All Submission Categories

Definite Integration and Summation Are #P-Hard

Authors: Leonid Gurvits, Warren D. Smith
Comments: 4 Pages.

We show that the common symbolic manipulation tasks of computing multiple partial derivatives, definite integration, and definite summation, are #P-hard, i.e, at least as hard as counting the accepting input strings for any Turing machine that halts in polynomial time. (The "multiple partial derivatives" part was previously known.)
Category: Combinatorics and Graph Theory

Accurate Circle Configurations and Numerical Conformal Mapping in Polynomial Time

Authors: Warren D. Smith
Comments: Sitting on my web pages since 1991; uploading to vixra for archival purposes.

According to a remarkable re-interpretation of a theorem of E.M. Andreev (1970) by W.P. Thurston (≈1982), there is a unique (up to inversive transformations) packing of interior-disjoint circles in the plane, whose contact graph is any given polyhedral graph G, and such that an analogous "dual" circle packing simultaneously exists, whose contact graph is the planar dual graph G*, and such that the primal and dual circle packings have the same set of tangency points and the primal circles are orthogonal to the dual ones at these tangency points.

This note shows that relatively and absolutely accurate coordinates for the primal and dual circles may be obtained in time polynomial in N, the number of vertices of the polyhedral graph, and D, the number of decimals of accuracy desired.

Consequently one may also accurately "midscribe"' a polyhedron – and simultaneously its dual – in polynomial time.

Also consequently, one may implement Riemann's conformal mapping theorem numerically, in polynomial time with provable accuracy.

Our result is obtained by generalizing and reformulating ideas found in the doctoral thesis of Walter Brägger [Math. Institut, Rheinsprung 21, CH-4051 Basel, Feb. 1991] to reduce our problem to maximizing a smooth convex function. This maximization problem is then solved by using Khachian's "ellipsoid method" or Vaidya's algorithm.
Category: Geometry

On the Nature of Light from the Original Meaning of the Antonyms "Bright" and "Dark"

Authors: Peng Xiaotao
Comments: 14 Pages.

Brightness and darkness are a pair of antonyms, both of which describe the state of the objective world related to light. Brightness refers to the state in which the observer can observe the surrounding things well when the light is abundant, while darkness refers to the state in which the observer can not perceive the surrounding things when there is no light. Therefore, the so-called light should be some kind of carrier that can change the state of things around the observer, but it is not something that the observer can directly perceive. Therefore, on the one hand, what the human eye sees can not be the so-called light; on the other hand, the light should be some carrier that can make the objective things bright, so that the human eye can see these things in a bright state. The objective things that can be seen by human eyes and are in a bright state are objective entities composed of various atoms, and it should be a force that can change their state. It can be seen that the essence of light should be the carrier responsible for transmitting some kind of force, which is most likely to exist only between charged particles. Therefore, there is good reason to think that the essence of light is a collection of some carrier or carriers responsible for the transmission of Coulomb force. This conclusion can explain all the physical phenomena and experimental results related to light at the same time, which is the most realistic conclusion at present. Hope to get the attention and support of experts, scholars and friends at home and abroad.
Category: Classical Physics

A Dual Extension for the Gamma Function and the Confinement of the Zeros of the Riemann Zeta Function

Authors: Julinho Jorge Luís
Comments: 14 Pages.

The Bohr-Mollerup Theorem establishes the uniqueness of the Gamma function on the right half-plane, but makes no assertion regarding extensions to the left half-plane that preserve the integral form. This work proposes a Dual Architecture consisting of two integral operators with complementary domains: the Classical Gamma and a Symmetric Factorial, connected by an operator derived from the Hankel contour integral. When applied to the Riemann zeta function, this architecture replaces the classical functional equation—which exhibits indeterminate forms at integer points—with a formulation that is directly evaluable and preserves all values of the Dirichlet series. Analysis of the connection operator reveals that its real part vanishes exclusively on the critical line within the critical strip. Assuming a non-trivial zero off this line leads, via a closed cycle of the dual functional equation, to a contradiction involving the modulus of the Gamma function, as established independently through the Weierstrass representation and the maximum modulus principle. The result forces all non-trivial zeros of the Riemann zeta function to lie on the critical line.Keywords: Gamma function, Riemann zeta function, critical line, Hankel contour, Weierstrass representation.
Category: Functions and Analysis

Arbitrary Approximation of the Shifted-LRC by the LRC

Authors: Deepak Ponvel Chermakani
Comments: 2 pages, 2 Theorems.

Consider an instance of the Shifted Lonely Runner Conjecture (S-LRC) where all n runners (except the stationary runner 0) have integer speeds and start from real values in [0,1[ at time t=0. We show that one can derive an alternative vector of starting points that can be made to be arbitrarily close to the initial vector of starting points. The alternative starting point of each runner i is a rational in [0,1[ and is expressible as (qi / P) where P is a large prime and qi is an integer in [0, P-1]. The S-LRC instance with the alternative starting points, allows a minimal loneliness gap of f, if and only if, the corresponding LRC allows a minimal loneliness gap of f, where f is a desired fraction in ]0,1[. This finding is important in the light of recent counter-examples to the shifted-LRC.
Category: Functions and Analysis

A "Good" Problem Equivalent to the Riemann Hypothesis

Authors: Warren D. Smith
Comments: This 1995 paper by me, heavily revised 2005, had been sitting on my web page but is now uploaded to vixra for archival purposes.

We exhibit a sequence c_n such that the convergence of ∑c_nzⁿ for all complex z with |z|<1 is equivalent to the Riemann Hypothesis. We argue that this particular RH-equivalent problem is "better" than most, or perhaps every, other RH-equivalent problem devised so far, in the sense that (we prove) there is a tremendous gap in behaviors of the c_n if the RH is true versus if the RH is false.
Category: Number Theory

Linear Transformations in the Reciprocal Gamma Function Quadrature

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

As an extension from my previous work, the paper attempts to generalize the Reciprocal Gamma Quadrature under the curve to general linear transformations on the argument itself. It extends further into the territory of Volterra Functions and Ramanujan's Log-Gamma integrals related to the Fransén-Robinson Constant.
Category: Number Theory

Identifying Natural Limits to Infinite Algebraic Singularities with Null Algebra

Authors: Robert S. Miller
Comments: 22 Pages. (Note by viXra Admin: Please cite and listed scientific references)

This paper introduces a framework which regularizes the classical algebraic singularity, using the essential hyperbola y=1/x to illustrate its application. Traditional, classical mathematics leaves the behavior at the origin for this function undefined due to divergence toward unachievable infinities. By using the transformational matrix defined in Null Algebra to map u=-1/y, the defined subspace of y, we may focus on a rate of information transfer implied by the function, as x→0. This is achieved by imposing a strict constraint upon dy/du which is required for any function y=f(x) and based upon chosen scale for the system defined by y=f(x). This shall show the singularity cannot actually be achieved due to natural self-limiting properties unique to a given function which emerge from Null Algebra, leaving a function, that is piecewise defined and continuous.
Category: General Mathematics

Entropic Origin of the Cosmological Constant A(t): Analytical Derivation of 10^122 Bits and Validation via Planck Data

Authors: Friedhelm M. Jöge
Comments: 14 Pages.

The discrepancy 0f 10^120 between the observed cosmological constant and quantum field theory (QFT) predictions remains one of the greatest enigmas in modern physics. The study provides a novel analytical derivation of this value by treating gravity as an entropic force arising from bits on a holographic screen. By establishing a direct link between the bit density of the universe and the dynamic nature of dark energy, the study offers a potential resolution to the cosmological constant problem. These findings bridge the gap between quantum information theory (QIT) and general relativity theory (GRT), suggesting that the accelerated expansion of the universe is a emergent phenomenon driven by the evolution of cosmic entropy.Since dark energy is not simply given as a number, but is derived from the age of the universe (13.82 billion years), the "naturalness problem" - one of the biggest problems in physics - can be solved.It is shown that all the information of the universe is encoded on the Planck-scale and is "unrolled" into spacetime by factor tu (Holographic Principle). The fact that the theoretically derived value of the Hubble constant (Ho) lies well within the range of astronomical measurements is the strongest indication that the connection between the Planck-scale and the age of the universe (tu) is not mere numerology, but a physical principle.
Category: Relativity and Cosmology

How a Matter-to-Vacuum Phase Transition Can Prevent Black-Hole Singularities

Authors: Rudi Van Nieuwenhove
Comments: 14 Pages.

The appearance of spacetime singularities during gravitational collapse remains one of the most important unresolved problems of General Relativity. In the standard picture, continued compression of matter inside a black hole leads to divergent densities, divergent spacetime curvature, and the breakdown of the classical gravitational description. In this work, we investigate an alternative phenomenological scenario in which gravitational collapse triggers a density-induced matter-to-vacuum phase transition once a critical density is reached.We assume that above this threshold ordinary matter is rapidly converted into a Vacuum Localized Structure (VLS) phase, representing a localized vacuum state that carries the mass-energy of the original collapsing matter. The detailed microscopic mechanism responsible for the transition is not specified. Instead, the transition is treated as an effective process that replaces the collapsing matter by a compact vacuum structure while conserving the total mass-energy of the system.The post-transition object is modeled as a static, spherically symmetric equilibrium configuration governed by the Einstein field equations and the Tolman-Oppenheimer-Volkoff equation. A Gaussian density distribution is adopted for the VLS phase, leading to finite central density, finite pressure, and a regular mass profile throughout the interior. The characteristic size of the VLS core follows directly from mass conservation and is uniquely determined by the total mass and the critical transition density.The resulting solutions replace the classical black-hole singularity by a finite-curvature core. The mass function approaches zero smoothly at the center, preventing the divergent gravitational compression associated with conventional collapse solutions. Consequently, all curvature invariants remain finite and the spacetime remains regular throughout the interior region. In this sense, the phase transition acts as a gravitational regulator, replacing continued compression by a stable vacuum-supported equilibrium configuration.Within this framework, singularity avoidance emerges without modification of the Einstein field equations and without the introduction of an explicit de Sitter vacuum core.
Category: Relativity and Cosmology

Atoms Through Nonlinear Dynamical Systems

Authors: Najib Chairi
Comments: 15 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org) Copyright © 2026 by the author(s), all rights reserved.

The atom is traditionally described by quantum mechanics through linear equations, especially the Schrödinger equation. Yet as soon as the number of particles increases, the atom no longer remains a simple one-body problem: electrons interact with one another, alter the effective potential in which they evolve, and give rise to global structures whose stability cannot always be understood as a mere addition of individual behaviors. This article proposes an exploratory reading of the atom and of the periodic table through the lens of nonlinear dynamical systems, threshold phenomena, collective modes, phase locking, and self-organization. The aim is not to replace standard quantum mechanics, but to examine whether certain atomic regularities - shell closures, noble gases, filling anomalies, transitions between periods, and the special stability of some configurations - can be interpreted as signatures of collective stability. The article also develops analogies with lasers, nonlinear optics, coupled oscillators, the fractional quantum Hall effect, and wave chaos. These analogies should not be understood as strict identifications. They are conceptual tools that help us think of atomic matter as a dynamic, resonant, and self-consistent organization.
Category: Quantum Physics

Predicting Low-Field Visibility Loss from Local Opposite-Polarity Field Coupling

Authors: Matthew Crane
Comments: 32 Pages.

Standard low-power optics treats visibility loss as a readout problem: the detector still records photon locations, but the measured hit pattern no longer separates cleanly into bright regions and dark regions.This paper controls that readout explanation before the prediction is tested. First, a stable visible interference pattern is made. Then the dark-region background, detector noise, false counts, pixel scale, position uncertainty, and minimum distinguishable bright-dark difference are measured. That calibration sets the measured visibility limit of the tested setup.After that calibration, detector sensitivity is part of the threshold test.This paper predicts that the measurable interference zone shrinks as the beam-waist to opposite-polarity + - coupling-event distance increases, until the setup reaches a measurable-visibility threshold.The predicted measurable-visibility threshold distance is:R_low = z_R sqrt(P/P_low - 1)
Category: Quantum Physics

Heisenberg Causes Gravity and Time Dilation

Authors: Leonardo Rubino
Comments: 16 Pages. (Note by ai.viXra.org Admin: For the last time, please cite and listed scientific references!)

Heisenberg causes gravity and time dilation.
Category: Quantum Physics

On Complex Dynamics and Standard Model Parameters

Authors: Ervin Goldfain
Comments: 16 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present numerical evidence that complex dynamics of nonlinear systems provides a coherent organizing principle for understanding the origin of Standard Model parameters, without introducing new fields or symmetries.
Category: High Energy Particle Physics

The Structure of Electrons and Photons

Authors: Michael Gunning
Comments: 19 Pages.

In this paper I propose a model for a physical explanation of the structure of the electron and the photon. The model explains what the charge of an electron is and why it has a total angular momentum of √3/2 ħ. It suggests what the nature of inertial mass is and explains the spin value of ħ for the photon as well as the origins of its alternating electric and magnetic fields. It includes explanations for what static electric and magnetic fields are and why the stress energy tensors for these fields used in General Relativity have the form that they do. It also explains the Lorentz force and the Stern Gerlach force. It gives a physical interpretation of Planck’s constant and proposes a physical mechanism for gravity which explains why it is so weak compared to the electric force. It also explains why the relativistic energy momentum formula has the form it does and also proposes a physical mechanism to explain the deBroglie wavelength of a particle.
Category: Quantum Physics

Diffraction: An Experimental Search for the Physical Mechanisms of Pattern Formation

Authors: Sergei P. Slukhayevskiy
Comments: 12 Pages. 5 figures

Diffraction is traditionally regarded as a consequence of the disruption of wavefront continuity by an obstacle, whereas experiments usually provide access only to the final intensity distribution observed on a distant screen. In the present work, an approach for the instrumental observation of the spatial evolution of the diffraction process was implemented through successive modifications of classical interference and diffraction arrangements adapted to new experimental objectives. It was experimentally established that, after interaction with a single half-plane obstacle, a finite layered structure is formed within the light beam. This structure remains confined to the beam cross-section and consists of alternating bright and dark regions oriented parallel to the obstacle edge. In the absence of spatial overlap with other disturbances, these layers gradually smooth out and the intensity distribution returns to a nearly uniform state. It is shown that, in more complex configurations, each half-plane generates its own system of spatial beam stratification. Signatures of these structures are observed at distances of approximately 15 cm before the geometrical edge of the obstacle and persist over a comparable distance after it. When spatial overlap occurs, mutual deflecting interactions between the layer systems arise, suppressing relaxation and leading to the formation of a stable wide-angle diffraction pattern. Experiments employing beams marked by a regular geometric light pattern revealed that dark-layer regions suppress the transmission of light from other sources in a manner similar to opaque objects. By varying the degree of spatial overlap between layer systems, a continuous transition was achieved from the classical distribution dominated by the central maximum to regimes exhibiting enhancement of higher-order maxima. Additional experiments revealed a spatially selective character of layer interactions and a weak dependence of the observed effects on the surface quality of macroscopic obstacles. The obtained results provide a basis for further investigation of the causal mechanisms responsible for the formation of diffraction structures and suggest potential practical applications of the observed regularities under controlled boundary conditions.
Category: Classical Physics

A Saturating Magnetic Switched Blumlein High Voltage Pulse Generator

Authors: Max Artusy
Comments: 2 Pages. (Note by viXra Admin: Author name is required in the article after the article title)

The Blumlein charged line generator is designed with a saturating magnetic switch. This allows rapid recharge and robust switching, which can tolerate arcing without switch damage. This shows the versatility of this unique circuit. High rep rate is intrinsic.
Category: High Energy Particle Physics

Architecture of Elementary Particles

Authors: Yvan Raverdy
Comments: 7 Pages. (Note by viXra Admin: Please cite and list scientific references of other authors)

The particles that constitute our Universe, in its so-called "ordinary matter and radiation" component, are all electromagnetic in nature, defined by the unification of their three possible interactions. We know that the fourth interaction (gravitational) is significantly different in nature from the other three. Here, we intend to describe how the so-called "stable" particles of ordinary matter can be composed of those that constitute their most fundamental building blocks. These particles decay in a time ranging from 10u207bu2076 s to 10u207b¹u2076 s, except for the proton, which is extremely stable.
Category: High Energy Particle Physics

Explaining the Complexity of Experimental Results on the Lifetimes of Free-Neutrons and Hyperons and the Masses of W-Bosons Based on the Atom-Like Structure of Baryons

Authors: Sylwester Kornowski
Comments: 14 Pages.

The complexities of the precise experimental data on the lifetimes of free neutrons and hyperons and the masses of W bosons have not yet been resolved within the quark model. These three extremely important problems concern the weak interactions. Here we present exact solutions to these problems within the atom-like structure of baryons described in the Scale-Symmetric Theory (SST). The SST solutions show that they are beyond the Standard Model, but in previous articles we have shown how the quark model emerges from the atom-like structure of baryons. The mean lifetimes of free neutrons are very important in nuclear physics, particle physics and cosmology. Within SST we calculated the ground state for mean lifetime of free neutrons that is 878.10 s — it follows from the transition from the nuclear weak interactions to the weak interactions of the electrons in the presence of dark matter. We showed that in a bottle, the central spacetime condensate in the neutron, which is responsible for the β decay, can be in different mass states that leads to two excited states of neutron lifetime, i.e. 880.36 s and 882.63 s. We showed that in neutron beams, mean lifetime of neutrons depends on neutron velocity because emissions of quanta by the central spacetime condensate with increasing neutron velocity are more and more suppressed. For neutron velocity equal to a threshold velocity 3.356 km/s we obtain a longer mean neutron lifetime equal to 888.89 s. For velocity 2.2 km/s we obtain 886.83 s. We showed that mass of the W boson depends on the place of creation — the two calculated basic values are 80,360.11 MeV and 80,378.96 MeV which lead to the mean value 80,369.5 MeV that is very close to the world average central value (80,369.2 MeV). We also calculated the exact lifetimes of the hyperons.
Category: High Energy Particle Physics

Emergent Gravity from Fundamental Triangles with Inner Torsion-Twist Degrees of Freedom — an Analogon to Structure of Penrose-Triangles

Authors: Holger Döring
Comments: 8 Pages.

Investigated is a model of spacetime in which fundamental triangles possess not only geometric properties such as area and edge lengths but also internal degrees of freedom representing twist, which encodes their relative orientation with respect to neighboring triangles. While local triangles are flat and consistent, global misclosures can accumulate, acting analogously to holonomies in curved spacetimes. This approach enables the construction of a spin-network-like model in which gravity can be interpreted as a statistical emergent phenomenon arising from these accumulated twists. The concept is inspired by Penrose-triangles: local consistency combined with global twist. Therefore this description is called the Penrose-triangle-ansatz (PTA).
Category: Quantum Gravity and String Theory

Special Relativity Violates Physical Identity

Authors: Antonio León Sánchez
Comments: 3 Pages.

The Theorem of Physical Identity demonstrated in this article is an almost immediate consequence of the Laws of Logic. However, it is incompatible with the theory of special relativity.
Category: Classical Physics

Recurrence Relations in the Tessellation of the Upper Half-Plane by the Full Modular Group

Authors: Hans Montanus
Comments: 11 Pages.

The successive actions of the generators S and T of the full modular group SL(2,Z) on the fundamental domain F lead to a tessellation of the upper half-plane H. Each image can be obtained by acting on the fundamental domain with a word consisting of solely S's and T's. For instance STTSTTT(F) is the image when the word STTSTTT acts on F. There is no shorter word that produces the image STTSTTT(F). A recurrence relation will be derived for the number of images for a given minimal word length.
Category: Combinatorics and Graph Theory

How to Derive the Fine Structure Constant Using Probability and Compton Equations

Authors: Colin James
Comments: 32 Pages.

I use the relativistic Compton equations to calculate the momentum response of a ‘target’ electron to vacuum photon collisions redirected from a ‘source’ electron. The equations give the ratio of the momentum of the ‘target’ electron after the collision divided by the momentum of the incoming photon over the range of all angles of the ‘target’ electron’s deflection. By summing evenly (over the maximum cross-section) over all angles we obtain the ratio of 1/2.1412 when using photon frequencies of 2 and 4 times the mass equivalence of an electron in the ratio of 5.6269 to 1. 4 times the mass equivalence may be 2 x (2 times electron mass equivalence photons acting simultaneously) or a double photon composite.The fraction 1/8 is a probability based on spherical geometry — the ratio of the maximum cross-sectional area of a sphere to its surface area (¼) and a further probability of (½) due to the even chance of the electromagnetic properties of a photon matching those of an electron. This gives a total probability of (¼) x (½) = 1/8. There are 2 such 1/8 probability collisions — one in which a photon is deflected by a ‘source’ electron towards a ‘target’ electron and a second 1/8 probability collision at the ‘target’ electron. The Fine Structure Constant is therefore divided into 3 parts.1/8 x 1/8 x 1/2.1412 = 1/137.0360 based on probability, spherical geometry and the use of the Compton scattering equations. 1/2.1412 {0.4670} is calculated using the Compton scattering equations. 1/2.1412 x 1/8 (probability) gives 1/17.1295 {0.05838} Coulomb’s Law. 1/17.1295 x 1/8 (probability) gives 1/137.0360 {0.007297} the Fine Structure Constant. A ‘free’ electron may be pictured/averaged as a speed of light particle contained in an approximately circular orbit with fixed angular momentum by collisions with vacuum momenta.
Category: High Energy Particle Physics

An Optimized Sech-Based Approximation of E^{-X^2}

Authors: Vladyslav Vasilache
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper introduces a new, highly accurate approximation for the function $e^{-x^2}$. By differentiating a known error function approximation and optimizing its parameters, we drastically reduce the maximum absolute error from $1.88%$ to less than $0.09%$ without using any exponential terms.
Category: Functions and Analysis

Towards a Floer Theory for Mars II Floer Hessian Field Almost Extends

Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 2 figures

In part I, [FW26a], we showed that collisional periodic orbits of twisted Zeeman systems can be detected variationally by a non-local Hamiltonian action functional. In this part II we show that the linearized gradient flow of this non-local functional is a Fredholm operator and prove a non-local elliptic regularity result. These results are obtained with the theory of almost extendability of weak Hessian fields introduced in [FW26c].
Category: Mathematical Physics

Inference Operators

Authors: A. Zelmer
Comments: 40 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Certainly the beauty of mathematics also lies in the precision of mathematical sentences, as well as in the proofs of theorems. However, this can only be fully achieved by formalizing sentences and proofs.Our computer-assisted proving system, which we have called "Logic", contains two fundamental modules: the sentence editor and the proof module. We presented the sentence editor in Mathematical Sentences as Matrices. The proof module of the "Logic" system is based on certain primitive functions that we have called inference operators. In this paper we present what inference operators are and how they can be used in formalized mathematical proofs.
Category: Set Theory and Logic

A Possible Solution to the Mystery of the Bermuda Triangle: a Nuclear Physics-Based Quark Transfer Model Leading to Perpetuity of Magnetic Force

Authors: Bijon Kumar Sen, Subha Sen
Comments: 5 Pages. 2 Figures

On the basis of a nuclear physics-based model, an attempt has been made to explain the neutron to proton (n — p) conversion in the nucleus of an atom and the way of transfer of a d- quark into a u- quark. From examination of their implications in the mechanism of low and high temperature superconductivity, we came across a stupendous conclusion which may lead to busting the mystery of the Bermuda triangle. This, however, assumes free quarks may have limited existence under special condition. It is the swarm of quarks produced from unlimited supply of free electrons, unhindered by the warmth and the depth of the ocean, unchecked by the Meissner effect, add up (aided and abated by mutual enforcement) to a strong attractive force which can explain the anomalous magnetic behaviour as noticed by Columbus during his voyage through Bermuda triangle. The appearance and disappearance of the hysteresis curve shows that the Bermuda Triangle serves as a natural channel, passing everything that comes into contact with it into eternal sleep leading ultimately to the perpetuity of magnetic force. It is advisable that the study of tectonic and geophysical processes should be carefully made by the scientists so as not to meet the swarm of quarks for their own safety, security and escape from becoming a part and parcel of perpetuity.
Category: Nuclear and Atomic Physics

Extended Lorentz Spacetime Approach to Gravity

Authors: Tomasz Kobierzycki
Comments: 13 Pages.

In this paper I will present simple model of gravity field not as spacetime curvature but as a motion of arrows or more precise set of vectors from each point of spacetime. It's rooted in special relativity and it extends Minkowski spacetime to three sectors.
Category: Relativity and Cosmology

Short Version of "Turing-Unsimulability & Cosmic-Censorship-Falsity for General Relativity"

Authors: Warren D. Smith
Comments: 6 Pages.

My paper http://vixra.org/abs/2605.0004 "Turing-Unsimulability, and instantaneous & sustained Cosmic-Censorship-falsity, for Einstein-Vacuum General Relativity", at 60, 74, and 78 pages for versions 1, 2, and 3, was too long for many stomachs. Therefore I here also provide a short introductory explanation (in the spirit of Phys.Rev.Letters summaries of fuller papers) of its main ideas to try to advertise it and to get expert readers oriented right before they start.
Category: Astrophysics

Emergent Time and the Elimination of Cosmological Singularities Via Clock-Field Deparametrization

Authors: Ruslan Yurkevich
Comments: 7 Pages. Distributed under the arXiv.org perpetual, non-exclusive license.

Context: In canonical quantum gravity, the Wheeler-DeWitt equation suffers from the notorious "problem of the frozen Universe," lacking an explicit time parameter. Methods: This paper introduces a novel pre-geometric quantum cosmological formalisation where the flow of time is an emergent property tracking microscopic transitions. We execute a canonical 3+1 ADM deparametrization of the gravitational constraint using a scalar clock-field (chi ), yielding a dynamic Schrödinger-type equation for quantum gravity. Results: We postulate a non-linear feedback loop where the local clock rate w slows down as the energy density (ho ) increases: (w(ho) = 1/(1 + xi ho)), where (xi > 0) is a universal coupling constant. Semi-classical WKB analysis of the homogeneous FRW mini-superspace reveals a singularity-free "bounce-plateau" state at the Big Bang and within black hole cores. In the low-density limit, this mechanism naturally acts as a dynamic negative pressure component, driving late-time cosmic acceleration without a cosmological constant (Lambda ). Significance: The modified Mukhanov-Sasaki equations predict explicit corrections for primordial perturbations ((n_{s}) and r) that fall precisely within the discovery thresholds of the upcoming CMB-S4 and DECIGO experiments, rendering the model fully falsifiable.
Category: Quantum Gravity and String Theory

Gravity as Spacetime Distortion: A Unified Framework from the Full Affine Connection

Authors: Luca Eliseo Pavesi
Comments: 26 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present a comprehensive geometric framework for gravity in which the fundamental dynamical variable is the distortion tensor encoding both torsion and non-metricity. After a thorough review of metric-affine geometry, we construct the most general action quadratic in the distortion and linear in the Levi-Civita curvature, supplemented by a Yang-Mills-type kinetic term. The theory propagates a massless graviton, a massive vector, and a massive scalar. We derive the full non-linear field equations, linearize them around Minkowski spacetime, perform a complete mode decomposition, and analyze the stability and unitarity of each sector. We study the low-energy limit and show that General Relativity is recovered exactly below the distortion mass scale. We then explore cosmological solutions, finding that the vector mode can drive late-time acceleration without a cosmological constant. Black hole solutions are analyzed perturbatively, revealing a possible mechanism for singularity regularization. We discuss gravitational wave signatures, including dipole radiation from the vector mode, and place preliminary constraints from LIGO/Virgo observations. Finally, we outline the power-counting renormalizability of the theory and its potential as an ultraviolet completion of General Relativity. Extensive appendices provide detailed derivations of all identities used in the main text.
Category: Relativity and Cosmology

The Optical Prison: Universal Physical Isolation as the Physical Solution to the Fermi Paradox

Authors: Hao Xu
Comments: 10 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

An Optical Prison hypothesis is proposed that would physically resolve the Fermi's Paradox. Three independent ground optical experiments verify the physical limitation of the astronomical observations caused by structural self-weight collapse and optical inherent constraints. Unlike conventional SETI concepts, the conclusion is quantitatively restricted by measurable experimental data, lacking empirical support, our conclusion is qualitatively restricted by neutron degradation and explaining the cosmic silence in SETI observations.
Category: Astrophysics

Testing the D.m. By Quantum Gravitation Theory by the Mass Associated to the Turnaround Radius

Authors: Manuel Abarca Hernandez
Comments: 9 Pages.

The DM by Quantum Gravitation theory (DMbQG hereafter), is a novel theory developed in the two main papers [1] and [2] Abarca,M.(2024). In the present work, in the framework of DMbQG theory it will derived the formula for the mass associated to the turnaround radius depending on the turnaround radius and it will be shown that the new expression has a deeper physical meaning regarding the same formula in the current LCDM paradigm. The DMbQG theory states a direct relation between the virial radius and the turnaround radius as well as the virial mass and the mass associated to the turnaround radius.The most important contribution of this work is placed in the chapter 2 where it has been demonstrated that the formula for the mass associated to the turnaround radius, using the DMbQG theory, is the same that the one in the current LCDM paradigm. However the new formula has a deeper physical meaning because its dimensionless factor is simpler regarding the one in the current LCDM paradigm. It is remarkable the fact that the both dimensionless factors depend on exclusively from the Universal omega parameters for the mass or for the DE and the both ones differ only a 5%. The fact that in the framework of DMbQG theory has been found a better formula for the mass associated to the turnaround radius is a strong support for the DMbQG theory whose hypothesis about the origin of DM is exclusively the gravitational field. The chapters 3, 4 and 5 are devoted to test the DMbQG theory in the clusters, Virgo, Coma and the Local Group of galaxies using recent data published about these clusters. The tests are mainly focused on the turnaround radius and its mass associated and all of them have been a complete success by the DMbQG theory.
Category: Astrophysics

Gravity as an Emergent Force Via the Uncertainty Principle

Authors: Morgan W. Weinberg
Comments: 51 Pages.

The core concept of this paper is the relation between an accelerating field and time uncertainty. This relation distills from the derivation of Newton's Law of Gravitation via the uncertainty principle. It's shown, further, that this relation can be used to derive the Coulomb Force, suggesting that it may be a general principle in nature. Taking this concept further, this paper draws a connection between expanding space and acceleration---offering an explanation for the missing-mass problem in galaxies. The paper goes on to draw a connection between the expansion of space and time uncertainty, leading to a startling conclusion: The expansion of space is not a function of the energy contained therein, but conversely, the mass of the universe is created in concert with the expansion of space. Further, because this expansion is a function of time, the mass of the universe is a function of time and increases in lockstep therewith. It's deemed that the model of the universe presented herein obviates the need for dark matter and dark energy to explain our observations of the cosmos.
Category: Astrophysics

Doppler Effect, Absolute Stellar Aberration, Stellar Velocity, Stellar Distance and Speed of the Light

Authors: Miloš Čojanović
Comments: 6 Pages.

Our assumption is that the Doppler Effect and Absolute Stellar Aberration are two complementary phenomena. This means that if we are able to use the result obtained by measuring $DE$ to determine the radial velocity, then by using the result obtained by measuring "ASA" we should be able to determine the transverse velocity with which the star moves in relation to the observer. We will prove that if we know the velocity of the star, we can determine its distance in relation to the observer and the speed of light emitted from the star in the direction of the observer.
Category: Astrophysics

Multi-Metric Wormholes: A No-Horizon Theorem and 1/N Suppression of Exotic Matter

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

We present a comprehensive study of traversable wormholes in multi-metric gravity, a ghost-free theory with N interacting metric tensors. The action, field equations, and constraints are derived step by step. We construct a static, spherically symmetric wormhole ansatz with a Gaussian deformation localised at the throat, and reduce the field equations to a system of ordinary differential equations. A central result is a no-horizon theorem: any stationary, asymptotically flat solution with a non-zero multi-metric charge Q, defined as the asymptotic flux of a conserved current built from the metric differences, cannot contain a Killing horizon and must therefore be a traversable wormhole. We show analytically and numerically that the null energy condition (NEC) violation is suppressed by a factor 1/N compared to the single-metric case, and that the exotic matter can be confined to an arbitrarily narrow shell. The deflection angle and Shapiro time delay are computed, and the stability under radial perturbations is analysed. The model satisfies Solar System constraints and makes falsifiable predictions for near-future instruments.
Category: Relativity and Cosmology

Shaking up the Theory of the Expanding Universe

Authors: Henk Dorrestijn
Comments: 11 Pages.

Obstruction Theory offers an alternative to the Newton/Einstein theory for cosmology. Assuming a rarefied mass density in the universe, the redshift we observe in distant light sources can be explained without assuming that the sources are moving away from us at high speed, causing the universe to expand. The redshift can be easily explained by the average mass density of the universe.It is known that a mass slows down the velocity of time at a point in its vicinity. This slowdown turns out to be equal to the reduction of direct radiation from more distant space due to the presence of the mass. We show that the amount of direct radiation reaching an observer from the universe is always partially lost along the way through scattering by protons and other small particles. This translates into the velocity of time, which we observe as redshift. We find the size of our visible universe by stating that the observed time velocity of the light sources at the boundary of the universe is reduced to zero. The value for the size that we find via a simple calculation is close to the value found in the traditional way. Furthermore, with this theory, a value for the Hubbleconstante can be found using the mass density of the universe. According to Obstruction Theory, there can furthermore be no question of a bounded universe. Every observer is the center of their own universe. Beyond its own universe, the universe extends infinitely far.
Category: Relativity and Cosmology

Collatz Conjecture: A Simple Proof for a Simple Problem

Authors: Ulrich Neuenschwander
Comments: 8 Pages.

A simple proof of the Collatz conjecture is proposed. The approach relies on the fundamental properties of N and on their fruitful interplay with the Collatz transformation.It will be interesting to see how the field receives the proposal and whether the reasoning and the conclusions are confirmed or need modification.
Category: Number Theory

Observation of D+D Fusion in Electromagnetically Self-Contained, Long-Lifetime Plasmoids

Authors: Dominik Kuryga, Paulina Nadia Weremczuk
Comments: 28 Pages.

We report the generation of self-contained, long-lived plasmoids in a low pressure coaxial diode of novel concept, driven by a ~5ns up to 1MV pulse, generating neutron bursts consistent with D+D fusion in discharges in deuterium. Neutrons were detected using a silver activation based detector. A correlation was observed between lifetime and neutron yield. Average neutron yields reached approximately 5—7x10u2075 neutrons per shot, with peak values up to 1,4x10u2076 neutrons/shot. Microwave emission measurements were done showing long decaying radiation. The demonstrated detectable nuclear fusion in this novel device opens new perspectives for compact neutron sources and alternative fusion concepts based on self-confined plasmoids.
Category: Nuclear and Atomic Physics

Traversable Wormholes in Quadratic Covariant Gravity: Localised Deformations, Shapiro Delay, and Stability

Authors: Luca Eliseo Pavesi
Comments: 19 pages. English.

We consider a covariant theory of gravity defined by the action S = ∫ d^4x √−g [(16πG)^{-1}(R + αR^2) + L_matter], which reduces to general relativity when α → 0. This theory, belonging to the class of f(R) gravities, is ghost-free and contains an additional massive scalar degree of freedom (the scalaron), and is treated as an effective field theory valid below the Planck scale. We derive the fourth-order field equations step by step, including all boundary terms. We then apply them to a static, spherically symmetric metric describing a traversable wormhole. The metric includes a Gaussian deformation X(r) = A exp[−(r − r0)^2/(2σ^2)] localised around the throat r = r0. The flare-out condition is satisfied for A > −1. We compute all Christoffel symbols exactly, derive the Ricci tensor and scalar, and solve the modified Einstein equations for an anisotropic fluid. The energy conditions are analysed: the null energy condition is violated only in an arbitrarily small region near the throat if α > 0 and the Gaussian parameters are chosen appropriately. We study null geodesics using the corrected radial equation, compute the deflection angle and the Shapiro time delay for light passing near the wormhole, and show that the Gaussian deformation introduces a characteristic shift compared to the Morris—Thorne case. Stability under radial perturbations is analysed in the scalar—tensor representation, showing that the wormhole can be stable for a range of parameters. The asymptotic limit is studied via a post-Newtonian expansion: the PPN parameters remain γ = β = 1, and the scalaron mass m^2 = 1/(6α) is constrained by Solar System tests to be m ≥ 10^{-3} eV. We discuss observational signatures such as lensing, Shapiro delay, and gravitational-wave echoes that make the model falsifiable. All calculations are presented in detail, with intermediate steps collected in appendices.
Category: Relativity and Cosmology

A Geometric Explanation of Dark Matter Based on General Relativity

Authors: Hao Shen, Ruipeng Ma
Comments: 19 Pages.

Within the framework of standard general relativity (Einstein 1915), under the assumptions of staticity, spherical symmetry and the strong energy condition, we prove that a geometric transition zone — the "reverse-bending zone" — must appear in the periphery of any finite self-gravitating system, where the t—r sectional curvature changes sign from negative to positive. This zone is bounded by the curvature zero r0, the curvature peak rpeak, and the matter boundary R; in the interval (r0, R) the sectional curvature smoothly transforms from matter-dominated spherical compression to vacuum saddle-shaped stretching. The reverse-bending zone is not a free vacuum but a forced geometry locked jointly by the interior baryonic potential well and the far-field boundary condition. Within this zone, the Misner—Sharp-type gravitational mass M(r) continues to grow: it grows faster than linearly in the region r0 → rpeak, and although the growth slows down in the region rpeak → R, it never ceases. The resulting geometric Weyl stretching together with the self-energy of the gravitational field provide an extra centripetal acceleration, which naturally manifests itself, in the weak-field approximation, as an approximately logarithmic potential and a flattening of the rotation curves. The theory yields parameter-free, falsifiable predictions that can be directly tested with existing rotation-curve and photometric data. These results show that, without introducing new particles or modifying the field equations, the forced geometry within general relativity can produce "dark-matter-like" gravitational effects on galactic scales.
Category: Relativity and Cosmology

Elementary Weak Solutions of the Navier—Stokes Equations and an Application of the Banach Fixed-Point Theorem

Authors: Masatoshi Ohrui
Comments: 23 Pages.

This is an application of functional analysis to the existence and smoothness of the Navier—Stokes equations using elementary weak solutions in Sobolev spaces.We solve the problem in mathematics. The problems are not in physics, so we do not use any physics or assumptions-falsified mathematics, such as other papers. We use mathematics only. We can solve the problem by using an exactly and completely FALSIFIED resolution, where large initial values destroy the earth, because uniqueness does NOT hold, or SMALL initial values love your cup of coffee.There are no long or complicated calculations; semi-groups, a priori estimates, and boundary conditions are not used at all. We apply the local solvability of linear partial differential operators with constant coeficients.
Category: Functions and Analysis

Proof of Hartog’s Phenomenon and Cohomology Vanishing Theorem

Authors: Masatoshi Ohrui
Comments: 2 Pages.

We can prove Hartog’s phenomenon by solving the ∂-bar equation for compactly supported forms. To solve the equation, we construct the solution using convolution.
Category: Functions and Analysis

Extended Standard-Model by the Coxeter Element of the Affine Weyl Group E˜8

Authors: Reinhard Kronberger
Comments: 20 Pages.

In this paper i will give an extension of the known Standard-Model.The shape of the extension is not arbitrary choosen.The shape explains gravity and more. I show that the symmetries generated by the coxeter-element of the affine Weyl group E˜8 which is the affine extension of the well known exceptional group E8 is a candidate which explains open questions like dark matter and gravity.
Category: Quantum Physics

Geometric Projection of Arithmetic Spirals Onto Logarithmic Manifolds: a Moiré Interference Framework for Studying Prime Distribution Without Complex-Analytic Tools

Authors: Jian-Yu Huang
Comments: 27 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We develop a geometric and spectral framework for studying structural fluctuations in discrete arithmetic sequences, operating entirely within real-variable analysis and without appeal to the Riemann zeta function, Euler products, explicit formulae, or analytic continuation. An arithmetic lattice is mapped onto a transcendental logarithmic manifold via an area-filling projection; the resulting Moiré-type interference field serves as the primary object of study. The principal contributions are as follows. (i) We prove, with explicit constants, that the projection map is injective and that successive images are uniformly separated (Propo-sitions 2.3-2.4). (ii) We establish a uniform L 2 near-orthogonality theorem for finite phase families, yielding a computable operator-norm bound on the associated Gram matrix via Gershgorin's circle theorem [5] (Theorem 3.3). (iii) We introduce an explicit Moiré di-lation operator T σ = −i(x ∂ x + σ) on L 2 ([1, ∞)), show that the geometric phasor family {x −(σ+it) } t∈R constitutes its formal eigenfunction family (Lemma 3.12), and prove by integration by parts that T σ is formally self-adjoint if and only if σ = 1 2 (Theorem 3.14). (iv) We derive quantitative variance bounds for node-count statistics, controlled by the pairwise phase-correlation bounds (Theorem 3.19). Complete exponential-sum estimates with explicit constants (Appendix C) and Abel-smoothing remainder formulae including an incomplete-Gamma bound (Appendix B) are provided. All theoretical claims are either proved using the above tools or explicitly designated as conjectural.
Category: Number Theory

Finite Bernoulli—Zeta Transforms for Fibonacci-Type Recurrence

Authors: Payam Danesh
Comments: 12 Pages.

Fibonacci and Lucas sequences are basic examples of second-order recurrences, and their behavior is closely connected to the golden ratio. Bernoulli numbers and special values of the Riemann zeta function also form a classical part of number theory. This paper connects these two areas through exact finite identities. The method starts from exponential generating functions, separates the odd-indexed terms, applies Bernoulli generating functions, and then compares coefficients. This gives a finite formula in which a weighted sum of zeta values at non-positive integers becomes an explicit Fibonacci expression. The same argument also gives a Lucas version, and then extends to every sequence satisfying the Fibonacci recurrence with arbitrary initial values. Exact symbolic checks and residual plot are included to show how the cancellation works. The result is a complete unconditional link between Fibonacci-type recurrences, Bernoulli numbers, and special zeta values.
Category: Number Theory

Dual Architecture of the Gamma Function: Complementary Extension to the Left Half-Plane and Regularization of Logarithmic Divergences

Authors: Julinho Jorge Luís
Comments: 20 Pages.

This work proposes a complementary extension of the factorial function to the real line, based on the separation of the bilateral integral of e^(-Ax) into two disjoint domains. For A>0, the classical Gamma function Γ(z) emerges in the right half-plane; for A<0, we introduce the Symmetric Gamma Function Γ ˉ(z)=e^(-iπ(z+1)) Γ(-z), defined in the left half-plane, with poles at the positive integers. The duality between the integral kernels underlies a regularization mechanism for logarithmic divergences: Γ_R (z)=1/Γ ˉ(z-1) and Γ ˉ_R (z)=1/Γ(z+1), replacing each pole by an exact finite value. An alternative real representation B(x)=∫_0^∞e^(-u) u^(-x) du (convergent for x<1) is constructed, together with a trigonometric factor C(x)=2sinu2061(πx)+cosu2061(πx), defining F(x)=C(x)B(x) for x≤0, yielding F(-n)=(-1)^n n!, thereby unifying the complex branch, real regularization, and Laurent expansion formalisms. The relation F(-n)⋅Resu2061(Γ,-n)=1 establishes the fundamental duality, which emerges directly from the construction of the integral kernels. The method is validated in arithmetic progressions, QED, and QCD. The extension to k-loops is systematic via exponentiation: Γ_R^((k) ) (-n)=[(-1)^n/n!]^k. Distinct physical prediction: In d=5 dimensions, the vacuum energy density changes sign — a repulsive force where the MS-bar predicts attraction. This inversion has direct implications for the stability of extra dimensions in string theory and brane models.
Category: Quantum Gravity and String Theory

The Atomic Structure of the Chemical Elements

Authors: Jozsef Garai
Comments: 68 Pages.

Based on the analysis of the well-known features of the atoms, the following conclusions can be deduced. The identical and invariant properties of the chemical elements can only be ensured if the charge distribution of the nucleus is invariant and identical for each of the elements, dynamic equilibrium between the opposite charges in the atoms cannot be stable in the time scale of the universe, classical electromagnetism is valid at atomic scale, since neither theory nor experiments sets limits on it. Taking these conclusions into consideration the following modifications of the contemporary atom models are proposed. Nucleus: The identical reproduction of the nucleus requires lattice arrangement for the nucleons. Protons and neutrons have the same size. These nucleons should occupy the space in the most efficient way, forming a closest packing arrangement. The smallest building blocks of this arrangement are tetrahedrons. Assuming alternate arrangement of the protons and the neutrons, and expanding a tetrahedron seed by adding additional layers to it, the number of protons in the layers reproduces the periodicity of the chemical elements. Electronegativity represents the average attraction of the unshielded proton/s on the valence electron/s. This physical description is even consistent with the irregularities of electronegativity. Electronic shell: In the time scale of the universe, dynamic equilibrium of the opposite charges in the atoms would be chaotic. This contradicts with the known stability of the atoms. Static equilibrium between the opposite charges can only be achieved if at least one of the charges is a distributed one. The physical behavior of the free and the bounded electrons are different. Thus, these electrons are not identical. These differences can be explained if the point charge free (unbounded) electron at capturing transfers and forms a surface charge electron shell around the nucleus, and vice versa. This phase transformation is energetically feasible. The electronic shell structure of the atoms is the consequence of the nuclear lattice. New electron shell is formed when the attraction of the added proton of an element is weaker on the captured electron than the average attraction on an electron in the existing shell.
Category: Nuclear and Atomic Physics

Completeness of the Metric Description of Gravitational Reality: An Radiative Generalization of Kerr-Newman Spacetime

Authors: Tanishq Chandu Khandare
Comments: 2 Pages.

I derive a non-vanishing, solution to the Einstein-Maxwell field equations representing a dynamical, radiating, rotating, and charged manifold. Utilizing the Newman-Penrose (NP) formalist, I project the metric onto a nulltetrad {l, n, m, m¯ } to evaluate the Weyl and Ricci scalars. We demonstrate that the resulting stress-energy tensor Tµν = T (null) µν + T(em) µν satisfies the Weak Energy Condition (WEC) and the local conservation law ∇µTµν = 0. By formalizing the EPR criterion for physical completeness, we argue that the stationary KerrNewman limit is a sub-manifold of the broader radiative reality. I further prove that the r = 0 singularity is a transient topological feature that resolves into a Minkowski vacuum in the limit of total evaporation.
Category: Relativity and Cosmology

Is the Central Valley of California an Elongated Impact Basin?

Authors: David E. Rutherford
Comments: 4 Pages.

In general, impact craters are circular in shape, but occasionally, they exhibit non-circular forms. One such form is the elongated impact crater. I suggest that the Central Valley of California may be a larger version of an elongated impact crater, an elongated impact basin. Its elongated shape might be the result of a very low angle of impact of one or more celestial objects with the surface of the Earth. The `central' peak (or uplift) of the original basin might be the Sutter Buttes, in the northern part of the Central Valley. In order to support these conclusions, images of lunar impact craters are compared to shaded relief maps of the Central Valley (and surrounding mountains) of California.
Category: Geophysics

Quantum Mechanics and The Subjective Nature of Mathematics

Authors: Joseph Palazzo
Comments: 3 Pages. (Note by viXra Admin: An abstract in the article labeled as such in the article is required)

In the historical debate between Einstein and Bohr, it is practically seen in every sentence that Einstein was debating ontology ("Do you really believe the moon is not there when you are not looking at it?")[1] while Bohr was debating epistemology (we only know until particles are observed, at which point the "wave function collapses" into a definite state). This is like as if one is talking about basketball, while the other is talking about hockey. It’s no surprise that they were talking passed each other, not aware of what was going on. Worse is that the whole physics community for the past 100 years did not see it. In 2022, the Nobel Prize in physics was headlined as: quantum mechanics is right, Einstein is wrong — indicating by all measures that we still don’t have it right.
Category: Quantum Physics

The Oscillations of a Particle in an Anharmonic Potential with Damping

Authors: L. A. Xamidullayeva, U. O. Muhammedov, X. N. Ismatullayev
Comments: 3 Pages.

The natural processes equations are nonlinear and have dissipating terms. In many cases they donot have an exact analytical solution. Using perturbation theory we solved the equation of anoscillating particle in an anharmonic potencial.
Category: Classical Physics

Kinematic Analysis of the Motion of an Ellipsograph Point Under Various Velocity Laws

Authors: Viktor Strohm
Comments: 5 Pages.

This paper investigates the kinematics of a fixed point on the connecting bar of an ellipsograph (Archimedes' trammel) under different driving motion regimes: uniform, uniformly accelerated, and Keplerian (elliptical). Based on differential constraint equations, analytical expressions for the velocity and acceleration vectors of the trajectory point are derived. A numerical approach, modeling the division of the orbital quadrant into equal time intervals, is utilized to calculate the corresponding areal velocities. It is rigorously demonstrated that the constancy of the areal velocity and the fulfillment of Kepler's second law occur exclusively under one specific law of angular velocity—the Keplerian regime—whereas under uniform and uniformly accelerated motions, the law of areas is violated. This work establishes a link between the mechanical modeling of trajectories and the author's fundamental theoretical research in the focal and central kinematics of the ellipse.
Category: Classical Physics

Decoupled Prompting and Topology-Aware Optimal Transport for CLIP-Based Unsupervised Cross-Modal Re-Identiffcation

Authors: Xiaohao Xie, Wenhua Jiao, Wei Meng
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Unsupervised Visible-Infrared Person Re-identification (USL-VI-ReID) is critical for cross-modal intelligent surveillance. While vision-language models (e.g., CLIP) present powerful representational capabilities, directly fine-tuning them for USL-VI-ReID often causes catastrophic feature collapse and prompt degradation due to massive domain gaps and noisy pseudo-labels. Furthermore, traditional discrete matching and heuristic denoising strategies suffer from severe cross-modal information starvation and numerical bias against hard positives. To address these challenges, we propose a robust, CLIP-based unsupervised cross-modal fine-tuning framework. First, we design an implicit adapter fine-tuning strategy coupled with decoupled multi-dimensional semantic prompting to isolate domain biases without destroying pre-trained priors. Second, a Cluster-Aware Cross-Modal Semantic Alignment (CCSA) mechanism maps dynamic visual centers to modality-shared textual proxies via visual-conditioned prompting, facilitating an implicit soft alignment decoupled from hard clustering noise. Third, we frame cross-modal association as a Topology-Aware Optimal Transport (TOTO) problem. Utilizing Fused Gromov-Wasserstein (FGW) constraints and Argmax assignments, TOTO injects potent hard regularization to overcome optimization inertia on difficult samples. Finally, our Pure Relative Confidence Ratio and Dual Adaptive Denoising (RCR-DAD) module eliminates numerical bias, formulating a robust self-paced learning trajectory. Extensive experiments on SYSU-MM01 and RegDB demonstrate our framework achieves state-of-the-art performance. The code will be released.
Category: Artificial Intelligence

Ramanujan Polynomial Expansion for Hurwitz Zeta Function

Authors: Payam Danesh
Comments: 29 Pages.

Polynomial expansions of zeta functions provide a natural way to connect analytic continuation, regularized summation, Mellin analysis, and orthogonal polynomial theory. In this paper we try to develop a shifted Ramanujan—Mellin expansion for the Hurwitz zeta function in the critical strip. The construction combines Abel—Plana regularization over the nonnegative integers, Ramanujan summation for shifted Dirichlet terms, the Cayley transform of the right half-plane, and Mellin transforms of Laguerre functions. The main result proves that the Hurwitz zeta function admits a locally uniformly convergent expansion in a universal polynomial basis that is independent of the shift parameter. The shift appears only through explicit coefficients involving the digamma function and shifted Hurwitz zeta values. The Riemann zeta function is obtained as a special case. On the critical line, the normalized basis forms a complete orthonormal system with respect to a hyperbolic weight, and every zero of each basis polynomial lies on the critical line. The final result gives an exact zero-free compact criterion equivalent to the Riemann Hypothesis.
Category: Number Theory

A New Home for Bivectors Geometric Algebra on a Sphere

Authors: Norm Cimon
Comments: 20 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

The Weakening of Earth's Magnetic Field is the Real Cause Driving Current Ocean Warming

Authors: Jamal S. Shrair
Comments: 21 Pages.

Earlier studies estimated that the Arctic region is warming around twice as fast as the global average. Yet, recent studies have found this figure to be wrong by a huge margin (hugely underestimated). Actually, in the last 45 years, the Arctic region has warmed almost four times faster than the rest of the planet, while the South Pole is warming three times faster than the global rate. On the other hand, since 2016, the Atlantic Ocean especially its northern part, has warmed faster than other ocean basins in the top 100 meters of ocean. Nonetheless, the real reason for the rapid warming of these regions is because of the huge decline in the strength of Earth's magnetic field, and the enormous flow of thermal energy from Earth's interior into the upper layers. Back in 2014, data from Swarm (three specialized satellites) revealed that Earth's magnetic field has weakened 10 times faster than expected. It was astonishing data, totally unexpected and unexplained by the current model that relies on self-generating dynamo. Specifically, Swarm found the biggest decline in the strength of Earth's magnetic field around the Arctic regions, the North Atlantic Ocean and also within the South Atlantic, as the South Atlantic Anomaly (SAA) shows. The decline in the strength of Earth's magnetic field, definitely implies that these regions would receive more solar radiation from above, and higher flow of thermal energy from the interior than when the field was strong and stable. Hence, one can say conclusively that the rapid weakening of Earth's magnetic field was the real cause that made the Polar Regions, and those close to them, warm faster in comparison to other regions of the planet. However, the most fundamental reason why the pseudoscience theory of greenhouse gases is the name of the game - in addition of course to the widespread corruption of our society - is because of the lack of understanding the most important scientific facts about the most important astronomical objects to us, namely our own planet and star. Basically, the origin and mechanism of the magnetic fields of the Earth and the Sun, including the reason for their reversal, are currently mysteries and will remain mysteries forever under gravity-dominated physics.
Category: Climate Research

Visual Space, Neural Networks, and AI Algorithm Models

Authors: Taiwei Song
Comments: 4 Pages. 4

This paper briefly discusses the concept of visual space discovered by the author [1-4], its transformation equation with the natural space-time, and points out that this transformation relationship is the key algorithm for AI embodied agents to automatically recognize the surrounding "world". It also briefly demonstrates that neural networks inherently possess the properties of "iterative convergence" and "self-learning evolution", and the "emergence of intelligence" in large AI models based on neural networks is inevitable.
Category: Artificial Intelligence

Hastings-Cody Approximations of the Integral of a Power Times the Complete Elliptic Integral of the First Kind

Authors: Richard J. Mathar
Comments: 16 Pages.

Hastings and later Cody tabulated minimax polynomial approximations for the Complete Elliptic Integral of the First Kind. The simplicity of this representation by polynomials and polynomials times a logarithm allows to integrate their terms analytically. We demonstrate how integrals of the Complete Elliptic Integral times a power of its argument achieve double precision accuracy for powers from 0 to 2 based on Cody's polynomials up to 9th order.
Category: Functions and Analysis

A Theory of Kinematic Gravitation, and Some Fundamental Consequences

Authors: Charles Ba Oumar
Comments: 14 Pages.

We will be concerned with the study of relativistic density and hence demonstrate from first principles the possibility of kinematic black hole formation in inertial systems of coordinates in Minkowski spacetime. We will discuss the applicability of these principles to elementary particles on the basis of a set of geometrical assumptions, some general consequences, and also present alternative gravitational equations on the basis of some related elementary considerations. Finally, we will conclude with some general remarks on the meaning of these results.
Category: Relativity and Cosmology

Once More on the Aether

Authors: Viktor Stetsovich
Comments: 12 Pages.

Based on the hypothesis of the aether's existence, this article proposes an explanation for the results of the Fizeau and Michelson experiments, as well as an experiment for detecting the aether.
Category: Relativity and Cosmology

Saturating Magnetic Max Bank Drives Mismatched Loads, Using the Method of Self Matched Lines

Authors: Max Artusy
Comments: 3 Pages.

Abstract: The saturating magnetic Max Bank, provides a versatile topology to produce rectangular high voltage pulses with little secondary distortion. The self matched line method, is employed to achieve this. Rapid recharge is intrinsic, allowing high rep rate operation.
Category: High Energy Particle Physics

Resolving the Cosmological Hubble Tension via Local Wave Impedance Fluctuations in a Hexagonal Close-Packed Lattice

Authors: Markov Efim Sergeevich
Comments: 5 Pages. License: CC BY 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The persistent cosmological discrepancy between early-universe cosmic microwave background (CMB) measurements (H0 approx 67.4 km/s/Mpc) and late-universe local distance ladder observations (H0 approx 73.0 km/s/Mpc) - known as the Hubble Tension - presents a fundamental crisis for the continuous Lambda-CDM paradigm. This paper resolves this conflict by shifting from expanding spacetime metrics to a stationary, non-singular Hexagonal Close-Packed (3HCP) discrete space crystal. We demonstrate that cosmological redshift is not a Doppler-like stretching of space, but a dissipative energy attenuation of electromagnetic wave packets undergoing sub-nodal friction across contacting cellular boundaries. By modeling the material vacuum as a discrete transmission network with a baseline register capacity Llimit = 256, we derive the propagation velocity and local wave impedance purely from first-principles lattice geometry. Through a multivariable Taylor series expansion, we establish a rigorous mathematical bridge proving that our discrete wave difference scheme converges onto the continuous Maxwell equations with a damping term as the lattice spacing approaches zero (h -> 0). Crucially, we show that local structural density fluctuations within the 3HCP matrix systematically alter the sub-nodal impedance along different lines of sight. Low-density intergalactic voids minimize wave friction, yielding an apparent higher local expansion rate (H0 approx 73.0), while deep CMB-scale averaging profiles smooth over macroscopic high-density clusters, converging onto the lower background global baseline (H0 approx 67.4). The Hubble Tension is thus completely eliminated, emerging as a predictable geometric artifact of measuring discrete wave impedance across a multi-scale, non-uniform spatial crystal.Creative Commons Attribution Non Commercial No Derivatives 4.0 International
Category: Astrophysics

The Final Theory

Authors: Nigel B. Cook
Comments: Corrected contents page links to sections and also a bibliography added.

We construct a complete quantum field theory in which all observed interactions - electromagnetic, weak, strong, gravitational, and cosmological - arise from a single mechanistic principle: energy conservation in vacuum polarization. The theory replaces the ad hoc structure of the Standard Model and the geometric assumptions of general relativity with a unified framework based on the group chain for Euclidean signature SO(3, 3) ~ SU(4) ⊃ SU(3) × U(1)G ⊃ U(2) ⊃ SU(2) × U(1)Y . Matter representations, gauge charges, running couplings, particle masses, gravity, and dark energy all emerge from this structure without arbitrary parameters. This paper is a new presentation of the ideas in vixra paper 1111.0111 dated 2011, with updates, a few corrections, and further development. That earlier paper should still be consulted for further references, graphics and details documenting the origins of the various nascent ideas.
Category: Quantum Gravity and String Theory

An Alternate Resolution of the Famous Grandmother Paradox Which Might be Also Validated Via a Classic Experiment

Authors: Moshe Segal
Comments: 16 Pages.

The nowadays Science of Physics still embeds unresolved paradoxes, and incompatibilities between various Physics branches.One significant unresolved paradox is the famous Grandmother Paradox, in which someone returns to the past, kills his grandmother and thus, inhibits his birth, which obviously, also inhibits his ability to travel to the past.In addition to paradoxes, as presented just above, the nowadays Science of Physics still also embeds incompatibilities between various Physics branches.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.Additional papers, by the author of this paper, present significant and reasonable arguments, which argue that the nowadays branch of the Classic Physics might be misleading in how it presents the concept of the Space-Time.By presenting an alternative view of how the Science of Physics should refer to the concept of the Space-Time, possible bridging between incompatible branches of the nowadays Science of Physics might be achieved, and also, a resolution to the famous Grandmother Paradox, might be presented.The above-mentioned additional papers, also propose experiments, which if implemented successfully, might provide validity, to the proposed alternative view of how the Science of Physics should refer to the concept of the Space-Time, which is presented in these additional papers.Thus, since a resolution of the famous Grandmother Paradox might be a significant step forward, and also the above-mentioned possible bridging between incompatible branches of the nowadays Science of Physics might also be a significant step forward, then, an implementation of the above-mentioned experiments, or any other experiments that might provide validity to the alternative view of how the Science of Physics should refer to the concept of the Space-Time, presented in the above-mentioned papers, should be an important and a significant endeavor.
Category: Relativity and Cosmology

Special Case of Law About Keep Moving of the Center of the Mass of а Closed System — Device from Two Bodies (Two Hulls), Uncompensated Moment and Propulsion in the Cosmic Space Without Propellant

Authors: L. Georgiev, D. Georgiev
Comments: 14 pages, 4 figures, In Bulgarian language

This article examines, special case of the law for conservation the motion of the center of the mass of а closed inertial system - device from two bodies (two hulls). Like in this special case, we obtain uncompensated moment for one of the hull of the device. As conditionally named first hull is standard rigid body. While on the second hull are connected two discs, which have equal masses and they can rotate free to the second hull. As when we apply the third law of Newton, between the two hulls, it’s uses the inertial of the two discusses. Like this way, because the kinetic energy is additive magnitude, it’s the hull with the discusses distribute the itself energy and for rotary motion of the discusses and for translational motion of the second hull. While for the first hull total kinetic energy, as a result of the applied third law is in the form of translational motion. As a result of the distribute of the energy of the second hull we obtain uncompensated moment for first hull. As a result of which is obtains and the special case of the law conservation motion of center of the mass of closed system — device from two bodies (two hulls). Like this way we have possibility for specific propulsion without propellant of the device in the cosmic space. Despite some shortcomings of the resulting specific propulsion, this is one of the possible ways of propulsion in cosmic space without "ejection" of propellant, and as only uses electrical energy from photovoltaics or nuclear energy.
Category: Classical Physics

Limitation in Ramanujan Positivity and Zeta Zeros of Riemann

Authors: Payam Danesh
Comments: 17 Pages.

Ramanujan’s divisor-sum identity gives one of the most analytical positivity arguments in the theory of the Riemann zeta-function: in Ingham’s work it yields the non-vanishing of ζ(s)on the line Rs=1. This paper revisits that mechanism and examines what is required to move it toward the critical strip. We first give a self-contained proof of the Ramanujan—Ingham zero-free line. We then prove that the direct critical-strip analogue fails for a precise Euler-factor reason: the positive Ramanujan square acquires an obstructing pole, while removing that pole destroys positivity already at prime level. This obstruction leads naturally to the Nyman—Beurling Hilbert-space formulation. Using Mellin transforms, we express the relevant closure problem through centered Ramanujan fractional-part functions and derive the exact finite-dimensional Gram system for optimal approximation. We prove fixed-window density of the associated boundary functions and separate the remaining problem into compact approximation and tail control. The main conclusion is a rigorous reduction: within this Ramanujan—Beurling framework, the remaining obstruction to the Riemann Hypothesis is an explicit uniform growing-window approximation estimate with controlled coefficient mass.
Category: Number Theory

Liniar Transformations on Multi-Vector Spaces

Authors: Constantin Scheau
Comments: 7 Pages.

A Smarandache multi-space is a union of spaces satisfying certain conditions. If the spaces beingunited are vector spaces, then we have a vector multi-space [3]. In [4] we defined the notion of a multimatrix and operations with multi-matrices, and in this paper we shall define linear mappings on a vector multi-space and study some of their properties.
Category: Algebra

Time vs. Duration: A Reinterpretation of Special Relativity

Authors: Ion Vlad
Comments: 23 Pages.

The twin paradox is often presented as a consequence of time dilation and the relativity of simultaneity, yet its standard interpretation frequently relies on simplified Minkowski diagrams and ambiguous coordinate assignments that obscure the physical meaning of the turnaround event. This paper re-examines the paradox by constructing a Lorentz-consistent spacetime diagram in which inertial and accelerated phases are treated separately and coordinate assignments are preserved consistently across reference frames. We show that a single spacetime event is invariant under Lorentz transformation; different observers may assign different coordinates to that event, but they do not describe different physical occurrences. The apparent contradiction arises not from simultaneity itself, but from conflating event identity with frame-dependent observation and from applying measurement transformations inconsistently after acceleration has ceased. This construction clarifies the operational meaning of simultaneity and demonstrates that the apparent paradox disappears once all measurements are analysed within a common comparison framework.
Category: Relativity and Cosmology

Geometric and Topological Approaches to Crystallography

Authors: Ellie Richwine, Lucian M. Ionescu
Comments: Pages.

This article explores the mathematical structures underpinning crystalline materials, bridging the gap between pure mathematics and materials science. Building upon Toshikazu Sunada’s breakthrough framework of topological crystallography and subsequent formalizations by John C. Baez, we provide a rigorous yet accessible introduction to the geometric and topological modeling of crystals. The study examines polyhedral geometry, duality, and lattice arrangements such as the Eisenstein and triangular lattices, framing them within the context of covering maps and Abel-Jacobi maps. Furthermore, we advance this foundation by introducing a simplified formulation of Graph Cohomology based on short exact sequences of graphs. This homological approach provides a unifying architectural template capable of tracking lattice defects via integer cohomology and modeling macroscopic continuous phenomena from discrete microscopic networks. The paper concludes by discussing the broader applications of these tools in molecular biology, theoretical physics, and fault-tolerant quantum engineering.
Category: Mathematical Physics

A Dynamic Model of Tidal Deformations of the Earth's Elastic Crust in the Central Force Field of the Earth-Moon System

Authors: Viktor Strohm
Comments: 8 Pages.

Traditional theories of Earth tides (such as the classical models of Clairaut, Love, and Darwin) describe geoid deformations via the differential potential of an isolated external disturbing body distributed across the volume of an elastic-plastic sphere. However, when attempting to interpret the physical meaning of forces acting on discrete crustal elements (mobile tectonic plates) within a real bound system, researchers inevitably encounter kinematic paradoxes—specifically, a theoretically unavoidable but empirically unobservable macro-displacement of the planet’s dense core toward its internal boundaries.The present work aims to describe the dynamics of the Earth’s shape variation based on generalizing the law of central forces and the kinematics of the system’s elliptical motion around the barycenter, as presented in [1]. The primary conceptual difference of the proposed approach is the transition from abstract scalar potentials to direct vector summation of actual gravitational accelerations acting on a rigid elastic shell of fixed thickness.The resolution of the apparent contradiction in the direction of individual particle force vectors during the transition from an abstract disk to the real Earth-Moon system lies within the framework of the classical three-body problem. As soon as we begin decomposing the monolithic mass of the planet M into an ensemble of discrete elements m_i, the system transforms into a hierarchical three-body configuration: two interacting bodies are located in immediate proximity (the analyzed crustal microparticle m_i and the residual mass of the planet M-m_i), while the third massive body (the Moon) is removed at a significant orbital distance.In such a formulation, the total force vector acting on each particle naturally decomposes into two components. The short-range (local) interaction binds the particle to the main mass distribution of the planet, directing its elastic retention vector strictly toward the center of the disk C (which, in a geocentric reference frame, manifests as radial compression in the lateral zones Y-Y' ). At the same time, the long-range (gravitational) field of the distant third body imparts the necessary centripetal acceleration to the entire bound system, directing the orbital force vector toward the system’s focus — the barycenter F. Thus, the formalism of force decomposition into focal and central components, proposed in [1] for the circle model O_E, receives a rigorous dynamic justification within the restricted three-body problem, linking the internal geodynamics of the lithosphere with Kepler's laws.
Category: Geophysics

From Ramanujan to Riemann Hypothesis

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

In this work we offer a careful framework for approaching the critical-line problem associated with the Riemann zeta function. At its heart is a long-standing divide in the subject. On one side are analytic approaches, which study the completed zeta function through its reflection symmetry. On the other side are arithmetic approaches, where related criteria often appear through extreme behavior in divisor functions. The purpose of this paper is not to claim a proof of the Riemann Hypothesis, but to place these two perspectives into a clearer and more usable relationship. The argument begins with reflected analytic data for the completed zeta function. It shows that such data can be described through an odd analytic perturbation, giving a more organized way to understand the analytic side of the problem. This also resolves a common point of confusion: the full complex defect is not required to vanish on the critical line. What matters is more subtle. Under a natural real-symmetry condition, the real part of the defect vanishes on the critical line, and this is the feature that becomes useful for the bridge argument. The arithmetic side is built around Ramanujan’s logarithmic divisor profile. The paper establishes the existence and positivity of the relevant extreme scale in the range needed for the proposed connection. These analytic and arithmetic pieces are then brought together through a real bridge functional, made up of a main sign term and a correction term. The main outcome is a conditional criterion for the critical line. If the bridge functional is zero-adapted at the nontrivial zeros, if the real analytic defect satisfies the required one-sided sign condition, and if the correction term remains strictly smaller than the main term, then every nontrivial zero must lie on the critical line. The contribution of this work is therefore structural rather than conclusive. It does not present the Riemann Hypothesis as solved. Instead, it separates what is already established from what still needs to be proved. The key sign law, the domination estimate, and the zero-adaptation identity remain open requirements for any future application of the framework. Its practical value is that it gives researchers a precise checklist for testing whether a proposed analytic or arithmetic strategy can genuinely support a critical-line argument.
Category: Number Theory

Big Gravity Remains Elusive

Authors: Clark M. Thomas
Comments: 5 Pages.

Big Gravity’s (G) Newtonian constant for the local universe seems to be something that eludes astrophysicists seeking better numbersfor the claimed four forces. The latest G data have failed to confront the hermeneutical limits of what their experimental tools measure.We need better multiversal causative precision in 4D dimensions, not weak mathematical correlations. Big Gravity, and Earth’s variablesurface gravities (g), include electromagnetism, along with the properly conceived net push/shadow kinetics. Unifying harmony among all physics dimensions is needed for any elegant multiversal paradigm.
Category: Astrophysics

Motion, Mass, Space and Time: An Emergent Vector Field Framework

Authors: Mangleshwar Thakre
Comments: 41 Pages.

The primary objective of this paper is to investigate the fundamental cause underlying the motion of a massive object. In other words, it seeks to elucidate the nature of momentum and how it originates. To achieve this, a comprehensive literature review on space, time, mass, and motion is presented, offering a novel perspective on these foundational concepts. The mathematical framework is constructed using the core principles and equations of classical mechanics and the special theory of relativity, drawing some direct and substantial indirect influences from continuum mechanics. To analyze physical phenomena within a four-dimensional space-time continuum, the Hodge decomposition theorem and tensor decomposition methods are employed. This paper derives a new set of governing equations for the state of motion of a massive object, providing an entirely new interpretation of its dynamics. Ultimately, this work establishes that mass-energy and momentum are manifested forms of the periodic change of a vector field defined to characterize the system's physics. Within this research paper, the Translational Gravitomagnetic Field Tensor is derived using an entirely novel method. Furthermore, the physical mechanism responsible for giving rise to space-time is explicitly detailed, thereby reinforcing the contemporary paradigm in physics that space-time is an emergent property rather than a fundamental entity of nature. Ultimately, the research paper appears to advocate for an absolute background throughout its entire exposition.
Category: Classical Physics