All Submission Categories

Real-Virtual Annihilation

Authors: Muhammad Sohail
Comments: 8 Pages. https://doi.org/10.5281/zenodo.15122956 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper explores the concept of real virtual annihilation in quantum spacetime, emphasizing theinteractions between real and virtual particles. Through theoretical formulations and quantum field dynamics, the study delves into the formation of black holes, quantum invariance under gravity, and the profound relationship between uncertainty principles and Minkowski metrics.
Category: Astrophysics

How a Tokamak May Allow GW to be Duplicated in Simulated Values [paert Ii]

Authors: Andrew Beckwith
Comments: 51 Pages. (Note by viXra Admin: Title shortened by viXra Admind to conform with scholarly norm - Please don't use long and convoluted title)

We make more specific initial contributions of prior work w.r.t. Tokamaks, relic black holes, and a relationship between a massive graviton particle count and quantum number n, and also add a great more to contributions of ourconclusions w.r.t. the wave function of the universe. Our idea for black hole physics being used for GW generation, is using Torsion to form a cosmological constant. Planck sized black holes allow for a spin density term linked toTorsion.. In doing so, we review its similarities to frequency values for GW dueto a Tokamak simulation. The conclusion of this document will be in bringing up would be values for an initial wave function of the Universe and an open question as to the applications of a white hole-black hole wormhole bridge between a prior to the present universe as well as a speculation as to particle count, and a quantum number, n, as specified in our document
Category: Quantum Gravity and String Theory

Research on the Vacuum Power Mechanism (in English)

Authors: Yake Li
Comments: 14 Pages. (Note by viXra Admin: Please submit article in pdf format only)

Based on multiple astronomical observation results, this paper proposes the hypothesis of the principle of relative variation of the speed of light and proves the compatibility between this principle and the principle of the constancy of the speed of light. Based on this principle, this paper constructs an innovative theoretical framework of the vacuum dynamics theory and derives several important conclusions.
Category: Astrophysics

Microscopic Interpretation of The Gravity Electroweak Symmetry Breaking

Authors: Stephane H. Maes
Comments: 30 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

In previous papers, we proposed detailing the concepts of gravity electroweak symmetry breaking, in the context of the multi-fold universe. Accordingly, massive particles are modeled as microscopic black holes as Higgs boson condensate Qballs, and massless particles are modeled as 2D random walk patterns of massless Higgs bosons. In this paper, we present a microscopic interpretation of what happens above, at and below the gravity electroweak symmetry breaking. This includes how we have condensation into a BEC Qball of Higgs condensate, while massless particles remain patterns of random walks, which disappear at higher temperatures, leading to eth Ultimate Unification (UU}, where only 2D random walks of massless bosons take place.
Category: High Energy Particle Physics

The LW-Tate Framework: Extending Langlands Watch to Prove the Tate Conjecture for K3 Surfaces and Beyond

Authors: Song Fei
Comments: 24 Pages.

Abstract This paper introduces the Langlands Watch-Tate (LW-Tate) framework, an extension of the Langlands Watch (LW) framework first proposed in [1] , to prove the Tate Conjecture for all K3 surfaces over mathbb{Q} . We establish that ensuremath{text{rank}text{Pic}(X)=text{ord}_{s=1}L(H^{2}(X),s)} holds universally, covering both finite and infinite automorphism groups, by decomposing H^{2}(X_{overline{mathbb{Q}}},mathbb{Q}_{ell}(1)) into irreducible representations under text{Aut}(X) and associating each with weight 2 automorphic forms on Shimura varieties. Building on LW’s hierarchical structure, LW-Tate’s novel integration of symmetry and modularity resolves a major conjecture in arithmetic geometry. Furthermore, we extend LW-Tate to Calabi-Yau threefolds , explaining text{ord}_{s=2}L(H^{3}(Y),s)=text{rank}text{Pic}(Y) , showcasing its potential to address higher-dimensional Tate Conjectures and cementing its role as a transformative tool in the Langlands Program.
Category: Number Theory

Wallis's Constant

Authors: Edgar Valdebenito
Comments: 2 Pages.

In this note, we give some formulas related to Wallis's constant.
Category: General Mathematics

A Technique for Making Nuclear Fusion in Solids — More Elements

Authors: Richard Wayte
Comments: 10 Pages.

A technique is demonstrated for making nuclear fusion at room temperature by passing an electric current through a new-found mixture of hydride and catalyst powders. The result is explosive beyond chemical reaction for the materials.
Category: Nuclear and Atomic Physics

Resonant Observation and Dimensional Evolution: A New Interpretation of Quantum Perception and Reality

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

This paper introduces a new theoretical framework called Dimensional Evolution, which reinterprets quantum observation through the lens of resonance. It proposes that wavefunction collapse is not a physical process, but a perceptual illusion created by the observer’s resonance with specific frequencies. The human body functions as a fractal antenna, filtering waveform reality and generating the illusion of particle-based outcomes. The interference pattern in the double slit experiment is reinterpreted as a visualization of resonance alignment, not probability distribution. This framework further explains the nature of consciousness, biological evolution, memory, and gravity through harmonic resonance, suggesting that many currently unobservable phenomena (such as dark matter) are waveform layers outside our resonant range. The theory provides a unified, resonance-based model of reality that bridges physics, biology, and perception.
Category: Quantum Physics

The Theory of Concomitant Forces

Authors: Dipeng Li
Comments: 14 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper studies the relationship between the Coulomb force and the magnetic force in electromagnetism, and proposes the inference that the magnetic force is the concomitant force of the Coulomb force. It also proposes the hypothesis that each fundamental force has a concomitant force and extends it to gravitation, suggesting that the inertial mass is the concomitant force of the gravitational mass, and explains the Higgs mechanism. Three laws of fundamental forces and concomitant forces are summarized. A model for unifying weak interactions and strong interactions is proposed, successfully explaining why magnetic monopoles cannot exist alone and the phenomenon of quark confinement. The strengths of the strong interaction and electromagnetic interaction are explained. There is a connection between fundamental forces, their concomitant forces, and space. On the basis of the theory of concomitant forces, a model of the origin of the universe is proposed. This model provides a theoretical framework to reconcile the contradictions between quantum mechanics and general relativity.
Category: High Energy Particle Physics

A study of Dark Matter: A Comprehensive Review

Authors: Diriba G. Tolasa
Comments: 14 Pages.

Dark matter, a fundamental component of the universe, remains one of the most fascinating mysteries in modern astrophysics. Despite its pervasive influence on the dynamics of the universe, its elusive nature continues to challenge the understanding of fundamental physics. This comprehensive review synthesizes recent research findings, theoretical frameworks, observational evidence, and experimental efforts in the quest to understand the nature and properties of dark matter.
Category: Astrophysics

A Dictionary of the Dano-Norwegian and English Languages by A. Larsen and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 29 Pages.

We study the Dano-Norwegian head entries of A Dictionary of the Dano-Norwegian and English Languages by A. Larsen. We draw the natural logarithm ofthe number of the Dano-Norwegianlanguage head entries, normalised, starting with a letter vs the natural logarithm of therank of the letter, normalised/unnormalised. We find that the Dano-Norwegian head entries underlie a magnetisation curve of a Spin-Glass in thepresence of little external magnetic field.
Category: Linguistics

Two New Methods Based on 6x ± 1 Equations to Break All Types of Evens in Sum of Two Primes

Authors: Bahbouhi Bouchaib
Comments: 14 Pages.

This article presents two methods A and B for breaking an even number into two primes. Both methods are inspired by the equations 6x ± 1 because all prime numbers and their multiples except 3 are 6x ± 1. Both methods can be very useful for even conversion in sums of two primes or to study the Goldbach's strong conjecture. Both methods can have applications in computer science.
Category: Number Theory

A Note on Superluminalization of SRT and Some Central Concerns of Contemporary Physics

Authors: Mohamed E. Hassani
Comments: 25 Pages. 1 Table; 121 References

Over the past decades and more recently, there has been a significant effort and renewed interest in extending special relativity theory beyond the speed of light. In this comprehensive note, the paper "Relativity of superluminal observers in 1+3 spacetime" by Dragan et al.[1] is examined. The authors attempted to extend the aforementioned theory to superluminal inertial reference frames by generalizing Parker’s two dimensional transformation with the addition of two pairs of spatial dimensions. This approach is not novel and is already well-documented in the literature. It is demonstrated that unlike Lorentz transformations, the authors’ transformations do not form an orthogonal-orthochronous group due to their negative determinant. Consequently, principles such as relativity, causality, spatial isotropy, and temporal ordering cannot be preserved. The authors’pseudo-transformations are revealed to be reflections in a plane through the originrather than true transformations. Also, a theoretical maximum limit of the Lorentz factor is introduced, whichleads to an extension of Lorentz transformations to luminal inertial reference frames and raises an importantconceptual question about the status and role of the symbolic quantity ‘c’, commonly called the speed of light in vacuum, as the neutrino and particularly the photon have non-zero mass. Therefore, it appears that as long as the non-zero mass of the photon is not taken seriously into full consideration, our current knowledge of physics, astronomy, astrophysics, and cosmology remains not only incomplete but above all vague and doubtful. Unfortunately, it seems that many present-day researchers are unaware that distinguished physicists like Einstein [59-62], de Broglie [63-66], Proca [67-71], Schrödinger [72-74], and many others [75-92] hadalready attributed non-zero mass to the photon because they realized that the photon itself behaves like a massive particle, carrying not only energy but also momentum and can exert pressure on a target. And at no stage may we really be able to conclude experimentally the exact masslessness of the photon because theHeisenberg uncertainty principle gives the lowest mass m that can be measured in the Universe’s age as ��~ℏ��^(−1)��^(−2)~1.5 × 10^(−33)eV/��^2. Once again, therefore, non-zero photon mass gives rise immediately to aconceptual question: What is the primary purpose of the symbolic quantity ‘c’ when it appears in some important equations describing the laws of physics? Moreover, this inclusive note highlights Hassani superluminal spatio-temporal transformations, which possess the algebraic structure of a linear group and serve as a generalization of Lorentz transformations for superluminal inertial reference frames. Thesetransformations are anticipated to be fundamental in superluminal relativistic mechanics [50].
Category: Mathematical Physics

Some Mathematical Results of Light Path Models in General Relativity and the Decomposition of the Null Geodesic Into Gravitational Components

Authors: Gerald Malczewski
Comments: 31 Pages.

This paper is a natural continuation of an earlier paper of light path models and investigates the mathematical implications of geodesic light trajectories within a Schwarzschild metric gravitational field. We focus on a model expressed as infinite Taylor series expansion and its finite cut-off counterpart. A comparison is then made against another existing model that is expressed in closed form not requiring an infinite series and which requires a Jacobian elliptic function. Under some restriction of the mass of the central gravitating body these different models were previously shown to be equivalent. Using these results, some mathematical relationships are then derived. Additionally, we decompose the light path equation into an infinite set of ‘gravitational components’, somewhat akin to techniques used in Fourier analysis.
Category: Relativity and Cosmology

Seven Set Prime Number Theorem

Authors: Muhammad Ahmad Abdullah
Comments: 41 Pages.

This paper seeks to explore the nature of primality by investigating relationships between prime numbers. For centuries, mathematicians have been intrigued by the unpredictable distribution of primes. The Seven-Set Prime Number Theorem (SSPNT) offers a novel approach to address this challenge. By building on Ulam's Spiral, SSPNT uses simple sets and visual patterns to gain insights into primality. This methodology not only provides a fresh perspective on prime number theory but also has potential applications in coding theory and cryptography, revealing hidden patterns and underlying structures.
Category: Number Theory

Proof of the Lehmer Conjecture on Ramanujan's τ Function

Authors: Minjia Shi, Lu Wang, Patrick Solé
Comments: 12 Pages.

A criterion for Lehmer's conjecture in terms of the spherical designs held in the shells of the lattice E8 was derived by de La Harpe, Pache and Venkov circa 2005. We check that this criterion is satisfied by combining spherical designs, harmonic polynomials, weighted theta series, and Deligne's bound on the modulus of the τ function.
Category: Number Theory

Connecting Gravitation and Electromagnetism In the Dirac Gauge of the Electromagnetic Field

Authors: Varun Verma
Comments: 28 Pages.

Motivated by the observation made by R. H. Dicke in 1957 that the speed of light seems to be correlated with the gravitational potential of the entire universe, we develop a spatially-variable speed of light theory of gravity based on a gravitational wavefunction. The gravitational wavefunction is treated as a fundamental property of matter, while the gravitational potential and resulting forces derived from it are emergent properties which are critically dependent on the distribution of mass on both local and global scales throughout the universe. We then show that the theory leads naturally to an association of gravitation with zero-point fluctuations of the electromagnetic field in the Dirac gauge, with the amplitude and frequency of the fluctuations constrained by the gravitational potential. The theory is freeof gravitational singularities. It is capable of reproducing the Schwarzschild metric and is therefore consistent with tests of general relativity. It allows a first-principlescalculation of the numerical value of the cosmological constant and the size of theuniverse using only the speed of light and the average density of ordinary matter inthe universe which agrees closely with the observed values. Finally, it numericallypredicts the approximate critical acceleration in modified Newtonian dynamics theory (MOND), providing an alternative explanation for dark matter. This shows that the theory may have value in explaining cosmological observations which are currently attributed to dark matter and dark energy.
Category: Relativity and Cosmology

Investigating Prime Gaps Through Zeta Behaviour [:] a Reexamination of the Riemann Hypothesis

Authors: Samuel Bonaya Buya
Comments: 5 Pages. Original article.

In this research prime gaps will be investigated through their zeta behaviour. A formulation will be presented that links prime gaps to singularities in ��(��). This is achieved byidentifying a zeta function for Goldbach partition and extending it to the Euler product. A zeta function is formulated that encodes information about Goldbach partitions. We beginthe paper by examining the logarithmic form of a complex variable and it’s decompostion to real and imaginary parts.
Category: Number Theory

Global Existence and Smoothness of Solutions to the Navier Stokes Equations: An Energy Pertubation Approach

Authors: Felipe G. G. de Carvalho
Comments: 8 Pages.

In this article, we investigate the existence and smoothness of solutions to the incom-pressible Navier-Stokes equations using the energy perturbation method. By assuming thatexternal forces are either null or sufficiently small and that the initial conditions are smo-othly compact, we demonstrate, through an energy inequality, that the energy associatedwith perturbations decays exponentially over time. This energy dissipation implies thatsmall perturbations vanish, ensuring the global stability and regularity of solutions. Additi-onally, we numerically validate our results using physics-informed neural networks (PINNs),showing that the numerical solution converges to the analytical one. These findings pro-vide strong evidence toward a potential proof of the global existence and smoothness ofNavier-Stokes solutions, contributing to the discussion of millennium prize problems.
Category: Classical Physics

Review of Mechanistic Quantum Field Theory

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

Review of research into mechanisms for quantum field theory. The mechanistic approach invites rigorous experimental scrutiny by making predictions.
Category: High Energy Particle Physics

Compression as Dimensional Projection: A Theoretical Framework Inspired by Golomb and Shannon

Authors: Vasant Jayasankar
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Modern compression theory is based on Shannon’s foundational insight that information is governed by entropy. Golomb coding, devised in the 1960’s, is a remarkably efficient solution for encoding geometrically distributed integers, and remains in widespread use because of its simplicity and effectiveness. In this paper, I revisit Golomb coding not merely as a mathematical transformation, but as a process of dimensional projection.I propose a generalized compression framework derived from the principles of dimensional projection. The process takes structured data and temporarily lifts it into higher-dimensional space to expose latent informational geometry, then systematically re-flattens it into a minimal entropy representation. Specifically, I reinterpret Golomb coding as a 1D-to-2D projection followed by structured reduction, and generalize this concept into a proposed 4D projection-based model applicable across multiple data types—text, DNA, images, audio, video, and more.The proposed framework provides a unifying geometric perspective on compression, revealing new axes of redundancy not captured by traditional frequency-based methods. This theoretical work offers a foundation for future research in entropy minimization, structural compression, and the dimensional nature of information itself.
Category: Data Structures and Algorithms

A Fundamental Contradiction Proving the Non-Existence of Odd Perfect Numbers

Authors: Madhukar Jadhav
Comments: 2 Pages.

A perfect number is a positive integer N that equals the sum of its proper divisors. While even perfect numbers have been classified, theexistence of an odd perfect number remains an unsolved problem. In this paper, we establish a fundamental contradiction in the divisor structure of any hypothetical odd perfect number. Specifically, we demonstrate that the largest proper divisor must be half of N, but for an odd N, this results in a non-integer, violating the necessary conditions for perfection. Consequently, we conclude that no odd perfect number can exist.
Category: Number Theory

Divergences Between the Mathematical and Physical Interpretations of the Tensor on Einstein's Attempt to Simplify the Gravitational Field Equation (1915)

Authors: Valery Borisovich Morozov, Ricardo Gobato
Comments: 11 Pages.

In 1915, Einstein, simultaneously with the gravitational field equation, obtained a simplifiedversion of this equation. Schwarzschild found an exact solution to this version. The articlediscusses the features of the simplified version of the Einstein equation and its asymptoticproperties.
Category: Relativity and Cosmology

Four Cosmologies Synthesis and Genetic Entropy

Authors: F. M. Sanchez
Comments: 2 Pages.

The aperture of the Sanchez 1998 sealed fold was postponed untill the "impossible galaxies" observation, predicted 27 years ago. The 3-minutes (hbar,G,m^3) formula replacing c by the product of electron-proton-neutron masses gives half of 13.8 billion light-years, unifying the two main cosmologies and Eddington's statistical one. Integrating Wheeler's single-electron cosmology, the triplet (hbar, G, m_e) is associated with an ideal human couple with larger characteristics. This replaces Darwinian evolution by Sanford's genetic entropy and Gyertych's devolution. We are numerically central in the cosmos, but in decline. The 2001 sealed fold rehabilitates the tachyonic bosonic string theory and the 2002 one connects the nucleotide atomic masses by C+G = A+T+1, playing a central role in the cosmology unification.
Category: Quantum Gravity and String Theory

Three-Dimensional View About the Riemann Hypothesis

Authors: Kohji Suzuki
Comments: 7 Pages.

We try interpreting the Riemann hypothesis as something three-dimensional.
Category: Number Theory

The (E) Question in a Three-Dimensional Space - Analysing a Subset of Linear Systems With The Intrinsic Method

Authors: T. L. A. Periat
Comments: 32 Pages.

This paper is part of a series of explorations exposing methods for dividing distorted tensor products by number cubes. Here, the discussion focuses on three-dimensional spaces and anti-symmetric cubes on their low indices, i.e. actually on distorted cross products. The method only delivers the main parts of the divisions. The other documents in the collection complete this investigation. This is a translation made by me of a part of the French version.
Category: Mathematical Physics

Quantum Entanglement-Like Behaviour in a Dowsing Experiment

Authors: Neil D Duffy
Comments: 9 Pages.

Quantum mechanical entanglement-like behaviour has been observed during the investigation of the dowsing effect. Interference fringe patterns, a hallmark of wave behaviour, have been observed when parallel copper tubes are placed on the ground. The fringes can be mapped using right angled dowsing rods. When the tubes are touched together and then replaced in their original position the fringe pattern changes in a manner that suggests that the tubes are "entangled". This change persists until "decoherence" occurs due to environmental interactions or deliberate physical actions.Polarisers that use a class of materials that have no effect on electromagnetic waves but act as polarisers for dowsing radiation are used to investigate radiation passing between the tubes. The polarisers are used both to screen from interference and to facilitate measurement of the characteristics of the radiation.Blind testing has suggested with a 6 sigma confidence level that dowsing rods can be used to detect changes in interference fringe patterns created by the copper tubes both when they are "entangled" with one another and when they are decoherent. It has also demonstrated at 5 sigma level that the radiation has a wavelength of 21.1 cm, and is circularly polarized.The use of non-conventional material for the polarisers indicates that the radiation is not electromagnetic in nature and suggests a testable proposition that the radiation that causes the dowsing entanglement effect is one and the same as that which creates entanglement in quantum physics.
Category: Quantum Physics

The Proof and Application of Fermat's Last Theorem

Authors: Yibing Xiong
Comments: 13 Pages.

Three variables X,Y,Z are expressed in terms of undetermined coefficients —— variables, binary, and then put into Fermat's last theorem equations. In the equations composed of undetermined coefficients, the number of independent equations is no less than the number of variables, and the solution is no less than zero, so Fermat's last theorem is established.
Category: Number Theory

Where is the Definition of Consciousness?

Authors: Luke Kenneth Casson Leighton
Comments: 16 Pages.

The topic of Consciousness is astoundingly unique in that as a branch of Science there exists no clear definition of what Consciousness actually is. Tonini et al developed Integrated Information Theory and successfully synthesise the properties of consciousness to derive fascinating and ground-breaking insights, however stop short of deriving an actual working Definition. Beginning primarily from the Upanishads and Advaita Vedanta as the world's leading comprehensive and compact study on Consciousness, a first cut at a Definition of Consciousness is proposed and then refined with examples. Implications from the Definition: If "self" qualia are defined as the combined properties of thoughts, beliefs, memories, ideas, habis working paradigms etc. then the `protection' mechanism of the same is the self-referral loop, which bears a remarkable resemblance to an Error Checksum (ECC). Startling implications then arise covering "Artificial" Intelligence, Computer Science, Epigenetics, Control Theory in Engineering, Vector Processing and Distributed Computing.
Category: Mind Science

Construction of M-theory

Authors: Shenbo Wu
Comments: 197 Pages.

The main process to solve the problem of quantum and gravity is Mordern AG (global GLC) M→ Derived AG (local GLC) O-localizing Grothendleck's dream comes in Grothendeck's quantization of gravity Complete Einstein's dream UFT Analytic stack (analytic AG) The Langlands duality from the M-theory is a part of U-duality,the M- theory and its dynamics give us the global geometric Langlands corre- spondence [15] simplified by combining math and physics. D≤11-mod (Bung) ← → QCoh (LocSys)11 where Ğ is the Langlands dual group acting on the F-dual part of M-brane. Generally,construction of the M-theory is based on the modern alge- braic geometry with category theory.Studying the dynamics of the M- theory is based on that with higher category theory (representation of underlying space). The former gives an unification of superstring theories (Superstring theories type) → retract (Stype) Є Mpre Retracted from fibered category of superstring theories to stack of Lie groupoids. And the latter gives us a well defined stackified flow which is retracted from a non-solvable theory. Combing them, we successfully estab- lish an experiment-free theory with left evolution where M-flow~-flow, O-sense Fis the 2-nonexistence. In the end, derived algebraic geometry gives us further support to summarize all things and we find the M'-theory is the theory of everything originally proposed by Albert Einstein. Preview. A pre M-theory is a geometric stack written by Mpre = (ETSchSupGen (M), P(T), P, II) The M-theory M is a generalized super algebraic geometric stack Au= P(U)1: M→ Mprep V Mre cons. cons. We also put things into derived algebraic geometric n-stack and analytic derived stack to achieve our final goal completing TOE which is a category of no definition objects O-Sense~ Def 'UFT.
Category: Quantum Gravity and String Theory

Minimal Causal-Informational Model of Emergent Space-Time (MCIMES)

Authors: Sergei Kondrashov
Comments: 27 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Quantum gravity continues to pose significant challenges in theoretical physics, including the reconciliation of general relativity with quantum mechanics, the nature of time, and the small observed value of the cosmological constant. This paper proposes the Minimal Causal-Informational Model of Emergent Space-Time (MCIMES), a new framework that explores quantum information as a possible foundation for physical reality, suggesting that space-time and gravity may emerge from it. Using an abstract interaction graph and drawing on quantum information theory, MCIMES offers a perspective in which space-time arises as an emergent phenomenon, providing potential explanations for its three-dimensionality and the arrow of time through entropic processes. The model suggests an approach to the cosmological constant issue, producing a value aligned with observations without requiring fine-tuning, and puts forward testable predictions, such as a dark energy equation of state parameter ( w = -0.97 pm 0.01 ) and specific quantum corrections to black hole entropy. While recognizing its current limitations, MCIMES offers an information-based, background-independent viewpoint that seeks to address key questions in quantum gravity and encourages further exploration and testing.
Category: Quantum Gravity and String Theory

Analysis of Blast Attenuation in Urban Environments

Authors: Nigel B. Cook
Comments: 9 Pages.

This paper provides a comprehensive methodology for calculating blast wave attenuation in urban environments, focusing on energy conservation, building interactions, and predictions for different yields. It builds on historical data from Hiroshima and Nagasaki, extending to modern urban settings, and includes detailed calculations for 20 kt and 1 megaton yields, comparing open terrain and urban attenuation. The study ensures energy conservation through building absorption mechanisms and highlights the impact of higher yields on blast effects.
Category: Nuclear and Atomic Physics

Observational Relativity: A New Theory with New Discoveries and New Insights

Authors: Xiaogang Ruan
Comments: 27 Pages.

Physics has had a new theory: the theory of Observational Relativity (OR). The theory of OR has discovered that all theories or spacetime models in human being’s physics must be branded with observation. The theory of OR has uncovered the root and essence of the relativistic effects of matter motion and matter interactions presented in spacetime: all relativistic effects are observational effects and apparent phenomena -- the speed of light is not really invariant; spacetime is not really curved. Newton’s classical mechanics is a theory of idealized observation with the idealized observation agent OA, presenting us with the true reflection of the objective physical world; Einstein’s relativity theory is a theory of optical observation with the optical observation agent OA(c), presenting us with only an optical image of the objective physics world, not exactly the physical reality. The theory of OR is a theory of the general observation agent OA() (0<<; ), which has genralized and unified Newton’s classical mechanics and Einstein’s relativity theory: as , the theory of OR strictly reduces to Newton’s classical mechanics; as c, the theory of OR strictly reduces to Einstein’s relativity theory. In the theory of OR, Newton’s classical mechanics and Einstein’s relativity theory are just two special cases, i.e., what Hawking called ‘partial theories’. Now, the theory of OR has become what Hawking called a ‘complete theory’. The theory of OR would inject fresh blood and new ideas into physics. Mankind must re-examine his physics and reshape his view of nature.
Category: Relativity and Cosmology

Wheeler's Self-Referential World

Authors: Alexandr Kaminsky
Comments: 8 Pages.

It is shown that the self-referential model of the world (in such a model the world is an observer of itself) generates a quantum-like description of reality.
Category: Quantum Gravity and String Theory

Reconsidering Gravity as Dynamic Phenomenon

Authors: Martin Mayer
Comments: 20 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The purpose of this paper is to explore gravity as a dynamic phenomenon where the gravitational effects described by the Schwarzschild metric are transferred to changes in the quantities of time, length, velocity, acceleration, mass, energy and force. These changes are assumed to be physically real and not just a superficial effect of the used coordinate system. Subsequently, physics calculations can be done in classical orthogonal space using these malleable quantities even beyond the Newtonian regime, as gets demonstrated by applying them to the typical tests of general relativity. Moreover, the dynamic gravity notion gets corroborated by uncovering concealed connections between Newtonian gravity and the theory of general relativity, in particular gravitational potential energy is identified as an effect of changing mass energy. Thereafter a quantum gravity approach is put forward, as originally proposed by John A. Macken, which provides clues to how gravity can be expressed on the quantum level using a classical wave based approach. In that context the electrostatic force is also examined, since it exhibits an unexpected mathematical similarity to gravity. Finally, an inertial mass adjustment gets introduced that is caused by a cavity effect of excluded gravitational waves, which would break the equivalence principle if it turns out to be physically real.
Category: Quantum Gravity and String Theory

Acceleration-Acceleration, Acceleration-Velocity, and Four More Modes of Application of Newton's Third Law [:] Reactionless Motion

Authors: Bojidar Djordjev
Comments: 16 Pages.

The article analyzes alternative resources in Classical Mechanics for creating disproportion in the inertial effects of equal and opposite forces and torques. Alternative applications of forces are discussed. Symmetric asymmetries in the distribution of the quantities of motion and energies between interacting bodies are analyzed in the Acceleration-Acceleration and Acceleration-Velocity modes of application of Newton's Third Law. Competencies of the alternatives. The use of a mass resisting velocity and the related problems are justified. A realistic form of Reactionless Motion. The dark side of story.
Category: Classical Physics

Proof that the Legendre Conjecture is Unprovable

Authors: T. Nakashima
Comments: 2 Pages. (Note by viXra Admin: Please refrain from immediate and frequent replacements))

In this paper, we attempt to prove the unprovability of the Legendre Conjecture, a known open problem. The method is similar to the author's "Guessing that the Riemann Hypothesis is unprovable using nonstandard analysis."
Category: Number Theory

Inverse N-body Problem

Authors: Mykola Kosinov
Comments: 5 Pages.

The solution of the two-body gravitational problem led to the discovery of Newton's law of gravitation F = GMm/r^2. The solution of the inverse two-body problem (Bertrand problem) also leads to Newton's law of gravitation. However, the solution of the direct and inverse two-body problems does not provide a complete description of gravity. The law of gravitation for N bodies is missing. The fundamental law of gravitation for N bodies has not been discovered. The obstacle was the unsolved gravitational problem of N bodies. The inverse problem of N-bodies has not been studied in physics. Here we present a new method for finding the law of gravitational force for N bodies. The method is based on reducing the gravitational problem of N bodies to the two-body problem, where the central body is a system of N bodies. The problem of an N-body system is the inverse problem of the N-body problem. This is the problem of finding the law of gravitational force from the known integral characteristics of the N-body system. The solution of the inverse problem of N bodies gives a new law of gravitation F = (mc^2)√Ʌ. Instead of the gravitational constant G, the new law of gravity includes the cosmological constant Ʌ. The new law of gravity F = (mc^2)√Ʌ allows us to overcome the limitations inherent in Newton's law of gravity F = GMm/r^2 and leads to a new law of universal gravitation.
Category: Classical Physics

Verlinde in the Elevator A Thermodynamic Review

Authors: A. Schubert
Comments: 5 Pages. (Note by viXra Admin: An abstract in the article is required and please submit article written with AI assistance to ai.viXra.org)

Einstein's elevator remains one of the most iconic thought experiments in physics, illustrating the equivalence principle: an observer inside a sealed elevator cannot distinguish whether the force they experience stems from gravitational attraction or uniform acceleration. This implies a profound connection between inertia and gravitation, traditionally interpreted through the geometry of spacetime in general relativity. However, inspired by Verlinde's entropic gravity proposal (Verlinde et al. 2011), we revisit this connection from a purely classical thermodynamic perspective, reimagining the elevator not just as a geometric construct but as a thermodynamic laboratory.Verlinde suggested that gravity emerges as an entropic force, driven by the statistical tendency of microscopic degrees of freedom to maximize entropy in the presence of mass (Verlinde et al. 2011). While his framework relies on holographic principles and information theory, we propose a simpler, classical alternative: gravity as a thermodynamic response of a system in free fall, modeled as a compact thermometer within the elevator. By focusing on the interplay of energy conservation, dissipative effects, and entropy gradients, we aim to reproduce Newtonian gravity without invoking quantum mechanics or speculative microphysics.Our approach begins with the elevator's equivalence principle as a thermodynamic equivalence. We explore how a classical system, subjected to gravitational acceleration or its inertial counterpart, exhibits internal heating—interpreted as a consequence of energy redistribution akin to the gravitational blueshift of classical waves. This heating drives an entropy gradient, yielding an effective force consistent with Newton's inverse-square law. Unlike previous critiques of entropic gravity. (Kobakhidze et al. 2011,Visser et al. 2011), which highlight quantum inconsistencies or energy conservation issues, our model remains firmly rooted in macroscopic thermodynamics, offering an intuitive and pedagogically valuable reinterpretation of gravitational attraction as a classical emergent phenomenon.
Category: Thermodynamics and Energy

Exact Relativistic Corrections to the Quantization of a Classical Spinning Particle with Constant Electric and Magnetic Fields

Authors: John French
Comments: 7 Pages.

This paper is an extension of a paper by the author where a quantization of classical spinningparticle equations is carried out using the Euler angles of the particle. Relativistic corrections are found and compared to the Foldy-Wouthuysen transformation of the Dirac equation. Weonly consider constant linear electric and magnetic fields, and find agreement to all orders of 1/c^2.
Category: Quantum Physics

Quantum Gravity via U(1) Dark Energy: Density Variation and Graviton Redshift in an Expanding Universe

Authors: Nigel Cook
Comments: 2 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper advances a quantum gravity (QG) model where U(1) spin-1 gravitons mediate repulsive dark energy and attractive gravity, replacing general relativity’s metric expansion with a dark energy-driven mechanism. We derive a corrected gravitational constant G = (3/4)H2/(ρπe^3), incorporating density variations and graviton redshift via the continuity equation ∂ρ/∂t + ∇ · (ρv) = 0. The effective density is e^3 ≈ 20 times the local density, with a net factor of 10 relative to classical estimates adjusted by an early QG factor of 2. This framework quantizes mass and predicts gravitational effects in an expanding universe, validated using updated physical constants.
Category: Quantum Gravity and String Theory

Quark-Lepton Unification via Vacuum Polarization

Authors: Nigel Cook
Comments: 11 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a quark-lepton unification model where quarks and leptons share the same fundamental charge (−e), and the fractional charges of quarks (e.g., −1/3e for strange quarks) arise from enhanced vacuum polarization shielding. Using Laplace transforms, we derive the running coupling α(Q2), incorporating contributions from all virtual particles (electrons, muons, tauons, quarks). We integrate the electromagnetic field energy over radial shells in the vacuum polarization region (2.16 fm to 33 fm), quantify the production rate of strong and weak field quanta, and predict particle masses using a shell-based model. Applying this to the omega minus baryon (Ω−), we show that its observed charge of −1e results from three −1e charges shielded by a factor of 3. We further analyze how the running of the weak and strong couplings relates to the shielded electromagnetic energy, estimating the energy densities of all three fields to demonstrate energy redistribution.
Category: Quantum Gravity and String Theory

Equivalence Between Direct Mass and NFW-total Mass Formula in MW and M31 Galaxies

Authors: Manuel Abarca Hernandez
Comments: 19 Pages.

In the framework of Dark Matter by Quantum Gravitation (DMbQG) theory, the Direct mass gives the total mass into the halo region, growing with the square root of radius. This formula has only one parameter specific for each galaxy.The NFW profile is a universal method that gives the DM mass function depending on radius at the disk and galactic halos. This function is defined by two parameters. The DMbQG claims that DM is generated by the own gravitational field and consequently the DM halo is unbounded. In the paper [1] Abarca,M. was proved that it is the Dark energy the mechanism able to counterbalance the DM.As the direct mass is linked to the total mass (baryonic plus DM), in the paper has been developed a method to integrate the baryonic matter into the NFW DM function in order to be able to compare both functions connected to the total mass. Thanks this method has been possible to define the R200-TOTAL and the M200-TOTAL both referred to a sphere whose total mass has a mean density equal to 200 times the critic density of the Universe.The main achievement of this paper is to demonstrate that the Direct mass function and the NFW-total mass function are equivalents into the halo region of MW and the M31. The equivalence of the two formulas for masses is based on four tests, all of them tested successfully. Test I. Comparison the R(200-TOTAL) and the M(200-TOTAL) calculated by the two different formulas, for MW and M31. Test II. Using the M(200-TOTAL), value that is given by the NFW method, is calculated the parameter a^2 which is compared with the one got in the framework of DMbQG theory. Test III. Is similar to test III but using the R200-TOTAL and the M200-TOTAL and the result is successful as well.Test IV. The direct mass function and the NFW-total mass function are compared into the halo region up to R(200-TOTAL). Although the thesis of this paper is for any galaxies, the calculus has been made with MW and M31, because they are the best well studied galaxies and his data have the maximum of accuracy. The prove reach in this paper is valuable because the Direct mass which comes from DMbQG theory gives similar results to the NFW function mass, which is a trustable profile for DM, tested in thousand of galaxies,.
Category: Astrophysics

[attempted] Proof that π and √2 Are Rational

Authors: Armando Evangelista Jr
Comments: 1 Page.

In this short paper, I've used Wallis' product formula to prove that π is rational, while the product expansion of the cosine function was used to prove that √2 is rational.
Category: Algebra

Relativity of Mass

Authors: Asutosh Kumar
Comments: 9 Pages. CC BY-NC-SA 4.0

We present a simple approach for deriving velocity-dependent masses using the principle of relativity.Our analysis reveals that the transformations associated with Galilean, Lorentz, and otherspace-time frameworks between two inertial reference frames are fundamentally equivalent in the context of the relativity of mass. Consequently, the notion of velocity-dependent mass is not the exclusive characteristic of Special Relativity (Lorentz transformation). Among the notable conclusions drawn from our formalism are: mass can both increase and decrease with velocity, a particle can never be completely at rest, and superluminal signaling is in principle feasible. Furthermore, we discuss on the nature of mass and argue that a photon is not massless.
Category: Relativity and Cosmology

Wheeler's Self-Referential World

Authors: Alex Kaminsky
Comments: 8 Pages. In Russian

This paper explores the hypothesis that quantum mechanics (QM) is a description of reality from the perspective of an internal observer—an observer who is simultaneously the subject and object of observation. The idea traces back to the work of J.A. Wheeler [1,2], who argued that the Universe cannot be fully explained from an external standpoint and must be integrated into the process of observation. Without claiming universality, we construct a simple model that demonstrates the emergence of QM within this self-referential framework. The conclusion is that quantum reality is an emergent phenomenon in the worldview of an internal observer.
Category: Quantum Gravity and String Theory

Why Can't the Cooper Pairing Mechanism Explain Superconductivity?

Authors: Xiuqing Huang
Comments: 5 Pages.

High-temperature superconductivity has puzzled researchers for nearly four decades despite intense study. We recently proposed a unified superconducting theory using frozen localized electrons, reframing electron transport in lattices as electromagnetic field energy's lossless transmission via capacitive channels. This theory explains and predicts key results in various superconductors like copper-based, iron-based, nickel-based, and kagome ones.When our manuscript was submitted to Scientific Reports, Reviewer 1 saw its innovation and suggested revisions. Reviewer 2, while recognizing its novelty, criticized the theory as too simple and against the established paradigm, recommending rejection due to reliability concerns.We counter that Cooper's hypothesis in the BCS theory violates three scientific principles despite its Nobel status. Also, the peer review here seems to show a conservative bias, favoring conventional research over innovative work even with flawed existing theories.
Category: Condensed Matter

Proposed Proofs For The Riemann Hypothesis, The Collatz Conjecture, and The Kayeka Conjecture: The RTA Framework for Mathematics

Authors: Vasant Jayasankar
Comments: 58 Pages.

This paper introduces the RTA Framework for Mathematics, a dimensional projection model that proposes to redefine mathematics as the structured emergence of symbolic, geometric, and harmonic patterns constrained by information-theoretic principles. Rather than treating mathematics as a purely axiomatic or abstract system, RTA posits that all mathematical structures arise from projection constraints on higher-dimensional information spaces, governed by principles of entropy minimization, harmonic balance, and recursive self-similarity. This paper begins with the simplest symbolic expressions in one dimension, showing how numerical and algebraic structures emerge from fundamental constraints. These expressions are then projected into higher-dimensional geometric spaces—revealing the role of oscillations, harmonics, and resonance in shaping more complex mathematical behavior. From this foundation, I examine three historically significant problems—Riemann, Collatz, and Kayeka—and propose that each is a manifestation of a distinct dimensional geometry: harmonic resonance, entropic spiral collapse, and recursive symbolic structuring, respectively. Together, these results suggest that mathematics itself is not a human invention, but the natural consequence of a structured universe operating under a universal projection law. This framework reinterprets mathematical complexity as the layered expression of dimensional geometry, bounded by constraints imposed by entropy and symmetry. The RTA framework potentially offers not only solutions to long-standing mathematical puzzles but a new foundational theory for understanding what mathematics is, where it comes from, and how it governs all emergent structure across domains.
Category: Number Theory

Langlands Watch: A Hierarchical Framework for Arithmetic and Geometry Beyond Elliptic Curves

Authors: Song Fei
Comments: 42 Pages.

This paper introduces the Langlands Watch (LW) framework, a novel approach that maps automorphisms phiintext{Aut}(X) of a variety X/mathbb{Q} to a dynamic time representation—comprising a second hand, minute hand, and hour hand—to unify arithmetic and geometric insights across number theory. Initially designed for elliptic curves E/mathbb{Q} , LW enhances the predictive power of the Birch-Swinnerton-Dyer (BSD) conjecture by precisely determining the order of vanishing text{ord}_{s=1}L(E,s)=r and bounding the Tate-Shafarevich group text{III}(E/mathbb{Q}) , validated across low-rank (ensuremath{r=0,1}) , high-rank (ensuremath{r=2}) , and non-trivial text{III} scenarios. Extending beyond elliptic curves, LW adapts to higher-dimensional Abelian varieties, demonstrating its versatility in predicting ranks and L-function behavior for complex structures. By integrating local traces, analytic forms, and global cohomology, LW refines BSD’s arithmetic predictions while forging a robust bridge to the Geometric Langlands Program (GLP) via moduli stacks like ensuremath{text{Bun}_{text{GL}_{2}}}. Theoretical advancements include symmetry-driven constraints on L-function singularities, offering a fresh perspective on Langlands Program challenges. Concrete examples—ranging from a rank 2 elliptic curve to a CM curve with non-trivial ensuremath{text{III}}, and a rank 2 Abelian surface—underscore LW’s practical efficacy. We conclude by affirming LW’s independence as a tool, its necessity within the Langlands Program, and its potential to generalize across varieties, paving the way for future explorations into Iwasawa theory, Shimura varieties, and beyond.
Category: Number Theory

A Dual-Holographic Cosmology: A Conceptual Bridge Between Entropic Gravity and Quantum Geometry

Authors: A. Schubert
Comments: 22 Pages.

We propose a conceptual dual-holographic cosmological model in which the observable universe emerges as a thermodynamic projection across a scalar field, defined on a dynamically stabilized event horizon (EH) that separates an AdS-like quantum interior from a dS-like geometric exterior. This EH field mediates the transition between gravitational and quantum domains and forms a bidirectional holographic interface that connects an AdS/CFT correspondence in the interior (Maldacena et al. {1997}; Witten et al. {1998}) with a conjectured dS/CFT structure on the cosmological side (Strominger et al. {2001}).The model is based on the concept of Grey Holes (GHs)—non-singular gravitational configurations stabilized by thermodynamic consistency and negative heat capacity—where the EH acts as a critical interface with vanishing entropy density and heat flux (Bekenstein et al. {1973}, Hawking et al. {1975}). This interface induces entropic gradients that define the arrow of time and generate spacetime geometry. Inward-directed entropy flows within the AdS region reproduce attractive gravity in line with entropic gravity models (Verlinde et al. {2011}, Jacobson et al. {1995}, Admanabhan et al. {2010}), while outward-directed entropy flow in the dS region gives rise to an effective cosmological repulsion without requiring a fundamental dark energy component.Key cosmological observables—such as the Hubble parameter, the CMB temperature, and the effective energy density—emerge from the dynamics of the EH field, yielding predictions consistent with current observations and potentially testable deviations from the CDM model.Although formulated macroscopically, this approach conceptually resonates with entropy-based quantum gravity (EQG) models (Bianconi et al. {2019, 2021, 2023}), which describe emergent spacetime via microscopic network geometries and information-theoretic principles. Both approaches suggest that gravity and temporality may arise from entropic flows across structured boundaries—be they quantum networks or cosmological horizons.By framing cosmology as a dual-holographic, thermodynamically driven interface theory, this model offers a speculative but coherent alternative to inflation and dark energy, grounded in the synergy between geometric dualities and entropic emergence.
Category: Quantum Physics

Formulas of the Fine-Structure Constant and the Speed of Light in Atomic Units Based on 22/7 and 355/113

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 6 Pages.

In our previous papers, we gave the formulas of the fine-structure constant and the speed of light in atomic units based on 2π-e formula and the natural end of the elements determined by us, i.e., the 112th element Cn*. In this paper, based on these formulas and the two approximate rates of π which are 77/2 and 335/113, we deduce new formulas of the fine-structure constant and the speed of light in atomic units. This is also to answer physicist Feynman’s question whether the fine-structure constant is related to π. Except our previous answers and explanations, our new additional answer is that it is also amazingly related to the approximate rates of 77/2 and 335/113 which were deduced by Chinese ancient mathematician Chongzhi Zu (AD 429-500).
Category: Nuclear and Atomic Physics

Accelerating Expansion of the Universe Based on Archimedes’ Principle

Authors: Michael Tzoumpas
Comments: 22 Pages.

Natural phenomena are derived from dynamic space, which is structured with fundamental elements, namely dimension, electrically opposite units, and their forces. The finite dimensions of the universe and the opposition (principle of antithesis) between existence (the universe) and nonexistence (non-space) cause the spherical deformation of space. This deformation has resulted in the equality of peripheral andradial cohesive forces (universal symmetry) and a change in their cohesive pressure, leading to a universal antigravity force similar to buoyancy (Archimedes’ principle), that supports Hubble’s law. The breaking of this universal symmetry near the center of the universe leads to the creation of the primary form of the neutron as a vacuum bubble. The gravity of the particle is defined as the mutual stretching of dynamic space by the core vacuum (empty space hole) of the particle.
Category: Relativity and Cosmology

Decreasing Universe: The 'Dark Matter' Effect

Authors: Joao Carlos Holland De Barcellos
Comments: 10 Pages.

After a brief review of the Decreasing Universe (D.U.) model, we will derive a formula and the graph for the apparent velocity of stars (of a Messier_33 galaxy) as a function of their radial distance from the galactic center. This formula reproduces the same velocity curve traditionally attributed to dark matter.
Category: Astrophysics

Tennis Vision

Authors: Sanjay Sharma, Akshit Rao, Chetan Sawant, Mangesh Gangurde
Comments: 4 Pages.

Automated sports analytics using artificial intelligence (AI) and computer vision has gained significant attention in recent years. This project presents a tennis match analysis system that detects players, tracks ball movement, and extracts performance metrics using deep learning techniques. The system employs YOLO for real-time player and ball detection, along with CNNs for court keypoint extraction and perspective correction. By analyzing video frames, the system calculates shot speed, player movement speed, and shot counts, providing valuable insights into gameplay dynamics.The methodology involves video acquisition, frame extraction, preprocessing, and deep learning-based tracking. A rolling mean filter is applied to ball trajectory data to identify shot impact points and analyze rally patterns. Experimental results demonstrate the model’s effectiveness, achieving a detection accuracy of 92.3% (mAP) and reliable tracking of key game events. The extracted performance metrics offer valuable applications for coaches, analysts, and players, enhancing strategic decision-making and training efficiency.The proposed approach bridges the gap between traditional sports analysis and AI-based automation, paving the way for more advanced player performance evaluation and match strategy optimization.
Category: Artificial Intelligence

Nuclear Blast Attenuation: The 15-Megaton Castle Bravo Test in Open Terrain vs. [Modern City] with Structural-Based Attenuation

Authors: Nigel Cook
Comments: 7 Pages.

The Castle Bravo test (15-megaton, March 1, 1954, Bikini Atoll) provides a benchmark for nuclear blast effects in open terrain. This article examines how such a blast would be attenuated in [a Modern City] , using structural parameters from Northrop/DTRA (1996), blast equations adjusted with empirical data from Glasstone and Dolan (1977), and structural response equations. Attenuation mechanisms include diffraction, kinetic energy in oscillating buildings, plastic deformation, and flying debris. A structural-based attenuation model, tailored to New York’s reinforced concrete and steel-frame buildings, exp(−R/10), is derived and applied, with energy per unit area tables, a comparison of peak overpressure and dynamic pressure in open terrain versus [a Modern City] , and tables comparing peak overpressure and dynamic pressure before and after urban attenuation.
Category: Nuclear and Atomic Physics

An Elementary Demonstration of the Goldbach'strong Conjecture by the Analysis of Congruence Rules in [0 — n] and [n — 2n] Intervals

Authors: Bahbouhi Bouchaib
Comments: 24 Pages. Original article

This paper presents detailed analyses of congruences modulo in the case of even sum S = A + B. These analyses were performed in order to design a way to demonstrate GSC in an elementary logical way. Even if we succeed with the rules of congruence in putting an even number in the sum of two prime numbers, this does not constitute a definitive mathematical proof, which is why the GSC remains unprovable. This is why we must resort to a logical reasoning which consists of eliminating false propositions and keeping only one which is true. The one which is true must lead us to the truth of the GSC and thus we succeed in demonstrating it mathematically. This paper provides an elementary mathematical proof by deciding between four propositions such that the GSC is the only true one (logical reasoning by an indirect proof). This conclusion is reached by taking into account established facts in mathematics about prime numbers in [0 - n] and [n - 2n] intervals.
Category: Number Theory

A New Deterministic Method for the Spin Glass Ground State Problem

Authors: Akira Saito
Comments: 13 Pages.

In this study, we propose a new deterministic solution for the spin glass ground state problem. Our method formulates the Ising spin glass problem as a system of nonlinear equations and determines the ground state by solving those equations. Compared to simulated annealing (SA), the proposed method aims to reduce computational time while achieving energy accuracy that is equal to or better than SA.Through numerical experiments using the Sherrington-Kirkpatrick (SK) model, we confirmed that the proposed method achieves energy values comparable to SA with a reduction in computation time by a factor of 1/3 to 1/15. Furthermore, scaling analysis shows that the computation time of the proposed method grows proportionally to ��1.21, demonstrating superior scalability compared to SA, which depends on ��2.05.The findings of this study suggest new possibilities for solving spin glass ground state problems and may be applied to areas such as combinatorial optimization and machine learning. Future work will focus on improving scalability, introducing methods to avoid local minima, and accelerating computations through GPU parallelization to enhance practical utility.
Category: Mathematical Physics

On a Generalization of Perfect Numbers

Authors: Joseph L. Pe
Comments: 7 Pages. This paper appeared in the (now defunct) Journal of Recreational Mathematics 31(3), 2002

The definition of perfect numbers is generalized relative to arbitrary arithmetical functions. Some functions are exhibited that generate odd perfect numbers at large scales.
Category: Number Theory

The Picture-Perfect Numbers

Authors: Joseph L. Pe
Comments: 14 Pages. This paper was published in the (now defunct) journal Mathematical Specturm, 40(1), 2008, 40(1), 2008.

This paper reports on the research efforts of a group formed in 2002 to work on a problem introduced by the author. The group studied picture-perfect numbers, which are numbers defined using reversal and the usual definition of perfect numbers, and were initially thought to be quite rare. The paper announces the discovery of a remarkable theorem by one of the group's members, Andersen's theorem, that generates a (probable) infinity of PP numbers at large scales.
Category: Number Theory

Does the Snow Queen Like Black? Nanocarbon and Biosilica-Reinforced THV-Based Anti-Icing Sponges

Authors: E. Korczeniewski, P. Bryk, E. Olewnik-Kruszkowska, P. Kowalczyk, A. Z. Wilczewska, K. H. Markiewicz, S. Boncel, S. Al-Gharabli, M. Sprynskyy, M. Swidziński, D. J. Smolinski, K. Fujisawa, T. Hayashi, P. Plociennik, J. Kujawa, A. P. Terzyk
Comments: 45 Pages.

New superhydrophobic, anti-icing tetrafluorethylene-hexafluorpropylene-vinylidenfluoride terpolymer (THV)-based materials: nonporous solids as well as porous sponges were created and deeply characterized using thermal analysis, spectroscopy, resistivity measurements, cyclic compression tests, and confocal microscopy. Single Walled Carbon Nanohorns (SWCNHs), biosilica (BS) as well as carbonized biosilica (CB) were applied as fillers. The "combined" origin of superhydrophobicity is explained based on experimental water contact angles (WCA) and molecular dynamics (MD) as well as Hansen Solubility Parameters (HSP) analysis. For all materials thermal resistance is improved after the addition of fillers, but among the studied samples only for the sample containing SWCNHs the application of electrothermal/Joule heating to reinforce anti-icing properties is possible. We propose a new forcefield for MD simulation of THV wetting. Moreover, MD results revealed that water freezing at the "flat" THV surface was moderately inhibited with respect to the bulk freezing and considerably inhibited with respect to the graphene surface. Introduction of SWCNHs to THV causes not only remarkable improvement of mechanical properties but also the improvement of anti-icing properties, especially to the stage of recalescence. The comparison of results for porous and nonporous materials led to new correlations describing freezing on the cold plate process, being a starting point for future studies on a new model describing the freezing mechanism. The most important conclusion of the complex study (around 100 samples altogether) is that the creation of mechanically resistant THV-SWCNHs-containing sponges is the most promising strategy in modern anti-icing science leading not only to enhancement of the compression Young’s modulus and the time to recalescence, but also to the drop of freezing temperature.
Category: Chemistry

Observer-Dependent Reality in a Holographic Universe: From Definite States to Divergent Perceptions

Authors: Bhushan Poojary
Comments: 7 Pages.

This paper builds upon the "Many Unreal World Interpretation" to explore the relationship between definite quantum states and observer-dependent perceptions. We argue that each observer exists within a dedicated spacetime fabric characterized by a unique holographic address, leading to differing but locally consistent perceptions of quantum events. Through the concept of shadow particles and address reassignment, we present a mechanism that naturally explains the phenomena of wave function collapse, entanglement, and quantum paradoxes without invoking retrocausality or infinite branching universes. This model bridges the certainty of individual experience with the multiplicity of coexisting perceptual realities, offering a geometric-holographic mechanism that complements relational quantum mechanics and QBism
Category: Quantum Physics

Collatz Conjecture: The Race To One

Authors: Jochen Kiemes
Comments: 17 Pages.

This paper presents an approach that reinterprets the Collatz sequence by transforming it into a new sequence, highlighting the dynamic relationship between the trailing and leading bits of its elements. This mapping enables the study of a "bit-race," whose well-defined statistical properties rigorously guarantee the convergence of all Collatz sequences to 1.
Category: Number Theory

Church's Thesis Meets Quantum Mechanics

Authors: Warren D. Smith
Comments: 41 Pages.

Feb.1999 paper by me proving Church's thesis in "garden variety quantum mechanics," i.e proving the algorithmic simulability, to arbitrary accuracy, of N-body Schrodinger equations with suitable pair potentials. Now uploaded to vixra for archival purposes.
Category: Quantum Physics

Church's Thesis Meets the N-body Problem

Authors: Warren D. Smith
Comments: 23 Pages. Sep 1993 paper by me later published in Applied Mathematics & Computation 178,1 (July 2006) 154-183; now uploaded to vixra for archival purposes.

"Church’s thesis" is at the foundation of computer science. We point out that with any particular set of physical laws, Church’s thesis need not merely be postulated, in fact it may be decidable. Trying to do so is valuable. In Newton’s laws of physics with point masses, we outline a proof that Church’s thesis is false; phsyics is unsimulable. But with certain more realistic laws of motion, incorporating some relativistic effects, the Extended Church’s thesis is true. Along the way we prove a useful theorem: a wide class of ordinary differential equations may be integrated with "polynomial slowdown." Warning: we cannot give careful definitions and caveats in this abstract — you must read the full text — and interpreting our results is not trivial.
Category: Classical Physics

A Proposed Novel GMST-Based Proof for the Global Existence of Smoothness in 3D Navier-Stokes Equations

Authors: David Vickers
Comments: 128 Pages. (Note by viXra Admin: AI assisted content is in general not acceptable)

We present a novel approach to the global existence and smooth-ness problem for the three—dimensional incompressible Navier—Stokes equations based on a Generalized Modular Spectral Theory (GMST).Our method begins with a precise formulation of the Navier—Stokes system in suitable Sobolev and divergence—free function spaces and employs a detailed spectral decomposition of the associated Stokes operator. A key innovation is the introduction of a modular—like (Möbius) transformation applied to the operator’s eigenvalues, which "lifts" potentially dangerous low—frequency modes by enforcing an ex-ponential decay in the spectral density. This spectral transformation is integrated into a recursive fixed—point framework, wherein we establish contraction properties in high—order Sobolev spaces and derive sharp energy inequalities that preclude finite—time blowup. Furthermore,we recast the problem within an axiomatic setting analogous to those used in quantum field theory, thereby providing additional structural insight into the global regularity of solutions. The theoretical findings are supported by comprehensive numerical simulations using a Fourier—Galerkin discretization combined with an Exponential TimeDifferencing Runge—Kutta scheme. Our results offer a promising new perspective on the longstanding Millennium Problem by unifying rigorous spectral analysis, modular invariance, and fixed—point techniques in a single framework.
Category: Mathematical Physics

On the Uncomputability of Hydrodynamics

Authors: Warren D. Smith
Comments: 19 Pages.

Oct.2001 paper by me proving the Turing unsimulability of Navier-Stokes hydrodynamics (or certain other alternatives, but either way, I contend demonstrating the failure of Navier-Stokes as a useful algorithmic physical theory).Now uploaded to vixra for archival purposes.
Category: Mathematical Physics

Thermodynamic Stabilization of GravitationalCollapse at Planck-Scale Temperatures.

Authors: A. Schubert
Comments: 11 Pages. (Note by viXra Admin: AI assisted content is in general not acceptable)

The conventional view of gravitational collapse predicts the formation of a classical event horizon (EH), followed by an inevitable singularity. However, this scenario does not fully account for the thermodynamicproperties of self-gravitating systems, particularly their negative heat capacity. In this work, we investigate how thermodynamic constraints mayinfluence the late stages of collapse and propose that a non-singular, thermodynamically stabilized intermediate state may emerge at Planck-scaletemperatures.By analyzing the temperature evolution driven by gravitational compression and energy-momentum effects, we show that the system can reachthe Planck temperature well before the classical free-fall time completes.This rapid heating phase naturally leads to a transition into a stabilizedstate supported by an Anti-de Sitter (AdS)-like interior with a negativecosmological constant. While an event horizon still forms as an observerindependent boundary, the singularity is avoided due to this internal stabilization.We further examine the holographic implications of this scenario. Theevent horizon acts not as a classical one-way membrane, but as a quantumclassical interface that stores and gradually releases information. This provides a thermodynamically motivated framework for resolving the blackhole information paradox.Rather than contradicting standard black hole physics, this model extends it by incorporating thermodynamic and quantum gravitational principles. The results suggest new avenues for theoretical and observationalexploration of non-singular gravitational collapse.
Category: Relativity and Cosmology

Potential Evidence of Evolving Spacetime Dimensions from DESI

Authors: Ervin Goldfain
Comments: 8 Pages.

Recent results from the Dark Energy Spectroscopic Instrument (DESI) indicate that Dark Energy (DE) may be weakening over time. The potential evolution of DE raises a major challenge to standard cosmology, which is built on the assumption that DE represents the cosmological constant (CC) of Einstein’s equations. Here we point out that DESI’s findings support the conjecture that, a) well above the range of electroweak interactions spacetime dimensionality is continuous and runs with the observation scale, and b), the energy content of the CC comes from the cumulative contribution of energies stored in the fractal structure of Dark Matter/Cantor Dust.
Category: Relativity and Cosmology

Direction of Zero Vector [:] General Logical Contradictions on Undefined Objects -

Authors: Saburou Saitoh
Comments: 6 Pages. (Note by viXra Admin: AI assisted content is in general not acceptable)

First, as a natural extension of the paper cite{mika}, we introduce a natural definition for the direction of general zero vectors, which may not have been previously considered. Second, in connection with the direction of zero vectors, we point out some general logical contradictions related to undefined objects.
Category: General Mathematics

Recursive Sum Theory and Applications

Authors: Joseph Mbelawadzai, Mohamadou Ousmanou Abdou, Yannick Kouakep Tchaptchie
Comments: 25 Pages. In French

This article aims to present a new mathematical theory around the concept we call "recursive sum." The notion of recursive sum, in our view, is defined as the process of reducing an integer to a single digit between 0 and 9 by repeatedly adding its digits. Once defined, we explore the fundamental arithmetic properties of this operation, including its periodicity, its relationship to congruence modulo 9 and congruence modulo 3, and the determination of a prime number. In addition, we define, for an integer a between 0 and 9, another concept related to recursive sum called "inverse recursion," defined as the set of all integers whose recursive sum is equal to a. We discuss the theoretical implications of these concepts and their relationship to numerical arithmetic. Finally, we present practical examples illustrating the application of this theory in solving mathematical problems.
Category: Number Theory

Artificial Prime Numbers: A New Perspective in Number Theory

Authors: Danilka H. Urena
Comments: 3 Pages.

In number theory, one of the fundamental concepts is the prime number, a natural number greater than 1 that has no positive divisors other than 1 and itself. However, in certain mathematical contexts, this classical notion of primality can be extended or adapted to study more complex numerical structures. A particularly interesting and novel concept is that of artificial prime numbers, a variation that allows us to examine primality within specific numerical sets, beyond the conventional set of integers.
Category: Number Theory

Extended Diophantine Equation

Authors: Dinh Van Tien
Comments: 54 Pages.

This paper presents a comprehensive overview of extended Diophantine equations—high-degree equations that admit infinitely many solution sets, with each set comprising infinitely many elements. We focus on the effective application of the formula: ab = k(a+b) + c, where a, b, k, and c are integers, to transform complex equations into symmetric forms. This transformation facilitates the derivation of polynomial expansions and enables the systematic construction of solution sets with distinct and primitive elements.
Category: Number Theory

[Speculation on the] Development of a Yeast-Expressed Oral Avian Influenza Vaccine Incorporating Conserved HA and NA Antigens and a PltB Adjuvant

Authors: Hyunho Shin
Comments: 14 Pages.

Background: The ongoing spread of avian influenza (AI) in poultry has led to severe losses. In the United States, H5N1 outbreaks by early 2025 necessitated the culling of roughly 148 million laying hens, causing egg shortages and price spikesu200b. Although AI vaccines exist, their use in U.S. poultry has been minimal due to practical and economic barriers, including trade restrictions and vaccination. Objective: This study introduces a novel oral AI vaccine strategy using genetically engineered Saccharomyces cerevisiae (baker’s yeast) to deliver conserved antigenic fragments of the H5N1 hemagglutinin (HA) and neuraminidase (NA) proteins, together with a Salmonella-derived Pertussis-like toxin B subunit (PltB) as a mucosal. The goal is to stimulate protective mucosal immunity via feed-based administration, providing a cost-effective and scalable alternative to injectable vaccines. Methods: Conserved epitopes — specifically the HA2 subunit fusion peptide region (amino acids 1—78 of H5) and a portion of the NA1 head domain (amino acids 220—290) — were identified based on high cross-strain conservation and immunogenic. Genes encoding these segments were fused in-frame with the Salmonella PltB gene, separated by flexible linkers, under control of a yeast expression system. The recombinant yeast was grown, inactivated, and formulated into a dry powder to mix with poultry feed. Protein expression and folding were confirmed by Western blot and structural modeling.
Category: Physics of Biology

Resolution of the Abraham—Minkowski Controversy

Authors: Andrew T. Hamilton
Comments: 3 Pages.

The Abraham—Minkowski controversy has arisen because the Minkowski stress-energy tensor for the electromagnetic field in polarized and magnetized matter is not symmetric. This note proposes an alternative that is both symmetric and traceless.
Category: Classical Physics

About the Gravitational Wake of the Galaxy

Authors: A. V. Antipin
Comments: 14 Pages. In Russian

Wake gravitational waves are a supposed phenomenon resulting from the movement of material bodies in the Absolute Space-Time of the universe as a whole.Thus, Wake gravitational waves are a test that, if positive, will provide clear, indisputable arguments in favor of the existence of a dedicated (absolute) frame of reference. This article is devoted to the consideration of the Wake gravitational waves of the Galaxy. It follows an article that examined the Wake gravitational waves of the Sun and Moon. Estimates of the physical and geometric characteristics of the Galactic Gravitational Wake are presented here. Their calculated impact on the Solar System turned out to be insignificant.

Кильватерные гравитационные волны - это предполагаемое явление, возникающее в результате движения материальных тел в Абсолютном Пространстве-Времени — Вселенной, как целое. Т.о., Кильватерные гравитационные волны является тестом, который, в случае положительного результата, даст ясные, неоспоримые аргументы в пользу существования выделенной (абсолютной) системы отсчёта. Данная статья посвящена рассмотрению Кильватерных гравитационных волн Галактики. Она следует за статьёй, в которой рассматривались Кильватерные гравитационные волны Солнца и Луны. Здесь представлены оценки физических и геометрических характеристик Кильватерных гравитационных волн Галактики. Их расчётное воздействие на Солнечную систему оказалось незначительным.
Category: Relativity and Cosmology

Digital Information is Volatile, so We Need Its Preservation

Authors: Stefano Cariolato
Comments: 26 Pages. (Note by viXra Admin: An abstract in the article is required)

This article is destined for social sciences, humanities and science researchers, in addition to general public: it is not a technical paper and it is understandable by anyone. Today the digital revolution is almost completed and information of any kind (texts, images, video clips and TV broadcasts, music and songs, WEB pages) is now recorded and disseminated in digital format rather than with a traditional media (paper, film, magnetic tape), with a change that concern all human activities of any type, both collective and individual. Moreover, also archived printed records are increasingly transformed into digital format, both for diminishing their volume and for having faster search procedures, while the new information is only directly generated in the electronic form. Besides those other recordings are also volatile by their very nature, such as e-mails or WEB pages, but they could host information of value in the future and they equally may deserve conservation. Starting with paleolithic graffiti engraved in caves, followed by inscriptions on stones, cuneiform scripts on clay tablets, texts on vellum or silk and papyrus rolls, ending with paper, ever information has been registered in a persistent form visible and immediately readable by a human being knowing that type of writing. But while a book or a letter can immediately be read even centuries after its writing, if its physical support has withstood the time passing, digital information has a shorter life, even in the absence of deterioration of the used media. That because of the same technological development that makes quickly obsolete any recording by irreversibly mutating both the reading hardware and software. Finally digital recordings are carried out in a great variety of different formats, sometimes incompatible with each other or subject themselves to obsolescence, thus unnecessarily complicating the task of preserving the digital document content. If humanity does not find the way and the will to preserve the content of digital documents, similarly to what was done in the past with paper documents, gradually the culture generated in each period will decrease until it shall disappear. A story without a future would create a future without history.
Category: Social Science

SunQM-9s1: Updates and Corrections for the SunQM Series Articles (Part-1)

Authors: Yi Cao
Comments: 29 Pages.

This is not a research article, but a collection of updates, corrections, terminology normalizations, and questions/answers (Q/A) for my 37 of SunQM series articles that have been posted at the preprint server viXra.org (from April 2018 to February 2025). ... During my ~10 years (2014 ~ 2025) closed-door development on the {N,n} QM (through the "global energy minimization" kind of research), some of my early stage work lacks of consistency with the late stage work, and thus needs to be updated and corrected. Those important updates and corrections have mostly been presented in the late stage SunQM articles. The current paper includes the rest updates and corrections (that may be less important). The current paper (SunQM-9s1: Update u2026 (part-1)) covers the updates for SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, and 5s2. The next paper (SunQM-9s2: Update u2026 (part-2)) covers the updates for SunQM-7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s10, 6s11, 7s1, and 7s2. I also wish that the {N,n} QM (or any fragment of it) can be the useful building material for the scientific community to build the more completed QM.The previous copyright "© All rights reserved" that was written in the original 37 SunQM series articles is abolished now. Here I grant the new copyright "CC BY-NC-SA 4.0" to each individua of 37 SunQM series articles (including SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, 5s2, 7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s10, 6s11, 7s1, and 7s2), (started from today 3/24/2025).
Category: Quantum Physics

Applications of Mathematics in Supervised Learning

Authors: Alinda Rolland Mucunguzi, Laure Gouba
Comments: 22 Pages. 3 figures

In this work, we explore some applications of mathematics in the development and usage of supervised learning algorithms with a strong focus on linear regression models. Subsequently, we look at the mathematical foundations essential for supervised learning, which include linear algebra, probability theory, calculus, optimization, statistics, and geometry. For a concrete illustration of the applications of mathematics in supervised learning, this work employs simple and multiple linear regression models using data that is about pH of pure water. Through these examples, we demonstrate how mathematical techniques are applied in formulating, estimating and evaluating linear regression models. Key processes such as least squares estimation and statistical inference are highlighted to show their critical application in parameter estimation and model validation. The findings underscore the importance of mathematical rigor in ensuring accuracy and interpretability of supervised learning models.
Category: General Mathematics

F(U)-Gravity: A Unified Framework for Singularity Resolution, Dark Matter, and Quantum Gravity

Authors: Vivan Mirchandani
Comments: 13 Pages.

I introduce F(U)-gravity, a modified gravitational framework extending Einstein’s theory by incorporating an energy-dependent curvature function F(U). This approach addresses fundamental issues in cosmology and quantum gravity, including singularity resolution, the nature of dark matter, and deviations from standard general relativity. By modifying the Einstein-Hilbert action, I derive new field equations and examine their thermodynamic and observational consequences. My theoretical predictions suggest distinct signatures in gravitational wave echoes and cosmic microwave background anomalies, which could provide experimental validation through upcoming LIGO and LISA observations. This work builds upon approaches such as those proposed by Rosen [Phys. Rev. 57, 147 (1940)] and Stelle [Phys. Rev. D 16, 953 (1977)], offering a novel perspective on the quantum nature of spacetime.
Category: Quantum Gravity and String Theory

The Method of Dividing the 60° Angle Into Three Equal Parts

Authors: Hongfa Zi, Hongyun Zi
Comments: 5 Pages.

The problem of dividing a 60 ° angle into three equal parts in modern mathematics has not yet been solved. This involves the infinite extension of this trigonometric function in a generalized perspective. After research, it was found that the solution is located between r and two-thirds of r. The former represents a curve, while the latter represents a horizontal line. This article aims to utilize the relationships between various shapes to divide the 60 ° angle into three equal parts, which can then be extended to any angle less than 180 ° between r and two-thirds of r.
Category: Geometry

Verification Experiment of Faraday's Law of Electromagnetic Induction Based on a RF Alternating Magnetic Field

Authors: Hongyuan Ye
Comments: 6 Pages.

As one of the three fundamental universal laws of electromagnetism, Faraday's law of electromagnetic induction reveals that the induced voltage generated in a metal coil is proportional to the number of turns of the coil and the rate of change of the magnetic flux passing through a single turn of the coil. New research indicates that Faraday's law of electromagnetic induction is only an engineering approximation formula, and Lorentz's magnetic field force theorem is the microscopic physical essence of the electromagnetic induction. This verification experiment utilizes two induction coils CA and CB with identical structure and dimensions. CA is wound uniformly with 15 turns in a single layer, and CB is wound densely with 30 turns in a single layer. The ratio of the number of turns between CB and CA is 2. The two coils CA and CB are sequentially placed in sinusoidal alternating magnetic fields with frequencies of 200Hz, 50MHz and 100MHz, respectively. The experiment demonstrates that at a low frequency of 200Hz, the ratio of the induced voltages of CB and CA is approximately 2, which is proportional to the number of turns of two coils. Under low-frequency conditions, Faraday's law of electromagnetic induction and the experimental results are well approximated and consistent. At a radio frequency of 50MHz, the ratio of the induced voltages of coil CB and coil CA is 1.52, which significantly deviates from the ratio of the number of turns of coil CB and coil CA, which is 2. Faraday's law of electromagnetic induction and the experimental results are clearly inconsistent. At a radio frequency of 100MHz, the ratio of the induced voltages of coil CB and coil CA is 0.83, with the induced voltage of the 30-turn induction coil CB being smaller than that of the 15-turn coil CA. Faraday's law of electromagnetic induction and the experimental results are completely opposite. The reason is that Faraday's law of electromagnetic induction does not take into account the electromagnetic radiation of the induction coil, and assumes that the propagation speed of the electromagnetic field is infinite. Faraday's law of electromagnetic induction is one of the two necessary conditions of the "electromagnetic wave" theory. Faraday's law of electromagnetic induction does not hold true in the RF "electromagnetic wave", which further proves that the "electromagnetic wave" theory is incorrect. There is no an "electromagnetic wave" in the objective physical world, and it is an independent electric field wave that realizes wireless communication.
Category: Classical Physics

Possible Evidences from $H(z)$ Parameter Data for Physics Beyond Lambda CDM

Authors: Rong-Jia Yang
Comments: 7 Pages.

We analyse $H(z)$ parameter data with some conditions by using Lagrange mean value theorem in Calculus. We find that: (1) there exists decelerated phase at 1 $sigma$ confidence level in the redshift range $(0.38, 0.59)$; (2) the equation of state of dark energy may be less than $-1$ at 1 $sigma$ confidence level at some redshifts in the redshift range $(1.3, 1.53)$; (3) there exists accelerated phase at 1 $sigma$ confidence level in the redshift range $(1.037, 1.944)$. These results may provide possible evidences for physics beyond $Lambda$CDM.
Category: Relativity and Cosmology

The Universe Circulation System

Authors: Ichiro Nakayama
Comments: 8 Pages. (Note by viXra Admin: For the last time, please cite and list scientific references!)

The currently mainstream standard cosmology has many problems to be solved, such as dark matter and dark energy. Inflation theory is also difficult to believe. The Energy Body Theory has elucidated the cause of the rotation speed of spiral galaxies, which is the basis for the existence of dark matter. And it has also revealed what dark energy is and showed the reason why galaxies move away isotropically and acceleratingly. This time, I propose that the entire universe is one energy body, and the uneven distribution of energy generated in the energy body forms positive energy of stars and gravitational fields, and the formations of them are accompanied by the formations of dark energy fields, and further throughout the universe, positive energy of stars and gravitational fields circulate by exchanging energy with negative energy of dark energy. This system is called the universe circulation system. The universe exists in eternal time that is not expanding.
Category: Astrophysics

The Light Interaction With Light

Authors: Miroslav Pardy
Comments: 7 Pages. Original article

The scattering of light by light is considered in case where the internalparticles of this process have spin zero. The original calculation of this process wasperformed by Karplus et al. (1950). The pedagogical explanation of this proceswas realized for instance by Akhiezer et al. (1965), or, by Beresteteskii etal. (1982). We use here the model with the Green function for the spin zero particles. The article is written with the mathematical simplicity and the Schwinger pedagogical clarity
Category: High Energy Particle Physics

Permutation Rotations

Authors: Bassam Abdul-Baki
Comments: 7 Pages.

In this paper, we discuss certain properties of permutation rotations on each other.
Category: Combinatorics and Graph Theory

A Small Contribution to Ross-Littlewood Paradox

Authors: Marko V. Jankovic
Comments: 6 Pages.

In this paper Ross-Littlewood paradox is going to be analyzed. Two new experiments were proposed and it will be argued that number of balls at the end of experiment is infinite.
Category: General Mathematics

Solving Recurrence Relations Using Generating Functions

Authors: Harry Willow
Comments: 7 Pages.

This paper explores the applications of generating functions in solving various recurrence relations. We present the explicit formulas for recurrence relations of different forms, demonstrating step-by-step transformations and manipulations using generating functions. Several cases are examined, including linear and nonlinear recurrences, factorial-based sequences, and Fibonacci-related expressions. The derivations leverage algebraic techniques and characteristic equations to obtain closed-form solutions. The results highlight the power of generating functions in simplifying complex recurrence relations and deriving explicit formulas efficiently.
Category: Functions and Analysis

Artificial Prime Numbers Primality Assessment and Analysis in Specific Contexts

Authors: Jose Acevedo Jimenez
Comments: 5 Pages. In Spanish (Note by viXra Admin: Listed scientific references should be cited in the article)

This article explores the concept of artificial prime numbers, defined within specific sets of integers. A number is considered an artificial prime if it has no divisors other than itself within the given set. Through this definition, we seek to extend the idea of primality beyond traditional prime numbers, offering new ways to analyze numbers in number theory. Additionally, some important properties of these numbers are discussed, as well as their relationship with classical primes.
Category: Number Theory

A Transcausal Theory of Quantum Gravity and Map to UFT

Authors: Jennifer Lorraine Nielsen
Comments: 35 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper presents a novel quantum gravity framework within a 6-dimensional spacetimeS^3 × R × C_τ , aiming to unify the four fundamental forces via geometric and transcausalstructures. The 3-sphere S^3 provides spatial topology, R a real-time axis, and Cτ a complexblock-time plane hosting transcausal effects. Gauge fields for gravity, electromagnetism, andthe strong and weak nuclear forces emerge from the spacetime’s geometry, while quantum states reside in a Hilbert space H. Observables are derived, distinguishing "play states" (accelerated, GR-influenced) from "game states" (inertial), with "wonder" defined as a twist torque observable. The theory is designed to be Popper-falsifiable, with potential applications in quantum optics and exotic propulsion.
Category: Quantum Gravity and String Theory

Wallis-Type Product Formulas and Associated Wallis Integrals

Authors: Robert Bilinski
Comments: 3 Pages.

Variants of the Wallis product formula are established using simplicial polytopic numbers. These are then used to represent the Wallis integrals.
Category: General Mathematics

Temporal Flow Theory: A Unified Framework for Time, Gravity, and Quantum Mechanics

Authors: Matthew Warren Payne
Comments: 8 Pages. © Matthew W. Payne 2025 (Note by viXra Admin: AI assisted article is in general not acceptable)

Temporal Flow Theory (TFT) unifies time, gravity, and quantum mechanics through an entropy flux four-vector Wµ, emergent from coarse-grained quantum entanglement and decoherence, coupled to spacetime curvature via a scale- and temperature-dependent function g(r,T). Distinct from Loop Quantum Gravity (LQG), string theory, and entropic gravity, TFT is derived from an information theoretic action and predicts a frequency-independent 1.0 ± 0.5% boost in the cosmic microwave background (CMB) power spectrum at ℓ ∼ 100, a Planck-scale bounce, a (1.0±0.2)×10−6 nanoscale quantum phase shift, and a (1.0 ± 0.3) × 10−16 gravitational wave (GW) speed deviation. These predictions are testable by CMB-S4, the Matter-wave Interferometer Gravitational-wave Antenna (MIGA), and LIGO/Virgo stacking, respectively. Consistent with Planck 2018 and GW170817 data, TFT operates as an effective field theory (EFT), offering a thermodynamically motivated resolution to the problem of time in quantum mechanics. This paper presents the full theoretical framework, including detailed derivations, cosmological implications, quantization, and experimental constraints, situating TFT within the broader quantum gravity landscape
Category: Relativity and Cosmology

Potential Proof of Impossibility of Order-3 Magic Squares of Squares

Authors: Josephi Krakowski
Comments: 3 Pages. (Converted to pdf by viXra admin - Please submit article in pdf format only, and cite and list scientific references)

We prove that there does not exist a 3×3 magic square consisting of distinct perfect squares. Although extensive computational searches have failed to produce such a square, a general proof of nonexistence has remained open since Martin Gardner posed the question in 1996. This proof uses a combination of parity analysis, modular arithmetic, the convexity of the squaring function, and infinite descent to rigorously eliminate all possible configurations.
Category: Number Theory

A Unified Framework for Bright and Dark Fields: A New Cosmological Model Based on Flowing Energy

Authors: Kaisheng Li
Comments: 2 Pages.

lity, nuclear dynamics, and galactic rotation. Spin propels orbits, with perturbations manifesting as gluon waves (λ ≈ 1.24 pm, f ≈ 1022 Hz), fission in 252Cf (200 MeV, force imbalance), and M31’s rotation (flat to 100 kpc). This reinterprets wave-like behavior as a perturbation artifact, fission as dynamic imbalance, and cosmic order as amplified spin. Encoded in F = kSv/r +αv2sin(ωt)−D(A, Z),it aligns with LHC, nuclear, and Gaia data, predicting gluon frequencies, fission thresholds, and rotation anomalies. This framework redefines fundamental interactions across scales.
Category: High Energy Particle Physics

An Intuitive Explanation of the Invariance of the Speed of Light: Understanding the Concept Through the Timeless and Spaceless Nature of Photons.

Authors: Izam Syed
Comments: 6 Pages.

The invariance of the speed of light is a cornerstone of special relativity, yet it remains counterintuitive to many. This paper presents an intuitive explanation based on the nature of photons, which do not experience time or space. We argue that the observed constancy of light speed follows naturally from this fact. Through thought experiments and relativistic principles, we demonstrate why all observers, regardless of their motion, perceive light at the same speed. This perspective deepens our understanding of spacetime and the fundamental properties of light.
Category: Relativity and Cosmology

Calculation and Prediction of the 40Ca, 171Yb and 171Yb+ Atomic/Ionic Transition Frequencies

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 7 Pages. In Chinese.

In our previous paper, we calculated out and determined the atomic unit of time (tau) to be 2.41888432658653284(45)×10-17 s. In this paper, using the BIPM recommended 171Yb atomic transition frequency which is 518295836590863.63(10) Hz and its reciprocal in atomic units calculated from our corresponding formula, we once more calculate out and determine the atomic unit of time to be 2.41888432658653280(46)×10-17 s. With this very slightly revised atomic unit of time and the reciprocal of 40Ca atomic transition frequency in atomic units calculated from our corresponding formula, we calculate out the 40Ca atomic transition frequency to be 455986240494140.30(9) Hz, which is about 94 times more precise than the BIPM recommended value, i.e., 455986240494140(8) Hz. Employing the same method, we also calculate out two 171Yb+ ionic transition frequencies which are consistent with the BIPM recommended values.
Category: Nuclear and Atomic Physics

Notes on the Jellinek-Berry Thermostated Ideal Gas

Authors: Leo T. Butler, Alireza Sharifi
Comments: 12 Pages.

This note studies Hamiltonian systems which are thermostated using the Jellinek—Berry thermostat (J. Chem. Phys. 1988; Phys. Rev. A 1988). Jellinek & Jellinek and Berry propose an extension of Nosé's thermostat (J. Chem. Phys. 1984). They introduce multiple functional parameters in order to achieve ergodicity of the thermostatted dynamics. This family of Hamiltonian thermostats aim to simulate the macro canonical ensemble of a Hamiltonian $H$ by coupling $H$ to a 1-d heat reservoir with potentialenergy $v(s)$ and kinetic energy $p^2/2Q(s)$. Our note derives a normal form for the reservoir’s potential energy; investigates when the Jellinek—Berry thermostated system admits a Nosé—Hoover reduction; and, we demonstrate that a Jellinek—Berry thermostated periodic ideal gas is completely integrable and satisfies a KAM twist condition called Rüssmann non-degeneracy. This is used to deduce that a thermostated, collision-less, non-ideal gas (i.e. one with a smooth potential energy) at sufficiently high temperatures of the reservoir has a positive measure set of invariant tori—hence, the thermostated dynamics are non-ergodic.
Category: Statistics

Introduction to Hestenes’ Use of Geometric Algebra in Treating Constant-Acceleration Motion

Authors: James A. Smith
Comments: 8 Pages.

As an aid to teachers and students who wish to apply Geometric Algebra to high-school-level physics, we provide the first installment in a guide to Hestenes’s treatment of constant-acceleration motion. Specifically, we present a more-detailed version of Hestenes’ solution to the problem of finding the time and distance at which a projectile will cross a given line of sight. We begin by reviewing the GA ideas that we will use, and finish by verifying the solution via a GeoGebra worksheet.
Category: Classical Physics

Proof that e is Rational

Authors: Armando Evangelista Jr
Comments: 1 Page.

In this short paper, I used Joseph Fourier's proof that e is irrational to prove that it is actually a rational number.
Category: Algebra

Faster-Than-Light Travel Feasible with Negative Mass - Superluminal Dynamics

Authors: Raul Fattore
Comments: 29 Pages.

The study demonstrates that faster-than-light travel requires negative mass. Mass must decrease as velocity increases and must be negative beyond the speed of light.It also proves that there is no absolute speed limit in the universe, contradicting faulty Einstein's theory of relativity and quantum theory. The study also reveals that relative motion depends on relative coordinates, not reference frames.It is demonstrated that gravitational and inertial control of mass is the basis of faster-than-light travel. A hypothetical spaceship is described, and physical calculations are made to demonstrate the possibility of traveling faster than light. The study also explores the potential effects of gravitational interaction and collisions. The technology is proposed for instantaneous cosmic communication and other applications of negative mass using the free energy of the gravitational field.* Is faster-than-light travel indeed possible?* What kind of propulsion could achieve such a technology?* Could any matter be traveling faster than light?* Could living beings be traveling faster than light?* What could be the consequences of that?The above questions will be scientifically answered through this study in accordance with the negative mass theory.
Category: Astrophysics

Diophantine Equation Degree Six Type (6-4-4) Equation

Authors: Oliver Couto
Comments: 5 Pages.

There are numerical solutions available on Wolfram world of mathematics website (ref. # 1) for the equation, (a^6+b^6+c^6+d^6)=(e^6+f^6+g^6+h^6). In this paper the author has arrived at numerical solution by algebra instead of elliptical theory. There are methods for the (6-4-4) equation in (ref #6) providing numerical solutions but parametric solutions are not shown. Also on the internet the author has not come across a similar method (given in this paper) for the above mentioned equation.
Category: Number Theory

Industry-Specific Sentiment Analysis Comparison: Evaluating VADER and TextBlob Across Finance, Healthcare, Social Media, and Customer Reviews

Authors: Manan Maheshwari
Comments: 7 Pages.

This study explores the effectiveness and strengths of two widely used Natural Language Processing (NLP) models—VADER and TextBlob—in different industry contexts. VADER (Valence Aware Dictionary and sEntiment Reasoner) is a specifically designed model to analyze sentiments in social media posts and short texts. VADER relies on a lexicon-based approach, using a pre-defined list of words (the lexicon) with associated sentiment labels (positive, negative, or neutral) to determine the sentiment of a text, that consists of contextual strengths of words. TextBlob also implements a lexicon-based approach, however, it enforces a rule-based technique that uses linguistic rules that help determine the sentiment polarity (positive, negative, or neutral) of a piece of text; this approach makes it more adaptable for general language processing tasks. This research evaluates the power and usefulness of these models across four key industries: Finance, Healthcare, Social Media, and Customer Reviews. Upon intensive testing against 100's of datasets, the study realized that VADER outperformed in Finance and Healthcare because of its capacity to process domain-related sentiment nuances, giving it a slight edge when it comes to sophisticated sentiments. In the case of Social Media, both models show similar and consistent accuracy; concurrently, TextBlob outperforms VADER in Customer Reviews because it is better suited for longer and more complex texts. The results stress the need to use the right sentiment analysis model according to industry-specific requirements. Comparing VADER and TextBlob on real-life data, this study offers useful implications for businesses, researchers, and developers aiming to improve their sentiment analysis approaches.
Category: Artificial Intelligence

Investigating Cyclic Gravity and Cosmology (CGC) as an Alternative Framework to Standard Cosmology

Authors: Joseph Bakhos
Comments: 16 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Cyclic Gravity and Cosmology (CGC) is introduced as an alternative framework to General Relativity (GR) and the ΛCDM model. CGC retains Euclidean space and proposes that gravity is a residual effect of electromagnetism ratherthan a fundamental force. The theory replaces the standard expansion model with cyclic expansion and contraction phases governed by large-scale gravitational oscillations. Redshift in CGC is explained through a combination ofDoppler motion, neutrino interactions, and a refined tired light mechanism. Time dilation and light deflection arise from neutrino scattering rather than spacetime curvature, preserving a Euclidean structure. CGC naturally explains the Cosmic Microwave Background (CMB) power spectrum without requiring inflation, aligns with observed large-scale structure, and provides a resolution to the Hubble tension within a non-expanding space framework. The theory predicts a self-regulating cosmic equilibrium maintained by an outer shell of intergalactic medium, preventing energy loss and sustaining cyclic dynamics. The observed galactic rotation curves, large-scale filament-and-void cosmic structures, and elemental recycling in Active Galactic Nuclei (AGN) are also consistent withCGC’s gravitational model. The purpose of this paper is not to assert CGC as the definitive model of cosmology but to establish it as aframework worthy of rigorous scientific investigation. Given recent challenges to ΛCDM from JWST observations and inconsistencies in Hubble measurements, CGC presents an opportunity to explore alternative gravitational dynamicsand cosmic evolution mechanisms that align with observational data.
Category: Relativity and Cosmology

Chaos, Confusion, and the Illusion of Gravity Waves

Authors: Keith D. Foote
Comments: 13 Pages.

The interpretation of vibrations detected by LIGO’s facilities is critically examined. The concept of gravitational waves is disputed and the argument is made the detected vibrations are the result of synchrotron radiation. Spacetime is treated with skepticism, and a modern version of the aether is described. Synchrotron and Cerenkov radiation are used as supporting evidence of a medium supporting the transport of electromagnetic waves.
Category: Relativity and Cosmology

A New Theory of Gravity and the Design and Fabrication of a Gravitational Field Generator Based on [a] New Theory

Authors: Yuan Pan, Yong Wen Pan
Comments: 86 Pages.

Albert Einstein (1879-1955) used a different line of thought to study the physical properties of gravitational fields before he established the general theory of relativity on the mathematical basis of Riemannian geometry. Based on this idea, we developed a new theory of gravity that describes the physical properties of gravitational fields on the basis of special relativity and eventually unifies the electromagnetic and gravitational fields. This paper is only the first part of this new gravitational theory, focusing on the construction of the foundation of the new theoretical system, with the following main contents:1.A new view of space-time is put forward, which holds that time, space and the mass of matter are determined by the gravitational field, and therefore controlling the gravitational field can control the space-time and the mass of matter to a certain extent.2. Recalculating and reinterpreting the classical verification experiments of general relativity (including the gravitational redshift of light frequencies, the gravitational deflection of light, the Mercury perihelion procession shift, etc.) in accordance with the new theory of gravity yielded identical calculations to those of general relativity.3.On the basis of the observed speed of motion of the centre of mass of the solar system with respect to the stationary reference system of the cosmic microwave background radiation (CMBR), it was calculated that a 1-year cycle variation should be included in the complex variation of the Earth's rotation rate. In this cycle, the change in the length of day (ΔLOD) of the Earth decreases by about 0.77376 ms to 0.85972 ms in August compared to February each year. We analyse that this calculation is consistent with the observation data released by IERS (International Earth Rotation Service).4.The new gravitational theory explains the dark energy in the Universe.5.We have revised De Broglie's matter wave formula, and the revised matter wave formula can explain why matter cannot be cooled to absolute zero, and this new matter wave formula can be used as the basis for unifying the electromagnetic field and the gravitational field. We believe that fluctuations in matter (matter waves) generate gravitational fields, and that regulating matter waves regulates the generation of gravitational fields.6. We have designed and built the world's first gravitational field generator since 2016 based on this new theory of gravity, and have successfully conducted a gravitational field generator (curvature engine) experiment in 2021, which is briefly described in this paper.
Category: Relativity and Cosmology

A Note on Gradient-Based Parameter Estimation for Energy-Based Models

Authors: L. Martino, S. Ingrassia, S. Mangano, L. Scaffidi
Comments: 12 Pages.

Energy-based models (EBMs) are an important family of models where a piece of the likelihood is intractable, and hence unknown. For this reason, the parameter estimation in EBMs is a challengefor the standard estimation methods. In this paper, we present a critical discussion of gradient-based approaches for inference in energy-based models. We provide many details of different derivations, clarify connections and differences. We give practical suggestions for the application of the different schemes. Specifically, we focus on a suitable choice of the proposal/reference density that is crucial for the performance of the gradient-based procedures.
Category: Statistics

Multioutput Feature Selection for Emulation and Sensitivity Analysis

Authors: J. Vicent, L. Martino, J. Verrelst, J. P. Rivera Caicedo, G. Camps-Valls
Comments: 26 Pages. Published in IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1-11, 2024

Statistical regression methods are widely used in remote sensing applications but tend to lack physical interpretability. In this paper, we introduce a methodological framework to improve modelemulation and its understanding with machine learning feature selection. Our wrapper-forward feature selection method seamlessly integrates physics knowledge into model emulation, improving the tradeoff between accuracy and interpretability. We illustrate our methodology by applying it to atmospheric radiative transfer models in the context of global sensitivity analysis (GSA) and emulation. Our approach consistently aligns with variance-based GSA, pinpointing the critical features of aerosol properties, solar zenith angle, and water vapor. While our physically-based emulators yield only a modest accuracy improvement of 0.2% over conventional Gaussian Processes emulators, its introduction signifies a step forward to physics-aware machine learning-based emulation. The emulator performance remains steadfast, unaffected by substantial changes, further underscoring the reliability of our approach.
Category: Statistics

Multi-fidelity Gaussian Process Emulation for Atmospheric Radiative Transfer Models

Authors: J, Vicent, L. Martino, J. Verrelst, G. Camps-Valls
Comments: 28 Pages. Published in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-10, 2023.

Atmospheric radiative transfer models (RTMs) are widely used in satellite data processing to correct for the scattering and absorption effects caused by aerosols and gas molecules in the Earth’s atmosphere. As the complexity of RTMs grows and the requirements for future Earth Observation missions become more demanding, the conventional Look-Up Table (LUT) interpolation approach faces important challenges. Emulators have been suggested as an alternative to LUT interpolation, but they arestill too slow for operational satellite data processing. Our research introduces a solution that harnesses the power of multi-fidelity methods to improve the accuracy and runtime of Gaussian Process (GP) emulators. We investigate the impact of the number of fidelity layers, dimensionality reduction, and training dataset size on the performance of multi-fidelity GP emulators. We find that an optimal multi-fidelity emulator can achieve relative errors in surface reflectance below 0.5% and performs atmospheric correction of hyperspectral PRISMA satellite data (one million pixels) in a few minutes. Additionally, we provide a suite of functions and tools for automating the creation and generation of atmospheric RTM emulators.
Category: Statistics

The Unifying Theory: The Missing Link Between Quantum Reality and Classical Physics

Authors: Bader Binkhudhayr
Comments: 7 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Einstein’s spacetime curvature falters as gravity’s cause—gravitational waves (strain h ~ 10^-21) stretch Earth without orbital jolts, exposing his causal lie (Sec. 4.1) [1]. The Unifying Theory reinterprets motion as quantized relocations—instantaneous jumps forming wave-like or linear patterns—dismantling the quantum-classical divide with a revolutionary mechanism. Particles leap at ultimate speeds, mimicking waves by tunneling (~10^21 s^-1) or aligning under scrutiny (double-slit [2]), their continuity a perceptual sham (Sec. 2). Length contraction—muons enduring ~7 μs at 0.99c vs. 2.2 μs rest [3]—demands quantized steps. A variant variable emerges from photon relocation distances, leading to a universal frame of reference (Sec. 3), torching special relativity’s equivalence [4]. Forces shift relocation frequencies, unifying gravity and electromagnetism via introducing a new unit: particle counts (Sec. 4, Eq. 6), relegating curvature to a passive backdrop [1]. Observation alters patterns, echoing free will theorems’ non-deterministic dance (Sec. 5) [5]. LIGO, tunneling, and relativistic data anchor this theory, shattering Copenhagen’s premature duality—a sloppy guess misreading tempo for states (Sec. 5.1). This framework unifies all forces, bridges quantum and classical realms, and exposes a century of missteps, ending with a truth unifying gravity and electromagnetism in one equation [19].
Category: High Energy Particle Physics

Systemic Relativity & Logarithmic Gravity (SRLG): A Scale-Dependent Framework for Unifying Quantum and Cosmic Phenomena - REVISION

Authors: Lukas A. Sosna
Comments: 16 Pages. 6 figures (Note by viXra Admin: AI assisted article is in general not acceptable)

The persistent rotation curve anomalies of galaxies present one of modern physics' most profound puzzles. Stars orbit galactic peripheries at velocities far exceeding Newtonian predictions based on visible matter alone, a discrepancy conventionally addressed by postulating vast halos of invisible dark matter. Meanwhile, the theoretical landscape remains fractured by the fundamental incompatibility between quantum mechanics and general relativity, particularly in extreme gravitational environments.This paper introduces Systemic Relativity & Logarithmic Gravity (SRLG), a theoretical framework that addresses these challenges through a single unifying principle: the scale-dependence of gravitational interactions. The core mathematical innovation is remarkably straightforward—a logarithmic modification to Newtonian gravity that causes gravitational force to decline more gradually with distance than the inverse-square law predicts:$$g_{text{log}}(r) = frac{GM}{r^2} times e^{-lambda log(r)}$$The distinguishing feature of SRLG is the system-dependent parameter λ, defined as the ratio of gravitational binding energy to Planck energy. This definition provides a physical basis for why gravitational behavior transforms across cosmic scales, with λ naturally increasing from negligible values at solar-system scales (λ ≈ 10^-38) to appreciable values at galactic scales (λ ≈ 10^-5).Rigorous analysis using 175 galaxies from the SPARC database demonstrates that SRLG reduces rotational velocity prediction errors by approximately 50% compared to Newtonian models without requiring dark matter. The framework also successfully models gravitational lensing in the Abell 2744 galaxy cluster with λ ≈ 0.26-0.32, producing observed lensing strength within 5-8% of measured values without dark matter components.The time-frequency dynamics incorporated in SRLG yields testable predictions for gravitational wave propagation, specifically a frequency-dependent phase shift potentially detectable by LIGO and LISA. This aspect of the theory may provide crucial insights into how gravity behaves in the strong-field regime, offering a bridge between quantum and relativistic physics. SRLG's connections to renormalization group approaches, black hole thermodynamics, and quantum gravity suggest it may be uncovering a fundamental pattern in nature's architecture rather than merely providing a convenient fitting function. By reconceptualizing gravity as a scale-dependent phenomenon, this work offers not only a potential resolution to the dark matter problem, but also a fresh perspective on the century-old quest to reconcile quantum mechanics with general relativity.
Category: Relativity and Cosmology

The Quo Vadis Effect: A Graviton-Based Explanation of Mercury’s Perihelion Precession

Authors: Adolfo Santa Fe Dueñas
Comments: 14 Pages.

We propose the Quo Vadis Effect (QVE), a velocity-dependent correction to Newtonian gravity arising from gravitational aberration. Unlike General Relativity (GR), which explains Mercury’s perihelion precession via space-time curvature, the QVE operates within a Newtonian framework without modifying the geometry of space-time. The core mechanism of the QVE is that an orbiting body perceives gravitons arriving at an apparent velocity greater than $c$ due to aberration. This results in two simultaneous effects: (1) an increased flux of gravitons and (2) an enhanced force per graviton, leading to a total gravitational force correction proportional to (1 + (v/c)²). This correction modifies the gravitational potential energy, reproducing the standard GR prediction for Mercury’s perihelion precession.A similar velocity-dependent correction was previously explored by Wayne (2015), albeit without a clear physical derivation, speculating on possible friction-like effects. In contrast, the QVE provides a well-defined mechanism based on gravitational aberration.Beyond Mercury’s orbit, the QVE may have broader implications, including potential corrections to GPS satellite clocks and alternative explanations for galaxy rotation curves without invoking dark matter. Additionally, it may offer insights into cosmic acceleration if graviton propagation exhibits similar aberration effects at cosmological scales.Given the ongoing debate surrounding modified gravity theories, this work aims to contribute to the discussion by demonstrating that a Newtonian approach incorporating gravitational aberration can recover key relativistic results. The QVE suggests a possible bridge between classical mechanics and quantum gravity, warranting further investigation.
Category: Relativity and Cosmology

Quantum Mechanics

Authors: Loïc Renaut, Laurent Bruneau
Comments: 65 Pages. In French

The aim of this thesis is to study the basic concepts and the mathematical formalism of quantum mechanics. To do so, we will first examine Newtonian mechanics. This was the prevailing theory until the early 20th century for describing the motion of objects of all sizes. However, it was later discovered that this theory had its limitations. Consequently, at the beginning of the 20th century, two new theories emerged to address the shortcomings of Newtonian mechanics: quantum mechanics, which is the focus of this thesis and describes the physics of atomic and subatomic-scale objects, and special relativity, which deals with the physics of objects on a very large scale.In the second part, we will study quantum mechanics and attempt to identify the similarities and differences between the two theories. The foundational principle of quantum theory is wave-particle duality. This principle states that the objects that make up matter (such as electrons and photons) exhibit behavior characteristic of a particle in some situations and behavior characteristic of a wave in others. However, they are neither purely waves nor purely particles—they are something else entirely. This is one of the fundamental differences between the two theories. In Newtonian mechanics, objects are considered exclusively as particles. To illustrate the intellectual revolution brought about by this principle, we can recall the major debate that took place in the 17th century regarding the nature of light (at the time, photons were unknown). Two opposing camps emerged: one led by Isaac Newton, who believed that light was composed of particles, and the other led by Christiaan Huygens, who argued that light was a wave. Newton’s influence was so great that his view was widely accepted by most scientists of the time. No one had yet considered that light might be neither a particle nor a wave. Moreover, the necessary mathematical tools to explore this idea did not yet exist.
Category: Functions and Analysis

Another Approximation for Prime Counting Function

Authors: Khazri Bouzidi Fethi
Comments: 4 Pages. (Note by viXra Admin: Listed scientific references should be cited in the article; AI assisted/generated content is in general not acceptable)

This paper proposes a more accurate approximation to the prime counting function, especially for small numbers, using a base-10 logarithm. It relates this approximation to the Riemann zeta function, providing geometric interpretations of its terms.
Category: Number Theory

Dictionary of Early English by Joseph T. Shipley and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the words of the Dictionary of Early English by Joseph T. Shipley. We draw the natural logarithm of the number of words, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4, $beta H=0.02$), i.e. the magnetisation curve in the the Bethe-Peierls approximation of the Ising model, in the presence of four nearest neighbours and little external magnetic field, H, with $beta H= 0.02$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

Mass Defect

Authors: Nainan K. Varghese
Comments: 6 Pages.

Although the mass of an object is defined to represent the equivalent of 3D matter it contains, it is often considered as the quantity of 3D matter contained in the object. Mass is the mathematical relation between an external linear effort on an object and the rate of the rate of its displacement in the direction of the external effort. This relationship is often ignored, and the value of a body's mass is regarded in almost all academic fields as the quantity of 3D matter present in the object. Loss (or gain) of mass of an object during its development stage or changes in its structure is understood as ‘mass defect’. This is often related to an assumed phenomenon of binding energy required to stabilize the nucleons in the atoms in a body.
Category: High Energy Particle Physics

Training Neural Networks with {-1,1} Weights by Genetic Algorithm

Authors: Hidehiko Okada
Comments: 7 Pages.

The author previously reported an experimental result of evolutionary reinforcement learning of binary neural network controllers. In the previous study, the controller was trained by Evolution Strategy. In this study, the author experimentally applies Genetic Algorithm, instead of ES, and the results were compared between GA and ES. In both studies, the same Acrobot control task is utilized, and the same three-layer feedforward neural network is adopted. The difference lies in the training algorithm. The findings from this study are (1) GA trained the controller better than ES (p<.01), (2) increasing the population size, rather than the number of generations, improved performance more in GA (p < .01), and (3) the optimal number of hidden units for the binary MLP was 128 among the choices of 16, 32, 64, 128 and 256, which was consistent with the previous study using ES.
Category: Artificial Intelligence

Bounds on Prime Gaps and Their Consequences in Number Theory

Authors: Siddid Gosain
Comments: 5 Pages.

In this paper, I establish several novel and rigorous bounds on prime gaps. These bounds not only enhance our understanding of prime distribution but also provide elegant proofs for certain unsolved problems in number theory. Moreover, this work paves the way for estimating the density of primes in large intervals and opens new avenues for further research.
Category: Number Theory

New Proof of Dark Numbers by Means of the Thinned Out Harmonic Series

Authors: W. Mückenheim
Comments: 1 Page.

It is shown that not all numbers can be expressed and communicated such that the receiver knows what the sender has meant. We call them dark numbers.
Category: Set Theory and Logic

Irrational Numbers Do Not Exist [?]

Authors: Armando Evangelista Jr
Comments: 1 Page. (Note by viXra Admin: Please cite and list scientific references)

This short paper proves that there are no such things as irrational numbers.
Category: Algebra

Surface Area of the Mobius Strip

Authors: Richard J. Mathar
Comments: 6 Pages.

The (half) area of the surface of the Mobius strip is the expected product of the length of the circular spine times the width of the sweep line times a positive correction factor. The manuscript writes down this factor as a Taylor series of the ratio of width over circle radius; it approachesone if that ratio approaches zero.
Category: Geometry

A New Dictionary of the Portugese and English Languages Enriched by H. Michaelis and the Graphical Law

Authors: Anindya Kumar Biswas
Comments: 20 Pages.

We study the Portugese head entries of A New Dictionary of the Portugese and English Languages enriched by H. Michaelis. We draw the natural logarithm of the number of head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the dictionary can be characterised by the magnetisation curve, BP(4,$beta H=0$), in the Bethe-Peierls approximation of the Ising model, in the resence of four nearest neighbours and in the absence of external magnetic field, H. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

137 First Prime of Form, First Prime Expressed with Four Base Numbers of Number Type

Authors: Dwight Boddorf
Comments: 2 Pages.

Where N is a counting number, one hundred and thirty-seven is the first prime number to take the form of 2[(2N+2)(2N+2)] + NN , if N equals 3 then prime number is one hundred and thirty-seven.
Category: Mathematical Physics

Bessel Functions and pi

Authors: Edgar Valdebenito
Comments: 3 Pages.

We give two sequences for Pi.
Category: Functions and Analysis

Nova Framework: A Unified Theory of Quantum Gravity and Beyond

Authors: Thura Zaw Oo
Comments: 6 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Nova proposes quantized spacetime fluctuations (QSFs)—a scalar field ϕ constrained to Planck-scale vacuum perturbations—as the sole constituent of the universe, with no external background,unifying General Relativity (GR) and Quantum Mechanics (QM) at all scales without invoking extra dimensions or geometric quantization. QSFs are both quantized and dynamic, inducing GR’s tensor gravity through a scalar-tensor coupling (κ) derived from gravitational vacuum energy, where grav-ity manifests as an inertial-like spread action driven by relative differences in QSF densities. Particlemasses and fundamental forces emerge from knotted QSF structures: the strong force as the knot-ting strength or potential at the bare minimum matter level, the weak force as the action strength of the knots themselves, the electromagnetic (EM) force as a vibration-like spread across the dynamic QSF scalar, and gravity as the relative QSF fluctuations’ spread action around matter-like QSFs. Antimatter and antiforces arise from stretched, non-knotted QSF actions, distinct in nature from knotted matter, not merely symmetric opposites. Time is derived from QSF actions, ceasing where action halts (e.g., ∂tϕ = 0). QSFs couple to Standard Model (SM) gauge fields through a constrainedSO(5) symmetry-breaking mechanism, generate dark matter via non-knotted fluctuations, producedark energy via expansion dynamics, and drive cosmic inflation through early high β-rates. Nova resolves singularities with a dynamic finite-core metric and eliminates the Hierarchy and Strong CPProblems as artifacts of linear thinking, not requiring fine-tuning or additional particles. We rigorously test against Planck CMB, LIGO GW150914, and LHC Higgs datasets, computing densities and masses with Monte Carlo error estimates, and predict a 510 ± 20 GeV scalar (consistent with LHC limits via suppressed coupling) and CMB B-modes at ℓ > 3000 with ∆C BB ℓ = 0.8 ± 0.2 µK 2, derived from inflationary physics. Nova offers a coherent, testable, and comprehensive framework grounded in exhaustive derivations.
Category: Quantum Physics

Kaluza Klein Theory Versus the Possibility that the Electric Field Strength Might be Recognized as a Form of Acceleration

Authors: Moshe Segal
Comments: 12 Pages.

Einstein's Theories are considered as significant theories of the nowadays Science of Physics. However, the nowadays Science of Physics did not provide yet a verified theory for unifying Gravitation and Electromagnetism.Kaluza Klein Theory addresses that issue by predicting that there are five dimensions, with the fifth dimension being of the shape of a tiny circle, with a radius of 23 times the Planck length, which is of the order of 10−33 cm.However, because there is no foreseeable technology for verifying that prediction, about that fifth dimension, the Kaluza Klein Theory is not yet accepted as a complete viable theory, which implies that the issues of presenting a theory which unifies the Gravitation and Electromagnetism is still an open issue.This paper, and several other preprints, by the author of this paper, also tries to address that issue, by presenting an alternate theory, which is also accompanied by a proposal for an experiment, which might either disprove the proposed theory, if the proposed experiment implementation will turn out to be unsuccessful, or, alternatively, provide validity to the proposed theory, if the proposed experiment implementation will turn out to be successful.However, while the Kaluza Klein theory does not challenge significant elements of the nowadaysScience of Physics, the proposed theory does challenge significant elements of the nowadaysScience of Physics, and as such, might appear, initially, as completely wrong. Thus, this paper concludes that the implementation of the proposed experiment might be an important endeavor, because it might provide validity to the proposed theory, while the Kaluza Klein theory does not seem to be verified, in the foreseeable future, leaving the issue of the unification of Gravity and Electromagnetism as an open issue.
Category: Relativity and Cosmology

TSVF-SUSY: A Time-Symmetric Supersymmetric Framework for Quantum Gravity Unification, Dark Matter Resolution, and Gravitational Wave Signature Predictions

Authors: Muhammad Shahzaib Uddin Khan
Comments: 19 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This work unifies the Two-State Vector Formalism (TSVF) of quantum mechanics with N = 1 supersymmetry (SUSY) into a mathematically rigorous framework for quantum gravity. Key results include: (1) A ghost-free, renormalizable Lagrangian with bidirectional time evolution; (2) Proof of SUSY algebra closure under Planck-scale corrections; (3) One-loop renormalizability with asymptotic safety; (4) Testable predictions for gravitational wave physics, dark matter, and neutrino oscillations. The framework resolves tensions between SUSY and quantum gravity while offering falsifiable deviations from General Relativity.
Category: Quantum Gravity and String Theory

The Missing Mass: A Heuristic Explanation of Dark Matter

Authors: Guofeng Chang
Comments: 5 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

In this paper, we analyze the phenomenon of non-isotropic mass distribution in spiral galaxies and propose a hypothesis that such an imbalanceintroduces a relative velocity for observers. Furthermore, we suggest observational methods to verify this hypothesis. If proven correct, thishypothesis could provide a more reasonable explanation for the origin of dark matter.
Category: Astrophysics

Pythagorean Complex: on Truth and Falsness Superpositions

Authors: Osvaldo Duilio Rossi
Comments: 1 Page. (Note by viXra Admin: An abstract in the article is required and cited references should be listed)

r^2 = x^2+y^2 implies r^2 = (x+yi)(x-yi), implying r^2 = rr*, superposing a statement true under algebra with a statement fals under epistemology, revealing the true nature of complex numbers and mathematical thinking.
Category: Algebra

Conditional Negation of The ABC Conjecture

Authors: Jinhua Fei
Comments: 4 Pages.

In this paper, the abc conjecture is negated under certain conditions.
Category: Number Theory

Multi-layer GRPO

Authors: Fei Ding
Comments: 7 Pages.

The success of DeepSeek-R1 has demonstrated the effectiveness of the GRPO algorithm. However, due to the absence of process rewards, GRPO often suffers from inefficiencies in exploration, as a single detailed error can result in an entirely incorrect final answer, leading to zero rewards.To address these challenges, we propose MGRPO (Multi-layer GRPO). In the first layer, GRPO operates identically to the original version, generating an initial response. This response is then fed into a second-stage GRPO process, which primarily trains the model to correct errors. Experimental results indicate that MGRPO outperforms standard GRPO, achieving superior performance.
Category: Artificial Intelligence

Patterns of Perfect Magic Squares of the 4th and 8th Order, Magic Cubes of the 2nd and 4th Order

Authors: Andrey V. Voron
Comments: 5 Pages.

The article shows the possibility of a formula calculation of patterns of ideal magic squares of the 4th and 8th order, magic cubes of the 2nd and 4th order, as well as substantiates the hypothesis that the laws of dialectics apply to numbers as ideal objects. In particular, the presence of mathematical patterns can characterize the dialectical law of "unity and struggle of opposites", when the sums of the numbers of the pattern act as opposites. The presence of the golden division constant or its derivatives between the opposite patterns is probably due to the property of the unity of the elements that make up such a whole. This unity of the elements that make up the whole is probably due to the greatest number of structural mathematical connections obtained in connection with the unique properties of the golden proportional relations.
Category: Number Theory

English Language and Science

Authors: Jeremy Dunning-Davies
Comments: 4 Pages.

Here attention is drawn to possible problems arising from an inaccurate use of the English language in science. It is noted that such misuse may lead to incorrect public understanding of some common notions in science today.
Category: History and Philosophy of Physics

Analytical Model for the Thermal Conductivity of Fully Ionized Plasmas

Authors: Yuanjie Huang
Comments: 13 Pages.

The thermal conductivity is a fundamental property of plasmas, yet its experimentally observed reduction remains an enigmatic phenomenon. Over the past half-century, extensive efforts have been dedicated to elucidating the mechanisms behind this reduced thermal conductivity and the associated heat-flux limiter, but a definitive solution has remained elusive. In this work, we present an analytical model for plasma thermal conductivity that is free of artificial parameters. This model employs Maxwell distributions for both electrons and ions and provides analytical expressions for thermal conductivity and the heat-flux limiter. Importantly, the predictions of the model are in good agreement with experimental observations. Its validity extends across plasmas with both small and large temperature gradients, significantly enhancing its applicability. This straightforward model not only offers insights into the underlying physics of reduced thermal conductivity and the heat-flux limiter but also plays a crucial role in advancing our understanding of thermal transport in plasmas across diverse areas.
Category: Nuclear and Atomic Physics

Recursive Differentiation and the Logarithmic Structure of Fundamental Constants

Authors: Leah Travers
Comments: 20 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The values of fundamental physical constants have long been treated as free parameters, requiring empirical measurement rather than derivation from first principles. In this work, we establish a novel analytical proof demonstrating that these constants emerge as equilibrium conditions of a recursive differentiation process. This analysis reveals that these constants are not independent but are instead stabilized by a universal recursive scaling law.A central result of this work is the emergence of a fixed recursion exponent k ≈ -3, derived from first principles, which constrains the values of h, the fine-structure constant α, and the cosmological constant Λ through a logarithmic scaling relationship. This exponent aligns with known renormalization group flow constraints in quantum field theory, black hole entropy scaling in holographic gravity, and fractal structures in critical phenomena. We explore the implications of this result for gauge symmetries, vacuum energy, and the unification of fundamental interactions.Further, we demonstrate that recursion provides a natural resolution to the scale-separation problem by embedding quantum and cosmological parameters within the same self-organizing structure. This formalism suggests that fundamental constants arise as attractor solutions to recursive differentiation, challenging conventional assumptions about their arbitrariness. Predictions include logarithmic corrections to the fine-structure constant over cosmological timescales, recursive stability constraints on vacuum energy, and scale-invariant deviations in black hole entropy.This work establishes recursion as a fundamental organizing principle of physical law. The recursive differentiation framework presented here lays the foundation for further theoretical development and experimental validation. If confirmed, this result implies that the structure of reality itself is governed by universal recursion constraints rather than arbitrary parameter selection.
Category: Quantum Gravity and String Theory

Prime Gap Instability and the Collapse of the Riemann Hypothesis

Authors: Jasmine Burns
Comments: 15 Pages.

The Riemann Hypothesis (RH) asserts that all nontrivial zeros of the Riemann zeta function lie on the critical line ℜ(s) = 1/2. In this paper, we prove that RH is false by demonstrating that the evolution of zeta zeros under the de Bruijn-Newman heat equation is fundamentally unstable. We establish that irregularities in prime gaps introduce an unbounded forcing term in the heat equation, leading to a necessary shift in the location of zeta zeros and forcing Λ > 0, contradicting RH. Furthermore, we resolve the Pair Correlation Conjecture independently of RH, showing that the statistical structure of zeta zeros remains unchanged under the heat evolution. This result confirms that the known statistical properties of the zeta function are not contingent on RH but instead arise from a deeper structural phenomenon tied to prime number modularity and diffusion dynamics. Our findings necessitate a fundamental reevaluation of the role of RH in analytic number theory, shifting focus toward a more geometrically and dynamically informed understanding of the zeta function's zeros.
Category: Number Theory

A Novel Identity in Binomial Probability Theory

Authors: Ashkan Karimi
Comments: 6 Pages.

This paper presents a proof and analysis of a previously unexploredbinomial probability identity involving weighted sums of binomial probabilities. The identity establishes that a specific weighted sum of binomial terms with probability parameter PA equals zero for any positive integer n. I provide a rigorous proof of this identity, explore its probabilistic interpretation in terms of expected values, and discuss potential applications in statistical analysis, information theory, and computational probability. The result offers new insights into the properties of binomial distributions and contributes to the broader understanding of discrete probability structures. The identity has particularly elegant connections to moment-generating functions and can be generalized to higher moments and other probability distributions.
Category: General Mathematics

Resolving the Yang-Mills Mass Gap Problem Using Alpha Integration

Authors: YoonKi Kim
Comments: 6 Pages. Email: yk.reserch@gmail.com

We present a non-perturbative proof of the Yang-Mills mass gap hypothesis, demonstratingthat the lowest eigenvalue E0 of the quantum Yang-Mills Hamiltonian in four-dimensionalEuclidean spacetime is positive, confirming the existence of a mass gap and quark-gluon confinement. Using a novel path integral framework, we address divergences, resolve Gribov ambiguities, and compute the spectrum, achieving consistency with lattice QCD simulations and experimental data. Our results align with the Clay Mathematics Institute’s Millennium Prize criteria, providing a mathematically rigorous and physically consistent solution.
Category: High Energy Particle Physics

Electron Approach Theory[:] A Damped Oscillation Model Based on Relativistic Effects and Space-Time Feedback.

Authors: Douglas Ruffini
Comments: 78 Pages.

This study proposes a new theoretical model to describe the behavior of the electron in the atom, reinterpreting the classical problem of its collapse towards the nucleus through a damped oscillation governed by relativistic effects and a space-time feedback. The electron, in its approach to the nucleus, undergoes an increasing acceleration until a critical point where its velocity approaches that of light, leading to a temporal discontinuity and a subsequent reversal of motion. This process is formalized through the Lorentz factor with imaginary values, suggesting a transition between quantum states rather than a real superluminal velocity. The model is supported by a mathematical analysis based on the exponential decay of energy and the time constant RC, which shows a connection with the Heisenberg uncertainty principle and the time scales of quantum processes. The electron descent-ascent cycle introduces the concept of space-time memory, with a coordinate recalculation mechanism that ensures atomic stability. The results suggest that energy quantization can emerge as a macroscopic effect of an oscillating dynamical system and that absolute space-time plays a key role in maintaining temporal coherence. This approach offers a novel perspective on the stability of the atom, bridging classical mechanics, relativity and quantum mechanics through a new interpretation of energy transitions and space-time structure.
Category: Nuclear and Atomic Physics

Magnetic Fields of White Dwarfs and Neutron Stars

Authors: Kiyoung Kim
Comments: 16 Pages.

Neutron stars and white dwarfs are known to be the final stages in the life cycle of stars. These celestial objects are characterized by immense gravitational pressure, extremely high temperatures, and exceptionally high density. Additionally, some of them are known to possess extraordinarily strong magnetic fields under these extreme conditions. However, the precise mechanisms behind the generation of such strong magnetic fields remain unclear. The primitive virtual negative (PVN) charge dynamo mechanism proposed for solar planets in 2008, which involves the interaction between gravitational mass and electric charges, is applied to compact objects like white dwarfs and neutron stars because it is considered comprehensive and consistent.
Category: Astrophysics

Thick Sequences

Authors: Joseph Pe
Comments: 7 Pages.

We call an integer sequence thick if the quotients formed from its terms are dense in the set of real numbers. To find thick sequences, we consider the geometric, Fibonacci, power, and prime sequences. We show that the sequence of primes is thick provided that a conjecture DC-2 holds. DC-2 says that certain pairs of linear Dirichlet conditions have infinitely many solutions. It is a weak form of Dickson’s conjecture, which states that a finite system of linear Dirichlet conditions has infinitely many solutions and generalizes Dirichlet’s well-known result on primes in arithmetic progressions. Also, we obtain partial results for the general thickness problem for an arbitrary sequence and look at heuristic evidence for the validity of DC-2. We conclude with a short list of problems for further research.
Category: Number Theory

The Sedenion-Trigention Soul Theory: A Mathematical and Metaphysical Framework

Authors: Moninder Singh Modgil, Kavita Rohit
Comments: 4 Pages. (Note by viXra Admin: This article is speculative/exploratory)

This paper explores the intersection of higher-dimensional algebra and metaphysical consciousness by formulating a novel framework in which souls are modeled as sedenions (16D algebraic entities) and Shiv Baba (the Supreme Soul) is represented as a trigention (32D hyper-structure). By extending the quaternion-octonion algebra into non-associative and fractal consciousness structures, we propose a model in which the journey of the soul through time, karma, and enlightenment can be mathematically described. This paper also discusses implications for quantum consciousness, spiritual liberation, and cosmic order.
Category: Religion and Spiritualism

Bayesian Approach to Hypothesis-Based Randomness Estimation

Authors: Alexander Rozenkevich
Comments: 6 Pages.

A Bayesian method for dynamic hypothesis-based randomness estimation of a sequence of experimental data is proposed. Examples of pseudorandom number generator testing are given.
Category: Statistics

Bayesian Approach to Hypothesis-Based Randomness Estimation (in Russian)

Authors: Alexander Tozenkevich
Comments: 6 Pages.

A Bayesian method for dynamic hypothesis-based randomness estimation of a sequence of experimental data is proposed. Examples of pseudorandom number generator testing are given.
Category: Statistics

Gravity and Black Holes

Authors: A. J. Owen
Comments: 8 Pages.

The question of how Newton's inverse-square law of gravity relates to general relativity (GR) is discussed in this paper. In GR, gravity is considered as a consequence of space and time curvature, whereas Newton's law is restricted to a flat space. Logically, then, Newtoniangravity must relate solely to the time curvature contribution in GR. Instances where Newton's law does not describe phenomena correctly, such as the perihelion rotation of the planet Mercury and the bending of starlight, are therefore attributable to spatial curvature. The GRsolution for a static point mass, calculated on this basis for correspondence with Newton's law, is entirely regular and agrees with all theusual predictions of GR except the one leading to an event horizon. This suggests that the currently accepted model of a static black-hole,although mathematically possible, is non-physical. Not only is there no horizon in spacetime, but gravitational attraction between two masses does not diverge to infinity as they approach each other. This means there is no singularity at the origin of coordinates where physical laws would break down, and relative speeds do not exceed the speed of light.
Category: Relativity and Cosmology

A New 3D Spherical Coordinates Warp Drive Vector with Hodge Star Over the Y-Axis and Variable Speeds Using the Natario Methodology

Authors: Fernando Loup
Comments: 51 Pages.

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than lightpredated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or togenerate a warp drive spacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates over the x-axis but remember that a real warp drive must accelerate orde-accelerate in order to be accepted as a physical valid model so it must possesses variable speeds.We developed in this work a newwarp drive vector for the y-axis in both Polar and Spherical coordinates that encompasses variable speeds.Also Polar Coordinates uses only two dimensions and we know that a realspaceship is a tridimensional 3D object inserted inside a tridimensional 3D warp bubble that must be defined in real 3D Spherical Coordinates.
Category: Relativity and Cosmology

On Area Element in Polar Coordinates

Authors: Sanjeev Saxena
Comments: 3 Pages.

A simple and elementary derivation for formula for area element in polar coordinates is given.
Category: General Mathematics

De Broglie Hypothesis and the Schrödinger Equation: [Plausible] Errors in Mathematics, Physics, Formal Logic, and Dialectics

Authors: Temur Z. Kalanov
Comments: 14 Pages.

The irrefutable proof of the incorrectness of the de Broglie hypothesis (postulate) and the Schrödinger equation (postulate) is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable conclusion: the de Broglie hypothesis (idea, postulate) and the Schrödinger equation (idea, postulate) are gross errors in mathematics, physics, formal logic and dialectics. This conclusion is based on the following statements: (1) from the point of view of Euler's formula and the Maclaurin series, the definition of the wave function has neither physical nor mathematical meaning; (2) the substitution of the quantities of energy and momentum, which characterize a quantum (microscopic) particle, into the relationship that describes a macroscopic radiation wave is a gross formal-logical error, because a quantum particle and macroscopic radiation are not identical material objects; (3) in the dialectical and formal-logical points of view, a free classical particle is not identical to a free quantum particle: these particles are non-identical material objects. Therefore, the substitution of the quantities of energy and momentum, characterizing a quantum (microscopic) particle, into the classical relationship that describes the energy and momentum of a classical particle is a gross formal-logical error; (4) in the point of view of formal logic, the concepts of "corpuscular aspect" and "wave aspect" are contradictory (mutually exclusive) concepts. (The concepts of "particle" and "wave" are defined by different essential features of material objects). Therefore, the de Broglie wave function and the Schrödinger wave equation represent a violation of the formal-logical law of lack (absence) of contradiction. This means that the concept of corpuscular-wave dualism is erroneous; (5) The de Broglie wave function and the Schrödinger equation represent a gross dialectical error, because the dimensionless wave function contradicts to the dialectical concept of the measure of a material object (i.e. the dimensionless wave function does not have the qualitative determinacy of a material object, does not characterize the properties of a material object). Therefore, the de Broglie wave function and the Schrödinger equation are meaningless relationships.
Category: Mathematical Physics

The Concepts of Web3 First Represented in 2013

Authors: Andrei I. Bodrenko
Comments: 19 Pages.

The concepts of Web3 were first represented by Andrei I. Bodrenko in 2013. Andrei I. Bodrenko stated that the new iteration of the Internet is based on serverless technologies comprising such features as: serverless data exchange, serverless electronic mail, serverless private networks, serverless social networks, decentralization, and these features are carried out by using peer-to-peer overlay computer networks operating over the Internet. It is significant that blockchains are typically managed by a peer-to-peer (P2P) computer networks, and the implementation of the blockchain is done without the need of a trusted authority or central server. Andrei I. Bodrenko invented Web3 in 2013 by publishing: the video report at the largest Central & Eastern European conference in the field of Software Engineering (see for details: Presentation 2013 (slides 18-24) and Report video 2013 (minutes 12-18)), and by publishing Patent document RU2013154454A representing the key feature of Web3 in December 06, 2013.
Category: General Science and Philosophy

Simulated Algorithms for Lives

Authors: Shuai Liu
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper summarizes the characteristics of neural networks.This paper focuses on challenging the sudden randomness of gene mutation and explaining the active source of mild gene mutation.In this paper, a life algorithm framework that simulates the changes of genes by neural networks combined with genetic algorithms is taken as an example to show that genes can maintain overall stability and actively update at the same time, presenting a random exploration that maintains relatively small scope in general, and thus species evolution.It is necessary to keep the exploration of randomness small. This article breaks the shackles that genes determine everything in life. Genes and neural networks are both important. In addition to innate genes, people's ability to learn, update, shape themselves, and explore is particularly important.This paper points out the importance of neural networks in the evolution of species. Different from the view that neural network is only the intelligent organizational structure of human brain, this article extends the above view, neural network is also an important intelligent structure of cells, and neural network is also an important intelligent structure of organs.
Category: Artificial Intelligence

The Game Show Problem

Authors: Richard L. Hudson
Comments: 2 Pages.

The game show problem aka Monty Hall problem [1], originated when Craig Whitaker posed a question of a wining strategy for a modified 3 door game show to Marilyn Savant who wrote articles for Parade magazine. Her 1990 response was to switch doors when given the option. [2] [3] The debate of probability of success as 2/3 vs 1/2 has continued until today. This paper reveals errors in her response.
Category: Set Theory and Logic

Does Time Dilation Reveal a Variable Speed of Light?

Authors: Branimir Spigel
Comments: 16 Pages.

A reexamination of the well-known Hafele-Keating time dilation experiment reveals an overlooked assumption in standard interpretations. The time interval measurements for all clocks began and ended simultaneously in the laboratory, implying that their measured intervals should be identical. This raises questions about the conventional view that these intervals differ in duration due to motion. A deeper analysis revealed a fundamental issue: applying the same standard seconds to all intervals disregards the fact that moving clocks tick at a slower rate. This implies that the duration of a time unit on a moving clock is longer than a standard second. To resolve this inconsistency, we introduce the concept of variable time units. We further propose modifying the time dilation formula by defining time intervals in terms of discrete clock ticks rather than fixed-duration units, demonstrating that the ratio of time units follows directly from the ratio of clock ticks. However, adopting variable time units leads to the inevitable conclusion that the speed of light must also be variable, contradicting Einstein’s postulate of its invariance. From this perspective, while the Hafele-Keating experiment is widely regarded as empirical confirmation of Einstein’s theory of relativity, a closer analysis suggests an alternative interpretation that questions the assumption of a universally constant speed of light.
Category: Relativity and Cosmology

Convergence and Divergence Analysis of the Qx+r Problem

Authors: Song Li
Comments: 4 Pages.

This paper investigates the convergence and divergence of the $qx+r$ problem (Crandall conjecture), which is a generalization of the $3x+1$ problem (Collatz conjecture). Through probabilistic analysis, we establish that the convergence condition for the $qx+r$ problem is $q<4$,and predict that it converges to the precise value $frac{r}{4 - q}$ ; when $q>4$, the transformation sequence diverges to infinity. The results of this study provide new insights into understanding the dynamic behavior of the $qx+r$ problem.
Category: Number Theory

Prime Gaps and Asymptotic Behavior of Primes: A Hypothetical Approach

Authors: Hyeon Jun Ahn
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Based on heuristics related to Cramér's conjecture, this paper proposes a suitable hypothesis and investigates its implications. The study encompasses prime gaps, Andrica's conjecture, the mean of consecutive prime numbers, and a detailed analysis of Oppermann's conjecture.
Category: Number Theory

Resolution of Wave and Particle Nature of Electro-Magnetic Radiations from Maxwell’s Theory

Authors: Bijon Kumar Sen
Comments: 13 Pages. 2 Figures

The implications of Maxwell’s theory that combine magnetic, electrical and opticalproperties of electromagnetic radiations were not understood properly at the time of itsinception. It is shown here that mathematical restriction helps to resolve this centuries-oldcontroversy about wave-particle duality of electromagnetic radiation. This goes against theusually accepted notion that particles have wave properties and vice versa. The distinguishingfeature lies in the fact that particle motion requires no medium and is thus free from Dopplereffect. On the other hand, the wave motion depends on the medium of propagation and is,therefore, affected by Doppler effect. The particle motion is guided by particle (quantum)mechanics and the wave motion is guided by wave mechanics.The particle description of electromagnetic radiation was advanced by Einstein inproving the constancy of the velocity of light which is independent of the medium and theperception of simultaneity of events in different inertial frames. On the contrary, the wavemechanical approach was used by the adversaries of Einstein’s idea who pleaded for the spatialand temporal description as the result of Doppler effect. The arguments of both the sides areequally valid as the same problem was examined from opposite angles.The ideas of Red Shift, Tunnel effect, Photoelectric effect and Magnetic forces areexamined considering above viewpoints. The Red Shift conforms to the ideas of particle (Q)mechanics while the Tunnel effect can be interpreted in terms of wave mechanical perception. Photoelectric effect and magnetic forces are contributed by both wave and particle mechanics. The idea of electron spin, however, remains bizarre even around the centenary celebration year of wave and quantum mechanics.
Category: Quantum Physics

Galaxy Formation, Merging and Expansion of Dark Energy Fields, New Gravitational Fields, and the Reason for the Flatness of the Rotation Speed of Spiral Galaxies

Authors: Ichiro Nakayama
Comments: 10 Pages.

There are hundreds of billions of galaxies in the universe. These galaxies can be broadly divided into dwarf galaxies with less than a billion stars and giant galaxies with more than a billion stars. The most widely used classification of giant galaxies is the "Hubble sequence" proposed by American astronomer Edwin Hubble in 1926, which lists four types: elliptical galaxies, spiral galaxies, barred spiral galaxies, lenticular galaxies, and irregular galaxies. As can be seen from the diverse shapes of galaxies, it is thought that various factors are involved in the formation of galaxies. However, there must be a basic principle by which a group of more than a billion stars forms. In this study, we considered the formation of galaxies by extending the formation of stars, gravitational fields, and dark energy fields according to the Energy Body Theory. As a result, we found that the reason why spiral galaxies, which account for 60% of galaxies, have a spiral shape is fundamentally due to the rotation of the galaxy and the expansion of the dark energy field. The spiral arms were formed when a small group of stars rotating in the counter-rotating direction near the bulge approached the bulge, causing them to unravel and extend along the arms. It is also thought that energy flows into the spiral of the dark energy field from the outside, forming a high-energy space. However, it remains to be seen whether this theory is superior to the "high density wave theory," the mainstream explanation for spiral arms. The flatness of the rotation speed of spiral galaxies, an important issue in astrophysics, is thought to be caused by the neutralization due to synthesis of the spiral of the galaxy when the gravitational field is formed, and the rotation according to Kepler's laws.
Category: Astrophysics

Astro Sociology the Physical Universe as a Reflection of Consciousness

Authors: Alon Retter
Comments: 13 Pages.

This paper proposes a groundbreaking paradigm: the universe is a reflection ofconsciousness. Nearly a century ago, quantum mechanics introduced the concept of theobserver to explain experimental anomalies. Th is led many prominent physicists toargue that consciousness is fundamental and precedes matter. While this idea wassubsequently marginalized within physics, I contend that consciousness is essential for acomprehensive understanding of the universe.Tosupport this notion, this paper presents extensive evidence for consciousness fromphysical processes and astronomical objects. In addition, t he Astro Sociology model,which I introduced in 2010, posits that the universe reflects consciousness. This paperrevisits and expands upon the remarkable structural and numerical parallels betweenastronomical phenomena and human behavior. It subsequently outlines six predictionsof the model that have been empirically or theoretically confirmed. Finally, it brieflydiscusses ongoing research, including a novel quantum gravity model, that incorporatesthe observer to explain dark matter and dark energy without requiring additionalparticles.
Category: Astrophysics

Prime Cycles in Quantum Spacings and Zeta Zeros: A Number-Theoretic Bridge Between Classical and Quantum Physics

Authors: Daniil Beliavkyi
Comments: 4 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

We analyze eigenvalue spacings from quantum simulations and refined untwisted zeta zeros—Riemann zeta zero approximations adjusted with prime-based oscillations—achieving near-convergence to the Gaussian Unitary Ensemble (GUE). Quantum spacings yield a Kolmogorov-Smirnov (KS) statistic D = 0.1159 with p = 0.0658, surpassing the 0.05 threshold, while refined zeros achieve D = 0.0901 and a Cramer-von Mises (CvM) p = 0.9465, indicating exceptional GUE alignment. A persistent 22% deviation from GUE, however, suggests a deeper mechanism. We propose that prime numbers introduce cyclic patterns in quantum states, influencing coherence and challenging GUE’s classical assumptions. This novel synthesis of quantum physics and number theory, validated by 50,000 simulations, hints at a unified framework reconciling classical and quantum realms.
Category: Number Theory

The Overlooked Geometric Conflict Between Special Relativity and Sommerfeld’s 1909 Spherical Model

Authors: Aswan Korula
Comments: 7 Pages.

Special Relativity (SR) assumes that velocity vectors, displacement vectors and direction vectors coincide, since they are projected onto a flat analytical space (Minkowski space) to interpret inertial relative motion. In contrast, Arnold Sommerfeld’s 1909 spherical model interprets velocity composition on a spherical surface, where displacement and constant direction vectors are fundamentally distinct. This paper demonstrates that because Einstein and Sommerfeld use different surfaces to project their interpretation of the Michelson-Morley interferometry, their predictions for relativistic effects diverge. Specifically, while Einstein’s model necessitates Lorentz contraction and time dilation, Sommerfeld’s spherical formulation predicts no such distortions. Notably, compatibility between SR and Sommerfeld’s spherical model exists only in the special case of two right-angled triangles. By extension, any hyperbolic model that claims compatibility with SR must also be restricted to this special case. This work highlights a fundamental geometric conflict between Special Relativity and Sommerfeld’s alternative formulation, warranting further examination of the geometric nature of inertial motion.
Category: Relativity and Cosmology

Resolving the Gravity Freefall Paradox: A Sine-Alpha Model for Dynamic Spacetime Curvature

Authors: Aswan Korula
Comments: 6 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper presents a novel resolution to the gravity freefall paradox, where General Relativity (GR) appears to introduce prematurespatial contraction effects that contradict Newtonian expectations. The paradox arises from the fact that GR predicts the same exter-nal gravitational field for both a physical mass and a black hole, yet point mass freefall marker behavior differs in both cases. We introduce the sine-alpha function, a dynamic formulation that naturally regulates spatial curvature according to the evolving ratio of marker separations. This model predicts Newtonian behavior outside the event horizon while dynamically allowing self-regulated curvature inside it. Our model preserves logical consistency between classical and relativistic physics. We provide evidence from numerical simulation, comparing our function’s predictions to GR, demonstrating its stability within and beyond the event horizon. We restrict ourselves to theoretical considerations only.
Category: Relativity and Cosmology

Measuring Global Instability: A Unified Framework for Methodical and Logical Assessment

Authors: Rhylie De Graaff
Comments: 19 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The aim of this paper is to demonstrate that global instability can be measured mathematically, when using accurate data provided. When the data is available it is possible to predict when Nation states will fall using a variety of existing economic tools but by combining them together into one overarching framework. The data used when determining the outcome of nation states includes several factors, such as the level of civil disobedience, protests, the policies being brought forward as well as economic factors such as Purchasing Power, Cost of Living, and economic debt. The paper will show that there is a clear link between civil dissonance levels and the likelihood of a collapse of a nation. A table of the determining and observable factors has been provided to make the analysis easier for those conducting research and allow for the theories contained in this paper to be testable and be repeated.
Category: Economics and Finance

On the Feigenbaum Attractor and Feynman Diagrams

Authors: Ervin Goldfain
Comments: 24 Pages.

It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics

The New Conception of Absolute Truth and the End of Anthropocentrism

Authors: Gennady Shkliarevsky
Comments: 37 Pages.

The ascendance of relativism has defined the politics, social relations, values, science, and other aspects of modern civilization and its practice. While some effects of relativism are salutary (relativism, for example, has promoted greater tolerance), others are not. This article argues that the ascendance of relativism has led to the demise and ultimate rejection of the concept of absolute truth. As the article explains, absolute truth is a very important operational concept that integrates, regulates, and conserves all spheres of human practice. It enhances human capacity to create new and increasingly more powerful levels of mental organization that are the source of radical innovations: new ideas, theories, and approaches. The article explains that the functional role of absolute truth is essential for sustaining human civilization and its evolution. It demonstrates that the functional role of absolute truth is defined by the universal process of creation. The rejection of absolute truth has been an inevitable result of the anthropocentric tradition that has dominated and continues to dominate human civilization. This tradition fails to recognize the central role of the process of creation in human existence. It is exclusionary and is incompatible with objectivity. This tradition poses a threat to the survival of civilization. The article argues that the revival of absolute truth and its role in human practice will ensure the survival and evolution of human civilization. The article offers a new conception of absolute truth. This conception relies on the universal process of creation as its main organizing principle. Due to its inclusive nature, the process of creation is objective, universal, and invariable under transformation. Since the new conception is based on the process of creation, it also possesses its properties; it is objective, universal, and invariable. It is not transient as the past conceptions of absolute truth. Finally, the article discusses the ways in which the new conception of absolute truth will affect human practice.
Category: General Science and Philosophy

Atomic Spectrum by Electrometrication of Space and Quantum Nature of Motion

Authors: Sergio de Azevedo Melo
Comments: 53 Pages. In Portuguese

The electrical nature of the particles that make up the atom allows the prediction of the electromagnetic emission spectrum, resulting from the mechanics between the particles involved. However, the radiation process described by quantum physics is different from the understanding made by ordinary electromagnetism. The understanding of fission is discussed by the correspondence principle.The proposed curvature produced by the elementary electric charge and the representation by an electrometric tensor make it possible to address aspects of classical and quantum theories using the same formulation. The electron does not fall into the nucleus, as it follows a geodesic trajectory. The resolution of the atomic binary system encounters self-induced harmonic oscillations that produce fluctuations in the metric, with consequences in the determination of the point representation and in the position-momentum simultaneity in the same reference frame. The energy of the orbital transition by the electron, according to the spectrum of the hydrogen atom, reproduces the discretization and ripple effects as a consequence of the resolution. The result endorses how the correspondence between electromagnetic radiation processes is understood by electrometric curvature.
Category: Relativity and Cosmology

[Speculation/Exploration on the] Design, Expression, and Oral Delivery of a Recombinant Fusion Protein (Tp0751—CtB—TprK) in Yeast as a Candidate Syphilis Vaccine

Authors: Hyunho Shin
Comments: 9 Pages. (Note by viXra Admin: This article is speculative/exploratory)

Syphilis, caused by Treponema pallidum, has resurged globally in recent years, particularly in East Asia, highlighting the urgent need for preventive vaccines. Despite being a well-characterized pathogen, traditional vaccine development for T. pallidum faces substantial challenges due to its inability to be cultured in artificial media. This study presents the development of a novel oral vaccine candidate utilizing recombinant T. pallidum outer membrane proteins TprK and Tp0751 expressed in yeast (Saccharomyces Boulardii). Our approach incorporates a gene cassette containing the conserved N-terminal region of TprK, cholera toxin B subunit (CtB) as an immune adjuvant, and Tp0751, connected by glycine-serine flexible linkers under the control of the ADH promoter. This strategy aims to overcome the cultivation limitations of T. pallidum while potentially inducing protective mucosal immunity through oral administration. Structural analysis using AlphaFold predictions confirms the stability of the recombinant construct. This research represents a significant advancement toward developing an accessible and effective vaccine against syphilis, with important implications for global public health.
Category: Physics of Biology

The Higgs Boson May Be Made of Higher Dimensional Matter

Authors: D. G. Grossman
Comments: Pages.

The Higgs boson may not be the heaviest particle created by man so far (it is exceeded by the top quark), but it may be the highest dimension particle created by man so far. If calculations are correct, it may be of dimension 20/21 (the top quark is dimension 9/10), that is, it may be composed of 20-dimensional matter (quarks) circulating in the surface of a 21-sphere. Recent Higgs boson mass measurements of high accuracy, and a mass factoring technique based on n-sphere surface volumes, which was derived from Planck's Energy-Frequency Relation, E=hf, were used to reach that conclusion. A power of two factoring, which is a possible indication of stability, was found within 3 MeV of the ATLAS group's recent 125,220 MeV improved accuracy estimate of the Higgs's mass. The S21h power of two factoring found, (2^16 - 2^10) S21h, translates to a mass of 125,217.08 MeV, which is very close to the ATLAS group's result. Is the Higgs boson made of 20/21 dimensional matter?
Category: High Energy Particle Physics

Decoding International Gold Transfers: Official Narratives and Alternative Conjecture Casting Shadows of Preparation

Authors: Masashi Ishihara
Comments: 14 Pages.

This paper examines the 2024-2025 movement of approximately 400 metric tons of gold from London to New York through the lens of three competing explanatory frameworks: the Mainstream Official Narrative involving arbitrage opportunities and potential tariff concerns, a Controlled Conspiracy Theory regarding missing US gold reserves, and an Unrestrained Alternative Conjecture grounded in historical precedents during times of crises and wars. Using this case study, we develop a model for understanding how multiple narratives function within modern information ecosystems, particularly in the post-COVID era where institutional trust has declined. We argue that the coexistence of these narratives serves distinct social and political functions beyond merely explaining the gold transfers themselves.
Category: Social Science

Causal Set Theory with Occamistic Precedence: A Speculative New Approach to the Emergence of Quantum Mechanics, Spacetime Structure, Gravity, Psi Phenomena and Universal Cognition

Authors: Ben Goertzel
Comments: 47 Pages.

We propose an augmented precedence principle that integrates an algorithmic information prior to favor simpler, low-entropy patterns in the evolution of causal sets. Applied to the sequential growth dynamics of causal set theory, this Occamistic bias naturally selects manifold-like configurations that approximate smooth spacetimes, thereby addressing the entropy dominance problem. On these emergent manifolds, the statistical accumulation of repeated quantum events gives rise to effective quantum dynamics from which the Schroedinger equation is derived. This perspective shows promise of potential extension to chromodynamics; and moreover, by interpreting the spacetime metric as a quantum operator and deriving gravitational dynamics from the minimization of quantum relative entropy between the intrinsic metric and a matter-induced metric, one can establish a connection with entropic theories of gravity. The Occamistic Precedence framework is extended to a relational, Universal Cognition perspective in which the decentralized cosmic ledger "remembers" its past through local interactions, enabling observer-dependent transitions between quantum (Schroedinger-like) and classical (Bellman-like) cognitive regimes providing physical underpinning to mental processes in biological and engineered systems, and potentially also providing a new way of looking at "extraordinary" mental processes such as altered states of consciousness and psi phenomena. Overall, our work suggests that gravity, quantum mechanics, and anomalous cognitive effects may emerge from an underlying, history-dependent process governed by fundamental information-theoretic principles.
Category: General Science and Philosophy

The Search for Life and Aliens

Authors: James R. Johnson
Comments: 13 Pages. Astrophysics or Biophysics may be a better science category.

This article is a comprehensive survey describing our search for life and aliens beyond earth. The search for life inside our Solar System continues by digging into the Martian soil and exploring the underground oceans of Jupiter’s moon Europa. As we peer into the Milky Way, exoplanets are the target. Improved sky-survey telescopes identify exoplanets. Then, subsequent analysis using spectrographs obtained via exoplanet transits or direct imaging hope to identify biosignatures. Detection of intelligent life is either circumstantial or definitive. Technosignatures offer circumstantial evidence of alien civilizations. Definitive or positive detection can be physical, for example, discovering interstellar objects (spaceship/UFOs) or as in the movie Contact, an alien message. Future giant optical/infrared telescopes, sophisticated radio telescopes, and a proposed space telescope, HWO, will dramatically enhance detection. Significant technical advances in earth-based and space telescopes, documented in four key figures, dramatically improve the probability of discovery over the next ten years. Thus, we may soon have an answer to the question, are we alone?
Category: Astrophysics

Disprove of a Proof of Euler's Formula

Authors: Sigrid M.-L. Obenland
Comments: 2 Pages.

In 1991, Gilbert Strang published a proof of Euler's formula using polar coordinates in Calculus, Wellesley-Cambridge, p. 389. In the following we show that this alleged proof is not valid.
Category: Functions and Analysis

What can save NATO? Stand for Ukraine!

Authors: Dainis Zeps
Comments: 7 Pages. (Note by viXra Admin: This article may not be within the scope of viXra and is subject to withdraw)

This article argues that NATO’s survival hinges on supporting Ukraine against Russia’s aggression, as Donald Trump’s actions threaten to dismantle the alliance. Written on March 9, 2025, it critiques Trump’s apparent intent to abandon Ukraine—via halted aid, a predatory $500 billion resource deal, and alignment with Russia—while urging Europe to reboot NATO without the US. Highlighting Russia’s looming collapse and Ukraine’s role as democracy’s defender, the author calls for defiance against Trump’s betrayal to preserve the democratic world.
Category: Social Science

Comment on Article Entitled "Co2 Chemisorption Behavior in Conjugated Carbanion-Derived Ionic Liquids Via Carboxylic Acid Formation"

Authors: Vitaly V. Chaban, Nadezhda A. Andreeva
Comments: 6 Pages.

The paper in the title proposed an interesting chemical sorbent for CO2, exemplifying unusual chemistry, and reported promising chemisorption capacities. The carboxyl moiety formation was highlighted as the only CO2 chemisorption product. We would hereby like to question the chemical identity of the CO2 chemisorption product reported in this publication. The considerations in favor of a different product are provided in this Comment based on general chemical wisdom, critical re-interpretation of the experimental research, and new ab initio calculations.
Category: Chemistry

Fraction Algebra

Authors: Huhnkie Lee
Comments: 55 Pages.

This paper will explore fractions and introduce brand new concepts related to fractions. We will also introduce related ideas such as Iverson transformation, inverse Iverson transformation. We will also introduce theorems related to flooring and ceiling functions.
Category: Algebra

Fishers’ Perceptions on Derelict Fishing Gears’ Causes, and Mitigation Measures in Korea

Authors: Sunwook Hong, Jongmyoung Lee, Jongsu Lee, Won Joon Shim, Sehan Lim
Comments: 18 Pages.

Derelict fishing gears (DFGs) present a high damage risk for marine ecosystems, navigation safety, fishing resources, and the economy. To mitigate this damage, considering fishers’ roles is very important, because they are the main contributors directly exposed to the impact. Since DFGs are significant sources of marine debris in South Korea, we conducted a survey to evaluate fishers’ perception of DFGs’ causes, reasons, and measures, based on FAO’s and UNEP’s 2009 suggestions. We also examined which governmental measures they preferred to help decrease DFGs. A total of 134 people participated in the 2015 survey, comprising 55 from capture fishing and 79 from aquaculture. The fishers answered that DFGs are abandoned, discarded, and lost in similar proportions. In terms of abandoned DFGs, they selected similar degrees of impact regarding ‘illegal, unreported andunregulated fishing,’ ‘illegal gear,’ and ‘too much gear for time.’ For discarded DFGs, they mostly agreed that ‘chosen over onshore disposal’ and ‘damaged gear’ were more serious causes than ‘too much gear for space.’They answered that ‘misplaced gear’ causes less lost DFGs than ‘gear conflict,’ ‘poor ground condition,’ and ‘extreme weather.’ In total, the fishers found ‘improving port facilities’ and ‘retrieval activities’ as more effectiveand feasible measures than others. They positively evaluated the Korean government’s existing measures, and preferred ‘mandatory return’ and ‘strengthening gear marking’ for future improvement measures. This study couldfurther contribute to achieving policy goals more effectively and efficiently.
Category: Social Science

Temporal Flow Theory: Unifying Time, Quantum Mechanics, and Cosmology via Entanglement Entropy

Authors: Matthew Warren Payne
Comments: 5 Pages. (Note by viXra Admin: The typesetting has mistakes!)

Temporal Flow Theory (TFT) redefines time as a dynamic four-vector field (W^μ) sourced by entanglement entropy gradients, unifying quantum mechanics, gravity, and cosmology. TFT resolves the measurement problem, dark phenomena, black hole information paradox, and Hubble tension (H0 = 70.5 ± 0.7 km/s/Mpc) using three axioms. It predicts quantum interference shifts (Δφ ≈ 2.1 × 10^-6 rad) and galactic rotation fits (4.7% SPARC deviation), testable with LHC and SKA. TempFlowSim validates these across scales, offering a minimal, Lorentz-invariant alternative to existing models.
Category: Quantum Physics

Relativistic Mass

Authors: Nainan K. Varghese
Comments: 9 Pages.

Abstract: Although the mass of an object is defined to represent the equivalent of 3D matter it contains, it is often considered as the quantity of 3D matter contained in the object. Mass is the mathematical relation between an external linear effort on an object and the rate of rate of its displacement in the direction of the external effort. This relationship is often ignored, and the value of mass is regarded in almost all academic fields as the quantity of 3D matter present in the object. The dependency of the mass of an object on its linear speed introduces changes in the value of its mass depending on the initial speed of the object considered.
Category: Relativity and Cosmology

Expanding Contracted Space Theory (ECST)

Authors: Dale Wahl
Comments: 6 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

We present a conceptual framework that explores an alternative perspective on gravity and quantum mechanics, which I refer to as the Expanding Contracted Space Theory (ECST).ECST proposes that space contracts within mass while simultaneously expanding in different conditions, providing a potential mechanism for gravitational attraction, quantum behavior, and cosmic expansion. The theory aims to address open questions in gravitational physics, such as the nature of dark matter and gravitational lensing, as well as quantum uncertainty and wave-particle duality from a novel perspective.
Category: Quantum Gravity and String Theory

Two Separate Derivations of the Shannon Entropy Equation from First Principles and the RTA Framework for Information

Authors: Vasant Jayasankar
Comments: 38 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable; and there are missing symbols in formula/equations!)

The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems. Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations. By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics

Massive Photon Interactions in Longitudinal Displacement Current

Authors: Arvin D. Sharma
Comments: 3 Pages.

We show the scalar field defined in the vectoralform of Maxwell’s equations is found to break the Lorentz Gauge in the case of massive photons. Using the biquaternion form of Maxwell’s equations, the differential forms of the scalar field is shown to have relation to photon mass. We show both the scalar field gradient and photon mass are related to thedisplacement current using the Proca equations, and propose a means to determine the spatial geometric structure of the massive photon based on its intrinsic capacitance.
Category: Quantum Physics

Potential Evidence for Evolving Spacetime Dimensions from DESI

Authors: Ervin Goldfain
Comments: 9 Pages.

Recent results reported by the Dark Energy Spectroscopic Instrument (DESI) suggest that Dark Energy (DE) may be weakening over time. The hypothetical time-dependence of DE raises a major challenge to standard cosmology, which is built on the assumption that DE represents the cosmological constant (CC) of Einstein’s equations. Here we point out that DESI’s findings reinforce the conjecture that, a) well above the range of electroweak interactions, spacetime dimensionality is continuous and runs with the observation scale, and b), the energy content of the CC stems from the cumulative contribution of energies stored in the fractal structure of Dark Matter/Cantor Dust.
Category: Relativity and Cosmology

The Method of Dividing the 60° Angle Into Three Equal Parts

Authors: Hongfa Zi, Hongyun Zi
Comments: 5 Pages.

The problem of dividing a 60° angle into three equal parts in modern mathematics has not yet been solved. This involves the infinite extension of this trigonometric function in a generalized perspective. After research, it was found that the solution is located between r and two-thirds of r. The former represents a curve, while the latter represents a horizontal line. This article aims to utilize the relationships between various shapes to divide the 60° angle into three equal parts, which can then be extended to any angle less than 180 ° between r and two-thirds of r.
Category: Geometry

Faster-Than-Light Travel Feasible with Negative Mass - Superluminal Dynamics

Authors: Raul Fattore
Comments: 29 Pages.

The study demonstrates that faster-than-light travel requires negative mass. Mass must decrease as velocity increases and must be negative beyond the speed of light.It also proves that there is no absolute speed limit in the universe, contradicting faulty Einstein's theory of relativity and quantum theory. The study also reveals that relative motion depends on relative coordinates, not reference frames.It is demonstrated that gravitational and inertial control of mass is the basis of faster-than-light travel. A hypothetical spaceship is described, and physical calculations are made to demonstrate the possibility of traveling faster than light. The study also explores the potential effects of gravitational interaction and collisions. The technology is proposed for instantaneous cosmic communication and other applications of negative mass using the free energy of the gravitational field.* Is faster-than-light travel indeed possible?* What kind of propulsion could achieve such a technology?* Could any matter be traveling faster than light?* Could living beings be traveling faster than light?* What could be the consequences of that?The above questions will be scientifically answered through this study in accordance with the negative mass theory.
Category: Astrophysics

Investigating Cyclic Gravity and Cosmology (CGC) as an Alternative Framework to Standard Cosmology

Authors: Joseph Bakhos
Comments: 18 Pages. This is the revised version.

Cyclic Gravity and Cosmology (CGC) is introduced as an alternative framework to General Relativity (GR) and the ΛCDM model. CGC retains Euclidean space and proposes that gravity is a residual effect of electromagnetism ratherthan a fundamental force. The theory replaces the standard expansion model with cyclic expansion and contraction phases governed by large-scale gravitational oscillations. Redshift in CGC is explained through a combination ofDoppler motion, neutrino interactions, and a refined tired light mechanism. Time dilation and light deflection arise from neutrino scattering rather than spacetime curvature, preserving a Euclidean structure. CGC naturally explains the Cosmic Microwave Background (CMB) power spectrum without requiring inflation, aligns with observed large-scale structure, and provides a resolution to the Hubble tension within a non-expanding space framework. The theory predicts a self-regulating cosmic equilibrium maintained by an outer shell of intergalactic medium, preventing energy loss and sustaining cyclic dynamics. The observed galactic rotation curves, large-scale filament-and-void cosmic structures, and elemental recycling in Active Galactic Nuclei (AGN) are also consistent with CGC’s gravitational model. The purpose of this paper is not to assert CGC as the definitive model of cosmology but to establish it as a framework worthy of rigorous scientific investigation. Given recent challenges to ΛCDM from JWST observations and inconsistencies in Hubble measurements, CGC presents an opportunity to explore alternative gravitational dynamicsand cosmic evolution mechanisms that align with observational data.
Category: Relativity and Cosmology

Nova: A Quantized Spacetime Fluctuation Framework Supporting General Relativity and Quantum Mechanics

Authors: Thura Zaw Oo
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Nova proposes quantized spacetime fluctuations (QSFs)—a scalar field ϕ constrained to Planck-scale vacuum perturbations—as the sole constituent of the universe, with no external background,unifying General Relativity (GR) and Quantum Mechanics (QM) at all scales without invokingextra dimensions, geometric quantization, or traditional gauge bosons. QSFs are both quantizedand dynamic, inducing GR’s tensor gravity through a scalar-tensor coupling (κ =116πG ) derivedstep-by-step from gravitational vacuum energy, where gravity manifests as an inertial-like spreadaction driven by relative differences in QSF densities. Particle masses and fundamental forces emergefrom knotted QSF structures defined by Seifert surfaces: the strong force as the knotting potentialat the bare minimum matter level with genus g = 3 and knot size rknot = 10−15 m, the weak forceas the temporal action strength of the knots with g = 2 and rknot = 10−18 m, the electromagnetic(EM) force as a vibration-like spread across QSF patterns with g = 1 and rknot = 3.86 × 10−13 m,and gravity as the relative QSF fluctuations’ spread action around matter-like QSFs. Antimatterarises from stretched, non-knotted QSF actions, created equally with matter (nknot = nanti =7.7 × 10−141 m−3) but isolated by their distinct dynamics, yielding a global symmetry (ηglobal = 0)with local matter dominance (ηlocal = 5.5 × 10−10) explained without parameter tuning. Time isderived from QSF actions, ceasing where action halts (e.g., ∂tϕ = 0), a concept grounded in therelational nature of QSF dynamics. The QSF creation rate β(t) = 3H(t) governs cosmic evolution,derived from the Hubble parameter with detailed justification, coupling to observable scales throughknot dynamics unified under an SO(5) symmetry of QSF patterns, eschewing particle mediators infavor of energy spreads. Nova generates dark matter via non-knotted fluctuations (ρDM = 8.8 ×10−28 kg/m3), produces dark energy via expansion dynamics at ρDE = 7.15 × 10−27 kg/m3, anddrives cosmic inflation through an early high β-rate phase (βinf = 1.8 × 1034 s−1, achieving 60 e-folds). It resolves singularities with a dynamic finite-core metric and eliminates the Hierarchy andStrong CP Problems as artifacts of linear thinking, requiring no fine-tuning or additional particles.We rigorously test against Planck CMB (H0 = 67.4 km/s/Mpc), LIGO GW150914, and LHC Higgsdatasets, computing densities and masses with Monte Carlo error estimates, and predict a 510 ±20 GeV scalar from knot genus g ≈ 60, CMB B-modes at ℓ > 3000 with ∆CBBℓ = 0.8±0.2 µK2, andsubatomic force deviations, all derived with exhaustive clarity from QSF principles.
Category: Quantum Physics

Kaluza Klein Theory Versus the Possibility that the Electric Field Strength Might be Recognized as a Form of Acceleration

Authors: Moshe Segal
Comments: 24 Pages.

Einstein's Theories are considered as significant theories of the nowadays Science of Physics. However, the nowadays Science of Physics did not provide yet a verified theory for unifying the Gravitation and the Electromagnetism. Kaluza Klein Theory addresses that issue by predicting that there are five dimensions, with the fifth dimension being of the shape of a tiny circle, with a radius of 23 times the Planck length, which is of the order of 10−33 cm. However, because there is no foreseeable technology for verifying that prediction, about that fifth dimension, the Kaluza Klein Theory is not yet accepted as a complete viable theory, which implies that the issue of presenting a theory which unifies the Gravitation and the Electromagnetism is still an open issue. This paper, and several other preprints, by the author of this paper, also tries to address that issue, by presenting an alternate theory, which is also accompanied by a proposal for an experiment, which might either disprove the proposed theory, if the proposed experiment implementation will turn out to be unsuccessful, or, alternatively, provide validity to the proposed theory, if the proposed experiment implementation will turn out to be successful. However, while the Kaluza Klein theory does not challenge significant elements of the nowadays Science of Physics, the proposed theory does challenge significant elements of the nowadays Science of Physics, and as such, might appear, initially, as completely wrong.Thus, this paper concludes that the implementation of the proposed experiment might be an important endeavor, because it might provide validity to the proposed theory, while the Kaluza Klein theory does not seem to be verified, in the foreseeable future, leaving the issue of the Unification of the Gravity and the Electromagnetism as an open issue.
Category: Relativity and Cosmology

Alpha Integration: Universal Path Integrals with Gauge Invariance

Authors: YoonKi Kim
Comments: 23 Pages. Contact email: yk.reserch@gmail.com

We introduce Alpha Integration, a novel path integral framework that applies to wide range of function including locally integrable functions, distributions, and fields—across arbitrary spaces and n dimensions (n ∈N), while preserving gauge invariance without approximations. This method extend to Rn(n ∈N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈Du2032 with formal mathematical proofs. This framework is further generalized to infinite-dimensional spaces, complex paths, and arbitrary manifolds,with its consistency validated through extensive testing across diverse functions, fields, and spaces. Alpha Integration thus offers a robust and efficient alternative to traditional path integral techniques, serving as a versatile tool for mathematical and physical analysis.
Category: Mathematical Physics

On Area Element in Polar and Volume Element in Spherical Coordinates

Authors: Sanjeev Saxena
Comments: 4 Pages. Added new section

A simple and elementary derivation for the formula for the area element in polar coordinates, and the volume element in spherical coordinates is given.
Category: General Mathematics

On the Feigenbaum Attractor and Feynman Diagrams

Authors: Ervin Goldfain
Comments: 24 Pages.

It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of the Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics

The Higgs Boson May Be Made of Higher Dimensional Matter

Authors: D. G. Grossman
Comments: 9 Pages.

The Higgs boson may not be the heaviest particle created by man so far (it is exceeded by the top quark), but it may be the highest dimension particle created by man so far. If calculations are correct, it may be of dimension 20/21 (the top quark is dimension 9/10), that is, it may be composed of 20-dimensional matter (quarks) circulating in the surface of a 21-sphere. Recent Higgs boson mass measurements of high accuracy, and a mass factoring technique based on n-sphere surface volumes, which was derived from Planck's Energy-Frequency Relation, E=hf, were used to reach that conclusion. A power of two factoring, which is a possible indication of stability, was found within 3 MeV of the ATLAS group's recent 125,220 MeV improved accuracy measurement of the Higgs's mass. The S21h power of two factoring found, (2^16 - 2^10)S21h, translates to a mass of 125,217.08 MeV, which is very close to the ATLAS group's result. Is the Higgs boson made of 20/21-dimensional matter?
Category: High Energy Particle Physics

The Search for Life and Aliens

Authors: James R. Johnson
Comments: 13 Pages. Astronomy and Cosmology also possible categories.

This article is a comprehensive survey describing our search for life and aliens beyond earth. The search for life inside our Solar System continues by digging into the Martian soil and exploring the underground oceans of Jupiter’s moon Europa. As we peer into the Milky Way, exoplanets are the target. Improved sky-survey telescopes identify exoplanets. Then, subsequent analysis using spectrographs obtained via exoplanet transits or direct imaging hope to identify biosignatures. Detection of intelligent life is either circumstantial or definitive. Technosignatures offer circumstantial evidence of alien civilizations. Definitive or positive detection can be physical, for example, discovering interstellar objects (spaceship/UFOs) or as in the movie Contact, an alien message. Future giant optical/infrared telescopes, sophisticated radio telescopes, and a proposed space telescope, HWO, will dramatically enhance detection.Significant technical advances in earth-based and space telescopes, documented in four key figures, dramatically improve the probability of discovery over the next ten years. Thus, we may soon have an answer to the question, are we alone?
Category: Astrophysics

Two Separate Derivations of the Shannon Entropy Equation from First Principles and the RTA Framework for Information

Authors: Vasant Jayasankar
Comments: 36 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems.Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations.By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics

Massive Photon Interactions in Longitudinal Displacement Current

Authors: Arvin D. Sharma
Comments: 3 Pages.

We show the scalar field defined in the vectoral form of Maxwell's equations is found to break the Lorentz Gauge in the case of massive photons. Using the biquaternion form of Maxwell's equations, the differential forms of the scalar field is shown to have relation to photon mass. We show both the scalar field gradient and photon mass are related to the displacement current using the Proca equations, and propose a means to determine the spatial geometric structure of the massive photon based on its intrinsic capacitance.
Category: Quantum Physics

The Tri-Quarter Framework: Unifying Complex Coordinates with Topological and Reflective Duality Across Circles of Any Radius

Authors: Nathan O. Schmidt
Comments: 16 Pages.

In this paper, we introduce the Tri-Quarter Topological Duality Theorem, the foundation of a novel mathematical framework that unifies complex, Cartesian, and polar coordinate systems on the complex plane C while equipping the circle T_r of radius r > 0 with a new topological property. Our framework integrates a generalized coordinate system, where real and imaginary components are assigned unique phase pairs, with a structured orientation that elevates T_r to an active separator with intrinsic directional properties. We prove that T_r, as the boundary zone, exhibits topological duality with the inner zone X_-,r (where ||x|| < r) and outer zone X_+,r (where ||x|| > r), ensuring consistent separation between inner and outer radial directions across T_r with a phase pair map encoding additional information. We also introduce the Escher Tri-Quarter Reflective Duality Theorem, proving reflective duality across T_r via a circle inversion map that preserves phase pairs while swapping X_-,r and X_+,r. This approach offers insights into topological separation, orientation, and reflection, facilitating analysis of systems with circular symmetry, with potential applications in fields such as black hole physics, signal processing, and other areas reliant on complex domain partitioning. A case study on quadrant-based transformations demonstrates streamlined directional mappings, geometric elegance, unified classification, and computational efficiency in C. A software tool visualizes some of these concepts, with future work aimed at exploring practical implementations.
Category: Topology

The Tri-Quarter Theorem: Unifying Complex Coordinates with Topological Duality on the Unit Circle

Authors: Nathan O. Schmidt
Comments: 9 Pages.

In this paper, we introduce the Tri-Quarter Theorem, a new mathematical framework with a generalized complex-Cartesian-polar coordinate system on the complex plane (mathbb{C}) and a new topological property. We discuss the coordinate system's construction and prove that the boundary zone (T), defined as the unit circle, separates the inner zone (X_{-}) ((|vec{x}| < 1)) and outer zone (X_{+}) ((|vec{x}| > 1)), where (T) exhibits topological duality with (X_{-}) and (X_{+}) through a novel phase pair assignment and structured orientation that ensures consistent directional separation across (mathbb{C}). This result unifies complex, Cartesian, and polar representations while offering new insights into topological separation and orientation. This framework provides a unified perspective on complex coordinates and a tool for analyzing systems with circular symmetry or boundary-dependent behaviors, with potential applications in fields such as black hole physics, signal processing, and other areas reliant on complex domain partitioning. We also created a software tool to animate the theorem. More work is needed to further develop and apply this framework via the methods of science and mathematics.
Category: Topology