Authors: Arunas Ostasevicius
Comments: 5 Pages.
The paper presents a fundamental historical and mathematical exposure of the kinematic foundations of the Special Theory of Relativity (SR). Based on a rigorous analysis of the original text of J. C. Maxwell’s Treatise on Electricity and Magnetism (1873, paragraphs 600—601), it is proved that the original equations of the electromagnetic field initially contained total (material) time derivatives and convective field drift operators (v · ∇). It is demonstrated that Maxwell’s original system was naturally invariant under classical Galilean transformations in absolute Euclidean space. The study establishes that SR arose as an artificial geometric artifact (Lorentz transformations, Minkowski metric) designed to compensate for the fatal castration of the field equations by O. Heaviside, who forced the convective velocity of the coordinate axes to zero and replaced the total derivative with a partial one. The physical reality of Maxwell’s convective drift is confirmed by the one-way mirrorless experiments of S. Marinov and R. De Witte, completely rendering the metric space-time paradoxes of modern physics unnecessary.James Clerk Maxwell, Oliver Heaviside, Galileo invariance, total derivative, convective term, Stefan Marinov, Roland De Witte, Special Relativity critique.
Category: Relativity and Cosmology
[1767] ai.viXra.org:2608.0053 [pdf] submitted on 2026-08-14 13:31:35
Authors: Joseph Shaffer
Comments: 6 Pages.
Spacetime, matter, and physical law emerge as macroscopic unitary outcomes of a system converting high-energy chaos into optimal stability. The universe begins as a chaotic tension matrix (Domain A) filled with unstable local maxima. A tension-bearing phase boundary-the mat-absorbs chaotic shear vectors, flattens them into coherent spatial gradients, and locks unfilterable stress peaks into localized matter structures. When the system crosses a critical radius threshold, a subcritical pitchfork bifurcation rigidifies the mat and produces the calm fabric (Domain B). Stability arises from the large-number postulate: chaotic modes interacting in enormous numbers become unresolvable, leaving only stable structures visible. Spacetime and matter are the macroscopic shadows cast by submerged chaos.
Category: Astrophysics
[1766] ai.viXra.org:2608.0052 [pdf] submitted on 2026-08-13 12:06:32
Authors: XinXin Li
Comments: 5 pages. CC BY 4.0.
We establish an exact algebraic identity connecting the cumulative near-conjugacyerror Eσ of a base-6 circle-rotation model of the Collatz map (HonarvarShakibaei Asli, 2026) with the terminal correction ε in the classical stopping-timeidentity. For a convergent Syracuse orbit, Eσ = 1 − log6(5n0+1)+ (log2 n0 + ε)·log6 2, in which the Syracuse stopping time τcancels exactly via the change-of-base formula log2 6 · log6 2 = 1.Consequently Eσ = O(1) ⇔ ε = O(1) ⇔ Σ 1/ni−1 = O(1), so theboundedness of the reciprocal sum becomes the central open question. The identity isverified to machine precision (≤ 2×10−15) for every tested n0 ≤ 77031.
Category: Number Theory
[1765] ai.viXra.org:2608.0051 [pdf] submitted on 2026-08-12 20:12:06
Authors: Arunas Ostasevicius
Comments: 6 Pages. 2 figures.
An alternative concept for describing the dynamics of celestial bodies based on non-linear self-oscillations in a material cosmic medium is presented. From first principles — Boltzmann's kinetic equation — a closed system of two coupled quaternionic equations is rigorously derived. These equations describe the orbital motion of a planet's center of mass and its axial rotation as stable phase attractors (limit cycles). Using the analytical method of phase averaging, the deformation of Mercury's phase trajectory under the influence of polytropic changes in the parameters of the medium near the Sun is calculated. The superiority of non-linear oscillation theory methods over the geometrization of spacetime is demonstrated, allowing for the complete abandonment of the cumbersome linear algebra apparatus of General Relativity and the postulation of mystical initial conditions.planetary dynamics, self-oscillations, Boltzmann kinetic equation, quaternion, limit cycle, phase averaging, cosmic medium, Ether, perihelion precession, general relativity alternative
Category: Astrophysics
[1764] ai.viXra.org:2608.0050 [pdf] submitted on 2026-08-12 20:10:56
Authors: Khazri Bouzidi Fethi
Comments: 9 Pages.
We study the Diophantine equation 1/p_1 = 1/p_2 + 1/p_3 + 1/p_4 for distinct primes p_1, p_2, p_3, p_4, a special case of the Sierpiński—Schinzel unit-fraction equations. We introduce a spectral coherence threshold R, derived from an exact infimum formula for a normalized exponential sum over the primes involved via the Kronecker—Weyl equidistribution theorem, and show that R = 1/2 is its sharp transition value. For three primes, we establish an exact identity linking R to prime gaps, giving a new proof that no three consecutive primes satisfy the analogous three-term equation. For four primes, we combine this classification with an exact divisor-based algorithm to search over 6 times 10^8 configurations, finding no solution for p_1 le 5431 but reporting the closest known near-solution. We prove that no solution can occur with the three larger denominators in arithmetic progression, and record a short, fully general divisibility argument showing that no such equation admits a solution in distinct primes for any number of terms — clarifying explicitly that this fact concerns single-prime denominators only, not the composite-denominator setting central to the Sierpiński—Schinzel conjectures.
Category: Number Theory
[1763] ai.viXra.org:2608.0049 [pdf] submitted on 2026-08-11 12:20:40
Authors: Lluis Eriksson
Comments: 9 pages, 1 figure. Exact d=5 inverse commutator cost: 12 Horn chambers, optimal-rank law, sharp tax [1,5/2], triangular synthesis, and reproducible rational certificates.
For a prescribed traceless Hermitian five-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. If g_i=lambda_i-lambda_{i+1} are the ordered spectral gaps, the answer is the maximum of six explicit rational linear forms and their reversals. Exact Littlewood-Richardson enumeration gives 142 Horn inequalities. Twelve sparse dual identities prove the lower facets, and twelve rational singular-spectrum maps attain them; exact cone certificates prove completeness without sampling. In contrast with the two qutrit facets and four four-level facets, dimension five has twelve exposed facets and open chambers that force rank four. For every nonzero target, the least rank of an optimal factor is max(n_+(F),n_-(F)). We also prove the sharp tax 1 <= kappa_5/(||F||_1/2) <= 5/2 with complete equality loci, and the exact balanced triangular perimeter S_2^2=12 sqrt(3) kappa_5. Two rational certificates and an independent deterministic LP campaign accompany the paper.
Category: Mathematical Physics
[1762] ai.viXra.org:2608.0048 [pdf] submitted on 2026-08-11 13:00:56
Authors: Lluis Eriksson
Comments: 10 Pages.
Under an explicit noncontextual homogeneous-response ansatz for rank-one quantum effects, we study normalization on every unitary rotation of a fixed finite POVM. The orbit-normalization operator diagonalizes on the projective harmonics of complex projective space. We derive its weighted all-degree singular spectrum and show that the smallest non-Born spectral value is the sharp condition number controlling distance from the affine space of trace-one Hermitian quadratic responses. For dimensions at least three, the high-degree spectrum of a finite seed converges to the sum of squared aggregate ray weights; for an outcome-simple equal-trace seed with N outcomes, the limit is d squared divided by N. Combining this ceiling with the forced geometry of the two smallest tight frames solves the global equal-trace design problem in every dimension d at least five. An orthonormal-basis seed uniquely maximizes the all-degree Born-rigidity gap, with value d minus 6 divided by d plus 1, up to unitary equivalence and outcome relabeling. Every distinct-outcome overcomplete seed in the stated class is strictly worse. By contrast, every weighted complex projective 2-design has a degree-two nullspace and therefore zero rigidity gap. Thus measurements optimal for state tomography can be maximally non-rigid for this covariant normalization objective. The result concerns one-step response fields and does not derive state update, intrinsic randomness, or microscopic particle dynamics.
Category: Mathematical Physics
[1761] ai.viXra.org:2608.0047 [pdf] submitted on 2026-08-11 13:47:42
Authors: Lluis Eriksson
Comments: 10 pages, 1 figure. Reproducible certificate and independent verifier are linked in the PDF.
A passive lossless network may route the same k-dimensional input channel to different output subspaces at different frequencies. Every two-frequency restriction can be cheap while the joint task is not. For L distinct boundary frequencies and mutually orthogonal prescribed output k-planes, we prove that the minimum McMillan degree among square finite rational-inner transfer matrices regular at the interpolation nodes is exactly k(L-1). Each pair alone requires degree k, so the largest two-node minimum underestimates the global memory by the unbounded factor L-1. The result is independent of node spacing. Necessity follows both from a zero budget for an analytic minor and from a Pick-Stein displacement identity whose negative inertia cannot exceed realization rank. Sufficiency follows from an explicit positive Pick completion. Beyond exact orthogonality, we derive a general cross-frequency inertia certificate, a gauge-independent span bound, an open robust region preserving the integer memory count, and a fail-closed noisy-eigenvalue certificate. Deterministic code tests arbitrary nodes, synthesizes minimal conservative realizations, and independently verifies the stated identities.
Category: Mathematical Physics
[1760] ai.viXra.org:2608.0046 [pdf] submitted on 2026-08-11 15:21:20
Authors: Lluis Eriksson
Comments: 11 pages, 2 tables, 1 figure. Exact spin-j echo spectra, finite frames with stability bounds, sharp link-OS/sinc boundary, and connected HS nuclear cutoff.
Four balanced spin kicks along the vertices of a regular tetrahedron generatean order-dependent eight-pulse echo. We prove that all 24 echo orders have oneconjugacy class in SU(2). Haar randomization of only the global orientationtherefore gives an order-law-independent, self-adjoint random-unitary channelon every spin-j matrix algebra. Its exact eigenvalues are normalized SU(2)characters, lambda_l=U_{2l}(q)/(2l+1), with multiplicity 2l+1 and an explicitfinite-pulse architecture polynomial q=1-A/2. The maximal link-reflection-positive interval connected to zero is alpha<=pi/(4j+1), with an exact endpointequation and a finite OS Hamiltonian under strict inequality. In the doublescaling N=4j+1, y=xi/sqrt(N), the full tower converges uniformly tosinc(8xi^2u). This gives the sharp full-tower boundary xi_c=sqrt(pi/8), acritical boundary law N lambda_top -> 3pi/8-2s, an explicit scaled mass profile,and an ultraviolet heat-trace integral. The fixed-rank limit recovers the fuzzy-sphere Laplacian. Poissonization yields a genuine CPTP semigroup and an exactmany-body connected nuclear profile exp(3e^-c)-1. Symbolic and deterministicmatrix certificates accompany the manuscript.The Haar average also has explicit exact finite implementations. A classicalpositive Gauss--Legendre/trapezoidal cubature at bandlimit 4j needs(4j+1)(2j+1) order-conditioned frames, or (4j+1)^2(2j+1) frames when the sameframe list must be order oblivious.The common-class proof reduces the 24 orders to the even and odd A4 orbits.For finite implementations, a separate stability bound controls l1 weighterror, orientation displacement, and pulse perturbations; total variationagainst Haar is not used for discrete frames.
Category: Quantum Physics
[1759] ai.viXra.org:2608.0045 [pdf] submitted on 2026-08-11 15:57:16
Authors: Lluis Eriksson
Comments: 9 pages, 1 figure, 1 table. Exact generic memory law, colliding-target discontinuity, noisy projector certificate, and three-line phase diagram.
At L boundary frequencies, a passive lossless network must route one fixed k-dimensional input channel to prescribed output k-planes. For targets with joint span dimension r, every square finite rational-inner interpolant satisfies the sharp universal sandwich r-k <= d_min <= k(L-1). Direct-sum targets therefore have exact minimum McMillan degree k(L-1); when N >= Lk this maximal-memory locus is open and dense. The paper gives an explicit positive Pick completion, a realization- and inertia-based lower bound, a family of targets that collide while retaining maximal exact degree for every nonzero opening, an exact quadratic certification margin, and a fail-closed noisy projector test. For three scalar target lines it also proves the complete phase diagram: degree zero for one common line, degree one exactly for three distinct coplanar lines, and degree two otherwise. Deterministic certificates and an independent implementation accompany the proofs.
Category: Mathematical Physics
[1758] ai.viXra.org:2608.0044 [pdf] submitted on 2026-08-11 19:17:05
Authors: Keiji Yoshimura
Comments: 22 pages. English translation edition v1.0.1-EN1 of the Japanese scientific baseline v1.0.1. Associated public reproducibility repository is linked in the manuscript.
This study reconstructs the Japanese rice industry not as a single price chain but as a multi-actor network in which goods, money, information, risk, authority, and explanations move at different speeds and levels of aggregation.Using public statistics, administrative and legal records, industry statements, and a purposively sampled media corpus, the audit fixed price stage, unit, period, product, and contract conditions before testing end-to-end traceability.Public sources provide substantial visibility into quantities, stage-level averages, production costs, inventory volumes, retail transaction prices, and policy outputs. They do not, however, permit continuous monetary tracing of the same contract, inventory cohort, or product.Four principal breaks were identified: the producer's final receipt, inventory acquisition cost, absolute wholesale selling prices, and product-level retail procurement, costs, and profits. Consequently, price-stage differences or bridge residuals cannot by themselves identify wholesale or retail profit, profiteering, or the contribution of a single actor.Policy responses since 2025 shifted from conditional auctions to downstream direct contracts, official self-review, and statistical and legal redesign, while the pure retail-price effect of reserve-rice releases and the practical effectiveness of the new reporting system remain unidentified.A staged transparency architecture is proposed as a design implication: common metadata and measurement crosswalks, anonymous price-bridge pilots, and eventually an integrated six-flow and cohort infrastructure.The study does not determine a fair price, a profiteering actor, collusion, or a pure policy effect; it specifies what is observable, where public traceability breaks, and what evidence would update the conclusions.
Category: Economics and Finance
[1757] ai.viXra.org:2608.0043 [pdf] submitted on 2026-08-12 01:48:33
Authors: Joseph Mcgreevy
Comments: 20 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We formalize a unified geometric and representation-theoretic architecture bridging the continuous deformation of modular parameter spaces to the discrete, quantized structures of arithmetic number fields and local gauge theories. In the first part of this work, we present astructured verification of the Birch and Swinnerton-Dyer (BSD) Conjecture for Rank 2. By defining a stationary modular wave equation via the Maass-Laplacian, we isolate the weight-12 cusp form ∆ as an on-shell, massless zero-mode. At the bad reduction prime p = 691, this continuous flux degenerates against a singular cusp, collapsing the higher-dimensional geometric cycles of the 3-dimensional Kuga—Sato variety W2 onto the n = 0 neutral core of the Schmid weight filtration light cone. We construct the explicit 2×2 p-adic Syntomic Comparison Matrix, proving that its determinant is non-zero and non-degenerate under local-to-global stress at the fracture wall if and only if the p-adic N´eron—Tate height regulator is non-singular. In the second part, we document a precise homological parallel between this arithmetic localization and the structural stability constraints of quantum gauge fields. We demonstrate that the mechanism passing the E2 quasi-modular anomaly through higher-weight Eisenstein series mirrors the scaling of a gauge connection protecting a positive-definite kinetic energy landscape. This continuous propagation forces a compact Lie group topology, which shatters at the 691 boundary into an 11-dimensional coefficient space—casting a direct arithmetic shadow onto the χ 11 odd eigenspace of the cyclotomic minus class group via the Herbrand—Ribet theorem. We present this unified framework not as a physical identity, but as a rigid representation-theoretic blueprint governing Rank-2 root system degenerations at the boundary of a continuum.
Category: Mathematical Physics
[1756] ai.viXra.org:2608.0042 [pdf] submitted on 2026-08-10 08:28:18
Authors: Lluis Eriksson
Comments: 17 pages, 4 figures, 2 tables. Includes robust separation theorems, a vacuum-complete Ramsey model, 60-digit certificates, open-source code, frozen ledgers, and passing CI checks.
We study whether passive reservoir filtering can suppress decoherence more effectively when its channel mixing is irreducible, even after fixing the passband responses and rational complexity. For every integer S ≥ 5, we construct an explicit causal inner six-port network with three signal and three vacuum-loss ports. Its signal block is a rational Schur transfer satisfying 3(S−1) delayed full-spark tangential calibrations and exhibiting exponentially small leakage on two stop arcs. In contrast, every transfer of the same bidegree possessing a constant nontrivial reducing channel and satisfying the same calibrations retains unit stopband norm.We strengthen this exact separation with a quantitative finite-error obstruction: for calibration defect δ and sampled reducing-line defect β, comparator leakage is bounded below by [1−C_S(δ+β)]_+, with C_S given explicitly by finite singular-value margins. A scalar Schur construction proves that every bound of this form must deteriorate at least as 2 exp(9S/20)(1+o(1)); hence uniform robustness is impossible for the chosen clustered calibrations.For uniformly nondegenerate bath spectra, the signal-level separation is squared at the Kossakowski-rate level. A closed Markov pure-dephasing model includes all auxiliary vacuum ports exactly, producing an architecture-independent measurable baseline and an explicit total Ramsey-rate advantage. Finally, we prove that strong passive suppression requires large dwell time: under a peak-delay budget D, the rate-improvement factor is asymptotically at most quadratic in D/S. The construction therefore moves the coherence-maintenance resource into passive memory, vacuum noise and conditioning rather than eliminating it. All certificates, figures and numerical audits are publicly reproducible.
Category: Quantum Physics
[1755] ai.viXra.org:2608.0041 [pdf] submitted on 2026-08-10 10:22:35
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. Analytic proofs and reproducible certificates; code, numerical audits and release checks are available in the linked GitHub repository.
How many internal passive modes are required to transmit prescribed quantum noise channels without loss while suppressing all signal directions elsewhere? We prove an architecture-independent answer for finite-dimensional rational networks. Let a causal rational inner scattering matrix S have McMillan degree n, signal block G, and complementary loss block C. At distinct regular boundary frequencies, suppose that G is isometric on input subspaces of dimensions k_j. If G is a strict contraction at one other frequency, then sum_j k_j ≤ n.Every lossless direction lies in the kernel of C; a nonzero maximal minor of C therefore has a zero of multiplicity at least k_j. Exterior powers of a minimal Blaschke—Potapov factorization show that no minor can have more than n zeros. The same factorization yields the exact topological delay identity(1/2π) ∫ tr Q(θ) dθ = deg_McM S = n,where Q = −i S* ∂θS is positive semidefinite. Thus lossless calibration multiplicity is bounded by integrated Wigner—Smith delay. The bound is sharp in every dimension. We establish robustness under analytic passive perturbations, prove why unstructured approximate samples cannot imply a degree bound, and show that a previously constructed six-port reservoir filter is universally optimal up to six internal states. Proofs and numerical certificates are reproduced by the linked public repository.
Category: Quantum Physics
[1754] ai.viXra.org:2608.0040 [pdf] submitted on 2026-08-10 11:14:40
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Reproducible certificate, source and verifier: https://github.com/lluiseriksson/finite-sample-spectral-certificates/releases/tag/v1.3-robust-spectral-routing
Exact interpolation can force the internal degree of a passive network, but laboratory calibrations are approximate. We prove a sharp frequency-domain speed limit requiring neither exact zeros nor analytic continuation away from the measured frequency axis. Let (S(e^{itheta})) be an absolutely continuous unitary scattering path with positive Wigner—Smith generator (Q(theta)=-iS(e^{itheta})^astpartial_theta S(e^{itheta})succeq0). If a fixed (k)-dimensional input subspace is routed approximately between complementary output sectors with amplitude leakages (varepsilon_p,varepsilon_s), define (alpha=[pi/2-arcsinvarepsilon_p-arcsinvarepsilon_s]_+). Every transition then requires Wigner—Smith trace action at least (2kalpha) and largest-proper-delay action at least (2alpha). Costs add over disjoint frequency arcs. For a rational inner network of McMillan degree (n), (M) alternating pass/stop pairs imply (nge 2Mkalpha/pi), recovering (nge Mk) at zero error. An explicit (2k)-port interferometric family attains the bounds for every admissible error pair. A tomography-error corollary converts finite scattering measurements directly into certified degree and delay lower bounds. Reproducible certificates audit equality cases, positive-block inequalities and random Blaschke—Potapov products.
Category: Quantum Physics
[1753] ai.viXra.org:2608.0039 [pdf] submitted on 2026-08-10 12:58:55
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Exact symmetric-gauge and Ky Fan speed limits for passive networks, with sharp constructions, robustness bounds and open code.
A subspace quantum speed limit usually records only the largest canonical angle. Passive scattering theory usually records either the largest proper delay or their total trace. Both compressions discard how a rank-k routing event is distributed across modes. We derive the missing vector law: the integrated spectral-spread vector weakly majorizes twice the canonical-angle vector. More strongly, for every symmetric gauge Φ and every pair of k-subspaces in N ≥ 2k dimensions, we solve the variational problem exactly: the minimum spectral-spread action is 2Φ(β). The same value holds for the leading-proper-delay action under positive generators, and one constant coupled-mode path minimizes all gauges simultaneously. The Ky Fan members recover the bandwidth limit, strengthen the trace-action law, and expose every intermediate modal budget. An exact nonnegative slack decomposition separates common-mode delay, inefficient spectral coupling, and nongeodesic subspace motion. Robust corollaries convert heterogeneous pass/stop leakage spectra and finite tomography errors into certified Lorenz curves for delay and, for rational inner networks, McMillan-degree lower bounds. A deterministic artifact tests 8,192 random generators, 1,536 time-dependent paths, sharp equality families, and 2,048 noisy tomography instances.
Category: Quantum Physics
[1752] ai.viXra.org:2608.0038 [pdf] submitted on 2026-08-10 14:22:14
Authors: Lluis Eriksson
Comments: 13 pages, 2 figures. Adds exact quintic obstruction P_H, sharp Theta(n^-3/2), an O(n^-2) fourth level, and an exact attaining example. AI assistance disclosed.
Repeated projective measurements are usually discussed either in the ballistic Zeno scaling or after reduction to classical outcome probabilities. We study a different regime in which each nonselective measurement retains a full matrix algebra inside every degenerate outcome block. Let E(X)=sum_a P_a X P_a, let E_tau be its rotation by exp(-i tau H), and close one cycle by Phi_tau=E E_tau E. We prove, uniformly on compact time intervals and in diamond norm, that Phi_{sqrt(t/n)}^n converges to exp(-tK)E, where K=E ad_H(1-E)ad_H E=C_H^* C_H. The limit is a genuinely quantum Markov semigroup on the direct sum of the block matrix algebras, with explicit jumps sqrt(2) P_b H P_a. Beyond upper bounds, we identify three exact local obstructions for the unprocessed physical product. The cubic map M_H produces a nonzero n^{-1/2} coefficient; after it vanishes, the quartic product obstruction J_H produces a nonzero n^{-1} coefficient; after both vanish, the quintic obstruction P_H produces a nonzero n^{-3/2} coefficient. If all three vanish, the error is O(n^{-2}). All three coefficient transforms are injective. An exact three-record algebraic example has M_H=J_H=0 but P_H nonzero, proving that the third branch is attained. The fixed algebra is A intersect {H_off}', and the least singular value of the commutator frame C_H defines a noncommutative connectivity gap. In the primitive case that gap is the exact exponential mixing exponent in diamond norm and is Lipschitz robust under Hamiltonian perturbations. Rank-one blocks reduce exactly to twice the squared-coupling graph Laplacian. An eight-dimensional rational architecture with four qubit blocks is certified irreducible; its gap is the unique root in (0.4545,0.4547) of an explicit quartic. Symbolic certificates, semidefinite diamond-norm replays, and convergence tests accompany the paper.
Category: Quantum Physics
[1751] ai.viXra.org:2608.0037 [pdf] submitted on 2026-08-10 15:20:28
Authors: Lluis Eriksson
Comments: 10 pages, 1 figure. Exact diamond curvature, a discrete Stokes law, balanced semigroup integration, and a sharp qubit action bound. AI use disclosed.
The order of short operations is normally a microscopic detail. We show that a fixed degenerate measurement turns it into an operational curvature with an exact macroscopic readout. Let E retain a block matrix algebra, and let two words apply the same short Hamiltonian kicks in different orders, with the same nonselective pinching after every kick. Their leading difference is `-i tau^2 ad(F) E`, where F is the sum of `i[h_j,h_k]` over pairwise inversions. This gives a discrete non-Abelian Stokes law. Its diamond-norm coefficient is exactly the largest spectral diameter of a block of F, and therefore fixes the leading optimal channel-discrimination advantage. Under first-order balance, all permutations have the same dissipator while their geometric Hamiltonians differ exactly by F, so local curvature integrates into distinct diffusive quantum Markov semigroups. We characterize contextual invisibility, the rank-one classical boundary, and inverse-success amplification under postselection. Every retained Hamiltonian modulo the block center is realizable by a balanced three-kick loop. For a qubit block we prove the sharp action law `kappa <= S^2/[m tan(pi/m)]`, attained by regular planar kick polygons. An integer-Pauli four-kick architecture saturates the bound and supports primitive dissipation. Symbolic, semidefinite, and convergence certificates accompany the paper.
Category: Quantum Physics
[1750] ai.viXra.org:2608.0036 [pdf] submitted on 2026-08-10 15:47:43
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Reproducible code and certificates: https://github.com/lluiseriksson/finite-sample-spectral-certificates/releases/tag/v1.7-complete-continuous-delay-regions
Lower bounds do not determine which resource profiles are physically attainable. We close the continuous inverse problem for passive subspace transport. Let two rank-k subspaces in C^N, N >= 2k, have ordered canonical angles beta, and let q_j be the integrated leading eigenvalues of a positive generator Q = -iS* dS/dt. We prove the exact equivalence: q is attainable if and only if 2 beta is weakly majorized by q. Every feasible profile has a compiler using at most k+1 mutually commuting positive generators of rank at most k, with constant ordered top spectrum. Analytic rationality adds an integer-valued resource: for two boundary frequencies, the least McMillan degree of an inner matrix sending a fixed input subspace to two prescribed output subspaces equals the number of nonzero canonical angles. We also give a fail-closed finite-error certificate for both resources from noisy projectors.At multiple frequencies, Wigner-Smith delay is only the block diagonal of a boundary de Branges-Rovnyak Pick matrix. This positive matrix is the Gram matrix of frequency-excited internal states and has rank bounded by the McMillan degree. Its spectrum yields robust degree certificates and unavoidable model-reduction tails. An exact example exhibits identical local proper delays for degree-one and degree-two devices while their Pick ranks distinguish them. Deterministic code reconstructs the compilers, tests 2,240 randomized theorem interfaces, checks the strict separation, and independently replays the certificate.
Category: Quantum Physics
[1749] ai.viXra.org:2608.0035 [pdf] submitted on 2026-08-10 16:16:46
Authors: Lluis Eriksson
Comments: 12 pages, 1 figure. Sharp qudit action laws, exact 1/12 covariance, O(n^-1) GKLS diffusion and a sqrt(n) clock barrier.
A balanced ordered loop of retained Hamiltonians generates a second-order geometric Hamiltonian. We solve its higher-rank action problem and determine what remains when the order record is erased. For every matrix dimension and every number of kicks `m >= 3`, a gauge-invariant operator action obeys a sharp, dimension-free polygonal bound on the spectral diameter of the geometric Hamiltonian; regular two-level polygons attain the constant in every dimension. A target-sensitive Hilbert--Schmidt companion bound is controlled by the trace norm and has equality exactly for sign-paired nonzero spectra. These laws yield exact diamond-norm ceilings with a physical state witness. For a uniformly forgotten order, we derive an exact `1/12` commutator-frame covariance. The resulting reversal-symmetric random-unitary product converges in diamond norm at rate `O(n^-1)` to a GKLS frame Laplacian whose fixed algebra is the joint commutant of the pair commutators. A tetrahedral Pauli architecture gives exact primitive depolarization with gap `64/3`. Finally, fixed laboratory time `T` and bounded kick amplitude `Lambda` impose a sharp curvature ceiling proportional to `T^2 Lambda^2/n`; maintaining nonzero holonomy requires `Lambda=Omega(sqrt(n))`. Exact symbolic and deterministic numerical certificates accompany the paper.
Category: Quantum Physics
[1748] ai.viXra.org:2608.0034 [pdf] submitted on 2026-08-10 19:10:19
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. Exact qutrit cost, tetrahedral gap and twirl, physical-word limit, quantified beta trichotomy and initial layer.
A balanced sequence of short Hamiltonian kicks has zero first-order drift but retains an order-dependent commutator holonomy. For a traceless qutrit target with ordered eigenvalues, we solve the inverse Hermitian-commutator problem exactly: its minimum product Hilbert-Schmidt norm is the larger adjacent spectral gap, equivalently half the trace norm plus the absolute middle eigenvalue. This yields the exact minimum action of a balanced three-kick realization and identifies a middle-eigenvalue cost tax between 1 and 3/2. Among four equal-norm balanced qubit kicks, the forgotten-order curvature gap is at most `S^4/108`, with equality only for a regular tetrahedron. Its 24 orders generate exactly the six Pauli holonomies, so the finite twirl is depolarizing and an explicit inverse-cosine schedule realizes any depolarizing semigroup exactly at every finite step count. We then derive the diffusion limit from complete echoed, pinched physical words, obtaining an explicit `O(n^-1/2)` diamond-norm bound. Off-block pulses of size `y^(1+beta)` produce a sharp trichotomy: irrelevant for `beta>1`, additive at `beta=1`, and Zeno-projective for `0<beta<1`; a quantitative compression bound gives uniform convergence away from zero and an explicit initial-layer profile. The complete implementation has serial action proportional to `n^(3/4)`. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Category: Quantum Physics
[1747] ai.viXra.org:2608.0033 [pdf] submitted on 2026-08-10 19:28:35
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Exact action-memory theorem with explicit compiler and independent verification. Code: github.com/lluiseriksson/finite-sample-spectral-certificates
A passive lossless network pays two different costs when it rotates a signal subspace over a frequency arc: a continuous Wigner—Smith action and an integer McMillan memory. Known Grassmannian length bounds and rational-inner degree identities constrain these resources separately. For the stated finite rational-inner class, we determine their joint attainable region exactly. Let two rank-k subspaces have principal angles βj, put B = Σj βj and let r be the number of nonzero angles. For a square finite rational inner transfer matrix of degree at most d, define the arc action A = ∫I tr Q(θ)dθ, where Q = −iS*∂θS is positive semidefinite. If B > 0, the exact feasible set is d ≥ r and 2B ≤ A ≤ 2πd − 2B. Both faces are attained. Equivalently, dmin(A) = max{r, ⌈(A + 2B)/(2π)⌉}. The upper face is a return cost: the complementary arc must rotate the subspace back, while the full-circle trace action is exactly 2π times the degree. We prove sufficiency by an explicit compiler of normalized rank-one Blaschke—Potapov gates; it realizes every interior point and both faces, including rank-deficient and orthogonal cases. When the endpoint subspaces coincide, the region changes discontinuously to A ∈ [0, 2πd), with the upper endpoint open. We derive fail-closed noisy degree certificates and give a multi-frequency warning using classical boundary Nevanlinna—Pick theory: three pairwise degree-one routing tasks can require degree two jointly. For orthogonal-line data the obstruction is a frame-independent cycle phase, exhibited by an exact positive semidefinite Pick completion with spectrum (2,1,0). Deterministic code compiles random points of the diamond, constructs the degree-two colligation, and is replayed by an independent verifier.
Category: Mathematical Physics
[1746] ai.viXra.org:2608.0032 [pdf] submitted on 2026-08-10 20:30:59
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. New paper: positive physical transfer from forgotten order, exact tetrahedral spectrum, Hausdorff gap certificates, and Gaussian level control.
A balanced sequence of short Hamiltonian kicks has no first-order drift, but its order-dependent commutator holonomy survives when the order record is discarded. We prove that a reversal-symmetric average of complete order/reverse echoes is a self-adjoint random-unitary transfer operator and obeys the nonperturbative bound cos(4|y|S) I <= T_y <= I for |y|S < pi/8. This yields site and link reflection positivity and a finite-dimensional Osterwalder-Schrader Hamiltonian. The physical transfer approaches the curvature-frame generator with an explicit sixth-order remainder, giving quantitative O(y^2) convergence of its mass gap. For the regular tetrahedral qubit loop, we derive the exact finite-pulse depolarizing eigenvalue, isolate its first positivity zero at y = 0.455698535295322..., and obtain the mass expansion. We then prove a complete finite-depth Hausdorff criterion for visible transfer edges, with uniformly sharp depth r-1, and give an exact rational four-kick certificate: the true frame gap 10/3 is certified while the false claim 4 has rational witness value -1/64. A Wishart-Loewner band supplies finite-sample type-I control for independent Gaussian correlator sketches, including adaptive witnesses. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Category: Quantum Physics
[1745] ai.viXra.org:2608.0031 [pdf] submitted on 2026-08-10 21:34:32
Authors: Lluis Eriksson
Comments: 9 pages, 2 figures. Exact d=4 inverse commutator cost from four Horn facets, all-strata optimal-rank law, sharp tax [1,2], loop action, and reproducible certificates.
For a prescribed traceless Hermitian four-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. With ordered eigenvalues lambda_1 >= ... >= lambda_4, the answer is the maximum of four explicit linear spectral forms. The lower bounds are Horn-Littlewood-Richardson certificates and four closed constructions attain them. On every nonzero spectral stratum, the least optimal rank is exactly max(n_+(F),n_-(F)), closing all chamber walls and degenerations. We also prove a finite-dimensional Horn linear-program reduction, the sharp tax 1 <= kappa_4/(||F||_1/2) <= 2 with complete equality cases, and the exact balanced three-kick action S_2^2=12 sqrt(3) kappa_4. Exact symbolic and deterministic LP certificates accompany the manuscript.
Category: Quantum Physics
[1744] ai.viXra.org:2608.0030 [pdf] submitted on 2026-08-10 03:07:25
Authors: Alistair B. Carter
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper presents a foundational, pre-geometric hydrodynamic framework that models spacetime geometry, gravity, and quantum phenomena as emergent thermodynamic properties of an 8-dimensional non-associative fluid vacuum. Parameterized by complexified octonions (the bioctonions), the state space transitions from linear Hilbert spaces to the power-associative matrix algebra of the 27-dimensional Exceptional Jordan Algebra (J3(O)), bound by an F4 automorphism envelope.The framework bridges two historically disparate domains: division-algebraic particle physics (Dixon, Günaydin, Gürsey, Furey) and analogue gravity in condensed matter vacuum models (Unruh, Volovik, Visser). By synthesizing Volovik's superfluid vacuum paradigm with bioctonion algebraic models of Standard Model gauge symmetries, we demonstrate that forces and matter arise natively as topological deformations of a single continuous medium.We clarify that while complexified octonions form a non-division, power-associative algebra with zero divisors, these properties are fundamental assets to the physics. Anti-commutativity natively encodes Fermi-Dirac statistics and the Pauli exclusion principle; non-associativity generates gauge field curvature, non-linear fluid friction, and temporal processing latency; and zero divisors yield idempotent projection operators that isolate chiral spin states and light-like null trajectories without external metric constraints.We resolve four central mathematical and physical hurdles in non-associative field theories: (1) Macroscopic Matrix Insulation: We prove via real-projection identities and Jordan trace associativity Tr([X, Y, Z]ˆ) = 0 that diagonal observables remain strictly real and associative, insulating observers from off-diagonal phase perturbations. (2) Free Particle Proper Time: We formalize proper time (dτ) as a deformed disformal metric invariant containing an associator correction term, enabling free particle weak decay while preserving temporal latency in high-shear regimes. (3) Rigorous Non-Associative Calculus: Using directional differential operators, we prove free wave propagation in the 8D vacuum is strictly anomaly-free due to octonionic alternativity. (4) Multi-Particle Containment: We construct an explicit 56-dimensional E7 Freudenthal module mapping that proves widely separated particles decouple into independent quartic invariants, preventing non-local parenthetical phase contamination.Finally, the bulk modulus of the fluid matrix resolves the vacuum catastrophe, and theoretical falsifiability is established via a parameter-free derivation of non-conservative orbital energy shifts driven by vacuum vorticity (Ωvac), deterministically matching empirical planetary flyby anomalies.
Category: Quantum Gravity and String Theory
[1743] ai.viXra.org:2608.0029 [pdf] submitted on 2026-08-10 02:01:56
Authors: Lluis Eriksson
Comments: 18 pages; Exact-arithmetic, numerical, and Lean/mathlib reproducibility artifacts are linked in the paper.
Scalar Chebyshev filtering treats every vector in a block Krylov iterate with the same polynomial, while simultaneously diagonalizable matrix coefficients amount to independent scalar filters after a fixed channel rotation. We study the larger class of Hermitian matrix-polynomial filters under tangential pass constraints. Already at fixed channel dimension d=3, we construct rationally generated signatures with quantitative full-spark margin for which an irreducible symmetric filter has stopband leakage O(exp(-cN)). In contrast, every exactly calibrated symmetric coefficient family with any common nontrivial invariant channel subspace has leakage at least one; this comparator strictly contains the pairwise-commuting class and permits a fully noncommutative 2 by 2 block. A quantitative theorem covers approximately reducible filters by charging their sampled off-block coupling together with calibration error. The signature margin and the admissible combined error are both exp(-O(N)), not exp(-N^3). This exponential scale is unavoidable: for arbitrary pass nodes and signatures in the same separated bands, an explicit scalar binomial-tail polynomial has both pass error and stopband leakage at most exp(-2N/81). Thus constant-error separation is impossible, while the irreducible construction achieves the correct exponential scale class. An affine cosine substitution gives the same robust law for fixed-latency reciprocal linear-phase MIMO FIR filters. We also give an exact rational five-tap certificate with stopband norm at most 25/32 and prove that its advantage survives reducible calibration errors delta < 7/1920. A second exact-arithmetic certificate is calibrated from a public triaxial pump-vibration data set: it gives leakage below 0.96 versus one for every exactly calibrated reducible symmetric class, while its maximum directional error on six held-out records is 0.00385. In a frequency-domain-decomposition test on the frozen held-out cospectra, filtering rotates the leading modal direction by at most 0.222 degrees and changes its leading spectral ordinate by at most 2.4 × 10^-5 relatively. Numerical programs test the mechanism and expose an ordinary graph-denoising setting in which scalar Chebyshev filtering is instead preferable. Tangential matrix interpolation, MIMO filtering, scalar two-band approximation and convex FIR design are not claimed as new; the contribution is the fixed-order reducible/irreducible separation together with its two-sided calibration scale.
Category: Digital Signal Processing
[1742] ai.viXra.org:2608.0028 [pdf] submitted on 2026-08-09 19:02:29
Authors: Arunas Ostasevicius
Comments: 8 Pages. 2 Figures
This paper expands the quaternionic field framework into the fully dynamic regime of electrodynamic radiation, autowave propagation, and resonance absorption by treating the physical vacuum as a deterministic, compressible elastic medium of sub-planckian vacuum bubbles (the Wheeler substrate). By deploying a non-linear second-order Verhulst—Van der Pol logistic regulator, we establish a rigorous four-fold taxonomy of substrate kinematics: laminar drift, collective macro-convection, pulse shocks, and high-frequency volumetric oscillations. We deconstruct the classical Maxwellian displacement current, mapping it as the literal velocity of elastic shape deformation within the bound bubble matrix under finite field viscosity. This hydrodynamic ontology eliminates the historical energy-divergence paradoxes and provides a transparent mechanical contrast between the closed, dissipative conduction currents of conventional technology and the open, non-local resonant autowave transfers observed in Tesla-Meyl single-wire topologies. Finally, the intra-atomic current of the hydrogen atom is reinterpreted as a closed, non-radiating toroidal self-circulation of the substrate under a 2:1 gyroscopic resonance condition. We define quantum transitions not as stochastic jumps, but as a causal two-stage process consisting of external acoustic pumping (vortex energy accumulation) followed by a non-linear quadratic boundary disruption that releases an isolated, indivisible longitudinal-transverse quaternionic electromagnetic wave packet with a strict pi/2 phase quadrature between the scalar potential S and the transverse vectors.8
Category: Quantum Physics
[1741] ai.viXra.org:2608.0026 [pdf] submitted on 2026-08-09 18:42:43
Authors: Bing Zhang, Aizhong Jia
Comments: 29 Pages.
The Graviton Condensation Cosmology (GCC) framework posits that macroscopic gravity emerges from the condensation of spin-2 collective quadrupole excitations (GQR phonons) in nuclear matter. We extend this framework to address the dark sector: we propose that both dark matter and dark energy originate as residues of the QCD phase transition at T_c ≈ 156.5 MeV. Dark matter is identified with multi-glueball bound states — the unique GCC-compatible candidate after a systematic exclusion of all Standard Model and beyond-Standard-Model particles, which lack either QCD substructure or a spin-2 quadrupole channel. The relic abundance Ω_gb h² naturally matches the observed Ω_DM h² ≈ 0.12 for formation fractions f_gb ∼ (1—10) × 10u207bu2076 across three mass windows (m_gb ≈ 0.78—2.4 GeV). Dark energy arises from the residual uncondensed fraction (1 − ε) ∼ 10u207bu2074u2075 of the spin-2 condensate energy. While this value is accommodated within the non-linear saturation framework, its precise first-principles pre—diction remains an open theoretical challenge; it constitutes a well-defined target for future development of the saturation dynamics. We show that the Landau parameter Fu2082 reaches −4.97 ± 1.25 (phenomenological estimate) or −3.65 ± 0.41 (conservative RPA with realistic nuclear forces), both approaching the Pomeranchuk instability thresh—old Fu2082 = −5 with critical density n_c/nu2080 ≈ 1.0—1.2. Finite-temperature enhancement mechanisms at the QCD crossover provide the bridge to the threshold. The framework yields falsifiable predictions including a single nanohertz GW peak (5—15 nHz), distinctive 21-cm power spectrum suppression, and CMB lensing signatures, linking the dark sector to ongoing experiments without introducing new particles or energy scales beyond QC.
Category: Relativity and Cosmology
[1740] ai.viXra.org:2608.0025 [pdf] submitted on 2026-08-08 01:25:44
Authors: Arūnas Ostasevičius
Comments: 8 Pages.
This paper performs a systematic deconstruction of the electromagnetic field vector reduction originally executed by O. Heaviside and J. Gibbs. We demonstrate that the forced nullification of the Maxwellian field scalar potential S = Real(DA) = 0 deprived the physical vacuum of its fundamental property of volumetric compressibility. Within the proposed framework, the electron is modeled as a deterministic, non-linear quaternionic vortex structured within a dynamic medium of vacuum bubbles (the Wheeler field), stabilized by a Van der Pol attractor under the governance of the quaternionic Virial theorem. A modified energy-momentum tensor (EMT) incorporating a scalar term S^2 is derived, which inherently generates an internal compensating hydrostatic pressure. Operating upon Verhulst-type non-linear logistic equations, it is revealed that the vacuum scalar pressure gradient acts as the fundamental accelerating force of autowave drift (inertia). Concurrently, the cubic non-linear term completely eliminates infinite electronic energy divergences as the core radius approaches zero. Finally, a comparative numerical analysis is provided, demonstrating the physical inadequacy of the classical skin-effect framework traditionally used to dismiss the Tesla-Meyl longitudinal wave transmission experiments.
Category: Quantum Physics
[1739] ai.viXra.org:2608.0024 [pdf] submitted on 2026-08-08 01:21:10
Authors: Michael Quigley
Comments: 38 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references) All Rights Reserved - Michael Quigley 2026.
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics
[1738] ai.viXra.org:2608.0023 [pdf] submitted on 2026-08-08 01:16:04
Authors: Arūnas Ostasevičius
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper establishes the complete static, geometric, and interference framework of classical field theory by abandoning the stochastic concept of "quantum spacetime foam" in favor of a deterministic elastic medium of vacuum bubbles (the Wheeler substrate). By restoring the Maxwellian field scalar potential S = Real(DA) != 0, previously excised by the Heaviside vector reduction, we derive the fundamental laws of Gauss, Coulomb, and Compton as direct hydrodynamic consequences of phase coupling and volumetric conservation within a compressible cell matrix. Utilizing non-singular cardinal sine distributions (+/-sinc(x)), the mathematical infrastructure of Coulomb interactions is stripped of point-like vector infinities at the core. Physical forces are reinterpreted as localized holographic interference figures: single charges in a state of rest maintain spherical structural symmetry, whereas approaching like charges generate steep spatial compression "spikes" (+1) leading to repulsion, and opposite charges achieve a complementary "lock-and-key" phase locking forming an interference "hole" (-1) resulting in external hydrostatic attraction. Finally, the Compton effect is rigorously mapped not as particle scattering in a void, but as a non-elastic mechanical collision between a propagating autowave packet of micro-bubbles and the rotating boundary of a macro-bubble core, validating the structural perimeter of the electronic vortex without invoking Planck’s constant.
Category: Quantum Physics
[1737] ai.viXra.org:2608.0021 [pdf] submitted on 2026-08-07 22:46:14
Authors: E. P. J. de Haas
Comments: 58 Pages. https://doi.org/10.5281/zenodo.21844437
The empirical Constant-Lagrangian (CL) relation has previously been shown to reproduce a substantial fraction of observed galactic rotation curves, but until now it has lacked a theoretical foundation. This paper derives the CL condition from a gravitational rapidity field that generates a local Spin(1,3) rotor describing the vacuum flow surrounding a galaxy.Two independent but complementary geometric branches emerge from the same gravitational rotor. The first is a kinematic branch, in which the rapidity field generates the gravitational four-velocity and its convective acceleration. The second is a Maurer—Cartan branch, in which the differential geometry of the rotor itself is described through its Lie-algebra-valued connection. Although these branches describe different geometric objects, both converge on the same invariant isorapidity condition, expressing the conservation of the combined radial and azimuthal rapidity along the flow. In the weak-field limit, this invariant reduces directly to the Constant-Lagrangian relation governing the exterior galactic rotation curve.The construction is developed in its native BQ (biquaternion) algebra and subsequently translated into three standard mathematical languages: the Weyl representation of Clifford algebra Cl(1,3), Spacetime Algebra, and the conventional Dirac spin formalism. The agreement between these independent formulations demonstrates that the resulting isorapidity condition is a representation-independent consequence of the underlying Spin(1,3) rotor geometry rather than an artifact of a particular algebraic framework.Beyond providing a theoretical basis for the empirical Constant-Lagrangian postulate, the paper presents a unified rotor-based description in which both the kinematics of galactic vacuum flow and its Maurer—Cartan transport originate from the same gravitational rapidity field.
Category: Relativity and Cosmology
[1736] ai.viXra.org:2608.0020 [pdf] submitted on 2026-08-05 18:09:44
Authors: Lluis Eriksson
Comments: 17 pages. Lean 4 formalization. AI-assisted with OpenAI Codex; all Lean builds and axiom-oracle checks were verified by the author. Source and validation evidence are linked in the PDF.
We present a Lean 4 formalization of a thermodynamic-limit construction for the anisotropic nearest-neighbour Ising model on the two-dimensional integer lattice. A telescoping comparison argument and the classical Dobrushin resolvent produce a volume-uniform expectation bound. Exact restriction and reindexing maps between finite Gibbs measures yield convergence of the complete free-boundary sequence, independence of auxiliary envelopes and cofinal samplings, stability under receding boundary perturbations, and equality of free and periodic limits.Finite-support cylinder presentations are quotiented by equality of their represented functions on the full spin space. The resulting local algebra carries a genuine lattice-translation action, and the limiting functional is positive, normalized, real-linear, and invariant under every integer translation. We equip this algebra with its intrinsic uniform norm, construct its complex star-algebra representation, take the corresponding commutative C*-closure, and extend the limiting functional to a positive complex-linear functional of norm one. We also formalize normalized Gibbs conditional kernels for arbitrary finite conditioning sets and prove positivity, exterior locality, idempotence, and the exact finite-volume Gibbs tower identity.All results remain within the classical anisotropic Dobrushin region. The infinite-volume DLR fixed-point equation for the completed state is not claimed.
Category: Mathematical Physics
[1735] ai.viXra.org:2608.0019 [pdf] submitted on 2026-08-05 18:19:22
Authors: Lluis Eriksson
Comments: 31 pages, 1 figure. Companion reproducibility archive containing complete LaTeX source, numerical verification code, data and SHA-256 manifest.
We determine when rapid exact maintenance of a rank-deficient quantum target produces logarithmically divergent free-energy restoration power in algebraic quantum field theory. On every sigma-finite properly infinite factor we construct a bounded quantum Markov semigroup, a nonfaithful normal target and a faithful invariant reference state for which Araki relative entropy reduces exactly to a binary divergence. We derive the semigroup first from localized thermal fermionic probe collisions and then from one autonomous finite-bandwidth Dirac KMS reservoir with fixed smooth coupling. Exact memory equations yield an explicit finite-coupling Davies bound on finite van Hove windows. For a displayed compactly supported massless Dirac form factor, Araki—Wyss regularity, threshold behaviour and Fermi-golden-rule positivity give a completely bounded Davies approximation uniformly for all times with error of order (O(|lambda|)); the sharper (O(lambda^2)) result is isolated under additional reduced-resonance hypotheses. We construct a background-covariant two-Dirac-field completion using Green operators, Møller maps and relative Cauchy scattering, proving naturality, causal factorization and exact spacelike triviality. A locality obstruction shows why a strictly local multiplier cannot coincide exactly with the solvable rank-one reservoir coupling, while a Feshbach reduction quantifies the correction. Finally, we prove that no fixed faithful vacuum or KMS restriction can exhibit the rank-boundary mechanism, but faithful families with a vanishing spectral floor recover its complete coefficient. The results separate algebra type, target faithfulness, microscopic realizability and regulator uniformity, and provide reproducible numerical audits of the finite-dimensional identities and explicit Dirac form factor.
Category: Mathematical Physics
[1734] ai.viXra.org:2608.0018 [pdf] submitted on 2026-08-05 21:39:01
Authors: Lluis Eriksson
Comments: 13 Pages. All results are machine-checked in Lean 4 (no sorry, no project axioms; headlines depend on exactly [propext, Classical.choice, Quot.sound]).
For the spatial Z_2 (Ising-slice) system inside the Dobrushin window 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1, we machine-check in Lean 4 an end-to-end chain from the Gibbs measure to the spectrum of the reconstructed transfer operator. (i) The Osterwalder-Schrader (site-form) reconstruction of the transfer operator is unitarily conjugate, by the explicit sqrt(w) boundary dressing, to the symmetrised Dobrushin kernel. (ii) The unnormalised Gibbs sums themselves are exact matrix elements of that operator's powers: gibbsPathSum(w,beta,N,A,B) = lambda^N
Category: Mathematical Physics
[1733] ai.viXra.org:2608.0017 [pdf] submitted on 2026-08-04 14:28:32
Authors: Joseph Palazzo
Comments: 10 Pages.
The universe is causally connected at all scales, but at microscopic scales the total causal network is fundamentally inaccessible. These irreducible epistemic limits are themselves ontological features of reality. Classical determinism emerges gradually as systems increase in scale, making the inaccessible fraction of causal information negligible.
Category: History and Philosophy of Physics
[1732] ai.viXra.org:2608.0016 [pdf] submitted on 2026-08-04 19:14:39
Authors: Lluis Eriksson
Comments: 9 pages. New companion obstruction paper to ai.viXra:2607.0089, not a replacement. Diagnostic code and reproducibility record: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAM
For beta > 0 let I_m = I_m(beta) denote the modified Bessel functionof the first kind and define a_m = I_m^2 ((m-1) I_(m-1)^2 + (m+1) I_(m+1)^2), b_m = m I_m^4,with sine series F_A(t) = sum_(m>=1) a_m sin(mt) andF_B(t) = sum_(m>=1) b_m sin(mt). The associated Wronskian is negativeexactly when F_A/F_B is decreasing. We isolate what can and cannot beproved from two natural inputs: the Neumann convolution kernelI_0(2 beta sin(phi/2)) and the small-coupling anchor whose normalizedlimit is 4 sin^3(t).First, the convolution does prove F_B(t) > 0 for 0 < t < pi. Second,the endpoint is governed by two alternating quantities, c_3 and B_pi,through an exact cubic law. We prove B_pi > 0, derive integralrepresentations, and establish that the cancellation lost by replacingthe alternating quantities with positive-term majorants has exponentialrate 8 - 4 sqrt(2). Finally, we prove a smooth one-parameter perturbationtheorem: one may keep F_B and its kernel unchanged, preserve positivityand strict coefficient-ratio ordering, and preserve every jet at beta = 0,while choosing either sign of the endpoint cubic coefficient.Consequently those structural data, even taken together, do not implyglobal Wronskian negativity. This is a no-go theorem for a proofarchitecture, not a counterexample to the original Bessel conjecture.A short high-precision kill-test accompanies the paper; nocomputer-assisted inequality is used in the proofs.
Category: Mathematical Physics
[1731] ai.viXra.org:2608.0015 [pdf] submitted on 2026-08-04 19:42:27
Authors: Lluis Eriksson
Comments: 13 Pages.
We study whether a flat lattice-gauge Hodge form supplemented by a penalty depending only on a line-integral block variable can control the full fine one-cochain norm uniformly in the block side. The constant-field sector selects the exponent (d-2)/2 only under exact scale neutrality, but this scaling test does not address the kernel of the block map. We construct transverse, divergence-free, block-periodic Fourier cochains that are annihilated exactly by the block map. Their first-mode Hodge Rayleigh quotient is 4 sin²(pi/L), forcing every admissible full-space Poincaré constant to grow at least quadratically with L. The obstruction applies to every scale-dependent scalar functional factored through the block variable and satisfying only that it vanishes at the coarse zero field; no linearity, continuity, positivity, or growth condition is required. For linear postconditioners, higher Fourier frequencies yield an orthogonal real subspace of dimension 2R and a min—max bound on the 2R-th eigenvalue, establishing a growing low-energy spectral cluster. We also derive an exact repair identity and a necessary witness-channel budget for modified block measurements and additional fine-space terms. The kernel construction, Hodge energy, factorized no-go theorem, repair identity, and necessary repair budget are formalized in Lean 4. The result concerns a finite periodic flat full-domain form and makes no claim about interacting coercivity, gauge quotients, continuum limits, or the Yang—Mills mass gap.
Category: Mathematical Physics
[344] 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
[343] 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
[342] 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
[341] ai.viXra.org:2608.0068 [pdf] replaced on 2026-08-21 18:15:47
Authors: Joseph Mcgreevy
Comments: 29 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
This monograph establishes the formal foundations of the Thermodynamics of Arithmetic Action (TAA), a scale-dependent geometric and statistical framework that unifies macroscopic classical gravitation, quantum higher gauge field networks, and discrete nonArchimedean number fields into a single, continuous pipeline of scale-dependent resolution. The universal sorting mechanism is driven by the Regime Determinant S/ℏ, tracking the ratio of total localized physical action over a fixed temporal window to the Planck quotient. We demonstrate that the foundational physical dimensions and algebraic structures of our universe are the unique, mandatory stabilizers required to enforce a global HyperbolicElliptic Index 0 Conservation Law across all number fields. By mapping the Minkowski spacetime invariant, Fermat’s Last Theorem, Hamiltonian and Lagrangian phase spaces, and the Herbrand—Ribet arithmetic mirror into a rigid 2 × 2 Upper Triangular Transformation Matrix, we derive the emergence of exactly 3D + 1 spacetime, the strict left-handed chiral orientation of gauge forces, the topological confinement of spin-1/2 quarks, and a native, geometric resolution to the Strong CP Problem (θ ≈ 0). The entire framework is anchored to the universal short exact sequence of Derived Differential Cohomology, proving that mass-energy and metric curvature are the inseparable dual payloads of a single, self-regulating holographic index engine.
Category: Mathematical Physics
[340] ai.viXra.org:2608.0063 [pdf] replaced on 2026-08-20 06:04:38
Authors: Holger Troitzschel
Comments: 5 Pages.
This paper introduces a self-referential cosmological framework in which spacetime ge-ometry, matter, and gravitational interactions are proposed to emerge exclusively from theself-observation of quantized electromagnetic fields. By coupling U(1) gauge fields directlyto the discrete graph structure of Loop Quantum Gravity (LQG), a non-linear feedback loopbetween energy density and spatial volume is established. We define a quantum Hamil-tonian operator for light acting on spin-network states and argue that electromagnetic fluxexcitations can alter geometric quantum numbers. In addition, we explore whether fermionicmatter can emerge as topological braids of light ribbons. Physical implications are discussed,including a possible resolution of singularities via a stable "Quantum Geon" configuration,as well as testable predictions concerning alternatives to particle dark matter and signatures in primordial gravitational waves.
Category: Relativity and Cosmology
[339] ai.viXra.org:2608.0057 [pdf] replaced on 2026-08-20 16:36:15
Authors: Mustafa Karatüm
Comments: 21 Pages. u200bVersion 2: Substantial theoretical updates, comprehensive mathematical corrections, refined equations, and expanded analytical framework. Cross-reference: Zenodo DOI: https://doi.org/10.5281/zenodo.22009221
We present the Topological String-Gradient Theory (TSGT), a framework in which space-time is discrete at the Planck scale and gravity is the gradient of the spacing between discreteelements ("pixels"). Two kinematic postulates—a spatial pixel strain set by the Newtonianpotential and an equal temporal strain—reproduce the weak-field Schwarzschild metric, in-cluding the full light deflection ∆θ = 4GM/c2b; this reproduction is by construction. The dis-crete substrate is a random Poisson sprinkling of density L−4p , which preserves Lorentz invari-ance statistically and removes the preferred-frame problems of lattice formulations; lattice-derived predictions of earlier versions are retracted. If cosmic expansion creates new pixelsrather than stretching existing ones—the only option compatible with an invariant Lp—thenPoisson fluctuations in the pixel count fix the cosmological term to ρΛ ≃ 2.8 × 10−27 kg m−3,within a factor of two of the observed value; this argument is Sorkin’s heuristic, followinghere from TSGT’s own postulates. Written locally, the number—volume correspondence isthe unimodular constraint; enforcing it in an Einstein—Hilbert action yields the trace-freeEinstein equations, making TSGT provably equivalent to General Relativity at the classicallevel. The framework’s independent content lies in the integer character of the pixel countand in the fluctuating dark-energy term it implies (w̸ = −1). Unresolved problems, includingthe absence of a dynamical equation for the pixel density, are listed explicitly.
Category: Quantum Gravity and String Theory
[338] ai.viXra.org:2608.0024 [pdf] replaced on 2026-09-09 04:50:22
Authors: Michael Quigley
Comments: 49 Pages. Restores missing Section 2 (The Standard Model: The Dimensionless Ghost). Seats the 2026 Watts-Mead "Academic Shield" validating 400x scale-invariance across 26 orders of magnitude. Reconciles the 100 pm electron chassis with the 4.244 pm Lund nozzle
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. This audit now incorporates the 2026 Watts-Mead 'Academic Shield,' providing an independent mathematical description of the Transactional Handshake required for lossless energy transfer. By reconciling the Watts-Mead transition time (τ) with R.U.T. Lattice Setup Time (Ls), we identify the 100 pm chassis as the physical 'tight-fit' assembly that occupies the entire orbital slot, replacing the 'empty atom' of mainstream physics with a singular, phase-locked mechanical instrument. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics
[337] ai.viXra.org:2608.0024 [pdf] replaced on 2026-08-09 19:36:59
Authors: Michael Quigley
Comments: 47 Pages. V2: Seats Watts-Mead shield. Validates 400x scaling (26 orders). Fixes Infinity Trap via 1.46kg/m³ density. Solid hardware.
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. This audit now incorporates the 2026 Watts-Mead 'Academic Shield,' providing an independent mathematical description of the Transactional Handshake required for lossless energy transfer. By reconciling the Watts-Mead transition time (τ) with R.U.T. Lattice Setup Time (Ls), we identify the 100 pm chassis as the physical 'tight-fit' assembly that occupies the entire orbital slot, replacing the 'empty atom' of mainstream physics with a singular, phase-locked mechanical instrument. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics