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 accordingly)

The ancients once said, "As above, so below." [This writing explores this notion and proposes three laws of spiritual mechanics.]
Category: Mathematical 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: 19 Pages.

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: CC BY-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 global heterogeneous aggregate 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

Statistical Gravity, Adm Splitting, and Affine Quantization

Authors: Riccardo Fantoni
Comments: 7 Pages.

In a recent publications I proposed a new statistical theory of gravity [Riccardo Fantoni, Quantum Reports, 6, 706 (2024)] which describes the fluctuations of the spacetime metric through a virial temperature. In a succeeding publication I discussed the foundations [Riccardo Fantoni, Stats, 8, 23 (2025)] of such theory. Here I propose a possible way to render numerically accessible the path integral Monte Carlo computations required in such Statistical Gravity theory. This requires the use of the Arnowitt, Deser, and Misner (ADM) splitting and of the Affine Quantization (AQ) method.
Category: Quantum Gravity and String Theory

What Does "Formally Verified" Actually Guarantee?

Authors: Stanislav Komarovsky
Comments: 12 Pages.

We prove that for any formal verification of any real system, the correspondence between the formal proposition and the system it describescannot be established within any finite tower of formal languages. The proof follows from Tarski’s undefinability theorem applied iteratively: verifying that a proposition correctly describes a system requires ex-pressing a correspondence claim that, by Tarski’s theorem, cannot be formulated within the proposition’s own language. Expressing the correspondence in a richer metalanguage generates a new correspondence claim that cannot be formulated in the metalanguage, producing an infinite regress that no finite extension of the formal framework can resolve. The result is structural, not contingent on current tooling or the complexity of the target system. We discuss five caveats—concerning human knowledge, the value of formal verification, partial gap closure, varying assumption strength, and the functionalist objection—and draw implications for the verification of AI-generated software artifacts.
Category: Artificial Intelligence

A Modular Zero-Knowledge Credential Framework for Multi-System Attribute Verification with Scoped Unlinkability and Efficient Accumulator-Based Revocation

Authors: Sayan Bairagi, Sayan Singha Roy, Abir Rakshit, Anik Bhowmick
Comments: 41 Pages.

This work presents a zero-knowledge credential framework designed to enable secure and privacy-preserving attribute verification across multiple independent systems. Theframework allows a user to prove statements of the form a ≥ t,where a ∈ Zq represents a secret attribute and t denotes a public threshold, without revealing the attribute value itself. At the sametime, the framework prevents the exposure of any globally stable identifier, thereby eliminating the risk of cross-domain tracking. The construction is based on Pedersen commitments, where each attribute is encoded as C = g^ah^r ∈ G, with G ⊆ Z^∗p denoting a cyclic group of prime order q. The generators g and h are selected such that the discrete logarithm relation between them is unknown. This ensures that the commitment is computationally binding under the discrete logarithm assumption and perfectly hiding due to the use of randomness r. As a result, the committed attribute remains concealed while still allowing verification of statements about it. Predicate verification is achieved using a sigma protocol, whichenables the prover to demonstrate knowledge of valid witnesses without revealing them. In particular, the protocol proves the relation C · g−t = g^δh^r, where δ = a − t. This transformation allows the system to verify threshold conditions such as a ≥ twithout disclosing the value of a. The zero-knowledge property of the protocol ensures that the verifier learns only the validity ofthe statement and no additional information about the underlying attribute or randomness.To prevent correlation of user activity across different verification domains, the framework introduces scoped pseudonyms defined as IDS = pkH(S), where pk = g^x is a public key derivedfrom a secret key x, and H is a cryptographic hash functionmodeled as a random oracle. The scope S represents a domain specific identifier. This construction produces a unique identifierfor each domain while ensuring that identifiers generated for different scopes cannot be linked without solving the discrete logarithm problem in G. Revocation is supported through an RSA accumulator constructed under the Strong RSA assumption. For a revoked set R={ri}, the accumulator value is defined as A = g^Qri mod N,where N is an RSA modulus. The system enables efficient non membership verification using witnesses derived from B´ezout coefficients1. This mechanism allows a verifier to confirm thata credential has not been revoked, while maintaining constant verification cost that does not depend on the size of the revoked set. (Truncated by viXra Admin)
Category: Artificial Intelligence

Infinite Flow Cosmology (IFC)

Authors: Bradley Stone
Comments: 7 Pages.

We present Infinite Flow Cosmology (IFC), a brane-world framework in which the observable universe is modelled as an open thermodynamic system embedded within a dynamic, radiating 5D Vaidya-Anti-de Sitter bulk spacetime. Rather than invoking a static cosmological constant, IFC drives late-time cosmic acceleration through continuous mass-energy flux projected from the bulk onto the 4D brane. Using the Shiromizu-Maeda-Sasaki projection formalism, we derive the modified Friedmann equations and a generalised energy conservation law governing bulk-brane exchange. We constrain the dimensionless bulk-brane coupling constant to α ≈ 2.2 by matching the observed late-time expansion history, and derive an effective quintessence-like equation of state w(z) ≳ −1 that is distinct from and testable against a pure cosmological constant. The model predicts a mild but measurable enhancement in the large-scale structure growth parameter fσu2088 at redshifts z < 0.5, forecasting a signal detectable by the Euclid satellite and DESI survey. Finally, we demonstrate that localised bulk flux preferentially couples to regions of extreme spacetime curvature, providing a two-channel gravity-based mechanism for super-Eddington black hole accretion that simultaneously explains anomalous mass growth rates and the persistence of bright X-ray coronae and radio jets — observations that challenge standard slim disk models
Category: Relativity and Cosmology

On Rényi Entropy and Foundational Physics

Authors: Ervin Goldfain
Comments: 13 Pages.

Rényi entropy is a generalization of the standard Shannon entropy and plays an important role in understanding complex dynamics of non-equilibrium systems. In line with [7], this brief report discusses the definition and application of Rényi entropy to Quantum Field Theory (QFT) and gravitational regime of primordial cosmology. In particular, we review the connection between Rényi entropy and entanglement entropy, on the one hand, and the maximal entropy principle (MEP), on the other. Remarkably, the latter enables derivation of the Higgs and W-boson masses in close agreement with experimental data. Appealing to multifractal analysis and the concept of generalized dimensions, we further bridge the divide between Rényi entropy and the "sum-of-squares" relationship of particle physics, corresponding to maximally entropy at index q=0. We emphasize the deep analogy between QFT entanglement and long-range correlations of complex dynamics and indicate that the MEP aligns with the universal route to chaos described by the Feigenbaum scenario. Finally, we review how Rényi entropy can be used to derive the four dimensionality of classical spacetime for q=1/2.
Category: Mathematical Physics

Quantum Molecular Dynamics

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

We formulate a new quantum many body simulation method for a general quantum fluid at any given temperature. Unlike path integral Monte Carlo our method evolves in imaginary time the density matrix from its initial delta function condition to its final thermal form at time equal to the inverse temperature. It does this with a molecular dynamics scheme on a classical Hamiltonian that has the same functional form as the one of the quantum mechanical Hamiltonian according to the properties of the continuous representation of John R. Klauder. We then end up with the thermal density matrix that can be used to extract thermal averages of observables using the Monte Carlo method equally well in any statistics.
Category: Data Structures and Algorithms

Very Accurate Formulas for the Light Velocity Dependent on the Figures 144 and 666 and on Wolfgang Pauli's Figure 137

Authors: Andreas Ball
Comments: 17 Pages.

Firstly a very accurate formula for the Light Velocity is presented, at which the figures 144 and 666 are applied. An extremely accurate formula for the Light Velocity is presented in additional dependence of the figure 137. Furthermore an investigation about the figure 137 and its connection to other figures are given. The Physicist Arnold Sommerfeld investigated the spectral lines of the hydrogen atom and derived a value, which he called the Fine Structure Constant and which became famous by its reciprocal 137. The Physician Wolfgang Pauli and also the Psychoanalyst Carl G. Jung were occupied with the significance of the figure 137 by a metaphysical view. Why their undertaking was not devious, that shows a proof at the end of this report.
Category: Mathematical Physics

Neutrino Masses, Custodial Symmetry and the Planck Energy

Authors: Bodo Lampe
Comments: 19 Pages.

A framework is analyzed where the Standard Model physics emerges as a low-energy effective field theory on a (7+1)D spacetime and Minkowski space is a monolayer composed of unresolvable tetrahedral unit cells at the Planck scale. We demonstrate that the SSB of the isospin cells into a chiral all-out configuration naturally generates a local O(4) isospin symmetry which governs the dynamics of the Higgs doublet and the mass hierarchy of the electroweak sector. By identifying the axial generators of the broken symmetry with massive vector bosons, we recover the electroweak phenomenology. The inherent handedness of the isospin vacuum provides a 7D origin for parity violation, establishing a direct link between the topology of the unresolvable spatial lattice and the observed chiral nature of weak interactions. The role of the O(4) symmetry of the Higgs potential is elucidated, and how the SM custodial symmetry is associated to neutrino masses, the latter being obtained from isospin-orbit coupling between isospins and the Planck lattice.
Category: High Energy Particle Physics

Parametric Analysis of Fin Geometry Effects on Stability and Performance of a Model Rocket

Authors: Ayush Samanta
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

Fin geometry plays a critical role in determining the aerodynamic stability andperformance of rockets, yet excessive fin area may reduce efficiency through added drag. In this study I investigated the effect of fin geometry on rocket flight characteristics using ten simulated variants analyzed in OpenRocket under controlled launch conditions with four wind levels in a hypothetical situation where we are in Guadalajara, Spain. Metrics including apogee altitude, maximum velocity, acceleration, and time to apogee were compared across designs, revealing measurable tradeoffs between stability margin and ascent performance. The results indicate that moderate fin configurations can outperform both oversized and undersized designs by balancing stability with reduced aerodynamic losses.
Category: Classical Physics

Scattering of the Spinless Particles

Authors: Miroslav Pardy
Comments: 7 Pages. Original article

The problem of scattering of the spinless by the spinless particles is considered under the condition that no other particles are created during the interaction. The matrix element of the scattering is defined and it is extracted fromthe general action of the current-current form. The differential cross section is then determined and the limiting formulas of it for the very high energy and very low energy is derived.
Category: High Energy Particle Physics

Non-inertial Relativity Theory, Finite Modified Newtonian Potentials and Asymptotic Freedom

Authors: Carlos Castro
Comments: 14 Pages.

After reviewing the basics of Non-inertial relativity theory based on the existence of a maximal proper force $b$, it allowed to postulate a modified Newtonian attractive gravitational force (and potential) which is $finite$ at the origin : $ | F ( r = 0 ) | = b$, and which vanishes at $r = infty$. Secondly, from the modified gravitational potential energy we were able to glean the expression for a running gravitational coupling $ G ( r ) $ which exhibits asymptotic-freedom-like properties : $ G ( r = 0) = 0$, and $ G ( r = infty) = G_N$. No quantum corrections were necessary to decrease the strength of gravity at short distances. Thirdly, we found that for very $large$ masses $m_1, m_2$ (compared to $ sqrt b $) the $threshold$ in the values of $r$ obeying $ kappa r^2 < < 1$, where the non-Newtonian regime becomes manifest, becomes larger and larger as $m_1, m_2$ become larger and larger. Whereas for very $small$ masses (compared to $sqrt b $) the $threshold$ in the values of $r$ obeying $ kappa r^2 < < 1$, where the non-Newtonian regime becomes manifest, becomes smaller and smaller as $m_1, m_2$ become smaller and smaller. In the $ b = infty$ limit one recovers the Newtonian gravitational force for all values of $ r>0$. These results were all possible by abandoning the weak equivalence principle at short distances.
Category: Quantum Gravity and String Theory

Coherent State Path Integral Monte Carlo

Authors: Riccardo Fantoni
Comments: 12 Pages.

We propose a new quantum simulation method for a many body quantum liquid of identical particlesat finite (non-zero) temperature. The new scheme expands the high temperature density matrix on the over complete set of single particles coherent states of John Rider Klauder instead of the usual plane waves as in conventional path integral methods. One is free to tune the elastic constant and/or the mass of the harmonic oscillator subtending the coherent states so as to maximize the computational efficiency of the algorithm. We prove that in the limit of an extremely stiff harmonic oscillator the results for the internal energy tends towards the correct expected values. Moreover we suggest that a stiff harmonic oscillator could allow the use of larger (imaginary) timesteps. This additional degree of freedom is the characteristic feature of our new algorithm and is not available in more conventional path integral methods.
Category: Data Structures and Algorithms

Comment on "Experimental Evidence that a Photon Can Spend a Negative Amount of Time in an Atom Cloud"

Authors: Vladimir Kuz'menko
Comments: 3 Pages.

Several interesting publications have appeared in the literature on the so-called "negative time" or "negative group delay" in experiments on the interaction of photons with cold atoms [1 - 6]. The physical meaning of this phenomenon is unclear. Such a physical explanation is proposed here and simple experiments for its further study are discussed.
Category: Quantum Physics

The Missing Rotation Angle of Rodrigues’ Rotation Formula

Authors: Russell P. Patera
Comments: 9 Pages.

Rodrigues’ Rotation Formula is used to rotate a vector based on the Axis-Angle parameterization of attitude transformation. Given an axis and angle about which an initial vector is rotated, Rodrigues’ Formula yields the final orientation of the vector. However, Rodrigues’ Formula does not include the associated rotation about the vector axis, which depends on the specific trajectory used in slewing the axis from its initial to final orientation. A theorem in attitude kinematics that was not available when Rodrigues developed his formula, contains attitude components that should be included with Rodrigues’ Formula. These attitude components were previously applied to the related problem of the Foucault Pendulum, which rotates with the Earth about the Earth’s spin axis. The methods to compute the rotation angle about the vector axis are the same as those used to compute the rotation of the Foucault Pendulum’s mounting fixture, since the trajectories are similar. This work presents the derivation of the formula for the missing rotation angle of Rodrigues’s Formula. Several numerical examples are presented to illustrate the use of the formula.
Category: Classical Physics

Shaking Tangled Dimensions - A Nascent Theory of Everything

Authors: David Welker
Comments: 46 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

Shaking Tangled Dimensions (TD) is a geometric and stochastic framework that seeks to unify particle physics, gravitation, and quantum behavior through a discrete, Planck-scale lattice of interconnected cores. Each core contains three spatial, three electrical, and three dark dimensions, whose local overlaps, bends, twists, and cross-connections are proposed to generate the observed structure of spacetime, particle properties, and force-like interactions. In this picture, fundamental particles arise as localized dimensional kinks and misconnections rather than as point-like objects existing independently of the lattice.Within TD, gravity is associated with the overlap volume and angular inclination of the spatial dimensions relative to a central reference point, while time is tied to local lattice update dynamics. Electromagnetic behavior emerges from the bending and twisting of the electrical dimensions, and photons, neutrino oscillations, spin, and several particle-family features are reinterpreted within the same geometric setting. Quantum uncertainty is attributed to continual Planck-scale lattice oscillations, providing a possible microphysical basis for the contingent ingredient in Barandes’ stochastic-quantum correspondence. Dark matter is treated primarily as a weakly self-ordering population of dark-dimensional kinks that contributes gravitationally through its effect on neighboring spatial overlap while remaining largely non-dissipative in the present cosmological epoch.Taken together, these ideas present TD as a developing candidate framework in which the phenomena normally assigned to separate formalisms may instead reflect different aspects of one underlying dimensional substrate. The model remains exploratory, but it offers a unified geometric program for relating spacetime structure, quantum contingency, particle behavior, and dark matter within a single lattice-based picture.
Category: Quantum Gravity and String Theory

The Geodesic Lines

Authors: Abdelmajid Ben Hadj Salem
Comments: 11 Pages.

In this article, we present the equations of the geodesic lines of a surface in $R^3$ and then we determine the calculation of the geodesic lines of the ellipsoid of revolution with a numerical example.
Category: Geometry

Selected Papers: [Book] IV Mathematical Contributions

Authors: Abdelmajid Ben Hadj Salem
Comments: 117 Pages.

This booklet is the tome IV of my Selected Papers. It is my mathematical contributions in the field of the Number Theory during the last 12 years.
Category: Number Theory

Gravitational Polarity Symmetry: Gravity, the Speed of Light, and Quantum Geometry from a Chiral Vacuum

Authors: Juraj Povazanec
Comments: 40 Pages. (Note by viXra Admin: Please DO NOT name any equation/formula after the author's name and submit article written with AI assistance to ai.viXra.org)

The vacuum energy problem is one of the central unresolved tensions between quantum theory and gravitation. Quantum field theory predicts a vacuum energy density near 10¹¹³ J/m³, which in General Relativity would generate severe spacetime curvature, yet observation finds space remarkably flat.This article argues that the discrepancy traces to a centuries-old conceptual error: the nature of energy itself has been misclassified.Energy has been treated as a universal scalar currency, a single real-valued quantity. Yet close examination of the quantum substrate reveals that energy possesses an irreducible two-component structure. Maxwell showed this through light's two orthogonal polarizations. Dirac demanded it with his positive and negative energy solutions.Consider the foundational statement: energy curves spacetime. If energy is complex, how does such curvature manifest? Equally along two internal axes. Within this framework, the vacuum, perfectly balanced, yields no net observable curvature—resolving the catastrophe.But what of the exquisite curvature GR predicts so accurately around planets and stars?Precisely there. In GR, energy curves spacetime. What produces this curvature? Planets and stars. The imbalance of the vacuum's perfect symmetry. Spacetime curvature emerges only where the two components of energy depart from equilibrium.What follows develops this construction and its implications for quantum gravity—one where the vacuum sets the speed of light through its total amplitude, and curvature arises solely from asymmetry.
Category: Quantum Gravity and String Theory

Generalization of A New Home for Bivectors

Authors: Norm Cimon
Comments: 19 Pages.

The impetus for the work is this quote:"...as shown by Gel’fand’s approach, we can only abstract a unique manifold if our algebra is commutative."[1]Geometric algebra is non-commutative. Components of different grades can be staged on different manifolds. As operations on those elements proceed, they can effect the promotion and/or demotion of components to higher and/or lower grades, and thus to different manifolds. This paper includes imagery that visually displays bivector addition and rotation on a sphere.David Hestenes interpreted the vector product or rotor in two-dimensions:"as a directed arc of fixed length that can be rotated at will on the unit circle, just as we interpret a vectoras a directed line segment that can be translated at will without changing its length or directionu2026"[2]Rotors can be used to develop addition and multiplication of bivectors on a sphere. For those rotational dynamics, rotors of lengthare the basis elements. The geometric algebra of bivectors — Hamilton’s "pure quaternions" — is thus shown to transparently operate on a spherical manifold.This paper also explores the possible generalizations that emerge from the placement of the graded elements which make up a geometric algebra onto separate manifolds.
Category: Geometry

Residual Cancellation in Ordered Abelian Groups

Authors: Theo Adebayo
Comments: 6 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper develops the ordered-structure core of the Theory of Residual Cancellation (TRC).The main idea is that, in a suitable ordered setting, the common part of two positive elements can be recovered from ordered difference and positive-part structure rather than assumed independently. Let G be an ordered abelian group equipped with a positive-part operation u → u+, and define u− := (−u)+. For x,y ∈ G, define the TRC common-part candidatem(x,y) := x−(x−y)+. Under a positive/negative-part decomposition axiom, this operation is symmetric and yields a two-sided residual/common decomposition. Under the additional assumption that the positive part map is monotone, the matched-content operation becomes monotone, maximal among common lower bounds, and equal to the meet on positive pairs. This gives an axiom-separated theorem ladder: one axiom governs the algebraic decomposition layer, while the second upgrades the decomposition into genuine order-theoretic meet recovery. The result identifies the abstract core of TRC as a compatibility principle between difference, positive part, and common part.
Category: Algebra

Nonlinear Spaces

Authors: Sergey Y. Kotkovsky
Comments: 33 Pages. In Russian

As a base for creating nonlinear algebra, we use vectors — mathematical objects with some predefined general properties, but without defining these objects in terms of numbers or numerical matrices. Next, we build our algebra based on the vector multiplication operation. Our approach allows us to obtain new and more generalized conceptions of vectors, scalars and related objects of a mixed scalar-vector type — generalized quaternions. We propose a fundamentally new perspective on such familiar concepts as space, vectors, quaternions, complexity, parallelism, orthogonality, and dimension. Within the framework of new nonlinear algebra, geometric concepts such as parallelism and orthogonality acquire the operator meaning of vector commutativity and anticommutativity. The essence of the transition from linear to nonlinear representations lies in the transition from static geometric representations to operational ones. Vector cycles, which are triples of vectors cyclically connected to each other, occupy a special place in our algebraic system. The axiomatic framework we have constructed allows us to prove a number of statements important for the further development of the theory of nonlinear spaces.
Category: Algebra

An Alternative to the Expanding Universe Theory

Authors: Jorma Jormakka
Comments: 13 Pages. (Note by viXra Admin: Please cite and list scientific references of other authors)

The article points out several errors in the expanding space theory that is currentlybelieved to explain the cosmological redshift. The article proposes a tired light theory thatgives the correct reduction factor. This tired light theory includes a mechanism that slowsdown transitions of electrons in the atomic level. The mechanism is not explained: it is only proposed that the fine structure constant changes over long time periods. The articlesuggests that Cosmic Microwave Background radiation did not come from the Big Bang and that it comes from lost energy of photons traveling through the space as in tired light theories.
Category: Relativity and Cosmology

Grand Unified Theories with Electro-Strong Interaction, New Su(5), and New So(10) Model

Authors: Wan-Chung Hu
Comments: 37 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Similar to electroweak interaction, strong force and electromagnetism can have similar Higgs mechanism mediated interaction. Thus, gluons can acquire mass. And, neural colored gluons have larger mass than colored gluons. Total, we can have eight gluons without red-anti-red gluon. The puzzle of proton or neutron mass can be solved. We can also derive a new SU(5) model to include all the above eight gluons, three W/Z bosons, photon, Higgs boson, three generations of leptons and quarks to make a new 5x5 SU(5) model. Wightman axioms can be fulfilled in this new SU(5) without causing proton decay crisis. !6f matter field construction is used to put all the particles. We can also add the 4x4 four dimensional spacetime tensor integrating mass-energy density, light pressure, electric fields, and magnetic fields as well as four gradients to make a new contravariant SO(10) model. Weyl tensor and Ricci tensor related to the new SO(10) model are also given. Thus, grand unified theory or theory of everything can be obtained, that is compatible with four dimensional spacetime without extra-dimension needed in string theories.
Category: Mathematical Physics

A Proof of Three Integral Representation of Riemann $xi$-Function Using Divergent Series Without Using Partial Integration

Authors: Yuhua Li
Comments: 12 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

In this paper,we proved that for classic integral representation of Riemann $xi$-function $xi(s)=frac{1}{2}+frac{s(s-1)}{2}int_1^inftypsi(x)(x^{s/2-1}+x^{(1-s)/2-1})dx=-4psi'(1)+int_1^inftypsi'(x)((1-s)x^{s/2}+sx^{(1-)/2})dx=2int_1^infty(frac{3}{2}psi'(x)+xpsi''(x))(x^{s/2}+x^{(1-s)/2})dx$ , the common lower limitation 1 of the three divergent series equals each other (including $frac{-1}{2}$ for the first and $(-4)psi'(1)$ for the second).This provides a new approach to prove the three integral representation without using partial integration.
Category: Number Theory

True ai Should not be a Winner, But a Loser

Authors: Dimiter Dobrev
Comments: 6 Pages. In Bulgarian

There is an inaccuracy in the modern definition of AI. Today's definition says that AI is a program that is successful. Indeed, for a program to be successful, it must be intelligent, but the opposite is not true. A program can be intelligent but not successful, simply because it has other goals and does not strive for the success in question. From a theoretical point of view, the modern definition of AI is good enough, because it gives us an answer to the question "What is AI" even though it does not describe all intelligent programs, but only some of them. From a practical point of view, however, this definition is not sufficient. The reason is that we are on the verge of creating true AI and we need to choose from all intelligent programs the one with which we will best live. It turns out that it is not good to choose one of the successful programs. It would be better to choose a program that does not blindly strive for victory. Such a program can be called a loser, because it will not be successful enough. However, in both humans and AI, reckless ambition is not a positive quality.
Category: Artificial Intelligence

[ Opinion on the] Divergence and Curl of Time-Varying Electromagnetic Fields

Authors: Hongyuan Ye
Comments: 7 Pages. (Note by viXra Admin: Please cite and list scientific references)

[In the author's opinion,] Maxwell’s equations are an integration of divergence, curl, and classical electromagnetism. Based on [this] definition, divergence and curl can apply to static electromagnetic fields, [but] not to dynamic, time-varying ones[?]
Category: Mathematical Physics

How Gravity Shapes the Structure of the Universe

Authors: Viktar Yatskevich
Comments: 20 Pages. figures 10, references 30

The Big Bang Theory (BBT) is currently widely accepted. The theory explains the expansion of galaxies by the action of "dark energy", a mysterious force that repels matter and causes space to expand at an accelerating rate. Within galaxies, the action of gravity prevails over the force of "dark energy" and no expansion occurs. This situation motivates the search for alternative physical interpretations based on verified observational data.A new physical interpretation of gravity is proposed to complement existing cosmological models. The theory is formulated both as a phenomenological framework and as a microscopic description explaining gravitational interaction at the atomic level. The proposed approach is constructed as a connected sequence of known physical phenomena, each of which has experimental confirmation. This provides a physically grounded basis for interpreting gravitational interaction across scales.A distinctive feature of the theory is its emphasis on the physical mechanisms underlying the formation and action of the gravitational field, while mathematical modeling is treated as a secondary descriptive tool. The theory offers a possible physical interpretation of the formation of cosmic structure driven by gravity alone. According to the proposed framework, gravitational interaction may manifest itself as either attraction or effective repulsion depending on the physical state of interacting matter. Within this interpretation, the observed expansion of the Universe may be described without invoking hypothetical forms of energy such as dark energy.
Category: Relativity and Cosmology

Resolution-Shifted Identity and the Mechanics of Persistent Formation

Authors: Richie DeMott
Comments: 8 Pages.

This manuscript offers a cross-scale framework for persistent formation in which dissipation-enabled capture, functional boundary, and coarse-grained inheritance jointly explain how stable higher-order units emerge from prior-scale dynamics under differing local mechanisms. The framework is interpretive and organizational, grounded in established physics—nonequilibrium thermodynamics, coarse-graining, and effective description—rather than proposing new fundamental laws.A central contribution is a functional boundary criterion combined with the concept of resolution-shifted identity. The paper argues that boundary appearance is systematically observer-relative due to timescale separation: systems may appear sharply localized or effectively diffuse depending on whether their characteristic recurrence dynamics are resolvable within the observer’s temporal window. This is formalized through a causality-normalized participation ratio, β* = L/(cτ), used to compare recurrence-governed participation across atomic, planetary, and galactic domains without invoking a universal scaling law.The aim of the manuscript is to clarify how persistent structure can be understood consistently across domains while remaining fully compatible with thermodynamics and effective-field-theoretic reasoning.
Category: Thermodynamics and Energy

Relativistic Model for Pion-Nucleon Scattering.

Authors: Joe Y. Haskian
Comments: 33 Pages.

For many years, particle and nuclear physicists have been especially interested in the pion-nucleon inter­action. The reason is twofold: the knowledge of pion-nucleon interaction comprises the foundation for any dynamical theory of nuclei and this knowledge provides clues to the understanding of the internal structure of hadrons.
Category: Nuclear and Atomic Physics

A Transport-Diffusion Kinetic Equation

Authors: Payam Danesh, Raoul Bianchetti
Comments: 16 Pages.

This paper studies a linear kinetic equation on a periodic phase space with free transport in position and Ornstein-Uhlenbeck relaxation in velocity. The equation is formulated in the weighted Hilbert space associated with the Maxwellian equilibrium. In that setting, the paper establishes the dissipation identity, conservation of mass, semigroup well-posedness, microscopic coercivity in velocity, and exponential convergence to equilibrium on the zeromass subspace. The spatially homogeneous problem is treated separately, where the entropy law and exponential entropy decay follow directly from the Gaussian logarithmic Sobolev inequality. A final numerical section presents a Fourier-Hermite discretization and illustrates the same relaxation mechanism at the level of decay curves, spectral localization, and density profiles.
Category: Mathematical Physics

dstr: A Small Language for Systems That Become Graphs

Authors: Sambuddha Majumder, Jayanta Majumder
Comments: 11 Pages.

dstr is a compact language for describing finite dynamic systems in a form that is both easyto write and semantically explicit. Its primary interface is a small s—expression DSL in which one states variables, initial conditions, actions, invariants, and reachability goals without the verbosity that often discourages exploratory modeling. The resulting description is not intended merely to support a checker run. It is intended to generate an explicit state graph that can subsequently be queried, transformed, filtered, and published. The central claim of this paper is that a state—action language becomes substantially more valuable when its semantics are treated as a first—class graph artifact, suitable not only for validation but also for downstream graph analysis and presentation.
Category: Data Structures and Algorithms

Simulations of Water Wave Generation Caused by Running Hydrofoil by Means of Wave-Making Green’s Function Due to 2-D Vortex

Authors: Tsutomu Hori, Manami Hori
Comments: 23 Pages, 13 Figures, 68 Equations, 10 References.

This paper conducts wave-making simulations for hydrofoils running at high speeds. The analysis is performed by constructing the wave-making Green's function due to a two-dimensional vortex filament by means of Fourier transform method. We adopt the developed Green’s function as the kernel function, and approach the problem using the boundary element method. The Green’s function is numerically computed by switching between three expansion forms, namely, Taylor expansion, continued fraction expansion, and asymptotic expansion, depending on the case.

Simulation calculations are performed on the lift force and wave-making resistance acting on the hydrofoil, the generated wave profile, the flow velocity vectors and the pressure distribution around the hydrofoil with a NACA airfoil. As a result, we gained concrete findings for the dependencies of wave-making phenomena upon the wing shape, running speed, submerged depth, angle of attack and other factors.
Category: Classical Physics

Space-Time Nature Might be Used to Bridge Between the Quantum and the Classic Physics

Authors: Moshe Segal
Comments: 14 Pages.

From the dawn of civilization Humans struggled to understand and explain their environment. The process of that struggle resulted in various branches of investigations and knowledge, which Humans denote as Science.Because the Human mind, which created this Science, is by itself composed of components which might be the same components that the environment is also composed of, Humans might be bound to never being able to understand and explain completely this environment, which is also denoted as the Existence, because one cannot explain an issue, if that explanation relies on this same issue. Nevertheless, Humans were still able to build a magnificent structure, of knowledge and explanations, which, as mentioned above, is denoted as Science which is still an ongoing endeavor, which continuously expands, reveals and explains more and more secrets embedded in the Existence.However, the nowadays Physics, which is the branch of Science which specifically focuses on understanding and explaining the Existence, is still composed of branches which are not fully compatible.One of these branches is the branch denoted as the Classic Physics, which focuses on understanding and explaining what is denoted as the Macroscopic Environment.Another such branch is the branch denoted as the Quantum Physics, which focuses on understanding and explaining what is denoted as the Microscopic Environment.And, as presented above, these two branches of Physics are not fully compatible, and Humans are still struggling, to expand the knowledge that might bridge the gap that still exists between these two branches of Physics.Moreover, even the branch of the Classic Physics itself, still embeds branches which are also not fully compatible, as for example, the Gravity and the Electromagnetism, and more must be done to bridge the gap that exists also between these two branches, which both belong, as stated above, to the branch of the Classic Physics.In the process of building the above-mentioned magnificent structure of Science, Humans detected in the Existence various components, and denoted these components as Entities, and used these Entities as the building blocks on which the Science of Physics was constructed.Two such Entities are the Entity of Space and the Entity of Time, which together were interweaved into one Entity, denoted as Einstein's four-dimensional Interwoven Space-Time Entity, by the Relativity Theories of Einstein.The branch of Classic Physics relates to the four-dimensional Interwoven Space-Time Entity as a real component, that really exists in the environment, or the Existence.Moreover, the branch of Classic Physics states that the environment embeds just one single four-dimensional Interwoven Space-Time Entity which is a real component of the environment, that really exists in the environment.However, this paper argues, that the branch of Quantum Physics, might also imply that the above-mentioned four-dimensional Interwoven Space-Time Entity might not be a component that really exists in the environment, or the Existence.Moreover, this paper also argues, that although the nowadays branch of Classic Physics does state that the four-dimensional Interwoven Space-Time Entity is a real existing Entity, a contrary conclusion can be also derived, a conclusion that the four-dimensional Interwoven Space-Time Entity might not be a component that really exists in the environment, or the Existence, and that contrary conclusion can be also derived from arguments based only on the nowadays Classic Physics.Thus, if it can be concluded that arguments based only on the Classic Physics might imply that the four-dimensional Interwoven Space-Time Entity does not really exists in the Existence, a conclusion which might be also in line, and compatible, with what the Quantum Physics also implies, then, by abandoning the conclusion that the four-dimensional Interwoven Space-Time Entity is a component that really exists in the environment, and by validating the assumption that the four-dimensional Interwoven Space-Time Entity might be only a facet or an attribute of another component of the Existence, which the Science of Physics denotes as Energy, this might provide also a lead for starting some bridging between the Classic Physics and the Quantum Physics, which, as already stated above, are still significantly incompatible.
Category: Relativity and Cosmology

The Spacetime Importance of the Neutron and Simple, Precise Calculation of the Energy Levels and Lifetimes of the Neutron and Deuteron 2H Using Natural Constants

Authors: Taiwei Song
Comments: 3 Pages.

Based on the Geometry of Spacetime Structures, this short paper briefly argues the importance of the neutron in the creation of natural spacetime. It also uses only the most fundamental natural constants to simply and precisely derive and calculate the energy levels and lifetimes of the neutron and deuteron 2H.
Category: High Energy Particle Physics

The Logic of Pi's Irrationality

Authors: Timothy Jones
Comments: 2 Pages. (Note by viXra Admin: Please cite listed scientific references)

The point on a unit circle that is associated with the arc Pi/2 is (0,1). We prove the bidirectional: every ordered pair of positive real numbers (a,b) corresponds to a point on the circumference of a circle of radius square root of a^2+b^2 with an associated radius with an arc length less than Pi/2. If Pi/2 is rational this gives a contradiction.
Category: Number Theory

Globoeconomics

Authors: N. S. Alsaud
Comments: 7 Pages.

The theatrical framework of globoeconomics is introduced in this paper as a global generalization of the economical analysis. This coherent treatment scientifically explains many perplexing economical, political and societal phenomena which necessitates rereading the historical development of humankind from novel perspective. Since the approaches used in this treatment provide more plausible and simpler justifications, they are suitable to be adopted based on the philosophical reasoning of Occam's razor.
Category: Economics and Finance

Calculate Universe 4 — Minimalistic Approach

Authors: Branko Zivlak
Comments: 3 Pages. 2 Tables (Note by viXra Admin: An abstract in the article is required)

Formulas are presented that connect known parameters in various fields of physics, thanks to the original concept and the Theory of Ruđer Bošković.
Category: Classical Physics

Nolekson Model: Derivation of Fundamental Constants from CMB Parameters and Jupiter's Perihelion

Authors: Victor Victorovich Oleksenko
Comments: 19 Pages. In Russian

This work presents a new physical paradigm based on the recognition of the substance "Nolekson" (Nl) — an inert gas occupying the 0-th position in the 0-th period of D.I. Mendeleev’s periodic table of chemical elements [1]. This is a quantum stationary cosmological model in which cosmic microwave background (CMB) photons and all particles are interpreted as vortex excitations (tori) in the Nolekson medium — an ultra relativistic gas filling all space [2, 3]. The mass of any particle or photon has the dimension of area [4, 5, 6] (kg = m^2), which resolves dimensional paradoxes and allows the Hubble constant (H_0) to be expressed via Planck constants. Precise relations are obtained linking the CMB temperature (T_CMB), Lorentz factors (γ ∼ 9×10^14 and γ^1 ∼ 7×10^14), the mean free path of noleksinos (L_nl — which is close to the perihelion of Jupiter, accounting for the barycenter, [3]) and the gravitational constant (G).
Category: Quantum Gravity and String Theory

Non-Closure of Doubling Vesica Chains: A Constructive Proof of Irreducible Remainder in Self-Similar Geometric Expansion

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

We present a constructive geometric proof demonstrating that a chain of Vesica Piscis figures following a doubling rule (R, 2R, 4R, u2026, 2n—1R) cannot be enclosed by a Vesica of radius 2nR that closes at the chain’s origin. The linear extent of n doubling iterations sums to 2n — 1, producing an irreducible remainder of exactly one base unit R. This remainder is invariant across all scales of the construction and cannot be eliminated by further iteration. We show that this non-closure property originates at the unit construction itself: the radius R, which generates the Vesica, cannot be consumed by the figure it produces. The result is established through direct lattice construction without appeal to limiting processes or infinite series. We discuss connections to self-similar fractal structures, aperiodic tilings, and renormalizationgroup theory. The construction arises from Geosectometry, a geometric framework developedby the author for investigating natural-state properties of constructive geometry.
Category: Topology

Motion of Bodies in an Energy Medium: A New Model of Gravity, Orbital Precession, and Cosmological Phenomena

Authors: Viktor Strohm
Comments: 5 Pages. (Note by viXra Admin: Please cite scientific references of other authors)

A mechanical model of gravity is proposed within the framework of an energy medium, in which every body continuously absorbs energy, creating a sphere of reduced energy density around itself. The pressure gradient of this medium generates a force that exactly reproduces Newton’s law for an appropriate choice of coefficient. The model naturally explains capture into elliptical orbits, perihelion precession (through violation of additivity of density in the region of overlapping spheres — "synergy"), and provides a physical interpretation of gravitational redshift/blueshift, cosmological redshift, the Hubble constant, and the negative result of the Michelson—Morley experiment. Analytical and numerical formulas for calculating trajectories, including precessing rosettes, have been obtained.
Category: Astrophysics

Regularized Gamma—Bernoulli Identities for the Riemann Zeta Function and a Conditional Critical-Line Criterion

Authors: Payam Danesh
Comments: 19 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

A Gamma—Bernoulli approach to the critical-line problem for the Riemann zeta function is developed. Starting from the Mellin—theta representation and the functional equation, one obtains explicit identities for the reflected Gamma quotient and for the regularization built into the Weierstrass product for Γ. On the Bernoulli side, the kernel (eu − 1)−1 is decomposed into its singular part and an analytic remainder, which yields a concrete zero-conditioned identity after continuation. The analysis shows that the harmonic divergence visible in raw finite Gamma products is a truncation phenomenon and therefore cannot by itself force Re(ρ) = 1/2. What remains is a coercive estimate which, if established, would convert the same mechanism into a critical-line theorem.
Category: Number Theory

The Quadripartite Classification of Triangles: A Unified Geometric and Numerical Field.

Authors: Jean-Yves Boulay
Comments: 12 Pages. (Note by viXra Admin: Please cite scientific references of other authors)

Grounded in a novel mathematical framework, this study demonstrates that any Euclidean triangle can be uniquely categorized into one of four canonical classes based on the intersection of isosceles and right-angled characteristics. We prove that these four classes form a complementary entanglement capable of saturating a rectangular space without voids. Furthermore, this geometric configuration is shown to be isomorphic with specific numerical assemblies in number theory, establishing a direct link between the fundamental sequence of whole numbers and the stability of geometric structures.
Category: Geometry

Achieving Ultra High Resolution Lithography via Intrinsic Equilibrium and Electron Driven Spin Resonance

Authors: Wim Vegt
Comments: 40 Pages.

This paper introduces Localized Intrinsic Field Equilibrium (LIFE), a unified field mechanical framework which posits that the photon is not merely a propagating wave, but a discrete electromagnetic wave packet maintained in dynamic equilibrium. Within this framework, field confinement is anisotropic: the electromagnetic forces maintaining equilibrium differ in the transverse and longitudinal planes. Consequently, the effective electromagnetic mass of the photon behaves as a vector quantity, dependent on the direction of propagation and external field interaction.Leveraging this framework, we propose a novel method for achieving ultra-high resolution photolithography by applying Electric Dipole Spin Resonance (EDSR) to bulk optical materials. While EDSR is traditionally utilized in quantum computing for single-electron spin manipulation, we demonstrate its application in a macroscopic "bulk" capacity to induce resonant light-matter coupling within a Sodium Chloride (NaCl) crystal lens at cryogenic temperatures. By driving the crystal lattice into a strong electromagnetic resonance, we alter the dispersion relation of the medium, creating a "Slow Light" regime where the propagation speed of light is reduced by a factor of 10 (v ≈ c/10).This massive deceleration results in a surge of the effective refractive index (n ≈ 10), which compresses the wavelength of standard red laser source light (650 nm) to an effective wavelength of 65 nm inside the lens. This hyper-refractive state allows the integrated lens to function as a solid immersion system with significantly enhanced optical power, projecting a demagnified image onto a silicon wafer 10 times smaller than the diffraction limit would normally permit. This approach offers a pathway to advanced integrated circuit scaling by achieving Extreme Ultraviolet (EUV)-class2resolution using standard optical frequencies, thereby bypassing the complexity and energy costs associated with high-energy photon sources.
Category: Quantum Gravity and String Theory

A Unified Force Density Framework for Plasma Confinement: Integrating Navier-Stokes with Local Interaction Field Equilibrium (LIFE)

Authors: Wim Vegt
Comments: 47 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Achieving stable magnetic confinement in nuclear fusion plasmas remains a profound theoretical and engineering challenge. Fundamentally, plasma confinement is a problem of macroscopic force density equilibrium. However, standard Magnetohydrodynamic (MHD) models treat mechanical fluid dynamics and electrodynamics as coupled but distinct systems, often relying on fragmented approximations that struggle to predict complex plasma instabilities.This paper introduces a unified theoretical framework that seamlessly integrates the mechanical fluid dynamics of the Navier-Stokes equations (governing mechanical pressure and fluid velocity) with the Local Interaction Field Equilibrium (LIFE) theory. By strictly expressing all physical interactions—including mechanical pressure, radiation pressure, electromagnetic field tensors, inertia, and gravitational coupling—in identical dimensions of force density (N/m3), we derive a single, continuous equilibrium field equation.This exact dimensional consistency eliminates the mathematical boundaries between the material plasma (Deuterium infusion) and the energetic confinement fields (microwave heating and magnetic containment). The resulting unified N/m3 equation provides a novel, rigorous analytical foundation for understanding high-energy plasma dynamics, offering new predictive pathways for mitigating instabilities in Tokamak and stellarator confinement systems.
Category: High Energy Particle Physics

A New Method for the Cubic Polynomial Equation

Authors: Jose Risomar Sousa
Comments: 4 Pages.

I present a method to solve the general cubic polynomial equation based on six years of research that started when, in the fifth grade, I first learned of Bhaskara's formula for the quadratic equation. I was fascinated by Bhaskara's formula and naively thought I could replicate his method for the third degree equation, but only succeeded after countless failed attempts. The solution involves a simple transformation to form a cube and which, by chance, happens to reduce the degree of the equation from three to two (which seems to be the case of all polynomial equations that admit solutions by means of radicals).
Category: Algebra

'show me the Mind of God', Said Einstein, so Let’s do it

Authors: Carl Littmann
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

Einstein, is likely one example of a few who asked, "Why is the universe, fundamentally, the way it is, instead of other possibilities we can imagine?" For example, "Why don’t we have a universe of solely empty space, i.e., all nothingness, total ‘void’, with no matter nor energy in it, instead of our universe with some mass?" Finding good answers may seem impossible, but let’s attack such problems creatively. Regarding the above question, for example, we note that the opposite of a ‘totally void universe’ is a ‘fully-filled universe’. But the ‘fully-filled’ option drags along with it, a huge load of other questions, possibilities, and problems to be worked out. Thus, perhaps those many other questions and issues, dragged along with it, is the main ‘reason’ why we have a universe with ’gross’ mass occupying only a very low fraction of all space, (i.e., only 10 to the minus 19 power, or less). But still, some fraction of space, indeed! So, below we formally present our analytic method, involving comparing different possibilities and their merits. And give examples of that. And we conclude, that "God did not ‘play dice’, so-to-speak, when ‘choosing our universe’."
Category: Relativity and Cosmology

A Synchronisation-Free Experiment to Test the One-Way Isotropy of Light Speed

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

We propose an experiment to test whether the one-way speed of light is isotropic, without relying on clock synchronisation between separated stations. Two identical stations separated by a fixed distance exchange laser beams through complementary shutters driven by independent atomic clocks. The phase relationship between the two stations' light maxima directly encodes any asymmetry in one-way light speed. No synchronisation signal is required and the measurement is not circular. Relative clock drift between stations is monitored by observing whether the inter-station timestamp offset remains constant over the measurement interval. This offset is not interpreted as a one-way propagation time and does not constitute a synchronisation convention -- it serves solely as a stability diagnostic. The known frequency precision of atomic clocks, combined with regular monitoring of this offset, provides sufficient warranty of system integrity. The experiment is sensitive to any preferred-frame velocity component along the baseline. The true velocity of the apparatus through such a frame -- if one exists -- is unknown. Earth's orbital velocity of approximately 30 km/s is a lower bound only; contributions from the motion of the solar system and galaxy relative to other astronomical reference points could raise the true figure substantially. A null result would constrain preferred-frame theories. A non-null result would warrant careful independent replication.
Category: Relativity and Cosmology

Numerical Study of Anharmonic Oscillator Using Python Code

Authors: Sahebabegum Pathan, Naveen K. Singh
Comments: 15 Pages.

In this work, we explore the python code to study the anharmonic oscillator. In obtaining the numerical solution for eigenvalues and eigen-functions, we discretize the spatial coordinates into the finite number of grid points and use the finite difference method. We observe that the effect of anharmonic term in hamiltonian in shifting energy level increases towards higher energy states. We compare eigen functions for ground, first excited and second excited state of the harmonic oscillator with anharmonic oscillator. Further, the corrected wave-functions using first order perturbationtheory are compared with wave-functions obtained from the numerical solutions of Schrodinger’s equations. The numerical Python code shows consistency of first order perturbation theory for the small value of anharmonic term.
Category: Quantum Physics

A Stronger Generalization of the Riemann Functional Equation

Authors: Jose Risomar Sousa
Comments: 12 Pages.

A generalization of the Riemann functional equation with a broader validity domain than the one available in the literature is introduced. The insight that led to this new relation came from a new formula for the zeta function created herein that implies the Riemann functional equation. A few minor developments that stem from new formulae introduced previously are also discussed.
Category: Number Theory

Energy Conservation Equation of Gravitational Retardation Potential Force

Authors: Xianxiang Duan
Comments: 3 Pages.

Following the analogy with the Feynman electromagnetic retardation potential formula,it is necessary to derive the energy conservation equation, which requires the concept of "repulsion." The four equilibrium forces governing Mercury's orbit consist of gravity, mass fieldforce, centripetal force, and another force; integrating this formula yields the energyconservation equation.
Category: Relativity and Cosmology

Explanation of Time Dilation in a GPS Satellite Without Using the Relativity Theor

Authors: Jorma Jormakka
Comments: 8 Pages.

In relativity theory the advance of an atomic clock in a GPS satellite of some38 microseconds in 24 hours is explained by time dilation because of velocity from the Special Relativity Theory and time dilation in a gravitational field from the General Relativity Theory. The article shows that the time advance of a GPS satellite can be explained without any relativity theory and the formulas are in the first order the same as inthe relativity theory. It is also shown that the calculation of the GPS clock advance from the relativity theory is incorrectly made: in relativity theory there is the equivalence principle and because of it, the time dilation caused by acceleration due to the curved orbitmust be included. When it is included, the clock advance is incorrect. It is also shown thatEinstein's 1907 calculation of the gravitational redshift is incorrectly made, though theresult is correct.
Category: Relativity and Cosmology

On a Converging Infinite Series Defined by Super-Exponentials

Authors: Rusin Danilo Olegovich
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We introduce and study the entire function $lambda(s) = sum_{n=1}^{infty} n^{s+1/2}/n^n$,defined by a Dirichlet-type series with super-exponential coefficients. We prove that$lambda(s)$ converges absolutely for all $s in mathbb{C}$, uniformly on compact sets,and is therefore an entire function of order zero. We establish a closed-form evaluationof the special value $lambda(-1/2) = int_0^1 x^{-x}, dx$, connecting $lambda$ to theclassical Sophomore's Dream identity of Bernoulli. We further prove that $lambda(s)$ isterm-by-term differentiable, with $lambda^{(k)}(s) = sum_{n=1}^{infty} (ln n)^k n^{s+1/2}/n^n$for all $k geq 0$, justified by the Weierstrass $M$-test. Finally, we propose a conjectureconnecting $lambda(s)$ to the Riemann zeta function.
Category: Number Theory

Perceived Downward Acceleration of Objects

Authors: Matt Guiney
Comments: 10 Pages.

Based on numerous physical experiments that can easily be performed by anyone, the arrangement of different matter of varying densities which are contained in a vessel are always arranged in a particular order when a force is applied to that vessel and that vessel is put into motion. The direction of the motion dictates the density gradient orientation. Based on other experiments it is also apparent that this arrangement of matter (based on density and dependent on the direction of motion) ceases when objects are in free fall. This would imply that when objects are in free fall there is no force present that is responsible for the apparent downward motion of objects, but rather the reference frame (earth) is moving upwards to meet the objects. This concept is explored (the upwards motion of the earth) and calculations are performed to understand how we (standing on earth) can perceive a downward acceleration (g) of objects in free fall if the earth is in motion upwards. Other concepts regarding the motion of the earth are also discussed.
Category: Relativity and Cosmology

Telomeres and Longevity

Authors: Clark M. Thomas
Comments: 7 Pages.

Telomeres in humans are caps at the two ends of chromosomes that largely determine our normal life expectancy. Chromosomal senescence typically approaches before our death, and no amount of botox can stop it. Interestingly, some people live longer than their seventies, with delayed senescence. Even though quality of life is more important than quantity, most of us want both quality and quantity, with minimal time spent in senescence. To what degree could this optimum be under our control? If we all could approach seeming immortality, what could that life extension mean for our individual and social lives?
Category: General Science and Philosophy

Quadrature Approximation to the Magnus Exponent for Numerical Solution of Non-Autonomous Coupled Linear Differential Equations

Authors: Kenneth C. Johnson
Comments: 14 Pages.

The Magnus-exponent method of solving non-autonomous (variable-coefficient) coupled linear differential equations is reviewed, and three quadrature approximation formulas are derived with residual errors proportional to the 3rd, 5th, and 7th power of the integration interval size.
Category: Functions and Analysis

Decreasing Universe Theory: Cosmological Time Dilation and the SN1A Explosion

Authors: Joao Carlos Holland De Barcellos
Comments: 16 Pages.

We will show that, within the "Decreasing Universe Theory" (DUT), time inside a gravitational field isaltered in the same way as spatial distance measurement scales. At the cosmic level (timescales of millions of years), this effect becomes perceptible and explains the variation in the measured duration of Type Ia Supernova (SN1A) explosions.
Category: Relativity and Cosmology

Euler Product-Power Series Representation of the Dirichlet Eta Function

Authors: Ryan Hackbarth
Comments: 4 Pages.

In this paper, I demonstrate how the Dirichlet Eta function may be represented as a sum of its fundamental frequencies through the use of a power series whose coefficients are the Euler Product representation of the Riemann Zeta function.
Category: Number Theory

DeepSlide: From Artifacts to Presentation Delivery

Authors: Ming Yang, Zhiwei Zhang, Jiahang Li, Haoseng Liu, Yuzheng Cai, Weiguo Zheng
Comments: 37 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Presentations are a primary medium for scholarly communication, yet most AI slide generatorsoptimize the artifact (a visually plausible deck) while under-optimizing the delivery process (pacing, narrative, and presentation preparation). We present DeepSlide, a human-in-the-loop multi-agent system that supports preparing the full presentation process, from requirement elicitation and time-budgeted narrative planning, to evidence-grounded slide—script generation, attention augmentation,and rehearsal support. DeepSlide integrates (i) a controllable logical-chain planner with per-node timebudgets, (ii) a lightweight content-tree retriever for grounding, (iii) Markov-style sequential rendering with style inheritance, and (iv) sandboxed execution with minimal repair to ensure renderability. We further introduce a dual-scoreboard benchmark that cleanly separates static artifact quality from dynamic delivery excellence. Across 20 domains and diverse audience profiles, DeepSlide matches strong baselines on artifact quality while consistently achieving larger gains on delivery metrics,improving narrative flow, pacing precision, and slide—script synergy with clearer attention guidance.
Category: Artificial Intelligence

The Non-Existence of Non-Trivial Periodic Orbitsin the Collatz Mapping

Authors: Xiaofeng Hu
Comments: 6 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

The Collatz conjecture states that for any given positive integer N,if N is even, divide it by 2; if N is odd, multiply it by 3 and add 1.Repeating this process,N will eventually become 1. This paper provesthat any positive odd integer O other than 1 cannot return to itself nomatter how many times the iteration is performed. We derive the generalformula satisfying this condition and rigorously prove by mathematicalinduction that this formula equals 1 uniquely in the set of positive oddintegers. We thus conclude that there are no non-trivial periodic orbitsin the Collatz mapping.
Category: Number Theory

Reducing Credit Assignment Variance via Counterfactual Reasoning Paths

Authors: Fei Ding, Yongkang Zhang, Yeling Peng, Youwei Wang, Guoxiong Zhou, Zijian Zeng
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Reinforcement learning for multi-step reasoning with large language models (LLMs) often relies on sparse terminal rewards, leading to poor credit assignment conditions where the final feedback is evenly propagated across all intermediate decisions. This results in high gradient variance, unstable training, and numerous ineffective updates, ultimately causing the model to fail and preventing sustained improvement. We introduce a counterfactual comparison-based credit assignment framework, which samples multiple reasoning trajectories under the same input. By treating their differences as an implicit approximation of alternative decisions, we construct an implicit process-level advantage estimator that transforms sparse terminal rewards into step-sensitive learning signals. Based on this, we propose Implicit Behavior Policy Optimization (IBPO), which significantly improves training stability and performance upper bounds on mathematical and code reasoning benchmarks, pointing to a promising direction for unlocking the performance potential of LLMs.
Category: Artificial Intelligence

Design Conditions for Intra-Group Learning of Sequence-Level Rewards: Token Gradient Cancellation

Authors: Fei Ding, Yongkang Zhang, Youwei Wang, Zijian Zeng
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In sparse termination rewards, intra-group comparisons have become the dominant paradigm for fine-tuning reasoning models via reinforcement learning. However, long-term training often leads to issues like ineffective update accumulation (learning tax), solution probability drift, and entropy collapse. This paper presents a necessary condition for algorithm design from a token-level credit assignment perspective: to prevent reward-irrelevant drift, intra-group objectives must maintain gradient exchangeability across token updates, enabling gradient cancellation on weak-credit/high-frequency tokens. We show that two common mechanisms disrupting exchangeability make "non-cancellation" a structural norm. Based on this, we propose minimal intra-group transformations to restore or approximate the cancellation structure in the shared token space. Experimental results demonstrate that these transformations stabilize training, improve sample efficiency, and enhance final performance, validating the value of this design condition.
Category: Artificial Intelligence

Flow-Oriented Programming and XF: A Preliminary Synthesis of Paradigm, Design, and Evaluation

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

Modern data processing increasingly relies on workflows centered on filtering, transforming, aggregating, and routing structured data, yet mainstream programming paradigms do not always treat explicit data flow and composable transformation as primary computational concerns. This paper synthesizes three related lines of inquiry: the conceptual formulation of Flow-Oriented Programming (FLOP), the design and implementation of XF as an experimental realization of that model, and the empirical evaluation of XF across representative data-oriented workloads. Through this synthesis,the paper examines the historical development of programming languages and paradigms through the lens of composability, abstraction, and data transformation, and positions flow-oriented programmingas a data-first model centered on explicit transformation pipelines. XF is then considered as a practical implementation of this model, emphasizing composable operations, decentralized control flow, and explicit value-state semantics. Benchmark results across CSV aggregation, transformation pipelines, pattern processing, and concurrency scaling suggest that while XF does not yet match the raw performance of mature language ecosystems, it demonstrates that flow-oriented programming is both expressively coherent and practically implementable as a distinct approach to data-intensive computation.
Category: Data Structures and Algorithms

An Experiment Proposal Testing ‘spooky Action at a Distance’

Authors: Xianming Meng
Comments: 13 Pages.

The results of numerous Bell tests are viewed as evidence of quantum entanglement: the instant inner connection between totally separated entangled particles, which explains the ‘spooky action at a distance’, a term coiled by Einstein. The paper proposes a variation to Bell tests, aiming to prove or disprove spooky action from a distance. The main variation is an added pair of half-waveplates, with which we can change the relative polarization angle of the entangled photon pairs and assess its impact. The paper has derived the quantum prediction of Bell tests due to the changes in both the relative polarization angle of the entangled photon pairs and in the relative angle of the polarization measurement devices. If the quantum prediction is proven correct by experiments, the claim of instant inner connection between entangled particles or spooky action from a distance must be false.
Category: Quantum Physics

How to Comprehend the Unphysical Quantum Superposition and Entanglement

Authors: Xianming Meng
Comments: 11 Pages.

The concepts of quantum superposition and entanglement are at the heart of quantum mechanics, but they often cause confusion. This paper shows that the concepts are intimately related to quantum coherence. Through examining the traditional arguments, the paper reveals that the essence of quantum superposition is a statistical superposition of coherent states, while quantum entanglement results from the coherence of entangled particles as well as the common rule governing the measurements.
Category: Quantum Physics

A Classical Mechanics Solution to Zeno's Arrow Paradox

Authors: Vladislav Smolenskij
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)

The flying arrow paradox states that motion is impossible, as the arrow is motionless at every instant of time. Although the paradox has a mathematical solution, a physical uncertainty remains: is time continuous, or does it consist of numerous infinitesimally small intervals? Within the framework of classical mechanics, it is shown that the assumption of instantaneous rest (zero velocity at any moment) inevitably violates the laws of conservation of momentum and kinetic energy. A flying arrow cannot stop or resume its motion without external input. Consequently, the arrow cannot be "at rest" within an infinitesimally small interval of time, and/or time does not contain any "zeros" and flows continuously.
Category: Classical Physics

Remarks on Vibrational Interpretations of the Schrödinger Equation

Authors: Martin Kraus
Comments: 8 Pages.

While the Schrödinger equation is one of the most important equations in physics, its interpretation is still being debated even one hundred years after its original publication. After summarizing Schrödinger's vibrational interpretations, this work remarks on three specific features that might be of particular interest for the development of future vibrational interpretations.
Category: History and Philosophy of Physics

On the Iterative Convergence of Fermat Numbers Through Continued Fractions

Authors: S. Mayank
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper presents a novel iterative representation of Fermat numbers, defined by the sequence Fn = 2^(2^n) + 1. By leveraging the fundamental recurrence relation F(n+1) - 2 = Fn(Fn - 2), we define a functional equation x = A/x - 2, where A = F(n+1) - 2. We demonstrate that this equation yields two integer solutions, x1 = Fn - 2 and x2 = -Fn. Through an analysis of the derivative of the map f(x) = A/x - 2, we prove that x = -Fn is an attractive fixed point and x = Fn - 2 is a repulsive fixed point, leading to a unique, convergent infinite continued fraction for the negative of any Fermat number. This provides a bridge between the rapid growth of Fermat sequences and the stability of iterative rational functions.
Category: Number Theory

The Twin Paradox Explained With the Acceleration

Authors: Leonardo Rubino
Comments: 8 Pages. In English and English (Note by viXra Admin: Please cite and list scientific references)

The Twin Paradox [is] Explained With the Acceleration.
Category: Relativity and Cosmology

Multiverse Idea in Cosmology

Authors: Kiyoung Kim
Comments: 7 Pages.

From the perspective of objective natural philosophy, cosmology should adopt a broader view consistent with nature's fundamental properties, such as continuity and cyclicity. It should move beyond the claim that the entire universe originated from a single event—an explosion of pure energy—that birthed time and space solely within the framework of general relativity. Such a shift suggests that our universe may be one of many, each following its own life cycle. We first review dark energy—long a subject of debate regarding its true nature and role in the universe's accelerating expansion—and explain how this expansion is possible within a 4-D complex space model. Additionally, we review the second law of thermodynamics to explain how the entropy of a cyclic universe evolves.
Category: History and Philosophy of Physics

Strictly Isolated Prime Constellations at Offsets {0, 8, 14, 18, 24, 32} and Their Associated Composite Pairs

Authors: Christoper Mututu
Comments: 13 Pages. (Note by viXra Admin: For the last time, please cite and list scientific references)

We introduce a deterministic construction for generating composite number pairs (A,B) from strictly isolated prime sextets, configurations of exactly six primes situated at fixed offsets {0,8,14,18,24,32} from a base value a≡9 (mod 10) with no additional prime existing anywhere within the interval [a,a+32]. We term such configurations strictly isolated prime constellations of order six.The structural constraint a≡9 (mod 10) forces the six primes to terminate in the digit pattern 9,7,3,7,3,1 respectively which is a consequence of the fixed offsets modulo 10. These six primes are arranged into a 2×4 rectangle whose columns are indexed by the digits {1,3,7,9}, the complete set of possible terminal digits of any prime greater than 5. Column wise addition and subtraction yield a Sums row and a Difference row from which the composite A and B are defined by their respective totals.We prove that this construction satisfies four universal invariants. First, the closed form identities A=6a+96 and B=2a+52 hold for every valid cluster. Second, A is always divisible by 1,2,3,5 and 6 while B is always divisible by 1,2,5 and 10, both following algebraically from a≡9 (mod 10). Third, the decimal expansion of A/B always carries a signature 2.9u2026 and B/A always carries initial signature 0.3u2026 for all a≥274 proven via closed form analysis. Fourth, both A/B and B/A always produce non terminating repeating decimal expansions guaranteed by the arithmetic structures of the reduced denominators.These four invariants are established algebraically and confirmed computationally across 17,138 valid clusters up to 100 billion with zero failures on every claim.
Category: Number Theory

The Existence of Hilbert-Pólya Operator

Authors: Amal Ladjeroud
Comments: 10 Pages.

Hilbert-Pólya conjecture is proved by constructing Hilbert-Pólya operator, the self-adjoint operatorwhere its eigenvalues are exactly the imaginary parts of zeros of Riemann zeta function on the critical line. Hence, the Riemann hypothesis is true.
Category: Number Theory

Proof of Collatz Conjecture

Authors: Pranshu Tripathi
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)

The collatz conjecture was introduced by Lothar collatz in 1937. It is also known as "3n + 1 problem". The conjecture states: Start from any positive integer, n. If n is even, divide by 2; if n is odd, multiply by 3 and add 1. Now, the conjecture says that if you keep repeating above steps, you will finally reach 1, no matter what value of n we choose. In this paper, we prove collatz conjecture using method of mathematical induction. We also use binary and trenary numbers to prove collatz conjecture.
Category: Number Theory

Lack of Cosmological Expansion Versus the Hubble Crisis

Authors: Michael A. Ivanov
Comments: 6 Pages.

Based on the low-energy quantum gravity model, it is shown that the overestimation of the Planck constant at small z, characteristicof the ΛCDMcosmological model, can be eliminated using a two parameter luminosity distance function that takes into account the change in the number of photons. This new function was fitted to a similar function in the ΛCDM model, which best describes observations. Estimates were obtained for the light attenuation parameter, which replaces the effect of dark energy, and for the Hubble constant in the new model without cosmological expansion. Such a resolution of the Hubble crisis could cause a serious conceptual crisis in moderncosmology.
Category: Quantum Gravity and String Theory

Verification Experiment of the "Electromagnetic Wave" Theory Based on a Half-Wave Dipole Dual-Antenna Pair

Authors: Hongyuan Ye
Comments: 15 Pages. (Note by ai.viXra.org Admin: Author name is required in the article after article title; and please cite and list scientific references)

Maxwell's equations theoretically introduce the hypothesis of "displacement current", stating that in a vacuum, a changing electric field can induce a changing magnetic field. Based on this, Maxwell predicted the existence of "electromagnetic waves" in a vacuum. The latest research indicates that the theory of "electromagnetic waves" has never been experimentally verified. The experiment conducted by German physicist Hertz in 1887 did not prove the existence of "electromagnetic waves" but rather demonstrated that wireless communication could be achieved by independent "electric field waves". Further research reveals that the hypothesis of "displacement current" is theoretically inconsistent. The simplest and most convincing way to verify the correctness of Maxwell's "electromagnetic wave" theory is to independently measure the electric field intensity and magnetic field intensity of electromagnetic radiation in wireless communication, and then determine through experiments whether the electric field energy density is equal to the magnetic field energy density. This verification experiment is based on the 3-meter method of EMC electromagnetic compatibility standards. A half-wave dipole dual-antenna configuration with reverse attenuation is used to cancel out the magnetic fields generated by the conduction currents of the two antennas, and the electric field intensity and magnetic induction intensity in the far-field of electromagnetic radiation are independently measured. The verification experiment shows that the electric field energy density is 137.6 times that of the magnetic field energy density, and the experimental result is 137.6 times the theoretical value of the "electromagnetic wave" theory. In this verification experiment, the relative error of the electric field intensity measurement is +/- 5%, and that of the magnetic field intensity measurement is +/- 40%. The experimental results are real and valid. This experiment fully proves that, whether in the near-field or far-field, the electromagnetic fields originate from the conduction current of the antenna. In a vacuum, without the participation of charges, a changing electric field cannot generate a changing magnetic field, and a changing magnetic field cannot generate a changing electric field. "Electromagnetic waves" do not exist in the objective physical world.
Category: Classical Physics

Duality in Physics

Authors: A. V. Kaminsky
Comments: Pages.

We propose an ontological interpretation of quantum mechanics based on the principle of subjective incompleteness—a fundamental limitation arising from the fact that the observer is part of the world being observed. By formalizing consciousness as a set of states Subj and the world as a self-mapping W:Subj→Subj, we construct an ontological configuration space whose structure naturally gives rise to the Hilbert space of quantum states. Within the proposed model, the hidden parameters in the representation of an observable operator are the eigenvalues of its canonical conjugate. In particular, the coordinate and momentum representations complement each other to form a complete ontological description, with the corresponding variables appearing as mutually hidden. From this perspective, the phenomenon of duality in physics, exemplified by pairs such as coordinate—momentum or time—energy, reflects the underlying subject—object structure of reality.The model offers a new justification of Bohr’s principle of complementarity and provides a geometrical account of noncommutativity in terms of subjective incompleteness. Furthermore, the entropic uncertainty relations of Hirschman—Everett are reinterpreted as quantitative measures of subjective incompleteness. This approach links the growth of thermodynamic entropy with the "motion" of the observer’s consciousness along the gradient of ontological states, thereby providing a natural explanation of the thermodynamic arrow of time.Thus, the key features of quantum mechanics emerge from the fundamental principle of subjective incompleteness. This article continues a series of works devoted to the role of the observer and consciousness in physics.
Category: Quantum Physics

Effective Field Dynamics and Quantum Emergence from Intrinsic Oscillations in a Bounded Vacuum

Authors: Tanuj Kumar, Vandana [Doe]
Comments: 16 Pages.

We extend the bounded-vacuum framework introduced in Ref. [1] by incorporating the intrinsic dynamical properties of localized vacuum configurations and deriving a unified effective field equation for the vacuum potential Φ(x,t). In this approach, matter is identified as a localized vacuum loading corresponding to a deficit of the vacuum potential. We show that stable vacuum loading configurations have their own intrinsic degrees of freedom associated with vibrations of definite frequency ω_0; small deviations from the equilibrium satisfy the Klein—Gordon-type equation, so that the dispersion relation gives the known energy-momentum dependence E^2=p^2 c^2+m^2 c^4, where mass originates due to the condition ℏω_0=mc^2. The field equation under discussion includes not only the wave propagation, but the effect of gravity and the restoring force which represents a sort of the vacuum capacity limitation; in such a way we get the unified treatment of the problem of both massive and massless particles. Within the nonrelativistic limit, the theory turns out to be nothing else but the Schrödinger equation with the effective potential associated with fluctuations of the vacuum potential.
Category: Quantum Gravity and String Theory

Definitive Proof of Brocard's Conjecture

Authors: Kenneth A. Watanabe
Comments: 19 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents a formal proof of Brocard’s Conjecture, which posits that there are at least four prime numbers between the squares of any two consecutive primes p_i² and p__i+1² for i>1. By defining the function π^*(n) that approximates the prime counting function π(n), we establish a lower bound for the number of primes in these intervals. Using mathematical induction, we demonstrate that the minimum number of primes in the interval, Δπ^*(p_i), is consistently greater than or equal to 4 for all p_i ≥ 3. The proof is further supported by a rigorous error analysis, bounding the maximum possible deviation between the estimated prime count π^*(n) and the actual prime counting function π(n).
Category: Number Theory

Turnover and Catalytic Cycle Frequency Determination based on Molar Mass-dependent Model Equations

Authors: Ikechukwu Iloh Udema
Comments: 23 Pages. [New version of] ChemRxiv via 10.26434/chemrxiv-2023-0sjpl

There were conflicting definitions and misrepresentations of turnover frequency (TOF), catalytic cycle frequency (CCF), and catalytic first-order rate constant (k_cat) in the literature. Based on the Benfield and Lineweaver-Burk methods, data were generated. The results indicated that the CCFs for the forward (~ 0.0025-1.58 exp. (+17)/s) and reverse (~ 0.0003-5.4 exp. (+18)/s) directions showed an increasing trend with higher concentrations of the enzyme; this was applicable to the TOF. The number of fragments per molecule of an enzyme in the forward direction was 0.19-1.23 exp. (+5). In conclusion, TOF and CCF are different parameters, and the former in particular was not the same as k_cat, while the latter was a constant; TOF and CCF vary. Strictly speaking, TOF was equal to f(M_3). Besides, CCF per molecule (> 1) of the enzyme is greater than TOF (< 1). This can be verified using sucrase in a future study; a larger data set is needed if starch is a substrate in order to reevaluate the models and address statistical concerns. PACS: 87.15.RJ; 87.14.ejKeywords: Aspergillus oryzae alpha-amylase; Catalytic cycle frequency; First-order catalytic rate constant; Gelatinized insoluble potato starch; Turnover number; Turnover number frequency.
Category: Biochemistry

A Note on the Structural Cancellation of Fourth-Order Singularities: Implications for Fluid Dynamics and Field Theory

Authors: Daniel Henrique Pereira
Comments: 7 Pages.

A recent work explores the Riemannian geometry of Victoria-Nash Asymmetric Equilibrium (VNAE) manifolds. A fourthu2011order cancellation in the curvature tensor follows from Schwarz's theorem and Riemann antisymmetry. This resolves the higheru2011order complexity that hindered Einstein's nonu2011symmetric field theory. The same mechanism suggests a conceptual parallel with the Navieru2011Stokes regularity problem, though no solution is claimed.
Category: Relativity and Cosmology

Riemannian Manifolds of Asymmetric Equilibria: Complete Geometric Structure and Curvature Signatures

Authors: Daniel Henrique Pereira
Comments: 25 Pages.

We develop the complete Riemannian geometry of Victoria—Nash asymmetric equilibrium manifolds (VNAE) for $n$-player games. The metric (g_{ij} = iota_i iota_j delta_{ij} + varepsilon H_{ij}(V,iota)) yields explicit Levi-Civita connection (Gamma^k_{ij}), Riemann tensor (R^i_{,jkl}) with fourth-order $V$-derivative cancellation, Ricci tensor (R_{ij} approx kappabigl(iota_{i,j} iota_i - kappa partial_i^2 iota_ibigr) delta_{ij}), and scalar curvature (K_s approx sum_{i<j} iota_i iota_j det H_{ij}^s + O(varepsilon^2)). Positive/negative/zero signatures classify stability geometrically. The Lyapunov—Morse functional (mathcal{L}) satisfies (frac{d^2}{dt^2}mathcal{L}big|_{mathrm{VNAE}} approx -2 operatorname{Ric}(dot{s}^perp,dot{s}^perp)) along gradient flows, establishing Ricci curvature as the normal contraction rate. Classical Nash, von Neumann’s minimax theorem, and Lyapunov stability emerge as degenerate flat limits as (varepsilonto0).
Category: Geometry

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

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

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

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

True AI Should Be a Loser, Not a Winner

Authors: Dimiter Dobrev
Comments: 6 Pages.

The modern definition of AI contains an inaccuracy. According to the definition we have nowadays, AI is a computer program which is successful. Indeed, for a computer program to be successful, it must be intelligent, but the opposite is not true. A program can be intelligent but not successful, merely because it pursues different goals and does not aim at the success in question. From a theoretical perspective, the modern definition of AI is good enough because it answers the question "What is AI?" even though it does not encompass all intelligent programs, but only some of them. From a practical standpoint, however, this definition is insufficient. The reason is that we are at the doorstep of creating True AI and among all intelligent programs we must choose the one we will be most comfortable with from now on. Thus, it is not a good idea to choose one of these successful programs. It would be better to choose a program that does not pursue victory at any cost. Such a program could be called a loser because it will not be successful enough. After all, both in humans and in AI relentless ambition is not a positive trait.
Category: Artificial Intelligence

New Research on Divergence and Curl

Authors: Hongyuan Ye
Comments: 7 Pages. (Note by viXra Admin: Please cite listed scientific references!)

Maxwell’s equations are an integration of divergence, curl, and classical electromagnetism. This study reveals that divergence and curl can apply to static electromagnetic fields, but not to dynamic, time-varying electromagnetic fields.
Category: Mathematical Physics

dstr: A Small Language for Systems That Become Graphs

Authors: Sambuddha Majumder, Jayanta Majumder
Comments: 19 Pages.

dstr is a compact language for describing finite dynamic systems in a form that is both easyto write and semantically explicit. Its primary interface is a small s—expression DSL in which one states variables, initial conditions, actions, invariants, and reachability goals without the verbosity that often discourages exploratory modeling. The resulting description is not intended merely to support a checker run. It is intended to generate an explicit state graph that can subsequently be queried, transformed, filtered, and published. The central claim of this paper is that a state—action language becomes substantially more valuable when its semantics are treated as a first—class graph artifact, suitable not only for validation but also for downstream graph analysis and presentation.
Category: Data Structures and Algorithms

Space-Time Nature Might be Used to Bridge Between the Quantum and the Classic Physics

Authors: u202aMoshe Segalu202cu200f
Comments: 16 Pages.

From the dawn of civilization Humans struggled to understand and explain their environment. The process of that struggle resulted in various branches of investigations and knowledge, which Humans denote as Science. Because the Human mind, which created this Science, is by itself composed of components which might be the same components that the environment is also composed of, Humans might be bound to never being able to understand and explain completely this environment, which is also denoted as the Existence, because one cannot explain an issue, if that explanation relies on this same issue. Nevertheless, Humans were still able to build a magnificent structure, of knowledge and explanations, which, as mentioned above, is denoted as Science which is still an ongoing endeavor, which continuously expands, reveals and explains more and more secrets embedded in the Existence. However, the nowadays Physics, which is the branch of Science which specifically focuses on understanding and explaining the Existence, is still composed of branches which are not fully compatible. One of these branches is the branch denoted as the Classic Physics, which focuses on understanding and explaining what is denoted as the Macroscopic Environment. Another such branch is the branch denoted as the Quantum Physics, which focuses on understanding and explaining what is denoted as the Microscopic Environment. And, as presented above, these two branches of Physics are not fully compatible, and Humans are still struggling, to expand the knowledge that might bridge the gap that still exists between these two branches of Physics. Moreover, even the branch of the Classic Physics itself, still embeds branches which are also not fully compatible, as for example, the Gravity and the Electromagnetism, and more must be done to bridge the gap that exists also between these two branches, which both belong, as stated above, to the branch of the Classic Physics. In the process of building the above-mentioned magnificent structure of Science, Humans detected in the Existence various components, and denoted these components as Entities, and used these Entities as the building blocks on which the Science of Physics was constructed. Two such Entities are the Entity of Space and the Entity of Time, which together were interweaved into one Entity, denoted as Einstein's four-dimensional Interwoven Space-Time Entity, by the Relativity Theories of Einstein. (Truncated by viXra Admin to <400 words)
Category: Relativity and Cosmology

Globoeconomics

Authors: N. S. Alsaud
Comments: 7 Pages.

The theoretical framework of globoeconomics is introduced in this paper as a global generalization of the economical analysis. This coherent treatment scientifically explains many perplexing economical, political and societal phenomena which necessitates rereading the historical development of humankind from novel perspective. Since the approaches used in this treatment provide more plausible and simpler justifications, they are suitable to be adopted based on the philosophical reasoning of Occam's razor.
Category: Economics and Finance

"Show me the Mind of Godu2026", Said Einstein, so Let’s do it

Authors: Carl Littmann
Comments: 5 Pages.

Einstein said, "I want to know how God created this world. I want to know His thoughts..." [1] So, I think Einstein sought answers to such basic questions as: "Why don’t we have a universe of solely empty space, i.e., all nothingness, total ‘void’, with no matter nor energy in it, instead of our universe with some mass?" Finding good answers may seem impossible, but let’s creatively try to. Regarding the above question, for example, we note that the opposite of a ‘totally void universe’ is a ‘fully-filled universe’. But the ‘fully-filled’ option drags along with it, a huge load of other questions, possibilities, and problems to be worked out. Thus, perhaps those many other questions and issues, dragged along with it, is the main ‘reason’ why we have a universe with ’gross’ mass occupying only a very low fraction of all space, (i.e., only 10 to the power of -19 or less). But still, some fraction of space, indeed! So, below we formally present our analytic method, involving comparing different possibilities and their merits. And give examples of that. And we conclude, like Einstein, that "God did not ‘play dice’, so-to-speak, when ‘choosing our universe’."
Category: Quantum Physics

Quadrature Approximation to the Magnus Exponent for Numerical Solution of Non-Autonomous Coupled Linear Differential Equations

Authors: Kenneth C. Johnson
Comments: 14 Pages. Added link to MATLAB code implementation.

The Magnus-exponent method of solving non-autonomous (variable-coefficient) coupled linear differential equations is reviewed, and three quadrature approximation formulas are derived with residual errors proportional to the 3rd, 5th, and 7th power of the integration interval size.
Category: General Mathematics

Reducing Credit Assignment Variance via Counterfactual Reasoning Paths

Authors: Fei Ding, Yongkang Zhang, Yeling Peng, Youwei Wang, Guoxiong Zhou, Zijian Zeng
Comments: 8 Pages.

Reinforcement learning for multi-step reasoning with large language models (LLMs) often relies on sparse terminal rewards, leading to poor credit assignment conditions where the final feedback is evenly propagated across all intermediate decisions. This results in high gradient variance, unstable training, and numerous ineffective updates, ultimately causing the model to fail and preventing sustained improvement. We introduce a counterfactual comparison-based credit assignment framework, which samples multiple reasoning trajectories under the same input. By treating their differences as an implicit approximation of alternative decisions, we construct an implicit process-level advantage estimator that transforms sparse terminal rewards into step-sensitive learning signals. Based on this, we propose Implicit Behavior Policy Optimization (IBPO), which significantly improves training stability and performance upper bounds on mathematical and code reasoning benchmarks, pointing to a promising direction for unlocking the performance potential of LLMs.
Category: Artificial Intelligence

A Classical Mechanics Solution to Zeno's Arrow Paradox

Authors: Vladislav Smolenskij
Comments: 3 Pages. Added References section as requested by viXra Admin

The flying arrow paradox states that motion is impossible, as the arrow is motionless at every instant of time. Although the paradox has a mathematical solution, a physical uncertainty remains: is time continuous, or does it consist of numerous infinitesimally small intervals? Within the framework of classical mechanics, it is shown that the assumption of instantaneous rest (zero velocity at any moment) inevitably violates the laws of conservation of momentum and kinetic energy. A flying arrow cannot stop or resume its motion without external input. Consequently, the arrow cannot be "at rest" within an infinitesimally small interval of time, and/or time does not contain any "zeros" and flows continuously.
Category: Classical Physics

Lack of Cosmological Expansion Versus the Hubble Crisis

Authors: Michael A. Ivanov
Comments: 6 Pages.

Based on the low-energy quantum gravity model, it is shown that the overestimation of the Hubble constant at small z, characteristic of the cosmological model, can be eliminated using a two-parameter luminosity distance function that takes into account the change in the number of photons. This new function was fitted to a similar function in the model, which best describes observations. Estimates were obtained for the light attenuation parameter, which replaces the effect of dark energy, and for the Hubble constant in the new model without cosmological expansion. Such a resolution of the Hubble crisis could cause a serious conceptual crisis in modern cosmology.
Category: Quantum Gravity and String Theory