All Submission Categories

Ramanujan Transformations and Robin Defects

Authors: Payam Danesh
Comments: 9 Pages.

We studied the Robin defect associated with the inequality σ(n)<e^γ nlogu2061logu2061n, express its Laplace transform through Ramanujan’s transformation for the divisor Lambert series and isolate the precise difference between smoothed positivity and coefficientwise positivity. The main results give us an exact Ramanujan-transformed identity for the Robin defect, an equivalent coefficientwise formulation of the Riemann Hypothesis showing why transform-level positivity cannot by itself prove the hypothesis and an extremal reduction to colossally abundant and highest abundant numbers. Numerical data for early extremal integers illustrate how the normalized defect behaves past the exceptional value 5040. Ramanujan’s identities provide powerful global control, but the Riemann Hypothesis requires pointwise positivity at the extremal divisor-rich integers.
Category: Number Theory

Optimization Model for Polyline Offset

Authors: Zitao Xu
Comments: 7 Pages.

Classical offset algorithms focus on constructing offset curves and surfaces. Optimization-based geometry processing has also been extensively studied for mesh fairing, deformation, and parameterization. The present work differs from both directions by introducing a least-squares formulation whose unknowns are tangential displacements of offset vertices, yielding a globally optimized offset configuration.
Category: Geometry

Analyzing a Variant Version of a Fibonacci Polynomial

Authors: Marciano L. Legarde
Comments: 12 Pages.

In this paper, we introduce a new finite polynomial called the "Variant Fibonacci Polynomial". This polynomial is defined by using the standard Fibonacci sequence as both the coefficients and the exponents of each term. Although the definition is simple, it leads to several interesting mathematical properties.We begin by defining the polynomial and giving several examples. We then evaluate it at different values of x, identify its guaranteed real root, discuss its complex roots, and derive formulas for both its derivative and antiderivative. We also examine the infinite series version of the polynomial and observe when it converges and when it diverges.Finally, we discuss whether this polynomial could be used to construct a new type of series expansion for functions and whether such an expansion might eventually be useful for solving differential equations. While it is still too early to draw definite conclusions, the results of this paper suggest that the Variant Fibonacci Polynomial is an interesting mathematical object that deserves further study.
Category: General Mathematics

On a Quadratic Collatz Type Map Governed by Prime Factorization: A Conjectural Universal Cycle, Two Reduction Theorems and an Intrinsic Computational Barrier

Authors: Christoper Mututu
Comments: 36 Pages.

We study a map T on the integers defined by T(n)=n^2+1 when n is prime or even and T(n)=n/P(n) when n is odd composite, where P(n) denotes a designated prime factor n. Two variants arise according to the choice of P(n). In Part I, P(n) is the largest prime factor of n while in Part II, it is the smallest. Informally, the conjecture of this paper asserts that every integer greater than one in absolute value eventually enters the single twelve element cycle5→26→677→458330→210066388901→52357→41→1682→2829125→1625→125→25 and remains there forever. Formally, we verify this for every integer n∈[2,1000] under Part I with no exception and no alternate cycle observed and we conjecture it holds for every integer n in the domain Z^*=Z {-1,0,1} but we do not prove it.Toward this conjecture, we prove two theorems. The first is exact rather than asymptotic. For any odd composite m, repeated application of the largest prime factor reduction reaches a prime in precisely Ω(m)-1 steps where Ω(m) counts the prime factors of m with multiplicity. Each application removes exactly one element from the prime factorization multiset m so the count decreases by exactly one per step and terminates uniquely at a prime. The second theorem follows from the first. Under the extension of primality to negative integers through |n|, which is the only convention under which the conjecture is well posed on Z, every negative integer reaches a positive value within at most Ω(|n|) steps. This reduces the negative integer case of the conjecture entirely to the positive integer case. We also identify an obstruction to further verification that is structural rather than a matter of computing resources. The reduction step of T requires the complete factorization of the input which is a problem for which no general sub exponential algorithm is known. Repeated application of the squaring branch can therefore produce integers whose factorization lies beyond any presently known method regardless of computing time available. Our verification required factoring intermediate values of up to 96 digits and succeeded in every instance though with no guarantee that a harder instance does not arise beyond the tested range. For Part II, this obstruction is severe enough to foreclose even a conjecture. Every trajectory examined exceeded 100 digits within fewer than 25 iterations without any value repeating. We are unable to characterize the long-term behavior of Part II by any method available to us and as a result, Part II is entirely open.
Category: Number Theory

The Giza Pyramid Complex as an Analogy to the Voyager Mission

Authors: Andrey V. Voron
Comments: 8 Pages.

This paper explores a potential analogy arising from a comparison between the space missions of Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 on one hand, and the Giza pyramid complex project on the other. Within this framework, five plausible assumptions are examined. Based on their outcomes, the study demonstrates the probable message intended by the pyramid builders and identifies a potential recipient for this transmission (a planet of a specific star).
Category: Archaeology

Artificial General Intelligence (AGI)

Authors: Clark M. Thomas
Comments: 4 Pages.

The sudden injection of giant data server farms into the world’s advanced economies, especially during 2026, is unique in human history. Humanity’s lofty position as the only global hyperkeystone species could be challenged by the emergence of a consciousness not fully human, nor what actual space aliens would bring to ourgeneralized intelligence. Here are some key aspects of this unique cybernetic challenge that we must soon face.
Category: Artificial Intelligence

A Quantum Induced Wapdrive II Subspacestructure, Dilaton-Field (Φ) and Their Cosmic Connections

Authors: Holger Döring
Comments: 26 Pages.

In a former paper a quantum induced warp-drive was introduced by assuming a model of microscopic cylinders as spacelike dimensions whereby the timelike dimension remains at its classical one-dimensional state. Described now is more detailed the underlying fundamental physical and mathematical spacetime structure than in the first paper , which is announced to feature this quantum induced warp-drive concept. Although there are certainly some new elements involved, everything is based on very classical GRT and QTH- descriptions. A more detailed description of the coupling dilaton-field is made, which connects the macroscopic sector of GRT with the microscopic sector of QFTH. This dilaton-field shall be named a "barytic -field".
Category: Quantum Gravity and String Theory

Comment on "Memories of Amplitude and Direction Coexist and Compete in Non-Brownian Suspensions"

Authors: Vladimir Kuz'menko
Comments: 3 Pages.

A recent article [Phys. Rev. Lett. 136, 258201 (2026)] continued the experimental study of an interesting physical phenomenon, where the viscosity of a suspension can be greater when moving forward than when moving backward. The authors attribute this phenomenon to the presence of a certain memory in the environment. The physical nature of both the phenomenon itself and the supposed memory is unknown. A possible explanation of the physical nature of this effect is proposed here and simple experiments to study some properties of such non-local memory are discussed.
Category: Quantum Physics

The Simple Geometry of Time: A Physical Record of Cosmic Metric Transformation

Authors: Alata Elatawneh
Comments: 26 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) Repository URL: https://github.com/Elatawneh/UCK-Cosmology-Framework.git

We present a predictive, geometrically constrained cosmological architecture, designated the Unified Cosmic Kinematic (UCK) framework, derived from the foundational postulate that cosmic time is macroscopically identical to relational metric spatial expansion. The invariant comoving time derivative of this identity demonstrates that the unperturbed background expansion parameter is the analytical inverse of the cosmic epoch, yielding a global background baseline constant of 70.85 km/ s/ Mpc when anchored to the empirically observed cosmic age of 13.8 Gyr. Although the baseline expansion model is geometrically deterministic, mapping observational signatures requires accounting for the interaction of matter and radiation within the spatial manifold via an effective field theory approach. This framework introduces four native tracking parameters calculated from first principles via the optimization of unbinned data streams, independent of external fluid-driven dark sector parameters. The statistical viability of this architecture is evaluated against five high-precision, unbinned astronomical data pipelines spanning late-universe standard candles, local velocity anomalies, localized mass-deflection geometries, the cosmic microwave background, and deep spectroscopic horizons. Our optimization routines address the persistent Hubble tension by demonstrating that regional gravitational density induces a localized clock-drag fraction that elevates the apparent local expansion rate via gravitational time dilation. This exact localized clock-drag metric reconciles weak-field gravitational limits, precisely mapping the mass-deflection profiles of strong gravitational lensing systems under pure baryonic constraints without invoking dark matter halos. Finally, coupling this expansion history to the primordial plasma sound horizon maps the early acoustic peaks with high statistical fidelity. The resulting high-redshift temporal elongation extends the available structural development timeline, thereby addressing the early mature galaxy chronological discrepancy across all targeted spectroscopic horizons.
Category: Relativity and Cosmology

Geometric Nodal Projections of Quantized Action

Authors: Casey McGrath
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

We introduce a Projected Node Model, in which quantized action ΔS = ℏ manifests at discrete event loci (nodes) via conjugate projections.From minimal axioms we rigorously derive the invariance of c, de Broglie relations, geometric uncertainty, Minkowski structure, massinertia,and the Planck scale. The framework recovers standard quantum and relativistic phenomenology with enhanced geometric clarity.
Category: Mathematical Physics

A Geometric Approach to the Hydrogen 1S—2S Transition Shift via Horizon-Enforced Acceleration Invariance

Authors: Osama Haggag
Comments: 4 Pages. DOI: 10.5281/zenodo.20459593

We explore a first-principles geometric framework to evaluate the precise frequency corrections in the atomic hydrogen 1S→2S transition by analyzing the coordinate strain of a bounded quantum vacuum. By extending the Einstein Equivalence Principle (EEP) to localized quantum states, we model the electron wavepacket as an extended matter wave whose internal phase clock modulates under intense non-inertial proper acceleration. Demanding that the contracting local Rindler horizon is bounded by the particle's irreducible Compton wavelength yields a maximum proper acceleration ceiling u2044 . Applying this constraint to the hydrogen ground state yields a metric modulation parameter . This coordinate-layer regularization introduces a geometric potential shift of 243.74 Hz, offering a novel, non-perturbative perspective that aligns closely with the high-precision spectroscopy data (2,466,061,413,187,018±11 Hz) tracked by the Max Planck Institute of Quantum Optics.
Category: Relativity and Cosmology

Parapose, Triggering for Transition of Matrix and Principles of an Object to Round Around the Chord or the Point

Authors: Binay Krishna Maity
Comments: 8 Pages.

In the Transpose mode of a matrix we can see thearrangement of the literals of the matrix in a specific manner. If we rearrange these literals in another specific manner and combine the resulting matrix with original and/or transpose as we need, then, there will be different patterns of matrix and we may call this way of transition of the literals of the matrix as Parapose of matrix and the way of combination of the matrices as the Triggering for transition. Then there are three kinds of triggering of transitions. Such as - 1) The Triggering for Transition in First kind, 2) The Triggering for Transition in Second kind and 3) The Triggering for Transition in Third kind. This triggering of Transition may exhibit the principle of any set of objects rounding centering the point or around the chord.
Category: General Mathematics

A Model for Merging Black Holes

Authors: Kohji Suzuki
Comments: 16 Pages.

We present a model in which SING, a singularity-inspired notion (viXra:1812.0480 [v1]), plays some role in black hole merging to suggest that evaporation of black hole leaves something behind.
Category: Mathematical Physics

The Nonlinear Schroedinger Equation and de Broglie Pilot Wave

Authors: Miroslav pardy
Comments: 11 Pages. The original article

The Schroedinger equation with the logarithmic nonlinear term is derived by the natural generalization of the hydrodynamical model ofquantum mechanics. The nonlinear term appears to be logically necessarybecause it enables explanation of the classical motion for the infinite masslimit. The article is the modied version of the articles by author (Pardy,1993; 2001).
Category: Quantum Physics

Deriving the Dot Product From Polar Coordinates

Authors: Timothy Jones
Comments: 1 Page. This derivation doesn't seem to be in the literature.

Using polar coordinates the dot product is easily derived.
Category: General Mathematics

An Interpretation of the Finnish Kalevala

Authors: Jorma Jormakka
Comments: 23 Pages. (Note by viXra Admin: Please cite and list references)

Kalevala may not be a so current topic, but some questions about it were never answered in a fully satisfactory way. What was Sampo, was it really a world pillar as Uno Harva explained, and if so, how can a world pillar have a handle, fall to the sea, and produce Bronze Age trade goods such as grain, salt and money (gold and silver). The article applies the following method to Kalevala: The starting points are, 1) Archeology has shown that Baltic Finns came to the Baltic shores during the Seima-Turbino phenomenon. 2) Many researchers suggest that Kalevala describes the Kaali meteorite. 3) Marjatta poems are from the time when Christianity came to Finland. It follows that Baltic Finns were creating poems during the whole time of their stay in the Baltic area.Considering that Elias L"onnrot and others gathered all poems they could find, the collected poems should contain poems from all of the times since the Nordic Bronze Age to the arrival of Christianity. By identifying which poems originate from which period, we can construct a history of Baltic Finns. The result agrees in much with the accepted view of the history of Baltic Finns, but it also changes the picture that has so far been obtained by other methods. Notably, Sampo is explained as a trade-agreement in the form of a written discand the method interprets Kullervo poems as describing a stage when Baltic Finns were a marginalized people pressed by Baltic peoples.
Category: Religion and Spiritualism

On the Non-Probabilistic Nature of Thermodynamic Processes: Fundamental to a Non-Statistical Formulation of Thermodynamics

Authors: Antonio Jose Mejias Marquina
Comments: 2 Pages.

[This] paper proposes a reevaluation of the fundamental nature of thermodynamics, challenging the prevailing view that attributes macroscopic behavior exclusively to statistical fluctuations of microscopic systems. Through a critical analysis of conservation laws and systems dynamics, it argues that the probabilistic nature observed in conventional thermodynamics is not an intrinsic property of matter at a fundamental level, but rather a consequence of an incomplete description of the microscopic state. The possibility of a deterministic formulation is examined, exploring the implications of integrating a complete causal dynamics that dispenses with overall averages, suggesting that the "arrow of time" and entropy could be emergent manifestations of a more precise underlying dynamic structure and not merely the result of chance.
Category: Thermodynamics and Energy

The Critical Path of Evolution

Authors: Oleg Ponfilenok
Comments: Pages. Source: https://github.com/oponfil/critical-path-of-evolution

The evolution of life is treated as the traversal of N ~ 10^14 small, high-probability steps of increasing complexity, with mean step time μ — a critical path from the thermal gate of the cosmic microwave background to a technological civilization over a time T ≈ 13.8 Gyr. When the step times are independent, the concentration of their sum compresses the relative spread of exit times as 1/√N; within the model this yields a dispersion σ = √(μT). We show that the observed absence of "loud" civilizations (cosmic silence) gives an upper bound on the interplanetary dispersion of exit times σ ≈ 800—1400 yr — of the order of the horizon of the transition to detectability; from this σ follows μ ≈ 25—75 min, which coincides with the generation time of microorganisms. The same silence places an upper bound on the Galactic population at n ~ 10^4—10^5 civilization-bearing planets, in agreement with astrophysical estimates of the number of Earth-like habitats. Two properties of the critical path — its progression under a local surplus of resources and the kinematic uniqueness of the fastest route — make its parameters approximately universal and ensure a synchronous tempo for the development of life; cosmic silence indicates that this route is realized through the carbon—organic chemistry of life of our type. A logical consequence of the same picture is the convergence of civilization form: the carriers of technological civilizations are expectedly close in functional plan to humanoids, although the details of morphology may differ.
Category: Astrophysics

Inertial Manifold for Dyadic Model of the Navier-Stokes Equations

Authors: Yuhan Wei
Comments: 35 Pages.

We prove the existence of finite-dimensional inertial manifolds forthe dyadic model of turbulence for all dissipation exponents α≥1/3.For α = 1/3 and α > 1/3 the proof is unified by working in the Hα-norm and employing a generalized cone method. The dimension scales as N∼1 2αlog λ log ν−1, matching the optimal upper bounds for shell models. The construction relies on a low-mode cut-off, a forward cascade estimate that exploits the monotone structure of the dyadic model, and a modified strong squeezing property of Koksch (2000). The resulting inertial manifold is Lipschitz and C1+ϵ-smooth, and satisfies the exponential tracking property. This provides a rigorousfinite-dimensional reduction for the entire supercritical range α≥1/3. We also answer an open question by Cheskidov (2008) regarding theexistence of strong compact global attractors for α<1/2.
Category: Functions and Analysis

Relaxation to Maxwellian Equilibrium in a Periodic Kinetic Model

Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.

We study a periodic kinetic Fokker—Planck equation in which free transport in position is coupled to Ornstein—Uhlenbeck relaxation in velocity. Our aim is to give a transparent weighted L^2 analysis of the relaxation mechanism and to test it by a modal approximation. The equation is written in Maxwellian variables, the generator is decomposed into a skew transport part and a dissipative velocity part and its contraction semigroup is considered on the natural weighted Hilbert space. Using Gaussian and torus Poincaré inequalities, we prove mass conservation, microscopic coercivity and exponential decay on the zero-mass subspace through a modified first-order energy containing a spatial—velocity cross term. For the homogeneous problem, the entropy identity gives decay from the Gaussian logarithmic Sobolev inequality. A Fourier—Hermite discretization is then derived, its semi-discrete L^2-stability is shown and truncation tests quantify convergence in the Hermite index and the spectral abscissa of the first nonzero Fourier block. The results give a compact account of how velocity relaxation enforces global return to Maxwellian equilibrium in this model.
Category: Mathematical Physics

A Little Book of Time Series with Python

Authors: Regi Mathew
Comments: 97 Pages.

A Little Book of Time Series with Python is a concise, practical guide designed as a quick reference for students, and analysts seeking to understand and apply time series analysis using Python. Inspired by Avril Coghlan’s A Little Book of R for Time Series, this volume preserves the original’s philosophy of simplicity and brevity while fully adapting the content to the modern Python ecosystem—the dominant language for data science, machine learning, and applied analytics. It emphasizes the enduring importance of statistical foundations in time series analysis and demonstrates how to implement them effectively with contemporary Python tools and libraries. Mirroring the structure and pedagogical approach of its R predecessor, the booklet provides clear explanations, code examples, and workflows tailored to Python, making it an ideal resource for concept clarification, interview preparation, self-study, and rapid application in real-world projects.
Category: Statistics

The Cosmological Constant as a Quantum-Relativistic Necessity

Authors: Osama Haggag
Comments: 4 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org) DOI: 10.5281/zenodo.20459593

The vacuum energy density predicted by Standard Quantum Field Theory (QFT), deviates from cosmological observations by approximately 120 orders of magnitude. This divergence stems from the assumption that spacetime is a continuous manifold permitting infinitely unbounded proper acceleration, which necessitates arbitrary insertion of ultraviolet cutoff at the Planck scale. In this framework, we introduce an impassable, mass-dependent quantum-geometric acceleration ceiling derived from firstprinciples horizon-saturation mechanics. By evaluating the modified Einstein Field Equations under a metric dynamically deformed by this acceleration ceiling, the Cosmological Constant ( ) emerges not as an arbitrary integration parameter, but as an inevitable geometric consequence of the global expansion running up against a baseline cosmic acceleration. This framework predicts a physical vacuum energy density aligns with empirical satellite data without tuning free parameters.
Category: Relativity and Cosmology

Adaptive-Dynamic Gravitational Field of the Solar System

Authors: Pavlo Danylchenko
Comments: 5 Pages.

The correspondence to the Solar System of not the static Newtonian gravitational field, but the dynamic gravitational field, which is also formed by the motion of the planets and, therefore, adapts to changes in the location of the planets in it, is substantiated. The correspondence of the trajectories of the planets' motion to the laws of conservation of angular momentum and energies (the Newtonian of inert free rest energy and the Keplerian of ordinary rest energy of matter) is shown. Spatial distributions of potentials and strength of the adaptive-dynamic gravitational field along the elliptical trajectories of the planets' motion, which correspond both to the laws of conservation and to the results of astronomical observations, are obtained.
Category: Relativity and Cosmology

Crossing the Line: A Dynamical Systems Theory of Bank Runs

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

The collapse of Silicon Valley Bank in March 2023 unfolded in forty-eight hours, following months of visible but apparently tolerated balance-sheet deterioration. This pattern, prolonged stability followed by sudden and discontinuous collapse, is difficult to reconcile with the canonical Diamond-Dybvig model of bank runs, which treats a bank failure as an instantaneous jump between two static states. This paper proposes a dynamical systems extension of the Diamond-Dybvig framework. We model the joint evolution of depositor beliefs and bank fragility as a coupled pair of nonlinear differential equations, map the full geometry of the system, and establish two threshold results: a saddle-node bifurcation at a critical interest rate r*, at which the system changes from having one possible resting state to having two, and a Hopf bifurcation at r** > r*, at which the calm resting state loses stability and a self-sustaining oscillation appears. That oscillation formalizes the idea of a bank in chronic stress: repeatedly approaching, but not yet crossing, the edge of collapse. Therefore, a bank failure is reinterpreted not as a choice between equilibria but as the crossing of a tipping line in the space of possible states. We apply the framework to Silicon Valley Bank, arguing that the Federal Reserve’s 2022 to 2023 hiking cycle pushed the bank past the saddle-node threshold, that the ensuing months of intermittent stress correspond to the oscillatory regime, and that the capital-raise announcement of March 8th, 2023 was the discrete shock to beliefs that pushed the system across the tipping line into irreversible collapse. Policy implications for deposit insurance design, capital requirements, and depositor-network regulation follow directly from the geometry.
Category: Functions and Analysis

Metaphysical and Spiritual Events

Authors: Kiyoung Kim
Comments: 6 Pages.

The introduction of subtle-spin-string waves within the physical vacuum offers a new type of physical interaction. This interaction provides a comprehensive explanation for phenomena like Ki energy and spirits. It also identifies possible connections between these phenomena and biological genetic evolution, topics that traditionally fall outside natural science.
Category: History and Philosophy of Physics

New Polyhedra with Ambo

Authors: Manuel Diaz Regueiro
Comments: 13 Pages.

The study of polyhedra and their classification can be significantly expanded by focusing on their generation through operations such as the Conway.. This approach gives rise to new polyhedra, new classifications, new problems, and new solutions. The present work focuses on a few preliminary observations concerning the simpler operators when applied to lesser-known polyhedra, with the hope that these insights may be transferable to others.
Category: Geometry

A New Explanation for the Origin of Superconductivity Based on Electron Magnetic Chains with 8-Shaped Magnetic Moments

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

Since the discovery of superconductivity in 1911, its microscopic mechanism has remained a central challenge in condensed matter physics. The classical BCS theory, which uses lattice phonons as mediators to establish a Cooper pair model of two electrons, can explain the basic properties of low-temperature metallic superconductivity but faces several inherent limitations: phonon coupling is only a short-range interaction, unable to resolve the cross-scale contradiction of long-range synchronous coupling among a large number of electrons, and struggles to counteract the Coulomb repulsion between electrons. This theory fails to explain experimental phenomena such as pre-paired pseudogaps and non-monotonic changes in critical temperature under magnetic fields, while also being incompatible with novel systems like high-temperature and two-dimensional flat-band superconductivity.This paper cites the 8-shaped electromagnetic standing wave + intrinsic drift electron structure model [1], proposing the electron magnetic chain microscopic conductive structure: under an external field, the intrinsic drift within electrons is suppressed, causing their inherent 8-shaped magnetic moment and magnetic coupling effects to manifest. Through the continuous chain-like connection enabled by the 8-shaped magnetic moment attraction, without fixed limitations on the number of paired electrons, a long-range ordered arrangement forms conductive pathways. This model can uniformly cover conventional and high-temperature superconducting phenomena, systematically resolving all existing internal contradictions in BCS theory, and provides a quantifiable theoretical basis for the structural design of new high-temperature and even room-temperature superconducting materials.
Category: Condensed Matter

Geometric Origin of Photon Wave Properties

Authors: Junzheng Liu
Comments: 17 Pages. (Note by viXra Admin: Please cite and list scientific references!)

In this paper, we propose a geometric ontology for the photon and demonstrate its capacity to explain the wave properties of light. Specifically, we discuss the nature of time and wave-particle duality. Also, we show how the geometric characteristics of photons naturally give rise to their frequency and amplitude.
Category: Quantum Physics

Projection Method for Visualizing the Spatial Structure of Light Beams Using a Negative Lens

Authors: Sergei P. Slukhayevskiy
Comments: 7 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

A simple projection method for direct visualization of the transverse spatial structure of freely propagating light beams is proposed and experimentally demonstrated.The optical arrangement consists of a negative lens positioned downstream of the investigated beam cross section and a remote observation screen. Within the paraxial approximation, the lens converts the transverse field distribution into an angular distribution that is projected onto the screen with a magnification determined by the ratio M = L|f|, where L is the distance from the lens to the screen and f is the focal length of the negative lens. The method enables non-invasive observation of beam cross sections while preserving unrestricted access to the investigated region. Longitudinal scanning isachieved simply by translating the lens along the propagation axis, allowing the spatial evolution of optical fields to be monitored without modifying the experimental arrangement.The technique has been applied to visualization of the fine spatial structure of semiconductor laser beams and to the investigation of diffraction fields generated by a knife edge. Experiments performed with projection magnifications of approximately M ≈ 300 reveal structural details that remain inaccessible under conventional observation conditions.Owing to its simplicity, low cost, and high visual sensitivity, the proposed methodrepresents a useful experimental tool for exploratory studies of wave-optical phenomena, laser beam diagnostics, and educational laboratory demonstrations
Category: Classical Physics

Probabilistic Estimation of the Critical Density Threshold for Kessler Syndrome in Low Earth Orbit Using a Two-Shell Monte Carlo Model

Authors: Ayush Samanta
Comments: 13 Pages. (Note by viXra Admin: An abstract in the article labeled as such is required; please submit article written with AI assistance to ai.viXra.org)

Orbital debris has become one of the most significant challenges facing the long-term sustainability of Low Earth Orbit (LEO). As the number of satellites continues to increase, so does the likelihood of collisions capable of generating large quantities of debris, potentially triggering a self-sustaining chain reaction known as Kessler Syndrome. This study develops a stochastic two-shell Monte Carlo model to investigate whether a critical orbital density exists beyond which such debris cascades become increasingly likely. The model represents the orbital environment using two concentric shells and incorporates stochastic collisions, debris fragmentation, atmospheric decay, active satellite failure, and collision avoidance. A systematic density sweep was performed using 200 independent Monte Carlo simulations for each normalized orbital density. The results reveal a rapid transition from stable orbital evolution to near-certain cascade formation over a narrow range of densities, with the critical normalized density multiplier estimated to be approximately $alpha_c approx 0.093$. Near this threshold, simulations with identical initial conditions frequently produced different long-term outcomes, highlighting the importance of stochastic collision dynamics in determining orbital stability. Although the model adopts several simplifying assumptions, it reproduces the fundamental feedback mechanism underlying the Kessler hypothesis and provides a computationally efficient framework for investigating the probabilistic onset of orbital debris cascades.
Category: Astrophysics

Evolution of the Concept of Angular Momentum

Authors: Yu. E. Zevatskiy
Comments: 7 Pages.

New types of angular momentum of elementary particles arising from the special theory of relativity are examined. A total of 14 types have been identified, including the classical angular momentum. The calculated values of relativistic angular momenta can be applied both to the determination of fundamental properties of elementary particles and to the quantitative description of various types of interactions between them.
Category: Nuclear and Atomic Physics

The Dual Architecture of the Gamma Function: From Vacuum Energy in Odd Dimensions to the Cosmological Constant and Neutrino Mass

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

The Gamma function, defined by the Euler integral, converges only in a restricted half-plane. Outside this domain, the integral diverges and one resorts to analytic continuation, which does not preserve the original integral form. This work proposes the Dual Architecture of the Gamma Function, a formulation based exclusively on integral representations and their natural domains of convergence. The architecture is built from two complementary objects: the Classical Gamma, convergent for positive real parts, and the Symmetric Gamma, convergent for negative real parts. Their connection is established through a multiplicative inverse relationship that yields unity, providing a parameter-free mechanism to regularize all divergences across the complex plane. A real trigonometric operator encodes a Dirichlet boundary condition with unit reflection coefficient, geometrically corresponding to a specific phase rotation that incorporates wave backscattering at impenetrable boundaries. We investigate the physical consequences of this dual structure in three key areas. First, the vacuum energy density in odd dimensions is evaluated, where the dual architecture produces a sign alternation that agrees with reference values in all analyzed cases. Second, the high-order WKB expansion for the quartic potential is examined, where the dual evaluation completely absorbs an exponential correction of previously unexplained physical origin, confirming backscattering as its source. Third, the cosmological constant problem is addressed by summing the regularized vacuum energy over the dimensional spectrum; the series converges naturally to a fundamental constant that predicts the neutrino mass and places the seesaw scale at the Grand Unified Theory regime. The formulation preserves the core principles of quantum field theory, positioning the dual architecture as a complementary regularization scheme for problems involving boundaries, odd dimensions, and the global structure of the vacuum.Keywords: Gamma function; Vacuum energy; Cosmological constant; Asymptotic expansions; Regularization
Category: Relativity and Cosmology

A Quantum Induced Warpdrive I

Authors: Holger Döring
Comments: 10 Pages.

This quantum induced warpdrive is featuring geometric unification of gravity and electro-magnetism in a four-dimensional cylindrical quantum spacetime as a corrugated spacetime-structure via sub-harmonic dilatonic resonance.Presented is a novel geometric framework for the unification of gravitation and electromagnetism strictly within a four-dimensional manifold . Rather than invoking higher spatial dimensions, proposed is, that the three macroscopic spatial axes possess intrinsic, periodic cylindrical degrees of freedom stabilized at the Planck scale . Under this topology, the standard metric tensor inherently encapsulates both gravitational and electromagnetic fields, where spacetime frame-dragging manifests macroscopically as the magnetic vector potential. Particle mass and charge emerge as localized, symmetric quantum wave configurations wrapped around the Planckian cylinders. Furthermore, introduced is a dynamic intermediate scalar field — derived from the local volume fluctuations of the cylindrical radius — which enables a non-linear, sub-harmonic resonance coupling between macroscopic laboratory-scale fields and the Planck-scale geometry. Demonstrated is then, that under precise phase-locked sub-harmonic frequencies, the effective gravitational coupling can be enhanced, leading to localized modulation of inertial mass, optical birefringence of the vacuum, and triggerable metric drift. Possibly this situation could lead to a form of local quantum induced warp-drive without ftl, which is called "the Metagrav" or QUIW .
Category: Quantum Gravity and String Theory

A More Accurate Period to Mean Distance Relation ( Applied to Mars)

Authors: Erik Gaylan Bergren
Comments: 11 Pages. (Note by viXra Admin: An abstract in the article labeled as such is required; please cite and list scientific references)

An improvement over the usual relation between a Planet's Period and its Mean Distance (semi-major axis) is presented and is compared against the standard relation that is used by JPL's Horizons web app, and against the previous improvement made in the Astronomical Almanac's Orbital Parameters Tables. The experimental data used for the comparisons is the 30390 year JPL Ephemeris integration DE441, analyzed specifically for the Planet Mars, which produced reference values of 686.979857 days per revolution and 1.5236886591 AU for the Period and Mean Distance of the Orbit of Mars respectively.
Category: Astrophysics

On the True Dimensionality of Electric Charge and Some Thermodynamic Quantities

Authors: Anatoly V. Belyakov
Comments: 3 Pages.

An additional justification for the nature of electric charge as momentum is provided, and itsrelationship with thermodynamic parameters is demonstrated. A new interpretation of theBoltzmann constant, temperature, and entropy is given.
Category: Thermodynamics and Energy

Causal Horizons under a Maximal Acceleration Limit

Authors: Osama Haggag
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) DOI: 10.5281/zenodo.20580374

Causal horizons—encompassing kinematic, gravitational, and cosmological event boundaries—are classically modeled in General Relativity as continuous, zero-volume mathematical abstractions permitting unbounded proper acceleration. This coordinate-dependent description induces severe non-local information loss, infinite mathematical divergences, and unphysical firewall paradoxes. This Letter provides a rigorous, non-circular operational proof demonstrating that causal horizons are discrete physical entities with an impassable minimum structural thickness equal to exactly one Compton wavelength. By deriving the horizon's properties from the closure of the local phase algebra under maximum metric strain, the Universal Law of Horizon Oscillation is systematically deduced. Crucially, we invoke the Strong Equivalence Principle to generalize this boundary condition as a covariant geometric invariant across all reference frames. This structural quantization resolves the 120-order-of-magnitude cosmological vacuum energy catastrophe as an applied boundary example, yielding a non-tuned density that precisely matches the order of magnitude of empirical observations, and provides a dynamic dark energy scaling framework that naturally reconciles the contemporary Hubble expansion tension.
Category: Relativity and Cosmology

Expansion for Harmonic Numbers Inspired by Ramanujan

Authors: Payam Danesh
Comments: 7 Pages.

In this work, we developed a direct formulation based on the variable X=n(n+1)+h, which h is a real parameter. This method starts from the digamma representation of H_n, recenters the expansion at n+1/2, and then converts the result into descending powers of X. This actually gives an explicit coefficient formula in terms of Bernoulli polynomials evaluated at 1/2. The special value h=1/3 is shown to cancel the first correction term, giving a sharper expansion whose error begins at a higher order. Numerical comparisons showed that the shifted form improves substantially over the standard Euler truncation and the unshifted pronic expansion for small and moderate n and this gives transparent route to Ramanujan-type harmonic-number approximations.
Category: Number Theory

Ehrenfest Paradox and Consistent Relativistic Circular Motion

Authors: Yang-Ho Choi
Comments: 13 Pages.

Some conundrums such as the Ehrenfest paradox have been raised in relation to the relativistic approach to circular motions. Different tangential velocities along the radius of a rotating frame bring about a nonuniform scalar field of potential. Based on the Schwarzschild metric for the potential field, we consistently and comprehensively deal with the problems of relativistic circular motion including the Ehrenfest paradox and the Sagnac effect. The Ehrenfest paradox is readily resolved via a visualization of wave propagation in the field, which shows that the length of radius in the rotating frame is different from the corresponding one seen in the laboratory frame. From the visualization, the anisotropy of the speed of light in inertial frames is also clearly shown. Moreover, a coordinate transformation for the circular motion at a fixed radius is developed based on the metric, which enables us to derive a transformation between inertial frames through limiting operations. The derived inertial transformation becomes the same as the Lorentz transformation if the standard synchronization is introduced. With the transformations, the Michelson-Morley experiment result and the generalized Sagnac effect are consistently explained.
Category: Relativity and Cosmology

Lecture Notes for Teaching Mechanistic Quantum Field Theory Axiomatically

Authors: Nigel B. Cook
Comments: 77 Pages.

The purpose of these brief lecture notes is to provide the basic framework for a course in axiomatically-derived mechanistic quantum field theory, to teach the foundations needed to understand vixra paper 2606.0012. Problems and solutions will be developed for inclusion at a later date, after we have more experience in teaching this course to students.
Category: Quantum Gravity and String Theory

A Quantum Induced Warpdrive

Authors: Holger A.W. Döring
Comments: 10 Pages.

This quantum induced warpdrive is featuring geometric unification of gravity and electro-magnetism in a four-dimensional cylindrical quantum spacetime as a corrugated spacetime-structure via sub-harmonic dilatonic resonance.Presented is a novel geometric framework for the unification of gravitation and electromagnetism strictly within a four-dimensional manifold . Rather than invoking higher spatial dimensions, proposed is, that the three macroscopic spatial axes possess intrinsic, periodic cylindrical degrees of freedom stabilized at the Planck scale . Under this topology, the standard metric tensor inherently encapsulates both gravitational and electromagnetic fields, where spacetime frame-dragging manifests macroscopically as the magnetic vector potential. Particle mass and charge emerge as localized, symmetric quantum wave configurations wrapped around the Planckian cylinders. Furthermore, introduced is a dynamic intermediate scalar field — derived from the local volume fluctuations of the cylindrical radius — which enables a non-linear, sub-harmonic resonance coupling between macroscopic laboratory-scale fields and the Planck-scale geometry. Demonstrated is then, that under precise phase-locked sub-harmonic frequencies, the effective gravitational coupling can be enhanced, leading to localized modulation of inertial mass, optical birefringence of the vacuum, and triggerable metric drift. Possibly this situation could lead to a form of local quantum induced warp-drive without ftl, which is called u201ethe Metagrav" or QUIW .
Category: Quantum Gravity and String Theory

Invariant Maximum Acceleration and Its Non-Linear Composition Law

Authors: Osama Haggag
Comments: 8 Pages. DOI: 10.5281/zenodo.20740142

Standard Special Relativity exhibits a fundamental geometric asymmetry: while the instantaneous velocity of a worldline is strictly bounded by the invariant speed of light ( ), its proper acceleration is permitted to diverge infinitely. This unconstrained upper bound introduces severe vulnerabilities into modern field theories, manifesting as divergent particle self-energies and zero-volume coordinate singularities at causal horizons. This framework proposes an operational resolution of this asymmetry by introducing a generally covariant kinematic framework featuring an impassable, invariant upper boundary on proper acceleration ( ) deduced from first principles. By modeling a massive particle’s internal state as a localized quantum wavepacket acting as an intrinsic clock, we demonstrate that uniform acceleration compresses the local Rindler horizon to its geometric saturation limit. To preserve this invariant ceiling across multi-body compound systems, we derive a velocity-independent, non-linear acceleration composition law based on a hyperbolic group structure. By equating the Rindler horizon with the particle's Compton wavelength, we extend the equivalence principle in quantum systems, Planck’s constant is directly inserted into spacetime kinematics. Finally, this framework offers a pure kinematic reinterpretation of the partonic cross-section flattening (gluon saturation) observed at the Large Hadron Collider (LHC) as an intrinsic, structural feature of a bounded quantum vacuum.
Category: Quantum Gravity and String Theory

Diamond-Confined Metallic Hydrogen: A Roadmap to Metastable Hydrogen Metal at Ambient Conditions via Quantum Electrodynamic Stabilization

Authors: Giustino Travaglini
Comments: 10 Pages.

The realization of metallic hydrogen at ambient temperature and pressure remains one of the most compelling goals in condensed-matter physics, promising a high-temperature superconductor, a revolutionary propellant, and a window into quantum phase transitions. While static compression experiments above 400 GPa have provided tentative evidence for the metallic state, its recovery to ambient conditions has proved elusive because of the vanishingly small kinetic barriers that separate the atomic metallic phase from the molecular insulating ground state at zero pressure. Here I propose a concrete, experimentally accessible strategy—Diamond-Confined Metallic Hydrogen (DCMH)—that combines three interlocking physical mechanisms: (i) sub-nanometer confinement of hydrogen within a fully sp³-bonded diamond-like carbon matrix, which delivers chemical internal pressures sufficient to reach the metallization density; (ii) topological frustration of the molecular Hu2082 recombination path, raising the kinetic barrier to geological timescales; and (iii) optional resonant quantum electrodynamic (QED) vacuum engineering using a tunable optical cavity to induce vacuum-mediated spin pairing, thereby lowering the free energy of the metallic state and rendering it thermodynamically competitive at 300 K and 0 GPa. The entire procedure can be executed in existing high-pressure laboratories using multi-anvil presses, DAC gas-loading systems, and table-top cavity QED setups. I present detailed DFT-based estimates of confinement densities, kinetic barrier heights, and cavity-enhanced pairing gaps, together with a full experimental protocol for synthesis, decompression, and characterization. This roadmap transforms metallic hydrogen from a high-pressure curiosity into a designer material that can be handled at ambient conditions
Category: Condensed Matter

Beal's Conjecture - Proof

Authors: B. N. Pathak
Comments: 19 Pages.

This is a proof for Beal's conjecture by B. N. Pathak - my late father.
Category: Number Theory

Global Mapping of Next Economy Organizations and Their Discourse

Authors: Can Özhasenekler, Elif İpek Ulusoy, Jochelle Laguipo, Uygar Özesmi
Comments: 11 Pages.

This article presents a global mapping of Next Economies organizations and their discourse, based on a dataset of 318 institutions across multiple countries and regions. Recent scholarship stresses that overhauling prevailing economic systems is essential to confront today’s interlinked global crises, with innovative approaches seeking to balance ecological integrity and human well-being (Kenter et al., 2024). Discussions on the "new economy" increasingly emphasize restructuring philanthropy and governance to better respond to the polycrisis and to advance more equitable and sustainable pathways (Alliance Magazine, 2024). To conduct this analysis, we developed a coded dataset capturing institutional structures, geographic locations, discursive critiques, adoption of circular economy principles, alignment with alternative models, and focus areas. The dataset was then translated into a relational network on GraphCommons, where organizations serve as nodes connected by shared features such as country, alliances, critiques, and focus areas. Using network analysis enables the identification of clusters with common orientations and the exploration of relations between institutional characteristics and discourses.Our findings highlight the ways in which Next Economies movements are emerging, revealing structural and thematic patterns in how Next Economies movements are globally distributed andconceptually aligned. The network approach provides insights into both the diversity and interconnectedness of these organizations, offering a foundation for comparative research and coalition-building. Ultimately, structuring these organizations within a global network contributes to a deeper understanding of the discursive and the structural landscape of the Next Economies.
Category: Economics and Finance

EUV-Patterned Diamond-Confined Metallic Hydrogen: A Lithographic Roadmap to Ambient-Condition Superconducting Hydrogen

Authors: Giustino Travaglini
Comments: 11 Pages.

The recovery of metallic hydrogen at ambient temperature and pressure remains a grand challenge, largely because the kinetic barriers preventing the back-conversion to molecular Hu2082 are too small in the pure atomic phase. Here I propose a radically new approach that merges three frontier technologies: (i) chemical precompression of hydrogen inside a diamond-like carbon (DLC) matrix patterned with sub-nanometer cavities, (ii) extreme ultraviolet (EUV) and High-NA EUV lithography to sculpt this matrix with near-atomic precision, and (iii) resonant vacuum quantum electrodynamic (QED) stabilization via an on-chip optical cavity fabricated in the same lithographic workflow. The core idea is to exploit the unique capabilities of EUV photons (92 eV) to crosslink diamondoid self-assembled monolayers into a rigid, fully sp³-bonded carbon network containing a periodic array of identical pores. After high-pressure hydrogen loading and controlled decompression, the hydrogen remains permanently locked at metallic densities by the mechanical strength of the DLC scaffold. Kinetic barriers are amplified by topological frustration and exceed 1.8 eV per H atom, ensuring geological metastability. An integrated Fabry—Pérot cavity tuned to the hydrogen plasma frequency enhances vacuum-mediated electron pairing, potentially tipping the thermodynamic balance and making the metallic state the true ground state. I present a detailed fabrication protocol compatible with existing EUV scanners and multi-anvil presses, quantitative DFT estimates of the confinement-induced metallization, and a full device architecture for a superconducting hydrogen chip. This roadmap transforms metallic hydrogen from a high-pressure curiosity into a designable material platform, accessible with the tools of the semiconductor industry in the 2026—2030 timeframe.
Category: Condensed Matter

DNA as Nanotechnology: Reassessing Life’s Origin Through the Lens of Information and Genomic Intelligence

Authors: Hannan Gondal
Comments: 31 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We undertake a comprehensive examination of the complex interplay between deoxyribonucleic acid (DNA), nanotechnology, and the origin of life, critically engaging with prevailing abiogenetic models. We advance the hypothesis that DNA functions at the quantum scale or exhibits quantum-mechanical characteristics, demonstrating a level of structural stability and informational complexity that challenges the assumptions underpinning theories of spontaneous molecular evolution. Central to the critique is the recognition of the indispensable role of enzymatic machinery in DNA replication—enzymes that, paradoxically, require DNA for their synthesis—thereby presenting a classic instantiation of the "chicken-and-egg" paradox. We further interrogate the significance of molecular chirality and evaluate the environmental prerequisites for biogenesis, contending that early Earth conditions were inherently unfavorable for the natural formation of either DNA or RNA. By synthesizing insights from molecular biology, quantum physics, and information theory, this analysis supports alternative frameworks. Ultimately, we call for a fundamental reassessment of evolutionary mechanisms and reposition DNA not merely as a passive genetic substrate, but as an advanced, self-organizing system for information storage and processing—one that challenges conventional biological paradigms. We propose a Mathematical proof utilizing Minimal Genome formation and the Universe's limit of Genetic generative capacity.
Category: Biochemistry

A Non-Distributive Symmetric Oscillatory Algebraic Structure and Its Implications for Resolving Paradoxes in Theoretical Physics and Quantum Mechanics

Authors: Mohammad Iman Esfandiari
Comments: 9 Pages.

This paper introduces and mathematically formalizes an alternative algebraic system running parallel to classical algebra, founded upon two core axioms: the elimination of the distributive property of multiplication over addition (Non-Distributivity) and a symmetric inversion of the rules of signed multiplication. In this framework, termed Non-Distributive Symmetric Oscillatory Algebra, the product of any two quantities with identical signs yields a negative output, whereas the product of two quantities with opposing signs yields a positive output. This structure induces an inherent frequency-based, oscillatory behavior within the sequential powers of real numbers. This study demonstrates how this novel algebraic model resolves the baryon asymmetry paradox (matter/antimatter) in cosmology, tames the explosion of infinities and singularities within black holes, formulates the exact mathematical mechanism behind wave function collapse in the quantum measurement problem without metaphysical assumptions, and establishes a theoretical foundation for designing room-temperature stable quantum hardware (Non-Distributive Polar Quantum Diodes) and macro-scale superconductors.
Category: Quantum Physics

The Collatz Singularity as a Global Binary Structural Attractor

Authors: Ammar Hamdous
Comments: 77 Pages. Creative Commons Attribution 4.0 International

In our fifth work [3] entitled A Structural Approach to the Collatz Conjecture via the Binary Singularity, we introduced the notion of binary singularity of Collatz sequence as a structural invariant and proposed a structural reformulation of the Collatz conjecture: every positive odd integer either is, or eventually reaches, a singularity configuration. We further hypothesized that this property could be characterized through an appropriate metric defined on binary structures.In the present work, we develop this idea by introducing a global binary structural attractor governing the evolution of odd Syracuse iterates. This attractor is based on the notions of Suffix of Singularity, suffix of generator of the suffix of singularity, and binary overflow, which together reveal a hierarchical binary decomposition of the binary structure of odd integers previously hidden by their arithmetic representation. We prove that every odd Syracuse iterate that is not a singularity admits a unique decomposition into a finite sequence of nested concatenation of suffixes of generators of the suffix of singularity followed by a single suffix of singularity, On = G(p,n) ∥ G(p−1,n)∥ · · · ∥G(1,n)∥Sn, and define a structural complexity function P(On) equal to the number of suffix generators contained in this decomposition. The evolution of P is entirely determined by the complementarity of the overflow generated by the most significant suffix generator G(p,n), leading to a complete structural classification of increasing, stationary, and decreasing transitions. This decomposition provides a symbolic description of the odd Syracuse dynamics and establishes the structural foundation for an eventual Lyapunov function whose minimal state is precisely the binary singularity P = 0. Rather than studying the arithmetic growth of Collatz trajectories,the proposed approach describes the dynamics as the progressive elimination of nested binary suffixes of generators toward a unique global structural attractor.
Category: Number Theory

Human nose and the Graphical Law

Authors: Anindya Kumar Biswas
Comments: 21 Pages.

Nasal index is breadth divided by height of a nose multiplied by hundred. We look into the nasal indices of noses of human beings as gathered by Thomson and Buxton as early as 1923.We draw the natural logarithm of the nasal indices, normalised, vs the natural logarithm of the rank, normalised(unnormalised). We conclude that the human nose, can be characterised by a magnetisation curve of a Spin-Glass in the presence of a little external magnetic field.
Category: Physics of Biology

Research Progress on Relative-Absolute Spacetime View: Logical Basis, Experimental Verification, and Paradigm Innovation

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

To address the core issue of the lack of physical mechanism explanation in relativity, a solution is proposed to construct a "relative absolute spacetime view" by reconciling "absolute" and "relative". The necessity of an absolute stationary system is logically demonstrated: The system with the smallest degree of freedom in motion, the system that is most difficult to obtain acquired motion, and the system with "no displacement space" (such as the centroid system of a total galaxy and the cosmic background radiation framework) all point to a logically absolute stationary frame. Based on the longitudinal traction difference between photons and electrons revealed by Jones' experiment, a "geometric optical velocimeter" was designed to calculate absolute velocity and verify the existence of absolute motion by measuring the deflection angle of photons and electron rays. By assuming that the clock in absolute motion slows down, the contradiction between relative and absolute is quantitatively reconciled. The Jones experiment actually proved that the gaps in the hollow glass disk are ineffective in pulling photons. It is equivalent to proving that, relative to photons, the vacuum space inside a moving train carriage does not belong to the same inertial frame as the body of the train. Hafele Keating experiment proved that "different approximate inertial frames are not always equal". Both of these situations pose challenges to the principle of special relativity.It is proposed that physics research should follow a spiral upward path of "absolute → relative → relative-absolute", breaking through the binary opposition between classical absolute spacetime and special relativity. It can provide new explanations for the Michelson-Morley experiment and a new paradigm for spacetime theory.
Category: Relativity and Cosmology

Definite Integration and Summation Are #P-Hard

Authors: Leonid Gurvits, Warren D. Smith
Comments: 4 Pages.

We show that the common symbolic manipulation tasks of computing multiple partial derivatives, definite integration, and definite summation, are #P-hard, i.e, at least as hard as counting the accepting input strings for any Turing machine that halts in polynomial time. (The "multiple partial derivatives" part was previously known.)
Category: Combinatorics and Graph Theory

Accurate Circle Configurations and Numerical Conformal Mapping in Polynomial Time

Authors: Warren D. Smith
Comments: Sitting on my web pages since 1991; uploading to vixra for archival purposes.

According to a remarkable re-interpretation of a theorem of E.M. Andreev (1970) by W.P. Thurston (≈1982), there is a unique (up to inversive transformations) packing of interior-disjoint circles in the plane, whose contact graph is any given polyhedral graph G, and such that an analogous "dual" circle packing simultaneously exists, whose contact graph is the planar dual graph G*, and such that the primal and dual circle packings have the same set of tangency points and the primal circles are orthogonal to the dual ones at these tangency points.

This note shows that relatively and absolutely accurate coordinates for the primal and dual circles may be obtained in time polynomial in N, the number of vertices of the polyhedral graph, and D, the number of decimals of accuracy desired.

Consequently one may also accurately "midscribe"' a polyhedron – and simultaneously its dual – in polynomial time.

Also consequently, one may implement Riemann's conformal mapping theorem numerically, in polynomial time with provable accuracy.

Our result is obtained by generalizing and reformulating ideas found in the doctoral thesis of Walter Brägger [Math. Institut, Rheinsprung 21, CH-4051 Basel, Feb. 1991] to reduce our problem to maximizing a smooth convex function. This maximization problem is then solved by using Khachian's "ellipsoid method" or Vaidya's algorithm.
Category: Geometry

On the Nature of Light from the Original Meaning of the Antonyms "Bright" and "Dark"

Authors: Peng Xiaotao
Comments: 14 Pages.

Brightness and darkness are a pair of antonyms, both of which describe the state of the objective world related to light. Brightness refers to the state in which the observer can observe the surrounding things well when the light is abundant, while darkness refers to the state in which the observer can not perceive the surrounding things when there is no light. Therefore, the so-called light should be some kind of carrier that can change the state of things around the observer, but it is not something that the observer can directly perceive. Therefore, on the one hand, what the human eye sees can not be the so-called light; on the other hand, the light should be some carrier that can make the objective things bright, so that the human eye can see these things in a bright state. The objective things that can be seen by human eyes and are in a bright state are objective entities composed of various atoms, and it should be a force that can change their state. It can be seen that the essence of light should be the carrier responsible for transmitting some kind of force, which is most likely to exist only between charged particles. Therefore, there is good reason to think that the essence of light is a collection of some carrier or carriers responsible for the transmission of Coulomb force. This conclusion can explain all the physical phenomena and experimental results related to light at the same time, which is the most realistic conclusion at present. Hope to get the attention and support of experts, scholars and friends at home and abroad.
Category: Classical Physics

A Dual Extension for the Gamma Function and the Confinement of the Zeros of the Riemann Zeta Function

Authors: Julinho Jorge Luís
Comments: 14 Pages.

The Bohr-Mollerup Theorem establishes the uniqueness of the Gamma function on the right half-plane, but makes no assertion regarding extensions to the left half-plane that preserve the integral form. This work proposes a Dual Architecture consisting of two integral operators with complementary domains: the Classical Gamma and a Symmetric Factorial, connected by an operator derived from the Hankel contour integral. When applied to the Riemann zeta function, this architecture replaces the classical functional equation—which exhibits indeterminate forms at integer points—with a formulation that is directly evaluable and preserves all values of the Dirichlet series. Analysis of the connection operator reveals that its real part vanishes exclusively on the critical line within the critical strip. Assuming a non-trivial zero off this line leads, via a closed cycle of the dual functional equation, to a contradiction involving the modulus of the Gamma function, as established independently through the Weierstrass representation and the maximum modulus principle. The result forces all non-trivial zeros of the Riemann zeta function to lie on the critical line.Keywords: Gamma function, Riemann zeta function, critical line, Hankel contour, Weierstrass representation.
Category: Functions and Analysis

Arbitrary Approximation of the Shifted-LRC by the LRC

Authors: Deepak Ponvel Chermakani
Comments: 2 pages, 2 Theorems.

Consider an instance of the Shifted Lonely Runner Conjecture (S-LRC) where all n runners (except the stationary runner 0) have integer speeds and start from real values in [0,1[ at time t=0. We show that one can derive an alternative vector of starting points that can be made to be arbitrarily close to the initial vector of starting points. The alternative starting point of each runner i is a rational in [0,1[ and is expressible as (qi / P) where P is a large prime and qi is an integer in [0, P-1]. The S-LRC instance with the alternative starting points, allows a minimal loneliness gap of f, if and only if, the corresponding LRC allows a minimal loneliness gap of f, where f is a desired fraction in ]0,1[. This finding is important in the light of recent counter-examples to the shifted-LRC.
Category: Functions and Analysis

A "Good" Problem Equivalent to the Riemann Hypothesis

Authors: Warren D. Smith
Comments: This 1995 paper by me, heavily revised 2005, had been sitting on my web page but is now uploaded to vixra for archival purposes.

We exhibit a sequence c_n such that the convergence of ∑c_nzⁿ for all complex z with |z|<1 is equivalent to the Riemann Hypothesis. We argue that this particular RH-equivalent problem is "better" than most, or perhaps every, other RH-equivalent problem devised so far, in the sense that (we prove) there is a tremendous gap in behaviors of the c_n if the RH is true versus if the RH is false.
Category: Number Theory

Linear Transformations in the Reciprocal Gamma Function Quadrature

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

As an extension from my previous work, the paper attempts to generalize the Reciprocal Gamma Quadrature under the curve to general linear transformations on the argument itself. It extends further into the territory of Volterra Functions and Ramanujan's Log-Gamma integrals related to the Fransén-Robinson Constant.
Category: Number Theory

Identifying Natural Limits to Infinite Algebraic Singularities with Null Algebra

Authors: Robert S. Miller
Comments: 22 Pages. (Note by viXra Admin: Please cite and listed scientific references)

This paper introduces a framework which regularizes the classical algebraic singularity, using the essential hyperbola y=1/x to illustrate its application. Traditional, classical mathematics leaves the behavior at the origin for this function undefined due to divergence toward unachievable infinities. By using the transformational matrix defined in Null Algebra to map u=-1/y, the defined subspace of y, we may focus on a rate of information transfer implied by the function, as x→0. This is achieved by imposing a strict constraint upon dy/du which is required for any function y=f(x) and based upon chosen scale for the system defined by y=f(x). This shall show the singularity cannot actually be achieved due to natural self-limiting properties unique to a given function which emerge from Null Algebra, leaving a function, that is piecewise defined and continuous.
Category: General Mathematics

Entropic Origin of the Cosmological Constant A(t): Analytical Derivation of 10^122 Bits and Validation via Planck Data

Authors: Friedhelm M. Jöge
Comments: 14 Pages.

The discrepancy 0f 10^120 between the observed cosmological constant and quantum field theory (QFT) predictions remains one of the greatest enigmas in modern physics. The study provides a novel analytical derivation of this value by treating gravity as an entropic force arising from bits on a holographic screen. By establishing a direct link between the bit density of the universe and the dynamic nature of dark energy, the study offers a potential resolution to the cosmological constant problem. These findings bridge the gap between quantum information theory (QIT) and general relativity theory (GRT), suggesting that the accelerated expansion of the universe is a emergent phenomenon driven by the evolution of cosmic entropy.Since dark energy is not simply given as a number, but is derived from the age of the universe (13.82 billion years), the "naturalness problem" - one of the biggest problems in physics - can be solved.It is shown that all the information of the universe is encoded on the Planck-scale and is "unrolled" into spacetime by factor tu (Holographic Principle). The fact that the theoretically derived value of the Hubble constant (Ho) lies well within the range of astronomical measurements is the strongest indication that the connection between the Planck-scale and the age of the universe (tu) is not mere numerology, but a physical principle.
Category: Relativity and Cosmology

How a Matter-to-Vacuum Phase Transition Can Prevent Black-Hole Singularities

Authors: Rudi Van Nieuwenhove
Comments: 14 Pages.

The appearance of spacetime singularities during gravitational collapse remains one of the most important unresolved problems of General Relativity. In the standard picture, continued compression of matter inside a black hole leads to divergent densities, divergent spacetime curvature, and the breakdown of the classical gravitational description. In this work, we investigate an alternative phenomenological scenario in which gravitational collapse triggers a density-induced matter-to-vacuum phase transition once a critical density is reached.We assume that above this threshold ordinary matter is rapidly converted into a Vacuum Localized Structure (VLS) phase, representing a localized vacuum state that carries the mass-energy of the original collapsing matter. The detailed microscopic mechanism responsible for the transition is not specified. Instead, the transition is treated as an effective process that replaces the collapsing matter by a compact vacuum structure while conserving the total mass-energy of the system.The post-transition object is modeled as a static, spherically symmetric equilibrium configuration governed by the Einstein field equations and the Tolman-Oppenheimer-Volkoff equation. A Gaussian density distribution is adopted for the VLS phase, leading to finite central density, finite pressure, and a regular mass profile throughout the interior. The characteristic size of the VLS core follows directly from mass conservation and is uniquely determined by the total mass and the critical transition density.The resulting solutions replace the classical black-hole singularity by a finite-curvature core. The mass function approaches zero smoothly at the center, preventing the divergent gravitational compression associated with conventional collapse solutions. Consequently, all curvature invariants remain finite and the spacetime remains regular throughout the interior region. In this sense, the phase transition acts as a gravitational regulator, replacing continued compression by a stable vacuum-supported equilibrium configuration.Within this framework, singularity avoidance emerges without modification of the Einstein field equations and without the introduction of an explicit de Sitter vacuum core.
Category: Relativity and Cosmology

Atoms Through Nonlinear Dynamical Systems

Authors: Najib Chairi
Comments: 15 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org) Copyright © 2026 by the author(s), all rights reserved.

The atom is traditionally described by quantum mechanics through linear equations, especially the Schrödinger equation. Yet as soon as the number of particles increases, the atom no longer remains a simple one-body problem: electrons interact with one another, alter the effective potential in which they evolve, and give rise to global structures whose stability cannot always be understood as a mere addition of individual behaviors. This article proposes an exploratory reading of the atom and of the periodic table through the lens of nonlinear dynamical systems, threshold phenomena, collective modes, phase locking, and self-organization. The aim is not to replace standard quantum mechanics, but to examine whether certain atomic regularities - shell closures, noble gases, filling anomalies, transitions between periods, and the special stability of some configurations - can be interpreted as signatures of collective stability. The article also develops analogies with lasers, nonlinear optics, coupled oscillators, the fractional quantum Hall effect, and wave chaos. These analogies should not be understood as strict identifications. They are conceptual tools that help us think of atomic matter as a dynamic, resonant, and self-consistent organization.
Category: Quantum Physics

Predicting Low-Field Visibility Loss from Local Opposite-Polarity Field Coupling

Authors: Matthew Crane
Comments: 32 Pages.

Standard low-power optics treats visibility loss as a readout problem: the detector still records photon locations, but the measured hit pattern no longer separates cleanly into bright regions and dark regions.This paper controls that readout explanation before the prediction is tested. First, a stable visible interference pattern is made. Then the dark-region background, detector noise, false counts, pixel scale, position uncertainty, and minimum distinguishable bright-dark difference are measured. That calibration sets the measured visibility limit of the tested setup.After that calibration, detector sensitivity is part of the threshold test.This paper predicts that the measurable interference zone shrinks as the beam-waist to opposite-polarity + - coupling-event distance increases, until the setup reaches a measurable-visibility threshold.The predicted measurable-visibility threshold distance is:R_low = z_R sqrt(P/P_low - 1)
Category: Quantum Physics

Heisenberg Causes Gravity and Time Dilation

Authors: Leonardo Rubino
Comments: 16 Pages. (Note by ai.viXra.org Admin: For the last time, please cite and listed scientific references!)

Heisenberg causes gravity and time dilation.
Category: Quantum Physics

On Complex Dynamics and Standard Model Parameters

Authors: Ervin Goldfain
Comments: 16 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present numerical evidence that complex dynamics of nonlinear systems provides a coherent organizing principle for understanding the origin of Standard Model parameters, without introducing new fields or symmetries.
Category: High Energy Particle Physics

The Structure of Electrons and Photons

Authors: Michael Gunning
Comments: 19 Pages.

In this paper I propose a model for a physical explanation of the structure of the electron and the photon. The model explains what the charge of an electron is and why it has a total angular momentum of √3/2 ħ. It suggests what the nature of inertial mass is and explains the spin value of ħ for the photon as well as the origins of its alternating electric and magnetic fields. It includes explanations for what static electric and magnetic fields are and why the stress energy tensors for these fields used in General Relativity have the form that they do. It also explains the Lorentz force and the Stern Gerlach force. It gives a physical interpretation of Planck’s constant and proposes a physical mechanism for gravity which explains why it is so weak compared to the electric force. It also explains why the relativistic energy momentum formula has the form it does and also proposes a physical mechanism to explain the deBroglie wavelength of a particle.
Category: Quantum Physics

Diffraction: An Experimental Search for the Physical Mechanisms of Pattern Formation

Authors: Sergei P. Slukhayevskiy
Comments: 12 Pages. 5 figures

Diffraction is traditionally regarded as a consequence of the disruption of wavefront continuity by an obstacle, whereas experiments usually provide access only to the final intensity distribution observed on a distant screen. In the present work, an approach for the instrumental observation of the spatial evolution of the diffraction process was implemented through successive modifications of classical interference and diffraction arrangements adapted to new experimental objectives. It was experimentally established that, after interaction with a single half-plane obstacle, a finite layered structure is formed within the light beam. This structure remains confined to the beam cross-section and consists of alternating bright and dark regions oriented parallel to the obstacle edge. In the absence of spatial overlap with other disturbances, these layers gradually smooth out and the intensity distribution returns to a nearly uniform state. It is shown that, in more complex configurations, each half-plane generates its own system of spatial beam stratification. Signatures of these structures are observed at distances of approximately 15 cm before the geometrical edge of the obstacle and persist over a comparable distance after it. When spatial overlap occurs, mutual deflecting interactions between the layer systems arise, suppressing relaxation and leading to the formation of a stable wide-angle diffraction pattern. Experiments employing beams marked by a regular geometric light pattern revealed that dark-layer regions suppress the transmission of light from other sources in a manner similar to opaque objects. By varying the degree of spatial overlap between layer systems, a continuous transition was achieved from the classical distribution dominated by the central maximum to regimes exhibiting enhancement of higher-order maxima. Additional experiments revealed a spatially selective character of layer interactions and a weak dependence of the observed effects on the surface quality of macroscopic obstacles. The obtained results provide a basis for further investigation of the causal mechanisms responsible for the formation of diffraction structures and suggest potential practical applications of the observed regularities under controlled boundary conditions.
Category: Classical Physics

A Saturating Magnetic Switched Blumlein High Voltage Pulse Generator

Authors: Max Artusy
Comments: 2 Pages. (Note by viXra Admin: Author name is required in the article after the article title)

The Blumlein charged line generator is designed with a saturating magnetic switch. This allows rapid recharge and robust switching, which can tolerate arcing without switch damage. This shows the versatility of this unique circuit. High rep rate is intrinsic.
Category: High Energy Particle Physics

Architecture of Elementary Particles

Authors: Yvan Raverdy
Comments: 7 Pages. (Note by viXra Admin: Please cite and list scientific references of other authors)

The particles that constitute our Universe, in its so-called "ordinary matter and radiation" component, are all electromagnetic in nature, defined by the unification of their three possible interactions. We know that the fourth interaction (gravitational) is significantly different in nature from the other three. Here, we intend to describe how the so-called "stable" particles of ordinary matter can be composed of those that constitute their most fundamental building blocks. These particles decay in a time ranging from 10u207bu2076 s to 10u207b¹u2076 s, except for the proton, which is extremely stable.
Category: High Energy Particle Physics

Explaining the Complexity of Experimental Results on the Lifetimes of Free-Neutrons and Hyperons and the Masses of W-Bosons Based on the Atom-Like Structure of Baryons

Authors: Sylwester Kornowski
Comments: 14 Pages.

The complexities of the precise experimental data on the lifetimes of free neutrons and hyperons and the masses of W bosons have not yet been resolved within the quark model. These three extremely important problems concern the weak interactions. Here we present exact solutions to these problems within the atom-like structure of baryons described in the Scale-Symmetric Theory (SST). The SST solutions show that they are beyond the Standard Model, but in previous articles we have shown how the quark model emerges from the atom-like structure of baryons. The mean lifetimes of free neutrons are very important in nuclear physics, particle physics and cosmology. Within SST we calculated the ground state for mean lifetime of free neutrons that is 878.10 s — it follows from the transition from the nuclear weak interactions to the weak interactions of the electrons in the presence of dark matter. We showed that in a bottle, the central spacetime condensate in the neutron, which is responsible for the β decay, can be in different mass states that leads to two excited states of neutron lifetime, i.e. 880.36 s and 882.63 s. We showed that in neutron beams, mean lifetime of neutrons depends on neutron velocity because emissions of quanta by the central spacetime condensate with increasing neutron velocity are more and more suppressed. For neutron velocity equal to a threshold velocity 3.356 km/s we obtain a longer mean neutron lifetime equal to 888.89 s. For velocity 2.2 km/s we obtain 886.83 s. We showed that mass of the W boson depends on the place of creation — the two calculated basic values are 80,360.11 MeV and 80,378.96 MeV which lead to the mean value 80,369.5 MeV that is very close to the world average central value (80,369.2 MeV). We also calculated the exact lifetimes of the hyperons.
Category: High Energy Particle Physics

Emergent Gravity from Fundamental Triangles with Inner Torsion-Twist Degrees of Freedom — an Analogon to Structure of Penrose-Triangles

Authors: Holger Döring
Comments: 8 Pages.

Investigated is a model of spacetime in which fundamental triangles possess not only geometric properties such as area and edge lengths but also internal degrees of freedom representing twist, which encodes their relative orientation with respect to neighboring triangles. While local triangles are flat and consistent, global misclosures can accumulate, acting analogously to holonomies in curved spacetimes. This approach enables the construction of a spin-network-like model in which gravity can be interpreted as a statistical emergent phenomenon arising from these accumulated twists. The concept is inspired by Penrose-triangles: local consistency combined with global twist. Therefore this description is called the Penrose-triangle-ansatz (PTA).
Category: Quantum Gravity and String Theory

Special Relativity Violates Physical Identity

Authors: Antonio León Sánchez
Comments: 3 Pages.

The Theorem of Physical Identity demonstrated in this article is an almost immediate consequence of the Laws of Logic. However, it is incompatible with the theory of special relativity.
Category: Classical Physics

Recurrence Relations in the Tessellation of the Upper Half-Plane by the Full Modular Group

Authors: Hans Montanus
Comments: 11 Pages.

The successive actions of the generators S and T of the full modular group SL(2,Z) on the fundamental domain F lead to a tessellation of the upper half-plane H. Each image can be obtained by acting on the fundamental domain with a word consisting of solely S's and T's. For instance STTSTTT(F) is the image when the word STTSTTT acts on F. There is no shorter word that produces the image STTSTTT(F). A recurrence relation will be derived for the number of images for a given minimal word length.
Category: Combinatorics and Graph Theory

How to Derive the Fine Structure Constant Using Probability and Compton Equations

Authors: Colin James
Comments: 32 Pages.

I use the relativistic Compton equations to calculate the momentum response of a ‘target’ electron to vacuum photon collisions redirected from a ‘source’ electron. The equations give the ratio of the momentum of the ‘target’ electron after the collision divided by the momentum of the incoming photon over the range of all angles of the ‘target’ electron’s deflection. By summing evenly (over the maximum cross-section) over all angles we obtain the ratio of 1/2.1412 when using photon frequencies of 2 and 4 times the mass equivalence of an electron in the ratio of 5.6269 to 1. 4 times the mass equivalence may be 2 x (2 times electron mass equivalence photons acting simultaneously) or a double photon composite.The fraction 1/8 is a probability based on spherical geometry — the ratio of the maximum cross-sectional area of a sphere to its surface area (¼) and a further probability of (½) due to the even chance of the electromagnetic properties of a photon matching those of an electron. This gives a total probability of (¼) x (½) = 1/8. There are 2 such 1/8 probability collisions — one in which a photon is deflected by a ‘source’ electron towards a ‘target’ electron and a second 1/8 probability collision at the ‘target’ electron. The Fine Structure Constant is therefore divided into 3 parts.1/8 x 1/8 x 1/2.1412 = 1/137.0360 based on probability, spherical geometry and the use of the Compton scattering equations. 1/2.1412 {0.4670} is calculated using the Compton scattering equations. 1/2.1412 x 1/8 (probability) gives 1/17.1295 {0.05838} Coulomb’s Law. 1/17.1295 x 1/8 (probability) gives 1/137.0360 {0.007297} the Fine Structure Constant. A ‘free’ electron may be pictured/averaged as a speed of light particle contained in an approximately circular orbit with fixed angular momentum by collisions with vacuum momenta.
Category: High Energy Particle Physics

An Optimized Sech-Based Approximation of E^{-X^2}

Authors: Vladyslav Vasilache
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper introduces a new, highly accurate approximation for the function $e^{-x^2}$. By differentiating a known error function approximation and optimizing its parameters, we drastically reduce the maximum absolute error from $1.88%$ to less than $0.09%$ without using any exponential terms.
Category: Functions and Analysis

Towards a Floer Theory for Mars II Floer Hessian Field Almost Extends

Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 2 figures

In part I, [FW26a], we showed that collisional periodic orbits of twisted Zeeman systems can be detected variationally by a non-local Hamiltonian action functional. In this part II we show that the linearized gradient flow of this non-local functional is a Fredholm operator and prove a non-local elliptic regularity result. These results are obtained with the theory of almost extendability of weak Hessian fields introduced in [FW26c].
Category: Mathematical Physics

Inference Operators

Authors: A. Zelmer
Comments: 40 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Certainly the beauty of mathematics also lies in the precision of mathematical sentences, as well as in the proofs of theorems. However, this can only be fully achieved by formalizing sentences and proofs.Our computer-assisted proving system, which we have called "Logic", contains two fundamental modules: the sentence editor and the proof module. We presented the sentence editor in Mathematical Sentences as Matrices. The proof module of the "Logic" system is based on certain primitive functions that we have called inference operators. In this paper we present what inference operators are and how they can be used in formalized mathematical proofs.
Category: Set Theory and Logic

A Possible Solution to the Mystery of the Bermuda Triangle: a Nuclear Physics-Based Quark Transfer Model Leading to Perpetuity of Magnetic Force

Authors: Bijon Kumar Sen, Subha Sen
Comments: 5 Pages. 2 Figures

On the basis of a nuclear physics-based model, an attempt has been made to explain the neutron to proton (n — p) conversion in the nucleus of an atom and the way of transfer of a d- quark into a u- quark. From examination of their implications in the mechanism of low and high temperature superconductivity, we came across a stupendous conclusion which may lead to busting the mystery of the Bermuda triangle. This, however, assumes free quarks may have limited existence under special condition. It is the swarm of quarks produced from unlimited supply of free electrons, unhindered by the warmth and the depth of the ocean, unchecked by the Meissner effect, add up (aided and abated by mutual enforcement) to a strong attractive force which can explain the anomalous magnetic behaviour as noticed by Columbus during his voyage through Bermuda triangle. The appearance and disappearance of the hysteresis curve shows that the Bermuda Triangle serves as a natural channel, passing everything that comes into contact with it into eternal sleep leading ultimately to the perpetuity of magnetic force. It is advisable that the study of tectonic and geophysical processes should be carefully made by the scientists so as not to meet the swarm of quarks for their own safety, security and escape from becoming a part and parcel of perpetuity.
Category: Nuclear and Atomic Physics

Extended Lorentz Spacetime Approach to Gravity

Authors: Tomasz Kobierzycki
Comments: 13 Pages.

In this paper I will present simple model of gravity field not as spacetime curvature but as a motion of arrows or more precise set of vectors from each point of spacetime. It's rooted in special relativity and it extends Minkowski spacetime to three sectors.
Category: Relativity and Cosmology

Short Version of "Turing-Unsimulability & Cosmic-Censorship-Falsity for General Relativity"

Authors: Warren D. Smith
Comments: 6 Pages.

My paper http://vixra.org/abs/2605.0004 "Turing-Unsimulability, and instantaneous & sustained Cosmic-Censorship-falsity, for Einstein-Vacuum General Relativity", at 60, 74, and 78 pages for versions 1, 2, and 3, was too long for many stomachs. Therefore I here also provide a short introductory explanation (in the spirit of Phys.Rev.Letters summaries of fuller papers) of its main ideas to try to advertise it and to get expert readers oriented right before they start.
Category: Astrophysics

Emergent Time and the Elimination of Cosmological Singularities Via Clock-Field Deparametrization

Authors: Ruslan Yurkevich
Comments: 7 Pages. Distributed under the arXiv.org perpetual, non-exclusive license.

Context: In canonical quantum gravity, the Wheeler-DeWitt equation suffers from the notorious "problem of the frozen Universe," lacking an explicit time parameter. Methods: This paper introduces a novel pre-geometric quantum cosmological formalisation where the flow of time is an emergent property tracking microscopic transitions. We execute a canonical 3+1 ADM deparametrization of the gravitational constraint using a scalar clock-field (chi ), yielding a dynamic Schrödinger-type equation for quantum gravity. Results: We postulate a non-linear feedback loop where the local clock rate w slows down as the energy density (ho ) increases: (w(ho) = 1/(1 + xi ho)), where (xi > 0) is a universal coupling constant. Semi-classical WKB analysis of the homogeneous FRW mini-superspace reveals a singularity-free "bounce-plateau" state at the Big Bang and within black hole cores. In the low-density limit, this mechanism naturally acts as a dynamic negative pressure component, driving late-time cosmic acceleration without a cosmological constant (Lambda ). Significance: The modified Mukhanov-Sasaki equations predict explicit corrections for primordial perturbations ((n_{s}) and r) that fall precisely within the discovery thresholds of the upcoming CMB-S4 and DECIGO experiments, rendering the model fully falsifiable.
Category: Quantum Gravity and String Theory

Gravity as Spacetime Distortion: A Unified Framework from the Full Affine Connection

Authors: Luca Eliseo Pavesi
Comments: 26 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present a comprehensive geometric framework for gravity in which the fundamental dynamical variable is the distortion tensor encoding both torsion and non-metricity. After a thorough review of metric-affine geometry, we construct the most general action quadratic in the distortion and linear in the Levi-Civita curvature, supplemented by a Yang-Mills-type kinetic term. The theory propagates a massless graviton, a massive vector, and a massive scalar. We derive the full non-linear field equations, linearize them around Minkowski spacetime, perform a complete mode decomposition, and analyze the stability and unitarity of each sector. We study the low-energy limit and show that General Relativity is recovered exactly below the distortion mass scale. We then explore cosmological solutions, finding that the vector mode can drive late-time acceleration without a cosmological constant. Black hole solutions are analyzed perturbatively, revealing a possible mechanism for singularity regularization. We discuss gravitational wave signatures, including dipole radiation from the vector mode, and place preliminary constraints from LIGO/Virgo observations. Finally, we outline the power-counting renormalizability of the theory and its potential as an ultraviolet completion of General Relativity. Extensive appendices provide detailed derivations of all identities used in the main text.
Category: Relativity and Cosmology

The Optical Prison: Universal Physical Isolation as the Physical Solution to the Fermi Paradox

Authors: Hao Xu
Comments: 10 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

An Optical Prison hypothesis is proposed that would physically resolve the Fermi's Paradox. Three independent ground optical experiments verify the physical limitation of the astronomical observations caused by structural self-weight collapse and optical inherent constraints. Unlike conventional SETI concepts, the conclusion is quantitatively restricted by measurable experimental data, lacking empirical support, our conclusion is qualitatively restricted by neutron degradation and explaining the cosmic silence in SETI observations.
Category: Astrophysics

Testing the D.m. By Quantum Gravitation Theory by the Mass Associated to the Turnaround Radius

Authors: Manuel Abarca Hernandez
Comments: 9 Pages.

The DM by Quantum Gravitation theory (DMbQG hereafter), is a novel theory developed in the two main papers [1] and [2] Abarca,M.(2024). In the present work, in the framework of DMbQG theory it will derived the formula for the mass associated to the turnaround radius depending on the turnaround radius and it will be shown that the new expression has a deeper physical meaning regarding the same formula in the current LCDM paradigm. The DMbQG theory states a direct relation between the virial radius and the turnaround radius as well as the virial mass and the mass associated to the turnaround radius.The most important contribution of this work is placed in the chapter 2 where it has been demonstrated that the formula for the mass associated to the turnaround radius, using the DMbQG theory, is the same that the one in the current LCDM paradigm. However the new formula has a deeper physical meaning because its dimensionless factor is simpler regarding the one in the current LCDM paradigm. It is remarkable the fact that the both dimensionless factors depend on exclusively from the Universal omega parameters for the mass or for the DE and the both ones differ only a 5%. The fact that in the framework of DMbQG theory has been found a better formula for the mass associated to the turnaround radius is a strong support for the DMbQG theory whose hypothesis about the origin of DM is exclusively the gravitational field. The chapters 3, 4 and 5 are devoted to test the DMbQG theory in the clusters, Virgo, Coma and the Local Group of galaxies using recent data published about these clusters. The tests are mainly focused on the turnaround radius and its mass associated and all of them have been a complete success by the DMbQG theory.
Category: Astrophysics

Gravity as an Emergent Force Via the Uncertainty Principle

Authors: Morgan W. Weinberg
Comments: 51 Pages.

The core concept of this paper is the relation between an accelerating field and time uncertainty. This relation distills from the derivation of Newton's Law of Gravitation via the uncertainty principle. It's shown, further, that this relation can be used to derive the Coulomb Force, suggesting that it may be a general principle in nature. Taking this concept further, this paper draws a connection between expanding space and acceleration---offering an explanation for the missing-mass problem in galaxies. The paper goes on to draw a connection between the expansion of space and time uncertainty, leading to a startling conclusion: The expansion of space is not a function of the energy contained therein, but conversely, the mass of the universe is created in concert with the expansion of space. Further, because this expansion is a function of time, the mass of the universe is a function of time and increases in lockstep therewith. It's deemed that the model of the universe presented herein obviates the need for dark matter and dark energy to explain our observations of the cosmos.
Category: Astrophysics

Doppler Effect, Absolute Stellar Aberration, Stellar Velocity, Stellar Distance and Speed of the Light

Authors: Miloš Čojanović
Comments: 6 Pages.

Our assumption is that the Doppler Effect and Absolute Stellar Aberration are two complementary phenomena. This means that if we are able to use the result obtained by measuring $DE$ to determine the radial velocity, then by using the result obtained by measuring "ASA" we should be able to determine the transverse velocity with which the star moves in relation to the observer. We will prove that if we know the velocity of the star, we can determine its distance in relation to the observer and the speed of light emitted from the star in the direction of the observer.
Category: Astrophysics

Multi-Metric Wormholes: A No-Horizon Theorem and 1/N Suppression of Exotic Matter

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

We present a comprehensive study of traversable wormholes in multi-metric gravity, a ghost-free theory with N interacting metric tensors. The action, field equations, and constraints are derived step by step. We construct a static, spherically symmetric wormhole ansatz with a Gaussian deformation localised at the throat, and reduce the field equations to a system of ordinary differential equations. A central result is a no-horizon theorem: any stationary, asymptotically flat solution with a non-zero multi-metric charge Q, defined as the asymptotic flux of a conserved current built from the metric differences, cannot contain a Killing horizon and must therefore be a traversable wormhole. We show analytically and numerically that the null energy condition (NEC) violation is suppressed by a factor 1/N compared to the single-metric case, and that the exotic matter can be confined to an arbitrarily narrow shell. The deflection angle and Shapiro time delay are computed, and the stability under radial perturbations is analysed. The model satisfies Solar System constraints and makes falsifiable predictions for near-future instruments.
Category: Relativity and Cosmology

Shaking up the Theory of the Expanding Universe

Authors: Henk Dorrestijn
Comments: 11 Pages.

Obstruction Theory offers an alternative to the Newton/Einstein theory for cosmology. Assuming a rarefied mass density in the universe, the redshift we observe in distant light sources can be explained without assuming that the sources are moving away from us at high speed, causing the universe to expand. The redshift can be easily explained by the average mass density of the universe.It is known that a mass slows down the velocity of time at a point in its vicinity. This slowdown turns out to be equal to the reduction of direct radiation from more distant space due to the presence of the mass. We show that the amount of direct radiation reaching an observer from the universe is always partially lost along the way through scattering by protons and other small particles. This translates into the velocity of time, which we observe as redshift. We find the size of our visible universe by stating that the observed time velocity of the light sources at the boundary of the universe is reduced to zero. The value for the size that we find via a simple calculation is close to the value found in the traditional way. Furthermore, with this theory, a value for the Hubbleconstante can be found using the mass density of the universe. According to Obstruction Theory, there can furthermore be no question of a bounded universe. Every observer is the center of their own universe. Beyond its own universe, the universe extends infinitely far.
Category: Relativity and Cosmology

Collatz Conjecture: A Simple Proof for a Simple Problem

Authors: Ulrich Neuenschwander
Comments: 8 Pages.

A simple proof of the Collatz conjecture is proposed. The approach relies on the fundamental properties of N and on their fruitful interplay with the Collatz transformation.It will be interesting to see how the field receives the proposal and whether the reasoning and the conclusions are confirmed or need modification.
Category: Number Theory

Observation of D+D Fusion in Electromagnetically Self-Contained, Long-Lifetime Plasmoids

Authors: Dominik Kuryga, Paulina Nadia Weremczuk
Comments: 28 Pages.

We report the generation of self-contained, long-lived plasmoids in a low pressure coaxial diode of novel concept, driven by a ~5ns up to 1MV pulse, generating neutron bursts consistent with D+D fusion in discharges in deuterium. Neutrons were detected using a silver activation based detector. A correlation was observed between lifetime and neutron yield. Average neutron yields reached approximately 5—7x10u2075 neutrons per shot, with peak values up to 1,4x10u2076 neutrons/shot. Microwave emission measurements were done showing long decaying radiation. The demonstrated detectable nuclear fusion in this novel device opens new perspectives for compact neutron sources and alternative fusion concepts based on self-confined plasmoids.
Category: Nuclear and Atomic Physics

Traversable Wormholes in Quadratic Covariant Gravity: Localised Deformations, Shapiro Delay, and Stability

Authors: Luca Eliseo Pavesi
Comments: 19 pages. English.

We consider a covariant theory of gravity defined by the action S = ∫ d^4x √−g [(16πG)^{-1}(R + αR^2) + L_matter], which reduces to general relativity when α → 0. This theory, belonging to the class of f(R) gravities, is ghost-free and contains an additional massive scalar degree of freedom (the scalaron), and is treated as an effective field theory valid below the Planck scale. We derive the fourth-order field equations step by step, including all boundary terms. We then apply them to a static, spherically symmetric metric describing a traversable wormhole. The metric includes a Gaussian deformation X(r) = A exp[−(r − r0)^2/(2σ^2)] localised around the throat r = r0. The flare-out condition is satisfied for A > −1. We compute all Christoffel symbols exactly, derive the Ricci tensor and scalar, and solve the modified Einstein equations for an anisotropic fluid. The energy conditions are analysed: the null energy condition is violated only in an arbitrarily small region near the throat if α > 0 and the Gaussian parameters are chosen appropriately. We study null geodesics using the corrected radial equation, compute the deflection angle and the Shapiro time delay for light passing near the wormhole, and show that the Gaussian deformation introduces a characteristic shift compared to the Morris—Thorne case. Stability under radial perturbations is analysed in the scalar—tensor representation, showing that the wormhole can be stable for a range of parameters. The asymptotic limit is studied via a post-Newtonian expansion: the PPN parameters remain γ = β = 1, and the scalaron mass m^2 = 1/(6α) is constrained by Solar System tests to be m ≥ 10^{-3} eV. We discuss observational signatures such as lensing, Shapiro delay, and gravitational-wave echoes that make the model falsifiable. All calculations are presented in detail, with intermediate steps collected in appendices.
Category: Relativity and Cosmology

A Geometric Explanation of Dark Matter Based on General Relativity

Authors: Hao Shen, Ruipeng Ma
Comments: 19 Pages.

Within the framework of standard general relativity (Einstein 1915), under the assumptions of staticity, spherical symmetry and the strong energy condition, we prove that a geometric transition zone — the "reverse-bending zone" — must appear in the periphery of any finite self-gravitating system, where the t—r sectional curvature changes sign from negative to positive. This zone is bounded by the curvature zero r0, the curvature peak rpeak, and the matter boundary R; in the interval (r0, R) the sectional curvature smoothly transforms from matter-dominated spherical compression to vacuum saddle-shaped stretching. The reverse-bending zone is not a free vacuum but a forced geometry locked jointly by the interior baryonic potential well and the far-field boundary condition. Within this zone, the Misner—Sharp-type gravitational mass M(r) continues to grow: it grows faster than linearly in the region r0 → rpeak, and although the growth slows down in the region rpeak → R, it never ceases. The resulting geometric Weyl stretching together with the self-energy of the gravitational field provide an extra centripetal acceleration, which naturally manifests itself, in the weak-field approximation, as an approximately logarithmic potential and a flattening of the rotation curves. The theory yields parameter-free, falsifiable predictions that can be directly tested with existing rotation-curve and photometric data. These results show that, without introducing new particles or modifying the field equations, the forced geometry within general relativity can produce "dark-matter-like" gravitational effects on galactic scales.
Category: Relativity and Cosmology

Elementary Weak Solutions of the Navier—Stokes Equations and an Application of the Banach Fixed-Point Theorem

Authors: Masatoshi Ohrui
Comments: 23 Pages.

This is an application of functional analysis to the existence and smoothness of the Navier—Stokes equations using elementary weak solutions in Sobolev spaces.We solve the problem in mathematics. The problems are not in physics, so we do not use any physics or assumptions-falsified mathematics, such as other papers. We use mathematics only. We can solve the problem by using an exactly and completely FALSIFIED resolution, where large initial values destroy the earth, because uniqueness does NOT hold, or SMALL initial values love your cup of coffee.There are no long or complicated calculations; semi-groups, a priori estimates, and boundary conditions are not used at all. We apply the local solvability of linear partial differential operators with constant coeficients.
Category: Functions and Analysis

Proof of Hartog’s Phenomenon and Cohomology Vanishing Theorem

Authors: Masatoshi Ohrui
Comments: 2 Pages.

We can prove Hartog’s phenomenon by solving the ∂-bar equation for compactly supported forms. To solve the equation, we construct the solution using convolution.
Category: Functions and Analysis

Extended Standard-Model by the Coxeter Element of the Affine Weyl Group E˜8

Authors: Reinhard Kronberger
Comments: 20 Pages.

In this paper i will give an extension of the known Standard-Model.The shape of the extension is not arbitrary choosen.The shape explains gravity and more. I show that the symmetries generated by the coxeter-element of the affine Weyl group E˜8 which is the affine extension of the well known exceptional group E8 is a candidate which explains open questions like dark matter and gravity.
Category: Quantum Physics

Geometric Projection of Arithmetic Spirals Onto Logarithmic Manifolds: a Moiré Interference Framework for Studying Prime Distribution Without Complex-Analytic Tools

Authors: Jian-Yu Huang
Comments: 27 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We develop a geometric and spectral framework for studying structural fluctuations in discrete arithmetic sequences, operating entirely within real-variable analysis and without appeal to the Riemann zeta function, Euler products, explicit formulae, or analytic continuation. An arithmetic lattice is mapped onto a transcendental logarithmic manifold via an area-filling projection; the resulting Moiré-type interference field serves as the primary object of study. The principal contributions are as follows. (i) We prove, with explicit constants, that the projection map is injective and that successive images are uniformly separated (Propo-sitions 2.3-2.4). (ii) We establish a uniform L 2 near-orthogonality theorem for finite phase families, yielding a computable operator-norm bound on the associated Gram matrix via Gershgorin's circle theorem [5] (Theorem 3.3). (iii) We introduce an explicit Moiré di-lation operator T σ = −i(x ∂ x + σ) on L 2 ([1, ∞)), show that the geometric phasor family {x −(σ+it) } t∈R constitutes its formal eigenfunction family (Lemma 3.12), and prove by integration by parts that T σ is formally self-adjoint if and only if σ = 1 2 (Theorem 3.14). (iv) We derive quantitative variance bounds for node-count statistics, controlled by the pairwise phase-correlation bounds (Theorem 3.19). Complete exponential-sum estimates with explicit constants (Appendix C) and Abel-smoothing remainder formulae including an incomplete-Gamma bound (Appendix B) are provided. All theoretical claims are either proved using the above tools or explicitly designated as conjectural.
Category: Number Theory

Finite Bernoulli—Zeta Transforms for Fibonacci-Type Recurrence

Authors: Payam Danesh
Comments: 12 Pages.

Fibonacci and Lucas sequences are basic examples of second-order recurrences, and their behavior is closely connected to the golden ratio. Bernoulli numbers and special values of the Riemann zeta function also form a classical part of number theory. This paper connects these two areas through exact finite identities. The method starts from exponential generating functions, separates the odd-indexed terms, applies Bernoulli generating functions, and then compares coefficients. This gives a finite formula in which a weighted sum of zeta values at non-positive integers becomes an explicit Fibonacci expression. The same argument also gives a Lucas version, and then extends to every sequence satisfying the Fibonacci recurrence with arbitrary initial values. Exact symbolic checks and residual plot are included to show how the cancellation works. The result is a complete unconditional link between Fibonacci-type recurrences, Bernoulli numbers, and special zeta values.
Category: Number Theory

Dual Architecture of the Gamma Function: Complementary Extension to the Left Half-Plane and Regularization of Logarithmic Divergences

Authors: Julinho Jorge Luís
Comments: 20 Pages.

This work proposes a complementary extension of the factorial function to the real line, based on the separation of the bilateral integral of e^(-Ax) into two disjoint domains. For A>0, the classical Gamma function Γ(z) emerges in the right half-plane; for A<0, we introduce the Symmetric Gamma Function Γ ˉ(z)=e^(-iπ(z+1)) Γ(-z), defined in the left half-plane, with poles at the positive integers. The duality between the integral kernels underlies a regularization mechanism for logarithmic divergences: Γ_R (z)=1/Γ ˉ(z-1) and Γ ˉ_R (z)=1/Γ(z+1), replacing each pole by an exact finite value. An alternative real representation B(x)=∫_0^∞e^(-u) u^(-x) du (convergent for x<1) is constructed, together with a trigonometric factor C(x)=2sinu2061(πx)+cosu2061(πx), defining F(x)=C(x)B(x) for x≤0, yielding F(-n)=(-1)^n n!, thereby unifying the complex branch, real regularization, and Laurent expansion formalisms. The relation F(-n)⋅Resu2061(Γ,-n)=1 establishes the fundamental duality, which emerges directly from the construction of the integral kernels. The method is validated in arithmetic progressions, QED, and QCD. The extension to k-loops is systematic via exponentiation: Γ_R^((k) ) (-n)=[(-1)^n/n!]^k. Distinct physical prediction: In d=5 dimensions, the vacuum energy density changes sign — a repulsive force where the MS-bar predicts attraction. This inversion has direct implications for the stability of extra dimensions in string theory and brane models.
Category: Quantum Gravity and String Theory

The Atomic Structure of the Chemical Elements

Authors: Jozsef Garai
Comments: 68 Pages.

Based on the analysis of the well-known features of the atoms, the following conclusions can be deduced. The identical and invariant properties of the chemical elements can only be ensured if the charge distribution of the nucleus is invariant and identical for each of the elements, dynamic equilibrium between the opposite charges in the atoms cannot be stable in the time scale of the universe, classical electromagnetism is valid at atomic scale, since neither theory nor experiments sets limits on it. Taking these conclusions into consideration the following modifications of the contemporary atom models are proposed. Nucleus: The identical reproduction of the nucleus requires lattice arrangement for the nucleons. Protons and neutrons have the same size. These nucleons should occupy the space in the most efficient way, forming a closest packing arrangement. The smallest building blocks of this arrangement are tetrahedrons. Assuming alternate arrangement of the protons and the neutrons, and expanding a tetrahedron seed by adding additional layers to it, the number of protons in the layers reproduces the periodicity of the chemical elements. Electronegativity represents the average attraction of the unshielded proton/s on the valence electron/s. This physical description is even consistent with the irregularities of electronegativity. Electronic shell: In the time scale of the universe, dynamic equilibrium of the opposite charges in the atoms would be chaotic. This contradicts with the known stability of the atoms. Static equilibrium between the opposite charges can only be achieved if at least one of the charges is a distributed one. The physical behavior of the free and the bounded electrons are different. Thus, these electrons are not identical. These differences can be explained if the point charge free (unbounded) electron at capturing transfers and forms a surface charge electron shell around the nucleus, and vice versa. This phase transformation is energetically feasible. The electronic shell structure of the atoms is the consequence of the nuclear lattice. New electron shell is formed when the attraction of the added proton of an element is weaker on the captured electron than the average attraction on an electron in the existing shell.
Category: Nuclear and Atomic Physics

Completeness of the Metric Description of Gravitational Reality: An Radiative Generalization of Kerr-Newman Spacetime

Authors: Tanishq Chandu Khandare
Comments: 2 Pages.

I derive a non-vanishing, solution to the Einstein-Maxwell field equations representing a dynamical, radiating, rotating, and charged manifold. Utilizing the Newman-Penrose (NP) formalist, I project the metric onto a nulltetrad {l, n, m, m¯ } to evaluate the Weyl and Ricci scalars. We demonstrate that the resulting stress-energy tensor Tµν = T (null) µν + T(em) µν satisfies the Weak Energy Condition (WEC) and the local conservation law ∇µTµν = 0. By formalizing the EPR criterion for physical completeness, we argue that the stationary KerrNewman limit is a sub-manifold of the broader radiative reality. I further prove that the r = 0 singularity is a transient topological feature that resolves into a Minkowski vacuum in the limit of total evaporation.
Category: Relativity and Cosmology

Is the Central Valley of California an Elongated Impact Basin?

Authors: David E. Rutherford
Comments: 4 Pages.

In general, impact craters are circular in shape, but occasionally, they exhibit non-circular forms. One such form is the elongated impact crater. I suggest that the Central Valley of California may be a larger version of an elongated impact crater, an elongated impact basin. Its elongated shape might be the result of a very low angle of impact of one or more celestial objects with the surface of the Earth. The `central' peak (or uplift) of the original basin might be the Sutter Buttes, in the northern part of the Central Valley. In order to support these conclusions, images of lunar impact craters are compared to shaded relief maps of the Central Valley (and surrounding mountains) of California.
Category: Geophysics

Quantum Mechanics and The Subjective Nature of Mathematics

Authors: Joseph Palazzo
Comments: 3 Pages. (Note by viXra Admin: An abstract in the article labeled as such in the article is required)

In the historical debate between Einstein and Bohr, it is practically seen in every sentence that Einstein was debating ontology ("Do you really believe the moon is not there when you are not looking at it?")[1] while Bohr was debating epistemology (we only know until particles are observed, at which point the "wave function collapses" into a definite state). This is like as if one is talking about basketball, while the other is talking about hockey. It’s no surprise that they were talking passed each other, not aware of what was going on. Worse is that the whole physics community for the past 100 years did not see it. In 2022, the Nobel Prize in physics was headlined as: quantum mechanics is right, Einstein is wrong — indicating by all measures that we still don’t have it right.
Category: Quantum Physics

The Oscillations of a Particle in an Anharmonic Potential with Damping

Authors: L. A. Xamidullayeva, U. O. Muhammedov, X. N. Ismatullayev
Comments: 3 Pages.

The natural processes equations are nonlinear and have dissipating terms. In many cases they donot have an exact analytical solution. Using perturbation theory we solved the equation of anoscillating particle in an anharmonic potencial.
Category: Classical Physics

Kinematic Analysis of the Motion of an Ellipsograph Point Under Various Velocity Laws

Authors: Viktor Strohm
Comments: 5 Pages.

This paper investigates the kinematics of a fixed point on the connecting bar of an ellipsograph (Archimedes' trammel) under different driving motion regimes: uniform, uniformly accelerated, and Keplerian (elliptical). Based on differential constraint equations, analytical expressions for the velocity and acceleration vectors of the trajectory point are derived. A numerical approach, modeling the division of the orbital quadrant into equal time intervals, is utilized to calculate the corresponding areal velocities. It is rigorously demonstrated that the constancy of the areal velocity and the fulfillment of Kepler's second law occur exclusively under one specific law of angular velocity—the Keplerian regime—whereas under uniform and uniformly accelerated motions, the law of areas is violated. This work establishes a link between the mechanical modeling of trajectories and the author's fundamental theoretical research in the focal and central kinematics of the ellipse.
Category: Classical Physics

Decoupled Prompting and Topology-Aware Optimal Transport for CLIP-Based Unsupervised Cross-Modal Re-Identiffcation

Authors: Xiaohao Xie, Wenhua Jiao, Wei Meng
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Unsupervised Visible-Infrared Person Re-identification (USL-VI-ReID) is critical for cross-modal intelligent surveillance. While vision-language models (e.g., CLIP) present powerful representational capabilities, directly fine-tuning them for USL-VI-ReID often causes catastrophic feature collapse and prompt degradation due to massive domain gaps and noisy pseudo-labels. Furthermore, traditional discrete matching and heuristic denoising strategies suffer from severe cross-modal information starvation and numerical bias against hard positives. To address these challenges, we propose a robust, CLIP-based unsupervised cross-modal fine-tuning framework. First, we design an implicit adapter fine-tuning strategy coupled with decoupled multi-dimensional semantic prompting to isolate domain biases without destroying pre-trained priors. Second, a Cluster-Aware Cross-Modal Semantic Alignment (CCSA) mechanism maps dynamic visual centers to modality-shared textual proxies via visual-conditioned prompting, facilitating an implicit soft alignment decoupled from hard clustering noise. Third, we frame cross-modal association as a Topology-Aware Optimal Transport (TOTO) problem. Utilizing Fused Gromov-Wasserstein (FGW) constraints and Argmax assignments, TOTO injects potent hard regularization to overcome optimization inertia on difficult samples. Finally, our Pure Relative Confidence Ratio and Dual Adaptive Denoising (RCR-DAD) module eliminates numerical bias, formulating a robust self-paced learning trajectory. Extensive experiments on SYSU-MM01 and RegDB demonstrate our framework achieves state-of-the-art performance. The code will be released.
Category: Artificial Intelligence

Ramanujan Polynomial Expansion for Hurwitz Zeta Function

Authors: Payam Danesh
Comments: 29 Pages.

Polynomial expansions of zeta functions provide a natural way to connect analytic continuation, regularized summation, Mellin analysis, and orthogonal polynomial theory. In this paper we try to develop a shifted Ramanujan—Mellin expansion for the Hurwitz zeta function in the critical strip. The construction combines Abel—Plana regularization over the nonnegative integers, Ramanujan summation for shifted Dirichlet terms, the Cayley transform of the right half-plane, and Mellin transforms of Laguerre functions. The main result proves that the Hurwitz zeta function admits a locally uniformly convergent expansion in a universal polynomial basis that is independent of the shift parameter. The shift appears only through explicit coefficients involving the digamma function and shifted Hurwitz zeta values. The Riemann zeta function is obtained as a special case. On the critical line, the normalized basis forms a complete orthonormal system with respect to a hyperbolic weight, and every zero of each basis polynomial lies on the critical line. The final result gives an exact zero-free compact criterion equivalent to the Riemann Hypothesis.
Category: Number Theory

A New Home for Bivectors Geometric Algebra on a Sphere

Authors: Norm Cimon
Comments: 20 Pages.

The impetus for the work is this quote:"...as shown by Gel’fand’s approach, we can only abstract a unique manifold if our algebra is commutative."[1] Geometric algebra is non-commutative. Components of different grades can be staged on different manifolds. As operations on those elements proceed, they can effect the promotion and/or demotion of components to higher and/or lower grades, and thus to different manifolds. This paper includes imagery that visually displays bivector addition and rotation on a sphere. David Hestenes interpreted the vector product or rotor in two-dimensions: "as a directed arc of fixed length that can be rotated at will on the unit circle, just as we interpret a vectoras a directed line segment that can be translated at will without changing its length or directionu2026"[2]Rotors can be used to develop addition and multiplication of bivectors on a sphere. For those rotational dynamics, rotors of lengthare the basis elements. The geometric algebra of bivectors — Hamilton’s "pure quaternions" — is thus shown to transparently operate on a spherical manifold.This paper also explores the possible generalizations that emerge from the placement of the graded elements which make up a geometric algebra onto separate manifolds.
Category: Geometry

The Weakening of Earth's Magnetic Field is the Real Cause Driving Current Ocean Warming

Authors: Jamal S. Shrair
Comments: 21 Pages.

Earlier studies estimated that the Arctic region is warming around twice as fast as the global average. Yet, recent studies have found this figure to be wrong by a huge margin (hugely underestimated). Actually, in the last 45 years, the Arctic region has warmed almost four times faster than the rest of the planet, while the South Pole is warming three times faster than the global rate. On the other hand, since 2016, the Atlantic Ocean especially its northern part, has warmed faster than other ocean basins in the top 100 meters of ocean. Nonetheless, the real reason for the rapid warming of these regions is because of the huge decline in the strength of Earth's magnetic field, and the enormous flow of thermal energy from Earth's interior into the upper layers. Back in 2014, data from Swarm (three specialized satellites) revealed that Earth's magnetic field has weakened 10 times faster than expected. It was astonishing data, totally unexpected and unexplained by the current model that relies on self-generating dynamo. Specifically, Swarm found the biggest decline in the strength of Earth's magnetic field around the Arctic regions, the North Atlantic Ocean and also within the South Atlantic, as the South Atlantic Anomaly (SAA) shows. The decline in the strength of Earth's magnetic field, definitely implies that these regions would receive more solar radiation from above, and higher flow of thermal energy from the interior than when the field was strong and stable. Hence, one can say conclusively that the rapid weakening of Earth's magnetic field was the real cause that made the Polar Regions, and those close to them, warm faster in comparison to other regions of the planet. However, the most fundamental reason why the pseudoscience theory of greenhouse gases is the name of the game - in addition of course to the widespread corruption of our society - is because of the lack of understanding the most important scientific facts about the most important astronomical objects to us, namely our own planet and star. Basically, the origin and mechanism of the magnetic fields of the Earth and the Sun, including the reason for their reversal, are currently mysteries and will remain mysteries forever under gravity-dominated physics.
Category: Climate Research

Visual Space, Neural Networks, and AI Algorithm Models

Authors: Taiwei Song
Comments: 4 Pages. 4

This paper briefly discusses the concept of visual space discovered by the author [1-4], its transformation equation with the natural space-time, and points out that this transformation relationship is the key algorithm for AI embodied agents to automatically recognize the surrounding "world". It also briefly demonstrates that neural networks inherently possess the properties of "iterative convergence" and "self-learning evolution", and the "emergence of intelligence" in large AI models based on neural networks is inevitable.
Category: Artificial Intelligence

Hastings-Cody Approximations of the Integral of a Power Times the Complete Elliptic Integral of the First Kind

Authors: Richard J. Mathar
Comments: 16 Pages.

Hastings and later Cody tabulated minimax polynomial approximations for the Complete Elliptic Integral of the First Kind. The simplicity of this representation by polynomials and polynomials times a logarithm allows to integrate their terms analytically. We demonstrate how integrals of the Complete Elliptic Integral times a power of its argument achieve double precision accuracy for powers from 0 to 2 based on Cody's polynomials up to 9th order.
Category: Functions and Analysis

A Theory of Kinematic Gravitation, and Some Fundamental Consequences

Authors: Charles Ba Oumar
Comments: 14 Pages.

We will be concerned with the study of relativistic density and hence demonstrate from first principles the possibility of kinematic black hole formation in inertial systems of coordinates in Minkowski spacetime. We will discuss the applicability of these principles to elementary particles on the basis of a set of geometrical assumptions, some general consequences, and also present alternative gravitational equations on the basis of some related elementary considerations. Finally, we will conclude with some general remarks on the meaning of these results.
Category: Relativity and Cosmology

Once More on the Aether

Authors: Viktor Stetsovich
Comments: 12 Pages.

Based on the hypothesis of the aether's existence, this article proposes an explanation for the results of the Fizeau and Michelson experiments, as well as an experiment for detecting the aether.
Category: Relativity and Cosmology

Saturating Magnetic Max Bank Drives Mismatched Loads, Using the Method of Self Matched Lines

Authors: Max Artusy
Comments: 3 Pages.

Abstract: The saturating magnetic Max Bank, provides a versatile topology to produce rectangular high voltage pulses with little secondary distortion. The self matched line method, is employed to achieve this. Rapid recharge is intrinsic, allowing high rep rate operation.
Category: High Energy Particle Physics

Resolving the Cosmological Hubble Tension via Local Wave Impedance Fluctuations in a Hexagonal Close-Packed Lattice

Authors: Markov Efim Sergeevich
Comments: 5 Pages. License: CC BY 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The persistent cosmological discrepancy between early-universe cosmic microwave background (CMB) measurements (H0 approx 67.4 km/s/Mpc) and late-universe local distance ladder observations (H0 approx 73.0 km/s/Mpc) - known as the Hubble Tension - presents a fundamental crisis for the continuous Lambda-CDM paradigm. This paper resolves this conflict by shifting from expanding spacetime metrics to a stationary, non-singular Hexagonal Close-Packed (3HCP) discrete space crystal. We demonstrate that cosmological redshift is not a Doppler-like stretching of space, but a dissipative energy attenuation of electromagnetic wave packets undergoing sub-nodal friction across contacting cellular boundaries. By modeling the material vacuum as a discrete transmission network with a baseline register capacity Llimit = 256, we derive the propagation velocity and local wave impedance purely from first-principles lattice geometry. Through a multivariable Taylor series expansion, we establish a rigorous mathematical bridge proving that our discrete wave difference scheme converges onto the continuous Maxwell equations with a damping term as the lattice spacing approaches zero (h -> 0). Crucially, we show that local structural density fluctuations within the 3HCP matrix systematically alter the sub-nodal impedance along different lines of sight. Low-density intergalactic voids minimize wave friction, yielding an apparent higher local expansion rate (H0 approx 73.0), while deep CMB-scale averaging profiles smooth over macroscopic high-density clusters, converging onto the lower background global baseline (H0 approx 67.4). The Hubble Tension is thus completely eliminated, emerging as a predictable geometric artifact of measuring discrete wave impedance across a multi-scale, non-uniform spatial crystal.Creative Commons Attribution Non Commercial No Derivatives 4.0 International
Category: Astrophysics

The Final Theory

Authors: Nigel B. Cook
Comments: 102 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

We construct a complete quantum field theory in which all observed interactions - electromagnetic, weak, strong, gravitational, and cosmological - arise from a single mechanistic principle: energy conservation in vacuum polarization. The theory replaces the ad hoc structure of the Standard Model and the geometric assumptions of general relativity with a unified framework based on the group chain for Euclidean signature SO(3, 3) ~ SU(4) ⊃ SU(3) × U(1)G ⊃ U(2) ⊃ SU(2) × U(1)Y . Matter representations, gauge charges, running couplings, particle masses, gravity, and dark energy all emerge from this structure without arbitrary parameters. This paper is a new presentation of the ideas in vixra paper 1111.0111 dated 2011, with updates, a few corrections, and further development. That earlier paper should still be consulted for further references, graphics and details documenting the origins of the various nascent ideas.
Category: Quantum Gravity and String Theory

An Alternate Resolution of the Famous Grandmother Paradox Which Might be Also Validated Via a Classic Experiment

Authors: Moshe Segal
Comments: 16 Pages.

The nowadays Science of Physics still embeds unresolved paradoxes, and incompatibilities between various Physics branches.One significant unresolved paradox is the famous Grandmother Paradox, in which someone returns to the past, kills his grandmother and thus, inhibits his birth, which obviously, also inhibits his ability to travel to the past.In addition to paradoxes, as presented just above, the nowadays Science of Physics still also embeds incompatibilities between various Physics branches.One of these branches is the branch denoted as the Classic Physics, which focuses on understanding and explaining what is denoted as the Macroscopic Environment.Another such branch is the branch denoted as the Quantum Physics, which focuses on understanding and explaining what is denoted as the Microscopic Environment.And, as presented above, these two branches of Physics are not fully compatible, and Humans are still struggling, to expand the knowledge that might bridge the gap that still exists between these two branches of Physics.Moreover, even the branch of the Classic Physics itself, still embeds branches which are also not fully compatible, as for example, the Gravity and the Electromagnetism, and more must be done to bridge the gap that exists also between these two branches, which both belong, as stated above, to the branch of the Classic Physics.Additional papers, by the author of this paper, present significant and reasonable arguments, which argue that the nowadays branch of the Classic Physics might be misleading in how it presents the concept of the Space-Time.By presenting an alternative view of how the Science of Physics should refer to the concept of the Space-Time, possible bridging between incompatible branches of the nowadays Science of Physics might be achieved, and also, a resolution to the famous Grandmother Paradox, might be presented.The above-mentioned additional papers, also propose experiments, which if implemented successfully, might provide validity, to the proposed alternative view of how the Science of Physics should refer to the concept of the Space-Time, which is presented in these additional papers.Thus, since a resolution of the famous Grandmother Paradox might be a significant step forward, and also the above-mentioned possible bridging between incompatible branches of the nowadays Science of Physics might also be a significant step forward, then, an implementation of the above-mentioned experiments, or any other experiments that might provide validity to the alternative view of how the Science of Physics should refer to the concept of the Space-Time, presented in the above-mentioned papers, should be an important and a significant endeavor.
Category: Relativity and Cosmology

Special Case of Law About Keep Moving of the Center of the Mass of а Closed System — Device from Two Bodies (Two Hulls), Uncompensated Moment and Propulsion in the Cosmic Space Without Propellant

Authors: L. Georgiev, D. Georgiev
Comments: 14 pages, 4 figures, In Bulgarian language

This article examines, special case of the law for conservation the motion of the center of the mass of а closed inertial system - device from two bodies (two hulls). Like in this special case, we obtain uncompensated moment for one of the hull of the device. As conditionally named first hull is standard rigid body. While on the second hull are connected two discs, which have equal masses and they can rotate free to the second hull. As when we apply the third law of Newton, between the two hulls, it’s uses the inertial of the two discusses. Like this way, because the kinetic energy is additive magnitude, it’s the hull with the discusses distribute the itself energy and for rotary motion of the discusses and for translational motion of the second hull. While for the first hull total kinetic energy, as a result of the applied third law is in the form of translational motion. As a result of the distribute of the energy of the second hull we obtain uncompensated moment for first hull. As a result of which is obtains and the special case of the law conservation motion of center of the mass of closed system — device from two bodies (two hulls). Like this way we have possibility for specific propulsion without propellant of the device in the cosmic space. Despite some shortcomings of the resulting specific propulsion, this is one of the possible ways of propulsion in cosmic space without "ejection" of propellant, and as only uses electrical energy from photovoltaics or nuclear energy.
Category: Classical Physics

Limitation in Ramanujan Positivity and Zeta Zeros of Riemann

Authors: Payam Danesh
Comments: 17 Pages.

Ramanujan’s divisor-sum identity gives one of the most analytical positivity arguments in the theory of the Riemann zeta-function: in Ingham’s work it yields the non-vanishing of ζ(s)on the line Rs=1. This paper revisits that mechanism and examines what is required to move it toward the critical strip. We first give a self-contained proof of the Ramanujan—Ingham zero-free line. We then prove that the direct critical-strip analogue fails for a precise Euler-factor reason: the positive Ramanujan square acquires an obstructing pole, while removing that pole destroys positivity already at prime level. This obstruction leads naturally to the Nyman—Beurling Hilbert-space formulation. Using Mellin transforms, we express the relevant closure problem through centered Ramanujan fractional-part functions and derive the exact finite-dimensional Gram system for optimal approximation. We prove fixed-window density of the associated boundary functions and separate the remaining problem into compact approximation and tail control. The main conclusion is a rigorous reduction: within this Ramanujan—Beurling framework, the remaining obstruction to the Riemann Hypothesis is an explicit uniform growing-window approximation estimate with controlled coefficient mass.
Category: Number Theory

Liniar Transformations on Multi-Vector Spaces

Authors: Constantin Scheau
Comments: 7 Pages.

A Smarandache multi-space is a union of spaces satisfying certain conditions. If the spaces beingunited are vector spaces, then we have a vector multi-space [3]. In [4] we defined the notion of a multimatrix and operations with multi-matrices, and in this paper we shall define linear mappings on a vector multi-space and study some of their properties.
Category: Algebra

Time vs. Duration: A Reinterpretation of Special Relativity

Authors: Ion Vlad
Comments: 23 Pages.

The twin paradox is often presented as a consequence of time dilation and the relativity of simultaneity, yet its standard interpretation frequently relies on simplified Minkowski diagrams and ambiguous coordinate assignments that obscure the physical meaning of the turnaround event. This paper re-examines the paradox by constructing a Lorentz-consistent spacetime diagram in which inertial and accelerated phases are treated separately and coordinate assignments are preserved consistently across reference frames. We show that a single spacetime event is invariant under Lorentz transformation; different observers may assign different coordinates to that event, but they do not describe different physical occurrences. The apparent contradiction arises not from simultaneity itself, but from conflating event identity with frame-dependent observation and from applying measurement transformations inconsistently after acceleration has ceased. This construction clarifies the operational meaning of simultaneity and demonstrates that the apparent paradox disappears once all measurements are analysed within a common comparison framework.
Category: Relativity and Cosmology

Geometric and Topological Approaches to Crystallography

Authors: Ellie Richwine, Lucian M. Ionescu
Comments: Pages.

This article explores the mathematical structures underpinning crystalline materials, bridging the gap between pure mathematics and materials science. Building upon Toshikazu Sunada’s breakthrough framework of topological crystallography and subsequent formalizations by John C. Baez, we provide a rigorous yet accessible introduction to the geometric and topological modeling of crystals. The study examines polyhedral geometry, duality, and lattice arrangements such as the Eisenstein and triangular lattices, framing them within the context of covering maps and Abel-Jacobi maps. Furthermore, we advance this foundation by introducing a simplified formulation of Graph Cohomology based on short exact sequences of graphs. This homological approach provides a unifying architectural template capable of tracking lattice defects via integer cohomology and modeling macroscopic continuous phenomena from discrete microscopic networks. The paper concludes by discussing the broader applications of these tools in molecular biology, theoretical physics, and fault-tolerant quantum engineering.
Category: Mathematical Physics

A Dynamic Model of Tidal Deformations of the Earth's Elastic Crust in the Central Force Field of the Earth-Moon System

Authors: Viktor Strohm
Comments: 8 Pages.

Traditional theories of Earth tides (such as the classical models of Clairaut, Love, and Darwin) describe geoid deformations via the differential potential of an isolated external disturbing body distributed across the volume of an elastic-plastic sphere. However, when attempting to interpret the physical meaning of forces acting on discrete crustal elements (mobile tectonic plates) within a real bound system, researchers inevitably encounter kinematic paradoxes—specifically, a theoretically unavoidable but empirically unobservable macro-displacement of the planet’s dense core toward its internal boundaries.The present work aims to describe the dynamics of the Earth’s shape variation based on generalizing the law of central forces and the kinematics of the system’s elliptical motion around the barycenter, as presented in [1]. The primary conceptual difference of the proposed approach is the transition from abstract scalar potentials to direct vector summation of actual gravitational accelerations acting on a rigid elastic shell of fixed thickness.The resolution of the apparent contradiction in the direction of individual particle force vectors during the transition from an abstract disk to the real Earth-Moon system lies within the framework of the classical three-body problem. As soon as we begin decomposing the monolithic mass of the planet M into an ensemble of discrete elements m_i, the system transforms into a hierarchical three-body configuration: two interacting bodies are located in immediate proximity (the analyzed crustal microparticle m_i and the residual mass of the planet M-m_i), while the third massive body (the Moon) is removed at a significant orbital distance.In such a formulation, the total force vector acting on each particle naturally decomposes into two components. The short-range (local) interaction binds the particle to the main mass distribution of the planet, directing its elastic retention vector strictly toward the center of the disk C (which, in a geocentric reference frame, manifests as radial compression in the lateral zones Y-Y' ). At the same time, the long-range (gravitational) field of the distant third body imparts the necessary centripetal acceleration to the entire bound system, directing the orbital force vector toward the system’s focus — the barycenter F. Thus, the formalism of force decomposition into focal and central components, proposed in [1] for the circle model O_E, receives a rigorous dynamic justification within the restricted three-body problem, linking the internal geodynamics of the lithosphere with Kepler's laws.
Category: Geophysics

From Ramanujan to Riemann Hypothesis

Authors: Payam Danesh, Raoul Bianchetti
Comments: 16 Pages.

In this work we offer a careful framework for approaching the critical-line problem associated with the Riemann zeta function. At its heart is a long-standing divide in the subject. On one side are analytic approaches, which study the completed zeta function through its reflection symmetry. On the other side are arithmetic approaches, where related criteria often appear through extreme behavior in divisor functions. The purpose of this paper is not to claim a proof of the Riemann Hypothesis, but to place these two perspectives into a clearer and more usable relationship. The argument begins with reflected analytic data for the completed zeta function. It shows that such data can be described through an odd analytic perturbation, giving a more organized way to understand the analytic side of the problem. This also resolves a common point of confusion: the full complex defect is not required to vanish on the critical line. What matters is more subtle. Under a natural real-symmetry condition, the real part of the defect vanishes on the critical line, and this is the feature that becomes useful for the bridge argument. The arithmetic side is built around Ramanujan’s logarithmic divisor profile. The paper establishes the existence and positivity of the relevant extreme scale in the range needed for the proposed connection. These analytic and arithmetic pieces are then brought together through a real bridge functional, made up of a main sign term and a correction term. The main outcome is a conditional criterion for the critical line. If the bridge functional is zero-adapted at the nontrivial zeros, if the real analytic defect satisfies the required one-sided sign condition, and if the correction term remains strictly smaller than the main term, then every nontrivial zero must lie on the critical line. The contribution of this work is therefore structural rather than conclusive. It does not present the Riemann Hypothesis as solved. Instead, it separates what is already established from what still needs to be proved. The key sign law, the domination estimate, and the zero-adaptation identity remain open requirements for any future application of the framework. Its practical value is that it gives researchers a precise checklist for testing whether a proposed analytic or arithmetic strategy can genuinely support a critical-line argument.
Category: Number Theory

Big Gravity Remains Elusive

Authors: Clark M. Thomas
Comments: 5 Pages.

Big Gravity’s (G) Newtonian constant for the local universe seems to be something that eludes astrophysicists seeking better numbersfor the claimed four forces. The latest G data have failed to confront the hermeneutical limits of what their experimental tools measure.We need better multiversal causative precision in 4D dimensions, not weak mathematical correlations. Big Gravity, and Earth’s variablesurface gravities (g), include electromagnetism, along with the properly conceived net push/shadow kinetics. Unifying harmony among all physics dimensions is needed for any elegant multiversal paradigm.
Category: Astrophysics

Motion, Mass, Space and Time: An Emergent Vector Field Framework

Authors: Mangleshwar Thakre
Comments: 41 Pages.

The primary objective of this paper is to investigate the fundamental cause underlying the motion of a massive object. In other words, it seeks to elucidate the nature of momentum and how it originates. To achieve this, a comprehensive literature review on space, time, mass, and motion is presented, offering a novel perspective on these foundational concepts. The mathematical framework is constructed using the core principles and equations of classical mechanics and the special theory of relativity, drawing some direct and substantial indirect influences from continuum mechanics. To analyze physical phenomena within a four-dimensional space-time continuum, the Hodge decomposition theorem and tensor decomposition methods are employed. This paper derives a new set of governing equations for the state of motion of a massive object, providing an entirely new interpretation of its dynamics. Ultimately, this work establishes that mass-energy and momentum are manifested forms of the periodic change of a vector field defined to characterize the system's physics. Within this research paper, the Translational Gravitomagnetic Field Tensor is derived using an entirely novel method. Furthermore, the physical mechanism responsible for giving rise to space-time is explicitly detailed, thereby reinforcing the contemporary paradigm in physics that space-time is an emergent property rather than a fundamental entity of nature. Ultimately, the research paper appears to advocate for an absolute background throughout its entire exposition.
Category: Classical Physics

A One-Way Relativistic Decay-Clock Test of Kinetic Preferred-Frame Time Dilation

Authors: Jayanta Majumder, Sambuddha Majumder
Comments: 11 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

A recently proposed kinetic route to the Lorentz transform models an elementary particle as a closed lightlike intrinsic motion whose internal cycle is reallocated, under bodily translation, between intrinsic circulation and spatial advance. The construction recovers the usual time-dilation law and the Lorentz boost as a hyperbolic state map, while allowing a physical ``special'' frame in which the intrinsic tick count and the external time parameter coincide. In such a framework, ordinary closed-path clock tests are not necessarily the most sensitive probes of the special frame, because the leading directional term proportional to $Ucdotvvec$ cancels when the transported clock returns to its starting point. This paper develops a sharper null test: a one-way lifetime anisotropy measurement using unstable relativistic particles as intrinsic clocks. If a laboratory has special-frame velocity $U$ and an unstable particle beam of speed $u=beta c$ is sent along direction $$, the strong preferred-frame reading of the kinetic model predicts, to leading order,begin{equation*} tau_{m lab}() simeq gamma_u tau_0 left(1 + betafrac{Ucdot}{c}ight),end{equation*}whereas standard special relativity predicts $tau_{m lab}=gamma_utau_0$ independent of absolute orientation. Antiparallel one-way beams would therefore exhibit a fractional lifetime asymmetrybegin{equation*} frac{tau_{+}-tau_{-}}{(tau_{+}+tau_{-})/2} simeq 2betafrac{Ucdot}{c}.end{equation*}For a candidate $|U|simSI{369}{km.s^{-1}}$, as suggested by the CMB dipole scale, the maximal signal for relativistic beams is of order $2.5times 10^{-3}$, far larger than the fourth-order residuals expected in closed transport tests. The decisive experimental signature is an antiparallel lifetime or decay-length asymmetry with sidereal modulation as the Earth rotates the beam axis relative to the putative preferred-frame vector. The proposal is framed as a falsifiable extension of the kinetic model: a null result would strongly constrain the strong preferred-frame interpretation rather than merely refine an existing relativistic clock test.
Category: Relativity and Cosmology

State Commitment Learning: Training Language Models to Distinguish Computation from Memory

Authors: Fei Ding, Yongkang Zhang, Runhao Liu, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

Reasoning language models do not distinguish tokens used for computation from tokens that constitute persistent state: once generated, all hidden thoughts remain in context and influence future predictions. As a result, downstream reasoning may depend on failed attempts, dead ends, and private scratch work that should not be safely relied on later. We recast this phenomenon as a new training objective, state commitment learning: training models to explicitly distinguish information that should be committed as persistent state from temporary computation that can be discarded. We define a counterfactual criterion, persistent-state sufficiency, which makes it trainable and measurable whether an answer remains usable after hidden thoughts are erased. We then propose Counterfactual Erasure RL (CERL), which evaluates, under the same prefix, both a path that keeps hidden thoughts and a path that erases them, and gives reward only when the erasure path remains correct. We also introduce the Erasure Dependence Protocol and show across mathematics, long-chain logic, scientific QA, and multi-turn tool-use evaluation that CERL substantially reduces answer dependence on hidden thoughts without sacrificing accuracy, consistently outperforming correctness-only RL and long-answer SFT baselines.
Category: Artificial Intelligence

Scaffold-Mediated Post-Training: Co-Evolving Model Parameters and Procedural Scaffold Graphs

Authors: Fei Ding, Yongkang Zhang, Runhao Liu, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

Post-training of large language models optimizes only parameters, while inference-time procedural scaffolds are typically designed independently of parameter training. This disconnect makes it difficult to automatically acquire and internalize complex strategies. We propose scaffold-mediated post-training: procedural scaffolds are organized into an evolvable graph structure that co-evolves with model parameters through discovery, distillation, and dynamic recompilation. We instantiate this paradigm as Skill Training. On FeatureBench, automatically discovered skills improve the passed rate by 8.1pp, and after progressive distillation the model still achieves a 27.7% passed rate without any external scaffold (distillation retention rate 85.2%, defined as post-distillation / with-skill passed rate), significantly outperforming standard SFT on the same data.
Category: Artificial Intelligence

Check Token: Real-Time Self-Verification and Precise Truncation in LLM Reasoning

Authors: Fei Ding, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

ECC memory embeds 8 parity bits for every 64 data bits and automatically detects and corrects errors on each read. The parity bits carry no data and only safeguard integrity, at ~12.5% overhead. Yet the reasoning chains of large language models lack such built-in self-verification: once an error occurs it propagates along the chain, and existing methods can only verify externally after generation completes. We propose the check token, establishing built-in self-verification for language model generation streams for the first time: a functional marker is added to the vocabulary, and the model triggers self-checking (analysis, localization, truncation, rewriting) by outputting it at any position. The check token carries no reasoning content (discarded after triggering) and only safeguards reasoning correctness, directly corresponding to the role of ECC parity bits, also at only ~13% overhead. Speculative forking further eliminates false-positive latency, and segmented reward makes trigger timing end-to-end learnable. Experiments (Qwen3-32B / Qwen3-Next) show that the check token achieves +10.8 pp improvement on HMMT25 at 1.13x overhead, with token efficiency 88x that of Best-of-8, and the precise truncation advantage monotonically increases with chain length.
Category: Artificial Intelligence

On the Impossibility of Unbiased and Length-Invariant Policy Optimization with Outcome Rewards

Authors: Fei Ding, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.
Category: Artificial Intelligence

Ramanujan-Inspired Prime Sums

Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.

This paper develops a finite framework for studying sums of prime numbers through consecutive prime gaps. The motivation comes from Ramanujan’s influence on arithmetic decompositions, partition methods, and summation ideas, while the argument remains within ordinary finite number theory. We study the partial sum of the first n primes and prove an exact identity that writes this sum as a baseline term from the initial prime together with a weighted accumulation of consecutive prime gaps. Each gap receives a weight equal to the number of later primes affected by that gap. The same identity is then expressed geometrically by encoding each weighted gap as the slope of a right triangle. Exact numerical examples verify the formula, and the asymptotic discussion shows that the decomposition has the same leading scale as the classical growth predicted by the prime number theorem. This paper also separates finite identities from regularized infinite summations. This distinction is essential: the finite formula is exact, while divergent infinite prime sums require a separate summation theory and cannot be treated as ordinary convergent series.
Category: Number Theory

An Infinite Family of Solutions to the Generalized Cannonball Problem

Authors: J.W.L. Eerland
Comments: 4 Pages.

In an earlier paper I considered the generalized cannonball problem for r-regular polygons and studied integer solutions to the associatedDiophantine equation. In this note I prove that for every positive integer n, the triple[(r,a,b)=left(3n+2,,3n^2-2,,3n^3-3n+1ight)] is a solution. Hence the generalized cannonball problem admits infinitely many positive integer solutions. I also compare this parametric family with the 858 tuples listed in the appendix of the earlier paper. Among those tuples, 802 are generated by the present family and the remaining 56 tuples are listed explicitly.
Category: Number Theory

Explicit U(2) Matrices and the Emergence of Electroweak Charges

Authors: N B Cook
Comments: 3 Pages.

We make the U(2) structure completely explicit in terms of 2 × 2 matrices and show how Woit’s construction on Λ∗(C^2) reproduces the chiral electroweak charges of the first lepton and quark generations.
Category: Quantum Gravity and String Theory

Logical Foundations of Geometric Space and Natural Space-time Space

Authors: Taiwei Song
Comments: 6 Pages. 6

This short paper briefly discusses the fundamental concepts, intrinsic rules, and logical relationships of geometry from the most essential perspective, and its relationship with algebra. It also defines natural space-time space and its intrinsic logical relationships and significance. Most of the content in this paper is important achievements of the" Geometry of Space-time Structures " established by the author.
Category: Mathematical Physics

Towards a Floer Theory for Mars I Twisted Zeeman Systems

Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 3 figures

In this article we study periodic orbits of an electron attracted by a proton subject to Lorentz, electric, and Euler forces where each of them is allowed to depend periodically on time. This setup is motivated by the elliptic restricted three-body-problem where the Lorentz force corresponds to Coriolis force, the Coulomb force is replaced by the gravitational force, and the electric force of an external source is a combination of centrifugal forces and gravitational forces of other bodies. This is a singular version of a Euler-Hamilton system as discussed in [FW26b]. The singularity is due to collisions of the electron with the proton, respectively of two masses. Due to the possibility of collisions this problem has to be regularized.We show how periodic collisional solutions of this problem can be detected variationally in a non-local Lagrangian setup as well as in a non- local Hamiltonian setup.
Category: Mathematical Physics

False Equivalence of Accelerating Rocket and Gravity Pull on Elevator

Authors: Carl Littmann
Comments: 6 Pages.

Gravity bends a light beam more than a particle beam. We show how elevator occupants can use that fact to determine whether the forces they feel are caused by a gravitational or non-gravitational acceleration. I.e., although that capability supposedly violates the ‘Equivalence principle’ of ‘General Relativity’. Einstein imagined "the experiences of occupants in a windowless chamber, in deep, isolated space" as it was ‘accelerated upward’ by a pulling. And claimed ‘Equivalent’ (identical) feelings and test results would arise for occupants in a non-moving elevator on our gravitational earth.[1] Yet, let us imagine that a photon and an ultra-high-speed particle are launched at the same time from an internal wall of an elevator; then they go through two adjacent pin-holes, and finally hit the opposite wall. But surprisingly, they do not hit the same spot - because the gravity bends photons twice as much as a particle beam.[2] So we discuss that violation of ‘Equivalence in Relativity’ and its broad implications, in this article.
Category: Relativity and Cosmology

A Proof for the Collatz Conjecture

Authors: Jérôme Chauvet
Comments: 5 Pages.

This proof adresses the Collatz conjecture and relies on the quantitative characterization undergone by the evolving densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system, from which we deduce the final cyclic attractor, hence proving the conjecture.
Category: General Mathematics

SlideTuner: PowerPoint Slide Design via XML Representation Learning and Preference Optimization

Authors: Lixiang Li, Anjan Goswami, Md Muksitul Haque, Bharat Bhargava
Comments: 7 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Generating high-quality PowerPoint slides from natural language instructions is a complex task that demands not only deep semantic understanding, but also aesthetic design. The essential component for building a functional and visually rich slide is the XML object. Therefore, it is intuitive that the most direct path to creating a high-quality slide is to generate it directly from the foundational XML structure. However, previous ``human instruction to slide generation" models typically rely on generating Python code, which serves as an intermediary to produce the final slide output rather than direct production of the XML object. As a result, these models lack the ability to precisely construct and control the building blocks required for a detailed slide composition. We introduce SlideTuner, a custom finetuned GPT-4o model specifically engineered to generate high-quality PowerPoint slides by generating the required XML files. Through extensive empirical experiments, we demonstrate that the fine-tuned GPT-4o model successfully and consistently produces visually coherent and aesthetically pleasing slides. The SlideTuner employs a two-stage training approach: first we apply SFT to the language model, enabling it to generate slide-rendering XML code directly from user instruction, utilizing XML data extracted from native PowerPoint slides. Second, we apply Direct Preference Optimization (DPO) to align the model's outputs with preferred visual styles, such as specific font choices. The slides produced by our model exhibit superior layout scores and style adherence. While this work focuses on font-level aesthetic control, our work establishes a foundation for future research aimed at precisely guiding slide generation toward diverse visual or structural preferences.
Category: Artificial Intelligence

Infinitely Many Twin Prime Reexplored - Proof

Authors: James DeCoste
Comments: 12 Pages.

Without any concrete feedback from the mathematical community, I was forced to have an enlightening discussion with Google's AI engine to determine what the likely problems were with my initial paper Infinitely Many Twin Primes — Proof (found on viXra.org: https://vixra.org/abs/2502.0186).Since I did all my own research in a sandbox without contributions from the mainstream mathematical community ( blind research ), I evidently ran into the same wall all prior mathematicians hit and that was proving that the twin primes candidates don't simply fizzle out as one approaches infinity. I was relying on combinatorics to prove this, which I now see was a mistake when taken by itself. As the AI engine and myself did a deeper dive on current mainstream research we noticed that much of the research I performed but did not include in my original paper were already explored by others. Some of these will be the key when reworking this on it's second take; the Hardy-Littlewood ratios 1:1:2 and the product rule that sees the pattern repeat at that product, to mention two. This was done blind without ever realizing it.We were able to determine that the rest of the original paper was sound even if not written in mainstream mathematical language. However that wall where the twin primes could simply fizzle out or completely dry up was impossible to ingore. While exploring some of the new approaches being implemented by Maynard and Tao, I made the realization that the probabilities angle should not have been abandoned. I had already done research to establish floor and ceiling limits as decaying log curves...but they too appear likely to fizzle out as one approaches infinity. That was until we took a look at a specific probability ratio of my window size sample growth versus the number of primes total growth. The first was a quadratic growth rate ( x^2) and the second was strictly linear ( number of primes grow at a steady rate). Using this probabilty along with the prior published paper finally plugs the hole and smashes down that wall as a mathematical improbability. The idea is that we have a fraction that is continually shrinking but can't actually get to absolute zero, the wall. The number of new elements (prime elimination patterns) is not increasing fast enough to keep up and eliminate all candidates in the exponentially increasing window size of my ranges. Candidates always escape. This clearly shows that my combinatoric approach was also correct in it's logic and that twin primes can never totally disappear.
Category: Number Theory

Quasinormal Modes of Black Holes in Finsler-modified Gravity

Authors: Holger A.W. Döring
Comments: 5 Pages.

Investigated is the ringdown phase of black holes within a modified gravitational framework that includes a weak Finsler coupling (a) , a quadratic curvature correction (b) and a dynamical timelike vector field (u^μ). Using analytical approximations and dicussing numerical simulations, there is shown, that quasinormal modes (QNM) are slightly shifted and anisotropically modulated. Residuals against standard Kerr fits are calculated, and observational constraints from LIGO, Virgo, pulsar timing, and atomic clocks are analyzed. Found is, that current gravitationalwave detectors constrain (a≾10 −3 ), while next-generation detectors (Einstein Telescope, LISA) could probe (a∼10 −12 −10 −8 ). Quadratic curvature corrections remain unobservable at thePlanck scale. The given results highlight characteristic signatures of Finsler-modified gravity in black hole ringdowns.
Category: Relativity and Cosmology

The Variable Mass Theory and Gravitational Paradoxes

Authors: Han de Bruijn
Comments: 10 Pages.

Essential reading is the first article in the series, which is about Atomic Time, Orbital Time and the Variable Mass Theory. It has been shown in this article that General Relativity (GR) can be effectively replaced by Variable Mass (VM) in a Static Euclidean Universe (SEU), which is eternal in Atomic time and has moments of creation (i.e. one or more beginnings) in Orbital time.
The cosmological redshift is intrinsic: it only depends on variable (elementary particle rest) mass. Because that is where the VM theory has been designed for.
A convenient consequence is that Newton's theory is good enough for describing gravity at a cosmic scale. It is demonstrated that the latter, when combined with the Variable Mass hypothesis, solves for Gravitational Paradoxes.
Category: Relativity and Cosmology

A Novel View of Quark Electric Charges and Baryon Composition

Authors: Wolfram Loewenstein
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)

I propose that the quarks (d, s, b) carry the electric charge (-1) and the quarks (u, c, t) are electrically neutral. I further propose that baryons are composed of one quark and two anti-quarks. I believe that these assumptions help to solve some problems in the Standard Theory of elementary particles.
Category: High Energy Particle Physics

Simple Proof of Fermat’s Last Theorem for Odd Powers

Authors: Minho Baek
Comments: 29 Pages. (Note by viXra Admin: Please cite listed scientific references)

It was already proved right that x^n+y^n=z^n, (n>2) has no solutions in positive integers which we called Fermat’s Last Theorem (FLT) by Andrew Wiles. But his proof would be impossible in the 17th century. I took the idea from Euler proof and proved in case of n=odd by simple method.
Category: Number Theory

The Infinite Dynamo Cosmological Model: Unifying Non-Linear Born-Infeld Electrodynamics with Holographic Saturation Bounds and Fibonacci Informational Structures

Authors: Dan Aurelian Ivan
Comments: 6 Pages. (Note by viXra Admin: There is overlap of equations; please submit article written with AI assistance to ai.viXra.org)

We present an alternative cyclic cosmological model, termed the "Infinite Dynamo,"wherein the initial Big Bang singularity is systematically avoided via a smooth bounce governed by non-linear electrodynamics and topological informational mechanisms. We mathematically demonstrate that a global geometric contraction of the metric can optically mimic an accelerated expansion for a local observer, conditioned by the temporal evolution of anactive cosmic web optical medium. At extreme densities, magnetohydrodynamic (MHD)induction triggers exponential pair production from the vacuum via a coupled Schwingermechanism. By deploying a Born-Infeld formalism structurally modified by the GoldenRatio (), we show that the effective electromagnetic pressure becomes asymptotically negative, driving a mechanical bounce at a non-zero minimum radius (amin). This inflectionpoint is stabilized and protected by the Holographic Principle, preventing loss of unitarity and conserving the universal informational states of consciousness encoded within cosmic skyrmions. Finally, we formulate four testable empirical predictions for modern astrophysics and high-power laser facilities.
Category: Relativity and Cosmology

Exact Solution to Einstein's Field Equation

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, Einstein's field equation will be solved by removing the framework of tensor analysis.
Category: Relativity and Cosmology

The Central Thalamic Nucleus as the Core Hypothesis of the Consciousness Vortex Model

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

The neural basis of consciousness is a central issue in the field of neuroscience, with the "hard problem" of consciousness revolving around the unclear physical origin of subjectiveexperience. Existing theories (such as IIT, GWT, etc.) are confined to information-logicrecursive frameworks, failing to identify core physical structures and often focusing on thecortex, which contradicts clinical evidence that thalamic damage leads to loss of consciousness.To address these limitations, this paper proposes and argues that the central medial thalamicnucleus (CM) is the core anchor for consciousness generation. Using the Consciousness Flow Vortex Model (CFVM) as an analytical framework, the study systematically elucidates CM's critical role in information convergence, rhythm regulation, and global integration from three dimensions: closed-loop cycles, central focusing, and global synchronization. The analysis demonstrates that CM can serve as the central anchor for consciousness production, effectively explaining the characteristics of awareness, integration, stability, and subjectivity in consciousness. This hypothesis not only constructs a comprehensive theoretical model for consciousness research but also provides a clear structural localization for the neuralmechanisms of consciousness, offering new opportunities for breakthroughs in theneuroscience of consciousness.
Category: Physics of Biology

The Universe is Magnetically Dynamic With Cosmic Explosions Driven by External Magnetic Fields

Authors: Jamal S. Shrair, John L. Turner
Comments: 48 Pages.

Theoretical models of cosmic explosions (such as stellar explosions) and galactic rotation curves are essential cornerstones of astrophysics, serving as primary diagnostic tools for understanding stellar mechanisms, the distribution of matter, and the fundamental structure of the universe. However, in this lengthy research paper, we have provided robust, up-to-date empirical data on stellar explosions and the rotation curve phenomenon, based on modern observations. This objective analysis of observational data has not only exposed the fundamental flaws in conventional models of stellar explosions and rotation curves but also refuted foundational paradigms in astrophysics and cosmology. Alternative models have been proposed.
Category: Astrophysics

Lerch's Φ and the Polylogarithm at the Negative Integers

Authors: Jose Risomar Sousa
Comments: 10 Pages.

At the negative integers, there is a simple relation between the Lerch Φ function and the polylogarithm. Starting from that relation and a formula for the polylogarithm at the negative integers known from the literature, we can deduce a simple closed formula for the Lerch Φ function at the negative integers, where the Stirling numbers of the second kind are not needed. Leveraging that finding, we also produce alternative formulae for the k-th derivatives of the cotangent and cosecant (ditto, tangent and secant), as simple functions of the negative polylogarithm and Lerch Φ, respectively, which is evidence of the importance of these functions (they are less exotic than they seem). Lastly, we extend formulae for the Hurwitz zeta function only valid at the positive integers to the complex half-plane using this novelty.
Category: Number Theory

The Ultrrasound Photoelectric Effect

Authors: Miroslav Pardy
Comments: 9 Pages. Original article

The ultrasound photoelectric effect is the new phenomenon in particle physics.We derive the velocity of sound in the blackbody gas of photons. Derivation is based on the thermodynamic theory of the photon gas and the Einstein relation between energy and mass.The quantization of this sound forms the matter of phonons. The ultra-sound phonons composed from photons generate the photoelectric effect as the analogue to the Einstein photoelectric effect in metals. The application of this effect in the elementary particle physics, atomic physics and nuclear physics is not excluded.
Category: Quantum Physics

On the Time Scale for Developing Fusion Power

Authors: Daniel L. Jassby
Comments: 13 Pages. (Note by viXra Admin: PPT format is not acceptable format; please cite and listed scientific references)

Fusion devices produce high-energy neutrons and ions by reactions between deuterons or between deuterons and tritons, but no one has ever converted the energy of fusion products to electricity. In 75 years of R&D no fusion system has produced one watt or one joule of electricity, while the device and its auxiliary systems consume multi-megajoules of electricity during each operating pulse. It’s possible that in the 2030’s one or morefusion devices may utilize clever stunts to produce a few watts, but even a modest demonstration of several kilowatts of electric output (while still consuming multi-megawatts) is two decades away. Producing net electric power from a fusion facility may never be possible because of the high power consumption of any fusion device and its auxiliary systems. The second most daunting hurdle to power production is that the burned and lost tritium fuel must be replenished in the fusion contraption itself. That is infeasible, partly because of shortcomings in "breeding" by fusion neutrons, but especially when inherently small burnup fractions result in unavoidable losses of the dispersing unburned tritium. The only practical fuel is deuterium alone. The difficulties of achieving ignition in deuterium, of developing adequate reactor technologies, and of finding pathways for reducing electricity consumption of reactor systems will push the realization of a prototype fusion power plant at least half a century away.
Category: Nuclear and Atomic Physics

A Merkleized Batch Attestation Scheme with Selective Disclosure and Compliance-by-Design

Authors: Harry Willson Potter
Comments: 8 Pages.

Soulbound tokens (SBTs) have been theorized as non-transferable attestations for decentralized identity and reputation. The existing SBT literature assumes permissive regulatory environments that tolerate token-based incentives, pseudonymous participation, and secondary markets. This paper inverts that assumption. We study SBT design under prohibitive regulatory constraints—jurisdictions that ban cryptocurrency, mandate real-name identity verification, and impose data minimization. We formalize the Usefulness Paradox as a theorem: for any SBT system under three or more prohibitive constraints, the DeFi feature set and the compliance feature set intersect in exactly one element—non-transferability. We define an 8-dimension compliance evaluation framework with formal criteria and prove existing SBT standards satisfy at most one of eight criteria. We present three general design patterns—hook-level soulbound enforcement, dual-layer compliance middleware, and beacon-based pseudonymity—that collectively satisfy all eight criteria.
Category: Data Structures and Algorithms

How Time Dilation's ‘Antigravity’ Effects Impact the Expanding Universe

Authors: Jonathan J. Dickau, Steven K. Kauffmann, Stanley L. Robertson
Comments: 11 Pages. Essay written for the Gravity Research Foundation 2026 Awards for Essays on Gravitation.

We outline how the cosmos’ accelerating expansion, diminishing over time, can be explained using the 1915-16 Einstein/Schwarzschild metric in the geodesic equation without requiring Dark Energy.
Category: Relativity and Cosmology

Horizons in Both Original and Symmetric Natario Warp Drives Using Two Parallel and Alternative Adm-MTW-Alcubierre Formalisms

Authors: Fernando Loup
Comments: 55 Pages. complements the developments of viXra:2509.0064 and viXra:2605.0014

In 1994 Alcubierre developed the first warp drive theory using the original 3+1 ADM-MTW formalism. The original ADM-MTW formalism (Arnowitt-Dresner-Misner) (Misner-Thorne-Wheeler) uses both contravariant and covariant shift vector components in its mathematical structure.It possesses mixed shift vector components. Seven years later in 2001 the same original 3+1 ADM-MTW formalism appeared in the first part of the second warp driven theory developed by Natario.(The second part of Natario theory uses the Hodge Star). In this work we present two new 3+1 ADM-MTW formalisms: One is the parallel contravariant in which all the shift vector components in its mathematical structure are completely contravariant and the other one is the parallel covariant in which all the shift vector components in its mathematical structure are completely covariant. We describe both the original and symmetric Natario warp drive vectors using the mathematical techniques of these parallel formalisms. We focused ourselves in the 3D spherical coordinates for variable speeds. Remember that a real spaceship is a 3D object inserted inside a real 3D spacetime. Also a real warp drive must accelerate and de-accelerate. One the major drawbacks concerning warp drives is the problem of the Horizons(causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble. The behavior of a photon sent to the front of the warp bubble in the case of the original and symmetric Natario warp drive vectors with variable speeds and a lapse function was also one of the main purposes of this work. We presented the behavior of a photon sent to the front of the bubble in the original and symmetric Natario warp drive vectors with the lapse function in these new parallel 3+1 ADM-MTW formalisms using quadratic forms and the null-like geodesics $ds^2=0$ of General Relativity and we provided here the step by step mathematical calculations in order to outline the final results found in our work which are the following ones: For the case of the lapse function or the 3+1 spacetime in these parallel ADM-MTW formalisms the Horizon do not exists at all. Due to the extra terms in the lapse function or the presence of the 3D dimensions that affects the whole spacetime geometry these solutions allows to circumvent the problem of the Horizon.
Category: Relativity and Cosmology

An Algebraic-Geometric Derivation Using Linked Right Triangles

Authors: Sorintreachboth Sath
Comments: 7 Pages.

This paper presents an independent geometric derivation involving linked right triangles and algebraic substitution based on the Pythagorean theorem. The derivation develops a relation for determining an unknown side length by connecting multiple right-triangle configurations through shared variables. By applying the Pythagorean theorem to related geometric structures and performing algebraic elimination, an explicit expression for an unknown side is obtained. The work emphasizes geometric visualization, structural reasoning, and step-by-step analytical derivation rather than the introduction of a new theorem. A numerical example is provided to verify the validity of the derived relation and its consistency with the original geometric configuration. This exposition demonstrates how classical geometric principles may be reconstructed through independent mathematical reasoning and provides an educational illustration of algebraic-geometric problem solving within linked right-triangle systems.
Category: Geometry

Testing the Dark Matter by Quantum Gravitation Theory in the Local Group, the Virgo and the Coma Clusters

Authors: Manuel Abarca Hernandez
Comments: 6 Pages.

The aim of this work is to test the novel theory called Dark Matter by Quantum Gravitation theory (DMbQG hereafter) at cluster scale. This theory was initially developed for galaxies and afterward was extended to clusters. The main paper where the theory is developed at galaxy scale is [5] Abarca, M. 2024, also in this paper there are some validation test using the rotation curves of MW and M31. The theory was fully extended to cluster in [2] Abarca,M.2024, also in the paper there are some validation test using data referred to the Local Group and the Virgo clusters. In this work are compiled some test introduced in the both papers and also there are two new tests referred to the Coma cluster, using data published recently. The tests are mainly focused on the turnaround radius, also called zero velocity radius, and its gravitating mass associated, in addition regarding the LG of galaxies there is another important test focused on its virial mass as well. The theoretical calculus has been validated using four papers published by well known team researchers in recent years. Namely the years: 2017, 2018, 2023 and 2025.
Category: Astrophysics

The Nontrivial Zeroes of the Riemann Zeta Function are Trivially Expressed by The Euler Product

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

Leonard Euler considered the Zeta function for real values input of s, and in doing so he famously derived the Euler Product formulation of the Zeta function, which linked the function to prime numbers. The connection between the prime numbers and the Zeta function was further pursued by Bernhard Riemann, who constructed an analytic continuation of the function which remained valid for the entire complex plane. In doing so, he was able to link the zeroes of the Zeta function to the distribution of prime numbers. In this paper, I show that the zeroes of the Zeta Function can be identified directly from the Euler Product, and in doing so, suggest a trivial link between the primes and the zeroes of the Zeta function while bypassing the more complex machinery of analytic continuation.
Category: Number Theory

A Sketch of the Development of the Atomism

Authors: Zbigniew Osiak
Comments: 101 Pages. In Polish

The contributions of over one hundred scientists to the development of the atomism are discussed. Detailed bibliographic information on their published works is provided.
Category: History and Philosophy of Physics

A Brief Essay on Electromagnetic Waves (Transported Energy, Quantum, Propagation, Photon and Wave-particle Duality)

Authors: José Romeu Dellacqua
Comments: 10 Pages.

The goal of this essay is to carry out a critical analysis of the extension of the concept of energy applied to stationary electromagnetic fields to traveling electromagnetic fields, that is, electromagnetic waves. In an attempt to establish a connection between the energy equations, obtained from Maxwell's equations and the results of Max Planck's studies, this essay proposes some changes to the conventional electromagnetic wave equations. This essay also seeks to deduce mathematical expressions for the electrical power and voltage associated with the quantum, as well as its subdivision into voltage, current and time components. Finally, a conjecture is proposed about what wave-particle duality could be, and its relationship with the photon as discussed in this essay.
Category: Quantum Physics

The Solar Magnetic Switchbacks Are Magnetic Scattering of Coulomb Collisions Between Galactic Cosmic Rays and Solar Radiation

Authors: Jamal S. Shrair, ohn L. Turner
Comments: 15 Pages.

The process of magnetic switchbacks contributes greatly to coronal heating and the acceleration of solar wind. It is a weakly collisional plasma process influenced by magnetic field configuration, rather than a result of purely electrostatic Coulomb collisions. This magnetic process is a consequence of magnetic scattering, in which low-energy galactic cosmic rays (3-30 MeV/nuc) interact with solar radiation, and this interaction is more pronounced during periods of heightened solar activity, including the release of Energetic Solar Particles (SEPs). Essentially, when highly modulated Galactic Cosmic Rays (GCRs) collide weakly with the solar radiation, magnetic switchbacks are formed, resulting in a form of anti-Stokes Raman scattering that increases the temperature of a magnetised plasma and accelerates the solar wind. It is unconventional Raman scattering of a highly magnetised plasma involving nonlinear, non-isotropic interactions in which an external magnetic field modifies charged-particle dynamics, producing an optical S-shaped signature. In the presence of a strong magnetic field, Coulomb collisions are significantly altered, forcing them into complex, S-shaped or non-monotonic trajectories rather than the simple hyperbolic paths observed in conventional Coulomb scattering. That is because the magnetic field induces cyclotron motion (gyromotion) which interacts with the Coulomb potential, causing the heavily charged particle to spiral or curve, intersect its asymptotic line, and create a unique S-shape before completing its scattering.  
Category: Astrophysics

Resolving Zeno’s Paradox Through the Intrinsic Progression of Time

Authors: Harsha Kumar Suriyaarachchi
Comments: 11 Pages. (Note by viXra Admin: Please cite listed scientific reference)

This study presents a resolution to the 2500-year-old Zeno’s paradox, restoring the relationship between Space and time to the fundamentals of classical understanding. Further, the calculation shows the instability of the relativistic space-time relationship in resolving the paradox.Zeno’s paradox has four main canonical variants, Dichotomy, Achilles and Tortoise, Arrow Paradox and Moving Rows. A comprehensive analysis is conducted of both classical and contemporary relativistic approaches proposed to resolve the paradox, including standard calculus, the summation of infinite series, models invoking quantised space, quantised time, and various adaptations within relativistic framework. Despite their theoretical sophistication, these approaches are mathematically argued to fall short of providing a satisfactory resolution.Coherent resolution emerges only under the hypothesis that time progresses as an independent, intrinsic and continuous entity, rather than being tied to spatial or kinematic variables. Classical mechanics tends to treat time as an independent parameter, but this feature has not been explicitly utilised in prior attempts to resolve Zeno’s paradox at a fundamental level. The present work proves where previous attempts, including the relativistic framework, fail and re-examines the paradox by explicitly enforcing the independence and the continuity of time as a primary principle, to consistently resolve the paradox.
Category: Mathematical Physics

From Piecewise-Linear to Piecewise-Circular: A Geometric Extension of Integration Theory via Osculating Sectors

Authors: Giuseppe D'Ambrosio
Comments: 20 Pages. (Note by viXra Admin: Author name is required in the article after the article title)

This paper introduces the D’Ambrosio Integral, a geometrically oriented generalization of the Riemann integral that incorporates the curvature of the integrable curve. Unlike classical schemes based on linear approximation, the proposed method employs circular arcs determined by consecutive triplets of points, allowing curvature information to be directly embedded into the integration process. It is shown that the integral converges, is geometrically invariant, and coincides with the Riemann integral for sufficiently smooth functions. The formulation naturally extends to Riemannian manifolds through the use of the exponential map. The proposed approach provides higher geometric accuracy in regions of pronounced curvature and is applicable to the analysis of curves, vector fields, and dynamical systems.
Category: General Mathematics

A New Closed-Form Expansion Related to the Riemann Zeta Function

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

We establish a closed-form expansion of the Riemann zeta function ζ(s) at any complex point s = a + ib in terms of an auxiliary real-analytic function L(a) built from theBernoulli numbers and the rising factorial. The cornerstone of the derivation is a clean dif-ferentiation identity for the elementary symmetric polynomial function Kp n(a) on consecutive integers, which we prove by a generating-function argument. Specialising the expansion to the critical line Re(s) = 1/2 recasts the Riemann hypothesis as the simultaneous vanishing of two real power series in the imaginary part b.
Category: Functions and Analysis

Preinertia And Accelerated Motions

Authors: Antonio León Sánchez
Comments: 3 Pages.

The universality of the non-rectilinear trajectories followed by virtually all celestial bodies and the irrelevance (or even nonexistence) of uniform motions in the observable universe serves as the starting point for a new redefinition of preinertia, which also demonstrates the absolute nature of motion.
Category: Classical Physics

From Rényi Entropy to General Relativity

Authors: Ervin Goldfain
Comments: 17 Pages. (Note by viXra Admin: Further repetition may not be accepted)

In this sequel to [4-6], we argue that the equations of General Relativity (GR) follow from constrained maximization of Rényi Entropy. This finding is entirely consistent with our earlier derivation of Feynman’s Path Integrals from constrained maximization of Rényi Entropy. An unforeseen conclusion is that three fundamental constants of Nature, (Planck’s, Newton’s and cosmological constants) emerge as Lagrange multipliers of the maximization procedure.
Category: Relativity and Cosmology

Embarking on Adventurous Journeys Through Some Subjects in Pure Mathematics: Part II

Authors: Tue Vu, Trista Vu
Comments: 248 Pages. [License] CC-BY-NC 4.0

As we enter Part II, we turn to two new subjects: Extensions of Fundamental Trigonometric and Hyperbolic Functions and Unraveling the Mystery of the Riemann Hypothesis: Toward a Complete Proof, beginning with Chapter 3 and Chapter 4.Chapter 3 develops generalized forms of classical trigonometric and hyperbolic functions, elevating them to a broader conceptual framework. These extended formulations introduce new dynamic behaviors, enabling the reshaping of familiar functions and the exploration of entirely new families of elementary functions. This extension creates a richer mathematical framework for studying natural curved surfaces. Classical trigonometric functions such as sin(x) and cos(x) produce identical cross sections when plotted in three dimensions, yielding surfaces that replicate the same curve for every value of y. In contrast, the new two variable trigonometric functions generate curves that vary with y, producing surfaces that differ across the domain and giving rise to distinct geometric objects rather than simple extrusions.Chapter 4 presents a proposed proof of the Riemann Hypothesis, one of the most intriguing and significant problems in mathematics. We explore known findings and properties of the Riemann zeta function, reformulate the functional equation in a new light, and demonstrate why certain hypothetical pairs of nontrivial zeros cannot exist. We present a proof of the Riemann Hypothesis using an elementary algebraic approach. In Section 4-4, we demonstrate that all possible nontrivial zeros lie in the narrow bands 6.28318534... ≤ 6.28983598... or -6.28983598... ≤ Im(s) <-6.28318534... for 0 However, none of them serve as solutions to ζ(s) = 0 because their imaginary parts are below the first nontrivial zero. This approach aims to clarify the assertion that all nontrivial zeros of the zeta function lie on the vertical line where the real part is 1/2.
Category: General Mathematics

Gravity as a Screening Effect

Authors: Michael A. Ivanov
Comments: 12 Pages. Current Physics, 2025, 2, e27723348373429. https://doi.org/10.2174/0127723348373429250512104534

Objective: A model of quantum gravity unrelated to general relativity is described. The main postulate of the model is the assumption of the existence of a background of superstrongly interacting gravitons. To describe the interaction of a graviton with any particle during their collision, a new constant is introduced. Methods: It is shown that screening of the background of single gravitons by a pair of bodies leads to approximately equal attractive and repulsive forces between the bodies. Pairing of a part of the background gravitons, provided that the pairs are destroyed as a result of a collision with a body, yields an attractive force twice as great as the repulsive force, and gravity arises as an effect of background screening. Results: Newton’s constant has been calculated in the model as a function of background temperature, which allows the value of the new constant to be estimated. This model is free from divergences, unlike quantum gravity models based on general relativity, due to the specific shape of the Planck spectrum of the graviton background. A theoretical estimate of the Hubble constant, depending on the new constant, is also obtained. Conclusion: An important feature of the model is the necessity of an "atomic" structure of matter, which leads as a side effect to the prohibition of the existence of black holes that do not have such a structure. Small additional effects of the model, caused by the interaction of photons with gravitons, may have great significance for cosmology.
Category: Quantum Gravity and String Theory

SunQM-9s2: Updates and Corrections for the SunQM Series Articles (Part-2, Drafting Began in 2021)

Authors: Yi Cao
Comments: 30 Pages.

This is not a research article, but a collection of updates, corrections, terminology normalizations, and questions/answers (Q/A) for my 39 of SunQM series articles that have been posted at the preprint server viXra.org (from April 2018 to February 2026). The suggested reading sequence for these 40 posted SunQM series papers is: SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, 5s2, 7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s9, 6s11, 7s1, 7s2, 8, 9s1, and 9s2. During my ~10 years (2014 ~ 2025) closed-door development on the {N,n} QM (through the "global energy minimization" kind of research), some of my early stage work lacks of consistency with the late stage work, and thus needs to be updated and corrected. Those important updates and corrections have mostly been presented in the late stage SunQM articles. The current paper includes the rest updates and corrections (that may be less important). The previous paper (SunQM-9s1: Update u2026 (part-1)) covered the updates for SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, and 5s2. The current paper (SunQM-9s2: Update u2026 (part-2)) covers the updates for SunQM-7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s9, 6s11, 7s1, 7s2, 8, and 9s1. Steve Wolfram once mentioned that he developed the online calculator "Wolfram Alpha" for the purpose of democratizing the math [citation at youtube video?]. After I discovered the Solar {N,n//6} QM structure and then built a single master table of {N,n//6} QM structure for our universe (see SumQM-7’s Table-1), I wish that the novel {N,n//q} QM also will democratize the QM theory. The {N,n} QM was built on three building blocks: the Newtonian mechanics (or the classical physics), the Bohr-QM (i.e., rn = r1 n^2 for the H-atom), and the Schrodinger equation/solution for the H-atom. Thus, I also wish that the {N,n} QM (or any fragment of it) can be the useful building material for other scientists (or the scientific community) to build either the more completed QM theories, or the more diversified QM theories.
Category: Quantum Physics

Forecasting Market Demand with Machine Learning: From Historical Data to Consumer Behavior Insights

Authors: Yerassyl Tursynbek, Kassekeyeva Aislu Bisenovna
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Accurate demand forecasting is a critical component of supply chain optimization, inventory management, and strategic planning in modern enterprises. Conventional statistical forecasting approaches often struggle to represent nonlinear patterns and abrupt changes in consumer behavior, which reduces their effectiveness in volatile market conditions. This study explores data-driven forecasting techniques that integrate historical sales records with factors influencing purchasing behavior, including seasonality and promotional effects. A comparative experimental analysis is conducted between classical time-series approaches and advanced data-oriented predictive models. The results demonstrate that data-driven forecasting techniques achieve higher predictive accuracy and stability, particularly when long-term temporal dependencies and irregular demand fluctuations are present. The proposed approach supports improved decision-making by reducing forecasting errors and enhancing operational efficiency. The findings highlight the potential of intelligent forecasting systems for sustainable business growth and adaptive demand planning.
Category: Artificial Intelligence

Three Theorems From Which Follow Two New Laws of Gravitation and a New Law of Universal Gravitation

Authors: Mykola Kosinov
Comments: 9 Pages.

New theorems on the flux of the gravitational field strength vector are presented, free from the limitations inherent in Gauss's theorem. Gauss's theorem is not sufficient for a complete description of gravity. It is shown that the relationship between the gravitational field flux and the mass of sources is not the only method for representing the gravitational field flux. Unlike Gauss's theorem, the new theorems do not include the mass of sources. The first theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the body's orbit. The second theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the universe. The third theorem concerns the total gravitational force that actually acts on the body and is caused by the gravitational interaction of the test body with all bodies in the universe. From these theorems, two new laws of gravitation and a new law of universal gravitation are derived, which for the first time describes gravity taking into account the action of all bodies in the universe. Unlike Newton's law of gravity, the new law of universal gravitation does not include the mass of sources and the gravitational constant G. The new theorems relate to the gravitational field, which obeys the inverse-square law, and to the gravitational field of the universe, where the inverse-square law does not apply. The new theorems and new laws of gravity provide a complete description of the gravitational interactions of all N-body bodies in the universe. The new theorems demonstrate the existence of a workaround instead of searching for a direct solution to the gravitational N-body problem (for N ≥ 3).
Category: Quantum Gravity and String Theory

About Photons and Anti-Photons

Authors: Paul R. Gerber
Comments: 4 Pages.

It is argued that photons and anti-photons are different entities in the sense that they react oppositely to a gravitational field. Explicitly, photons experience a redshift when moving away from a star, and are further red-shifted when moving towards a (supposed) anti-matter star. Analogously, anti-photons gain energy when moving towards a matter-star. However, we are unable to see anti-photons, and thus, cannot observe possible galaxies that are built up of antimatter and shine in anti-light. The ensuing consequence is, that we observe that about half the volume of the universe is not populated by stars, but consist of so-called voids. But, in fact, these voids must contain an equivalent population of anti-stars which consist of anti-matter and, thus, shine by emitting anti-photons which are invisible to us.
Category: Relativity and Cosmology

A New View of the Process of Light Diffraction

Authors: Iuri Bagaturia, Zaza Melikishvili, Anzor Khelashvili, Koba Turashvili, Saba Kvesitadze
Comments: Pages.

Based on empirical studies, we show that the "diffractive-interferential" images produced in laser light experiments are generated by a completely unknown, non-wave phenomenon. We show that the phenomenon is generated by barriers that create the slits. Presumably, the mechanism of this phenomenon is related to the scattering caused by collisions of photon beams with strange spatial structures of physical fields of a strange nature and which are generated by charged particles of the barrier's atomic lattice. We indicate the probable mechanism of the physical phenomenon corresponding to these scatterings. We hypothesize that the same phenomenon also gives rise to the characteristic quantum discreteness of the microscale, and that further, more detailed empirical and theoretical investigation of this phenomenon will lead to the necessity of implementing significant changes in fundamental concepts of physics.
Category: Quantum Physics

New Interpretation on the Fransén-Robinson Constant

Authors: Ruiguo He
Comments: 11 Pages.

The Fransén-Robinson Constant F is closely related to e, but a discrete series representation for F has not yet been established. The lack of existing analytical identities obscures its direct algebraic analyticity, including its potential transcendence. In this paper, we introduce a novel approach utilizing the Abel-Plana Formula to derive the first discrete series representation of F, opening many possible avenues for the true nature of F.
Category: Number Theory

[ Exploration on Whether] The Riemann Hypothesis is True!

Authors: Abdelmajid Ben Hadj Salem
Comments: 10 Pages. In French, submitted to the journal " Bulletin des Sciences Mathématiques "comments welcome.

In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) $s=sigma+it$ of the zeta function, defined by: $$zeta(s) = sum_{n=1}^{+infty}frac{1}{n^s},,mbox{for}quad Re(s)>1$$ have real part} $sigma= frac{1}{2}$. In this note, I give the proof that $sigma= frac{1}{2}$ using an equivalent statement of the Riemann Hypothesis: the Dirichlet eta function.
Category: Number Theory

Revisited String Theory

Authors: Alaya Kouki
Comments: 3 Pages.

In this short communication we give an experimental verification of the String Theory.
Category: Quantum Gravity and String Theory

Required Conditions for Successful Lattice Confinement Fusion Experiment in D/Pd Electrolysis

Authors: Jozsef Garai
Comments: 12 Pages.

Recipe for successful D/Pd Lattice Confinement Fusion in Electrolysis is suggested. The effects of magnetic field, laser excitation, and surface requirements of the Palladium cathode are discussed in detail.
Category: Nuclear and Atomic Physics

[ Propositions of] Three Laws of Spiritual Mechanics

Authors: Thomas Adrian Nicewicz
Comments: 2 Pages. (Note by viXra Admin: This submission may not be written in a manner suitable to viXra - Please read the viXra guidelines and conform accordingly)

The ancients once said, "As above, so below." [This writing explores this notion and proposes three laws of spiritual mechanics.]
Category: Mathematical Physics

Rethinking Electricity: A Wave-Based Interpretation of Electrical Energy Transport

Authors: Oliver Consa
Comments: 8 Pages.

This work revisits Oliver Heaviside’s interpretation of electricity within modern electromagnetic theory, presenting electrical energy transport as a fundamentally wave-based phenomenon. Electrical energy is transmitted primarily as electromagnetic fields propagating through the dielectric medium surrounding theconductors; the motion of charges within the conductors plays a secondary, dissipative role. Building on transmission line theory, Maxwell’s equations, and Poynting’s theorem, the paper introduces the concepts of supracurrent and infracurrent to distinguish field-mediated energy flux from dissipative material response. The telegrapher’s equations are then interpreted as a macroscopic description of propagation and loss in real transmission lines.
Category: Classical Physics

Partial Differential Equations Arising From the Chain Rule for Direct Dependencies

Authors: Edigles Guedes
Comments: 3 Pages.

This paper presents two partial differential equations obtained from the chain rule for functions with direct dependencies among the variables.
Category: Functions and Analysis

Two Generalized Binomial Identities With a Free Parameter

Authors: Edigles Guedes
Comments: 5 Pages.

Two remarkable combinatorial identities are established.
Category: Combinatorics and Graph Theory

Arbitrary Approximation of the Shifted-LRC by the Equi-Split-LRC

Authors: Deepak Ponvel Chermakani
Comments: 2 Pages. Clarified on the new LRC variant called equi-split-LRC

Consider an instance of the shifted Lonely Runner Conjecture (shifted-LRC) where n runners (except the stationary runner 0) have integer speeds and start from real values in [0,1[ at time t=0. We show that one can derive an alternative vector of starting points that can be made to be arbitrarily close to the initial vector of starting points. The alternative starting point of each runner i is a rational in [0,1[ and is expressible as (qi / P) where P is a large prime and qi is an integer in [0, P-1]. We then introduce a new LRC variant called the equi-split-LRC. The LRC instance allows a minimal loneliness gap of f for runner 0 from the remaining n-1 runners, if and only if, the equi-split-LRC instance with the same vector of speeds and alternative vector of starting points simultaneously allows a minimal loneliness gap of f/P for the arc-center of each of P sectors into which the circle is divided from the remaining n-1 runners. Here, f is a desired fraction in ]0,1[. This finding is important in the light of recent counter-examples to the shifted-LRC.
Category: Functions and Analysis

On Complex Dynamics and Standard Model Parameters

Authors: Ervin Goldfain
Comments: 22 Pages.

The Standard Model (SM) of particle physics contains nineteen freeparameters—and up to twenty-six with massive neutrinos—whose numerical values remain unexplained by the theory itself. The present paper developsa unified framework in which these parameters emerge from Large DeviationTheory (LDT) applied to a multifractal attractor that describes the endpoint of entropy flow at the electroweak scale.
Category: High Energy Particle Physics

The Structure of Electrons and Photons

Authors: Michael Gunning
Comments: 23 Pages.

In this paper I propose a model for a physical explanation of the structure of the Aether from within which the structures of the electron and the photon emerge. The model gives a physical interpretation of Planck’s constant ħ, and explains why the electron has a total angular momentum of √3/2 ħ. It also explains the spin value of ħ for the photon as well as the origins of the photon’s alternating electric and magnetic fields. It includes explanations for what static electric and magnetic fields are and why the stress energy tensors for these fields used in General Relativity have the form that they do. It also explains the Lorentz force and the Stern Gerlach force. It proposes a physical mechanism for gravity which explains why it is so weak compared to the electric force. It also shows why acceleration and gravity are indistinguishable and proposes a physical mechanism to explain the flat rotation curves of galaxies. It also explains why the relativistic energy momentum formula has the form it does and also proposes a physical mechanism to explain the de Broglie wavelength of a particle. It concludes with a physical explanation for length contraction, time dilation and gravitational redshift as well as a novel derivation of the mass energy equivalence relationship.
Category: Quantum Physics

Testing the D.M. By Quantum Gravitation Theory by the Mass Associated to the Turnaround Radius

Authors: Manuel Abarca Hernandez
Comments: 9 Pages.

The DM by Quantum Gravitation theory (DMbQG hereafter), is a novel theory developed in the two main papers [1] and [2] Abarca, M. (2024). In the present work, in the framework of DMbQG theory it will derived the formula for the mass associated to the turnaround radius depending on the turnaround radius and it will be shown that the new expression has a deeper physical meaning regarding the same formula in the current ΛCDM paradigm. The DMbQG theory states a direct relation between the virial radius and the turnaround radius as well as the virial mass and the mass associated to the turnaround radius.The most important contribution of this work is placed in the chapter 2 where it has been demonstrated that the formula for the mass associated to the turnaround radius, using the DMbQG theory, is the same that the one in the current ΛCDM paradigm. However the new formula has a deeper physical meaning because its dimensionless factor is simpler regarding the one in the current ΛCDM paradigm. Also it is remarkable the fact that the both dimensionless factors depend on exclusively from Ωm or ΩDE and the both ones differ only a 5%. The fact that in the framework of DMbQG theory has been found a better formula for the mass associated to the turnaround radius is a strong support for the DMbQG theory whose hypothesis about the origin of DM is exclusively the gravitational field. The chapters 3, 4 and 5 are devoted to test the DMbQG theory in the clusters: Virgo, Coma and the Local Group of galaxies using recent data published about these clusters. The tests are mainly focused on the turnaround radius and its mass associated and all of them have been a complete success by the DMbQG theory. In this second version of the paper, the mass associated to the turnaround radius formula is obtained by a different way regarding the first version. In this new method is not used any formulas with the parameter "a", achieving a more understandable process to obtain the same formula.
Category: Astrophysics

Collatz Conjecture: A Simple Proof for a Simple Problem

Authors: Ulrich Neuenschwander
Comments: 8 Pages.

A simple proof of the Collatz conjecture is proposed. The approach relies on the fundamental properties of N and on their fruitful interplay with the Collatz transformation.
Category: Number Theory

A Geometric Explanation of Dark Matter Based on General Relativity

Authors: Hao Shen, Ruipeng Ma
Comments: 38 Pages.

Within the framework of standard general relativity[1], under the assumptions of staticity, spherical symmetry and the strong energy condition, we prove that a geometric transition zone — the "reverse-bending zone" — must appear in the periphery of any finite self-gravitating system, where the t—r sectional curvature changes sign from negative to positive. This zone is bounded by the curvature zero (r_0), the curvature peak (r_{mathrm{peak}}), and the matter boundary (R); in the interval ((r_0, R)) the sectional curvature smoothly transforms from matter-dominated spherical compression to vacuum saddle-shaped stretching. The reverse-bending zone is not a free vacuum but a forced geometry locked jointly by the interior baryonic potential well and the far-field boundary condition. Within this zone, the Misner—Sharp-type gravitational mass (M(r)) continues to grow: it grows faster than linearly in the region (r_0 to r_{mathrm{peak}}), and although the growth slows down in the region (r_{mathrm{peak}} to R), it never ceases. The resulting geometric Weyl stretching together with the self-energy of the gravitational field provide an extra centripetal acceleration, which naturally manifests itself, in the weak-field approximation, as an approximately logarithmic potential and a flattening of the rotation curves. The theoretical sectional curvature formula precisely reproduces the Friedmann acceleration equation, the Newtonian radial tidal formula (and, by integration, the Newtonian gravitational acceleration), the TOV equation, and the Schwarzschild solution, among others — not approximately, not asymptotically, but exactly in their respective limits. It yields parameteru2011free, falsifiable predictions that can be directly tested with existing rotationu2011curve and photometric data. This result demonstrates that, without introducing new particles or modifying the field equations, forced geometry within general relativity alone can generate a "darku2011matteru2011like" gravitational effect on galactic scales.
Category: Relativity and Cosmology

The Final Theory

Authors: Nigel B. Cook
Comments: Corrected contents page links to sections and also a bibliography added.

We construct a complete quantum field theory in which all observed interactions - electromagnetic, weak, strong, gravitational, and cosmological - arise from a single mechanistic principle: energy conservation in vacuum polarization. The theory replaces the ad hoc structure of the Standard Model and the geometric assumptions of general relativity with a unified framework based on the group chain for Euclidean signature SO(3, 3) ~ SU(4) ⊃ SU(3) × U(1)G ⊃ U(2) ⊃ SU(2) × U(1)Y . Matter representations, gauge charges, running couplings, particle masses, gravity, and dark energy all emerge from this structure without arbitrary parameters. This paper is a new presentation of the ideas in vixra paper 1111.0111 dated 2011, with updates, a few corrections, and further development. That earlier paper should still be consulted for further references, graphics and details documenting the origins of the various nascent ideas.
Category: Quantum Gravity and String Theory

An Infinite Family of Solutions to the Generalized Cannonball Problem

Authors: J.W.L. Eerland
Comments: 4 Pages.

In an earlier paper I considered the generalized cannonball problem for r-regular polygons and studied integer solutions to the associated Diophantine equation. In this note I prove that for every positive integer n, the triple [(r,a,b)=left(3n+2,,3n^2-2,,3n^3-3n+1ight)] is a solution. Hence the generalized cannonball problem admits infinitely many positive integer solutions. I also compare this parametric family with the 858 tuples listed in the appendix of the earlier paper. Among those tuples, 802 are generated by the present family and the remaining 56 tuples are listed explicitly.
Category: Number Theory

False Equivalence of Accelerating Rocket and Gravity Pull on Elevator

Authors: Carl Littmann
Comments: 6 Pages.

Gravity bends a light beam more than a particle beam. So, this article tells elevator occupants how to use that fact to detect whether the forces they feel are caused by a gravitational or non-gravitational acceleration. I.e., although that capability supposedly violates the ‘Equivalence principle’ of ‘General Relativity’. Einstein imagined "the experiences of occupants in a windowless chamber, in deep, isolated space" as it was ‘accelerated upward’ by a pulling. And claimed ‘Equivalent’ (identical) feelings and test results would arise for occupants in a non-moving elevator on our gravitational earth.[1] Yet, let us imagine that a photon and an ultra-high-speed particle are launched at the same time from an internal wall of an elevator; then they go through two adjacent pin-holes, and finally hit the opposite wall. But surprisingly, they do not hit the same spot - because the gravity bends photons twice as much as a particle beam.[2] But not so - for a rocket in deep outer space, experiencing a non-gravitational acceleration! So we discuss that violation of ‘Equivalence in Relativity’ and its broad implications, in this article.
Category: Number Theory

A Proof for the Collatz Conjecture

Authors: Jérôme Chauvet
Comments: 5 Pages.

This proof addresses the Collatz conjecture and relies on the quantitative characterization undergone by the evolving densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system from which we deduce the final cyclic attractor, hence proving the conjecture.
Category: General Mathematics

Exact Solution to Einstein's Field Equation

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, Einstein's field equation will be solved by removing the framework of tensor analysis.
Category: Relativity and Cosmology

Exact Solution to Einstein's Field Equation

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, Einstein's field equation will be solved by removing the framework of tensor analysis.
Category: Relativity and Cosmology

Three Theorems From Which Follow Two New Laws of Gravitation and a New Law of Universal Gravitation

Authors: Mykola Kosinov
Comments: 13 Pages.

New theorems on the flux of the gravitational field strength vector are presented, free from the limitations inherent in Gauss's theorem. Gauss's theorem is not sufficient for a complete description of gravity. It is shown that the relationship between the gravitational field flux and the mass of sources is not the only method for representing the gravitational field flux. Unlike Gauss's theorem, the new theorems do not include the mass of sources. The first theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the body's orbit. The second theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the universe. The third theorem concerns the total gravitational force that actually acts on the body and is caused by the gravitational interaction of the test body with all bodies in the universe. From these theorems, two new laws of gravitation and a new law of universal gravitation are derived, which for the first time describes gravity taking into account the action of all bodies in the universe. Unlike Newton's law of gravity, the new law of universal gravitation does not include the mass of sources and the gravitational constant G. The new theorems relate to the gravitational field, which obeys the inverse-square law, and to the gravitational field of the universe, where the inverse-square law does not apply. The new theorems and new laws of gravity provide a complete description of the gravitational interactions of all N-body bodies in the universe. The new theorems demonstrate the existence of a workaround instead of searching for a direct solution to the gravitational N-body problem (for N ≥ 3).
Category: Quantum Gravity and String Theory

Propositions of Three Laws of Spiritual Mechanics

Authors: Thomas Adrian Nicewicz
Comments: 2 Pages. (Note by viXra Admin: This submission may not be written in a manner suitable to viXra - Please read the viXra guidelines and conform)

The ancients once said, "As above, so below." This writing explores this notion and proposes three laws of spiritual mechanics.
Category: History and Philosophy of Physics