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Any replacements are listed farther down
[46116] viXra:2609.0075 [pdf] submitted on 2026-09-25 19:09:14
Authors: Bert Morrien
Comments: 15 Pages.
Standard cosmological models face severe theoretical crises: the Vacuum Catastrophe, the Black Hole Information Paradox, and the unresolved nature of Dark Matter. These issues stem from a foundational misalignment—treating the observable universe as an isolated, expanding single-universe system while applying continuous, non-quantized geometry at black hole horizons. This paper introduces the framework of Reality (R) as an absolute, eternal, non-egocentric, and gravitationally closed thermodynamic system. By resolving Hawking’s semiclassical continuum approximation through strict Planck-scale boundary discretization (Δx≥l_P), black holes are re-evaluated not as information sinks, but as quantized thermodynamic pumps that compress high-entropy matter into net-zero entropy fluxes. Furthermore, by accounting for the unshielded gravitational influence of external cosmic zones within an infinite expanse, the ambient background tension naturally accounts for dark matter phenomena without invoking hypothetical particles. Finally, by treating the zero-point energy baseline (0" Kelvin" ) as an active thermodynamic floor rather than a localized non-extractable vacuum, mass-energy equivalence (E=mc^2) satisfies the baseline energy density of the cosmos. Through strict adherence to the Law of Non-Contradiction and Ockham's Razor, this model unifies general relativity and quantum field operations into a continuous, self-sustaining thermodynamic engine.
Category: Relativity and Cosmology
[46115] viXra:2609.0074 [pdf] submitted on 2026-09-25 19:07:34
Authors: Edgar Valdebenito
Comments: 5 Pages.
In this note, we analyze a binomial series established by R. Zurita in 2026.
Category: General Mathematics
[46114] viXra:2609.0073 [pdf] submitted on 2026-09-25 19:05:32
Authors: Mat Hunt
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Claims of "scalar", "longitudinal" or "Tesla" electromagnetic waves often combine threedistinct phenomena: longitudinal electric-field components in anisotropic media, superluminalphase or group velocities, and an additional propagating scalar degree of freedom. Weseparate these questions and derive the relevant results from first principles. First, source-free Maxwell electrodynamics with tensor permittivity and permeability is reduced to itsplane-wave eigenvalue problem. The Gauss constraint is shown to make the displacementfield, rather than the electric field, transverse to the wave vector; an explicit anisotropicexample consequently has a predominantly longitudinal electric field and a phase velocityexceeding the vacuum light speed. The Poynting theorem is then derived for a dispersiveanisotropic medium, leading to the Brillouin energy density and energy velocity and showingwhy a superluminal phase velocity does not imply superluminal energy or signal propagation.Second, a genuine scalar degree of freedom is introduced through a Lorentz- and gauge-invariant dilaton-like action. All Euler—Lagrange equations are derived explicitly. Gauge,translation and Lorentz symmetries are treated with Noether’s theorem, yielding charge,energy—momentum and angular-momentum/boost conservation laws. Linearisation about astatic electric background gives the full mixed scalar—electromagnetic dispersion relation, itsnearly massless distinguished limit, and a scalar-associated branch which is purely longitudinalelectrically and has zero magnetic perturbation for propagation parallel to the backgroundfield. The same action gives a finite-electrode voltage-dependent capacitance; this predictionis derived using the Green function of the scalar equation. Existing scalar—photon andresonator searches already constrain the coupling strongly, making large effects in the minimalunscreened theory implausible. We finally formulate direct static and dynamical experimentaltests of the remaining longitudinal mode.
Category: Mathematical Physics
[46113] viXra:2609.0072 [pdf] submitted on 2026-09-25 18:54:17
Authors: Solomon Khmelnik
Comments: 15 Pages. In Russian
The device is designed to generate electricity without the use of mechanical energy. It was first proposed and registered in 2010, but its details were not published. Here, it is presented with additional explanations.
Category: Classical Physics
[46112] viXra:2609.0071 [pdf] submitted on 2026-09-25 18:50:32
Authors: Marcin Barylski
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Prime numbers can be represented in many ways. This work focuses on representing them using other primes: p, q, and r as: p×q±r. The aim of this research is to explore interesting properties of such prime representation, including the smallest product of p, q, and r that can represent a given prime number and 4 related hypotheses that were formulated when exploring this topic.
Category: Number Theory
[46111] viXra:2609.0070 [pdf] submitted on 2026-09-25 18:59:39
Authors: Dimiter Dobrev
Comments: 5 Pages. In Bulgarian
It is difficult to imagine a being with unlimited mental capabilities, because none of us have encountered anything like it in our lives. However, we live with the idea of an omnipotent and all-powerful being who cares for us. We call this being God. Each of us knows what God is, regardless of whether we believe in His existence. The superintelligence will be very similar to a god and will possess one of his main characteristics — omnipotence. As much as it will be similar, it will also be very different. We will probably feel sorry for the good old God who took care of us and forgave our sins. Now, before we take the final step, it's good to stop and think about whether we have a choice and what that choice is.
Category: Artificial Intelligence
[46110] viXra:2609.0069 [pdf] submitted on 2026-09-23 23:34:03
Authors: Volodymyr Krasnoholovets
Comments: 28 Pages.
This work briefly reviews the main achievements of theoretical particle physics obtained using approaches based on symmetry and topology, and then highlights the weighty errors present in these theories. Particle theories are very abstract and developed within the framework of physical mathematics, which has no solid physical basis. However, real particles and real physical processes require finding a real basis on which fundamental physics should stand, and this is very important. The primary mathematical structure must be such that it is possible to apply mathematical physics to describe the physical picture of the world in real parameters that are actually present in particles and their interactions. It is precisely such a mathematical theory that is described in this work, the suitable geometry and topology are revealed, and references are provided to the corresponding physical theories developed by the author within the framework of mathematical physics, which already have a number of reliable experimental confirmations.
Category: High Energy Particle Physics
[46109] viXra:2609.0068 [pdf] submitted on 2026-09-24 01:37:44
Authors: Deng Ke
Comments: 35 Pages.
Current research on the distribution of prime numbers either narrows down to counting due to a focus on applied fields, meaning it only counts without knowing which numbers are prime, or it explores patterns but, because of a cause-from-effect order, leads to unclear results and only approximate rather than definitive distribution patterns. This paper attempts to discuss a common type of multiplication—multiplication whose factors do not contain 1, called skip-multiplication—introducing skip-numbers and skip-products, to explain the essence of prime numbers as full-skip numbers and their distribution patterns, and to achieve a fundamental grasp of prime numbers in terms of identity rather than merely quantity through the method of reverse selection from the skip-product table. Furthermore, because tables rely on enumeration, their role in application is at most auxiliary rather than a replacement for any tool; thus, this paper mainly provides a new number-theoretic understanding of prime and composite numbers in the pure mathematical theory domain. The appendix supplements some patterns of the skip-multiplication theory tables and discussions on the oddness of primes and the Riemann Hypothesis.
Category: Number Theory
[46108] viXra:2609.0067 [pdf] submitted on 2026-09-24 20:38:43
Authors: Hyoyoung Choi
Comments: 69 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This study begins with the recognition that the Standard Model particle-antiparticle classification lacks a universal physical principle that determines the particle orientation of each charge-conjugate pair while grouping the proton, neutron, and electron into the same particle sector. Motivated by the weak-isospin doublet structure of weak fermion transitions, we introduce a new weak-isospin-based quantum number, N=2T_3L, where T_3L is the third component of left-handed weak isospin. States with N > 0 are assigned to the particle sector, states with N < 0 to the antiparticle sector, and states with N=0 to an N-neutral sector. In this classification, the proton and neutrino are particles, whereas the electron and neutron are antiparticles. The representative weak, hadronic, stellar, and early-Universe processes examined here consistently preserve the total additive N balance while redistributing N among different species. For fermion species defined by their left-handed weak-doublet orientation, the electroweak charge assignments give N=2Q−(B−L), where Q, B, and L denote electric charge, baryon number, and lepton number. Hence, for charge-conserving processes, exact additive N conservation requires ∆(B−L)=0. Accordingly, the same Universe that appears strongly particle-antiparticle asymmetric under the conventional classification is reinterpreted in the weak-isospin-based classification as a Universe in which positive-N and negative-N components cancel globally, yielding the global N-symmetry condition N_tot=0. This work further proposes a possible particle physics mechanism for the species-level particle-antiparticle and baryon asymmetry problems. A proposed N-conserving 1 → 3 decay process such as 'n̄ →p + e^− + ν_e' can generate, in a single decay event, the asymmetry direction required to account for the present cosmic particle abundance pattern, (δ∆p, δ∆n, δ∆e, δ∆ν) = (+1, +1, +1, +1). Related 2 → 2 scattering processes such as 'n̄ + e^+ → p +ν_e' and 'n̄ + v̄u2091 → p +e- ' produce the same asymmetry direction. Accordingly, this work recovers global particle-antiparticle symmetry through the N=2T_3L classification and proposes a possible solution to the species-level particle-antiparticle asymmetry through new N-conserving particle-conversion processes. The proposed mechanism can be tested directly through searches for N-conserving 1 → 3 decay and 2 → 2 scattering channels and their CP-conjugate rate asymmetries, while cosmic neutrino asymmetry, B−L violation, and the nature of neutrinos provide additional tests of the broader framework.
Category: High Energy Particle Physics
[46107] viXra:2609.0066 [pdf] submitted on 2026-09-24 20:37:46
Authors: Nigel B. Cook
Comments: 5 Pages. (Note by viXra.org Admin: Please cite listed scientific references)
In standard quantum field theory, the Ward—Takahashi identity expresses the quantum version of Noether’s theorem and guarantees the decoupling of unphysical ghost states, preserving unitarity. In this paper we reformulate the Ward identity inside a mechanistic, vacuum—polarisation—driven QFT, where the fundamental ensemble weight is real (e.g. cos S rather than exp(iS)), and where gauge bosons arise as coherent waves of routing bias in a discrete spinor network associated with the real forms of SL(4, C). We show that the Ward identity emerges as a dynamical constraint: the vacuum couples only to conserved gauge currents, and the vacuum—polarisation energy functional is strictly gauge invariant. As a consequence, ghost—like, non—conserving excitations cannot couple to the vacuum and therefore have zero physical amplitude. This provides a physical, mechanistic implementation of the Ward identity compatible with discrete SL(4, R) spinor routing, finite subgroup quantisation (including Wilson’s H288), and the continuous SU(4) gauge structure arising in the coarse—grained limit.
Category: Quantum Physics
[46106] viXra:2609.0065 [pdf] submitted on 2026-09-23 09:30:42
Authors: Naili Cui
Comments: 9 Pages.
This paper constructs the G-L integer-charge microstructure system and defines the G fundamental particle as the underlying fermionic unit of cosmic matter. Secondary composite L-quark structures are formed by the coupling of G fundamental particles. The standard L-quark configurations for proton and neutron are presented. The configuration evolution mechanisms for proton-neutron transformation in β^- decay, β^+ decay and electron capture are fully revealed. A self-consistent novel framework for hadron microstructure is established without ad-hoc assumptions. Based on the microscopic mechanism of the 1022 keV threshold in proton β^+ decay, the Cui Charge Symmetry Threshold Conservation Law for β^+ Decay under Weak Interaction (CZ Law) is derived. Observations from deep inelastic scattering experiments can be interpreted as regional average charge effects inside nucleons, which are highly consistent with the G-L integer-charge model. Based on the G-L model, it is predicted that the X(2370) resonance discovered by BESIII is a brand-new hadronic state formed by many-body direct condensation of G fundamental particles. It opens a new theoretical paradigm for hadron spectroscopy and glueball physics.
Category: Nuclear and Atomic Physics
[46105] viXra:2609.0064 [pdf] submitted on 2026-09-23 10:19:08
Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.
In this paper, we develop an observation into a precise operator-theoretic program. For a zero written as ρ=σ+it, the imaginary part of the energy is t(1-2σ). Hence, for every non-real zero in the critical strip, E_ρis real precisely on the critical line. The result shows the Riemann hypothesis is the assertion that all quadratic zeta energies are real. This paper then formulates the Hamiltonian structure required to turn this equivalence into a proof. The proposed operator is not a finite spectral fit, instead, it is a modular-arithmetic Hamiltonian built on logarithmic space, prime translations, an arithmetic boundary domain, a prime-power trace formula and determinant closure with the completed zeta function. The main theorem is conditional since if such a self-adjoint operator has determinant ξ(s) in the spectral coordinate s(1-s), then all non-trivial zeros lie on critical line.
Category: Mathematical Physics
[46104] viXra:2609.0063 [pdf] submitted on 2026-09-23 20:05:33
Authors: Renato Vieira dos Santos
Comments: 17 Pages. 10.1016/j.chaos.2026.119179
The prevalence of sexual reproduction in nature remains an evolutionary paradox, given its substantial costs compared to asexual alternatives. While genetic explanations such as the Red Queen hypothesis emphasize coevolution with parasites, the role of spatiotemporal discreteness and population structure has been underexplored. Spatial structure matters because real populations are finite, interact locally, and are subject to demographic noise, factors that can fundamentally alter evolutionary outcomes. Here, we show that the discrete, nonlinear character of interactions between hosts and pathogens, when combined with spatial diffusion in low-dimensional habitats, naturally favors sexual reproduction. Using stochastic reaction—diffusion models and renormalization group analysis, we demonstrate that asexual populations face certain extinction in dimensions d≤2 due to discreteness-induced extinction (DIE), whereas sexual populations can persist and form stabilizing clusters. The mechanism hinges on the recurrence of random walks in low dimensions, which ensures pathogen-host encounters for asexuals but promotes protective clustering for sexuals. Our results suggest that the advantage of sex may emerge from purely physical and demographic constraints, independent of genetic mechanisms, thereby offering a new perspective on this classic evolutionary puzzle.
Category: Quantitative Biology
[46103] viXra:2609.0062 [pdf] submitted on 2026-09-23 20:26:27
Authors: Renato Vieira dos Santos
Comments: 10 Pages.
The time-dependent electric Aharonov-Bohm effect, where shielded potentials vary while electrons are in transit, offers a unique test of the Lorenz condition $partial_mu A^mu=0$. We introduce a phenomenological coupling $kappa$ between the scalar $partial_mu A^mu$ and the electron. In the field-free interior of shielded cylinders, $partial_mu A^mu = dot{Phi}/c^2$, giving an additional phase $Deltaphi_{lorenzScalar} = -kappa[Delta V(T)-Delta V(0)]$. For sinusoidal modulation this yields a $1-cos(omega T)$ term orthogonal to the standard $sin(omega T)$ Aharonov-Bohm phase. We propose a realistic electron interferometer, analyse fringe-field systematics, and project a sensitivity $|kappa|sim10^{-6},text{V}^{-1}$, the first such probe. A null result would confirm the scalar mode's decoupling from matter; a positive signal would uncover a new electromagnetic degree of freedom.
Category: Quantum Physics
[46102] viXra:2609.0061 [pdf] submitted on 2026-09-22 01:05:53
Authors: A. E. Mammadov
Comments: 22 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Lattice Tension Theory (LTT) is a theoretical framework that explores the possibility that observable space is composed of discrete quantum-scale cells whose structural response gives rise to gravitational phenomena. Matter is modeled as persistent configurations of quantum energy packets occupying this cellular network, while occupation modifies the elastic state of the surrounding structure.A central feature of LTT is the distinction between an empty cell, an occupied cell, and a missing or non-operative cell. Under sufficiently strong and sustained loading, the cellular structure may undergo fracture and lose its ability to support ordinary three-dimensional propagation. Such a persistent cell-free region is proposed as a spatial rupture, with black holes interpreted as spatial ruptures surrounded by an active, gravitating boundary.The paper develops both discrete and continuum descriptions of the framework. A variational scalar action leads to a nonlinear gravitational field equation with a load-dependent elastic coefficient, while a corresponding discrete lattice energy provides a microscopic counterpart. The formulation reproduces the Newtonian weak-field limit and admits an exact spherical exterior solution. A surface-source formulation demonstrates how an attractive exterior gravitational field can arise around an excised region without requiring an ordinary matter source in its interior.The study also introduces candidate mechanisms for lattice fracture and repair, higher-dimensional energy exchange, boundary radiation, area-scaling entropy, and a universal ordering parameter distinct from physical clock readings.This work is intended as a foundational formulation rather than a completed alternative to general relativity. Its purpose is to define the physical assumptions and mathematical structure of LTT clearly enough for subsequent numerical simulations, compact-object studies, galaxy-scale tests, propagation analyses, and comparison with observational constraints.
Category: Quantum Gravity and String Theory
[46101] viXra:2609.0060 [pdf] submitted on 2026-09-22 01:02:37
Authors: Maodong Ye
Comments: 16 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper proposes a new representation of integers, revealing significant information regarding their divisibility. Based on this novel integer representation, it provides necessary and sufficient conditions for numbers of the form $n^2+1$ to be prime. Meanwhile, the Goldbach's conjecture has been proven.
Category: Number Theory
[46100] viXra:2609.0059 [pdf] submitted on 2026-09-22 00:49:04
Authors: Hamid Simon
Comments: 41 Pages. In French
[T]he spatial "x-field" which exerts no influence on electromagnetic waves and has no effect on living matter, regardless of its intensity—is [theorized as] a reality. For it is through this field, acting in conjunction with the gravitational field, that celestial bodies and groups of celestial bodies move along their equilibrium orbits and rotate on their axes. In other words, the movement of celestial bodies along their equilibrium orbits and their rotation on their axes are analogous to the rotation of an electric motor's rotor under the influence of a magnetic field combined with an electric field. This study also demonstrates that without the spatial x-field, the Universe could not exist.
Category: Astrophysics
[46099] viXra:2609.0058 [pdf] submitted on 2026-09-20 13:00:18
Authors: Marko V. Jankovic
Comments: 8 Pages.
In this paper, entropy of natural numbers is going to be introduced. It will be shown that every natural number canbe associated with a family of discrete probability distributions and their entropies. After an introduction of a new Tesla'sentropy measure, a usefulness of the concept is going to be demonstrated by a short proof of Fermat's Last Theorem, basedon a simplified ABC theorem for prime numbers.
Category: Number Theory
[46098] viXra:2609.0057 [pdf] submitted on 2026-09-21 01:31:40
Authors: Viktor Strohm
Comments: 23 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)
Classical and relativistic physics treat gravitational interaction either as action at a distance between static masses, or as a geometric property of curved spacetime. However, the nature of inertia, the equality of inertial and gravitational mass, the mechanisms of momentum transfer in vacuum, and the origin of quantum and gauge structures remain dualistic postulates.The present work proposes the Local Energy Deficit Model (LEDM) — a deductive mechanical approach based on the concept of a dynamic elastic energy medium (vacuum substrate) in a state of elastic thermodynamic equilibrium. Developing the ontological principle of the objective reality of space and time, the author transitions from a purely geometric description of trajectories to the physics of spatial pressure gradients in a real medium. This allows for a consistent mechanical interpretation of action at a distance, unification of macroscopic gravity with optical phenomena, and extension of the model to quantum and gauge dynamics.Part I. Classical Mechanics of the Elastic Substrate1.Derivation of Newton's law. The gravitational force is derived from the pressure gradient of the elastic medium, created by the superposition of energy deficit fields of individual bodies. It is shown that the background energy density of vacuum ρu2080 completely cancels out in the final expression for weak fields. The absorption coefficient is fixed as σ = 16πGρu2080, ensuring dimensional and quantitative consistency.2.Orbital precession. In the nonlinear synergistic regime of the medium, an additional cubic force (1/r³) arises, leading to secular pericenter shift. The precession formula coincides with empirical data for Mercury (43u2033 per century). The normalization of the nonlinear modulus γ/ρu2080 = 1 receives microscopic justification.3.Optical and cosmological consequences. Gravitational lensing, the Shapiro effect, and cosmological redshift are interpreted as consequences of changes in optical density and interaction of photon wave packets with the elastic medium. The broadening (stretching) of Type Ia supernova light curves is explained without invoking geometric expansion of empty space.4.Casimir effect. The mechanism of the Casimir force is interpreted as a result of pressure difference between the external medium and the shielded gap; an explicit regularization transition is provided.Part II. Quantum and Gauge Extension5.Derivation of the Schrödinger equation. It is shown that the Schrödinger equation can be obtained from the stochastic wave equation of MLDE as its non-relativistic limit via the envelope approximation procedure. Energy quantization in bounded regions arises as a consequence of boundary conditions for waves in the elastic medium.6.Hierarchy of gauge structures. A three-level scheme for introducing charge has been developed:Level 1 — minimal gauge coupling (charge as an external sink parameter);Level 2 — complex field δu with U(1) symmetry; charge as a Noether current; relation of |ψ|² to the density of conserved charge in the envelope approximation;Level 3 — SU(3) color generalization; structural analogies with confinement and limitations of the envelope approximation applicability.7.Fundamental limitations of the model. It is emphasized that MLDE remains a local theory and, according to Bell's theorem, does not explain the violation of Bell inequalities. This fundamental limitation of the model clearly delineates its applicability boundaries.Keywords: Model of Local Energy Deficit (MLDE); vacuum elasticity; strain tensor; orbital precession; Shapiro effect; Casimir effect; gravitational lensing; cosmological redshift; stationary Universe; Schrödinger equation; envelope approximation; U(1); SU(3); Bell's theorem. IntroductionIn the absence of material objects, physical space represents an elastic energy medium in elastic thermodynamic equilibrium: points of the continuum exchange equal momenta, and the average vacuum pressure remains constant. This equilibrium is maintained through background isotropic elastic oscillations of the medium — an analogue of quantum zero-point oscillations.The model proposed in this work differs fundamentally from historical predecessors (Descartes, Euler, Le Sage). In it, the energy medium is considered not as viscous, but as ideally elastic, in dynamic thermodynamic equilibrium. It is the elasticity of the medium, not its viscosity, that is the source of the pressure gradient, and therefore of the attractive force. This allows not only to strictly derive Newton's law, but also to explain the secular precession of orbits as a nonlinear effect in the elastic substrate — without violating the stability of trajectories.The methodological foundation of MLDE rests on four principles:1.Logical deduction of dynamic forces from kinematics.2.Objective reality of the medium and dynamic nature of mass.3.Formation of radial energy deficit (gravitational wells).4.Sub-nuclear additivity of quantized forces and the equivalence principle.Structure of the work. This article consists of two parts. Part I develops the classical mechanics of the elastic vacuum substrate: derivation of Newton's law, orbital precession, optical and cosmological effects, Casimir effect. Part II extends the model to quantum and gauge dynamics: derivation of the Schrödinger equation, hierarchy of U(1) and SU(3) gauge structures, discussion of fundamental limitations (Bell's theorem).
Category: Classical Physics
[46097] viXra:2609.0056 [pdf] submitted on 2026-09-19 09:25:12
Authors: Vitaly V. Chaban
Comments: 30 Pages.
The rapid evolution of energy storage technology has necessitated the exploration of alternatives to conventional Li-ion batteries. It is driven by the limitations of resource scarcity, safety concerns, and sustainability challenges. This chapter critically discusses the technical, economic, and environmental aspects of emerging battery technologies. While Li-ion batteries are instrumental in powering electronics, electric vehicles, and renewable energy systems, their reliance on limited lithium and cobalt deposits, flammability risks, and recycling hurdles necessitate the development of next-generation solutions. A compelling alternative is solid-state batteries based on non-flammable ceramic, polymer, and glasses. These batteries feature enhanced safety, higher energy density, and improved thermal stability. These parameters satisfy applications in vehicles. Yet, challenges related to manufacturing scalability, interfacial resistance, and cheap production persist. Na-ion batteries gain researchers’ attention due to the low cost of sodium. Despite their lower energy density compared to Li-ion, recent advancements in cathode and anode materials can decrease the performance gap. Another promising avenue is lithium-oxygen and zinc-air systems. The latter offer theoretical energy densities surpassing the ones of Li-ion systems. Oxygen management, electrolyte degradation, and limited cycle life remain limiting barriers. Redox flow batteries, particularly vanadium and organic redox flow systems, provide scalable solutions for long-duration performance, though their bulkiness and lower energy density eliminate their compatibility with tablets and smartphones. Mg , Ca , and Al ions are cheap and offer high theoretical capacities. A slow-ion kinetics must be dealt with in the future. Organic and biodegradable batteries leverage eco-friendly materials and designs, while their current performance limitations restrict them to niche applications. Presently, Li-ion remains the dominant player due to its established infrastructure and cost-effectiveness. Therefore, recycling and sustainability efforts, such as closed-loop recovery systems and ethical sourcing initiatives, are critical in minimizing the ecological footprint of Li. Technological optimizations and machine-learning optimizations are essential for the future of energy storage and portable devices.
Category: Chemistry
[46096] viXra:2609.0055 [pdf] submitted on 2026-09-19 23:04:30
Authors: Sylwester Kornowski
Comments: 11 Pages. (Note by viXra Admin: Further repetition will not be accepted))
By combining the quark model and the atom-like structure of baryons described in the Scale-Symmetric Theory (SST) we have described the solar neutrino problem and generations of quarks. According to SST, there is a similarity of shapes and equality of mass ratios of the components of the three fundamental cores, i.e. of the core of lightest neutrinos, core of baryons, and the core of the Protoworld that was composed of dark matter. Within such a similarity we described the origin of the large mixing angle 33.089 degrees and the origin of the mass-squared splitting that define the solar neutrino oscillations. In our description, there appears imaginary mass and activation of the solar neutrino oscillations that can be damped. We showed that survival probability for the solar electron-neutrinos decreases from 1/2 at low energies of the electron-neutrinos (it is a mean value) to 1/3 for electron-neutrino energy equal to or higher than 9.345 MeV. We also described the atmospheric neutrino oscillations. SST leads to a minimum in the curve describing the dependence of the survival probability on neutrino energy for the atmospheric muon-like neutrinos for ∼500 km/GeV — it is consistent with experimental data. From SST follows that there are three generations of leptons and four generations of quarks and that the eight quarks combine into four pairs, i.e. d and u, s and c, b and t, and b’ ≈ 2.68 TeV and t’ ≈ 14.76 TeV. We described also the dark-matter (DM) field.
Category: High Energy Particle Physics
[46095] viXra:2609.0054 [pdf] submitted on 2026-09-19 13:11:33
Authors: Miloš Čojanović
Comments: 4 Pages. This work is licensed under a Creative Commons Attribution 4.0 International License.
The Lorentz-FitzGerald contraction is the physical phenomenon where an object becomes contracted along the axis of motion. We will test this hypothesis by observing the movement of the Earth relative to the CMB rest frame.
Category: Relativity and Cosmology
[46094] viXra:2609.0053 [pdf] submitted on 2026-09-19 22:56:11
Authors: Andrey V. Voron
Comments: 38 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Modern positional numeral systems suffer from zero code redundancy, making internal data verification impossible. While the classical Fibonacci numeral system features natural redundancy, its level varies drastically across different numbers. To optimize and stabilize this mathematical framework, this paper formulates the Parity Constraint Rule to restrict code redundancy. Based on this rule, we develop a New Fibonacci Numeral System (NFNS) with a dual basis designed specifically for fault-tolerant computing environments.
Category: Data Structures and Algorithms
[46093] viXra:2609.0052 [pdf] submitted on 2026-09-19 01:18:08
Authors: Henning Thielemann
Comments: 26 Pages. In German
We calculate the number of ways to arrange the ships in the game "Battleship." The answer: On a 10 × 10 grid, there are 26,509,655,816,984 (approximately 26.5 trillion) ways to place one ship of length 5, two ships of length 4, three ships of length 3, and four ships of length 2, with spaces between them. Rotations and reflections are not excluded from this count.
Category: Combinatorics and Graph Theory
[46092] viXra:2609.0051 [pdf] submitted on 2026-09-18 16:30:53
Authors: V. V. Chaban
Comments: 31 Pages.
Electrolytes are pivotal components of Li-ion batteries. Electrolytes enable ion transport between electrodes. The chemical composition and thermodynamic phase of an electrolyte directly influence performance, safety, and longevity. This chapter discusses challenges and advancements in liquid and solid electrolytes with an accent on their roles in shaping next-generation energy storage systems. Liquid electrolytes, composed of lithium salts dissolved in organic solvents remain the present industry standard, thanks to their desirable ionic conductivity and mature manufacturing infrastructure. Flammability, toxicity, and chemical reactivity under extreme conditions pose risks, such as thermal runaway and fire hazards. In turn, solid electrolytes offer non-flammable alternatives. They exhibit enhanced thermal stability and compatibility with highly energy-dense anodes like lithium metal. Ceramic electrolytes boast promising conductivity and electrochemical stability. Thus far, high production costs and processing challenges hinder the scalability of ceramic alternatives. Polymeric Li-ion electrolytes are flexible and easy to process, yet face limitations, such as relatively low ionic conductivity. Liquid Li-ion electrolytes dominate due to established supply chains and cost-effectiveness. Alternatively, solid electrolytes steadily gain traction amid modern demand for safer and higher-capacity batteries. The synthesis of solid Li-ion electrolytes involves costly processes and requires rare materials. Safety represents a critical driver for solid electrolytes, as they eliminate flammability risks and mitigate lithium dendrite formation. Sustainability and recyclability limitations are common challenges across both electrolyte types. Ionic liquids dissolving lithium salts can be considered to represent the third type of Li-ion electrolyte due to their non-volatility and broad voltage tolerance. Liquid Li-ion electrolytes contribute harshly to environmental pollution due to toxic solvent leakage, whereas solid electrolytes face obvious hurdles in material recovery.
Category: Chemistry
[46091] viXra:2609.0050 [pdf] submitted on 2026-09-18 17:34:11
Authors: Uri Lachish
Comments: 3 Pages.
Scattered light polarization, which is generally conserved on dark surfaces, provides evidence for single-event scattering. The conservation observed in dark terrestrial stones extrapolates to single-event scattering of moonlight. Single-event scattering offers a natural explanation for both the uniform appearance of the full Moon and the opposition effect, which are two manifestations of the same underlying phenomenon. Comparable near-uniformity is observed in full images of all the planets and their moons, as well as in terrestrial images of similar geometry. There are no real images that are consistent with Lambert’s cosine law of scattering.
Category: Classical Physics
[46090] viXra:2609.0049 [pdf] submitted on 2026-09-18 19:25:40
Authors: Fran De Aquino
Comments: 12 Pages.
It is demonstrated that gravitational and inertial masses are correlated by an electromagnetic factor. Some theoretical consequences of the correlation are: incorporation of Mach's principle into Gravitation Theory; new relativistic expression for the mass ; the generalization of Newton’s second law for the motion; the deduction of the differential equation for entropy directly from the Gravitation Theory. Another fundamental consequence of the mentioned correlation is that , in specific ultra-high energy conditions, the gravitational and electromagnetic fields can be described by the same Hamiltonian , i.e., in these circumstances, they are unified Such conditions can have occurred inclusive in the Initial Universe , before the first spontaneous breaking of symmetry.
Category: Quantum Physics
[46089] viXra:2609.0048 [pdf] submitted on 2026-09-17 23:07:23
Authors: Gordon Stewart Watson
Comments: 1 Page.
Taking all elements of physical reality to be beables (things that exist), our local-realistic study of Bell (1964) rests on two core principles: Einstein-locality (no beable travels superluminally) and Bohr-realism (some beables change interactively). This note (with expectation E, probabilities P, spin-half particles p), exposes the physical laws that correct Bell's error and refute his theorem.
Category: Quantum Physics
[46088] viXra:2609.0047 [pdf] submitted on 2026-09-17 23:02:29
Authors: Theophilus Agama
Comments: 23 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
An addition chain of length $h$ that leads to a number $n$ is a sequence of positive integers $s_0=1,s_1=2,ldots,s_h=n$ such that $s_i=s_j+s_k$~($i>jgeq k$) for each $1leq ileq h$. We introduce a matrix-theoretic framework for studying the properties of arbitrary addition chains that lead to a target integer $ngeq 2$ by associating each chain and the sequence of dominant and lower weight summands that calculate each term in the chain an adjacency matrix that encodes the internal geometry. In this linear-algebraic and matrix theoretic framework, we investigate how rank, rank profiles, singular values, eigenvalues, matrix norms, predecessor depths, and track-interaction terms encode the combinatorial and arithmetic structure of addition chains.
Category: Algebra
[46087] viXra:2609.0046 [pdf] submitted on 2026-09-17 08:10:08
Authors: Florian Michael Schmitt
Comments: 9 Pages.
The Hafele—Keating experiment and GPS technology exhibit a time-dilation effect that has traditionally been explained in terms of special and general relativity. We show, based on a Newtonian concept of a gravitationally entrained ether, that atomic clocks intrinsically exhibit this time-dilation effect when moving relative to gravitational fields. To this end, we develop a mathematical framework that reproduces the values observed in the aforementioned experiments for the apparent time dilation within a Newtonian-physics framework.
Category: Relativity and Cosmology
[46086] viXra:2609.0045 [pdf] submitted on 2026-09-16 20:51:40
Authors: Hyoyoung Choi
Comments: 57 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Black Hole Cosmology has traditionally been challenged by the apparent incompatibility between black hole interiors and cosmic expansion. However, because classical general relativity, on which this criticism is based, is itself incomplete in black hole interiors, the criticism rests on an incomplete premise. We reformulate this problem using total gravitational self-energy (GSE). The total GSE functional U_{gs−T}(R) = − (βGM_fr^2/R)[1 − (5β/7 )GM_fr/ Rc^2] contains a negative GSE term and a positive matter-GSE interaction term responsible for the repulsive radial response, where β denotes the structural coefficient of the GSE functional. For a matter-filled black hole interior, this energy landscape yields finite radii, including R_gs=(5β/7)R_S, R_{min,BH} = 5βR_S/(14−5β), and R_{min,E}=(5β/14)R_S. Thus, the point singularity is replaced by a finite-radius structure, allowing sufficiently massive black holes to contain macroscopic nonsingular interiors. This supports the possibility of closed black hole universes whose interiors exhibit weak local curvature and small tidal gradients. For our observable universe, the relevant configuration is not an isolated vacuum black hole, but a cosmological black hole embedded in a much larger, nearly homogeneous matter distribution. The matter-sector mass enclosed within the present particle horizon gives a Schwarzschild-equivalent event horizon radius R_S≃150.4 Gly, whereas the causal radius is R_U≃46.5Gly, giving R_S/R_U≃3.23 > 1. In this compactness sense, the observable universe lies within its own Schwarzschild-equivalent radius. The cosmological application of total GSE yields the dark energy density ρ_{Λ_m}= (βρ_m/2)(R_S/R_U)[(5β/14)R_S/R_U − 1]. Under the matter-dominated background approximation with w_{Λ_m}≃−1, the condition for accelerated expansion is ρ_{Λ_m} > ρ_m/2, or equivalently, R_U< R_{crit,U}≃0.279 βR_S. The framework provides a three-stage interpretation of cosmic history: early accelerated expansion driven by total GSE, a decelerating phase during the radiation era and the matter era, and late-time accelerated expansion driven by total GSE dark energy. Thus, accelerated cosmic expansion is not evidence against Black Hole Cosmology, but rather a central signature of a cosmological black hole. The predicted dark energy density provides a direct observational test of this interpretation of the observable universe.
Category: Relativity and Cosmology
[46085] viXra:2609.0044 [pdf] submitted on 2026-09-16 20:49:48
Authors: Enrico Stretti
Comments: 20 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)
This work introduces a discrete geometric model for the construction of a circle, basedon the hypothesis of a quantized space and the strict exclusion of the analytical continuum. The circular domain does not emerge as the limit of regular polygons, but rather from the progressive development of elementary circular sectors of increasing angular width associated with a step-by-step elongation of discrete radius; these sectors extend from the vertical axis of the circle, structuring their evolution into a numerical staircase pattern. A rectification procedure for the profile of thisstaircase is defined by means of a cutting line passing through the midpoints of the individual steps, thereby isolating right-trapezoid-shaped sections equivalent to the circular sectors of the discrete circle. The ordered accumulation of these elements reduces the measurement of the enclosed area to that of a corresponding equivalent isosceles right triangle. Under specific conditions of structural proportionality—and using a geometric equivalence constant (γ = 5/2) derived from the intrinsic properties of the configuration—it is demonstrated that the construction of this specific discrete model is governed by the exact dimensionless constant k = 25/8, which operates independently of the traditional analytical value of π.
Category: Mathematical Physics
[46084] viXra:2609.0043 [pdf] submitted on 2026-09-14 20:41:36
Authors: David Adam, Guillaume Estienne
Comments: 10 Pages. In French
Chang introduced Carlitz multiple polylogarithms (CMPs), generalizing in positive characteristic the Carlitz polylogarithms of Anderson and Thakur, and established a linear independence result for their ∞-adic algebraic values, from which follows the function field analogue of Goncharov's direct sum conjecture for multiple zeta values u200bu200b(MZV). Chen showed the analogue of this result in the v-adic setting, under the assumption that the place v is of degree one. The aim of this article is to show that Chen's result is valid for any finite place.
Category: Number Theory
[46083] viXra:2609.0042 [pdf] submitted on 2026-09-14 20:34:47
Authors: Izzie Boxen
Comments: Pages.
A model is presented here to help explain quantum wave-particle duality and two-slit one-at-a-time interference in a classical way and without resorting to the complex mathematics that is used in quantum field theory and even classical wave theory. This model avoids wave function collapse during measurement, the measurement problem.
Category: Quantum Physics
[46082] viXra:2609.0041 [pdf] submitted on 2026-09-15 13:12:18
Authors: Andrej Liptaj
Comments: 33 Pages.
The usual power series sumalpha_{n}x^{n} are generalized by the substitution xto g(x) to power series built from a function sum a_{n}g^{n}(x). The key feature of our approach consists in using functions g with free parameters g(x)=g({p_{i}},x); the resulting expansions thus keep the Taylor—like behavior (i.e., they match derivatives at the expansion point), but can also be tuned to adjust the far—away behavior. We present six specific cases g_{X}, Xin{A,dots,F}, each containing five free parameters. We use examples to demonstrate that the generalization can improve the convergence (rate and domain), mimic branch points and branch cuts and have other interesting properties. Because the partial Bell polynomials are a necessary ingredient in our method, our results can be interpreted as new formulas for specific values of the Bell polynomials.
Category: Functions and Analysis
[46081] viXra:2609.0040 [pdf] submitted on 2026-09-15 20:48:48
Authors: Mauro Alfonso Montenegro
Comments: 73 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Spacetime is conventionally treated as a four-dimensional background within which matter and gravitational phenomena occur. Space-Clock Field Theory (SCFT-A) advances a field-first alternative: the Lorentzian metric is the gravitational field, and physical space is the clock-orthogonal spatial state of that field, rather than an independent background container in which gravity resides. A dynamical scalar clock T selects the physical foliation and distinguishes cosmological clock-field time T from matter proper time t, the invariant time measured along material worldlines. Along homogeneous clock-comoving trajectories, the two physical times satisfy dT= Q dt, so that NT → dt/dT= Q→1 and HT = H/Q. Because T carries stress, conjugate momentum, conserved charge, and gravitational backreaction, this distinction changes relational observables and cannot be removed by a coordinate transformation. The theory’s central reciprocal statement is: As physical space expands, cosmological time contracts or moves slower; as physical space contracts, cosmological time expands or moves faster. The expanding branch obeys the on-shell response dNT /dH < 0. An explicit unbraided contracting branch has˙ Q > 0; this clock-rate statement has a different response sign and is proved only on its stated branch. This gravitational—clock architecture motivates the proposed extended equivalence principle, gravity= proper acceleration= physical space= relativistic aether= vacuum, where= denotes identity of physical sector rather than mathematical equality among curvature, acceleration, spatial geometry, causal structure, and vacuum states. SCFT-A realizes these principles using one universally coupled metric and one shift-symmetric scalar clock. The same operator family admits specified approximately matter-like regimes, a late self-accelerating endpoint, and a controlled local stationary MOND/AQUAL operator limit, without a separate cold-dark-matter action, dark-energy fluid, bare cosmological constant, or second matter metric. These are classical branch results, rather than a completed dark-sector unification theorem. A convex kinetic interpolation and positive spatial derivative operators define a deliberately constructed classical example. An explicit revised coe"cient point, ωm/H2 d = 1030 , ε = 10→140 and ϑ = 10→6, replaces uncertified numerical extrema by proved su"cient bounds. It preserves all-momentum local scalar positivity and a positive tensor spectrum. A generalized endpoint polynomial proves positive scalar kinetic and restoring coe"cients, and an exact decreasing energy controls every endpoint scalar mode despite redshifting momentum. The revised stationary correction ratio is strictly below 10→14 at a declared subhorizon scale. (Truncated to < 400 words by viXra Admin)
Category: Relativity and Cosmology
[46080] viXra:2609.0039 [pdf] submitted on 2026-09-13 09:32:25
Authors: Volodymyr Krasnoholovets
Comments: 24 Pages.
In this paper, the submicroscopic deterministic concept developed by the authoris applied to the problem of the neutrino mass. A particle appears from spaceconsidered as a mathematical lattice of primary topological balls, and induces adeformation coat in its surrounding. The principles of the interaction of particleswith space and through space between themselves are considered in detail. Theapproach states that real quarks possess only an integer charge (±e) and whenmoving they periodically change to the monopole state (⇄g) and hence, canonicalparticles are dynamic dyons. A neutrino emerges as a squeezed quark when it isin a monopole state, or in other words, the quark monopole state (a bubble in thetessellattice) is transferred to the appropriate lepton monopole state (a speck in thetessellattice). The self-mass (a ‘rest’ mass) for each neutrino flavour is calculated.The calculated value of the self-mass for the electron anti-neutrino is 1.222874 × 10^{−36} kg = 0.69893 eV/c^2. The concept of neutrino oscillations is revised, and another postulation is proposed, namely, that the transition from lighter to heavier flavours is due to the inelastic scattering of neutrinos on oncoming scatterers. As a result, the neutrino captures the mass defect, becomes heavier, and therefore the transitions ν_e → ν_µ and ν_µ → ν_τ occur; thus, the number of light neutrinos decreases in the neutrino flux studied.
Category: High Energy Particle Physics
[46079] viXra:2609.0038 [pdf] submitted on 2026-09-13 09:59:31
Authors: Volodymyr Krasnoholovets
Comments: 22 Pages.
Real physical space, as a purely mathematical structure built according tothe rules of set theory, topology, and fractal geometry, was proposed by MichelBounias (1943-2003) and the author. It emerges as a mathematical lattice ofprimary topological balls, which was named a tessellattice, and the size of acell/ball in the tessellattice is comparative with the Planck length, ∼ 10^{−35} m.Discrete fractal properties of the lattice allow the prediction of scales at whichsubmicroscopic to cosmic structures should occur. This approach allows thedevelopment of a submicroscopic concept of physics, which describes Natureat a much deeper level than offered by the quantum-mechanical formalismdeveloped at the atom scale, ∼ 10^{−10} m. In addition, the approach makesit possible to define such fundamental physical notions as mass and chargefrom first submicroscopic principles, and this actually means that fundamentalmathematics lays down the basic concepts of physics.
Category: Mathematical Physics
[46078] viXra:2609.0037 [pdf] submitted on 2026-09-13 10:01:01
Authors: Haruto Aoki
Comments: 5 Pages.
This paper examines moral responsibility for mistranslations of technical terms by large language models (LLMs) in light of expert contributions to public lexical resources. It argues that providing normatively appropriate translations in Wikipedia and Wiktionary may improve translation by LLMs that use these resources, and proposes the notion of deferentialism on terminological translation. It also questions the exclusive attribution of moral responsibility for mistranslation to model developers.
Category: General Science and Philosophy
[46077] viXra:2609.0036 [pdf] submitted on 2026-09-13 13:03:32
Authors: Johann Albers
Comments: 8 Pages.
As early as 1687, Isaac Newton published the law of gravitation named after him. This law includes the so-called ‘universal gravitational constant’, also named after him. With the help of this law, it was possible, amongst other things, to calculate the orbital paths of the planets in our solar system with such precision that perturbations in the orbit of Uranus were detected. These perturbations led to the prediction of the existence of another planet. In 1883, the new planet Neptune was indeed discovered at the predicted position, with a deviation of barely 1 degree.In recent decades, many new measurement results with ever-decreasing errors have been published. Unfortunately, the results often differed by more than the sum of their uncertainties. The results often do not merely represent a fixed value, but also time-varying components. Of particular interest are, for example, short-term variations, as their exact date is helpful in the search for their cause. Even more interesting, however, are periodic variations, as knowledge of the period length greatly narrows the search for the cause. One such variation with a period length of 5.9 years is well established. Based on the ‘Alternative Reflections on Gravitation’ (ARG), the search quickly leads to the suspected polluter: Jupiter, the largest planet in the solar system. Perhaps this planet is involved also in a non-gravitational effect, the Solar Cycle with a period of about 11 years.
Category: Astrophysics
[46076] viXra:2609.0035 [pdf] submitted on 2026-09-13 18:18:25
Authors: Fernando Salmon Iza
Comments: 3 Pages.
The controversy surrounding the existence of a non-accelerating universe—contrasting with the prevailing view of recent decades that we inhabit an accelerating, expanding universe—has resurfaced following recent discoveries by South Korean and Indian scientists. At the same time, the position held by U.S. scientists regarding an accelerating universe has been reaffirmed; the debate is likely to persist until more reliable data on dark energy become available in the coming years, ultimately settling the matter. The new Nancy Grace Roman Telescope, launched into orbit just weeks ago, is poised to resolve the issue in the near future. For now, new studies and opinions continue to emerge, supporting one position or the other. The work presented here is a theoretical study arguing for the existence of a non-accelerating universe; to this end, it examines the solutions to the Friedmann equations in detail. This study analyzes the expansion of the universe using a mathematical approach that leads to the following conclusion: the only valid solutions to the Friedmann equations are those describing non-accelerating universes.
Category: Relativity and Cosmology
[46075] viXra:2609.0034 [pdf] submitted on 2026-09-13 15:42:12
Authors: Tadeusz Pastuszek
Comments: 15 Pages.
This article presents a proposed unified description of physical interactions within the framework of the special theory of relativity. The starting point is the principle of minimum potential energy, interpreted equivalently as the principle of minimum rest mass. According to this approach, every interaction can be described by a general force formula containing the charges of the given interaction, an interaction constant, and a dimensionless function of distance. The commonly used inverse-square dependence is treated here as an experimentally established approximation valid only within a limited range of distances, rather than as a universal law extending from zero to infinity.After the finite propagation speed of interactions is taken into account, interactions become one-sided: the force exerted by a source charge on another charge is determined by the state of the source at the point from which its interaction ray reaches the affected object. Therefore, the interaction must first be described in the rest frame of the source charge and then transformed to other inertial frames by means of Lorentz transformations. Using general vectorial Lorentz transformation formulas for U-spaces of arbitrary dimension, together with a relativistic form of Newton's second law of motion, unified vector formulas are derived for the acceleration and force acting on a point object carrying an arbitrary interaction charge. The appendix presents the derivation of the rest-mass derivative used in these formulas and provides numerical checks confirming the consistency of the transformations.
Category: Relativity and Cosmology
[46074] viXra:2609.0033 [pdf] submitted on 2026-09-12 00:50:54
Authors: Richard D. Lockyer
Comments: 32 pages plus 8 appendices
Attempts to apply Octonion Algebra to the Standard Model have involved creating a matrix algebra representing Octonion Algebra operating on itself, an adjacent algebra. Each used only one of sixteen Octonion division algebra orientations, and favored left application. This manuscript first demonstrates how proper use of Octonion Algebra for mathematical physics must give consideration to all sixteen in an algebraic orientation covariant fashion if one is to avoid pathological outcomes when the same analysis is repeated using another orientation.Properly constructed 8x8 adjacent algebra matrices generate an algebraic orientation covariant left/right application inclusive group also closed for all Octonion algebraic orientation changes. Orientation closed pairs of conjugacy classes lead to sixteen class equivalence partitions. Eight bracket/orientation closed Lie algebras are created from them, which demonstrate the orientation of each 8x8 adjacent algebra matrix position is fixed. Seven Lie algebras have four ideals in 4x4 submatrices that pair up to occupied rows/columns directly related to the seven Quaternion subalgebra indexes or their basic quad index set. From these, fourteen unique skew-Hermitian Dirac gamma matrix bases for su(4) are created, and within each six skew-Hermitian Pauli matrix su(2) bases. 28 unique su(2) bases span the 8x8 matrix format with a bracket/orientation closed Lie algebra. Skew-Hermitian bases for adjacent algebra su(n: 2-8) Lie algebras can be placed in any nxn submatrix position using linear combinations of su(2) Lie algebras. Two distinct representations of su(2) ⨁ su(3) are presented that combine into the direct sum su(2) ⨁ su(3) ⨁ su(3).
Category: Mathematical Physics
[46073] viXra:2609.0032 [pdf] submitted on 2026-09-12 06:56:25
Authors: Carl Littmann
Comments: 9 Pages.
In his book, ‘Opticks’, 1700, Newton made a respectable estimate for both ether’s pressure and density — the best up to about 1905, after which interest in ether sadly waned. Ether pressure is, in fact, the energy per volume in space, and thus is very fundamentally important. But this paper explains, sadly, how the scientists of the 1800’s largely failed to address ether’s pressure. I.e., not even appreciating ether’s causing the high-pressures near the center of the earth and inside more massive bodies. So, Einstein’s great (mc^2) was welcomed even more than otherwise. ((I also give my reasons for my own rough estimate of ether pressure of (10^+34) N/sq.m., (coincidentally, same as scientists use for inside neutron stars.) [1] And for my ether density estimate of (10^-20) Kg/cu.m., (consistent with the highest-to-lowest densities in Nature — roughly equaling the highest-to-lowest forces found in Nature).)) Some 1800’s scientists made good estimate of ether’s density. ((It is said of Einstein’s gravitational theory that "two adjacent bodies bend space more than otherwise". But my view is that the available space for ether flow is naturally more constricted between two close bodies, so ether’s flows must speed-up there to maintain flow continuity. And that causes the well-known ‘Venturi flow effect’ -- reduced pressure, a suction effect, ‘attraction’, i.e., known as ‘gravity’.))
Category: Relativity and Cosmology
[46072] viXra:2609.0031 [pdf] submitted on 2026-09-12 07:04:58
Authors: Hans Hermann Otto
Comments: 8 Pages.
It is recommended joining together existing models for the structure of the electron to an elegant geometric relativistic wave-manifold model by support of artificial intelligence. The final model should reproduce the experimentally verified fundamental properties of the electron with high accuracy, including Sommerfeld’s omnipresent structure constant and the anomalous gyromagnetic factor of the electron, where the properties are generated by the internal geometric or topological constraints of the object itself. We will then better understand how electron pairing or pairing of holes works and how it does not.
Category: Classical Physics
[46071] viXra:2609.0030 [pdf] submitted on 2026-09-12 18:08:50
Authors: Piren Mo
Comments: 6 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
A constructive refinement of prime-type classification via nested primorial sievematrices. We introduce a primorial-based additive representation of integers (Mo numbers)and prove a residue separation property: for any prime q, primes in the arithmetic progressionq mod ps# cannot lie outside the nested Mo-type MTq. The Mo-types form a strictly descendinghierarchy MT2 ⊃ MT3 ⊃ MT5 ⊃ MT11 ⊃ ···, and we prove each deepest-type class containsinfinitely many primes (a constructive refinement of Dirichlet’s theorem without analytic densityestimates).We further classify twin prime candidates into coupled types such as MT(5,7) and MT(11,13),showing that the Twin Prime Conjecture is equivalent to the divergence of true twin pairs withinMT(5,7). As a rigorous corollary, Zhang’s bounded-gap theorem admits a Mo-type formulation:some even gap N ≤ 246 yields infinitely many prime pairs in a coupled Mo-type progression.The framework reframes classical distribution problems as explicit sieve-matrix counting,leaving open the quantitative density of twin pairs for future work
Category: Number Theory
[46070] viXra:2609.0029 [pdf] submitted on 2026-09-12 12:27:30
Authors: Peter Cameron
Comments: 10 Pages.
This essay traces the history of impedance matching as an overlooked core organizing principle in quantum physics. Impedance matching governs amplitude and phase of the flow of energy, of information transmission, in both classical and quantum mechanics. Although quantum mechanics retained the associated phenomena of amplitude, phase, reflection, transmission, resonance, tunneling, and scattering, it did not assimilate the organizing principle of impedance matching. Convergence with particle physics phenomenology and geometric algebra illustrates how ideas arising in separate traditions can unexpectedly meet. The essay reveals how a physical organizing principle can remain present in the phenomena while becoming largely invisible in the language used to describe them.
Category: History and Philosophy of Physics
[46069] viXra:2609.0028 [pdf] submitted on 2026-09-11 02:47:58
Authors: Xiao Lin Li
Comments: 9 Pages.
Particles in quantum mechanics have the property of quantum wave entropy. Similar to stretching a spring, under the specific conditions of cosmic expansion, particle wave entropy exhibits a negative entropy force that resists expansion. This negative entropy force provides particles with an attractive effect different from gravity. Like a spring constant, the negative entropy force has a proportional factor. The negative entropy force is proportional to the Hubble constant and also proportional to gravitational rotational speed. The effect of this negative entropy force is roughly the same as that of dark matter, serving as the physical origin of dark matter effects. Negative entropy force leads to a result where the rotation speed of a galaxy is proportional to the fourth root of the distance, showing an approximately flat and slowly rising curve. Negative entropy force also can explain the Tully-Fisher relation. Galaxies have properties of a flat radius and a cutoff radius. Galaxies only show noticeable dark matter effects within a limited range. The dark matter effect becomes noticeable starting from the flat radius and begins to decline noticeably from the cutoff radius. The flat radius and cutoff radius of a galaxy are determined by its mass. Galaxies of different masses and sizes will show different behaviors of dark matter. Negative entropy force also applies to photons and can explain the dark matter effects in gravitational lensing. Therefore, without assuming the existence of dark matter or modifying gravity theory, we can still normally explain the observed dark matter phenomena in galaxies. Dark matter doesn't exist, and MOND isn't needed.
Category: Astrophysics
[46068] viXra:2609.0027 [pdf] submitted on 2026-09-11 20:47:48
Authors: Agum Abdillah
Comments: 40 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)
This work develops a theta-geometric framework for studying the Hankel positivity problem associated with the Riemann Hypothesis.Starting from the centered Riemann xi-function, the framework exploits the even spectral symmetry to introduce a folded spectral coordinate and a meromorphic resolvent whose poles encode the squared centered zeros. Passing to reciprocal spectral variables leads to a canonical moment sequence whose Stieltjes moment property is characterized by the positivity of two associated families of Hankel matrices.The framework then connects this spectral-moment structure with the theta-function representation of the xi-function. A tilted theta measure is introduced, yielding an exact expectation representation for the folded resolvent and a differential hierarchy governing its derivatives. The resulting analysis leads to an adjoint differential operator and a two-variable kernel representation, together with an exact inhomogeneous differential identity in which boundary contributions are retained explicitly.The central outcome is an exact reduction of the spectral question to an all-orders Hankel positivity problem. The work distinguishes rigorously established identities and equivalences from numerical diagnostics and does not claim a proof of the Riemann Hypothesis. Instead, it provides a structured theta-geometric and moment-theoretic framework for investigating the remaining positivity problem.
Category: Number Theory
[46067] viXra:2609.0026 [pdf] submitted on 2026-09-11 20:43:44
Authors: Moshe Segal
Comments: 11 Pages.
Modern physics is caught in a profound conceptual schism between deterministic, continuous classical frameworks and probabilistic, discrete quantum mechanics. While recent advancements—such as Nicolas Gisin’s application of intuitionistic mathematics to classical mechanics [1] — might have provided some bridging of this gap by exposing classical physics as fundamentally probabilistic, they continue to rely on the static assumption of a fundamental, singular space-time background. This paper argues that space-time might not be a primary entity. Instead, this paper argues that what Humans perceive as space-time might only be an emergent cognitive interface used to interpret and explain energy interactions. To break the logical paradox of using a brain embedded in space-time to disprove space-time, this paper proposes that science must look for an internal algorithmic "bug" in the existing frameworks. This paper proposes a Charged Lense-Thirring Effect Experiment, which is designed to observe a possible anomaly in the spin-precession of a charged particle beam orbiting a rapidly rotating charge distribution, which, if this anomaly is detected, might also support the assumption that space-time might be a secondary property of localized energy interactions and a cognitive construct stemming from energetic interactions. This paper does not present that a successful implementation of the proposed experiment, will, by itself, assert that the space-time is not a primary entity. But this paper argues that a successful implementation of the proposed experiment, with possible successful implementations of additional properly proposed experiments, might support the already ongoing research endeavors to present the space-time as an emerging entity, which might conclude in a more reasonable view of the universe, and also resolve issues related to the existing view of the space-time as a primary entity.
Category: Relativity and Cosmology
[46066] viXra:2609.0025 [pdf] submitted on 2026-09-11 16:09:24
Authors: Volker W. Thürey
Comments: 5 Pages.
Many people dream of establishing a settlement on the planet Mars, especially the American entrepreneur Elon Musk. However, I believe this is nearly impossible because of the planet's extremely harsh environmental conditions. Compared with Mars, Earth is far more hospitable to human life.
Category: Astrophysics
[46065] viXra:2609.0024 [pdf] submitted on 2026-09-11 20:36:06
Authors: Pawel Jan Piskorz
Comments: 4 Pages.
We propose a procedure which allows to determine the only admissible exponents in Diophantineequations of three kinds: Fermat, Markov and Catalan. First, we use a set of rewriting rules for each Diophantine equation. Second, we obtain the parametrized versions of the Diophantine equations. Next, we differentiate each of parametrized equations obtaining the identities for Fermat, Markov and Catalan equations.
Category: Number Theory
[46064] viXra:2609.0023 [pdf] submitted on 2026-09-10 02:12:16
Authors: Peter Shushmaruk
Comments: 11 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)
This paper presents a reverse-engineered model of the Great Pyramid of Giza and proposes how each of the internal components functioned as part of a cohesive acoustic-resonant cavity circuit. It begins in the King’s Chamber, driving a continuous acoustic pressure wave that is filtered and amplified before ultimately being used to activate a metallic transmitter at the apex. This paper focuses on the function of each internal component and the progression of acoustic responses between them.
Category: Classical Physics
[46063] viXra:2609.0022 [pdf] submitted on 2026-09-08 06:47:50
Authors: Yong Zhao
Comments: 4 Pages.
For any integer n greater than 1 such that 2n+1 is prime, we construct interval (n,2n). By synthesizing the prime number theorem, the Bertrand—Chebyshev theorem and Euler's proof to analyze the gap between 2n+1 and primes in the interval (n,2n), we prove the Polignac's Conjecture.For any integer greater than 1, we construct intervals (n,2n) and (2n,4n). By synthesizing the Bertrand—Chebyshev theorem and the prime number theorem to analyze the gap of primes between the consecutive intervals, we prove the Polignac's Conjecture.
Category: Number Theory
[46062] viXra:2609.0021 [pdf] submitted on 2026-09-09 00:10:19
Authors: Joshua Dizon
Comments: 5 Pages. (Note by viXra Admin: Please cite and listed scientific references!)
We show that the decay of the energy envelope in a damped harmonic oscillator can be explicitly connected to the increase of entropy in the surroundings. The result is a simple, pedagogical bridge between mechanics and the Second Law of Thermodynamics.
Category: Thermodynamics and Energy
[46061] viXra:2609.0020 [pdf] submitted on 2026-09-08 23:35:02
Authors: Francesco Prandel
Comments: 12 Pages.
If interpretation is a metacognitive process, interpreting a physical theory means identifying the metaphysical concepts suitable for representing its theoretical terms. From this perspective, given the linearity of the formalism of quantum mechanics, its natural interpretation is the one suggested by W. Heisenberg, according to whom quantum mechanics governs the potential level of physical reality, not its actual level.
Category: Quantum Physics
[46060] viXra:2609.0019 [pdf] submitted on 2026-09-09 00:20:40
Authors: Xiaodong Liu, Qichang Liang, Yu Liang
Comments: 1 Page.
In this study, we found that a cathode-ray tube can drive a circuit containing a capacitor to generate a direct current. Furthermore, the system requires no external power input.
Category: Classical Physics
[46059] viXra:2609.0017 [pdf] submitted on 2026-09-07 05:26:48
Authors: Harris V. Georgiou
Comments: 21 Pages.
In Urban Search & Rescue (USAR) operations after large-scale earthquakes, time is of essence for the survival of trapped victims. There are too many parameters that define the conditions, severity and survivability window for each victim entombed under debris. Hence, worksite assessment and triage is primarily an empirical procedure that is based on incomplete and mostly qualitative information. On the other hand, if statistical rescue data from previous USAR missions are available, appropriate probabilistic models can be developed for estimated rescue counts and live victims remaining over time. This study explores the availability of such historic data and, based on these, several probabilistic models are designed. These include Exponential and Weibull for inter-rescue times, non-homogenous Poisson for rescue counts and Generalized Extreme Value (GEV) for the tails of the underlying data distributions. All the models converge to very similar results for survival windows and in accordance to real rescue data. Namely, the 95% and 99% quantiles point to 115-118 hours (4.8-4.9 days) and 177-181 hours (7.4-7.5 days), respectively. A mixed-model approach is proposed for more accurate approximations, selecting GEV for the beginning (up to day 2) and ending phases (days 5-8), Weibull for the middle (days 3-4) and non-homogenous Poisson everywhere else (days 2-3, 4-5), with a relative approximation error no more than 4.5% compared to real rescue data throughout the typical USAR operational period of eight days. Finally, the GEV model is also used for investigating the effect of under-reporting live rescues during the first 24-hour window of USAR operations, providing hints of a factor at the order of 1-in-5 to 1-in-8 or more, especially during the first six hours. These results provide valuable insights for better planning and team deployment in such USAR missions after large-scale earthquakes.
Category: Statistics
[46058] viXra:2609.0016 [pdf] submitted on 2026-09-07 18:15:38
Authors: Min Min Oo
Comments: 19 Pages. (Note by viXra Admin: Please cite and listed scientific references!)
This paper develops a Prime Pair Framework for studying twin primes using structured sequences of odd composites. The base sequenceO_1=9+6r_1, r_1≠((1+2x)^2-13)/6 " or" ((1+2x)^2-7)/6 provides intervals containing two odd integers, which may form twin primes if both are prime. When the general sequencesO_a=(2a+1)^2+(2+4a) r_a (a={2ⓜ,3ⓜ,4ⓜ,u2026ⓜ,k})and O_1are in proper alliance, the conditions are formed through lower, upper and double twin prime formation mechanisms.
Category: Number Theory
[46057] viXra:2609.0015 [pdf] submitted on 2026-09-07 18:09:48
Authors: Hadrijan Crnčić Jurasić
Comments: 14 Pages. hadrijan.crncic-jurasic@skole.hr
In this paper we formally construct (mathbb{M}), a number system that contains three dimensions and forms a bridge between the complex numbers and the quaternions. In this system we define the operation of division by zero (1/0=infty). The third dimension of the system is the scalar infinity (s), which does not mix with real or complex numbers.Historically, a system with exactly three dimensions was impossible because of the multiplication of two new axes. In the quaternions these are (i) and (j), whose product must give (k), creating a new dimension because (ij) cannot be displayed in those three dimensions. Historically, taking the square root of (-1) was not allowed. This was solved by the new number (i), which introduced the complex numbers and achieved the transition from (mathbb{R}) to (mathbb{C}) by adding the new number (i) such that (i^2 = -1). (mathbb{R}) is one-dimensional, and (mathbb{C}) is a two-dimensional number system, so the question arises whether there are number systems above (mathbb{C}).The answer was first found by William Rowan Hamilton when he tried to construct a three-dimensional number system. By adding one new axis (j) such that (j^2 = i^2 = -1), he encountered the problem of what the product of (i) and (j) would give. He realized that it would give (k), a new spatial axis, and so he constructed a four-dimensional number system with axes (1,i,j,k) such that (k^2 = j^2 = i^2 = -1). Thus the three-dimensional algebra was skipped because no matter which axis we add, the product of two axes must always give something new, namely a fourth dimension.Later Frobenius and Hurwitz formalized this and proved that number systems are possible only in dimensions (2^n), where (n) is a natural number: namely 1 ((mathbb{R})), 2 ((mathbb{C})), 4 ((mathbb{H})), 8 ((mathbb{O})), and so on, up to 256 dimensions and beyond. This is the Cayley-Dickson construction, and the number systems obtained after the sedenions are no longer particularly interesting or useful for study because they lose critical properties such as associativity, alternativity, and commutativity.All these systems do not solve the problems for which new systems are introduced, namely the definition of undefined numbers. Just as the complex numbers define the square root of (-1), which was undefined in the real numbers, so the definition of (n/0) brings with it the definitions of other undefined numbers, such as the zeroth root and zero to the zeroth power.
Category: General Mathematics
[46056] viXra:2609.0014 [pdf] submitted on 2026-09-07 18:34:15
Authors: Ayush Samanta
Comments: 37 Pages.
Finite-time transport in the circular restricted three-body problem (CR3BP) can change qualitatively under perturbations to initial conditions, making robustness difficult to characterize using smooth trajectory sensitivities alone. This work investigates whether geometric distance to an outcome-change boundary can provide a usefulmeasure of transport robustness for a two dimensional family of invariant-manifold seeds generated from planar L1 Lyapunov orbits in the Earth—Moon CR3BP. A 160 × 33 parameter atlas comprising 5280 initial conditions was classified by first-passage outcome, and adaptive refinement produced 484 numerical samples of the resultingoutcome boundaries. To avoid arbitrary Euclidean distance in the family parameters, the seed-state map was used to induce a local pullback metric, defining a family-constrained boundary-distance diagnostic ρη. The metric construction was numerically consistent, and ρη revealed strongly nonuniform proximity to the resolved transportinterfaces. Its ordering, however, depended on the prescribed state weighting, with Spearman correlations ranging from approximately 0.794 to 0.999 across the tested metrics. Direct perturbation tests also rejected a guaranteed-radius interpretation: one outcome change occurred at approximately 0.5ρη, while finite directional searches at five representative points recovered no independent minimum flip distance. These results support ρη as a family- constrained geometric diagnostic of proximity to resolved finite-time outcome boundaries, but not as a certifiedoutcome-preserving radius or validated transport condition number. A stronger robustness measure requires converged boundary resolution, physically specified uncertainty geometry, and direct computation of minimum outcome-changing perturbations.
Category: Astrophysics
[46055] viXra:2609.0013 [pdf] submitted on 2026-09-08 00:52:38
Authors: Clark M. Thomas
Comments: 3 Pages.
The recent Phase 3 trial of a customized Moderna mRNA cancer vaccine, along with Merck’s Keytruda, to fight melanoma skin cancer, points to possible long-term remission, if not yet a permanent cure. The hope is that future mRNA vaccines can work similarly for other types of cancer, along with Keytruda. This 2026 medical news points toward the general promise of AI in other medical areas, and for understanding cellular life itself. This essay points to emerging synergies between human and AI research tools.
Category: Artificial Intelligence
[46054] viXra:2609.0012 [pdf] submitted on 2026-09-06 09:13:25
Authors: Jacqueline Fernandes
Comments: 4 Pages.
This paper explores the transition boundary where classical escape velocity thresholds intersectwith relativistic coordinate transformations. Using observational mass configurations from Sagittarius A*, we analyze how super luminal escape velocities (ve > c) force a geometric inversion ofthe local Minkowski metric tensor. We demonstrate that the information loss paradox is fundamentally a consequence of the future light cone compressing and tilting past the vertical axis, renderingoutward spatial paths geometrically non-existent to an external observer.
Category: Astrophysics
[46053] viXra:2609.0011 [pdf] submitted on 2026-09-06 14:39:55
Authors: Herbert Weidner
Comments: 10 Pages.
We report the detection of continuous microhertz waves originating from Jupiter, recovered from two decades of atmospheric pressure measurements across Germany. Barometers act as largeu2011aperture antennas for lowu2011frequency signals, allowing coherent recovery of a carrier near 55.97 $mu$Hz, which corresponds to twice the rotation frequency of Jupiter’s solid core. A directu2011conversion receiver iteratively compensates all known phase modulations caused by Earth’s orbit and the four Galilean moons, concentrating the wave’s energy into a narrow spectral line with a signalu2011tou2011noise ratio of 100. We measure the longu2011term frequency drift of Jupiter’s core and determine the modulation indices associated with each moon. The phaseu2011modulation pattern is stable across 318 independent realizations. Additional spectral features indicate that Jupiter hosts multiple internal oscillators with distinct frequencies. These results demonstrate that Earth’s atmosphere responds coherently to microhertz waves generated by nearby planets.
Category: Astrophysics
[46052] viXra:2609.0010 [pdf] submitted on 2026-09-06 21:45:10
Authors: Volodymyr Krasnoholovets
Comments: 49 Pages. Journal of Advanced Physics 5, No. 2, 145—167 (2016). DOI: 10.1166/jap.2016.1232
This paper reviews major approaches to the description of subatomic particles, suchas leptons, quarks, hadrons and nucleons. Among these approaches are quantum chromodynamics, soliton models, bag models and others. The main accent is on a theory of thereal physical space that acts as a scene on which all high-energy events take place. Wediscuss how a lepton and quark appear in the space constituted as a tessellation lattice ofprimary topological balls — the only structure that mathematics (i.e. set theory, topologyand fractal geometry) offers to the constitution of ordinary physical space. Since leptonsand quarks emerge in the tessellattice from a topological ball, they must interact withthis substrate. The principles of the interaction of subatomic particles with space andthrough space between themselves are considered in detail. The approach: i) states thatreal quarks possess the integer charge ±e and they periodically change to the monopolestate (hence, canonical particles are dynamic dyons); ii) naturally solves the problem ofconfinement of quarks; iii) reveals the dynamics of quarks in hadrons; iv) discloses an innerstructure of the proton and neutron; v) calculates the radius of the proton; and vi) derivesthe nuclear forces as the result of both direct coalescence of surfaces of the nucleons andthe overlapping of spatial excitations (named inertons) generated by the nucleons at theirmotion through the tessellattice. Experimental results showing nuclear transformationsin samples affected by artificially generated inerton fields are demonstrated.
Category: High Energy Particle Physics
[46051] viXra:2609.0009 [pdf] submitted on 2026-09-06 22:07:09
Authors: Teo Banica
Comments: 400 Pages.
This is an advanced introduction to the various types of normal random variables, with most of the needed preliminaries included. We first discuss the probability basics, standard central limits, and the theory of the usual, real normal variables, with examples, illustrations and numerous formulae. Then we go on a similar discussion regarding the complex normal variables, and the Rayleigh variables too. We then move to arbitrary dimensions, with a discussion regarding the Gaussian vectors, and related probability laws, featuring some functional analysis, and geometry and physics too. Finally, we provide an introduction to the quantum versions of the normal variables, and notably to those coming from free probability and random matrices.
Category: Statistics
[46050] viXra:2609.0008 [pdf] submitted on 2026-09-05 08:44:33
Authors: Anatoly V. Belyakov
Comments: 10 Pages. 4 Fig.
Physical models based on J. Wheeler’s geometrodynamics, when applied to planetarysystems and pulsars, agree well with modern observational results and predict new ones.The current geometrodynamic model explains the appearance of the "hot Neptunian desert"region, the existence of an "airy super-Earth", the construction of compiled pulsar spectra,the calculation of their "death line", the calculation of braking indices for various pulsarpopulations, and much more.
Category: Astrophysics
[46049] viXra:2609.0007 [pdf] submitted on 2026-09-06 00:56:45
Authors: Edward Larson
Comments: 24 Pages. (Note by viXra Admin: Future submission of AI assisted article will not be accepted)
Gödel's intuition accurately zeroed in on a core truth: that the expressiveness of non-trivial mathematical theories outpaces the efficacy of any inference engine. His paradoxical form of argumentation, however, begat immense confusion and pessimism, which this essay examines critically and aims to undo. His actual technical analysis exposed a historic oversight in classical set theory: the lack of internal structural variation within the Cantor sets $aleph_{0}$, $aleph_{1}$, etc. The paradoxical argumentation amounts to an indirect proof (reductio ad absurdum) of internal differentiation within $aleph_{0}$.This paper introduces a new concept of structural grade separation (SGS) within the Cantor sets and examines their foundational role and implications within formal mathematical frameworks, challenging the traditional conception of coarse set cardinality. By introducing a comprehensive SGS scheme, we demonstrate how structural stratification illuminates transfinite set theory without sacrificing logical consistency. The theoretical bounds of this construction against established axioms of arithmetic and set theory are analyzed, illustrating how explicit structural hierarchy resolves ambiguities inherent in standard set theory and cardinal assignments. The broader mathematical significance of graded set structures for decision algorithms and formal reasoning engines are explored.
Category: Set Theory and Logic
[46048] viXra:2609.0005 [pdf] submitted on 2026-09-03 04:06:45
Authors: Dave E. Dunstan
Comments: 4 pages. 3 Figures.
The Pantheon + SHOES data is interpreted using transformed coordinates with distances that have origin at the beginning of the Universe. Distances (R) taken from the beginning of the Universe (R~0 and t~0) increase toward Earth and reveal a Newtonian Gravitational redshift (z<0.1). Distances determined in this way are the inverse of the luminosity distances measured from Earth. The revised coordinate frame yields a 1/R dependence of the redshift consistent with a Newtonian gravitational redshift. An alternative to the Hubble-Lemaitre expanding Universe is presented. The alternative Universe suggested is determined by Gravity, is static in size and contains Galaxies that show a Gaussian distribution of velocities. This is the model of the Universe first considered by Einstein.
Category: Relativity and Cosmology
[46047] viXra:2609.0004 [pdf] submitted on 2026-09-03 15:49:44
Authors: Martin Kraus
Comments: 9 Pages.
According to a recently proposed vibrational interpretation of the Schrödinger equation for hydrogen-like atoms, stationary single-electron wave functions describe vibrations that are driven by phase waves associated with a bound electron moving on precessing orbits similar to orbits of the old quantum theory by Bohr and Sommerfeld. Based on this interpretation, the objective of this work is to provide insights into the structure of these wave functions by constructing similar wave functions from the corresponding electronic orbits and their associated phase waves without explicitly solving the three-dimensional Schrödinger equation. The proposed construction extends solutions of the two-dimensional Schrödinger equation into three dimensions and takes precession of the orbital angular momentum into account by a weighted average over all rotations about the quantization axis. The constructed wave functions are structurally similar to the standard wave functions of hydrogen-like atoms in spherical coordinates; thus, the proposed construction provides a new way of understanding the structure of these wave functions.
Category: History and Philosophy of Physics
[46046] viXra:2609.0003 [pdf] submitted on 2026-09-04 00:18:43
Authors: Antoine Khai Nguyen
Comments: 17 Pages. (Note by viXra Admin: For the last time please cite and list scientific references!)
The Cosmic wavefunction model that governs the cosmic world, and the Nuclear wavefunction model that governs the quantum world.These two discovery-postulated Quantum wavefunction models are separated by their action realms but very similar in their ingrained structural mechanisms.The core element of this Quantum wavefunction model set is the concept of orbital/motion frequencies for both cosmic and quantum objects, and the quantization principle of the ingrained feature determination mechanisms for these objects.Each wavefunction model can demonstrate that the orbital positions (from the captor out) of all the captives inside their system are not random, but are coordinated according to the model's mechanism which uses the orbital/motion frequencies as the shared factor.
Category: Quantum Gravity and String Theory
[46045] viXra:2609.0002 [pdf] submitted on 2026-09-01 20:46:50
Authors: Nigel B. Cook
Comments: 5 Pages.
Reference 1 shows that when multipath interference is treated correctly, the imaginary term, i sin S, is unnecessary; the real term cos S suffices, therefore Euler’s exp(iS) = i sin S + cos S reduces to exp(iS) → cos S. Can this same principle be applied to complex phase amplitudes in gauge theory phase ransformations? Gauge invariance only requires a continuous group action in real space, not the complex phase structure suggested by textbooks. The complex exponential hides the physics. The conversion of gauge theory to real space phase changes makes explicit the physical mechanism of gauge theory.
Category: Quantum Physics
[46044] viXra:2609.0001 [pdf] submitted on 2026-09-02 11:37:02
Authors: Aleksandr Nikitin
Comments: 4 Pages.
My theoretical developments of the new scientific paradigm lead to the conclusion that any movement of matter, including gravity and low-energy nuclear reactions (LENR), occur as matter-neutrino induction.Any fundamental prime mover (sail, water wheel, steam engine, internal combustion engine, gas turbine, jet engine, nuclear reactor, electric current generator) is a nuclear fusion generator.The motion of matter, i.e. any change, including gravitational, electromagnetic and low-energy nuclear reactions LENR, the description of which is the task of science, can be further cognized solely on the basis of a new scientific paradigm:
Category: Nuclear and Atomic Physics
[46043] viXra:2608.0109 [pdf] submitted on 2026-08-31 12:30:45
Authors: Xiaogang Ruan
Comments: 18 Pages.
The theory of Observational Relativity (OR) is a new theory in physics. For ease of understanding, the author reports the significant discoveries and new insights of OR to physicists and readers in the form of serial reports. Now, OR Serial Report 6 reports that, similar to relativistic effects, the quantum effects in the quantum mechanics based on Planck's quantum hypothesis, including wave-like nature and uncertainty, are also sorts of observational effects. But the difference is that relativistic phenomena are caused by the observational locality of observation agents, while quantum phenomena are caused by the observational perturbation of observation agents. The OR axiom system, taking the definition of OR time as the most basic premise or first principle, has not only deduced the theory of OR, including the inertial OR (IOR) and the gravitational OR (GOR), but also deduced the theory of observational quantum (OQ). The theory of ORQ is that of the general observation agent. The informons of observation agents with momentum and energy must perturb the observed object P, causing P to exhibit quantum effects. The theory of OQ has discovered that Planck's quantum theory is a theory of optical observation, i.e., a special case of the theory of OQ, in which the quantum effects, including wave-like nature and uncertainty, are observational effects caused by the perturbation of the informons (photons) of the optical agent, not the intrinsic nature of the physical world or P; the Planck constant h is not a cosmological constant, but rather the energy-frequency ratio of photons, representing the minimum scale or resolution for the optical agent to determine the mass, momentum and energy of P. Now, the whole theoretical system of ORQ has not only generalized and unified Newtonian mechanics and Einstein's theory of relativity, but also generalized and unified Einstein's formula E=mc2 and Planck's equation E=hf, marching towards the unification of relativity theory and quantum theory.
Category: Quantum Physics
[46042] viXra:2608.0108 [pdf] submitted on 2026-08-31 20:40:36
Authors: Miroslav Pardy
Comments: 15 Pages. Original article
It is shown that all spin possibilities can be constructed by combining the fundamental spin 1/2 system a sufficient number of times. In order to express all spin possibilities mathematically we introduce the multispinor source. All component spins are on the same footing and additional symmetry requirements can be imposed on the multispinor. The multispinor description provides a unified approach to all spin values, with the first-order differential equation of spin 1/2 setting the pattern of field equations.
Category: Mathematical Physics
[46041] viXra:2608.0107 [pdf] submitted on 2026-08-31 20:36:26
Authors: Jamal S. Shrair
Comments: 13 Pages.
An objective and empirical analysis of the data collected from different detectors over four decades reveals that the so-called solar neutrino problem is far from being solved. Contrary to the assessment of the Nobel Committee, the experimental results from the Sudbury Neutrino Observatory cannot be regarded as a confirmation of the Standard Solar Model. However, the obsolescence of the current model (SSM) has recently been exposed by so much observational data, for instance, the crisis in solar abundance. Furthermore, using images obtained by the Solar Dynamics Observatory, researchers found the convective motions (the motions within the Sun's interior) to be nearly 100 times smaller than current theoretical expectations. This is a clear verdict on the notion of thermonuclear reactions that are supposed to be the processes that generate solar neutrinos.
Category: Astrophysics
[46040] viXra:2608.0106 [pdf] submitted on 2026-08-31 20:39:34
Authors: Kiyoung Kim
Comments: 6 Pages.
Viewed as an ontological reality in physics, the biological morphic field—whose existence has long been hypothesized in biology—is interpreted as a structural template for matter. In this context, for a living organism, this field acts as the ontological counterpart to its physical body in an energy resonance state. Through the organism's mental activities, the field and physical body interconnect to interact with the external environment. Moreover, if we can assume that the life cycles of organisms are a natural process selected through evolution to help them adapt to changing environments, the genetic data inherent to both this field and the physical body should be passed down to subsequent generations.
Category: General Science and Philosophy
[46039] viXra:2608.0105 [pdf] submitted on 2026-08-31 01:03:09
Authors: Blair D. Macdonald
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)
This paper introduces a unique possible cause of religion and similar secular beliefs. It suggests they are an emergent manifestation derived from the universal ‘life-force to survive’. It argues that, given the highly developed human brain, ‘survival’ must be catered for both during life and in the afterlife. At this time of evolution, only the human mind can imagine an afterlife. This void must be survived in, must be filled; humans are the first to fill this gap with belief, and later, with religion. Religions have evolved to meet the demand for this new space. This survival theory may also explain secular belief systems in which the pattern of survival repeats with dual, same-yet-different characteristics.
Category: Religion and Spiritualism
[46038] viXra:2608.0104 [pdf] submitted on 2026-08-30 09:00:00
Authors: Volodymyr Krasnoholovets
Comments: 20 Pages.
This paper shows how Maxwell’s equations can be derived from first submicroscopic principles, which involves understanding the detailed structure of real physical space, that is, introducing basic concepts such as charge, electric and magnetic fields. Consideration at the level of elementary particles indicates that particles can be studied without involving the concept of electric current, although the presence of current density is an important component in Maxwell’s equations used in classical electrodynamics. A moving charged particle interacts with space organised in the form of a tessellattice, and this allows the identification of subtle nuances of the behaviour of the particle within the particle’s de Broglie wavelength λ = h/(mυ). Namely, a charged particle behaves like a dynamic dyon, whose state periodically changes from the state of an electric charge to the state of a magnetic monopole with the spatial period λ. Thus, Maxwell’s equations explicitly include the magnetic monopole as a source of the magnetic field, and therefore monopoles should appear in experiments conducted by particle physicists, although until now they have not focused on the direct manifestation of magnetic properties of elementary particles.
Category: Quantum Physics
[46037] viXra:2608.0103 [pdf] submitted on 2026-08-30 17:02:35
Authors: Richard F. Cronin
Comments: 9 Pages.
On a global average, the Earth’s magnetic field has weakened approx. 9 to 10 % over the last 160 to 200 years. Most notable is the teardrop-shaped South Atlantic Anomaly (SAA), centered due east of Porto Alegre, Brazil, but extending from South Africa to the waters of the eastern Pacific. Magnetic field strength in this region is measured at 22 micro-Teslas and lower. The weakened magnetic field allows greater solar proton penetration into the lower layers of the ionosphere, formation of HOx, NO, and NOx, ozone destruction and increased Ultraviolet (UV) radiation to the surface. Moreover, the Dalton Minimum, with negligible solar activity, spanned from 1790 to 1830. We have enjoyed sustained Solar Cycles since then. Solar Maximum # 25 (2024 to 2026) has been particularly powerful. Thus, continuous Forbush Decreases have also contributed to ozone reduction, reduced cloud cover, brighter skies and greater Ultraviolet radiation reaching the surface. Earth’s most recent magnetic field breakdown was the Laschamps Excursion, 41000 to 42000 years ago, triggering a near collapse of Earth’s protective ozone layer and bathed the planet in Ultraviolet (UV) radiation. The magnetic dipole broke apart and magnetic anomalies (weak points) wandered across the Earth. This led to dramatic climate change, violent weather, and the final great migration of Homo Sapiens out of Africa. UV radiation evaporated water from the Southern Oceans and delivered snows across the far northern latitudes to build the Ice Age glaciers. In fact, conditions across southern Europe were mostly cool and Alpine. Africans sought out shelter in the limestone caves of Eurasia to escape the extreme UV. Armed with bow and arrow, Homo Sapiens evicted cave bears and Neanderthals. Hunting and fishing was conducted at night. Humans who ventured out in daylight "covered their nakedness" and applied red ochre clay on exposed limbs and faces as sun block. With minimum exposure to daytime radiation and Ultraviolet, Eurasians develop paler skin (lower melanin) in order to produce adequate Vitamin D. This paper will discuss in greater detail the role of magnetic field variations, ozone destruction, UV radiation increases, warming of the Southern oceans, and degassing of dissolved CO2. Multiple papers have disputed the claims of Anthropogenic Global Warming / Climate Change -- allegedly due to "greenhouse gases" and "downwelling" or "back scatter" of Infrared radiation. I will leave that discussion to others.
Category: Climate Research
[46036] viXra:2608.0102 [pdf] submitted on 2026-08-29 03:54:54
Authors: Sergio de Azevedo Melo
Comments: 225 Pages. In Portuguese
Covariance implies invariance under coordinate transformations, and its application within inertial reference frames enables the resolution of a wide range of relativistic spacetime problems. However, its application to gravitation restricts its use to spherical coordinate systems. Conventional transformation to a Cartesian system leads to issues regarding symmetry and commutativity, resulting in spacetime discontinuity due to the emergence of torsion.Coordinates lack physical significance, and the transformation between Cartesian and spherical representations should be trivial. Resolving the metric tensor in Cartesian coordinates via an imaginary group allows for the resolution of the Levi-Civita connection's torsion and, consequently, leads to a series of reconsiderations regarding spacetime.The structure of spacetime is revealed as a topological construction through Minkowski's hyperbolic foundation -- a formalism that allows for the representation of both the wave-like properties of gravitation and the metric characterization of electrodynamics.The normalized formalism proves productive both in demonstrating its consistency -- through the normalized formulation of the hydrostatic equilibrium of compact bodies, which supports the absence of singularities (as an alternative to the Tolman-Oppenheimer-Volkoff equation) -- and in its treatment of geodesics and rotating bodies (as an alternative to the Kerr metric). Formulation of the self-organization of spacetime via the normalized energy-momentum tensor, as well as cosmological issues regarding inertia, time and its irreversibility, entropic characterization, and large-scale behavior. Normalized metric is a continuous group that allows for the metric derivation of the Dirac equation, Yukawa coupling, and Hubble's law, while also offering insights into various conceptual issues, such as symmetry and vacuum polarization.
Category: Relativity and Cosmology
[46035] viXra:2608.0101 [pdf] submitted on 2026-08-29 09:04:48
Authors: Shanzhong Zou
Comments: 4 Pages.
We study the projection geometry induced by a singular point on the boundary of a three-dimensional fan-shaped cylinder. The cylinder is defined in the first quadrant of the real coordinate plane, with x and y both between zero and one, and a singular point located at x=1 on the boundary. Through an iterative projection process involving the angle bisector of the quadrant, we prove that the continuous interval [0,1] is precisely discretized to an infinite set of boundary points.
Category: Geometry
[46034] viXra:2608.0100 [pdf] submitted on 2026-08-29 10:41:23
Authors: Pavlo Danylchenko
Comments: 8 Pages.
It is substantiated that the Solar System corresponds not to a static Newtonian gravitational field, but to a dynamic gravitational field that is also formed by planetary motion and therefore adapts to changes in the positions of the planets within it. It is because of this that gravitational pseudo-forces, just like centrifugal pseudo-forces of inertia, are orthogonal to the superharmonic quasi-circular orbits of the planets at every point. The correspondence of the superharmonic trajectories of the planets' motion exclusively to the laws of conservation of angular momentum and energies (the Newtonian of inert free rest energy and the Keplerian of ordinary rest energy of matter) is proven. The inconsistency of two-focus elliptical orbits with the law of conservation of angular momentum is substantiated. Equations for superharmonic single-focus quasi-circular (asymmetric oval) planetary orbits have been derived, consistent with both the laws of conservation and astronomical observations. Modernized and substantially improved versions of Kepler's laws have been formulated.
Category: Relativity and Cosmology
[46033] viXra:2608.0099 [pdf] submitted on 2026-08-28 20:03:11
Authors: Peng Gao
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Modern natural-language systems determine the meaning of a word or a sentence statistically, by training large language models on extensive corpora and massive graphics-processor(GPU) resources. In the present work we pursue an altogether different route: we ask whetherthe meaning of written text is a physical quantity that can be registered directly by a torsion field detector, without any training of a statistical model. The study is carried outwithin the framework of torsimetry developed by Shkatov, in which the torsion field (TF)of physical objects and processes is recorded as the torsional contrast (TC) of the measuredobject with respect to the measuring instrument by means of single- and multi-coordinatetorsimeters. To suppress the spurious informational phantoms that otherwise accumulate inobject—instrument—operator systems and smear the readings of repeated measurements, weadopt the Method of Differential Test Assertions (MDTA), which composes the object undertest from pairs of textual assertions of opposite meaning and records their differential torsion response. We show that this differential response is a stable and reproducible signature of the semantic content of the text, and that the detector is able to discriminate the meanings of different words and sentences without any GPU-based training. In 19 independent measurement sessions, an impossible assertion (a total score greater than a physically unrealisable threshold) produced a consistently higher torsional contrast than the correspondingtrue assertion, with a positive sign in all 19 sessions and a mean difference of +112 arbitraryunits (p ≈ 2 × 10−6 ). The results support the hypothesis that the meaning of a word or asentence is an objective and stable property of the text, carried by its torsion field, and thatit can therefore be read directly from the instrumental signal rather than inferred from atraining corpus.
Category: Quantum Physics
[46032] viXra:2608.0098 [pdf] submitted on 2026-08-28 19:58:00
Authors: Shashankaditya Upadhyay
Comments: 21 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Network of oscillators are studied to understand if graph (vertex) colouring can be obtained upon synchronization when a strong negative coupling is applied between oscillators when there is an edge present in the network and a small positive coupling is applied between oscillators when there is no edge. We find that oscillators with simple equations such as Thomas' systems are best suited for such couplings. We further observe that introducing a degree of variance in coupling strength improves synchronization to a great extent in favour of returning optimal graph colouring in such networks. We further study the role of parameters (which are obtained as a result of varying coupling strength) on synchronization. The present article thus ends up proposing a polynomial time heuristic method to solve the graph colouring problem.
Category: Combinatorics and Graph Theory
[46031] viXra:2608.0097 [pdf] submitted on 2026-08-26 21:54:00
Authors: Rafael Cañete Mesa
Comments: 3 Pages.
In this paper, we will demonstrate that relativistic kinetic energy follows an expression that is just as precise as the non-relativistic one, that one is related to the other, and that a corpuscular topology can be derived from it.
Category: High Energy Particle Physics
[46030] viXra:2608.0096 [pdf] submitted on 2026-08-27 21:31:35
Authors: Jose Risomar Sousa
Comments: 20 Pages.
The discovery of a generalization of the Riemann functional equation obtained by exploiting symmetries of a new formula for the Hurwitz zeta function with respect to the shift parameter, $b$, has led to the search for a similar relation for the Lerch $Phi$ function, $Phi(e^z,k,b)$, where a new formula is used as starting point and the symmetries with respect to $b$ are exploited again. To this end, we uncover surprising new ways of producing analytic continuations of finite summations.
Category: Number Theory
[46029] viXra:2608.0095 [pdf] submitted on 2026-08-27 03:35:26
Authors: Matt Guiney
Comments: 50 Pages.
This paper examines two different explanations of what the horizon is and how it is formed. The first explanation is that the horizon is a physical location, more specifically it is an occluding edge of a spherical surface which obstructs objects below and beyond it from being viewed. The second explanation is that the horizon is an optical phenomenon involving human visual perception and the behavior of light.
Category: General Science and Philosophy
[46028] viXra:2608.0094 [pdf] submitted on 2026-08-27 21:27:01
Authors: Manish Kumar
Comments: 40 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Cancer is a complex genetic disease involving uncontrolled cell growth and proliferation, necessitating the effective targeting of dysregulated cellular pathways underlying cancer progression. Multiple genetic and epigenetic alterations characterize tumor progression and define the hallmarks of cancer. This may result in the dysregulation of growth factors, regulatory proteins, cell adhesion molecules, and immune system molecules driven by alterations in the expression profile of tumor suppressor genes and oncogenes, which may vary among different cancer types. Importantly, patients with the same cancer type respond differently to available cancer treatments, likely due to tumor-specific DNA, RNA, and proteins, indicating the need for patient-specific treatment options. Precision oncology has evolved as a form of cancer therapy that focuses on the genetic and molecular profiling of tumors to identify specific molecular alterations involved in carcinogenesis for tailored individualized cancer treatment. Advances in high-throughput technologies, including next-generation sequencing, have enabled gene expression profiling, providing detailed molecular characterization of various tumors. Moreover, the application of multiomic technologies, including genomics, proteomics, metabolomics, and single-cell multiomics, constitutes a novel approach for the identification and quantification of a comprehensive set of biological molecules to study their translation into cellular functions and tissue pathologies. The integration and analysis of various multiomic sequencing data are crucial in this regard, as they can reveal critical molecular changes, such as cancer-driving mutations, post-translational modifications, gene fusions, amplifications, and alterations in signaling networks within tumors. Furthermore, the role of computational techniques, such as artificial intelligence and deep learning, in analyzing complex data and identifying patterns of disease development for better outcomes, is now well established in precision medicine. Additionally, AI-powered multi-omics and network biology have been harnessed to integrate and analyze biological data through networks, which may prove crucial in solving key problems in precision oncology. This article aims to briefly explain the foundations and frontiers of precision oncology in the context of cutting-edge developments in tools and techniques associated with it and assess its scope and importance in achieving the intended goals over time.
Category: Quantitative Biology
[46027] viXra:2608.0093 [pdf] submitted on 2026-08-27 21:24:20
Authors: Hongyuan Ye
Comments: 8 Pages.
In the two definitions of divergence，the flux-density divergence provides the physical definition of divergence, whereas the nabla-operator divergence serves as a mathematical tool for calculation and derivation. Using examples derived from Coulomb’s law of electrostatics, and based on the theory of limits, this paper reveals that the flux-density divergence and the nabla-operator divergence are non-equivalent. The differential form of Gauss’s flux theorem in Maxwell’s equations does not hold. Furthermore, keeping or discarding relatively higher-order infinitesimals yields different results of the flux-density divergence, which contradicts the theory of limits in calculus. This paper proposes the effective order infinitesimal theorem to enhance the theory of limits. In the expression of the flux-density divergence, the effective order of its infinitesimal variables is 3. However, during the mathematical derivation of the nabla-operator divergence from the flux-density divergence, only 2nd-order infinitesimal variables are retained. Gauss’s flux theorem in differential form does not hold, and the theory of limits in calculus exhibits deficiencies. Physics and mathematics are undergoing a revolutionary scientific transformation.
Category: Mathematical Physics
[46026] viXra:2608.0092 [pdf] submitted on 2026-08-27 21:21:49
Authors: Jose Risomar Sousa
Comments: 10 Pages.
A formula for the Hurwitz zeta function at the positive integers k, ζ(k, b), is createdby solving the real and the imaginary parts separately and then combining them. Afew different formulae for the Hurwitz zeta function are known from the literature, butthey are very general and usually hold for ℜ(k) > 1. The advantage of formulae thatonly hold at the positive integers is the fact that they are simpler and easier to workwith. P An analytic continuation of the generating function of ζ(k, b) is also obtained as k≥2 xk(ζ(k, b) − 1/bk), where the term 1/bk was subtracted for convenience.
Category: Number Theory
[46025] viXra:2608.0091 [pdf] submitted on 2026-08-27 16:40:44
Authors: Madison Brown
Comments: 14 Pages.
Argentina occupies a paradoxical position in the comparative literature on trust: a country with one of Latin America's oldest continuous democratic periods since 1983, yet one whose citizens report chronically low confidence in one another and in the state. This article presents a narrative literature review of empirical and theoretical scholarship on interpersonal, institutional, and political trust in Argentina, drawing on Latinobarómetro survey data, World Values Survey findings, and peer-reviewed studies indexed on Google Scholar. The review traces four interlocking patterns. First, generalized interpersonal trust in Argentina, while comparatively higher than the regional Latin American average in recent survey rounds, remains low by global standards and has been shaped by decades of recurrent economic crisis. Second, institutional and political trust has followed a long-run downward trajectory punctuated by short-lived recoveries around new administrations, with a persistent gap between broad normative support for democracy and specific satisfaction with its performance. Third, this erosion is driven by an interacting cluster of factors: entrenched corruption and high-profile prosecutions of political elites, recurrent monetary and economic crises that have produced a durable narrative of monetary distrust, income inequality, and a closed political elite characterized by high incumbency and family-based succession. Fourth, Argentina's deep political polarization, commonly referred to as "la grieta" (the crack), both reflects and reinforces the erosion of generalized institutional trust. The review also considers how the COVID-19 pandemic and the 2023 election of Javier Milei illustrate the practical stakes of this trust deficit, and it identifies gaps in the literature that future longitudinal and comparative research should address.
Category: Social Science
[46024] viXra:2608.0090 [pdf] submitted on 2026-08-26 20:44:05
Authors: Shashankaditya Upadhyay
Comments: 6 Pages.
A method to find prime factors of a given arbitrary number $n$ is proposed. When $n$ is semiprime, the method is shown to run in $O(n^2log(log(n)))$ time. Eigenvalue distribution of matrices utilized in the proposed method is conjectured.
Category: Number Theory
[46023] viXra:2608.0089 [pdf] submitted on 2026-08-26 20:33:28
Authors: David Robert Somervell
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references)
The Feynman-Stueckelberg interpretation equates negative energy with negative time, but since −E = h(−ν) = h/(−t) it is better to think of this view as a mathematical statement, rather than an interpretation. What is required is to determine what negative time represents, not dismiss its existence as mere mathematics. The immediate implication is that time as it is represented in the equations of motion cannot be time in the fundamental sense. If it were, we would expect anti-matter to travel backwards in time, but we do not observe this. The mathematics of this dimension are startlingly similar to the 3 spatial dimensions, so it is reasonable to assume that this dimension is actually a 4th spatial dimension, and that it has a symmetric relationship with the flow of time. We measure time indirectly with the motion of clocks, and in the same vein, the 4th dimension has become the clock that we use in physics. Using this insight, possible solutions to both the "Arrow of Time" and the "Measurement Problem" become immediately apparent.
Category: Quantum Physics
[46022] viXra:2608.0088 [pdf] submitted on 2026-08-26 11:52:02
Authors: Junghwan Jun
Comments: 14 Pages. Please post next to the accompanying manuscript
We present new static solutions of SU(2) Yang-Mills equations for $n$ point sources aligned in a common isospin direction. The solutions possess a gauge field structure analogous to the BPST instanton while constituting a distinct class of static solutions, and satisfy the Coulomb gauge condition. They are either self dual or anti-self dual. Substitution of the solutions into the Yang-Mills equations yields localized source terms corresponding to a non-Abelian electric charge but also a magnetic monopole charge associated with each source. Furthermore, the resulting gauge fields generate a confining potential for quarks. These properties suggest that the present solutions provide a new class of nonperturbative configurations in Yang-Mills theory.
Category: High Energy Particle Physics
[46021] viXra:2608.0087 [pdf] submitted on 2026-08-26 20:29:37
Authors: Junghwan Jun
Comments: 23 Pages.
A Dirac equation for the $qbar{q}$ system is formulated in the presence of the confining potential derived from a static solution of the SU(2) Yang-Mills equations. The resulting radial equations define an eigenvalue problem with singular behavior at $r=0$ and $r=ho$, leading to a discrete spectrum of confined states.The system reduces to four sets of coupled radial equations for each of quark and antiquark components, which do not appear to admit closed-form solutions in terms of standard special functions. An approximate treatment is therefore developed to determine the corresponding energy spectrum. The calculated bound-state energies are found to be largely insensitive to the current quark masses and are of the same order as the observed meson masses, suggesting that the dominant contribution to the meson masses originates from the confining dynamics described by the present Yang-Mills solution. The quark and antiquark spectra exhibit an asymmetry associated with the gauge orientation of the underlying monopole-like configuration, although the individual energy eigenvalues are not gauge invariant observables.
Category: High Energy Particle Physics
[46020] viXra:2608.0086 [pdf] submitted on 2026-08-26 20:21:59
Authors: Yonglin Tong
Comments: 6 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)
We report a universal geometric identity for charged particles: the product of the classical electron radius r_e and the Schwarzschild radius r_s is fixed by the Planck length and the fine-structure constant: r_e r_s = 2 alpha l_P^2. The mass m completely cancels, indicating that this constraint is independent of the specific particle mass and represents a universal relation between charged matter and spacetime geometry. Two independent paths provide cross-validation: (1) an algebraic path—direct multiplication of the classical definitions; and (2) a dynamical path—Dekker (2014) derived the characteristic radius r_c = l_P sqrt(alpha) from exact solutions of the Einstein—Maxwell equations, which is algebraically equivalent to the identity above. From this identity, a natural length scale r_res = l_P / sqrt(2 alpha) is defined, corresponding to the Compton energy E_res = sqrt(2 alpha) E_P approx 1.47 x 10^18 GeV, which contains no free parameters and lies within a potentially testable window of ultra-high-energy cosmic-ray physics. We also propose an S^3 x R^3 fiber-bundle geometry as a heuristic framework providing a geometric picture for the resonance scale.
Category: History and Philosophy of Physics
[46019] viXra:2608.0085 [pdf] submitted on 2026-08-25 12:46:38
Authors: Peter Cameron
Comments: 9 Pages.
This essay explores a historical question: did twentieth-century physics gain extraordinary predictive power at the cost of losing a unified geometric language? It traces the development of Grassmann's exterior algebra and Clifford's geometric algebra, their eclipse during the rise of vector analysis, and the subsequent evolution of relativity, quantum mechanics, and gauge theory. This change in mathematical language also changed the direction in which theoretical physics sought explanation—from beginning with geometry and asking how physical law emerges, to beginning with physical law and deriving wavefunctions as solutions of field equations. It concludes by suggesting that recovering the geometric representation of the vacuum wavefunction may reopen a complementary bottom-up tradition in theoretical physics.
Category: History and Philosophy of Physics
[46018] viXra:2608.0084 [pdf] submitted on 2026-08-25 14:33:40
Authors: Igor Hrnčić
Comments: 1 Page.
This paper identifies a century old error in math.
Category: Number Theory
[46017] viXra:2608.0083 [pdf] submitted on 2026-08-24 14:27:56
Authors: Uwe Saint-Mont
Comments: 22 Pages.
Much has been written about the notion of probability, and how this concept may be interpreted. In contrast, philosophers of science seem to have neglected the concept of (stochastic) distribution, although distributions are at least as fundamental. One the one hand, they generalize the basic mathematical notion of number, on the other, from a structuralist perspective, distributions precede probabilities and their interpretation.
Category: Statistics
[46016] viXra:2608.0082 [pdf] submitted on 2026-08-25 01:07:06
Authors: Nana Abeka Otoo, Asirifi Boa
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Prototype based one-class learners such as Supervised Vector Quantization for One-Class Classification (SVQ-OCC) utilise squared Euclidean distance without metric adaptation and cannot adapt to the spatial structure of the data. Moreover, these learners are unable to capture relevant variation when the target distribution presents anisotropic structure in the feature space. This paper proposes One-Class Generalized Learning Vector Quantization (OC-GLVQ), whose discriminant substitutes the negative-class distance in GLVQ with a per-prototype visibility threshold, yielding a cost function that is jointly differentiable in prototypes, thresholds and metric parameters. A hierarchy of distance formulations from diagonal relevance weighting through global and local matrix projections to tangent subspace metrics is developed within the OC-GLVQ framework. The resulting classifiers adapt their geometry to the target distribution while retaining prototype-level interpretability. This paper identifies a gradient-magnitude mismatch between the prototypes and threshold parameters in high-dimensional settings and resolves it through a square-root reparameterisation. Experimental assessment on four practical datasets indicates the metric-adaptive variants consistently surpass both SVQ-OCC and Support Vector Data Description (SVDD), with local matrix adaptation yielding the strongest overall performance.
Category: Artificial Intelligence
[46015] viXra:2608.0081 [pdf] submitted on 2026-08-24 18:13:07
Authors: Uwe Saint-Mont
Comments: 8 Pages.
Goodman's new riddle of induction has mainly been treated in verbal terms. Its core concept, projectabiliy, has much in common with statistical estimation. Therefore, understanding when and why the latter approach works, also sheds much light on Goodman's riddle.
Category: General Science and Philosophy
[46014] viXra:2608.0080 [pdf] submitted on 2026-08-23 20:14:50
Authors: Moshe Segal
Comments: 11 Pages.
Modern physics is caught in a profound conceptual schism between deterministic, continuous classical frameworks and probabilistic, discrete quantum mechanics. While recent advancements—such as Nicolas Gisin’s application of intuitionistic mathematics to classical mechanics [1] —have bridged this gap by exposing classical physics as fundamentally probabilistic, they continue to rely on the static assumption of a fundamental, singular space-time background. This article argues that space-time is not a primary entity but an emergent cognitive interface used to interpret energy interactions. To break the logical paradox of using a brain embedded in space-time to disprove space-time, we propose that science must look for an internal algorithmic "bug" in existing frameworks. We propose a specific high-precision experiment: testing whether the mathematical sign of an electric charge induces an asymmetry in gravitational time dilation, aiming to reveal a "bug" in general relativity. By testing whether positive and negative charges produce asymmetric time dilation, the proposed experiment aims to falsify the current Q2-dependent Reissner—Nordström metric and demonstrating that space-time is a secondary property of localized energy interactions and a cognitive construct stemming from energetic interactions.
Category: Relativity and Cosmology
[46013] viXra:2608.0079 [pdf] submitted on 2026-08-23 21:15:40
Authors: Rick Burger
Comments: 9 Pages.
This paper proposes a mechanism for cosmic genesis wherein a daughter universe is birthed via a white hole ejection sourced by a parent black hole collapse. We hypothesize that as macroscopic matter undergoes gravitational collapse toward the parent singularity, extreme tidal forces and Planck-scale quantum gravity effects resolve the singularity by completely dissociating complex matter states into their most fundamental quantum constituents. This extreme deconstruction acts as an information-scrambling and homogenization phase, stripping the infalling mass-energy of its structural history. Consequently, when this fundamental plasma undergoes a quantum bounce and is expelled from a white horizon, it emerges in a highly uniform, low-entropy configuration. This mechanism provides a physical basis for the low-gravitational entropy boundary conditions required at the onset of a new inflationary epoch, offering a novel resolution to the Past Hypothesis.
Category: Relativity and Cosmology
[46012] viXra:2608.0078 [pdf] submitted on 2026-08-21 11:46:41
Authors: Payam Danesh
Comments: 8 Pages.
Stirling transforms inherit modular periodicity from their fixed columns only when the weights suppress the additional prime-power factors in the column periods. We establish a local p-adic valuation criterion for an integer-weight Stirling transform and prove that, for every modulus greater than two, Euler’s totient is an eventual period. The proof involves truncating the transform modulo each prime power, applying Kwong’s fixed-column period bounds and handling the exceptional third column at the prime two on its own. We then apply the criterion to the signed binomial-recurrence sequence; the formal exponential generating function of this sequence yields integral Stirling weights such that the odd and even prime valuations satisfy the criterion, thereby proving Bala’s modular-periodicity conjecture for this sequence. For every integral substitution G(e^x-1), we obtain the stronger universal eventual period given by the Carmichael function.
Category: Number Theory
[46011] viXra:2608.0076 [pdf] submitted on 2026-08-23 00:32:00
Authors: Rouven Metternich
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We propose that dark matter is not an exotic new substance, but a geometric necessity of four-dimensional spacetime. Prior to the electroweak Higgs phase transition, all fundamental particles were massless and propagated at the speedof light c. In this pre-Higgs epoch, the four dimensions of spacetime were fully equivalent— no dimension was geometrically privileged as "time". Upon Higgs condensation, the acquisition of mass froze each particle’s instantaneous propagationaxis as its individual time dimension, while the remaining three orthogonal dimensions became its spatial dimensions. Since exactly four basis dimensions are available, this produces four distinct dimensional sectors: one visible sector (our own) and three geometrically equivalent dark sectors. Particles across sectors share thesame four-dimensional manifold and thus interact gravitationally. Electromagnetic interactions— being confined to a shared three-dimensional spatial hypersurface— are geometrically forbidden between sectors. Dark matter thus requires no newparticles, no new forces, and no modifications to gravity: it is a direct consequence of the combinatorial geometry of (3+1)-dimensional spacetime. The predicted dark to-visible matter ratio of 3 : 1 is consistent with cosmological observations. The structural co-distribution of dark and visible matter emerges naturally from their shared gravitational manifold. Furthermore, the hypothesis provides a geometric explanation for the Hubble tension, predicts gravitational wave events without electromagnetic counterparts, and accounts for the persistent null results of all direct dark matter detection experiments.
Category: Relativity and Cosmology
[46010] viXra:2608.0075 [pdf] submitted on 2026-08-21 00:58:57
Authors: Roger L. Mc Murtrie
Comments: 1 Page.
John Bell’s 1964 article On The Einstein Podolosky Rosen Paradox concludes that a discrepancy between quantum theoretical and Kolmogorov-type expectation values is due to non-locality. On the other hand, this document concludes that the discrepancy is due to information loss rather than non-locality.
Category: Quantum Physics
[46009] viXra:2608.0074 [pdf] submitted on 2026-08-21 00:49:19
Authors: Wenhao Xiong
Comments: 7 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We consider an effective gravitational potential whose extra term is a regularised two-dimensional logarithmic potential — the logarithmic Green''s function of the two-dimensional Poisson equation. We derive its source surface density, Σ(R) ∝ rc^2/[(R^2 + rc^2)^2] (a two-dimensional Plummer-like distribution), and show that its total mass satisfies M = Vflat^2/G2 exactly, so that the model has a well-defined physical normalisation. The circular-velocity contribution is V2D^2(R) = Vflat^2 R^2/(R^2 + rc^2), which differs from a pseudo-isothermal (PI) halo in the approach to the flat asymptote (1/R^2 vs. 1/R corrections). We fit this model, MOND (two interpolating functions), NFW, PI and Burkert halos to the SPARC sample of 175 disk galaxies (3391 velocity measurements), with the stellar mass-to-light ratio free per galaxy and a systematic error floor scanned over 0—15%. At the reference 10% floor, the cored models give lower total χ^2 than NFW and both MOND forms: χ^2/N = 0.57 (2D), 0.57 (Burkert), 0.60 (PI), versus 0.79 (NFW), 1.38 (MOND-simple) and 1.66 (MOND-standard). The three cored models (2D, Burkert, PI) have similar goodness of fit, but the information criteria moderately favour the 2D model over PI (∆AIC ≃ 93) and provide only a modest preference over Burkert (∆AIC ≃ 13); the present data do not establish a decisive physical distinction among them. The discriminating observable is the shape of the transition to the flat asymptote: 1/R^2 for the 2D potential, 1/R for PI, and a peak followed by a slow decline for Burkert. We show that SPARC covers the relevant radial range only partially (23% of data points in the discrimination zone). Against MOND the result depends on the model-selection criterion, because MOND has substantially fewer global parameters. Among the models evaluated at each error-floor value, the 2D model gives the lowest total χ^2; MOND-standard is evaluated only at the reference 10% floor. We conclude that the soft-logarithmic potential is a viable, normalised member of the cored-model family, with a specific falsifiable prediction for the transition region.
Category: Astrophysics
[46008] viXra:2608.0073 [pdf] submitted on 2026-08-21 00:43:27
Authors: Tanuj Kumar, Vandana [Doe], Jyoti [Doe]
Comments: 34 Pages. (Note by viXra Admin: Both the first and last names of the authors are required; please submit article written with AI assistance to ai.viXra.org)
We develop an effective continuum framework in which the physical vacuum is characterized by a bounded scalar capacity field Φ(x,t), with normalized remaining-capacity fraction f=Phi /c^{2}. Matter is represented by localized depletion of this capacity, while gravitation arises from the associated redistribution of the remaining vacuum response. In the weak-field limit, the governing equation reduces to the Poisson equation and reproduces Newtonian gravity. A nonlinear capacity-dependent response yields the exterior solution Phi (r)=c^{2}sqrt{1-2Gm/(rc^{2})}, or equivalently f(r)=sqrt{1-2Gm/(rc^{2})}. Relating the local capacity fraction to temporal and reciprocal radial scaling reconstructs the Schwarzschild exterior line element ds^{2}=-f^{2}c^{2}dt^{2}+f^{-2}dr^{2}+r^{2}d{Omega }^{2}, together with its standard weak-field gravitational optical response. The same continuum dynamics admit localized intrinsic oscillations which, under the quantum normalization mathrm{hbar }{omega }_{0}=mc^{2}, yield the Planck—Einstein and de Broglie relations through Lorentz transformation of the intrinsic phase. The resulting dispersion relation takes the Klein—Gordon form and reduces to the Schrödinger equation in the nonrelativistic limit. Massive excitations propagate subluminally, whereas massless disturbances remain nondispersive with limiting propagation speed c. The framework thus provides a common continuum description of vacuum depletion, emergent gravitation and spacetime scaling, and relativistic matter-wave dynamics, while identifying strong-field dynamical phenomena as a potential regime for distinguishing predictions.
Category: Quantum Gravity and String Theory
[46007] viXra:2608.0072 [pdf] submitted on 2026-08-18 13:31:27
Authors: Holger Döring
Comments: 17 Pages.
Investigated is a hypothetical mathematical framework describing a dynamical crossing between two otherwise orthogonal and causally unbridged (n)-dimensional spaces or spacetimes, interpreted here as distinct universes. The crossing is represented by a localized, time-dependent kernel that temporarily modifies the effective mode spectrum of the coupled system.The central object is a non-homogeneous para-topological crossing kernel which induces a transient mixing between the two spaces without requiring a permanent geometric bridge. In an effective field description, the crossing may generate a temporarily negative effective squared frequency,, thereby producing a transient tachyonic regime. Shown is, that this does not necessarily imply a persistent tachyonic degree of freedom after the crossing. Instead, the process can be represented by a Bogoliubov transformation characterized by coefficients and . Subsequently introduced ergo is an effective entropy/information sector and investigated is its feedback on the crossing dynamics. The resulting system admits stabilizing, destabilizing and potentially symmetry-breaking regimes. In particular, entropy transport between the two universes can be distinguished mathematically from entropy production, allowing the possibility of asymmetric post-crossing states even when the initial configuration is symmetric. May be, that the phenomenon of matter transportation or of radiation energy could occur between the two space manifolds over the crossing zone ("skip effect") but this special situation is discussed in a later paper. Two similiar crossing zones between the same universes then will be defined as a u201econgruence".The present work however concentrates on and constitutes a phenomenological mathematical framework rather than a claim of an established physical theory. Its principal purpose is to identify the necessary dynamical structures, stability criteria and falsifiable mathematical consequences of such a crossing scenario. Some more treatises to this theme discussing intesively these sort of phenomena, will follow.
Category: Relativity and Cosmology
[46006] viXra:2608.0071 [pdf] submitted on 2026-08-18 17:09:02
Authors: Bing Lin
Comments: 12 Pages.
In this paper, actions and language are closely bound together. Action sequences could be coded and act as fundamental building block of language. Action language describes the world. Thus, the world has been mapped into action space.Language Image Natural Modeling Architecture (LINMA) contributes laws to construct the mapping engineering: law of head, law of limb posture, law of hand shape, law of motion trajectory.Language token could be action token. Action language could directly drive humanoid robot to perform actions.
Category: Artificial Intelligence
[46005] viXra:2608.0070 [pdf] submitted on 2026-08-17 22:55:18
Authors: Mnoz Pathibharaman
Comments: 23 Pages.
A derivation, once completed, is typically treated as settling the question it was undertaken to answer. This paper argues that this is not generally true, and that the gap between a completed derivation and a settled physical question is easy to overlook precisely because it has no name and leaves no formal trace once crossed. We develop the point through a case in which the gap is unusually visible: a citation, in Hawking’s canonical 1976 physics paper, offered as the source of an extension the citing paper needs but does not itself derive, which turns out oninspection to point to two unsupported sentences in an earlier paper. We use this case not toadjudicate the underlying physical claim, but to isolate two distinct achievements that citationpractice, and derivation itself, can silently conflate: extending a mathematical formalism to abroader domain, and showing that the extended formalism answers a question about a physicalsystem, in the operational sense that connects a model’s terms to what an observer would measure. We argue, drawing on Bridgman’s operational analysis and the model/target-system distinction in philosophy of science, that even a fully executed derivation closing the citation gap we identify would establish the first achievement without thereby establishing the second: a frequency-resolved extension of Hawking’s formalism cannot characterize the polarization structure of the emitted state, and so cannot by itself be used to evaluate the unitarity question the citation is invoked to support, whatever that question’s true answer turns out to be. The dependency this creates is not merely evidentiary but constitutive of Hawking’s own 1976 formal apparatus: that paper’s superscattering operator is built from Hilbert spaces the paper does not construct for the higher-spin sectors, so its own formal question, for those sectors, remains a construction the citation was invoked to supply and does not. We do not argue that this precise structure recurs throughout physics; doing so responsibly would require the same case-by-case verification this paper insists on. We do argue that the case examined here is nota bibliographic curiosity but an instance of a general and underappreciated distinction in whatclosing a derivation can and cannot be shown to achieve.
Category: History and Philosophy of Physics
[46004] viXra:2608.0069 [pdf] submitted on 2026-08-17 22:53:11
Authors: Farid Abrari
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The Rindler Horizons are known to causally disconnect regions of the flat spacetime from an accelerating observer. In this article it is shown that the past and future horizons of such observer indeed meet at the event horizon of the Unit Black Hole (UBH) of the c-SRQM theory. Furthermore, the Unruh temperature registered by an accelerating observer is shown to be the red shifted Hawking temperature of the UBH at such a hovering distance where the local UBH gravity is equal to the acceleration of the observer. Thermodynamics of the gravity and acceleration are unified.
Category: Relativity and Cosmology
[46003] viXra:2608.0068 [pdf] submitted on 2026-08-17 04:55:20
Authors: Sougata Jana
Comments: 17 Pages.
Time is conventionally treated as a fundamental parameter of physical reality.We propose an alternative axiomatic framework in which the universe is postulated as a closed, maximally entangled quantum many-body system with nofundamental notion of time. In this framework, observers are finite quantumsubsystems with limited information-processing capacity, preventing access tothe complete universal state. We argue that the perceived flow of time emergesfrom observer-dependent reconstruction of incomplete information rather thanfrom an intrinsic temporal dimension. This perspective establishes a timelessinformation-theoretic description of the universe and provides a mathematicalfoundation for investigating the emergence of temporal order, observation, andclassical reality within a unified quantum framework.
Category: Quantum Physics
[46002] viXra:2608.0067 [pdf] submitted on 2026-08-17 22:46:16
Authors: Yvan-Claude Raverdy
Comments: 5 Pages.
We present here elements which validate the identification of what is called "dark matter" to the classical gravitational energy. The corpuscular gravitation theory [1],[2] gives a very concrete interpretation to this energy which concerns the space void of all known matters, black holes and radiation. Measuring the energy density of the vacuum by the Casimir effect may be an experimental verification.
Category: Astrophysics
[46001] viXra:2608.0066 [pdf] submitted on 2026-08-17 22:41:34
Authors: Osama Haggag
Comments: 12 Pages. 10.5281/zenodo.21979604
This work establishes a unified operational framework bridging Special Relativity (SR), General Relativity (GR), and Quantum Mechanics (QM) by introducing two fundamental extensions to relativistic mechanics while demonstrating explicit reduction to standard physics in correspondence limits. First, we resolve the historical kinematic asymmetry in relativity—where speed is universally bounded by while proper acceleration a remains unphysically unbounded—by deriving an invariant maximum proper acceleration scale directly from horizon dynamics and quantum localization limits. Second, we extend the Einstein Equivalence Principle into the quantum domain via the Unified Equivalence Principle (UEP), establishing a three-way operational equivalence. By modeling a massive particle as a localized quantum clock oscillating at its Compton frequency, the canonical Hamiltonian Legendre transform partitions total relativistic energy into an internal-clock component and a motion-dependent time-dilation component. We demonstrate that physical acceleration forces a progressive de-excitation of internal quantum clock states, where internal phase depletion acts as an equivalent acceleration manifesting macroscopically as observable quantum phase shifts. Applying the Heisenberg energy—time uncertainty principle across the co-moving Rindler horizon demonstrates that the maximum acceleration amax corresponds to the complete evacuation of the clock to its vacuum ground state. At this critical threshold, the Rindler horizon stabilizes precisely at the reduced Compton wavelength, preventing geometric collapse into naked singularities. In the standard physical regime, the framework reduces continuously to standard Special Relativity, General Relativistic weak-field potentials, and Newtonian kinetic dynamics.
Category: Relativity and Cosmology
[46000] viXra:2608.0065 [pdf] submitted on 2026-08-17 22:34:33
Authors: Po Hu
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Let X and Y be independent geometric random variables on Z≥0 with P(X = k) = p(1 − p)k. For positive integers a, b, we determine the global modes of Z = aX + bY . The probability mass function may have gaps and local rises and falls. We prove that every global mode is a multiple of lcm (a, b) and that there are at most two global modes. A logarithmic threshold gives their exact locations and determines whether one or two modes occur. We also give an exact formula for every probability and a small-p asymptotic formula for the mode. The proof parametrizes the solutions of ax + by = n by residue classes and then compares the maxima of consecutive blocks.
Category: Statistics
[45999] viXra:2608.0064 [pdf] submitted on 2026-08-17 13:18:28
Authors: Sylwester Kornowski
Comments: 9 Pages.
Incompleteness of mainstream theories narrows the scope of their applicability. We showed the origin of indestructibility of the cores of baryons described in the Scale-Symmetric Theory (SST) that leads to the true internal structures of black holes (BHs). Here we show that black holes are some associations of the neutron black holes (NBHs) with an invariant mass that is equal to 24.81 solar masses. The catalogs of binary mergers suggest that the NBHs can absorb the excited stellar black holes described in this article. Calculated here masses of such excited states are 2.68, 3.66, 4.87, 6.21, 10.16 solar masses. There also can be mergers only of the excited states. The excited stellar BHs are built of the cores of baryons packed to maximum. We showed that masses of the stellar black holes decrease when their mass density increases. We also calculated the coupling constant and involved energies in the quantum entanglement. We showed also the origin of the black hole star MoM-BH*-1 and that in the early Universe, due to the massive collisions of NBHs and created repulsive dark energy, masses of massive black holes rapidly decreased rather than increased.
Category: Quantum Gravity and String Theory
[45998] viXra:2608.0063 [pdf] submitted on 2026-08-17 22:26:54
Authors: Christian Ricordeau
Comments: 54 Pages. (Note by viXra Admin: Please cite and list scientific references) In English & French - License: Creative Commons CC BY-NC-ND
Living beings are made of atoms, and we know that atoms were created at a stage in the evolution of the universe when living beings did not yet exist. Atoms are therefore still present inside living beings, but what's more, they continue to live their life as atoms, with their own way of functioning and with their own properties. In the same way, the stage of the universe that preceded the birth of atoms would still exist, and it would still function inside atoms in the same way it did before atoms existed, just as atoms function within us in the same way they did before living beings appeared.According to this hypothesis, the pre-atomic universe would not be the frightening pre-Big-Bang world we are usually presented with, i.e. a universe subjected to unheard-of conditions of density and heat. This earlier universe would still be living inside us, in the atoms that constitutes us, and under the conditions of temperature and pressure that are usually those of the atoms that constitutes us. We will attempt to describe this pre-atomic universe, and to guess how it might have functioned to have generated, through its inevitable evolution, the universe of atoms and radiation.
Category: Classical Physics
[45997] viXra:2608.0062 [pdf] submitted on 2026-08-17 22:18:18
Authors: Jamal S. Shrair
Comments: 37 Pages.
Almost all observations clearly show the condensed matter nature of the Sun. Regrettably, empirical solar data are always interpreted with the Standard Solar Model (SSM) in mind. Basically, the interpretation of solar features and phenomena must be compatible with the SSM. For instance, sunspots, granules, and faculae are regarded as optical illusions within a gaseous mass, yet they are actually real physical structures formed by condensed crystal lattices. Besides that, the Sun’s average density (1.41g /cm^3) —which is comparable to Earth's oceans and slightly denser than water—is ignored or rather deliberately misinterpreted by being considered a mathematical illusion. In fact, not only is the overall density of the Sun perfectly aligned with the condensed liquid state, but pure gases of this composition would also not inherently maintain the observed structural rigidity required for the solar dynamo to operate. Moreover, a continuous solar spectrum cannot be produced by gaseous bodies. That is because a continuous spectrum requires dense, opaque matter (like solids or liquids) in order to emit light across all wavelengths, behaving as a blackbody. In contrast, isolated, low-density gases or plasmas produce distinct, discrete emission lines. Furthermore, and most importantly, it is physically impossible for the observed solar-dynamic phenomena such as sunspots, solar prominences, coronal rain, sunquakes, and solar tsunamis to occur without a liquid surface and a solid core.
Category: Astrophysics
[45996] viXra:2608.0061 [pdf] submitted on 2026-08-16 00:17:33
Authors: Ahcene Ait Saadi
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We study a self-contained combinatorial equality, discovered by the author some forty years ago, which extends [(n, p)^T)]to negative integer indices without invoking any extension of the factorial...
Category: Combinatorics and Graph Theory
[45995] viXra:2608.0060 [pdf] submitted on 2026-08-16 20:17:20
Authors: Theophilus Agama
Comments: 15 Pages.
An addition chain of length $h$ that leads to an integer $ngeq 2$ is a strictly increasing sequence of positive integers $s_0=1,s_1=2,ldots,s_h=n$ such that $s_i=s_j+s_k$ with $i>jgeq kgeq 0$ for each $iin {1,ldots,h}$. We denote the minimal length of an addition chain that leads to an integer target $cdot$ by $ell(cdot)$. Combining a generalized version of the Brauer method with a multi-step minimization approach, we verify the speculative inequality $$ ell(2^n-1)leq n-1+ell(n) $$for all $ngeq 2$.
Category: Number Theory
[45994] viXra:2608.0059 [pdf] submitted on 2026-08-16 18:17:16
Authors: Adriana Mišúthová, Zuzana Lukačová, Ramin Mehrabifard, Zdenko Machala
Comments: 38 Pages.
Cold atmospheric plasma generates reactive oxygen and nitrogen species (RONS) that dissolve in water, forming plasma-activated water (PAW) and inducing complex chemical changes and biological responses. PAW, enriched with nitrogen (N) species, emerges as a sustainable alternative to fertilisers by combining signalling (ROS) and N supplementation (RNS). This study aims to investigate the dual role of PAW in lettuce, Lactuca sativa (cv. Matilda), grown under either N-sufficient or N-deprived half-strength Hoagland solutions. Four treatments were evaluated: control, seed priming in PAW-activated Hoagland, PAW-activated Hoagland cultivation, and the combination of the latter two, under both N-content regimes.Under N-sufficient conditions, seed priming in PAW increased the lettuce head fresh weight up to 40%, chlorophyll a+b by 25%, and the sensory scores (freshness, juiciness), compared to the control. Under N-deprived conditions, PAW partially compensated for N-deficiency, increased the plant growth up to 50%, photosynthetic pigments and quercetin (up to 20%), and antioxidant enzymes (e.g., APX and G-POX increased up to 2x). Principal component analysis confirmed N-content as the primary variance driver (PC1 69—71%), with PAW modulating redox homeostasis tissue-specificity.Our results demonstrate the capacity of PAW to enhance plant growth, metabolism, and quality, even in N-deprived conditions, to address gaps in plasma agriculture by highlighting the PAW nutritional and signalling contributions. PAW thus represents a promising, eco-friendly strategy.
Category: Nuclear and Atomic Physics
[45993] viXra:2608.0058 [pdf] submitted on 2026-08-13 23:51:46
Authors: Ken Gonder
Comments: 30 Pages, 8 Diagrams
The universe's inferred expansion is based almost entirely on cosmological redshift. If it's found that it does not originate from space's stretching then the big bang would of course become unworkable. If it's found that other red/blue shift sources also emanate from galaxies then it'd be virtually impossible to know how much shift to attribute to each. So the big bang would again become untenable. If it turns out that the speed of light is not constant but varies everywhere then the entire concept of cosmological redshift collapses, taking along with it the big bang. If any one of these undermining conditions is true, we're forced to concede the fallacy of universal expansion, which returns us back to the very beginning. We're left wondering what it is exactly that causes a galaxy's redshift. Viable, practical, readily apparent alternates do exist. But they only become evident by recognizing the ever-decreasing density of a galaxy's gravity field.
Category: Relativity and Cosmology
[45992] viXra:2608.0057 [pdf] submitted on 2026-08-14 20:49:35
Authors: Leonardo Rubino
Comments: 142 Pages.
Ramanujan Pi series — proof, and other subjects of interest in the Appendix I.
Category: General Mathematics
[45991] viXra:2608.0056 [pdf] submitted on 2026-08-14 11:16:29
Authors: Claudio Piantanida
Comments: 35 Pages.
In standard treatments of the Michelson—Morley experiment, the round-trip time is calculated along a central path that identifies reflection with the geometric center of the mirror. This choice is adopted without proof: the reflector is treated as point-like, or the central ray is selected on symmetry grounds, without verifying that the reduction preserves the property being calculated.This article provides that verification. By parameterizing the reflecting surface with a continuous coordinate, the total round-trip time is calculated as a function of the reflection point. In the geometric time-of-flight model with point-like source and receiver, the physically relevant path is the one that minimizes the total time. In general, the corresponding minimum point coincides neither with the geometric center of the reflector nor with the first point reached by the incident wavefront.The main result is that, although the minimum-time reflection point is displaced from the geometric center by an amount of order O(β^2 )L, the round-trip time evaluated along the central path differs from the minimum time only at order O(β^4 ), with β=vu2044c, whereas the anisotropy predicted by Galilean kinematics already appears at order O(β^2 ).As a corollary, not all geometrically plausible reductions have the same status. The first-contact construction—which identifies the relevant reflection point with the first point reached by the incident wavefront during the outward propagation alone—produces an error already at order O(β^2 ) and cancels the entire angular dependence. Two geometrically analogous reductions of the same system therefore have opposite methodological status, and the difference can be diagnosed from the perturbative structure of the error.The immediate motivation for this work comes from an acoustic analogue proposed by Norbert Feist. In that context, the author had previously adopted the first-contact construction as an explanation of an experimentally reported isotropic result. The present article shows that this construction was incorrect and identifies the error: minimizing the outward propagation time alone is not equivalent to minimizing the total round-trip time.
Category: Classical Physics
[45990] viXra:2608.0055 [pdf] submitted on 2026-08-14 20:41:21
Authors: Fei Ding, Runhao Liu, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.
In verifier-style RLVR, group-relative optimization often treats advantage scale as an implementation detail. This paper separates two low-variance cases: sub-resolution jitter that should not become a preference signal, and credible but small cardinal gaps that should be learned without distorting KL calibration. We propose an advantage-scale three-way calibration interface: the same within-group scale denominator simultaneously determines the reward-branch strength, prompt-level batch weight, and the effective KL calibration induced when the reward branch is re-expressed on the original cardinal scale. This interface explains why RLOO / Dr.GRPO can let credible small gaps become KL dominated, whereas GRPO's standard-deviation denominator can amplify tiny gaps without bound. Based on this interface, we further introduce the Reward-Resolution Protocol and MaxNorm-AC, respectively filtering sub-resolution gaps and providing bounded cardinal recovery on credible nonzero gaps. Across dense / MoE architectures and math / code reasoning, MaxNorm-AC improves over the prespecified percentile-scale reference (p = 90, hereafter the p90 reference) while truncating the low-variance inverse-scale tail.
Category: Artificial Intelligence
[45989] viXra:2608.0054 [pdf] submitted on 2026-08-14 20:34:54
Authors: Andrey V. Voron
Comments: 7 Pages.
The study demonstrates that projecting order-4 and order-8 magic squares onto a tesseract preserves their fundamental numerical invariants. Similarly, the 4×4 Dürer's magic square is projected onto the vertices of an octagonal prism with internal spatial connections. The results obtained in this study open up prospects for utilizing multidimensional geometry to develop new data distribution algorithms. The presented mathematical symmetries can find practical applications in high-tech and theoretical disciplines.
Category: Combinatorics and Graph Theory
[45988] viXra:2608.0053 [pdf] submitted on 2026-08-14 20:32:51
Authors: Sangwha Yi
Comments: 11 Pages.
We present a formulation of Cosmological Special Theory of Relativity(CSTR) in with the standard Lorentz transformation is extended to incorporate the expansion of the universe via the Robertson-Walker scale factor.
Category: Relativity and Cosmology
[45987] viXra:2608.0052 [pdf] submitted on 2026-08-13 01:50:04
Authors: Zhenghao Wu, Wenjun Wu
Comments: 6 Pages.
Background: Adolescent depression has reached epidemic proportions in urbanChinese cohorts, with prevalence estimates exceeding 20% in some regions. Standard interventions achieve only partial remission in a substantial minority of cases,and treatment resistance is especially common when family-system dynamics perpetuate the depressogenic environment.Case Presentation: We report the case of "Z.," a 17-year-old male adolescent withmajor depressive disorder, generalized anxiety, school refusal, and disordered gaming, who had declined pharmacotherapy and electroconvulsive therapy. The patientpresented following academic setback, romantic dissolution, and familial conflict exacerbated by the COVID-19 pandemic.Intervention: Treatment consisted of 18 months of weekly video-based psychotherapy grounded in the Universal Law of Subconscious State Change (ULSSC), delivered concurrently to the patient and his mother. The intervention integrated cognitive training, behavioral activation, and family-systems restructuring.Results: The patient resumed educational engagement, achieved university admission, and demonstrated sustained functional recovery at 18-month follow-up. Depressive symptomatology reduced from severe to subclinical levels; suicidal ideationresolved by month four and did not recur.Conclusion: This case illustrates the potential efficacy of family-integrated subconsciousstate therapy for treatment-resistant adolescent depression. Controlled trials arewarranted.
Category: Mind Science
[45986] viXra:2608.0051 [pdf] submitted on 2026-08-13 20:28:31
Authors: Leonardo Rubino
Comments: 113 Pages.
In physics the use of the spherical or cylindrical coordinates is often the only way to develop a subject at an acceptable level of difficulty, as such a use allows us to benefit from the simplifications coming from the existing symmetry (spherical or cylindrical, indeed). Here is a treatise with tensors and also a classical one, without tensors.
Category: General Mathematics
[45985] viXra:2608.0050 [pdf] submitted on 2026-08-13 20:24:16
Authors: Anindya Kumar Biswas
Comments: 12 Pages.
In this paper, we study the Fifa World Cup 2026 matches up to the Final. In the Group Stage, for the decided matches, the probability for a team with lower relative Gini coefficient to win was 28/52. In the next stages up to final i.e. in the Round of Thirty Two stage, the Round of Sixteen stage etc, the probability for a team with lower relative Gini coefficient to win were 6/15, 6/8, 1/4, 0/2, 0/1, 1/1 respectively. In the Group Stage, the probability to win with lower HDI was 19/52 i.e. less than half. In the Round of Thirty Two stage, theprobability to win with lower HDI was 6/16.In the Round of Sixteen stage, the probability to win with lower HDI was 1/8. In the Quarter Final stage, the probability for a team with lower relative HDI to win was 3/4 i.e. swung to the right. In the Semi Final stage, the probability for a team with lower relative HDI to win was 2/2. In the Third Place Play-off, the team with higher relative HDI won i.e. the probability swung to the left. In the Final, the team with lower relative Gini coefficient, higher HDI won. The overall probability to win with lower relative Gini coefficient was 42/53 i.e. 0.506 i.e. more than half. In the previous World Cups 2022, 2018, 2014, the overall probability to win with lower relative Gini coefficient were 0.556, 0.627, 0.519 respectively.
Category: Economics and Finance
[45984] viXra:2608.0049 [pdf] submitted on 2026-08-13 20:17:13
Authors: Mykola Kosinov
Comments: 8 Pages.
"Big G" is a constant of the Universe; this is its fundamental meaning. "Big G" is not measured directly; it is calculated from Newton's law of gravitation. However, this law has a limitation: it does not take into account the gravity of the Universe. All laboratories obtain G values that are outside the permissible error limits. It is shown that the reason for the discrepancies lies in the fact that the gravitational background of the Universe is not taken into account in the calculation: (mc^2)√Ʌ. This leads to a shift in the G values by varying amounts, depending on the contribution of (mc^2)√Ʌ. In essence, metrologists were the first to experimentally detect an external factor of a gravitational nature, which is not included in Newton's law. Physics has traditionally posed challenges to metrology and developed thanks to the results of precise measurements. As R. Davis [2] notes, an increase in accuracy by even one decimal place reveals new physical realities and confirms or refutes existing theories. In the situation with measuring "big G," metrology has outpaced physical theory. Discrepancies in G values showed that Newton's local law of gravity does not allow for its precise value. For the first time in the history of science, metrology had grounds to pose a challenge to theoretical physics: "We have no doubt about the accuracy of our instruments; we have discovered an unaccounted cosmological factor that is not included in your law; a new law of gravity is needed that will allow us to correctly calculate the value of Big G." The Big G crisis is not caused by "bad instruments," but by the imperfection of the physical law from which it is calculated.
Category: Quantum Gravity and String Theory
[45983] viXra:2608.0048 [pdf] submitted on 2026-08-12 02:22:15
Authors: J. W. A. Zwart
Comments: 15 Pages.
The dark matter mediating medium for the pseudo vectors carries by definition four independent vector cells of the components for acceleration, spin and precession making up twelve combinations of pseudo vectors cells. The conjugated medium at the absolute zero energy state consists of solely pseudo e-neutrino triplets as a dynamic non destructible equilibrium in cubic pyramid symmetry. At a relativistic thermodynamic level of electron energy the pseudo vector medium consists of pseudo μ-triplets in cubic symmetry mixed to a triplets of τ-pseudos in cubic symmetry together guided by the pseudo e-neutrinos. Both the μ- and τ- triplets carry always the rotations for τ-triplets perpendicular to the μ-triplets suggesting orthogonal cubic pyramid symmetry. The top in equilateral pyramid symmetry of equal dimension for the base triangle in the cubic symmetry provides the dynamic electric charge in one polarity following the acceleration vector component of the pseudo vector cells. The time intervals for the electric charge dynamics give the sequential conjugated inversion shifts along the rotation axis of the height of the equilateral pyramid. Common sense reasoning for the some scaling calculations shows the validity of the statement in this abstract and explained in the paper below. Extension in par 7.0 and 7.1. For the conclusion see 9 for the limit of quantum gravity.
Category: Quantum Gravity and String Theory
[45982] viXra:2608.0047 [pdf] submitted on 2026-08-12 20:48:35
Authors: Lin Hu Zhong
Comments: 10 Pages. (Note by viXra Admin: Please cite listed scientific reference)
This paper proposes "Fame Theory," arguing that no fame means no success, where "fame" specifically refers to good fame, positive fame, and honorable fame — the reputation bestowed upon an individual by society based on recognition of positive value. This paper explicitly excludes bad fame, ill fame, and infamous fame. Using wealth as a reference framework, the argument unfolds across four dimensions: visibility, permanence, independence, and distinctiveness. The essence of fame is a positive symbolic consensus in society; it transcends material accumulation and becomes the highest expression of an individual's life value.
Category: Social Science
[45981] viXra:2608.0046 [pdf] submitted on 2026-08-12 20:48:11
Authors: Clark M. Thomas
Comments: 4 Pages.
Potential energy and kinetic energy are related, yet very distinct. From the widest-angle perspectives they are equals. Last centuryRichard Feynman shocked the world by talking about the great energy everywhere in a seeming vacuum. He was partially correct within his quantum mechanics perspective. This century brings a better model for the potential and kinetic energies within individual y/y spheres, and along beaded-string frequency waves.
Category: Astrophysics
[45980] viXra:2608.0045 [pdf] submitted on 2026-08-11 02:10:14
Authors: Kutlumuratov Atabek Bekchanovich
Comments: 106 Pages.
In the treatise main principles of propaedeutics of modern clinical medicine and human physiology are discussed. Nowadays the official medicine considers them the sciences which are based on a biomedical paradigm. But the real basis the medicine as practical science (science of doctoring) is u2026a) the clinical paradigm which applies the philosophical preconditions of knowledge of the world, of the own nature, and of the reality constituted by person, b) system of auxiliary paradigms among which the basic place is occupied nowadays with a biomedical paradigm, andc) the clinically registered data about a current state of health of each patient. Doctor uses the philosophical preconditions, and the clinical paradigm, and the auxiliary paradigms, and data of current clinical inspection of the patient in interests of each patient in each clinical case.Being based on a clinical paradigm, the medicine obviously and implicitly develops system of auxiliary paradigms. Each doctor reproduces and uses auxiliary paradigms in each clinical case by considering the professional possibilities and abilities. Each doctor subjects to individuation each clinical case in interests of health of each patient in conformity with the possibilities given to them by a society, a science and professional conditions. Doctors obviously and implicitly use (at least during 1000 years) the model of psychophysical unique human nature, generalised by Avicenna as an ontological and epistemological basis of medical thinking. During the individuation of dotoring of each patient the doctor develops the clinical diagnosis adequately to the current nature (condition) of health of each patient. Each clinical discipline obviously and implicitly develops own clinical paradigm that allows the doctor to supervise the own thinking in interests of health of each patient in each clinical case. Thus the doctor considers mental and physical perception patterns by patient of own health status and obviously or implicitly subjects individuation auxiliary paradigms, first of all - biomedical one, and supervises current data of clinical inspection of the patient. During doctoring of each patient the modern doctor regularly and, as a rule, implicitly, usesideas Alcmeon, and Hippocrates, and Galen about psychophysical (psychophysiological) nature of the clinical paradigm, and it was explicitly formulated by Avicenna. In an obvious kind the modern doctor constitutes judgements in language of the biomedical paradigm. Keywords: science philosophy; clinical medicine; clinical paradigm; psychophysical model of the patient; undividuation of doctoring; biomedical paradigm.
Category: General Science and Philosophy
[45979] viXra:2608.0044 [pdf] submitted on 2026-08-11 02:04:43
Authors: Hongyuan Ye
Comments: 13 Pages.
In classical electromagnetism, Gauss’s flux theorem in integral form states that the electric flux through a closed surface is proportional to the charge enclosed by that surface. Recent research points out that Gauss’s flux theorem in integral form applies to static electric fields but not to time-varying electric fields. This paper reveals that when Gauss’s flux, characterized by three-dimensional space, is compressed to a single point, the divergence of a field no longer retains its original meaning of the flux. Based on the divergence of the electric field at a point in space, Gauss's flux theorem in differential form contradicts Coulomb's law and violates the superposition principle of the electric fields. Therefore, the differential and integral forms of Gauss’s flux theorem are not equivalent. In conclusion，Gauss’s flux theorem in differential form does not hold in both static and time-varying electric fields, and has no definite mathematical and physical significance. Theoretical physics and mathematics will undergo a revolutionary scientific transformation.
Category: Mathematical Physics
[45978] viXra:2608.0043 [pdf] submitted on 2026-08-11 01:56:57
Authors: Carlos Castro, E.I Guendelman
Comments: 39 Pages.
The string tensions can be dynamical as one of us (EG) has studied in recent publications. For example, in the case when string theories are formulated in the modified measure formalism where string and brane tensions appear as an additionaldynamical degree of freedom. It is found that the tension values assigned to these strings and branes may not fixed (universal), but rather that each string and brane acquires its own tension with a different value for each string and brane. We havedisplayed cases where the spontaneous breaking of target space scale invariance is produced in the process of string-tension-generation, except for some limits where the tensions dynamically approach infinity. The introduction of internal gauge fieldsgoverns the dynamical tensions of the strings, and specific sources for these gauge fields provide diverse tensions. In this work it is shown that in special cases where the tensions have the exponential form exp(ασ1) or exp(ασ0), in the conformal gauge, the target space scale invariance can be restored by considering shifts in either the (spatial) σ1 or (temporal) σ0 string world-sheet coordinates. In the first case, the (open) strings must be of infinite length and cannot have boundaries in order to respect target space scaleinvariance. While in the second case we can consider closed or open strings without breaking target space scale invariance. World sheet conformal invariance implies a Ricci flat condition for an effective metric and which is consistent with the expected equations of motion of the strings. Boundary conditions can be introduced by introducing charges that couple to the internal gauge fields. Point like sources break the scale invariance point-wise which can lead to very interesting consequences, like the construction ofsemi-open strings which are strings which connect to a charge only at one point and where along the other direction the tension decays. These serve as models of deconfined quarks. Generalizations of these effects to brane like solutions in Milne and Wesson spaces, etc. are also discussed.
Category: Quantum Gravity and String Theory
[45977] viXra:2608.0042 [pdf] submitted on 2026-08-11 01:45:32
Authors: Abdelmajid Ben Hadj Salem
Comments: 10 Pages. Submitted to Ramanujan Journal. Comments welcome.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called the Riemann hypothesis : textit{The nontrivial roots (zeros) $s=sigma+it$ of the zeta function, defined by:} $$zeta(s) = sum_{n=1}^{+infty}frac{1}{n^s},,mbox{for}quad Re(s)>1$$ textit{have real part} $sigma= frac{1}{2}$. In this paper, I give the proof that $sigma= frac{1}{2}$ using an equivalent statement of the Riemann hypothesis: the Dirichlet $eta$ function and the functional relation verified by the zeta function.
Category: Number Theory
[45976] viXra:2608.0041 [pdf] submitted on 2026-08-11 02:53:06
Authors: Teo Banica
Comments: 400 Pages.
This is an introduction to probability, written with a quantum idea in mind, namely that the semicircle law comes first. We first discuss discrete probability, notably with the binomial and hypergeometric laws, positive and negative, and the Poisson and compound Poisson laws. Then we get into the continuous case, with the basics of the theory explained, and with as starting examples the exponential, semicircle and beta distributions. Afterwards, we investigate the central limits and normal variables, both real and complex, and with a look at Rayleigh laws, and hyperspherical laws too. Finally, we discuss a number of more specialized distributions, and more specialized techniques too, and we end with an introduction to random matrices and freeness.
Category: Statistics
[45975] viXra:2608.0040 [pdf] submitted on 2026-08-09 21:29:01
Authors: Viktor Voevodov
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)
This paper proposes a fundamentally new approach to investigating the structure of the set of natural numbers based on the concept of alternative and connected numerical sets, one of which is the set of prime numbers. The method of dynamic sieves is described. By utilizing the proposed kinematic model and the theory of connected sets, a theorem is proven on the infinity of sets of n-tuple primes of arbitrary length and configuration. While the theory of connected sets expands the theorem, the theory of alternative sets deepens it, rendering the theorem global.
Category: Number Theory
[45974] viXra:2608.0039 [pdf] submitted on 2026-08-09 21:22:28
Authors: Sangwha Yi
Comments: 10 Pages.
Companion reviews of the Cosmological Special Theory of Relativity(CSTR) have repeatedly identified the extension of the equal-time Klein-Gordon field quantization to a genuinely two-time(multi-epoch) propagation as the central open problem of the theory's quantum sector(Yi,2020,2021,2025).
Category: Relativity and Cosmology
[45973] viXra:2608.0038 [pdf] submitted on 2026-08-09 13:18:50
Authors: George Athanasiou
Comments: 19 Pages.
We develop a residue-based method for recovering the coefficients of aDirichlet series from the singularities of its analytic continuation. Startingfrom the classical vertical-line inversion formula, we introduce a conformaltransformation that converts coefficient extraction into a contour integraland yields a spectral representation in terms of poles and residues. Weapply this framework to the von Mangoldt, prime characteristic, Möbius,and Euler totient functions, obtaining representations involving the zerosand poles of the Riemann zeta function. We also introduce generalized vonMangoldt functions associated with arbitrary Dirichlet series and extendthe approach to finite and Dedekind zeta functions, leading to formulas forpoint counts, prime-ideal counting functions, and characteristic functionsover number fields. Finally, we examine prime-pair, Goldbach, andprime-tuple counting functions and derive conditional error estimatesunder the Riemann hypothesis. These results present contour integrationand zeta-function factorizations as a unified mechanism for translatinganalytic spectral data into arithmetic information.
Category: Number Theory
[45972] viXra:2608.0037 [pdf] submitted on 2026-08-10 02:53:44
Authors: Nana Abeka Otoo, Asirifi Boa
Comments: 22 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Supervised Neural Gas (SNG) introduces the margin-optimized cost function of Generalized Learn-ing Vector Quantization (GLVQ) equipped with neighborhood cooperation from Neural Gas (NG).This yields a highly interpretable learner that is less sensitive to the prototype initialization problem observed in the LVQ family of classification algorithms. Although Hammer, Strickert and Villmann presented the SNG framework as an extension applicable to any differentiable dissimilarity measure, the diagonal relevance weighting adaptation remains the only scheme to have been explored. In this paper, we investigate extensions of SNG with full matrix, local matrix, tangent and class-wise matrix distances by examining how rank-based cooperation interacts with metric parameterization learning. We provide gradient-level analysis of two failure modes: (I) gradient dilution and (II) subtraction amplification, which explain learning behavioral challenges in cooperation-based metric learning. We propose a Supervised Class-Wise Matrix Neural Gas variant (SCMNG) that identifies three structural conditions under which rank-based metric relevance learning can be achieved in light of these recorded failure modes. Ablation experiments against non-cooperative reference models indicate that the impact of rank-based cooperation depends on initialization quality, metric structureand class-wise conditions. When prototypes are placed in a representative manner, NG coopera-tion mainly results in gradient interference. In contrast, with poor initialization, NG cooperationfacilitates the distribution of prototypes across class regions.
Category: Artificial Intelligence
[45971] viXra:2608.0036 [pdf] submitted on 2026-08-08 05:03:56
Authors: Runsheng Tu
Comments: 10 Pages.
Classical mechanics and quantum mechanics are considered to be binary oppositions. This kind of understanding has never brought us any real benefits, only trouble. The fundamental equations of quantum mechanics cannot logically delineate the boundary between quantum and classical mechanics. On the contrary, the mass m and potential energy V in the Schr ö dinger equation can easily cross the boundary between microscopic and macroscopic levels. The electromagnetic potential energy in the Schrödinger equation can be replaced with the potential energy of the interaction force. Potential energy can be further transformed into force based on F=V/r. This operation can establish Newton's second law wave equation (e.g., Eq.(30)) and force containing wave mechanics equation (e.g., Eq. (31) ) ψ =Fψ). This result more directly indicates that quantum and classical are compatible. Eliminating the historical absence of the concept of "force" in quantum mechanics, bridging the gap between macroscopic classical and microscopic quantum frameworks, and changing people's perceptions. Can explain why nanoscale particles have quantum properties. Simplify the calculation of quantum forces. This lays the foundation for the generalized wave mechanics that unifies mechanics across scales.
Category: Quantum Physics
[45970] viXra:2608.0035 [pdf] submitted on 2026-08-09 00:42:56
Authors: Yijia An, Preet Sharma
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This study is about applying the fundamentals of physics using the concepts of friction to understand and describe dance shoes and dance floor interaction. We have used sliding friction, skidding friction and rotational friction to describe our model independent study. Since we are performing a general and model independent study so we have taken the dancer to be of a uniform cylindrical shape. The various frictions used are time dependent.
Category: Classical Physics
[45969] viXra:2608.0034 [pdf] submitted on 2026-08-09 00:40:30
Authors: Slavik Avagyan
Comments: 11 Pages.
This paper analyzes a fundamental geometric oversight in the classical interpretation of the Michelson -Morley experiment. We demonstrate that in a frame moving with velocity u , the reflection of light from a mirror follows a specific angular deviation. By introducing the formula sinu2061〖β=u/c〗 √(1-u^2/c^2 ), we prove the optical paths are asymmetrical. This geometric shift provides a new basis for understanding the "null result" of the Michelson-Morley experiment without necessitating postulate of absolute constancy of light in all frames. In other words, the Michelson-Morley experiment is a failed experiment and the physical-mathematical conclusions drawn from its "results" have no scientific basis.The question of the nature of light is directly related to the Michelson-Morley experiment. Since the aforementioned experiment can be considered a failure, the idea of the ether becomes relevant. For this reason, a new idea is proposed to solve the problem of light propagation. Light is attributed only a wave nature in the form of spherical waves, and the propagation medium is dark matter. The idea is substantiated by appropriate calculations. . The mass of a dark matter particle has also been determined, which is found to be equal to M_dm≈4.〖10〗^(-34) kg.Keywords: Light, Michelson-Morley, experiment, theory, law, ether, wave, dark matter.
Category: Astrophysics
[45968] viXra:2608.0033 [pdf] submitted on 2026-08-08 17:32:27
Authors: Bertrand Wong
Comments: 9 Pages.
Reality is highly important to us for we would prefer to live with reality rather than live with the imaginary world or the world of dreams, e.g., we would prefer ideas and concepts to be realistic, i.e., rooted in the real-life situation, rather than being merely theoretical and not practicable. Reality is apparently a slippery concept which is difficult to have a firm grasp on. Hence, there are many quizzical questions asked in this paper in order to be able to really come to terms with the very abstract, slippery concept of reality. There could be different ways of interpreting reality resulting in differing concepts of reality, which would be a problem as logically there should be only one true, valid, consistent concept of reality - the author posits such a concept of reality in the conclusion, a reasoned concept which is apparently more logically consistent.
Category: General Science and Philosophy
[45967] viXra:2608.0032 [pdf] submitted on 2026-08-08 17:37:42
Authors: Bertrand Wong
Comments: 4 Pages.
This paper emphasizes the importance of intuition, which is apparently frequentlygiven little attention. It appears that logic is equated with intelligence and is regarded as themost important aspect of thinking by many. The author here attempts to raise the status ofintuition vis-à-vis logic or reasoning and in doing so he is presenting intuition from a different and perhaps unique perspective. The paper explains the importance of intuition though it may not be perfectly effective in bringing the desired outcomes, a state of affair which applies also to logic. Nevertheless, intuition plays an important part in our intellectual and creative endeavors, apparently aided by logic, which is explained in this paper.
Category: Mind Science
[45966] viXra:2608.0031 [pdf] submitted on 2026-08-08 23:37:15
Authors: Minghao Ruan, Junhao Fu
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Background Literature screening constitutes a critical component in evidence synthesis; however, it typically requires substantial time and human resources. Artificial intelligence (AI) has shown promise in this field, yet the accuracy and effectiveness of AI tools for literature screening remain uncertain. This study aims to evaluate the performance of several existing AI-powered automated tools for literature screening.Methods This diagnostic accuracy study employed a cohort to evaluate the performance of five AI tools—ChatGPT 4.0, Claude 3.5, Gemini 1.5, DeepSeek-V3, and RobotSearch—in literature screening. We selected a random sample of 1,000 publications from a well-established literature cohort, with 500 as randomized controlled trials (RCTs) group and 500 as others group. Diagnostic accuracy was measured using several metrics, including the false negative fraction (FNF), time used for screening, false positive fraction (FPF), and the redundancy number needed to screen.Results We reported the FNF for the RCTs group and the FPF for the others group. In the RCTs group, RobotSearch exhibited the lowest FNF at 6.4% (95% CI: 4.6% to 8.9%), whereas Gemini exhibited the highest at 13.0% (95% CI: 10.3% to 16.3%). In the others group, the FPF of the four large language models ranged from 2.8% (95% CI: 1.7% to 4.7%) to 3.8% (95% CI: 2.4% to 5.9%), both of which were significantly lower than RobotSearch's rate of 22.2% (95% CI: 18.8% to 26.1%). In terms of screening efficiency, the mean time used for screening per article was 1.3 s for ChatGPT, 6.0 s for Claude, 1.2 s for Gemini, and 2.6 s for DeepSeek.Conclusions The AI tools assessed in this study demonstrated commendable performance in literature screening; however, they are not yet suitable as standalone solutions. These tools can serve as effective auxiliary aids, and a hybrid approach that integrates human expertise with AI may enhance both the efficiency and accuracy of the literature screening process.
Category: Artificial Intelligence
[45965] viXra:2608.0030 [pdf] submitted on 2026-08-06 19:08:53
Authors: Manuel Uruena Palomo, Juan David Santander
Comments: 18 Pages.
Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration $a_0$. It is well known that increasing $a_0$ by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters. Within a parameter-free Machian interpretation of MOND, in which $a_0sim GM_u/R_u^2$ arises from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote $a_0$ to a variable influenced by mass external to a locally enclosed region in the spherically symmetric case. Instead of a boost of $a_0$ in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters. We conclude by beginning to generalize the proposed formulation beyond spherical symmetry.
Category: Relativity and Cosmology
[45964] viXra:2608.0029 [pdf] submitted on 2026-08-08 02:41:13
Authors: Theophilus Agama
Comments: 10 Pages.
An addition chain of length $h$ that leads to an integer $ngeq 2$ is a strictly increasing sequence of positive integers $s_0=1,s_1=2,ldots,s_h=n$ such that $s_i=s_j+s_k$ with $i>jgeq kgeq 0$ for each $iin {1,ldots,h}$. We denote the minimal length of an addition chain that leads to an integer target $cdot$ by $ell(cdot)$. In this paper, we introduce the concept of emph{quasi closed} addition chains and show that numbers $ngeq 2$ that admit a minimal-length quasi closed chains that are also a minimal-length addition (quasi complete numbers) satisfy the Scholz conjecture, precisely the inequality $$ ell(2^n-1)leq n-1+ell(n).$$
Category: Number Theory
[45963] viXra:2608.0028 [pdf] submitted on 2026-08-07 05:37:17
Authors: Iz Tecum
Comments: 26 Pages.
We analyze one coupling of single-site Glauber dynamics for proper (q)-colorings of the cycle (C_n) in two ways.Drift on the Hamming disagreement count and path coupling on Hamming-adjacent pairs give the one-step contractions[mathbb{E}bigl[d_{H}(X_1,Y_1)bigr]lealpha_{mathrm{cl}}(q,n),d_{H}(X_0,Y_0),qquadmathbb{E}bigl[d_{G}(X_1,Y_1)bigr]lealpha_{mathrm{pc}}(q,n),d_{G}(X_0,Y_0),]with (alpha_{mathrm{cl}}(q,n)=1-(q-4)/bigl(n(q-2)bigr)) and (alpha_{mathrm{pc}}(q,n)=1-(q-6)/bigl(n(q-2)bigr)), both attained. The thresholds are(qge5) and (qge7), and the constants separate by (2/bigl(n(q-2)bigr)) uniformly in (n). The gap is geometric.Transposing two colors across an edge produces a pair at Hamming distance (2) that no single recoloring connects,so the path metric (d_{G}) of the color graph charges a created disagreement (+2) rather than (+1); such pairspack (lfloor n/2floor) to a cycle, giving (operatorname{diam} d_{H}=n) and (operatorname{diam} d_{G}=lfloor3n/2floor) for(qge5), hence closed (O(nlog n)) bounds for both methods. The loss is attributable to the sparse edge setrather than to path coupling, since the complete edge set recovers (alpha_{mathrm{cl}}). Exact enumeration on (C_4)confirms every bound and gives worst-start (t_{mathrm{mix}}(0.05)=57,29,22,19,18) for (q=3,dots,7).
Category: Statistics
[45962] viXra:2608.0027 [pdf] submitted on 2026-08-07 14:04:51
Authors: Martin Kraus
Comments: 10 Pages.
Physicists have been searching for a vibrational interpretation of the Schrödinger equation for a century; so far with limited success. This work presents a speculative vibrational interpretation in the special case of the Schrödinger equation for a hydrogen-like atom. Solutions of this equation are interpreted as high-frequency stationary vibrations of the atom’s electromagnetic field driven by de Broglie’s internal clock of the atom’s electron, which is assumed to orbit around the atom’s nucleus. The proposed vibrational interpretation challenges existing interpretations of the Schrödinger equation in various ways, which pose interesting research questions for future work.
Category: History and Philosophy of Physics
[45961] viXra:2608.0026 [pdf] submitted on 2026-08-07 14:09:31
Authors: Md Razib Talukder
Comments: 9 Pages.
This paper presents a proof of Fermat's Last Theorem using the symmetry properties of the cosine rule. It is demonstrated that the structural invariance of the cosine rule prevents any transformation that would yield nontrivial integer solutions for exponents greater than two. The argument establishes that no such solutions exist, thereby confirming Fermat's assertion.
Category: Algebra
[45960] viXra:2608.0025 [pdf] submitted on 2026-08-08 02:21:38
Authors: Fischel Bloom
Comments: 2 Pages. (Note by viXra Admin: Please cite and listed scientific references)
We solve the open problem of proving Fermat’s Last Theorem (FLT) for n > 2 using only tools available to Fermat. We infer from Euclid’s formula an n-th power generalization that is equivalent to equation z^n− y^n = x^n. This generalization clearly shows that FLT is correct for integral {(z,y,x)}with integral n>2.
Category: Number Theory
[45959] viXra:2608.0024 [pdf] submitted on 2026-08-07 21:37:19
Authors: Mikhail Batanov-Gaukhman
Comments: 7 Pages.
The article proposes to use all 12 metric solutions of the Einstein’s vacuum equation with the Λ-term within the framework of constructing a single system consisting of metric-dynamic models of one stable convex vacuum formation and one stable concave vacuum formation. This approach is a prerequisite for the creation of a Hierarchical Cosmological Model as part of a unified project "Geometrized Vacuum Physics Based on the Algebra of Signature" [5,6,7,8,9,10,11,12,13,14,15,16,17, 18,19,20], aimed at developing the Clifford-Einstein-Wheeler program for the complete geometrization of physics
Category: Relativity and Cosmology
[45958] viXra:2608.0023 [pdf] submitted on 2026-08-06 15:54:03
Authors: Arūnas Ostasevičius
Comments: 11 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper introduces an alternative, deterministic paradigm for the micro-world by modeling the hydrogen atom as an open, non-linear dissipative system embedded within the hydrodynamic substratum of Wheeler’s quantum foam. By replacing the abstract complex-valued wave function of standard quantum mechanics with a modified three-dimensional Van der Pol system formulated via Hamilton’s quaternions (H), we resolve the fundamental paradoxes of stationarity, instantaneous quantum jumps, and wave-particle duality. In this framework, the stable ground state of the atom emerges naturally as a stable limit cycle (attractor), where the classical Coulomb potential acts as an active negative-friction energy pump that balances velocity-dependent radiative dissipation at the Bohr radius (a0). We present a non-quantum, electrodynamic derivation of the Bohr radius and link the emission frequency directly to radiation intensity via the characteristic impedance of free space (Z0) without invoking Planck’s constant (h). Furthermore, the four traditional quantum numbers (n, l, m, s), the Zeeman splitting, and the Pauli exclusion principle are decoded as explicit geometric and topological properties of a phase-locked spatial rotator, bypassing the necessity of both the Schrödinger probability density and the complex Dirac matrices.
Category: Quantum Physics
[45957] viXra:2608.0022 [pdf] submitted on 2026-08-06 15:44:16
Authors: Richard Michael Blaber
Comments: 22 Pages. (Note by viXra Admin: Author name is required in the article) Creative Commons License BY-NC-ND 4.0
For the majority of its existence, our species did not live in settlements, did not have agriculture, writing or metallurgy. These are all features of the Holocene Epoch, and the global human population during most of the time since the start of that epoch remained both low and relatively constant until the beginning of the 19th Century, accelerating through the 20th Century, following the Industrial and Agrarian Revolutions. The enormous population, and the complex, planet-wide capitalist technological civilisation on which they depend, but which also exploits them, are now faced with numerous dangers, which are likely to prove insuperable.
Category: Social Science
[45956] viXra:2608.0021 [pdf] submitted on 2026-08-06 15:40:32
Authors: Kevin Elijah Valentine
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Graph theory plays a vital role in the study of mathematical structures and their applicationsin communication networks, optimization, and computer science. Among the variousdomination parameters, the Double Roman Domination Number has attracted significant attentiondue to its enhanced defensive strategy compared with classical domination concepts.This paper investigates the Double Roman Domination Number of Degree-Centric Graphsobtained from several standard graph families. The degree-centric transformation is firstconstructed for each graph, and the corresponding Double Roman Domination Numbers aredetermined. Based on these results, general observations and formulas are established fordifferent classes of graphs, illustrating the relationship between the degree-centric transformationand the domination parameter. The obtained results extend the study of dominationin transformed graphs and provide a foundation for future research in degree-centric graphtheory.
Category: Combinatorics and Graph Theory
[45955] viXra:2608.0020 [pdf] submitted on 2026-08-06 06:49:38
Authors: Hidehiko Okada
Comments: 8 Pages.
Discrete-valued neural networks have attracted increasing attention because they require less memory and lower computational cost than conventional floating-point neural networks. While discrete weights are often obtained by quantizing pretrained continuous-valued networks, such approaches are not applicable to reinforcement learning tasks that cannot be trained by gradient-based methods. This paper investigates the training of multilayer perceptrons (MLPs) with ternary connection weights {−1,0,1} using Genetic Algorithm (GA) for the Atari Space Invaders reinforcement learning task. The performance of ternary-weight networks is compared with that of binary-weight networks {−1,1} under identical network topologies and GA configurations. Experimental results show that GA configuration employing a smaller population size and a larger number of generations significantly outperforms a configuration with a larger population size and fewer generations when the total number of fitness evaluations is fixed. Furthermore, no statistically significant difference is observed between ternary and binary weight representations in terms of game performance. Although ternary weights exhibit slightly better median and worst-case performance, binary weights occasionally achieve higher best scores while requiring less memory. These findings suggest that binary-weight neural networks provide an attractive trade-off between performance and memory efficiency, making them an attractive representation for evolutionary reinforcement learning.
Category: Artificial Intelligence
[45954] viXra:2608.0019 [pdf] submitted on 2026-08-06 09:11:46
Authors: Gerald Vones
Comments: Title page not included in number of pages
It is argued that the known physical fields themselves can be comprehended as extra dimensions attached to spacetime. This is achieved by copying the basic structure of Special Relativity related to objects, and pasting it at the level of fields. The role of the conversion factor played by the velocity of light there is played by Newtons constant here. This leads to a permutation of the roles of established concepts.
Category: High Energy Particle Physics
[45953] viXra:2608.0018 [pdf] submitted on 2026-08-04 20:55:57
Authors: Sergey Shevchenko, Vladimir V. Tokarevsky
Comments: 30 Pages. https://arxiv.org/abs/0707.4657v6 , PACS numbers: 03.50; 12.60.-i; 12.90.+b; 14.60.Cd; 03.70.
This paper is the presentation of the 2007-2026 Planck scale informational physical model, which is based on philosophical "The Information as Absolute" concept, which was formulated mainly in 2007. In the concept it is rigorously proven that nothing exists besides some informational patterns/systems of the patterns that are elements of the absolutely fundamental, and absolutely infinite, "Information" Set. Thus Matter for sure is nothing else than some informational system of informational patterns/sub-systems — particles, fields, bodies, etc. The other fundamental base of the model is the outstanding findings of von Weizsäcker and Fredkin-Toffli, who proved that Matter is based on some binary logics ("UR hypothesis"), and that if a system consists of reversible elements, then this system doesn’t dissipate energy outside, whereas the conception above makes these findings as completely natural. That allowed to define scientifically a number of fundamental phenomena/notions, first of all "Space", "Time", "Matter", "Energy", "Inertia", and so to solve, or essentially to clarify, a number of fundamental physical problems, considering everything in Matter as some specific disturbances in Matter’s ultimate base — dense lattice of fundamental logical elements (FLE) that is placed in real Matter’s (here utmost universal "kinematical") [5]4D spacetime) — what are particles and antiparticles, what are physical senses of basic equations ib kinematics, first of all of Lorents transformations and in dynamics., etc.
Category: Relativity and Cosmology
[45952] viXra:2608.0017 [pdf] submitted on 2026-08-04 20:53:23
Authors: Michel Van de Gaer
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This note proposes a path toward knot-like organized structure in an Adaptive Medium (AM): a recursively adapting field whose local state responds to both external drive and its own neighbourhood. Within that Medium, microscopicvibrational degrees of freedom can phase-lock on steep density slopes into compact, particle-like cohorts. Cohort emission leaves a local vacancy; that vacancy is filled by vacancy backfillfrom the cell behind the shot (opposite the emission direction). Backfill steepens the upstream face, so emission regenerates andthe active lip retreats into remaining dense fuel—a kickback cascade—until a weaker valley brakes the process. Cohorts, wakes, and cascades are presented as the dynamical bridge from a continuous Adaptive Medium toward string- and knotlike organization. The account is conceptual and illustrated by interactive GPU simulations; it is not offered as a closed continuum theorem.
Category: High Energy Particle Physics
[45951] viXra:2608.0016 [pdf] submitted on 2026-08-04 17:10:30
Authors: Krrish Choudhary
Comments: 7 Pages.
The Initial Entropy Problem asks why the early universe began in an exceptionally low gravitational entropy state despite matter and radiation being at thermal equilibrium. Standard cosmology accepts Penrose's Past Hypothesis as a brute empirical fact, without a dynamical mechanism that enforces it. This paper presents a candidate Center Origin White Hole Cyclic Cosmology, built from thirteen explicit axioms, offered as an axiomatic framework, not a resolution of the problem it addresses. The model proposes that the Big Bang is the time-reversed quantum-gravity bounce of a single, monolithic universal black hole. Three axioms carry the model's real explanatory weight and are flagged plainly rather than hidden in notation: Axiom 9 stipulates an explicit exception to the Second Law of Thermodynamics at the transition; Axiom 11 stipulates repulsive anti-gravity that cannot be derived from time-reversal of the Einstein field equations and is grounded only in current untestability; Axiom 13 stipulates that dark energy is dynamical rather than a true cosmological constant, an explicit, falsifiable bet on an open question in dark energy research that current measurements do not support under a constant &Lambda. The paper derives the model's recollapse dynamics as an exact consequence of the Friedmann equation for a dust-dominated closed universe and shows explicitly where this derivation fails to match a universe dominated by dark energy. The framework does not derive low initial entropy from more fundamental principles; it relocates the Past Hypothesis to a named, falsifiable transition.
Category: Astrophysics
[45950] viXra:2608.0015 [pdf] submitted on 2026-08-04 18:15:23
Authors: Herbert Weidner
Comments: 6 Pages.
Gravitational waves in the microhertz regime represent an unexplored window into slow dynamical processes in planetary interiors and the longu2011period tidal interactions within the Solar System. Jupiter, whose rotation period of 9.925 h is known with high precision, should generate a gravitational wave near 55.97 $mu$Hz if its mass distribution departs from perfect axial symmetry. Such a signal is far below the sensitivity of existing gravitationalu2011wave detectors and is strongly Doppleru2011shifted by the synodic Earth—Jupiter motion, making direct detection challenging.Using 20 years of barometric pressure data from DWD stations, we extract Jupiter’s gravitational wave through coherent demodulation of the phase modulations induced by Earth’s orbit and by the four Galilean moons. The recovered carrier frequency exhibits SNR $approx100$ and reveals a previously unknown longu2011term frequency drift associated with Jupiter’s deep interior. The modulation indices and phases of Io, Europa, Ganymede, and Callisto are stable across 752 independent realizations, demonstrating that Earth’s atmosphere responds coherently to microhertz gravitational forcing.The measured modulation indices exceed linearized Doppler predictions by a factor of 12.7, implying a propagation speed of $vapprox 0.08 c$ for the wave along the Jupiter—Earth path. Because this path lies entirely within the Sun’s gravitational potential, our results suggest that microhertz gravitational waves may experience dispersive propagation in strongly curved spacetime. No additional longu2011term phase modulations were detected. These findings open a new observational channel for studying gravitational phenomena in the Solar System at ultrau2011low frequencies.
Category: Astrophysics
[45949] viXra:2608.0014 [pdf] submitted on 2026-08-03 20:39:38
Authors: Sangwha Yi
Comments: 10 Pages.
The Cosmological Special Theory of Relativity (CSTR) re-derives the Lorentz transformation, relativistic quantum mechanics, quantumfield theory, and general relativity within a cosmological inertial frame, in which a local, unexpanded spatial coordinate is related to thephysically expanded coordinate of a Robertson-Walker universe through a cosmological expansion function τ (t0) (Yi, 2020, 2025). Fivecompanion reviews have each examined a different sector of this program — special-relativistic kinematics, relativistic quantum mechanics andfield quantization, the Cosmological General Theory of Relativity’s black-hole solutions, the group-theoretic structure of the transformationitself, and the theory’s observational status — and each has found that CSTR’s predictions reduce, in a precise and recurring sense, tothose of the corresponding standard theory. This paper collects that recurring correspondence into a single, systematic set of comparisontables, juxtaposing every principal CSTR equation against its special-relativistic, quantum-mechanical, quantum-field-theoretic, or generalrelativisticcounterpart, and identifies the single limit — evaluation at a fixed cosmological epoch, equivalently τ (t0) → const — responsiblefor every instance of correspondence. We further collect, in a final comparison, the specific respects in which CSTR is not merely a relabelingof standard theory: the multi-epoch groupoid structure and the associated open questions identified in a companion review. The result isintended as a single reference synthesizing the correspondence structure of the entire CSTR program.
Category: Relativity and Cosmology
[45948] viXra:2608.0013 [pdf] submitted on 2026-08-03 09:25:56
Authors: Holger Döring
Comments: 16 Pages.
Galactic rotation-curves shows in many spiral- and dwarfgalaxies deviations in movement from the expectation of baryonic matter alone. Usually these deviations are explained by supposing a domination of a "dark-matter" halo. Here, in this treatise an alternative scenario is discussed in the sense of Ockams Razor: not to speculate new things to safe the phenomena but to try an explanation of observed phenomena by very well-known contributions. Therefore a global galactic magnetic plasma-halo is able by supposing a magnetic pressure and stress-term to deliver an additional dynamical term to movement of stars. This model doesn’t substitute gravity but elaborates the eeffective dynamics by magnetohydrodynmical effects (MHD).
Category: Astrophysics
[45947] viXra:2608.0012 [pdf] submitted on 2026-08-03 10:03:47
Authors: Benjamin de la Fontaine
Comments: 19 Pages. Distributed under CC BY-NC-ND 4.0
By interpreting inertia and gravity in terms of both classical electrodynamics and hydrodynamics, novel and accurate formulae for inertia, gravity and the gravitational constant can be derived from a Higgs field with precise geometric properties. Extending these formulae to general relativity, it is shown that the speed of light, the vacuum energy density, the cosmological constant, and 4-dimensional space-time curvature can also be derived from the same assumptions. A new model of general relativity and universal expansion based on a dynamically oscillating space-time is proposed.
Category: Relativity and Cosmology
[45946] viXra:2608.0011 [pdf] submitted on 2026-08-03 19:16:21
Authors: Igor Hrnčić
Comments: 3 Pages.
This paper disproves the Riemann Hypothesis by a different method.
Category: Number Theory
[45945] viXra:2608.0010 [pdf] submitted on 2026-08-02 09:14:48
Authors: Yuanjie Huang
Comments: 29 Pages.
A long-standing puzzle in plasma physics is the universally fast rate of magnetic reconnection, observed to be of order 0.1 across diverse environments yet unexplained by classical resistive magnetohydrodynamics (MHD). We propose a new analytical model for two-dimensional steady-state reconnection based on two concepts: the magnetic moment force as the gyro-averaged Lorentz force, and the semi-free electron constraint arising from quasi-neutrality. We show that the inflow is driven by the magnetic moment force rather than resistive diffusion, while the outflow is governed by the ion pressure gradient. The model yields a closed-form reconnection rate that depends only on the electron-to-ion temperature ratio and ion charge state, independent of system size, field strength, density, and resistivity. For a thermal equilibrium hydrogen plasma, the rate is approximately 0.2, consistent with satellite observations and simulations. The model also reproduces the bipolar electrostatic field at the current sheet center. Compared with Sweet-Parker, Petschek, and Hall-MHD models, our framework offers a first-principles kinetic explanation for the universal reconnection rate. Finally, we propose a corresponding modification to the two-fluid MHD equations, removing the electron pressure gradient and replacing the Lorentz force with the magnetic moment force.
Category: Nuclear and Atomic Physics
[45944] viXra:2608.0009 [pdf] submitted on 2026-08-02 12:54:22
Authors: MingLai Man
Comments: 9 Pages.
An axiomatic framework for the temporal structure of quantum pure states is formulated. In addition to time-reversal symmetry, two ontological postulates are introduced: binary reality and coherent composition. A physically complete pure state is required to contain two distinct time-reversal-related branches with a definite relative phase. We prove that, for a time-reversal-covariant Hamiltonian, the reversed branch obtained by applying the antiunitary time-reversal operator to the time-reflected forward solution satisfies the same Schrödinger equation. Linearity and coherent composition then imply a coherent superposition of the two partners. The theorem does not require different energy eigenvalues: the partners may lie in the same degenerate eigenspace. The result is therefore a conditional theorem of the enlarged axiomatic framework rather than a derivation of quantum superposition from standard time-reversal symmetry alone.
Category: Quantum Gravity and String Theory
[45943] viXra:2608.0007 [pdf] submitted on 2026-08-02 00:36:14
Authors: Taha Muhammad
Comments: 3 Pages.
For centuries, the existence of a Perfect Cuboid—an Euler Perfect Box where the three edges, three face diagonals, and the internal space diagonal are all positive integers—has remained one of the most resilient open challenges in number theory. This manuscript delivers a definitive proof establishing the absolute non-existence of such a system. By decomposing the structural framework into three exhaustive geometric classes (scaloid, isosceles, and equilateral), we implement an original polynomial transformation to isolate unbreakable irrationality barriers. We demonstrate that the arithmetic parameters governing the system are mutually exclusive across all integer domains, proving that an Euler Perfect Box is structurally impossible.
Category: Number Theory
[45942] viXra:2608.0006 [pdf] submitted on 2026-08-02 00:34:14
Authors: Xiaohao Xie, Wei Meng, Wenhua Jiao
Comments: 16 Pages.
Person Re-Identification (ReID) under severe occlusion remains a formidable challenge, primarily because existing discriminative models lack the capacity to infer missing topological structures, inevitably leading to fragmented feature representations and compromised metric spaces. To break this perceptual limitation, we propose a novel end-to-end Diffusion-Driven Dual-stream Framework ($text{D}^3text{F}$), which seamlessly integrates generative structural priors from Diffusion Transformers (DiT) into vision-language ReID. To overcome the high computational overhead and semantic gaps inherent in diffusion models, we first design a truncated prior extraction mechanism alongside a Cascaded Inverted Modality Shuffle Network (CIMSN) to achieve lightweight and deep cross-modal interaction. Furthermore, recognizing that divergent generative features can severely contaminate the strict distance metric space, we propose an Asymmetric Decoupled Feature Guidance (ADFG) strategy. ADFG strictly utilizes the fused generative prior as a contextual lens to update text prompts, while reverting to pure discriminative features for mask localization and final metric pooling. This restrained decoupling strategy strikes an optimal balance between occlusion-resistant inference and metric space purity. Extensive experiments demonstrate that the proposed $text{D}^3text{F}$ significantly outperforms existing methods, achieving state-of-the-art (SOTA) performance on both occluded and holistic ReID benchmark datasets.
Category: Artificial Intelligence
[45941] viXra:2608.0005 [pdf] submitted on 2026-08-01 07:11:58
Authors: Manuel Abarca Hernandez
Comments: 10 Pages.
This work presents the first application of the Dark Matter by Quantum Gravitation (DMbQG) theory to the study of dark matter (DM) at cosmological scales. In Section 2.1, the first Friedmann equation is introduced within the DMbQG framework. A key feature of this approach is the explicit separation between baryonic matter density and dark matter density. It is shown that, in this theory, the dark matter density evolves with the cosmological scale factor, a, following a power-law exponent of −2.5, in contrast to the ΛCDM model, where total matter density is not differentiated and scales as a with exponent -3.In Section 2.2, the second Friedmann equation and the cosmological conservation equation are presented. From the latter, the equation-of-state parameter w is derived for baryonic matter, dark matter, and dark energy. A novel result of this work is that, for dark matter, w = −1/6, which implies that its effective density is one-half of its physical density.In Section 3, the age of the Universe is calculated first within the standard ΛCDM model and subsequently using the DMbQG framework. A central result is that the age integral obtained with DMbQG is approximately 11.5% larger than that derived from ΛCDM. This difference allows for consistency with the Hubble constant measured by the SHOES project, based on Type Ia supernovae in the local Universe, with Hu2080 = 73 km/s /Mpc, yielding an age of 14.7 Gyr. In contrast, applying this same value within ΛCDM leads to an age of 12.8 Gyr, in tension with the oldest known astrophysical objects. Consequently, ΛCDM relies on the Planck Collaboration value, Hu2080 = 67.4 km/ s/Mpc, which gives an age of 13.85 Gyr.Given that the SHOES method provides a more direct measurement of the present-day expansion rate, while the Planck value is inferred from early-Universe data (cosmic microwave background), the former may better represent the current Hubble parameter. The Hubble tension remains one of the major open problems in cosmology, and this work suggests that the DMbQG framework may offer a partial resolution by reconciling a higher Hu2080 value with a consistent estimate of the Universe’s age.
Category: Astrophysics
[45940] viXra:2608.0004 [pdf] submitted on 2026-08-02 00:26:38
Authors: Arunas Ostasevicius
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper proposes a deterministic macroscopic model of thermal radiation from condensed matter, offering an alternative to stochastic noise approaches of fluctuational electrodynamics. Based on the concept of a continuous cascade buildup of intermittent self-oscillations of the electron subsystem during slow heating (the Bolero principle) and first-order linearized Maxwell equations, a rigorous analytical derivation of Wien’s spectral law is obtained. The thermal response parameter of a substance is expressed for the first time in terms of its fundamental macroscopic properties: the dynamic stiffness of the electron shell of the emitting center, the volumetric heat capacity of the lattice, and the unit cell volume. Numerical verification of the model using the high-temperature parameters of tungsten (W) is performed, demonstrating the exact convergence of the equations. An analytical relationship is established between the macroscopic rate of change of the medium’s temperature and the baseline amplitude of the radiation current.
Category: Quantum Physics
[45939] viXra:2608.0003 [pdf] submitted on 2026-08-02 00:24:12
Authors: Julinho Jorge Luís
Comments: 16 Pages.
The Gamma function diverges at negative integer and half-integer arguments, posing a fundamental obstacle for both perturbative and non-perturbative theories. Analytic continuation, while guaranteeing uniqueness, does not preserve the Euler integral representation in the left half-plane, as noted by Hardy and Titchmarsh. We present a continuous regularization technique - the Dual Architecture - that addresses this limitation through a complementary function F(z) with directional vector opposite to that of the Gamma function. The phase function C(z)=cosu2061(πz)-sinu2061(πz) is uniquely determined by the boundary conditions F(0)=1 and F(1/2)=-√π, and its periodicity is established by Lemma 2.1. The regularized function RΓ(z)=1/[C(z)Γ(1-z)] for R(z)≤0 is finite by construction at all points where the classical Gamma function diverges, unifying regulation and subtraction within a single definition. We demonstrate the physical applicability of the technique across six systems: the cosmological constant, the Higgs boson mass, the strong CP problem, the Casimir effect, dimensional regularization in d=3, and a divergent Gaussian integral. In each case, the algebraic development is presented in full, yielding analytical results consistent with experimental values. The technique offers a unified framework for treating Gamma-function divergences across perturbative and non-perturbative regimes.Keywords: Continuous regularization, Gamma function, uniqueness theorem, Casimir effect, Standard Model.
Category: Quantum Physics
[45938] viXra:2608.0002 [pdf] submitted on 2026-08-02 00:16:55
Authors: Johannes Debouto
Comments: 13 Pages. In French
The field of real numbers is essential to many scientific disciplines. The first formal constructions—which appeared long after the field's initial discovery—involve properties crucial to its modern application, most notably the property of completeness. One of the most famous of these constructions implicitly relies on the Cantor-Dedekind axiom, a concept that has often sparked controversy within the mathematical community. This work aims to demonstrate the validity of the Riemann hypothesis within the axiomatic framework of ZF plus the Cantor-Dedekind axiom, utilizing a result concerning Euler's totient function derived from the study of cyclotomic polynomials.
Category: Number Theory
[17092] viXra:2609.0025 [pdf] replaced on 2026-09-21 10:42:15
Authors: Volker W. Thürey
Comments: 6 Pages.
Many people dream of establishing a settlement on the planet Mars, especially the American entrepreneur Elon Musk. However, I believe this is nearly impossible because of the planet's extremely harsh environmental conditions. Compared with Mars, Earth is far more hospitable to human life.
Category: Astrophysics
[17091] viXra:2608.0099 [pdf] replaced on 2026-09-07 18:20:16
Authors: Peng Gao
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Modern natural-language systems usually represent linguistic meaning through statisticalmodels trained on large text corpora with substantial graphics-processor (GPU) resources.The present work examines a different, instrument-based hypothesis: that semantic differences between written assertions may be registered directly as differential torsion-fieldresponses, without training a statistical model. The study is formulated within Shkatov’storsimetry framework, in which the torsion field (TF) of physical objects and processes isrecorded as the torsional contrast (TC) between the measured object and the instrumentby means of single- and multi-coordinate torsimeters. To reduce spurious informationalphantoms that can accumulate in object—instrument—operator systems and affect repeatedmeasurements, we use the Method of Differential Test Assertions (MDTA). In this method,the object under test is composed from paired textual assertions with opposite meanings,and the differential torsion response between the two assertions is analysed. In 19 independent measurement sessions, a high-threshold assertion ("the total score is greater than θ"),treated as false under the experimental conditions, produced a higher torsional contrast thanthe paired true assertion ("the total score is less than θ") in every session. The mean paireddifference was +112.1 arbitrary units, and the exact one-sided sign-test probability for 19positive differences out of 19 was p = 2−19 ≈ 1.9 × 10−6. These results show a reproducibledifferential response between the paired textual assertions in the present protocol. Withinthe torsimetry framework, they support the working hypothesis that semantic content cancontribute to the measured torsional contrast of a written text; independent replication andexpanded controls will be required to determine the generality and physical mechanism ofthe effect.
Category: Quantum Physics
[17090] viXra:2608.0096 [pdf] replaced on 2026-09-22 00:21:17
Authors: Jose Risomar Sousa
Comments: 20 Pages.
The discovery of a generalization of the Riemann functional equation obtained by exploiting symmetries of a new formula for the Hurwitz zeta function with respect to the shift parameter, b, has led to the search for a similar relation for the Lerch Φ function, Φ(e^z, k, b), where a new formula is used as starting point and the symmetries with respect to b are exploited again. As a secondary objective, we address the problemof obtaining the analytic continuation of a finite summation that appears in a formula for the Lerch Φ function. Above all, this paper demonstrates, with clear elementary mathematics, how a functional equation can be derived.
Category: Number Theory
[17089] viXra:2608.0096 [pdf] replaced on 2026-09-07 05:21:56
Authors: Jose Risomar Sousa
Comments: 20 Pages.
The discovery of a generalization of the Riemann functional equation obtained byexploiting symmetries of a new formula for the Hurwitz zeta function with respectto the shift parameter, b, has led to the search for a similar relation for the Lerch Φ function, Φ(e^z, k, b), where a new formula is used as starting point and the symmetries with respect to b are exploited again. In addition, we uncover surprising new ways of producing analytic continuations of finite summations. Above all, this paper demonstrates, with clear elementary mathematics, how a functional equation can be derived.
Category: Number Theory
[17088] viXra:2608.0073 [pdf] replaced on 2026-08-27 21:53:46
Authors: Tanuj Kumar, Vandana [Doe], Jyoti [Doe]
Comments: 35 Pages. (Note by viXra Admin: Both the first and last names of the authors are required; please submit article written with AI assistance to ai.viXra.org)
We develop an effective continuum framework in which the physical vacuum is characterized by a bounded scalar capacity field Φ(x,t), with normalized remaining-capacity fraction f=Phi /c^{2}. Matter is represented by localized depletion of this capacity, while gravitation arises from the associated redistribution of the remaining vacuum response. In the weak-field limit, the governing equation reduces to the Poisson equation and reproduces Newtonian gravity. A nonlinear capacity-dependent response yields the exterior solution f(r)=sqrt{1-2Gm/(rc^{2})}. Relating the local capacity fraction to temporal and reciprocal radial scaling reconstructs the Schwarzschild exterior line element ds^{2}=-f^{2}c^{2}dt^{2}+f^{-2}dr^{2}+r^{2}d{Omega }^{2}, together with its standard weak-field gravitational optical response. The same continuum dynamics admit localized intrinsic oscillations which, under the quantum normalization mathrm{hbar }{omega }_{0}=mc^{2}, yield the Planck—Einstein and de Broglie relations through Lorentz transformation of the intrinsic phase. The resulting dispersion relation takes the Klein—Gordon form and reduces to the Schrödinger equation in the nonrelativistic limit. Massive excitations propagate subluminally, whereas massless disturbances remain nondispersive with limiting propagation speed c. The framework thus provides a common continuum description of vacuum depletion, emergent gravitation and spacetime scaling, and relativistic matter-wave dynamics, while identifying strong-field dynamical phenomena as a potential regime for distinguishing predictions.
Category: Quantum Gravity and String Theory
[17087] viXra:2608.0049 [pdf] replaced on 2026-08-21 18:36:43
Authors: Mykola Kosinov
Comments: 10 Pages.
"Big G" is a constant of the Universe; this is its fundamental meaning. Despite more than 200 years of sophisticated experiments, it remains the least precise fundamental constant in physics. "Big G" is not measured directly; it is calculated from Newton's law of gravitation. However, this law has a limitation: it does not take into account the gravity of the Universe. All laboratories obtain G values that are outside the permissible error limits. It is shown that the reason for the discrepancies lies in the fact that the gravitational background of the Universe is not taken into account in the calculation: (mc^2)√Ʌ. This leads to a shift in the G values by varying amounts, depending on the contribution of (mc^2)√Ʌ. In essence, metrologists were the first to experimentally detect an external factor of a gravitational nature, which is not included in Newton's law. Physics has traditionally posed challenges to metrology and developed thanks to the results of precise measurements. As R. Davis [2] notes, an increase in accuracy by even one decimal place reveals new physical realities and confirms or refutes existing theories. In the situation with measuring "big G," metrology has outpaced physical theory. Discrepancies in G values showed that Newton's local law of gravity does not allow for its precise value. For the first time in the history of science, metrology had grounds to pose a challenge to theoretical physics: "We have no doubt about the accuracy of our instruments; we have discovered an unaccounted cosmological factor that is not included in your law; a new law of gravity is needed that will allow us to correctly calculate the value of Big G." The Big G crisis is not caused by "bad instruments," but by the imperfection of the physical law from which it is calculated.
Category: Quantum Gravity and String Theory
[17086] viXra:2608.0045 [pdf] replaced on 2026-08-25 01:18:16
Authors: Kutlumuratov Atabek Bekchanovich
Comments: 111 Pages. In Russian
In the treatise main principles of propaedeutics of modern clinical medicine and human physiology are discussed. Nowadays the official medicine considers that these sciences are based on a biomedical paradigm. But the real basis of the medicine (it is understood as the practical science, or the doctoring, science) are constituted byu2026a) the clinical paradigm (it applies the philosophical preconditions of knowledge on the world, nature of person and of the nature formed by person), b) the system of supplementary paradigms among which the basic place is occupied nowadays by the biomedical paradigm, and alsou2026c) by clinically registered data about a current state of health of each patient. Physician applies the philosophical preconditions of medicine, and the clinical paradigm, and the supplementary paradigms, and data of current clinical inspection of the patient. In each doctoring the physician's thinking is directed by interests of each patient in each clinical case. Being based on a clinical paradigm, the medicine explicitly and implicitly develops system of supplementary paradigms. Each doctor reproduces and uses supplementary paradigms in each clinical case by using own professional abilities and possibilities. Each doctor exposes to individuation each clinical case in interests of health of each patient, and uses possibilities given to him (to her) by a society, a science and professional opportunities and abilities.Doctors explicitly and implicitly (at least during 1000 years) use the model of psychophysical unique human nature, generalized by Avicenna as an ontological and epistemological bases of the doctor's thinking. During the individuation of doctoring of each patient the doctor develops the clinical diagnosis which expresses the current nature of health of each patient. Each clinical discipline explicitly or implicitly develops own clinical paradigm that allows the doctor to supervise the own thinking in interests of health of each patient in each clinical case. Thus the doctor considers mental and physical perception patterns by patient of own health status and explicitly or implicitly exposes to individuation supplementary paradigms, first of all - biomedical one, by supervising the current data of clinical inspection of the patient.During doctoring of each patient the modern doctor regularly and, usually, implicitly, uses ideas of Alcmeon, and Hippocrates, and Galen about psychophysical (psycho-physiological) nature of the clinical paradigm, and these ideas were explicitly integrated by Avicenna. But in an explicit kind the modern doctor constitutes judgments in language of the biomedical paradigm.
Category: General Science and Philosophy
[17085] viXra:2608.0042 [pdf] replaced on 2026-09-25 19:11:04
Authors: Abdelmajid Ben Hadj Salem
Comments: 10 Pages. In French. Submitted to the journal " Quarterly Journal of Mathematics ". Comments welcome. S
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called the Riemann hypothesis : The nontrivial roots (zeros) $s=sigma+it$ of the zeta function, defined by: $$zeta(s) = sum_{n=1}^{+infty}frac{1}{n^s},,mbox{for}quad Re(s)>1$$ have real part} $sigma= 1/2$. In this paper, I give the proof that $sigma= 1/2$ using an equivalent statement of the Riemann hypothesis: the Dirichlet eta function and the functional relation verified by the zeta function.
Category: Number Theory
[17084] viXra:2608.0024 [pdf] replaced on 2026-09-22 07:48:44
Authors: Mikhail Batanov-Gaukhman
Comments: 13 Pages.
This article proposes treating the Kottler family of 10 metric solutions of the Einstein vacuum equation with a ±Λ-term within a single system. To this end, we propose the invariant averaging of the scalars associated with each solution of this Kottler family. As a result, averaged scalars and curvature invariants of the region of space under study are obtained: 〈C_μνρσ C^μνρσ 〉=12r_b^2/ru2076, 〈R_μν R^μν 〉=36/r_a^4,⟨g_00⟩=1 , ⟨R⟩ = 0, ⟨Ru2080u2080⟩ = 3c²r²/rau2074, ⟨K⟩ = 12rb²/ru2076 + 24/rau2074, 〈l_r^((+)) 〉=〈Δr/r〉=〈√(g_11 )-1〉 and others. On the basis of these averaging results, mathematical models of two mutually opposite stable spherical vacuum formations are considered, and contradictions of this method are identified. To overcome the resulting difficulties, an extended Einstein vacuum equation with a finite difference of a large number of positive and negative ±Λ-terms is proposed. This approach may serve as a basis for a Hierarchical Cosmological Model, as part of a unified study entitled "Geometrized Vacuum Physics Based on the Algebra of Signatures", aimed at the development of the Clifford—Einstein—Wheeler program for the complete geometrization of physics.
Category: Relativity and Cosmology
[17083] viXra:2608.0024 [pdf] replaced on 2026-08-22 17:26:14
Authors: Mikhail Batanov-Gaukhman
Comments: 9 Pages.
The article proposes to use all 12 metric solutions of the Einstein’s vacuum equation with the Λ-term within the framework of constructing a single system consisting of metric-dynamic models of one stable convex vacuum formation and one stable concave vacuum formation. This approach is a prerequisite for the creation of a Hierarchical Cosmological Model [16—31], aimed at developing the Clifford-Einstein-Wheeler program for the complete geometrization of physics.
Category: Relativity and Cosmology
[17082] viXra:2608.0022 [pdf] replaced on 2026-08-28 09:08:20
Authors: Richard M. Blaber
Comments: 22 Pages. CC-BY-NC-ND.
For the majority of its existence, our species did not live in settlements, did not have agriculture, writing or metallurgy. These are all features of the Holocene Epoch, and the global human population during most of the time since the start of that epoch remained both low and relatively constant until the beginning of the 19th Century, accelerating through the 20th Century, following the Industrial and Agrarian Revolutions. The enormous population, and the complex, planet-wide capitalist technological civilisation on which they depend, but which also exploits them, are now faced with numerous dangers, which are likely to prove insuperable.
Category: Social Science
[17081] viXra:2608.0018 [pdf] replaced on 2026-09-19 23:13:03
Authors: Sergey Shevchenko, Vladimir Tokarevsky
Comments: 32 Pages. PACS numbers: 03.50; 12.60.-i; 12.90.+b; 14.60.Cd; 03.70.
This paper is the presentation of the 2007-2026 Planck scale informational physical model, which is based on philosophical "The Information as Absolute" concept, which was formulated mainly in 2007. In the concept it is rigorously proven that nothing exists besides some informational patterns/systems of the patterns that are elements of the absolutely fundamental, and absolutely infinite, "Information" Set. Thus Matter for sure is nothing else than some informational system of informational patterns/sub-systems — particles, fields, bodies, etc. The other fundamental base of the model is the outstanding findings of von Weizsäcker and Fredkin-Toffli, who proved that Matter is based on some binary logics ("UR hypothesis"), and that if a system consists of reversible elements, then this system doesn’t dissipate energy outside, whereas the conception above makes these findings as completely natural. That allowed to define scientifically a number of fundamental phenomena/notions, first of all "Space", "Time", "Matter", "Energy", "Inertia", and so to solve, or essentially to clarify, a number of fundamental physical problems, considering everything in Matter as some specific disturbances in Matter’s ultimate base — dense lattice of fundamental logical elements (FLE) that is placed in real Matter’s (here utmost universal "kinematical") [5]4D spacetime) — what are particles and antiparticles, what are physical senses of basic equations in kinematics, first of all of Lorentz transformations and in dynamics, etc.
Category: Relativity and Cosmology
[17080] viXra:2608.0012 [pdf] replaced on 2026-08-05 16:28:15
Authors: Benjamin de la Fontaine
Comments: 19 Pages. Distributed under CC BY-NC-ND 4.0.
By interpreting inertia and gravity in terms of both classical electrodynamics and hydrodynamics, novel and accurate formulae for inertia, gravity and the gravitational constant can be derived from a Higgs field with precise geometric properties. Extending these formulae to general relativity, it is shown that the speed of light, the vacuum energy density, the cosmological constant, and 4-dimensional space-time curvature can also be derived from the same assumptions. A new model of general relativity and universal expansion based on a dynamically oscillating space-time is proposed.
Category: Relativity and Cosmology
[17079] viXra:2608.0005 [pdf] replaced on 2026-09-10 16:22:06
Authors: Manuel Abarca Hernandez
Comments: 26 Pages. The chapter 5 is a step forward to solve the Hubble tension problem
This work presents the first application of the Dark Matter by Quantum Gravitation (DMbQG) theory to the study of dark matter at cosmological scales.Section 2.1 introduces the first Friedmann equation within the DMbQG framework. In this framework, the dark matter density evolves with the cosmological scale factor according to a power-law exponent of −2.5, in contrast to the ΛCDM model.Section 2.2 presents the second Friedmann equation and the cosmological conservation equation. From the latter, the equation-of-state parameter w is derived for dark matter. A novel result of this work is that, for dark matter, w = −1/6, which implies that its effective density is one-half of its physical density.Section 3 calculates the present-day deceleration parameter in both the ΛCDM and DMbQG frameworks and compares the results with published studies. The cosmological deceleration parameter as a function of redshift z is also investigated within both theoretical frameworks.Section 4 first calculates the age of the Universe using the standard ΛCDM model and subsequently using the DMbQG framework. A central result is that, within DMbQG, the age of the Universe is 14.3 Gyr when Hu2080 = 73.4 km/s/ Mpc, the value obtained from the Pantheon+ project. In contrast, using the same Hu2080 value within ΛCDM yields an age of 12.8 Gyr, which is in tension with the ages of the oldest known astrophysical objects.Since Pantheon+ provides a direct low-redshift determination of Hu2080, this result is compared with the value inferred by the Planck Collaboration from early-Universe data. The DMbQG theory therefore offers the possibility of reconciling a higher Hu2080 value with a consistent estimate of the age of the Universe.Section 5 investigates the Hubble tension by calculating Hu2080 within both theoretical frameworks. The values obtained are consistent with the Planck-inferred Hu2080 in the ΛCDM framework and with the Pantheon+-based Hu2080 in the DMbQG framework.The dataset consists of 34 [z, H(z)] measurements obtained using the Cosmic Chronometers method. Although the mathematical procedure is based on a simple statistical method, it yields the two results described above.This work provides a potentially important contribution to the study of the Hubble tension, which has remained unresolved for more than a decade.
Category: Astrophysics
[17078] viXra:2608.0005 [pdf] replaced on 2026-08-25 01:19:49
Authors: Manuel Abarca Hernandez
Comments: 19 Pages.
In this versionV2 Universe`s age goes down 14.3Gyr This work presents the first application of the Dark Matter by Quantum Gravitation (DMbQG) theory to the study of the dark matter (DM) at cosmological scales. In the section 2 are introduced the Friedmann equations using the DMbQG theory, a key feature of this approach is the explicit separation between baryonic matter density and dark matter density. It is remarkable how in the DMbQG framework is demonstrated using the second Friedmann equation and the cosmological conservation equation that the effective DM density is a half of the physical DM one. This theoretical finding has several successful consequences studied in the sections 3 and 4. Also in this section, it is calculated the transition between the decelerating- accelerating eras, according to the DMbQG theory and the ΛCDM model. The theoretical calculus are tested with other published results. In the section 3, it is calculated the current cosmologic deceleration parameter by the two theoretical frameworks, being tested this calculus with other published results. Also it is studied the cosmological deceleration function depending on the z red-shift according to the two frameworks, yielding two quite different functions that could be tested by the recent results of the DESI project. In the section 4, the Universe`s age is calculated first within the standard ΛCDM model and subsequently using the DMbQG framework. A central result is that the age integral obtained with DMbQG is approximately 12.5% larger than that derived from ΛCDM. This difference allows for consistency with the Hubble constant measured by the PANTHEON project, based on Type Ia supernovae , with Hu2080 = 73.5 km /s/ Mpc, yielding an age of 14.3 Gyr. In contrast, applying this same value within ΛCDM leads to an age of 12.8 Gyr, in tension with the oldest known astrophysical objects. Consequently, ΛCDM relies on the Planck Collaboration value, Hu2080 = 67.4 km /s/ Mpc, which gives an age of 13.85 Gyr.Given that the SHOES or PANTHEON+ projects provide a more direct measurement of the present-day expansion rate, while the Planck value is inferred from early-Universe data (cosmic microwave background), the former may better represent the current Hubble parameter. The Hubble tension remains one of the major open problems in cosmology, and this work suggests that the DMbQG framework may offer a partial resolution by reconciling a higher Hu2080 value with a consistent estimate of the Universe’s age.
Category: Astrophysics
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