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Previous months:
2025 - 2503(1) - 2504(2) - 2505(7) - 2506(1)
Any replacements are listed farther down
[10] ai.viXra.org:2506.0008 [pdf] submitted on 2025-06-02 01:25:05
Authors: Rafael Eliahu Vaidergorn
Comments: 5 Pages.
This paper introduces the Vaidergorn Number (Ts), denoted by theHebrew letter Tzadi Sofit (Unicode U+05E5), as a novel mathemati-cal construct representing an absolute magnitude beyond all infinities. We formalize Ts within an extended Zermelo-Fraenkel (ZF) framework with new axioms, leveraging forcing and non-standard analysis, and prove its uniqueness via a new theorem, distinguishing it from Cantor’s cardinals (ℵ0, ℵ1) and Robinson’s hyperreals. Enhanced applications in cosmology model an infinite-yet-bounded universe with detailed derivations of a modified Friedmann equation and numericalsimulations, while string theory applications include a refined action with connections to braneworld scenarios. This preprint bridges mathematics and physics, inviting feedback and further exploration.
Category: Mathematical Physics
[9] ai.viXra.org:2505.0198 [pdf] submitted on 2025-05-30 01:06:52
Authors: Robert Loiseau
Comments: 5 Pages.
We present a minimal construction of a self-adjoint operator Hjk = αlogpj + βlog2pj, whose entries are determined entirely by the logarithmic structure of the prime numbers. This operator yields a discrete, strictly positive lowest eigenvalue that remains stable across increasing matrix sizes. Without invoking spacetime, gauge fields, or conventional Lagrangian dynamics, we interpret this result as a candidate solution to the Yang—Mills mass gap problem. The construction is purely arithmetic and offers a novel pathway to mass gap realization.
Category: Mathematical Physics
[8] ai.viXra.org:2505.0122 [pdf] submitted on 2025-05-20 20:25:31
Authors: Justin Sirotin
Comments: 16 Pages. Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
We present a comprehensive exposition of the Spinor-Mediated Universal Geometry(SMUG) framework that resolves the Clay Mathematics Institute's Yang--Millsexistence and mass gap problem through torsion-induced four-fermion interactionson a Euclidean lattice. This novel approach establishes a mathematically rigorousconnection between spacetime geometry and quantum field dynamics, demonstratinghow spinor-sourced torsion naturally generates the mass gap.
Category: Mathematical Physics
[7] ai.viXra.org:2505.0071 [pdf] submitted on 2025-05-13 23:45:00
Authors: Romeo Prince
Comments: 50 Pages.
It has A Morphic Riemann Tensor, there is a damping term which dams qft at large x and vise versa, flow time, Morphic flow, stress, pressure, exp, theory of temperature, quantum gravity, particles, QCD, QFT.
Category: Mathematical Physics
[6] ai.viXra.org:2505.0059 [pdf] submitted on 2025-05-11 20:41:01
Authors: Faysal EL Khettabi
Comments: 9 Pages. Also see https://ai.vixra.org/abs/2505.0054
This report outlines a foundational shift in mathematics, proposing a framework groundedin finite, constructive principles—the "Arithmetic of Order"—emerging from the progression 1 → n → n + 1 and the combinatorial structure of powersets P(Ωn). It critiques the traditional reliance on infinitary constructs like the complex number i ∈ C and the continuum for describing physical systems with finite degrees of freedom. Instead, it posits haracter-istic functions as the true empirical interface, and demonstrates how optimal mathematical structures—such as the Golay code G24, the Leech lattice Λ24, and the Mathieu group M24—emerge deterministically from this finitistic basis through processes of constraint-guided differentiation. This approach offers a new foundation for understanding hypercomplex numbers, projective geometries emergent from powersets, universal principles of communication and information stability, and the potential architectures for advanced artificial intelligence. Crucially, it reinterprets the continuum not as an *a priori* given, but as an asymptotic limit of the nested powerset hierarchy. The principles underlying theoremslike Gleason’s are viewed not merely as specific results at a particular n (such as n = 24),but as exemplars of universal rules of emergence that guide the formation of order acrossall degrees of freedom. The entire framework operates without recourse to unobservableinfinities or the subjective concept of "noise."
Category: Mathematical Physics
[5] ai.viXra.org:2505.0055 [pdf] submitted on 2025-05-10 21:18:10
Authors: Taylor Pablo Federico
Comments: 60 Pages. In Spanish
This work introduces the theoretical framework of Algebraic Engineering, centered on the Fundamental Theorem of Algebraic Synchronism (FTAS). The theory categorizes algebraic structures as elemental (internally closed) and essential (dependent on external data), and proposes a metric-entropy formulation based on a (1,1) deformation tensor. A Ricci-type dynamic flow is defined, blending geometric evolution with algebraic synchronism. Applications include the synchronization of metrics from General Relativity and Quantum Mechanics, and a reformulation of stress-strain behavior in material science via entropy and metric functors. The document includes 17 chapters, a complete glossary, symbolic conventions, and a dedicated section on the role of artificial intelligence in the development of the work. It is written in Spanish with a full English summary, and is structured, self-contained, and open to collaboration.
Category: Mathematical Physics
[4] ai.viXra.org:2505.0054 [pdf] submitted on 2025-05-10 21:21:53
Authors: Faysal EL Khettabi
Comments: 12 Pages.
Can we derive a Modern Mathematical Framework for Hypercomplex Numbers? Hypercomplex numbers, such as quaternions and octonions, expand beyond traditional real and complex numbers by introducing additional imaginary units. These numbers have unique algebraic properties and applications in mathematical and physical theories for describing transformations, symmetries, and geometric concepts in higher-dimensional spaces. However, there is a noticeable gap in the robust mathematical foundation related to hypercomplex numbers. This research project aims to establish a comprehensive mathematical framework for hypercomplex numbers, specifically focusing on their intrinsic relationship with physical systems having a natural number of degrees of freedom. By enhancing the understanding and application of hypercomplex numbers in this context, deeper insights into complex systems and phenomena in various fields can be uncovered
Category: Mathematical Physics
[3] ai.viXra.org:2504.0129 [pdf] submitted on 2025-04-30 19:46:43
Authors: Hamed Mehrabi
Comments: 33 Pages.
The universe presents us with a profound paradox: while the second law of thermodynamicspredicts increasing disorder, complex organized systems—from living cellsto galactic structures—emerge and persist throughout cosmic history. We resolve thisparadox by proposing a fundamental extension to Einstein’s mass—energy equivalence,incorporating organizational information as an intrinsic physical quantity that carriesmeasurable energy. Our central principle establishes that the total energy of a systemcomprises both its rest energy (Erest = mc2) and an additional energy associatedwith maintaining organizational information (Eorg = kBT ln(2)Ω), where Ω quantifiesnon-random correlations in bits. Together, these energy components form a completeaccounting of the system’s energetic requirements: Etotal = Erest + Eorg. This frameworkmakes three remarkable quantitative predictions: (1) human brain power consumptionof 20.1W (measured: 20W), (2) E. coli basal metabolic rate of 4.1 × 10−12W(measured: 3.8-4.5 × 10−12W), and (3) quantum decoherence times within 8% of experimentalvalues across different qubit technologies. Through rigorous mathematicalderivation and cross-scale validation, we demonstrate that organizational informationrequires continuous energy expenditure against entropic decay. This fundamental insightnot only resolves longstanding puzzles in bioenergetics and quantum foundations,but also suggests a new understanding of cosmic fine-tuning without invoking multiversehypotheses. By recognizing that maintaining order has an irreducible energeticcost, we reveal a deeper symmetry in nature that bridges thermodynamics, informationtheory, and fundamental physics.
Category: Mathematical Physics
[2] ai.viXra.org:2504.0072 [pdf] submitted on 2025-04-19 22:57:37
Authors: Jon Curry
Comments: 6 Pages.
Differential equations underpin countless physical systems, from chaotic pendulums to cosmic fields, yet classical numerical solvers struggle with stiff, nonlinear, or tensorial problems due to their reliance on time-stepping and derivative approximations. We introduce the Four-Dimensional Iterative Prediction (4DIP) framework, a novel symbolic method that uses geometric residual contraction to solve diverse differential systems with high precision. By iteratively refining a guess toward the true solution using a fixed rule, 4DIP eliminates time discretization, achieving residuals below 10−14 across 13 challenging systems—including chaotic triple pendulums, Dirac fields in curved spacetime, and noisy quantum turbulence—using 50-digit precision. This revised paper enhances theoretical rigor, expands comparisonsto modern solvers, and clarifies failure modes, demonstrating 4DIP’s potential to transformcomputational physics, engineering, and beyond.
Category: Mathematical Physics
[1] ai.viXra.org:2503.0012 [pdf] submitted on 2025-03-29 16:09:34
Authors: Nigel Cook
Comments: 4 Pages. (AI Assistance: Grok 3 xAI; correction made by ai.viXra.org Admin. Note by ai.viXra.org Admin: Conditions of submission are that AI is used as a research tool & the authors understand the AI generated data, equations & graphs etc & have verified them to be correct/true)
Peter Woit’s 2002 paper, "Quantum Field Theory and Representations Theory: A Sketch" (arXiv:hep-th/0206135), proposes a geometric framework for the Standard Model using Clifford algebras in Euclidean space-time. This paper aims to elucidate the mathematical foundations of Woit’s approach, focusing on the role of the Clifford algebra Cl(2), its extension to Cl(4), and the construction of the spin representation that yields the quantum numbers of a Standard Model generation of leptons and quarks. By breaking down the algebraic structures and their physical interpretations, we make Woit’s ideas more accessible to a broader audience, including students and researchers in particle physics and mathematical physics.
Category: Mathematical Physics
[1] ai.viXra.org:2505.0089 [pdf] replaced on 2025-05-20 06:04:14
Authors: Justin Sirotin
Comments: 25 Pages. 25p Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
We present a unified theoretical framework—Spinor Mediated Universal Geometry (SMUG)—in which intrinsic spin is the foundational generative principle from which spacetime, gauge symmetries, mass, and matter interactions emerge. The formalism is constructed within Riemann—Cartan geometry, where spinor fields act as sources for torsion, which in turn modifies the affine connection and curvature structure of spacetime. The fundamental operators—spin $hat{S}_i$ and torsion $hat{T}_i$ (where $i in {1,2,3}$ denotes spatial components in the internal algebra)—obey a closed non-Abelian algebra:begin{equation*}[hat{S}_i, hat{S}_j] = ihbar epsilon_{ijk} hat{S}_k, quad [hat{S}_i, hat{T}_j] = ihbar epsilon_{ijk} hat{T}_k, quad [hat{T}_i, hat{T}_j] = -ihbar epsilon_{ijk} hat{S}_k,end{equation*}which embeds naturally into the Clifford algebra $mathcal{C}ell(3,1) otimes mathcal{C}ell(2,0)$ and generates the $mathfrak{spin}(5,1)$ algebra. A spontaneous torsion condensate $langle T^a angle eq 0$ (where $T^a$ is the two-form torsion field related to but distinct from the operators $hat{T}_i$) breaks this symmetry down to $mathfrak{su}(3)_c oplus mathfrak{su}(2)_L oplus mathfrak{u}(1)_Y$, the precise gauge algebra of the Standard Model. We provide explicit spin-torsion constructions of the gauge generators and demonstrate that the U(1) hypercharge generator arises as a composite operator $gamma^5 sigma^3$, where $sigma^3 = -isigma^1sigma^2$ is derived from the $mathcal{C}ell(2,0)$ generators.A unique eigenmode selection principle is introduced via the Preservation Constraint Equation (PCE) $mathcal{P}(sigma,tau,upsilon) = -2sigma^2 + 2tau^2 + 3tau = 0$ (assuming $tau=upsilon$), which filters allowed modes based on spin-torsion projections. Only the $lambda = 4$ mode satisfies this constraint, leading to algebraic and topological exclusion of higher gauge symmetries such as SU(5), SO(10), and E(6).We derive an effective Lagrangian incorporating spin-torsion interactions,begin{equation*}mathcal{L} = frac{1}{16pi G} left[ R + alpha_S S^2 - beta_{ST} S cdot T + gamma_T T^2 ight],end{equation*}and show that integrating out torsion induces NJL-type four-fermion terms that generate fermion masses dynamically. The equation of state $P = ho - alpha_E ho^2$ (where $alpha_E$ is an effective coupling distinct from $alpha_S$) naturally emerges from the recursive spin-torsion dynamics, preventing singularities in both gravitational collapse and early-universe cosmology. Furthermore, torsion backreaction yields quantized gravitational wave echo frequencies and decoherence dynamics derivable from Lindblad-type master equations.Collectively, these results establish SMUG as a self-consistent, recursively closed, and observationally testable framework that unifies geometry, quantum field theory, and gauge structure through the primacy of spin.
Category: Mathematical Physics