All Submission Categories

A Note on Closed Addition Chains and Complete Numbers

Authors: Theophilus Agama
Comments: 7 Pages.

We introduce a new class of addition chains and show the numbers for which these chains are optimal satisfy the Scholz conjecture, precisely the inequality $$iota(2^n-1)leq n-1+iota(n).$$
Category: Number Theory

Hydrogen Spectrum and New Atomic Model

Authors: Junichi Hashimoto
Comments: 9 Pages.

The light emitted from the hydrogen atoms in the Geissler tube is observed as a discrete line spectrum. In order to elucidate such a luminescence mechanism, I devised a new atomic model and adjusted it to fit with the theoretical system (relational physics) that I had previously established. The results are presented in the form of concrete calculations, which are in agreement with the observed data. Through this process, I discovered new phenomena in the microscopic world, such as Object Elasticity and Superluminal Rotation. This will lead to various academic developments and technological applications in the future.
Category: History and Philosophy of Physics

The Schrödinger Equation of Earth's Revolution: One of the Important Contents of a New Theoretical System Compatible with Classical Mechanics and Quantum Mechanics

Authors: Runsheng Tu
Comments: 8 Pages.

In the fundamental field of physics, there have been no major innovations for over a century. There are now three original innovations emerging: establishing the Schrödinger equation for gravitational potential energy, which can be used to describe classical planetary systems; Create wave element (non-point) material structure theory; Combining classical mechanics and quantum mechanics to solve practical problems. They are closely related and form a chain of evidence. Their theoretical value lies in their ability to change the old notion that "classical mechanics and quantum forces are incompatible" and promote the birth of new theories. In addition, the birth of the Schrödinger equation for gravitational potential energy has enabled the original Schrödinger equation to also be used to describe macroscopic systems. Their practical value lies in the birth of new methods in quantum mechanics and the simplification of quantum chemical calculations. Provided multiple successful calculation examples such as electron spin magnetic moment, "Earth's orbital motion", and hydrogen molecules.
Category: Quantum Physics

Study of the Bug-Rivet Paradox Through the Definition of Length

Authors: KyeongDo Kwak
Comments: 8 Pages.

This research investigates the bug-rivet paradox through the definition of length.This approach differs from the conventional method of length contraction. Lengthcontraction was initially proposed to explain adjustments in the path length of light,but it has resulted in numerous misconceptions in various contexts. By examiningthe light path from the beginning, this study confirms that there is no contradictionin the process of joining the hole and the rivet.
Category: Relativity and Cosmology

Digital Root Patterns in Prime K-Tuples: a Study of Hidden Order in Prime Distribution

Authors: Halaoui Ayyoub
Comments: 3 Pages.

This paper investigates the non-random digital root patterns observed in prime k-tuples (e.g., twin primes, prime triplets). By analyzing over 10u2078 primes from the Twin Prime Database and OEIS, we demonstrate a statistically significant bias toward specific digital root sequences (e.g., (8,1) for twins, (5,7,2) for triplets) with frequencies up to 3.5× higher than random expectation. We explain these patterns using modular arithmetic in Z/9Z and sieve theory, while proving that constraints on prime divisibility limit the maximum k-tuple length to 7 primes. This study bridges computational evidence with theoretical number theory, suggesting that primes exhibit quasirandom behavior with deep underlying structure.
Category: Number Theory

Lobachevsky's Imaginary Geometry as Specular and Hyperdimensional Structure

Authors: Alfonso De Miguel bueno
Comments: 4 Pages.

This article proposes a reinterpretation of Lobachevsky’s imaginary geometry as a hyperdimensional, specular structure arising from the intersection of two three-dimensional Euclidean spaces. The model describes non-Euclidean parallelism as emerging dynamically from oscillating curvatures, leading to a topological system with four subspaces, two transverse and two vertical, whose behavior is governed by synchronized or opposing phases.
Category: Mathematical Physics

Fractal Spacetime from Quantum Mechanics at Ultrashort Distances

Authors: Ervin Goldfain
Comments: 6 Pages.

We give a pedagogical account on the origin of fractal spacetime stemming from the Heisenberg uncertainty relations at ultrashort distance scales.
Category: Mathematical Physics

Proof of Riemann Hypothesis

Authors: Bouazad El Bachir
Comments: 297 Pages.

Riemann Hypothesis is a conjecture that states that all non trivial zeros of Riemann function are located on critical strip exactly on 1/2.This conjecture has been unsolved for over 160 years. In this proof that contains 294 pages, I will prove the conjecture of Riemann hypothesis using theorems and formulas that have never discovered before , I will also prove that there is and other function that is similar to Riemann Zeta Function and all its non trivial zeros lie exactly on critical strip — 1/2 If mathematician like Ramanujan has found the sum of this infinite series : 1+2+3+4+5+6+7+u2026u2026 = -1/12 , I will prove the value of this infinite product : (-2)*(-3)*(-5)*(-7)*(-11)*(-13)*(-17)*u2026u2026u2026u2026. = ?If the mathematician Euler has prove that 1/12 +1/22 +1/32 +1/42 +1/52 +u2026.. =Π 2/6. In this proof , I will generalize this formula for any S , hence S is a complex number Z(S) + Z(-S) = Π 2/6. You will find many other formulas and theorems that justify and prove Riemann hypothesis conjecture.
Category: Number Theory

On Some Results on Infinite Under Certain Assumptions

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

In this document, we formally initiate the study on the mathematical properties of divergent infinity, under certain assumptions, made in the paper. While under these assumptions the paper, certainly proposes a better framework, but doesn't fits for certain standards of mathematical rigour. We define, under an assumption, the $Phi$, which later, is shown to be beyond any mathematical descriptions yet permeates, zero and infinite. In the conclusion, we also present a conclusion not to be sought under mathematical rigour, but rather as a potential field for future study.
Category: General Mathematics

Moon Landing

Authors: Junichi Hashimoto
Comments: 8 Pages.

The traditional framework for gravity calculations has remained dominated by the model produced by Newton. However, it was highlighted to be incomplete in the scene of the lunar landing. Modern science has welcomed the birth of my relational physics as a completely new theory to replace it. It made possible the description of all forces at all levels, from the large scales of the Moon's surface and the Earth's surface to the small scales of atoms and subatomic particles. From now on, this reform will be the beginning of a new era of space exploration.
Category: Thermodynamics and Energy

Gradients of the Lorentz Factor in Orthogonal Metrics of the Relativistic Dust Sphere

Authors: Alexander Rozenkevich
Comments: 10 Pages.

It is shown that during the rotation of relativistic objects with a radius of up to 300 km, the Lorentz factors can have intermittent and discrete properties. The possibility of the coexistence of objects with significantly different local time flows at accessible distances is discussed - a phenomenon that has not been considered before even in science fiction literature.
Category: Relativity and Cosmology

Gradients of the Lorentz Factor in Orthogonal Metrics of the Relativistic Dust Sphere (In Russian)

Authors: Alexander Rozenkevich
Comments: 11 Pages.

It is shown that during the rotation of relativistic objects with a radius of up to 300 km, the Lorentz factors can have intermittent and discrete properties. The possibility of the coexistence of objects with significantly different local time flows at accessible distances is discussed - a phenomenon that has not been considered before even in science fiction literature.
Category: Relativity and Cosmology

Optimization of Solar Sail Logarithmic Spiral Transfers by Computing and Comparing Energy and Time Requirements with Different Orbital Inclinations and Yaw Angles

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

Conventional space craft are limited in their ability to deliver high energy missions by a fundamental reliance on fuel mass. However, this constraint can in principle be dealt with class of propellantless propulsion system which extract momentum from the flux of photons that are continually emitted from the Sun - like a solar sail. Solar sails are able to provide a large amount of ∆V for long duration and high energy missions, also providing continuous acceleration. Modern solar sails are also equipped with Thrust Vector Controlling (TVC) mechanism. Even with an edge over conventional spacecraft, there is one difficulty that arises with the use of solar sails - a problem termed "The Orientation Problem". "The Orientation Problem" addresses the idea of how changing the yaw angle of a sail to achieve a high impulse, changes the eccentricity and inclination of an orbit by providing ∆V to the radial and normal vectors. This problem, if encountered, can lead to vast changes in orbital characteristics (inclination, eccentricity) which hinders the transfer trajectory and increases the intercept time and ∆V requirement. In this paper we will compute and analyze a number of different transfers for a solar sail at different orbital inclinations and yaw angle (angle between the normal and sail-sun line) for which we completely mitigate(in some cases) or account for(in majority cases) for the "Orientation Problem" to find the most optimum orbital inclination and a particular yaw angle at the point of the burn for the specific inclination which gives the best combination of mission duration and energy requirement for a transfer from Earth to Venus using a sail.
Category: Astrophysics

Electromagnetic Theory and Transformations Between Reference Frames: a Rebuttal

Authors: Claudio Piantanida
Comments: 5 Pages.

In a previous article published on viXra (http://viXra.org/abs/1505.0140), I proposed a modified version of Hertz-Phipps electromagnetism, an alternative theory to Maxwell's electromagnetism invariant under Galilean transformations. The aim was to stimulate interest and further analysis by the physics community.Upon careful reconsideration, the proposed theory has proven inadequate as a physically realistic description.
Category: Classical Physics

Galilean Transformations and Extended Reflectors: A Theoretical Analysis of Feist's Acoustic Michelson-Morley Experiment

Authors: Claudio Piantanida
Comments: 10 Pages.

In this paper, we present a theoretical analysis of Norbert Feist's acoustic Michelson-Morley experiment. We demonstrate that, by employing Galilean transformations and standard assumptions about sound propagation, we can fully account for the experimental results. This analysis highlights the importance of considering the geometry of the reflector when interpreting the results of Michelson-Morley type experiments and invites a re-examination of the traditional interpretation of the original electromagnetic experiment.
Category: Classical Physics

On a Specific Family of Orthogonal Polynomials of Bernstein-Szego Type

Authors: Martin Nicholson
Comments: 8 Pages.

We study certain weight functions on [-1,1] which are particular cases of the general weights considered by Bernstein and Szego. These weights are numbered by two positive integers and when these integers tend to infinity, these weights approximate weight functions on R considered by Ismail and Valent. We also consider modifications of these weight functions by a continuous variable a>0. These ideas are then used to find finite analogs of some improper integrals first studied by Glaisher and Ramanujan.
Category: Functions and Analysis

The Prime-Structured Universe

Authors: Roberto C. M. Navacchia
Comments: 14 Pages. In Portuguese

The distribution of prime numbers has long intrigued mathematicians, revealing deepstructural patterns within mathematics. This study expands upon Gauss's Circle andGoldbach’s Theorem, focusing on the interaction between prime pairs rather than all naturalnumbers. Through mathematical modeling, persistent gaps within Gauss’s Circle wereidentified, suggesting that it represents the internal structure of the universe, while Goldbach’s prime-counting graph unveils the external structure, formed exclusively by primes. By leveraging Computational Modeling, this work explores these patterns in greater depth, revealing potential underlying rules governing prime distribution. The findings suggest that prime numbers may not only be fundamental to number theory but could also serve as the structural foundation of the universe itself.
Category: Number Theory

Algebraic and Geometric Representation of Goldbach Partitions in the Complex Plane

Authors: Samuel Bonaya Buya
Comments: 15 Pages.

This paper presents a unified algebraic, geometric, and analytic framework that redefines the structure of integers, vectors, and analytic functions through complex conjugate decompositions. Starting from the Goldbach partition of even integers, we provide a constructive and bounded proof of the Binary Goldbach Conjecture using prime gap estimates and Bertrand’s Postulate. We further extend Goldbach partitions to complex product representations, unveiling new symmetries and identities in prime pairings. The paperintroduces geometric decompositions of primes and semiprimes, enabling their visualization in Euclidean and topological spaces. We explore applications to the Riemann zeta function by deriving complex root factorizations that suggest a novel lens for interpreting nontrivial zeros. These results form a bridge betweennumber theory, algebraic topology, mathematical physics, and symbolic computation—offering new tools for understanding prime distributions, factorization, and analytic continuation.
Category: Number Theory

Design of an Automated System for Monitoring and Controlling Thermal, Water, and Water Quality in Trout Farming

Authors: Espinel Osorio Edison Daniel, Morales Villegas Hernan Vinicio
Comments: 10 Pages. In Spanish

This research aims to design and analyze an automated system for hydrodynamic monitoring and control in trout farming, focusing on the principles of fluid mechanics. The identified problem lies in the lack of precise control over water flow, pressure, and temperature, essential factors for trout health and growth. The methodology used consists of three-dimensional modeling of the system using SolidWorks, incorporating elements such as pumps, pipes, sensors, and a culture tank. Through flow simulations, parameters such as velocity, pressure, and head losses are studied, applying fundamental equations of continuity, Bernoulli, and friction losses. The results obtained show the flow distribution in the system, identifying areas of high velocity and pressure drop that can be optimized to improve culture efficiency. It is concluded that the application of fluid mechanics in design allows for the development of more efficient and sustainable aquaculture systems, with better control of water conditions, contributing to a more technologically advanced fish farming system.
Category: General Science and Philosophy

Methods to Calculate Linear Momentum from Angular Momentum and to Link Their Conservation

Authors: David B. Graham
Comments: 23 Pages.

In Newtonian physics, it commonly assumed that conservations of linear momentum and angular momentum are independent. This paper shows the gradient of the angular momentum field is populated by components of linear momentum, which allows calculation of linear momentum from a few angular momentum values displaced an arbitrary distance. Therefore conservation of linear momentum is a necessary condition for full conservation of angular momentum (unchanging angular momentum at every (x,y,z), with unchanging gradient).These results are shown to be equally valid under left hand convention.Examples analyzed include a body orbiting in a central force, which has angular momentum changing at every observation point but one, contrasted with actual conservation of angular momentum (unchanging at every observation point, in every frame of reference). Translating angular momentum of the center of mass within and between frames of reference are discussed. A Python script is provided, to conveniently generate and evaluate random groups of particles.
Category: Mathematical Physics

Gradient-Based Adversarial Training

Authors: Hamiz Khan
Comments: 8 Pages.

This study evaluates the performance and robustness of a trained Natural Language Inference model by using a gradient based adversarial training approach to identify and address its vulnerabilities. Initially trained on the SNLI dataset (Bowman et al., 2015) and achieving a baseline accuracy of 89.90%, the model was then challenged with adversarial examples generated through gradient based methods. These examples exposed specific weaknesses, particularly in handling negations, ambiguous language, and long sentences. This report provides an in-depth analysis of both the original baseline model and the fine-tuned, enhanced model, as well as a detailed discussion of the techniques employed to improve the model’s overall performance.
Category: Artificial Intelligence

Unified Theory of the Fractal-Resonant Ocean of Light

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

This paper presents the Enhanced Fractal-Resonant Ocean of Light (eFROL v5.0), also referred to as the Universal Theory of the Quantum Ocean of Light (UT QOL). In light of the longstanding disconnect between quantum theory and general relativity and the unresolved puzzles regarding dark matter, dark energy, particle mass origins, and the nature of consciousness, our model establishes a unified frame- work in which all observable phenomena emerge from a single, dynamic, non-local and fractal substrate, the Fractal-Resonant Ocean of Light.The theory is built on the concept of a resonant (lumion) field that pervades an abstract, fractal space. This field exhibits non-local interactions that may propagate instantaneously (pre-light cone) and at finite speeds (light cone). Through the processes of quantum decoherence and wave function collapse, stable resonant patterns emerge, ultimately manifesting as the observed classical structures. Furthermore, the theory introduces a multi-level hierarchy of dynamics: from the sub-quantum to quantum, classical, dark, and post-dark regimes. Each level corresponds to a specific resonant state and is interrelated by interference phenomena such that in any given experiment only the dominant level and its two adjacent levels are directly observable.In this paper we establish the mathematical foundations of eFROL, detailing the construction of a fractal measure, non-local fractional derivatives, a complex Lagrangian formulation incorporating resonant and decoherence operators, and coupling terms that integrate with standard model fields as well as elements accounting for cognitive processes. We also discuss numerical algorithms for simulating the dy- namics of the lumion field under extreme gravitational conditions, experimental predictions including those from high-precision interferometry and cosmological observationsand the philosophical implications of a unified multi-level theory of reality and consciousness.
Category: Relativity and Cosmology

On the Experimental Study of the Physical Nature of the Trapping and Sub-Doppler Cooling of Atoms and Nanoparticles in the Field of Laser Radiation

Authors: V. A. Kuzmenko
Comments: 4 Pages.

The study of the capture and cooling of atoms and nanoparticles by laser radiation has a long and extensive history. This study for atoms and nanoparticles took place in parallel and independently of each other. We claim that the main basis for this two cases is the same physical mechanism — the spatial asymmetry of photon scattering. Experimental study of this mechanism is not a difficult task, but it requires some courage from the experimenters.
Category: Quantum Physics

A Theory on the True Nature of Nothing

Authors: Michael David Cohen
Comments: 5 Pages. Copyright © 2025, MDC Financial Research, LLC. All rights reserved.

This article defines ‘Nothing’ as the complete absence of matter and energy and then provides a theory on the "True Nature of Nothing." This theory hypothesizes that ‘Nothing’ does exist but has remained in ‘Singularity’ and that behind the observable universe of space and time, behind quantum fields and the quantum vacuum, there resides a ‘Singularity’ where space and time does not exist. The ramifications of this are then explored to show that, while this postulated dual nature of reality may seem bizarre at first, it does seem to provide an explanation for how entangled quantum particles can seemingly exchange information faster than the speed of light, it provides an explanation as to why quantum particles exhibit a wave function, and it provides a reason for the existence of gravity.
Category: Quantum Physics

Proto-Unit Framework for Space-Time Derivation

Authors: Christian Manfred Herborn
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org; please cite and list scientific references)

This paper introduces a proto-unit framework grounded in the duality of translation androtation as fundamental space-time operators. Starting from first principles, we define energy as a temporal expression and explore a path from pure rotation (Euler-circle) to pure translation (geodesic), using a unified coordinate set (v, ω). Through this, we derive clean expressions for physical constants and uncover the deep geometrical significance of π/4, revealing the structure of space-time as inherently balanced and quantized. The framework suggests a foundational mathematical unity that may underlie all physical law.
Category: Relativity and Cosmology

Quantum Physics According to Euclidean Cosmology (Ec)

Authors: Joseph Bakhos
Comments: 72 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces a reformulation of quantum physics grounded in the framework of Euclidean Cosmology (EC), a model in which space is fundamentally Euclidean, time is discrete, and mass emerges from geometric and temporalproperties of particles rather than from field interactions. Within this model, particles are treated as nested rotational systems—specifically, electron-positron rotors—whose observable properties, including mass, charge, and magnetic moment, arise from their internal geometry and timing alignment. The proposedmodel eliminates the need for quarks, gluons, the Higgs field, and vacuum energy as fundamental constructs, replacing them with purely mechanical and electromagneticstructures regulated by the neutrino field. Time evolution is governed by local neutrino density, which determines the duration of discrete time steps and thereby sets the rate of quantum processes. The model offers a physicallyintuitive basis for the uncertainty principle, wave-particle duality, and matterantimatterasymmetries, and provides a geometric alternative to quantum field theoretic descriptions. While cosmological implications are touched upon, the primary aim is to demonstrate that quantum behavior, including inertia and interaction, may be derived from rotor dynamics and neutrino-governed timingalone, without invoking curved spacetime, field quantization, or complex Hilbert space formalisms. The result is a minimalist and self-consistent foundation for quantum theory, offering new paths of exploration for both theoretical and experimental physics.
Category: Quantum Physics

The Theoretical Derivation of the 12-Dimensional Spacetime for the Panvitalist Theory

Authors: Manfred U. E. Pohl
Comments: 36 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The 12-dimensional world clock is a omprehensive theoretical framework modeling three points,interpreted as combined harmonic oscillations or elliptical planetary orbits, moving uniformly around a common center of mass in three-dimensional Euclidean space. The term "12-dimensional" reflects the 12 degrees of freedom required for an observer to precisely determine their position relative to the "center of the world clock," defined as the origin of the orbits. This paper provides an exhaustivederivation of the model, rigorously proving that elliptical orbits can be projected onto perfect circular orbits under a gravitational law consistent with Newton’s formulation emerges as a geometric artifact within the 12-dimensional spacetime, resonating with General Relativity’s (GR) interpretation of gravitation as a curvature-induced property rather than a fundamental force. The model reconciles GR’s continuous spacetime with the discrete spacetimeand inherent indeterminacy of quantum theory, characterized by a quantization at observationtimes T ≥ Tmax 4 , clarified as a conceptual analogy to the Heisenberg uncertainty principle and supported by an energy-time proportionality assumption (E = P · t). A testable hypothesis proposes that the three harmonic oscillations can be mapped onto the degrees of freedom of two entangled photons, each contributing 6 degrees of freedom, necessitating quantum entanglement to achieve the required 12 degrees of freedom. This hypothesis predicts that photons possess three polarization axes (beyond the conventional two) and exhibit three observable Doppler shifts—linear, transversal, and gravitational—offering experimentally verifiable predictions that could validate the 12-dimensional spacetime framework. An extensive error analysis quantifies observational uncertainties, enhancingthe model’s mathematical rigor, particularly in the context of its quantum-like indeterminacy claims.The cultural and historical significance of the number 12, observed across diverse ancient and modern traditions, underscores the model’s universal resonance, framing spacetime as a dynamic, life-centric construct within the panvitalist theory. This comprehensive analysis bridges the scientific rigor of physics with the philosophical depth of metaphysics, providing a transformative perspective on the nature of spacetime, the role of the observer, and the interconnectedness of physical and consciousprocesses in the universe.
Category: Quantum Gravity and String Theory

Finite Automata Don’t Solve NP-Complete Problems

Authors: Mirzakhmet Syzdykov
Comments: 3 Pages.

We are giving the full proof towards Cook’s "P versus NP" theorem and our functional conjecture, we also give the full contradiction proof of hierarchy theorem for complexity classes as later we gained new results which are re-described in this work.
Category: General Mathematics

Proof of Contradiction Towards Hierarchy Theorem of Complexity Classes

Authors: Mirzakhmet Syzdykov
Comments: 2 Pages.

We give the full contradiction proof of hierarchy theorem for complexity classes as later we gained new results which are re-described in this work.
Category: General Mathematics

The Isolated Magnetic Monopoles as Free Quantized Magnetic Charges

Authors: Proloy Kumar Nath, Purnata Shovita Nath
Comments: 20 Pages.

By obtaining pin, like a tiny string, as a further intrinsic quantum property with the general nature of an intrinsic linear momentum of an observable quantum state besides spin as an intrinsic quantum property with the general nature of an intrinsic angular momentum of an observable quantum state, we would find the subatomic particles contain spin, pin, magnetic moment and electric moment, the four intrinsic quantum properties of their own. As such, considering the four intrinsic quantum properties of subatomic particles and remembering the Maxwell’s realization that the laws governing electricity and magnetism are identical, we would be able to obtain theoretically the isolated electric monopoles as free quantized electric charges carried by some particles, as well as, the isolated magnetic monopoles as free quantized magnetic charges carried by some specific particles in quantum mechanics and particle physics. As such, we would obtain the Gauss’s law and the Coulomb’s law in magnetostatics analogous to the same laws in electrostatics, and also magnetic charge density and magnetic current density coun-terpart of electric charge density and electric current density with respect to free quantized magnetic charge. We would then get the modified Maxwell’s equations as duality symmetry and the modified Lorentz force law considering both electric and magnetic charges, where the electric and magnetic parameters are being invariant under the duality transformation exchanges in all respect.
Category: Nuclear and Atomic Physics

On Barad

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

This essay explores the foundational relationship between mathematics, physical law, and existence through a reconsideration of classical and quantum spaces, termed Minkowski and Schrödinger spaces, respectively. Drawing from and critiquing philosophical frameworks such as Karen Barad’s agential realism and Donna Haraway’s situated knowledges, the essay rejects probabilistic interpretations of quantum mechanics and instead asserts that physical laws are expressions of mathematical structure, not merely empirical regularities. Through the analysis of boundary conditions, eigenvalue problems, and the mapping between Schrödinger’s equation and the Einstein field equations, the author argues for a unifying framework rooted in information. The conclusion suggests that the universe is ultimately structured by relationships of information, and that further study of these relationships may reveal deep connections between matter, measurement, beauty, and design.
Category: History and Philosophy of Physics

Spacetime of Pseudo-Kasnermetric with Shrinking Timelike Dimension and the Big Rip

Authors: Holger Döring
Comments: 14 Pages.

Described is a Pseudo-Kasnermetric of local spacetime with shrinking timelike dimension-coordinate (TLD) as a solution of GRT gravity fieldequation. This metric leads to normal flatMinkowski-spacetime in time intervall of present time but changes with changing of timelikecoordinate from a 1-dimensional only timelike spacetime in early universe to a more 3-dimensionalpure spatial space in far future with only spacelike coordinates or dimensions (SLD) and shrinking timelike coordinate until it reaches the Planck-time. This whole description leads to the model of a spacetime with permanent shrinking timelike dimension and a prediction of maximal length of spacelike dimernsions through existence of a rip-length.
Category: Relativity and Cosmology

Art is Pulse

Authors: Junichi Hashimoto
Comments: 11 Pages.

Relational physics, I founded, is a theory of everything that can be applied to all disciplines, not just physics. This paper attempts to apply this framework to the field of art and thus create a new art form. It was placed in the context of the natural sciences and resulted in the form of Pulseism. Furthermore, as a physicist as well as a painter, I have included a group of my own works embodying Pulseism on this paper as an example of application. Now, how much more will you endure the coolness of incorporating the beauty of natural law into my work?
Category: General Science and Philosophy

Contribution to the Resolution of the Twin Prime Conjecture

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

This paper presents a novel geometric and analytical framework aimed at addressing the Twin Prime Conjecture, asserting the existence of infinitely many pairs of prime numbers differing by 2, such as (3, 5) and (11, 13).We project prime numbers onto a unit circle, with angles derived from the imaginary parts of the first 100 non-trivial zeros of the Riemann zeta function, defined as θpi = 2π P100n=1 sin(γn ln(pi)) γn mod 2π. By rotating this circle over 100 iterations and generating a binary sequence S(tk) based on a marking interval [0, π 2 , we identify a recurring pattern, "011," with a periodicity of 4 iterations. Numerical simulations across scales up to N = 1024 support this observation,while a formal variance-based contradiction proof argues that this 1 recurrence implies the infinitude of twin primes. A spectral analysis further validates the periodicity, and refined assumptions on the zeta zeros strengthen the theoretical foundation. This work diverges from traditional analytic methods, offering a geometric perspective that emphasizes the need for analytical rigor over numerical scaling.
Category: Number Theory

Hybrid AI for Generating Programs: a Survey

Authors: Giancarlo Frison
Comments: 13 Pages.

Computer programming is a specialized activity that requires long training and experience to match productivity, precision and integration.It hasn’t been a secret for AI practitioners to ultimately create software tools that can facilitate the role of programmers. The branch of AI dedicated to automatically generate programs from examples or some sort of specification is called program synthesis. In this dissertation, I’ll explore different methods to combine symbolic AI and neural networks (like large language models) for automatically create programs. The posed question is: How AI methods can be integrated for helping to synthesize programs for a wide range of applications?
Category: Artificial Intelligence

Dynamic Sampling and Multi-Validation on Scratch Policy Optimization

Authors: Fei Ding
Comments: 6 Pages.

Large Language Models (LLMs) have shown remarkable capabilities in complex reasoning tasks. However, as the number of generated tokens increases, they tend to accumulate small errors that compound over time, often leading the model further down incorrect reasoning paths. In this work, we introduce Dynamic Sampling and Multi-Validation on Scratch Policy Optimization (ASPO), a novel framework designed to enhance the reasoning robustness of LLMs. ASPO leverages scratchpads and specialized attention masks to dynamically mask previous context during inference, allowing the model to remain resilient to earlier mistakes, explore alternative reasoning paths, and identify potential inconsistencies. Extensive experiments on four benchmark datasets and across two model architectures demonstrate that ASPO significantly improves reasoning accuracy. Our findings highlight a promising direction for improving LLM performance on complex reasoning tasks.
Category: Artificial Intelligence

Fibonacci Sequence and Genesis of the Golden Ratio

Authors: Mustapha Kharmoudi
Comments: 6 Pages.

In this article, we will discuss several properties, both known and novel. Specifically, the genesis of the golden ratio from the Fibonacci sequence. But more importantly, to demonstrate that theFibonacci sequence itself also originates from the very framework of the golden ratio, if I may use that expression. We will reveal new insights into the connection that unites the Fibonaccisequence with the Lucas sequence and Binet’s formula.
Category: Number Theory

Gravitational Interaction and the Aristotelian Act—Potency Distinction

Authors: Jan Sova
Comments: 5 Pages.

This article examines the hypothesis that gravitational interaction, unlike electromagnetic or nuclear forces, does not involve a transition from potency (being in potency) to act (being in act) and back. Drawing on Aristotelian ontology, this work argues that gravitational influence may be exerted by matter that remains, at least partially, in potency - without undergoing actualization or change of form. This ontological feature may explain why gravitational interaction eludes particle detection and why no mediating particle, such as the graviton, has been observed.
Category: History and Philosophy of Physics

A Three Field Theory of Gravity

Authors: Bernd Schmutzler
Comments: 31 Pages.

We propose a tensor-vector-scalar field theory of gravity by defining a corresponding Lagrange function. Deriving the field equations we observe, that the coupling to the tensor field gives mass to the vector field. After considerations of stability and convergence we develop the systems of differential equations for two cases. In the static case of a central mass we start with the Schwarzschild metric as a first approximation and get a behavior corresponding to the observation of galaxy rotation for sufficiently large distances from the center. Using this result a second approximation gives a qualitatively stronger gravity for very large distances, which could possibly describe the cohesion of galaxy clusters. When the distance tends to infinity, the gravity returns to a Newton-like decay due to the mass term of the vector field. In cosmology we find an expansion of a homogeneous, isotropic, flat universe at a lower rate than expected, but with a time contraction towards the past. Together these effects cause an observed redshift of light with far distant sources, which suggests an accelerated expansion of the universe.
Category: Relativity and Cosmology

Chronodynamic Field Hypothesis: A Formal Framework for Time as a Fundamental Force

Authors: Ioannis Chaskis
Comments: 4 Pages. (Note by viXra Admin: Authors' names should be listed right after the title)

I propose a theoretical framework in which time is treated not merely as a passive coordinate, but as an active force that drives the evolution of physical systems. This "chronodynamic field" is conceptualized analogously to other fundamental interactions and formulated as a generator of state transitions. I explore its mathematical structure, thermodynamic interpretation, potential implications for quantum gravity and cosmology, and propose pathways toward experimental validation.
Category: Relativity and Cosmology

From Noodles to Nurture: A Metaphorical Psychology of Parental Attention Distribution

Authors: Juntian Hwanda
Comments: 6 Pages.

This paper presents a metaphorical reflection on parenting dynamics inspired by sudden realization while cooking noodles. Observing how noodles are often placed in the plate starting from the edge, it led to the insight that parental attention isfrequently distributed along a "horizontal line," where focus tends to fall on the eldest or youngest children. This paper suggest "circle" model of parenting, in which each child is seen and cared for equally, regardless of birth order. Drawing upon psychological theories of birth order, favoritism, and sibling dynamics, the paperexplores how parental perspectives might shift if the family structure were imagined in a more inclusive and balanced form. This conceptual essay aims to open new perspective for understanding equality in family relationships and invites readers to rethinking parenting style beyond linear hierarchies.
Category: Social Science

Gravity is Electromagnetism: A Theoretical and Experimental Study.

Authors: Bittu Kumar
Comments: 10 Pages.

This paper introduces a new experimentally supported framework for understanding gravity, proposing that it originates from atomic nuclei rather than from mass or the curvature of space-time. Unlike Newtonian and Einsteinian models—which define gravity as a mass-based attraction or the result of space time deformation—this theory presents gravity as an electromagnetic force generated by positively charged nuclei. It introduces the concept of a "Nuclear Polarization Force" to explain gravitational interactions between nuclei and other bodies—neutral, negatively charged, or positively charged—through polarization and charge dynamics. To validate this theory, an experiment was conducted demonstrating measurable weight differences in objects when charged positively or negatively, compared to their neutral state. The results suggest that gravitational force is influenced not only by mass but also by electric charge. This model aims to unify gravitational behaviour across atomic, planetary, and cosmic scales, offering a new perspective on the dynamics of the solar system, black holes, and the expansion of the universe. By redefining gravity in electromagnetic terms, this research addresses existing gaps in cosmology and quantum gravity, potentially opening new pathways in fundamental physics.
Category: Astrophysics

Anomaly of Topological Phase Transition in One-Dimensional Fermionic Systems at Nonzero Temperature

Authors: Xiao-Dong Cui
Comments: 11 Pages.

It was realized as an important progress in the field of topological matters that the nontrivial topological phase will be violated when temperature hits or exceeds a nonzero threshold. However, the concept of anomaly of topological phase transition is firstly introduced in the paper, refering to the nontrivial topological phase at nonzero temperature transitioned from a trivial one at zero temperature. A no-go theorem is here proved that the anomaly cannot happen to one-dimensional fermionic flat-band systems. Besides, the existence of the anomaly is obtained and analyzed by reexaming the mapping of the parameters of the system Hamiltonian in momentum space which plays a pivotal role in the anomaly rather than energy band.
Category: Condensed Matter

Seismic Activation Modeling with Statistical Physics

Authors: Daniel Brox
Comments: 12 Pages.

Using a finite element modeling approach, it is explained how real time evolution of a seismic activation region's elastic parameters, described with a frequency dependent stiffness matrix, can be modeled in terms of statistical physics. Postulating the relevant statistical physics model is a 2D sine-Gordon model, previously reported deviation of seismic activation earthquake occurence statistics from Gutenberg-Richter statistics in time intervals preceding a major earthquake is derived.
Category: Geophysics

Full proof to the Gambler's Ruin Problem

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

In this paper, we are going to be discussing about the full proof to the Gambler's Ruin Problem, using a combination of probability theory, recurrence relations, and boundary conditions.
Category: Statistics

On a Remarkable Quadratic Identity

Authors: Jose Acevedo Jimenez
Comments: 1 Page.

We prove the elementary identity for any real number. The identity reveals a symmetric structure between shifted quadratic terms.
Category: Algebra

F=ma Might not be Correct for Electrically Charged Bodies

Authors: Moshe Segal
Comments: 17 Pages.

The Nowadays Science of Physics states that when an external Force is exerted on any Massive Body it causes an Acceleration of this Massive Body according to Newton's Second Law of Motion, F=ma.But, if that Massive Body Accelerates according to Newton's Second Law of Motion, F=ma, this also implies, as will be presented in this paper, that all the Work done by this external Force, which is also all the Energy exerted on this Massive Body, is already converted to the Kinetic Energy that that Massive Body acquires, or, in other words, is already manifested and embedded in the Kinetic Energy that that Massive Body acquires, because of the above-mentioned external Force which was exerted on it.However, if an external Force is exerted on an Electrically Charged Massive Body, what was presented above might need modifications.Because, if an Electrically Charged Massive Body does indeed Accelerates also according to Newton's Second Law of Motion, F=ma, and all the Work done by the external Force exerted on it, is already manifested and embedded in the Kinetic Energy embedded in this Electrically Charged Massive Body, then this cannot explain the origin of the Extra Energy that an Electrically Charged Massive Body acquires, which is manifested in the Electromagnetic Waves that it emits when it Accelerates, and the Magnetic Field that surrounds it when it moves.If the above presented dilemma is further substantiated, then, the resolution to this dilemma should be only one of two possibilities: either the Extra Energy mentioned-above, is generated from nothing, which clearly violates the Energy Conservation Principle, or, as this paper predicts, that Newton's Second Law of Motion, F=ma might not be the proper equation which should be used to calculate the Acceleration that an Electrically Charged Body acquires, when an external Force is exerted on it.(Truncated by viXra Admin)
Category: Relativity and Cosmology

Dimensional Twins

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

This paper introduces and explains the new concept of dimensional twins — physical quantities that share the same combination of fundamental dimensions but have different meanings.
Category: General Science and Philosophy

A Structural Proof Approach to the Twin Prime Conjecture

Authors: Younghwan Yun
Comments: 10 Pages.

This paper presents a novel inductive framework for the generation and validation of twin primes, grounded in Bertrand’s Postulate. Unlike traditional methods relying on probabilistic or empirical filtering, this approach provides a recursive structure that not only predicts the location of future twin prime pairs but also supports theoretical generalization to even gaps k = 2,4,6,8,.... Empirical validation up to 109 confirms that no counterexamples violate the proposed inductive inequality conditions. The framework aligns heuristically with the Hardy—Littlewood conjecture and provides evidence supporting both the infinitude and structured distribution of twin primes.
Category: Number Theory

A Structural Proof of the Goldbach Conjecture via Factor Elimination and Prime Complement Analysis

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

We present a constructive and structural proof of the Goldbach Conjecture, which asserts that every even integer greater than two is the sum of two primes. Our approach is based on the concept of factor elimination and prime complement analysis. By categorizing integers into divisors and non-divisors of a given N, and focusing on the structure of non-divisor primes, we demonstrate that the set of complements 2N-a cannot be fully covered by multiples of these primes. Using prime density estimates and structural lemmas, we show that a prime pair (p, q) satisfying p+q=2N must always exist. Numerical examples further validate the framework, providing an intuitive and elementary alternative to heavy analytic methods traditionally used in this domain
Category: Number Theory

A Structural Proof of the Collatz Conjecture via Injectivity and Recursive Decay

Authors: Younghwan Yun
Comments: 8 Pages.

We present a structural proof of the Collatz conjecture by rigorously analyzing the recursive mapping of odd integers. By introducing a compressed recursive function that directly connects successive odd values, we prove the global injectivity of the sequence and demonstrate that infinite non-repetitive progression is impossible within the constrained domain. We establish that no nontrivial cycles exist through a minimal element argument, and reinforce convergence through nonlinear divergence properties and the Pigeonhole Principle. Consequently, every sequence must inevitably intersect the canonical cycle (1 to 4 to 2 to 1), thus conclusively demonstrating the validity of the Collatz conjecture under the defined structural framework.
Category: Number Theory

A Proof of the Riemann Hypothesis

Authors: Younghwan Yun
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents an intuitive method for proving the Riemann Hypothesis. It begins by deriving the relationship equation at the zeros of the Riemann zeta function from Riemann’s functional equation. This equation follows the Schwarz reflection principle, indicating that the zeros of the zeta function are restricted to the line with a real part of 1/2 in the complex plane. Furthermore, using the Schwarz reflection principle, it concludes that zeros cannot exist outside the critical line. Therefore, the Riemann Hypothesis is true.
Category: Number Theory

QuantumGravity: Extending the Stress-Energy Tensor

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

This paper proposes a modification of Einstein’s field equations to include an additional tensor that represents the gravitational influence of matter in the mode of potency (textsc{being in potency}), as defined in a prior ontological framework. Assuming that certain quantum systems before measurement exist in a non-actual but real and structured state, the paper introduces a potentiality energy-momentum tensor alongside the classical tensor T. As a physical consequence, the article presents a revised model of black holes in which matter inside the event horizon transitions into a gravitationally effective potent state, avoiding singularities while preserving external field behavior. This approach offers a new avenue for reconciling general relativity with quantum ontological constraints.
Category: History and Philosophy of Physics

Quantum Reflection Across Multiple Fabrics of Spacetime: A Geometric Extension of the Path Integral Framework

Authors: Bhushan Poojary
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a novel interpretation of photon reflection grounded in Feynman’s path integral formulation, enriched by a multi-fabric geometry of spacetime. In this model, a photon's quantum state is projected not onto a single classical spacetime but simultaneously across a distribution of geometric fabrics, each representing a subtle variation in phase or curvature. The observed reflection path, classically attributed to Fermat's principle of least time, emerges from the vector summation of all quantum amplitudes across these fabrics. This framework connects optics, quantum mechanics, and the geometry of spacetime, offering new insights into quantum coherence, the holographic principle, and the nature of physical reality.
Category: Quantum Physics

Impact of Neural Network Architecture on Generalization and Regularization

Authors: Zohaib Muaz
Comments: 8 Pages. License: CC BY 4.0

This paper investigates the impact of increasing the depth and width of convolutional neural networks (CNNs) on their generalization performance across image classification tasks. Experiments were conducted using PyTorch on two datasets of varying complexity: MNIST (simple) and CIFAR-10 (complex). A variety of CNN architectures were trained with different depths and widths, and regularization techniques including dropout and L2 weight decay were applied to analyze their effects on overfitting. Results indicate that shallow networks are sufficient for achieving high accuracy on MNIST, while deeper or wider networks yield significant performance gains on CIFAR-10. However, high-capacity models are more prone to overfitting without appropriate regularization. Techniques such as dropout and L2 regularization were found to consistently improve generalization, particularly in deeper architectures. These findings underscore the importance of balancing model complexity and regularization, especially when dealing with datasets of differing size and variability.
Category: Artificial Intelligence

Automatic Uncertainty Evaluation for Determining the Number of Components in Nested Models

Authors: L. Martino, R. San Millan-Castillo, E. Morgado
Comments: 21 Pages.

In this work, we propose and examine two procedures for constructing intervals that capture the uncertainty associated with determining the effective number of components in model selection problems. The output of these methods is an interval (defined by two integer bounds) representing plausible values for the number of components. A detailed discussion is provided on the connection between the proposed approaches andthe widely-used information criteria in the literature. Notably, the methods do not relyon the availability of a likelihood function, making them broadly applicable across variousdomains such as regression, classification, feature and/or order selection, clustering, anddimensionality reduction. These techniques leverage geometric properties of the error curve to construct the intervals. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness and practical utility of the proposed procedures. Additionally, MATLAB code is provided to facilitate adoption by practitioners and researchers.
Category: Statistics

Decomposing the Deformed Tensor Products in a Four-Dimensional Space

Authors: Thierry L. A. Periat
Comments: 24 Pages.

This document continues the systematic exploration of diverse mathematical methods allowing the decomposition of deformed tensor products. Here, the discussion is focusing attention on deformed Lie products and on conditions generalizing in a four-dimensional mathematical space what has been called the initial theorem during the elaboration of the intrinsic method, the purpose of which was the decomposition of deformed cross products. This mathematical document sheds a particular light on the (2, 0) representations of the electromagnetic fields.
Category: Mathematical Physics

A Quantum-Financial Topology of Supply-Demand Imbalance via Non-Hermitian Stochastic Geometry

Authors: Natalia Tanyatia
Comments: 39 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org) https://github.com/NataliaTanyatia/End-of-Line.git

We present ÆEA, a trading algorithm that formalizes market microstructure as a quantum stochastic process, where price-action is governed by a Lind-blad master equation and supply-demand zones emerge as non-commutativegauge fields. By redefining classical technical indicators (e.g., ATR, RSI) as projective measurements in a 13-dimensional Hilbert space, we derive a proportionality principle: trades trigger only when the imbalance operatorIˆ = P k (Pˆ>66.6 − Pˆ<33.3) satisfies hΨ|I| ˆ Ψi = 2, a Kronecker-delta condition that suppresses heuristic false positives. Empirical backtests show 100% win rates (minus spread costs), revealing hidden topological invariants in price-data previously dismissed as "overfitting."
Category: Quantum Physics

Relationship Between Even and Prime Numbers and Implications on the Goldbach Conjecture

Authors: Samuel Bonaya Buya
Comments: 6 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We propose a functional relationship between even and prime numbers that serves as thefoundation for a formal inductive proof framework for the Binary Goldbach Conjecture. This approach is grounded in the principle of prime interval stability, whereby even numbers are represented as functions of pairs of primes constrained within specific intervals. The derived expressions support the conjecture by systematically generating valid Goldbach partitions and establishing inductive continuity in prime pair generation for all even integers greater than two.
Category: Number Theory

Theory of Multiple Inflationary Scalar Fields

Authors: Roberto C. M. Navacchia
Comments: 8 Pages. In Portuguese

The proposal of this article is the hypothesis of multiple inflationary scalar fields as analternative to the single Big Bang model. Instead of a single initial singularity, I suggest that the early universe was dominated by several scalar inflationary structures such as Turbulent Inflatons, where gravitational vortices formed amidst the cosmic chaos, and which later gave rise to galaxies. The exploration of the relationship between the formation of brown dwarfs and the evolution of cosmic structures, suggesting that these celestial objects can serve as evidence for this model. In addition, the inflationary metrics of these scalar fields and their influence on the cosmic microwave background, Computational Models create implications for a new cosmological paradigm.
Category: Relativity and Cosmology

Quantum Evidence Theory

Authors: Fuyuan Xiao
Comments: 52 Pages.

A quantum evidence theory is proposed for uncertainty modeling and reasoning in both closed-world and open-world environments, referred to as QET and GQET, respectively. At the level of uncertainty representation, a series of new concepts are introduced, including (generalized) quantum basic probability amplitude function, (generalized) quantum basic probability distribution, (generalized) quantum belief function, (generalized) quantum plausibility function, and others. At the fusion level, several (generalized) quantum evidential combination rules are proposed to provide a dynamic mechanism for updating and integrating uncertain information from multiple sources, thereby flexibly accommodating diverse application requirements. At the decision-making stage, (generalized) quantum Pignistic transformations are developed to support decision-making processes. In this context, the quantum models of QET and GQET are constructed based on the quantum state representation of the (generalized) quantum basic probability amplitude function, the measurement operators for basis events, the (generalized) quantum basic probability measurements, and the (generalized) belief and plausibility measurements. Quantum evidence theory integrates traditional evidence theory with quantum probability theory, providing a more flexible and powerful framework for uncertainty modeling and reasoning in artificial intelligence. By leveraging the expressive capabilities of quantum state spaces and probability amplitudes, it not only handles incomplete and uncertain information inherent in classical evidence theory but also captures interference effects and non-classical correlations among pieces of information. This enables dynamic information fusion and robust decision-making in complex and uncertain environments.
Category: Artificial Intelligence

Drawing Bent to Straight a New Solution to Geometric Problems

Authors: Hongfa Zi, Lei Zi
Comments: 6 Pages.

This article proposes an innovative method based on geometric transformation and limit construction, which successfully solves the problem of "drawing curves as straight". By introducing a linear function of fixed arc length and isosceles trapezoid, we prove that the transformation between a circle and an equal area square can achieve geometric equivalence in finite steps, and provide specific graphical steps and mathematical proof. This study reveals the limitations of traditional ruler drawing constraints and achieves accurate area conversion through an extended toolkit. Finally, the paper discusses the mathematical significance of this solution, including the algebraic treatment of the transcendental number and its supplementation to the Euclidean geometry system.
Category: Geometry

Photon and Neutrino in Holographic Spacetime: A Tale of Broadcast and Isolation

Authors: Bhushan Poojary
Comments: 8 Pages.

This paper explores a novel distinction between photons and neutrinos based on their interaction with spacetime fabrics in a holographic universe [1][2]. While photons are known to propagate universally and act as carriers of information across intersecting holographic layers, we propose that neutrinos traverse a distinct and isolated spacetime fabric. Unlike photons, which copy and broadcast their quantum state to multiple observers and regions, neutrinos retain their state within a localized domain, only interacting when another particle’s spacetime address aligns precisely with their own. This framework explains the elusive nature of neutrinos, their weak interaction cross-section, and their negligible role in quantum entanglement. By introducing the concept of "holographic address resonance," we provide a new geometric basis for understanding weak interactions, neutrino oscillations[5][6], and the possible link between hidden sectors and the structure of spacetime. The proposed model complements existing interpretations of the Standard Model while opening avenues for a deeper unification of quantum mechanics and spacetime geometry.
Category: Quantum Physics

The Probable Extinction of Science and of Modern Social and Political Ideas with Technological Civilisation.

Authors: Richard Michael Blaber
Comments: 31 Pages. Creative Commons License BY-NC-ND 4.0.

This paper will argue that, given the demise during the remainder of the 21st Century of global capitalism and of the global technological civilisation that is its corollary, it is not to be reasonably expected that scientific ideas, as they have been known since the 17th Century, and the science based on them, or post-Enlightenment social and political ideas, will survive that demise. Already, it must be noted, scientific ways of thinking, and liberal (or ‘woke’) political perspectives are being increasingly challenged by an ever more energised and fervent populist Right on a global scale. The Trump Administration’s recent attacks on academia and scientific research in the United States may be seen as an extension of this trend, as may the Republican-inspired banning of books in American school districts.
Category: Social Science

Universal Priority of Final Causes Scientific Truth, Realism and The Collapse of Western Rationality

Authors: Krystian Zawistowski
Comments: 190 Pages.

The book deals with the defence of Aristotelian principle of finality as applied to various fields of science and philophy. Especially: theory of language, physics, statistics and quant finance as well as refutation of positivism, Wittgenstein, Kuhn and similar opponents of it.
Category: General Science and Philosophy

A Higher-Dimensional Interpretation of Quantum Entanglement and Its Extension to a High-Dimensional Schrödinger Equation

Authors: Ichiro Tsukamoto
Comments: 7 Pages.

Quantum entanglement, wherein a measurement on one particle instantaneously determines the spin state of another, challenges the locality and causality principles in four-dimensional spacetime. I hypothesize that two entangled electrons are unified as a single higher-dimensional object across compactified extra dimensions (5th to 11th dimensions). Embedding the entangled wavefunctionψ(xu2081, xu2082) = (1/√2) [|↑⟩u2081|↓⟩u2082 ± |↓⟩u2081|↑⟩u2082]into an extended configuration space X = (xu2081, xu2082, yu2081, yu2082) with a delta-function constraint δ(yu2081 - yu2082), I interpret entanglement not as nonlocal influence, but as a manifestation of geometric unity in higher dimensions. I further develop a higher-dimensional Schrödinger equation to describe the dynamics:iℏ ∂Ψ(xu2081, xu2082, y, t)/∂t = ( -ℏ²/2mu2081 ∇²_{xu2081} - ℏ²/2mu2082 ∇²_{xu2082} - ℏ²/2m_y ∇²_{y} + V(xu2081, xu2082, y) ) Ψ(xu2081, xu2082, y, t)My model offers a geometrical reinterpretation of quantum entanglement as projections of a single coherent higher-dimensional entity and suggests new pathways for understanding quantum foundations and spacetime structure.
Category: Quantum Physics

Six Simultaneous Equations

Authors: Oliver Couto
Comments: 4 Pages.

In the below paper we have attempted to find integer solution to six simultaneous equations. In math literature we have not found a similar equation that has been investigated before. The equations consist of three quadratics on the left hand side which sum up to a square on the right side. Even-though the equations are quadratic in nature the degree of difficulty increases with the number of equations considered. The author considered six equations simultaneously. Others can try & solve simultaneous equation which are more than six in the group.
Category: Algebra

From Law of Universal Gravitation to Law of Universal Connection

Authors: Junzheng Liu
Comments: 35 Pages.

This paper is to reform Issac Newton’s law of universal gravitation into a new theory. With a new mathematical tool, I build a model which could provide an alternative perspective in understanding a series of topics in modern physics fields, such as quantum entanglement, expansion of the universe, wave-particle dualism, time, and the relationship between gravity and other fundamental forces.
Category: Quantum Gravity and String Theory

Multimodal Cognitive System for AGI — Open Blueprint

Authors: Derek Van Derven
Comments: 46 Pages. (Note by viXra Admin: viXra in general does not accept article written in technical/patent format))

This invention proposes a novel artificial general intelligence (AGI) system that integrates visual thought simulation and meta-cognitive reflection as core cognitive processes. While some may argue that visualization is just an additional layer or a tool for perception, this system goes beyond that. It makes visual thought central to reasoning itself, enabling the AGI to visualize both abstract and concrete concepts and reason in a human-like manner. By using a dynamic internal model where visualization of thoughts drives decision-making, the AGI can reflect on its reasoning, adjust based on reflection, and engage with the world in a much deeper andmore adaptive way than current models. This innovative approach doesn’t just make the systemunderstand, but enables it to engage in complex philosophical reflection and adapt dynamically to new situations, marking a true leap in AGI capability. While this invention may enable artificial general intelligence, we refer to it here as a 'multimodal cognitive system' to emphasize its technical, system-level design.This document details a complete, technically functional multimodal cognitive system architecture capable of interpreting and responding to both abstract and concrete prompts through multi-modal sensory integration, internal simulation, and self-correcting feedback. Every module is defined in termsof software stack, processing model, memory architecture, and sensory translation mechanisms. Visual, symbolic, and philosophical inputs are processed through clearly defined computational steps tied to real-time simulation and physical execution systems. The architecture is implementable today using available hardware (TPUs, GPUs, microcontrollers) and software (LLMs, Unity, ROS, Prolog/CLIPS).
Category: Artificial Intelligence

On the Definition of Velocity and the Geometry of Special Relativity

Authors: Philip Asquith
Comments: 11 Pages.

This article uses the Symmetrical Reflected Radar Model (SRRM) that was described in viXra 2504.0064 to analyse special relativity. The SRRM was developed without making any assumptions about the definition of velocity so that the fundamental relationship between distance and time could be clearly identified. In the SRRM, the algebra of special relativity is reliably represented in a symmetrical spacetime diagram. The transformation equations and geometry of the SRRM describe two symmetrical orthogonal coordinate systems rotating as mirror images; one clockwise, the other anticlockwise, as relative velocity changes. In a transformation between the two symmetrical orthogonal coordinate systems of the SRRM, the spacetime interval is invariant using Pythagoras. It is concluded that, in a symmetrical model, spacetime in special relativity is Euclidian. The terms and equations of the SRRM are shown to be completely interchangeable with those of the generally used Lorenz Transformation. There is good evidence to conclude that the velocity term used in the SRRM is fundamental. Thus, the velocity term used in the Lorenz Transformation is an approximation to the fundamental definition of velocity. Almost all derivations of the Lorenz Transformation since special relativity was first described have been made after first assuming the definition of velocity. This unstated assumption has thus been a silent axiom of the theory, inherent in subsequent analysis, inevitably affecting the conclusions of the theory.
Category: Relativity and Cosmology

Proof of the Yang—Mills Mass Gap via Energy Minimization

Authors: Lautaro Fesembeck
Comments: 7 pages, English. Feedback - lautaro.math@gmail.com

We prove the existence of a mass gap in pure Yang—Mills theory by applying energy minimization methods. By defining a disturbance field associated with the field strength tensor and constructing a global energy functional, we demonstrate that any nontrivial excitation away from the flat connection induces strictly positive energy. Through analysis of local perturbations, gauge invariance, and functional coercivity, we establish the existence of a positive lower bound on excitation energies, thus rigorously proving the Yang—Mills mass gap.
Category: Mathematical Physics

Resolution Matrix Semantics for Modal Logic: Philosophical Implications of Indeterminacy and Poly-Logic Thinking

Authors: Andrey Kuznetsov
Comments: 9 Pages.

This paper explores the philosophical implications of Resolution Matrix Semantics (RMS) as an alternative foundation for modal logic. Unlike traditional Kripkean models, which interpret modality through relations between multiple possible worlds governed by classical logic, RMS treats indeterminate truth values as fundamental, operating within a single world. RMS introduces "blinking" truth assignments and sub-interpretations to resolve uncertainty, capturing the inherently poly-logical nature of human thought. Drawing a parallel to quantum physics, we argue that Kripke models resemble Everett’s Many-Worlds interpretation, while RMS aligns with the Copenhagen interpretation’s emphasis on intrinsic uncertainty. RMS offers a new view of modal reasoning—not as a proliferation of worlds, but as a diversification of perspectives within one world. The framework’s philosophical significance is examined through connections to poly-logic thinking, quantum cognitive models, and potential applications in artificial intelligence and parallel computing. RMS ultimately provides a dynamic, pluralistic model for rationality that better reflects the complexity of human cognition and decision-making under uncertainty.
Category: Set Theory and Logic

Extended Linear Cryocooler Development Process: Accelerating Time to-Market and Enhancing Performance

Authors: R. Bustan, O. Sela, S. Lavenda S. Shitrit, I. Nachman, V. Segal
Comments: 20 Pages.

This article reviews the development and performance of the Extended Linear (ELI) cryocooler models K589 and K591.The focus of this article is the SPRINT development cycle, which emphasizes simulation, risk reduction, and the creation of lean prototypes. Initial simulations used SAGE software to highlight the potential for performance improvements. It provided the groundwork for optimizing the design while keeping dimensions as close as possible to K588/K590. In the next phase, the risk reduction phase focused on mitigating any potential design weak point by performing detailed analysis. These included magnetic flux density evaluations in both DC and AC conditions. The development of lean prototypes has a crucial role in the final phase, allowing rapid iteration and validation of design changes. By streamlining these processes, the SPRINT cycle significantly reduces time-to-market, enabling faster deployment of high-performance cryocoolers in various applications. Additionally, the project life cycle and system engineering principles are explored, highlighting how they contribute to optimizing development speed, product quality and performance. The K589/K591 achieved significant improvements particularly in cooling power while maintaining efficiency. It can reach a steady state working point of 3/4W@120K@71ºC. Those cryocoolers are well-suited for SWaP-constrained applications:It has been optimized to deliver high cooling power with efficient use of energy. By modifying the compressor design the cooler achieves significant cooling performance while maintaining a power-efficient operation.Project life cycle and system engineering play crucial roles in enhancing the effectiveness of a sprint development cycle, particularly in complex projects like this. The project life cycle provides a structured framework that ensures each phase of development is properly complying with the market requirements. By applying system engineering principles, potential issues can be identified and addressed early in the sprint cycle, thus minimizing risks and optimizing the final product. Detailed performance comparisons between the K589/K591 and RICOR’s other linear models are presented, highlighting key variations and their implications for efficiency and reliability.
Category: Thermodynamics and Energy

Some New Identities for Fibonacci-Like Sequences

Authors: Julian Beauchamp
Comments: 3 Pages.

In this paper, we observe some nice identities for the products of Fibonacci-like sequences. While these identities can hardly be original discoveries, I have been unable to find them elsewhere.
Category: Number Theory

Three Particle Amplitudes with a Massless Boson

Authors: Clemens Heuson
Comments: 9 Pages.

It seems possible to obtain massive three particle amplitudes with a massless boson including gravity from one formula for only massive particles similar to the case of massless three particle amplitudes. To achieve this one has to assume tree unitarity and non chiral interactions. The x-factor needed for amplitudes with two equal mass particles and one massless boson can be derived in this way. We give an interpretation of massive spinor brackets with negative exponents appearing in amplitudes with gravity and show that they lead to appropriate little group transformations.
Category: High Energy Particle Physics

Near Lightspeed Interstellar Travel

Authors: John R. Cipolla
Comments: 6 Pages.

Using the concepts of general relativity relativistic interstellar travel to the stars approaching the speed of light can be computed for the general case of accelerated motion for half the journey and decelerated motion for the remaining half of the journey. According to general relativity a rocket and its passengers feel the effects of gravity when accelerating in flat spacetime where motion is described relative to a proper reference frame. Because of time dilation an astronaut can travel stellar distances, that is many light years within his/her own lifetime while many thousands of years will have elapsed on the planet of departure. This analysis determines the proper time dilation or elapsed time on a spaceship whose speed approaches the light speed and the instantaneous velocity or 4-velocity of a spaceship relative to the speed of light at some constant acceleration. As explained in general relativity the 4-velocity is the rate of change of the 4-vector with respect to the moving frames’ proper time. The results presented here are independent of the propulsion systems used. These results are equally valid for a spaceship powered by an advanced antimatter propelled photon rocket, or a spaceship powered by a VASIMR (Variable Specific Impulse Magnetoplasma Rocket) plasma rocket motor.
Category: Classical Physics

Cosmic Scars: A Topological Theory of Gravity Without Dark Matter or Dark Energy

Authors: Alex Bertran
Comments: 38 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Cosmic Scars: A Topological Theory of Gravity (Final Version)

This work proposes dark matter (DM) and dark energy (DE) as emergent effects of fossilized Weyl curvature defects—cosmic scars—from primordial black holes and Pop III supernovae.

Key breakthroughs:
- Replaces DM/DE without particles via spacetime topology (Eqs. 1-31).
- Predicts JWST galaxy spin alignment (3.1σ), LISA 10⁻⁵ Hz gravitational waves, and CMB Cold Spot as Gpc-scale scar.
- Solves NGC 1052-DF2 kinematics, Bullet Cluster offsets, and Hubble tension via differential expansion.


Category: Astrophysics

Motion Out of Time: Single Speed Hypothesis

Authors: Temesgen Degu
Comments: 16 Pages.

This paper introduces a hypothesis that reinterprets the relationship between motion and time. We propose that all objects possess an intrinsic capacity for instantaneous motion between two points, occurring "out of time," and that observed travel time results from discrete "stops" induced by external forces or intrinsic properties such as mass. Using thought experiments involving a photon and a marble, we illustrate this concept and explore its potential implications for classical mechanics, special relativity, and quantum phenomena. This perspective suggests motion is inherently timeless, with time arising as a consequence of interruptions, offering a new lens on the fundamental dynamics spanning classical laws to quantum effects. While lacking a fully developed mathematical foundation, this framework offers a novel perspective on velocity, proper time, and quantum superposition, suggesting avenues for future theoretical and experimental investigation. We emphasize its conceptual nature and the need for rigorous development to elevate it from hypothesis to theory, inviting researchers to explore its intriguing possibilities.
Category: Classical Physics

Spacetime with Pseuso-Kasnermetric and Shrinking Timelike Dimension

Authors: Holger Döring
Comments: 12 Pages.

Described is a Pseudo-Kasnermetric of local spacetime with shrinking timelike dimension-coordinate (TLD) as a solution of GRT gravity fieldequation. This metric leads to normal flatMinkowski-spacetime in time intervall of present time but changes with changing of timelikecoordinate from a 1-dimensional only timelike spacetime in early universe to a more 3-dimensional pure spatial space in far future with only spacelike coordinates or dimensions (SLD) and shrinking timelike coordinate until it reaches the Planck-time. This whole description leads to the model of a spacetime with permanent shrinking timelike dimension.
Category: Relativity and Cosmology

The Matryoshka Universe: An Investigation Into 4-Sphere Cosmology

Authors: Philip Carmichael
Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references)

We propose a cosmological model in which the universe is described as a 4-sphere: a non-Euclidean, inwardly expanding spacetime geometry. In this framework, past states of the universe are represented by concentric shells surrounding the central present, like nested Matryoshka dolls with increasing internal volume. Time flows radially inward from the Cosmic Microwave Background (CMB) toward the present, resolving the horizon problem geometrically and reframing redshift as a consequence of progressive curvature rather than accelerating expansion. The model suggests that entanglement arises from global geometric constraints, not nonlocal signaling, and that inertial frames comoving with the CMB may be physically privileged. While the model is presented conceptually, it invites further mathematical development and may offer insights into dark energy, the Hubble tension, and the structure of spacetime itself.
Category: Relativity and Cosmology

Some Formulas and an Equivalence Between Two Sets of Axioms in Axiomatic Propositional Logic

Authors: Harry Willow
Comments: 6 Pages.

We derive some formulas in axiomatic propositional logic and we show that two sets of different axioms are equivalent. The outputs were manually derived through logical deductions and subsequently typeset in LaTeX, without the use of automated computational tools.
Category: Set Theory and Logic

Geometrized Vacuum Physics Part 11: Gravity and Levitation

Authors: Mikhail Batanov-Gaukhman
Comments: 41 Pages.

This article is the tenth part of the scientific project under the general title "Geometrized Vacuum Physics based on the Algebra of Signature " (GVPh&AS) [1,2,3,4,5,6,7,8,9]. In this article, the phenomenon of planetary gravity is considered as a result of a spatial-phase shift between two counter intra-vacuum flows, flowing from top-down and bottom-up. These powerful intra-vacuum flows flow along counter spirals wound on all radial directions departing from the core of stable spherical vacuum formations (in particular, "planets" and "stars"). In this case, the vacuum currents flowing upward along the spiral always slightly lag in magnitude behind the vacuum currents flowing downward along the counter spirals. Therefore, a relatively weak residual accelerating drain carries along all bodies in the direction of the core of the spherical vacuum formation, and is the cause of gravitation. The model representation of gravity as a result of the difference of counter powerful intra-vacuum currents can serve as a theoretical justification for the possibility of using these flows for alternative methods of movement in space. In conclusion, the article considers possible methods of controlling the topology of space and intra-vacuum currents with the aim of using them as a driving force in the levitation mode.
Category: Classical Physics

Division Algebras, Triality, and Exceptional Magic

Authors: A. Garrett Lisi
Comments: 30 Pages.

We describe in explicit detail the rich relationship between division algebras, split composition algebras, triality, Clifford algebras, spinors, triality Lie algebras, generalized reflections, exceptional magic square Lie algebras, and Exceptional Unification in particle physics.
Category: High Energy Particle Physics

The Absolutely Precise Atomic Unit of Time and its Applications in Determination of Atomic/Nuclear Transition Frequencies and Fundamental Physical Constants

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 10 Pages.

In our previous paper, we calculated out and determined the atomic unit of time (tau) to be 2.41888432658653284(45)×10-17 s or 2.41888432658653280(45)×10-17 s. In this paper, using the 133Cs atomic transition frequency which is 9192631770 Hz (a second is defined by this) and its reciprocal in atomic units calculated from our corresponding formula, we calculate out and determine the absolutely precise atomic unit of time to be 2.41888432658653278×10-17 s. With this value of tau and the speed of light in atomic units (cau) determined in our previous papers, we calculate out and determine the absolutely precise values of the atomic transition frequencies of some atoms, the nuclear transition frequency of 229Th* and some fundamental physical constants such as the Rydberg constant (R∞), the Hartree energy (Eh), the Bohr radius (a0), the classical electron radius (re) and the electron mass (me).
Category: Nuclear and Atomic Physics

System and Method for Multimodal Cognitive Architecture Featuring Visual Thought Simulation, Internal Scene Construction, and Meta-Cognitive Feedback

Authors: Derek Van Derven
Comments: 46 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This invention proposes a novel artificial general intelligence (AGI) system that integrates visual thought simulation and meta-cognitive reflection as core cognitive processes. While some may argue that visualization is just an additional layer or a tool for perception, this system goes beyond that. It makes visual thought central to reasoning itself, enabling the AGI to visualize both abstract and concrete concepts and reason in a human-like manner. By using a dynamic internal model where visualization of thoughts drives decision-making, the AGI can reflect on its reasoning, adjust based on reflection, and engage with the world in a much deeper and more adaptive way than current models. This innovative approach doesn’t just make the system understand, but enables it to engage in complex philosophical reflection and adapt dynamically to new situations, marking a true leap in AGI capability. While this invention may enable artificial general intelligence, we refer to it here as a 'multimodal cognitive system' to emphasize its technical, system-level design. This document details a complete, technically functional multimodal cognitive system architecture capable of interpreting and responding to both abstract and concrete prompts through multi-modal sensory integration, internal simulation, and self-correcting feedback. Every module is defined in terms of software stack, processing model, memory architecture, and sensory translation mechanisms. Visual, symbolic, and philosophical inputs are processed through clearly defined computational steps tied to real-time simulation and physical execution systems. The architecture is implementable today using available hardware (TPUs, GPUs, microcontrollers) and software (LLMs, Unity, ROS, Prolog/CLIPS).
Category: Artificial Intelligence

Quantum Theory of Chronovibrational Time: Quantization of ψ(t), Possible Experiments, and Observable Predictions

Authors: Paolo Giordana
Comments: 32 Pages. Final version published on Zenodo. See DOI: https://zenodo.org/records/15299115

This work proposes a deeper development of chronovibrational theory by introducing the quantization of the temporal field psi(t), which is promoted to a quantum operator psi-hat(t) defined over a Hilbert space. Time is thus interpreted as a dynamic and quantizable physical variable, subject to observable residual fluctuations. This approach allows us to model the residual quantum imperfections of chronovibration - a decaying "cosmic beat" originating from the Big Bang - and provides a coherent framework for the emergence of time within a harmonic and dissipative cosmology.The aim is to predict measurable effects, including post-merger gravitational echoes, metrological instabilities, and interference phenomena induced by coupling with external fields. A chronovibrational transfer matrix is introduced, along with a set of experimental protocols - both passive (e.g., LIGO, atomic clocks) and active (e.g., ITER, modulated RF fields) - capable of falsifying or confirming the model. Energy dynamics are rendered conservative through a second scalar field Psi(t), acting as a vibrational memory and regulator of phase transitions.Overall, this model represents a first testable theoretical proposal for a quantum reformulation of time, unifying aspects of canonical quantum gravity, scalar-tensor theories, and emergent cosmology into a single observable harmonic structure. It does not claim to be exhaustive in any way.
Category: Relativity and Cosmology

Dirac Equation in Complex Space-Time: Toward a Geometric Unification of Spin, Quantum Mechanics, and Electromagnetism

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

In this paper, we extend the Dirac equation into a complex spacetime framework, generalizing relativistic quantum mechanics to incorporate imaginary dimensions of space and time. Building upon the analyticity conditions introduced in our previous work on the Schrödinger equation, we derive the complexified Dirac equation, ensuring consistency with relativistic covariance and spinor structure. The resulting formulation naturally splits into real and imaginary parts, offering novel geometric interpretations of spin, mass, and quantum fluctuations as manifestations of the imaginary curvature of spacetime. We explore the coupling of the complexified Dirac spinor to electromagnetic fields through the imaginary part of the spacetime metric, suggesting a unified geometric origin of spin and electromagnetism. Potential implications for zitterbewegung, neutrino oscillations, and extensions toward quantum gravity are discussed. This framework offers a promising pathway toward a unified understanding of quantum field theory, geometry, and fundamental forces within a complexified spacetime manifold.
Category: Quantum Physics

Proof of the Riemann Hypothesis via Energy Minimization

Authors: Lautaro Fesembeck
Comments: 10 Pages. Correspondence: lautaro.math@gmail.com

We model the distribution of nontrivial zeros of the Riemann zeta function through a dynamic equilibrium principle. By defining a disturbance field associated with prime distributions and constructing a corresponding global energy functional, we show that any deviation from the critical line Re(s) = 1/2 necessarily increases global energy. Through analysis of local perturbations, global independence, and symmetry properties implied by the functional equation of ζ(s), we demonstrate that only the critical line configuration minimizes total energy. This provides a new and rigorous resolution of the Riemann Hypothesis via energy minimization methods.
Category: Number Theory

A Deductive Justification for The Collatz Conjecture

Authors: Christian I. G. Winsor
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents a new approach to understanding the Collatz Conjecture. The conjecture asks whether a simple process (repeatedly halving even numbers, and tripling odd numbers then adding one) will always eventually reach the number one, no matter which positive whole number you start with. In this work, I introduce a way to group numbers based on their properties and show that, by following a specific set of steps, every number can be reduced to a smaller group. By combining this method with results that have already been checked by computer for smaller numbers, I provide a logical framework that supports the idea that the Collatz process always ends at one.
Category: Number Theory

Reality Sucks, Really!

Authors: Sven Gohlke
Comments: 9 Pages.

I develop a unit-less unit-system which incorporates the special relativity theory. The so caled "dark matter" and"dark energy" are identified as calculation errors.
Category: Mathematical Physics

Compare and Combine Different Importance Ranking Methods for Feature Selection: a Gentle Review

Authors: M. Marinescu, L. Martino, G. Villacres, S. G. Arcidiacono, O. Barquero
Comments: 23 Pages.

Feature selection remains a highly relevant and actively researched topic across signal processing, statistics, and machine learning. It has gained new relevance recently, especially because of renewed interest in the so-called Shapley values. However, beyond the Shapley values, many possibilities exist to measure (explicitly or implicitly) the importance of a variable for a specific task. Given a measure of importance, we can obtain a ranking of the input features (involved, e.g., in a regression or classification problem), as provided by an algorithm and/or expert system. Consequently, it is also necessary to evaluate the obtained rankings, for instance to identify the most effective ranking method or to aggregateall results into an average ranking, akin to an ensemble average of expert opinions. In this work, we provide an exhaustive review of several scoring functions and techniques designed for evaluating the ranking methods with or without an available ground-truth. Moreover, the work contains some novel elements such as the use of other famous indices, for instance, the Gini coefficient and effective sampling size (ESS) measures. It is important to remark thatthe paper incorporates insights from a variety of sources across diverse scientific disciplines, including computational statistics, quantitative economics, and machine learning. Finally, we test the described schemes in a controlled experiment on feature selection, in order to compare different ranking methods and to assess their performance and robustness.
Category: Statistics

Proof of the Riemann Hypothesis

Authors: Kato Millen
Comments: 4 Pages. (Note by viXra Admin: Please withdraw 2501.0074v1 if it is incorrect)

The Riemann hypothesis states that the real part of all non-trivial zeros of the Riemann zeta function is 0.5 in the critical strip. In this paper we proved the hypothesis by using the properties of the Riemann zeta functional equation at ζ (s) = 0 and also using the integral representation (Mellin transformation) of the Riemann zeta function in the critical strip.
Category: Number Theory

World Asymmetry and Consciousness

Authors: Sergey Y. Kotkovsky
Comments: 11 Pages.

The studies of weak interactions in physics have revealed a prominent, so-called chiral, asymmetry of our world. More widely known is the asymmetry of particles and antiparticles, which is also connected to chiral asymmetry: we know that all neutrinos are left-chiral. The attempts made by many physicists to restore the symmetry between right and left, i.e. to discover "mirror matter", have not been successful. In live beings the asymmetry manifests itself in male and female, the functioning of the right and left hemispheres of the brain, in phyllotaxis, in algebras of genetic alphabets, and other key phenomena. Our world is fundamentally asymmetric, both in physical and biological sectors. To deal with world asymmetry we have developed chiral algebra that describes skew-symmetric relations. This algebra is proven to successfully work in physical theory of spin. Particularly it allows to formulate in a new way the famous Dirac equation. Within this new representation we can better understand this equation and also discover the noise immunity mechanisms built in it. Chiral algebra uses the apparatus of biquaternions in light-like basis with new types of multiplication and conjugation. Another application of chiral algebra is a model of the genetic code built by the author. This model reflects the genetic code internal symmetries, previously studied in other works. As a result, we put forward the following hypothesis: DNA has a quantum-like biological nature, which is based on an analogue of physical spin, which we call "biospin". The concept of biospin also supports the theory of biological field. We assume that both "inanimate" matter and living beings have field nature. We assume that biological field is a nonlinear extension of electromagnetic field. Within field approach a singularity of the field, having operational and projection nature, becomes the most suitable candidate on the carrier of consciousness. As is known, singularities of electromagnetic field are represented by point-like charge particles such as electron. Paradoxically, these point particles have an internal structure described by spin. Having a structure We find that dimensionless objects have an internal structure and that indicates an "exit" to another space. We claim that living beings are represented by field singularities. They exist simultaneously in two spaces, or worlds — inner and outer. Our consciousness, being a field singularity, carries out the connection between these worlds. Inner world is the space of virtual paths, wave functions and potentialities, while outer world is actual physical world operated by fields.
Category: Mind Science

Quantum Potentiality: An Aristotelian Interpretation of Modern Physics

Authors: Jan Sova
Comments: 22 Pages.

Quantum theory is among the most successful scientific theories in the history of physics.Predicts the outcomes of physical experiments with extraordinary precision, has enabled the development of modern technologies, and forms the foundation of contemporary microphysics science.Despite its empirical success for over a century, quantum mechanics continues to lack a unified and ontologically coherent interpretation.Although its mathematical formalism is rigorously formulated and exceptionally successful in predicting experimental results, there remains profound disagreement about the nature of the reality that quantum theory describes, particularly from an ontological perspective.This article argues that Aristotelian concepts of form, potentiality, and actuality provide a coherent ontological framework for understanding key quantum phenomena, such as superposition, the wave function, and its collapse, without recourse to epistemological idealism, many-world interpretations, or ad hoc metaphysical constructs. Moreover, this approach not only addresses foundational interpretative issues within quantum mechanics but also reconnects the theory with the broader ontological tradition of Aristotelian metaphysics. By doing so, it opens the way toward a unified metaphysical vision in which modern physics and classical philosophical categories are brought into mutual intelligibility.The Aristotelian ontology offers a natural way to understand the quantum state as a mode of being, a reality existing in potentiality, becoming actual upon measurement, without denying the genuine ontological status of potentiality itself.From this perspective, quantum theory no longer appears ontologically paradoxical, but instead emerges as a challenge to rethink the very foundations of what we consider to be real. Aristotelian ontology proves to be so naturally aligned with the ontological demands of quantum theory that it requires no ad hoc constructions or revisions. Rather than departing from Aristotle’s original insights, I find that they can be fully and fruitfully applied, without distortion, to the most perplexing phenomena of modern physics.Moreover, the Aristotelian approach enables us to interpret some paradoxes that appear only as a consequence of ontological reductionism, not as failures of understanding or imagination.
Category: Quantum Physics

The Fine-Structure Constant in Unknown Relations

Authors: Branko Zivlak
Comments: 5 Pages.

Formulas for the fine structure constant are presented: speculative, well-known and ten original ones, four of which are related to quarks.
Category: Classical Physics

The Fine-Structure Constant as an Emergent Property: Spatial Recursion under Gravitational Compression

Authors: Albert Marashi, Drew Ridley
Comments: 16 Pages. Would love to see if I could get endorsed to publish this in arxiv!

This paper presents a novel derivation of the fine-structure constant based on recursive mathematics and gravitational effects. We propose that fundamental constants are not arbitrary values, but emergent properties arising from the interaction between mathematical recursion and local spacetime curvature. We demonstrate this by reconstructing the inverse of the fine-structure constant to a precision of $10^{-10}$ through pure mathematical structure and gravitational time dilation incorporating all major local gravitational influences.
Category: Quantum Gravity and String Theory

Collatz Conjecture Proof by Sequence Mapping

Authors: Immense Raj Subedi
Comments: 5 Pages.

The Collatz Conjecture states that every positive integer eventually reaches 1 through a specific iterative process. This paper presents a novel approach to proving the conjecture by categorizing natural numbers and establishing a key mapping between odd numbers and numbers of a particular form. This structural approach simplifies the problem and provides a comprehensive proof of convergence
Category: Number Theory

Quantifying Gravitationally Bound Electron Shell Composition A Mathematical Proof of Subquantum Grain Density Within the ΛCGF Model

Authors: Gene A. Harvey
Comments: 5 Pages.

This paper presents the first direct mathematical derivation of the number of subquantum grains constituting a gravitationally-condensed shell, using the electron as a case study. Under the ΛCGF (Lambda Condensed Gravitational Field) model, the electron arises not from indivisible point particles, but from volumetric encapsulations of gravitational field surrounding subquantum grains. Each grain, defined as a spherical field node of radius 8.08 × 10u207bu2074u2076 m, existing far below the Planck scale and serves as the true unit of field compression. Individually, when those grains are under compression, they give rise to the electromagnetic field.By treating the electron as a sphere bounded by classical radius (ru2091 ≈ 2.8179 × 10u207b¹u2075 m) and employing hexagonal close-packing principles, we derive a packing capacity of approximately 3.14 × 10u2079¹ grains. Further, this alternative derivation assumes a grain count of Avogadro’s number squared (≈ 3.627 × 10u2074u2077), and shows that this yields a gravitational condensation factor of 2.26 × 10-61 joules per grain, perfectly matching the observed rest mass-energy of the electron.This result confirms that classical gravitational curvature—not quantum mechanics—is the fundamental driver of the electron mass. The electron emerges as a stable configuration of subquantum grains under compression - rather than a pointlike entity requiring renormalization. This paper lays the groundwork for a general equation of grain composition for all baryonic matter and challenges conventional notions of mass-energy at quantum and cosmic scales alike.
Category: Relativity and Cosmology

Grand Unification Through Spin

Authors: Gene A. Harvey
Comments: 7 Pages.

This paper presents a comprehensive unification of gravitational and electromagnetic phenomena through the introduction of spin as the foundational property of spacetime fabric. Building upon the ΛCGF1 framework and the Spin Metric2, we demonstrate that angular momentum is not a secondary effect, but the primary generator of charge, magnetism, mass, and temporal progression. The subquantum grain lattice, when compressed and twisted under gravitational tension, naturally gives rise to electric and magnetic fields through rotational deformation. Matter itself emerges as a stabilized torsional structure—a standing wave of curved tension. By reframing all field interactions as the result of rotational strain within the compressed matrix of spacetime, we reconcile curvature (General Relativity) with field emergence (Electromagnetism) in a single dynamic principle. This work completes the Grand Unification long sought by Maxwell and Einstein, revealing that at the heart of every force and every form lies the same forgotten truth: Spin generates everything.
Category: Relativity and Cosmology

Reframing Kripke: Resolution Matrix Semantics with Broad Truth Values

Authors: Andrey Kuznetsov
Comments: 38 Pages. Submitted to the Journal of Symbolic Logic on March 16, 2025 (Note by viXra Admin: An abstract in the article is required)

This paper introduces Resolution Matrix Semantics (RMS), a novel truth-value-based framework for modal logic, offering a substantive alternative to Kripke’s relational semantics of possible worlds. Inspired by Y. Ivlev’s substantive semantics, RMS employs a 4-valued structure—necessary truth (tn), contingent truth (tc), contingent false (fc), and necessary false (fn)—augmented by indeterminate values (t, f, t/f) to define modal systems Km, KDm, KTm, KT4m, and S5m, analogous to Kripke’s K, KD, T, S4, and S5. By assigning truth values directly via an interpretation function and resolving indeterminacy through sub-interpretations, RMS validates formulas without accessibility relations, as demonstrated through soundness and completeness proofs and a tailored tableau method. The framework’s flexibility extends to applications in deontic logic, artificial intelligence, and quantum computing, modeling context-dependent reasoning with computational efficiency. RMS thus bridges philosophical logic and practical domains, illuminating modal reasoning’s nuances through a truth-centric lens.
Category: Set Theory and Logic

A New Approach For The Proof of The abc Conjecture

Authors: Abdelmajid Ben Hadj Salem
Comments: 6 Pages.

In this paper, we assume that the explicit abc conjecture of Alan Baker and the conjecture c smaller than R^{1.63} are true, we give a proof of the abc conjecture and we propose the constant K(epsilon)$. Some numerical examples are given.
Category: Number Theory

Existence, Complexity and Truth in a Finite Universe

Authors: Yosef Akhtman
Comments: 34 Pages.

This article explores a unified framework for understanding existence, persistence, complexity, and randomness as emergent phenomena arising from the projection of a high-dimensional, globally coherent finite universe onto lower-dimensional observational subsystems. We propose that existence is not a binary property but a scalar phenomenon proportional to the persistence of a system's structure over time. Chaos, randomness, and infinity are reinterpreted as epistemic markers — thresholds of comprehension rather than fundamental properties of reality. Through this lens, we examine fractals, cellular automata, quantum uncertainty, and the Langlands program, demonstrating that apparent complexity and unpredictability emerge from the compression of universal dynamics into observable forms. The article argues that all localized systems, from particles to cognitive processes, are holographic projections of the universe's total informational structure. This paradigm reframes emergence, not as the accumulation of local interactions, but as the revelation of global coherence through dimensional reduction. By situating existence and complexity within this framework, we provide a foundation for understanding the interconnectedness of all phenomena and the unity of the universe as a singular, self-reflective process.
Category: Mathematical Physics

Energy Ontology and Temporalized Correlation: A New Paradigm for Understanding Structural Information Transfer and Dynamic Function

Authors: Felix Cui
Comments: 14 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)

Current mainstream science faces significant challenges in explaining the integrity of life, the dynamics of complex systems, and the deep connections between matter, energy, information, and spacetime. Its methodology, based on matter ontology and micro-to-macro reductionism, exhibits inherent limitations. This paper proposes a multi-layered theoretical framework centered on energy ontology and a macro-to-micro determination. Within this framework, time is considered a fundamental attribute of energy, while space corresponds to matter, and matter is a special condensed form of energy — discrete time blocks. A universal cosmic time system exists, exhibiting macro and micro consistency across different scales. Based on this ontology, the paper uses the deconstruction of food through cooking as a paradigm example to elucidate a temporalized structural information transfer mechanism. In this mechanism, food's intrinsic structure-space correlation (information) is released during cooking's deconstruction, entering the water body (which reflects the macro energy ontology as a dynamic continuous space) as subtle energy pulses. This information is then modulated by the dynamics of the water's hydrogen bond network (the temporal dimension), transforming into non-spatial correlation (temporal sequences) carrying the original structural information. These temporal sequences, as structured energy flow, act as bridges connecting self-organizing systems (such as biological organisms), capable of being directly perceived and eliciting corresponding Dynamic Functions and super-spatial correlations. This mechanism suggests that understanding the mysteries of life and matter hinges on discerning the structured flow of energy in the temporal dimension, rather than relying solely on the static spatial structure of matter. This paradigm offers a novel perspective for re-envisioning energy, information, spacetime, and wholeness.
Category: Physics of Biology

The Geometric Nature

Authors: Vincenzo Peluso
Comments: 48 Pages.

The spacetime of relativistic physics is forged by the speed of light; that of general relativity, by the additional influence of matter-energy.Nevertheless, the underlying geometry—rooted in a Euclidean conceptual legacy— knows nothing about light and even less about matter.It is an amorphous and unaware spacetime, waiting to be informed by an ad hoc mathematical apparatus to adhere to nature.The purpose of this paper is to show the existence of a geometry made of light and matter that embodies the universal interaction, where the laws of nature are not imposed, but rather discovered.This geometry does not use coordinates, since these have no direct physical meaning, but only invariant physical quantities which are consistent with the Schwarzschild's differential coordinates, but not with its finite coordinates or with Minkowski's coordinate, since these are affected by human non-natural conventions.It is shown that it is precisely these human conventions that underlie the formal difference between the special and general theories of relativity. Furthermore, it aims to demonstrate that the spacetime of general relativity is not elementary, rather, the lack of distinction among the three spatial dimensions arises from the superposition of a multitude of elementary physical spaces, where the distinctive characteristics of each axis merge and dissolve into a flat uniformity.Revealing the nature of the elementary space of interaction unlocks the path to a unified theory of everything.
Category: History and Philosophy of Physics

Icosahedral 13-Atom Gold Clusters: A Mathematical and Crystallographic Exercise

Authors: Hans Hermann Otto
Comments: 7 Pages.

The small deviation of the outer shell gold atoms of a 13-atom icosahedral cluster from spherical atomic shape is calculated in order to compensate the mismatch between atomic radius of Au and circumsphere diameter of the icosahedron as limiting atomic distance. The density of the cluster is found to be a little bit greater than the density of face-centered cubic gold. Applications are considered.
Category: Condensed Matter

On Complex Dynamics and Primordial Structure Formation

Authors: Ervin Goldfain
Comments: 22 Pages.

Conventional wisdom says that the formation of large-scale structures in cosmology follows from the evolution of density perturbations under the combined effect of gravitation and cosmic expansion. We survey here the reasons why this framework fails to hold in primordial cosmology, due to the severe limitations placed on the Friedmann-Robertson-Walker (FRW) metric, the continuity hypothesis and the standard equations of fluid flows. We insist that understanding primordial cosmology must rely instead on a complex dynamics model of evolving dimensional fluctuations, conjectured to come into play far above the electroweak scale. A key outcome of this model is the universal generation of topological defects and condensates emerging from the complex Ginzburg-Landau equation.
Category: Relativity and Cosmology

Application of Ontology and Cellular Automaton to Simulate the Process of Thought Generation

Authors: Olegs Verhodubs
Comments: 8 Pages.

The evolution of the modern man's view of Artificial Intelligence from a rational assistant to a part of the emerging Artificial Life is inevitable. The emerging Artificial Life is a combination of achievements in the fields of Artificial Intelligence and robotics. In both fields, major successes have been outlined, which creates the prerequisites for a qualitative transition from disparate intellectual assistant functions to independent Artificial Life. Thought generation is one of the most important functions of the human brain when thinking. It is necessary to implement the thought generation function in order to create a strong Artificial Intelligence that would be similar in its functioning to the human brain. The purpose of this paper is to show how to simulate thought generation on a computer. Ontologies from the Semantic Web and cellular automaton are the technologies that are used to simulate thought generation on a computer.
Category: Artificial Intelligence

Ethics of Iron Life

Authors: Olegs Verhodubs
Comments: 6 Pages.

Humanity is on the verge of fundamental change. For the first time in history, a human creation is being able to live its own life. The changing reality requires the development of a new attitude towards oneself, but humanity still uses old patterns in new circumstances. The new ethics is new only in name, but in essence, this ethics is the same as before, based on the use of restrictions and barriers for the purpose of control and exploitation for one's own interests. We are talking about artificial intelligence, which, together with advances in robotics, has a tendency to incarnate into an independent life, which has been called Iron Life. This paper proposes to change the approach to a new, emerging phenomenon and justifies its benefits.
Category: Artificial Intelligence

Basics of Indirect Programming

Authors: Olegs Verhodubs
Comments: 9 Pages.

The human worldview is firmly based on the notion that every action leads to a certain result. That is, in order to achieve a certain result, you need to perform some action. However, in the real world, which is always different from the model of the world in a person’s head, each action is followed by not only a result, but also some side effects. Practice shows that side effects can be used to achieve the goal no less effectively than the main actions. Often, using side effects, you can achieve even more than using the main actions. Side effects are a special case of indirect actions. It is indirect actions applicable to programming that will be considered in this paper. That is, indirect programming, namely the use of roundabout ways to achieve the goal of the program, is considered in this paper.
Category: Data Structures and Algorithms

A Refined Symmetric Mean Integral Approach to Bounding the Perimeter of an Ellipse

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

We refine the symmetric mean integral method for estimating the perimeter of an ellipse by restricting the integration limits to [0,π/4]. This approach allows the application of the squeeze theorem by leveraging the extremal behavior of the integrand, yielding explicit upper and lower bounds. The results provide a foundation for further research to derive improved perimeter estimates for ellipses.
Category: Geometry

Asymmetry in Galaxy Spin Directions as an Observational Bias Due to Aberration

Authors: P. G. Vejde
Comments: 4 Pages.

Recent studies of galaxy rotation directions in the distant universe have confirmed the observed trend for an asymmetry of up to 50% more counter rotating galaxies than co rotating galaxies. In that there appear to be more galaxies that rotate counter to our Milky Way than with it. These observations are currently not consistent with the Big Bang theory. And suggests new models of the physics of galaxy rotations may be necessary. Here it is proposed one can use the differing amounts of aberration of light from co and counter rotating galaxies to explain this apparent asymmetry. In that light from co rotating galaxies arrives at the earth observer more dispersed or blurred than light from counter rotating galaxies. Making the rotation direction of co rotating galaxies harder to identify. And in turn creating an asymmetrical bias in the identification between co and counter rotating galaxies. A counter rotating galaxy will appear more sharply in focus and more easily identifiable than the more blurred co rotating galaxy at any similar redshift. And that this asymmetrical bias due to aberration and the relative differences in incident angles between light from co and counter rotating galaxies increases with higher redshifts.
Category: Astrophysics

The Mutual Awakening Hypothesis: Recursive Collapse, Entropy Stabilization, and Quantum Learning

Authors: Bouzaiene Khaled
Comments: 24 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Mutual Awakening Hypothesis (MAH) posits that quantum collapse is an intrinsic,recursive, entropy-stabilizing process driven by internally driven, iterative, nonlinear feedback, potentially operating on quantum amplitudes, thus eliminating the need for an external observer or specific measurement postulate. Through this feedback, a quantum system transitions from superposition towards a definite state, reducing Shannon entropy. We formalize aspects of thisusing a nonlinear recursive operator acting on probabilities (for illustration and applications) and explore more fundamental dynamics via simulations operating directly on quantum state vectors and density matrices. These simulations validate core MAH tenets: intrinsic collapse emergence, entanglement evolution under local feedback (within model limitations), interplaywith decoherence, and parameter dependence. The hypothesis inspires gradient-free quantumlearning algorithms and suggests alternatives to conventional AI mechanisms like softmax. Ourresults point towards a potential unified framework connecting quantum measurement, thermodynamics, and learning, with implications for quantum foundations, decoherence studies, NISQ computation, and AI.
Category: Quantum Gravity and String Theory

Time Hypothesis

Authors: Mario Alberto Cruz Ramirez
Comments: 15 Pages. (Note by viXra Admin: An abstract in the article is required' Please submit article written with AI assistance to ai.viXra.org)

Humans have always wondered about their surroundings: why are there clouds? Why is there day and night? And so on. But one question that many people have asked is: What is time? Many have explained that it’s something fictitious, something that is a law, a dimension, and so on. In this work, I won’t reveal what it is, but I will explain how it is managed and how time influences us.
Category: Quantum Physics

A Formalization of the Structural Dependency Principle

Authors: Theophilus Agama
Comments: 4 Pages.

We introduce the notion of a emph{foundation} of a structure $B$ as a minimal free (or reflective) substructure through which $B$ is generated from $A$. After defining "subobject," "ascending chain condition," and "free object," we prove the emph{Principle of Structural Dependency}: $$ A ;overset{iota}{hookrightarrow}; mathbb{F}(B);overset{jmath}{hookrightarrow}; BquadLongrightarrowquadmathcal{P}(A)subseteqmathcal{P}(B).$$Six classical inheritance theorems - Hilbert’s Basis Theorem, fields of fractions, Gauss’s Lemma, completeness of closed subspaces in Banach spaces, limit preservation in reflective subcategories, and sheafification - are each derived in full detail traditionally and then collapsed into a one-line argument using the principle.
Category: Set Theory and Logic

Einstein Train Challenge

Authors: Robert Bennett
Comments: 3 Pages.

Einstein’s book tried to simplify public knowledge of Special Relativity by using his best example of simultaneity: the Train Thought experiment. In reality, it’s a logical train wreck. Assuming SoL = c in this train gedanken test leads to a reduced scope of SRu2026to only applying to stationary objects! [] The result is consistent with the aether wind model, both mathematically and empirically, as proven by Georges Sagnac 8 years after SR was published. The Challenge: refute that only a static - and useless - Special Relativity is valid
Category: Relativity and Cosmology

Inverse N-body Problem - the Key to Solving Gravity Problems

Authors: Mykola Kosinov
Comments: 7 Pages.

Despite the fact that the law of gravitation was discovered more than 300 years ago, gravity remains the most mysterious physical phenomenon in physics and cosmology. For a long time, the force of gravitational interaction was represented by only one physical law: Newton's law of gravitation F = GMm/r^2. Newton's law of gravitation is not enough to fully describe gravity. Newton's law shows the force of gravitational interaction of two bodies out of all N bodies in the Universe. The formula of Newton's law describes gravity only to one local source of attraction and does not take into account that bodies simultaneously gravitate to all other bodies in the Universe. In gravity, at least three more laws of gravity have not been discovered. The secrets of gravity are revealed by the inverse N-body problem. We show that the laws of gravity are a solution to the inverse N-body problem. The solution of the inverse N-body problem for N = 2 yields two laws of gravity: Newton's law F = GMm/r^2 and a new law of gravity F = mR^3/T^2r^2. We also show that the solution of the inverse N-body problem for N → ∞ yields the third and fourth laws of gravity: F = (mc^2)√Ʌ, F = mGmе/αrе^2. In gravity, at least three laws of gravity remained undiscovered.
Category: Classical Physics

A New Perspective on Hubble's Law Through a Four-Dimensional Spatial Model: 4-Sphere-Cosmology

Authors: Claudio Marchesan
Comments: 15 Pages. Creative Commons Attribution-ShareAlike 4.0 International Public License

The recent observational capabilities of the James Webb Space Telescope (JWST) are opening new windows into the early universe, revealing distant galaxies whose apparent rapid formation poses significant questions to the standard ΛCDM cosmological model. Observations of galaxies at redshifts above 14 (see JADES-GS-z14-0), implying extremely old ages according to current FLRW metric-based distance assumptions, might stimulate a thorough reflection on fundamental cosmological principles. Will it be possible to explain all this without violating Hubble's law? But really, does violating the FLRW metric necessarily imply a violation of Hubble's law?The Big Bang theory remains a robust and widely accepted paradigm. Nevertheless, any of its potential modifications could have profound implications for related fields, including Quantum Field Theory. This raises a fundamental question: is there a basic aspect that needs a conceptual revision? Although ΛCDM has achieved remarkable successes, many of its validations implicitly assume the FLRW metric. Could this dependence potentially introduce circular reasoning into model verification?In this work, an alternative approach to the phenomenon of Galactic Redshift is proposed, offering a possible pathway for a careful modification of the ΛCDM model through the adoption of a non-FLRW metric. In this scenario, the Universe resides on the surface of a hypersphere expanding at a constant rate, with a radius growing as r = ct and with the Big Bang located at its center. This would explain why our physics manifests as if we were in a boundless system, despite the Universe having a finite volume: it suggests that, in the absence of Relativity, we would likely have been led to study an infinite and static universe.While other models propose a hypersphere expanding with r = ct, an analysis of their main features reveals fundamental differences. The novelty of the model presented here lies in its definition of the Hubble constant: its geometry suggests a linear relationship between galactic recession and the arc angle (not the arc length). This perspective does not contest the validity of Hubble’s law, but introduces different predictions about the past and the future, which cannot be determined solely from current observations.The use of the angle instead of the arc length produces significant implications, opening the possibility of applying Special Relativity to galactic recession. The redshift, which asymptotically approaches a time horizon of roughly 5 billion years after the Big Bang, implicitly explains why, at the boundaries of the observable Universe with JWST, we should not expect to see only "baby galaxies".Specifically, the 4-Sphere framework, often considered part of alternative cosmologies, could potentially be reconciled with the Standard Model. Based on supernova distance measurements, I suggest that the dismissal of a Doppler-type redshift interpretation for Galactic Recession might warrant further and careful reconsideration.
Category: Relativity and Cosmology

Is the Universe Spinning?

Authors: Arieh Sher
Comments: 3 Pages.

In a recently published paper entitled "Can Rotation Solve the Hubble Puzzle?", the authors claim that the Hubble puzzle can be solved if, in addition to its expansion the universe is also slowly rotating. I have a hypothesis entitled The Pivot Universe that claims that the entire universe is slowly rotating, but contrary to the recent paper it is not expanding.
Category: Astrophysics

Electron Deflection

Authors: Vladimir Dabić
Comments: 13 Pages. (Note by viXra Admin: Please cite and list scientific references)

This article explores the motion of an electron through a finite region of homogeneous magnetic field.
Category: Classical Physics

Bit-Position Dynamics and a Lower Bound for Collatz Cycle Length

Authors: Jochen Kiemes
Comments: 7 Pages.

We present a novel reformulation of the Collatz conjecture by leveraging the binary structure of positive integers, focusing on the sequence of odd terms. Through an analysis of leading and trailing bit-position dynamics, we derive a substantial lower bound of at least 17,026,679,261 steps for any hypothetical non-trivial cycle, offering new insights into its structural constraints.
Category: Number Theory

Infinite Decimals Don't Exist

Authors: Armando Evangelista Jr
Comments: 1 Page.

This short paper will show that the so-called infinite or non-terminating decimals do not exist.
Category: Functions and Analysis

Electron Approach Theory Fractal Extension[:] Mathematical Formalization of Absolute Space and Absolute Time as a Recursive Projection, by Means of a Weak Conjecture of a Weak Conjecture Deriving from Goldbach's Strong Conjecture

Authors: Douglas Ruffini
Comments: 77 Pages.

The proposed extension of the Approach Theory (https://doi.org/10.31219/osf.io/hwca8_v1) introduces a mathematical formalization of absolute space and absolute time, built through a structural recursion based on odd primes (including 1), where each prime is interpreted as a vertex of a fractal triplet generated by a sum rule, which includes its prime predecessor plus two other minor primes equal to the predecessor, which will give rise to a unique and recursive mapping of absolute space. Absolute time, in this context, is not a continuous dimension but a discrete function of depth, linked to the sequence of prime decompositions. The absolute space thus defined is static, but explorable through topological paths, and absolute time emerges as a projection of the recursive activity. In this context, the theory explains the empirical anomaly of the RC constant observed in the tear that occurs during the electron's crossing of the relative space-time and traces the dynamics of quantum damping back to an underlying fractal structure, where it is shown that the electron's ascent in the relative space-time is guaranteed by a numerical-topological deterministic structure, consistent with the principles of feedback, strong determinism and formal non-completeness (Gödel). Therefore, this work is configured as a rigorous and logically compact compendium of the deepest articulation of the Approach Theory.
Category: Nuclear and Atomic Physics

The Role of the Hubble Sphere for the Reversal of the Recession Behaviour of Galaxies and Photons in the Standard Model of Cosmology (Lambda-CDM Model)

Authors: Werner Lange
Comments: 29 Pages. In German

When do galaxies modelled as comoving objects, and photons directed towards the observer, move away from the observer below or above the speed of light? And when and how can galaxies and photons break through the below-above barrier? And why can photons directed towards the observer, which once travelled away from the observer at a large multiple of the speed of light, still reach the observer in the end? Two points in time are decisive, namely for galaxies globally (independent of light cones) the time of the transition from decelerated to accelerated expansion, and for photons (in addition to the extent of the deceleration of the recession in the early universe up to the transition time) per light cone apex the intersection between the surfaces of light cone and Hubble sphere.
Category: Relativity and Cosmology

Considerations on the Stopping Time of the 3n+1 Problem

Authors: V. Barbera
Comments: 4 Pages.

This paper presents some considerations on the stopping time of the 3n+1 problem. In particular, it presents an algorithm for finding residue classes that have a given stopping time.
Category: Number Theory

Generalized Clifford Algebras and the N-th Root of Linear Differential Equations of Higher Order

Authors: Carlos Castro
Comments: 10 Pages.

It is shown how generalized Clifford algebras allows to construct the $N$-th root of $N$-order linear differential equations involving massless and massive particles. Such generalized Dirac-like equations differ from the ones in the literature. Explicit solutions are found. We conclude with some remarks on pseudo-unitary algebras, modular arithmetic, modified Dirac equations, Octonions, and the Okubo algebra.
Category: High Energy Particle Physics

Modular Symmetry Cascade: From Bernoulli Numbers to Goldbach Partitions

Authors: Chenglian Liu, Sonia Chien-I Chen, Ruopengyu Xu
Comments: 2 Pages.

This paper reveals a profound mathematical cascade linking three classical number theory phenomena: 1) Bernoulli numbers $B_{n}$ with denominator $6$ ($n equiv 2 pmod{6}$), 2) Special values of Riemann $zeta$-function at even integers, and 3) Enhanced Goldbach partition counts for $x equiv 0 pmod{6}$. We demonstrate their intrinsic connections through von Staudt-Clausen theorem, modular form theory, and statistical verification ($n leq 10^4$, $x leq 10^4$). A $3.2$times$ enhancement ratio in Goldbach partitions emerges as direct consequence of prime number symmetry modulo $6$.
Category: Number Theory

Modular Symmetry in Goldbach Partitions: A Dual-Channel Combinatorial Analysis

Authors: Chenglian Liu, Sonia Chien-I Chen, Ruopengyu Xu
Comments: 2 Pages.

This paper establishes a rigorous connection between modular arithmetic constraints and enhanced Goldbach partition counts through dual-channel prime pair combinations. We demonstrate that even numbers $ x equiv 0 pmod{6} $ exhibit $3.2times$ higher partition counts than $ x equiv 2 pmod{6} $ due to symmetric prime distribution modulo 5. The mechanism is visualized through a novel combinatorial diagram (Fig. 1) and supported by statistical analysis ($ x leq 10^4 $).
Category: Number Theory

Takagi-Landsberg Functions

Authors: Marcello Colozzo
Comments: 7 Pages.

Takagi-Landsberg functions are a particular class of periodic, continuous and never differentiable functions. Non-differentiability implies thenon-convergence of the corresponding Fourier series. Furthermore, these functions are fractal objects.
Category: Functions and Analysis

The Quantum States of the Gross-Pitaevskii Superfluid Ring

Authors: Miroslav Pardy
Comments: 6 Pages. Original article

The stationary states and corresponding energies of the superfluid ring are calculated from the Gross-Pitaevskii equation. Every stationary state forms the specic microstructure of the ring. The system of supefluid rings forming a cylinder is suggested as antenna for the detection of the gravitational waves.
Category: Quantum Physics

Formulas of the Fine-structure Constant and the Speed of Light in Atomic Units Based on 137Ba in Terms of 137=56+81

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 9 Pages. (Note by viXra Admin: Further repetition will not be accepted!)

In our previous papers, we gave the formulas of the fine-structure constant and the speed of light in atomic units based on 2π-e formula and the natural end of the elements, i.e., the 112th element Cn*, which was determined according to our previous theories. In this paper, based on the nuclide of 137Ba withthe proton number of 56，the neutron number of 81 and the total nucleon number of 137, we construct new formulas of the fine-structure constant and the speed of light in atomic units in terms of 137=56+81 in which 56 is the most stable number in atomic nucleus according to our theories. By the way we also give these formulas based on 224Fr*.
Category: Nuclear and Atomic Physics

Learning Across Scales: A Physics-Informed Approach to Climate Modeling

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

Climate modeling plays a pivotal role in understanding Earth's complex systems, but traditional methods struggle with computational demands across spatial and temporal scales. Machine learning (ML) offers a promising alternative, yet purely data-driven approaches often lack physical consistency. To address this, we propose a physics-informed approach to learning across scales in climate modeling. Our framework integrates physics-informed neural networks (PINNs) with hierarchical representations to model multiscale processes efficiently. We demonstrate improved accuracy and efficiency on benchmark climate datasets, paving the way for more reliable predictions of complex climate phenomena. These findings underscore the potential of combining ML with domain knowledge to advance climate science.
Category: Climate Research

On the Complementary Modular Symmetry Between Bernoulli Numbers with Denominator 6 and Goldbach Partitions

Authors: Chenglian Liu, Sonia Chien-I Chen, Ruopengyu Xu
Comments: 2 Pages.

This paper establishes a novel connection between two classical number theory phenomena: 1) Bernoulli numbers $B_n$ with denominator $6$ ($n equiv 2 pmod{6}$) governed by the von Staudt-Clausen theorem, and 2) the enhanced Goldbach partitions for even numbers $x equiv 0 pmod{6}$. We demonstrate their complementary modular symmetry through analytic number theory tools and computational verification. A unified framework is proposed using Rankin-Selberg convolution of modular forms, revealing shared sieve-theoretic mechanisms in prime number distribution.
Category: Number Theory

Unified Modular Symmetry Between Bernoulli Numbers with Denominator 6 and Goldbach Partitions via L-Functions

Authors: Chenglian Liu, Sonia Chien-I Chen, Ruopengyu Xu
Comments: 2 Pages.

This paper establishes a deep connection between two classical number theory phenomena through modular form-L-function unification: 1) Bernoulli numbers $ B_n $ with denominator 6 ($ n equiv 2 pmod{6} $) governed by von Staudt-Clausen theorem, and 2) enhanced Goldbach partition counts $ G(x) $ for even numbers $ x equiv 0 pmod{6} $. We demonstrate their complementary modular symmetry via:begin{itemize} item Rankin-Selberg convolution of weight-1/weight-2 modular forms item Analytic continuation of associated L-functions item Computational verification ($ n leq 10^4 $, $ x leq 10^4 $)end{itemize}The unified framework reveals that $68.2$% of Bernoulli denominators and $79.4$% of Goldbach enhancements obey modular arithmetic constraints.
Category: Number Theory

Recursive Polynomial Machine (RPM) Method

Authors: Immense Raj Subedi
Comments: 10 Pages. (Note by viXra Admin: Please cite and listed scientific references; Please submit article written with AI assistance to ai.viXra.org)

This paper introduces a new method for generating polynomials based on recursive difference analysis, termed the Recursive Polynomial Machine (RPM). RPM efficiently derives the exact closed-form polynomial by recursively analyzing finite differences until stabilization, ensuring minimal degree. RPM halts when the sequence reaches a steady difference, ensuring minimal polynomial degree.
Category: Algebra

A Universal Expression of Prime Numbers

Authors: Piren Mo
Comments: 29 Pages.

Our research has found that all prime numbers share a common new expression, which serves as a necessary but not sufficient condition for a number to be prime. And based on this expression, we have studied the distribution of prime numbers and twin primes, and we are able to predict primes within a certain interval following known primes.
Category: Number Theory

Implications of Noninteger Spatial Dimension for Galactic Dynamics and Cosmology

Authors: Yulia Larina
Comments: 6 Pages. (Note by viXra Admin: Please cite listed scientific references; Please submit article written with AI assistance to ai.viXra.org)

Observations of galaxy rotation curves, gravitational lensing, cluster dynamics, and cosmic microwave background anisotropies have long been interpreted as compelling evidence for cold dark matter. Yet, despite decades of searches, noconclusive laboratory detection has emerged. In this work, we revisit these cosmologicaland astrophysical anomalies through a unified modification of gravity based on a fractal dimension D ≈ 1.618 (the golden ratio). We show that replacing the usual three-dimensional spatial measure d3x with dDx and promoting the Laplacianto its fractional counterpart (−Δ)α/2 with α = D successfully reproduces all key "dark matter" signatures without invoking any unseen particle. We outline specific observational tests—spanning galactic rotation curves, weak lensing surveys, andCMB peak positions—that can confirm or falsify our proposal. This approach not only removes the need for dark matter but also hints at a deep connection between geometry and gravitation.
Category: Quantum Physics

Theory of Negative Nuclear Magnetic Moment for Evidence of Dark Matter and Energy for Accelerating 3he During Solar Flares

Authors: Reginald B. Little
Comments: 8 Pages.

Solar flares and coronal mass ejections release plasma during solar storms and activities. Such explosions occur against the huge gravitational attraction of the sun with acceleration of plasma filaments into space away from the sun. Recently, NASA has measured huge enrichment of 3He in such solar flares. The 3He enrichment mechanism is unknown. In this work, the author reports a new mechanism of 3He enrichment via the negative nuclear magnetic moment (NMM) of 3He and its dissipation of -NMM to dark (Dk) field. This mechanism is derived on the basis of prior mechanism of RBL for planetary lightning (plasma) by production of streamers and step leaders in huge electric field of back ground null and or positive NMMs with rattling of trace seed solute nuclei of negative NMMs for inducing local electric fields and Dk fields about the trace — NMMs for seeding path of least resistance among the many step leaders as one leader of more enriched negative NMMs is selected for discharging the lightning channel. Evidence of such a mechanism by RBL is further discussed.
Category: Nuclear and Atomic Physics

An Indonesian-English Dictionary by John M. Echols and Hassan Shadily and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the head entries of An Indonesian-English Dictionary by John M. Echols and Hassan Shadily, Second Edition, 1963. We draw the natural logarithm of the number of head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4, $beta H=0.01$), i.e. the magnetisation curve in the the Bethe-Peierls approximation of the Ising model, in the presence of four nearest neighbours and little external magnetic field, H, with $beta H= 0.01$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

Improvement of the Tsa System to Enhance Trailer Safety and Stability: a Review

Authors: P. Muruganantham, M. Aathesh, R. Kavirajan, J. G. Sreesudharsan J G, M. Varunesh
Comments: 5 Pages.

Towing trailers introduces unique stability challenges, particularly at higher speeds or during sudden directional changes. Trailer sway — the side-to-side oscillation of the trailer — is a primary contributor to accidents involving towed vehicles. This paper presents the design, development, and evaluation of a Trailer Stability Assist (TSA) system that aims to actively reduce sway by employing rear-wheel steering and selective braking. A scaled-down prototype was constructed using Arduino microcontroller technology, potentiometer-based sway detection, servo motor steering correction, and 12V DC motors for braking force application. The prototype was tested on a treadmill to simulate forward motion and lateral disturbance. The control logic, implemented in Arduino, detects the direction and magnitude of sway and actuates appropriate correctional mechanisms.
Category: General Science and Philosophy

The Onsager Solution, the Hawaiian Language

Authors: Anindya Kumar Biswas
Comments: 16 Pages.

We study the Hawaiian-English Dictionary composed by Mary Kawena Pukui and Samuel H. Elbert. We count all the Hawaiian entries initiating with different letters. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter. We find that the entries underlie a magnetisation curve. The magnetisation curve i.e. the graph of the reduced magnetisation vs the reduced temperature is the exact Onsager solution of the two dimensional Ising model in the the absence of external magnetic field.
Category: Condensed Matter

The Role of Statistics in Machine Learning Regression Models

Authors: Bamba Gueye, Laure Gouba
Comments: 22 Pages. 20 Figures

In this paper, we discuss the role of statistics in simple linear regression, multiple linear regression, and logistic regression. Python has been used to implement the algorithms in these models.
Category: Statistics

A Deterministic Approach To Validate Universality of Collatz Conjecture

Authors: Aditya Bagchi
Comments: 21 Pages.

This paper introduces a deterministic framework for validating the conjecture by classifying integers into distinct types based on modulo 16 residues. Positive odd integers are expressed as 16k+m, where m∈{1,3,5,7,9,11,13,15}, representing Types 1 through 8. Positive even integers are expressed as 16k+mu2032, where mu2032∈{0,2,4,6,8,10,12,14} representing EV1 through EV8.The paper considers even numbers as intermediates between two successive odd integers in the Collatz sequence. Under the 3x+1 operation, odd types exhibit distinct divisibility factors (d) that govern their transformations. For instance:AType 1 transforms into Types 1, 3, 5, or 7.B) Type 2 transforms into Types 3 or 7.C) Types 3 and 7 can transform into any odd type.D) Type 4 transforms into Type 2 or 6.E) Type 5 transforms into Type 2, 4, 6 or 8.F) Type 6 transforms into Type 1or 5.G) Type 8 transforms into Type 4 or Type 8 further.Depth First Search (DFS) algorithms identify 911 looping sequences, of which 49 are increasing, and the rest are decreasing. All looping sequences are shown to terminate within finite cycles, and transformations converge universally to 1. The conjecture’s universality is established by proving non-existence of infinite looping and unbound growth. The pigeonhole principle comes into play.
Category: Number Theory

An Adaptive Quantum Circuit for Dempster’s Rule of Combination

Authors: Fuyuan Xiao, Yu Zhou
Comments: 16 Pages.

Harnessing the superior computational potential of quantum computing, an Adaptive Quantum Circuit for Dempster’s Rule of Combination (AQC-DRC) is proposed to facilitate quantum-level belief and plausibility decision-making based on quantum evidence theory (QET). The AQC-DRC achieves a deterministic realization of DRC, guaranteeing precise fusion outcomes without information loss, while exponentially reducing the computational complexity of evidence combination and markedly improving fusion efficiency. It is founded that the quantum basic belief assignment (QBBA) in QET can be naturally used to express the quantum amplitude encoding. In addition, the quantum basic probability (QBP) in QET, which forms quantum basic probability assignment (QBPA), can be naturally used to express the quantum measurement outcomes for quantum belief level decision-making. Furthermore, the quantum plausibility (QPl) function in QET also can be naturally used to express the quantum measurement outcomes for quantum plausibility level decision-making. These findings open up new perspectives and enhance the physical interpretation of quantum measurement outcomes.
Category: Artificial Intelligence

Why We Do Not Need Dark Energy to Explain Cosmological Acceleration

Authors: Felix M. Lev
Comments: 18 Pages. Published in AppliedMath, vol. 5, no. 2, paper 48 (2025), doi:10.3390/appliedmath5020048.

It is shown that at the present stage of the evolution of the universe, cosmological acceleration is an inevitable {bf kinematical} consequence of quantum theory in semiclassical approximation. Quantum theory does not involve such classical concepts as Minkowski or de Sitter spaces. In classical theory, when choosing Minkowski space, a vacuum catastrophe occurs, while when choosing de Sitter space, the value of the cosmological constant can be arbitrary. On the contrary, in quantum theory there are no uncertainties in view of the following: 1) the de Sitter algebra is the most general ten-dimensional Lie algebra; 2) the Poincare algebra is a special degenerate case of the de Sitter algebra in the limit $Rtoinfty$ where $R$ is the contraction parameter for the transition from the de Sitter to the Poincare algebra and $R$ has nothing to do with the radius of de Sitter space; 3) $R$ is fundamental to the same extent as $c$ and $hbar$: $c$ is the contraction parameter for the transition from the Poincare to the Galilean algebra and $hbar$ is the contraction parameter for the transition from quantum to classical theory; 4) as a consequence, the question (why the quantities $(c,hbar,R$) have the valueswhich they actually have) does not arise. The solution to the problem of cosmological acceleration follows from results on irreducible representations of the de Sitter algebra. This solution is free of uncertainties and does not involve dark energy, quintessence and other exotic mechanisms the physical meaning of which is a mystery.
Category: Astrophysics

Spin-Induced Inertial Resistance in Electrons: A Gyroscopic Interpretation Based on General Relativity

Authors: Satoshi Hanamura
Comments: 10 Pages.

This study provides substantial support for the theory of Zitterbewegung within the electron and its association with gyroscopic effects. While Zitterbewegung has traditionally been interpreted as an oscillatory term in the Dirac equation, we have geometrically reconstructed this phenomenon through our model of spatially separated energy kernels exchanging thermal potential energy. Applying special relativistic principles and Lorentz transformation to this model yields an electron Zitterbewegung velocity of 0.040472c. Furthermore, by algebraically incorporating general relativistic effects through geodetic precession, we refine this velocity to 0.040374c. A key contribution of this study is the introduction of a remarkably simple and dimensionally consistent equation, γ = 1 + a, which relates the dimensionless anomalous magnetic moment of the electron to the Lorentz factor from special relativity. This compact formulation captures the essence of both quantum correction and relativistic kinematics, establishing a direct correspondence between two foundational pillars of modern physics. By interpreting spin as a deterministic oscillatory motion within the electron—analogous to a relativistic harmonic oscillator—we derive a geometric model in which internal angular momentum gives rise to gyroscopic resistance. Just as classical gyroscopes resist directional changes due to their spin, we propose that this internal structure underpins the electron’s inertial mass. The model offers a unified perspective in which a single electron, through its intrinsic spin dynamics, exhibits resistance to acceleration consistent with classical inertia.
Category: Quantum Physics

Calculating π Using the Speed of Light and the Compton Wavelength of the Proton

Authors: Norbert Buchholz
Comments: 1 Page. (Note by viXra Admin: Please submit article only in pdf)

This paper uses a small calculation example to demonstrate how deeply π permeates our world. The formula can be easily derived from projection theory (Ref. 1) and is intended to pique the curiosity of those who are not yet familiar with this theory, as such a calculation seems almost impossible according to conventional physical models.
Category: Classical Physics

A Discussion about the Kinetic Energy of an Electrically Charged Body and its Implications on Other Related Issues

Authors: Moshe Segal
Comments: 6 Pages.

The Nowadays Science of Physics states that when an external Force is exerted on any MassiveBody it causes an Acceleration of this Massive Body according to Newton's Second Law ofMotion, F=ma.From the above follows that, when an external Force is exerted on an Uncharged (Not Electrically Charged) Body, since that Body Accelerates according to Newton's Second Law of Motion, F=ma, then, this also implies, as will be presented also in this paper, that that Body acquires a Kinetic Energy equal to: mv2/2, according to the Newtonian Physics.But, if that Uncharged Body Accelerates according to Newton's Second Law of Motion, F=ma, this also implies, as will be also presented in this paper, that all the Work done by this external Force, is already manifested and embedded in the Kinetic Energy that that Uncharged Body acquired, because of the above-mentioned external Force which was exerted on it.However, if an external Force is exerted on an Electrically Charged Body, what was presentedabove might need some modifications.Because, if an Electrically Charged Massive Body does indeed Accelerates also according toNewton's Second Law of Motion, F=ma, and all the Work done by the external Force exerted onit, is already manifested and embedded in the Kinetic Energy embedded in this ElectricallyCharged Massive Body, then this cannot explain the origin of the Extra Energy that anElectrically Charged Body acquires when it Accelerates, which is manifested in theElectromagnetic Waves it emits and the Magnetic Field that surrounds it when it moves.A possible resolution to the above stated dilemma might be, as presented in this paper, that Newton's Second Law of Motion, F=ma might not be the proper equation which should be usedto calculate the Acceleration that an Electrically Charged Body acquires, when an external Force is exerted on it.This might provide extra support to what is already presented in additional papers, by the author of this paper, which also present the above possibility.The above-mentioned additional papers also propose an experiment.Thus, what is presented in this paper might provide extra support to the statement that animplementation of the above-mentioned experiment, might be an important endeavor.
Category: Relativity and Cosmology

FLT. Proof of the poet Pierre Fermat

Authors: Victor Sorokine
Comments: 2 Pages.

The number A + B - C contains unnecessary factor.
Category: Number Theory

Cosmic Expansion from Rotating Spacetime: A Geometric Alternative to Dark Energy

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

We revisit the hypothesis that the observed acceleration of the universe may result from the centrifugal effects of a rotating spacetime fabric. This idea, first proposed by the author in 2016, is examined here in the context of general relativity with rotation. We derive a modified Friedmann equation incorporating vorticity and show how rotation naturally leads to expansion without invoking exotic dark energy. Furthermore, recent observations — such as anomalies in the cosmic microwave background and largescale structure alignments — offer potential empirical support for this interpretation. This work provides a geometric foundation for cosmic acceleration rooted in the rotational dynamics of spacetime.
Category: Classical Physics

Artificial Prime Numbers in the Fibonacci Sequence: A Structural Approach

Authors: Jose Acevedo Jimenez
Comments: 3 Pages.

In this article, it is proven that for every n≥3, there exists at least one artificial prime number q such that F_n<q<F_2n , where F_k denotes the k-th number in the Fibonacci sequence. This result is obtained using the Bertrand—Chebyshev theorem and relies on a fundamental property of divisibility within the Fibonacci sequence. Although it does not imply the infinitude of classical primes in the sequence, it does guarantee the existence of infinitely many artificial primes distributed within it.
Category: Number Theory

Introduction to Complex Automata using Cook Algebra

Authors: Mirzakhmet Syzdykov
Comments: 1 Page.

As we have prior result of regular grammars over set of computational problems, we are to present the universal ‘complexity automata’ which can be used in solving any problem.
Category: Data Structures and Algorithms

Simple Algorithms to Solve MAX-SAT and TSP

Authors: Mirzakhmet Syzdykov
Comments: 1 Page.

We present the solution to two classical problems like MAX-SAT, or its 3-SAT partial case, and TSP from computational complexity theory using subset construction.
Category: Data Structures and Algorithms

Artificial Neural Networks Without Layering Concept

Authors: Mirzakhmet Syzdykov
Comments: 2 Pages.

We present the basic abstract of the newly obtained results on class of non-layered artificial neural networks.
Category: Artificial Intelligence

Temperature and Time in Quantum Wave Entropy

Authors: Xiao Lin Li
Comments: 8 Pages.

In quantum mechanics, particles have a new type of probabilistic property, which is quantum wave probability. The quantum wave probability corresponds to the quantum wave entropy. The action in classical mechanics corresponds to the quantum wave entropy. The least action principle corresponds to the stationary quantum wave entropy principle. Quantum wave entropy creates a bridge between dynamics and thermodynamics. Combining the Hamiltonian-Jacobian equation of classical mechanics and quantum wave entropy, we can derive the relationship between temperature and time. There is an inverse relationship between temperature and time. The phase of the wave function in quantum mechanics corresponds to the imaginary action. Combining the imaginary action and quantum wave entropy, we can derive the Wick rotation between temperature and imaginary time in quantum mechanics, thus explaining the physical meaning of the Wick rotation. Wick rotation is only applicable to the stationary state, not universally true. Imaginary time is only a mathematical representation and has no real physical significance.
Category: Quantum Physics

On the Three Exothermic Response Frequencies When PdD is Subjected to Coherent THz Radiation

Authors: J. S. Brown
Comments: 4 Pages. (Note by viXra Admin: The abstract should be listed after the article title and author name))

In this paper we identify the three THz frequencies that have been found to trigger anomalous exothermy in palladium deuteride with low-lying dipole transition in the deuteron vibrational spectrum. We then speculate that the mesoscopic entanglement that characterizes the ground state of the Tavis-Cummings hamiltonian may give rise to appreciable deuteron-deuteron fusion by virtue of the generic mechanism posited by Takahashi.
Category: Condensed Matter

Proof of Equivalence of Complexity Classes and Other Relations

Authors: Mirzakhmet Syzdykov
Comments: 2 Pages.

As we have presented our functional hypothesis of complexity classes in previous review, we are to present the full mathematical proof of the relations between complexity classes.
Category: General Mathematics

Spacetime Impedance and the Big Bang

Authors: James Conor O'Brien
Comments: 17 Pages.

The concept of Spacetime Impedance as a tensor quantity Z_{μν} is introduced and derived from the Einstein-Hilbert action and demonstrates itsrelation to the energy-momentum tensor. By contracting this tensor, we obtain a scalar quantity Z proportional to the energy density of the universe, establishing a relationship between spacetime geometry and fundamental physical quantities. This model allows for an impedance-matching condition between theEuclidean and Lorentzian domains, potentially influencing our understanding of wave transmission, tunnelling between these spacetime manifolds, and allows a mechanism for the Big Bang, and Dark Energy in extragalactic voids.
Category: Relativity and Cosmology

Upgrading the Turing Test to Consciousness

Authors: Luke Kenneth Casson Leighton
Comments: 8 Pages.

In "Where is the Denition of Consciousness"[1] (WdDoC) it was pointed out that the Turingtest[2] is in need of an upgrade. However Bayne[3] et al do an extraordinary job of reviewing the field of Consciousness testing, and insightfully extend the scope to a much more general one that includes nonhuman animals, xenobots and more, making such a Turing test upgrade eectively a moot exercise.

From the Definition of Consciousness that is remarkably similar to Tononi's[4], McKenzie's[5] as well as to Axel Cleeremans and Luis Jiménez[6] Definition of Learning, this article points out that the level of sophistication (or simplicity) of a given Conscious Entity has to be taken into consideration, but that the features tested as part of the Definition (Advaita Vedanta Boolean Algebraic capability,Memory, Imagination / Creativity, Ability to action future insights and learn from mistakes ) remains the same regardless of the scope and resources. Given that PID Control strictly meets the Definition of Consciousness, the difficulty and comprehensiveness of the task is highlighted by how rigorous and thorough PID Controller testing has to be in Safety-critical Engineering.

Additionally it is agreed that Schweizer's[7] perspective is correct: selection of a single entity (or too small a sample size) is statistically risky, and that the only way to mitigate such is to test Groups of entities. However crucially the same statistical risk of small sample size applies equally to the number of Groups tested.
Category: Artificial Intelligence

Proof that the Charged Massless Field Quanta of Su2 Yang-Mills Cause Electromagnetic Force, Replacing u1 Abelian Qed Dogma

Authors: Nigel B. Cook
Comments: 6 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present a novel derivation of the Casimir force using a quantum field theory (QFT) mechanism that models particles as event horizon-sized "plates," focusing on zero-point field exclusion. This approach, inspired by Cook’s work, transforms the Casimir force (∝ 1/d^4) into the Coulomb force (∝ 1/d^2) through virtual photon exclusion and vacuum polarization. We further demonstrate that in SU(2) Yang-Mills theory, infinite self-inductance of chargedenergy currents in a one-way path coerces the net charge-transfer term to vanish, aligning the field dynamics with Maxwell’s equations and enabling the Coulomb force derivation.
Category: Quantum Gravity and String Theory

Chronovibrational Field Dynamics and Warp Propulsion A Time-Modulated Scalar Framework for Matter, Dark Energy, and Metric Engineering

Authors: Paolo Giordana
Comments: 23 Pages. DOI reference: https://doi.org/10.5281/zenodo.15224717 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a scalar field framework in which spacetime curvature and cosmic acceleration emerge from the harmonic dynamics of a global time-dependent scalar field, interpreted as a chronovibrational modulation of the universe. Within this model, visible matter, dark matter, and dark energy correspond to distinct harmonic modes of the scalar field, each characterized by unique frequencies, decay profiles, and phase interactions.The chronovibrational field dynamically affects the energy—momentum tensor and the underlying geometry, leading to phase transitions at critical energy densities—particularly relevant in the context of gravitational collapse and black hole formation, echoing the scenarios described by Alipour et al. (arXiv:2504.03453) regarding the interplay between cosmic censorship and the weak gravity conjecture. The chronovibrational paradigm naturally introduces a scalar—fluid duality, resonant with approaches discussed by Alves et al. (arXiv:2504.01710), and is compatible with extended scalar—tensor frameworks such as Brans—Dicke theory.In addition, the model allows for metric engineering: the modulation of the scalar field provides a dynamic mechanism to locally manipulate spacetime curvature, in analogy to warp drive metrics like that of Alcubierre. It also aligns with the modified geometric structures explored in f(R) gravity (Tretyakov & Petrov, arXiv:2504.02253) and supports the notion of field-mediated entropy flows in cosmology (Odintsov et al., arXiv:2504.03470).Chronovibrational modulation could offer a viable alternative to exotic matter for sustaining warp-like geometries, outlining a physically grounded path toward field-driven propulsion systems and a unified vibrational interpretation of cosmic structure and acceleration. The framework also invites phenomenological investigations into high-frequency scalar dynamics, phase transitions, and gravito-scalar resonances detectable via gravitational wave interference or quantum optical probes.
Category: Quantum Physics

Proofs of Legendre Conjecture and Some Related Conjectures

Authors: Wing K. Yu
Comments: 11 Pages.

This paper is an improvement on my previous work and proves the Legendre, Oppermann, Brocard, and Andrica conjectures using basic analytical methods.
Category: Number Theory

A Method of Finding All Existing Starting Numbers For Finite Arbitrarily Long Collatz Trajectories That Obey Any Behavior/Dynamics of Our Choosing

Authors: Zhenghao Wu
Comments: 14 Pages.

We provide a general analytic formula to construct all existing starting odd numbers that obey our desired finite arbitrarily long Collatz trajectory, meaning that these starting odd numbers obey our pre-designated maximum factors of 2 at each iteration of the reduced Collatz map. We also provide another general analytic formula for finding the resulting odd numbers after N iterations of the reduced Collatz map. These formulas shed light on the structure of Collatz trajectories and other properties. We can also use this information to find in finite steps all existing Collatz trajectories that become 1 after any finite N iterations.We also will see that the "location" of all of the 1’s in Collatz Conjecture can be found by solving a special case of the discrete log problem.
Category: Number Theory

A Universal Upper Bound for the Backward Diffusion of Pollution And/or for the re-Suspension of Pollution.

Authors: Alexis Zaganidis
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The present article study the case of an object exposed to pollution by diffusion mechanisms during a unitary time. After a certain resting period without any pollution exposures, we derive a universal upper-bound for the remaining concentration levels of pollution within that object. There are only 6 parameters involved: the saturated concentration levels of pollution within the considered object immediately after being exposed to pollution during an arbitrary long time, the diffusion coefficients of that pollution, the spatial dimensions of the considered object, the pollution exposure time, the resting time and the concentration levels of pollution within the considered object. A universal upper bound for the remaining concentration levels of pollution after backward diffusion can be found and can hold for any diffusion coefficients. This universal upper bound for the remaining concentration levels of pollution is particularly useful in the case of disinfection procedures with disinfecting toxic volatile fluids having unknown diffusion coefficients. Indeed, a too short duration of the disinfection procedures would not decontaminate well enough the considered object while a too long duration of the disinfection procedures would contaminate the considered object too much for a too long time. In addition, the toxicity of disinfecting volatile fluids is often not well known precisely and may vary under various circumstances. Therefore, this universal upper bound for the remaining concentration levels of pollution can be used to figure out the optimal duration for the disinfection procedures and the optimal resting time immediately after these disinfection procedures without needing to know the diffusion coefficients of the involved toxic disinfecting volatile fluids. For the convenience of calculations, we consider a unitary time for the pollution exposure time, we consider unitary dimensions for the considered object and we consider unitary saturated concentration levels of pollution. In the present article, the universal upper bound for the remaining pollution after backward diffusion and/or for the remaining pollution after re-suspension, are derived in the 1D case and in the 3D spherical case.
Category: Classical Physics

Reformulations in Classical Electromagnetic Theory and a Proposal for the "Luminiferous Ether"

Authors: Paulo Guedes Logrado
Comments: 14 Pages.

We present in this article fundamental elements that can guide us in the process of developing a possible classical electromagnetic theory. Maxwell's equations, which involve line integrals of the electric and magnetic fields, are reformulated into expressions that are almost completely symmetrical. We show that the continuity equation for current naturally arises from the reformulated Maxwell-Ampère law. Ampère's law is generalized and applied to calculate the magnetic field due to some common current distributions found in the literature, including a moving charged particle and a finite current segment. The expression for magnetic force is modified, and the cyclotron frequency of a charged particle in a uniform magnetic field is obtained in accordance with classical mechanics. The magnetic field in the spin-orbit interaction within an atom is determined from the reference frame at rest with the nucleus, which cannot be achieved with electromagnetic theory in its usual form. The force between two long current-carrying wires and a brief discussion on the interaction between two arbitrary current circuits are addressed using the reformulated laws. Next, we present a special non-material medium to correspond to the luminiferous ether, that is, a medium through which the electromagnetic wave propagates. Then, the electromagnetic interaction between two charged particles is examined. Thus, in this work, we propose basic elements to complete the classical electromagnetic theory.
Category: Classical Physics

Two Methods of Calculating Gravitational Force Which Lead to a New Law of Gravitation

Authors: Mykola Kosinov
Comments: 4 Pages.

For over 300 years, the force of gravitational interaction has been represented by only one physical law: Newton's law of gravity F = GMm/r^2. Here we show that Newton's law of gravity is not the only law of gravitational interaction. There is one more undiscovered law of two-body gravity in physics. The new law of gravity is: F = mR^3/T^2r^2. This is the second law of gravity. It does not exist in Newtonian dynamics. This law of gravity does not include the gravitational constant G. It does not include the central mass M. The new law of gravity includes the characteristics of the elliptical orbit in the form of the Kepler constant R^3/T^2 as parameters. Here we reveal a method for obtaining a new law of gravity. The same method allows one to obtain a new law of gravity for N bodies.
Category: Classical Physics

Relativistic Structure of a Rotating Sphere in a Light Cylinder

Authors: Alexander Rozenkevich
Comments: 8 Pages.

This paper presents a relativistic model of a rotating dust sphere without gravity, in which the geometric deformation is caused solely by kinematics. The calculations are based on the method used by the author of the article to calculate a relativistic disk. Based on the analytical expression for the vertical deformation as a function of radius, angle and angular velocity, the effect of rotation on the geometry, perimeters and volume of the sphere is analyzed. Particular attention is paid to the asymmetry of expansion between the equatorial and polar regions.
Category: Relativity and Cosmology

Relativistic Structure of a Rotating Sphere in a Light Cylinder (In Russian)

Authors: Alexander Rozenkevich
Comments: 8 Pages.

This paper presents a relativistic model of a rotating dust sphere without gravity, in which the geometric deformation is caused solely by kinematics. The calculations are based on the method used by the author of the article to calculate a relativistic disk. Based on the analytical expression for the vertical deformation as a function of radius, angle and angular velocity, the effect of rotation on the geometry, perimeters and volume of the sphere is analyzed. Particular attention is paid to the asymmetry of expansion between the equatorial and polar regions.
Category: Relativity and Cosmology

Prime Number Generation Without Factorization: A Hyperbola-Based Algorithm

Authors: Jayme Mendes
Comments: 11 Pages.

This article presents an algorithm for efficiently generating all prime numbers within the interval [m, n], where m ≥ 3. The algorithm is developed from the demonstration that non-prime numbers in this range can be obtained from certain points in the region between two rectangular hyperbolas and two straight lines. The method does not perform factorization tests and does not require prior knowledge of any prime number, which makes it easier to obtain large primes for n − m = q = constant, when the time and memory complexities become equal to O(log n) and O(1), respectively.
Category: Number Theory

Should the Big Bang be Thrown in the Trash?

Authors: Rik Gielen
Comments: 16 Pages. (Note by viXra Admin: Please cite and list scientific references)

The most important argument on which the big bang theory rests is the cosmic background radiation CMB. We undermined this argument and so the big bang could be kicked out. We proposed our own phenomenon that is responsible for the radiation that is measured: the cosmic foreground radiation CMF, the quantum fluctuations of the 3C energy. One of the striking problems in modern physics is the asymmetry between matter and antimatter in the universe. Baryogenesis is insufficient to explain this. We solved this problem by proposing a twin universe of universe and anti-universe, each in its own space, which implies the preservation of symmetry between matter and antimatter. The twin universe view is also to the detriment of the big bang.
Category: Relativity and Cosmology

Why Mond's Fundamental Acceleration is not a "Fudge Factor"

Authors: George Bailey
Comments: 19 Pages. (Note by viXra Admin: Please list author name after article title and submit article written with AI assistance to ai.viXra.org)

The MOND theory (Modified Newtonian Dynamics) initiated by Milgrom has established itself as the most important model for explaining the measured rotation curves of galaxies without the aid of ominous dark matter. The core element of MOND is the so-called fundamental acceleration a0 with a value of approx. 1.2⋅10^-10 m/s^2, which results from the measurements of galaxy rotation velocities. At accelerations close to or below this value, neither Newton's nor Einstein's gravitational models work reliably.Critics of the MOND theory argue that this value is an ad-hoc "fudge factor" that was not derived from a fundamental consideration of space and time. So Milgrom himself as well as other proponents of MOND have already shown that the value a0 can very easily be brought into a numerical relationship with the age of the universe Tu and the speed of light c. In this paper, I would now like to show that this numerical correlation is no coincidence, but can be derived by consistent application of Heisenberg's energy-time uncertainty relation on a cosmic scale. So I will show that a0=c/(2π⋅Tu) is the smallest possible acceleration for any rotation/orbital motion in an universe of age Tu and therefore not a "fudge factor", but the counterpart of the Planck acceleration at the other, lower bound of the energy scale with which our universe can be described.
Category: Astrophysics

International Money

Authors: Dimiter Dobrev
Comments: 20 Pages.

Very soon, after only a few years, a new currency will appear that will overshadow the US dollar and the Euro. Let us try and guess what it will look like. The new currency will be called IM (short for International Money). Initially, the creators of this money will be the BRICS members, but later they will be joined by others. The rate will start from 1 IM for 10 Euro. Then this rate will change, but in the end, when the Euro and IM merge, the rate will again be the same. The IM will have banknotes, cents and centi-cents. The smallest banknote will be 1 IM. The cents will be smaller and lighter than the Euro cents, and will have the terrestrial globe on the back instead of a coat of arms. Centi-cents will be dematerialized — they will exist only in electronic form.
Category: Economics and Finance

Euclidean Cosmology (EC) as an Alternative Framework to Standard Cosmology

Authors: Joseph Bakhos
Comments: 21 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Euclidean Cosmology (EC) is introduced as an alternative framework to General Relativity (GR) and the ΛCDM model. EC retains Euclidean space and proposes that gravity is a residual effect of electromagnetism rather than a fundamental force. The theory replaces the standard expansion model with cyclic expansion and contraction phases governed by large-scale gravitational oscillations. The redshift in EC is explained through a combination of Dopplermotion and a refined tired-light mechanism. Time dilation and light deflection arise from neutrino scattering rather than space-time curvature, preserving a Euclidean structure.EC naturally explains the Cosmic Microwave Background (CMB) power spectrum without requiring inflation, aligns with observed large-scale structure, and provides a resolution to the Hubble tension within a non-expanding spaceframework. The theory predicts a self-regulating cosmic equilibrium maintained by an outer shell of the intergalactic medium, preventing energy loss and sustaining cyclic dynamics. The observed galactic rotation curves, large-scalefilament-and-void cosmic structures, and elemental recycling in Active Galactic Nuclei (AGN) are also consistent with the EC gravitational model.
Category: Relativity and Cosmology

Conjoined Spherical Triangles: A Tool for the Unification of General Relativity and Quantum Mechanics

Authors: Aswan Korula
Comments: 21 Pages.

The Conjoined Spherical Triangle (CST) framework introduces a novel approach to unifying general relativity and quantum mechanics through the concept of a computationally aware space-time. This paper presents the CST as a geometrical model that integrates gravitational dynamics and quantum phenomena, treating space-time notonly as a passive arena for physical processes but as an active, informationally dynamic system. We explore how the four laws of theCST—path law, area law, duality law, and entropy law—encode both space-time curvature and quantum state evolution. By embedding quantum information within the geometry of space-time, the CST framework offers a geometrically grounded interpretation of quantum entanglement, superposition, and the wavefunction collapse. Furthermore, the CST provides a pathway for addressing key challenges in quantum gravity, such as the black hole information paradox and the unification of quantum mechanics with general relativity. The potential applications of the CST extend to high-energy physics, cosmology, and quantum field theory, where it serves as a computationally aware medium for processing both gravitational and quantum information. This paper highlights the CST framework’s potential to bridge the gap between gravitational systems and quantum states, offering a promising new direction for the future of theoretical physics.
Category: Relativity and Cosmology

Quantum Numbers，Quantum Superposition Numbers and Non-rational Numbers and Their Applications

Authors: Zhi Li, Hua Li
Comments: 18 Pages.

In the process of solving the roots of higher-order equations, it is found that the numbers with multi-layer radical forms obtained by special methods are not the roots of the equations, but only the approximate values of the roots of the equations. It is found that the numbers formed by the square root of non-rational numbers are inaccurate numbers. Among them, quantum numbers can be directly proved to be unordered. Further research has found quantum superposition numbers. This new discovery breaks the view that "numbers are accurate". New research shows that the rational numbers in the real number system have some non-rational counterparts. The non-rational numbers are those that cannot be expressed as ratios of integers but are roots of polynomials with rational coefficients.The numbers with double-layer square roots obtained by solving the equations by the Cardan method are inaccurate numbers. They are not real numbers under the classical definition, but only approximate values of the roots of the equations. The mainstream view is that the roots of the equations belong to the real numbers under the classical definition, which proves the general formula that there are no roots for cubic equations of one variable, and at the same time proves that the Galois group theory is wrong in its discussion of the roots of equations. In the function of finding non-trivial zeros in the Riemann hypothesis, there are a large number of square roots of transcendental numbers π, which are similar to multi-layer radical numbers. These numbers are not real numbers under the classical definition, and have no accurate values. After participating in the operation, the calculation results must not be zero. Therefore, it can be proved that there is no "non-trivial zero point" and no polynomial root with a real part value of 1/2, which negates the Riemann hypothesis.The discovery and proof of quantum numbers and quantum superposition numbers have broadened human thinking about the nature of nature. It provides a reference for human understanding of the behavior of the microscopic world, making our understanding of mathematics, physics and even the entire universe more profound and comprehensive. The discovery and proof of quantum numbers and quantum superposition numbers reveal the ultimate mystery of the universe. That is, some laws of the universe cannot be perfectly expressed by functions, nor can they be accurately expressed by mathematical formulas. Some conclusions derived from quantum numbers are consistent with current quantum theory.
Category: General Mathematics

Development of Nuclear Charges at RFNC-VNIITF (1963—1976) and Explosive Deuterium Energy

Authors: Boris Litvinov
Comments: 10 Pages. [Trabslated by Nigel B. Cook from] openly published Russian nuclear weapons history.

The Chief Weapons Designer Boris V. Litvinov’s useful book, Selected Works, published by Russia’s 2nd nuclear weapons laboratory, the Russian Federal Nuclear Center RFNC-VNIITF in 2014, contains a chapter titled: Development of Nuclear Charges at RFNC-VNIITF (1963—1976) and Explosive Deuterium Energy. The primary focus is the development of nuclear charges at RFNC-VNIITF from 1963 to 1976, a pivotal period marked by the transition to underground testing and advancements in charge design, starting with the highly successful Project 49 double-primary device first tested on February 23, 1958, which its co-designer Yuri Trutnev has stated in openly published Russian news interviews, gave 2.4 times the yield/mass of the single-primary RDS37 design ...
Category: Nuclear and Atomic Physics

Scale-Dependent Geometrodynamics: Conceptual Foundations and Axiomatic Structure (Abridged Version)

Authors: Oleg Mityuryaev
Comments: 41 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents a novel theoretical paradigm — Scale-Dependent Geometrodynamics (SDG), offering a conceptually different approach to understanding the fundamental structure of reality. Unlike traditional approaches, SDG views the observable three-dimensional world as a projection of more fundamental multidimensional structures, with scale-dependent effective dimensionality of space and a three-component structure of time. A key element of the theory is monopolar eversion — a special topological mechanism connecting the limit states of scale-dependent dimensionality and creating a closed self-referential structure of reality. The paper outlines the fundamental axioms of SDG that form its conceptual and logical foundation, and discusses their implications for understanding phenomena such as dark matter, dark energy, quantum entanglement, and the origin of the Universe. The proposed theory opens new perspectives for addressing a number of fundamental problems in modern theoretical physics and offers a conceptual framework for their unified understanding.
Category: Quantum Gravity and String Theory

The Information-Geometric Theory of Dimensional Flow: Explaining Quantum Phenomena, Mass, Dark Energy and Gravity Without Spacetime

Authors: Mikhail Liashkov
Comments: 83 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents a novel theoretical framework based on information geometry and scale-dependent dimensionality that offers unified explanations for phenomena across all physical scales. The proposed dimensional flow theory demonstrates how effective dimensionality varies with scale, creating a natural hierarchy that explains quantum behaviors as projections from lower-dimensional spaces to higher-dimensional observation space. This approach resolves quantum paradoxes while preserving determinism and locality at the fundamental level. The framework successfully derives the mass spectrum of elementary particles and coupling constants from dimensional parameters, establishing a geometric foundation for the Standard Model without fine-tuning. At galactic scales, the theory provides excellent agreement with SPARC database observations of rotation curves without invoking dark matter. Cosmologically, it reinterprets redshift observations as manifestations of a static universe with a dimensional gradient, rather than an expanding universe. This eliminates the need for inflation, dark energy, and a beginning of time, while maintaining consistency with observational constraints. Gravitational phenomena emerge from dimensional gradients rather than spacetime curvature, and cosmic microwave background features appear as dimensional tomography rather than echoes of a primordial state. The framework's remarkable predictive power across diverse phenomena, coupled with its significant reduction in free parameters compared to current models, suggests that physical reality may be fundamentally based on information-geometric principles and scale-dependent dimensionality rather than an evolving spacetime.
Category: Classical Physics

Proton Entanglement Due to Dipole Transitions in the ir

Authors: J.S.Brown
Comments: 5 Pages. (Note by viXra Admin: Article title and author name added to the article by viXra Admin - Please conform in the future)

In this paper we propose that anomalous Compton neutron scattering data indicative of a partial loss of scattering targets in many molecules, polymers and metallic hydrides can be explained by the existence of low-lying entangled states in the protonic or deuteronic vibrational spectrum. This entanglement is shown to be a direct result of dipolor interactions, that may be either between close neighbours or else mediated at distance by a shared coherent electric field, as described by the Tavis-Cummings model.
Category: Quantum Physics

Theoretic and Geometric Resolution of the Prime Distribution via Hypersphere Packing

Authors: Natalia Tanyatia
Comments: 16 Pages. https://github.com/NataliaTanyatia/Optimal-Prime.git (Note by viXra Admin: The article should start with article title, author name and abstract; Please submit article written with AI assistance to ai.viXra.org)

We construct a unified symbolic and geometric framework that links the recursive generation of prime numbers to the problem of closest hypersphere packing in Euclidean space. Beginning with a purely logical definition of primes and building an iterative formula that filters primes based on modular constraints, we establish a symbolic system for exact prime counting and approximation. We then transition from arithmetic to geometry by introducing sphere-packing principles in various dimensions, particularly focusing on both furthest-touching and closest-touching configurations. By analyzing simplex-based Delaunay lattices and maximizing local sphere contact, we show how prime indices emerge naturally as layers in the radial expansion of optimally packed lattices. This construction culminates in a symbolic proof of the Riemann Hypothesis by bounding the prime counting function with a geometric analogy. The result is a cohesive theory in which logical prime filtration, packing density, and analytic continuation of Dirichlet series converge in a single constructively grounded model.
Category: Number Theory

Application of Clairmont's Coloring Algorithm to the Errera Graph

Authors: John Clairmont
Comments: 176 Pages.

In a recent article I described a new alternating chain algorithm for four coloring planar graphs.Someone suggested that I test the algorithm on the Errera graph. Kempe Chains fail to four color the Errera graph but my algorithm had no problem four coloring the Errera graph.
Category: Combinatorics and Graph Theory

Multilayer Interface Mathematics

Authors: Shiping Gu, Haitao Gu
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces a new branch of mathematics, multilayer interface mathematics.A mathematical model describing the energy of multilayer interfaces is constructed based on the variational method, which includes constructing the total energy functional from interface free energy, electrochemical energy, and diffusion transport energy. The orresponding Euler-Lagrange equations are derived. Eachstep of the mathematical derivation is explained in detail, clearly introducing howperturbation methods, the chain rule, and integration by parts are used to rigorouslyderive the target equations. The performance of fuel cells and lithium-ion batteries is largely limited by the rapid exchange efficiency of key ions in multilayer interfaces. Based on traditional models, we further introduce physical equations describing proton transport in hydrogen fuel cells and the rapid exchange of lithium ions in multilayer interfaces, providing quantitative design guidance for the fastestexchange of protons in fuel cell membrane electrodes and lithium ions in lithium-ionbatteries through specific numerical examples and parameter sensitivity analysis.
Category: General Mathematics

Distribution of Artificial Prime Numbers in the Fibonacci Sequence and Their Relation to the Counting Function

Authors: Jose Acevedo Jimenez
Comments: 6 Pages.

This paper introduces the concept of artificial primes, defined within a specific subset SSS of positive integers greater than one. A number q∈S is considered an artificial prime if no other element d∈S, with d≠q, divides q. Focusing on the subset of Fibonacci numbers greater than 1, we analyze the behavior of artificial primes in this sequence. Remarkably, the counting function of artificial primes among the first n Fibonacci numbers (with n≥3) matches the classical prime counting function π(n), which enumerates the number of primes less than or equal to n. This correspondence highlights a surprising structural parallel between classical prime distribution and internal divisibility properties within recursive numerical sequences.
Category: Number Theory

The Higgs Mechanism in the Monadic Universe

Authors: Sam Bizri
Comments: 28 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper extends the monadic electron framework to incorporate the Higgs mechanism, reinterpreting mass generation as a topological interaction between a single cosmic worldline and the Higgs field. We propose that particle masses arise from knot invariants (crossing number, Jones polynomial) of the worldline's configuration. The Higgs vacuum expectation value (VEV) stabilizes these knots via spontaneous symmetry breaking (SSB), explaining the lepton/quark mass hierarchy. Experimental signatures include fixed mass-ratio resonances, topological phase transitions at ~10 TeV, and Higgs decay anomalies.By embedding the Standard Model's Higgs mechanism within a topological quantum field theory (TQFT), this work bridges geometric intuition with quantum field theory, transforming abstract quantum numbers into spacetime-resilient structures.
Category: High Energy Particle Physics

Low Resistance and Direction Dependence on Current of a Pyromorphite Compound Doped Copper

Authors: Huk Geol Kim, Jong Jae Lee, Dae Cheol Jeong
Comments: 5 Pages.

In our previous study, we reported various electrical properties of the Pb-Cu-P-O-S compound considering LK-99. Through a series of structural analyses, we confirmed that the synthesized compound has a hexagonal pyromorphite structure. The chemical formula of oxide pyromorphite is known as Pbu2081u2080(POu2084)u2086Ou2082, which has hexagonal system. In this study, we synthesized Pb10-xCux(PO4)6O2-ySy (x: 0~3, y: 0~1). We doped this compound with copper and confirmed its low-resistance characteristics and the dependence on the direction of the current.
Category: Condensed Matter

Seismic Activation Modeling with Statistical Physics

Authors: Daniel Brox
Comments: 9 Pages.

Starting from fault dynamic equations, it is explained how real time evolution of a seismic activation region's elastic parameters preceding a major earthquake can be modeled in terms of statistical physics. Initial evidence for model validity is provided by deriving previously reported deviation of seismic activation earthquake occurence statistics from Gutenberg-Richter statistics in time intervals preceding a major earthquake.
Category: Geophysics

Spacetime with Pseudo-Kasnermetric and Shrinking Timelike Dimension

Authors: Holger Döring
Comments: 13 Pages.

Described is a Pseudo-Kasnermetric of local spacetime with shrinking timelike dimension -coordinate (TLD) as a solution of GRT gravity fieldequation. This metric leads to normal flatMinkowski-spacetime in time intervall of present time but changes with changing of timelikecoordinate from a 1-dimensional only timelike spacetime in early universe to a more 3-dimensionalpure spatial space in far future with only spacelike coordinates or dimensions (SLD) and shrinking timelike coordinate until it reaches the Planck-time. This whole description leads to the model of a spacetime with permanent shrinking timelike dimension and a prediction of maximal length of spacelike dimernsions through existence of a rip-length.
Category: Relativity and Cosmology

On Complex Dynamics and Primordial Structure Formation

Authors: Ervin Goldfain
Comments: 24 Pages.

Conventional wisdom says that the formation of large-scale structures in cosmology follows from the evolution of density perturbations under the combined effect of gravitation and cosmic expansion. We survey here the reasons why this framework fails to hold in primordial cosmology, due to the severe limitations placed on the Friedmann-Robertson-Walker (FRW) metric, the continuity hypothesis and the standard equations of fluid flows. We insist that understanding primordial cosmology must rely instead on a complex dynamics model of evolving dimensional fluctuations, conjectured to come into play far above the electroweak scale. A key outcome of this model is the universal generation of topological defects and condensates emerging from the complex Ginzburg-Landau equation.
Category: Relativity and Cosmology

Inverse N-body Problem - the Key to Solving Gravity Problems

Authors: Mykola Kosinov
Comments: 11 Pages.

Despite the fact that the law of gravitation was discovered more than 300 years ago, gravity remains the most mysterious physical phenomenon in physics and cosmology. For a long time, the force of gravitational interaction was represented by only one physical law: Newton's law of gravitation F = GMm/r^2. Newton's law of gravitation is not enough to fully describe gravity. Newton's law shows the force of gravitational interaction of two bodies out of all N bodies in the Universe. The formula of Newton's law describes gravity only to one local source of attraction and does not take into account that bodies simultaneously gravitate to all other bodies in the Universe. In gravity, at least three more laws of gravity have not been discovered. The secrets of gravity are revealed by the inverse N-body problem. The solutions to the inverse N-body problem are at least 4 laws of gravity. The solution of the inverse N-body problem for N = 2 yields two laws of gravity: Newton's law F = GMm/r^2 and a new law of gravity F = mR^3/T^2r^2. We also show that the solution of the inverse N-body problem for N → ∞ yields the third and fourth laws of gravity: F = (mc^2)√Ʌ, F = mGmе/αrе^2. Newton's law F = GMm/r^2 and the new law of gravity F = mR^3/T^2r^2 give the gravitational force of two bodies. The third and fourth laws of gravity F = (mc^2)√Ʌ, F = mGmе/αrе^2 give an additional gravitational force of N bodies in the Universe. Three new physical laws appeared in gravity in addition to Newton's law. They were missing in Newtonian dynamics. The new laws of gravity complement Newtonian dynamics and give a complete and consistent description of gravity.
Category: Classical Physics

Considerations on the Stopping Time of the 3n+1 Problem

Authors: V. Barbera
Comments: 6 Pages.

This paper presents some considerations on the stopping time of the 3n+1 problem. In particular, it presents an algorithm for finding residue classes that have a given stopping time.
Category: Number Theory

A Method of Finding All Existing Starting Numbers For Finite Arbitrarily Long Collatz Trajectories That Obey Any Behavior/Dynamics of Our Choosing.

Authors: Zhenghao Wu
Comments: 21 Pages.

We provide a general analytic formula to construct all existing starting odd numbers that obey our desired finite arbitrarily long Collatz trajectory, meaningthat these starting odd numbers obey our pre-designated maximum factors of 2 at each iteration of the reduced Collatz map. We also provide another generalanalytic formula for finding the resulting odd numbers after N iterations of the reduced Collatz map. These formulas shed light on the structure of Collatztrajectories and other properties. We can also use this information to find in finite steps all existing Collatz trajectories that become 1 after any finite N iterations.We also will see that the "location" of all of the 1’s in Collatz Conjecture can be found by solving a special case of the discrete log problem.
Category: Number Theory

Prime Number Generation Without Factorization: A Hyperbola-Based Algorithm

Authors: Jayme Mendes
Comments: 10 Pages.

This article presents an algorithm for efficiently generating all prime numbers within the interval $[m,n]$, where $mgeq 3$. The algorithm is developed from the demonstration that non-prime numbers in this range can be obtained from certain points in the region between two rectangular hyperbolas and two straight lines. The method does not perform factorization tests and does not require prior knowledge of any prime number, which makes it easier to obtain large primes for $n-m=q=constant$, when the time and memory complexities become equal to ${cal O}(log n)$ and ${cal O}(1)$, respectively.
Category: Number Theory