viXra.org e-prints

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

2026-06-08 00:56:25

reference: viXra:2606.0029v1
title: Dual Architecture of the Gamma Function: Complementary Extension to the Left Half-Plane and Regularization of Logarithmic Divergences
authors: Julinho Jorge Luís
category: Quantum Gravity and String Theory
type: submission
date: 2026-06-08 00:56:25
abstract: 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.

The Atomic Structure of the Chemical Elements

2026-06-08 20:11:22

reference: viXra:2606.0028v1
title: The Atomic Structure of the Chemical Elements
authors: Jozsef Garai
category: Nuclear and Atomic Physics
type: submission
date: 2026-06-08 20:11:22
abstract: 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.

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

2026-06-08 19:46:29

reference: viXra:2606.0027v1
title: Completeness of the Metric Description of Gravitational Reality: An Radiative Generalization of Kerr-Newman Spacetime
authors: Tanishq Chandu Khandare
category: Relativity and Cosmology
type: submission
date: 2026-06-08 19:46:29
abstract: 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.

Is the Central Valley of California an Elongated Impact Basin?

2026-06-08 15:29:47

reference: viXra:2606.0026v1
title: Is the Central Valley of California an Elongated Impact Basin?
authors: David E. Rutherford
category: Geophysics
type: submission
date: 2026-06-08 15:29:47
abstract: 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.

Quantum Mechanics and The Subjective Nature of Mathematics

2026-06-08 19:36:21

reference: viXra:2606.0025v1
title: Quantum Mechanics and The Subjective Nature of Mathematics
authors: Joseph Palazzo
category: Quantum Physics
type: submission
date: 2026-06-08 19:36:21
abstract: 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.

The Oscillations of a Particle in an Anharmonic Potential with Damping

2026-06-05 18:10:42

reference: viXra:2606.0024v1
title: The Oscillations of a Particle in an Anharmonic Potential with Damping
authors: L. A. Xamidullayeva, U. O. Muhammedov, X. N. Ismatullayev
category: Classical Physics
type: submission
date: 2026-06-05 18:10:42
abstract: 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.

2026-06-05 18:03:18

reference: viXra:2606.0023v1
title:
authors: Viktor Strohm
category: Classical Physics
type: submission
date: 2026-06-05 18:03:18
abstract: 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.

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

2026-06-05 18:00:10

reference: viXra:2606.0022v1
title: Decoupled Prompting and Topology-Aware Optimal Transport for CLIP-Based Unsupervised Cross-Modal Re-Identiffcation
authors: Xiaohao Xie, Wenhua Jiao, Wei Meng
category: Artificial Intelligence
type: submission
date: 2026-06-05 18:00:10
abstract: 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.

Ramanujan Polynomial Expansion for Hurwitz Zeta Function

2026-06-06 03:28:18

reference: viXra:2606.0021v1
title: Ramanujan Polynomial Expansion for Hurwitz Zeta Function
authors: Payam Danesh
category: Number Theory
type: submission
date: 2026-06-06 03:28:18
abstract: 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.

A New Home for Bivectors Geometric Algebra on a Sphere

2026-06-06 03:25:23

reference: viXra:2606.0020v1
title: A New Home for Bivectors Geometric Algebra on a Sphere
authors: Norm Cimon
category: Geometry
type: submission
date: 2026-06-06 03:25:23
abstract: 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.

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

2026-06-07 02:04:16

reference: viXra:2606.0019v1
title: The Weakening of Earth's Magnetic Field is the Real Cause Driving Current Ocean Warming
authors: Jamal S. Shrair
category: Climate Research
type: submission
date: 2026-06-07 02:04:16
abstract: 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.

Visual Space, Neural Networks, and AI Algorithm Models

2026-06-06 14:18:10

reference: viXra:2606.0018v1
title: Visual Space, Neural Networks, and AI Algorithm Models
authors: Taiwei Song
category: Artificial Intelligence
type: submission
date: 2026-06-06 14:18:10
abstract: 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.

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

2026-06-06 18:49:02

reference: viXra:2606.0017v1
title: Hastings-Cody Approximations of the Integral of a Power Times the Complete Elliptic Integral of the First Kind
authors: Richard J. Mathar
category: Functions and Analysis
type: submission
date: 2026-06-06 18:49:02
abstract: 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.

A Theory of Kinematic Gravitation, and Some Fundamental Consequences

2026-06-06 18:59:43

reference: viXra:2606.0016v1
title: A Theory of Kinematic Gravitation, and Some Fundamental Consequences
authors: Charles Ba Oumar
category: Relativity and Cosmology
type: submission
date: 2026-06-06 18:59:43
abstract: 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.

Once More on the Aether

2026-06-04 20:13:36

reference: viXra:2606.0015v1
title: Once More on the Aether
authors: Viktor Stetsovich
category: Relativity and Cosmology
type: submission
date: 2026-06-04 20:13:36
abstract: 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.

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

2026-06-05 01:22:28

reference: viXra:2606.0014v1
title: Saturating Magnetic Max Bank Drives Mismatched Loads, Using the Method of Self Matched Lines
authors: Max Artusy
category: High Energy Particle Physics
type: submission
date: 2026-06-05 01:22:28
abstract: 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.

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

2026-06-03 20:24:38

reference: viXra:2606.0013v1
title: Resolving the Cosmological Hubble Tension via Local Wave Impedance Fluctuations in a Hexagonal Close-Packed Lattice
authors: Markov Efim Sergeevich
category: Astrophysics
type: submission
date: 2026-06-03 20:24:38
abstract: 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

The Final Theory

2026-06-04 20:19:31

reference: viXra:2606.0012v2
title: The Final Theory
authors: Nigel B. Cook
category: Quantum Gravity and String Theory
type: replacement
date: 2026-06-04 20:19:31
abstract: 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.

The Final Theory

2026-06-03 20:54:14

reference: viXra:2606.0012v1
title: The Final Theory
authors: Nigel B. Cook
category: Quantum Gravity and String Theory
type: submission
date: 2026-06-03 20:54:14
abstract: 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.

2026-06-03 03:10:06

reference: viXra:2606.0011v2
title:
authors:
category: Classical Physics
type: withdrawal
date: 2026-06-03 03:10:06
abstract:

64 Spirals Across 12 Science Domains, Same Three Equations. Nobody Was Looking.

2026-06-01 22:00:03

reference: viXra:2606.0011v1
title: 64 Spirals Across 12 Science Domains, Same Three Equations. Nobody Was Looking.
authors: James Lucas
category: Classical Physics
type: submission
date: 2026-06-01 22:00:03
abstract: We present a catalog of 64 spiral phenomena spanning 12 domains of science — from quantum spin (10u207b³u2075 m) to cosmic filament rotation (10²u2076 m). Three equations describe all observed instances: the logarithmic spiral r = ae^(bθ), Fibonacci packing at the golden angle θu2099 = n × 137.508°, and angular momentum conservation L = Iω. No free parameters are introduced beyond the growth rate b, which varies by scale. The same functional form appears across quantum mechanics, atomic structure, chemistry, biology, neuroscience, Earth science, planetary dynamics, stellar evolution, galactic structure, cosmology, multiverse models, and pure mathematics. We argue this is not metaphor but mechanism: spin is the only behavior available to energy in a rotational spacetime. The catalog was assembled without targeted search; a systematic survey would likely expand it. All source code for interactive visualizations is included.

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

2026-06-02 03:54:54

reference: viXra:2606.0010v1
title: An Alternate Resolution of the Famous Grandmother Paradox Which Might be Also Validated Via a Classic Experiment
authors: Moshe Segal
category: Relativity and Cosmology
type: submission
date: 2026-06-02 03:54:54
abstract: 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.

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

2026-06-02 07:07:35

reference: viXra:2606.0009v1
title: 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
category: Classical Physics
type: submission
date: 2026-06-02 07:07:35
abstract: 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.

Limitation in Ramanujan Positivity and Zeta Zeros of Riemann

2026-06-03 00:06:14

reference: viXra:2606.0008v1
title: Limitation in Ramanujan Positivity and Zeta Zeros of Riemann
authors: Payam Danesh
category: Number Theory
type: submission
date: 2026-06-03 00:06:14
abstract: 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.

Liniar Transformations on Multi-Vector Spaces

2026-06-03 00:04:47

reference: viXra:2606.0007v1
title: Liniar Transformations on Multi-Vector Spaces
authors: Constantin Scheau
category: Algebra
type: submission
date: 2026-06-03 00:04:47
abstract: 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.

Time vs. Duration: A Reinterpretation of Special Relativity

2026-06-02 14:23:16

reference: viXra:2606.0006v1
title: Time vs. Duration: A Reinterpretation of Special Relativity
authors: Ion Vlad
category: Relativity and Cosmology
type: submission
date: 2026-06-02 14:23:16
abstract: 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.

Geometric and Topological Approaches to Crystallography

2026-06-02 14:44:15

reference: viXra:2606.0005v1
title: Geometric and Topological Approaches to Crystallography
authors: Ellie Richwine, Lucian M. Ionescu
category: Mathematical Physics
type: submission
date: 2026-06-02 14:44:15
abstract: 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.

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

2026-06-02 17:26:30

reference: viXra:2606.0004v1
title: 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
category: Geophysics
type: submission
date: 2026-06-02 17:26:30
abstract: 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.

From Ramanujan to Riemann Hypothesis

2026-06-01 20:52:50

reference: viXra:2606.0003v1
title: From Ramanujan to Riemann Hypothesis
authors: Payam Danesh, Raoul Bianchetti
category: Number Theory
type: submission
date: 2026-06-01 20:52:50
abstract: 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.

Big Gravity Remains Elusive

2026-06-01 20:50:54

reference: viXra:2606.0002v1
title: Big Gravity Remains Elusive
authors: Clark M. Thomas
category: Astrophysics
type: submission
date: 2026-06-01 20:50:54
abstract: 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.

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

2026-06-01 14:50:19

reference: viXra:2606.0001v1
title: Motion, Mass, Space and Time: An Emergent Vector Field Framework
authors: Mangleshwar Thakre
category: Classical Physics
type: submission
date: 2026-06-01 14:50:19
abstract: 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.

A One-Way Relativistic Decay-Clock Test of Kinetic Preferred-Frame Time Dilation

2026-05-31 01:54:37

reference: viXra:2605.0121v1
title: A One-Way Relativistic Decay-Clock Test of Kinetic Preferred-Frame Time Dilation
authors: Jayanta Majumder, Sambuddha Majumder
category: Relativity and Cosmology
type: submission
date: 2026-05-31 01:54:37
abstract: A recently proposed kinetic route to the Lorentz transform models an elementary particle as a closed lightlike intrinsic motion whose internal cycle is reallocated, under bodily translation, between intrinsic circulation and spatial advance. The construction recovers the usual time-dilation law and the Lorentz boost as a hyperbolic state map, while allowing a physical ``special'' frame in which the intrinsic tick count and the external time parameter coincide. In such a framework, ordinary closed-path clock tests are not necessarily the most sensitive probes of the special frame, because the leading directional term proportional to $Ucdotvvec$ cancels when the transported clock returns to its starting point. This paper develops a sharper null test: a one-way lifetime anisotropy measurement using unstable relativistic particles as intrinsic clocks. If a laboratory has special-frame velocity $U$ and an unstable particle beam of speed $u=beta c$ is sent along direction $$, the strong preferred-frame reading of the kinetic model predicts, to leading order,begin{equation*} tau_{m lab}() simeq gamma_u tau_0 left(1 + betafrac{Ucdot}{c}ight),end{equation*}whereas standard special relativity predicts $tau_{m lab}=gamma_utau_0$ independent of absolute orientation. Antiparallel one-way beams would therefore exhibit a fractional lifetime asymmetrybegin{equation*} frac{tau_{+}-tau_{-}}{(tau_{+}+tau_{-})/2} simeq 2betafrac{Ucdot}{c}.end{equation*}For a candidate $|U|simSI{369}{km.s^{-1}}$, as suggested by the CMB dipole scale, the maximal signal for relativistic beams is of order $2.5times 10^{-3}$, far larger than the fourth-order residuals expected in closed transport tests. The decisive experimental signature is an antiparallel lifetime or decay-length asymmetry with sidereal modulation as the Earth rotates the beam axis relative to the putative preferred-frame vector. The proposal is framed as a falsifiable extension of the kinetic model: a null result would strongly constrain the strong preferred-frame interpretation rather than merely refine an existing relativistic clock test.

State Commitment Learning: Training Language Models to Distinguish Computation from Memory

2026-05-31 18:47:17

reference: viXra:2605.0120v1
title: State Commitment Learning: Training Language Models to Distinguish Computation from Memory
authors: Fei Ding, Yongkang Zhang, Runhao Liu, Yuhao Liao, Zijian Zeng, Huiming Yang
category: Artificial Intelligence
type: submission
date: 2026-05-31 18:47:17
abstract: Reasoning language models do not distinguish tokens used for computation from tokens that constitute persistent state: once generated, all hidden thoughts remain in context and influence future predictions. As a result, downstream reasoning may depend on failed attempts, dead ends, and private scratch work that should not be safely relied on later. We recast this phenomenon as a new training objective, state commitment learning: training models to explicitly distinguish information that should be committed as persistent state from temporary computation that can be discarded. We define a counterfactual criterion, persistent-state sufficiency, which makes it trainable and measurable whether an answer remains usable after hidden thoughts are erased. We then propose Counterfactual Erasure RL (CERL), which evaluates, under the same prefix, both a path that keeps hidden thoughts and a path that erases them, and gives reward only when the erasure path remains correct. We also introduce the Erasure Dependence Protocol and show across mathematics, long-chain logic, scientific QA, and multi-turn tool-use evaluation that CERL substantially reduces answer dependence on hidden thoughts without sacrificing accuracy, consistently outperforming correctness-only RL and long-answer SFT baselines.

Scaffold-Mediated Post-Training: Co-Evolving Model Parameters and Procedural Scaffold Graphs

2026-05-31 03:02:06

reference: viXra:2605.0119v1
title: Scaffold-Mediated Post-Training: Co-Evolving Model Parameters and Procedural Scaffold Graphs
authors: Fei Ding, Yongkang Zhang, Runhao Liu, Yuhao Liao, Zijian Zeng, Huiming Yang
category: Artificial Intelligence
type: submission
date: 2026-05-31 03:02:06
abstract: Post-training of large language models optimizes only parameters, while inference-time procedural scaffolds are typically designed independently of parameter training. This disconnect makes it difficult to automatically acquire and internalize complex strategies. We propose scaffold-mediated post-training: procedural scaffolds are organized into an evolvable graph structure that co-evolves with model parameters through discovery, distillation, and dynamic recompilation. We instantiate this paradigm as Skill Training. On FeatureBench, automatically discovered skills improve the passed rate by 8.1pp, and after progressive distillation the model still achieves a 27.7% passed rate without any external scaffold (distillation retention rate 85.2%, defined as post-distillation / with-skill passed rate), significantly outperforming standard SFT on the same data.

Check Token: Real-Time Self-Verification and Precise Truncation in LLM Reasoning

2026-05-31 03:04:00

reference: viXra:2605.0118v1
title: Check Token: Real-Time Self-Verification and Precise Truncation in LLM Reasoning
authors: Fei Ding, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
category: Artificial Intelligence
type: submission
date: 2026-05-31 03:04:00
abstract: ECC memory embeds 8 parity bits for every 64 data bits and automatically detects and corrects errors on each read. The parity bits carry no data and only safeguard integrity, at ~12.5% overhead. Yet the reasoning chains of large language models lack such built-in self-verification: once an error occurs it propagates along the chain, and existing methods can only verify externally after generation completes. We propose the check token, establishing built-in self-verification for language model generation streams for the first time: a functional marker is added to the vocabulary, and the model triggers self-checking (analysis, localization, truncation, rewriting) by outputting it at any position. The check token carries no reasoning content (discarded after triggering) and only safeguards reasoning correctness, directly corresponding to the role of ECC parity bits, also at only ~13% overhead. Speculative forking further eliminates false-positive latency, and segmented reward makes trigger timing end-to-end learnable. Experiments (Qwen3-32B / Qwen3-Next) show that the check token achieves +10.8 pp improvement on HMMT25 at 1.13x overhead, with token efficiency 88x that of Best-of-8, and the precise truncation advantage monotonically increases with chain length.

On the Impossibility of Unbiased and Length-Invariant Policy Optimization with Outcome Rewards

2026-05-31 03:05:42

reference: viXra:2605.0117v1
title: On the Impossibility of Unbiased and Length-Invariant Policy Optimization with Outcome Rewards
authors: Fei Ding, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
category: Artificial Intelligence
type: submission
date: 2026-05-31 03:05:42
abstract: Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.

Ramanujan-Inspired Prime Sums

2026-05-31 18:40:17

reference: viXra:2605.0116v1
title: Ramanujan-Inspired Prime Sums
authors: Payam Danesh, Raoul Bianchetti
category: Number Theory
type: submission
date: 2026-05-31 18:40:17
abstract: This paper develops a finite framework for studying sums of prime numbers through consecutive prime gaps. The motivation comes from Ramanujan’s influence on arithmetic decompositions, partition methods, and summation ideas, while the argument remains within ordinary finite number theory. We study the partial sum of the first n primes and prove an exact identity that writes this sum as a baseline term from the initial prime together with a weighted accumulation of consecutive prime gaps. Each gap receives a weight equal to the number of later primes affected by that gap. The same identity is then expressed geometrically by encoding each weighted gap as the slope of a right triangle. Exact numerical examples verify the formula, and the asymptotic discussion shows that the decomposition has the same leading scale as the classical growth predicted by the prime number theorem. This paper also separates finite identities from regularized infinite summations. This distinction is essential: the finite formula is exact, while divergent infinite prime sums require a separate summation theory and cannot be treated as ordinary convergent series.

An Infinite Family of Solutions to the Generalized Cannonball Problem

2026-05-31 18:39:00

reference: viXra:2605.0115v1
title: An Infinite Family of Solutions to the Generalized Cannonball Problem
authors: J.W.L. Eerland
category: Number Theory
type: submission
date: 2026-05-31 18:39:00
abstract: In an earlier paper I considered the generalized cannonball problem for r-regular polygons and studied integer solutions to the associatedDiophantine equation. In this note I prove that for every positive integer n, the triple[(r,a,b)=left(3n+2,,3n^2-2,,3n^3-3n+1ight)] is a solution. Hence the generalized cannonball problem admits infinitely many positive integer solutions. I also compare this parametric family with the 858 tuples listed in the appendix of the earlier paper. Among those tuples, 802 are generated by the present family and the remaining 56 tuples are listed explicitly.

Explicit U(2) Matrices and the Emergence of Electroweak Charges

2026-05-31 18:28:27

reference: viXra:2605.0114v1
title: Explicit U(2) Matrices and the Emergence of Electroweak Charges
authors: N B Cook
category: Quantum Gravity and String Theory
type: submission
date: 2026-05-31 18:28:27
abstract: We make the U(2) structure completely explicit in terms of 2 × 2 matrices and show how Woit’s construction on Λ∗(C^2) reproduces the chiral electroweak charges of the first lepton and quark generations.

Logical Foundations of Geometric Space and Natural Space-time Space

2026-05-29 01:02:12

reference: viXra:2605.0113v1
title: Logical Foundations of Geometric Space and Natural Space-time Space
authors: Taiwei Song
category: Mathematical Physics
type: submission
date: 2026-05-29 01:02:12
abstract: This short paper briefly discusses the fundamental concepts, intrinsic rules, and logical relationships of geometry from the most essential perspective, and its relationship with algebra. It also defines natural space-time space and its intrinsic logical relationships and significance. Most of the content in this paper is important achievements of the" Geometry of Space-time Structures " established by the author.

Towards a Floer Theory for Mars I Twisted Zeeman Systems

2026-05-29 20:37:55

reference: viXra:2605.0112v1
title: Towards a Floer Theory for Mars I Twisted Zeeman Systems
authors: Urs Frauenfelder, Joa Weber
category: Mathematical Physics
type: submission
date: 2026-05-29 20:37:55
abstract: In this article we study periodic orbits of an electron attracted by a proton subject to Lorentz, electric, and Euler forces where each of them is allowed to depend periodically on time. This setup is motivated by the elliptic restricted three-body-problem where the Lorentz force corresponds to Coriolis force, the Coulomb force is replaced by the gravitational force, and the electric force of an external source is a combination of centrifugal forces and gravitational forces of other bodies. This is a singular version of a Euler-Hamilton system as discussed in [FW26b]. The singularity is due to collisions of the electron with the proton, respectively of two masses. Due to the possibility of collisions this problem has to be regularized.We show how periodic collisional solutions of this problem can be detected variationally in a non-local Lagrangian setup as well as in a non- local Hamiltonian setup.

False Equivalence of Accelerating Rocket and Gravity Pull on Elevator

2026-05-27 04:47:08

reference: viXra:2605.0111v1
title: False Equivalence of Accelerating Rocket and Gravity Pull on Elevator
authors: Carl Littmann
category: Relativity and Cosmology
type: submission
date: 2026-05-27 04:47:08
abstract: Gravity bends a light beam more than a particle beam. We show how elevator occupants can use that fact to determine whether the forces they feel are caused by a gravitational or non-gravitational acceleration. I.e., although that capability supposedly violates the ‘Equivalence principle’ of ‘General Relativity’. Einstein imagined "the experiences of occupants in a windowless chamber, in deep, isolated space" as it was ‘accelerated upward’ by a pulling. And claimed ‘Equivalent’ (identical) feelings and test results would arise for occupants in a non-moving elevator on our gravitational earth.[1] Yet, let us imagine that a photon and an ultra-high-speed particle are launched at the same time from an internal wall of an elevator; then they go through two adjacent pin-holes, and finally hit the opposite wall. But surprisingly, they do not hit the same spot - because the gravity bends photons twice as much as a particle beam.[2] So we discuss that violation of ‘Equivalence in Relativity’ and its broad implications, in this article.

A Proof for the Collatz Conjecture

2026-06-04 09:32:39

reference: viXra:2605.0110v2
title: A Proof for the Collatz Conjecture
authors: Jérôme Chauvet
category: General Mathematics
type: replacement
date: 2026-06-04 09:32:39
abstract: This proof addresses the Collatz conjecture and relies on the quantitative characterization undergone by the evolving densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system from which we deduce the final cyclic attractor, hence proving the conjecture.

A Proof for the Collatz Conjecture

2026-05-27 12:32:03

reference: viXra:2605.0110v1
title: A Proof for the Collatz Conjecture
authors: Jérôme Chauvet
category: General Mathematics
type: submission
date: 2026-05-27 12:32:03
abstract: This proof adresses the Collatz conjecture and relies on the quantitative characterization undergone by the evolving densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system, from which we deduce the final cyclic attractor, hence proving the conjecture.

SlideTuner: PowerPoint Slide Design via XML Representation Learning and Preference Optimization

2026-05-27 22:10:46

reference: viXra:2605.0109v1
title: SlideTuner: PowerPoint Slide Design via XML Representation Learning and Preference Optimization
authors: Lixiang Li, Anjan Goswami , Md Muksitul Haque , Bharat Bhargava
category: Artificial Intelligence
type: submission
date: 2026-05-27 22:10:46
abstract: Generating high-quality PowerPoint slides from natural language instructions is a complex task that demands not only deep semantic understanding, but also aesthetic design. The essential component for building a functional and visually rich slide is the XML object. Therefore, it is intuitive that the most direct path to creating a high-quality slide is to generate it directly from the foundational XML structure. However, previous ``human instruction to slide generation" models typically rely on generating Python code, which serves as an intermediary to produce the final slide output rather than direct production of the XML object. As a result, these models lack the ability to precisely construct and control the building blocks required for a detailed slide composition. We introduce SlideTuner, a custom finetuned GPT-4o model specifically engineered to generate high-quality PowerPoint slides by generating the required XML files. Through extensive empirical experiments, we demonstrate that the fine-tuned GPT-4o model successfully and consistently produces visually coherent and aesthetically pleasing slides. The SlideTuner employs a two-stage training approach: first we apply SFT to the language model, enabling it to generate slide-rendering XML code directly from user instruction, utilizing XML data extracted from native PowerPoint slides. Second, we apply Direct Preference Optimization (DPO) to align the model's outputs with preferred visual styles, such as specific font choices. The slides produced by our model exhibit superior layout scores and style adherence. While this work focuses on font-level aesthetic control, our work establishes a foundation for future research aimed at precisely guiding slide generation toward diverse visual or structural preferences.

Infinitely Many Twin Prime Reexplored - Proof

2026-05-27 22:09:00

reference: viXra:2605.0108v1
title: Infinitely Many Twin Prime Reexplored - Proof
authors: James DeCoste
category: Number Theory
type: submission
date: 2026-05-27 22:09:00
abstract: Without any concrete feedback from the mathematical community, I was forced to have an enlightening discussion with Google's AI engine to determine what the likely problems were with my initial paper Infinitely Many Twin Primes — Proof (found on viXra.org: https://vixra.org/abs/2502.0186).Since I did all my own research in a sandbox without contributions from the mainstream mathematical community ( blind research ), I evidently ran into the same wall all prior mathematicians hit and that was proving that the twin primes candidates don't simply fizzle out as one approaches infinity. I was relying on combinatorics to prove this, which I now see was a mistake when taken by itself. As the AI engine and myself did a deeper dive on current mainstream research we noticed that much of the research I performed but did not include in my original paper were already explored by others. Some of these will be the key when reworking this on it's second take; the Hardy-Littlewood ratios 1:1:2 and the product rule that sees the pattern repeat at that product, to mention two. This was done blind without ever realizing it.We were able to determine that the rest of the original paper was sound even if not written in mainstream mathematical language. However that wall where the twin primes could simply fizzle out or completely dry up was impossible to ingore. While exploring some of the new approaches being implemented by Maynard and Tao, I made the realization that the probabilities angle should not have been abandoned. I had already done research to establish floor and ceiling limits as decaying log curves...but they too appear likely to fizzle out as one approaches infinity. That was until we took a look at a specific probability ratio of my window size sample growth versus the number of primes total growth. The first was a quadratic growth rate ( x^2) and the second was strictly linear ( number of primes grow at a steady rate). Using this probabilty along with the prior published paper finally plugs the hole and smashes down that wall as a mathematical improbability. The idea is that we have a fraction that is continually shrinking but can't actually get to absolute zero, the wall. The number of new elements (prime elimination patterns) is not increasing fast enough to keep up and eliminate all candidates in the exponentially increasing window size of my ranges. Candidates always escape. This clearly shows that my combinatoric approach was also correct in it's logic and that twin primes can never totally disappear.

Quasinormal Modes of Black Holes in Finsler-modified Gravity

2026-05-27 01:06:39

reference: viXra:2605.0107v1
title: Quasinormal Modes of Black Holes in Finsler-modified Gravity
authors: Holger A.W. Döring
category: Relativity and Cosmology
type: submission
date: 2026-05-27 01:06:39
abstract: Investigated is the ringdown phase of black holes within a modified gravitational framework that includes a weak Finsler coupling (a) , a quadratic curvature correction (b) and a dynamical timelike vector field (u^μ). Using analytical approximations and dicussing numerical simulations, there is shown, that quasinormal modes (QNM) are slightly shifted and anisotropically modulated. Residuals against standard Kerr fits are calculated, and observational constraints from LIGO, Virgo, pulsar timing, and atomic clocks are analyzed. Found is, that current gravitationalwave detectors constrain (a≾10 −3 ), while next-generation detectors (Einstein Telescope, LISA) could probe (a∼10 −12 −10 −8 ). Quadratic curvature corrections remain unobservable at thePlanck scale. The given results highlight characteristic signatures of Finsler-modified gravity in black hole ringdowns.

The Variable Mass Theory and Gravitational Paradoxes

2026-05-26 09:42:40

reference: viXra:2605.0106v1
title: The Variable Mass Theory and Gravitational Paradoxes
authors: Han de Bruijn
category: Relativity and Cosmology
type: submission
date: 2026-05-26 09:42:40
abstract: Essential reading is the first article in the series, which is about Atomic Time, Orbital Time and the Variable Mass Theory. It has been shown in this article that General Relativity (GR) can be effectively replaced by Variable Mass (VM) in a Static Euclidean Universe (SEU), which is eternal in Atomic time and has moments of creation (i.e. one or more beginnings) in Orbital time.
The cosmological redshift is intrinsic: it only depends on variable (elementary particle rest) mass. Because that is where the VM theory has been designed for.
A convenient consequence is that Newton's theory is good enough for describing gravity at a cosmic scale. It is demonstrated that the latter, when combined with the Variable Mass hypothesis, solves for Gravitational Paradoxes.

A Novel View of Quark Electric Charges and Baryon Composition

2026-05-27 01:01:50

reference: viXra:2605.0105v1
title: A Novel View of Quark Electric Charges and Baryon Composition
authors: Wolfram Loewenstein
category: High Energy Particle Physics
type: submission
date: 2026-05-27 01:01:50
abstract: I propose that the quarks (d, s, b) carry the electric charge (-1) and the quarks (u, c, t) are electrically neutral. I further propose that baryons are composed of one quark and two anti-quarks. I believe that these assumptions help to solve some problems in the Standard Theory of elementary particles.

Simple Proof of Fermat’s Last Theorem for Odd Powers

2026-05-27 00:47:00

reference: viXra:2605.0104v1
title: Simple Proof of Fermat’s Last Theorem for Odd Powers
authors: Minho Baek
category: Number Theory
type: submission
date: 2026-05-27 00:47:00
abstract: It was already proved right that x^n+y^n=z^n, (n>2) has no solutions in positive integers which we called Fermat’s Last Theorem (FLT) by Andrew Wiles. But his proof would be impossible in the 17th century. I took the idea from Euler proof and proved in case of n=odd by simple method.