All Submission Categories

Exact Solution to Einstein's Field Equation

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, Einstein's field equation will be solved by removing the framework of tensor analysis.
Category: Relativity and Cosmology

The Central Thalamic Nucleus as the Core Hypothesis of the Consciousness Vortex Model

Authors: Zhaole Sun
Comments: 21 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The neural basis of consciousness is a central issue in the field of neuroscience, with the "hard problem" of consciousness revolving around the unclear physical origin of subjectiveexperience. Existing theories (such as IIT, GWT, etc.) are confined to information-logicrecursive frameworks, failing to identify core physical structures and often focusing on thecortex, which contradicts clinical evidence that thalamic damage leads to loss of consciousness.To address these limitations, this paper proposes and argues that the central medial thalamicnucleus (CM) is the core anchor for consciousness generation. Using the Consciousness Flow Vortex Model (CFVM) as an analytical framework, the study systematically elucidates CM's critical role in information convergence, rhythm regulation, and global integration from three dimensions: closed-loop cycles, central focusing, and global synchronization. The analysis demonstrates that CM can serve as the central anchor for consciousness production, effectively explaining the characteristics of awareness, integration, stability, and subjectivity in consciousness. This hypothesis not only constructs a comprehensive theoretical model for consciousness research but also provides a clear structural localization for the neuralmechanisms of consciousness, offering new opportunities for breakthroughs in theneuroscience of consciousness.
Category: Physics of Biology

The Universe is Magnetically Dynamic With Cosmic Explosions Driven by External Magnetic Fields

Authors: Jamal S. Shrair, John L. Turner
Comments: 48 Pages.

Theoretical models of cosmic explosions (such as stellar explosions) and galactic rotation curves are essential cornerstones of astrophysics, serving as primary diagnostic tools for understanding stellar mechanisms, the distribution of matter, and the fundamental structure of the universe. However, in this lengthy research paper, we have provided robust, up-to-date empirical data on stellar explosions and the rotation curve phenomenon, based on modern observations. This objective analysis of observational data has not only exposed the fundamental flaws in conventional models of stellar explosions and rotation curves but also refuted foundational paradigms in astrophysics and cosmology. Alternative models have been proposed.
Category: Astrophysics

Lerch's Φ and the Polylogarithm at the Negative Integers

Authors: Jose Risomar Sousa
Comments: 10 Pages.

At the negative integers, there is a simple relation between the Lerch Φ function and the polylogarithm. Starting from that relation and a formula for the polylogarithm at the negative integers known from the literature, we can deduce a simple closed formula for the Lerch Φ function at the negative integers, where the Stirling numbers of the second kind are not needed. Leveraging that finding, we also produce alternative formulae for the k-th derivatives of the cotangent and cosecant (ditto, tangent and secant), as simple functions of the negative polylogarithm and Lerch Φ, respectively, which is evidence of the importance of these functions (they are less exotic than they seem). Lastly, we extend formulae for the Hurwitz zeta function only valid at the positive integers to the complex half-plane using this novelty.
Category: Number Theory

The Ultrrasound Photoelectric Effect

Authors: Miroslav Pardy
Comments: 9 Pages. Original article

The ultrasound photoelectric effect is the new phenomenon in particle physics.We derive the velocity of sound in the blackbody gas of photons. Derivation is based on the thermodynamic theory of the photon gas and the Einstein relation between energy and mass.The quantization of this sound forms the matter of phonons. The ultra-sound phonons composed from photons generate the photoelectric effect as the analogue to the Einstein photoelectric effect in metals. The application of this effect in the elementary particle physics, atomic physics and nuclear physics is not excluded.
Category: Quantum Physics

On the Time Scale for Developing Fusion Power

Authors: Daniel L. Jassby
Comments: 13 Pages. (Note by viXra Admin: PPT format is not acceptable format; please cite and listed scientific references)

Fusion devices produce high-energy neutrons and ions by reactions between deuterons or between deuterons and tritons, but no one has ever converted the energy of fusion products to electricity. In 75 years of R&D no fusion system has produced one watt or one joule of electricity, while the device and its auxiliary systems consume multi-megajoules of electricity during each operating pulse. It’s possible that in the 2030’s one or morefusion devices may utilize clever stunts to produce a few watts, but even a modest demonstration of several kilowatts of electric output (while still consuming multi-megawatts) is two decades away. Producing net electric power from a fusion facility may never be possible because of the high power consumption of any fusion device and its auxiliary systems. The second most daunting hurdle to power production is that the burned and lost tritium fuel must be replenished in the fusion contraption itself. That is infeasible, partly because of shortcomings in "breeding" by fusion neutrons, but especially when inherently small burnup fractions result in unavoidable losses of the dispersing unburned tritium. The only practical fuel is deuterium alone. The difficulties of achieving ignition in deuterium, of developing adequate reactor technologies, and of finding pathways for reducing electricity consumption of reactor systems will push the realization of a prototype fusion power plant at least half a century away.
Category: Nuclear and Atomic Physics

A Merkleized Batch Attestation Scheme with Selective Disclosure and Compliance-by-Design

Authors: Harry Willson Potter
Comments: 8 Pages.

Soulbound tokens (SBTs) have been theorized as non-transferable attestations for decentralized identity and reputation. The existing SBT literature assumes permissive regulatory environments that tolerate token-based incentives, pseudonymous participation, and secondary markets. This paper inverts that assumption. We study SBT design under prohibitive regulatory constraints—jurisdictions that ban cryptocurrency, mandate real-name identity verification, and impose data minimization. We formalize the Usefulness Paradox as a theorem: for any SBT system under three or more prohibitive constraints, the DeFi feature set and the compliance feature set intersect in exactly one element—non-transferability. We define an 8-dimension compliance evaluation framework with formal criteria and prove existing SBT standards satisfy at most one of eight criteria. We present three general design patterns—hook-level soulbound enforcement, dual-layer compliance middleware, and beacon-based pseudonymity—that collectively satisfy all eight criteria.
Category: Data Structures and Algorithms

How Time Dilation's ‘Antigravity’ Effects Impact the Expanding Universe

Authors: Jonathan J. Dickau, Steven K. Kauffmann, Stanley L. Robertson
Comments: 11 Pages. Essay written for the Gravity Research Foundation 2026 Awards for Essays on Gravitation.

We outline how the cosmos’ accelerating expansion, diminishing over time, can be explained using the 1915-16 Einstein/Schwarzschild metric in the geodesic equation without requiring Dark Energy.
Category: Relativity and Cosmology

Horizons in Both Original and Symmetric Natario Warp Drives Using Two Parallel and Alternative Adm-MTW-Alcubierre Formalisms

Authors: Fernando Loup
Comments: 55 Pages. complements the developments of viXra:2509.0064 and viXra:2605.0014

In 1994 Alcubierre developed the first warp drive theory using the original 3+1 ADM-MTW formalism. The original ADM-MTW formalism (Arnowitt-Dresner-Misner) (Misner-Thorne-Wheeler) uses both contravariant and covariant shift vector components in its mathematical structure.It possesses mixed shift vector components. Seven years later in 2001 the same original 3+1 ADM-MTW formalism appeared in the first part of the second warp driven theory developed by Natario.(The second part of Natario theory uses the Hodge Star). In this work we present two new 3+1 ADM-MTW formalisms: One is the parallel contravariant in which all the shift vector components in its mathematical structure are completely contravariant and the other one is the parallel covariant in which all the shift vector components in its mathematical structure are completely covariant. We describe both the original and symmetric Natario warp drive vectors using the mathematical techniques of these parallel formalisms. We focused ourselves in the 3D spherical coordinates for variable speeds. Remember that a real spaceship is a 3D object inserted inside a real 3D spacetime. Also a real warp drive must accelerate and de-accelerate. One the major drawbacks concerning warp drives is the problem of the Horizons(causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble. The behavior of a photon sent to the front of the warp bubble in the case of the original and symmetric Natario warp drive vectors with variable speeds and a lapse function was also one of the main purposes of this work. We presented the behavior of a photon sent to the front of the bubble in the original and symmetric Natario warp drive vectors with the lapse function in these new parallel 3+1 ADM-MTW formalisms using quadratic forms and the null-like geodesics $ds^2=0$ of General Relativity and we provided here the step by step mathematical calculations in order to outline the final results found in our work which are the following ones: For the case of the lapse function or the 3+1 spacetime in these parallel ADM-MTW formalisms the Horizon do not exists at all. Due to the extra terms in the lapse function or the presence of the 3D dimensions that affects the whole spacetime geometry these solutions allows to circumvent the problem of the Horizon.
Category: Relativity and Cosmology

An Algebraic-Geometric Derivation Using Linked Right Triangles

Authors: Sorintreachboth Sath
Comments: 7 Pages.

This paper presents an independent geometric derivation involving linked right triangles and algebraic substitution based on the Pythagorean theorem. The derivation develops a relation for determining an unknown side length by connecting multiple right-triangle configurations through shared variables. By applying the Pythagorean theorem to related geometric structures and performing algebraic elimination, an explicit expression for an unknown side is obtained. The work emphasizes geometric visualization, structural reasoning, and step-by-step analytical derivation rather than the introduction of a new theorem. A numerical example is provided to verify the validity of the derived relation and its consistency with the original geometric configuration. This exposition demonstrates how classical geometric principles may be reconstructed through independent mathematical reasoning and provides an educational illustration of algebraic-geometric problem solving within linked right-triangle systems.
Category: Geometry

Testing the Dark Matter by Quantum Gravitation Theory in the Local Group, the Virgo and the Coma Clusters

Authors: Manuel Abarca Hernandez
Comments: 6 Pages.

The aim of this work is to test the novel theory called Dark Matter by Quantum Gravitation theory (DMbQG hereafter) at cluster scale. This theory was initially developed for galaxies and afterward was extended to clusters. The main paper where the theory is developed at galaxy scale is [5] Abarca, M. 2024, also in this paper there are some validation test using the rotation curves of MW and M31. The theory was fully extended to cluster in [2] Abarca,M.2024, also in the paper there are some validation test using data referred to the Local Group and the Virgo clusters. In this work are compiled some test introduced in the both papers and also there are two new tests referred to the Coma cluster, using data published recently. The tests are mainly focused on the turnaround radius, also called zero velocity radius, and its gravitating mass associated, in addition regarding the LG of galaxies there is another important test focused on its virial mass as well. The theoretical calculus has been validated using four papers published by well known team researchers in recent years. Namely the years: 2017, 2018, 2023 and 2025.
Category: Astrophysics

The Nontrivial Zeroes of the Riemann Zeta Function are Trivially Expressed by The Euler Product

Authors: Ryan Hackbarth
Comments: 3 Pages. (Note by viXra Admin: Further repetition may not be accepted)

Leonard Euler considered the Zeta function for real values input of s, and in doing so he famously derived the Euler Product formulation of the Zeta function, which linked the function to prime numbers. The connection between the prime numbers and the Zeta function was further pursued by Bernhard Riemann, who constructed an analytic continuation of the function which remained valid for the entire complex plane. In doing so, he was able to link the zeroes of the Zeta function to the distribution of prime numbers. In this paper, I show that the zeroes of the Zeta Function can be identified directly from the Euler Product, and in doing so, suggest a trivial link between the primes and the zeroes of the Zeta function while bypassing the more complex machinery of analytic continuation.
Category: Number Theory

A Sketch of the Development of the Atomism

Authors: Zbigniew Osiak
Comments: 101 Pages. In Polish

The contributions of over one hundred scientists to the development of the atomism are discussed. Detailed bibliographic information on their published works is provided.
Category: History and Philosophy of Physics

A Brief Essay on Electromagnetic Waves (Transported Energy, Quantum, Propagation, Photon and Wave-particle Duality)

Authors: José Romeu Dellacqua
Comments: 10 Pages.

The goal of this essay is to carry out a critical analysis of the extension of the concept of energy applied to stationary electromagnetic fields to traveling electromagnetic fields, that is, electromagnetic waves. In an attempt to establish a connection between the energy equations, obtained from Maxwell's equations and the results of Max Planck's studies, this essay proposes some changes to the conventional electromagnetic wave equations. This essay also seeks to deduce mathematical expressions for the electrical power and voltage associated with the quantum, as well as its subdivision into voltage, current and time components. Finally, a conjecture is proposed about what wave-particle duality could be, and its relationship with the photon as discussed in this essay.
Category: Quantum Physics

The Solar Magnetic Switchbacks Are Magnetic Scattering of Coulomb Collisions Between Galactic Cosmic Rays and Solar Radiation

Authors: Jamal S. Shrair, ohn L. Turner
Comments: 15 Pages.

The process of magnetic switchbacks contributes greatly to coronal heating and the acceleration of solar wind. It is a weakly collisional plasma process influenced by magnetic field configuration, rather than a result of purely electrostatic Coulomb collisions. This magnetic process is a consequence of magnetic scattering, in which low-energy galactic cosmic rays (3-30 MeV/nuc) interact with solar radiation, and this interaction is more pronounced during periods of heightened solar activity, including the release of Energetic Solar Particles (SEPs). Essentially, when highly modulated Galactic Cosmic Rays (GCRs) collide weakly with the solar radiation, magnetic switchbacks are formed, resulting in a form of anti-Stokes Raman scattering that increases the temperature of a magnetised plasma and accelerates the solar wind. It is unconventional Raman scattering of a highly magnetised plasma involving nonlinear, non-isotropic interactions in which an external magnetic field modifies charged-particle dynamics, producing an optical S-shaped signature. In the presence of a strong magnetic field, Coulomb collisions are significantly altered, forcing them into complex, S-shaped or non-monotonic trajectories rather than the simple hyperbolic paths observed in conventional Coulomb scattering. That is because the magnetic field induces cyclotron motion (gyromotion) which interacts with the Coulomb potential, causing the heavily charged particle to spiral or curve, intersect its asymptotic line, and create a unique S-shape before completing its scattering.  
Category: Astrophysics

Resolving Zeno’s Paradox Through the Intrinsic Progression of Time

Authors: Harsha Kumar Suriyaarachchi
Comments: 11 Pages. (Note by viXra Admin: Please cite listed scientific reference)

This study presents a resolution to the 2500-year-old Zeno’s paradox, restoring the relationship between Space and time to the fundamentals of classical understanding. Further, the calculation shows the instability of the relativistic space-time relationship in resolving the paradox.Zeno’s paradox has four main canonical variants, Dichotomy, Achilles and Tortoise, Arrow Paradox and Moving Rows. A comprehensive analysis is conducted of both classical and contemporary relativistic approaches proposed to resolve the paradox, including standard calculus, the summation of infinite series, models invoking quantised space, quantised time, and various adaptations within relativistic framework. Despite their theoretical sophistication, these approaches are mathematically argued to fall short of providing a satisfactory resolution.Coherent resolution emerges only under the hypothesis that time progresses as an independent, intrinsic and continuous entity, rather than being tied to spatial or kinematic variables. Classical mechanics tends to treat time as an independent parameter, but this feature has not been explicitly utilised in prior attempts to resolve Zeno’s paradox at a fundamental level. The present work proves where previous attempts, including the relativistic framework, fail and re-examines the paradox by explicitly enforcing the independence and the continuity of time as a primary principle, to consistently resolve the paradox.
Category: Mathematical Physics

From Piecewise-Linear to Piecewise-Circular: A Geometric Extension of Integration Theory via Osculating Sectors

Authors: Giuseppe D'Ambrosio
Comments: 20 Pages. (Note by viXra Admin: Author name is required in the article after the article title)

This paper introduces the D’Ambrosio Integral, a geometrically oriented generalization of the Riemann integral that incorporates the curvature of the integrable curve. Unlike classical schemes based on linear approximation, the proposed method employs circular arcs determined by consecutive triplets of points, allowing curvature information to be directly embedded into the integration process. It is shown that the integral converges, is geometrically invariant, and coincides with the Riemann integral for sufficiently smooth functions. The formulation naturally extends to Riemannian manifolds through the use of the exponential map. The proposed approach provides higher geometric accuracy in regions of pronounced curvature and is applicable to the analysis of curves, vector fields, and dynamical systems.
Category: General Mathematics

A New Closed-Form Expansion Related to the Riemann Zeta Function

Authors: Ayoub Zaroual
Comments: 6 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We establish a closed-form expansion of the Riemann zeta function ζ(s) at any complex point s = a + ib in terms of an auxiliary real-analytic function L(a) built from theBernoulli numbers and the rising factorial. The cornerstone of the derivation is a clean dif-ferentiation identity for the elementary symmetric polynomial function Kp n(a) on consecutive integers, which we prove by a generating-function argument. Specialising the expansion to the critical line Re(s) = 1/2 recasts the Riemann hypothesis as the simultaneous vanishing of two real power series in the imaginary part b.
Category: Functions and Analysis

Preinertia And Accelerated Motions

Authors: Antonio León Sánchez
Comments: 3 Pages.

The universality of the non-rectilinear trajectories followed by virtually all celestial bodies and the irrelevance (or even nonexistence) of uniform motions in the observable universe serves as the starting point for a new redefinition of preinertia, which also demonstrates the absolute nature of motion.
Category: Classical Physics

From Rényi Entropy to General Relativity

Authors: Ervin Goldfain
Comments: 17 Pages. (Note by viXra Admin: Further repetition may not be accepted)

In this sequel to [4-6], we argue that the equations of General Relativity (GR) follow from constrained maximization of Rényi Entropy. This finding is entirely consistent with our earlier derivation of Feynman’s Path Integrals from constrained maximization of Rényi Entropy. An unforeseen conclusion is that three fundamental constants of Nature, (Planck’s, Newton’s and cosmological constants) emerge as Lagrange multipliers of the maximization procedure.
Category: Relativity and Cosmology

Embarking on Adventurous Journeys Through Some Subjects in Pure Mathematics: Part II

Authors: Tue Vu, Trista Vu
Comments: 248 Pages. [License] CC-BY-NC 4.0

As we enter Part II, we turn to two new subjects: Extensions of Fundamental Trigonometric and Hyperbolic Functions and Unraveling the Mystery of the Riemann Hypothesis: Toward a Complete Proof, beginning with Chapter 3 and Chapter 4.Chapter 3 develops generalized forms of classical trigonometric and hyperbolic functions, elevating them to a broader conceptual framework. These extended formulations introduce new dynamic behaviors, enabling the reshaping of familiar functions and the exploration of entirely new families of elementary functions. This extension creates a richer mathematical framework for studying natural curved surfaces. Classical trigonometric functions such as sin(x) and cos(x) produce identical cross sections when plotted in three dimensions, yielding surfaces that replicate the same curve for every value of y. In contrast, the new two variable trigonometric functions generate curves that vary with y, producing surfaces that differ across the domain and giving rise to distinct geometric objects rather than simple extrusions.Chapter 4 presents a proposed proof of the Riemann Hypothesis, one of the most intriguing and significant problems in mathematics. We explore known findings and properties of the Riemann zeta function, reformulate the functional equation in a new light, and demonstrate why certain hypothetical pairs of nontrivial zeros cannot exist. We present a proof of the Riemann Hypothesis using an elementary algebraic approach. In Section 4-4, we demonstrate that all possible nontrivial zeros lie in the narrow bands 6.28318534... ≤ 6.28983598... or -6.28983598... ≤ Im(s) <-6.28318534... for 0 However, none of them serve as solutions to ζ(s) = 0 because their imaginary parts are below the first nontrivial zero. This approach aims to clarify the assertion that all nontrivial zeros of the zeta function lie on the vertical line where the real part is 1/2.
Category: General Mathematics

Gravity as a Screening Effect

Authors: Michael A. Ivanov
Comments: 12 Pages. Current Physics, 2025, 2, e27723348373429. https://doi.org/10.2174/0127723348373429250512104534

Objective: A model of quantum gravity unrelated to general relativity is described. The main postulate of the model is the assumption of the existence of a background of superstrongly interacting gravitons. To describe the interaction of a graviton with any particle during their collision, a new constant is introduced. Methods: It is shown that screening of the background of single gravitons by a pair of bodies leads to approximately equal attractive and repulsive forces between the bodies. Pairing of a part of the background gravitons, provided that the pairs are destroyed as a result of a collision with a body, yields an attractive force twice as great as the repulsive force, and gravity arises as an effect of background screening. Results: Newton’s constant has been calculated in the model as a function of background temperature, which allows the value of the new constant to be estimated. This model is free from divergences, unlike quantum gravity models based on general relativity, due to the specific shape of the Planck spectrum of the graviton background. A theoretical estimate of the Hubble constant, depending on the new constant, is also obtained. Conclusion: An important feature of the model is the necessity of an "atomic" structure of matter, which leads as a side effect to the prohibition of the existence of black holes that do not have such a structure. Small additional effects of the model, caused by the interaction of photons with gravitons, may have great significance for cosmology.
Category: Quantum Gravity and String Theory

SunQM-9s2: Updates and Corrections for the SunQM Series Articles (Part-2, Drafting Began in 2021)

Authors: Yi Cao
Comments: 30 Pages.

This is not a research article, but a collection of updates, corrections, terminology normalizations, and questions/answers (Q/A) for my 39 of SunQM series articles that have been posted at the preprint server viXra.org (from April 2018 to February 2026). The suggested reading sequence for these 40 posted SunQM series papers is: SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, 5s2, 7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s9, 6s11, 7s1, 7s2, 8, 9s1, and 9s2. During my ~10 years (2014 ~ 2025) closed-door development on the {N,n} QM (through the "global energy minimization" kind of research), some of my early stage work lacks of consistency with the late stage work, and thus needs to be updated and corrected. Those important updates and corrections have mostly been presented in the late stage SunQM articles. The current paper includes the rest updates and corrections (that may be less important). The previous paper (SunQM-9s1: Update u2026 (part-1)) covered the updates for SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, and 5s2. The current paper (SunQM-9s2: Update u2026 (part-2)) covers the updates for SunQM-7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s9, 6s11, 7s1, 7s2, 8, and 9s1. Steve Wolfram once mentioned that he developed the online calculator "Wolfram Alpha" for the purpose of democratizing the math [citation at youtube video?]. After I discovered the Solar {N,n//6} QM structure and then built a single master table of {N,n//6} QM structure for our universe (see SumQM-7’s Table-1), I wish that the novel {N,n//q} QM also will democratize the QM theory. The {N,n} QM was built on three building blocks: the Newtonian mechanics (or the classical physics), the Bohr-QM (i.e., rn = r1 n^2 for the H-atom), and the Schrodinger equation/solution for the H-atom. Thus, I also wish that the {N,n} QM (or any fragment of it) can be the useful building material for other scientists (or the scientific community) to build either the more completed QM theories, or the more diversified QM theories.
Category: Quantum Physics

Forecasting Market Demand with Machine Learning: From Historical Data to Consumer Behavior Insights

Authors: Yerassyl Tursynbek, Kassekeyeva Aislu Bisenovna
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Accurate demand forecasting is a critical component of supply chain optimization, inventory management, and strategic planning in modern enterprises. Conventional statistical forecasting approaches often struggle to represent nonlinear patterns and abrupt changes in consumer behavior, which reduces their effectiveness in volatile market conditions. This study explores data-driven forecasting techniques that integrate historical sales records with factors influencing purchasing behavior, including seasonality and promotional effects. A comparative experimental analysis is conducted between classical time-series approaches and advanced data-oriented predictive models. The results demonstrate that data-driven forecasting techniques achieve higher predictive accuracy and stability, particularly when long-term temporal dependencies and irregular demand fluctuations are present. The proposed approach supports improved decision-making by reducing forecasting errors and enhancing operational efficiency. The findings highlight the potential of intelligent forecasting systems for sustainable business growth and adaptive demand planning.
Category: Artificial Intelligence

Three Theorems From Which Follow Two New Laws of Gravitation and a New Law of Universal Gravitation

Authors: Mykola Kosinov
Comments: 9 Pages.

New theorems on the flux of the gravitational field strength vector are presented, free from the limitations inherent in Gauss's theorem. Gauss's theorem is not sufficient for a complete description of gravity. It is shown that the relationship between the gravitational field flux and the mass of sources is not the only method for representing the gravitational field flux. Unlike Gauss's theorem, the new theorems do not include the mass of sources. The first theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the body's orbit. The second theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the universe. The third theorem concerns the total gravitational force that actually acts on the body and is caused by the gravitational interaction of the test body with all bodies in the universe. From these theorems, two new laws of gravitation and a new law of universal gravitation are derived, which for the first time describes gravity taking into account the action of all bodies in the universe. Unlike Newton's law of gravity, the new law of universal gravitation does not include the mass of sources and the gravitational constant G. The new theorems relate to the gravitational field, which obeys the inverse-square law, and to the gravitational field of the universe, where the inverse-square law does not apply. The new theorems and new laws of gravity provide a complete description of the gravitational interactions of all N-body bodies in the universe. The new theorems demonstrate the existence of a workaround instead of searching for a direct solution to the gravitational N-body problem (for N ≥ 3).
Category: Quantum Gravity and String Theory

About Photons and Anti-Photons

Authors: Paul R. Gerber
Comments: 4 Pages.

It is argued that photons and anti-photons are different entities in the sense that they react oppositely to a gravitational field. Explicitly, photons experience a redshift when moving away from a star, and are further red-shifted when moving towards a (supposed) anti-matter star. Analogously, anti-photons gain energy when moving towards a matter-star. However, we are unable to see anti-photons, and thus, cannot observe possible galaxies that are built up of antimatter and shine in anti-light. The ensuing consequence is, that we observe that about half the volume of the universe is not populated by stars, but consist of so-called voids. But, in fact, these voids must contain an equivalent population of anti-stars which consist of anti-matter and, thus, shine by emitting anti-photons which are invisible to us.
Category: Relativity and Cosmology

A New View of the Process of Light Diffraction

Authors: Iuri Bagaturia, Zaza Melikishvili, Anzor Khelashvili, Koba Turashvili, Saba Kvesitadze
Comments: Pages.

Based on empirical studies, we show that the "diffractive-interferential" images produced in laser light experiments are generated by a completely unknown, non-wave phenomenon. We show that the phenomenon is generated by barriers that create the slits. Presumably, the mechanism of this phenomenon is related to the scattering caused by collisions of photon beams with strange spatial structures of physical fields of a strange nature and which are generated by charged particles of the barrier's atomic lattice. We indicate the probable mechanism of the physical phenomenon corresponding to these scatterings. We hypothesize that the same phenomenon also gives rise to the characteristic quantum discreteness of the microscale, and that further, more detailed empirical and theoretical investigation of this phenomenon will lead to the necessity of implementing significant changes in fundamental concepts of physics.
Category: Quantum Physics

New Interpretation on the Fransén-Robinson Constant

Authors: Ruiguo He
Comments: 11 Pages.

The Fransén-Robinson Constant F is closely related to e, but a discrete series representation for F has not yet been established. The lack of existing analytical identities obscures its direct algebraic analyticity, including its potential transcendence. In this paper, we introduce a novel approach utilizing the Abel-Plana Formula to derive the first discrete series representation of F, opening many possible avenues for the true nature of F.
Category: Number Theory

[ Exploration on Whether] The Riemann Hypothesis is True!

Authors: Abdelmajid Ben Hadj Salem
Comments: 10 Pages. In French, submitted to the journal " Bulletin des Sciences Mathématiques "comments welcome.

In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called 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} $sigma= frac{1}{2}$. In this note, I give the proof that $sigma= frac{1}{2}$ using an equivalent statement of the Riemann Hypothesis: the Dirichlet eta function.
Category: Number Theory

Revisited String Theory

Authors: Alaya Kouki
Comments: 3 Pages.

In this short communication we give an experimental verification of the String Theory.
Category: Quantum Gravity and String Theory

Required Conditions for Successful Lattice Confinement Fusion Experiment in D/Pd Electrolysis

Authors: Jozsef Garai
Comments: 12 Pages.

Recipe for successful D/Pd Lattice Confinement Fusion in Electrolysis is suggested. The effects of magnetic field, laser excitation, and surface requirements of the Palladium cathode are discussed in detail.
Category: Nuclear and Atomic Physics

Propositions of Three Laws of Spiritual Mechanics

Authors: Thomas Adrian Nicewicz
Comments: 2 Pages. (Note by viXra Admin: This submission may not be written in a manner suitable to viXra - Please read the viXra guidelines and conform)

The ancients once said, "As above, so below." This writing explores this notion and proposes three laws of spiritual mechanics.
Category: History and Philosophy of Physics

Rethinking Electricity: A Wave-Based Interpretation of Electrical Energy Transport

Authors: Oliver Consa
Comments: 8 Pages.

This work revisits Oliver Heaviside’s interpretation of electricity within modern electromagnetic theory, presenting electrical energy transport as a fundamentally wave-based phenomenon. Electrical energy is transmitted primarily as electromagnetic fields propagating through the dielectric medium surrounding theconductors; the motion of charges within the conductors plays a secondary, dissipative role. Building on transmission line theory, Maxwell’s equations, and Poynting’s theorem, the paper introduces the concepts of supracurrent and infracurrent to distinguish field-mediated energy flux from dissipative material response. The telegrapher’s equations are then interpreted as a macroscopic description of propagation and loss in real transmission lines.
Category: Classical Physics

Partial Differential Equations Arising From the Chain Rule for Direct Dependencies

Authors: Edigles Guedes
Comments: 3 Pages.

This paper presents two partial differential equations obtained from the chain rule for functions with direct dependencies among the variables.
Category: Functions and Analysis

Two Generalized Binomial Identities With a Free Parameter

Authors: Edigles Guedes
Comments: 5 Pages.

Two remarkable combinatorial identities are established.
Category: Combinatorics and Graph Theory

Geometric Scaling Laws in Block Decompositions of the Dirichlet Eta Function

Authors: Min Min Oo
Comments: 9 Pages. (Note by viXra Admin: Author name is required in the article after the article title and the abstract should be labeled as such)

This paper presents a block-structured decomposition of the Dirichlet eta functionη(s)=∑_(n=1)^00 (-1)^(n-1) n^(-s), where s=σ+it, based on an exponential partitioning of the summation index into intervals of the form N_k∼2e^(2kπ/t). The series is reorganized into finite segments, which are analyzed as dynamically scaling components with approxipmately geometric decay behavior.A ratio structure between successive block contributions is derived, leading to an approximate exponential scaling law of the form R_k (s)∼e^(-2πσ/t). This allows the eta function to be expressed as a coupled system of real and imaginary components, each defined over partitioned summation blocks. Using this decomposition, a real—imaginary interaction structure is introduced, where intersection-type conditions between the real and imaginary parts are studied through a determinant-based formulation. The resulting system suggests a structured relationship between block interactions and phase behavior in the complex plane. The framework provides a new perspective on the analytic structure of η(s)through interval scaling, phase coupling, and approximate geometric recursion. In particular, the model highlights a special role of the parameter σ=1/2within the interaction structure, emerging from symmetry considerations in the decomposed representation. This work is exploratory in nature and aims to develop a structured analytical model for studying oscillatory behavior in alternating Dirichlet series via block decomposition techniques.
Category: Functions and Analysis

A Conjecture about Primes with Primitive Root 2

Authors: Julian Beauchamp
Comments: 3 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In this paper, we conjecture that a Collatz-like ("if odd/if even") function can be used to test whether a prime number has primitive root 2.
Category: Number Theory

Population Coding: Using Fixed Additive Lattice Group of 2 × 2 Matrices as Data Composite

Authors: Derrick Donkor
Comments: 7 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We introduce a finite, structure-driven framework for neural population coding based on a fixed additive lattice of 2 × 2 matrices. The model defines a predetermined set of sixteen basis matrices whose admissible linear combinations generate stimulus representations in the real number space R. Information encoding is achieved by selecting lattice combinations that maximize entropy, consistent with efficient coding principles. In this proposal, Population coding is formulated as a probabilistic inference problem governed by a Markov state-space model, where transitions occur over lattice states (distinct matrices in the lattice group), as shown in equation (1). Model parameters are inferred via maximum likelihood estimation. Since the compositional structure of the lattice is fixed a priori, the framework decouples population coding computationalcapacity from stringent network connectivity, enabling a fully computable and classical probabilistic formulation of population coding. Beyond the conventional role of population codes as output representations in [11], the proposed population-coded lattice is conceived as a structured input representation for deeplearning architectures, with cross-entropy optimization serving as an objective for pattern classification. This work demonstrates a direct relation between random analog timed-series data and it’s probability encoding, P(si(t)). This work unifies population coding and information theory within a finite matrix-basedframework, offering a computational reinterpretation of neural representation and inference.
Category: Artificial Intelligence

Gravity as an Emergent Average Force from Quark Fields Interactions

Authors: Lucian M. Ionescu
Comments: 11 Pages. Essay submitted to the Gravity Research Foundation contest 2026.

Gravitational force is established as an average force resulting from quark field interactions, specifically functioning as a nuclear spin-spin interaction. This perspective is consistent with the Standard Model quark model of nucleons and the Nuclear Force Lagrangian. It was experimentally verified by Frederick Alzofon and theoretically predicted by a general framework based on the Standard Model. At present, a multitude of researchers have documented, based on experiment, the dependence of the Gravitational constant on the type of material, specifically on the nucleon content of the material’s nuclei. There is a critical need to extend the Stan- dard Model formalism with the appropriate interpretation of Nuclear Force resulting from a quark-to-quark tensorial interaction. By deriving the Gravitational constant as the electric permittivity for nucleon spin-to-nuclear spin polarization effects, we can reformulate the current Quantum Chromodynamics (QCD) framework. This reformulation avoids pointwise premises regarding quarks, operating instead in the spirit of Einstein-Cartan connections with torsion for the Differential Geometry of the frame bundle, as in Einstein-Cartan-Sciama-Kibble Theory, which corresponds directly with Yang-Mills Gauge Theory based solely on the SU(2) gauge group.
Category: Nuclear and Atomic Physics

Se-ReID: Spatially Enhanced Representation Learning for Scalable Person Re-identification

Authors: Xiaohao Xie, Wenhua Jiao
Comments: 10 Pages. (Note by viXra Admin: Author name is required in the article after the article title and please submit article written with AI assistance to ai.viXra.org)

Person Re-Identification (ReID) struggles with discriminative feature learning due to extreme intra-class variance and ambiguous boundary samples. Existing metric losses are often constrained by local mini-batch mining or rigid distance margins that ignore contextual data structures. To address these issues, we propose Se-ReID, a unified framework that enhances feature space representation through instance-level and centroid-level innovations. At the instance level, we introduce TriHard+ Loss with dynamic routing to prevent manifold collapse, alongside an alternative TriWeight Loss utilizing hard-adapted soft weighting to preserve dense intra-class structures. At the centroid level, we propose CentroidM Loss, which leverages learnable global proxies to transcend mini-batch limitations and effectively soften inter-class boundaries. These core metric modules are further supported by 1st & 2nd order mask techniques to eliminate sampling bias, and a streamlined cross-camera centroid retrieval strategy to filter gallery noise. Extensive experiments demonstrate that Se-ReID achieves remarkable performance on standard benchmarks (Market1501 and DukeMTMC-ReID) without relying on ReRank. Notably, it yields state-of-the-art (SOTA) results when integrated with the SOLIDER Transformer baseline, confirming its robust effectiveness and broad applicability across diverse architectures.improvements on MNIST. The code will be released.
Category: Artificial Intelligence

A Moment Framework for the Riemann Hypothesis

Authors: Payam Danesh
Comments: 17 Pages. (Note by viXra Admin: For the last time, please submit article written with ANY AI assistance to ai.viXra.org!)

The Riemann Hypothesis remains one of the deepest open problems in mathematics because it connects the hidden geometry of complex zeros with the distribution of prime numbers. This paper develops a structured analytic framework that transfers the problem from its usual complex form into a real-variable setting where the desired zero structure can be studied through positivity. The central idea is to work with the completed zeta function after normalization and transformation, and to identify a precise positivity principle that would force the corresponding zeros into the correct location. The framework reduces the problem to a compact moment condition for the central logarithmic coefficients of the normalized completed function. This condition is then connected with complete Bernstein functions, Stieltjes functions, Hankel positivity, finite-difference inequalities, and an equivalent logarithmic integral representation. Each step is formulated as a rigorous implication, so the remaining difficulty is isolated in one concrete positivity theorem rather than hidden inside formal manipulation. The approach is designed to avoid the common weaknesses of many proposedarguments for the Riemann Hypothesis. It does not use the Euler product outside its valid region, does not infer the result from symmetry alone, does not replace the original zeta function with a modified object, and does not rely on numerical evidence as proof. Instead, it gives a connected chain from central derivative positivity to a Stieltjes logarithmic derivative, from there to a negative-real-axis zero structure, and finally back to the critical-line statement. The paper does not claim a completed proof of the Riemann Hypothesis. Its contribution is a clean reduction that identifies a single remaining positivity problem in a form suitable for rigorous verification. This gives a clear and testable route for future work, with finite conditions that can be studied through moment theory, operator theory, and the analytic theory of special functions.
Category: Number Theory

Finite Product Limits for Elementary and Gamma Functions

Authors: Edigles Guedes
Comments: 22 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 series of novel finite product limit representations for several fundamental functions: power function, gamma function and reciprocal gamma function.
Category: Functions and Analysis

General Formula Solution for Quintic Equations

Authors: Zhi Li, Hua Li
Comments: 10 Pages.

This paper discovers and proves the existence of a general, non-radical-based formulaic solution for the general quintic equation with complex coefficients. The method involves transforming the general form of the equation into a formulaically solvable form—referred to herein as standard form— given by x^5−px+ 1 = 0 , where p is an arbitrary complex number. When the modulus of p satisfies |p|≥1.65, the solution is derived using a series expansion involving negative integer powers with its coefficients of an integral series; conversely, when |p|< 1.65 , a series expansion involving positive powers with its coefficients of a fractional series is employed. These two approaches form a complete and logically closed loop. This method is purely algebraic in nature, requiring neither root searching nor iterative procedures. Furthermore, since any general quintic equation with complex coefficients can invariably be transformed into this standard form, the proposed method possesses universal applicability. Numerical results demonstrate that the method presented in this paper is highly practical and easy to implement.
Category: General Mathematics

Refactoring the Periodic Table: A Deterministic Derivation of the Complete Atomic Mass Registry from Superfluid Vacuum Mechanics

Authors: Claude Pellerin
Comments: 7 Pages. EPJA-108887, Zenodo-10.5281.20200833 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

While the standard shell model of the nucleus relies on highly complex, semi-empirical fitting parameters to estimate nuclear binding energies, the Hydrodynamic Vacuum Framework (HVF) approaches the nuclear landscape from a perspective of pure continuum fluid mechanics. In this paper, we report a remarkable empirical convergence: the masses of all 119 elements across the periodic table can be derived deterministically from a single, unified continuum expression representing the hydraulic interaction of nucleons with a superfluid substrate plenum. This single-equation continuum architecture evaluates continuously across all synthesized elements, matching the experimental AME2020 mass database from Hydrogen (Z=1) through to the predictive boundary horizon of Ununennium (Z=119) with a highly robust global average residual profile of -1.66%
Category: Nuclear and Atomic Physics

The Mistaken Assumption of a Lorentzian Spacetime Manifold in Quantum Gravity

Authors: René Friedrich
Comments: 4 Pages.

Current theories of quantum gravity are based on the assumption of a Lorentzian (pseudo-Riemannian) spacetime manifold. However, incredibly, this assumption proves to be a 100-year-old optical illusion, an impossible object: Light rays and light cones in a spacetime manifold confirm its Euclidean metric, because if it were Lorentzian, the length of lightlike phenomena would be reduced to zero. Starting from the observer-dependent Euclidean spacetime, the invariant Lorentzian metric may be retrieved by calculation, however, the Lorentzian metric does not in any way parameterize the spacetime manifold, but only its worldlines and fields. - These concerns have been known informally for nearly ten years (viXra:1612.0056), but they have been disregarded by official research. As a non-physicist, the author argues that the assumption of Lorentzian spacetime manifold should be reviewed by professional physicists on the basis of the objections raised, because in case of their confirmation, this could possibly pave the way to quantum gravity.
Category: Relativity and Cosmology

The Lonely Runner Conjecture: A Trivial Construction and a Geometric Model

Authors: Bin Zhang
Comments: 8 Pages.

The Lonely Runner Conjecture states that if n runners with distinct speeds start at the same point on a unit circle, each runner will be at least 1/n away from the others at some moment. This paper provides a novel constructive analysis framework for this conjecture. We first propose the concept of a "trivial construction" — a speed configuration scheme where all non-zero runner speeds form an arithmetic progression. Using the Pigeonhole Principle, we rigorously prove that for any given threshold 1/n, this trivial construction only requires n+1 runners to ensure that the designated runner is never lonely. Furthermore, through Galilean relative transformations, this result is extended to a situation where all runners are never lonely, proving that the effectiveness of this construction remains valid after multiplying each numerator by any positive rational number. Based on this construction, we introduce a "Time-Position" geometric model, mapping the runner's motion onto a polyline on a plane. By combining features such as constant slope, speed, and the seamless splicing of the region covering the threshold curves, this model intuitively demonstrates the uniqueness and optimality of the trivial construction among all geometric configurations. It provides a solid foundation for rigorously proving that n runners must be lonely. This paper does not prove the original conjecture but provides rigorous results under specific speed configurations.
Category: Number Theory

Twin Paradox with Symmetric Acceleration

Authors: Yannan Yang
Comments: 4 Pages.

Conventional treatments of the twin paradox in special relativity typically employ an asymmetric setup: one twin at rest in an inertial frame, the other twin undergoing accelerated space travel. The standard resolution attributes the younger age of the traveling twin to the breaking of inertial symmetry via acceleration, often invoking general relativity for a complete account. This paper presents a modified thought experiment in which both twins execute symmetric, oppositely directed relativistic journeys with identical acceleration profiles. We show that the paradox persists even under full general—relativistic treatment, because acceleration effects remain symmetric. Furthermore, we introduce a gedanken experiment involving rod—clocks with lengths perpendicular to the direction of relative motion, linking time dilation to transverse length observation. This configuration yields an independent, logically irreconcilable contradiction: each observer must simultaneously judge the other’s clock as longer and capable of leaving a physical scratch, creating an unambiguous inconsistency that cannot be eliminated by frame transformations.
Category: Relativity and Cosmology

Periodic Table of Prime Number Intervals: A Systems Approach

Authors: Viktor Strohm
Comments: 8 Pages.

In accordance with the general systems theory of Yu.A. Urmantsev, systems of objects are constructed on the set of prime numbers. The relation between objects is taken as the difference of primes. Each prime number (except the first and the last) is assigned two normalized intervals: the left interval — the difference with the previous prime divided by 2, and the right interval — the difference with the next prime also divided by 2. The third coordinate (sequential number) records the multiplicity of a given combination of intervals. A three dimensional array is obtained, whose projection onto the plane (x, y) reveals a strict periodicity: in the table of residues modulo 6, cells with equal non zero residues (x mod 3, y mod 3) are empty, while the remaining cells contain only 1 or 5. A lemma is proved that explains these regularities. It is shown that the systematisation does not provide a deterministic algorithm for finding the next prime, yet it reveals deep structural constraints.
Category: Number Theory

Probabilistic Performance Profiling for Non-Deterministic Agentic AI Systems

Authors: Raghavendra Venkateshappa
Comments: 16 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Non-deterministic agentic AI systems present fundamental challenges for traditional performance testing methodologies that rely on deterministic metrics and reproducible measurements. We propose a novel probabilistic performance profiling framework that models agent performance as probability distributions rather than point estimates. Our approach leverages Monte Carlo sampling to generate comprehensive performance distribution profiles across diverse execution contexts, while employing Bayesian inference for continuous model refinement based on observed system behavior. The framework provides confidence intervals, performance bounds, and probabilistic guarantees that enable robust decision-making under uncertainty. Extensive evaluation on multiple agent frameworks demonstrates that our approach captures performance variability more accurately than traditional methods, providing 95% confidence intervals with mean absolute errors below 8% across different task complexities. This work establishes the foundational framework for probabilistic performance assessment in agentic systems, enabling more reliable deployment and monitoring of non-deterministic AI agents.
Category: Artificial Intelligence

An Inconsistency in Birkhoff's Theorem re Spherical Shells

Authors: Jeff Sorensen
Comments: 7 Pages.

According to Birkhoff's theorem the interior and exterior vacuum intervals for a spherically symmetric shell are the flat Minkowski metric and the static Schwarzschild solution respectively. Although these results are generally accepted individually, they should be considered in conjunction with each other. Here we examine the junction of the interior and exterior vacuum intervals across a thin spherical shell. The results show Birkhoff's theorem is not self consistent. The interior interval cannot be the Minkowski metric and, for a non-static shell, the overall solution cannot be static. As such, Birkhoff's theorem should not be relied upon as a basis for determining the properties of a given space-time.
Category: Relativity and Cosmology

Structural Link Between Sophie Germain Numbers and Triangular Numbers

Authors: Jean-Yves Boulay
Comments: 6 Pages.

This work highlights a simple yet remarkably overlooked connection between the arithmetic structure underlying Sophie Germain numbers and the classical theory of triangular numbers. Although these two notions arise in distinct contexts, one in the study of prime constellations, the other in figurate number theory, they share a common algebraic backbone that becomes explicit once one examines the product x(2x + 1) arising from the transformation mapping x to (2x + 1).
Category: Number Theory

Integral Reduction Formulas Enhanced With a TI84

Authors: Timothy Jones
Comments: 4 Pages.

The TI84 has both a definite integral function and a recursive list generator. We explore whether the combination can be used to solve single and double integral problems that reference recursive formulas for integral evaluations.
Category: General Mathematics

Einstein-Cartan Cosmology and the Matter Kinematic Dipole Anomaly

Authors: Davor Palle
Comments: 8 Pages.

The recent precise measurements of the kinematic dipole of radio galaxies and quasarsreveal that its magnitude is much larger than the CMB dipole and the expectationfrom the standard LCDM cosmological model.We show that the Einstein-Cartan cosmology predicts the matter dipole in accordancewith the observations. The reason for the discrepancy between the predictions ofthe LCDM model based on the General Relativity and the Einstein-Cartan cosmologylies on the fact that the massless CMB photons, unlike the massive CDM, baryonsand light neutrinos consisting the matter of the Universe, do not couple to torsionof spacetime.
Category: Relativity and Cosmology

On the Cauchy Problem for the Harmonic Oscillator Equation

Authors: Igor Shchitov
Comments: 4 Pages.

The article proves that the solution to the Cauchy problem for the harmonic oscillator equation is not unique, and can have the most unusual properties.
Category: Mathematical Physics

Some New Collatz-like Sequences: If Odd Add d, if Even Divide by 2

Authors: Julian Beauchamp
Comments: 4 Pages. (Note by viXra Admin: Author name is required in the article; please cite and list scientific references)

In this paper, we describe what seems to be a new Collatz-like ("if odd/if even") function, and propose some related conjectures. For any arbitrary positive number, x, iterative operations can be made such that, when even, x is divided by two, and when odd, it is added to odd integer, d. It appears that when x = 1, after sufficient iterations, the sequence always reaches 1, creating a loop. The iterative function can be stated as follows: f(x) = x/2 if x is even, x+d if x is odd.
Category: Number Theory

Relative Set Theory: Definitions of Finite and Infinite Sets

Authors: Wenjie Wu
Comments: 18 Pages. In Chinese (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In response to Russell's Paradox, which arises from the a priori assumption of actual infinity and the unrestricted comprehension principle in classical set theory, this paper proposes a novel foundational framework: Relative Set Theory. Taking the concept of potential infinity as its ontological core, this theory strictly defines finite sets from the bottom up based on the dynamic generation logic of determined elements, and abolishes the absolute universal set to eradicate the logical root of the paradox. On this basis, the paper innovatively and uniformly defines an infinite set as the "limit of a strictly increasing sequence of finite sets," pointing out that static infinity divorced from a specific evolutionary process lacks logical validity. By introducing an algebra of relative magnitudes benchmarked against the standard sequence of natural numbers, this theory establishes the "principle of relativity" for infinite metrics, revealing that the size of an infinite set is essentially equivalent to the asymptotic growth rate of its generating sequence. This framework not only resolves the counterintuitive dilemmas of classical equipotence theory at the algebraic level but also provides a rigorous and self-consistent relativistic new paradigm for fundamentally circumventing the third foundational crisis of mathematics and re-examining the concept of infinity in mathematical philosophy.
Category: Set Theory and Logic

Theory of Matrix and Graph Combination ("matregraph")

Authors: Abdoul Kader Adamou
Comments: 96 Pages. In French; Licence: CC BY-SA 4.0 (Note by viXra.org Admin: Please cite listed scientific references)

This new word "matregraph" comes from the combination of two terms already known in the field of mathematics which are: matrix and graph. A "matregraph" is precisely u200bu200ba new mathematical tool with several functions that assemble, rank and perform arithmetical calculations between real numbers (IR) in order to reach to a general result located in the structure of this "matregraph" at the place of n-line and n-column. It’s an algorithm that is able to select some values among a lot of values reducing consequently a long calculation by getting quickly a result. This new theory may be used in many fields such as physics, chemistry, computer science, telecommunications, electricity, cryptography, mechanics, transportation ...etc. Finally, "matregraph" is u200bu200ba mathematical model that is flexible and may help us solve many problems of science and engineering.
Category: General Mathematics

Mechanical, Topological, and Quantum Theory in the Universe of Natural Numbers

Authors: Abdoul Kader Adamou
Comments: 36 Pages. In French; Licence: CC BY-SA 4.0 (Note by viXra.org Admin: Please cite listed scientific references)

Natural numbers used here in mechanics, topology and quantum context is a new branch of modern mathematics whose deep abstraction and revolutionary nature make a great change in our underderstanding of mathematics field’s fundamental knowledge. This new theory applies principles from mechanics, topology and quantum field to natural numbers. It invites us to explore a new type of reasoning where we will use new calculation methods with innovative tools that are useful for mathematical research, particularly for complex open problems and likely useful for other fields of science and technology.
Category: General Mathematics

On Centrifugal Forces and Newton's Third Law of Mechanics

Authors: Antonio León Sánchez
Comments: 2 Pages.

This article presents two brief arguments regarding the reality of centrifugal forces: the first based on Newton’s Third Law of Mechanics, and the second on the Law of Dimensional Homogeneity. As a consequence, either centrifugal forces are real, or both the Law of Action and Reaction and the Law of Dimensional Homogeneity are not universal laws.
Category: Classical Physics

An Observational Study of Localized Optical Intensity Features Under Natural Environmental Conditions

Authors: Yelda Davran
Comments: 7 Pages. 4 figures (Note by viXra Admin: Author name is required in the article after the article title)

Although the particle nature of light has long been established through phenomena such as Compton scattering and double-slit experiments, there are relatively few reports of its direct observability under natural environmental conditions. In this work, we report a novel observational phenomenon suggestive of particle-like behavior of light occurring in a natural outdoor setting. The observations were conducted during the winter of 2020 in Ağrı, Türkiye, at an altitude of 1,640 m and ambient temperatures ranging between −10 °C and −20 °C. During afternoon hours, within deeply shadowed regions formed by surrounding buildings, bright, point-like micro-flashes resembling scattered water droplets were observed impinging on the ground and exhibiting multidirectional dispersion. These features were not detected in areas directly exposed to sunlight. It is suggested that the combination of extreme cold climatic conditions, reduced atmospheric pressure associated with high altitude, dark ground surfaces, and strong shadow—contrast conditions contributes to the enhanced visibility of particle-like optical effects. The observed micro-flashes are interpreted as a phenomenon in which localized light intensity features become macroscopically distinguishable under specific environmental conditions, representing a rare natural observational instance relevant to discussions of the wave—particle duality of light.
Category: Classical Physics

Volume of General Spherical Wedges

Authors: Richard J. Mathar
Comments: 26 pages, including 13 pages of a C++ listing.

A sphere cap is constructed by slicing a sphere with a plane. Slicing a sphere cap again with a second plane splits it into a pair of spherical wedges.This work evaluates spherical wedge volumes, i.e., the triple integrals over essentially the intersection of the two sphere caps established by the two cut planes. The integrals are closed forms of square roots and inverse sines as a function of sphere radius, heights of the sphere caps, and dihedral angle between the cut planes.
Category: Geometry

A Modular Structure Theorem for Goldbach Representations and a Computational Study of Shift-propagating Prime Pairs in the Arithmetic Progression N≡8 (Mod 30)

Authors: Christoper Mututu
Comments: 25 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We study a structural property of Goldbach representations which are expressions of even integers as sums of two primes within two specific arithmetic progressions modulo 30.We prove the following theorem by elementary modular arithmetic alone requiring no unproven hypothesis and no computation.Theorem. Let n≡8 (mod 30) with n≥38. Then every Goldbach pair (p,q) with p+q=n and p,q prime satisfies p≡q≡1 (mod 6). Furthermore, for any n≡28 (mod 30) within n≥28, every Goldbach pair (p,q) of n satisfies p≡q≡2 (mod 3) which forces both p+10 and q+10 to be divisible by 3 and therefore composite.As a consequence, no Goldbach pair of any n≡28 (mod 30) can produce a Goldbach pair of n+10 via the shift (p,q)↦(p+10,q+10).We then investigate the coupled pairs (n,n+20) where n≡8 (mod 30) observing that n+20≡28 (mod 30) always. For such a coupled pair, the shift (p,q)↦(p+10,q+10) maps a Goldbach pair of n to a Goldbach pair of n+20 automatically in terms of the sum since (p+10)+(q+10)=n+20 provided both p+10 and q+10 are prime.We define the shift-propagation count,R(n)=#{p≤n/2 ∶p prime,n-p prime,p+10 prime,n-p+10 prime}and present the following conjecture supported by extensive computation.Conjecture. For every even integer n≡8 (mod 30) with n≥38, we have R(n)≥1. That is, at least one Goldbach pair of n always shifts by +10 to produce a Goldbach pair of n+20.We verify this conjecture computationally for all 33,332 values of n≡8 (mod 30) in the range38≤n≤999,980 finding zero exceptions. The minimum value R(n)=1 occurs only at n=128 across this entire range and the average value of R(n) grows consistently with the scale of n from an average of 2.00 at the smallest values to an average of 197.69 across the full range to 10^6.We present the modular structure theorem with complete proof, state the conjecture precisely and provide full computational verification. We make no claim of proving Goldbach’s conjecture. We propose that this modular structure and the coupled pair phenomenon may serve as a foundation for future analytic work toward Goldbach’s conjecture.
Category: Number Theory

An Elementary Proof of the Infinitude of Twin Primes Based on Interwoven Mersenne Chains

Authors: Defeng Han
Comments: 6 Pages. In Chinese (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper constructs three classes of deeply intertwined recursive sequences for Mersenne primes, encompassing all Mersenne-type core structures of the forms 2p-3, 2p-1, and 2p+3. These three classes of sequences share a common pool of prime exponents and serve as mutual recursive foundations for one another, thereby forming an organically unified recursive network. The derivations are rigorously established by relying on elementary modular arithmetic, Fermat's Little Theorem, and the $6n pm 1$ prime configuration, combined with mathematical induction and the Fundamental Theorem of Arithmetic. The terms of these sequences naturally differ by 2 from their respective "plus-two" counterparts, thereby constituting candidates for twin primes. By demonstrating the super-exponential growth property of this recursive network, the interchange of infinite quantifiers is rigorously executed within an elementary framework; this establishes the existence of a unified steady-state time and, consequently, proves the infinitude of twin primes. Simultaneously, the standard Mersenne recursive chain itself directly generates an infinite number of Mersenne primes, thereby synchronously resolving the conjecture regarding the infinitude of Mersenne primes. The entire process employs exclusively elementary number theory tools—eschewing analytic number theory and advanced sieve methods—and is logically self-consistent, free of logical gaps or leaps, and fully compliant with the axiomatic system of elementary number theory.
Category: Number Theory

Behavior of a Decimal-Parity-Based 3n+1 Mapping

Authors: J. Adnan, S. A. Dar
Comments: 9 Pages. Licensed under CC BY 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In this paper, we investigate and evaluate the Collatz conjecture, traditionally based on positive integers, under a suitable convergence condition in which the numbers converge towards one. In our derivations, we extend the 3n+1 problem to the decimal values via a scaling factor, for showing behaviour of the last decimal digit, either even or odd. Where the numbers diverges to infinity (∞). From which it follows that between zero and one, the sequence diverges such that its limit approaches infinity.
Category: Number Theory

From Rényi Entropy to the Feynman Path Integral

Authors: Ervin Goldfain
Comments: 17 Pages.

In this sequel to [17 - 18], we argue that Rényi Entropy is organically tied to the FeynmanPath Integral formalism of Quantum Field Theory (QFT).
Category: Quantum Physics

Dynamic Gravitational Field and Its Attributes

Authors: Pavlo Danylchenko
Comments: 20 Pages. Updated equations, and references

The correspondence of the parameter b of the Schwarzschild solution of the gravitational field equationsto the square of the relative frequency of electromagnetic interaction of micro-objects of a stationarymatter and its equivalence to the square of the maximum possible (limit) velocity of this matter on asingular surface are substantiated. The error in linking the parameter b with the coordinate velocity oflight of the General Relativity (GR) has been exposed. It has been proven that GR can correspond toreality only if it uses a dynamic gravitational field, which ensures the invariance of the flow of the propertime of matter during its inertial motion, instead of a static one. The necessity of using in physics ofrelativistically invariant Newtonians of the free inert rest energy of matter and Keplerians of the ordinaryrest energy of matter, respectively, instead of relativistically non-invariant Hamiltonians and Lagrangians,has been justified. It has been proven that the thing inherent to the Lorentz transformations is not theredshift, but the blueshift of the frequency of centripetal radiation from matter that is at rest in thepeople’s world and is evolutionarily self-contracting in the frame of references of spatial coordinate andtime comoving with the expanding Universe (CFREU). The suitability of Lorentz transformations for thepeople’s world is justified only for the quasi-equilibrium motion of micro-objects of gradually coolingmatter. Ordinary synchronization-compensation transformations of increments of spatial coordinate andtime (OSCT) are provided. They, unlike Lorentz transformations, allow proportional synchronization ofall clocks moving in a gravitational field by inertia and provide compensation (by the motion by inertia)of the concomitant change in the gravitational deceleration of the flow of time counted by these movingclocks. The redshift of the frequency of radiation from distant galaxies that are at rest in the CFREU isindeed inherent exactly to OSCT. And this is in good agreement not only with relativistically invariantthermodynamics, but also with the equations of the dynamic gravitational field of both the Solar Systemand flat galaxies. Newton’s law of gravity is obtained directly from the condition of no change in the flowof the proper time of matter during its inertial motion in a gravitational field. The fallacy of ignoring thecompensation for comoving changes in gravitational dilation of time by the inertial motion of matter ismost thoroughly substantiated. Based on the analysis of the motion of the planets, the compensation bythe centrifugal pseudo-force of inertia not only of the gravitational pseudo-force, but also of the pseudoforceof evolutionary self-contraction of the matter to the center of gravity is confirmed.
Category: Relativity and Cosmology

Hilbert’s 6th Problem New re-Interpretation

Authors: Payam Danesh, Raoul Bianchetti
Comments: 26 Pages.

The axiomatization of physics, particularly the connection between microscopic dynamics and macroscopic laws, remains a central challenge of Hilbert’s Sixth Problem. A persistent conceptual gap in this program is that probability is typically introduced as a fundamental assumption rather than derived from physical evolution itself. To close this gap, we develop Viscous Time Theory (VTT), an evolutionary framework structured around admissibility, coherence, and recoverability. When paired with an informational action principle, VTT allows probability to emerge naturally as an induced statistical measure over bundles of admissible trajectories. To test this proposed mechanism, we analyze a viscous-time kinetic transport operator, establishing its contraction semigroup structure, spectral gap, and hypocoercive convergence. We then extend the model to nonlinear interaction kernels and evaluate its hydrodynamic scaling limit. The analysis proves that this diffusion-driven operator achieves strict spectral stability, exponential entropy decay, and global nonlinear stability, with the macroscopic scaling limit rigorously yielding nonlinear diffusion dynamics for the coherence density. By providing an analytically tractable layer between microscopic and macroscopic behavior, this work demonstrates how probability, irreversibility, and transport laws can cohesively emerge from informational geometry.
Category: Mathematical Physics

Initial Velocities of Hydrated Ions Under an Electropotential Field, Their Molar Masses, and Total Hydration Numbers

Authors: Ikechukwu Iloh Udema
Comments: 17 Pages. License: CCBY-NC-ND

The inner hydration shell, where water is electrostricted, has always been the main area of study. But it appears that the bulk water, which is affected by the ion electric field, is not given the same degree of attention. This largely theoretical study aims to develop equation-based models that can be used to calculate the initial velocities of ions when an electrical potential gradient is applied, as well as the total number of water molecules pulled to the ions and their molar masses (including the mass of the electrostricted water). Theoretical and computational approaches were employed to analyze literature-based data. The initial velocity was approximately 3.8 exp. (—8) m/s for cobalt ions and 26 exp. (—8) m/s for oxonium ions. The equivalent total hydration number ranged from 4 for oxonium ions to 60 for cobalt ions. Initial velocities ranged from 1.65 exp. (—8) m/s for epinephrine to 2.88 exp. (—8) m/s for glycinate, and the corresponding total hydration number ranged from 38 for glycinate to 64 for epinephrine. The molar masses of the hydrated ions ranged from 765 g/mol for glycinate to 1,333 g/mol for epinephrine and from 85.81 g/mol for oxonium ions to 1,137.8 g/mol for cobalt ions. The trajectory and biological function of biomolecules can be impacted by their hydrated mass. The lowest and highest velocities are associated with the highest and lowest total hydration numbers per unit charge. Future research could focus on determining the electrophoretic mobilities of all physiologically active biomolecules at physiological pH and body temperature.
Category: Condensed Matter

The Vortex of Consciousness: The Physical Origin of Subjective Experience

Authors: Zhaole Sun
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

How neural activity generates subjective experience—the "hard problem" of consciousness—remains unresolved [1]. This paper proposes the Consciousness Flow Vortex Model Hypothesis(CFVM-H), positing that subjective experience arises from vortex dynamics formed by closedrecursive structures in the thalamocortical loop. This vortex exhibits three core characteristics:closed-loop circulation, vortex core focusing, and global synchronization. These featuresdirectly map to three fundamental elements of subjective experience: self-boundary, firstperson perspective, and a unified field of sensation. CFVM-H provides a testable, physicsbased framework for the "hard problem" of consciousness, defining subjective experience asan inevitable product of vortex structure rather than a mysterious emergent property
Category: General Science and Philosophy

The Classical Electromagnetic Standing Wave Model of the Electron: Energy Self-Consistency and Implications for the Mass—Energy Relation

Authors: Chunshu Li
Comments: 5 Pages.

Within the framework of classical electrodynamics, a spherical electromagnetic standing-wave model is constructed. Based on Maxwell equations in vacuum, the lowest-order transverse electric (TE) mode with l=1 in spherical coordinates is adopted, and the half-wave standing-wave condition kru2091=π is imposed as the geometric constraint. Integrating the electromagnetic energy density over the whole domain yields a total field energy exactly equal to the electron rest energy, with the ratio precisely 1.000000. The model gives the fine-structure constant α=ru2091/λc=0.00729735 from geometric relations, consistent with experimental values. No free parameters are introduced; the derivation relies entirely on classical electromagnetic theory. The results show that a self-confined, localized field configuration exists in the solution space of classical electrodynamics, whose numerical characteristics match the known properties of the electron with high fidelity.
Category: Mathematical Physics

Emergent Spacetime and Protomatter from Ollivier-Ricci Flow with Discrete Cartan Torsion

Authors: Fabrizio Vassallo
Comments: 38 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a discrete geometric model in which classical spacetime and matter emerge from a discrete random network equipped with two combinatorial structures: Ollivier-Ricci curvature (ORC), a metric-free notion of curvature defined via optimal transport on the network, and discrete Cartan torsion, a 2-cochain on a weighted simplicial complex measuring holonomy defects of parallel transport around elementary triangles. Both structures are intrinsically combinatorial and require no background geometry; classical geometry is an output, not an input, of the model. Building on Trugenberger's ORC-based network model, which exhibits a phase transition between a random hyperbolic phase and a geometric phase, we augment the Ricci flow with a nonlinear torsion coupling and demonstrate, in an explicit four-node toy model, that the resulting dynamical system possesses two distinct basins of attraction whose separation is topologically robust and independent of the specific toy model chosen. Regions of the network with vanishing torsion condense into a one-dimensional geometric phase (embryonic spacetime), while regions with non-vanishing torsion condense into a localized, topologically non-trivial configuration identified as a torsion defect carrying all quantum numbers equal to zero. A key structural result is that the torsion-bearing fixed point P T is a saddle point of the linearized discrete flow, with one expanding and one contracting direction in the (w, T) plane. The Jacobian entry J T w = 8λ/9 > 0 is derived exactly from the Wasserstein optimal transport, yielding real eigenvalues µ = 1 ± 8λη sech 2 (T *)/9 and a determinant det(J) = 1 − (8λη/9) sech 2 (T *) < 1. We conjecture-as a structural analogy motivated by the geometry of Einstein-Cartan theory, but not derivable from the linearized dynamics-that this fixed point is geometrically associated with the parametrization of the Cartan helix. This conjecture motivates, but does not rigorously imply, the hierarchical level model introduced in Section 7, in which the rotation angle and expansion factor of the helix are tentatively associated with spin halving and mass scaling between levels. We further propose a hierarchical particle spectrum-the level model-in which each level is characterized by doubled spacetime dimension, halved spin, and mass scaling by a factor 4α, where α is the 1 electromagnetic fine-structure constant and δ F ≈ 4.6692 is the Feigenbaum period-doubling constant. The conservative flow has a saddle-like structure at P T and cannot produce a Feigenbaum period-doubling cascade. We introduce a physically motivated dissipative extension of the torsion equation-a −ξ sin(T) restoring term-and show that the resulting effective torsion dynamics reduces, in the strongly dissipative limit, to the sine mapT → ξ sin(T) on [0, π], which belongs to the Feigenbaum universality class. The Feigenbaum constant δ F ≈ 4.6692 therefore emerges dynamically from the flow, and the empirical relation α ≈ 1/(2πδ 2 F) is found to be numerically consistent with this scaling, with the factor 2/π from the sine map amplitude. The physical origin of the dissipation is the geometric coarse-graining at each RG step: information is globally conserved, but the geometric distinguishabil-ity of sub-Planckian torsion configurations is reduced, creating equivalence classes in the sense of 't Hooft's dissipative quantum gravity program [82]. Our results and 't Hooft's program converge toward the same conceptual conclusion by independent routes: quantum-mechanical behavior can emerge from an effectively dissipative underlying structure, with information globally conserved. The continuum limit of the full construction is argued to reproduce Einstein-Cartan gravity in four dimensions. Falsifiable numerical predictions are formulated for simulation on synthetic networks.
Category: High Energy Particle Physics

Problems with Nontrivial Symmetrizations of Hamiltonian Operators

Authors: Jouni Puuronen
Comments: 11 Pages.

We discover an example of an infinite collection of simple quantum systems that all have the same classical limit, and recognize this as a problem, because the correct quantization of the example classical system is then not known. Our example contradicts Born-Jordan quantization theory, meaning that at least other one must contain a mistake. We discuss the related possible difficulties with the quantum mechanical description of a charged particle in a magnetic field, but eventually conclude that these difficulties maybe are not so severe after all.
Category: Quantum Physics

Analysis of Solution of Equations for Magnetic Field of Rotating Ball Using Polynomials

Authors: Sergey G. Fedosin
Comments: 62 Pages.

The exact form of the solution for the vector potential and magnetic field of a rotating uniformly charged ball is explicitly found. Expressions for specific vector spherical polynomials associated with the corresponding components of the potential are used to represent the solution. Inside and outside a charged ball uniformly rotating around its axis, the components of the potential and magnetic field are determined up to terms containing the sixth power of the speed of light in the denominator. To do this, it was necessary to use spherical coordinates and eight polynomials of each type. In addition, the solutions inside and outside the ball were equated to each other on the surface of the ball, taking into account the symmetry of the ball. The accuracy of the approach used can be increased, since it is determined only by the number of polynomials used, whose contribution to solutions decreases rapidly as the degree of the polynomials increases. To calculate the vector potential and magnetic field of a rotating ball within the framework of special relativity, it is sufficient to substitute the coordinates of the observation point, the invariant volumetric charge density, the angular velocity of rotation and the radius of the ball into the formulas.
Category: Classical Physics

A Simple 2 X 2 Neural Network with Linear Algebra, by Hand

Authors: Han de Bruijn
Comments: 5 Pages.

An extremely simple single-layer feedforward 2 x 2 neural network is the subject of this article. Because I feel it is important to understand some essential features of neural networks without the help of a computer. The network at hand can be completely described, mathematically, by elementary linear algebra. A working example with two inputs and one output is leading to the general case. A counter example with two outputs instead of one is presented as well. It is concluded that the network with one output has learning capability and the network with two outputs has not. The behaviour of the first network can be formulated in geometric terms: all points on a straight line through two given points in the input plane give the desired output. There are no other inputs that do the job. The network with two outputs, on the contrary, is not able to make any generalization. It does not learn from experience, so to speak. It's kind of surprising that the more intelligent network is characterized by a singular matrix, and the dumber network by a regular matrix of weights.
Category: Artificial Intelligence

Much Ado About Nothing When it Comes to Fractional Energy Levels: is Coulomb Law in Conflict?

Authors: Udema Ikechukwu Iloh
Comments: 14 Pages. License: CCBY-NC-ND

From a theoretical viewpoint, this investigation examined fractional energy levels and velocities that surpass the speed of light in a vacuum. These phenomena have received limited attention. Using a classical framework, the study aims to validate these phenomena by computing relevant parameters using fundamental constants and their multiples in derived equations. The presence of fractional energy levels and superluminal velocities (SVs) is validated within a classical framework aligned with the mass-energy equivalence principle. SVs are directly proportional to the masses of fundamental and baryonic particles when the first energy level is set to one. Conversely, if a constant luminal velocity is considered, the irrational energy levels (n_i) are proportional to the square of the particles' masses. For example, the values for the proton and the top quark are 3.022436467 exp. (+8) and 556.3297886 exp. (+8) m/s, respectively. The corresponding energy levels are 1.0164718078 and 34,436.83251, respectively. With the first atomic energy level, the energy levels are equal to the corresponding atomic numbers. For each atomic number, the fractional energy levels are inversely related to the subluminal kinetic energy. From Z=1 to Z=4, however, the energy levels showed an increasing trend. Even though the classical theoretical framework considers the distance between two centers of mass, determining the mass radius of the proton remains a possibility at specific fractional energy levels for certain atomic numbers. Future research may explore achieving the proton's mass radius at higher atomic numbers and lower fractional energy levels (below 0.1).
Category: Nuclear and Atomic Physics

SignaVision (Sign Language Interpreter)

Authors: Aashraya Man Singh, Bhuvanesh S, Tanikanti Dinesh Babu
Comments: 5 Pages.

This report presents the design and implementation of a real-time American Sign Language (ASL) recognition system using computer vision and deep learning techniques. We use MediaPipe for hand landmark detection, OpenCV for image pre-processing and a Convolution Neural Network (CNN) for gesture classification. The system provides a solution to bridge the communication gap between sign language users and non-signers by converting hand gestures into text and speech output in an accessible and affordable way.The project presents a lightweight webcam-based solution that does not require any specialized hardware like sensor gloves or depth cameras. The system uses skeletal hand landmark rendering to improve robustness and accuracy, reducing the effect of background noise and lighting changes. Experiments show that the method has high recognition accuracy and efficient real-time performance, which makes it applicable to practical applications such as educational support, assistive communication, and public service interaction. This work showcases the promise of the integration of artificial intelligence, computer vision and human-computer interaction technologies for the development of scalable and inclusive communication systems. The report also discusses system limitations and future enhancements, including dynamic gesture recognition, sentence-level translation, and deployment on mobile and embedded platforms.
Category: Digital Signal Processing

Longitudinally Polarized Same-Sign W Boson Pairs Scattering and Noncontractibility of the Physical Space

Authors: Davor Palle
Comments: 8 Pages.

The production of the longitudinally polarized same-sign W boson pairs at the LHCpp collisions presents the unique opportunity to study and verify in detail the mechanism ofthe symmetry breaking in the Standard Model and beyond.We compare at leading order the electroweak contribution to this productionin the Standard Model and in the theory of the noncontractible space containing the zero-normmassless zeta particle. It appears that the difference between differential cross sectionsis huge with the possibility to measure it in Run 3 and high-luminosity runs of the LHC.
Category: High Energy Particle Physics

On the Nature of the Superfluid Phase in Liquid He4

Authors: Alekseenko Viktor Viktorovich
Comments: 14 Pages.

A hypothesis on the physical nature of the superfluid phase in liquid helium is presented. It is shown that atomic delocalization is possible only along one coordinate, rather than along three, as is currently accepted in classical concepts of helium's transition to a superfluid state. Filamentous coherent states of atoms form the basis of the superfluid component of liquid helium. The hypothesis is supported by the justification of the critical velocity during rotation of cylindrical vessels and thermodynamic calculations.
Category: Condensed Matter

An Alternative to Light's Limiting Speed

Authors: Ken Gonder
Comments: 10 Pages, 1 Diagram

Another perplexing dilemma in special relativity has recently emerged. Under ordinary conditions, multiple objects/reference frames with different relative motion would cause an unresolvable conflict in their motion-created mass. This article elaborates on the finding, suggesting an explanation for the disparity while providing a realistic resolution.
Category: Relativity and Cosmology

The Speed Limit for a Rotating Object

Authors: Yannan Yang
Comments: 4 Pages.

This paper presents a new kinematic analysis of relativistic rotating objects within the framework of special relativity. By examining the Lorentz contraction of concentric circumferences on a spinning disk, we show that when the edge speed approaches the speed of light, the outer circumference may paradoxically become shorter than the inner one. To eliminate this geometric inconsistency, we derive a strict upper speed limit for rotating bodies: the linear velocity of any point must not exceed the speed of light divided by the square root of 2. This constraint arises purely from special relativistic kinematics, independent of material strength or mechanical properties, offering a novel resolution to the Ehrenfest paradox complementary to existing approaches.
Category: Relativity and Cosmology

On Gravitational Binding Energy Evaluation

Authors: Nicolas Poupart
Comments: 19 Pages.

We develop a hierarchical formulation for evaluating gravitational binding energy from the internal organization of matter, volume conservation, and mass--energy equivalence. Rather than relying only on pairwise interaction terms defined relative to infinity, the proposed estimator assigns an intrinsic energy scale to compact configurations of matter. We then test whether the corresponding mass-equivalent contribution can reproduce the effective dark mass inferred in galaxies.We test this formulation using SPARC rotation-curve data together with independent GALEX and SDSS photometric observations. Stellar population mixtures are reconstructed from dynamical information alone, without using photometric data as input, and are then used to predict integrated galaxy colors. The resulting colors show significant correlations with observations, indicating that the reconstructed populations encode non-trivial information about stellar structure.A systematic exploration of the estimator reveals structured regions of high-quality solutions in parameter space. In particular, the results favor a hierarchical recursive interpretation in which class-level binding energies are preserved, while the binding energy associated with the global aggregation of heterogeneous stellar classes may contribute with an effective virial factor. The dynamical reconstruction varies only weakly across a broad range of parameters, whereas the photometric constraints provide greater discrimination between candidate forms.These results suggest that gravitational binding energy provides a physically motivated contribution to the effective dark mass inferred in galaxies, while also explaining why dynamical information can encode stellar population structure.
Category: Astrophysics

Asymptotic Regularization of Poles and Closed-Form Generalization for Arithmetic Progressions in the Gamma Function

Authors: Julinho Jorge Luís
Comments: 25 Pages.

This paper proposes a novel analytical framework for the Gamma and Factorial functions, extending their consistent application beyond the domain of positive real numbers. Traditionally, these functions encounter singularities (poles) at non-positive integers, limiting their continuity. Through an asymptotic regularization method, this work demonstrates that the ratio of Gamma functions can yield finite and unique values at these critical points, effectively bypassing traditional meromorphic constraints.The core contribution is the derivation of a universal closed-form formula for the product of arithmetic progressions, valid across the entire real line without the need for manual domain adjustments. Furthermore, the concept of a "Rising Gamma Function" ($check{Gamma}$) is introduced as a dual operator. By establishing the zero point as an inversion axis, a functional symmetry is revealed, integrating the properties of the function into a complete and continuous structure. This approach provides new insights into analytical continuity and simplifies calculations in complex analysis and number theory.Keywords: Gamma Function, Factorial, Asymptotic Regularization, Arithmetic Progressions, Functional Symmetry, Analytical Continuity.
Category: Functions and Analysis

An Identity with Symmetry in Basic Hypergeometric Series and Its Applications

Authors: Edigles Bezerra Guedes
Comments: 4 Pages. (Note by viXra.org Admin: Please cite listed scientific references)

This paper determines a symmetry relation between basic hypergeometric series that has escaped the scrutiny of other mathematicians.As a direct application of this identity,we derive a double-sum symmetry and present a particular case as an exercise. Theseresults contribute to the understanding of hidden symmetries in ��-series. Moreover, it may be useful in the study of basic hypergeometricfunctions and ��-analogues of special functions.
Category: Number Theory

Mathematical Description of the Oscillations of the Radius Difference Modulus at Symmetrical Orbital Points

Authors: Viktor Strohm
Comments: 11 Pages.

The provided materials demonstrate an empirical study (Figs. 1-12) identifying mysterious "envelope waves" through the analysis of distance differences at symmetrical points of planetary orbits. Additionally, a rigorous kinematic apparatus [2] has been developed to derive a force law applicable not only to closed ellipses but also to precessing orbits (rosettes).Using the kinematic apparatus from work [2], we can construct a mathematical description of the observed oscillations. The key idea is that the envelope wave in the graphs is a direct consequence of orbital precession, "decomposed" through an original methodology of symmetrical differences.
Category: Astrophysics

Horizons in a 3D Alternative and Symmetric Natario Warp Drive Vector Using the Adm-MTW-Alcubierre Formalism

Authors: Fernando Loup
Comments: 96 Pages. complements the developments in viXra:2509.0064

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than lightpredated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates but remember that a real warp drive must accelerate or de-accelerate in order to beaccepted as a physical valid model so it must possesses variable speeds.We developed the extension for a symmetric alternative warpdrive vector that encompasses variable speeds. Also Polar Coordinates uses only two dimensions and we know that a real spaceship is a 3D object inserted inside a 3D warp bubble that must be defined in real 3D Spherical Coordinates.In this work we present the alternative warp drive vector in 3D Spherical Coordinates for variable speeds.One the major drawbacks concerningwarp drives is the problem of the Horizons (causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble. The behavior of a photon sent to the front of the warp bubble in the case of the alternative warp drive with variable velocity and a lapse function is also one of the main purposes of this work. We present the behavior of a photon sent to the front of the bubblein the alternative warp drive in the 3+1 spacetimes with the lapse function using quadratic forms and the null-like geodesicsds^2=0 of General Relativity and theADM (Arnowitt-Dresner-Misner) formalism equations with the approach of MTW(Misner-Thorne-Wheeler) and Alcubierre.
Category: Relativity and Cosmology

A Complete Proof of the Rational Distance Problem for the Unit Square

Authors: Song Li
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper studies the following classical geometric problem: does there exist a point inside the unit square whose distances to all four vertices are rational? We first prove that if such a point exists, its coordinates must be rational. Through a scaling transformation, the original problem is equivalently reduced to a Diophantine problem involving an integer square with integer coordinates and integer distances. Based on the parity alignment of common legs, we discuss three cases and derive contradictions using the parameterization of primitive Pythagorean triples and parity analysis. Combined with known results for boundary cases, we prove that no such point exists inside the unit square.
Category: Number Theory

The Scholz Conjecture is True for 2^n-1 for Almost All N

Authors: Theophilus Agama
Comments: 9 Pages.

An addition chain of length h that leads to a number n is a sequence of positive integers s_0 = 1, s_1 = 2,. .. , s_h = n such that s_i = s_j + s_k (i > j ≥ k) for each 1 ≤ i ≤ h. A Brauer addition chain is the one where j = i − 1 for each 1 ≤ i ≤ h. Let l(·) and l* (·) denote the minimal length of an addition chain and the Brauer addition chain, respectively, that leads to an integer ·. Applying probabilistic methods to the iterated factor method, we show that l(2^n − 1) ≤ n − 1 + l(n) for almost all positive integers n as n −→ ∞.
Category: Number Theory

An Average Loneliness Gap of 1/n Can Allow a Minimum Loneliness Gap of 1/(2n)

Authors: Deepak Ponvel Chermakani
Comments: 6 Pages. 7 Theorems and 2 Algorithms

Consider n runners R0, R1, ... Rn-1, with distinct constant integer speeds S0, S1, ... Sn-1 respectively, where S0=0, running around the circumference of a circle of unit circumferential length from arbitrary starting points at time t=0. At time t, denote gi(t) be the minimum absolute distance along the circumference of Ri from R0. We first use aresult on prime numbers to obtain special cases of runners speeds, for which the Lonely Runner Conjecture (LRC) is true. We then develop an approach to the LRC that derives a time at which, some subset of the runners is placed at the extremities of arcs of sectors ensuring implicit separation from R0, while the remaining runners are directly separated from R0. We use this approach to show that in the general case for large n, there exists a time T at which, gi(T) > 1/(2n) for all integers i in [1,n-1], and (g1(T) + g2(T) + ... + gn-1(T))/(n-1) tends to 1/n.
Category: Number Theory

The Theory of Observational Relativity Serial Report 5: Is the Big Bang a Theory in Scientific Sense?

Authors: Xiaogang Ruan
Comments: 31 Pages.

The theory of Observational Relativity (OR), as a new theory of physics, reports its significant findings and new insights in the form of serial reports in F1000Research. Now, OR Serial Report 5 focuses on the Big Bang theory of modern cosmology. Human beings always believe that the universe was bestowed by the Creator: no matter time or space must have a starting point. So, cosmologists have invented the Big Bang model: the universe that human beings rely on for survival originated from a Big Bang 13.8 billion years ago. Einstein's theory of relativity is the most important theoretical basis of modern cosmology, and the invariance of light speed and the doctrine of spacetime curvature play important roles in the Big Bang theory. The Big Bang theory is not only a product of logical deduction and mathematical formulization, but also has empirical evidences such as cosmic expansion and cosmic microwave background radiation. However, the theory of OR has discovered that the speed of light is not really invariant, and spacetime is not really curved. From the broad perspective of the general observational agent, the theory of OR has clarified that Einstein's theory of relativity, including the special and the general, is that of optical observation adopting the optical agent, which has the observational locality, presenting us with only optical images of the physical world and not representing the objectively physical world. The doctrine of Big Bang, or even the entire modern cosmology, is only a mirage based on such optical images. Since the speed of light is not really invariant, the doctrine of spacetime curvature, the doctrine of cosmic expansion, and Einstein's theory of relativity, including the special and the general, cannot hold true. Can the Big Bang theory still hold up without Einstein's theory of relativity as the theoretical basis? Can the Big Bang theory still hold up without Hubble's doctrine of cosmic expansion as the empirical basis? This article has elucidated for readers from the perspectives of both science and philosophy that the doctrine of Big Bang is not only contrary to science but also contrary to philosophy.
Category: Relativity and Cosmology

Energy-Anti-energy,Matter-AnnihilatingMatter:FoundationalConceptReconstructionandTestableExperimentalSchemes

Authors: Jian Yang
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Based on respect for the classical physical conclusion that matter-antimatter annihilation produces photons, this paper redefines the logical boundaries of fundamental concepts such as energy-anti-energy and matter-annihilating matter. Itstrictly distinguishes between two types of physical processes: first, the traditional mass-energy conversion process when matter and antimatter meet, which leaves behind energy and photons; second, the field-configuration-annihilation process proposed herein, which after interaction completely returns to the quantum vacuum ground state, leaving no observablephysical remnants. This paper introduces two hypothetical physical entities — matter-annihilating matter and electron-annihilating electron—and clarifies their symmetric annihilation relationship. Based on the philosophy of binaryopposition and unity, a theoretical framework of Chaos Theory is constructed, proposing three core foundational rules with mathematical expressions. On this basis, two major directions are outlined: experiments feasible with current technology and research directions verifiable with future technology. A set of falsifiable scientific predictions is also proposed. All theoretical inferences are ultimately judged by physical experiments, providing a theoretical reference forfundamental physics and new physics beyond the Standard Model.
Category: Relativity and Cosmology

The Problem of Cosmological Constant Correlation Between Observation and QFT-Measurement as a Fixpoint-Description Spectral Self-Adjustment of the Cosmological Constant from Quantum Vacuum Structure

Authors: Holger A.W. Döring
Comments: 31 Pages.

Discussed is a trying to solve the obvious contradiction in discrepance between the measuring of cosmological constant (CC) from GRT-description and its calculated prediction in classical QFT.Either then the coupling of CC to theory is wrong or the physical and mathematical methods tocalculate CC by QFT in flat Minkowskispace-background are wrong. Tried is a fixpoint-method tocome to a calculated value of CC which better fits to observation. In this context the sum-rules for1-loop/2-loop in BSM-QFT are solved, three new scalarons ("Stooges") and two new heavyfermione ("Tweedles") are introduced to couple matter-field beyond SM to CC and to look atdiscrepances between measuring and calculation in a more consistent way.
Category: Quantum Gravity and String Theory

A Short Formula to Discover the Real Evolution of the Expansion of the Universe

Authors: Dino Bruniera
Comments: 4 Pages. In English and Italian (Note by viXra Admin: Please cite and list scientific references)

A short formula to find the real travel time of photons from Type Ia supernovae and, therefore, the real epoch relative to the scale factor of the expansion of the Universe, indicated by their redshift. This, thanks to the thousands of ob-servations of Type Ia supernovae of all epochs already available, would allow us to obtain a graph showing the real evolution of the expansion of the Universe.
Category: Relativity and Cosmology

For All Hyperoperations, 2^4 = 4^2 is The Only Whole Number Pair Exception to their Anticommutativity

Authors: Anthony Veglia
Comments: 7 Pages.

All higher-order hyperoperations beyond multiplication are anticommutative, featuring a pair of distinct input values being the base and the power, such as x^y. Using real whole numbers, other than the infinite trivial examples where x = y, it has been proven that 2^4 = 4^2 is the only exception to the anticommutativity property of the hyperoperation exponentiation. This proof shows that for all higher-order hyperoperations, including tetration, pentation, and beyond, thatsingular exception, H3(2, 4) = H3(4, 2), remains the sole example of "anti"-anticommutativityusing real whole number inputs.
Category: Number Theory

Eigenvalues of Transpose of a Matrix

Authors: Sanjeev Saxena
Comments: 1 Page.

A proof without using determinants is given to show that the eigenvalues of a square matrix A are the same as those of its transpose A^T. The proof only uses the fact that the row and column ranks of a matrix are same.
Category: Algebra

Turing-Unsimulability, and Instantaneous and Sustained Cosmic-Censorship-Falsity, for Einstein-Vacuum General Relativity

Authors: Warren D. Smith
Comments: 60 Pages.

(I) We construct instantaneous counterexamples to Penrose's "cosmic censorship conjecture" (CCC) in Einstein's vacuum field equations (EVFEs) in general relativity (GR).

(II) We also construct ones that persist for a positive timespan (e.g. 1 million years). More precisely, II demonstrates either (1) the existence of a solution of EVFEs – note, no matter is involved – for a million years, throughout which there are any desired arbitrary number (including infinity as a number") of "naked" point-singularities, or(2) Einstein solutions suddenly stop existing, or(3) solutions of Einstein that ought to be well described by Newton-law dynamics, are not, or(4) "stability" of Newton law solutions does not work the way everybody thought based both on many experiments and KAM/Nekhoroshev mathematical theory.

Consequently, if Penrose's CCC is physically valid,then the reason is not Einstein gravity alone – some other physics must play a crucial role. The construction for II shows as corollaries that GR can have everywhere non-analytic metrical solutions, maximally-refuting an unfortunately-widely-believed myth; and also indicates that naked singularities arise from generic initial data – at least with some people's notions of the word "generic" (but possibly not yours).

(III) We sketch a proof of the "Turing unsimulability" of EVFEs. More precisely, either (1) the metric of spacetime time-evolves during a finite timespan (e.g. 1 year) in a manner which no Turing machine can simulate to within arbitrary user-specified accuracy bound in any finite timespan, or (cases 2, 3 basically same as in II), or (4) "chaos lifetime" in Newtonian 3-body scenarios behaves very differently than everybody had thought based on extensive experiments. It probably should be possible to get rid of case (4) via a different, chaos-avoiding, proof technique based on more-explicitly defined motions with perturbation bounds devised with computer aid – I sketch how but do not actually do this. The argument also suggests that unsimulability happens with generic initial data, at least with some people's notions of the word "generic" (but possibly not yours). All these scenarios I, II, III involve finite and bounded total mass-energy.

Crucial to I-III is the fact that the EVFEs permit storing an infinitude of information in a compact finite-volume region using finite mass-energy; and furthermore (for III) an infinitude that's dynamically relevant, i.e. changing any single bit of that information will yield an easily-observable macroscopic consequence within a fixed timespan. That mathematical fact probably is unphysical, in which case the EVFEs are not the laws of gravity in our universe, but rather only an approximation to truer (e.g. "quantum gravity") laws.

I believe case 1 is the truth in both theorems II and III; cases 2-4 were added to handle my inability to prove case 1 fully rigorously.(Theorem I, however, is fully rigorous and does not need extra cases.) Key obstacles to rigor: Humankind presently is usually unable to prove eternal existence and uniqueness of solutions to the Einstein equations; and cannot prove or disprove (for any particular N≥3) that a positive-measure set of Newton N-body solutions can exhibit "eternal chaos." And although there has been progress on problems resembling "proving stability of the solar system" for Newton N-body problems (at least in a Nekhoroshev long-time-survival sense), that progress has not yet been good enough to handle N=∞. But regardless of which cases happen, I contend theorems I, II, III signify the failure of the EVFEs as an algorithmic theory of gravitational physics. Some lessons are drawn from that, e.g. everybody trying to combine standard model with GR whilekeeping the latter nonquantum, is misguided. Also includes(a) an introduction reviewing previous works in my "computational complexity status of physics" aka "Church's thesis meets physical law X" research programme;(b) a long survey of useful facts about Newtonian N-body problems, in some respects the best currently available, and highlighting the important open question of whether a positive-measure set of "eternal chaos" N-body solutions exist.
Category: Relativity and Cosmology

Some of the Biggest Problems for the Theory of Relativity

Authors: Lars Frølund Jensen
Comments: 4 Pages.

According to experts in special relativity, it is ‘mathematically self-consistent’, and therefore it should be impossible to demonstrate any inconsistency in the theory. Supposedly, only physical experiments have the possibility of disproving it! — However, I and other researchers have demonstrated several inconsistencies in both the special and general theory of relativity, and in this paper I will show examples that are so simple and clear that experts will easily be able to understand the arguments. So — unless they can demonstrate crucial errors in my argumentation — they will be able to realize that there are serious inconsistencies in the theory of relativity!
Category: Relativity and Cosmology

Pythagorean Theorem: an Alternative Formula

Authors: Muhammad Roy Asrori
Comments: 2 Pages.

In this note we give a formula for the pythagorean theorem.
Category: Number Theory

About Possibilities of Physical Unrealizability of Cosmological and Gravitational Singularities in General Relativity and in Relativistic Gravithermodynamics

Authors: Pavlo Danylchenko
Comments: 34 Pages.

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) and in its improved version — the relativistic gravithermodynamics (RGTD) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not comoving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in the comoving with expanding Universe FR (CFREU), when it has hollow topological form in the space of CFEU and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed. And there is antimatter instead of matter in this internal part of the space. Inevitability of self-organization in physical vacuum of spiral-wave structural elements, which correspond to elementary quasiparticles, and universal electromagnetic nature of all non-fictive quasiparticles are substantiated. Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter. It is proved that only in the case of the joint application in the Universe of a physically homogeneous exponential scale of unified gravithermodynamic time and a dynamic gravitational field, which ensure the invariance in space and time of the vacuum velocity of light and the Hubble constant, is it possible to ensure not only the general covariance of all physical laws, but also the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter. Although the use in the Universe of a metrically homogeneous uniform scale of the proper time of matter and of a static gravitational field ensure the eternity of the existence of the Universe and the non-exceeding of the values of the false coordinate velocities of light of the GR by the radial velocities of distant galaxies, it does not ensure both the general covariance of all physical laws and the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter.
Category: Relativity and Cosmology