All Submission Categories

A Proof of the Collatz Conjecture via Thermodynamic Entropy Decay, Modular Arithmetic, and 2-Adic Analysis

Authors: Faustino Malena
Comments: 14 Pages. (Note by viXra Admin: Some cited references are not listed; AI assisted article is in general not acceptable))

The Collatz Conjecture is proven using a novel framework combining thermo-dynamic entropy decay (via logarithmic energy potentials and expectation bounds), modular arithmetic (phase space compression in Z/2kZ), and 2-adic analysis (contraction mappings on Z2). This proof demonstrates that all positive integers eventually reach 1 under the Collatz process, entering the cycle 1 →4 →2 →1, as codified by the Banach Fixed-Point Theorem and entropy monotonicity. Rigorous connections are established between ergodic theory (through Lyapunov function construction), algebraic dynamics (via projective limits in modular rings), and non-archimedean analysis (utilizingultrametric contraction properties).
Category: Number Theory

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: 11 Pages.

The Higgs boson is not only the heaviest particle created by man so far, it may also be the highest dimension particle created by man so far. If calculations are correct, it may be of dimension 20/21, 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

Tri-Quarter: Coordinates and Topological Zones with a Structured Orientation and Consistent Directional Separation Across the Complex Plane

Authors: Nathan O. Schmidt
Comments: 5 Pages.

In this paper, we introduce the Tri-Quarter Theorem, a new mathematical framework for defining a generalized complex-Cartesian-polar coordinate system on the complex plane ℂ. We discuss the coordinate system's construction and prove that the boundary zone T, identified as the unit circle, exhibits topological duality with the inner zone X_- (|x| < 1) and outer zone X₊ (|x| > 1), with a trichotomy-defined structured orientation that ensures consistent directional separation. This result unifies complex, Cartesian, and polar representations while offering new insights into topological separation and orientation. Its development was originally intended for quark confinement and black holes, but additional potential applications may include technologies that rely on complex numbers, boundary behaviors, or spatial partitioning in engineering, computing, and applied sciences. We discuss the coordinate system's construction and the theorem's proof. More work is needed to further develop and apply this framework via the methods of science and mathematics.
Category: Topology

Observer Effect and Hidden Variables

Authors: I. Prusis, P. Prusis
Comments: 5 Pages. 3 figures

In modern physics, it is assumed that all particles have both corpuscular and wave properties. The double slit experiment shows that when the properties of a particle are measured, it inexplicably turns into a particle that has no wave properties, i.e. it loses its duality. The analysis of the experiment shows that any particle performs many different motions at the same time. Chaotic thermal fluctuations, part of which is in the transverse direction, zitterbewegung and longitudinal movement (drift) in the direction of the slit. The measuring instrument cancels the transverse oscillations, so the interference pattern fades
Category: Quantum Physics

The Hubble Diagrams Limitations and Surprises

Authors: Martin Schauer
Comments: 12 Pages.

In 1929, Edwin Hubble measured the brightness and redshift of distant stars to calculate their distance and escape velocity. The resulting data, plotted on the now famous Hubble diagram, showed a proportional relationship between distance and redshift. It is important to note, however, that any measurement of a star's brightness (magnitude) also gives its corresponding lookback time. But is the correlation between redshift and lookback time causal or spurious, or is even the correlation between redshift and distance spurious ?In other words, does the redshift brightness plot reflect the spatial or the temporal evolution of the Universe or both, and to what extent? This article shows that there are many different possible events that could lead to the same redshift brightness diagram. For example, the redshift could depend almost entirely on changes in distance, or almost entirely on changes in lookback time. It turns out that the more redshift depends on changes in distance, the less it depends on changes in lookback time, and vice versa. However, due to a lack of data, no one knows what really happened. But many things would be simpler, if one assumed that the redshift depends almost exclusively on the lookback time: The amazing idea of an expanding space would not be necessary. The expansion rate of the universe would be steadily decreasing.Dark energy and the cosmological constant (Einstein's biggest blunder) would not be necessary. Until new discoveries are made, it is not possible to determine what conclusions can be drawn from a redshift brightness diagram.But these inferences are a key pillar of the ΛCDM model. If this pillar wobbles, the whole structure could collapse.
Category: Relativity and Cosmology

PhytoIntelligence: An Open-Source AI-Driven Mathematical Framework for Diagnostic-Specific Phytochemical Formulation for Any Diagnostic

Authors: Marie Seshat Landry
Comments: 15 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

PhytoIntelligence is an innovative, open-source, AI-driven framework designed to revolutionize the development of plant-based nutraceuticals. By systematically integrating advanced techniques in literature mining, molecular docking, pharmacokinetic modeling, bioavailability optimization, synergy analysis, and regulatory compliance, this framework enables the creation of diagnostic-specific nutraceutical formulations for a wide range of health conditions. This document outlines the complete scientific methodology underlying PhytoIntelligence—from initial observations and research questions to hypothesis formulations, methodological design, experimentation, discussion, and final conclusions. While the LC-Phyto formulation for lung cancer prevention and support (comprising 10 bioactive compounds) is used as an illustrative case study, the framework’s modular design makes it universally applicable to any diagnostic.
Category: Quantitative Biology

Interpretation-Independent Proof That Decoherence Is Not Collapse

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

This paper presents an interpretation-independent proof that neither detection nor decoherence explains quantum state collapse. The argument is grounded in experimental results from Proietti et al. (2019), which demonstrate the persistence of quantum coherence despite environmental decoherence. By analyzing the logical consequences of entanglement, detection, and decoherence, this work demonstrates the fallacy of equating detection or decoherence with observation in quantum foundations and establishes a necessary condition for viable interpretations.
Category: Quantum Physics

Collatz Conjecture: A Coordinate System Based Approach

Authors: Eric M. Kelleher
Comments: 24 Pages. (Note by viXra Admin: Author's nameis required on the article)

The Collatz conjecture states any number, N0, after successive computations will always yield one, initiating the recursive sequence of 1→4→2→1→4 because 1 equals itself via (3n+1) 2 for n = 1. Finding a separate recursive sequence excluding 1 would prove the conjecture false. Analysis of the Collatz conjecture with a dual coordinate system (beta tables and gamma tables) revealed only one such recursive sequence is possible. For n, x = N0, the number sequence (6n + 5) forms beta table 2, column 1 and (6n + 1) creates beta table 3, column 1 with each successive column increasing by 22x. The formula (n−1) 3 was used on each beta entry to produce the gamma tables defined by the following sequences, for n = N0: (4n + 3) = m forms gamma table 2, column 1 and (8n + 1) = m forms gamma table 3, column 1 where each successive column increases by 4m + 1. This reveals the (3n+1)2 quotients of all odd numbers connect as follows: (4n + 3) → (6n + 5) and (8n + 1) → (6n +1), accounting for all possible unique connections between odd numbers via (3n+1)2. The differences between connecting sequences are (4n +3)−(6n+5) =2m and (8n+1)−(6n+1)= −2m where the difference only equals zero for n = 0 as follows: (8 × 0 + 1) − (6 × 0 + 1) = 0, indicating the recursive loop as found with (3n+1)2 for n = 1. Using the coordinate system, I herein demonstrate the uniqueness of the only known recursive loop and prove it is the only one of its kind thus solving a major part of the Collatz Conjecture.
Category: Number Theory

Corrections of Exercises and Problems, Part 1: Chapters of Topography, Astronomy and Curves and the Theory of Surfaces

Authors: Abdelmajid Ben Hadj Salem
Comments: 95 Pages. In French

This booklet includes in the first part thecorrections of the exercises and problems of the following three chapters : topography, astronomy and curves and the theory of surfaces.
Category: Geophysics

Detection of Oscillatory Time Dynamics Through Cross-Correlation Analysis of GW170817gfvv Data

Authors: Maksym Strygun
Comments: 4 pages, English. Independent research. Includes detailed cross-correlation analysis of GW170817 data with graphical illustrations. No journal submission. License: CC BY-SA 4.0.

This paper presents a correlation analysis of publicly available gravitational wave data from event GW170817 recorded by the LIGO detectors H1 and L1. The analysis aims to identify periodic oscillations predicted by a recently proposed novel time oscillation model, which describes time as possessing intrinsic spiral and oscillatory dynamics. Cross-correlation between the H1 and L1 signals revealed a maximum correlation at a time lag of approximately -14.37 seconds. This time shift is consistent with the theoretical predictions of the proposed model, suggesting possible intrinsic oscillatory dynamics of time. These findings, if confirmed across multiple events, could provide crucial insights into the fundamental nature of time and its relation to quantum gravity.
Category: Quantum Gravity and String Theory

The Simplest Proof of Fermat's Last Theorem the Proof of Wiles Was Unrelated to the Fermat’s Last Theorem

Authors: Xiaochun Mei
Comments: 13 Pages.

This paper discusses the complex extensions of Riemann Zeta function and complementary formulas of Gama function. By re-writing the Zeta function equation, it is proved that the equation described a relation between the original Zeta function Z(s) and a now function Z(s)=Z(1-s) . But the domains of these two function does not the same and incompatible, so the Riemann Zeta function equation does not hold. It is also proved that the complex extension formula of the present complementary formula of Gama function is wrong. The correct formula is given by strict calculation. The condition 01. Therefore, Riemann Zeta function equation does not hold at any point in the complex plane, and it is meaningless to discuss it.
Category: Number Theory

Transition Predication Models - Literature Review

Authors: Shlomy Shitrit, Eran Arad
Comments: 30 Pages.

The transition of a boundary layer from laminar to turbulent impacts the characteristics of aflow field, but its underlying physics has yet to be well understood. This literature review aims to give an overview of the more widely used approaches to model transition in ComputationalFluid Dynamics (CFD). Several different methods are reviewed: the linear stability analysismethod, the low Reynolds number turbulent closure approach, the correlation-based methods,the intermittency transport method and the laminar fluctuation energy method. The approaches are compared to one another, highlighting their respective advantages and drawbacks.
Category: Mathematical Physics

Root Finding Problem

Authors: Edgar Valdebenito
Comments: 2 Pages.

In this note, we consider the alternative form of the rootfinding problem known as the fixed-point problem.
Category: General Mathematics

Resolution of the Yang-Mills Mass Gap Problem via the Wave Oscillation-Recursion Framework (WORF)

Authors: James Fruit
Comments: 8 Pages. Copyright Licensed under CC BY 4.0. NC © 2025 James Fruit.

This paper presents a rigorous, non-perturbative proof of the Yang-Mills Mass Gap Problem,demonstrating the existence of a strictly positive lower bound for the spectrum of SU(3) gauge boson excitations. The proof is formulated within the Wave Oscillation-Recursion Framework(WORF), introducing a recursive Laplacian operator that governs the spectral structure of gauge field fluctuations. By constructing a self-adjoint, gauge-invariant operator within a well-defined Hilbert space, this approach ensures a discrete, contractive eigenvalue sequence with a strictly positive spectral gap.A recursive contraction mapping theorem is established, showing that the eigenvalues of theLaplacian satisfy a recursive relation of the form lambda(n+1) = rho * lambda(n) with 0 < rho < 1, preventing the accumulation of eigenvalues at zero. The application of the Banach Fixed-Point Theorem guarantees that the lowest eigenvalue remains strictly positive, resolving the core issue of massless gauge bosons in Yang-Mills theory. The transition from classical spectral bounds to the quantized mass spectrum is explicitly derived. The quantum excitation energy of gauge bosons follows E(n) = hbar * sqrt(lambda(n)), leading directly to a nonzero mass gap given by m_gap = (hbar / c) * sqrt(lambda_1) > 0. This result establishes a non-perturbative proof of the mass gap problem, independent of renormalization group methods or numerical simulations. This work represents the first direct application of WORF to a fundamental problem in quantum field theory. The proof is mathematically self-contained and is submitted for formal review by the Clay Mathematics Institute. If validated, this approach provides a transformative new methodfor addressing open problems in high-energy physics and gauge theory.
Category: Mathematical Physics

Noetic Morphisms

Authors: Dara O. Shayda
Comments: 8 Pages.

In March of 1845 Gauss described the conception of an action at a distance, propagated with a finite velocity, the natural generalization to electrodynamics view of Newtonian force. Unsuccessfully, Wheeler and Feynman attempted a new theory for Absorber in 1945 [9]. In their paper there is a detailed reference provided by Prof. Einstein about a relatively unknown physicist named Hugo Tetrode[10,11] and quoted: "The sun would not radiate if it were alone in space and no other bodies could absorb its radiation... If for example I observed through my telescope yesterday evening that star which let us say is 100 lights years away, then not only did I know that the light which it allowed to reach my eyes was emitted 100 years ago, but also the star or individual atoms of it knew already 100 years ago that ‘I’, who then did not even exit, would view it yesterday evening at such and such timeu2026"[11]. The process by which the verb "knew"occurs is modelled by the Noetic morphisms of the arr(Decay) Arrow Category. However this treatise is not about energy emission absorption in nature, rather about their mechanism of information knowledge exchange to make the emission possible.This treatise and its categorical constructions, Universal Properties and symbols pave the way for grammars and functions and operators and Formal Systems (algebras, calculi) of de novo programming languages to describe the nature of specific Emitter Absorber coupling.
Category: Mathematical Physics

A Simple Approach to Understanding the Stress-Energy Tensor

Authors: Mueiz Gafer KamalEldeen
Comments: 4 Pages.

The common method of defining the stress-energy tensor is confusing and inconsistent. In this article, an alternative simple method for definition is presented. The connection between the stress-energy tensor used in general relativity and the stress tensor used in material mechanics contains errors, as all stresses occurring in the material cause an increase in the fields that bind the microscopic parts of the material and affect only the material's density.
Category: Relativity and Cosmology

The Cosmological Constant Problem is not a Problem: it is a Misconception

Authors: Rudi Van Nieuwenhove
Comments: 6 Pages.

The persistent discrepancy between quantum field theoretical predictions of vacuum energy density and the observed value of the cosmological constant suggests a fundamental issue in our understanding of their gravitational effects. We argue that General Relativity developed without quantum mechanical input, is not suited to accommodate zero-point energy as a source term in the Einstein field equations. Instead, we propose that the cosmological constant arises from large-scale curvature effects rather than an intrinsic vacuum energy density. This approach naturally resolves the cosmological constant problem without requiring fine-tuning or exotic physics. Furthermore, we outline how this perspective aligns with the idea that only energy contributions with physical boundaries (e.g., mass-affected zero-point fluctuations) gravitate, while uniform vacuum fluctuations do not.
Category: Relativity and Cosmology

Introducing Pn Power Series in Number Theory: a Novel Way to Classify Natural Numbers

Authors: Pradeep Pant
Comments: 12 Pages. The supplementary file (Table S1) is available at https://bennettu-my.sharepoint.com/:x:/g/personal/pradeep_pant_bennett_edu_in/EcL2EjaiGNJFqyyLEo-SqqcBqEle9TZA32Wk3IAmC0Cy0A?e=LVosYs

Mathematics is a constantly evolving field where the search for new knowledge never stops. Discovering new mathematical series has been crucial for progress, leading to breakthroughs in many areas and offering fresh insights into the world of numbers. In this paper, we describe a new series called the Pn power series. The Pn power series is a superset of many series depending on the value of n. In number theory, we hypothesize a natural number X belongs to a power series Pn if its proper positive divisors (d1 , d2 , d3 ,. . . , X) follow; X^n = d1 * d2 * d3 *. . . * X (where n = 1, 1.5, 2, 2.5, 3, etc.). To illustrate this concept, 12 is a member of the P3 power series as its proper positive divisors, namely 1, 2, 3, 4, 6, and 12, satisfy the equation: 12^3= 1 * 2 * 3 * 4 * 6 * 12 = 1728. Similarly, 196 belongs to the P4.5 power series, with its divisors 1, 2, 4, 7, 14, 28, 49, 98, and 196,following the equation: 196^4.5 = 1 * 2 * 4 * 7 * 14 * 28 * 49 * 98 * 196 = 20,661,046,784. We believe that the implications of this observation are far-reaching, extending beyond number theory into various mathematical disciplines, and have the potential to open up new avenues of research and mathematical exploration.
Category: Number Theory

A New Approach to the Collatz Conjecture:Proof of the Absence of Cycles

Authors: Kwangsun Song
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)

The Collatz conjecture posits that for every natural number, a specific iterative rule leads to 1 or forms a cycle. This paper introduces a simplified Collatz function, inverse Collatz, and double inverse Collatz to prove that no cycles exist beyond the known 1 → 4 → 2 → 1. By analyzing number generation through parameters a and k, we demonstrate the logical impossibility of additional cycles.
Category: Number Theory

The Natural Laws of Compressed Euler Wave Equations

Authors: Marciano Laoang Legarde
Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references)

the Natural Laws of Compressed Euler Wave Equations, it describes how trigonometric functions behave when their inputs are transformed exponentially. It explores how sine, cosine, secant, cosecant, tangent, and cotangent waves undergo extreme compression along the positive x-axis, leading to predictable patterns in their peak values, oscillations, and asymptotic behavior. The paper establishes three fundamental laws governing these transformations, revealing deeper insights into wave behavior under exponential scaling.
Category: General Mathematics

Two Theorems to Verify Goldbach's Strong Conjecture or Refute it by an Uninterrupted Sequence of Composite Odd Numbers in the Interval [n ─ 2n]

Authors: Bahbouhi Bouchaib
Comments: 17 Pages.

Let's assume an even number E that is one unit larger than to the largest prime number we know today. Let's call this prime number Pl. Now we have 0—E/2—E and therefore Pl > E/2. For GSC to be true E must be sum of two primes P1 and P2 such that P1 < E/2 and P2 > E/2. Therefore we have to calculate E — P2 = X. If X is composite GSC is not verified; if X = P1 then GSC is verified. We then calculate E — P2 starting with Pl and all P2 till the one which is the closest to E/2. The question is: are all the Xs resulting from calculated E — P2 = X composites? Is it possible that all Xs might be composite which means non-verification of GSC? By contrast, if only one X is prime, then GSC is true. We see that GSC is much more likely to be verified in this case because a very long sequence of composite numbers is very unlikely to be continuous from E — Pl to E — P2 which is the closest to E/2. In other words there is at least one P2 prime in [E/2—E] such that E — P2 = P1 → E = P1 + P2. The small primes are those that give the most composite numbers because their multiples are the most frequent but it is unlikely that all P2 of [E/2—E] would give composite numbers when calculating E — P2. If anyone, using this procedure, is able to find a sequence of composite numbers E - P2 = X in the whole E/2 — E interval; then He will be the first one who finds the solution to Goldbach's strong conjecture because this means its final rejection, and no mathematician can cast any doubt on his result. However, let us not forget that if only one X is prime, then GSC is true. As long as we cannot find this very precious and historical counterexample of an uninterrupted sequence of composite numbers by E — P2 = X (P2 is in E/2-E interval); Goldbach's strong conjecture will remain true although unprovable. This article gives the TWO THEOREMS of CONGRUENCE-MODULO which always predetermine whether GSC is true or not when calculating E - P2 = X. These two theorems described in this article will predict whether X is prime or composite. Nevertheless, these two theorems require the use of euclidean divisions in series with the calculation of the remainders for each P2.
Category: Number Theory

Experimental Validation of TSVF-SUSY Induced Phase Shifts in Gravitational Waves

Authors: Muhammad Shahzaib Uddin Khan
Comments: 5 Pages.

This paper presents the first statistically significant evidence for a TSVF-SUSY induced phase shift in gravitational waves detected by the LIGO—Virgo—KAGRA (LVK) Collaboration. Through numerical simulations and statistical analysis, using time-domain and Fourier analysis techniques, I find a consistent phase shift of approximately **0.002 radians** across multiple events, including GW150914, GW170817, and GW190521. With a **corrected signal-to-noise ratio (SNR 433.34), recalculated using an improved integration method over the LIGO noise power spectral density**, and a p-value confirming statistical significance, Ianalyze the correlation of this effect with binaryparameters. I find that the TSVF-SUSY phase shift scales with **mass (r = 0.992), spin (r = 0.996), and redshift (r = 0.977)**, suggesting a non-universal effect linked to black hole properties and cosmic expansion. These results provide a testable prediction for future GW detections, particularly with upcoming observatories such as **LISA and the Einstein Telescope (ET)**, which will have enhanced sensitivity to phase shifts in different frequency regimes.
Category: Quantum Gravity and String Theory

Angles Associated with Primes Numbers

Authors: Khazri Bouzdi Fethi
Comments: 1 Page.

This article explores a géometric interpretation of the Riemann zêta function as angle measures.This perspective could explain the spiral arragement of prime numbers,as observed in Ulam’s spiral (1963).
Category: Number Theory

New Wireless Technology not Covered by the Existing Ieee Standards of 2017

Authors: Andrei I. Bodrenko
Comments: 5 Pages.

A new type of wireless computer network is presented in this article. This wireless network, for data transmission, uses visible light, and does not use intensity modulation of optical sources, such as light-emitting diodes and etc. Thus represented wireless network differs substantially from wireless networks covered by the existing IEEE standards of 2017, and its ongoing revisions, for visible-light communication (VLC) technologies, Li-Fi technology and optical camera communication (OCC) technologies. This new wireless technology can be used for the next generation of wireless communication networks such as 5G networks.
Category: Digital Signal Processing

Reasonable Alternatives to the Two Big Problems in 20th-Century Physics

Authors: Gocho V. Sharlanov
Comments: 105 Pages. The content of this monograph is based on 3 published articles.

The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks the real advance in science ("The Evolution of Physics", Einstein & Infeld, 1938). The root cause of the biggest problem in 20th century physics, the "special theory of relativity", is actually the incorrectly accepted and maintained for more than 100 years "postulate of the constancy of the speed of light for all reference frames". The reason for the emergence of this postulate is the incorrect interpretation of the famous "Michelson-Morley experiment". This experiment was based on the inappropriate conceptual design used in Michelson’s "two-way interferometer". All other known experiments: the Sagnac experiment in 1912, the "Michelson-Gale-Pearson" experiment in 1925, and the "One-way measurement of the speed of light" experiments carried out in recent years, indisputably prove that the speed of light is not the same for all frames of reference. The measured speed of light in the frame of reference related to the Earth’s surface differs from the "speed of light in vacuum" and this difference varies depending on the latitude (proven by Michelson himself back in 1925). Michelson published the results of the "Michelson-Gale-Pearson" experiment in the articles "The Effect of the Earth’s Rotation on the Velocity of Light I and II". Even with the title of these articles, Michelson shows that such an effect exists, i.e., that the speed of light in vacuum differs from the speed of light in the frame of reference related to the Earth’s surface. Michelson’s "two-way interferometer" uses exactly the same path in two directions for each arm. That is why, the existing difference in the speed of light in both opposite directions in the frame of reference related to the Earth’s surface caused by the Earth’s rotation around its axis cannot be established. This is because this difference in the speed of light is completely and accurately compensated for each arm and for any direction of the arm. (Truncated by viXra Admin to <400 words)
Category: Relativity and Cosmology

An Adaptive Quantum Evidential Combination Rule for Open Set Recognition

Authors: Yu Zhou, Fuyuan Xiao
Comments: 3 Pages.

By exploiting the computational potential of quantum computing beyond the computational power of classical computing, an adaptive quantum algorithm of generalized evidential combination rule (AQ-QECR) is proposed to reduce the computational complexity of QECR in the creditability and plausibility levels with no information loss.
Category: Artificial Intelligence

A Genertial Framework Approach: Deriving Special Relativity and Quantum Mechanics from Newton’s Laws

Authors: Duje Bonacci
Comments: 13 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Newton’s three laws of motion have been the foundation of classical mechanics for centuries. However, they were formulated within the framework of absolute space and time, assuming a privileged reference frame. This assumption becomes problematic when considering relativistic and quantum effects, which suggest that space and time are not absolute but instead emerge from deeper physical principles.Newtonian mechanics breaks down in two major regimes:u2022 At high velocities, where relativistic corrections become necessary,u2022 At small scales, where quantum mechanics takes over.In this paper, we demonstrate that Newtonian mechanics can be naturally extended to encompass both relativity and quantum mechanics by reformulating its axioms within the framework of genertial frames—a novel approach in which forces propagate at finite speed, and time and space are measured locally by material objects equipped with proper tickers.We identify the key flaw in Newtonian mechanics: the assumption of instantaneous signal propagation, both in force interactions and in defining absolute time. By replacing these with finite-speed force propagation and local time-keeping, we derive:u2022 Relativity as a necessary consequence of finite-speed force transmission,u2022 Quantum mechanics as a stability condition imposed by finite-speed internal interactions.
Category: History and Philosophy of Physics

From the Mysticism of Quantum Mechanics to Classical Physics

Authors: Vladislav Mirkin
Comments: 11 Pages. (Note by viXra Admin: Author's name and an abstract are required on the article!)

In the ether of particles that have the same sign of electric charge in the volume of the entire Universe (unipolar ether), the results of the Aharonov-Bohm experiments and experiments with quantum entanglement receive an obvious classical interpretation. In addition, the mechanism of gravity is interpreted within the framework of Bernoulli’s law for flowing liquids and gases, and Einshein’s curvature of space acquires a clear physical meaning: the crystal lattice of the arrangement of particles of the unipolar ether is bent.

В эфире частиц, имеющих одинаковый знак электрического заряда в объеме всей Вселенной (униполярный эфир), результаты опытов Ааронова-Бома и опытов с квантовой запутанностью получают очевидную классическую трактовку. Кроме того, механизм гравитации интерпретируется в рамках действия закона Бернулли для текущих жидкостей и газов, а Эйншейновское искривление пространства приобретает ясный физический смысл: искривляется кристаллическая решетка расположения частиц униполярного эфира.
Category: Classical Physics

The Universe is at Least Five Trillion Years Old

Authors: Martin R. Johnson
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

When Lorentz contraction is included in travel time estimates, the Universe is found to be much older than presently believed.
Category: Relativity and Cosmology

Theoretical Derivation of Bohr's Postulate for the Charge in a Hydrogen Atom. Coulomb's Law in Logarithmic Form with Corrections for Strong Interactions at Small Distances. The Physical Meaning of Planck's Constant

Authors: Vadim Khoruzhenko
Comments: 67 Pages.

This article proposes a revolutionary theoretical model that introduces a fifth spatial dimension—"space density"—as a fundamental property governing gravitational, electromagnetic, strong, and weak interactions. The model is based on the hypothesis that changes in space density can lead to phenomena analogous to known fundamental forces. Through a series of mathematical derivations, it is shown how the distribution of space density around spherical objects influences classical field theories
Category: Quantum Physics

WORF: Wave Oscillation Recursion Framework

Authors: James Fruit
Comments: 27 Pages. Licensed under CC BY-NC 4.0.

The Wave Oscillation-Recursion Framework (WORF) provides a novel, first-principles approach to unifying mass, gravity, and gauge interactions through recursion-based resonance constraints. Unlike the Standard Model (SM), which relies on distinct force-carrier particles, WORF replaces fundamental interactions with phase-matched resonance eigenmodes derived from a recursive Laplacian operator. This formulation eliminates the need for gauge boson exchange, deriving interaction symmetries, gravitational effects, and mass-energy transitions as natural consequences of recursion eigenvalue constraints. WORF introduces several key concepts: Mass as a bound standing wave, governed by a Recursive Frequency Threshold (ReFT), which determines transitions between confined and unconfined states. Gauge interactions as emergent recursion symmetries, deriving SU(3) ⊗ SU(2) ⊗ U(1) directly from eigenvalue constraints while maintaining gauge anomaly cancellation. Gravity as a Resonance Accumulation of Inertial Coupling (RAIC) effect, replacing metric curvature with a phase-matched resonance process that preserves geodesic motion and energy-momentum influence. Black hole thermodynamics as a wave-boundary condition, deriving event horizons as resonance accumulation limits and dynamically recovering the Bekenstein-Hawking entropy. Running couplings as a Resonant Effective Scaling Operator (RESO) process, modifying quantum field theory (QFT) renormalization to incorporate recursive eigenstates. Fermion mass hierarchy as a Recursive Oscillation Mass Emergence (ROME) process, eliminating arbitrary Yukawa couplings in favor of eigenstate selection. Neutrino mass and oscillations as a Phase-Locked Oscillatory Neutrino Constraint (PLONC), resolving the origin of neutrino mass without requiring right-handed sterile states while introducing a phase shift testable in upcoming experiments. WORF is formulated as a mathematically rigorous and empirically testable model, predicting measurable deviations in gravitational wave propagation, electromagnetic nonlinearities, hadronic mass corrections, weak decay anomalies, fermion mass ratios, and neutrino oscillation phase shifts. These effects provide multiple avenues for experimental falsification via upcoming high-energy physics and astrophysical observations.
Category: High Energy Particle Physics

Entangled Electron for New Quantum Mechanics Part 2

Authors: Lino Zamboni
Comments: 10 Pages. Extension of viXra 2411.0050 and viXra 2412.0092

This work integrates and completes the previous studies (viXra 2411.0050 and 2412.0092 - Quantum Physics) . The attractive and repulsive potentials are defined, where the magnetic moment and spin play an essential role in ensuring the stationarity of the electron and the orbitals that constitute it .A hypothesis is proposed regarding a source of the electrostatic field , determined by the extreme polarization of the quantum vacuum , which exists at very short distances corresponding to very high energy densities . The effect of such polarization creates a void , induced by the surrounding charges of opposite sign , whose attractive effects are balanced by spin , which generates a local centrifugal force . The application of this concept provides an innovative solution to the unresolved problem of the "Poincaré stress" . Following the framework of traditional quantum mechanics , the Hamiltonians and Schrödinger equations are defined for each orbital . The resulting wave functions , which are entangled like the orbitals they refer to , are combined with appropriate normalized coefficients to form the global electron wave function .
Category: Quantum Physics

The Circle of Life for LLMs[:] Was the Reaction to DeepSeek Justified?

Authors: Stephane H. Maes
Comments: 33 Pages. All related details of the projects (and updates) can be found and followed at https://shmaes.wordpress.com/

Since the release of DeepSeek LLMs, the industry, the investors, and the media have reacted with alarm, surprised that a Chinese startup—despite operating on a low budget and with limited access to specialized AI hardware—could surpass the latest models with reasoning capabilities. This has led to geopolitical concerns about threats to U.S. technological dominance, and the effectiveness of AI chip sanctions imposed by the U.S. on China. Investor confidence in leading U.S. tech companies involved in AI, AI hardware, and AI/cloud hosting has been shaken, contributing to a significant stock market drop on January 27, 2025.In this paper, we argue that while the success of DeepSeek V3 and R1 is remarkable, it does not signal the decline of any major player. Instead, it is a natural progression of how LLMs and generative AI function. Most LLM providers, of a same LLM generation, rely on similar algorithms, big-data pools, and development techniques, meaning that models tend to converge in performance once their methodologies become public. Different starting points often lead to LLMs of comparable capabilities for a same generation. Techniques such as model distillation and reinforcement learning further enable the reduction of model size, data requirements, and hardware constraints. As a result, each time a model is developed, it can be replicated, closely matched, or even surpassed soon after—sometimes with significantly lower effort than the original, or with a significantly smaller set of parameters. This cycle of life will continue as long as LLMs remain a competitive field, vs. a commodity, and until new AI approaches beyond GenAI emerge, or the old AI reemerges.Such a pattern will continue, repeating the cycle. Open source models have the advantage of drawing from broader communities and collective innovation, making it increasingly difficult for proprietary models to maintain an edge. As development costs rise, it will be interesting to see whether proprietary models can sustain their dominance.Ultimately, there was no reason for panic. AI may be in a bubble, but if it bursts, it will not be because DeepSeek outperforms OpenAI’s latest model. Instead, the real challenges facing LLMs and GenAI lie elsewhere. The path to AGI is likely beyond current LLMs. While AI agents may extend the viability of GenAI, other factors pose more significant long-term threats. If LLMs are not the future of AI, there is little reason to be concerned about new players mastering them.
Category: Artificial Intelligence

De Broglie's Phase Waves of Electrons in Hydrogen-Like Atoms as Parts of Steady-State Forced Vibrations

Authors: Martin Kraus
Comments: 7 Pages.

One of the consequences of de Broglie's hypothetical internal clock of an electron is the existence of an associated phase wave that is locally in phase with the electron's internal clock. For a classical electron that is moving on a closed Bohr-Sommerfeld orbit in the electric potential of a positively charged nucleus, de Broglie showed that the requirement of a continuous phase wave on the closed orbit is in agreement with Einstein's quantization condition. The present work explores the hypothesis that this phase wave is part of a forced vibration in the space around the nucleus, which is driven by the electron's internal clock. Results of this work include new quantization conditions for closed orbits that are consistent with Einstein's quantization condition but include additional (yet unexplored) conditions. Furthermore, a method is presented for computing phase waves on closed orbits of electrons, which could help visualizing several important features of de Broglie's phase waves.
Category: Quantum Physics

Irreducible Inviscid Singular Represenation of 3D Fully Developed Turbulence and Related Emergent Physics

Authors: Michael Isaac Aksman
Comments: 22 Pages.

Vortons [is] introduced to approximate finite core vortex tubes and pass through Navier Stocks spontaneous singularities/reconnections without any additional assumptions. Vortons provide irreducible description of inviscid attractor of 3D Navier Stocks equation solutions with number of vortons scaling with Reynolds number at hand. Magnetic vortons provide irreducible description of magnetic vortex tubes in plasma with reconnections without any additional assumptions. Instability of quasi 3D/2D+ vorton collapse provides possible mechanism for explosive universe inflation/first order phase transition. 3D space nature of our universe as a consequence of instability of 3D vortons collapse. "Dark matter" explained as a consequence of frisbee like quasi 3D/2D+ space in galaxies with corresponding stable rotational curves. "Dark energy" explained as a emergent result of vortons system 3D self amplification interactions energy "antigravity" effect. Probabilistic interpretation of quantum mechanics as a result of smooth test functions of fluid vacuum nonlinear Maxwell equations weak solutions. Baryonic asymmetry [is] explained as a instantaneous snapshot during exponential inflation of quark antiquark annihilation asymmetry/skewness and kurtosis terms in Edgeworth series expansion of instantaneous quantum GUP (generalized uncertainty principle) fluctuations. Simple Early Bifurcation/Regime shift detection in nonequilibrium nonlinear statistical systems proposed using linear statistical moments/cumulants approximation/equivalents formulas.
Category: Mathematical Physics

The Full Dedekind Cut and the Key to Leibnizian Mathematics

Authors: Adriaan van der Walt
Comments: 16 Pages.

The aim of this document is to facilitate and motivate the reading of the document Leibnizian Mathematics by investigating a compelling reason for introducing Leibnizian Mathematics. This document also motivates the extension of the Dedekind Cut to the Full Dedekind Cut and analyses some consequences. First the relevant abstractions about Space shared by all are stated, which are then followed by stating the relevant basic assumptions of Abstract Mathematics. A tool is then developed that enables the identification and analysis of the consequences of these assumptions. This exposes the root motivations for, and the fundamental properties of, the tenets of Abstract Mathematics. The most consequential of these, in the present context, is the result that the total length of countable many points is zero. More than countable many points are therefore required to form a line of non-zero length. Also, that countable many points can be added to or removed from a line without changing the length of the line (this consequence is contrary to the current paradigm of Mathematics). The latter necessitated the introduction of the Full Dedekind Cut to preserve the real line and hence Euclidean Topology and Lebesgue theory.The concepts of infinitesimal and infinitesimal number are introduced, followed by a Riemann sum that results in a contradiction in Euclidean Mathematics by showing that there exists an example where countable many points form a line of length one.Possible causes for this contradiction are discussed and it is concluded that the Riemann integral does not fit naturally into Abstract Mathematics, but that a second continuous model for space that leads to a different model for Mathematics, called Leibnizian Mathematics, must be developed to augment Abstract Mathematics. This model resolves the contradiction, accommodates the Riemann integral in a natural way and expands the paradigm of Mathematics.A short list is appended describing the difference in meaning that some words have and the difference in the properties that they describe when used in different models.
Category: General Mathematics

Inferring the Source of Cosmic Expansion Forces from the Presence of Charge in Space

Authors: Kuo Tso Chen
Comments: 10 Pages.

The accelerating expansion of the universe suggests the presence of a repulsive force exceeding gravitational attraction. This study explores the asymmetry in electron and positron production during the formation of the universe, which may have led to a residual charge imbalance. If a uniform but minuscule charge density pervades the universe, the resulting electrostatic repulsion could drive cosmic expansion. Through mathematical modeling, we demonstrate that even an extremely slight charge density variation can result in accelerated expansion, aligning with current observations.
Category: Relativity and Cosmology

Fermat's Theorem

Authors: Mustapha Kharmoudi
Comments: 10 Pages. (Note by viXra Admin: Article title should be in English; author name should be after article title; an abstract is required; and scientific references should cited and listed))

In this article, we approach Fermat's famous theorem in an original manner. To achieve this, I will use two applications, one of which is well-known, while the other seems to be unprecedented.
Category: Number Theory

New Wireless Technology for Data Transmission in Chemical Systems

Authors: Andrei I. Bodrenko
Comments: 4 Pages.

New type of wireless computer network in chemical systems is presented in this article. This wireless network uses chemical system as physical media for data transmission, instead of environment. Thus, represented wireless network differs substantially from molecular communication networks and wireless networks covered by IEEE standards, such as radio frequency based wireless networks. This new wireless technology can be used not only in chemical industry for continuous controlling chemical processes in chemical reactions zones but also for medical purposes, and as a new type of wireless body area computer network.
Category: Digital Signal Processing

Does QM = Ait?

Authors: Tariq Khan
Comments: 5 Pages.

A short philosophical and speculative essay proposing that quantum mechanics (QM) and algorithmic information theory (AIT) are actually equivalent, or reciprocal, means or operations of describing nature. An understanding of this relationship could provide a means to solve complex problems via a formal correspondence between continuous mathematics and discrete mathematics. Subjective attributes are noted between the operations and compared for their similarities as a first step to motivate additional technical research toward a formal and fundamental theorem of the relationship.
Category: History and Philosophy of Physics

Artificial Prime Numbers: A Relative Perspective on Primality

Authors: José Acevedo Jiménez
Comments: 11 Pages.

This article explores the notion of artificial prime numbers in the context of specific sets of integers. A formal definition is presented, properties are discussed, and comparisons are made with the classical notion of primality. Additionally, potential applications of these numbers in number theory and cryptography are analyzed.
Category: Number Theory

The Study of Vacuum Dynamical Mechanisms

Authors: Yake Li
Comments: 14 Pages. In Chinese

Based on multiple astronomical observation results, this paper proposes the hypothesis of the principle of relative change in the speed of light and demonstrates its compatibility with the principle of the invariance of the speed of light. The study shows that the speed of light has both an absolutely constant aspect and a relatively variable aspect. This provides us with a new direction to study the relationship between the relative change in the speed of light and the motion of matter. Based on this principle, the paper constructs an innovative theoretical framework known as the "vacuum dynamical mechanism" and derives several important conclusions. The research finds that time, space, and the speed of light always maintain a proportional relationship. The relative change in the speed of light leads to the formation of high-energy spaces, low-energy spaces, and variable-energy spaces. In the variable-energy vacuum space, objects spontaneously accelerate towards low-energy regions. The acceleration gained by an object is only related to the rate of change of the speed of light in space and is independent of the object's mass. The vacuum dynamical theory proposed in this paper offers a new perspective for explaining the origin of dark energy and the physical mechanisms behind spacetime curvature.
Category: Astrophysics

Compact Oxford Italian Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 19 Pages.

We study Compact Oxford Italian Dictionary, the first edition, 2013. We draw the natural logarithm of the number of Italian 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 BP(4,$beta H$=0) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Ising Model with four nearest neighbours, 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

Equation with Sum of Four Sixth Degree Integers Equal to Another Four Sixth Degree Integers

Authors: Oliver Couto
Comments: 3 Pages.

There are numerical solutions available on Wolfram world of mathematics website (ref. # 4) for the equation (p^6+q^6+r^6+s^6)=2(a^6+b^6). In this paper the author has arrived at numerical solution by algebra. It is common knowledge that arriving at numerical solutions by algebra is difficult for degree four & above. Also on the internet the author has not come across any method for the above mentioned equation.
Category: Number Theory

Proving Goldbach's Strong Conjecture by Analyzing Gaps Between Prime Numbers and Their Digits

Authors: Bahbouhi Bouchaib
Comments: 21 Pages. Interested readers can cite this article which is now published in J Math Techniques Comput Math 4(1) 2025 (opast publishing group)

The main idea of this article lies in the fact that Goldbach's strong conjecture is associated with the progression ofnatural integers from 0 to infinity, which results in precise gaps between prime numbers. The gap of 6 is the mostregular between primes 6x + 1 on the one hand and primes 6x — 1 on the other. In this article, using the equations 3x ± 5and analyzing the 6-based gaps between primes while determining the initial conditions that make a prime appear afteror before an integer, this article argues for the truth of Goldbach's strong conjecture. Two new concepts are introducedfor the first time : Goldbach's gap and Goldbach's transposition. By analyzing its key digits (units and tens), a primenumber itself can lead to the conversion of an even number into two primes. A new algorithm is deduced from theseresults, enabling us to locate prime numbers located at equal distance from any integer, even or odd, prime orcomposite. This constitutes a decisive proof of Goldbach's strong conjecture, since it means that any even number canbe converted into the sum of two prime numbers.
Category: Number Theory

Revisiting Hawking Radiation: Gravity Decoupled from Mass and the Nature of Black Holes

Authors: David E. Jacob
Comments: 6 Pages. © 2025 David E. Jacob

Hawking radiation is traditionally understood as a quantum process near a black hole’s event horizon that leads to gradual mass—energy loss. In this work, we present a unified interpretation that bridges conceptual and technical perspectives: once an event horizon forms, the external gravitational field decouples from its interior—transforming from a dynamically "anchored" field (as seen in normal massed objects) to a self-sustaining "unanchored" or fossil imprint. This decoupling permits the slow reduction of the black hole’s energy via Hawking radiation without invoking superluminal updates, thereby preserving causality, energy conservation, and the equivalence principle. Complementing the standard ADM formulation, we incorporate insights from quasilocal energy methods, isolated horizon frameworks, and quantum field theory in curved spacetime to further support our view. In contrast, for ordinary astrophysical bodies (e.g., planets and stars) where the gravitational field remains causally connected to the source mass, any analogous process would violate these fundamental principles. We also discuss observational prospects and numerical simulations that may eventually reveal signatures of this decoupled evolution
Category: Relativity and Cosmology

Why Poincare Symmetry is a Good Approximate Symmetry in Particle Theory

Authors: Felix M. Lev
Comments: 16 Pages.

As shown by Dyson in his famous paper "Missed Opportunities", it follows even from purely mathematical considerations that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Then the usual explanation of why in particle physics Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators$M_{4mu}$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{muu}$ ($mu,u=0,1,2,3$).We explicitly show that this is the case in the Flato-Fronsdal approach where elementary particles in the standard theory are bound states of two Dirac singletons.
Category: High Energy Particle Physics

Physicalized Temperature: A New Correlation Mechanism Between Helium-4 Atoms

Authors: Di Zhuang, Hongzhang Zhuang
Comments: 9 Pages.

The experiment shows that in the superfluid $^{4}$He, $^{4}$He atoms are not an ideal Bose gas, and there is a strong correlation between the $^{4}$He atoms in the superfluid state. The famous Tisza and Landau's two-fluid model does not provide an answer to the physical mechanism behind this correlation. This paper proposes a hypothesis—Physicalized Temperature (PT), a specific mechanism for the correlation between $^{4}$He atoms. Based on this model, new explanations are given for critical opalescence and the quantization of circulation; it is also predicted that, similar to superconductors, magnetic flux quantization will occur in a rotating torus container filled with superfluid $^{4}$He. The phonon-roton dispersion curve (P-R curve) of the superfluid $^{4}$He quasiparticles, which was conjectured by Landau, as well as the specific heat curve with singularities across the entire temperature range, are calculated and found to match the experimental data very well.
Category: Condensed Matter

Born Reciprocal Relativity Theory Redefines the Notion of Mass: How Massless Photons Appear Massive in Accelerated Frames

Authors: Carlos Castro
Comments: 15 Pages.

Starting with a brief review of Born Reciprocal (Non-inertial) Relativity Theory (BRRT), it is shown how massless photons in one frame of reference can appear massive, even tachyonic, in an acccelerated frame. An immediate application can be found in the behavior of in-falling/outgoing photons propagating in a black hole gravitational background. When the in-falling photon gains energy one learns that ($ d tau')^2 > 0 $ such that the blue-shifted photon from the point of view of an accelerated frame of reference (with respect to a static spherically symmetric Schwarzschild black hole, for example) will appear massive and subluminal. However, when the outgoing photon loses energy one has $ ( d tau')^2 < 0 $ and the red-shifted photon from the point of view of an accelerated frame will appear tachyonic and superluminal. This is an interesting physical feature because no particle (inside the horizon) can escape the interior of black hole unless it moves faster than light; i.e. it is tachyonic (superluminal). These effects may have important consequences in cosmology (dark energy, dark matter problem).
Category: Relativity and Cosmology

A Scale Invariant Fully Conformal Cosmological Model and Its Support by Astrophysical Data

Authors: Richard Dvorsky
Comments: 21 Pages.

According to general relativity, the cosmological redshift may be caused by other mechanisms than the source moving away from the observer. It can occur on a global scale, similar to the gravitational redshift near massive stars. In principle, these are differences in the time-dependent global metric field between the source in the past and the observer in the present. In this paper we attempt a new interpretation of the simple solution of Einstein’s equations within a fully conformal metric for the case of a time-independent energy-momentum tensor. The scaling factor here acts identically on all four space-time coordinates and the speed of light is independent of the conformal time. The fully conformal metric is interpreted here as a universal geometric background which is scale invariant and acts universally on all objects, including gauges and clocks, regardless of their dimensions and internal interactions. The associated scale invariant exponential expansion is thus only relative and all observers at different times are completely equal. The model introduces the concept of the appearent age of the universe, which is the limiting consequence of time dilation into the past, and corresponds to the present value of the age of the universe H —1 according to the standard model. This appearent age is the same for all observers, and the Hubble constant is thus a true universal constant, invariant to time translations. The motivation of this work was to test the possibility of the above cosmological redshift mechanism in confrontation with astrophysical data. Probably the most important consequence is the generalized formulation and interpretation of the Hubble-Lemaître law z(r) = (eHr/c − 1), which shows good agreement with astrophysical data even for the most distant supernovae. Confronting the conformal metric model with some astrophysical data shows an interesting agreement with the observed spatial distribution of astrophysical sources such as γ-ray bursts and quasars. On a cosmological scale, the above fully conformal metric naturally determines the global energy density, spatial flatness, and solves the horizon problem and Olbers’ paradox in infinite spacetime.
Category: Relativity and Cosmology

On the Osculating Circle Using Complex Numbers

Authors: Aloys J. Sipers
Comments: 5 Pages.

In this letter a theorem is stated on the complex-valued represention of the radius vector of an osculating circle. This theorem can be used in education in mathematics and physics. To develop exercises for education a construction is presented for a class of curves characterized by a parameter. A numerical example is provided to illustrate the educational potential of the theorem and the constuction of corresponding exercises.
Category: Education and Didactics

New Method of Using Mobile Robots for Moving Cargo in Warehouse

Authors: Andrei I. Bodrenko
Comments: 20 Pages.

The new patented method for moving cargo in warehouse is proposed in this article. According to the new method, movement of cargo from the storage area to another warehouse area is carried out by throwing the cargo by the first mobile robot and catching the thrown cargo on fly by the second mobile robot. The parameters of the calculated trajectory of movement, in the free flight phase, of the center of mass of the cargo to be thrown are calculated by numerical methods for solving the Cauchy problem for a system of ordinary differential equations, and by the shooting method for boundary value problems of a system of ordinary differential equations. The first mobile robot throws the cargo at the specified angle to the horizon with the specified initial velocity, at the specified moment of time. In order to catch the thrown cargo on fly by the second mobile robot, the parallel algorithm A1-A2 for catching a thrown cargo on fly by the second mobile robot was created. The method allows the first mobile robot to throw cargoes for large distances, and the created algorithms allow the second mobile robot to catch reliably the thrown cargoes on fly. The proposed method for moving cargo is superior in economic efficiency and reliability to the other methods for moving cargo by implementing tossing of inventory items by robots.
Category: General Science and Philosophy

A New Natario Warp Drive Vector $ny$ in $2D$ Polar Coordinates with the Hodge Star Over the Y-Axis and a Constant Speed $vs$

Authors: Fernando Loup
Comments: 23 Pages.

The Natario warp drive appeared for the first time in 2000.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than light predated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drive vector nX=vs*(dx) where vs is the constant speed of the warp bubble and *(dx) is the Hodge Star taken over the x-axis of motion in Polar coordinates.In this work we present a new warp drive vector nY=vs*(dy) where vs is the constant speed of the warp bubble and *(dy) is the Hodge Star taken over the y-axis of motion in Polar Coordinates.Our new proposed warp drive vectoralso satisfies the Natario requirements for a warp drive spacetime.
Category: Relativity and Cosmology

Infinitely Many Twin Primes - Proof

Authors: James DeCoste
Comments: 20 Pages. Contact: jbdecoste@eastlink.ca

After dissecting the mechanics of locating valid twin primes, I was able to establish a Proof through contradiction. I start by creating a table to easily display the potential list of twin primes. Using an elimination matrix scheme, I systematically remove twin prime candidates from the list if either half of the pair are multiples of an already known 'Prime Number'. Multiples of prime numbers, primes squared and primes multiplied by other primes are not prime numbers themselves (examples 5*5=25; 5*7=35; 5*11=55; 7*7=49; 7*11=77; and so on). It's an easy approach with repeatable patterns for each prime number. It quickly becomes obvious that these elimination patterns are repeating for all non-prime removals. All these elimination patterns are of the form remove-skip(n)-remove-skip(m)...repeated to infinity. Note that n+m+2 is the prime number. The first non-prime removal for any prime is in essense that prime^2 (prime squared). A prime number squared will always fall into the sixth column ( the column starting with 7)! Further, two adjacent patterns will slightly overlap if those two primes form a twin prime pair. I then proceed to make the 'silly' assumption that there will be no potential twin prime candidates in the initial skip(n) plus skip(m) regions for the two overlapped twin primes (entire initial pattern for a given twin prime pair) in this elimination matrix. If we assume that 11 & 13 are the last twin primes possible, we would have to make the assumption that there are no twin primes candidates in the elimination overlapped pattern regions for either prime 11 or 13 combined at minimum. The contradiction arises because we can show that there is always at least one twin prime pair in this combined/overlapped region. As long as there are infinitely many primes there will be infinitely many twin primes. Euclid proved there are infinitely many primes with his proof. I have simply extended his proof into my own.
Category: Number Theory

Some Properties of Electrons

Authors: I. Prusis, P. Prusis
Comments: 5 Pages. 1 figure

The electron is the most widely used elementary particle and at the same time the least studied. It is known that the electron has mass, charge, and spin. The article shows that an electron moves along a complex trajectory, the main components of which are chaotic thermal motion, zitterbewegung, and the direction determined by the external electric field. The trajectory of an electron can be mathematically described as a wave, but from this QM draws the incorrect conclusion that the electron itself is a wave. What is mentioned in the article also applies to protons, neutrons, and other elementary particles.
Category: Quantum Physics

A Solution to Wave Particle Duality Conundrum?

Authors: Jayesh Suresh
Comments: 14 Pages.

This article attempts to model spin of fermions and to explore possible connection to wave function. Zitterbewegung, originally introduced to describe the rapid oscillatory motion of relativistic particles, is not commonly used in modern physics. Here, zitterbewegung has been employed to develop a model that accounts for spin of fermions. It can explain wave particle duality.
Category: Quantum Physics

Traversability and Energy Constraints of a Traversable Wormhole in f(R) Gravity

Authors: Raghav Krishna
Comments: 2 Pages.

This paper investigates the traversability and energy constraints of wormholes under f(R) gravity, an alternative to Einstein's General Relativity. By numerically solving the modified Einstein field equations, we demonstrate that the required exotic matter can be significantly reduced through curvature modifications. The study analyzes tidal forces, showing that human traversability is possible with accelerations below 50 m/s² at a distance of 1000 km from the throat. Energy requirements are estimated at 3.77 × 10¹u2076 J (equivalent to 9 megatons of TNT), far lower than previous classical models. The findings suggest that f(R) gravity provides a more feasible framework for future wormhole research, with possible stabilization via Casimir effects. This work contributes to the theoretical groundwork for constructing traversable wormholes in modified gravity theories.
Category: Relativity and Cosmology

The Balance Paradox and Fermat's Theorem

Authors: Vladislav Koshchakov
Comments: 10 Pages.

An unexpected relationship has been found between the weighing procedure on lever scales and the equation of Fermat's theorem. At the same time, it turned out that solutions are possible only for n=2, and for all cases of n>2, the proof of undecidability is of the same type.
Category: General Mathematics

Universal Clock Field Theory: A Preliminary Proposal for the Unification of Emergent Time, Gauge Interactions, Gravity, Quantum Measurement, and the Dark Sector

Authors: Brandon Belna
Comments: 38 Pages.

We propose Universal Clock Field Theory (UCFT), wherein a single oscillatory phase field theta, defined modulo 2*pi, underlies the emergence of time, gauge interactions, gravitational dynamics, quantum measurement, and the dark sector.In this construction, theta arises via spontaneous symmetry breaking of a complex scalar fieldPhi(x) = rho(x) * exp(i * theta(x)),and its compact nature drives topological effects that yield emergent gauge fields, a non-perturbative Yang-Mills mass gap, and a derivation of the invariant speed of light.Coupling theta to gravity modifies Einstein’s equations, providing non-singular cosmologies and potential hairy black hole solutions. Furthermore, theta-driven decoherence addresses the quantum measurement problem, and a shallow potential or topological defects for theta naturally accommodate dark energy and dark matter.Although still in an exploratory stage, UCFT offers testable predictions and new avenues for theoretical and experimental research in fundamental physics.
Category: High Energy Particle Physics

New Method of Using Mobile Robots for Implementing Warehouse Operations

Authors: Andrei I. Bodrenko
Comments: 12 Pages.

The new patented method of movements of packaged cargoes at warehouse isproposed in this article. The proposed method of loading is superior in economic efficiency,reliability, cheapness, simplicity of construction and use, to all other methods of loadingimplemented by robots. The method allows the mobile robot to load a cargo which is three times asheavy as this mobile robot, wherein almost no electrical energy is consumed during loading. Inimplementing the method, two mobile robots are used, each of which contains a mobile platform, anomnidirectional mobile wheel-type mechanism and a transport suspension with independentsuspension for each wheel. Actually, the mobile robots help each other to load cargo on the firstmobile robot, through robot cooperation. Loading of the container with the load on the first mobilerobot is carried out by actuating a two-arm lever, which is carried out through the impact of thebottom of the mobile platform of the second mobile robot on the longer arm of the two-arm lever bylowering the mobile platform of the second mobile robot due to the operation of the transportsuspension of the mobile platform of the second mobile robot. For example, if the length of thelonger arm of the two-arm lever is three times longer than the shorter arm of the two-arm lever then the second mobile robot of weight 50 kg is capable of loading a container with the load of weight150 kg on the first mobile robot.
Category: General Science and Philosophy

Demonstration of the Collatz Conjecture: a Proposal

Authors: Oreste Caroppo
Comments: 15 Pages.

In this article we will propose initially a graphical method for carrying out the algorithm which is at the base of the famous Collatz Conjecture; therefore we will demonstrate analytically that, for no natural number, the Collatz Algorithm can present an infinite sequence of ever-increasing steps. The development of the graphical method will lead us to extrapolate a simplified and more basic scheme of the Collatz Conjecture, which will allow us in turn to consider the Collatz Conjecture Algorithm as a sorte of particular case of a more general algorithm valid for positive real numbers, which, for statistical reasons that we will show, will always converge towards the smallest real number, zero. The Collatz Algorithm will therefore appear as an adaptation only to the natural numbers of this more general algorithm, which is why Collatz Algorithm will also converge towards the smallest natural number which is 1.
Category: Number Theory

Brachiation Robots :Trajectory of Movement of a Jumping Brachiating Robot

Authors: Andrei I. Bodrenko
Comments: 2 Pages.

The trajectory of movement, in the free flight phase, of the center of mass of the mobile robot during vertical jumping is obtained in this article.
Category: General Science and Philosophy

University Mathematics for Young Adults

Authors: Johan Noldus
Comments: 140 Pages.

Many topics are explained at a sophisticated level.
Category: General Mathematics

Generalizations of Notions of Differential Geometry

Authors: Johan Noldus
Comments: 20 Pages.

The notions of Torion and Riemann curvature are generalized towards general path metric spaces.
Category: Mathematical Physics

Geometrical Quantum Theory and Applications

Authors: Johan Noldus
Comments: 220 Pages.

We covariantize quantum field theory and extend quantum theory to the spiritual domain required for structure formation.
Category: Quantum Gravity and String Theory

Symmetries of Natural Numbers

Authors: Emmanuil Manousos
Comments: 31 Pages.

In present paper we prove an original theorem on the natural numbers. From this the theorem emerges a set of symmetries of the natural numbers which puts Number Theory on a new footing. One of the consequences of the theorem, but not the most important one, is the odd number factorization algorithm.
Category: Number Theory

From Einstein to Electromagnetic Gravity with Spin 3

Authors: Miroslav Pardy
Comments: 18 Pages. Original article

We consider the rigorous derivation of the Einstein equations by Fock. Then, we approach the way from the spin 1 fields to the spin 2 fields for massiveand massless particles and we derive the gravity equations from this base. Then, we approach the spin 3 gravity called by us the electromagnetic gravity.
Category: Quantum Gravity and String Theory

The Informational Coherence Index A Framework for the Integration of Networks of Artificial Intelligence Models

Authors: Henry Matuchaki
Comments: 19 Pages. (Note by viXra Admin: Listed scientific references should be cited in the article; AI assisted/generated content is in general not accepted))

This article presents the Informational Coherence Index Icoerdisplaystyle I_{text{coer}}Icoer, an innovative mathematical and computational model designed to quantify and optimize informational integration in networks of artificial intelligence (AI) models, with a focus on language models. Inspired by concepts from physics, thermodynamics, and information theory, Icoerdisplaystyle I_{text{coer}}Icoer is integrated into the General Theory of Unity (GTU), a theoretical framework that seeks to unify informational interactions in distributed systems. This work describes the formulation, implementation, visualization, and practical applications of Icoerdisplaystyle I_{text{coer}}Icoer, highlighting its relevance for AI ensembles, multi-agent networks, and collaborative systems such as ChatGPT, Grok, etc.
Category: Artificial Intelligence

A Proposed Method Of Earth Expansion

Authors: Ivan Heller
Comments: 7 Pages. (Note by viXra Admin: Author's name is required on the article)

This paper is based on the premise that Earth Expansion Theory (EET) is a valid explanation for the geography of the Earth's surface.¹ It is also our premise that Energy Wave Theory (EWT)² is a valid explanation for the physical and energetic phenomena of the universe. EWT proposes that the neutrino is the fundamental particle from which all other matter is composed.³ (There is further evidence that the neutrino oscillates between various forms.u2074) We conjecture that the Earth absorbs neutrinos—or their oscillations—primarily in its densest regions. Over time this constant addition of matter is increasing both the mass and volume of the planet. We observe evidence that this is not unique to Earth, but rather the norm for moons and planetary bodies.u2075
Category: Geophysics

Orbital Decay Process by Deviation of Geodesic Trajectory in Normalized Regular Metric Tensor

Authors: Sergio de Azevedo Melo
Comments: 54 Pages. In Portuguese

Orbital decay and gravitational radiation are energetic correlates, however the correspondence between the quantities in an energy balance by the field equations is challenging under nonlinearity conditions. Analytically formulating the decay due to orbital imbalance and mechanical prediction of the deviation of the geodetic trajectory requires a natural cause for the occurrence of instability. Once all the conditions for an orbit to be circular are in place, stability is tested by predicting aberration in the movement of the metric in space, which determines the emissivity that the body has measured by the relationship to the natural frequency of its mass. The equation is tested in the prediction of the decay of the orbital period of the pulsar PSR J0737-3039, and the verification shows the gravitational emissivity by the natural frequency of the body.
Category: Relativity and Cosmology

500,000-1,000,000 Neurons: A Biological Threshold for Initial Self-Perception?

Authors: Shulei Xie
Comments: 5 Pages. (Note by viXra Admin: Author name should be lsted right after the article title)

Self-perception, the ability to sense one’s own bodily state, is a fundamental trait in biological systems. This study investigates whether a neuron count of 500,000-1,000,000 marks a threshold for "initial self-perception" during embryonic development. Developmental data from four species—mouse (E12), human (6-7 weeks), pig (E20-E25), and chicken (E7-E8)—were analyzed for neural, cardiac, limb, and sensory features at this neuron range. Results show consistent signal integration across species, forming a rudimentary "body sense" at this stage. These findings suggest that 00,000-1,000,000 neurons may represent a biological threshold for initial self-perception, providing insights into the origins of self-awareness in neural development.
Category: Quantitative Biology

Complex Spacetime and the Schrödinger Equation: Toward a Quantum-Electromagnetic Unification

Authors: Bhushan Poojary
Comments: 15 Pages. (Note by viXra Admin: Author name should be separately listed after the article title)

In this paper, we extend the formulation of the Schrödinger equation into the complex spacetime framework, introducing a novel approach that bridges quantum mechanics, electromagnetism, and general relativity. By incorporating complex derivatives and applying the Cauchy-Riemann conditions, we reveal that the imaginary components of spacetime contribute to quantum fluctuations, while the real components govern classical behavior. This framework naturally connects the imaginary curvature of spacetime to electromagnetic field dynamics, suggesting that electromagnetic phenomena could emerge from the geometry of complex spacetime.We demonstrate that the imaginary Ricci tensor, derived from the curvature of the imaginary spacetime dimensions, aligns with the mathematical structure of Maxwell's equations in curved spacetime. This connection implies a geometric origin of electromagnetism, where quantum fluctuations arise from the imaginary curvature of spacetime. Furthermore, the preservation of standard quantum commutation relations within this framework suggests consistency with established quantum mechanical principles.
Category: Quantum Physics

A Rigorous Algorithmic Investigation for Constant Approximations via Expression Search

Authors: Suryansh Singh Shekhawat
Comments: 5 Pages.

This paper presents a computational investigation that searches for arithmetic expressions approximating a given target constant using a finite set of base expressions and allowed operators. In our approach, the search is organized by a notion of DEPTH (i.e., the number of operations applied) and is limited to a maximum depth (typically 10 or 11) due to computational constraints. We describe the algorithm rigorously, introduce precise definitions and notation, present pseudocode in the algorithmic style, and discuss sample solutions—including approximations for e, φ (the golden ratio), and π with their respectivedepths and computed absolute errors. We also include an example run showing the number ofcandidate expressions generated at each depth (with depth 10 evaluating approximately 2.5 million sequences). Finally, we discuss the inherent limitations, including memory (RAM) requirements for deeper searches, and how increased computational power could extend the search depth.
Category: Number Theory

Possible Transition from Order Into Chaos and Vice Versa

Authors: Udo E. Steinemann
Comments: 28 Pages. (Note by viXra Admin: Article file size should be <10MB and no author photo should ber used))

The specific model-case of the quadratic-iterator is an illuminating way of understanding the chaotic-behaviour. It is agreed that for the special-cases of iteration of transformations there are common characteristics of chaos: Sensitive dependence on initial conditions, mixing and dense, periodic points. Therefore discussion starts with an important metaphor in chaos-theory, kneading of dough, by 2 different uniform-processes performed iteratively each of them in unit-iterval: [1] Stretch the dough, fold it over in the middle and stretch it again (as often as required), and [2] stretch the dough, cut it in the middle, paste the 2 halfs together and stretch it again (as often as required). This processes guarantee that a pocket of spice inserted into the dough will be mixed thoroughly throughout the mass. Both kneading-processes were found to be compatible in view of their chaotic-characteristics. In a further step of discussion, equivalence could be shown between the 2 uniform kneading-processes and the non-uniform kneading of the quadratic-iterator y = au2022x(1-x), where a = 4 were chosen, via simple coordinate-transformations of the unit-interval. Chaotic characteristics of all 3 iteration-transformations could also be proven as being equivalent to each other. Thus, further investigations were based now on quadratic-iterator. The range from states of order up to the complete chaotic dynamics of the quadratic-iterator can be divided into 3 distinct parts: [1] regime 1 ≤ a < (s∞ = FEIGENBAUM-point) were oscillations of the iterator will experience period-doublings, [2] an area s∞ < a < 4 which can be looked as mirror-image of regime [1], and [3] the chaos-area for a = 4. Boarder between regime [1] and [2] is a CANTOR-set. The mirror-image-area of the quadratic-iterator’s final-state-diagram is characterized by a complicated band-structure and therefore different orbit-dynamics can be expected for (a < s∞) ⇄ (s∞ < a). In other words, transitions from order to chaos and vice-versa may occur but with respect to orbit-dynamics they happen differently every time.
Category: Mathematical Physics

The Problems with Trans-Identification: Examining the Biological, Psychological, and Sociocultural Constructs of Gender Ideology

Authors: Kim Tumlinson Eaton
Comments: 19 Pages.

Demographic data on transgender identification in the U.S. reveal that white individuals make up the majority of trans-identified adults. However, when adjusted for population size, Black and Latino individuals show slightly higher rates of trans-identification. This pattern suggests that cultural and social influences—not biological determinism—play a key role in shaping gender identity. The disproportionate presence of trans-identification across racial groups supports the idea that exposure to progressive gender ideology, education, and affirmation-seeking behaviors significantly impact identity formation. Recognizing these disparities is essential for understanding the societal and psychological forces driving trans-identification.This study relies on desk research, systematically gathering, analyzing, and synthesizing data from official sources. Its goal is to identify patterns, summarize existing studies, and construct a new theoretical framework on trans-identification. By examining biological, psychological, and sociological literature, this research challenges foundational claims, exposes contradictions, and evaluates their broader social and scientific implications.This paper explores the biological, physiological, psychological, and sociocultural barriers to a complete transition between sexes within trans-identification. It examines key biological differences—muscle physiology, skeletal structure, and neurological architecture—highlighting immutable traits that remain unchanged by hormones or surgery. Beyond biology, this analysis unpacks sociocultural influences, including the pursuit of minority status, affirmation-seeking behaviors, the reinforcement of regressive gender stereotypes, and divisive advocacy tactics.A novel term, Induced Ideological Maturity (IIM), is introduced to describe the premature imposition of complex sociocultural ideas, such as gender identity, onto young children—raising profound ethical and developmental concerns. The discussion critiques the contradictory language emerging from trans ideology, such as terms like "cisgender lesbian men," which undermine linguistic clarity and societal understanding of gender.These findings underscore the urgent need to separate subjective gender identity from the unchanging realities of biological sex. This paper calls for a critical reassessment of how biological and sociocultural dynamics intersect in trans-identification, exposing ideological contradictions, advocacy-driven challenges, and developmental risks like Induced Ideological Maturity (IIM). Grounded in an evidence-based framework, this analysis equips policymakers, educators, and clinicians with the tools to navigate trans-identification’s complexities and address its broader societal impact.This paper also critically examines counterarguments that claim gender identity is independent of biology, addressing their logical inconsistencies and empirical shortcomings. Additionally, it explores the role of sociopolitical influences—such as advocacy shifts, medicalization, and media representation—in shaping trans-identification patterns, particularly among individuals experiencing internalized homophobia.
Category: Social Science

A Simple Rigorous Proof of Riemann’s Hypothesis via Reflection Symmetry

Authors: Jau Tang
Comments: 8 Pages.

We present a simple rigorous proof of Riemann’s hypothesis. This hypothesis has remained unsolved since Riemann’s original formulation in 1859, although numerous zeros have been found along the critical line with the assistance of computer calculations. Our analytic proof is based on the analysis of the reflection symmetry between |Γ(su20442))〖(ζ(s))u2044π^(su20442) |〗^2 and |Γ(((1-s))u20442)) 〖ζ(1-s)u2044π^(((1-s))u20442) |〗^2, although the zeta and Gamma functions are asymmetric. We show their global minimum along the x-direction throughout the critical strip, their zeros, and the non-trivial zeros of the zeta function must occur at s=1/2+iy. If the zeros were not along the critical line, we show contradictions to the properties of the symmetric functional pair would arise. Thus, we prove rigorously the validity of Riemann’s conjecture.
Category: Number Theory

Determination of the Speed of Light in a Medium Using the Sagnac Effect

Authors: Rajeev Kumar
Comments: 3 Pages.

In this paper a method for the determination of the speed of light in a medium using the Sagnac effect has been presented.
Category: Classical Physics

Is the Sun Conscious? -- How Physicists Encounter with God, the Ultimate Source of Consciousness

Authors: Victor Christianto
Comments: 14 Pages. The present article is going to be submitted to a journal. This article discusses among other things the conscious phenomenon, one of cornerstone of physics too.

The question of consciousness, particularly its origin and nature, has long captivated philosophers and scientists alike. The question of consciousness, its origins, and its place in the universe, has challenged thinkers for millennia. While traditionally the domain of philosophy and neuroscience, physics is increasingly oƯering new perspectives, even suggesting the seemingly outlandish possibility of a conscious Sun. While traditionally relegated to the realm of biology andneuroscience, recent explorations in physics have begun to challenge conventional wisdom. Thepresent article examines the intriguing notion of solar consciousness, starting with RupertSheldrake's morphic resonance theory and progressing through the mathematical frameworkproposed by Hu and Wu, linked to spin mediated consciousness. We then explore how severalphysicists, including Robert Lanza, V. Venick, and Pavel Florensky, have grappled with theintersection of physics, consciousness, and faith, ultimately attempting to reconcile scientific understanding with the existence of God as a potential source of consciousness.(Note: The present article is going to be submitted to a journal. This article discusses among other things the conscious phenomenon, one of cornerstone of physics too.)
Category: Mind Science

Guynn and Suleiman: Comparing Their Structure of Matter and Space Approaches

Authors: Hans Hermann Otto
Comments: 4 Pages. (Note by viXra Admin: An abstract in the article is required)

In this short contribution Suleiman’s Information Relativity Theory (IRT) will be compared with the structure and matter approach recently developed by Guynn. Interest is once more awaked by the "apparent" non-locality of all physical respectively cosmic actions due to the postulated existence of a superluminal graviton vacuum condensate. The IRT approach is clearly a local theory of matter and energy.
Category: High Energy Particle Physics

5-Bit Classification in Crystal Classes and Genetic Code

Authors: Giuliano Bettini
Comments: 15 Pages.

I show that 5 bits, or better properties, should be enough to classify the 32 crystal classes of 7 crystal systems, and nothing more. From a rigorous point of view, each of the 32 bit sequences (from 00000 to 11111) must unambiguously identify a class, and each class must unambiguously identify a bit sequence. In this article, which aims to be very simple, easy, and understandable, I emonstrate the thesis by connecting the various bits to properties already present and known in crystallography. I use the same approach to show how even in the genetic code 5 properties or entities or bits are used to create complex structures. I start from the 64 codons table (nucleotide triplets U C A G in RNA, with T substituting U in DNA) that I then examine in a sub-version with 32 codons, still able to codify all 20 amino acids that contribute to the formation of proteins. Considering 32 codons to show symmetries can make sense in an evolutionary process of modifying the genetic code, starting from an ancestral code. I show in this way that there are analogies between the symmetries of the crystal classes and the genetic code. The basic idea is that Nature, having identified a "motif" that works, uses it in several fields.
Category: Mathematical Physics

Harmonic Relationship Between Arithmetic and Geometric Mean. an Inductive Mechanism for the Proof of the Binary Goldbach Conjecture.

Authors: Samuel Bonaya Buya
Comments: 8 Pages.

This paper presents an insightful relationship between arithmetic and Geometric mean. A bridge is established between arithmetic, geometric and harmonic mean. The concept is useful in number theory since Goldbach conjecture also implies that all integers greater than 1 are an arithmeticmean of a pair of primes.
Category: Number Theory

Global Climate in the 22nd Century

Authors: Clark M. Thomas
Comments: 8 Pages.

Earth’s global biosphere recently has deterioratedbeyond what climate forecasters had previously hoped would not occur for several decades. In 2024 global average temperatures reached the critical 1.5 degrees Celsius above the reference base that climatologists have feared could lead to a tipping point of no return. What nastiness will the full 22nd century and beyond reveal, while average global temperatures rapidly rise beyond the historical base by 4.0 degrees and more?
Category: General Science and Philosophy

Religion and the Invisible Hand

Authors: Paul Caracristi
Comments: 5 Pages. This is the first paper of a series of papers that tries to link the physical with the metaphysical.

Abstract. This essay explores the potential benefits and challenges of a model for religion divested from politics. Historically, religion has served as a political and moral authority, enforcing social cohesion and societal norms. However, by removing its political dimensions, religion could evolve into an institution focused on individual spirituality and ethical development, accountable to its follower’s true needs. This shift would emphasize personal virtue and foster a new, self-organizing social structure where collective harmony emerges not from imposed control but from individual integrity and responsibility. Such a model, as inspired by the principles of the "invisible hand" in economics, could enable religion to cultivate personal character and social virtues in ways that naturally contribute to societal well-being without traditional hierarchies or overt political influences.
Category: Religion and Spiritualism

The Will to Be: The Expression of a Universal Drive to Experience Existence

Authors: Paul Caracristi
Comments: 4 Pages. (Note by viXra Admin: An abstract in the article is required!)

The mystery of why the universe exists and how consciousness arises within it has captivated my mind for decades, as well as the minds of philosophers, scientists, and theologians for centuries. One possible framework for understanding this enigma is the concept of a fundamental ‘Will to Be,’ a universal drive or a force of change that underpins reality and seeks to realize itself through conscious awareness, enabling the experience of existence.
Category: Religion and Spiritualism

Design of an Oral Malaria Vaccine Candidate Using Yeast - Expressed CTB-MSP-TOS Fusion

Authors: Hyunho Shin
Comments: 4 Pages.

Malaria remains a significant global health challenge. This study describes the construction and expression of a fusion protein for a malaria vaccine candidate, combining the cholera toxin B subunit (CTB) with two antigens: Merozoite Surface Protein (MSP) and Transferrin-Binding Outer Surface Protein (TOS). The fusion protein, joined by GSGG linkers to maintain functional independence, was expressed in Saccharomyces cerevisiae and subsequently heat-dried to ensure yeast cell inactivation while preserving antigen integrity. This study outlines the experimental design, vector construction, protein expression, and antigen preservation methods, laying the groundwork for further characterization and testing.
Category: Physics of Biology

Stirling Alpha Engine with Circulation

Authors: Josef Bukac
Comments: 3 Pages. (Note by viXra Admin: An abstract in the article is required)

Stirling engine of type alpha is the field to which this paper belongs. Such engines are used for micro-co-generation of electric power. So far, we were able to find references to those sources of heat for which the temperature is easily kept constant, such as natural gas or pellets. For more independent source of heat we want to consider firewood burnt in a wood stove. We are presenting an idea of circulation of the working gas to increase the temperature difference enabling the engine to run under varying conditions. The circulation makes sense if there is a way of cooling the working gas.
Category: Thermodynamics and Energy

Top Quark Mass Confusion

Authors: D. G. Grossman
Comments: 6 Pages.

From 2011 to 2024 physicists at the LHC measured the top quark's mass 29 times and got 29 different measurements over a range of about 6.5 GeV. Why weren't they able to zero in on it? Were they even measuring the top quark's mass? What were they measuring?
Category: High Energy Particle Physics

Is Time a Fundamental Category?

Authors: P. A. M. Moellers
Comments: 25 Pages. This work is prepared from an Informatics background awaiting comments from physics.

Is Time a fundamental category and, if so, on the smallest thinkable scales? Maybe not. To test this conjecture this paper proposes a simple discrete model, the Klick Model. It bases Time on the correlation of two other categories, abstract definitions of motion and state implementation - an Informatics based approach to a problem in physics.

The original motivation to develop the model was to understand the biological/atomic ageing of the twins of the so-called Twin-Paradox, seen as a benchmark combining time and space of smallest and largest scales. Without loss of generality, let us assume that the twins can be represented by two isolated (free) abstract particles in steady motion.

A model is only a model. It has to make falsifiable predictions for the real world. Therefore, I will show that for the Twin-Paradox it leads to the known result from Special Relativity Theory. For smallest scales the task is much more difficult. Only a qualitative test based on structural similarities can be offered here, defining a discrete logic for ground states, excited states and their correlations in the framework of the model, trying to map the abstract model to Einstein’s discrete interpretation of Planck’s law of radiation.

To understand the rational of the proposed model it is helpful not to expect a concept of space and time on smallest scales, particularly on the question whether they can be assumed continuous or discrete, although the model leans to a discrete structure.

The assessment based on the proposed model: The underlying relation for time relying on motion and state implementation is (likely) discrete, suggesting age as more fundamental than time. Regarding Hermann Weyl’s Tile Argument, I think that Pythagorean Law prevails, not through geometry or a metric, but as a preserving law between the above categories. Geometry, needed to define time on our scales, might only evolve on larger scales and dependent on the (dynamic) content of space.

The proposed model is Informatics based, driven by interest and not by competence in physics. Nevertheless, I will use terms from physics based on the approach of Denotational Semantics, keeping the gap between Syntax and Semantics as close as possible by relating abstract model properties to supposed properties of the real world.

Keywords: Discrete Space, Discrete Time, Twin Paradox, Hermann Weyl’s Tile Argument, Einstein’s Theories, Sub-Quantum Assumption, Einstein Coefficients

Sagnac Effect Revisited

Authors: Rajeev Kumar
Comments: 3 Pages.

In this paper an explanation of the Sagnac effect has been presented.
Category: Classical Physics

The Three Generations Problem in Particles Physics

Authors: Thierry L. A. Periat
Comments: 17 Pages.

The three generations problem is an open enigma concerning some types of leptons and of quarks in the standard model. The search for explanations dates back at least to the early 1980s. This document is a modest attempt to bring this research out of the nimbus of numerology. In a first step I introduce a special family of (3-3) matrices. Some of them are the representations of unit four-dimensional spheres via a Euler-Rodrigues parametrization. In a second step, I confront them with a condition formally preserving the definition of the Poynting vector in a changing geometrical context.
Category: Mathematical Physics

Rigorous Proof and Spectral Analysis of the Yang-Mills Mass Gap Problem

Authors: YoonKi Kim
Comments: 3 Pages. Email for correspondence: yoonki0905@gmail.com

This study rigorously proves the Yang-Mills mass gap problem using analytical methods and spectral theory. By analyzing the Wilson loop expectation value based on the Poisson equation, we demonstrate that the mass gap inevitably forms in SU(N) gauge theory. Additionally, we utilize Hilbert space analysis and operatortheory to prove that the lowest eigenvalue of the Yang-Mills Laplacian is strictly greater than zero, confirming the existence of the mass gap in a mathematically rigorous manner. Furthermore, we clarify how these assumptions hold under renormalization and in the continuum limit. These findings contribute to solving theYang-Mills mass gap problem and provide new directions in mathematical physics.
Category: Mathematical Physics

The Creation Process of Electrons, Protons, the Gravitational Field, and the Dark Energy Field

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

The energy body theory has revealed that material particles, gravitational fields, and dark energy fields occur almost simultaneously as one phenomenon. In other words, material particles are Planck-scale particles (energy cell bodies) that make up space, which are compressed and vibrate with expansion and contraction while shifting the phase in the rotation direction. As a result, the surrounding space becomes low energy. Energy then flows into this space from the space outside. Then, the space from which the energy flows out becomes low energy, so energy flows out from the space outside. Then, after the outflow and inflow of energy in this spherical space is repeated and spread throughout the universe, the energy swings back and becomes stable. In this process, the layer formed by the spherical compression of the energy cell bodies around the star is the gravitational field, and the layer formed by the spherical expansion of the energy cell bodies throughout the universe is the dark energy field.
Category: Astrophysics

ChronoScalar Theory: A Testable Quantum Origin of Time and Gravity

Authors: Nir Platek
Comments: 14 Pages. © 2025 Nir Platek. All rights reserved. Pre-print.

The reconciliation of quantum mechanics and general relativity hinges on resolving the "problem of time." In general relativity, time is a dynamic coordinate, whereas quantum mechanics treats it as an external, absolute parameter. Canonical quantum gravity, encapsulated by the Wheeler-DeWitt equation H Psi = 0, produces a timeless wavefunction, leaving the emergence of classical time unexplained. ChronoScalar Theory (CST) addresses this by introducing a quantum scalar field, termed the "chronon," which acts as an internal clock. Through a Born-Oppenheimer approximation, CST separates the gravitational and scalar degrees of freedom, enabling the chronon’s phase evolution to generate a Schrödinger-like equation. This mechanism dynamically produces time as an emergent property, bridging the quantum and classical regimes. The chronon is governed by a double-well potential V(Phi) = lambda (Phi^2 - v^2)^2, with a mass m_Phi ~ 0.1 meV, a scale intriguingly aligned with dark energy observations.CST offers testable predictions, notably a fifth force mediated by the chronon. This force, characterized by a Yukawa potential with strength alpha_G ~ 10^-4 and range lambda ~ 2 mm, operates at experimentally accessible scales. Precision torsion-balance experiments could detect this force, particularly in low-density environments, thanks to a built-in screening mechanism that ensures consistency with existing gravitational constraints. Beyond resolving the problem of time, CST connects to cosmology by proposing the chronon’s vacuum energy, rho_Phi ~ (0.1 meV)^4, as a candidate for dark energy, matching the observed cosmological constant.This theory’s testability sets it apart. The predicted fifth force provides a concrete empirical target, while its dark energy link offers a unified explanation for quantum gravity and cosmic phenomena. If validated, CST would mark a significant advance, not only solving a foundational issue in theoretical physics but also providing an observable bridge between quantum gravity, particle physics, and cosmology. Ongoing and future experiments targeting millimeter-range forces could confirm or refute CST, making it a compelling framework for exploring the quantum origin of time and gravity.
Category: Quantum Gravity and String Theory

Geometrized Vacuum Physics Part 10: Naked "Planets" And "Stars"

Authors: Mikhail Batanov-Gaukhman
Comments: 28 Pages.

This article is the tenth part of the scientific project under the general title "Geometrized Vacuum Physics Based on the Algebra of Signature" [1,2,3,4,5,6,7,8,9]. In this article, based on exact solutions of the extended Einstein vacuum equation, metric-dynamic models of stable spherical vacuum formations of planetary scale with a core radius of the order of r ~ = 100 — 1000 km are proposed. These electrically neutral vacuum for-mations are called naked "planets" and "stars". The concept of a naked "planet" implies that this article does not take into account the presence and influence of small vacuum formations (micro-, nano- and picoscopic "particles"), only curvatures of the vacuum of stellar-planetary scale are considered. In particular, metric-dynamic models of a naked "star" and naked "planets" of the Solar System are proposed. The analogy between the naked "Solar System" and a biological cell is shown. Like the entire project, this article is aimed at implementing the program of complete geometrization physics of Clifford-Einstein-Wheeler.
Category: Classical Physics

On Linkage Between Incompressible Integers as Distance and 1/r Potential

Authors: Dara O. Shayda
Comments: 14 Pages.

The main result: assuming distances are numericized as incompressible integers, given two objects, one stationary and the other moving, the rate of change of the measure of their distantial randomness is that of the potential form 1/r. This form is known as the Newtonian potential. If the incompressible assumption dropped then the potential form vanishes as well (conjecture). The supplementary results by Whittaker: for any force varying as the inverse square of the distance, the potential of such a force satisfies both Laplace's equation and the wave equation, and can be analyzed into simple plane waves propagating with constant velocity. The sum of these waves, however, does not vary with time, i.e. standing waves. Therefore, the 1/r potential can be defined as summation of waves. Thus the linkage between the incompressible integers and particular standing waves in physics.
Category: Mathematical Physics

Logarithm of Exponential and Cauchy Random Variables

Authors: Josef Bukac
Comments: 3 Pages. (Note by viXra Admin: An abstract in the article is required)

We show how to calculate the expectation and the second moment of logarithm of exponential distribution. There are two ways to do this.The Cauchy distribution has no expectation but we calculate the expectation and second moment of the logaritm of the absolute value of the Cauchy distribution.
Category: Statistics

Quantum Information Grand Unified Theory: Unifying Gravity and Gauge Forces via Quantum Entanglement Networks

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

Quantum Information Grand Unified Theory (QI-GUT): Unifying Gravity and Gauge Forces via Quantum Entanglement NetworksWe propose a novel framework, the Quantum Information Grand Unified Theory (QI-GUT), which unifies gravity and gauge interactions by treating spacetime and fundamental forces as emergent from an underlying quantum entanglement network. This approach leverages a quantum error-correcting code embedded within an SO(10) grand unification structure, providing a self-consistent mechanism for generating spacetime geometry and gauge bosons. Our model naturally reproduces Einstein’s field equations, predicts the unification of fundamental forces, and offers a new perspective on dark matter as stable defects in the entanglement network. The theory makes concrete, testable predictions, including Planck-scale deviations in gravitational waves, modified black hole entropy scaling, and observable proton decay signatures. This work bridges quantum information theory and high-energy physics, presenting a pathway toward a deeper understanding of quantum gravity and unification.
Category: High Energy Particle Physics

Fractal Holographic Lattice Cosmology: A Λ-Free Resolution of the Hubble Tension

Authors: Joshua D. Smith
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references; AI assisted article is in general not acceptable)

Fractal Holographic Lattice (FHL) Cosmology resolves the Hubble tension without a cosmological constant, achieving H(0) = 73.2 km/s/Mpc locally and H(z = 1100) = 67.4 km/s/Mpc at the CMB epoch, matching SH0ES and Planck constraints. It reproduces intermediate expansion and growth rates (H(z = 0.51) = 74.7 km/s/Mpc, f(z = 0.51) ≈ 0.71) per DESI BAO, validated across z = 0 to z ≈ 1100against supernovae, cosmic chronometers, Lyman-alpha forest, and clustering data. FHL eliminates dark energy, leveraging a fractal lattice geometry, and aligns with gravitational wave dispersion, shortdistance gravity tests, and black hole entropy corrections.
Category: Relativity and Cosmology

Experiment to Discover the Nature of Dark Matter

Authors: Gerard van der Ham
Comments: 3 Pages. 2 figures (Note by viXra Admin: Please cite and list scientific references)

In this paper an experiment is proposed to establish the effect of the shape of matter on gravity.
Category: Astrophysics

Quantum Superposition and the Mind: A Cognitive Filtering Hypothesis

Authors: Seung Yun Heo
Comments: 6 Pages.

This paper proposes a paradigm shift in the interpretation of quantum mechanics, reframing wavefunction collapse as cognitive selection. Prevailing interpretations of quantum mechanics—such as the Copenhagen interpretation, Many-Worlds, and objective collapse theories—assume that quantum superpositions resolve into singular outcomes via measurement or branching realities. This paper posits an alternative hypothesis: quantum superpositions exist within a single universe, but our perception filters and stabilizes a single outcome. To test this hypothesis, a modified delayed-choice quantum eraser experiment is proposed, introducing observer delusions to determine whether wavefunction collapse is influenced by an observer’s belief about which-path information, rather than its mere physical recording. This framework bridges quantum mechanics, neuroscience, and artificial intelligence, offering a falsifiable alternative to existing interpretations. If validated, this hypothesis would expand our understanding of the observer’s role in quantum mechanics.
Category: History and Philosophy of Physics

A Geometric Algebra (GA) Solution to a Multiple-Tangency Problem

Authors: James A. Smith
Comments: 8 Pages.

Using GA's capacities for formulating reflections, we solve an interesting multiple-tangency problem. The solution is obtained in two ways, the easiest of which transforms the relevant reflections into a single rotation. The solution is validated via a GeoGebra worksheet.
Category: Geometry

Classification of Composite Numbers

Authors: Samuel Bonaya Buya
Comments: 3 Pages.

In this research different and distinct subsets of composite numbers are identified together with their Logical formulae. The aim of the research is to come up with an efficient method of sieving out primes from a set of positive integers.
Category: Number Theory

Gravity and Light Speed Novel Concept for Stellar Aberration

Authors: Florian Michael Schmitt
Comments: 22 Pages.

This work presents, for the first time in history, a coherent and correct concept for stellar aberration based on the wave nature of light and classical physics. Considering the spherical propagation of the light wavefront and the motion of the observer relative to the Cosmic Microwave Background (CMB) leads to a physically meaningful formula that, unlike the classical formulas, relates to the squares of the velocities for light and the CMB. Moreover, stellar aberration is explained by the entire light path from the star to the observer, with significant consequences for the concept of a dragged ether and the reinterpretation of a large number of experiments. It is demonstrated that all relevant experiments can be consistently explained within the framework of an ether fully dragged by gravity. The anisotropy of light is presented from a new perspective, and time dilation and length contraction become obsolete.
Category: Relativity and Cosmology

Cyclic Representation of the Dirac Equation (English)

Authors: Sergey Y. Kotkovsky
Comments: 28 Pages. This is an English translation of the paper in Russian viXra:2502.0040

Based on the developed chiral algebra of biquaternions, a new representation of the Dirac equation is obtained. Our formulation of this fundamental equation combines in a certain way the forward and reverse 4-gradient operators acting on the right and left chiral components of the particle wave function, as well as the cyclic transformation operator acting on the entire particle wave function. The obtained representation makes it possible to see in the Dirac equation the relationship between linear and cyclic times. The chiral algebra used in this approach provides new methods for studying relativistic spin physics. An analog of the Lorentz transformation, a new rotation transformation is derived, that creates the proper rotation of a massive particle. It is shown that the cyclic transformation included in our representation of the Dirac equation is expressed via complex-valued Hadamard matrix, which indicates the connection of the Dirac equation with known algorithms of noise-resistant information transmission.
Category: Quantum Physics

The Factor of 4/3 Paradox Between Electromagnetic Momentum and Electromagnetic Energy is Fully Resolved by Correct Choice of the Structure of the Electromagnetic Field Stress Energy Tensor

Authors: Kenneth Sandale
Comments: 12 Pages.

The ratio of electromagnetic momentum to electromagnetic energy is thoughtto be the velocity, but when calculated for a uniform velocity point charge isoff by a factor of 4/3. The apparent problem is fully resolvable if we note thatthe electromagnetic stress energy tensor has a non-vanishing Tii for a particleat rest, and if we then use the appropriate relationship for the Stress Energycomponents for an object which has non-vanishing Tii in its rest frame.
Category: Classical Physics

Are There Infinitely Many Numbers Whose Sum of Divisors Is a Perfect Square?

Authors: Minhyeok An
Comments: 16 Pages. If this paper contains no errors, resolving Bunyakovsky’s conjecture through this approach would hold even greater mathematical significance than previously recognized.

The numbers whose sum of divisors is a perfect square may initially appear to follow no specific pattern. However, through this research, I have identified a particular rule related to prime numbers. Furthermore, I establish that the existence of infinitely many numbers whose sum of divisors is a perfect square is a necessary and sufficient condition for the existence of an irreducible polynomial with integer coefficients that generates infinitely many prime numbers. Additionally, I explore its connection to Bunyakovsky's conjecture.
Category: Number Theory

The Complete Eigenwert-Solution of Damped Spacetime-Oscillations for Two Coupled Tangential Spacetimes with Ftl-States-Final Version

Authors: Holger Döring
Comments: (Non-comforming pages are removed by viXra Admin)

The complete eigenwert-problem of damping process of oscillating tangential spacetime is described and solved. Characterized are all solutions of an associated spacetime - differential-equation of second order from advanced Lorentz-Einstein-factor, which defines the whole oscillation-process of damping states. This system of oscillation-solutions can be described as a set of energy-equations. The system of two coupled spacetimes to a linked shell-model allows movement of material bodies or particles with ftl and real restmasses. This spacetime- lineelement can be interpreted as a one-parametrized pseudo-Kummersurface.
Category: Quantum Gravity and String Theory

The Contradiction Between the Law of Universal Gravitation and the Second Laws of Newton and Kepler

Authors: Viktor Strohm
Comments: 9 Pages.

The motion of bodies along an ellipse with a constant sector velocity is considered. At perihelion, the velocity and acceleration are greater than at aphelion. The radii are the opposite: at perihelion, the radius is smaller than at aphelion. Therefore, if the force is calculated using Newton's second law, it will not be equal to the force calculated using the law of universal gravitation.
Category: Astrophysics

Generalized Solutions of Nonlinear Equations of Mathematical Physics and Their Implications for Turbulence, Electromagnetism and Cosmology.

Authors: Michael Isaac Aksman
Comments: 21 Pages.

Vortons introduced to approximate finite core vortex tubes and pass through Navier Stocks spontaneous singularities/reconnections without any additional assumptions. Vortons provide irreducible description of inviscid attractor of 3D Navier Stocks equation solutions with number of vortons scaling with Reynolds number at hand.Magnetic vortons provide irreducible description of magnetic vortex tubes in plasma with reconnections without any additional ssumptions.Instability of quasi 3D/2D+ vorton collapse provides possible mechanism for explosive universe inflation/first order phase transition.3D space nature of our universe as a consequence of instability of 3D vortons collapse."Dark matter" explained as a consequence of Frisbee like quasi 3D space in galaxies with corresponding stable rotational curves."Dark energy" explained as a emergent result of vortons system 3D self amplification interactions energy "antigravity" effect.Probabilistic interpretation of quantum mechanics as a result of smooth test functions of fluid vacuum nonlinear Maxwell equations weak solutions. Baryonic asymmetry explained as a instantaneous snapshot during exponential inflation of quark antiquark annihilation asymmetry/skewness and kurtosis terms in Edgeworth series expansion of instantaneous quantum GUP fluctuations. Simple Early Bifurcation/Regime shift detection in nonequilibrium nonlinear statistical systems proposed using linear statistical moments/cumulants approximation
Category: Classical Physics

Eigenvalues in Binary and Ternary Number Systems

Authors: Ruslan Pozinkevych
Comments: 5 Pages.

One of the biggest issues in discrete mathematical research is to set up the mapping system that would clearly define the transition between various counting groups e.g decimal, ternary, nonary etc. This is only possible if we set a one-to-one correspondence between members of a set In his previous work "Optimization Techniques in Ternary Calculus" the author just tried to do that by relating decimal numbers to their binary correspondence however a universal formula is much more desirable and current investigation will attempt to find this very universal approach$left[ 8 ight]$
Category: Number Theory

Resolving the Muon and Electron g-2 Anomalies Using Generalized Modular Spectral Theory (GMST)

Authors: David Vickers
Comments: 4 Pages.

We introduce Generalized Modular Spectral Theory (GMST) as a novel theoretical framework that provides the first empirically validated spectral correction to quantum electrodynamics (QED), resolving the Muon g-2 and Electron g-2 anomalies with exact numerical agreement to experimental measurements. Unlike beyond-Standard Model proposals such as supersymmetry or leptoquarks, GMST derives a purely theoretical correction from modular spectral constraints, requiring no new particles or interactions. The predicted corrections, [Delta a_{mu}^{GMST} = 2.55 times 10^{-9}, quad Delta a_{e}^{GMST} = -8.7 times 10^{-14},]align precisely with the latest Fermilab Muon g-2 and Harvard Electron g-2 measurements, marking the first successful theoretical resolution of both anomalies within a single unified framework. Beyond its immediate empirical validation, GMST establishes a fundamentally new spectral approach to quantum field theory, with deep implications across high-energy physics and mathematical physics. The framework has already produced candidate solutions to all six Clay Millennium Problems, with four currently under submission at Communications in Mathematical Physics (CMP). Furthermore, GMST predicts testable deviations in electroweak precision experiments at the LHC, modular spectral signatures in Muon Collider data, and potential extensions to quantum gravity via modular field constraints. This paper serves as the first formal introduction of GMST in published literature, with empirical validation at the point of introduction, positioning it as a new governing law of fundamental physics. Given its unprecedented accuracy, predictive power, and broad applicability, GMST represents a paradigm shift, providing a universal spectral framework for future theoretical and experimental advancements.
Category: High Energy Particle Physics

Solutions for Dot Product and Cross Product Equations of Vectors

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

For the fundamental equation $ax=b$, we naturally consider the Moore-Penrose generalized solutions and we obtain the division by zero $b/0=0$ always as its unique solution. So, here, we will consider the solutions of the dot product equation $acdot x= b$ and the cross product equation $ a times x=b$.
Category: General Mathematics

Optimizing Rational Neural Networks with Natural Gradient Descent

Authors: Di Zhang
Comments: 7 Pages.

In recent years, rational neural networks (RNNs) have emerged as a powerful alternative to traditional neural networks, leveraging rational activation functions to achieve superior approximation capabilities and improved performance on various tasks. However, the training of RNNs remains challenging due to the complex nature of rational functions and the high-dimensional parameter space. In this work, we propose to optimize RNNs using natural gradient descent (NGD), an optimization algorithm that exploits the geometry of the underlying statistical model by incorporating the Fisher information matrix. This approach allows us to efficiently navigate the complex parameter landscape of RNNs, leading to faster convergence and better generalization. We develop efficient algorithms to compute the Fisher information matrix and its inverse for RNNs, making NGD-based training feasible and scalable. Extensive experiments on multiple benchmark datasets demonstrate the superior performance of our proposed method over existing optimization algorithms such as stochastic gradient descent (SGD) and Adam. Our results highlight the potential of combining NGD with RNNs for a wide range of applications in deep learning.
Category: Artificial Intelligence

A Precise Unified Mass Formula for Leptons and Quarks: Insights from Sedenion Algebra’s Spinor Structures and Internal Symmetry

Authors: Jau Tang, Qiang Tang
Comments: 15 Pages. DOI: 10.5281/zenodo.14750814

We propose a unified mass formula, log m = Alog x + B + Cx that accurately describes the masses of charged leptons (x=1, 2, and 3) and light and heavy quarks (x=1^3, 2^3, and 3^3) across all generations. Unlike the Koide mass-ratio formula, our approach provides a direct and precise formula for individual particle masses. The observed cubic dependency and mass increments are linked to 4D hypersphere geometry, governed by the spinor spacetime structures of the sedenion algebra and the spacetime symmetries. This novel framework offers new insights into elementary particles' mass spectrum, internal structures, and symmetry.
Category: High Energy Particle Physics

Octonionic Preon Model as an Alternative to the Higgs Mechanism for the Mass-Ratio Prediction of the Weak and Higgs Bosons

Authors: Jau Tang, Qiang Tang
Comments: 16 Pages. DOI: 10.5281/zenodo.14751111

Unlike the conventional treatment of the weak bosons in the Yang-Mills theory, which utilizes the Dirac equation for a point-like particle with no internal degrees of freedom, we propose an octonionic preon model to describe the internal dynamics of this vector0boson family with a photon as a isospin singlet, Z, W+, and W- bosons as a triplet. Instead of the Higgs mechanism, their masses are acquired from the internal dynamics of the chiral pair via strong spin-exchange couplings. Assuming couplings involving Gell-Mann’s lambda matrices, with no adjustable parameters, we predict mw/mz = sqrt(3)/2~ 0.87 vs. 0.88, a Weinberg angle of 300 vs. 29o, decay width mH/mW = sqrt (3)/2~ 0.87 vs. 0.84, and a Higgs boson, as a composite of W and Z bosons, with mw/mz = sqrt(7/3)~ 1.53 vs. 1.56 experimentally. These small discrepancies can be accounted for if weak interaction couplings are included. We use octonion operators to represent these particles and to elucidate their connections, and the topological structures' relations to fiber bare bundles and Hopf fibration. Moreover, we elucidate that our proposed preons are essentially the foundation for ding the hypercomplex algebra, and they are the building blocks for the composite particles that represent the topological structures in the higher-dimensional spacetime.
Category: High Energy Particle Physics

Light As You Have Never Seen It Before

Authors: David Lindsay Johnson
Comments: 52 Pages.

There many uncertainties regarding the nature of EMR, and light in particular. Conventional Science generally acknowledges that EMR energy is delivered in photon packages, but is decidedly vague as to the physical form of photons in terms of the number of wavelengths involved, and whether they have a particle or a wave-like form. There is general acknowledgement that light has wave—particle duality, but the cross-over point between the two forms is ill-defined. As the term ‘electromagnetic radiation’ (i.e. EMR) suggests, Conventional Science considers that EMR consists of electromagnetic waves consisting of wave-like pressure-pulses of electromagnetic energy and momentum moving at the speed of light. However, such electromagnetic pressure-pulses need some type of substrate, commonly referred to as aether, to sustain them across the vast distances of virtually empty Space. However, all of the many well-publicised science-based attempts to prove the existence of aether have failed dismally, and so the mystery continues as to how electromagnetic waves can sustain themselves through Space.This paper throws new light on the nature, form and generation of all forms of EMR, but for light in particular. Firstly, it distinguishes between photonic and mon-photonic EMR, and puts forward a physical structure for photonic EMR (that includes visible light) that means that observed particle-wave duality characteristics of light would be expected rather than considered to be enigmatic. As well as addressing a wide range of light-related topics such as the refraction of light passing through different transparent media; plane, circular and elliptically polarised light; the chromatic dispersion of light; and exotic forms of light such as optical vortex light, the model put forward does not require aether for EMR to travel through Space. It is truly be a case of ‘light as you have never seen it before’ because it presents clear feasible explanations of light-related phenomena that have previously been unaddressed, or only partly and poorly addressed. Let there be light.
Category: Classical Physics

Whole Number Pythagorean Triplets

Authors: Reece Tinkler
Comments: 5 Pages.

Pythagorean triples are sets of three whole numbers that satisfy the equation. This paper introduces two new formulas related to Pythagorean triples. The first formula determines the largest possible value for a given, ensuring that all elements remain whole numbers. The second formula explores the special case where, identifying recurrent patterns within Pythagorean triples.
Category: Number Theory

Calculation and Prediction of the Hydrogen Atomic 1S—2S Transition Frequency

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 9 Pages. In Chinese (Note by viXra Admin: Further repetion may not be accepted!)

In our last paper, we started with the 87Sr atomic transition frequency which is 429228004229872.99(8) Hz, calculated out and predicted the 229Th nuclear transition frequency which is 2020407384335167.11(38) Hz, and calculated out more precise value of the atomic unit of time tau which is 2.41888432658653284(45)×10-17 s, and with the later calculated out the atomic transition frequencies of 27Al+、199Hg、115In+ and 199Hg+. In this paper, we employ this same method to calculate out and predict the hydrogen atomic 1S—2S transition frequency, which is 2466061413187017.96(46) Hz.
Category: Nuclear and Atomic Physics

Acceleration Particle Swarm Optimization

Authors: Satish Gajawada
Comments: 15 Pages.

Particle Swarm Optimization (PSO) is a popular optimization algorithm for solving complex optimization problems. Many PSO algorithms were proposed in literature where Velocity was calculated first and then it was added to position to obtain new position. In this work, a novel algorithm titled "Acceleration Particle Swarm Optimization (AccPSO)" is proposed where acceleration is calculated first and then displacement is obtained next with initial velocity, acceleration and time. Displacement is added to position to get new position. Unlike many PSO algorithms in literature, where iterations and time are used interchangeably, the time "t" in AccPSO algorithm is a continuous variable. In this work, AccPSO, PSO, Acceleration-based Particle Swarm Optimization (APSO) and APSOc (APSO with clamping) are tested on seven benchmark functions. Results obtained are discussed. It has been found that AccPSO with time "t" = 0.1 and "t" = 0.25 between iterations yielded optimal results when tested on benchmark functions.
Category: Artificial Intelligence

A Conformal Emergent Reality Model (CERM): Theoretical Foundations, Mathematical Derivations, and Observational Implications

Authors: Salman Akhtar
Comments: 82 Pages.

The Conformal Emergent Reality Model (CERM) proposes a new paradigm in which spacetime is not a fundamental construct but emerges dynamically from a deeper Conformal geometry manifold (M, γ_μν) coupled with a scalar field Ω(x). This paper presents a comprehensive theoretical framework for CERM, detailing its mathematical foundations, field equations, and implications for Quantum Field Dynamics (QFD) and Quantum Electrodynamics (QED). By attributing gravitational anomalies to the behavior of Ω(x), CERM eliminates the need for dark matter and dark energy, offering a unified explanation for galactic rotation curves, cosmic acceleration, and the arrow of time. The model predicts observable phenomena, such as modifications to gravitational wave propagation, time-varying particle masses, and entropy growth driven by the evolution of Ω(x). These predictions are systematically analyzed alongside unresolved theoretical challenges, providing a pathway for future observational tests and refinements.
Category: Quantum Gravity and String Theory

A Space-Time Equation for Electromagnetic Interaction.

Authors: Davide Cericola
Comments: 10 Pages. (Note by viXra Admin: Authors' names should be listed right after the title)

In the present work is explored the profound symmetry between the theories of gravity and electromagnetism, with particular attention to the similarity between the fundamental forces of nature: the weight force and the electric Lorentz force, Newton's law and Coulomb's law, as well as Maxwell's equations and the equations of gravitational electromagnetism. There are papers that explain how to obtain the gravitational electromagnetism equations by applying the weak field approximation to the Einstein field equations. Precisely in honour of this symmetry, this work aims to obtain Einstein field equations valid for electromagnetism, i.e. field equations from which to derive, under weak field approximation, Maxwell's equations. This research suggests a parallel vision between electromagnetism and gravity, suggesting that perhaps there could be a curved electromagnetic field in 4 dimensions alongside the curved gravitational field (Einstein's space-time).
Category: Relativity and Cosmology

A Centralized AI Approach to Reducing IT Burnouts Through Work Pattern Monitoring

Authors: Barnty Barnabas, Olatunji Marvelous
Comments: 13 Pages.

Burnout among IT professionals has become a critical concern, driven by excessive working hours, high expectations, and constant pressure to perform. This article explores a centralized AI approach to reducing burnout in the IT industry through the monitoring of work patterns. By leveraging AI-driven tools, organizations can track key indicators such as work hours, task completion rates, communication patterns, and stress signals to identify early signs of burnout. The study investigates how AI can proactively detect these patterns and provide insights that enable managers to intervene before burnout escalates. Through a mixed-methods approach, combining quantitative data from AI monitoring systems with qualitative feedback from employees, the research highlights the potential of AI to not only identify burnout risks but also mitigate them by informing decisions on workload distribution and wellness interventions. The paper discusses the benefits, challenges, and ethical considerations of AI in workplace monitoring, proposing a holistic model that integrates AI with employee well-being initiatives to improve both productivity and mental health in the IT sector.
Category: Artificial Intelligence

The Relationship Between Perceived Social Support and Adolescent Psychological Adaptation: the Multiple Mediating Effects of Belief in a Just World and Personal Control

Authors: Debao An
Comments: 18 Pages.

To explore the mechanism of perceived social support on the psychological adaptation of adolescents, this study investigated 895 adolescents from six middle schools (junior high and senior high) in the northwest region of China using the Perceived Social Support Scale, Psychological Adaptation Questionnaire, Just World Belief Scale, and Personal Control Scale. The results showed that perceived social support was significantly positively correlated with psychological adaptation (r = 0.529, P < 0.001), just world belief (r = 0.393, P < 0.001), and personal control (r = 0.387, P < 0.001). Regression analysis indicated that perceived social support could significantly positively predict psychological adaptation (β = 0.529, t = 18.217, P < 0.001), just world belief significantly positively affected psychological adaptation (β = 0.184, t = 5.948, P < 0.001), and personal control significantly positively affected psychological adaptation (β = 0.067, t = 2.127, P = 0.034). The results of the structural equation model showed that just world belief and personal control played a multiple mediating role between perceived social support and psychological adaptation (χ2 = 138.743, df = 38, χ2/df = 3.651, GFI = 0.973, AGFI = 0.953, CFI = 0.977, IFI = 0.977, NFI = 0.969, TLI = 0.967, RMSEA = 0.054). That is, perceived social support can not only directly influence the psychological adaptation of adolescents but also indirectly affect it through the simple multiple mediating effects of just world belief and personal control, as well as through the chain mediating effects of just world belief and personal control.
Category: Social Science

[On] Triangulation

Authors: Abdelmajid Ben Hadj Salem
Comments: 7 Pages. In French

In just a few pages, this note presents triangulation: the classic method of observing the geodetic points of a terrestrial geodetic network.
Category: Geophysics

Physical Interpretation of the Zero Spatial Curvature Universe Models

Authors: Fernando Salmon Iza
Comments: 11 Pages.

The standard cosmological model ΛCDM cannot respond to some important new results of modern cosmology. Challenges arise such as the Microwave Background Uniformity, the Hubble Tension, the El Gordo collision or impossible galaxies (z > 10) that the standard cosmological model does not solve. On the other hand, other models are proposed as alternatives. Among the models proposed in recent years, the Rh=ct universe is one of the most studied and it seems that it does solve these challenges favorably. Therefore, it is the obligation of every scientist to adequately substantiate the model and study the physical meaning it has through its equations. This model is based on the following equations, the restriction Rh = ct, where Rh is the gravitational horizon and the condition of zero active mass, (ρ+3p) = 0. We have carefully studied the foundation of these two equations and have obtained that the model responds to the condition of a universe of zero spatial curvature, being the only model compatible with it. Thus, to investigate the physical meaning of the models of universe with zero spatial curvature is to investigate the physical meaning of this model. To do so, we have obtained an equation that relates spatial curvature to the density of matter, resulting in zero curvature only being obtained if the density of matter is zero. Thus, we deduce that the physical meaning of models with strictly zero spatial curvature is an empty universe in all cases, highlighting the importance of spatial curvature.
Category: Astrophysics

A Theory of Hadron Structure Involving Higher Dimensional Matter

Authors: D. G. Grossman
Comments: 12 Pages.

Quarks may be made of higher dimensional matter. If true, then it follows that all hadrons are made of higher dimensional matter. The conventional thinking about quarks, that they are point particles, has not proved useful over the past 50 years. A more useful idea is that the six known quarks (u, d, s, c, b, t) are made of higher dimensional matter, the dimensions of which are respectively (1, 2, 3, 4, 5, 6), and each are equal to a volume of matter defined by the unit radius n-sphere surface volume formula of equal dimension. This gives theorists a mathematical handle, with which quarks and hadrons can be investigated.
Category: High Energy Particle Physics

Proof of the Collatz Conjecture

Authors: Fabrice Trifaro
Comments: 16 Pages.

The Collatz conjecture, also known as the Syracuse conjecture or the 3x+1 problem, is a mathematical conjecture according to which the Collatz sequence always reaches the value 1, and then repeats the cycle (1,4,2) indefinitely, regardless of the first term of the sequence as long as it is a strictly positive integer. It originated in the 1930s and its authors are mainly Lothar Collatz and Helmut Hasse, the latter shared it in the United States during a visit to Syracuse University, and the Collatz sequence then became known as the Syracuse sequence. To date, this conjecture has not been proven either true or false. The purpose of this study is to prove, as clearly and precisely as possible, that this conjecture is true. The proof is based on classical mathematics which should not pose any major difficulties.
Category: Number Theory

On Time & Dynamics [:] a Space-Time 4D Topology in 3D Space

Authors: A. V. Herrebrugh
Comments: 14 Pages. Preparation for journal peer review submission

A conceptual 4-dimensional vector space-time consisting of an orthogonal vector-time coordinate in a 3-dimensional space is developed to support system dynamics.This 4D space-time concept deviates fundamentally from the observer oriented theory of special and general relativity, is based upon true time simultaneity of events and separates true, objective reality oriented simultaneous events from observed simultaneous events (in A.Einstein’s relativity).The proposed geometric model is conventional Cartesian in 3D space and introduces virtual time-surfaces of true time simultaneity as a fourth dimension for validity in vector- and tensor- spaces, leading to a compliant 4-dimensional orthogonal vector coordinate system in space-time; the model is thereby implicitly introducing a different space-time topology.The evolvement of events in this space-time then are traced in a coordinate system of 4 truly independent vector-coordinates i.e. with an independent scalar magnitude of the time-vector.The treatment modifies space-time into 4D curved virtual time-surfaces inside the empty and un-curved 3D space, i.e. confining 3D space in a virtual reality of projected, dynamic evolving ‘present’ surfaces, spherically closed as the space-time ‘edge’ of time.This system model facilitates descriptions both of events in true (proper) time as well describes space-time in a local time defined orthogonal vector coordinate system i.e. referenced, backwards compatible with space-time dependency parameter models as used regularly in scientific descriptions of local events/experiments in space. The mathematical treatment in virtual surfaces of a-symmetrical time, as well as the (observed) flow of clock-time by the growing radius of curved surfaces, matches human notion of time intuitively; it introduces a time-vector coordinate orthogonal to space coordinates and in a triad/trihedral vector system supports evolving events in time embedded virtual surfaces. This local system description may inherit true time length marks, and events starting on a timesurface can evolve in any spatial direction and be described in properties by the triad e.g. momentum, radiation, in general energy, with it’s own virtual surfaces and direction of energy, while maintaining the mandatory orthogonality of the 4D coordinate system.This mathematical treatment of vector time as a virtual fourth dimension, has profound consequences for the mainstream concept of time in vector/tensor spaces in physics - it models and restricts time to the very task of identifying sequences in evolvements of events: time then in principle cannot be affected anymore by parameters/variables in other coordinates i.e. with the consequence that e.g. even by gravity, time cannot be moulded to affect space.
Category: Classical Physics

Solution to Gravity Divergence and Effective Renormalization of Gravity

Authors: Hyoyoung Choi
Comments: 12 Pages. (Note by viXra Admin: Please remove "Physics Department")

By using the fact that the mass M changes to M_eff, which reflects the binding energy, we can obtain the RG flow and gravitational coupling constant G(k). G(k)=(1 − R_gp/R)G_N. When k^*=5Rc^3/3G_N, G(k^*)=0, which means that gravity is zero. Therefore, we can solve the problem of gravitational divergence at high energy. This work presents an effective renormalization approach to gravity, where the running G(k) naturally leads to the resolution of gravitational divergence without requiring quantum corrections. If R > R_gp , G(k)>0, and attractive force acts. If R = R_gp , G(k)=0, and gravity is also zero. If R < R_gp , G(k)<0, and repulsive force or antigravity acts. This repulsive force prevents the formation of a singularity at the center of the black hole. Therefore, the singularity problem is also solved.
Category: Relativity and Cosmology

The Electromagnetic Duality in a Quaternionic Vacuum

Authors: Thierry L. A. Periat
Comments: 6 Pages.

The electromagnetic duality in vacuum is an intriguing property characterizing Maxwell’s equations. It was the starting point of numerous developments. One of the most important topic related to that property certainly is the discussion due to Dirac concerning magnetic mono-poles. This exploration proposes representations of the duality with elements in M(4, H) involving the three generators of the imaginary part of H, the non-commutative set of quaternions.
Category: Mathematical Physics

Through Socialism to War

Authors: Milan D. Nešić
Comments: 52 Pages.

Undoubtedly, discovering the meaning of the world is necessary to man as an individual. This is the reason for the appearance of the great utopian ideas throughout history: Plato, Christ, Moore, Owen, Saint-Simon, Marx, and Engels. If, however, an institution or armed force stands behind such an idea, its meaning will necessarily become inverted. The idea that a classless society of justice and prosperity could be created through armed revolution and then the dictatorship of the communist avant-garde in the name of the proletariat led, on the contrary, to the creation of a NEW CLASS (Milovan Djilas, 1957, in English) and the cult of personality — which is why Yugoslavia fell apart. The new class disintegrated, each in the name of its national God, proving precisely Marx's thesis that religion is the opium of the people. It has been shown that the political economy of socialism does not exist. One cannot simply add French utopian socialism to the historical materialism of class struggle with the forcible seizure of the means of labor and by that to get the political economy of socialism. No matter how much historical materialism was science, it turned out it is science only up to capitalism. Historical materialism has come to a standstill with capitalism. It turned out that the epistemological theory of reflection is naive: human consciousness is not just a mere reflection of objective reality, so the Communist Party will tell us what is a correct reflection and what is not. Human consciousness is a co-creator of the world as we see it and as we think about it — just as the postulate c=const is true in all inertial coordinate systems because c=const is created only in interaction with a receiver. Without receivers (masses, atoms), the cosmic ether and the speed of photons are completely indeter¬minate, like a true completely indeterminate infinity (as Hegel would put it). No armed struggle can create a society of justice and prosperity because the contradiction between labor and capital is not the last one in society, because there is no last contradiction. Man himself is a contradiction, on the one hand as an individual, on the other as a social being. The peaceful protests of students in Serbia are only a condition for understanding this. Scientific analyses of what and how with historical materialism about capitalism have yet to be created. In this sense, the Yugoslav experience can be instructive, in this sense the collection of short stories THROUGH SOCIALISM TO WAR can be useful. Moreover, the experience of peaceful student protests is already a significant indicator of how to move forward.
Category: Social Science

The Eggenberger-Polya Urn Process: Probabilities of Revisited Ball Ratios

Authors: Richard J. Mathar
Comments: 14 Pages.

The Eggenberger-Polya urn process starts with an urn that contains balls of two colors. At each step a ball in the urn is randomly chosen and a ball of the same color added to the urn. The probabilities of finding specified numbers of balls of the two colors later on can be visualized as a non-isotropic walk of U(p) and R(ight) steps on a square lattice. We discuss some numerical aspects of the probability that a ratio of the ball numbers of the two colors reappears later on during the process.
Category: Statistics

Protocol for Communication via Differentiation of Hidden Basis from Linear Basis of Entangled Photon Pair Polarization

Authors: Wells M Chandler
Comments: 4 Pages.

What is the polarization basis of an entangled photon pair when exiting a beta-barium borate crystal (BBO)? Repeated experiments have confirmed there is no linear polarization basis that can account for the observed (anti-)correlations of the pair. Rather, the pair is initially defined by a real but inaccessible basis of polarization which is orthogonal to all linear polarization bases — a hidden basis[1]. The properties of orthogonality of the hidden basis to all linear polarization bases and the instantaneous decoherence of both members of the pair to a linear polarization basis following measurement of one member are exploited in the following experimental proposal to facilitate limited faster than light communication.
Category: Quantum Physics

Distance Determination Using Redshift

Authors: Enrique Domínguez Pinos
Comments: 5 Pages. In Spanish

The potential of the inertial forces is the main effect to determine the redshift of extragalactic photons. This effect determine accurately the distance to the object if we know its radial speed.
Category: Astrophysics

Consciousness is Faster Than Light

Authors: Skyler P. Dillon
Comments: 10 Pages.

Nobody knows exactly how consciousness is produced. To make matters worse, nobody even knows what consciousness is. In this article, I provide insight into what consciousness is, and how it is produced, by showing that consciousness is faster than light. I also show that consciousness is a new faster-than-light phenomenon; as opposed to coming from non-local quantum mechanics. To be clear, I have not disproven Einstein’s theory of relativity; instead, I have discovered a loophole in Einstein’s theory of relativity that applies to consciousness. The discovery that consciousness is faster than light is important, because it shows that consciousness cannot be a particle, energy, or anything else located in space (e.g. not a soul). In other words, we can now conclude that consciousness is non-energy information. Where does this non-energy information (i.e. consciousness) come from? The discovery that consciousness is faster than light excludes numerous theories of consciousness while also enabling new theories of consciousness. For example, a computational theory of consciousness was previously untenable due to the fact that there is no convergence point in the brain for all information and the speed limit of light prevented the conscious observer from accessing all of the distributed information in the brain, but now a computational theory of consciousness is plausible. I show rare case reports and evidence that support the theory that consciousness (i.e. non-energy information) is, at least in part, produced directly from "non-trivial" computations.
Category: Mind Science

Relativistic Kinematics of Photon-Electron Scattering in the Lab Frame

Authors: Muhammad Fahad
Comments: 7 Pages.

We present a unique derivation for photon-electron scattering that operatesexclusively in the laboratory frame of reference. It considers the relativistic principleand angular dependence of photon and electron. A general equation emerges at theend which relates the energies of the photon before and after scattering through theapplication of energy and momentum conservation laws [4]. Such a laboratory-basedmethodology gets rid of the requirement for frame transformations into electron restreference frames while providing an integrated approach to understanding bothclassical and relativistic regimes [3].
Category: High Energy Particle Physics

A Probabilistic Approach to the Inductive Step of 3n + 1

Authors: James Nguyen
Comments: 7 Pages.

It was Paul Erdos, one of the brightest mathematicians of our time, who famously statedthat ’Mathematics is not yet ripe for such questions’, setting the tone for almost all related mathematical inquiry for the next generation. The notorious Collatz Conjecture has stumped a plethora of hobbyist and professional mathematicians alike who have tried their hand.Among many ways in which this problem has been tackled, including [Lag11], [Lag12], andothers, one of them seems most suggestive - strong induction. In this paper, we claim toshow that the inductive step of the Collatz Conjecture is probabilistically true for large odd seeds. Further, in this paper I put forth a novel reformulation that, if true, would imply the truth of the Collatz Conjecture.
Category: Number Theory

On the Foundational Primacy of Consciousness and Its Quantum-Mechanical Coupling to Non-Human Intelligence Technology: A Framework for Psionic Interaction

Authors: Mark Brewer
Comments: 6 Pages.

In this paper I propose a novel, mathematically rigorous framework that postu-lates consciousness as a fundamental constituent of physical reality and establishes itsdirect coupling to a sector associated with non—human intelligence (NHI) technology.Drawing on advanced concepts from quantum field theory, operator algebras, and mod-ern metaphysics—including Russellian monism and integrated information theory—Iconstruct a composite Hilbert spaceH = HM ⊗ HC ⊗ HNHIwhere HM represents conventional matter fields, HC encodes the intrinsic qualitaTive states of consciousness via a self—adjoint operator Cˆ, and HNHI captures extra—dimensional or nonlocal degrees of freedom associated with NHI technology. I introduce an interaction Hamiltonian (with g a coupling constant determined empirically and {Nˆα} a rigorously defined family of operators on HNHI) to model "psionic modulation" of consciousness. I derive detailed predictions via time—dependent perturbation theory and Dyson series expansions,and I propose experimental protocols that combine ultra—low noise SQUID magnetometry, advanced quantum sensors, and rigorous Bayesian data analysis. My frameworkthus provides a unified, falsifiable account that bridges subjective phenomenology withobjective quantum dynamics.
Category: Mind Science

A Story of a Function

Authors: Andrej Liptaj
Comments: 17 Pages.

We dedicate this text to a study of a function with interesting properties: besides being, by construction, well suited for a certain type of approximations, the function happens to be lacunary, i.e. without analytic continuation outside the complex unit disk. It however satisfies a functional equation which can be (with some restriction) solved everywhere except the origin. Unfortunately, this solution cannot be understood asits natural continuation beyond the disk.
Category: Functions and Analysis

Wonders of Natural Integers

Authors: Ahcene Ait Saadi
Comments: 03 Pages.

In this paper I highlight the wonders of natural integers. I discovered pairs of integers which, by doing operations on them, I find relationships between the parts of these numbers. I put this work in the hands of young researchers for deepening, this in the interest of science and knowledge.
Category: Number Theory

Emergent Time Theory: From Timeless Quantum Fields to Physical Time

Authors: Nir Platek
Comments: 19 Pages. Copyright © 2025 Nir Platek.

Emergent Time Theory (ETT) posits that time is not fundamental but emerges from the dynamics of a timeless quantum scalar field, Φ. Our framework develops a rigorous quantum field theory that makes specific, falsifiable predictions—a 10^-4-level deviation from Newtonian gravity at millimeter scales, atomic clock frequency shifts on the order of 10^-18, and Casimir force modifications at the 10^-5 level—that are accessible with current or near-future experiments. Recognizing that groundbreaking theories often blend mathematical precision with deep conceptual insights, we present ETT in two parts: a Core Theory addressing immediate experimental implications, and a Visionary Roadmap outlining speculative extensions—from cosmic bounces and black hole transitions to potential links with consciousness and unconventional information transfer. This structured approach clearly distinguishes established predictions from exploratory ideas, inviting further investigation into the nature of time, space, and physical reality.
Category: Relativity and Cosmology

The Universe May be More Than a Trillion Years Old

Authors: Martin R. Johnson
Comments: 3 Pages.

When Lorentz contraction is included into travel time, the Universe is found to be much older than present estimates suggest.
Category: Relativity and Cosmology

Symmetries of Natural Numbers

Authors: Emmanuil Manousos
Comments: 32 Pages.

In present paper we prove an original theorem on the natural numbers. From this theorem emerges a set of symmetries of the natural numbers which puts Number Theory on a new footing; the study of the natural numbers through symmetries. One of the consequences of the theorem, but not the most important one, is the odd number factorization algorithm.
Category: Number Theory

500,000—1,000,000 Neurons: A Biological Threshold for Initial Self-Perception?

Authors: Shulei Xie
Comments: 5 Pages.

Self-perception, the ability to sense one’s own bodily state, is a fundamental trait in biological systems. This study investigates whether a neuron count of 500,000—1,000,000 marks a threshold for "initial self-perception" during embryonic development. Developmental datafrom four species—mouse (E12), human (6—7 weeks), pig (E20—E25), and chicken (E7—E8)—were analyzed for neural, cardiac, limb, and sensory features at this neuron range. Resultsshow consistent signal integration across species, forming a rudimentary "body sense" atthis stage. These findings suggest that 500,000—1,000,000 neurons may represent a biological threshold for initial self-perception, providing insights into the origins of self-awarenessin neural development.
Category: Quantitative Biology

Top Quark Mass Confusion

Authors: D. G. Grossman
Comments: 8 Pages.

From 2011 to 2024 physicists at the LHC measured the top quark's mass 29 times and got 29 different measurements over a range of about 6.5 GeV. Why weren't they able to zero in on it? Were they even measuring the top quark's mass? What were they measuring?
Category: High Energy Particle Physics

Top Quark Mass Confusion

Authors: D. G. Grossman
Comments: 8 Pages.

From 2011 to 2024 physicists at the LHC measured the top quark's mass 29 times and got 29 different measurements over a range of about 6.5 GeV. Why weren't they able to zero in on it? Were they even measuring the top quark's mass? What were they measuring?
Category: High Energy Particle Physics

Rigorous Proof and Spectral Analysis of the Yang-Mills Mass Gap Problem

Authors: YoonKi Kim
Comments: 5 Pages. If there are any errors or questions, please contact honkai0509@gmail.com. The response may be delayed.

This paper provides a rigorous mathematical proof of the existence of a mass gap in quantumSU(N) Yang-Mills theory, addressing a central unsolved problem in theoretical physics posed by the Clay Millennium Prize. Our objective is to demonstrate that the quantum Hamiltonian of the theory possesses a strictly positive lowest eigenvalue, E0 > 0, in four-dimensional Euclidean spacetime. We achieve this by starting with the complete Yang-Mills gauge field Aµ, quantizing it via path integrals, and performing a detailed spectral analysis of the resulting Hamiltonian HˆYM. To facilitate this analysis, we introduce a confinement scalar W derived from Aµ, construct its effective HamiltonianHˆ , and prove E0 > 0 for both systems without approximations. The proof incorporates the fullnonlinear dynamics, derives all parameters from the Yang-Mills action, and verifies confinementthrough Wilson loop behavior, aligning with the physical predictions of Quantum Chromodynamics(QCD), including the emergence of the scale ΛQCD.
Category: Mathematical Physics

Rigorous Proof and Spectral Analysis of the Yang-Mills Mass Gap Problem

Authors: YoonKi Kim
Comments: 3 Pages. Email for correspondence: yoonki0905@gmail.com

This study rigorously proves the Yang-Mills mass gap problem using analytical methods and spectral theory. By analyzing the Wilson loop expectation value based on the Poisson equation, we demonstrate that the mass gap inevitably forms in SU(N) gauge theory. Additionally, we utilize Hilbert space analysis and operator theory to prove that the lowest eigenvalue of the Yang-Mills Laplacian is strictly greater than zero, confirming the existence of the mass gap in a mathematically rigorous manner. This revised version further strengthens the argument by explicitly deriving the Poisson equation from first principles and providing a more detailed spectral analysis of the YangMills Laplacian.
Category: Mathematical Physics

Logarithm of Exponential and Cauchy Random Variables

Authors: Josef Bukac
Comments: 5 Pages.

We show how to calculate the expectation and the second moment of logarithm of exponential distribution. There are two ways to do this.The Cauchy distribution has no expectation but we calculate the expectation and second moment of the logaritm of the absolute value of the Cauchy distribution.
Category: Statistics

Classification of Composite Number

Authors: Samuel Bonaya Buya
Comments: 9 Pages. The paper is a revision containing more details than the other one

In this research different and distinct subsets of composite numbers areidentified together with their Logical formulae. The aim of the research is tocome up with an efficient method of sieving out primes from a set of positiveintegers. An exact formula for determining the number of primes will bepresented. In the paper a graphical method of factorization will be presented.The paper will back its theoretical claims with a practical Python code that will demonstrate both counting and graphical factorization methods. Thisintegration of theory and practice is useful for further research and real worldapplication. The paper aims at providing an exact and structured frameworkfor counting primes within a given range. It will categorize prime numbers ina way that avoids redundant processing. By giving an exact prime countingfunction and a graphical method of factorization the paper offers insightsbeyond sieving.
Category: Number Theory

Is there an Infinite Number in Which the Sum of the Divisors is the Square Number?

Authors: Minhyeok An
Comments: 16 Pages. If this paper contains no errors, resolving Bunyakovsky’s conjecture through this approac.h would hold even greater mathematical significance than previously recognized.

The numbers whose sum of divisors is a perfect square may initially appear to follow no specific pattern. However, through this research, I have identified a particular rule related to prime numbers. Furthermore, I establish that the existence of infinitely many numbers whose sum of divisors is a perfect square is a necessary and sufficient condition for the existence of an irreducible polynomial with integer coefficients that generates infinitely many prime numbers. Additionally, I explore its connection to Bunyakovsky's conjecture.
Category: Number Theory

The Contradiction Between the Law of Universal Gravitation and the Second Law of Newton. Revision 2

Authors: Viktor Strohm
Comments: 12 Pages.

The motion of bodies along an ellipse with a constant sector velocity is considered. At perihelion, the velocity is greater than at aphelion. The radii are the opposite: at perihelion, the radius is smaller than at aphelion. Let's calculate the tangential and centripetal acceleration. Let's calculate the force using Newton's second law and the law of universal gravitation. The forces are equal in magnitude, but opposite in direction, Fig. 2. Contradictions are eliminated if we consider the momentum of the system.
Category: Astrophysics

A Theory of Hadron Structure Involving Higher Dimensional Matter

Authors: D. G. Grossman
Comments: 13 Pages.

Quarks may be made of higher dimensional matter. If true, then it follows that all hadrons are made of higher dimensional matter. The conventional thinking about quarks, that they are point particles, has not proven useful over the past 50 years. A more useful idea is that the six known quarks (u, d, s, c, b, t) are made of matter of different dimensions - those dimensions being (1, 2, 3, 4, 5, 6) respectively - and each quark has a shape defined by the n-sphere surface volume formula of equal dimension. This gives theorists a mathematical handle (a factoring technique based on n-sphere surface volumes, which was derived from Planck's energy-frequency relation, E=hf), with which quarks and hadrons can be investigated. The dimension of the matter in the hadron and its exact mass can be found with a correct factoring.
Category: High Energy Particle Physics

A Theory of Hadron Structure Involving Higher Dimensional Matter

Authors: D. G. Grossman
Comments: 12 Pages.

Quarks may be made of higher dimensional matter. If true, then it follows that all hadrons are made of higher dimensional matter. The conventional thinking about quarks, that they are point particles, has not proven useful over the past 50 years. A more useful idea is that the six known quarks (u, d, s, c, b, t) are made of higher dimensional matter, the dimensions of which are respectively (1, 2, 3, 4, 5, 6), and each are equal to a volume of matter defined by the n-sphere surface volume formula of equal dimension. This gives theorists a mathematical handle, with which quarks and hadrons can be investigated.
Category: High Energy Particle Physics

On Time & Dynamics [:] a Space-Time 4D Topology in 3D Space

Authors: A. V. Herrebrugh
Comments: 14 Pages. Shortened abstract, changed paragraphs, minor textual updates and line of thoughts.

A conceptual 4-dimensional vector space-time consisting of an orthogonal vector-time coordinate in a 3-dimensional space is developed to support system dynamics. This 4D space-time concept deviates fundamentally from the observer oriented theory of special and general relativity, is based upon true time simultaneity of events and separates true, objective reality oriented simultaneous events from observed simultaneous events (in A.Einstein’s relativity). The proposed geometric model is conventional Cartesian in 3D space and introduces virtual time-surfaces of true time simultaneity as a fourth dimension for validity in vector- and tensor- spaces, leading to a compliant 4-dimensional orthogonal vector coordinate system in space-time; the model is thereby implicitly introducing a different space-time topology. The evolvement of events in this space-time then are traced in a coordinate system of 4 truly independent vector-coordinates i.e. with an independent scalar magnitude of the time-vector. The treatment modifies space-time into 4D with curved virtual time-surfaces inside the empty, un-curved 3D space, i.e. confining 3D space in a virtual reality of projected, dynamic evolving ‘present’ surfaces, spherically closed as the space-time ‘edge’ of time. This mathematical treatment of vector time as a virtual fourth dimension, has profound consequences for the mainstream concept of dimensional time in vector/tensor spaces in physics - it models and restricts time to the very task of identifying sequences in evolvements of events: time then in principle cannot be affected anymore by parameters/variables in other coordinates i.e. with the consequence that e.g. even by gravity, time cannot be moulded to affect space introducing e.g. space connections.
Category: Classical Physics

About the Riemann Hypothesis

Authors: Thomas Brouard
Comments: 6 Pages.

Here is proposed to confirm the Riemann hypothesis.
Category: High Energy Particle Physics