All Submission Categories

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

Thinking Over the Goldbach Conjecture Solution from a Probabilistic Point of View

Authors: Rosario D'Amico
Comments: 12 Pages. Keywords: Goldbach's conjecture; Prime number; Probability

This paper aims to provide a set of considerations that allow us to see a possible solution to the problematic issue of Goldbach's "strong" conjecture, which amounts to asserting that any even natural number greater than 2 can be written as the sum of two prime numbers that are not necessarily distinct. Specifically, we will show mathematically that a hypothetical scenario in which no even composite number exists as a sum of two primes is impossible. This will be done by adopting a probabilistic method by far simpler than the arithmetical attempts already present in literature.
Category: Number Theory

The Existence of Chance

Authors: Rosario D'Amico
Comments: 14 Pages. Doi: 10.23756/sp.v12i2.1667 (Note by viXra Admin: Please submit in preprint format only - No journal header etc))

This paper aims to study a particular case to provide a rational basis for recognizing the existence of chance by finding its real trace, that is, specifying its practical meaning, which consists of the following statement known as the Statistical Law of Large Numbers: If an event E has a constant probability p of occurrence on any one trial, and has occurred m times in n trials, then, if the relative frequency of E, m/n, approaches the value of a limit point l and the accuracy of the approximation increases as the number of trials increases, we have l = p. The argument we propose is based on the concepts of "event" and "trial", formulated by the author himself, and their direct implications.
Category: General Science and Philosophy

Coulomb Force from Zero-Point Field Exclusion Using Casimir Force Approach

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

We propose that the Coulomb force emerges from the zero-point field, initially manifesting as the Casimir force (∝ 1/d^4) between two event horizon-sized "plates" (electrons or an electron-positron pair), which is then converted to the Coulomb form (∝ 1/d^2) via total exclusion of virtual photon exchange between charges. Using Heisenberg’s uncertainty principle and a black hole cutoff (λ_min = 2Gm/c^2), we derive the Casimir force, then show how vacuum polarization shielding—quantified by the running coupling α(Q2)—adjusts the magnitude and distance dependence to match Coulomb’s law. This energy-conservation-based mechanism unifies the Casimir and Coulomb forces within quantum field theory, supporting quark-lepton unification.
Category: Quantum Physics

BEIPE: Block Entropic Information Pressure Engine

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

This paper proposes a foundationally minimalist framework aiming to unify quantum, gravitational, and in- formational concepts using only one driver (an "Entropic Gradient"), one process ("Translation"), and one ingredient ("Information"). At the quantum level, it re-derives Tsirelson’s bound and Bell-type correlations (in- cluding GHZ) by treating particles as geometric "streaks," without invoking probabilistic postulates. From this basis—and using the framework’s ontological flexibility—a finite, 4D manifold is posited in which Planck-scale quantities can be recovered from geometric arguments alone.The paper outlines how large-scale observables such as the baryon acoustic scale and gravitational effects (e.g., lensing) emerge from the same entropic structure, deriving the deflection of light by the Sun (1.75 arcseconds) through geometric grooving of the entropy gradient, though it does not exhaustively re-derive all lensing scenar- ios or the detailed profiles of galactic rotation curves. It demonstrates that these phenomena can be explained by the same geometry without invoking dark energy, dark matter, or extra fields. The framework’s entropy gradient—steep and rapid in early phases, easing into a slower progression—naturally aligns with the redshift- distance relation, as photons on steeper, helical paths yield higher redshifts, while gentler slopes produce lower ones, offering a flexible geometric fit to observations. In this model, time is replaced by entropic descent, the Big Bang is replaced by a persistent "Main Vent", and particles are conjectured to be "streaks" of information interacting deterministically with the entropic gradient.Potential tests include deviations from the predicted correlation bounds or direct evidence for a graviton, either of which would falsify the proposal. By relying strictly on standard mathematical functions and a min- imal set of core principles, the framework strives for both conceptual parsimony and ontological flexibility in addressing fundamental physics.
Category: Relativity and Cosmology

The Physics of Energy Transfer

Authors: Henok Abatihun Birhane
Comments: 19 Pages.

Isaac Newton defined the laws of motion and gravity, which were later expanded upon by Albert Einstein through his deeper understanding of time and gravity. However, Einstein himself was not fully satisfied with his theory. He believed that the theory of relativity offered only a limited perspective, aimed at improving measurement and relative observation, and that it still left certain aspects of time and gravity un-explained. This paper discuss narrower view of the cause for time, inertia and gravity based on newton, Einstein and multiple experiment results. The questionu2032of why’ for time, inertia and gravity will be discussed
Category: Mathematical Physics

Mass Law of Leptons and Quarks based on Hypercomplex Algebra: Topological Scaling and Generation Geometry

Authors: Jau Tang, Qiang Tang
Comments: 15 Pages.

This study presents an empirical and geometric approach to accurately modeling the mass hierarchy of leptons and quarks using a three-parameter logarithmic relation involving the fine-Structure constant (α ≈ 1/137), the mathematical constant π, and internal spinor projection geometry. The mass of each fermion is fitted to the form: log(m) = A·log(αu207b¹) + B·log(π) + C·log(D), where D represents a geometric factor derived from compactified internal spinor volumes. The coefficients A, B, and C are found to scale systematically with the generation number and Cayley Dickson algebraic embedding. Each generation corresponds to a deeper layer in the spinor structure—from complex numbers to sedenions—mirroring their increasing mass. Leptons and quarks display similar geometric patterns, with fitting errors consistently below 0.001%, supporting the hypothesis that fermion masses arise from fundamental internal symmetry projections. These coefficients align with Clifford algebra spinor spaces and suggest embeddings into grand unified symmetry groups such as SU(5), SO(10), and Eu2088. This model offers a potentially unifying framework linking particle mass, internal curvature, and the algebraic structure of spacetime, with implications for understanding triality, mass generation, and symmetry breaking in a geometric context. Based on the simple mass law, due to the hypercomplex-base framework, our view shares the view of Takizawa-Yosue’s theory regarding these particles as composites.
Category: High Energy Particle Physics

What Tells Geometric Reciprocity about the Mass Constituents of the Universe and the Universe Itself?

Authors: Hans Hermann Otto
Comments: 35 Pages.

The universe is the result of long-lasting stochastic processes in nature, and life is the most complex result of such combined actions of statistics and probability. All these processes occur in the corset of geometry. In this way, natural numbers and their combinations play a dominant role in understanding the fractal universe and its cyclic behavior. We must consider all underlying exact or almost exact relations and reciprocity relations between fundamental numbers that importantly influence statistics, probability and pairing as well as de-pairing behavior. The folding of DNA, for example, is a result of such geometric (besides energetic) considerations. In the parlance of photosynthesis or its newly created artificial pendant such number systems may be considered as number catalysts.
Category: General Science and Philosophy

Investigating Prime Gaps Through Zeta Behaviour[:] Investigating the Stringent Conditions Under Which the Riemann Hypothesis is True

Authors: Samuel Bonaya Buya
Comments: 13 Pages.

This paper explores the relationship between prime gaps and the behavior of the Riemann zeta function. We analyze key logarithmic formulations of the zeta function and their decomposition to real and imaginary parts.A zeta function is formulated that encodes information about Goldbach partitions. An exact prime gap equation is generated. It is shown the prime gaps are determined using the zeroes of the Riemann zeta function. With the exact prime gap formula, an exact formula for counting the number of primes is presented. The mystery of prime numbers is solved.
Category: Number Theory

A Symmetrical Reflected Radar Model of Special Relativity using Euclidian Geometry

Authors: Philip Asquith
Comments: Pages.

A Symmetrical Reflected Radar Model (SRRM) for Special Relativity is described. It analyses radar reflection using the Bondi k-calculus in a symmetrical spacetime diagram. Complete agreement is shown between the algebra of Special Relativity and its geometrical representation in the SRRM using Euclidian geometry. In the SRRM, the pairs of orthogonal axes; t’, x, and t, x’, which all have the same scale, can be considered as a symmetrical pair of Euclidian coordinate systems. The invariance of the spacetime interval in a transformation from the t’, x to the t, x’ coordinate system is shown using Pythagoras. Thus, in a transformation from the t’, x to the t, x’ system (and vice versa) spacetime is Euclidian.
Category: Relativity and Cosmology

Integrabily And Cohomology And 6-Sphere

Authors: Jun Ling
Comments: 6 Pages.

We construct a differential from Nijenhuis tensor of any almost complex structure on a differentiable manifold, and show a relationship between the integrability of the almost complex structure and the cohomology of the manifold. For the case of 6-sphere, we first show that this form does not vanish for a special almost complex structure, and then show that this form does not vanish for any almost complex structure on the 6-sphere. Therefore all almost complex structures on 6-sphere are not integrable.
Category: Geometry

Reversibility and Determinism in an Expanding Universe

Authors: J. Vianney Koelman
Comments: 9 Pages.

A graph-theoretical toy model is presented that allows us to study the degrees of freedom in globally hyperbolic discrete causal structures governed by a deterministic local rule. We observe that expanding structures compared to structures static in sizes behave markedly dierent. In expanding causal structures, the degrees of freedom can not all be localised in the past, and it is not meaningful to treat these degrees of freedom as initial conditions. As a result, the past no longer determines the future and determinism loses its meaning. This invalidates the argument of free will being incompatible with deterministic laws.
Category: Mathematical Physics

On Experimental Proof of "P Versus NP" Theorem

Authors: Mirzakhmet Syzdykov, Yannick Leon Kardeis
Comments: 31 Pages.

We propose a simple and intuitive algorithm for solving md-DFA problem using algorithm concepts within extended operators, our approach shows quadratic polynomial time and hence proves the equivalence between polynomial and non-polynomial classes, we have also shown that minimal non-emptiness of automata problem can be solved in polynomial time with help of modified subset construction, rather that building a product automaton, which lead to factorial size of the memory and time, in this work we also have used many non-tractable existing examples and computed them in polynomial time, which guarantees that our algorithm solves NP-complete problem in almost linear polynomial time, we have also avoided the problem of product automata by an algorithmic approach, we are also giving the starting ground for the proof of back-reference problem which was discussed before, notion to the globally local increment is also given as the main argument towards the resolution of "P versus NP" theorem, which coincides with the finitarity term in general mathematics.
Category: General Mathematics

From Notre-Dame to Norton Dome: Collapse and Reconstruction of a Cathedral of Determinism

Authors: K. Ben Letaïef
Comments: 13 Pages.

The Norton Dome is a beautiful problem in theoretical physics that is supposed to challenge the principles of causality, inertia and determinism in Newtonian mechanics. A static undeformable ball at the top of a dome of a given shape seems to move spontaneously at a certain moment, without the help of any external net force. We try to show here that the perfect rotational symmetry of the problem has not been taken into account as it should be in its solving. In this approach, we distinguish between trajectory study plan and real trajectory plan: the section of the dome in which the object will evolve or not isn't the result of a free choice or a probability but the pure consequence of physics. The differential equations of motion integrated over the entire dome precisely tell us that, if it moves, the ball should take all directions, which brings us back to a basic logical contradiction not with determinism or completeness of Newtonian theory, but between the solutions themselves: under penalty of ubiquity of the ball, its stable rest at the top remains the only known true solution to the Norton problem.
Category: Classical Physics

Reevaluating Viral Transmission: A Critical Examination of Virological Methods and Assumptions

Authors: Matthew North
Comments: 30 Pages.

This paper critically evaluates the foundational principles of virology, focusing on viral transmission, which underpin the broader scientific claims about the existence and pathogenicity of viruses. A thorough examination reveals significant empirical gaps and methodological limitations. Historical and contemporary studies are reviewed to highlight the lack of consistent evidence supporting person-to-person viral transmission, often relying on proxies such as molecular detection rather than direct causality. By addressing these shortcomings, this paper challenges the conventional paradigms of virology and their implications for public health strategies, including vaccination and quarantine measures. This work aims to foster a critical reassessment of virological methods and assumptions, promoting a more robust scientific framework for understanding diseases.
Category: Quantitative Biology

The Apex Proof to Fermat's Last Theorem

Authors: D. Ross Randolph
Comments: 40 Pages. (Note by viXra Admin: Please cite and list scientific references)

This proof uses modular analysis of exponent P, and congruence of the variables A, B and C to show no possible solutions exist for both Sophie Germain Cases 1 and 2. Basic number theory, not involving elliptic curves, makes this colorful proof relatively easy to follow, for both advanced and mid-level mathematicians.
Category: Number Theory

Spinning Electrons on Pendulum-Paths in Hydrogen Atoms

Authors: Martin Kraus
Comments: 9 Pages.

While electronic orbitals with zero orbital angular momentum are a standard feature of modern quantum mechanics, the corresponding linear electron paths with zero orbital angular momentum ("pendulum-paths") were explicitly excluded in the "old quantum theory" because of concerns that an electron on such paths would collide with the atom's nucleus. Recently, Rivas hypothesized that his model of spinning electrons allows for electrons on pendulum-paths without collisions with the nucleus. In the present work, the scenario of a spinning electron in a hydrogen atom on a pendulum-path was numerically simulated using relativistic equations of motions by Beck. The resulting trajectories were evaluated by comparing time-averaged powers of the distance between electron and proton with corresponding time-averaged values in an improved variant of the Bohr-Sommerfeld model as well as with quantum mechanical expectation values. The numerical results for a spinning electron were in better agreement with quantum mechanical expectation values than the results for the improved Bohr-Sommerfeld model.
Category: Quantum Physics

U(2) × U(3) Unified Field Theory

Authors: Nigel B. Cook
Comments: 5 Pages.

The Standard Model of particle physics is built on the symmetry groups U(1) × SU(2) × SU(3), describing electromagnetism, the weak force, and the strong force. This paper explores a speculative unified theory using U(2) × U(3), which may encompass the Standard Model while suggesting an extra U(1) group for dark energy and gravitation via a "Casimir-type shielding" effect. We use simple, concrete matrices to explain the idea, avoiding abstract math for clarity.
Category: Quantum Gravity and String Theory

Supplemented Newtonian Gravitational Equation

Authors: Istvan Polgar
Comments: 3 Pages.

Gravitational equation, and new theory based on the effect of gravitational fields to each other.The calculated attractive force eliminates the need for dark matter.
Category: Astrophysics

The Monadic Electron Universe: A Single Braided Worldline Approach to Spin-½, Multi-Fermion States, and Pauli Exclusion

Authors: Sam Bizri
Comments: 35 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We revisit the classic Wheeler—Feynman "one-electron universe" speculation—where all electrons and positrons are manifestations of a single zigzagging worldline in 4D spacetime—and develop it into a rigorous framework using worldline methods and Grassmann variables to account for spin-½. We show how: Dirac spinors and the standard QED fermion propagator naturally emerge from a single, braided worldline with local supersymmetry (the "spinning particle" formalism).The Pauli exclusion principle arises from topological and Grassmann constraints, eliminating the need to impose antisymmetrization by hand.Multi-electron processes (e.g., scattering, multi-point correlators) appear as segments of the same cosmic thread, reproducing the usual results of second-quantized QED.The Schwinger correction to the electron’s magnetic moment (g−2) arises from loop-like self-interactions of the worldline, demonstrating the calculational power of the framework.Gauge interactions are generalized to non-Abelian symmetry via color-carrying Grassmann variables, allowing confinement and asymptotic freedom to emerge geometrically.Knot invariants and topological quantum numbers (e.g., Gauss linking number, Jones polynomial) provide a new layer of observable structure, predicting testable deviations in spectroscopy, scattering, and quantum interference.This single-entity picture remains fully consistent with known quantum field theory yet offers a fresh geometric/topological interpretation of fermionic statistics, gauge invariance, and the role of spin—all within 3+1-dimensional spacetime, echoing Penrose’s insistence on retaining geometric intuition and building on our earlier work reinterpreting the "one-electron universe" hypothesis [Bizri, 2025],. We also propose a shift in this framework—from reinterpretation to prediction—and outline how this model could unify aspects of the Standard Model in a purely topological and spacetime-realistic manner.
Category: High Energy Particle Physics

The Physical Meanings Behind Wick Rotation and the Energy-Momentum Complex Functions

Authors: Zhuopeng Xian
Comments: 11 Pages.

Through Wick rotation, and the holomorphic and residue theory of energy-momentum complex functions, some formulas for wave theory, relativity, and quantum mechanics are derived. Also, the connections implied by various branches of physics such as classical mechanics, relativistic mechanics, wave theory, thermodynamics, and quantum mechanics are sought.
Category: Relativity and Cosmology

On the Nature of Logic and the P vs NP Problem

Authors: Natalia Tanyatia
Comments: 12 Pages. https://github.com/NataliaTanyatia/Logical-Manifesto.git (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We prove P = NP by demonstrating that NP-completeness arises from an avoidable computational overhead: the exponential cost of constructing higher-order logical (HOL) frameworks from first-order primitives. By formalizing the logical realizability ofall NP problems within HOL, we show these problems become polynomial-time solvable when their logical structure is known in advance. The apparent hardness of NP problems is thusrevealed as an artifact of forcing deterministic Turing machines to reconstruct HOL representations from Boolean logic (∧, ∨, ¬)rather than an intrinsic property of the problems themselves. Key to this result is the Perspective-Dependent Logical Realizabil-ity Theorem, which establishes that:1. Every NP problem’s HOL formulation has an equivalent first-order logic (FOL) representation. 2. A deterministic Turing machine (DTM) can solve any NP problem in polynomial time if provided with its HOL framework. 3. The P ≠ NP separation occurs only when DTMs are restricted to bottom-up FOL construction. We validate this with Boolean satisfiability (SAT), proving its polynomial-time tractability under HOL and introducing Deciding by Zero (DbZ) as a further example of how logical reframing eliminates classical intractability. This work does not merelysuggest P = NP as a possibility but demonstrates it as a direct consequence of logical representation theory.
Category: Set Theory and Logic

The Escherichia Coli Zinc Exporter Zitb of the Cation Diffusion Facilitator (CDF) Protein Family: Properties, Cloning, Amplified Expression, Purification

Authors: Muhammad Ali, Roshan Ali, Israr Ali Khan, Irshad Ahmad, Nighat Nawaz, Simon G. Patching
Comments: 25 Pages.

The trace metal zinc is essential in all types of organisms, where it has many catalytic, structural and regulatory functions. Zinc homeostasis in cells and organelles is maintained by various types of zinc transport protein. These include Cation Diffusion Facilitator (CDF) family proteins, which export zinc to the extracellular space or to the cytoplasm. Homologous CDF proteins are found in both prokaryotes and eukaryotes, where the human variants are the ZnTs or SLC30 family. One of the first and best characterised prokaryotic CDFs is the Escherichia coli zinc exporter ZitB, which is driven by the proton motive force in an antiport manner. In this article we provide an analytical review and expand on the biochemical and computational characterisation of ZitB and assess its potential for high-resolution three-dimensional structure determination. Consistent with structures determined for other CDF proteins (YiiP, ZnTs 3, 4, 7 and 8), the 313 residues of ZitB are predicted to form six transmembrane spanning α-helices with a long cytoplasmic C-terminal tail. An unusual feature of ZitB is an exceptionally high (8.0%) content of histidine residues. Using the IPTG-inducible plasmid pTTQ18, we demonstrate the cloning and amplified expression in E. coli of non-tagged, wild-type ZitB at levels of ~15% of total protein in preparations of inner membranes. ZitB was solubilised in the mild detergent n-dodecyl-β-D-maltoside (DDM) and purified by immobilised metal affinity chromatography in yields of ~1.8 mg per litre of culture medium. The structural integrity of purified ZitB was confirmed by mass spectrometry and circular dichroism spectroscopy.
Category: Biochemistry

An Argument Against Quantum Computers (Or Against Certain Decoherence Models)

Authors: Warren D. Smith
Comments: 4 Pages.

We present a fundamental theoretical obstacle that prevents quantum computers obeying 4 axioms from being more than a constant factor more powerful than classical ones. All presently known quantum error correction and quantum fault tolerant circuit ideas are defeated by this obstacle. The crucial question is whether "axiom #4" (concerning the nature of decoherence) is true in our universe. There are numerous previous decoherence models that both obey and disobey axiom 4. Previous arguments against quantum computers were of the form "although quantum computers may be valid theoretically, they seem extremely difficult to build in practice." In constrast, the present obstacle is theoretical, but may leave plenty of room for engineers to build quantum computers. That is because it merely shows there is some maximum number N_max of qubits in which one can hope to maintain coherence – but this upper bound might be enormous.Our argument also may be thought of as a partial explanation of why the macroscopic world appears classical. For that purpose, even a bound as weak as N_max<10³⁰ still seems interesting.[This resided on my web page since Mar.2003, and earlier versions of the manuscript were much older, e.g. I showed one to Peter W. Shor in the mid-1990s; now copying to VIXRA for archival purposes.]
Category: Quantum Physics

Enhancing Depression Detection using BERT Models Pre-trained on Reddit Corpora

Authors: Yuan Gao
Comments: 16 Pages.

Depression is a pervasive and severe mental health disorder affecting millions worldwide, with its often covert nature making early detection challenging (World Health Organization, 2021). The proliferation of social media platforms, particularly Reddit, has created unprecedented opportunities for individuals to express their mental health concerns and seek support online (De Choudhury & De, 2014). This digital footprint provides a unique avenue for leveraging natural language processing techniques to automatically identify users potentially suffering from depression, facilitating early intervention. This study builds upon the model architecture proposed by Chen et al. (2023), which utilizes BERT (Bidirectional Encoder Representations from Transformers)(Devlin et al., 2019) for feature extraction from individual user posts, followed by a Convolutional Neural Network(Krizhevsky, Sutskever, & Hinton, 2017) for user-level classification. While this approach has shown promise, we hypothesize that the pre-trained BERT model, typically trained on formal corpora such as books and Wikipedia(Devlin et al., 2019), may not optimally capture the nuanced language patterns prevalent in social media discourse. To address this potential limitation, we propose a novel approach of pre-training the BERT model on a large corpus of Reddit data before integrating it into the BERT+CNN architecture. This study aims to evaluate whether this Reddit-specific pre-training can enhance the model's performance in detecting depression through social media content analysis. We conducted extensive experiments comparing the performance of the original BERT+CNN model against our Reddit-pre-trained variant. Performance metrics including accuracy, recall, F1 score, and validation loss were meticulously analyzed. Our findings indicate a significant improvement in performance, with the Reddit-pre-trained model achieving a 2.1 point increase in F1 score compared to the baseline model. This research contributes to the growing body of literature on digital mental health assessment and demonstrates the potential of domain-specific language model pre-training in improving the accuracy of depression detection in social media contexts. The implications of this study extend to both clinical practice and public health policy, offering insights into more effective, data-driven approaches for early mental health intervention strategies.
Category: Artificial Intelligence

Geometric Origin of the Cepheid Variables: Time Varying Light Cones

Authors: S. Panda, M. S. Modgil
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Cepheid variable stars are among the most important standard candles in observational cosmology, exhibiting periodic variation in brightness. In this work, we propose a novel geometric model to explain their pulsation using a time-periodic spacetime with modulated causal structure. Specifically, we introduce a time-dependent metric coefficient $g_{tt}(t)$ driven by a brightness-inspired function that mimics asymmetric Planck-like emission. This leads to oscillating light cones, whose angles encode the gravitational basis for observed Cepheid variability, as a consequence of causal dynamics in the spacetime geometry.
Category: Relativity and Cosmology

Generalized Dirac Delta Impulse and Determinism Obtained from the Multivariate Gaussian

Authors: Ait-Taleb nabil
Comments: 6 Pages.

In this paper, we will propose to generalize the Dirac delta impulse to several dimensions. This generalization will be done by taking into account the one-dimensional version of the Dirac delta impulse. From a projection of the variance-covariance matrix, located inside the cone of positive semi-definite matrices, onto the boundary of the cone of positive semi-definite matrices, we will make the transition from Gaussian probability theory to determinism.
Category: Artificial Intelligence

A Novel Proof of the ABC Conjecture: It is easy as abc!

Authors: Abdelmajid Ben Hadj Salem
Comments: 5 Pages. Submitted to the journal Bulletin of the London Mathematical Society. Comments welcome.

In this paper, we consider the abc conjecture. Assuming that the conjecture c<rad^{1.63}(abc) is true, we give the proof that the abc conjecture is true.
Category: Number Theory

An Inductive Proof of the Riemann Hypothesis

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

This paper presents a rigorous inductive proof that all non-trivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 0.5, thereby proving the Riemann Hypothesis. We introduce a novel induction method based on the"impossibility of zero migration," ensuring that zeros cannot deviate from σ = 0.5. Additionally, we provide an exhaustive analysis excluding zeros at σ ̸= 0.5 across 0 < σ < 1, using both analytical and numerical validations. Every derivation is detailed to establish the method’s validity and the hypothesis’s truth.
Category: Number Theory

New Explanation of the Physics of Tunnel Effect Processes

Authors: Viktar Yatskevich
Comments: 31 Pages.

The tunnel effect, commonly defined as the phenomenon in which a microparticle overcomes a potential barrier that exceeds its total energy, is often cited in quantum mechanics. However, this effect does not actually occur in its described form in nature, and the quantum mechanical interpretation of tunneling does not accurately represent the real physical processes involved, but rather provides a mathematical model. The true physical mechanism of the tunnel effect remains unidentified.An analysis of the tunnel effect reveals that its manifestation creates a "paradox" in classical physics. Explanations based on the Heisenberg uncertainty principle and the wave nature of particles fail to offer a comprehensive understanding of the actual physical process.This study proposes a new explanation of the tunneling phenomenon based on the principles of classical physics and electrodynamics. It is shown that the overcoming of the Coulomb barrier by low-energy microparticles occurs exclusively due to brief localized decreases in potential within the Coulomb barrier, allowing certain charged microparticles to penetrate.The formation mechanism of these short-lived localized regions, which manifest as volume channels with lower potential within the Coulomb barrier, is examined. It is established that the creation of these channels is linked to the properties of atomic nuclei and their associated electric fields. This facilitates the suprabarrier penetration of the Coulomb barrier by individual low-energy microparticles, which pass through these channels while experiencing a reduction in their total energy.This explanation resolves the "paradox" of the tunneling effect, eliminating the contradiction with classical physics laws. Moreover, the derived estimates of the tunneling process parameters are in qualitative agreement with the results obtained from quantum-mechanical models. The proposed framework aligns with nuclear physics findings, is supported by experimental evidence, and provides a new mechanism for controlling the tunneling effect in various energy-related applications.
Category: Quantum Physics

The Geometry of Complex Spacetime: Emergence of Real Time from Imaginary Deformations

Authors: Bhushan Poojary
Comments: 12 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We propose a geometric framework for understanding complex spacetime, where classical space is represented by a deformable Cartesian grid. In this model, expansion and contraction of grid cells are interpreted as movements into the imaginary component of spacetime. These deformations introduce complex coordinates, with imaginary displacements corresponding to a pre-collapse, probabilistic regime. We argue that real time only emerges when overlapping deformed grids—representing moving reference frames—collapse into a consistent configuration. This collapse corresponds to the classical observation of time and events. The approach offers a novel, visualizable mechanism for wave function collapse and may provide insight into the interface between quantum mechanics, relativity, and the emergence of reality.
Category: Quantum Physics

Corpuscle-Simple Theory of Everything (Physical Models)

Authors: V. F. Chibisov, I. V. Chibisov
Comments: 38 Pages.

A physical model of the quantum of space-time is proposed, equivalent to the properties of the modern Theory of physical vacuum (TFV) and the Theory of Lorentz ether (TLE), on the basis of which, as a consequence, physical models of virtual photons, lines of force of electric and magnetic fields, vortices of electromagnetic radiation (EMR), preons (protoparticles of substance) are built, elementary and fundamental particles of substance, atomic nuclei, basic nuclear reactions, including LENR, neutron matter, central objects of Black holes, the cosmological stages of the formation and evolution of the universe, the great unification of fundamental interactions.
Category: High Energy Particle Physics

'Conventional Wisdom' and Academia

Authors: Jeremy Dunning-Davies
Comments: 10 Pages.

It might, and indeed should, be of interest for practising scientists to wonder how and why some theories are followed up while others are seemingly dismissed before being even properly examined or checked. There are many examples which could be cited in order to examine this question but here attention will be focused on three such examples — one from each of the last three centuries. A further speculation regarding how the attitudes seemingly exposed in these three examples might be affecting modern ideas concerning climate change will be addressed and several myths concerning this particular topic will be brought to light..
Category: History and Philosophy of Physics

Translation of the Kimberling's Glossary Into Barycentrics ("le Glossaire de Pierre")

Authors: Pierre L. Douillet
Comments: 503 Pages.

Described at https://faculty.evansville.edu/ck6/encyclopedia/ETC.html by "if you're unsure of a term, click Glossary or Pierre Douillet's much expanded and very useful version".
Category: Geometry

Beyond Quantum: The Case for a Continuous Universe

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

This paper proposes a novel framework that unifies space, time, energy, and entropy into a single continuous field, eliminating the necessity for quantum discreteness. It argues that quantization arises from human perception and mathematical formalism rather than being an intrinsic property of the universe. Gravity is reinterpreted as the curvature of space itself rather than a separate force acting within it. Time is conceptualized as a manifestation of energy distribution, with entropy governing its evolution. A new mathematical framework is required to describe this continuous field, integrating curvature, time dilation, and entropy dynamics. The implications of this model are explored in relation to black holes, cosmology, and the limitations of existing quantum theories.
Category: Quantum Physics

The Schrödinger Equation of Earth's Revolution

Authors: Runsheng Tu
Comments: 7 Pages. (Note by viXra Admin: Further repetition will not be accepted)

By replacing the electromagnetic interaction potential energy in the original Schrödinger equation with the gravitational interaction potential energy, the gravitational potential energy Schrödinger equation can be obtained. It is a product of the combination of classical mechanics and quantum mechanics, suitable for describing macroscopic and microscopic systems. A quantum chemistry method that combines classical mechanics and quantum mechanics can be established. Multiple computational examples have been provided for the application of this method. The basic particle structure configuration of wave elements can explain the source of electron spin magnetic moments. These three facts constitute a new theoretical system of quantum mechanics - a localized realism quantum mechanics system that combines classical mechanics and quantum forces. This has a positive impact on promoting the development of material structure theory and quantum theory.
Category: Quantum Physics

Graviton-Based Mass Relativity via the Quo Vadis Effect

Authors: Adolfo Santa Fe Dueñas
Comments: 10 Pages.

We present a graviton-based reinterpretation of relativistic mass increase grounded in the Quo Vadis Effect (QVE), a framework in which gravitational interactions are mediated by finite-speed messengers, without invoking spacetime curvature or Lorentz transformations. Applied to the Bertozzi experiment, where electrons accelerated through known voltages exhibit an asymptotic velocity limit, we show that the observed behavior arises from Doppler-like modulation of gravitational signaling.In this view, the effective mass perceived by the calorimeter is not an intrinsic property, but a result of the timing and momentum of incoming gravitons. The familiar relativistic correction factor γ(v) emerges naturally as a geometric average of two distinct signal regimes: a blue-shifted approach phase, termed the "Mustard Seed Effect", and a red-shifted attenuation phase during deceleration.This mechanism reproduces the predictions of Special Relativity while offering a Newtonian interpretation rooted in finite-speed information transfer. The QVE also generalizes to other phenomena, such as Mercury’s perihelion precession and cosmic expansion, where apparent mass varies with interaction geometry and duration. These findings suggest a broader framework in which relativistic-like effects emerge from the dynamics of signal perception, bridging classical, relativistic, and potentially quantum domains.
Category: Relativity and Cosmology

On the Possible Existence of Superluminal P and S Waves Within the Quantum Vacuum, and a Resolution to the Entanglement Problem

Authors: Christopher H. Pilot
Comments: 27 Pages.

Within the framework of Winterberg’s model for space where the vacuum consists of a very stiff two-component superfluid, made up of very massive, positive as well as negative mass, Planck particles, we offer an explanation for quantum entanglement. We make use of the hypothesis,that Planck charge, ������ , was created at the same time as Planck mass, ������. Moreover, the repulsive force that Planck particles of a similar mass experience is, in reality, the electrostatic force of repulsion between like charges. There is also a gravitational force of attraction between two Planck particles of similar mass, but this will be shown to be related to the electrostatic force. We can prove that there is an electrostatic restoring force, ��+,�� =(������) ��̈ = −�� �� , acting on a Planck particle within this, two-component, non-viscous fluid (sea), which forces the individual Planck particle back into its equilibrium positions when disturbed (displaced). Moreover, it can be derived from the electrostatic force between individual Planck particles, �� ������^2/��^2 = ħ ��/��^2 = �� ������^2/��^2 . In fact, the spring constant, �� , can be shown to equal, 4 ��(3)ħ�� ��+(0) , where ��(3) equals Apery's constant, 1.202 ...., an irrational number.The, ��+(0) = ��−(0) , is the relaxed, present day, number density for the positive, as well as for the negative mass Planck particle, making up the vacuum. In the present epoch, we estimate that, ��+(0) equals, 7.848 ��54 ��^−3. The relaxed distance of separation between nearest-neighbor positive, as well as negative, Planck particle pairs is, ��+(0) = ��−(0) = 5.032 ��−19 ������������. We will argue that space is the arbitrator of quantum interactions, and not photons or gravitons, as is commonly thought. Space is inherently electrostatic (and gravistatic, at the same time) because these are the forces that hold it together. Moreover, space will allow for superluminal �� and �� waves to propagate, once the space is disturbed or otherwise disrupted (as in wave function collapse). We prove that the vacuum will thus allow for an almost instantaneous transmission of energy and information between two particles separated by a great distance using our two-component superfluid model. This may solve the quantum entanglement problem.
Category: Quantum Physics

Refuting the Principle of Relativity

Authors: Azzam Almosallami
Comments: 2 Pages.

In this paper we shall prove how the Galilean principle of relativity is not true physically and according to that by refusing the Galilean principle of relativity in Special relativity theory SRT, and according to the constancy of the speed of light, then this is leading to SRT to be conformally invariant.
Category: Relativity and Cosmology

The Electron Monad: The One-Electron Universe Revisited. A Monistic Model of Quantum Spacetime

Authors: Samer Elbizri
Comments: 20 Pages. (Note by viXra Admin: Please cite and list scientific references; Please submit article written with AI assistance to ai.viXra.org)

The persistent asymmetry between matter and antimatter, alongside foundational quantum mysteries like wave-particle duality and measurement collapse, suggests a deeper unity underlying observable physics. We revisit John Wheeler’s speculative "one-electron universe" hypothesis, proposing a geometric reinterpretation where all electrons and positrons are manifestations of a single, Planck-scale braided worldline in spacetime. By treating antiparticles as time-reversed segments of this worldline and the vacuum as a self-annihilating network of unobserved interactions, we derive quantum phenomena—including double-slit interference and wavefunction collapse—as emergent consequences of the electron’s spacetime topology. This model eliminates the need for extra dimensions or abstract wavefunctions, offering a monistic explanation for quantum mechanics, antimatter rarity, and the arrow of time.
Category: Quantum Gravity and String Theory

TSVF-SUSY: A Testable Time-Symmetric Quantum-Gravity Framework

Authors: Muhammad S. U. Khan
Comments: 57 Pages.

This paper presents TSVF-SUSY, a novel framework that unifies the Two-State Vector Formalism (TSVF) of quantum mechanics with N=1 Supersymmetry (SUSY), forming a time-symmetric, CPT-invariant, and renormalizable theory for quantum gravity. By incorporating retrocausal boundary conditions and supersymmetric closure, the theory resolves long-standing paradoxes in quantum mechanics and cosmology. We demonstrate how TSVF-SUSY naturally preserves information through retrocausal interactions, offering a holographic resolution to the black hole information paradox. The framework’s dualities—TSVF-T (Temporal T-Duality), TSVF-S (Weak-Strong Duality), and TSVF-U (Universal Duality)—are explored, with connections drawn to quantum entanglement, gravitational wave physics, and the deep structure of spacetime. Additionally, we investigate testable predictions, such as gravitational wave echoes, neutrino oscillation anomalies, and graviton scattering amplitudes, paving the way for experimental verification via current and future observational platforms like LIGO/Virgo, DUNE, and the Einstein Telescope. This theory offers a self-consistent, holographically-encoded framework for reconciling quantum gravity with information conservation, providing new insights into the nature of spacetime, quantum entanglement, and fundamental physics.
Category: Quantum Gravity and String Theory

Divisor Convolution Prime Power Theorem

Authors: Naman Chaudhary
Comments: 11 Pages. (Note by viXra Admin: Please cite and list scientific references; Please submit article written with AI assistance to ai.viXra.org)

The Divisor Convolution Prime Power Theorem explores the relationship between divisors of prime powers and their applications in mathematical optimization, network systems, and cryptography. For any positive integer n, the theorem defines a function f(n) based on the sum of the divisors of n, weighted by both the divisor and the number of divisors of n/d. For any prime number p and non-negative integer k, the theorem provides an explicit formula for f(����), which is expressed as f(����) = ��^��+2 − (�� + 2)�� + (�� + 1)/(�� − 1)^2 This formula plays a crucial role in optimizing load balancing, hierarchical network routing, and fault tolerance in decentralized systems. By understanding the divisibility properties of prime powers, the theorem allows for more efficient distribution of traffic or data across multiple nodes in a network, ensuring scalability and redundancy. The applications extend to areas such as cloud computing,distributed storage systems, and blockchain technologies, where optimized access routes or permissions are vital for system performance. This paper delves into the mathematical formulation of the Divisor Convolution Prime Power Theorem and its practical significance in modern computational and network-based systems.Keywords: Divisor Convolution, Prime Power Theorem, Network Load Balancing, HierarchicalStructures, Cryptography, Optimization, Divisors, Traffic Distribution, Distributed Systems, Fault Tolerance, Cloud Computing, Blockchain, Network Routing, Mathematical Optimization, Access Permissions.
Category: Functions and Analysis

A Static, Infinite Universe: Gravitational Redshift and the Tolman Test Revisited

Authors: Marco Aurelio De Cunha
Comments: 3 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper revisits the application of the Tolman surface brightness test in the con-text of a static, homogeneous, and isotropic universe with a uniform mass density D.The gravitational redshift z(R, D) is derived using the exact spherical metric withoutweak-field approximations. The apparent velocity v(R, D) is calculated relativistically,leading to the derivation of the luminosity distance RL through an integral approach.The implications of this framework on the Tolman test are explored, revealing a correc-tion that accounts for gravitational curvature effects. A detailed discussion is providedon the philosophical motivations behind Einstein’s original static model and its topo-logical finiteness, which aligns with modern LCDM models. Special attention is givento the historical oversight of gravitational redshift in static universe models, which ledto misinterpretations of observational data.
Category: Relativity and Cosmology

Why None of the Record Breaking Galaxies Observed by JWST Are Ovals?

Authors: Dmitriy S. Tipikin
Comments: 11 Pages.

One of the problems of Big Bang cosmology is necessity to explain the events at the beginning of time (soon after Big Bang) as taking place at very high rate (very fast development of the mature galaxies with high metal content, very big black holes, too many galaxies etc). This is because the Plank’s temperature of cooled light (measured at ~2.7 K) may only be what it is measured if the expansion rate corresponds to 13.6 billions of years for total age. Since James Webb already reached z=14 (corresponding to 13.4 billions of years back in time) almost no time is left for normal, slow as we observed in nearby cosmos rate of galaxies and black holes etc formation. Big Bang theory can not "move" this time threshold further in time (accepting this would be suicide for Big Bang because it means the light itself may somehow be thermalized and red shifted according to tired light theory). Thus Big Bang theorists are inventing numerous "epicycles" like primordial black holes, black dark matter, even unification of Big Bang and tired light [1] - all in attempts to either accelerate the processes in the very beginning or move age of Universe further (say up to 27 billions of years [1]) to allow slow and well known growth of galaxies. The contradiction easily observed in James Webb Space Telescope images is discussed here - and it also because of the presence of this ~13 billions of years time boundary condition — in Big Bang cosmology the geometrical distance (what determines the optical resolution) to the galaxies with Z=8 and Z=14 is around 13 billions of light years with very high accuracy (13.1 billions of light years to z=8 objects and 13.4 billions of light years for Z=14 objects). From astronomy point of view the angular resolution of such objects is the same — yet at Z=8 galaxies are mainly ovals (as expected for poorly resolved objects) while at z=12-14 they are unresolved circles (which is not possible in either developed galaxies or so called primordial fast merging galaxies — in both cases ovals would be observed for poorly resolved galaxies). Such simple images like dots or circles hints onto the much further distance to the observed record breaking galaxies, where even JWST angular resolution is not enough to resolve at least something.
Category: Astrophysics

Geometric Interpretation of Multi-Qubit States on Complex Spacetime-Deformed Bloch Manifolds

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

The Bloch sphere provides an elegant geometric visualization for single-qubit quantum states but fails to scale intuitively to multi-qubit systems. In this paper, we propose a novel framework where Bloch spheres are reinterpreted as dynamic manifolds embedded within complex spacetime. Compression and expansion along the imaginary axis represent curvature due to quantum evolution, enabling a physical geometric model for entanglement and spin. We extend this idea to multiple qubits, where their states correspond to intersecting or entangled deformed manifolds. We also reinterpret the electron’s 720-degree rotation property as traversal of a Möbius-like loop in complex spacetime. This work aims to unify geometric visualization with the formal structure of quantum mechanics through complex geometry.
Category: Quantum Physics

The Terminator of a Sequence: A Constructive Approach to Infinity

Authors: Gabriele Bonamini
Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references; Please submit article written with AI assistance to ai.viXra.org)

In this paper, we introduce and develop the concept of "the terminator of a sequence", defined as the term that would be reached by extending the construction of a given infinite succession indefinitely. Unlike the traditional limit, whose value may be abstract or not defined in the target domain, the terminator is an actual element of the sequence.This approach leads to the introduction of new operators which formalize the ideas of "infinity by construction" and "infinitesimal by construction", respectively, which allows to re-design infinite and infinitesimal quantities as concrete mathematical entities that arise directly from the sequence’s construction, rather than as mere abstract mathematical concepts.
Category: Number Theory

Real-Virtual Annihilation

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

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

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

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

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

Research on the Vacuum Power Mechanism (in English)

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

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

Microscopic Interpretation of The Gravity Electroweak Symmetry Breaking

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

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

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

Authors: Song Fei
Comments: 24 Pages.

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

Wallis's Constant

Authors: Edgar Valdebenito
Comments: 2 Pages.

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

A Technique for Making Nuclear Fusion in Solids — More Elements

Authors: Richard Wayte
Comments: 10 Pages.

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

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

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

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

The Theory of Concomitant Forces

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

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

A study of Dark Matter: A Comprehensive Review

Authors: Diriba G. Tolasa
Comments: 14 Pages.

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

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

Authors: Anindya Kumar Biswas
Comments: 29 Pages.

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

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

Authors: Bahbouhi Bouchaib
Comments: 14 Pages.

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

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

Authors: Mohamed E. Hassani
Comments: Pages.

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

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

Authors: Gerald Malczewski
Comments: 31 Pages.

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

Seven Set Prime Number Theorem

Authors: Muhammad Ahmad Abdullah
Comments: 41 Pages.

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

Proof of the Lehmer Conjecture on Ramanujan's τ Function

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

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

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

Authors: Varun Verma
Comments: 28 Pages.

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

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

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

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

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

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

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

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

Coulomb Force from Zero-Point Field Exclusion Using Casimir Force Approach

Authors: Nigel B. Cook
Comments: 6 Pages. Diagrams added to aid understanding QFT mechanism ((Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org))

We propose that the Coulomb force emerges from the zero-point field, initially manifesting as the Casimir force (∝ 1/d^4) between two event horizon-sized "plates" (electrons or an electron-positron pair), which is then converted to the Coulomb form (∝ 1/d^2) via total exclusion of virtual photon exchange between charges. Using Heisenberg’s uncertainty principle and a black hole cutoff (λ_min = 2Gm/c^2), we derive the Casimir force, then show how vacuum polarization shielding—quantified by the running coupling α(Q2)—adjusts the magnitude and distance dependence to match Coulomb’s law. This energy-conservation-based mechanism unifies the Casimir and Coulomb forces within quantum field theory, supporting quark-lepton unification. Diagrams aid understanding this QFT mechanism.
Category: Quantum Gravity and String Theory

Prime Gaps, Zeta Function Behavior, and Counterexamples to the Riemann Hypothesis

Authors: Samuel Bonaya Buya
Comments: 20 Pages.

This paper investigates the relationship between prime gaps and the Riemann zeta function, focusing on the stringent conditions under which the Riemann Hypothesis (RH) holds and the circumstances under which it is falsified. Through the analytic continuation of primes, we derive an exact prime gap theorem and an alternative formulation of the zeta function. A key result reveals that the zeta function ��(log �������� + ����) generates infinite number of zeroes outside the critical strip. Other result reveals that a zero is generated independently of ��, providing a potential counterexample to RH. This challenges the assumption that all non-trivial zeta zeros lie on the critical line ℜ(��)=1 2 . Numerical analysis supports thetheoretical framework, demonstrating that prime gaps and zeta zeros are deeply interconnected. These findings suggest that while RH is useful in number theory, it cannot be an absolute truth, requiring a revised understanding of prime number distribution.
Category: Number Theory

From Notre-Dame to Norton Dome : Destruction and Reconstruction of a Cathedral of Newtonianism

Authors: K. Ben Letaïef
Comments: 14 Pages.

The Norton Dome is a beautiful problem in theoretical physics that is supposed to challenge at the same time the principles of causality, inertia and determinism in Newtonian mechanics. A static undeformable ball at the top of a dome of a given shape seems to move spontaneously at a randommoment, without the help of any external net force. We try to show here that the perfect rotational symmetry of the problem has not been taken into account as it should be in its solving. In this approach, we distinguish between trajectory study plan and real trajectory plan: the section of the dome in which the object will evolve or not isn't the result of a free choice or a probability but the pure consequence of physics. The differential equations of motion integrated over the entire dome precisely tell us that, if it moves, the ball should take all directions, which brings us back to a basic contradiction not with determinism or completeness of Newtonian theory, but between the indeterministic solutions themselves: under penalty of ubiquity of the ball, its permanent immobility at the dome’s summit remains, in accordance with the principle of inertia, the unique physical solution to the Norton’s paradox.
Category: Classical Physics

[ A] Proof to Fermat's Last Theorem

Authors: D. Ross Randolph
Comments: 40 Pages.

This proof uses modular analysis of exponent P, and congruence of the variables A, B and C to show no possible solutions exist for both Sophie Germain Cases 1 and 2. Basic number theory, not involving elliptic curves, makes this colorful proof relatively easy to follow, for both advanced and mid-level mathematicians.
Category: Number Theory

Supplemented Newtonian Gravitational Equation

Authors: Istvan Polgar
Comments: 4 Pages.

Gravitational equation, and new theory based on the effect of gravitational fields to each other.The calculated attractive force eliminates the need for dark matter. Tested on the rotational velocity of an average disc-shaped galaxy.
Category: Astrophysics

Generalized Dirac Delta Impulse and Determinism Obtained from the Multivariate Gaussian

Authors: Ait-Taleb Nabil
Comments: 9 Pages.

In this paper, we will propose to generalize the Dirac delta impulse to several dimensions. This generalization will be done by taking into account the one-dimensional version of the Dirac delta impulse. From a projection of the variance-covariance matrix, located inside the cone of positive semi-definite matrices, onto the boundary of the cone of positive semi-definite matrices having only the last eigenvalue equal to zero, we will make the transition from Gaussian probability theory to determinism.
Category: Artificial Intelligence

How a Tokamak May Allow GW to be Duplicated in Simulated Values, with Torsion Cosmology and Cosmological Constant

Authors: Andrew W. Beckwith
Comments: 58 Pages. [Article expanded and submitted to JHEPGC]

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

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

Authors: Varun Verma
Comments: 28 Pages.

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

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

Authors: Varun Verma
Comments: 29 Pages.

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

Review of Mechanistic Quantum Field Theory

Authors: Nigel B. Cook
Comments: 14 Pages. Completely rewritten, updated and corrected with better explanations (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents a comprehensive mechanistic quantum field theory (QFT) framework that unifies quarks and leptons, particle masses, and quantum gravity through two fundamental dynamical processes: (1) discrete momentum transfers via gauge boson exchanges, analogous to billiard-ball collisions, averaging to continuous forces on macroscopic scales, and (2) energy conservation in vacuum polarization, where pair production above the infrared (IR) cutoff (1.022 MeV, $sim 33$ fm) shields core charges, redistributing energy into particle masses and nuclear forces.
Category: High Energy Particle Physics