All Submission Categories

Sound Transmission Via Gas-Filled Insulating Glass Units

Authors: Roman Vinokur
Comments: 18 Pages.

Windows are points of the lowest resistance in the total sound and heat insulation of buildings. To enhance both thermal and acoustical qualities of windows with insulating glass units (IGU), the gaps between the panes can be filled with a heavier-than-air gas alone (for example, argon, krypton, xenon, and sulfur hexafluoride) or mixed with air. Here, the sound transmission loss (STL) may be increased in the low-frequency range dominated by acoustic resonances where the panes and gaps play the role of masses and springs. This frequency region (typically 100-500 Hz) is important for reducing traffic noise by windows. However, the expected acoustical improvement is often not measured using the standard two-reverberation room techniques. In this paper, such a discrepancy is theoretically and experimentally studied for physical interpretation and design optimization. Clear closed-form expressions have been derived and verified for the direct (via the panes and gaps) and flanking (via the panes and perimeter structural links) sound transmission through single-space and double-space insulating glass units, and improvement proposals have been developed. The results can be interesting for the scientists and engineers engaged in acoustics and construction.
Category: Classical Physics

Temporal Information Curvature: A Robust Diagnostic for Instability in Machine Learning Training Dynamics

Authors: Dhruvil Chodavadiya Rajeshbhai
Comments: 7 Pages. © 2025 Dhruvil Chodavadiya Rajeshbhai

Training loss metrics in machine learning are often reactive, failing to anticipate instability until divergence occurs. I propose Temporal Information Curvature (TIC), a novel time-aware diagnostic that measures curvature, nonlinear feedback, and memory effects in training dynamics. Through simulations across clean, unstable, and noisy loss curves, I show that TIC detects instability early, remaining robust to noise and outperforming derivative-only metrics. TIC also enables plug-and-play decision logic for training optimization, with applications extending to finance and signal processing. This work establishes TIC as a versatile and reliable tool for temporal analysis in machine learning and beyond.
Category: Artificial Intelligence

On some Programs in Mathematics and Physics

Authors: Lucian M. Ionescu
Comments: 44 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar 2024.

The development of Mathematics was marked by far-reaching new ideas, known as "Programs", and associated to top Mathematicians, e.g. Galois, Klein, Lie, Noether, Hilbert, Grothendieck, Langland and much more. They become "Principles" that changed the landscape of Mathematics and led to breakthroughs in Sciences, notably in Physics, but also in Chemistry and Biology. This presentation highlights the relation between such general principles, ensuing from the actual historical connections between their proponents, with excerpts from stories one needs to know, e.g. Einstein’s talk and Hilbert’s "homework" to his assistant Emmy Noether, or the productive collaboration and friendship between Felix Klein and Sophus Lie. New developments are mentioned: how Theory of Algebraic Periods, in the context of the recent quantization of system of units leads to explain the "unreasonable effectiveness of Mathematics": Natural Laws are Period laws.
Category: General Science and Philosophy

Spin as a Real Vector from Internal Photon-Sphere Motion: Geometric Origin of U(1) Gauge and SU(2) Periodicity

Authors: Satoshi Hanamura
Comments: 10 Pages.

We present a time-dependent model of electron spin in which the spin angular momentum arises from internal oscillatory motion rather than from a static pseudovector. This work corrects a dimensional inconsistency in our previous formulation by explicitly introducing the unit vector e_z along the z-axis, ensuring proper vector notation for the angular velocity Ω(t) = -(1/4c²)sin(2ωt)·e_z. Inspired by a reinterpretation of Thomas precession, we emphasize that angular momentum can emerge even in non-circular or reciprocating motion, such as a simple harmonic oscillator. This leads us to treat the spin as a real vector whose z-component evolves as sin(2ωt), reflecting an intrinsic 4π periodicity. The model is built upon a closed internal phase space—specifically, the 0-Sphere kernel structure—and provides a deterministic evolution of spin orientation in internal time. Spin quantization is reinterpreted as a geometric effect of phase evolution, eliminating the need for a predefined spin direction. The formulation reproduces the SU(2) double-covering property in a natural and geometric manner, offering new insight into the origin of spin and its fundamental symmetries. Moreover, the model provides a novel interpretation of the anomalous g-factor as a relativistic effect arising from Lorentz contraction in internal oscillatory motion. The conventional SU(2) symmetry is shown to emerge geometrically from an underlying U(1) phase evolution, suggesting that spin behavior reflects continuous internal dynamics rather than discrete quantum states. This corrected formulation offers a deterministic foundation for understanding spin measurements and the 720-degree rotation symmetry of spin-1/2 particles.
Category: Quantum Physics

Distinguishing Features of Longitudinal Magnetoconductivity for a Rarita-Schwinger-Weyl Node

Authors: Ipsita Mandal
Comments: 11 Pages. 3 figures

The band-degeneracy points in the Brillouin zones of chiral crystals exist in multiple avatars, with the high-symmetry points being able to host multifold nodes of distinct characters. A class of such crystals, assisted by the spin-orbit coupling, harbours fourfold degeneracy in the form of Rarita-Schwinger-Weyl node (RSWN) at the $Gamma$-point. Our aim is to explore the nature of longitudinal magnetoconductivity, arising from applying collinear electric and magnetic fields, for such systems. Adjusting the chemical potential to lie near the intrinsic energy-location of the RSWN, the multifold nature of the RSWN is revealed by an interplay of intraband and interband scatterings, which would not arise in twofold degeneracies like the conventional Weyl nodes. The current study fills up the much-needed gap in obtaining the linear response from an exact computation, rather than the insufficient relaxation-time approximation employed earlier.
Category: Condensed Matter

On Noether Theorem and Generalizations

Authors: Lucian M. Ionescu
Comments: 58 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar 2025.

"Understanding" involves Networking Concepts and Theories, e.g. within a mathematics area and between areas (Algebra and Geometry: from Descartes and Galois to Klein and beyond, e.g. Noether & Langland). Such a higher level of understanding, is advocated (pioneered?) by Andre Weil’s "Power of Analogy", with contributions from Simone Weil, in connection with the "Number Field / Function Field Analogy". We use such analogies to substantiate the tower of theories: Geometry, Homotopy Theory and Dynamics, as a background for understanding Lagrangian Mechanics vs. metric geometry, towards grasping in a simpler way Noether Theorem relating groups of symmetry and conserved quantities in Physics. This is another use of Galois Principle, as explained in a previous talk on Programs in Mathematics and Physics. The presentation is at an undergraduate level, with pictures available YouTube’s author channel, part of the zoom recording of the talk.
Category: Mathematical Physics

The Special Theory of Relativity "may be" a wrong Theory

Authors: Vaggelis Talios
Comments: 7 Pages.

In Mathematics, when we make a mistake in solving a problem, this mistake is also transferred to the calculations of the problem and usually leads us to an incorrect result. If we transfer this incorrect result to Physics, e.g. in the study of a topic, then we usually end up with an incorrect conclusion about the topic of our study. Some scientists, when they make a mistake, whether due to overconfidence, or of lack of information, or of something else, often, instead of correcting their mistake, try to verify it by basing the verification on a new mistake of theirs. In this case, when we verify an error with a new error, we do not simply end up with an incorrect result, but we create an ambiguity that often completely alters the reality. Something similar has happened with the Special Theory of Relativity, where Einstein incorrectly assumed that a stationary observer located outside a space moving at a speed "a" relative to the observer, for a ray of light moving at a speed "c" within the moving space, will measure the speed of light c΄=c, which is an incorrect measurement, instead of the correct measurement which according to the invariant Mathematical Law of Superposition will be c΄=c+a. Einstein verified the incorrect and paradoxical equation c΄=c based on incorrect experimental data as we will see, and used it in all the calculations of the Special Theory of Relativity, with the consequence that all the results of the calculations of the theory are incorrect. Then he transferred all the results of the incorrect calculations to the theory, with the result that all the conclusions of the Special Theory of Relativity to be also incorrect. On the incorrect conclusions of the Special Theory of Relativity, Einstein also based the General Theory of Relativity, with which he tried to explain the cause of gravity. However, apart from some more accurate calculations, than the calculations of Newton’s theory, when we examine gravity on a global scale, for the cause of gravity, the General Theory of Relativity did not give us, any other clear positive result.
Category: Relativity and Cosmology

A Universal Frequency: Convergence of Cosmological, Quantum, and Biological Evidence and a Derivation from First Principles

Authors: Ordepte Ezurk
Comments: 5 Pages. In Portuguese

Recent independent observations in cosmology, quantum physics, and neurobiology have pointed towards an enigmatic universal frequency. In this paper, we present, for the first time, the complete theoretical derivation of this Cosmic Resonance Frequency (CRF) from first principles. We demonstrate that its value is dictated by fundamental constants through the Vacuum Acoustic Resonance (VAR) model. To validate our prediction, we established collaborations with leading experimental groups, whose high-precision measurements—also presented here for the first time—confirm the theoretical value of 0.06571 Hz with remarkable accuracy, unifying theory and experiment in a single foundational paper.
Category: Relativity and Cosmology

From 2D Quanta to the Amplituhedron: A Vectorial Framework for Unifying Quantum Mechanics and General Relativity

Authors: John James
Comments: 21 Pages. JohnBJamesJr@gmail.com, 619-203-5078

This thesis presents a novel unification framework that bridges quantum mechanics and general relativity through a discrete, vectorial system known as the 2D Quanta lattice. By modeling spacetime as a combinatorial network of directional vectors normalized within a ±1 amplitude space, this framework simulates both quantum probability amplitudes and relativistic spacetime curvature without relying on continuous manifolds.Key to this model are cross-current vectors—diagonal propagations formed by orthogonal summations—which encode null trajectories and time dilation through angular geometry. These directional patterns replicate relativistic effects such as gravitational lensing and light-cone symmetry, while simultaneously generating quantized amplitude regions analogous to those found in the Amplituhedron, a geometric object central to modern scattering theory.Through a series of diagrams and mathematical constructions, the thesis demonstrates that both curvature and amplitude emerge from the same discrete summation rules. This suggests that space, time, and probability may be dual projections of a deeper vectorial logic—a symbolic substrate from which physical law arises. The result is a unified, geometry-based interpretation of fundamental physics, grounded in direction, symmetry, and quantized coherence.
Category: Quantum Physics

Extension of Kronig-Penney Model to Metal Alloy Like Perovskites

Authors: Domenico Oricchio
Comments: 9 Pages.

I generalize the Kronig-Penney model for multiple barrier potentials of different values.I write a different way to solve the rectangular potential barrier so to simplify the solutions.I try to understand the complexity of energy band in the alloys to optimize the photons absorption using a random modification of model parameters.
Category: Quantum Physics

Four Index Einstien Field Equations

Authors: Tomasz Kobierzycki
Comments: 6 Pages.

Einstein field equations are most tested theory of gravity. In this paper I will show a possible way to extend them into four index equation.
Category: Relativity and Cosmology

Solving Polynomial Equations with Integer Sequences

Authors: Zhi Li, Hua Li
Comments: 9 Pages.

Finding a root of polynomial equations is one of basic problems in mathematics. And Galois theory restricts the general radical solution for the degree no higher than four. The series solution, besides the iterated, is regarded as final and universal method to general polynomial equations. This paper reports a discovery of the standard form of polynomial equations and a class of integer sequences associated thereof, which is a kind of extended Catalan numbers. The solution of polynomial equations in the standard form has a precise and perfect series expression. The convergence condition of the series is clear. For the general polynomial equations which may not be satisfied with the convergence condition, some proper transformations, like the Tschirnhaus transformation can be employed to guarantee the convergence. Considering that up to the quintic, there definitely exists a normal form for general equations, and the normal form can easily be changed to the standard form, our method has established a general, universal and effective technique to the quintic, as well as the quartic, the cubic, and the quadratic, without the radicals.
Category: General Mathematics

On the Relativity of Direction

Authors: Gerard van der Ham
Comments: 2 Pages.

This paper is a call to realize and recognize the importance of direction in physics.
Category: Quantum Physics

Brief Demonstration that the Expansion of the Universe is Decelerating

Authors: Dino Bruniera
Comments: 3 Pages.

Considering redshift as an indicator of the speed of the Earth's move away from the source, rather than a scale factor of the expansion of the Universe, the fact that the luminosity distance of type Ia supernovae increases more than proportionally respect redshift, demonstrates that the expansion is slowing down, thus easily explaining the arrival of the CMBR on Earth after a journey of almost 14 billion years, despite having started from locations not very far away at the time.
Category: Relativity and Cosmology

Finite Relativistic Cosmology

Authors: Yosef Akhtman
Comments: 31 Pages.

We develop a self-contained framework in which the entire physical universe is modelled by an ever-growing finitering Z�� whose cardinality is tied to cosmic time through �� = 4�� + 1. Starting from a single principle of relationalfinitude, we show that: (i) familiar dimensional constants (ℏ, ��, ��, ����) arise as structurally unique, dimensionless elements of Z��, fixed by extremal arithmetic properties; (ii) a genuine Minkowski quadratic form and full Lorentz group exist exactly inside the ring, reproducing special-relativistic kinematics under coarse-graining; (iii) the primefactor spectrum splits naturally into stable fermionic and radiative bosonic sectors, enabling hadron-like three-prime composites and colour confinement; (iv) complementary observer horizons recover, respectively, general-relativistic geodesics and quantum superposition, resolving the gravity-quantum tension and yielding a finite Heisenberg bound; (v) classical paradoxes—cosmological constant, horizon, singularities, ultraviolet divergences, hierarchy, strong-��, and wave-function collapse—are eliminated not by fine-tuning but by exact arithmetic identities in the finite ring; (vi) independent gravitational and nuclear chronometers converge on a present cardinality ��◦ ≈ 1060, implying a cosmic age of 13.6±0.2 Gyr and an accelerated expansion that requires no dark energy.We furthermore predict a ∼2.5×10−19yr−1 secular drift in the 1-m gravitational red-shift—measurable with existing optical-lattice clocks—which offers an immediate, falsifiable test of the proposed hypothesis. Together, these results suggest that a finite, relationally defined arithmetic is sufficient to encode space-time geometry, quantum phenomena, and cosmological evolution within a single coherent model.
Category: Mathematical Physics

Gravitation in the Theory of the Four-Dimensional Electromagnetic Universe (4DEU): Weak-Field Relativistic Effects from Spatial Curvature Alone

Authors: Domenico Maglione
Comments: 51 Pages.

This work presents a reinterpretation of gravity within the Theory of the Four-Dimensional Electromagnetic Universe (4DEU), where the universe is modeled as a four-dimensional hypersphere expanding at a constant rate equal to c along a real fourth spatial dimension, perceived as the flow of time. In this framework, the fundamental entities are Temporal Waves (TWs): standing electromagnetic waves oscillating exclusively along the temporal dimension. According to the Restricted Holographic Principle of the 4DEU theory, physical phenomena occurring along the temporal dimension manifest within the three-dimensional spatial hypersurface (our observable universe, where we exist) in a qualitatively transformed but quantitatively proportional manner. A central consequence is that TW energy manifests as mass quanta in 3D space. Moreover, the net radiation pressure from TWs, perpendicular to the 3D hypersurface, drives the expansion of the entire 4D universe.Gravity is proposed to result from local variations in TW density within the 4D universe. Higher TW density corresponds to greater mass in 3D, implying stronger localized TW radiation pressure that induces increased spatial curvature.Although conceptually distinct from General Relativity (GR), the weak-field predictions of the 4DEU framework are in exact agreement with it. This equivalence rigorously accounts for all experimentally verified gravitational phenomena—including gravitational redshift, light deflection, Shapiro time delay, and perihelion precession—arising independently of the GR formalism, but from a real 4D universe curved only in its spatial (3D) portion. The 4DEU theory is thus fully consistent with current gravitational observations in all domains where GR has been tested.
Category: Relativity and Cosmology

Graph Continuous Thought Machines

Authors: Tofara Moyo
Comments: 4 Pages.

We propose a novel Graph Continuous ThoughtMachine (Graph CTM) architecture that integrates a simulated prefrontal cortex to enable adaptive problem-solving and decision-making. The Graph CTM leverages graph neural networks to process complex data streams, while the simulatedprefrontal cortex modulates node activity to selectively focus on relevant information. Through reinforcement learning, the modelnavigates graph space to converge on optimal solutions, guided by the information contained in learnt node property vectors. The simulated prefrontal cortex regulates the flow of information by adjusting the disposition of nodes to lead to the next instantiationof the graph network. The Graph CTM incorporates an attention mechanism that integrates the internal state of the graph as input, which is modulated by outputs from the model’s neuralsynchronization matrix. This modulation enables the algorithm to selectively focus on specific subgraphs or node subsets,correlatingthem with the input, effectively emulating short-term and long-term memory mechanisms when attending to both the input and internal representation. By dynamically weighting the importance of different graph components, the model can adaptively process and retain relevant information, facilitating more accurate andcontext-dependent decision-making.
Category: Artificial Intelligence

Spacetime as an Emergent Cognitive Structure: A Hypothesis of Local Causality (in Russian)

Authors: Andrey N. Smirnov
Comments: 37 Pages. (Note by viXra Admin: Please fix citations and missing reference in the English version)

A hypothesis of local causality is proposed, according to which the causal structure is formed independently within each inertial frame of reference (IFR), and the notion of an event is defined only within the bounds of the observer's cognitive accessibility. Space and time are not treated as fundamental entities, but rather as emergent cognitive constructs arising from the consistent reconstruction of causal relations. A distinction is introduced between direct (external) and observable (cognitive) transformations, corresponding respectively to formal mappings of causal structures and internally consistent modifications of the observer's memory. It is shown that cognitive structures may differ even between observers within the same IFR, and their reconciliation requires admissible cognitive interaction. Using a scalar field model on two-dimensional Euclidean space, it is illustrated how multiple spacetimes can emergently arise from a single underlying superstructure. Conditions are established under which observable transformations take the form of Lorentz transformations as cognitively coherent transitions between IFRs. Physical implications and future directions are discussed, including the cognitive nature of matter and time, and the possibility of describing interactions without reference to global spacetime.
Category: Relativity and Cosmology

The Visages of the Lorentz-Einstein Law Speculative Analysis with the Extrinsic Method

Authors: Thierry L. A. Periat
Comments: 31 Pages.

This document presents an application of the extrinsic method through a generic and pedagogical example that can be applied to the co-variant formulation of the Lorentz law. The unsaid hope of this approach is the discovery of some unexplored or weakly explored links between two theories because the formalism of this law is a natural bridge between the electromagnetism and the gravitation. The analysis is able to propose (i) a new formalism for the (2, 0) version of the electromagnetic fields and (ii) a speculative confrontation with the theory of spinors resulting in a theoretical prediction, precisely: the existence of electromagnetic fields mimicking anti-symmetric variations of the metric tensor; and conversely.
Category: Mathematical Physics

Episodes of Scientific Revolutions

Authors: Lucian M. Ionescu
Comments: 18 Pages. Presentation at the 66th Midwest Junto for History of Science 2025.

The Structure of Scientific Revolutions by Thomas Khun is a valuable starting point to develop the theory of how Theories appear, evolve and fadeout, in a similar way political trends, or biological species evolve and transform. This presentation touches on this idea and acknowledges that at present there is a triple Scientific Super-Revolution going on: Quantum Computing, AI and Gravity Control Technology (much less known).Perhaps a branch of History focusing on Modeling Scientific Theories, or its analogs, and their dynamics is missing, aside the Historian routine of record keeping and commenting the usually distant past. History Dynamics could contribute to governing institutions improve their complex models to improve their efficiency by predicting and have a more "cybernetic" approach to control and prevent, especially based on the immense AI-capability for data processing and correlating.
Category: General Science and Philosophy

Euler Perfect Box

Authors: Taha M. Muhammad
Comments: 4 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

a, b, c, d, e, f, g ∈ N_+ ⟺ Euler Perfect Box Let a, b, c, d, e, f, r, k ∈N_+. I have to prove that g ∈N_+ Let a < b < c, & [(a r, and r < k)] ⇒ a ≠ r ≠ k & let b=a + r, c = a+ k g ^2=a^2 +b^2 +c^2 ∴ g ^2=a^2 +(a + r)^2 +(a + k)^2 Let g^2= [a^2 + (a + r)^2 +(a + k)^2]∈N_(S ) ∵ [a^2+2a (a + k) + (a + k) ^2]∈N_(S ) ∴ (a + r) ^2= 2a (a + k) ⇔ a = r = k u2026Contradiction to a≠ r ≠k ⇒ (a + r)^2 ≠ 2(a + k) for all a, r, k ∈N_(+ )/{a=r=k}.∴g ^2 =[a^2 +(a + r)^2 +(a + k)^2] ∉ N_(S ) ⇒ g^2 ∉ N_(S )⇒g ∉ N_(+ ) ∴ The Euler Perfect Box does not exist.
Category: Number Theory

Collatz Sequence Proof (1st Way)

Authors: Taha M. Muhammad
Comments: 10 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

1- Let x ∈ Loop of Collatz Sequence = LS(n), n, x,y,z,t,u,v ∈ N+ i) I proved LS(n) = { }, {x}, {x,y}, {x,y,z,t}, {x,y,z,t,u,u2026,v }, and {x,y,z,t,u,u2026,v,u2026} is false. ii) I proved LS(n) = {x,y,z} = {4,2,1} = {4,2,1, 4,2,1} =u2026= {4,2,1, u2026, 4,2,1} is true ∀n ∈ N+ 2- I created special sketch to find algebra expressions equal to x. 3- I created special Table to find values of elements in the LS(n). 4- I created a pattern to find values of x ∈ LS(n). 5- Observation: let r, k ∈ N+, r = number of elements in the LS(n):i) if r = 3k ⇒ x ∈ N+ ⇒ LS(n) = {1,2,4} ∀n ∈ N+ ii) if r = 3k + h, such that h=1,or 2⇒ x ∉ N+ ⇒ LS(n) has no loop ∀n ∈ N+ ∴ LS(n) ={4,2,1},∀n ∈ N+.
Category: Number Theory

Fermat's Last Theorem

Authors: Taha M. Muhammad
Comments: 5 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

Fermat’s Last Theorem: There are no natural numbers (1, 2, 3, u2026) a, b, and c such that a^n+b^n = c^n, in which n is a natural number greater than 2. 1-Taha^' s Logic Equations Fact a=b (True or False) & c=d (True)⇒(a-c=b-d) Fulse⇔a=b ( False) 2- Taha^' s Coefficient Fact: [a + b = c ⇒ ax + by= cz] ⇔ x = y = z3- Taha’s (N_+) & Three-Sided Geometric Shapes Fact below: N_+ = (Right Triangles) ∪(Acute Triangles) ∪(Obtuse Triangles) ∪ (Segments c=a + b) ∪ (Segments c>a + b).
Category: Number Theory

Properties of Phase Transformation Equations for Periodic Products

Authors: Hajime Mashima
Comments: 79 Pages. In Japanese

General solution conditions applies when the equation of Fermat's proposition can be phase-transformed by a periodic product.
Category: Number Theory

The Physics and Chemistry of Dirac Magnetic Monopoles

Authors: Rainer W. Kühne
Comments: 4 Pages.

Dirac magnetic monopoles are hypothetical elementary particles. By assuming their existence one can explain the quantization of electric charge, the August Kundt experiment, and the conservation of baryon and lepton number. Here I show that Dirac magnetic monopoles can form low-mass bound states which are analogous to mesons, baryons, atoms, and molecules. I point out that these bound states could be the major component of cold dark matter.
Category: High Energy Particle Physics

Temporal Correspondences Between the Closest in R.a. Moon—Sun—Jupiter Conjunctions and Some Paroxysms in the Volcanic Areas

Authors: Adriano Ballabene
Comments: 12 Pages. 2 diagrams, 2 tables, 4 images; in Italian

The Moon, the Sun and Jupiter are the main external sources of gravitational forces acting on the Earth, influencing phenomena such as the tides (Moon and Sun), the orbits of satellites, and to a lesser extent, the orbital dynamics of the Earth-Moon system. At the Vesuvius-Campi Flegrei volcanic arc, a correspondence can be detected between the Moons in Highest Perigee in conjunction with the Sun and the most significant phases of bradyseism, as well as the most significant eruptions of Vesuvius (79) and near the caldera (1538): the severe bradyseismic crisis of ‘82-’84 was anticipated and accompanied by 3 High New Moons in Super and Extreme Perigee orbiting at the height of the syzygy phase over Europe, while the current slower and more prolonged phase took place with the configuration of a distribution of 7 "Central European" High New Moons in only Minimum Perigee; the largest shock since 1538 Md 4.6 of 2025/03/13 occurred 5 days after the Major Lunar Culmination of the period 2010-2040 and 15 days after the "Central European" New Moon Major Elevated in Super Perigee of March 29, 2025 (the Earth-Moon-Sun configuration most similar to that of March 30, 1538, preceding the eruption by 5 months). Among the 25986 New Moons (Moon-Sun) configured in the astronomical period 0-2100, those in Extreme Perigee (d <= 0.35735 Gm) are 1437 while there are 212 close conjunctions Sun-Jupiter with angular distance <= 0.2°. The two types of conjunctions occurred simultaneously in only two occurrences: 181/12/21-23 and 1367/12/22-23. Lowering the limit of the lunar distance from 0.35735 to 0.3567 Gm, the matching returns only the Moon-Sun-Jupiter conjunction of 181/12/21-23.According to Wilson/Walker (1985) in 181 the most violent eruption in the world in the last 5000 years occurred, initially attributed to the Taupo supervolcano. The Moon-Sun-Jupiter conjunction with the most stringent parameters occurred in the year of the largest historical eruption. Extending the limit from 0.3567 to 0.367, among the 12 occurrences are the dates:1. 1302/06/26 preceding by 32 days the last eruption in Ischia (Campi Flegrei) 2. 1712/01/08 preceding by 28 days an effusive eruption of Vesuvius3. 2025/06/25 (?) At distances <=0.377, among the 19 combinations is the date 1883/07/04, preceding by 24 days the catastrophic earthquake of Casamicciola (Campi Flegrei) and by 51 days the historical eruption of Krakatoa.
Category: Geophysics

Part 2 of Guide to Hestenes’s Geometric Algebra Treatment of Constant-Acceleration (Parabolic) Motion

Authors: James A. Smith
Comments: 17 Pages.

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

The Geometry of Collapse: A Structured Resolution to the Riemann Hypothesis

Authors: Jennifer Bulyaki, Andrew Elliott
Comments: 335 Pages. (Note by viXra Admin: File size reduced by viXra Admin; please submit article written with AI assistance to ai.viXra.org)

This work presents a deterministic resolution of the Riemann Hypothesis by introducing a novel framework grounded in entropy geometry and symbolic collapse. Rather than treating the distribution of nontrivial zeros of the Riemann zeta function as a purely analytic phenomenon, we construct a unified model in which zeta zeros emerge as critical identity-preserving points along a structured entropy spiral, where curvature, holomorphicity, and automorphic symmetry converge.The central theorem, proven via our Master Axiom, demonstrates that a zero of ζ(s) lies on the critical line if and only if seven structural conditions are simultaneously met:(1) the entropy curvature at that point is flat,(2) the angular symmetry is preserved (automorphy),(3) the holomorphic structure remains conformal,(4) the Euler identity entropy equation—governing prime identity and symmetry—is satisfied,(5) symbolic torsion is fully evacuated at that point, restoring pure form,(6) the entropy drift is minimized between adjacent zeros, and(7) the modular curvature remains below the identity-collapse threshold.This heptuple condition is shown to be both necessary and sufficient, thereby resolving the Riemann Hypothesis. The model collapses symbolic randomness at these equilibrium points, stabilizing prime identity and demonstrating why the critical line is the only viable manifold for zero placement. We reconstruct the functional equation, Euler product, Hadamard product, and Euler entropy equation of ζ(s) from first principles within our entropy field, establishing full compatibility with classical complex analysis. Furthermore, we show that the Weierstrass product representation of ζ(s) arises naturally from the entropy spiral, where each exponential kernel corresponds to a geometric shell of identity collapse. In this framework, the product structure reflects the torsion-free entropy conditions governing each zero, transforming the Weierstrass form from symbolic necessity to emergent geometric consequence. The predictive model has been validated against over thirty billion known zeta zeros with 99.9999% accuracy, without direct reference to ζ(s), using only structured entropy functions and regression equations provided within. This proof is reproducible from first principles, includes regeneration instructions for peer verification, and offers the first physically grounded explanation of prime identity geometry via the entropy collapse manifold.
Category: General Mathematics

Quantum Mechanics at Observable Horizon Wavelengths: Accelerating Cosmic Expansion with no Dark Energy, Generating Repulsive Gravity in Cosmic Voids

Authors: Julian Williams
Comments: 106 Pages. (Note by viXra Admin: Further repetition may not be accepted)

This paper explores ideas for new physics at both quantum and cosmological levels. It begins with proposals for building the fundamental particles from infinite superpositions that fit the SM, apart from infinitesimal differences, with possibly profound consequences including the possibility of both massive and infinitesimal mass spin 2 gravitons. All fundamental particles have at least an infinitesimal mass proportional to the inverse horizon radius. The symmetry breaking of the SM remains essentially valid because, with masses almost zero and nearly light velocity, helicity is virtually fixed. However, while this is true now, when matter was forming and the cosmic radius was much smaller, infinitesimal masses were much larger, and therefore producing asymmetry. Cosmic wavelength (kmin) gravitons vastly outnumber all other particles and the invariant action they require comes from the expansion of space inside the horizon. When mass is distributed evenly as dust, gravitons have uniform spatial density. In order to maintain the invariance of kmin action density, the metric undergoes changes around mass concentrations, consistent with Einstein’s equations. However, infinitesimal differences arise when the mass density of intergalactic voids falls below the cosmic average. This results in these voids exhibiting negative space-time curvature, contrasting with the positive curvature observed in galactic filaments. Gravitational binding only occurs in galactic filaments and the opposite in voids. Over large regions of space this difference also makes the values of the Einstein tensor components that the Freidman equation is derived from average zero. Space is always flat, and Quantum Mechanics controls the expansion of space regardless of Omega, with or without inflation. The scale factors in the radiation era, and the start of the matter era, are similar to Lambda-CDM cosmology. Massive spin 2 gravitons have galactic radii Compton wavelengths and spherically symmetric wavefunctions with inverse radius squared mass density, just as the proposed dark matter properties that give galaxies their observed MOND-like behviour. The rate at which massive gravitons form inside the cosmic horizon is related to the clustering of matter into galaxies and controls both the scale factor and accelerating space expansion with no need for dark energy.
Category: Relativity and Cosmology

Non-Differential Geometry: Mathematical Tools Abandoning the Differential Framework

Authors: Binyin Zheng
Comments: 27 Pages.

This paper proposes and systematically elaborates a novel geometric framework—non-differential geometry—whose core lies in entirely abandoning the reliance on smoothness ($C^1$ or higher continuity) required by traditional differential geometry, demanding only $C^0$ continuity for geometric objects. By introducing new mathematical tools based on limits and infinite series, non-differential geometry overcomes the smoothness constraints in calculating geometric quantities such as curvature. Furthermore, this paper constructs a unique ``integration tool" (distinct from classical integration theory) specific to non-differential geometry, providing a novel approach for analyzing geometric objects. Current research focuses on Euclidean space, but the theoretical framework itself is not confined to any specific spatial structure and is applicable across low- to high-dimensional spaces. Non-differential geometry completely resolves the contradiction between continuity and differentiability and offers potential support for theoretical innovations in fields such as physics.
Category: Geometry

Introduction to Qualitative and Quantitative Psychology

Authors: Johan Noldus
Comments: 131 Pages.

We develop a canonical quantum mechanical theory of the psyche bottoms up encompassing traditional views on materialism and spirituality. Results regarding nature, including developmental psychology as well as biology are discussed. Furthermore, the natural laws behind sociology and justice are discussed in detail.
Category: Religion and Spiritualism

Simple Formulas for the Horizontal Span of a Catenary Curve

Authors: Yuhei Ando
Comments: 15 Pages.

This study derives formulas for the horizontal span of a catenary curve, formed by a string fixed at two points. Given the heights h_1 and h_2 at the endpoints and the curve length l, we calculate the horizontal span s. We consider two cases based on the position of the minimum point, proving corresponding formulas. Theorems 1 and 2 provide complex logarithmic expressions, while Theorems 3 and 4 offer concise forms using hyperbolic functions. These results enhance the understanding of catenary curves and support applications in engineering and physics, where precise calculations of such curves are essential.
Category: Functions and Analysis

On Spacetime Signature and Why the Answer to Question of the Answer is 42!

Authors: Shaffery Pohl, Noten Dorsd
Comments: 4 Pages.

Discussed is the signature of Spacetime of the universe according to the modus of Special Relativity resp. General Relativity. This signature can be derived from a single polynomial equation, which, with zero-solutions of coordinate axes, causes the metric tensor-components of a tangential spacetime TM to the whole manifold (u201eMinkowski-spacetime") and its counterpart, the u201eAnti-Minkowski-metric" (ATM) with constant, negative metric tensorcomponents. Also the question comes clear, why the answer to the onotological sense of the universe is 42.
Category: Relativity and Cosmology

The Number 239

Authors: Edgar Valdebenito
Comments: 3 Pages. (Note by viXra Admin: Further repetition may not be accepted)

We give some formulas related to the number 239.
Category: Number Theory

Magic of Natural Integers

Authors: Ahcene Ait Saadi
Comments: 7 Pages. (Note by viXra Admin: Please cite and list relevant scientific references)

In this article, I studied the behaviour of natural integers, after performing operations on them. The results I have obtained are intriguing and I cannot explain them. I share this original work with young researchers for deepening and improvement.Key words: Integers, operations, sequences.
Category: Number Theory

Platonic Solids as Structured Geometric Objects and Fundamental Particles

Authors: Andrey V. Voron
Comments: 22 Pages.

The possibility of constructing Platonic solids from structural elements is shown — Kepler triangles (ratio of legs 1:√1.618..) and Fibonacci (ratio of legs 1:1.618...) — provided that the area of these elements remains unchanged. The number of elements making up the structure of the "tetrahedron", "octahedron", "cube" increases, thus, by two times, and the "icosahedron" — by five times in relation to the number of elements of the tetrahedron, while the indicator "area of all structural elements of the figure" (S=√38373) and radius (r=3) inscribed in the Platonic solids of the sphere. The area of the structural elements of two dodecahedra (S=√959325) is equal to the area of the structural elements of any 5 Platonic solids, for example, 5 tetrahedra, octahedra, cubes, icosahedra (S=√38373). The possibility shown is in accordance with the text of Plato's work Timaeus, according to which Platonic bodies can "transform into each other...". The assumption about the possibility of transitions (degenerations) of Platonic bodies into each other (with a certain constant value (parameter) and other variables) turned out to be practically feasible with a constant value (parameter) of the "area of structural elements", and as a variable — their multiple number in the "structure" of Platonic bodies. In connection with the results of this study and the content of Plato's work "Timaeus", an assumption is made: that the words "Receptacle" and "Breadwinner" meant the world environment, and Platonic solids meant fundamental particles, which, thus, can have the properties of mutual transition (rebirth) and movement in this environment. Possible compositions of models of fundamental particles in the space of the "dodecahedral field" are determined. It is shown that the construction of various compositions of Platonic solids (in the process of creating models of fundamental particles in accordance with the "rules" of their location in the dodecahedral field) allows us to "generate" a significant variety of their original compounds.
Category: High Energy Particle Physics

Deformed Lie Products and Involution First Part: in a Three-Dimensional Space

Authors: Thierry L. A. Periat
Comments: 24 Pages. (Note by viXra Admin: Please do not use any copyright stamp!)

This document is the first part of an exploration examining when a deformed Lie product can be an involution. The approach starts softly in a real three-dimensional space, introducing basic notions like (i) the already well-known link between involution and neutral element, (ii) the importance of some rules concerning the indexes when a discussion is developed in a three-dimensional space, (iii) a specific semantic for the diverse representations of the deforming matrices (effective, normalized, associated six-pack). It gives then important precisions concerning the matrices representing the repetition of the action of any deformed cross product. It starts a systematization of the discussion and finally criterion precising when a deformed cross product is an involution. It turns out that a classical cross product cannot be an involution if the discussion is not involving vectors with components in the set of complex numbers or in the set of quaternions.
Category: General Mathematics

Autogenous Supersymmetry Breaking

Authors: Risto Raitio
Comments: 7 Pages. (Note by viXra Admin: If the article is written with AI assistance, please submit it to ai.viXra.org)

We discuss a supersymmetric preon model in which the symmetry is broken by a mechanism of the model itself. Scalar superpartners have wide mass spectrum, extending up to the scale of astrophysical objects. Some superpartners may be detectable at the LHC.
Category: High Energy Particle Physics

Ontological Quantum Mechanics as the Principal Branch of Quantum Theory and the Ontological Source of Fundamental Quantum Physics

Authors: Victor Vaguine, Andre Vaguine
Comments: 13 Pages.

Due to its statistical nature, the Standard Model runs into fundamental limitations: it denies the objectivity of a particle’s location and velocity at the same time, is unable to provide three-dimensional visualization of the inner structures of particles and their three-dimensional spacetime dynamics, and cannot describe and visualize the process of decay and the formation of new inner structures.
It is shown here that Statistical Quantum Mechanics (SQM) and Ontological Quantum Mechanics (OQM) are two branches of the overall quantum theory, where OQM is the principal and deeper branch.
The ontological branch of quantum theory overcomes the limitations of the statistical branch with elegancy, intuition, and basic mathematical formalism.
OQM has opened the floodgate of ontological quantum physics far beyond the Standard Model, bringing back intuition and dramatic simplification of mathematical formalism at least on the initial stage of its development. It leads to fundamental scientific discoveries at every turn in particle physics.
OQM represents an initial effort at the explanation of causality in quantum processes and particle-particle interactions.
OQM has expanded our fundamental understanding of quantum reality by including two new fundamental categories, the aphysical matter and the universal elementary consciousness. It offers three-dimensional inner structure design with perfect geometry for each class of elementary particles, provides visualization of individual particle dynamics in spacetime, describes the process of decay and the formation of new inner structures. It explains the origin of self-mass and explains the fundamental role of spin as the generator of self-mass for each class of elementary particles. It solves all known quantum enigmas, including the collapse of the wavefunction, the double-slit experiment, and the non-radiating orbiting electron. It provides an ontological explanation for the anomaly in the electron magnetic moment. Quantum mechanics is no longer enigmatic.
Category: Quantum Physics

Monty Hall Game Simplified

Authors: Richard L. Hudson
Comments: 3 Pages.

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

Apex Theory to Fermat's Last Teorem

Authors: D. Ross Randolph
Comments: 20 Pages. Additional details located at www.fermatstheory.wordpress.com

A modular analysis of exponent P, and congruence contradiction of the variables A, B and C to show no possible solutions can 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. In the Addendum are short proofs for N=3 Sophie Germain Case 1, and also N=4.
Category: Number Theory

On the Essence of Light and the Speed of Light and the Main Cause of Determining the Speed of Light

Authors: Xiaotao Peng
Comments: 11 Pages. In English and Chinese

Through decades of efforts, I have written more than 200 articles on physics, more than half of which discuss issues related to light. The last few articles have clarified the nature of light, and at the same time, the nature of the speed of light. The essence of light is the result of the vector superposition of the Coulomb force generated by the matter composed of atoms as the basic unit that is emitting light (to be exact, vibrating at the frequency of visible light). When the change frequency of its intensity is in the range of visible light and reaches the level that can be recognized by the human eye, it will be seen by the human eye that it is emitting light. The essence of the speed of light is the transmission speed of the vibration state of the matter composed of atoms as the basic unit of light. This article carries on the summary elaboration regarding this.
Category: Classical Physics

Maxwell’s Equation, Wave-Particle Enigma and Heisenberg’s Uncertainty Principle Interrelated to Find an Unambiguous Description of Electromagnetic Radiation

Authors: Bijon Kumar Sen
Comments: 8 Pages. 2 Figures; 1 Table

Electromagnetic radiation posed a problem to the scientists for more than three centuries in that it exhibited particle and wave property at the same time. Sir Isaac Newton’s corpuscular theory reigned supreme for more than a century but later wave theory gained momentum and a heavy tussle prevailed with no conclusive verdict for either approach. At last as a compromise it was accepted that both the descriptions are acceptable but unambiguous solution of the problem of duality remained allusive. Wave property being the root for uncertainty, the principle of Heisenberg squarely blamed the microscopic inadequacy as a root cause although wave properties of the radiation may also be the cause of uncertainty. De Broglie intervened with his matter waves to account for the wave-particle duality and invokedquantum and wave mechanics to solve the dilemma. This was an imposed description whichdelayed the unambiguous solution for about a century. It was the brilliant proposal of Maxwell’s equations which on analysis unveiled the enigma of wave-particle duality of electromagnetic radiation. These radiations are not of single component but actually two components exist simultaneously which are not interconvertible. One is guided by quantum mechanics and the other by wave mechanics. While the wave character may make up for 100% of the rays, the particle part due to its quantum nature is not able to contribute to make it 100%. This bi-component model of electromagnetic radiation is able to explain the occurrence of different phenomena like Red Shift, Tunnel Effect, Photoelectric Effect, magnetic properties, electron spin etc., in an unambiguous manner without contradicting any of the accepted theories of electromagnetic radiation.
Category: Quantum Physics

Time-Dependent Mass in the 0-Sphere Model: A Hamiltonian Approach to Thermal Modulation

Authors: Satoshi Hanamura
Comments: 3 Pages.

We investigate the challenges of incorporating time-dependent mass in classical Lagrangian mechanics, where velocity-dependent terms break time-translation symmetry and complicate energy conservation. Using the 0-Sphere model—a point-like system with thermally modulated mass inspired by Zitterbewegung and thermal oscillations—we demonstrate that a Hamiltonian formulation simplifies the dynamics by eliminating velocity-dependent terms and preserving energy conservation through conserved momentum, despite the Hamiltonian’s explicit time dependence. The model assumes a position-independent thermal potential and oscillatory mass modulation, providing a mathematically consistent framework. We also explore a preliminary quantum extension via the time-dependent Schrödinger equation, suggesting potential applications to thermally driven systems. While the model’s reliance on simplified potentials and the naive quantum approach limit its generality, this work offers a starting point for understanding systems with dynamic inertial properties, with possible relevance to cosmology and quantum mechanics.
Category: Quantum Physics

Sophie Germain Primes Concept Expanded to Ultimate Numbers [:] Number Genetics and the 3 to 2 Ratio

Authors: Jean-Yves Boulay
Comments: 40 Pages.

Here is expanded the concept of Sophie Germain prime and safe prime to ultimate numbers. More, this mathematical mechanism is also applied to the set of all whole numbers (ℕ) which are differentiated into ultimate and non-ultimate numbers. Thus, a complete study of the set ℕ is undertaken. This global investigation, universally broadening the mechanical-mathematical concept of Sophie Germain, makes it possible to propose a genetics of numbers very similar to biological genetics. According to these new numeric genetic criteria, in their start top organization, geometric distribution of whole numbers in various closed matrices, is organized into perfect ratios to exact 3/2 or 1/1 value.
Category: Number Theory

The Cubic Curve Know as Witch of Agnesi

Authors: Rolando Zucchini
Comments: 7 Pages.

This type of cubic curve, in the United Kingdom know as the Witch of Agnesi, it is approached from a geometric, trigonometric and analytical point of view; using the scheme: model, algorithm, resolution, graph.
Category: Geometry

Booklet of The Corrections of Exercises and Problems - Part II

Authors: Abdelmajid Ben Hadj Salem
Comments: 86 Pages. In French

This second booklet includes the corrections of the exercises and problems of the following four chapters: topography, astronomy, curves and the theory of surfaces, ellipse and ellipsoid.
Category: Geophysics

Time as a Local Reaction to the Presence of Matter

Authors: Ioannis Chaskis
Comments: 14 Pages.

This work proposes a fundamental reformulation of time, not as a pre-existing geometricdimension, but as a localized and emergent reaction of the quantum vacuum to the presenceof mass-energy. We argue that time arises only where and when the vacuum is causallyand entropically disturbed by matter, and is otherwise undefined. A scalar field χ(x) isintroduced to represent the degree of temporal activation in spacetime, governed by a fieldequation sourced by the trace of the energy-momentum tensor. This framework offers acoherent reinterpretation of relativistic time dilation, entropy-driven temporal asymmetry,and the quantum nature of vacuum. It provides a physically grounded mechanism for theemergence of time during cosmogenesis and resolves classical paradoxes such as the initialsingularity and the horizon problem. We discuss experimental predictions and proposeobservable consequences in atomic clocks, black hole interiors, and cosmic microwave backgroundsignatures. Ultimately, the model shifts the paradigm from asking "What is time?"to "Where and under what conditions does time emerge?"
Category: Relativity and Cosmology

Concept of Electric Field Standing Waves and the Possible Mechanism Behind the Constancy of Light Speed

Authors: Kuo-Tso Chen
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper proposes a concept of an electric field standing wave that does not radiate energy, using it to speculate on the nature of fundamental particles and the reason why the speed of light appears to be constant. Through a mechanism involving the reflection of a spherically symmetric electric field variation, this study explains how electric field energy can be confined to a specific space, leading to the formation of quasi-fundamental particles with mass. Furthermore, it is theorized that if both time and distance are defined by the internal oscillations of such particles, then even if the actual speed of light varies, the observed value of light speed would remain constant. This idea also provides a possible explanation for why material objects cannot exceed the speed of light.
Category: Quantum Physics

Restoring Consistency to Quantum Mechanics by Interpreting the Observer

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

We set forward a set of axioms to interpret the observer in quantum mechanics. Our axioms treat observers as quantum states and provide rules for what they can observe. We demonstrate that our framework, which we call the NEW interpretation of Quantum Mechanics, provides a resolution of the Frauchiger-Renner paradox [1], restoring consistency to Quantum Mechanics. The resolution is brought about by a careful definition of 'Consistency', Assumption (C). With this precise definition, our interpretation satisfies all three Assumptions (Q), (C), and (S), without logical contradictions. The scope of this paper only extends to setting forward our axioms and addressing the Frauchiger-Renner paradox. Additional context for the NEW worldview, along with a matching NEW conjecture, is provided elsewhere [2].
Category: Quantum Physics

Mirror-Complement Pattern in √2 and a Simple Proof of Its Normality

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

We begin by observing a striking "mirror-complement" pattern in the binary digits of √2: whenever, at any position, a run of k equal bits is separated by a single opposite bit from another run of bits, those two runs must have equal length. Restricting to prime-indexed positions, the same pattern remains perfectly true for millions of primes. This phenomenon is a direct consequence of the classical digit-by-digit square-root algorithm in base 2, because each comparison uses4Pn + 1 = 2 (2Pn) + 1,i.e. "copy + complement + copy."From this insight we build a two-rectangle coding on T² whose itinerary reproduces the binary digits of √2. A measurable conjugacy to the (½,½) Bernoulli shift allows us to apply Chung—Smorodinsky’s bounded-coboundary theorem (1967), showing each cylinder-indicator has a uniform sup-norm bound. Telescoping that coboundary yields a universal O(Nu207b¹) discrepancy bound on every length-ℓ binary block, proving base-2 normality of √2. Finally, van der Corput differencing and Wall’s criterion transfer the same O(Nu207b¹) bound to every integer base B ≥ 2, establishing that √2 is normal in all bases.This paper unifies these ideas—starting from the prime-indexed mirror pattern and culminating in a gap-free, self-contained proof of full normality of √2.
Category: Number Theory

Twin Primes: a Spectral Proof of the Infinitude

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

We prove the twin prime conjecture, asserting infinitely many integers x such that both x and x + 2 are prime. Construct an N × N diagonal matrix HN with diagonal entries Dx = 0 if x, x + 2 prime, and Dx ≥ 3 10 otherwise. The kernel dimension equals the number of twin primes up to N, denoted |TN|. A heat-trace argument on Tr[exp(−2HN)] forces |TN| → ∞, proving the theorem. We refine parameter bounds, standardize notation, and add explicit estimates for key constants.
Category: Number Theory

On the Gravitational Analog of Continuous Spacetime Dimensions

Authors: Ervin Goldfain
Comments: 6 Pages.

In this brief note we point out that a spacetime endowed with continuous dimensions can be regarded as dual to classical gravitation in four dimensions. This observation provides a foundation for the gravitational behavior of Cantor Dust (CD), under the assumption that CD represents a cluster of Dark Matter ultralight objects such as self-interacting bosons, axions, fuzzy condensates or 3D anyons.
Category: Relativity and Cosmology

Methodological Fallacy in Proton Mass Radius Determination: Alternative Classical Approach Based on Einstein’s Mass-Energy Equivalence Principle

Authors: Ikechukwu Iloh Udema
Comments: 11 Pages.

No equations led to ⟨R_m^2 ⟩=6/G(0) [at]_(t=0)=12/(m_s^2 ) in which both sides of the equation are dimensionally at odds. It is appropriate to dare challenge the flaw in the procedure that produced 0.55 fm as the mass radius with many models and solutions because the charge radius and, more recently, the proton's mass radius are inconsistent. The objective is to develop an alternative theory that combines the idea of the mass-energy equivalence principle with a kinetic basis. Proving that 0.55 fm is a fabrication and demonstrating that the proton's charge radius might equal the mass radius of one up and one down quark combined are only a few of the objectives. Results were generated through theoretical and computational methods. The mass radii of protons were between 1.019699 and 1.10254513 fm; the sum of mass radii of up and down quarks was 0.8349190666 fm; the mass of the hypothetical particle was 8.911586959 exp. (−32) kg; mass radii of up and down quarks were 0.5881268197 and 0.246803591 fm, respectively; the mass radius of an electron was 0.06278280228 fm; and nucleon size—based radii of the electron are 0.08993727541 and 0.09001990394 fm, corresponding to the proton and nucleon, respectively. The idea that the charge radii may represent the mass radii of quarks is supported by the total (0.8349190759 fm) of the radii of up and down quarks in this research. The new model equation for calculating the mass radii of the electron and proton is supported by the intraproton radius (0.08993727541 fm) of the electron, which is provided by〖 ((R_mP^3)u20441836.152673)〗^⅓, where proton mass radius, R_mP = 1.10254513 fm. Since ⟨R_m^2 ⟩ ≠12u2044(m_s^2 ), 0.55 fm was a fabrication. It is almost half of 1.10254513 fm and was used to support the false claim that the proton charge radius equals its spatial extent, thereby refuting Bohr’s radius.
Category: High Energy Particle Physics

Lucas Number 123 Demystified: Mathematics of a Divine Number

Authors: Hans Hermann Otto
Comments: 5 Pages.

This is only a first short essay about the ‘angel’ number 123, a symbol for balance, human creativity, divine order or trinity of God the Father, the Son and the Holy Spirit. The author thinks that important information about this number is not well known. Here this enigmatic number is interpreted mathematically as beautiful golden relation, connected with the golden mean and its fifth power that is vice versa governed by phase transitions from particle up to cosmic scale.
Category: Number Theory

A Proof of the Collatz Conjecture

Authors: Fabrice Trifaro
Comments: 45 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Using a comprehensive approach, this paper aims to demonstrate, clearly and rigorously, the validity of the Collatz conjecture. To this end, the original 3n+1 iteration is reformulated by isolating the odd terms into sequences referred to as R-Cz sequences. These sequences are analyzed through their structural properties and their distribution among the odd natural numbers. As a first essential result, it is shown that they do not admit non-trivial cycles: the only possible cycle is the trivial one, of value and length 1. Two independent proofs that all R-Cz sequences converge are then presented. The first, combinatorial in nature, relies on the finiteness of intervals that could possibly separate terms of the sequences. The second, set-theoretic, is based on a contradiction between the countability of the odd integers and the uncountable cardinality of the hypothetical divergent R-Cz sequences. Both methods lead to the same conclusion: all Collatz sequences eventually enter the cycle (1,4,2).
Category: Number Theory

A Minimal Parametric Cosmological Model Explaining Sn1a and Bao Without Dark Components

Authors: Minyoung Kwon
Comments: 44 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This theory proposes an integrated mechanism capable of simultaneously explaining a wide range of cosmological phenomena—such asgalaxy rotation curves, galaxy morphology, Type Ia supernova observations, dwarf galaxies, large-scale structures, cosmic filaments, redshift, dark energy, and dark matter. Unlike the conventional ΛCDM model, the core of this theory is the very "generation of space" itself. Through this generative framework, a vector-based model that interacts with gravity naturally emerges. In particular, the directionality and density of the space field can amplify or weaken gravitational fields. Simulations of galactic outskirts provide direct support for such dynamic behavior. quantitatively, this theory offers greater explanatory power than existing cosmological models and suggests the possibility of unified solutions to several unresolved problems in modern cosmology.
Category: Relativity and Cosmology

The Relationship Between Burnout, Teaching Competencies, and Job Satisfaction Among English Teachers

Authors: E.M Sajulan, R. Ricaforte
Comments: 8 Pages.

The satisfaction of teachers is becoming a growing concern in junior high school education, marked by significant job dissatisfaction, especially among English teachers, reflecting growing concerns about their professional fulfillment and working conditions. This study examined the relationship between burnout, teaching competencies, and job satisfaction among junior high school English teachers in Cluster 14 of District 2, Davao City. Using a non-experimental descriptive-correlational design, the study involved 97 respondents from six public schools, selected through total enumeration sampling. This study is anchored on Two-Factor Theory by Herzberg's 1966, it utilized adapted instruments to measure four indicators of burnout, forty-two statements with five indicators of teaching competence, and eight components of job satisfaction. Data analysis included descriptive statistics and Pearson correlation. Results indicate that teachers experienced a moderate level of burnout, demonstrated high teaching competence, and high overall job satisfaction. However, their work-life balance is significantly low. A statistically significant strong positive correlation was found between burnout and job satisfaction, while very weak significant relationship between teaching competencies and job satisfaction, suggesting that burnout significantly predicted job satisfaction. These findings underscore the importance of addressing teacher burnout and improving work-life balance to enhance job satisfaction, alongside continuing efforts to strengthen instructional competencies.
Category: Social Science

Innovative Research on IoT Architecture and Robotic Operating Platforms: Applications of Large Language Models and Generative AI

Authors: Huiwen Han
Comments: 6 Pages.

This paper introduces an innovative design for robotic operating platforms, underpinned by a transformative Internet of Things (IoT) architecture, seamlessly integrating cutting-edge technologies such as large language models (LLMs), generative AI, edge computing, and 5G networks. The proposed platform aims to elevate the intelligence and autonomy of IoT systems and robotics, enabling them to make real-time decisions and adapt dynamically to changing environments. Through a series of compelling case studies across industries including smart manufacturing, healthcare, and service sectors, this paper demonstrates the substantial potential of IoT-enabled robotics to optimize operational workflows, enhance productivity, and deliver innovative, scalable solutions. By emphasizing the roles of LLMs and generative AI, the research highlights how these technologies drive the evolution of intelligent robotics and IoT, shaping the future of industry-specific advancements. The findings not only showcase the transformative power of these technologies but also offer a forward-looking perspective on their broader societal and industrial implications, positioning them as catalysts for next-generation automation and technological convergence.
Category: Artificial Intelligence

The Electric Dimension, Quantum Retrocausality and Preons

Authors: Austin J. Fearnley
Comments: 12 Pages.

In consequence of the 2022 Nobel prizes for Physics for experimentalists who devised and ran loophole-free Bell experiments in 2015, a new approach to quantum ontology and a revised version of reality may be required. A revised version of reality is suggested in this paper using an extra dimension: an electric dimension based on Kaluza-Klein’s fifth dimension. Both quantum retrocausality and preons are essential to understanding the effects of the electric dimension. Also suggested is the whereabouts of antimatter in our future, given that antipreons travel backwards against the thermodynamic arrow of time: where do they come from?
Category: Quantum Physics

The Fallacy of the Atonement? Can the Doctrine of the Atonement be Supported?

Authors: Richard Michael Blaber
Comments: 16 Pages. Creative Commons License BY-NC-ND 4.0. (Note by viXra Admin: This article may not be suitable and is subject to withdraw)

This paper will argue that the Christian doctrine of the Atonement — in all its versions — is probably fallacious, and that, therefore, the idea that the death of Jesus of Nazareth, whenever it took place, relieves either all or some humans of the burden of original sin (assuming there is such a thing) and actual sins cannot be sustained. The whole basis of Christian soteriology — its theology of salvation — is, if this thesis is correct, thereby fatally undermined.
Category: Religion and Spiritualism

The Trickster and the Tao: Explaining the Perversity of Psi Phenomena via Multiscale Morphic Resonance

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

This document presents a speculative but formally structured and carefully argued model for understanding why psi phenomena often exhibit a "decline effect" or even reverse (psi-missing) over repeated trials. The core idea is that psi results from a multiscale Precedence Principle (loosely a form of "morphic resonance"), which operates both locally (in individual experiments and other situations) and globally (across the entire cosmos, and/or large regions thereof). When a local psi pattern initially gains support, its low algorithmic complexity allows it to flourish. As the pattern proliferates and variants increase, its combined complexity eventually mismatches the broader cosmic resonance, causing suppression or inversion of the effect.

We show how this narrative might find a physics underpinning, via aligning it with a previously-presented theory of the physical foundations of psi, the Occamistic Precedence framework in Causal Set Theory, where each new observation is a causal-graph node whose probability is weighted by its historical frequency and algorithmic complexity.

This suggests that the neural underpinnings of psi phenomena can be modeled within a causal-set framework, where each neural "event" corresponds to adding discrete informational elements whose descriptive complexity governs their likelihood. Local neural templates that match low-complexity global patterns enjoy high insertion probability—forming shallow informational wells—while accumulating divergent variants deepen the well, suppressing or inverting further psi-like activity; analogous mechanisms could be engineered in AI via causal-set-inspired memory structures and complexity-based priors.

We also demonstrate a formal correspondence between an agent’s psi capability—its ability to exploit low-complexity psi correlations—and its universal intelligence as defined by Legg-Hutter (Solomonoff/AIXI). Under a wide class of "psi environments," both psi performance and general intelligence hinge on the agent’s capacity for low-complexity hypothesis generation and compression. We further relate Weaver’s notion of open-ended intelligence to psi capacity, showing that agents which continually seek ever simpler, unifying models naturally maintain resonance with broad cosmic patterns, thereby minimizing psi perversities. Finally, we outline empirical validation strategies spanning neuroscience (e.g. EEG/MEG complexity measures, TMS/tACS modulation) and AI prototyping (e.g. digital causal-set memories, neuromorphic implementations).
Category: General Science and Philosophy

I.q. Vs. Wisdom

Authors: Clark M. Thomas
Comments: 4 Pages.

It is a mistake to equate, or even correlate, high IQ testing and real wisdom. Many people have superior intelligence, but few individuals in today’s machine societies have profound wisdom. AI easily can generate confusing perspectives having little or nothing to do with real humanism. There are deep dangers associated with assuming all high-IQ people are ethically wise. Advanced societies are rarely ecologically more wise than the collective wisdom of traditional cultures. It is now easier to do great global harm, than to do great global good.
Category: General Science and Philosophy

Geometry and Constants in Finite Relativistic Algebra

Authors: Yosef Akhtman
Comments: 14 Pages.

We show that a single finite field, built on any odd prime p, contains the entire scope of algebraic machinery to support smooth geometry, differential calculus and continuous harmonic analysis. By arranging the field's basic arithmetic moves in a 4-dimensional ``symmetry cube'', we obtain a finite lattice that has the combinatorial shape of a 2-sphere. Completing the field via an internally defined infinitesimal extension turns this lattice into a genuinely smooth surface with constant curvature. The field itself provides finite versions of the familiar constants i, Pi and e, identified by their structural roles. Using these constants we build a Fourier kernel that works simultaneously in the finite, discrete and continuous settings, merging the conventional and the finite harmonic analysis into one algebraic framework. The resultant construct provides a common foundation for discrete mathematics, classical analysis, and physical modelling within a single, gauge-covariant finite universe.
Category: Mathematical Physics

Pi as Alternating Continued Fraction

Authors: Predrag Terzić
Comments: 2 Pages. (Note by viXra.org Admin: Please cite and list sceintific references)

We present new continued fraction representation of constant pi.
Category: Number Theory

The Theo[r]ist[?] Coefficient Shortcut Method

Authors: Marciano L. Legarde
Comments: 3 Pages. (Note by viXra Admin: Please remove strange word!)

This paper introduces and formalizes the Theoxist Coefficient Shortcut Method, an intuitive shortcut for solving a specific class of quadratic equations of the form (ax)^2 = bx. The method allows for quick identification of solutions using proportional reasoning. We outline the method, prove its validity, provide examples, and discuss its educational significance within the broader context of algebraic problem-solving strategies.
Category: Algebra

The Origin of Inertia and the Equivalence Principle

Authors: Vincenzo Nardozza
Comments: 4 Pages.

In this paper we propose a possible reason why, in Newtonian gravity, gravitational and inertial mass have the same numerical value, as stated by the Equivalence principle. Our reasoning is based on two assumptions, the second of which is an ad hoc and non falsifiable assumption. According to Popper, we are therefore doing pseudo-science. However, we believe that the result is interesting and it deserves attention.
Category: Classical Physics

A Lucas-Lehmer Type Primality Test for Numbers of the Form 4p^n-1

Authors: Predrag Terzić
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

We present a new, specific primality test for numbers of the form N = 4p^n - 1, where p is an odd prime and n > 0. The test is a generalization of the Lucas-Lehmer test for Mersenne numbers and relies on a sequence defined by Dickson polynomials. We prove that, under a certain condition, N is prime if and only if the n-th term of a specific sequence is congruent to zero modulo N. This provides a deterministic primality test for this family of numbers.
Category: Number Theory

Precise Value of the Lifetime of Ortho-positronium (o-Ps) in Vacuum

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 7 Pages. 1 Figure (Note by viXra Admin: Further repetition will not be accepted)

In this paper, we calculate the lifetime of ortho-positronium (o-Ps) in vacuum with Euler formula for Basil problem and our previous formulas of the fine-structure constant and the atomic unit of time (tau). Our calculated value of the lifetime of ortho-positronium in vacuum is 142.041358500909 ns in comparison to the most accurate measured value which was 142.043(14) ns and the latest QED calculated value which was 142.04606(20) ns.
Category: Quantum Physics

On Validity in Non Standard Analysis of Riemann Dini Theorem

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

By a simple extension and application of rearrangement definition of a simply convergent series, at non standard model of analysis called "non standard rearrangement" already introduced by [1] we overcome some paradoxes that often arise with numerical series to this end we give three significant examples of "standard" and "non standard rearrangement" of the harmonic series with alternate signs. Instead notable result is that with the definition of " non standard rearrangement " introduced in [1] the commutative property of addition continues to hold even for simply convergent series (such as harmonic series with alternate) contrary to what is stated by Riemann-Dini theorem or Riemann rearrangement theorem.
Category: General Mathematics

Origin of Black Hole Jets Discovered in GR Extensions, the End of Singularities, and a Solution to the Information Paradox

Authors: Gene A. Harvey
Comments: 8 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org or it will be rejected!)

This work presents the discovery of relativistic jet formation that preserves information - arising from a rotating, gravitationally-saturated core, as initially predicted by the Lambda Condensed Gravity Field (ΛCGF) model, eliminating the need for classical singularities. Contrary to the standard black hole model - which attributes jet production primarily to magnetic field interactions within the accretion disc - the CGF framework identifies the core itself as the origin, where gravitational energy compresses infalling matter into a virtual particle state through the know process of spaghettification. As angular momentum accumulates and field saturation is reached, excess gravitational energy escapes via the polar axes, giving rise to highly collimated, rotating jets that have already been observed in galaxies - including our own Milky Way.Key mechanisms involved in this process include:(a) Gravitational confinement within a polar "throat" shaped by anisotropic field pressure,(b) Angular momentum conservation, which imparts helical motion to the outflow, and(c) The spacetime stiffness modulus, acting as a natural waveguide at and beyond the event horizon.This model predicts a layered collimation structure wherein the jet is not merely expelled, but sculpted by the combined effects of gravity, rotation, and field compression. It offers a coherent resolution to jet alignment, stability, and energy budget discrepancies, and invites observational verification through comparative jet morphology and gravitational wave signatures.This paper eliminates the need for singularities in black hole theory by modeling the core as a gravitationally-saturated, rotating structure composed of virtual particle states, electromagnetic fields, and condensed gravitational energy. Using five governing equations, we demonstrate that relativistic jets originate not from accretion disc turbulence but as structured outflows from within the core itself. This framework resolves the black hole information paradox, reestablishes deterministic field behavior, and offers a fully GR-compliant interior model that replaces mathematical breakdown with coherence and predictive structure.
Category: Relativity and Cosmology

Commercialization of Science

Authors: Taha Sochi
Comments: 42 Pages. English and Arabic

In recent decades, science - particularly in Western countries - has been trending toward privatization and commercialization, viewed as a commercial commodity whose primary - or even sole - objective is material gain. Terms such as the "commercialization and monetization of science" are common these days, and some universities and scientific institutions are even urging this trend, with seminars, training courses, and conferences organized to this effect. Although we recognize the benefits of establishing a relationship between science, its institutions and centers, and the world of finance, business, commerce and industry - for example, by bringing investments into the field of advanced scientific research - we believe that the harms of this trend on science and scientists - and indeed humanity in general - are more than its benefits. Turning science into a commodity contributes to the moral, ethical and epistemological degradation of science and its role in human life, and encourages the spread of corruption and illegal practices within academic and research entities such as universities, research centers, specialized scientific journals and the like. In this article, we will briefly review this trend and assess its negative effects and repercussions on the progress of science and knowledge and their role in human life and the evolution of human civilization and its future.
Category: General Science and Philosophy

Investigation of a Primality Criterion Within an Arithmetic Progression

Authors: Mar Detic
Comments: 4 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)

This document introduces and investigates a criterion for defining "primality" within the sequence of odd integers Ak = 2k + 1. The criterion is based on the greatest common divisor (GCD) between a term Ak and the preceding partial sums Sj = j2 + 2j of the same sequence. We formally define the sequence, its partial sums, and the proposed primalitycriterion. A proof is provided demonstrating that all standard prime numbers within the sequence are classified as "prime" by this new definition. Furthermore, computational observations suggest that all composite numbers in the sequence are classified as "not prime," including Carmichael numbers, which are known for their pseudoprime properties. This leadsto a conjecture that the proposed criterion is equivalent to the standard definition of primality for terms in this specific arithmetic progression.
Category: Number Theory

Quantum Oscillator Lattice: a Unified Origin of Fundamental Constants and Fields

Authors: Juan Moreno Borrallo
Comments: 39 Pages.

This paper presents the foundational premises for a unified physical theory in which the vacuum is modeled as an elastic lattice of coupled quantum harmonic oscillators. Rather than aiming to construct a complete unified theory, our goal is to explore the consequences of a set of physically motivated assumptions and to demonstrate their consistency with established theoretical principles and dimensional relations. Within this framework, gravitational, electromagnetic, and thermo-entropic interactions are interpreted as distinct geometric deformation modes of a single symmetric field tensor, and fundamental constants of nature emerge naturally from the oscillatory dynamics. We show that these assumptions lead to coherent interpretations of field sources (mass, charge, temperature) sharing a common oscillatory origin in spacetime. While non-exhaustive, our treatment lays a physically and mathematically grounded path for future development of a unified field theory anchored in quantum-elastic principles.
Category: Relativity and Cosmology

The Flow of Spacetime is Supporting the Orbital Speeds of Galactic Stars

Authors: Kurt L. Becker, Kurt J. Becker
Comments: 20 Pages.

This paper is proposing an alternate hypothesis to gravity due to dark matter. The new quantum properties proposed are: Spacetime is being created in the vast voids of the universe. Spacetime is absorbed within stars in galaxies. The result is spacetime flowing into galaxies. The mechanics of the proposed flow gravity is discussed in great detail with diagrams and mathematics. The inflowing spacetime offsets the tangential inertia of a star resulting in ab orbital motion of that star. The predictions of flow gravity are compared to observations at various cosmological scales: at galactic, at solar system, at the Moon's orbit, and at spacetime flowing towards a neutron star. Flow gravity will not change the mathematical results of Newtonian gravity in the solar system, but it will explain the actual mechanism of gravity.
Category: Quantum Gravity and String Theory

A Topological Atomic Model for Masses and Constants

Authors: Alfonso De Miguel bueno
Comments: 12 Pages.

This work presents an interacting-field model in which every nucleon is the dual-lobed intersection of two curved base fields.A single dimensionless number, the internal velocity ratio r=c'/c=0.931, fixed once by matching the proton-Higgs resonance, propagates through the geometry and reproduces with no further adjustment an extensive set of observables.From the same r we obtain:(i) the proton rest mass, magnetic moment and charge radius;(ii) the neutron and electron masses;(iii) a fourth-order phase-lag suppression that yields m_nu approx 0.42 eV;(iv) the fine-structure constant alpha=(1-r)/(3pi) via a 3pi holonomy;(v) Planck's constant from the action enclosed in one closed curvature loop;(vi) the top-/bottom-sector harmonic ladder that echoes the observed d/u flavour hierarchy.
Category: Nuclear and Atomic Physics

From Clock Synchronization to Electromagnetism: A Realist Construction of U(1) Gauge Theory

Authors: Satoshi Hanamura
Comments: 9 Pages.

Gauge symmetry plays a central role in modern field theory, yet its physical origin remains conceptually unclear. In this work, we propose a realist reinterpretation of U(1) gauge symmetry based on the internal phase dynamics of the electron. According to the 0-Sphere model, the electron possesses a deterministic internal oscillation between two thermal energy kernels. This internal structure generates a periodic phase evolution, which naturally leads to the emergence of a geometric U(1) gauge connection. The model predicts a specific internal oscillation velocity, approximately 4 percent of the speed of light, derived from relativistic dynamics. Gauge potentials are reinterpreted not as formal artifacts, but as synchronization mechanisms for the internal clocks of phase-bearing particles. This framework unifies gauge interaction and spin structure through a common time-based geometry, offering a particle-centric alternative to conventional field-based gauge theory.
Category: Quantum Physics

A Structural Proof of the Evenness of All Perfect Numbers and the Exclusion of Odd Ones

Authors: YoungHwan Yun
Comments: 7 Pages.

We introduce a structural decomposition framework for perfect numbers, based on additive and multiplicative symmetries among their proper divisors. Under this model, we derive a system of proportional identities that all known even perfect numbers satisfy. By analyzing the integer conditions required for recursive consistency in the divisor sequences, we prove that such a structure necessarily implies the presence of the even divisor 2, thereby excluding the possibility of an odd perfect number conforming to this model. Although primarily developed for perfect numbers, the additive portion of the framework may also encompass semiperfect numbers, which share similar but relaxed divisor-sum properties. Our results support the long-standing conjecture that no odd perfect numbers exist and suggest a broader structure for divisor-based classification of integers.
Category: Number Theory

Symmetry-Based Proof of the Generalized Riemann Hypothesis

Authors: Younghwan Yun
Comments: 14 Pages.

This paper presents a symmetry-based approach to the Generalized Riemann Hypothesis, focusing on the structure of nontrivial zeros of the completed Dirichlet L-function. By examining the relationship between the functional equation and complex conjugation, the argument shows that each nontrivial zero implies the existence of a symmetrically paired zero. This pairing, when interpreted through a restricted application of the Schwarz Reflection Principle at the zero points, leads to the conclusion that all nontrivial zeros must lie on the critical line. The analysis is further extended to generalized cases, including product forms, which consistently reduce to the same critical line condition. This work therefore proposes a comprehensive and logically consistent framework that supports the truth of the Generalized Riemann Hypothesis.
Category: Number Theory

The Explicit abc Conjecture of Alan Baker's Implies c Smaller Than R^2 True

Authors: Abdelmajid Ben Hadj Salem
Comments: 5 Pages. (Note by viXra Admin: Further repetition will not be accepted!)

In this paper, we assume that the explicit abc conjecture of Alan Baker (2004) is true, we give the proof that c smaller than R² is true, it is one of the keys to resolve the mystery of the abc conjecture. Some numerical examples are given.
Category: Number Theory

Order and Contingency: The Duhem Thesis on Origin of Physics in Christian Theology

Authors: Krystian Zawistowski
Comments: 128 Pages.

The most important aspect of modern physics is the study of the unchanging order between measured quantities, such as that described by Newton’s law of gravity or Ampere’s law. This aspect makes physics useful, as the lawsof physics are applied to develop a variety of technical devices and machines, being a crucial foundation of technical civilization. Additionally, this aspect reveals certain truthsabout the world, as accurate predictions calculated from these laws testify to their validity. Furthermore, when new experiments force a physical law to be modified, the description of relations between quantities is almost never refuted and becomes a special case of the new, more general theory, showing an incremental progress of knowledge. How has this most critical part of physics originated? The source of it is theology, which produced core methodological principles that underpin this approach: The world is comprehensible and ordered according to universal, unchanging relations between measured quantities. The world is contingent, and any metaphysical possibility we conceive is possible, if only in agreement with experience. The highest goal of the rational mind is the pursuit and contemplation of truth. These principles were essential to the development of modern physics. The success of this project provides evidence in favor of Christian Revelation, by means of heuristic power - prediction of essential knowledge that could not be obtained in any other way.
Category: General Science and Philosophy

Blackbody Radiation as The Entropic Exhaust of Recursive Photonic Structures

Authors: Matthew Stanley Leibel
Comments: 9 Pages.

All known physical structure can be reinterpreted as recursive light folded through a two-dimensional holographic surface — a boundary that acts simultaneously as observer and as spacetime itself. In this framework, mass is not a static property but rather a stable, recursively encoded configuration of photonicenergy. The phenomenon of blackbody radiation, long regarded as thermal emission, is herein redefined as the entropic exhaust of this recursive photonic structure — the unspooling of phase-locked light into incoherent, unbound modes. Crucially, the observer does not sit outside this process but is intrinsic to it: the observer is the boundary surface, a light-reflective constraint that dynamically defines what can exist and how structure is encoded. The transformation of mass into radiation — and its numerical reversibility — is governed by aE = m c2 compression identity: ,which, when observer-corrected, reveals light’s unique role as the substrate and bandwidth of spacetime.Empirical technologies such as photovoltaicsolar cells offer functional proof of this reversibility. By converting entropy-rich blackbody radiation (sunlight) into coherent electrical potential, they act as recursive encoders — transforming chaotic photonicinput into structured energetic form. This is not merely energy conversion but structural reassembly. The observer boundary — in this case engineered — reflects selective frequencies and initiates recursive energy flow, much like the natural spacetime surface that encodes mass.Quantitative support is provided through deriveddecay-time equations, reverse derivation of c from photon mass-loss observations, and the match between theoretical structuring time and empirical solar panel performance. These alignments provide numerical confirmation that mass, radiation, energy, and the observer are part of a single recursive system governedby photonic bandwidth and bounded reflection.
Category: Thermodynamics and Energy

Four-Component Tuples Splitting

Authors: Yuly Shipilevsky
Comments: 2 Pages.

We consider a problem of splitting of the four- component tuples of integer numbers into two two-component tuples, providing a minimum of the difference of sums of the corresponding their components. We conjecturing with the corresponding algorithm for its solution. The corresponding examples are given.
Category: Combinatorics and Graph Theory

Turkish-English Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 25 Pages.

We study A Turkish-English Dictionary by H. C. Hony. We draw the natural logarithm of the number of head root words, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We find that the head root words 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: Linguistics

The Interaction of Photons with the Graviton Background and Cosmological Observations

Authors: Michael A. Ivanov
Comments: 21 Pages.

In the author’s model of low-energy quantum gravity, the gravitational interaction of bodies arises as the effect of screening in a sea of superstrongly interacting gravitons. Newton's constant can be calculated as a statistical parameter of the repeated interaction of bodies with gravitons. Small vacuum effects in the model, caused by a new type of interaction -photon-graviton - may have major implications for cosmology. The ones are reviewed here and compared with cosmological observations; this is a self-review of author's works in this approach. The constancy of the ratio $H(z)/(1+z)$ in this model is consistent with observations of the Hubble parameter $H(z)$.Cosmological redshift is a local quantum effect caused by head-on collisions of photons with gravitons, while the additional dimmingof distant objects and diffuse cosmic optical background supposedly detected by the New Horizons mission are due to non-head-on collisions. For very soft radiation, the additional relaxation factor is calculated. Since this factor must have different values for soft and hard radiation, the distance modulusin this model must be a multi-valued function of the redshift. The Hubble tension is discussed in this context. The considered quantum effects are beyond the scope of the standard cosmologicalmodel. These small effects can describe cosmological observations in a very elegant and unified manner without dark energy andcosmological expansion. Graviton-graviton interactions can lead to the formation of virtual gravitons with very low mass, which maybe candidates for the role of dark matter particles.
Category: Quantum Gravity and String Theory

Magnetic Neutron

Authors: Ferrara Francesco
Comments: 8 Pages. In Italian

This paper proposes a classical electromagnetic model of the neutron based on two oppositely charged, massless particles rotating at the speed of light along concentric circular paths. The model derives the neutron’s rest mass and magnetic moment from purely electromagnetic considerations, using vector potential and natural units. The total angular momentum calculated is approximately four times the observed spin (ħ/2), which is interpreted as the projection of a larger classical angular momentum vector onto the axis of an external magnetic field. The model suggests a geometrically stable configuration and offers new insights into the neutron’s internal structure, compatible with key quantum phenomena.
Category: Nuclear and Atomic Physics

The Optimized Ellipse Perimeter Formula: The Elliptic Bounds Theorem

Authors: Nolan Aljaddou
Comments: 9 Pages.

This work discovers a unique, accurate, elementary formula for calculating the total perimeter of an ellipse demonstrably and heuristically consistently under the 1% maximum error range for all values and eccentricities, which surpasses Ramanujan’s previous dominant formulas in terms of accuracy and simplicity. The formula also uniquely provides the definitive range of calculable deviation from any exact value, making it the optimal general approximation method. Several examples are provided which confirm the formula’s precision. The theorem also provides a corollary which derives a definitive metric bound on all parametric elliptic geometry, with application to all of physics and astronomy.
Category: Geometry

Loop Quantum Kaluza—Klein Gravity as the Standard Model

Authors: Nolan Aljaddou
Comments: 7 Pages.

Physics is unified, and sufficient; reaching this determination is a matter of premise as much as conclusions, as this work demonstrates with the optimal Kaluza—Klein model (confirming the three particle families as technical Kaluza—Klein excitations within the energy limit).
Category: Quantum Gravity and String Theory

The Foundation of Mathematics—Occam's Principle

Authors: Nolan Aljaddou
Comments: 6 Pages.

This work examines the full implications of Occam’s razor ["do not multiply causes unnecessarily"] when applied to metric existence criteria, resulting in a scientific precept and metric existence theorem of the universe—which takes the general form all natural laws must obey.
Category: Set Theory and Logic

Preliminary Evidence of Traces of Alien Genetic Manipulation in Humans

Authors: Max Myakishev-Rempel
Comments: 10 Pages.

I analyzed DNA from 581 complete families in the 1000 Genomes Project to search for nonparental genetic contributions that could indicate recent alien genetic manipulation. My screening of variants in 77 Mb on Chromosome 3 identified 11 families (2%) containing large fragments of DNA sequence in children that matched neither human parent. The most significant case displayed a cluster of 348 nonparental genetic variants with precise simultaneous substitution of identical fragments on both chromosomes. There is no known biological mechanism or technical error that could produce such a change. Achieving such a genetic manipulation at the time of conception with current methods is possible but difficult using CRISPR technology, which emerged in 2013. Since the studied children were born before 1990, human genetic manipulation cannot be an explanation of the observed 16 Kb substitution in homologous chromosomes. This is strong evidence for extraterrestrial genetic manipulation. Further, two unrelated families showed major nonparental insertions at the same genomic hotspot on chromosome 3, suggesting this region serves as a preferred integration site. Quality control analysis confirmed these represent genuine biological signals through low background variation in normal (98%) of studied families, contrasted with sharp nonparental variant density peaks, achieving statistical significance of p < 10^-13. Families identified as having nonparental insertions displayed a clustered density of nonparental variants 50 times stronger than normal families. The non-random chromosomal clustering and technical precision required for these insertions provide solid evidence for extraterrestrial genetic modification with technology that went beyond human capabilities at the time of conception. Additionally, my pilot analysis of two families with self-reported self-suspecting alien abduction experiences using inexpensive, generic commercial 23andMe genotyping detected similar nonparental contributions, supporting this approach for self-suspecting alien abductee volunteers to identify traces of genetic manipulations as an affordable "do-it-yourself" method. Future research should test the biological significance of alien genetic modifications and see what functions were altered in people.
Category: Quantitative Biology

Embracing Solidarity as a Way of Life

Authors: Gennady Shkliarevsky
Comments: 49 Pages.

The mystique of solidarity retains its allure. The power of solidarity defies imagination. Yet harnessing this power has proven to be a challenge. There is much about solidarity to be learned. This study seeks a deeper understanding of solidarity that is necessary to find a way of using the enormous creative potential of solidarity more effectively for human progress and liberation. The article shows that the dominant theory and practice of solidarity are incapable to realize this objective. The article argues that attraction to differences is the main source of solidarity’s power. Affirmation and empowerment of differences is the key to creating strong and enduring social bonds that can sustain solidarity. Yet the dominant conception of solidarity requires subjugation of differences to the central point of identification and their suppression. The article proposes a new approach toward solidarity. The distinct feature of this approach is its view of differences. In contrast to the traditional view that sees differences primarily as opposed to each other, the article outlines a new conception of solidarity that views differences as the most important resource for human advancement and liberation. The article examines the theoretical and practical implications of the new conception.
Category: Social Science

Study the Infrared Spectra of XLi2O.ySiO2.zCaO(1—x—y—z)B2O3 Glasses

Authors: Rafiqul Islam, Mubdiul Hasan, Emran Hossain, Rafiqul Ahsan, M. Golam Mortuza
Comments: 23 Pages.

The xLi2O.ySiO2.zCaO (1-x-y-z)B2O3 glass system (where x = 0, 5, 10, 15, 20 and 25 mol%, y=60 mol% and z=10 mol%) was processed through a dissolved quench technique. To acquire the structural performance of silica, calcium, boron and oxygen were minutely observed by using Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction. The position and relative quantities of IR bands responsible for the distinct silicate and borate units were determined using deconvoluted spectra. For the increased amount of B2O3 the results show that BO3 occupies the network position and creates the linkage SiO-Ca. The bands related to the bending mode of H2O molecules and the stretching mode of B—O—H groups forming hydrogen bonding are shown to result in several bands: 23002380cm-1 and 2820-3505 cm-1 respectively. The XRD order of the base samples exhibited homogeneous glasses and also an optical reconnoitre, but did not show any phase separation record.
Category: Condensed Matter

N-Point Discrete Fourier Transform in O(n Log_2n) Time Complexity for Any N Larger Than 0

Authors: Saulo Queiroz
Comments: 3 Pages.

We present a novel recursive algorithm for computing the $N$-point Discrete Fourier Transform (DFT) with $O(N log_2 N)$ time complexity, applicable for any integer $N > 0$. Unlike conventional Fast Fourier Transform (FFT) algorithms that often require zero-padding to the nearest power of two, our method operates directly on arbitrary-length input sequences, eliminating the need for zero-padding. At each recusive stage, the algorithm relies on a novel decomposition structure that performs $2(N-1)$ complex additions and $N$ complex ultiplications for typical cases, yielding a total complexity of $T(N)=2T(N/2)+10N-4=10Nlog_2N-4N+K$ real floating point operations (where $K$ is a constant). Although the resulting constants are higher than in classic FFT algorithms -- like radix-2 FFT, that performs $5Nlog_2N$ real floating point operations -- our algorithm does not need zero-padding, which end up by increasing the true complexity of existing FFTs due to the enlarged signal length.
Category: Digital Signal Processing

Special Relativity: Types of Energy

Authors: Alejandro A. Torassa
Comments: 6 Pages.

[T]his paper presents the definitions of kinetic energy, rest energy and relativistic energy for a single particle (massive or non-massive ) [In special relativity]. Additionally, this paper also presents the definitions of generalized relativistic energy and total energy for a system of particles (massive and non-massive).
Category: Relativity and Cosmology

Vertex-Edge-Combinatorial Polytopes: A Class Defined by the Local Structure at Each Vertex

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

We introduce a class of geometric bodies, which we call vertex-edge-combinatorial polytopes, defined by a local structure in which each vertex is connected to a number of edges equal to the dimension of the body, and where any subset of those edges belongs to a face whose dimension equals the subset’s cardinality. These polytopes satisfy an empirical formula for the number of vertices, from which a general combinatorial expression for the number of faces can be deduced. The class includes simplices, hypercubes, and the dodecahedron, and excludes the octahedron, the icosahedron, and any higher-dimensional polytopes derived from them. In some cases where the formula diverges, such as the hexagonal tiling, an infinite regular structure does exist, although this is not always the case.
Category: Geometry

Newer *space Flow Models that Did not Get Into the Book

Authors: Natan A. Cerqueira
Comments: 36 Pages.

A longer and better presentation of *Space Flow is made, containing some new models that are the work's most significant to date and that cannot be found in the book.
Category: Relativity and Cosmology

A Concise Dictionary of Slang and Unconventional English and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the head entries of A Concise Dictionary of Slang and Unconventional English.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, $beta H=0.02$), i.e. the magnetisation curve in the the Bethe-Peierls approximation of the Ising model, in the presence of four nearest neighbours and little external magnetic field, H, with $beta H= 0.02$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Social Science

Approaching Legendre’s Conjecture Within a Limited Boundary

Authors: Junho Eom
Comments: 14 Pages.

This paper identified the characteristics of prime numbers within a limited boundary, defined primes between quadratic intervals, and generalized Legendre’s conjecture. Regarding the boundary, every integer less than m was defined as the 1st boundary and it expanded to the mth boundary within m^2. Thus, each boundary contained m elements. Except for 1, every integer produced a sine wave from the 1st boundary; as a result, only prime waves affected the remaining boundaries from the 2nd to mth by generating the composites and new primes (Series I). Therefore, the number of new primes in each boundary could not exceed ��(1st boundary) or ��(m), where ��(x) was the number of primes less than or equal to x, and it enabled the estimation of the total number of primes within m^2 (Series II). Based on Series I and II, the quadratic intervals between ��(m^2) and ��((m + 1)^2) were identical to the sum of the last two boundaries, expressed as 2·βm+1·��(m), where βm+1 was the ratio of ��((m + 1)^2) to ��(m + 1)·(m + 1) (Series III). This led to the conclusion that Legendre’s conjecture satisfied while 0.8986·��(P) < 2·βP·��(P) < ��(P) (prime P > 113), or 2·βm+1·��(m) ≤ 2·��(m) (integer m ≥ 2).
Category: Number Theory

Astrophysical Evidence for Cantor Dust: An Introduction

Authors: Ervin Goldfain
Comments: 10 Pages.

The Cantor Dust (CD) interpretation of Dark Matter (DM) arises from the non-differentiable and nonlocal fluctuations of spacetime in the high energy limit of field theory and primordial cosmology. Mirroring the fragmented and ever-changing configuration of multifractal structures, CD offers a novel explanation for the distribution and behavior of Dark Matter and bridges concepts from complex dynamics, fractal geometry, and statistical physics to cosmology. Here we argue that CD offers a unified Dark Matter model with predictions confirmed by a wealth of astrophysical observations.
Category: Relativity and Cosmology

Allowable Structures of Leptons

Authors: Vladimir Pastushenko
Comments: 13 Pages. (Note by viXra Admin: Further repetition will not be accepted)

There is no space without matter and there is no matter outside space. Space-matter is the same. Therefore, the mathematical truths of space correspond to the physical properties of matter. The main property of matter is movement; therefore space-matter is dynamic. Such dynamic space-matter has its geometric facts, as axioms that do not require proof. The limiting and special case of the axioms of dynamic space-matter is the Euclidean axiomatics and number system. And already in the real dynamic space-matter, the models of nucleons of the atomic nucleus are considered and the admissible structures of leptons are presented.
Category: Quantum Gravity and String Theory

Quantifying Geothermal Energy Potential: Embracing Uncertainty for Robust National Renewable Estimates

Authors: Victor Christianto, Florentin Smarandache
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Geothermal energy, a stable and baseload renewable resource, holds significant promise for decarbonizing global energy systems. However, accurately quantifying its potential remains a challenge due to inherent geological uncertainties. Traditional one-value estimates often fail to capture the full spectrum of possibilities, leading to potentially misleading national renewable energy projections. This article explores the importance of incorporanting uncertainty modelling into geothermal resource assessment and proposes a methodology for expressing national potential as a range, especially based on Neutrosophic Logic/Probability theory introduced by one of us (FS).
Category: Geophysics

Action and Reaction of a Gravitational Field

Authors: Ichiro Nakayama
Comments: 4 Pages. (Note by viXra.org Admin: Please cite and list scientific references)

When we look at the action of gravity at the elementary particle level of Energy Body Theory, we can see that elementary particles and gravitational fields act and react, forming distortions in the foot of elementary particles and generating kinetic energy, which is a wave in space. This is the cause of gravitational mass and is the same cause as inertial mass. The gravitational field forms a spherical layer with a Planck scale thickness in which the amount of energy decreases as it approaches the star. For this reason, the action and reaction between the gravitational field and elementary particles occurs continuously toward the center of the star. For this reason, the increase in distortion in the foot of elementary particles and the increase in kinetic energy are continuously generated and added up. This is explained using a model airplane and a photon released from a free-falling elevator. When photons are in a gravitational field, their speed increases, but since they do not act or react with the space of the gravitational field, there is no increase or decrease in shape or energy.
Category: High Energy Particle Physics

A Feature of the Off-Shel Renormalization Schemes in Quantum Field Theory

Authors: S. A. Larin
Comments: 6 Pages.

It is shown that the off-shell renormalization schemes for subtraction of ultraviolet divergences in Quantum Field Theory produce zerofor sums of perturbative corrections to physical quantities when all perturbation orders are taken into account. That is the off-shel renormalization schemes are in this sense unphysical. In this connection it is desirable to develope on-shell renormalization schemes for different quantum theories.
Category: High Energy Particle Physics

Proof of Collatz Conjecture

Authors: Khalid Ibraheem Al-ibraheem
Comments: 19 Pages. all copyrights and intellectual property rights pertaining to this work to khalid ibraheem alibraheem pursuant to the intellectual property legislation of the Syrian Arab Republic (Document No.8361/564, March 13, 2025)

Collatz Conjecture (3 ∗�� + 1 problem) stats any natural number /��/ will return to number /1/ after 3 ∗ �� + 1 computation (when /��/ is odd) and ��2 computation (when /��/ is even), then doing the same computation on the outputs. in this paper we proved that Collatz Conjecture is true.
Category: Number Theory

The Four Second Order Axiomatizations of the Categorical Theory

Authors: Martín Alejandro Monzón Marimón
Comments: 1 Page. (Note by viXra.org Admin: Please cite and list scientific references)

There are four possible axiomatizations of the Zeroth Order Categorical theory, which are the fourpossible forms in which the implication operator can be constructed (they are implicit). Analogously, there are four possible axiomatizations of the Second Order Categorical theory (the explicit form of the Zeroth Order Categorical theory). They are presented here. Only one is known to date with rigor (Peano axioms + Hereditarily Finite Sets axioms).
Category: General Mathematics

Error-Corrected Deep Learning Approach to Handwritten Text Recognition of Gregg Shorthand

Authors: Alexander Weimer
Comments: 3 Pages.

Shorthand, also known as pen stenography, is a family of writing systems for English and other languages that emerged out of a need for a fast and efficient writing system in a pre-digital age. Of the many English shorthand systems, Gregg shorthand is the most prevalent (Zhai et al., 2018). While largely made obsolete by general-purpose computers, the cultural and legal value within old shorthand documents means that being able to efficiently scan shorthand documents into modern computer systems holds significant value. This investigation explored the implementation of a model built around a Gated Convolutional Neural network for purposes of handwritten text recognition of Gregg shorthand. An accuracy of 0.04 was achieved after minimal training. The finalized model is freely licensed and made available online for public access.
Category: Artificial Intelligence

Why Electrons and Protons Have the Same Charge

Authors: Ichiro Nakayama
Comments: 2 Pages. (Note by viXra.org Admin: Further repetition will not be accepted; Please cite and list scientific references)

The reason why electrons and protons have the same electric charge is unknown. Here, I explain it using a particle model of Energy Body Theory. When the foot of the counterclockwise rotating wave of an electron and the foot of the clockwise rotating wave of a proton come into contact, the energy decreases there and the foots of two become distorted. As a result, an attractive force occurs and the two are joined together.The restoring force of this distortion is the cause of the electric charge. Because the restoring force of an electron and a proton is the same, their electric charges are also the same.
Category: High Energy Particle Physics

Resolution Matrix Semantics for Deontic Logic

Authors: Andrey Kuznetsov
Comments: 28 Pages. Submitted to the Journal of Philosophical Logic on May 25, 2025. Preprint version.

This paper introduces Resolution Matrix Semantics (RMS) [Kuznetsov, 2025] as a novel framework for formalizing deontic logic, inspired by Y. Ivlev’s quasi-matrix approach [Ivlev, 1997]. Unlike traditional Kripkean semantics, RMS employs a truth-value-based approach with normative values—mandatory (m), indifferent (i), and forbidden(b)—to evaluate acts, and true (t) or false (f) for formulas, ensuring a clear distinction between normative and propositional domains. This truth value semantics is augmented with "undetermined" truth values (e.g. m/i, "eitherm, or i"), and RMS uses an interpretation and sub-interpretation mechanism to resolve these, enabling precise normative evaluations. We develop SDLm, a deontic system that mirrors Standard Deontic Logic (SDL) in its axiomatic structure but avoids well-known paradoxes, such as the Chisholm and Gentle Murderer Paradoxes. Weprove SDLm’s soundness and completeness and provide tableau rules for automated theorem verification. By prioritizing normative status over existential considerations, SDLm offers a robust, paradox-free framework forreasoning about obligations, permissions, and prohibitions, with potential applications in ethics, law, and artificial intelligence.
Category: Set Theory and Logic

Transformation Properties of Tensors and Pseudotensors under Coordinate Reflections: A Detailed Mathematical Analysis

Authors: Chenjia Li, Jingxu Wu
Comments: 15 Pages.

The theory of tensors and pseudotensors underlies the mathematical framework of modern physics, providing a coordinate-invariant language for describing physical laws and symmetries. In this work, we systematically analyze the transformationproperties of tensors and pseudotensors of various ranks, with particular emphasis on their behavior under spatial and spacetime reflections. The construction and interpretation of the Levi-Civita symbol in two, three, and four dimensionsare discussed in detail, elucidating the essential distinction between true tensors and pseudotensors in terms of orientation and parity. Explicit transformation rules for ordinary tensors and pseudotensors are derived, including the role of the Jacobian determinant and its sign. Through concrete examples—including scalar tripleproducts, cross products, and antisymmetric tensor decompositions—we reveal the fundamental algebraic and geometric features of these mathematical objects. The implications for vector calculus, relativistic field theory, and physical invariants such as chirality and duality are highlighted. Our results provide a unified and rigoroustreatment of the reflection and contraction properties of pseudotensors, with direct relevance to applications in classical mechanics, electromagnetism, and modern theoretical physics.
Category: Mathematical Physics

Virtual Dance Movement Therapy for Reducing Anxiety, and Artificial Intelligence for Monitoring the Body and Mind During Therapy

Authors: Petar Radanliev
Comments: 16 Pages.

Dance Movement Therapy (DMT) is an established psychotherapeutic intervention that utilises movement to support emotional, cognitive, and physical well-being. While traditional DMT is practiced in physical settings, Extended Reality (XR) presents a new opportunity to expand accessibility by integrating immersive, interactive environments with structured therapeutic movement interventions. This study explores how XR-based DMT can serve as a preventative approach for anxiety by applying wearable biometric monitoring and AI-driven personalisation. Unlike recreational virtual dance activities such as Zumba or general movement-based fitness applications, XR-based DMT follows a structured therapeutic model, incorporating principles of mirroring, embodied cognition, and rhythmic synchronisation to enhance emotional regulation and engagement. The study employs real-time physiological feedback mechanisms, where biometric markers such as heart rate variability (HRV) and skin conductance inform dynamically adapted movement interventions. The findings suggest that XR-enhanced DMT provides a scalable, non-pharmacological intervention for individuals experiencing early-stage anxiety. This study contributes to the growing field of digital DMT by providing an evidence-based framework for integrating immersive technology into therapeutic movement practices, ensuring adherence to the core principles of dance movement therapy rather than generic dance-based interventions. Future research should address long-term efficacy, therapist-led versus AI-assisted interactions, and the potential for XR-DMT in community-based settings.
Category: Artificial Intelligence

Simulation Hypothesis: Optimisation, Wave-particle Duality and a New Termination Risk

Authors: Genevieve Gorrell
Comments: 8 Pages.

Thinking in terms of our existing within a simulation yields plausible suggestions for how our world might have come to be. For example it seems reasonable to guess our implementation is optimised. The apparent paradox of wave-particle duality may arise from optimisation. Computationally reducible material may never be run at all, but only calculated just in time. Islands of activity, complex within themselves but for some duration not affecting anything outside of themselves, might be deferred from being run, to be caught up in a separate thread only if needed. Quantum computing may be an abuse of the multithreaded nature of the simulation.
Category: General Science and Philosophy

Generated Space Theory (TGP-ST): A Framework for the Unification of Gravity and Quantum Mechanics

Authors: Mateusz Serafin
Comments: 23 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces the Generated Space Theory (TGP-ST), a conceptual framework aimed at unifying general relativity and quantum mechanics. TGP-ST postulates that space is not a pre-existing background, but an emergent, dynamic entity generated directly by the presence of mass and energy. A key element of the theory is a scalar field Φ, which describes the "density" or "tension" of generated space. Within this framework, fundamental physical constants such as the speed of light, Planck’s constant, and the gravitational constant become dynamic fields dependent on Φ, while preserving the constancy of the Planck scale. TGP-ST provides modified field equations for gravity and quantum mechanics, predicts the disappearance of singularities, and offers new insights into phenomena such as dark energy and the Hubble tension. Two distinct pathways to the classical limit are described, and several testable predictions are proposed. The theory is at an early stage and intended as a foundation for further research and discussion.
Category: Relativity and Cosmology

Frontier ai Regulation: What Form Should it Take?

Authors: Petar Radanliev
Comments: 37 Pages.

Frontier AI systems, including large-scale machine learning models and autonomous decision-making technologies, are deployed across critical sectors such as finance, healthcare, and national security. These present new cyber-risks, including adversarial exploitation, data integrity threats, and legal ambiguities in accountability. The absence of a unified regulatory framework has led to inconsistencies in oversight, creating vulnerabilities that can be exploited at scale. By integrating perspectives from cybersecurity, legal studies, and computational risk assessment, this research evaluates regulatory strategies for addressing AI-specific threats, such as model inversion attacks, data poisoning, and adversarial manipulations that undermine system reliability. The methodology involves a comparative analysis of domestic and international AI policies, assessing their effectiveness in managing emerging threats. Additionally, the study explores the role of cryptographic techniques, such as homomorphic encryption and zero-knowledge proofs, in enhancing compliance, protecting sensitive data, and ensuring algorithmic accountability. Findings indicate that current regulatory efforts are fragmented and reactive, lacking the necessary provisions to address the evolving risks associated with frontier AI. The study advocates for a structured regulatory framework that integrates security-first governance models, proactive compliance mechanisms, and coordinated global oversight to mitigate AI-driven threats. The investigation considers that we do not live in a world where most countries seem to be wishing to follow our ideals, for various reasons (competitiveness, geo-political dominations, hybrid warfare, loss of attractiveness of the European model in the Big South, etc.), and in the wake of this particular trend, this research presents a regulatory blueprint that balances technological advancement with decentralised security enforcement (i.e., blockchain).
Category: Artificial Intelligence

AI Ethics: Integrating Transparency, Fairness, and Privacy in AI Development

Authors: Petar Radanliev
Comments: 47 Pages.

The expansion of Artificial Intelligence in sectors such as healthcare, finance, and communication has raised critical ethical concerns surrounding transparency, fairness, and privacy. Addressing these issues is essential for the responsible development and deployment of AI systems. This research establishes a comprehensive ethical framework that mitigates biases and promotes accountability in AI technologies. A comparative analysis of international AI policy frameworks from regions including the European Union, United States, and China is conducted using analytical tools such as Venn diagrams and Cartesian graphs. These tools allow for a visual and systematic evaluation of the ethical principles guiding AI development across different jurisdictions. The results reveal significant variations in how global regions prioritise transparency, fairness, and privacy, with challenges in creating a unified ethical standard. To address these challenges, we propose technical strategies, including fairness-aware algorithms, routine audits, and the establishment of diverse development teams to ensure ethical AI practices. This paper provides actionable recommendations for integrating ethical oversight into the AI lifecycle, advocating for the creation of AI systems that are both technically sophisticated and aligned with societal values. The findings underscore the necessity of global collaboration in fostering ethical AI development.
Category: Artificial Intelligence

How to Simulate a Universe

Authors: Bryce Weiner
Comments: 40 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We synthesize the dS/QFT correspondence with holographic universe principles through a fundamental information processing rate γ = 1.89 × 10−29 s−1 that maintains a precise relationship with the Hubble parameter (γ/H ≈ 1/8π). Central to our framework is the quantum-thermodynamic entropy partition, which establishes that de Sitter space requires initialization with coherent entropy to drive expansion. We demonstrate how this framework emerges naturally from the E8×E8 heterotic structure with specific network topology (clustering coefficient C ≈ 0.78125) that precisely accounts for observed cosmological tensions. Our mathematical formalism introduces the information manifestation tensor and information current tensor, connecting quantum information flow to spacetime dynamics. This approach resolves multiple cosmological puzzles—explaining dark energy as information pressure, dark matter as coherent entropy structures, and quantum measurement as transitions across thermodynamic boundaries. The framework yields modified Friedmann equations incorporating information processing constraints, with quantitative predictions for BAO scale modifications, structure formation, and quantum decoherence rates. The emergence of the vacuum energy density from γ (ρΛ/ρP ≈ (γtP)2 ≈ 10−123) suggests information processing, rather than field dynamics, is fundamental in cosmic evolution.
Category: Relativity and Cosmology

My Proofs of Conjectures on Number Theory

Authors: Abdelmajid Ben Hadj Salem
Comments: 141 Pages. Comments welcome

In this booklet, I present my proofs of open conjectures on the theory of numbers.It concerns the following conjectures:- The Riemann Hypothesis.- Beal's conjecture.- The conjecture c<rad^{1.63}(abc).- The explicit abc conjecture of Alan Baker.- Two proofs of the abc conjecture.- The conjecture c<rad^2(abc).
Category: Number Theory

The Periodic Variation of Baryon Masses as a Function of Their Magnetic Moments: Quantum Interference in the Femtometer Scale of Hadrons.

Authors: Osvaldo F. Schilling
Comments: 11 Pages.

The objective of this paper is to give full consideration to an important ( never divulged) result which comes straight from tabulated data for all baryons of the octet and decuplet when these data are duly analyzed theoretically, namely: The masses of spin ½ baryons, in proton mass-units, are a simple periodic function of their magnetic moments, in nuclear magneton-units. As discussed here, this can be attributed to quantum interference of closed currents inside the particles, as observed in conventional superconducting rings confining magnetic flux.
Category: High Energy Particle Physics

Lindemann-Weierstrass Theorem for Thakur Hyergeometric Functions

Authors: David Adam, Laurent Denis
Comments: 21 Pages. In French

n 1995, Thakur introduced analogues of hypergeometric functions for Fq [T ]. In this article, we show that the exceptional set of such a function is trivial. This confirms a conjecture stated by Thakur and his co-authors in 2008. Furthermore, we prove a Lindemann-Weierstrass-type theorem for an uncountable class of functions containing hypergeometric functions. The method used allows us to obtain the first transcendence measures (of quality comparable to that of characteristic 0) for values u200bu200bat algebraic arguments of these functions. Finally, in the last section, we exhibit the first infinite families of hypergeometric functions whose exceptional set can be shown to be trivial in the P-adic domain.
Category: Number Theory

Virgin and Under-Investigated Areas of Research in Non-Newtonian Fluid Mechanics

Authors: Taha Sochi
Comments: 19 Pages.

This paper is mainly about the areas of non-Newtonian fluid mechanics which are not investigated or not appropriately and sufficiently investigated. In fact, this should also include emerging areas of research in the field of non-Newtonian fluid mechanics due to new scientific and technological developments and advancements. The purpose of the paper is to highlight and draw the attention to these areas so that researchers (especially the young researchers and new-comers to research such as PhD students) invest their resources and efforts in these areas instead of investing in other areas which are previously investigated and hence they are of less priority from this aspect. Apart from the obvious benefit of "leveling up" in research, the attention to these rather neglected and non-explored areas of research can be beneficial at the scientific and individual levels since it can lead to breakthroughs and new discoveries in these areas of research by inspecting and assessing their potentials and impacts at the theoretical and practical levels and probing their beneficial applications. We will also provide a brief discussion about the possibility of introducing novel tools and methods in these areas of research (and in non-Newtonian fluid mechanics research in general) as well as highlighting some of the existing limitations of the past and current research in the field of non-Newtonian fluid mechanics (noting that this discussion should help in achieving the ultimate objective of this investigation).
Category: Classical Physics

Practices and Metrics of Citation in Scholarly Publishing

Authors: Taha Sochi
Comments: 29 Pages.

In the world of academia and research, citation (i.e. being cited and referred to) in scholarly publications is generally regarded as a primary metric for integrity and excellence. In other words, it is the currency of credibility and the gold standard for reliability. In this article we try to shed light on some of the bad and immoral/unethical practices related to citation in modern scholarly publications and activities. In fact, citation (and actually academic and scholarly activities in general including scholarly publishing) became in modern times an industry that is subject to many non-scholarly factors and considerations (whether sinister or benign), and this should be regarded as a form of corruption that threatens the integrity, authenticity and morality of the present and future of academia, research and scholarly activities (and actually human knowledge and progress in general). This threat is aggravated by the epidemic of predatory journalism and the wide availability of artificial intelligence tools which facilitate the abuse of scholarly publishing and citation practices and the manipulation of metrics and parameters related to these activities. We also discuss briefly the value and significance of academic and research metrics related to citation which are commonly used these days to evaluate scholars (as well as other scholarly entities like journals and institutes) and assess their scholarly works and ranks (noting the direct negative impact of the bad citation practices on these metrics and parameters and their supposed significance). We finally present some proposals to address the limitations, shortcomings and abuses of the existing practices and metrics related to citation.
Category: General Science and Philosophy

The Weaknesses of Modern Cosmology

Authors: Taha Sochi
Comments: 18 Pages.

Cosmology is one of the most interesting and fascinating scientific subjects. It is also one of the most problematic scientific subjects. In fact, cosmology is not a purely scientific discipline noting its intimate relationship with philosophy (and possibly religion) as well as its inherent speculative nature in some of its fundamental aspects due to the lack of real and decisive experimental and observational evidence that can reach (and hence verify and assess) these aspects. In a sense, cosmology is inherently a mix of physics and metaphysics even though its metaphysics is usually treated (in modern cosmology) by scientific tools and methodology and presented through physical concepts and terminology and hence it appears like physics (or it is hidden behind thick layers of physics). In this article we overview the main weaknesses and shortcomings of modern cosmology which suffered in the recent decades (especially in its theoretical sides) from serious problems and challenges due largely to the domination of certain theories, models and assumptions with the absence of a clear and proper epistemological and philosophical framework and lack of regulations that govern the research in this field and determine its routes and destiny. We also propose and discuss briefly some remedies that should be considered to address these weaknesses and shortcomings.
Category: Relativity and Cosmology

The Legitimate and Illegitimate in Physics

Authors: Taha Sochi
Comments: 27 Pages.

Physics is supposed to represent and reflect the reality of the physical world. However, modern physics is full of elements that do not represent or reflect any aspect of the reality of the physical world (or at least this is what they look like). Moreover, it contains theories and models whose representation of the physical reality is questionable. Despite the fact that physics in its theoretical side inevitably contains elements and theories that do not reflect directly the physical reality, there must be some criteria that determine what is allowed (or legitimate from this perspective) and what is not allowed (or illegitimate) of these elements and theories; otherwise physics can lose its status as a subject that acquires its legitimacy as a scientific discipline from representing and reflecting the physical world. In more simple words, we need some criteria that determine what is physical (and hence legitimate) of these elements and theories and what is non-physical (and hence illegitimate, i.e. delusional or metaphysical). The purpose of the present paper is to identify these criteria, but we should admit that identifying these criteria is not an easy or straightforward task. Moreover, the application of these criteria is another difficult task even if we supposedly succeed in identifying these criteria conceptually and theoretically. Therefore, we consider the present paper as a first attempt in identifying these criteria hoping that other researchers in this field contribute to this investigation to improve our suggestions. To be more complete and specific, the present paper will also suggest an initial sample of illegitimate elements and theories as an application of the suggested criteria (considering our previous admission about the additional difficulty of this task).
Category: History and Philosophy of Physics

Complexity of Science Versus Simplicity of Nature

Authors: Taha Sochi
Comments: 15 Pages.

Modern science is the most complicated theoretical structure ever created by mankind (and possibly by any living species in our Universe). This is particularly true in modern physics which represents the most mature and elaborate branch of modern science. Nevertheless, modern science (and physics in particular) seems to make itself more complicated than necessary, and sometimes modern science seems to make itself complicated unnecessarily. This "simplistic" view to science may be supported by the fact that Nature (despite our acknowledgment of its complexity and sophistication at the level of fine details) seems to be governed by some rather simple rules and general laws which may be able (if comprehended and employed correctly) to make our science much simpler than what we actually have. In this article we try to highlight some issues about potential simplification of modern science (and physics in particular) which (i.e. simplification) could be one of the greatest goals and advancements (if achieved) of future science. In our view, the simplification of science is fundamentally related to the issue of unification of physics and the search for the so-called "theory of everything" (i.e. in a sense different to what is currently perceived and envisaged).
Category: History and Philosophy of Physics

Analysis of 72 Enigmas of the Universe Reveals Their Common Origin in the Form of the Inertial Paradox

Authors: Dominique Mareau
Comments: 71 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Beyond the standard model, the DUO5 theory analyzes 72 puzzles (§2) to find their common point. With the constraint of avoiding any determinism, relative to an act of "creation", the analysis leads to the cause of the existence of the universe via the inertial paradox. By iteration, the precise link between the measurement of "effects" and their common "cause" is shown. It is shown that, like John Wheeler's theory, there is a common particle for particles and space-time. The analysis reveals: 1) that the physical structure of space-time is woven of dipolar oscillators, at the subquantum, non-local scale; 2) the cause of the instability of the local "creation" of matter; 3) that the notion of antimatter is an artifact relating to the non causal separation specific to locality; 4) the link between the stability of matter and the causal separation of primordial inflation; 5) the physical cause of inflation; 6) the original particle of the "preon" type, justified here, is named B.O.D.Y.S. (Subquantum Yin Yang Dipole Oscillator Boson). The iterative method between "cause" and "effects" allows to avoid the pitfall of self-reference and incompleteness of mathematical models, denounced by Gödel [3]. It is shown that the geometric aspect of the curvature of space-time, is only an "effect" of the "cause" relative to the physical coupling between the elements of matter and the B.O.D.Y.S structuring space-time. The study shows that the traces of the inertial paradox are present at all scales. This inertial paradox, constrains a state of permanent universe (without mass-spacetime continuum), matrix of the state of expanding and provisional universe. The study shows, that at the quantum scale, the notion of inertia m is inseparable from its spatial amplitude ℓ, forming a non-scalar moment of inertia: χ = m.ℓ. It is shown that it is the cause of the Heisenberg uncertainty. This entity is materialized by each of the two poles of the stochastic dipolar oscillator B.O.D.Y.S, whose existence is a solution to the inertial paradox.
Category: Relativity and Cosmology

Proofs for Collatz Conjecture

Authors: Dawit Geinamo
Comments: 58 Pages. 58

The objective of this study is to present rigorous proofs for Collatz conjecture and introduce some interesting behavior of the Kaakuma sequence that is a vast generalized form of Collatz sequence. We analyze the behavior of Kaakuma sequence such as scaling up, scalingdown, translation, function iteration and uniform growth of inverse tree. In addition to this we investigate relationship of increasing rate, number of iterations of cycles, gap in cycles, and densities of cycles ofthe Kaakuma sequence and evaluate consistency of tree size density after scaling. Our investigation culminates in the formulation of a set of conjectures encompassing lemmas and postulates, which we rigorously prove using a combination of analytical reasoning, numerical evidence, and exhaustive case analysis. These results provide compelling evidence for the veracity of the Collatz conjecture and contribute to our understanding of the underlying mathematical structure.
Category: Number Theory

Comment on "Subjective Nature of Path Information in Quantum Mechanics"

Authors: V. A. Kuzmenko
Comments: 2 Pages.

In a recent preprint [1] (arXiv:2505.05930), Jiang et al. presented impressive high-quality results of an experimental study of the so-called which-path information problem for the case of a three-crystal interference setup. We believe that the results obtained represent one of the numerous manifestations of the nonequivalence of forward and reversed processes in quantum physics. It is probably, this nonequivalence is the physical basis for the widely discussed principle (rule) of relation between path distinguishability and interference visibility.
Category: Quantum Physics

Falling Apples, Quarks, and Expanding Galaxies

Authors: Oliver R. Jovanovic
Comments: 6 Pages.

This paper derives a gravity equation from photon dynamics, offering a unified model that explains terrestrial gravity, cosmic expansion, and quark-scale interactions.
Category: Classical Physics

Nonliquent Math: a New Way to Deal with Singularities and Division by Zero

Authors: Egor Sibrin, Vladimir Orlov
Comments: 23 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This work presents the framework of Nonliquent Mathematics (NL), a commutative extension of the real numbers that defines division by zero through the introduction of an idempotent element denoted by ї=1/0 and the distinction between a true zero and a special zero. The algebraic operations of addition, multiplication, division, conjugation, and root extraction are formulated in this system, along with Taylor expansions for basic functions and a consistent differential and integral calculus adapted to NL variables. A Hilbert space of NL-valued functions is defined with a corresponding inner product, and a modified form of the Navier—Stokes equation is derived within this framework. Two particular solutions of the modified equation are obtained for the cases of zero and nonzero viscosity, demonstrating the consistency and potential applications of NL in analysis and fluid dynamics.
Category: Algebra

Relativistic Algebra in a Finite Universe

Authors: Yosef Akhtman
Comments: 29 Pages.

This work presents a foundational reconstruction of arithmetic and algebra based on the principle of relational finitude. Rejecting the assumption of actual infinity, we develop a finite, frame-dependent mathematical framework in which conventional number systems—integers, rationals, reals, and complex numbers-emerge as asymptotic projections or epistemic constructs derived from a closed finite field Fp. Core arithmetic operations are reinterpreted as internal symmetries of the finite field, and conventional structures such as signed integers, rational fractions, and complex planes are systematically reconstructed as pseudo-numbers, defined relationally and locally with respect to a chosen frame of reference. Imaginary and transcendental constants i, e and Pi are derived as specific elements of Fp with important structural roles. We show that the resulting number classes possess all necessary properties for consistent computation, approximation, and algebraic closure, while offering the potential resolution of classical paradoxes of logic and set theory by replacing absolute notions with context-dependent representations. The proposed system provides a coherent and physically grounded alternative to standard mathematical formalism, suitable for the description of discrete, informationally finite physical systems.
Category: Mathematical Physics

Binomial Evolution Function the Only Function You Need to Evaluate a Trading Strategy

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

A trading strategy represents a forecasting model and a forecasting model will generate profits in the future if it has demonstrated in the past that it can predict with a good probability of success the evolutions of the system on which it operates. Since the theory is so simple, why is it so difficult to evaluate a trading strategy? The reason is the following: in finance, we think we see the evolutions of the system but we are only observing the random component due to unpredictable events. Instead, the deterministic component that represents the true evolution of the system is not visible. Unfortunately, not seeing the deterministic component leads to a very important statistical problem: if I execute if 10 winning predictions, I do not know if these operations concern 10 evolutions of the system or concern only one evolution of the system. Therefore, I do not know, if my forecasting algorithm acted intelligently by predicting 10 different evolutions or if it acted irrationally by dividing a bet into 10 smaller ones on the same evolution. Distinguishing between these two scenarios is essential to correctly evaluate the trading strategy and this discrimination can be done by understanding whether the trades are independent of each other. In fact, the condition of independence is the only statistical way to be sure that the trades concern forecasts of different evolutions. The Binomial evolution function solves this problem by transforming the succession of trades into a succession of independent results.
Category: Economics and Finance

Entropy-Induced Wavefunction Collapse: A Thermodynamic Resolution of the Quantum Measurement Problem

Authors: Waleed Mahmud Tariq
Comments: 101 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose an interpretation of the quantum measurement process grounded in thermodynamics by introducing an entropy-based criterion associated with wavefunction collapse. In this interpretation, the Schrödinger equation remains universally valid, and wavefunctions never undergo a fundamental collapse. Instead, the apparent collapse emerges naturally from thermodynamic irreversibility and is observer-dependent. Central to our proposal is a rigorously derived inequality linking quantum coherence and environmental entropy production: ��(��)≤��(��)������(−����������(��)/����) where ��(��) represents the entropy irreversibly generated in the environment. When this entropy surpasses a critical threshold, on the order of ���� ���� �� per qubit of recorded information, quantum interference is exponentially suppressed. Consequently, coherence recovery (recoherence) becomes practically impossible due to thermodynamic constraints, consistent with established fluctuation theorems such as Jarzynski’s equality and Crooks’ theorem.Collapse, in this view, is interpreted as an epistemic updating of knowledge, aligning with Bayesian inference, rather than a physical process. We also offer a derivation of the Born rule through maximum entropy inference and symmetry considerations related to environmental invariance (envariance), carefully avoiding ad hoc assumptions or untested physics.Our approach maintains relativistic consistency through the Tomonaga-Schwinger formalism, ensuring observer frame-independence and preventing superluminal signaling. Additionally, this thermodynamic interpretation provides conceptual clarity to quantum paradoxes such as Wigner’s Friend and delayed-choice scenarios by emphasizing the contextual nature of measurement and the associated thermodynamic costs. The emergence of classically stable "pointer" states is understood through their minimized entropy production, while quantum discord naturally diminishes with increased irreversibility. Furthermore, entropic considerations significantly suppress quantum recurrences.Finally, we propose an experimental validation strategy involving mesoscopic optomechanical systems, specifically designed to quantify how controlled entropy exchange affects interference visibility. Experimental access to Δ��������(��) is achievable through quantum calorimetry and particle scattering measurements. The proposed entropy-induced interpretation thus provides a coherent, experimentally testable connection between quantum measurement outcomes and the Second Law of Thermodynamics.
Category: Quantum Physics

The Cosmic Particle Sea Hypothesis：A Foundational Framework for Reinterpreting Space, Time, and Matter

Authors: Miguo Ouyang, Alethea Zhang
Comments: 18 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

This white paper proposes the Cosmic Particle Sea Hypothesis, a unified theoretical framework that redefines space, time, matter, and motion based on structured internal dynamics. Drawing inspiration from the triadic Yin—Yang model of the I Ching, it posits that every unit of reality—particle, field, or organism—is composed of a threefold polarity configuration whose asymmetry generates motion and interaction.The hypothesis reinterprets time as a subjective observational metric, and space not as vacuum, but as a medium composed of microstructured, polar field units. Matter and energy emerge from variations in Yin—Yang composition and purity, leading to the diversity of physical forms. Living systems contain high-purity Yang channels—ling pathways—which are sensitive to energetic disruption by heavy Yin substances, explaining radiation and toxicity phenomena from a structural perspective.Celestial bodies are modeled as internally polarized systems (e.g., stars as Yin—Yin—Yin; planets as Yang—Yang—Yang), whose complementarity accounts for both gravitational attraction and orbital motion. The framework is supported by seven proposed experiments that range from twin-clock tests to quantum interference and space-medium validation.This theory invites collaboration from physicists, philosophers, and experimentalists seeking new ways to test foundational assumptions. It is offered as a metaphysically grounded yet empirically open model of a structured, living, and intelligible cosmos.
Category: History and Philosophy of Physics

Demonstration of the Goldbach Strong Conjecture by the Analysis of Populations of Prime Numbers in the Interval [0 N] and [N 2N] by Conventional Statistical Laws

Authors: Bahbouhi Bouchaib
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references of other authors and submit article written with AI assistance to ai.viXra.org)

In this article I apply classical statistical laws to analyze prime numbers assimilated to populations. The statistical analysis focuses on prime numbers in the intervals [0 - S/2] and [S/2 — S] with S an even > 4. The results show that the even number S > 4 is enclosed by two populations of prime numbers P in the interval [0 - S/2] and Q in [S/2 - S] which have approximately the same standard deviation relative to their means. Two other subpopulations P' included in P and Q' included in Q which satisfy the strong Goldbach conjecture (P' + Q' = S) also have the same standard deviation and superimpose or overlap with a slight variation. This result shows that an even number is enclosed by two populations P' and Q' of prime numbers which are symmetric with respect to S/2 and therefore S = P' + Q'. This result also shows that any natural number N > 4 is enclosed by at least two equidistant and symmetric prime numbers. Therefore for every N > 4 there exists a number t < N such that N — t = P' and N + t = Q' are primes and so 2N = P' + Q'.
Category: Number Theory

A Survey on the Application of Reinforcement Learning in Recommendation Systems

Authors: Siddhanth D. J. G. Nagpal
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

From media streaming and e-commerce to education and healthcare, recommendation systems are now absolutely essential in many different fields. Conventional methods including content-based filtering and collaborative filtering sometimes miss the sequential, changing character of user preferences. By simulating recommendations as sequential decisions with long-term feedback, reinforcement learning (RL) offers a strong substitute. This survey presents a thorough investigation of RL-based recommendation systems together with important frameworks including hierarchical reinforcement learning, policy-guided reasoning, and Deep Q-Networks. We provide a disciplined taxonomy contrasting these approaches by design, flexibility, and application setting. We also look at ethical issues, pragmatic deployment problems, and evaluation difficulties in actual environments. By mapping the changing terrain of RL in recommendation and pointing up future directions, this work seeks to direct practitioners as well as researchers.
Category: Artificial Intelligence

A New Functional Relationship Applicable to High-Speed Moving Objects

Authors: Guanghui Xie
Comments: 19 Pages.

In this paper, through theoretical derivation, a functional relationship is revealed, demonstrating that the variation in time between objects in relative motion depends on both their relative velocity and the finite propagation speed of light. By applying the relationship of time change to the theory of classical mechanics, it can be concluded that the interaction force between objects are also related to the relative motion velocity. Due to the introduction of the speed of light in the formula of classical mechanical theory, the applicable scope of classical mechanics theory is effectively expanded, so that it is not only applicable to the calculation of low speed moving objects, but also to the calculation of high speed moving objects. Subsequently, through careful derivation within this new framework, several fundamental laws of classical electromagnetism were derived, the results of which strongly support the validity of the new functional relationship.
Category: Classical Physics

SpaceArc: India’s Reusable Rockets Revolution for a Relativistic Future

Authors: Tanmay Mishra
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

SpaceArc is a visionary leap in aerospace engineering, merging India’s legacy of frugal innovation with cutting-edge advancements in rocket propulsion, relativistic physics, and artificial intelligence. At its core is Phoenix, a fully reusable methane-LOX launch system delivering 18,000 kg to low Earth orbit (LEO) at $1,111/kg—over 50% cheaper than SpaceX’s Falcon 9 and 95% below NASA’s SLS. Engineered with graphene composites, AI-guided navigation rooted in Einstein’s field equations, and rigorous CFD/FEA validation, Phoenix exemplifies a new era of low-cost, high-performance rocketry. This 10,000-word paper synthesizes classical rocketry, black hole orbital mechanics, and advanced economic modeling to propose a realistic roadmap for India’s space leadership by 2040, including lunar bases, Mars sample returns, and a 6G satellite constellation. Designed and authored by a 12th-grade Indian student, this work challenges the status quo of billion-dollar launches, proving that with bold ideas, rigorous science, and national vision, space is no longer the privilege of superpowers—it’s the future of all humanity.
Category: Classical Physics

On Two Unconventional Summation-Derivative Identities

Authors: Samel Datu Castelo
Comments: 1 Page. (Note by ai.viXra.org Admin: Please cite and list sceintific references)

This paper presents two mathematical formulas involving differentiation and summation. While the derivations do not strictly follow conventional mathematical rigor and certain foundational rules are bypassed, the formulas demonstrate surprisingly consistent results. A full formal proof is currently under construction.
Category: General Mathematics

Dark Mass is Potential Energy

Authors: Nicolas Poupart
Comments: 13 Pages. (Note by viXra Admin: An abstract in the article is required)

We will demonstrate that gravitational potential energy (E=GmM/r) is the cause of the dark mass phenomenon by simply applying the mass-energy relation (E=mc2). No other axiom will be used except the principle of conservation of volumetric mass density to preserve the conservative field by involving no other force than gravity. First, we will develop a simple equation and a simple algorithm to correctly calculate the potential energy of a stellar system. Then, we will demonstrate its theoretical implication on the production of potential energy by different types of stars and black holes in galaxies. Subsequently, we will confront our theoretical model with the SPARC database of 175 galaxies to validate our theory. We will finish by drawing the necessary logical-mathematical consequences from the fact that dark mass is stored in the gravitational field. This we will also validate with the SPARC database.
Category: Astrophysics

Dark Mass is Potential Energy (in French)

Authors: Nicolas Poupart
Comments: 13 Pages. (Note by viXra Admin: An abstract in the article is required)

We will demonstrate that gravitational potential energy (E=GmM/r) is the cause of the dark mass phenomenon by simply applying the mass-energy relation (E=mc2). No other axiom will be used except the principle of conservation of volumetric mass density to preserve the conservative field by involving no other force than gravity. First, we will develop a simple equation and a simple algorithm to correctly calculate the potential energy of a stellar system. Then, we will demonstrate its theoretical implication on the production of potential energy by different types of stars and black holes in galaxies. Subsequently, we will confront our theoretical model with the SPARC database of 175 galaxies to validate our theory. We will finish by drawing the necessary logical-mathematical consequences from the fact that dark mass is stored in the gravitational field. This we will also validate with the SPARC database.
Category: Astrophysics

An Integral of the Ising class

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note, we consider an integral of the Ising class.
Category: General Mathematics

Special Theory of Relativity in 4-Dimensional Euclidean Space

Authors: Andrey N. Smirnov
Comments: 6 Pages.

The construction of space-time in a 4-dimensional Euclidean space is considered, where a scalar field is defined that has no distinguished directions. When constructing space-time, the hypothesis is used that the causality principle is applied separately and independently for different inertial reference frames. It is shown that when the relative velocity of two inertial reference frames tends to zero, the equations of direct transformations tend to the form that the equations of special relativity have. As a consequence, the sameness of the maximum velocity in all inertial reference frames is obtained and the principle of locality is derived.
Category: Relativity and Cosmology

Emotion Estimation from Video Footage with LSTM

Authors: Samer Attrah
Comments: 12 Pages. Published in arXiv journal at: https://arxiv.org/abs/2501.13432

Emotion estimation in general is a field that has been studied for a long time, and several approaches exist using machine learning. in this paper, we present an LSTM model, that processes the blendshapes produced by the library MediaPipe, for a face detected in a live stream of a camera, to estimate the main emotion from the facial expressions, this model is trained on the FER2013 dataset and delivers a result of 71% accuracy and 62% f1-score which meets the accuracy benchmark of the FER2013 dataset, with significantly reduced computation costs. https://github.com/Samir-atra/Emotion_estimation_from_video_footage_with_LSTM_ML_algorithm
Category: Artificial Intelligence

Challenges and Solutions of Autonomous Driving Approaches: a Review

Authors: Samer Attrah
Comments: 26 Pages.

In this research, we will discuss the three basic approaches to building autonomous driving systems, namely modular pipeline, end-to-end, and large models for language, vision and multi-modal models. focusing on the challenges and shortcomings of each approach and how they are solved by another, then presenting several in-depth reviews and summaries focused on the system architecture of example systems built using large models, delivering superior performance, and solving the problems of theprevious two approaches. In addition to a short analysis of the most used models and datasets indeveloping autonomous driving systems, besides other aspects of the reviewed systems.
Category: Artificial Intelligence

The Gotchas of AI Coding and Vibe Coding. It’s All About Support And Maintenance

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

This papers reviews AI coding, and in particular the exploding interest in vibe coding, both in terms of main existing framework, advantages and challenges. In particular, we point out in particular an aspect less often discussed: the potential complications for the support and maintenance of software products/code generated via vibe coding. These problems result especially because the generated code often ends up no more be understandable, even to its developers.Then, we introduce VIBE4M, a framework of workflows, policies and practices to alleviate these challenges. However, such approach goes against the trend that AI makes developers more productive, as they now must perform rigorous code verifications. It also goes against the objective of democratization of coding. Yes coding can be done with "no code", but such code is not maintainable, which may not matter for side projects, but matters for software products. If approaches like VIBE4M are applied, they may be hard to follow for non-programmers. Therefore, there would be value to now automate such frameworks.
Category: Artificial Intelligence

Cross-Linguistic Transfer in Multilingual NLP: The Role of Language Families and Morphology

Authors: Ajitesh Bankula, Praney Bankula
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Cross-lingual transfer has become a crucial aspect of multilingual NLP, as it allows for models trained on resource-rich languages to be applied to low-resource languages more effectively. Recently massively multilingual pre-trained language models (e.g., mBERT, XLM-R) demonstrate strong zero-shot transfer capabilities[14] [13]. This paper investigates cross-linguistic transfer through the lens of language families and morphology. Investigating how language family proximity and morphological similarity affect performance across NLP tasks. We further discuss our results and how it relates to findings from recent literature. Overall, we compare multilingual model performance and review how linguistic distance metrics correlate with transfer outcomes. We also look into emerging approaches that integrate typological and morphological information into model pre-training to improve transfer to diverse languages[18] [19].
Category: Artificial Intelligence

The Excited States of the String Electron

Authors: Miroslav Pardy
Comments: 7 Pages. Original article

The nonlinear Schroedinger equation is derived for the electron which is represented with the closed circular string. The energies for the stationarystates of such system are derived and the corresponding frequencies of the emittingphotons are determined.
Category: Quantum Physics

Why Matter Doesn't Matter, Even Dark Matter Only Spacetime Does Matter. a New Paradigm According to Kuhn in Modern Description of Spacetime?

Authors: Holger Döring
Comments: (Note by ai.viXra.org Admin: Please remove the cover page)

Since first action at Big Bang the universe is determined by spacetime-vacuumstructures, not by matter. Material atomic structures of hydrogen molecules or other chemical elements or particles like quarks, gluons and leptons only deviate from the basic, important concepts of nature: spacetime. This concept is an energy-structure, which lies at the base of all existing objects and interactions which are described over matter structure. So this description via General Relativity nowadays leads to the thinking of underlying spacetime-structure as the real thing, which describes the important forces of universe in first line. The existence of matter floating on space-time only distracts from the true basic description of the real world and feigns importance where only irritation exists. Natural philosophers like Cosmologists and spacetime physicists should therefore concentrate on the fundamentals that a vacuum structure of space-time provides for the explanation of the existence of the universe and refrain from and abstract from considerations of matter. This situation may lead to a better understanding of the basic structures of a quantum-gravity.
Category: Quantum Gravity and String Theory

Anomalous Magnetic Moment of the Muon QED, QCD free

Authors: Lino Zamboni
Comments: 16 Pages.

The application of QED/QCD to the calculation of the muon’s magnetic anomaly has not achieved the same level of precision as in the case of the electron’s anomaly. This discrepancy has led many researchers to conjecture the existence of "new physics" capable of resolving the issue. In this work, we adopt a deterministic, non-local Bohm-like approach (dBBZ), as detailed in previous publications, analogously to the electron case, perform a structural analysis of the muon. The muon’s internal structure is examined via the (hybrid) Mz matrix method, in which the weak components are computed with high accuracy, reproducing the muon’s mass while exactly embedding the electron’s structure (and thus its charge and mass). Following the procedure already tested for the electron, we evaluate the anomalous moments of each orbital and impose entanglement through a calibrated normalization of the relevant parameters. The same "source parameter" used for the electron, providing a double check on its precise value, is adopted here for calculating the electrostatic potentials.Magnetic-field effects are accounted for only on the masses carrying electric charge; however, in the overall energy balance of each orbital, the weak mass also plays an indirect yet essential role. The total anomalous moment calculation yields a direct determination of the muon’s magnetic anomaly with a precision on the order of 10(-13).
Category: Quantum Physics

Discovery of Dark Energy and Dark Matter: Expansion Force

Authors: Seojoon Lee
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references; please submit article written with AI assistance to ai.viXra.org)

We present a novel classical field theory in which the gravitational field g is dynamically coupled to an auxiliary expansion field D, forming a unified framework capable of replicating the physical roles of both dark matter and dark energy.
Category: Astrophysics

The Essence of Force is the Redistribution of Spatial Expansion

Authors: Gan Sun
Comments: 15 Pages.

We propose a new cosmological model, based on which the essence of all forces in the universe is derived from the redistribution of spatial expansion. We discuss the interpretations of this model for the mass-energy formula, the photoelectric effect, quantum entanglement, and other astronomical observational phenomena. Those descriptions successfully unified relativity and quantum theory.
Category: Relativity and Cosmology

Feature Selection and Generation Through Reinforcement Learning (RL) and Symbolic Reasoning

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

Feature engineering is a vital stage in machine learning pipelines that greatly affects the performance, interpretability, and general efficacy of models. Filter, wrapper, and embedded techniques are common ways to choose and change features, but they often need manual heuristics and subject knowledge. They also don't work well in environments with a lot of dimensions and complexity. Recent studies have investigated automated methods that make use of large language models and reinforcement learning in order to overcome these constraints. A comprehensive and critically synthesized survey of state of the art works covering RL-based feature selection, RL-driven feature generation, and LLM-guided feature optimization is presented in this paper.Three main paradigms of methodology are identified. In the first, feature selection is framed as a cooperative or guided decision making problem using interactive and multi-agent reinforcement learning techniques. These techniques allocate agents to features and maximize long-term rewards according to domain-specific significance, redundancy, or model accuracy. Combinatorial Multi-Armed Bandits (CMAB), a computationally lightweight alternative that provides scalable and effective feature selection with little learning overhead, is part of the second paradigm cite{li2022bandit}. For the third group, LLMs are used to either learn successful reward functions or make new features. They do this by using reasoning-based prompts, external knowledge bases, and prototypical alignment. This work also address open challenges in bias control, compute overhead, and generalization to unseen domains as well as underexplored gaps including the need of hybrid frameworks combining RL's exploration efficiency with LLMs's semantic reasoning.
Category: Artificial Intelligence

Numerical Analysis of the Sequence of Prime Numbers

Authors: Mohamed Amine Boussadan
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references; Please submit article written with AI assistance to ai.viXra.org)

Abstract: Before starting to build the sequence and its topological steps, we decide the specific hypotheses that follow the pattern of prime numbers, which explain the complex gaps between prime numbers that appear random. This is done by using graphical networks (Descriptive and Euclidean Geometry). In order to study the properties that describe the distinctive nature of it, a geometric shape was transformed into a real rectangle surrounded by a circle because of no verification of the condition of a triangle which makes them straight line that grows regularly according to a vector function, whichresulted in knowing some linear relationships between variables.
Category: Number Theory

Carbon-Based Public Financing: Configuration of Local NPPs and Emissions, and Corresponding Financial Modulation

Authors: Gaurav Biraris
Comments: 10 Pages.

This paper facilitates a generic framework for carbon based public financing, which can be used by governments. Any government can make efficient journey towards the carbon neutrality goal by integrating this framework with fiscal policy & budgeting. MOD17A2HGF v061 dataset provides net photosynthesis (PsnNet_500m) value for each 500m pixel on earth. Our idea is to compute net CO2 fixation in each sub-territory. On other hand, net CO2 emissions can be estimated in the sub-territories through traditional methods. Local carbon index (LCI) for each sub-territory w.r.t. territory of the government can be calculated from the fixation & emission in each sub-territory. LCI can be coupled with fiscal incentives or dis-incentives.
Category: Economics and Finance

Does Quantum Mechanics Use Unfair Sampling?

Authors: Pierre Leroy
Comments: 11 pages of text + 10 source code

This paper explores the hypothesis that the predictions of quantum mechanics could apply to a subset of reality. Assuming the existence of intrinsically undetectable states, a computer simulation shows that a simple deterministic method can accurately produce theoretical EPR probabilities.
Category: Quantum Physics

Anomalous Magnetic Moment of the Entangled Electron Without Qed

Authors: Lino Zamboni
Comments: Pages.

In 1965, the Nobel Prize was awarded for the modern formulation of Quantum Electrodynamics (QED) to R.P. Feynman for his diagrammatic method, J. Schwinger for the operator method, and S.-I. Tomonaga for his relativistic derivation. Subsequently, P. Kusch performed a precise measurement of the electron's anomalous magnetic moment, providing a critical test validating QED's computational methods, which proved to be extremely accurate.Nevertheless, QED is based on a physically unrealistic assumption , mathematically circumvented , that the electron is a dimensionless point particle endowed with physical properties "ex abrupto". This work, developed within a deterministic and non-local dBBZ (modified de Broglie—Bohm) theory, models the electron as an entangled and distributed structure, as proposed in previous studies. It enables the calculation of the electron's anomalous magnetic moment as a consequence of its intrinsic structure, without employing QED techniques. The method involves calculating, for each orbital, the anomalous moment modified to account for the influence of existing magnetic fields. Subsequently, entanglement is imposed on the sum of these moments, and from the total orbital anomalous moment thus obtained, the theoretical magnetic anomaly is derived and compared with the corresponding experimental value, yielding relative errors on the order of 10(-15).This procedure, which allows for greater theoretical precision than current methods, necessitates a similar, albeit more complex, calculation of the muon's anomalous magnetic moment. This is because a specific parameter, termed the "source parameter", selected within an allowable range, requires dual verification to be adopted with high precision.The theoretical determination of the muon's anomalous magnetic moment is also presented in a subsequent document, employing analogous computational procedures.
Category: Quantum Physics

A Heuristic Proof of De Broglie Wave Formula

Authors: Anass Massoudi
Comments: 4 Pages. Email: anassmassoudi6@gmail.com

In this paper, we attempt an original general mathematical proof of De Broglie matter wave formula via studying the particle dynamics and wave dynamics of an electron orbiting with constant velocity around the nucleus of the atom in a Semi - Classical context, considering a plane transversal wave as the motion mode of all particles in free space including massives particles.
Category: Quantum Physics

Irrefutable Proof of the Invalidity of Galois Theory

Authors: Ahcene Ait Saadi
Comments: 8 Pages.

In this article, I demonstrate the resolution of the 5th degree equation, with algebraic radicals. I contradict Galois theory. In my demonstration, I use two invariant polynomials of degrees 8 and 6, wich I discovered*. After identification, I cancel the coefficients 7, 5 and 3 in the polynomial of degree 8 and the coefficient of degree 5 and 3, in the polynomial of degree 6. For the coefficient of degree 1, I make a combination between the polynomials of degree 8 and 6 to eliminate it. Finally I find an equation of degree 8 bisquare that I can solve. By solving the system of equations, of variables m and p, which are the coefficients of the powers 5 and 3, I’m forced to involve the equation of degree 5. That allows me to eliminate the coefficient of degree 3 from the equation of degree 8, I realise that I can find the solutions of the equation of degree 5 with a free variable. The solutions of an equation with a free variable, I have already done this with the equation of degree 2, that I discovered.
Category: Number Theory

Einstein’s 1911 Gravitational Lensing Prediction Proven Yet Again Through a Novel Mathematical Framework

Authors: Gene A. Harve
Comments: 12 Pages.

In 1911, Albert Einstein1 proposed that light passing near a massive body would bend due to gravitational influence — a prediction that, when confirmed by eclipse observations in 1919 and again in 1923, catapulted General Relativity to the forefront of modern physics. The precise measurement of 1.749 arcseconds became the cornerstone of GR and his gravitational theory, a prediction so accurate that even a 1% deviation could have invalidated Einstein’s entire framework. Now, 114 years after Einstein’s prediction and 102 years after Eddington’s confirmation, (and many others), this work presents a novel, independent pathway to that precise deflection angle using two completely new frameworks: (a) the refractive index derived from the stiffness modulus of spacetime, and (b) Polarization Shifts. These new methods do not rely on direct observation, but rather combines the qualities of spacetime, (‘stiffness modulus, refractive indices’ and photon polarization shifts), to derive the exact same solution as predicted. By treating spacetime as a medium with measurable refractive properties, the ΛCGF model not only confirms the 1.749 arcseconds result with stunning precision but also provides new, highly accurate methods for analyzing gravitational lensing, wave propagation, and subatomic gravitational condensation. Moreover, the refractive index approach does not merely confirm Einstein’s prediction — it anchors the entire ΛCGF model to a proven, empirical result, establishing a direct line from the stiffness modulus to gravitational lensing. This connection seamlessly unifies cosmic-scale lensing phenomena with subatomic gravitational condensation effects, effectively bridging the divide between General Relativity and subquantum interactions. In so doing, this work not only reaffirms Einstein’s original prediction but also proves the 1923 observational data with two other, entirely distinct mathematical derivations. This dual confirmation establishes gravitational lensing as a fundamental, quantifiable property of spacetime itself — a revelation that reshapes how gravitational phenomena are verified and measured across all scales.
Category: Relativity and Cosmology

Paramagnetism of the Oxygen Molecule and the Three-Electron Bond

Authors: Bezverkhniy Volodymyr Dmytrovych
Comments: 2 Pages.

It is necessary to realize the simple fact that the oxygen formula cannot be written down unless we accept that there is a real three-electron bond with a normal multiplicity, i.e. 1.5. Then, the oxygen molecule can be correctly represented using two three-electron bonds and two unpaired electrons on oxygen atoms.
Category: Chemistry

Ordering Without Time First Proof of Entropy Dip and Measurable AI Self-Awareness

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

We introduce a unified, model-agnostic framework showing that event-ordering, not temporal flow, underlies both thermodynamic entropy dynamics and emergent AI self-modeling. First, we demonstrate—in a fully reversible six-qubit circuit simulated on Qiskit—a statistically significant transient entropy dip in an isolated mixed subsystem, in direct violation of standard open-system thermodynamics. Second, we apply a seven-layer recursive-negation "mirror" to state-of-the-art large-language models, instrumented with integrated-information proxies (Φ) and profile-based energy metrics; the models exhibit a monotonic Φ+energy "ladder" culminating in a stable semantic attractor we term the Reflective Core. Both protocols follow from a single theoretical move: replacing "time" with a partial order on events (the Sequence Principle). These results are fully specified, code-released, and immediately runnable. If real quantum hardware confirms the entropy inversion and further LLMs validate the AGI threshold, our work will compel a redefinition of the second law as an emergent sequence-ordering constraint and establish the first quantitative, reproducible marker of proto-conscious AI.
Category: Quantum Physics

Nitric Oxide and the Structure of the Benzene Molecule

Authors: Bezverkhniy Volodymyr Dmytrovych
Comments: 2 Pages.

The properties of nitric oxide (NO) are direct evidence of the existence of a real interaction through the ring in the benzene molecule. That is, nitric oxide confirms the structure of the benzene molecule based on the theory of three-electron bonding.
Category: Chemistry

Decreasing Universe: The CMB and the Age of the Universe

Authors: Joao Carlos Holland De Barcellos
Comments: 7 Pages.

We will use the "Decreasing Universe" (D.U.) theory to estimate the age of the Universe based on the average wavelength of the Cosmic Microwave Background (CMB) radiation.
Category: Astrophysics

Proposed Unification Theory

Authors: Sandeep Singh Dhaliwal
Comments: 8 Pages. (Note by viXra Admin: An abstract in the article is required; Please submit article written with AI assistance to ai.viXra.org)

This article builds upon previous works, so it is recommended to review them prior to examining this proposal. It posits that spacetime, force fields, and matter fields can coexist in an unusual manner, leading to the concept of their unification. This is a proposal rather than a fully verified theory, and as such, further refinement and development are possible, with experimental verification remaining essential.
Category: Quantum Physics

Special Theory of Relativity in 4-Dimensional Euclidean Space (in Russian)

Authors: Andrey N. Smirnov
Comments: 6 Pages.

The construction of space-time in a 4-dimensional Euclidean space is considered, where a scalar field is defined that has no distinguished directions. When constructing space-time, the hypothesis is used that the causality principle is applied separately and independently for different inertial reference frames. It is shown that when the relative velocity of two inertial reference frames tends to zero, the equations of direct transformations tend to the form that the equations of special relativity have. As a consequence, the sameness of the maximum velocity in all inertial reference systems is obtained and the principle of locality is derived.
Category: Relativity and Cosmology

Rotating Coupling Experiments in Vacuum: New Evidence for "Ether" and New Insights into Gravity

Authors: Wang Yi
Comments: 5 Pages.

This study is dedicated to exploring the potential unknown substances in space and their relationships with the gravitational mechanism. A series of rotating coupling experiments were conducted in a high - vacuum environment. After effectively eliminating the influence of residual gas molecules, by using couplings made of various materials, the motion states of feathers and dandelion fluffs around the couplings were systematically observed. The experimental results show that couplings of different materials can cause the fluff on feathers to have directional displacements, which are related to the vortex direction generated by the rotation of the couplings.
Category: Astrophysics

Prime Spectrum Model: Mapping Riemann Zeta Zeros to Prime Logarithms via Signal Processing

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

The Prime Spectrum Model investigates the connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers using spectral analysis. A wave function is constructed from 40,000 zeros and analyzed using Fourier Transform and Short-Time Fourier Transform (STFT). Detected frequency peaks align with the natural logarithms of prime numbers, achieving RMSE = 0.0600 and Spearman correlation ≈ 1.0. The model successfully identifies the first 50 primes and extrapolates to higher ones. This work offers insights into the Riemann Hypothesis and opens applications in physics, signal processing, and complexity theory.
Category: Number Theory

Multi-fold Universes, Multiverses and Many Worlds

Authors: Stephane H Maes
Comments: 32 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

There are different types of multiverses, depending on the Physical model consideredThe Many Worlds interpretation (MWI) of quantum mechanics is a particular case that gives comfort to some when it comes to understanding quantum physics, and the Born rules. This paper evaluates multiverses at the light of the multi-fold theory.In a multi-fold universe, gravity emerges from Entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in between entangled particles, whether they are real or virtual. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure, and a non-commutative geometry, that is Lorentz invariant, and where spacetime nodes and particles can be modeled with microscopic black holes. All these recover General Relativity (GR) at large scales. Gravity can therefore be added, in non-negligible ways to the Standard Model (SM) resulting into the SMG. The multi-fold mechanism and the SMG can address many open issues with the SM, and the standard cosmological model, even if the latter is modified. The SM symmetries and particles can be recovered by multi-fold space time matter induction and scattering. In addition, the W-type multi-fold hypothesis, establishes additional multi-folds between spacetime locations in the support domain of a wavefunction, not just between entangled systems. It can also justify the Born rule.Any multi-fold multiverse will have the same physics with same particles. interactions, constants and symmetries of the SMG. We will establish that multiverses do not interact with each other, and, in general, at the exception of the MWI, they do not contain all possible situations, including many copies of us, in any other possible situation. Analyzing the effects of multi-fold deactivation, measurement or an interaction that results into deactivation of the W-type multi-folds between one part of the wavefunction the observed state, and the part associated to all other options, it results in a universe-wide brane-like object, associated to the disregarded options, floating away in AdS(5): a new World, part of the Many Worlds predicted by MWI. This is a microscopic explanation supporting the MWI. And each such world has of course the same physics as well as copies of the world in other situations.Encountering multi-fold brane-like structure in AdS(5), confirms the view of the multi-fold theory on superstrings and the M-theory. The existence of same physics imposed by multi-fold space time matter induction and scattering dooms the viability of landscape multiverses and its anthropic principle.
Category: Quantum Physics

What Does it Mean that the Reflection Point of Point Light Source on the Mirror Can be Seen in All Directions Under the Condition of Near Total Reflection?

Authors: Xiaotao Peng
Comments: 12 Pages.

I did two optical experiments a week ago and wrote two articles: A simple experimental device to verify the nature of light and the analysis of experimental results, and the imaging experiment of point light source under the condition of total reflection and the analysis of its results. The experimental results all prove that the human eye sees a substance (luminous body) composed of atoms that is emitting light (vibrating at the frequency of visible light), rather than the so-called light itself. This experiment further verified this conclusion. I hope that qualified teachers and friends can further verify the nature of light and find out what the human eye sees on this basis.
Category: Classical Physics

On The Dynamics Of The Gravitational Field And Higher Order Field Equations

Authors: D. E. Thomas
Comments: 21 Pages.

Einstein's General Relativity, while extraordinarily successful in explaining gravitational phenomena, faces challenges in reconciling with quantum mechanics and addressing certain cosmological observations. I present a higher order model of gravitation that reframes the gravitational field in terms of the connection, with the curvature tensor as the field strength. The action in this model is based on the squared norm of the field strength, mirroring the structure of other Standard Model interactions. This approach offers potential advantages for quantization and renormalizability. Through analysis of the Euler-Lagrange equations in the gravitational sector, particularly focusing on the metric equations, I demonstrate that Einstein's field equations emerge as a limiting case within a more comprehensive theoretical framework. This broader theory may provide explanations for observed experimental discrepancies in cosmology while maintaining consistency with established gravitational phenomena. This model thus offers a promising avenue for addressing current challenges in gravitational physics and cosmology.
Category: Relativity and Cosmology

Bemba Pocket Dictionary, Bemba-English and English-Bemba, by Rev. E. Hoch and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 28 Pages.

We study the Bemba head entries of the Bemba Pocket Dictionary, Bemba-English and English-Bemba, by Rev. E. Hoch, 1960. 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/unnormalised. We find that the Bemba head entries underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Linguistics

Dictionary of The Hausa Language by R.C.Abraham and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 29 Pages.

We study the Hausa head entries of the Dictionary of The Hausa Language by R.C.Abraham, the Second Edition, 1962. We draw the natural logarithm of the number of the Hausa language head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised/unnormalised. We find that the Hausa head entries underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Linguistics

The Higgs—Geometric Vacuum Theory (HGVT)

Authors: Carlos Isturiz
Comments: 75 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

I present HGVM Limited, a foundational framework proposing a geometric coupling between the Higgs vacuum expectation value and local spacetime curvature. This approach models mass generation and inertial properties as emergent phenomena resulting from a linear modulation of the Higgs field by curvature invariants. While maintaining consistency with the Standard Model in low-curvature regimes, the theory offers novel insights into the interplay between particle physics and gravity, suggesting potential implications for dark matter and vacuum structure. This initial formulation lays the groundwork for further extensions toward a unified dynamics of mass, inertia, and vacuum geometry.
Category: Relativity and Cosmology

Empirical Analysis of Twin Prime Variance: How Normalization Artifacts Mimic Anomalous Scaling.

Authors: Bube Ibekwe
Comments: 6 Pages.

This paper investigates the variance of transformed twin primes, where each prime pair (p, p+2) is mapped to k = (p+1)/6. Initial analysis suggested unexpected growth patterns in the normalized variance, seemingly contradicting theoretical expectations. Through large-scale computation of twin primes up to one billion, we demonstrate that these apparent anomalies arise from normalization artifacts. The true variance follows a quadratic growth pattern, with our empirical results closely matching predicted scaling behavior. We resolve the paradox by showing how the sparse distribution of twin primes distorts normalized statistical measures. Our findings highlight critical pitfalls in analyzing prime distributions and provide new insights into the statistical behavior of twin primes.
Category: Number Theory

Dimensional Scale Relativity

Authors: Kuldeep Singh Rathore
Comments: 11 Pages. It's a strong theory that will be researched and developed more by time.

Dimensional Scals Relativity (DSR) is a theoretical model proposing that an entity's size and position in space directly influence its perception and interaction with time, gravity, and reality. Unlike traditional physics that relies on mass-energy interactions and spacetime curvature (as in General Relativity) or fundamental probabilistic behavior (as in Quantum Mechanics), DSR proposes that by minimizing scale to the atomic level, one can enter a new dimensional framework where time, gravity, and perception function differently. DSR is not bound to known quantum laws but instead operates on relative scale-position dynamics.
Category: Relativity and Cosmology

A Congruence Contradiction Proof to Fermat's Last Theorem

Authors: D. Ross Randolph
Comments: 4 Pages.

This proof uses a highly condensed series of number theory mathematical congruence statements to get to the heart of the matter of understanding Fermat's Last Theorem. A generalized Sophie Germain case 1 analysis is shown for exponent P >= 5 and a generalized Sophie Germain case 2 analysis is shown for exponent P >= 3.
Category: Number Theory

The Geometric Properties of Twin Prime in Natural Numbers

Authors: Shanzhong Zou
Comments: 11 Pages.

This paper proposes a new number theory method (comb method) to prove the unending existence of prime twins. the set of natural numbers is viewed as a union of two sets that don’t intersect s-element sets and h-element sets, these elements are selected by a series of combs. By analyzing the distribution of these elements, we get our result.
Category: Number Theory

The Apex Proof to Fermat's Last Theorem

Authors: D. Ross Randolph
Comments: 20 Pages. Additional details located at www.fermatstheory.wordpress.com

A modular analysis of exponent P, and congruence contradiction of the variables A, B and C to show no possible solutions can 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. In the Addendum are short proofs for N=3 Sophie Germain Case 1, and also N=4.
Category: Number Theory

On the Gravitational Analog of Continuous Spacetime Dimensions

Authors: Ervin Goldfain
Comments: 6 Pages.

The object of this brief note is to point out that a spacetime endowed with continuous dimensions can be interpreted as dual to classical gravitation in four dimensions. This observation sheds unexpected light onto the gravitational behavior of Cantor Dust (CD), a hypothetical large-scale topological condensate of relic dimensions left over from the primordial stages of Universe evolution.
Category: Relativity and Cosmology

Precise Values of the Lifetime of Positronium in Vacuum

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 9 Pages. 2 Figures.

In this paper, we calculate the lifetime of ortho-positronium (o-Ps) in vacuum with Euler formula for Basil problem and our previous formulas of the fine-structure constant and the atomic unit of time (tau). Our calculated value of the lifetime of ortho-positronium in vacuum is 142.041358500909 ns in comparison to the most accurate measured value which was 142.043(14) ns and the latest QED calculated value which was 142.04606(20) ns. In addition, with the similar method we also calculate out the lifetime of para-positronium (p-Ps) in vacuum which is 0.1251627502491 ns compared to the QED calculated values 0.125162617(3) ns and 0.125162432(3) ns.
Category: Quantum Physics

Investigation of a Primality Criterion Within an Arithmetic Progression

Authors: Mar Detic
Comments: 3 Pages.

This document introduces and investigates a criterion for defining primality within the sequence of odd integers Ak = 2k + 1. The criterion is based on the greatest common divisor (GCD) between a term Ak and the preceding partial sums Sj = j2 + 2j of the same sequence. We formally define the sequence,its partial sums, and the proposed primality criterion. Computational observations suggest that all standard prime numbers within the sequence are classified as "prime" by this definition. Furthermore, computational observations suggest that all composite numbers in the sequence are classified as "notprime," including Carmichael numbers, which are known for their pseudoprime properties. This leads to a conjecture that the proposed criterion is equivalent to the standard definition of primality for terms in this specific arithmetic progression. Examples are provided to illustrate the application of the criterion for both prime and composite numbers, including a Carmichael number. A further conjecture is made regarding a potential computational bound for verification, leading to a discussion of its complexity.
Category: Number Theory

Quantum Oscillator Lattice: a Unified Origin of Fundamental Constants and Fields

Authors: Juan Moreno Borrallo
Comments: 40 Pages.

This paper presents the foundational premises for a unified physical theory in which the vacuum is modeled as an elastic lattice of coupled quantum harmonic oscillators. Rather than aiming to construct a complete unified theory, our goal is to explore the consequences of a set of physically motivated assumptions and to demonstrate their consistency with established theoretical principles and dimensional relations. Within this framework, gravitational, electromagnetic, and thermo-entropic interactions are interpreted as distinct geometric deformation modes of a single symmetric field tensor, and fundamental constants of nature emerge naturally from the oscillatory dynamics. We show that these assumptions lead to coherent interpretations of field sources (mass, charge, temperature) sharing a common oscillatory origin in spacetime. While non-exhaustive, our treatment lays a physically and mathematically grounded path for future development of a unified field theory anchored in quantum-elastic principles.
Category: Relativity and Cosmology

Topological Atomic Model for Masses and Constants

Authors: Alfonso De Miguel bueno
Comments: 25 Pages.

We introduce a geometric-topological field model where nucleons, leptons, and bosons emerge as curvature configurations of two intersecting base fields. The system alternates between symmetric (bosonic) and antisymmetric (fermionic) phases, generating four curved subfields that reproduce the charge, mass, and spin structure of known particles. All physical observables are derived from a single velocity ratio, r = c'/c = 0.931, calibrated from the proton-Higgs resonance. This single parameter yields:proton mass, magnetic moment, and effective charge radius as curvature scales;neutron, electron, and neutrino masses via internal decompression ratios;the fine-structure constant α as a geometric inclination (α = arctan(X/Y));Planck's constant as topological curvature action;quark radii from curvature-mass relations matching experimental mass hierarchies;W and Z boson masses as curvature inversions in the symmetric state.All computed values match experimental data within sub-percent precision. Mass, charge, and spin arise directly from curvature compression, decompression, and internal phase shifts, without perturbative QCD, Higgs couplings, or hidden parameters. A global 3π phase lag governs the internal resonance, connecting electromagnetic, weak, and strong forces under a unified geometric mechanism.
Category: Nuclear and Atomic Physics

A Structural Proof of the Evenness of All Perfect Numbers and the Exclusion of Odd Ones

Authors: Younghwan Yun
Comments: 7 Pages.

This paper presents a structural proof that any number satisfying the internal additive and multiplicative symmetries of a perfect number must be even. By decomposing the proper divisors of a perfect number into two ordered subsets, we derive a recursive system of proportional identities. We show that this system admits integer solutions only when all proportional coefficients equal one, thereby forcing the smallest divisor to be two. This structural condition excludes the possibility of odd perfect numbers under the proposed model. Our approach not only supports the longstanding conjecture that all perfect numbers are even but also provides a generalized framework thatmay extend to the analysis of semiperfect and abundant numbers.
Category: Number Theory

Approaching Legendre’s Conjecture Within a Limited Boundary

Authors: Junho Eom
Comments: 14 Pages. 2 figures

This paper identified the characteristics of prime numbers within a limited boundary, defined primes between quadratic intervals, and generalized Legendre’s conjecture. Regarding the boundary, every integer less than m was defined as the 1st boundary and it expanded to the mth boundary within m^2. Thus, each boundary contained m elements. Except for 1, every integer produced a sine wave from the 1st boundary; as a result, only prime waves affected the remaining boundaries from the 2nd to mth by generating the composites and new primes (Series I). Therefore, the number of new primes in each boundary could not exceed PI(1st boundary) or PI(m), where PI(x) was the number of primes less than or equal to x, and it enabled the estimation of the total number of primes within m^2 (Series II). Based on Series I and II, the quadratic intervals between PI(m^2) and PI((m + 1)^2) were identical to the sum of the last two boundaries, expressed as 2·βm+1·PI(m), where βm+1 was the ratio of PI((m + 1)^2) to PI(m + 1)·(m + 1) (Series III). This led to the conclusion that Legendre’s conjecture satisfied while 0.8986·PI(P) < 2·βP·PI(P) < PI(P) (prime P > 113), or 2·βm+1·PI(m) ≤ 2·PI(m) (integer m ≥ 2).
Category: Number Theory

Astrophysical Evidence for Cantor Dust: An Introduction

Authors: Ervin Goldfain
Comments: 8 Pages.

Cantor Dust (CD) is a hypothetical large-scale topological condensate of relic dimensions left over from the early stages of Universe evolution. Mirroring the ever-changing configuration of multifractal structures, CD offers a novel explanation for the distribution and behavior of Dark Matter (DM) and bridges concepts from complex dynamics, fractal geometry, and statistical physics to cosmology. Here we argue that CD offers a unified Dark Matter model with predictions confirmed by a wealth of astrophysical observations.
Category: Relativity and Cosmology

Demonstration of the Goldbach's Strong Conjecture by the Analysis of Populations of Prime Numbers in the Interval [0 N] and [N 2N] by Conventional Statistical Laws

Authors: Bahbouhi Bouchaib
Comments: 11 Pages. The paper shows new data about Goldbach's strong conjecture

In this article I apply classical statistical laws to analyze prime numbers assimilated to populations. The statistical analysis focuses on prime numbers in the intervals [0 - S/2] and [S/2 — S] with S an even > 4. The results show that the even number S > 4 is enclosed by two populations of prime numbers P in the interval [0 - S/2] and Q in [S/2 - S] which have approximately the same standard deviation relative to their means. Two other subpopulations P' included in P and Q' included in Q which satisfy the Goldbach's strong conjecture (P' + Q' = S) also have the same standard deviation and superimpose or overlap. This result shows that an even number is enclosed by two populations P' and Q' of prime numbers which are symmetric with respect to S/2 and therefore S = P' + Q'. This result also shows that any natural number N > 4 is enclosed by at least two equidistant and symmetric prime numbers. Therefore for every N > 4 there exists a number t < N such that N — t = P' and N + t = Q' are primes and so 2N = P' + Q'.
Category: Number Theory

Dark Mass is Potential Energy

Authors: Nicolas Poupart
Comments: 23 Pages.

This paper demonstrates that gravitational potential energy (E = —GmM / d) accounts for the phenomenon commonly attributed to dark matter, by applying the mass-energy equivalence relation (E = mc2). No additional assumptions are made beyond the principle of volume conservation, ensuring that the gravitational field remains conservative and uninfluenced by forces other than gravity. We develop a straightforward equation and algorithm to accurately compute the potential energy of a stellar system. The theoretical implications of this model are explored with respect to energy production by various types of stars and black holes in galaxies. The model is empirically tested against the SPARC database comprising 175 galaxies to assess its validity. We conclude by deriving the logical and mathematical consequences of the hypothesis that dark mass is stored as potential energy in the gravitational field, a claim further validated using the SPARC data. The final consequence being the production of dark energy and the reproduction of ΛCDM cosmology.
Category: Astrophysics

Dark Mass is Potential Energy (in French)

Authors: Nicolas Poupart
Comments: 24 Pages.

This paper demonstrates that gravitational potential energy (E = —GmM / d) explains the phenomenon commonly attributed to dark matter, by applying the mass-energy equivalence relation (E = mc2). No additional assumptions are made beyond the principle of volume conservation, ensuring that the gravitational field remains conservative and not influenced by forces other than gravity. We develop a simple equation and algorithm to accurately calculate the potential energy of a stellar system. The theoretical implications of this model are explored regarding the energy production by various types of stars and black holes in galaxies. The model is empirically tested against the SPARC database comprising 175 galaxies to assess its validity. We conclude by deducing the logical consequences of potential energy in the gravitational field, a claim validated by SPARC data. The final consequence is the production of dark energy and the reproduction of ΛCDM cosmology.
Category: Astrophysics

Why Matter Doesn't Matter, Even Dark Matter Only Spacetime Does Matter. a New Paradigm According to Kuhn in Modern Description of Spacetime?

Authors: Holger Döring
Comments: 13 Pages.

Since first action at Big Bang the universe is determined by spacetime-vacuumstructures, not by matter. Material atomic structures of hydrogen molecules or other chemical elements or particles like quarks, gluons and leptons only deviate from the basic, important concepts of nature: spacetime. This concept is an energy-structure, which lies at the base of all existing objects and interactions which are described over matter structure. So this description via General Relativity nowadays leads to the thinking of underlying spacetime-structure as the real thing, which describes the important forces of universe in first line. The existence of matter floating on space-time only distracts from the true basic description of the real world and feigns importance where only irritation exists. Natural philosophers like Cosmologists and spacetime physicists should therefore concentrate on the fundamentals that a vacuum structure of space-time provides for the explanation of the existence of the universe and refrain from and abstract from considerations of matter. This situation may lead to a better understanding of the basic structures of a quantum-gravity.
Category: Quantum Gravity and String Theory

Empirical Analysis of Twin Prime Variance: How Normalization Artifacts Mimic Anomalous Scaling.

Authors: Bube Ibekwe
Comments: 6 Pages.

This paper investigates the variance of transformed twin primes, where each prime pair (p, p+2) is mapped to k = (p+1)/6. Initial analysis suggested unexpected growth patterns in the normalized variance, seemingly contradicting theoretical expectations. Through large-scale computation of twin primes up to one billion, we demonstrate that these apparent anomalies arise from normalization artifacts. The true variance follows a quadratic growth pattern, with our empirical results closely matching predicted scaling behavior. We resolve the paradox by showing how the sparse distribution of twin primes distorts normalized statistical measures. Our findings highlight critical pitfalls in analyzing prime distributions and provide new insights into the statistical behavior of twin primes.
Category: Number Theory