All Submission Categories

Dilating Loop Relativity: Mathematical Derivation for a Gauge-Gravity Spinfoam Mapping

Authors: Andrew Evans
Comments: 27 Pages.

Dilating Loop Relativity (DLR) connects the Bern-Carrasco-Johansson double copytheory1 with Loop Quantum Gravity (LQG). The framework recognizes physical mass as the source of unconfined kinematic potential density operating on LQG spinfoam cells. At aspinfoam vertex, this potential triggers localized spatial loop dilations that emergemacroscopically as the Schwarzschild metric. At a black hole, vertex dilation increasescontinuously down to the black hole centre. The event horizon acts as a filter, where nodes havedilated sufficiently that shorter-wavelength photons cannot execute the discrete hops required for propagation, while ultra-long Hawking radiation wavelengths span the node gaps and escape. Dark matter is the frozen remnant of early fluctuations in the strong force, acting similarly on LGQ spacetime. Finally, we propose a laboratory test using polarized solid hydrogen to detect an anisotropic, equatorial time-dilation signature.
Category: Quantum Gravity and String Theory

A Test of the Cosmological Scaling of MOND’s Critical Acceleration

Authors: Wenhao Xiong
Comments: 4 Pages.

Modified Newtonian Dynamics (MOND) is built on a universal critical acceleration a0, with a long-standing numerical coincidence between the local best-fit a0 and cH0/(2π). Previous tests of a0’s cosmic evolution have been limited by baryonic modeling systematics and the narrow applicability of the deep-MOND approximation. Here we define a dimensionless observable B(z) ≡ a2 tot/(cH(z)aN), which cancels structural systematics and directly probes a0(z)/(cH(z)) in the weak-acceleration regime. Under the hypothesis a0(z) = cH(z)/(2π), B(z) is predicted to be a universal constant 1/(2π) ≈ 0.159. We test this prediction with three complementary datasets: 175 nearby SPARC galaxies, 1207 radial acceleration points from the SPARC sample in the strict deep-MOND regime (atot < 0.1a0), and 5 high-redshift regular rotating disk galaxies (z = 0.56 − 2.10) from the ALMA ALPAKA survey. We find the deep-MOND local sample yields B = 0.158±0.020, in agreement within uncertainties with the theoretical prediction. For high-redshift galaxies in the strong-acceleration regime, we apply an analytical correction based on the standard MOND interpolation function, with uncertainties propagated via Monte Carlo error propagation to ensure rigorous error estimation. Corrected values are fully consistent with 1/(2π) within uncertainties. We find no statistically significant evidence for redshift evolution of B(z), with a linear slope of 0.010 ± 0.009 (consistent with zero at 1.1σ).This result is robust to selection criteria and cosmological parameter choices. Our findings serve as a preliminary consistency check for the proposed cosmological scaling of a0. With the current small high-redshift sample, we cannotplace strong constraints on evolution; future high-resolution observations with JWST and ALMA will be needed to test the redshift dependence more robustly.
Category: Astrophysics

Quantum Field Theory with Integer Spins

Authors: Miroslav pardy
Comments: 15 Pages. The original article

The analogy with the spin 1, 2 and 3 situation enables us to introduce actionfor the arbitrary integer spin situation. It is not excluded that the theory haspossible application in quantum cosmology with spin stars.
Category: High Energy Particle Physics

Collatz Sequence Proof

Authors: Taha Muhammad
Comments: 13 Pages.

A Collatz sequence is a series of numbers generated by taking any positive integer and repeatedly applying two simple arithmetic rules [Collatz Sequence Rule (CSR)] until the number reaches 1:1- If the current number is even, divide it by 2: (n /2). 2- If the current number is odd, multiply it by 3 and add 1: (3 n + 1). Taha^' s Collatz Sequence Fact 1 (TCSF1): if any sequence S(n)={a,b,c,u2026x,u2026,t}u2026by sequence rule ⇒lS(n)=lS(a)=lS(b)=⋯lS(x)=lS(t)u2026by (TCSF1) This paper presents a systematic evaluation of the localized boundary layers governing the classical Collatz Conjecture ((3n+1)) utilizing Taha’s Sketch and a comprehensive Loop Table state matrix. We evaluate the algebraic behavior of the sequence within an isolated loop structure containing exactly (r) elements, where (k) is defined strictly as a positive integer serving as the cofactor of 3 when (r = 3k) ((r, k in mathbb{N}^+)). By partitioning the entire positive integer domain into two mutually exclusive sets ((mathbb{N}_{3k} cup mathbb{N}_{text{non}_3k} = mathbb{N}^+)), we solve the general loop equation (x = text{(potential loop element)}) to show that any alternative configurations outside of this strict ratio consistently yield fractional values, breaking integer closure properties ((x otin mathbb{N}^+)). Consequently, we demonstrate that alternative or non-trivial integer loops are structurally impossible, concluding that all trajectories over the valid domain must uniquely collapse to the classical ({1, 4, 2}) attractor cycle.
Category: Number Theory

A Geometric Limit Theory for Closed Discrete Spaces

Authors: Satoshi Nakamoto, Nicolas Bourbaki
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

We propose a geometric limit theory for discrete spatial configurations where continuous curves cannot exist, leaving a deterministic boundary error termed the "Pi residual." By balancing the root-mean-square deviation of discrete vertices against system coordinate resolution, we derive critical boundary constraints
Category: Mathematical Physics

The Mathematical Structure of the Cosmological Special Theory of Relativity: Coordinate Transformations, Group Structure, and Invariants

Authors: Sangwha Yi
Comments: 10 Pages.

The Cosmological Special Theory of Relativity (CSTR) relates a local, unexpanded spatial coordinate to the physically expanded coordinateof a Robertson-Walker universe through a cosmological expansion function τ (t0) of the cosmological time t0, and re-derives the Lorentztransformation, relativistic wave equations, and electrodynamics within the resulting cosmological inertial frame (Yi, 2020, 2025). Thispaper examines the purely mathematical structure of that construction: the explicit form of the cosmological Lorentz transformation andits matrix representation; whether the set of such transformations closes under composition to form a genuine group, both at a single fixedcosmological time and across different cosmological times; the four-vector and tensor formalism appropriate to the cosmological inertialframe; the invariant and non-invariant quantities of the theory; and the status of energy and momentum conservation under Noether’s theoremgiven the explicit time dependence introduced by τ (t0). We show that at fixed cosmological time the cosmological Lorentz transformationsreduce, after a coordinate relabeling, exactly to the ordinary Lorentz group, but that composing a boost with the passive evolution of τ (t0)between two different cosmological times does not, in general, close within the class of cosmological Lorentz transformations, so that the fullset of transformations used across the CSTR literature is more naturally described as a groupoid than as a Lie group. We relate this structureto the mainstream distinction between comoving and physical coordinates and to the conformal (Weyl) group of transformations, and discussthe implications for the open composition question raised in companion reviews of CSTR (A Critical Review, 2025).
Category: Relativity and Cosmology

Cosmological Special Theory of Relativity: A Consolidated Review of the Formalism

Authors: Sangwha Yi
Comments: 10 Pages.

Over a series of papers published between 2018 and 2025, the author has developed a framework, the Cosmological Special Theory of Relativity(CSTR), that incorporates the time-dependent expansion of the Robertson—Walker universe directly into the coordinate transformations,differential operators, and relativistic wave equations of special relativity, by way of an auxiliary "cosmological inertial frame" in whichphysical (expanded) coordinates are related to a local, unexpanded coordinate through a cosmological expansion function τ (t0) of the cosmologicaltime t0 (Yi, 2020,?). This paper consolidates the central results of that program into a single, self-contained review. We present thespace-time relations that define the cosmological inertial frame, the cosmological Klein-Gordon equation and its free-particle wave functionand Yukawa-potential solution (Yi, 2020, 2021), the corresponding non-relativistic Schr¨odinger limit and cosmological uncertainty relation,the Dirac equation in the cosmological inertial frame and its consistency with the Klein-Gordon equation (Yi, 2021), the Klein-Gordon—Maxwell theory of interacting complex scalar and electromagnetic fields (Yi, 2021), the canonical quantization of the Klein-Gordon scalarfield (Yi, 2021), the particle’s kinetic energy and force in the cosmological frame, and the extension to a Cosmological General Theory ofRelativity (CGTR), including cosmologically embedded Schwarzschild and Kerr-Newman solutions (Yi, 2021, 2025). We close with a discussionof the relationship between this formalism and the standard comoving-coordinate treatment of Robertson-Walker cosmology, and ofopen questions raised in the literature regarding CSTR’s consistency and standing (A Critical Review, 2025).
Category: Relativity and Cosmology

Cosmologically Embedded Black Holes: Schwarzschild and Kerr-Newman Solutions in the Cosmological General Theory of Relativity

Authors: Sangwha Yi
Comments: 10 Pages.

The Cosmological General Theory of Relativity (CGTR) extends the Cosmological Special Theory of Relativity (CSTR) to curved spacetime byembedding a localized mass, or a rotating charged mass, within a spatially flat, spatially homogeneous Robertson-Walker background whosescale factor is denoted the cosmological expansion function τ (t0) (Yi, 2020, 2021). This paper concentrates specifically on the black-holesolutions of this framework: the cosmologically embedded Schwarzschild solution and the cosmologically embedded Kerr-Newman solution(Yi, 2021, 2025). We present the CGTR field equation and its perturbative metric ansatz, derive the Schwarzschild and Kerr-Newman metricfunctions and their horizon structure, work out the radial and circular photon and massive-particle geodesics, the ergosphere and extremalitycondition of the rotating solution, and the homogeneous (source-free) limit that recovers the background Robertson-Walker cosmology.We show that, in every case considered, the physically measured horizon radii, extremality condition, and photon-sphere radius reduce totheir ordinary, epoch-independent general-relativistic values once expressed in the physically expanded radial coordinate, even though thecorresponding local-coordinate expressions carry explicit τ (t0)-dependence. We close with a comparison to the mainstream McVittie andSchwarzschild-de Sitter embeddings of a point mass in an expanding or accelerating universe, and with the open questions raised by anindependent critical review of the underlying CSTR framework (A Critical Review, 2025).
Category: Relativity and Cosmology

Cosmological Quantum Physics: RelativisticWave Equations, Field Quantization, and the Uncertainty Principle in the Cosmological Inertial Frame

Authors: Sangwha Yi
Comments: 10 Pages.

The Cosmological Special Theory of Relativity (CSTR) re-derives the relativistic wave equations of quantum theory within an auxiliarycosmological inertial frame, in which a local, unexpanded spatial coordinate is related to the physically expanded coordinate of an expandingRobertson-Walker universe through a cosmological expansion function τ (t0) of the cosmological time t0 (Yi, 2020,?). This paper focusesspecifically on the quantum-theoretic content of that program: the cosmological Klein-Gordon equation, its plane-wave solutions, conservedcurrent, and Yukawa-potential solution (Yi, 2020, 2021); the non-relativistic Schr¨odinger limit and the associated cosmological positionmomentumand time-energy uncertainty relations (Yi, 2020); the Dirac equation in the cosmological inertial frame, its consistency with theKlein-Gordon equation, its non-relativistic (Pauli) reduction, and its negative-energy spectrum (Yi, 2021); the Klein-Gordon-Maxwell theoryof an interacting charged scalar and electromagnetic field, together with its gauge invariance and static Coulomb limit (Yi, 2021); and thecanonical quantization of the free Klein-Gordon field, including its Fock space, vacuum energy, and equal-time propagator (Yi, 2021, 2025).We conclude with a discussion of how this formalism compares with the treatment of quantum fields in curved and expanding spacetimes inthe mainstream literature, and with the open questions raised by an independent critical review of CSTR (A Critical Review, 2025).
Category: Relativity and Cosmology

Performance of AI Tools for Automated Literature Screening in Evidence Synthesis

Authors: Minghao Ruan, Junhao Fan
Comments: 10 Pages.

Background Literature screening constitutes a critical component in evidence synthesis; however, it typically requires substantial time and human resources. Artificial intelligence (AI) has shown promise in this field, yet the accuracy and effectiveness of AI tools for literature screening remain uncertain. This study aims to evaluate the performance of several existing AI-powered automated tools for literature screening.Methods This diagnostic accuracy study employed a cohort to evaluate the performance of five AI tools—ChatGPT 4.0, Claude 3.5, Gemini 1.5, DeepSeek-V3, and RobotSearch—in literature screening. We selected a random sample of 1,000 publications from a well-established literature cohort, with 500 as randomized controlled trials (RCTs) group and 500 as others group. Diagnostic accuracy was measured using several metrics, including the false negative fraction (FNF), time used for screening, false positive fraction (FPF), and the redundancy number needed to screen.Results We reported the FNF for the RCTs group and the FPF for the others group. In the RCTs group, RobotSearch exhibited the lowest FNF at 6.4% (95% CI: 4.6% to 8.9%), whereas Gemini exhibited the highest at 13.0% (95% CI: 10.3% to 16.3%). In the others group, the FPF of the four large language models ranged from 2.8% (95% CI: 1.7% to 4.7%) to 3.8% (95% CI: 2.4% to 5.9%), both of which were significantly lower than RobotSearch's rate of 22.2% (95% CI: 18.8% to 26.1%). In terms of screening efficiency, the mean time used for screening per article was 1.3 s for ChatGPT, 6.0 s for Claude, 1.2 s for Gemini, and 2.6 s for DeepSeek.Conclusions The AI tools assessed in this study demonstrated commendable performance in literature screening; however, they are not yet suitable as standalone solutions. These tools can serve as effective auxiliary aids, and a hybrid approach that integrates human expertise with AI may enhance both the efficiency and accuracy of the literature screening process.
Category: Artificial Intelligence

Mechanical Equations of a Particle Group in a General Reference Frame

Authors: Jinyong Liu
Comments: 22 Pages.

In the framework of classical noninertial mechanics, the theoretical construction is predicated on the existence of a special reference frame, the "inertial frame", as a priori. Its essence is to extend the dynamical laws in the inertial frame to noninertial frames through coordinate transformation and formal modification, thus inherently relying on the definition and existence of the inertial frame, making it difficult to achieve a fundamental breakthrough in the inertial frame paradigm. This paper proposes a dynamic reconstruction path based on the intrinsic relations within the system, aiming to establish a new system of particle dynamics that is logically self-consistent and physically self-sufficient and does not presuppose an absolute space-time background. On the basis of Newton's laws of motion, in this paper, the equations of particle mechanics applicable to any translational reference frame (i.e., a reference frame with an origin acceleration that can be any function of time) are derived. Through systematic analysis, it is proven that core physical quantities such as force, momentum, and the kinetic energy of a particle group all possess intrinsic properties independent of the choice of reference frame. By further introducing a particle subsystem grouping mechanism, this paper reveals the dynamical essence of internal interactions within the system and its coupling with the external environment, clarifying the physical origin of the energy hierarchy structure (internal kinetic energy and external kinetic energy) and its conservation conditions in general reference frames, thereby providing a solid theoretical foundation and an operational, verifiable mathematical framework for constructing a truly universal noninertial mechanics theory that does not require the introduction of fictitious inertial forces.
Category: Mathematical Physics

The Mathematical World

Authors: Bernard Riley
Comments: 5 Pages. Current data used.

The measurement value of a quantity arises in the judgement of a single observer, in the synthesis of a sensible intuition (an immediate representation upon observation) and a mathematical concept conceived for the purpose. The value is then objectively and universally valid. Values judged for various notable physical quantities are presented in terms of the author’s concept. A consistent mathematical system (the Mathematical World) built from valid mathematical statements made in the phenomenal world of our experience is hypothesised to underlie the phenomenal world and to regulate cognition in order to maintain the consistency of all measured values and their interrelationships. The Mathematical World is the analogue of Kant’s noumenal world, which is the world as it is in itself, independent of human perception.
Category: History and Philosophy of Physics

Spectral Analysis of Arithmetic Functions

Authors: George Athanasiou
Comments: 9 Pages.

This paper explores the normalization of Fourier series kernelsassociated with elementary arithmetic functions. By analyzing keyfunctions such as divisor related functions, the prime gap function andthe inverse prime counting function. With these results, a framework fortheir spectral decomposition in terms of complex exponential functionswas developed. Through contour integration techniques and normalizationof the Dirac delta function, new methods can be derived from the analyticstructure of these functions. These findings contribute to the broaderunderstanding of arithmetic functions and their link to Fourier series.
Category: Number Theory

Determining the Proportion of Dark Matter Using Information Economics

Authors: Bernd Ganter
Comments: 8 Pages. In German language. Comments please to: bernd.ganter.fsk@gmx.de

This paper explains in German language how Dark Matter covers 85% of all the total matterin the universe. It does so by applying the mathematics of consecutive optimal power towersto the relative sizes of the strengths of interactions between elementary particles.The same procedure was used with the fine structure constant in vixra 2607.0104which allowed the derivation and very exact calculation of that constant.Based upon that procedure a formula can be developed to calculate the relative valueof spacetime volume and information density (=strength) of gravity as an interaction.
Category: Mathematical Physics

Derivation of the Correct Chiral Dirac Equation for Leptons and Quarks from Su(4), Motivated by Critical Discussion with Robert a Wilson

Authors: Nigel B. Cook
Comments: 67 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

SO(3,1) has the double cover SL(2,C), which is the symmetry for the pair of Weyl spinors in a Dirac spinor. Dirac gamma matrices contain two copies of SU(2), and this is exactly why the spin group of the Lorentz group is SL(2,C). SO(3,1) is the group of real 4 × 4 matrices, while SL(2,C) is the group of complex 2 × 2 matrices with determinant 1. They arise dynamically, then no gauge group is required to contain them as real forms. That is precisely why SU(4) is viable. Dirac gamma matrices are the SU(2) × SU(2) structure of the Lorentz algebra, because the Dirac’s spinor matrices content are two copies of SU(2). Dirac’s original antimatter prediction was too symmetric; Nature’s stable first generation is chiral and asymmetric; SU(4) vacuum-polarisation dynamics explain this asymmetry and yield the corrected Dirac equation. The writing of this paper is motivated by the kind critical discussion with mathematician Robert A Wilson, who very helpfully pointed out key problems in the mainstream physics approach, as well as critically clarifying the theoretical physics group and lie algebras underlying Dirac’s spinor. (However, any errors in this paper are not due to Dr Wilson, but to the author.)
Category: Quantum Gravity and String Theory

Obtaining and Proving an Uncompensated Momentum for a Closed Mechanical System Device Consisting of Two Hulls: A Theoretical Overview

Authors: Lozko Georgiev, Daniel Georgiev
Comments: 8 Pages. In Bulgarian; 5 figures

This article examines a closed mechanical system consisting of two hulls. Using this system, we can obtain an uncompensated momentum for one of the hulls in the closed system by employing the design described below and performing the required processes in sequence. It should be noted that, according to the laws of classical mechanics, Newton in "The Principia: Mathematical Principles of Natural Philosophy" discusses the law of conservation of the center of mass’s motion, but only for classical bodies. The device under consideration, however, consists of two hulls, each with different properties. In this case, to simplify this brief theoretical discussion, we have omitted some of the processes. This is because obtaining a single uncompensated momentum for one of the hulls in the closed system is sufficient to demonstrate the device’s functionality.
Category: Classical Physics

[ Critical Analysis of] the Derivation of Lorentz Transformations and the Dynamics of Ether Drag in D. Miller's Experiments

Authors: Arunas Ostasevicius
Comments: 5 Pages. ([ ] added by viXra Admin)

This paper provides a critical analysis of the geometric and physical assumptions underlying the derivation of the Lorentz transformations. It is demonstrated that the classical derivation, based on the geometry of the Michelson-Morley interferometer arms, contains a fundamental kinematic error [?] caused by a misconception of the nature of the luminiferous medium (the World Ether). Applying the Pythagorean equation to the spatial displacements of a moving system, rather than utilizing a vector analysis of a spherical wave front of an elastic wave in the medium, led to a false hypothesis regarding the deformation of space-time. An alternative quaternion description of a wave packet in absolute Euclidean space is presented. The invalidity of the relativistic postulate of the constancy of the speed of light is proven by the results of long-term high-altitude experiments conducted by Dayton Miller, which recorded a real ether drift and the dynamics of a partial drag of the medium within a hydrodynamic boundary layer. The long-standing paradox of stellar aberration is rigorously resolved without invoking the four-dimensional Minkowski metric.
Category: Relativity and Cosmology

A Temperature-Derived Solar Mass Model and Running Parameters Resolve Dark Matter

Authors: Terry J. McMahon
Comments: 8 Pages. Part 3 of a series

Gravitational lensing and galactic rotation curve data evidence that galactic mass calculations, via the centripetal force method, obtain results significantly less than total matter indicated, by about 5.35:1. This major invisible component is known as dark matter, interacting gravitationally. Newtonian and general relativity gravitational models diverge on multiple fronts, suggesting neither model is complete. Dimensional analysis, when reduced to units of length and time only, identifies the scaling mode for dimensional parameters. Gravity is accordingly modified. Speed of light c is shown to be the velocity of least energy for fundamental particles. Modified gravity reveals that galactic mass calculations via the centripetal force method are incorrect. Comparison of solar volumetric temperature slices against atomic hydrogen temperature, provides a method for calculating solar mass. Recalculating galactic mass via running parameters, and solar temperature analysis in atomic hydrogen terms, fully resolves dark matter.
Category: Quantum Physics

Fibonacci Code Redundancy and the Design of a New Fibonacci Numeral System — NFNS

Authors: Andrey V. Voron
Comments: 40 Pages.

It is shown that modern number systems suffer from a significant drawback in the form of zero code redundancy. Unlike the classical binary code, the Fibonacci code is inherently redundant. Furthermore, its redundancy manifests through the property of multi-valued representation (as a binary code) of natural numbers and is not constant: the code redundancy varies significantly for individual numbers. Based on the Fibonacci number system featuring Fibonacci codes with unrestricted redundancy, a rule for limiting the Fibonacci code redundancy has been formulated: numbers with an even digit weight can only be represented alongside numbers with an odd digit weight. Consequently, natural numbers can be represented by exactly two (and only two) code variants due to the introduced Rule. The development of an optimal arithmetic algorithm for the New Fibonacci Number System (NFNS) must be based on the fundamental principles of classical Fibonacci arithmetic (developed by A.P. Stakhov), while strictly integrating the author's rule: a prohibition on adjacent positions of identical parity. In the NFNS, where consecutive odd numbers of zeros are forbidden (except at the end of the code string), the mathematical framework shifts toward dual representation. The paper presents: the architecture of the NFNS arithmetic algorithm; the mathematical description of the NFNS arithmetic algorithm; and an example of adding specific numbers (7 + 8) in the NFNS. The primary advantage of the presented addition algorithm for the NFNS is that redundancy is utilized for error control directly during the computation process. If, at stage 3, the finite-state machine detects that an intermediate number lacks exactly 2 representation options (or the code shifts into a forbidden combination), the processor instantly diagnoses a fault (an attack or an error).
Category: Data Structures and Algorithms

Arithmetic Dimensionality of Real Numbers

Authors: Robert S. Miller
Comments: 33 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper will explore the concept of Arithmetic Dimensionality, D_A, for real numbers, whose analog is the fractal dimensionality of geometric constructs, D_G. Beginning with a short review of how the dimension of a geometric object is calculated, it will be shown how this same concept can be applied to real numbers, and that the current understanding of numbers having a geometric dimension of 0 is not accurate. Instead it is show,, that although the point on a number line, like the x-axis is 0 dimensional, the numbers themselves may possess a fractal dimension. It is beyond to scope of this paper to prove the exact Geometric Fractal Dimension of transcendental numbers (like π and e) or irrational numbers (like √2). The goal however is to show (1) there exists a D_A and D_G for real numbers, (2) that D_A→D_G as the number of decimal digits considered n→∞ and (3) where D is a generic stand in for both D_A and D_G, it exists in Information Space or Sub-Hilbert Space of Geometric Dimension such that 0≤D<1.
Category: General Mathematics

The Michelson-Morley Experiment and the Gravity

Authors: Miloš Čojanović
Comments: 3 Pages.

The Michelson-Morley experiment was designed to detect the Earth's motion relative to the "aether". The experiment yielded a null result a fundamental proof that a speed of light is invariant. This ultimately paved the way for Einstein's theory of special relativity. Our assumption is that Earth's own gravity creates a preferred frame , which rotates around Earth's axis in relation to an infinitely distant fixed point. This directly affects the result of "MM" experiment. In order to test this hypothesis, it is necessary to perform "MM" in an environment where gravity is approximately equal to zero
Category: Astrophysics

The Refractive Plenum Gradient: Replacing the Spacetime Metric with Field Refraction

Authors: Carl Max Reed
Comments: 3 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Within the strict, three-dimensional constraints of the Electromagnetic Energy Onlyverse (EMEO), physical paths of translation are entirely liberated from the abstract geometric constraints of a curved spacetime metric. Utilizing Robert Dicke's 1957 polarizable medium framework, space is recognized as nothing other than the electromagnetic field itself extending outward, while the localized velocity of light is governed entirely by the variable permittivity (ε) and permeability (µ) of this continuous field substrate. This paper demonstrates that a concentrated, self-sustaining toroidal soliton node modifies the local electromagnetic density of the surrounding continuous plenum, naturally generating a structural refractive index gradient (n = √εµ/ε0µ0). When an independent electromagnetic wavefront passes through this high-density region, its velocity drops non-linearly, forcing the wavefront to refract and steer symmetrically inward toward the density of the field concentration. Field Refraction and orbital trajectories emerge natively as a pure optical steering phenomenon within a material medium, completely eliminating the necessity for a curved geometric fabric or abstract quantum graviton exchanges.
Category: Classical Physics

Plasma-Activated Water and Phenolic Compounds: a Potent Combined Strategy Against Yeast Resilience

Authors: Bernard Gitura Kimani, Ramin Mehrabifard, Oleksandr Galmiz, Zdenko Machala
Comments: 12 Pages.

Effective fungal control is essential to prevent spoilage, contamination, and infections in the realms of food, healthcare, and industry. This study explores the antifungal activity of plasma-activated water (PAW) generated by transient spark (TS) electrical discharge combined with natural phenolics bioactive compounds on the planktonic growth, biofilm formation, and surface adhesion of yeast Saccharomyces cerevisiae and Wickerhamomyces anomalous. The phenolics were assayed at 1 or 2u202fmg/mL for planktonic growth after determining their minimum inhibitory concentration. The biofilms were grown on sterile microscope slides for 48u202fh, stained with acridine orange or calcofluor stain, and observed under a fluorescence microscope. PAW was used immediately after plasma treatment of tap water to create PAW-phenolic solutions. The combination of PAW with cinnamic acid and vanillin showed the most significant antiyeast activity against planktonic and biofilm growth, as well as surface adhesion. The biofilms formed with the PAW-phenolic combination were notably fragmented, and residual cells were structurally damaged. A complete inhibition of biofilm formation was observed when 500u202fμg/mL of cinnamic acid was used in combination with PAW. The findings indicate a strong potential of combining PAW with phenolic compounds that represents an effective novel strategy for preventing fungal growth.
Category: Nuclear and Atomic Physics

Forces and Vectors

Authors: Teo Banica
Comments: 400 Pages.

This is a joint introduction to mathematics and physics, guided by the dimensionality of the ambient space, and with the mathematics and physics chapters alternating. We start with a discussion on what happens in 1 dimension, namely the basics of calculus, and some physics too, including 1D collisions, relativity, gravity, waves and heat. Then we go on a similar discussion in 2D, featuring this time plane vectors, complex numbers, and more advanced physics, such as elliptic orbits under gravity. We then discuss what happens in 3 dimensions, namely standard vector calculus, and 3D classical mechanics, and the basics of electromagnetism. Finally, we discuss 4D and curved spacetime, and we end with a brief introduction to quantum mechanics.
Category: History and Philosophy of Physics

Decreasing Universe Theory: Dark Matter X Gravitational Gradient

Authors: Joao Carlos Holland De Barcellos
Comments: 8 Pages.

In the Decreasing Universe Theory ("DUT"), "Dark Matter" is explained as an illusory effect caused by the differential contraction of stars relative to their distance from a galaxy's massive nucleus[1][17]. This article presents a systematic analysis of 47 galaxies, demonstrating that the apparent dark matter fraction (fDM) correlates with a gravitational gradient factor derived from DUT principles. Weshow that galaxies with massive bulges and large radial extents exhibit high dark matter fractions, while compact galaxies with dense bulges (NGC 1277) and diffuse galaxies without bulges (NGC 1052-DF2, DF4, DF9) show negligible dark matter effects — exactly as predicted by the DUT model.
Category: Astrophysics

Toward the Physical Nature of the Self-Healing Effect of Light

Authors: Vladimir Kuz'menko
Comments: 3 Pages.

When a narrow beam of light meets an opaque obstacle, then part of the beam is scattered, and the other part behind the obstacle can restore its initial shape. This interesting and counterintuitive self-healing effect has long been studied theoretically and experimentally. There is a detailed mathematical description, but no clear physical explanation. Such a simple and universal physical explanation is discussed here.
Category: Quantum Physics

Some Exams for the Students of ENIT, Faculty of Science of Tunis and ISET of Nabeul

Authors: Abdelmajid Ben Hadj Salem
Comments: 16 Pages. In French. Comments welcome.

This article presents some exams given to the students of the ENIT, Faculty of Sciences of Tunis and the ISET of Nabeul concerning geodesy, astronomy of position and mathematical cartography.
Category: Geophysics

Confirming Beal's Conjecture

Authors: Francesco Aquilante
Comments: 15 Pages.

We present a complete, unconditional proof of Beal's Conjecture by introducing a novel hybrid framework that bridges classical Euclidean geometry, the rational parametrization of orthogonal vectors, and Gaussian integer arithmetic. By mapping a hypothetical coprime counterexample triple $a^k + b^m = c^n$ onto a two-dimensional geometric construction split by a rational altitude, we derive two fundamental algebraic identities. We show that the geometric sign clash inherent to these identities can be non-trivially satisfied only within the Gaussian integer domain $mathbb{Z}[i]$. Applying localized $pi$-adic valuation analysis reveals a powerful, invariant parameter symmetry relation across the coordinate space. Systematically evaluating this symmetry across inert ($3 pmod 4$), split ($1 pmod 4$), and ramified ($q=2$) prime instances demonstrates that any valid parameter distribution forces a scale explosion ($a^k > b^{2m}$).This parameter growth contradicts the strict mathematical limits required to bridge consecutive perfect powers, proving that no such counterexamples can exist and completing the proof.
Category: Number Theory

Die Entschlüsselung Der Feinstrukturkonstante (Deciphering The Fine Structure Constant Update)

Authors: Bernd Ganter
Comments: 99 Pages. In German. Comments please to: bernd.ganter.fsk@gmx.de

This paper is about dimensions and fundamental forces in the universe, and especially the fine structure constant, the value of which has remained unexplained for over 100 years now. The paper is the German parent document of the condensed version viXra:1405.0226 in English translation. It contains the derivation and exact calculation of the value of the fine structure constant which is 1/137.035999100.
Category: Mathematical Physics

Dynamic Clifford Fiber Transitions and a Spin-2 Signature Order Parameter: a Possible Framework for Emergent Spacetime Phases

Authors: Holger Döring
Comments: 11 Pages.

Investigated is a possible model in which spacetime signature is not a fixed background property but emerges from a dynamical Clifford-fiber structure. The fundamental object is assumed to be a local Clifford module with an internal two-state fiber. The two fiber orientations correspond to different realizations of the underlying Clifford structure. A degenerate vacuum state with vanishing signature order parameter undergoes a phase transition into two non-degenerate signature phases, whereby the norm of signature is assumed as a conservation quantity (law) of zero during the splitting in phase transition of different signature states.
Category: Relativity and Cosmology

Ramanujan Primes as Stability Thresholds

Authors: Payam Danesh
Comments: 16 Pages.

Ramanujan primes encode a persistent form of prime abundance: after the nth threshold, every interval of the form (x/2,x] contains at least n primes. Existing work establishes their existence, global bounds, and leading asymptotic equivalence to the 2nth prime, yet the exact discrete mechanism and the next asymptotic correction are usually treated separately. This work provides a general framework for the analysis of stability and thresholds. It uses a prime window counting process as an event-driven step function and describes the latest deficit as well as the finite sieve process with a known upper bound guaranteeing its completeness. Asymptotic inversion of the prime-counting expansion formula provides the second-order approximation of the threshold with respect to a constant window value c from the interval (0, 1). In the classical case, the approximation shows that the difference between the 2n-th prime number and 2n converges to log 2. Exact computation of the first 100,000 Ramanujan primes confirms the predicted scale; at n=100,000, the second-order approximation has relative error 3.37×10^4. The framework separates rigorous asymptotics, certified finite computation, and historical terminology, providing a reproducible basis for further explicit estimates.
Category: Number Theory

Finding the Maximum of a Polynomial Time Computable Bounded Smooth Function on an Interval is NP-Complete

Authors: Warren D. Smith
Comments: 3 Pages.

Ker-I Ko in his 1991 book "Complexity theory of real functions" (Birkhauser) defined the notions of polynomial-time computable (P.T.C.) real numbers and real functions. On p.106 he posed as an open question "whether differentiability helps in computing maximum values." We argue the answer is "no."

But in order to make this argument, Ko's theory needs to be extended to encompass notions of the codelength of a P.T.C. real number, and the code transformation time for various real arithmetic operations. The question in Ko's unextended theory remains unsolved.

Our result is: If F(x) is C and bounded and P.T.C. on [0,1], then the maximum M of F on [0,1] either

1. is not P.T.C.,
2. or if it is, then the code of M is not produceable by a polytime algorithm from the code for F, or
3. P=NP.

Linear-Time Algorithms to Color Topological Graphs

Authors: Warren D. Smith
Comments: On www since 2005; uploading to VIXRA for archival purposes. Figure on last page 22 with caption on p.21.

We describe a linear-time algorithm for 4-coloring planar graphs. We indeed give an O(V+E+|χ|+1)-time algorithm to C-color V-vertex E-edge graphs embeddable on a 2-manifold M of Euler characteristic χ where C(M) is given by Heawood's corrected (minimax optimal) formula. Finally, there is a linear-time algorithm to 5-color a graph embedded on any fixed surface M except that an M-dependent constant number of vertices are left uncolored. All the algorithms are simple and practical and run on a deterministic pointer machine, except for planar graph 4-coloring which involves enormous constant factors and requires an integer RAM with a random number generator. All of the algorithms mentioned so far are in the ultraparallelizable deterministic computational complexity class "NC." We also have more practical planar 4-coloring algorithms that can run on pointer machines in O(VlogV) randomized time and O(V) space, and a very simple O(V)-time coloring algorithm for planar graphs which conjecturally uses 4 colors.
Category: Data Structures and Algorithms

A Fixed-Port Recursive Construction for Superpermutations

Authors: Yang Liu
Comments: 18 Pages.

We present a bottom-up recursive construction for superpermutations on n symbols, based on a fixed-port invariant of length n−2 and a layer-wise merging procedure where overlap decreases from n−2 down to 1. Starting from (n−1)! directed cycles as base units, the construction iteratively groups units by port matching, closes each group into a cycle, and cuts it to restore fixed-length ports. A key structural property—the self-port property—emerges after the first layer: every merged unit has identical head and tail ports, which greatly simplifies subsequent matching. Reverse-cycle pairs remain separated at every layer due to their fixed maximum overlap of 1, ensuring exactly two units survive to the final step. The construction yields explicit linear superpermutations of length Σu2096u208cu2081u207f k! for all n, matching the classic upper bound and the known minimum for n ≤ 5. The same framework naturally produces three variants—linear, directed cycle, and undirected cycle—each with a closed-form length. While not improving the n=6 record of 872, the construction is fully explicit, manually verifiable, and offers a novel invariant-based perspective that unifies all three variants within a single combinatorial framework.
Category: Combinatorics and Graph Theory

1. Aes Seems Weak. 2. Linear Time Secure Cryptography,

Authors: Warren D. Smith
Comments: On www since 2007. Uploading to VIXRA for archival purposes. Figure on last page 26. Also Markus Grassl computed an accompnying 171-page table of BCH codes which I wish I could upload as "accompanying data."

We describe a new simple but more powerful form of linear cryptanalysis. It appears to break AES (and undoubtably other cryptosystems too, e.g. SKIPJACK). The break is "nonconstructive," i.e. we make it plausible (e.g. prove it in certain approximate probabilistic models) that a small algorithm for quickly determining AES-256 keys from plaintext-ciphertext pairs exists – but without constructing the algorithm! The attack's runtime is comparable to performing 64^w encryptions where w is the (unknown) minimum Hamming weight in certain binary linear error-correcting codes (BLECCs) associated with AES-256. If w<43 then our attack is faster than exhaustive key search. Probably w<10. (Also there should be ciphertext-only attacks if the plaintext is natural English.)

Even if this break breaks due to the underlying models inadequately approximating the real world, we explain how AES still could contain "trapdoors" which would make cryptanalysis unexpectedly easy for anybody who knew the trapdoor. If AES's designers had inserted such a trapdoor, it could be very easy for them to convince us of that. But if none exist, then it is probably infeasibly difficult for them to convince us of that.We then discuss how to use the theory of BLECCs tobuild cryptosystems provably1. not containing trapdoors of this sort,2. secure against our strengthened form of linear cryptanalysis,3. secure against ``differential'' cryptanalysis,4. secure against D.J.Bernstein's timing attack.Using this technique we prove a fundamental theorem:it is possible to thus-encrypt $n$ bits with security$2^{cn}$, via an circuit $Q_n$ containing $le c n$two-input logic gatesand operating in $le c log n$ gate-delays, where the three $c$s denote(possibly different) positive constants and $Q_n$ is constructiblein polynomial$(n)$ time.At the end we give tables of useful binary codes.
Category: Data Structures and Algorithms

Understanding Euclidean Quantum Mechanics and the Path Integral of Quantum Force Fields

Authors: Nigel B. Cook
Comments: 48 Pages.

Quantum mechanics, as historically formulated, rests on a mathematical shortcut introduced by Weyl in 1918. Weyl attempted to quantize the gravitational metric by replacing it with Euler’s complex phase exp(iX), a move later adopted by Schrödinger in 1926 to model atomic spectra. Although Weyl’s unification of electromagnetism and gravity was physically incorrect and rejected by Einstein, its mathematical residue, the use of complex configuration space and a single complex wavefunction, became entrenched in quantum mechanics. This groupthink formalism obscures the true dynamical mechanism of quantum phenomena. Feynman’s path integral formulation reveals the correct relativistic structure: quantum behaviour arises from multipath interference, not from a single complex wavefunction: quantum mechanics and quantum field theory can be formulated entirely in Euclidean spacetime using real interference kernels. Euclidean Schrödinger equation emerges as a coarse-grained approximation to the double-path interference dynamics. The hydrogen atom spectrum is derived within this framework, demonstrating full equivalence with standard quantum mechanics. This paper compiles key objective evidence for a scientific revolution, and proves precisely where the errors in mainstream orthodoxy lie, and the benefits of correcting them (rather than attempting to "explain" them using spurious epicycle type inventions such as superstring).
Category: Quantum Gravity and String Theory

Double Stochastic Quantization in Minkowski Spacetime. Non Perturbative Approach for Stochastic Quantization λϕ_{d}²u207f,n≥2,d≥4 Model Quantum Field Theory in Minkowski Spacetime

Authors: Jaykov Foukzon
Comments: 24 Pages.

In this paper, we show how the finite formulation of quantum field theorybased on Langevin equations can be generalized to the case of nonrenormalizabletheories.The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu,is put in a path-integral form in [5]. The procedure of taking the limit τ→∞ is analyzed and based on new grounds through the introduction of the vacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}²u207f,n≥2,d≥4 model quantum field theory in Minkowski spacetime is considered.
Category: Mathematical Physics

A Characterization of Gaussian Compositeness in Arithmetic Progressions: A Generalized Rational Sieve

Authors: Jatin Dharkar
Comments: 4 Pages. (Note by viXra Admin: Please cite and listed scientific references)

This paper introduces an algebraic sieve for identifying Gaussian primes within arithmetic progressions of the form N = ax + b. By mapping the primality of N onto a one-dimensional integer index x, we establish a parameterization x = (ap + b)n + p. We extend the domain of the parameters p and n to the field of Gaussian rationals Q(i), subject to specific integrality constraints on the resulting factors. We provide a formal proof of the sieve's completeness, demonstrating that the existence of a valid parameter pair (p, n) is both a necessary and sufficient condition for the compositeness of ax + b within the ring of Gaussian integers Z[i].
Category: Number Theory

Resolution of the Yang-Mills Millennium Problem: The Solution via Full General Relativity and its Surrounding Equation

Authors: Frederic Lassiaille
Comments: 9 Pages.

We present the solution to the Yang-Mills existence and mass gap problem by incorporating full General Relativity into Quantum Field Theory via its surrounding equation. By replacing the idealized single-source, asymptotically flat approximation with a multi-source surrounding energy distribution vector D^μ(x), the local field operator calibration is dynamically governed through the purely algebraic structure of the global background environment via the scale-invariant ratio v/c. We show that this ratio possesses an intrinsic scale invariance property under global energy rescalings λ ∈ ℝ*, preventing field configurations from collapsing into zero-energy or infinitesimal states. In low-density vacuum environments, the surrounding background dynamically amplifies the effective gauge interaction energy in inverse proportion to the background density, guaranteeing a strictly positive mass gap Δ > 0. Furthermore, at high energy scales and short distances, the accumulation of local surrounding energy in D^μ(x) induces an intrinsic saturation of the v/c ratio, dynamically damping high-momentum interaction amplitudes and providing a non-perturbative UV regularization scheme without ad hoc cutoffs or counterterm subtractions. This algebraic embedding links full relativistic background constraints directly to the resolution of fundamental open problems in subatomic quantum field theory.
Category: Mathematical Physics

AI Accountability Infrastructure: Cryptographically Verifiable Decision Provenance for High-Stakes AI Systems

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

Consequential decisions in law, medicine, finance, and public services are increasingly mediated by AI systems, yet no widely adopted infrastructure allows an authorized third party to later verify, with cryptographic assurance, what observable factors caused a specific AI output. Explainable AI (XAI) methods characterize model behavior in general, not a single transaction; governance frameworks specify process, not evidentiary mechanism; and forensic/audit logging is rarely designed for AI-specific provenance (retrieved context, tool invocation, policy evaluation) or for graduated, privacy-preserving legal disclosure. We systematize this gap and propose the AI Accountability Infrastructure (AAI), centered on a formally defined, hash-chained, digitally signed AI Accountability Record (AAR) and a graduated, threshold-cryptography-enforced disclosure model in which no single party — including the AI provider — holds unilateral access to evidentiary content. We give (i) a formal model of record integrity and non-repudiation with informal correctness arguments grounded in established cryptographic primitives; (ii) a STRIDE-based threat model spanning both AI-specific and classical evidentiary risks; (iii) a privacy analysis using established data-minimization and disclosure-control concepts; (iv) a complexity and overhead analysis of the proposed mechanisms; and (v) an evaluation methodology intended for future empirical validation. This paper is explicitly a framework and formal-model contribution: it does not report novel experimental results, and we state this limitation directly rather than fabricate benchmark figures. We situate AAI against the NIST AI Risk Management Framework, ISO/IEC 42001, and the EU AI Act, and identify open problems suitable for a doctoral research program.
Category: Artificial Intelligence

A Dimensionless Gravitational State Parameter from a Planck-Scale U(1) Lattice

Authors: Wenhao Xiong
Comments: 2 Pages.

We derive a dimensionless gravitational state parameter R from a discrete U(1) lattice with Planck spacing. From H=J[sum][1−cos(Δφ)] with J=ℏc/ℓP, point defects interact via the 3D Coulomb potential, yielding Newton’s law with n=m/mP. The parameter R≡Fr2/FP(FP=c4/G) decomposes into a defect rigidity term Rm=n2r/ℓP and the lowest-order compact U(1) vacuum contribution 2πℓP/r: R={[m/(m^P)]^2}r/(ℓ^P)−2π(ℓ^P)/r.(1) [for] R larger than 0: classical attraction. R smaller than 0: repulsion. R=0 defines a critical line mr=2πℏ/c. The effective force F=FPR/r2 acquires a mass-independent r−4 correction. At laboratory scales this effective correction is estimated to be [about 10^(130) N.
Category: Quantum Gravity and String Theory

Born's Rule and the Path Integral from a Phase-Consistency Condition

Authors: N. Gurappa
Comments: 7 pages, no figures

Born's rule is the only probabilistic postulate of quantum mechanics that is not derived from its unitary dynamics. The phase-consistency condition (PCC) introduced here treats a quantum state's global phase as a beable — an intrinsic, particle-associated element of reality rather than an observable. Being individually inaccessible, this phase functions as a contextual (supplementary) hidden variable that deterministically maps each state onto a single eigenstate of the corresponding observable for a given measurement context. Over an ensemble, the detection frequencies yield the Born rule and its quadratic form, with no distribution over the phase assumed at any step. Applying Hamilton's principle of stationary action to the PCC yields a dimensionless-action formulation of the Feynman path integral. Therefore, both the probabilistic and dynamical contents of quantum mechanics follow from a single-phase condition.
Category: Quantum Physics

Aliquot Spectral Basis

Authors: Walter A. Kehowski
Comments: 9 Pages.

The author observed belatedly that {9,4} is the spectral basis of n=sigma(9)−1=12, where sigmau2032(9)=sigma(9)−9=4, the aliquot sum of 9. The author provides examples of m such that {m,sigmau2032(m)} is the spectral basis of n=sigma(m)−1, called the aliquot spectral basis of n.
Category: Number Theory

Is a Spontaneous Contraction of the Universe Thermodynamically Possible?

Authors: Fernando Salmon Iza
Comments: 4 Pages.

In this work, we study the expansion and contraction of the cosmic fluid from a thermodynamic perspective. We make general considerations about both processes by calculating their Gibbs free energy function and analyzing its sign. The sign determines whether the process is spontaneous or non-spontaneous. The result is that, while the expansion of the universe is a spontaneous process at any temperature, the contraction process is not. To carry out this study, we derive an equation that relates the entropy generated by these processes to the redshift and the adiabatic index. Using this equation, we calculate the Gibbs free energy function, studying the spontaneity of the expansion and contraction processes. The result is that, while the expansion process is always spontaneous, the contraction process is never spontaneous, requiring external energy to make it possible.
Category: Relativity and Cosmology

Branch-Dependent Proper Time

Authors: Oleg Ponfilenok
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) https://github.com/oponfil/branch-dependent-proper-time

We propose tying the fundamental scale of gravitationally induced space-time blurring to proper time rather than to spatial length, and postulate that, under an ensemble reading of the quantum state in which each branch carries its own world line, proper-time fluctuations are statistically independent across branches. Interference is sensitive to the difference of branch phase contributions; with independent clocks this difference accumulates at the frequency ω_eff = E_br/ℏ. For a composite system we define branch-sensitive energy operationally after removing the Hamiltonian sector common to both branches and measuring the remaining split-sector energy from its physical vacuum or ground state. This prescription is invariant under a global shift of the total Hamiltonian. It yields V/V_0 = exp(−χ) with χ ∝ m² t^(2/3) for a centre-of-mass interferometer. Confronted with sodium-nanoparticle interferometry of the Vienna group, this gives an upper bound ξ ≲ 1.1. A decisive test is near: at m ~ 1 MDa and v ≈ 25 m/s the model predicts practically complete loss of interference, whereas standard quantum mechanics expects measurable fringes.
Category: Quantum Physics

Introduction to First Mechanics: Physics Presuppositions

Authors: Deng Ke
Comments: 30 Pages.

Traditional theoretical physics typically only describes phenomena, rather than investigating mechanisms, or examines surface mechanisms without deeply investigating causes. This paper attempts to investigate the causal level of physics, to discuss a kind of First Mechanics—a foundational system that takes quantity of occupation and its substitution motion as its object of study, explaining phenomena rather than merely describing them, and constructs a corresponding formal mathematical system—in order to supplement the foundational theories of traditional physics. From this, the topic of dynamicity is discovered. Finally, from the study of Quantity of Occupation, spatial dimensionality is discovered, and from spatial dimensionality and unknown phenomena, the Unsolvability Principle is discovered: namely, that we are uncertain about everything. After the main text, a hypothesis explaining dynamicity is appended.
Category: History and Philosophy of Physics

Reductiones ad Absurdum of the "P Versus NP Problem" and P = Np/ap/ch

Authors: Deng Ke
Comments: 17 Pages.

There exist latent meta-axioms concerning propositions in mathematics that are often overlooked. A discussion of these axioms simultaneously brings to light the secondarity of mathematics with respect to reality. Applying one of these axioms to the "P/NP problem" can reduce the problem to absurdity; however, precisely due to this secondarity of mathematics, such a dissolution can only ever be a "dissolution" rather than a "solution." To approach the "P/NP problem", we again adopt a reductio ad absurdum method: understanding the limitations of polynomial-time algorithms and identifying such limitations within NP-complete problems, thereby obtaining P≠NP. Extending this reductio from the specific contradiction between polynomial-time algorithms and NP-complete problems to the more general contradiction between guarantee of winning and symmetric mutually-exclusive games, we arrive, in the computational and purely logical domains respectively, at the conclusions P≠AP and P≠CH.
Category: Set Theory and Logic

Introduction to Neo-Agnosticism: Ontological Reductio ad Absurdum and the Omniscient Drive

Authors: Deng Ke
Comments: 12 Pages.

The critique of idealism has long centered on its failure to recognize the primacy of practice—that is, the materialist critique. This paper discusses a non-materialist critique of idealism, one that proceeds solely from the internal logic of idealism itself, without invoking the primacy of practice. This critique operates at the level of transcendental logic, and its core method is reductio ad absurdum: it confirms the existence of an unknowable term that can affect "knowable" terms, and thereby demonstrates that reasoning based solely on "knowable" terms is philosophically illegitimate. After carrying out this critique, the method is abstracted to reveal its universal applicability—not only to idealism, but to all current ontologies. All existing systems of thought harbor an illegitimate intermediate state in which they tolerate the non-omniscient while claiming partial knowledge, a state exposed by this reductio. Consequently, all philosophy must arrive at a more radical ontological posture—agnosticism. Because this agnosticism, derived through ontological reductio, differs from traditional agnosticism, it is termed Neo-Agnosticism. Finally, since critique requires an anchor point of "known correctness," it is shown that Neo-Agnosticism is statically and logically necessarily connected to an Omniscient Drive.
Category: General Science and Philosophy

Origins of Nonlinear Physics

Authors: Terry J. McMahon
Comments: 9 Pages.

Nonlinear physical processes arise via dimensional parameters scaling with energy. Parameter dimensions determine the scaling character at speed of light c, and at velocities < c. Reducing dimensional analysis to time and length dimensions only, resolves this scaling paradigm. A mode change occurs for running parameters for wave-particle velocities < c, consistent with symmetry breaking, where scaling is determined by the exponent on the length component. The fine structure constant alpha is found to have dimensions Hz, requiring dimensional amendments to a number of fundamental parameters. The gravitational constant G is found to have dimensions m-1, implying that gravity is not a force. Gravity is shown to have dimensions of linear density. Running parameters ought to resolve multiple anomalies within the standard model, leading to unification of gravity with electromagnetism.
Category: Quantum Physics

Primordial Code in the Universe

Authors: Terry J. McMahon
Comments: 20 Pages. Part 2 of a series

Dimensional analyses identify running modes for dimensional parameters. Relationships with the gravitational parameter G introduce an apparent primordial code, designated the ‘interaction constant’ for now, which appears to be embedded within every wave-particle duality, process and interaction. Dimensional parameters are emergent from this interaction constant. Least energy occurs at speed of light (c) for quantum wave-particles (wavicles). Wavicle-specific, dimensional quantum parameters scale mostly linearly at c with energy. Scaling becomes non-linear < c for many parameters (including mass, gravity, and the Planck ‘constant’), synonymous with symmetry breaking. This feature of the standard model ought to resolve dark matter. Quantum wavicles appear to be fractally related. Gravity is emergent, forming the spatial field interaction with matter, contracting locally, which unites with quantum theory. Multiple constants are amended and several new relationships introduced. These amendments to the standard model, with the ubiquitous interaction constant embedded as a primordial code, are invariant under multiple systems of simultaneous assessment. A finely tuned, encoded universe with emergent parameters, is inconsistent with a chaotic big bang cosmology.
Category: Quantum Physics

Loop Diassociativity Has no Finite Basis

Authors: Warren D. Smith
Comments: 13 Pages. Paper on www since 2004, now uploading to VIXRA for archival purposes.

No finite set of equations characterizes diassociativity in either finite or infinite loops. This settles a 52-year-open problem.
Category: Algebra

Inclusions Among Diassociativity-Related Loop Properties

Authors: Warren D. Smith
Comments: 15 Pages. On www since 2004, now uploading to VIXRA for archival purposes.

We attempt to find all implications among 19 commonly used diassociativity, Moufang, Bol, alternativity and inverse-related properties in loops. There are 6 among these that appear to be valid in finite but not infinite loops. Under that assumption, we completely settle the problem. We study in detail the apparently-simplest among the 6 nasty cases: the "LRalt⇒2SI" question of whether a left- and right-alternative loop necessarily has 2-sided inverses. We construct an infinite loopin which this is false. However, X must have a 2-sided inverse in any LRalt loop with ≤50 elements or in which Xⁿ=1 with n≤13 – results suggesting this is the case in all finite loops. The problem of fully resolving this might be the hardest natural problem in mathematics that is this simply posed!
Category: Algebra

Secrets Of Sphere Packings And Figurate Numbers

Authors: Joerg Moesch
Comments: 70 Pages.

This paper is about the arrangement and stacking of equal-sized spheres into geometric figures, and the sequences an remarkable yet largely unknown insights that can be obtained as a result.
Category: Number Theory

Pi is Irrational: Without Words

Authors: Timothy Jones
Comments: 1 Page.

Venn diagrams show an argument for the irrationality of pi.
Category: Geometry

Thermonuclear Fusion

Authors: Vladimir Pastushenko
Comments: 9 Pages. (Note by viXra Admin: Please cite listed scientific references)

A new technology for space-matter theories is presented, the limiting case of which is the technology of Euclidean space-time axiomatics. Within the framework of this technology of theories, the difficulties of existing problems of thermonuclear fusion are presented and new principles of thermonuclear fusion are proposed.
Category: Nuclear and Atomic Physics

Triunism

Authors: D. J. Larson
Comments: 30 Pages.

Western civilization rests on foundational belief systems of religion, philosophy, and science that once pursued a unified truth. Over recent centuries, science rose to dominate over philosophy and religion as new observations challenged old paradigms and technological advances delivered many benefits. Commitments to objective reality, God, and the immortal human soul gradually yielded to a worldview in which scientific formulas and empirical tests became the dominant path to knowledge. Truth came to be seen as a human construct shaped by power. In many intellectual circles, Christianity is now viewed as an outdated and sometimes dangerous myth.This paper traces the historical path that led to the present dominance of nihilistic, monistic, materialistic, atheistic, relativist instrumentalism, including the role science has played in appearing to support these philosophical positions. It then discusses the many unsolved problems in presently dominant science and philosophy.Triunism is presented as a return to objective reality, Christianity, and a single coherent truth. Its ontology consists of a primary triune of absolute space, absolute time, and matter. Within matter lies a secondary triune: M1 (ordinary matter), M2 (aetherial matter), and M3 (spiritual matter). The human being is understood as an M3 immortal soul united to an M1 body during earthly life, with the soul surviving bodily death. M3 interacts with M1 through preferential collapse of quantum states, enabling genuine free will while preserving M1 conservation laws.The paper discusses how a return to absolute theory and an aetherial M2 is consistent with existing scientific data. It notes that science deliberately excludes M3 from its experiments; physics therefore finds no evidence of M3. This absence leads to the mistaken materialist conclusion that M3 (including God and the soul) does not exist. The paper presents ample positive evidence that M3 does exist, including evidence for the soul. The life, death, and Resurrection of Jesus Christ, along with arguments concerning the existence of God, are also discussed. Finally, the paper discusses how Triunism offers promising solutions to many persistent problems in physics and philosophy.Triunism is not a finished product. What is offered here is a foundation, not an encyclopedic replacement. Much work remains.By recovering metaphysics, objective reality, and a spiritual M3, Triunism addresses many vexing problems while providing a path toward reuniting physics, philosophy, and Christianity under the pursuit of a single coherent truth.
Category: General Science and Philosophy

Particle Flow Model for Diffraction and Its Experimental Verification

Authors: Jiankun Lai
Comments: 24 Pages.

To explore the evolutionary law between single-filament diffraction fringes and double-slit diffraction fringes, a self-made experimental device with dynamically and symmetrically adjustable slit widths was adopted to carry out comparative laser diffraction experiments. (Background) Single-filament and double-slit diffraction have long lacked a unified particle-based theoretical framework to explain fringe evolution[1][2][3][4][5]. (Methods) Self-adjustable double-slit equipment and three sets of comparative optical experiments were designed, together with a complete set of dynamic mathematical derivation based on near-field electromagnetic gradient force. (Results) The experimental results show that double-slit diffraction fringes can be continuously evolved from single-filament diffraction fringes, and both have the structural characteristics of enveloping fine fringes. The particle flow model derived in this paper can uniformly explain the diffraction laws of photons and electrons, which is highly consistent with measured data. (Conclusions) This particle-trajectory interpretation provides a new theoretical perspective for basic optical experiment teaching and diffraction mechanism research. Based on the local near-field interaction characteristics of microscopic particles, a particle flow model with particle trajectory deflection is established. Starting from the action mechanism of near-field electromagnetic gradient force, a complete set of mathematical and physical relational expressions for particle deflection angle, transverse momentum increment and diffraction fringe spacing are derived. Model parameter calibration and self-consistency test are completed by using measured xperimental data. Two groups of differentiated comparative experiments prove that microscopic particles have definite propagation paths when passing through obstacles. The established particle flow model can coherently explain the diffraction imaging laws of photons and electrons uniformly, and is highly consistent with the measured fringe changes. It can provide new reference ideas and theoretical interpretation perspectives for the research on physical mechanism of diffraction and physics experiment teaching.
Category: Quantum Physics

Quantum is Composite

Authors: Asutosh Kumar, Vishal Arya
Comments: 11 Pages.

The wave-particle duality of light and matter remains a cornerstone of quantum mechanics.The Standard Model of particle physics defines both the photon and the electron as strictly elementary, indivisible point particles. In this paper, we propose a composite model of quanta wherein these purported elementary particles are composed of multiple, underlying vibratory entities. We introduce a topological wave-packet framework and examine how this sub-structural hypothesis can naturally recover wave-particle duality by explaining the wave and the particle phenomena of light simultaneously without changing models, address theoretical singularities, and propose potential testable predictions. We also consider the physical reason and origin of the relativity of mass and energy, and the physical meaning of Planck's constant within this framework.
Category: Quantum Physics

Adaptive-Dynamic Gravitational Field of the Solar System Consistent with Conservation Laws and Physical Reality

Authors: Pavlo Danylchenko
Comments: 6 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. It is because of this that gravitational pseudo-forces, like centrifugal pseudo-forces of inertia, are orthogonal at all points to the quasicircular (pseudo-elliptical) orbits of the planets.. 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 proven. The inconsistency of elliptical orbits with the law of conservation of angular momentum is substantiated. Spatial distributions of potentials and strength of the adaptive-dynamic gravitational field along the quasicircular 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

Relativistic Geometrical Horizons in the 3D Spherical Natario Warp Drive

Authors: Fernando Loup
Comments: 42 Pages.

In 1994 Alcubierre developed the first warp drive work using the original 3+1 ADM-MTW formalism.Seven years later in 2001 the same original 3+1 ADM-MTW formalism appeared in thefirst part of the second warp drive work developed by Natario. But in 1997 the concept of the Relativistic Geometrical Horizon RGHwas introduced by Hiscock in his work about the Alcubierre warp drive. According to Hiscock if the time component of a given spacetime metric tensor becomes null g_(00)=0 a Horizon similarto the Event Horizon of the Schwarzschild black hole appears. Hiscock computed the Relativistic Geometrical Horizon RGH for the Alcubierre warp drive.We present in this work the RelativisticGeometrical Horizon RGH for the 3D version of the Natario warp drive with both constant and variable speeds.Remember that a real spaceship is a 3D object and a spaceship must accelerate or de-accelerate in order to be accepted as a physical valid model. Due to the presence of three spatial dimensions the g_(00)=0 never appears however in a dimensional reduction from a 3+1 spacetime to a 1+1 spacetime the Relativistic Geometrical Horizon RGH g_(00)=0 appears again.
Category: Relativity and Cosmology

Light Through the Geometric Memory of Spacetime: Optical Signatures in Gravitational Lensing

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

This work proposes an alternative way to think about gravitational lensing. Instead of assuming that weak-field spacetime geometry responds instantly to baryonic matter, it proposes that geometry needs a finite time to relax to its new configuration. From this perspective, part of the lensing signal may come from light traveling through a residual geometric "memory": spacetime curvature that has not yet fully relaxed to the current baryonic distribution. The manuscript develops this idea and tests it with weak lensing, strong lensing, and colliding galaxy clusters.
Category: Relativity and Cosmology

Proving & Teaching Collatz Conjecture

Authors: A. A. Frempong
Comments: 18 Pages. Copyright © by A. A. Frempong

Collatz conjecture states that beginning with a positive integer, if one repeatedly performs the following operations to form a sequence of integers, the sequence will eventually reach the integer one; the operations being that if the integer is even, divide it by 2, but if the integer is odd, multiply it by 3 and add one; and also, use the result of each step as the input for the next step One would note the patterns of the sequence terms as the Collatz process reaches the equivalent powers, 2^(2k) (k = 2, 3,...) and the sequence reaches the integer 1 by repeated division by 2. Two main cases are covered. In Case 1, the integer can be written as a power of 2 as 2^(k) (k=1,2,3,u2026), and in this case, the sequence would reach the integer one by repeated division by 2, i.e., 2^(k-1), 2^(k-2), 2^(k-3,),u2026,2^(k-k). In Case 2, the integer cannot be written as a power of 2, but the sequence terms reach the equivalent power, 2^(2k) (k = 2, 3,...) and by repeated division by 2, the sequence will reach the integer 1. In Case 2, when the sequence terms reach some particular integers such as 5, 21 and 85, the application of 3n + 1 to these integers will result in the powers, 2^(2k). One would call these integers, the 2k-power converters. There are infinitely many 2k-power converters as there are 2^(2k) powers. There are infinitely many paths for converting integers to 2^(2k) powers. Of these paths, the integer 5-path, is the nearest 2^(2k) converter path to the integer 1 on the 2^(2k)-route. Other integers can follow the integer 5-path to 16 as follows: Let n be an integer whose sequence terms would reach 16, and let n ± r = 5, where r is the net change in the sequence terms before the integer 5; and one uses the positive sign if n<5, but the negative sign if n > 5. One will call the following, the 5-path 2k-converter formula: 3(n ± r) + 1 = 16. By the substitution axiom, using this formula, the sequence of every positive integer that cannot be written as a power of 2, would reach the integer, 16, and continue to reach the integer 1. Therefore, the sequence of every positive integer would reach the integer 1.
Category: Number Theory

The Mystery of the Gravitational Constant G: The Greatest Metrological Impasse in History, or Evidence That Gravity Is More Complex Than Newton Thought?

Authors: Mykola Kosinov
Comments: 10 Pages.

The "Big G" problem remains an unsolved mystery in modern metrology and physics. Scientists have yet to obtain a precise value for the gravitational constant. Various laboratories use impeccable equipment that achieves record-breaking measurement accuracy, yet their results consistently diverge beyond the permissible error margins. It is shown here that the problem of the gravitational constant G is directly related to the incompleteness of the Newtonian model of gravity. The gravitational constant G refers to the gravity of the entire universe—this is its fundamental meaning. However, "Big G" is calculated from Newton's law of gravity, which does not take into account the gravity of the universe. Using the local law of two-body gravity F = GmM/r^2 without taking into account the gravity of the enormous mass of the universe leads to an error. To eliminate this error, it is proposed to use the law of gravity FU = GmM/r^2 + (mc^2)√Ʌ, which takes into account the gravity of the universe. It has been shown that the discrepancy between the values of G lies in the fact that the second component of the gravitational force, (mc^2)√Ʌ, is not taken into account when calculating it. This leads to a shift in the values of G by varying amounts, depending on the contribution of the second component, (mc^2)√Ʌ. The measured value of the constant G depends not only on technical limitations but also on how adequately the physical law from which it is calculated describes gravity.
Category: Classical Physics

How Gravity's Puzzles Enticed Some of the Greatest Physicists into Mistakes

Authors: Jonathan J. Dickau, Steven K. Kauffmann, Stanley L. Robertson
Comments: 12 Pages.

Einstein's ponderings on gravity led in 1907 to his principle of the equivalence of gravitation and inertia, illustrated by his famous elevator prop. For Newtonian gravity, it is impeccable. But his elevator illustration of gravity's bending of light implicitly allows light to be accelerated to a speed greater than c, violating his 1905 Lorentzian relativity. In 1913, Einstein decided that general relativity supplants Lorentzian relativity, and proceeded to his famous gravity theory. But his Einstein equation has no unique solution, hampering his effort to explain Mercury's perihelion precession. He overcame that obstacle in 1915 with a simple Lorentz-invariant coordinate condition which isn't mentioned in textbooks, honoring his insistence that coordinate conditions are irrelevant. Friedmann, also honoring that insistence, found a new coordinate condition in 1922 that can make the Einstein equation easier to solve; it was eagerly adopted by cosmologists. But it makes gravity essentially Newtonian, which is drastically wrong at high redshifts. In 1962, Feynman elucidated general relativity's physical role in gravity theory; it generates the gravity field's self-interaction in the context of an action principle, which is a fundamental prerequisite for quantization. But Feynman missed the very large constant in that action, the key to gravity's classical-field nature and the absence of gravitons, so he tried quantum-gravity perturbations, which are a physical dead end.
Category: Relativity and Cosmology

Growth Versus Equity in a Stochastic Multiplicative Wealth Model: the Cost of Redistribution and the Emergence of an Inequality Laffer Curve

Authors: Renato Vieira dos Santos
Comments: 12 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

A stochastic multiplicative wealth model with taxation and redistribution is extended to include two channels through which fiscal policy can reduce the economy's average growth rate: productive disincentive (a taxu2011dependent mean return) and administrative inefficiency (loss of part of the collected revenue). For uniform redistribution, the stationary density of normalized wealth remains an inverseu2011gamma law, but its shape parameter acquires a richer dependence on the tax rate. The central finding is the emergence of an emph{inequality Laffer curve}: when the disincentive is sufficiently strong, the Gini coefficient first decreases, reaches a minimum at a finite tax rate, and then increases again as taxation intensifies. In the extreme limit the stationary state collapses back to the condensed phase, restoring the oligarchic transition. Both channels also create a direct tradeu2011off between inequality and longu2011run average wealth, giving rise to a welfareu2011maximizing tax rate. The two channels are combined into a single analytically tractable model, and all predictions are validated by agentu2011based simulations. The results show that the qualitative existence of an optimal tax rate is robust whenever the aggregate growth rate responds to fiscal policy, while the inequality Laffer curve is a specific prediction of the productiveu2011disincentive channel.
Category: Condensed Matter

Dual Architecture in Yang-mills Theory: Algebraic Regularization, Wightman Axioms, and Mass Gap

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

This article presents the Dual Architecture, an algebraic regularization method for divergent integrals in quantum field theory. The method rests on two functions defined over complementary domains: the Euler integral for the Gamma function over the positive real axis, and a companion integral over the negative real axis. When one integral representation diverges, its dual converges, and the regularized value is taken as the reciprocal of the convergent one. The sign alternation is encoded by an entire function without zeros on the negative real axis. Applied to Yang-Mills theory with gauge group SU(N), the method demonstrates the existence of a mass gap persisting to all orders of perturbation theory. The perturbative series of the Dual Architecture converges absolutely because the regularized Gamma values at negative integers decay factorially, in contrast to the factorial growth of the traditional Dyson series. Evidence for the proposal comes from two independent anomalies that the established method leaves unexplained. The first is a residual error in the WKB expansion of the quartic anharmonic oscillator, computed numerically to high order and documented in the literature. The second is the sign of the vacuum energy density, which the traditional analytic continuation yields as negative, contradicting the observed accelerated expansion of the Universe. The Dual Architecture corrects both anomalies, and they share a common origin in the same negative half-integer argument of the Gamma function. The method eliminates the renormalization scale because integrals are evaluated directly in four dimensions, producing finite values without pole subtraction. Correspondence with quantum electrodynamics at one loop is verified. The Wightman axioms are satisfied.
Category: Mathematical Physics

There is Nothing Beyond the Edge of the Universe — What Does that Mean ?

Authors: Henok Tadesse
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references other than the author's own!)

Imagine a finite universe. This view raises the questions: what exists beyond the edge of the universe? What does it even mean by the edge of the universe? Many physicists say that there is nothing beyond the edge of the universe, without comprehending what they mean by this. We propose a solution to this incomprehensible puzzle as follows. The universe is made of finite amount of matter contained in a finite spherical volume of space. What would happen to a spacecraft going to the edge of the universe for exploration? As the spacecraft goes far outside this sphere, it experiences that space gradually loses its property with increasing distance from matter. The permittivity and permeability of space continue to decrease with distance from matter. The electrostatic forces between and within atoms and molecules of the spacecraft gradually decrease, and eventually diminish to zero, at which point the atoms, molecules and elementary particles that make up the spacecraft and thereby the spacecraft eventually 'dissolve' and go out of existence. We propose this to be interpretation of the statement that there is nothing beyond the edge of the universe. No matter, no space exists outside the universe. We propose that matter and space have no independent existence.
Category: Relativity and Cosmology

Geometrized Vacuum Physics. Part 14: "The Hydrogen Atom"

Authors: Mikhail Batanov-Gaukhman
Comments: 42 Pages.

This article is the fourteenth part of the scientific project under the general title "Geometrized Vacuum Physics Based on the Algebra of Signature" (GVPh&AS) [1,2,3,4,5,6,7,8,9,10,11,12,13]. In this article, the stochastic metric-dynamic model (SMDM) of the "hydrogen atom" is considered, constructed on the basis of the principles and mathematical apparatus of GVPh&AS. A similar methodology can be applied to study the internal structure of all known "atoms" and "molecules" of both the picoscopic level of matter organization (~10^—11 — 10^—14 cm), and other levels: microscopic, planetary, galactic, etc. A stochastic Schrödinger equation for the "hydrogen atom" with effective potentiality is proposed, which may allow for a refinement of the fine structure of the emission spectrum of this stable vacuum formation without the use of radiative corrections. A distinctive feature of the SMDM from the quantum mechanical approach (in the Copenhagen interpretation) is that the mathematics of the GVPh&AS allows for the creation of a visual simulation of intra-atomic processes in a form convenient for our perception, i.e., as if peering inside the "atom" and mentally observing the cosmic grandeur of the processes occurring there.
Category: Nuclear and Atomic Physics

Mostly-Destructive Consequences of Non and Nowhere Analyticity of the Spacetime Metric; and New "2-Sided Mirror Paradigm" Hypothetical Grandiose Universe Picture

Authors: Warren D. Smith
Comments: 34 Pages.

We explore consequences of my previous discovery (http://vixra.org/abs/2605.0004 Smith 2026) that Einstein general relativity vacuum solutions are not necessarily real-analytic, and indeed can be (hence presumably generically are, since the analytically-smooth spacetime metrics form an infinitesimally tiny subset of the much wider class of permitted functions) nowhere-analytic. These consequences are hugely destructive for many former physics ideas that implicitly or explicitly assumed analyticity – such as "ER=EPR," "AdS-CFT," or "maximal analytic extensions" – and I will duly obliterate them! A Monte Carlo estimate is that 1-20 thousand general-relativity papers are invalidated. However, in an unexpected brief creative interlude during that apocalyptic demolition, I invented the promising new "mirror paradigm," which might be crazy, but if valid offers a simple nice way to resolve most or all famous "paradoxes" associated with black holes, and also provides a whole new mental picture of the entire universe. Amazingly, I found out soon after posting v1 that almost exactly the same idea (under the name "black mirror") was invented independently 1.5 years before by Tzanavaris, Boyle, and Turok (TBT) although mostly for different reasons. At the end I attempt to reconcile all Smith-versus-TBT discrepancies while showing all apparent obstacles to this picture are only apparent, to produce a mirroring hypothesis we hopefully all can agree is the right proposal and makes sense. I also, surprisingly, make new observations even about the hugely-studied Schwarzschild/Kruskal black hole, including proposing arguably-local metrical tests for event-horizons (a feat often claimed impossible by prior authors).
Category: Quantum Gravity and String Theory

Plank’s Constant

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

Multivectors change the paradigm of electromagnetic theory. Multivectors derive not only Maxwell's equations but also energy density, Poynting vectors, Joule heat and electromagnetic force solely through calculation without the aid of experimental laws. Moreover, this process can be repeated three more times by changing the dimension of multivector in 4-dim. And these four Maxwell equations tell us what charge, spin, quarks, and mass are. The 2-vector rotor and booster transform the coordinate system and derive the ladder operator without quantum mechanics. The commutative relation of the angular momentum operator, the uncertainty principle, and the reason photons can be counted in the photoelectric effect are explained by the infinitesimal rotor and booster. These three phenomena, including Planck's constant, indicate that the infinitesimal rotor and booster are always operating. The universe is vibrating, and the current magnitude of cosmic background vibration is Planck's constant.
Category: Quantum Physics

Self-Approximation for Riemann Hypothesis

Authors: Payam Danesh, Raoul Bianchetti
Comments: 6 Pages.

We present a rigorous formulation of that idea through shifts generated by the continuous Gram function. We study the set of parameters τ for which ζ( s+itτ) uniformly approximates ζ( s) on compact subsets of D with connected complements. The method is based on Gram-shift universality, weak convergence of probability measures on the space of analytic functions and the support theorem for the random Euler product. The support is precisely the analytic functions that vanish nowhere in D and the identically zerofunction. This structure leads to two precise equivalences: The Riemann hypothesis is true if and only if the Gram-shift self-approximation holds with positive lower density for each admissible compact set and each approximation radius; and equivalently, when the limiting density exists and it is positive except at mostcountably many radii.
Category: Number Theory

Pi-Greek

Authors: Rolando Zucchini
Comments: 13 Pages.

This paper reports the most significant studies on the knowledge of Pi-Greek. The number that has stimulated mathematicians throughout the centuries, from Archimedes to Descartes to Euler. It was the numerous attempts to prove the squaring of the circle that led to increasingly precise approximations of Pi. The proofs continued even after the Royal Academy of Sciences in Paris, in 1775, abandoned examining the many alleged "solutions" to this problem. The irrationality of π was demonstrated by Ferdinand von Lindemann in 1882. This article is mainly a historical research on the number Pi-Greek.
Category: Number Theory

Nuclear Shell Model Composed of Spin-coupled Dinucleon

Authors: Naili Cui
Comments: 6 Pages.

This paper constructs a Nuclear Shell Model composed of spin-coupled dinucleon nuclei. Using pn (proton-neutron) and nn (neutron-neutron) pairs formed by antiparallel spin coupling as the basic structural units of the atomic nucleus, a shell model isomorphic to the outer electron orbitals is established. By comparing the microscopic orbital configurations of various typical magic number nuclei, the formation of magic numbers is explained from the perspective of nuclear structure. This paper distinguishes between orbital shell configurations and the actual steady state of the atomic nucleus, thus resolving paradoxes that magic number models cannot explain, such as the instability of certain double magic number nuclei and the stability of isotopes in non-magic number nuclei. Research shows that a complete inner neutron cores is a necessary condition for maintaining the stable state of the atomic nucleus. Magic numbers merely represent the geometric characteristics of fully occupied orbitals and cannot be used as a standard for judging nuclear stability. This model can construct a unified nuclear shell system applicable to nuclei within the magic number range without the need for artificial fitting of empirical parameters, providing a new theoretical framework for studying nuclear structure and isotope stability.
Category: Nuclear and Atomic Physics

Parametric Mathematical Model for the Human's Brain Global Shape

Authors: Jérôme Chauvet
Comments: 17 Pages.

Using two generative key components, i.e. self-similarity and sigmoidal functions, we showhow to build an idealized artero-veinous system that accurately encompasses the cortical hull of a human brain measured on real patient through angiographic imagery. Our algorithm, based on the constructal principle, demonstrates that, despite the complexity and sophistication of the human cerebral organ, it appears possible to gauge its general morphology by means of a theoritical model justified with pure mathematical approach and biophysical arguments. Our result might as well fit for both medical purpose and studies in evolutionary neuroscience.
Category: Quantitative Biology

Some Remarks on the Riemann Hypothesis, Concerning the Zero-Finding Theorem II

Authors: Holger Döring
Comments: 22 Pages.

At first, this second description also is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical, more physical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory.
Category: Mathematical Physics

Inverse of the Square Wave Matrix

Authors: David J. Grabiner, Warren D. Smith. Sushanta Srivastava
Comments: 5 Pages. Based on At&T Bell Labs tech report we wrote in 1989, now uploaded to VIXRA for archival purposes.

The FFT (Fast Fourier Transform) is a very important conversion of a N-datapoint digital signal into a linear combination of Fourier waves (or vice versa) than can be implemented algorithmically in O(NlogN) operations. This paper describes a different signal↔wave conversion that also runs in O(NlogN) operations, but now involving "square waves."
Category: Digital Signal Processing

Rating Systems for Gameplayers, and Learning

Authors: Warren D. Smith
Comments: 20 Pages. Based on my 1984 bachelor thesis at MIT and the basis for the rating system used by the "internet chess club." Now uploaded to VIXRA for archival purposes.

This report studies rating systems: systems that produce quantitative measures, called "ratings," of the ability of players in a league, based on game results. By "quantitative,", it is meant that win odds for a game between two players in the league may be estimated from their ratings. We consider both "static" and "dynamic" systems. The latter update the ratings after each game. Attention is given to noise in rating systems and to thedistribution of ratings in the player population. Some real-world data is also included. This subject may be of interest to gamblers, gaming leagues, psychologists, consumer groups, and industry.
Category: Statistics

Prompt Injection Attacks in Large Language Model Systems: Threats, Mechanisms, and Defense Strategies

Authors: Iqra Zulfiqar
Comments: 7 Pages.

AI systems based on Large Language Models are now everywhere, from chatbots to autonomous agents that can book flights, send emails, and make financial decisions. But this power comes with a serious problem.These models cannot tell the difference between real instructions and fake ones hidden inside data. Attackers exploit this weakness through what researchers call prompt injection attacks. This paper reviews how these attacks work, what damage they can cause, and what defenses exist today. We look at different attack types, from simple text tricks to complex automated attacks that spread across multiple AI agents. Wealso review what current defenses can and cannot do. The conclusion is not comfortable: no defense today fully solves the problem, and the attacks keep getting smarter.
Category: Artificial Intelligence

Electrohydrodynamic Wind Generation in Planar DBDs: Role of Electrode Symmetry and Geometry

Authors: Farshad Sohbatzadeh, Saeed Ranjbar Malekshah, Hamed Soltani Ahmadi, S. Mirzanejhad, Ramin Mehrabifard, Samira Mavvadati, Zdenko Machala
Comments: 19 Pages.

This study experimentally and numerically investigates the electrohydrodynamic (EHD) interaction induced by a surface dielectric barrier discharge (SDBD) actuator at atmospheric pressure. The EHD effect, driven by non-thermal plasma in a dielectric barrier discharge (DBD), generates ionic wind, which is characterized here for a symmetric annular-type DBD actuator. A symmetric annular-type DBD actuator, consisting of concentric ring—disk electrodes that generate a predominantly vertical ionic wind rather than a tangential jet. Despite extensive studies on linear and tangential SDBD actuators, the influence of annular electrode geometry on vertically induced ionic wind and associated ozone generation remains insufficiently explored. We analyze the induced wind velocity perpendicular to the electrode plane, focusing on the influence of geometric parameters—electrode diameter (D) and thickness (δ)—on performance. Experimental results reveal a maximum wind velocity of 3.42 m s−1 ± 1% for an optimized configuration (D = 32 mm, δ = 0.06 mm), corroborated by numerical simulations. The simulations further elucidate the velocity profile, volumetric force, electron temperature, and gas pressure distribution within the plasma region. Complementary diagnostics, including O3 concentration measurements and Schlieren imaging, demonstrate that larger electrode diameters (e.g., 32 mm and 22 mm) enhance vertical flow height but concurrently increase ozone production. These findings provide actionable insights for designing DBD-based systems in applications such as plasma flow control, air purification, and biomedical plasma technologies.
Category: Nuclear and Atomic Physics

Delegated Agency and Moral Responsibility in Artificial Intelligence

Authors: Petar Radanliev
Comments: 53 Pages.

Across historical contexts, artificial agents exhibit consistent structural features: bounded autonomy, delegated authority, explicit override mechanisms, and dependence on human oversight. These features directly correspond to contemporary AI ethics concerns, including alignment failures, responsibility gaps, human-in-the-loop control, and system interruptibility.
Category: General Science and Philosophy

Cryptography, Romance, and War

Authors: Petar Radanliev
Comments: 49 Pages.

The study develops a four-component model of cryptographic intimacy, Exclusive Sharedness, Double Audience, Adversary Ecology, and Cultural Scripting, and articulates five propositions explaining how secrecy practices adapt to risk, coordination cost, temporal ethics, and power asymmetry. These patterns recur across historical, literary, and technical domains as structured responses to threats against intimacy.
Category: Social Science

Plumbing the Pudding Model of the Atom

Authors: Eric Stanley Reiter
Comments: 11 Pages.

We will explore in this sequence: 1) the experimental evidence initiating the nuclear model, 2) ER’s (author) experimental repeat, 3) threshold model vs quantization, 4) ER’s past experiments with gamma ℽ and alpha α rays, 5) ER’s recent tests splitting the α upon a crystal surface, and 6) conclusion. In addition to a serious challenge to quantization, this report reveals how so-called nucleons can diffract. We know of experiments that show what appears to be nucleon interference (1, 2). If you do not think this is a problem, please read up on the measurement problem. The short answer to this problem is: if it diffracts, it is a wave. We explain particle-like effects as thresholds.
Category: Quantum Physics

Charge Quantization, the Topology of the Universe, and the Hopeful Abolition of Monopoles

Authors: Warren D. Smith
Comments: 18 Pages. Paper on internet since 2000, now uplaoded to VIXRA for archival purposes.

This is the first of a 3-part series of papers on "the shape of the universe." Inspired by P.A.M.Dirac's discovery that the existence of even one "magnetic monopole" would logically force electric charge to be quantized (explaining why all electrons have the same charge, protons the exactly-opposite charge, etc), I show that a tiny magnetic field "trapped in the topology of the universe" also would logically force that. Which universes does this idea work in? We show it works for every compact 3-manifold topology for the universe except two. We then re-examine monopoles, showing their existence would cause a lot of nasty problems, and none have ever been detected.
Category: Relativity and Cosmology

On the Shape of the Universe

Authors: Warren D. Smith
Comments: 10 Pages. Paper on internet since 2003, now uplaoded to VIXRA for archival purposes.

This is the second of a 3-part series of papers on "the shape of the universe." Bright objects such as quasars are observed to be uniformly distributed on the sky-sphere. We prove a theorem that if this is true for almost every observer-location (i.e. the location of the Earth is not special in this respect) then the universe must be a "harmonic manifold." We also argue that the universe must be an orientable 3-manifold not containing any closed geodesic whose traversal causes "twist." We also discuss incompletely-convincing evidence that the universe contains a nonzero finite number of short closed geodesics passing through the Earth. If that is genuine, we prove our assumptions winnow down the possible topologies for the universe to only 3 possibilities: "flat 3-torus" and its degenerate versions with some paralelipiped sidelengths infinite.
Category: Relativity and Cosmology

Discrete Random Variables

Authors: Teo Banica
Comments: 400 Pages.

This is an introduction to probability and discrete random variables. We first discuss games, counting and basic probability, with the mathematics of the binomials and factorials recalled, and with everything explained with numerous illustrations. Then we get into the theory of discrete random variables, with the basic theory explained, with illustrations, notably with results about the binomial and Poisson laws. Then we discuss more advanced distributions, such as the Bessel, hypergeometric and beta binomial ones, with methods from both algebra and analysis. We end with an introduction to continuous phenomena, advanced combinatorics, random matrices and freeness.
Category: Statistics

On the Finiteness and Shape of the Universe

Authors: Warren D. Smith
Comments: 31 Pages. Paper on internet since 2004, now uploaded to VIXRA for archival purposes.

This is the last of a 3-part series of papers on "the shape of the universe" and includes summary of the prior two. At the end is a chart allowing you to choose your favorite set of assumptions (from among those we consider) whereupon it tells you the conclusions deducible from those assumptions about the topology of the universe. This and the prior papers also includeddiscussion of "reasons the universe is 3-dimensional." As far as I know my analyses of these matters go considerably beyond all others; but quite possibly if "real topologists" got involved then considerably more could be said.
Category: Relativity and Cosmology

The Einstein and Landau-Lifshitz Pseudotensors — a Mathematical Note on Existence

Authors: Stephen J. Crothers
Comments: 4 Pages.

For a closed system, the conservation of energy and momentum has been affirmed through a vast array of experiments. In an attempt to reconcile the General Theory of Relativity with these findings, Einstein constructed, ad hoc, his so-called pseudotensor [A. Einstein, Ann. Phys. 49, 769 (1916)]. Yet this solution fell outside the tensorial mathematical structure of his theory. Landau and Lifshitz also constructed, ad hoc, an even more complex pseudotensor, as a proposed improvement upon the work of Einstein [The Classical Theory of Fields (Addison-Wesley Press, Inc., Cambridge, MA, 1951)]. Their pseudotensor is symmetric, unlike that proposed by Einstein. They advance that their pseudotensor yields a conservation law which also included angular momentum. However, once again, this approach leads to a mathematical construct which is not a tensor and thereby falls outside the very mathematical structure of Einstein’s theory. Both pseudotensors, whether that advanced by Einstein or by Landau and Lifshitz, violate the rules of pure mathematics and therefore can hold no place in physics.
Category: Relativity and Cosmology

Vaccum Unified Solitonic Condensate Theory

Authors: Ibrahim Khalid, M. Golebiowski
Comments: 98 Pages. License: CC BY NC ND (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Vacuum Unified Solitonic Condensate Theory is a way to understand the world around us. It says the space or the Vacuum Unified Solitonic Condensate Theory is like a liquid. You can squeeze it. Move it around. The Vacuum Unified Solitonic Condensate Theory has some rules that physicists know. These rules help us understand how things like electrons and protons and neutrons work.These tiny things are like knots in the Vacuum Unified Solitonic Condensate Theory. They have properties like mass and charge and spin. The Vacuum Unified Solitonic Condensate Theory helps us understand where these properties come from. We can use the Vacuum Unified Solitonic Condensate Theory to figure out the mass of electrons and protons and neutrons. We just need to use some ideas about the Vacuum Unified Solitonic Condensate Theory.The Vacuum Unified Solitonic Condensate Theory also helps us understand charge. Electric charge is like a twist in the Vacuum Unified Solitonic Condensate Theory. This twist is always the same. The Vacuum Unified Solitonic Condensate Theory can help us understand the weak forces too. It can help us understand how they are related to the Vacuum Unified Solitonic Condensate Theory.The Vacuum Unified Solitonic Condensate Theory even helps us understand gravity. Gravity happens when the Vacuum Unified Solitonic Condensate Theory gets dense in some places and not in others. The Vacuum Unified Solitonic Condensate Theory can help us understand how atoms work. It can help us understand why some things decay. The Vacuum Unified Solitonic Condensate Theory makes some predictions. We can test these predictions to see if the Vacuum Unified Solitonic Condensate Theory is correct.
Category: High Energy Particle Physics

A Problem in the Theory of Surfaces

Authors: Abdelmajid Ben Hadj Salem
Comments: 2 Pages. In French. Comments welcome.

In this note, we present a problem in the theory of surfaces. The equations for the surface $(Sigma)$ were inspired by the monograph cited in the references, published by the eminent Japanese mathematicians Katsumi Nomizu and Takeshi Sasaki.
Category: Geometry

Post-Carroll Algebra, Conformal Extensions, and Field Theories

Authors: Mojtaba Najafizadeh
Comments: 32 Pages.

By incorporating leading c -dependent corrections to the Carroll transformations, we introduce the post-Carroll transformations". We demonstrate that these transformations are consistent with post-Carrollian mechanics [1]; furthermore, they give rise to the so-called post-Carroll algebra". We show that, unlike the Carroll algebra, this new structure allows for a central charge in higher dimensions; we refer to it as the Carroll{Bargmann algebra". To construct conformal extensions, we first build the conformal extension of the post-Carroll algebra and study field theories invariantunder this symmetry. We then construct the conformal extension of the Carroll{Bargmann algebra, referred to as the Carroll{Schrodinger algebra", and demonstrate that it precisely matches the symmetry algebra of the higher-dimensional Carroll{Schrodinger theory [2]. Finally, we derive the general form of two-point functions in a post-Carrollian CFT, which in 1 + 1 dimensions exhibits both electric and magnetic sectors, while in higher dimensions only the magnetic sector survives.
Category: High Energy Particle Physics

The Missing Electric Aharonov-Bohm Test and the Search for the Electromagnetic Scalar Mode

Authors: Renato Vieira dos Santos
Comments: 8 Pages.

The electromagnetic four-potential $A^mu = (Phi/c, mathbf{A})$ comprises a scalar potential $Phi$ and a vector potential $mathbf{A}$. In gauge-invariant electrodynamics, gauge symmetry together with the Lorenz condition $partial_mu A^mu = 0$ ensure that only the two transverse photon polarizations are physical, while the scalar degree of freedom decouples. Whether this elimination holds in all physical regimes is an empirical question that has never been tested in configurations where the electric field vanishes but the potentials vary in time. We ask whether the scalar mode, described by the quantity $lorenzScalar = partial_mu A^mu$, can leave a physical imprint on matter that is detectable in the electric Aharonov-Bohm effect. The original configuration proposed in 1959---time-dependent potentials applied to shielded conducting cylinders---has never been experimentally realized. We show that a phenomenological coupling $propto lorenzScalar,bar{psi}psi$ yields a phase shift proportional to $1-cos(omega T)$, orthogonal to the standard $sin(omega T)$ prediction. A frequency sweep can cleanly separate the two contributions. We outline a realistic electron interferometry experiment, analyze the dominant systematic (fringe fields), and argue that such a test is within reach of existing technology. The question is testable: a null result would provide the first empirical bound on a physical scalar mode in a field-free regime; a positive signal would indicate that the gauge-fixing procedure discards a genuine degree of freedom. Either outcome illuminates the foundations of gauge theory.
Category: Quantum Physics

Toward Charge-Dependent Tests of the Equivalence Principle: a Phenomenological Parameter and an Unexplored Frontier

Authors: Renato Vieira dos Santos
Comments: 15 Pages. Published in PRD: https://doi.org/10.1103/frfk-vp26

We introduce and define the phenomenological parameter $kappa$, defined by $Delta a/g = kappa , Delta(q/m)$, to quantify potential linear coupling between electric charge and gravitational acceleration. A synthesis of existing precision equivalence principle experiments yields the first quantitative estimate of the effective sensitivity to this coupling: $|kappa| < 2.1 times 10^{-4}~si{kilogrampercoulomb}$ at 95% confidence level. This constraint is approximately 11 orders of magnitude less stringent than corresponding bounds on composition-dependent violations, revealing that the electromagnetic axis remains a largely underexplored frontier in empirical gravity. We connect $kappa$ to established frameworks---the Standard-Model Extension and the $THepsilonmu$ formalism---showing that it occupies a region of parameter space untouched by existing high-precision tests. An effective field theory analysis shows that dimension-six operators that couple curvature directly to the electromagnetic field strength are suppressed by the minuscule terrestrial spacetime curvature ($G_N ho_oplus sim 10^{-55}~text{GeV}^2$) and are therefore phenomenologically irrelevant. Consequently, a future measurement of $kappa$ at an accessible level would not probe minimal geometric couplings but would signal physics beyond minimal gravitational EFT, such as mediation by light scalar fields as in Einstein-Maxwell-Dilaton theory. We examine the Schiff-Barnhill effect, the primary systematic background for any such measurement, and show how it can be separated from a genuine signal. We outline the necessary experimental strategy, focused on maximizing charge-to-mass ratio differences, to transform this overlooked axis into a targeted probe for new physics.
Category: Relativity and Cosmology

A Preprint Republic at a Crossroads: Governance, Transparency, and the Future of arXiv as a Public Good

Authors: Renato Vieira dos Santos
Comments: 8 Pages.

The arXiv preprint repository, founded in 1991, has become the de facto dissemination platform for physics, mathematics, computer science, and increasingly other quantitative disciplines, hosting over 2.4 million articles and serving millions of users worldwide. In mid-2026, its governance will transition from Cornell University Library to an independent nonprofit entity governed by a board of directors and supported by private philanthropy. This article provides a data-driven examination of that transition, placing it within the history of the repository and the broader political economy of scholarly communication. Drawing on public submission statistics, moderation records, documented controversies, and historical precedents from academic publishing, we identify six structural risks: opaque governance, centralized editorial control, financial unsustainability, systemic bias, erosion of scientific pluralism, and potential mission drift toward privatized gatekeeping. We argue that the moment before institutional inertia sets in is precisely when the research community must insist on binding transparency and accountability mechanisms. We propose a set of concrete safeguards---a community-elected advisory council, mandatory transparency reporting, an independent moderation ombuds, a free-access charter, and periodic external audits---that can preserve arXiv's identity as a public good without compromising operational agility. The manuscript itself has been submitted to arXiv as a real-time test of the moderation system's openness to self-examination.
Category: General Science and Philosophy

A Pedagogical Reconstruction of Maxwell's Equations: How Charge Conservation, Helmholtz's Theorem, and the Speed of Light Make Them Natural

Authors: Renato Vieira dos Santos
Comments: 8 Pages.

Maxwell's equations are traditionally introduced as four independent postulates, each grounded in a distinct experimental law. Although empirically sound, this approach can obscure the logical structure that unifies them. This paper offers a pedagogical reconstruction based on local charge conservation, Helmholtz's theorem, and the experimental fact that electromagnetic disturbances propagate in vacuum with speed (c). A few natural auxiliary assumptions -- linearity, locality, and the simplest possible coupling to sources -- are stated explicitly. From the continuity equation and the physical necessity of a mediating field we argue that the electric and magnetic fields must be introduced. Helmholtz's theorem then demands that both divergences and curls of these fields be specified; coupling them to the available scalar and vector sources yields the inhomogeneous equations. Consistency with charge conservation forces the displacement current, making it a logical requirement rather than an empirical addition. The homogeneous equations follow from the same framework: (abla cdot mathbf{B} = 0) is the most parsimonious choice consistent with experiment, and requiring wave propagation at speed (c) fixes Faraday's law uniquely as (abla times mathbf{E} = -partial_t mathbf{B}). Once Maxwell's equations are established, the Lorentz force density (homathbf{E} + mathbf{J}timesmathbf{B}) emerges as the only dimensionally consistent expression compatible with the local conservation of momentum derived directly from the field equations. The argument employs only elementary vector calculus and is accessible to advanced undergraduates. We suggest that this unified narrative, which reveals the internal coherence of electromagnetism, can serve as a valuable complement to the traditional empirical presentation.
Category: Education and Didactics

Charge-Dependent Equivalence Principle Violation from Kinetic Mixing of the Photon with a New Long-Range Vector Field

Authors: Renato Vieira dos Santos
Comments: 11 Pages. https://doi.org/10.1142/S0218271826500458

The weak equivalence principle (WEP) has been tested with extraordinary precision over the past decades, but invariably with electrically neutral bodies. This leaves a fundamental blind spot: does gravity feel electric charge? A recent phenomenological analysis introduced a parameter $kappaphen$ to quantify this unexplored sector, but lacked a consistent field-theoretic origin. In this work we show that the simplest mechanism is kinetic mixing between the standard photon and a new massless vector field $X_mu$ that mediates a long-range fifth force coupled to the ordinary mass current. The single gauge-invariant dimension-four operator $frac{xi}{2}F_{muu}X^{muu}$ preserves causality and unitarity. By adopting the action in which both fields couple to their respective currents with the same sign convention, the two-body potential is fully symmetric and exactly satisfies Newton's third law, rendering the model free of any mathematical pathology.The fifth force between equal masses is repulsive, a known property of vector-mediated interactions, but its contribution to the neutral gravitational acceleration is absorbed into the measured Newtonian constant.For a static, spherically symmetric source, the mixing induces an electric field proportional to the Newtonian gravitational field, leading to a charge-dependent acceleration from which we identify $kappaphen = -ximu_0,G_X/G_N$, where $G_X$ is the fifth-force coupling strength.The symmetric cross term $propto q_1m_2+q_2m_1$ in the two-body potential gives rise to dipole radiation from compact binaries, providing a direct link to pulsar-timing constraints.We derive explicit constraints from the Cassini bound on the PPN parameter $gamma$, from lunar laser ranging on $alpha_1$, and from the Hulse--Taylor pulsar, showing that the model is compatible with all existing data while providing a clear roadmap for future experimental tests.
Category: High Energy Particle Physics

Cosmology from a Rastall-Inspired Variational Theory of Gravitation

Authors: Renato Vieira dos Santos
Comments: 9 Pages.

We propose a novel gravitational theory inspired by Rastall's idea of non-conserved energy-momentum, but formulated through a consistent variational principle. After developing a Lagrangian density that naturally incorporates matter-geometry coupling, we study cosmological consequences and fit parameters using recent Hubble function $H(z)$ data. According to model selection criteria (AICc and BIC), we obtain competitive models relative to $Lambda CDM.$ In our framework, the cosmological constant emerges from energy exchange between spacetime geometry and matter content, providing an alternative to vacuum energy interpretations. Our formulation provides a self-consistent variational foundation for non-conservative gravity, offering a potential resolution to the cosmological constant problem through dynamical energy exchange rather than vacuum energy.
Category: Relativity and Cosmology

A Least-Squares Optimization Model for Quad Mesh Offset

Authors: Zitao Xu
Comments: 10 Pages.

This article presents a least-squares optimization model for quadrilateral mesh offsets. Starting from an initial offset mesh generated from a base quad mesh, the method improves offset quality by introducing tangential corrections at offset vertices and solving for them globally. Each correction is represented by two scalar variables associated with two independent directions taken from the corresponding base quad, so that the optimization preserves the intended offset distance while allowing the offset mesh to adjust tangentially.For each quad, the objective function is constructed from local shape-preservation terms together with a center-consistency term, so that the optimized offset quad remains as consistent as possible with the shape and size of the corresponding base quad while reducing local crimping and shearing. The resulting formulation is a global least-squares problem over the mesh and leads to a sparse linear system. Examples in both convex and concave regions show that the method can significantly improve the quality of quad-mesh offsets and can be applied iteratively for further improvement.
Category: Geometry

TauPhi Numbers

Authors: Walter A. Kehowski
Comments: 8 Pages.

Let tau(n) be the number of divisors of n and let phi(n) denote the number of relatively prime numbers less than n. A number is called refactorable if and only if tau(n) divides n. It is known that phi(n) divides n if and only if n is 3-smooth. Furthermore, n/phi(n)=2 when n is a power of two and n/phi(n)=3 otherwise. Define lambda(n)=lcm(tau(n),phi(n)). Then n/lambda(n) is in {1,2,3} and n is called a tauphi-number. It is the purpose of this note to show when lambda(n)=n, called the unital tauphi-numbers.
Category: Number Theory

Quantifying Relational Structure in Quantum Measurement: An Axiomatic Account of Recursive Observation Depth

Authors: Agus Mulia Bakti
Comments: 20 Pages.

We formalize the relational pair (O, M), observer and observed system, as a primitive mathematical object governed by three operational axioms. From this structure we define Recursive Observation Depth (n^k), the length of the longest informative measurement chain an observer O can perform on a system M through a Positive Operator-Valued Measure (POVM). Five propositions about n^k are proved: monotonicity, relational dependence, a characterization of superposition, an exact value for a compatible (classical) observer, and, for a generic informationally complete observer, the impossibility of a terminal state, from which the divergence of n^k follows. Rank appears only as a special case, attained when the observer's measurements are mutually compatible; once they become informationally complete and incompatible, n^k diverges. We test the framework against four no-go theorems. It is consistent with Bell, Kochen—Specker, and No-Cloning on independent structural grounds, and consistent with PBR conditionally, provided the quantum state is taken to be a property of the relation (O, M) and not of the system alone. Wigner's Friend is resolved within this framework without further postulates. The Born rule is not derived, and no new experimental predictions are offered.
Category: Quantum Physics

Reasons the Photon Mass Should be Exactly Zero

Authors: Warren D. Smith
Comments: 5 Pages.

We argue from general relativity that if photons had mass, then charged black holes could not exist. But there is evidence they do exist. Also, big violations of Maxwell's laws would occur, even in regions far from black holes. This is the first evidence that photons really have zero, as opposed to just very small, mass. We also point out that the presence of extragalactic magnetic fields suggests |m_γ|⪅10^-64kg. Two independent lines of argument, one based on extragalactic magnetic fields and very conservative bounds on current densities, the other based on Voyager spaceprobe magnetometer measurements,both find |m_γ|⪅1.7×10^-56kg. These numbers are respectively 10¹⁰ and 60 times stronger than the best previous experimental bound. Finally, we consider the fact that massless quantum fields have additional symmetries. While it is tempting to try to use that as further justification for masslessness, it ultimately seems wrong.
Category: Classical Physics

Invisibility is Uncomfortable

Authors: Warren D. Smith
Comments: 3 Pages. Paper on www since 1993 now uploaded to VIXRA for archival purposes.

As a consequence of information-theoretic limitations arising from thermodynamics form a previous paper, we conclude that the sustained wearing of a "cloak of invisibiliity" is impossible.
Category: Thermodynamics and Energy

Perturbative String Theory and Its Non-Perturbative Probes

Authors: Sutirtha Mukherjee
Comments: 292 Pages.

Perturbative string theory treats a moving string as a two-dimensional surface and studies the quantum field theory of the fields living on it. Removing the two gauge freedoms of that surface, the freedom to relabel its points and the freedom to rescale its metric, by the Faddeev--Popov method produces a nilpotent BRST charge $Q_B$, and its cohomology $H(Q_B)$ is the physical spectrum of the string. The condition $Q_B^2=0$ fixes the number of spacetime dimensions at twenty-six for the bosonic string and ten for the superstring. At one loop the surface is a torus, and its modular invariance chooses the allowed spectrum, the GSO projection of the superstring, and the charge lattices the theory can carry. The same degeneration limit gives unitarity, since the amplitude factorizes on physical intermediate states. When that intermediate state is a massless one emitted into the vacuum, its coefficient is a tadpole, and requiring the tadpole to vanish is what picks out an allowed background. For the unoriented open string, this condition, equivalently the cancellation of gauge anomalies, forces the gauge group $SO(32)$. These results, and the tree and loop amplitudes built from them, make up the perturbative theory. Perturbation theory is limited to weak coupling, and reaching strong coupling relies on a set of non-perturbative probes that supersymmetry protects. A single cylinder stretched between two D-branes can be understood in two ways, as a loop of open string and as a closed string exchanged across the gap, and equating the two fixes the tension of a D-brane and shows that its Ramond-Ramond charge is quantized in the smallest unit Dirac allows. The masses of the bound states the branes form, the $(p,q)$ strings, and the D0-brane threshold bound states are set exactly by the supersymmetry algebra. Because these tensions, charges, and masses do not move with the coupling, they can be compared across two descriptions of the physics. The $(p,q)$ strings fill out the $SL(2,mathbb Z)$ multiplet behind the S-duality of type~IIB, and the D0-branes become the momentum modes of an eleventh dimension that opens up in strongly coupled type~IIA. The same protected states count the microstates of a black hole and reproduce its Bekenstein-Hawking entropy, and D-branes sourcing a warped throat give a four-dimensional gauge theory that confines while keeping one massless particle.
Category: Quantum Gravity and String Theory

Viscous Time Theory & Birch—Swinnerton-Dyer

Authors: Raoul Bianchetti, Payam Danesh
Comments: 10 Pages.

We develop a precise arithmetic version of Viscous Time Theory by replacing the original Sobolev field space with a finite Hilbert model of the Selmer complex. The VTT passive Hessian creates an anchored space for arithmetic. When we use a Schur complement it gets rid of the memory coupling. This results in an operator. The Bloch-Kato Selmer group is a sector, for this operator. The VTT passive Hessian and the Bloch-Kato Selmer group are connected in this way. The free part of the Bloch-Kato Selmer group gives us the Mordell-Weil rank. The finite arithmetic memory is what captures the Tate-Shafarevich and the Tamagawa contributions. The height-energy layer is also important. It connects with the Néron-Tate regulator. This connection happens through Arakelov and nonarchimedean potential theory. The VTT passive Hessian and the Néron-Tate regulator are related in this way. The main result is a rigorous VTT—BSD reduction theorem: after the active determinant germ is compared with L(E,s) at s=1, the BSD rank formula and refined leading coefficient follow. In this paper, we establish the variational, cohomological, height-theoretic and determinant-line structure needed for that comparison and it identifies the remaining analytic theorem.
Category: Algebra

Complexity of Minimization

Authors: Warren D. Smith
Comments: 15 Pages. On internet since 2000; uploading to VIXRA for archival purposes.

An important problem in numerical analysis is trying to minimize (or maximize) a real function F(x₁,x₂,...,x_d) of d real variables. We investigate (and survey) its computational complexity borderlines.

Results include (precise theorem statements are in the text): Minimizing, e.g., functions specified by polynomial formulas involving both trigonometric and ordinary arguments, is undecidable. Hence consider plain rational functions; we'll show minimizing these (more precisely, deciding whether the minimum lies below some threshold) is in NP. If the sum of the numerator and denominator degrees of a (multivariate) rational function is ≤4, then finding all its local minima is in P, except for the 4+0 case of a quartic polynomial (or its reciprocal) in which case it is NP-complete. (There is a slight caveat for the case 3+1; the "polynomial" runtime unfortunately depends also on an additional parameter, but for practical purposes this does not matter.) Indeed, even deciding whether a specified point is a localmin is NP-complete for a quartic. Minimizing a linear function in a cube is polynomial, but minimizing a quadratic in a cube is NP-complete. Minimizing a quadratic in a ball is in P, but it is NP-complete for a quartic (cubics: unknown). In all theseNP-completeness results, even approximating the value of the min is NP-complete, and the problems remain NP-complete even if all integers are input in unary. The P minimization algorithms for low degree rational functions involve new techniques of "multi-stage minimization" and "dimension reduction."

Minimizing functions "unimodal on lines," is in P. Solving systems of nonlinear equations F&8407;(x⃗)=0 is in P, if all the nonlinear functions $F_k are monotonic on lines. We present evidence that minimizing strictly unimodal functions (with exactly one minimum, and no saddlepoints) is exponentially hard; but if additionally the function obeys certain derivative bounds, then hardness seems to occur precisely when there are extremely long "winding valleys."
Category: Data Structures and Algorithms

Some Short Remarks on the Riemannian Hypothesis, Concerning the Zero-Finding Theorem

Authors: Holger Döring
Comments: 3 Pages. In German

At first, this description is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory. A more detailed paper will follow.
Category: Mathematical Physics

Computational Complexity of Synthetic Chemistry Basic Facts

Authors: Warren D. Smith
Comments: 8 Pages. On internet since 1997; uploading to VIXRA for archival purposes. Related paper: Molecular tinkertoys.

Three negative results:

1. Given a set of allowed starting materials and allowed chemical reactions, the problem of determining whether a chemical of specified structure is synthesizable is Turing undecidable.
2. The question of whether it is synthesizable in N steps is NP-complete. These 2 results apply in a general abstract setting and do not prove anything about how hard the problem is with any specific set of starting materials and allowed reactions. In particular we prove nothing about the case when the starting materials are all commercially available chemicals and the reactions are all known reactions!
3. The IUPAC naming scheme for assigning names to organic compounds will assign ambiguous names to most N-atom compounds and requires great chemical expertise. We show that both these problems are avoidable with alternative naming schemes, There are unquestionably {it far} simpler and better methods to name chemical compounds than the IUPAC scheme.

All 3 of these facts are almost trivial from the viewpoint of modern computer science, but I don't think they've been mentioned in the chemical literature.

Positive results: We discuss algorithms for finding out how to solve the synthesis problem (of determining whether something is synthesizable, and what the best synthetic process is). An interesting generalization of the famous "shortest path problem" in directed graphs arises in which the paths become synthetic trees, the graphs become hypergraphs, and the distances become synthetic costs. This problem is soluble either by generalizing Dijkstra's algorithm or the dynamic programming algorithm. Despite the fact that these algorithms are highly efficient as a function of the size of the hypergraph, in practice because the hypergraph arising from chemistry is enormous, that is inadequate. We discuss methods for ameliorating this.
Category: Chemistry

The Payment Verification Model for Digital Cash Point of Sale Systems

Authors: Lukas Saul, Robert Gludo, Jonathan Gludo
Comments: 6 Pages.

With public ledger digital cash payments comes a new type of point of sale (POS) system which has been implemented by several devices and apps. The "payment verification model" for POS minimizes security risk and associated fees while enabling merchants to adopt their point of sale system to different numéraires and different payment currencies. In this paper we outline this system and its advantages and operation. We provide the first systematic security taxonomy, privacy mitigation strategies, and accounting integration guidance specifically for payment verification POS systems.
Category: Economics and Finance

Relativistic Geometrical Horizons(rgh) in Both the Original Versions of Alcubierre and Natario Warp Drives

Authors: Fernando Loup
Comments: 26 Pages.

In 1994 Alcubierre developed the first warp drive work using the original 3+1 ADM-MTW formalism.Seven years later in 2001 the same original 3+1 ADM-MTW formalism appeared in the first part of the second warp drive work developed by Natario. But in 1997 the concept of the Relativistic Geometrical Horizon RGH was introduced by Hiscock in his work about the Alcubierre warp drive. According to Hiscock if the time component of a given spacetimemetric tensor becomes null g_(00)=0 a Horizon similar to the Event Horizon of the Schwarzschild black hole appears. The Alcubierre warp drive suffers from this pathology because in a given point of the Alcubierre warped regionthe g_(00)=0 appears generating the Alcubierre Horizon equivalent to the Event Horizon of the Schwarzschild black hole.The Natario warp drive was formulated in polar coordinates in a2+1 spacetime.A dimensional reduction of the Natario warp drive from a 2+1 to a 1+1 spacetimes in a given point of the Natariowarped region the g_(00)=0 appears generating the Natario Horizon in a 1+1 spacetime.But in the original Natario warp drive in polar coordinates in a 2+1 spacetime the g_(00)=0 never appears.Due to the presence of a second spatial dimension the g_(00)=0 can be avoided.
Category: Relativity and Cosmology

Eddington’s Mass-Luminosity Relation and the Laws of Thermodynamics

Authors: Stephen J. Crothers, Pierre-Marie Robitaille
Comments: 8 Pages.

Ever since its formulation by A. S. Eddington, the mass-luminosity relation has been viewed as a triumph for theoretical astronomy and astrophysics. The idea that the luminosity of the stars could be controlled solely by their mass was indeed a revolutionary concept. The proof involved two central aspects: (1) the belief that stars could be treated as ideal gases in hydrostatic equilibrium, and (2) that the opacity of Capella could be used as a reference mark applicable to other stars. Yet, when the mass-luminosity relation was advanced, no thought was given to the need for thermodynamic balance. Within thermodynamic expressions, not only must the dimensions (hence units) be consistent on each side of the equals sign, but the extensive nature of the properties must also balance. Namely, thermodynamic expressions must be balanced by properties which are extensive to the same degree. In this regard, mass is an extensive thermodynamic property and can be represented by a homogenous function of degree 1. Conversely, the luminosity of a star is neither extensive nor intensive, but rather can be represented by a homogenous function of degree 2/3. Consequently, the mass-luminosity expression is thermodynamically unbalanced and stands in violation of the laws of thermodynamics.
Category: Astrophysics

The Electrodynamic Origin of Black Holes (Part 1)

Authors: Raul Fattore
Comments: 17 Pages.

The electrodynamic origin of black holes as well as the electrodynamic origin of the gravitational force developed in the present study will contribute to a better understanding of how our universe works and obeys the real-world physics demonstrated by the more than proven laws of electrodynamics.This study presents a new perspective that will clarify and demystify many aspects about the origin of the gravitational force through a newly derived equation with terms that are absent in basic Newton’s gravitational law. It will also be demonstrated the decay of the gravitational force, the origin of black holes, what they really are, how they are formed, how they evolve, the real radiation spectrum, what particles are the constituents of black holes, what particles are to be found outside a black hole, the wavelength shift (or redshift) of black holes, and other properties.- Do "receding" galaxies really mean that the universe is expanding?- Is it scientifically serious to accept that gravity is not a force, but a "geometrical effect" caused by mass?- Is it scientifically serious to accept that "geometrical gravity" lacks a unique unit of calculation, because it depends on what is being calculated?- Can it be scientifically acceptable that a lump of Newtonian mass bends EM radiation?- Can monochromatic radiation emission from black holes be scientifically acceptable?- Can it be scientifically acceptable that some types of black holes do not rotate?
Category: Astrophysics

The Electrodynamic Origin of Black Holes (Part 2)

Authors: Raul Fattore
Comments: 37 Pages.

The electrodynamic origin of black holes as well as the electrodynamic origin of the gravitational force developed in the present study will contribute to a better understanding of how our universe works and obeys the real-world physics demonstrated by the more than proven laws of electrodynamics.This study presents a new perspective that will clarify and demystify many aspects about the origin of the gravitational force through a newly derived equation with terms that are absent in basic Newton’s gravitational law. It will also be demonstrated the decay of the gravitational force, the origin of black holes, what they really are, how they are formed, how they evolve, the real radiation spectrum, what particles are the constituents of black holes, what particles are to be found outside a black hole, the wavelength shift (or redshift) of black holes, and other properties.- Do "receding" galaxies really mean that the universe is expanding?- Is it scientifically serious to accept that gravity is not a force, but a "geometrical effect" caused by mass?- Is it scientifically serious to accept that "geometrical gravity" lacks a unique unit of calculation, because it depends on what is being calculated?- Can it be scientifically acceptable that a lump of Newtonian mass bends EM radiation?- Can monochromatic radiation emission from black holes be scientifically acceptable?- Can it be scientifically acceptable that some types of black holes do not rotate?
Category: Astrophysics

Best Play for Imperfect Players and Game Tree Search: Part I (Theory)

Authors: Eric B. Baum, Warren D. Smith
Comments: 41 Pages.

This is part I (theory) of a 2-part paper about a new, non-minimaxing, approach to search in game-trees such as Chess and Go. Its first point is that minimaxing is NOT the best decision-making (i.e. chess-move-selection) process based on inexact merely-statistical estimates about the "goodness" of the chess positions at the leaves of a search tree. Its second point is that going down the game tree to some fixed depth, then stopping, is NOT the best choice of chess-positions for your search to explore. "BPIP search" is a way to make better decisions based on any particular search tree, and a way to explore better trees. As of year 2026, BPIP still has not yet been used by chess and go programs, but if were might enable them to get substantially stronger. Would it? I would like to know, but never found out because I abandoned my attempts to write strong chess and go programs as just too difficult a programming task for me.

I originally wrote this paper and put it on the internet in 1993, and at that time "Monte Carlo game tree search" and today's highly advanced selective alphabeta variants did not yet exist, computer chess was weaker than the best humans, and computer go far weaker than decent human amateurs. Later, go programmers invented "Monte Carlo game tree search" which can be regarded as a "poor man's BPIP" (although they did not realize that). MCGTS has been used in go programs with great success.
Category: Artificial Intelligence

Fermi-Born-Infeld Electrodynamics: a Nonlinear Theory with Physical Gauge

Authors: Renato Vieira dos Santos
Comments: 12 Pages.

We construct a nonlinear extension of Fermi's electrodynamics by incorporating a Born--Infeld structure that depends directly on the four-potential $A_mu$ rather than on the field strength $F_{muu}$. The resulting theory, which we call Fermi--Born--Infeld (FBI) electrodynamics, eliminates the $U(1)$ gauge redundancy by elevating the Lorenz gauge to a dynamical condition. The Lagrangian is built from the determinant of a metric-like tensor $g_{muu} = eta_{muu} + 2kappa, partial_{(mu} A_{u)}$, ensuring that the canonical energy--momentum tensor and the spin density remain unique and free of gauge ambiguities. We derive the field equations, which reduce to $partial_u(sqrt{-g}, g^{muu}) = 0$, and show that the Lorenz condition $partial_mu A^mu = 0$ emerges dynamically from retarded boundary conditions and the requirement of a positive-energy spectrum. The nonlinearities modify the propagation of longitudinal modes; we argue, via a Vainshtein-like mechanism, that the nonlinear self-interactions may stabilize the longitudinal mode, opening the possibility of a stable massive scalar photon under extreme field conditions. We also compute the spin density from the Noether current and discuss its properties. The FBI theory preserves the physical gauge of Fermi's original formulation while incorporating the regularization features of Born--Infeld electrodynamics, making it a candidate for describing electromagnetic phenomena in strong-field regimes.
Category: Relativity and Cosmology

Best Play for Imperfect Players and Game Tree Search: part II (experiments)

Authors: Warren D. Smith, Eric B. Baum, Charles Garrett, Rico Tudor
Comments: 39 Pages.

This is part II (experiments) of a 2-part paper about a new, non-minimaxing, approach to search in game-trees such as Chess and Go. Its first point is that minimaxing is NOT the best decision-making (i.e. chess-move-selection) process based on inexact merely-statistical estimates about the "goodness" of the chess positions at the leaves of a search tree. Its second point is that going down the game tree to some fixed depth, then stopping, is NOT the best choice of chess-positions for your search to explore. "BPIP search" is a way to make better decisions based on any particular search tree, and a way to grow better trees to explore. As of year 2026, BPIP still has not yet been used by chess and go programs, but if were might enable them to get substantially stronger. Would it? I would like to know, but never found out because I abandoned my attempts to write strong chess and go programs as just too difficult a programming task for me. However in this paper we did program BPIP and alphabeta gameplayers for a number of simpler games, achieving strengths apparently stronger than any human and also among the strongest year-1995 computer programs. For some games BPIP indeed outperformed alphabeta, sometimes hugely. Games large enough that full solves of game positions are usually out of reach, and which can have "smart and slow" position evaluators, and in which large searches are done, are the games favoring BPIP versus alphabeta.

I originally wrote this paper and put it on the internet in 1995, and at that time "Monte Carlo game tree search" and today's highly advanced selective alphabeta variants did not yet exist, computer chess was weaker than the best humans, and computer go far weaker than decent human amateurs. Later, go programmers invented "Monte Carlo game tree search" which can be regarded as a "poor man's BPIP" (although the MCGTS inventors did not realize that). MCGTS has been used in go programs with great success.
Category: Artificial Intelligence

The Influence Mechanism of Weight Allocation and Test Set Design on Open-Source Large Model Evaluation Results

Authors: Dong Zhang, Yang Sun, Fei Lyu, Xiaofeng Liu, Xin Li
Comments: 22 Pages.

The evaluation results of open-source large language models are not only influenced by model parameter scale, training corpus, and alignment strategies, but also significantly constrained by the test set architecture and the weight allocation of evaluation metrics. To address this issue, this paper leverages multiple types of real-world evaluation data collected from engineering projects to investigate the evolution mechanism of open-source large model evaluation scores and rankings under the coupled effects of weight allocation and test set design. This paper selects four mainstream frontier open-source models—DeepSeek-V3.2, MiniMax-M2.5, Qwen3.6-35B-A3B, and gpt-oss-120b—to conduct controlled experiments. All models uniformly employ 8 96G H20 GPUs for local offline inference evaluation, and weighted aggregation is performed after unifying the scoring criteria to eliminate evaluation interference caused by third-party API rate limiting, version differences, and inconsistent scoring standards. The native capabilities of the models are supplemented with official model card information from the ModelScope platform: MiniMax-M2.5 focuses on code engineering, intelligent agents, and office interaction, with inference speed improved by 37% over the previous generation and inference cost at only 10% of Claude Opus 4.6; gpt-oss-120b is an OpenAI open-source MoE architecture model that natively supports hierarchical reasoning, tool invocation, and MXFP4 quantized deployment. The experimental datasets cover five major tasks—social bias discrimination, common misconception fact-checking, lifestyle question answering, contextual semantic understanding, and basic logical reasoning—corresponding to five evaluation capabilities: bias identification, fact verification, knowledge response, contextual interpretation, and mathematical reasoning. Specifically, this paper operationalizes "task type"as an observational variable into five categories of questions: ：social bias discrimination is used to measure the Bias Identificationconcept（characterized by bias judgment accuracy and harmful tendency response rate），common misconceptionFact-Checkingfact-checking is used to measure the fact verification concept（characterized by fact judgment accuracy），lifestyle question answering is used to measure the knowledge response concept（characterized by answer correctness rate and completeness score），contextual semantic understanding is used to measure the contextual interpretation concept（characterized by semantic consistency and coreference resolution accuracy），basic logical reasoning is used to measure the mathematical reasoning concept（characterized by reasoning step accuracy and final conclusion accuracy）。This paper constructs three evaluation weighting schemes: average baseline weights、performance-oriented weights、, and robust compliance-oriented weights，to analyze the variation patterns of model tier rankings under differentiated weight allocations。The experimental results show that：when the test set task categories are homogeneous、and question types are uniform，model rankings are highly susceptible to local sample perturbations；test sets with diverse task types、and balanced difficulty levels，exhibit stronger evaluation stability，and can objectively characterize comprehensive model capabilities。The study further confirms that，metric weights、sample structure、and task distribution are not auxiliary evaluation variables，but core elements determining the credibility of evaluation conclusions、and applicability。
Category: Artificial Intelligence

Non-Hermitian Quantum Mechanics Fundamentals & Lennard-Jones Potential

Authors: Larry Lee, Preet Sharma
Comments: 8 Pages.

Non-Hermitian quantum mechanics is a fairly new field and has been of great interests to theorists and experimentalists alike. In this study we have shown the basics of Non-Hermitian quantum mechanics and have put forward a scenario in which Non-Hermitian quantum mechanics can be applied to the well known Lennard-Jones potential. We have not shown explicitly what the results would be but when we apply Lennard-Jones potential to the Non-Hermitian scenario, but we have given one idea as to how it can play a part. This idea is also our continuing research.
Category: Quantum Physics

A Network-Based Microscopic Interpretation of Vacuum Localised Structures

Authors: Rudi Van Nieuwenhove
Comments: 10 Pages.

Vacuum Localised Structures (VLS) have recently been proposed as self-gravitating solutions of the Einstein field equations. Such structures have been investigated in connection with galactic dark matter distributions, filamentary gravitational configurations, and black-hole-like vacuum solutions without baryonic matter sources. Although the corresponding solutions are mathematically consistent within General Relativity, the physical interpretation of the underlying stress-energy tensor remained unclear.In the present work, a microscopic interpretation of VLS structures is explored using a dynamical network framework. Space is interpreted as an emergent structure arising from an underlying discrete connectivity network, in which effective metric properties are associated with local link configurations and shortest-path relations. Curvature is interpreted as a spatial variation of effective network connectivity.Within this framework, a VLS is described as a self-sustained coherent network configuration maintained by local reconnection dynamics. This surface-dominated dynamical behaviour naturally leads to the effective equation of state in which the radial pressure equals minus one-third of the energy density, thereby providing a possible microscopic interpretation of the peculiar stress-energy properties associated with VLS solutions.
Category: Relativity and Cosmology

Introduction to Pseudo Vector Theory of the Mediating Medium for Dark Matter

Authors: J. W. A. Zwart
Comments: 12 Pages. (Note by viXra Admin: Please cite and list scientific references)

The dark matter mediating medium for the pseudo vectors carries by definition four independent vector cells of the components for acceleration, spin and precession making up twelve combinations of pseudo vectors. The conjugated medium at the absolute zero energy state consists of solely pseudo e-neutrino triplets as a dynamic non destructible equilibrium in cubic pyramid symmetry. At a relativistic thermodynamic level of electron energy the pseudo vector medium consists of pseudo μ-triplets in cubic symmetry mixed to triplet ensembles of τ-pseudo triplets in cubic symmetry together guided by the pseudo e-neutrinos. Both the μ- and τ- triplets carry always the rotations for τ-triplets perpendicular to the μ-triplets suggesting orthogonal cubic pyramid symmetry. The top in equilateral pyramid symmetry of equal dimension for the base triangle in the cubic symmetry provides the dynamic electric charge in one polarity following the acceleration vector component of the pseudo vector cells. The time intervals for the electric charge dynamics give the sequential conjugated inversion shifts along the rotation axis of the height of the equilateral pyramid. Common sense reasoning of some scaling calculations shows the validity of the statement in this abstract explained in the paper below.
Category: High Energy Particle Physics

Quaternions, Octonions, and Now, 16-Ons and 2^n-Ons: New Kinds of Numbers

Authors: Warren D. Smith
Comments: 68 Pages. Placing this 2004 paper on vixra for archival purposes.

"Cayley-Dickson doubling," starting from the real numbers, successively yields the complex numbers (dimension 2), quaternions (4), and octonions (8). Each contains all the previous ones as subalgebras. Famous Theorems, previously thought to be the last word, state that these are the full set of division (or normed) algebras with 1 over the real numbers. Their properties keep degrading: the complex numbers lose the ordering and self-conjugacy (x̅=x) properties of the reals; at the quaternions we lose commutativity; and at the octonions we lose associativity. If one keeps Cayley-Dickson doubling to get the 16-dimensional "sedenions," zero-divisors appear.

We introduce a different doubling process which also produces the complexes, quaternions, and octonions, but keeps going to yield 2ⁿ-dimensional normed algebraic structures, for every n≥0. Each contains all the previous ones as subalgebras. We'll see how these evade the Famous Impossibility Theorems. They also lead to a rational "vector product" operation in 2^k-1 dimensions for each k≥2; this operation is impossible in other dimensions.

But properties continue to degrade. The 16-ons lose distributivity, right-cancellation yx·x^-1=y, flexibility a·ba=ab·a, and antiautomorphism (c̅=b̅a̅ where c=ab). The 32-ons lose the properties that the solutions of generic division problems necessarily exist and are unique, and lose the "Trotter product limit formula." We introduce an important new notion to topology we call "generalized smoothness." The 2ⁿ-ons are generalized smooth for n≤4.

All 2ⁿ-ons have 1 and obey numerous identities including weakenings of the distributive, associative, and antiautomorphism laws. In the case of 16-ons these weakened distributivity laws characterize them, i.e. our 16-ons are, in a sense, unique and best-possible. Our 2ⁿ-ons also are unique, albeit in a much weaker sense. The 2ⁿ-ons with n≤4 support a version of the fundamental theorem of algebra. Normed algebras (rational but not nec. distributive) over the reals are impossible in dimensions other than powers of 2.
Category: Algebra

Embedding Space Construction of Conformal Field Theory From First Principles

Authors: Sutirtha Mukherjee
Comments: 104 Pages. (Note by viXra Admin: Please cite listed scientific references)

This work presents a systematic development of conformal field theory from first principles in quantum field theory, emphasizing complete derivations of the conformal group in arbitrary dimensions from the conformal Killing equation, proving its isomorphism to $mathrm{SO}(d+1,1)$, and develop the embedding space formalism as a tool for constructing conformally covariant correlation functions constrained by Ward identities. In two dimensions, conformal symmetry enhances to an infinite-dimensional algebra: we derive the Virasoro algebra $[L_m, L_n] = (m-n)L_{m+n} + frac{c}{12}(m^3-m)delta_{m+n,0}$ from infinitesimal generators $ell_n = -z^{n+1}partial_z$, computing the central charge explicitly for free theories (boson $c=1$, Majorana fermion $c=1/2$, $bc$-ghosts $c = 1-3(2lambda-1)^2$) and demonstrating its physical interpretation as vacuum energy. Through radial quantization, we establish the operator-state correspondence and construct the Hilbert space via Virasoro descendants of primary states $|h,bar{h}angle$, deriving the transformation law $T'(w) = (dw/dz)^{-2}[T(z) - (c/12){w;z}]$ that reveals the geometric origin of the conformal anomaly. Unlike conventional treatments, we develop all mathematical machinery from standard QFT without relying on unexplained results from string theory or representation theory, exhibiting all intermediate steps explicitly to provide a detailed continuation beyond introductory QFT texts.
Category: Quantum Gravity and String Theory

Entanglement, Common-Origin Correlations, and the Interpretation of Bell Violations

Authors: Ion Vlad
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Bell's theorem demonstrates that no local deterministic theory can reproduce the complete set of correlations predicted by standard quantum mechanics. The present work accepts Bell's theorem as mathematically correct but questions the physical interpretation of the quantum correlation function used in Bell analyses. It is argued that entangled particles inherit a complete common physical state at their creation and that subsequent measurements reveal selected observables of this state rather than generating new information or requiring superluminal communication. The paper further proposes that the standard quantum correlation function, (E(θ)=−cosθ), incorporates additional angular dependence beyond the information physically established at the source. Under this interpretation, the observed violation of Bell inequalities arises from the mathematical structure of the correlation function rather than from nonlocal information transfer between distant particles. An explicit local common-source model is presented, leading to a piecewise linear correlation function and motivating a decomposition of the standard quantum prediction into a local component and a supplementary angular term.
Category: Quantum Physics

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