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| ai.viXra.org > Mathematical Physics > 2511 |
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[7] ai.viXra.org:2511.0081 [pdf] submitted on 2025-11-24 01:03:23
Authors: Pedro A. Kubitscheck Homem de Carvalho
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
Classical planetary timekeeping relies on the solar day and the synodic period, two historically Earth-based units. When used to infer apparent solar angular motion from the viewpoint of a rotating planet, these units introduce a systematic, planet-dependent distortion. Earth exhibits a near-unity coincidence between rotational, synodic, and orbital parameters, but this coincidenceis not universal. We formalize the distortion through a dimensionless error functional depending only on the rotational period τP , the apparent solar period T⊙,P , and the planetary radius DP. We derive a universal referential correction,Du2032P = pτP T⊙,P , which collapses the apparent solar angular velocity to a single reference value across different planets when expressed in physical (non-local) time. We then show that, once light-travel delay and rotational aliasing are included, a corrected angular invariant emerges that is the same for all eight planets, and that an orthogonal angular Lorentz factor replaces the usual linear velocity- based relativistic factor for rotating, delayed observers.
Category: Mathematical Physics
[6] ai.viXra.org:2511.0075 [pdf] submitted on 2025-11-23 00:09:56
Authors: J. W. McGreevy
Comments: 3 Pages.
We report a striking numerical coincidence between the graded dimensions of the moon-shine module V ♮ (associated with the Monster group) and the energy levels of the hy-drogen atom, as described by the Rydberg—Ritz combination principle. Using the cumulative dimensions T (n) = P k≤n dim V ♮ k and a Cardy-refined effective quantum number neff (n) = q 3 16π2 log T (n), the Balmer and Lyman series are reproduced to within current experimental precision (∼ 10−6 relative error) for low n, with deviations following the Cardy asymptotic of the c = 24 theory. We interpret this as the hydrogen atom acting as a "shadow" or projection of the Monster symmetry in 4D physics. The unique Monster-invariant weight-2 vector is conjectured as the archetype of the photon, the Runge—Lenz vector as a Monster generator preserving the third quadratic form, and the Dirac equation as an orbifold projection of the 24-dimensional Clifford algebra embedded in V ♮. These connections suggest a deeper unification of quantum mechanics with monstrous moonshine,with testable predictions for high-n spectral deviations.
Category: Mathematical Physics
[5] ai.viXra.org:2511.0053 [pdf] submitted on 2025-11-17 01:19:21
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 6 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a unified geometric framework (Principium Geometricum, PG) in which vacuum, light, inertia, gravity, and the cosmological constant arise from a single Planck—scale oscillatory law on a compact toroidal manifold T³. Each Planck cell (area (A_P = ell_P^2 = hbar G / c^3)) behaves as a harmonic geometric oscillator with frequency (Omega = 1/t_P = c^5 / (hbar G)) and geometric tension (tau_U). The mean kinetic term (langle dot T^2 angle = kappa_0 A_P^2 Omega^2) defines a finite vacuum density (ho^{PG}*v = beta kappa_0 ho_P) with (beta = (H_0 t_P)^2) and (ho_P = c^7 / (hbar G^2)). Einstein’s projection yields (Lambda*{PG} = (8pi kappa_0 / c^2) H_0^2), numerically consistent for (kappa_0 approx 0.1) without fine—tuning. Inertia and gravity emerge as temporal and spatial coherence gradients of the same geometric field; light is the universal update rate of the vacuum, (langle dot T^2 angle = sqrt{kappa_0} A_P Omega = sqrt{kappa_0} c ell_P). The unified constant (alpha_U equiv k_e A_P = (4pivarepsilon_0)^{-1} hbar G / c^3) acts as a geometric impedance linking electromagnetism and curvature; a Planck—unit projection (baralpha_U = (k_e/Z_0)(A_P Omega / hbar) = (1/4pi)(c G / hbar)) quantifies the EM—GR mismatch at the Planck interface. We provide closed-form calculations and two testable predictions: (i) a cosmological fit (Lambda propto H^2) and (ii) a torsion-balance signal scaling with material coherence.
Category: Mathematical Physics
[4] ai.viXra.org:2511.0041 [pdf] submitted on 2025-11-13 21:42:59
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please refrain from frequent submisions of highly speculative articles)
We propose a geometric framework in which matter transmission arises as a natural extension of wave propagation under the Principium Geometricum (PG). The vacuum is not an empty background but a geometric medium endowed with intrinsic tension, characterized by the unified constant alpha_U = ke * A_P. Light and radio waves are open modes of this tensional field, while matter corresponds to stationary toroidal oscillations. We introduce a triplet (A, Theta, Psi) that encodes the tensional amplitude, toroidal phase, and helicoidal topology of the vacuum. The associated signal S(t) = integral over V of Phi(x,t) dx, with Phi(x,t) = A(x,t) * exp(i * Theta(x,t)) * Psi(x,t), acts as a "vacuum radio": a modulation of temporal tension capable of propagating the geometric signature of matter through space. At the receiving end, when the local vacuum reaches phase coherence with the incoming signal, a stationary toroidal pattern self-organizes and the corresponding atom or structure is recreated as a new instance of the same geometric state. No mass or charge is transported; only coherence information is. This framework suggests a deep equivalence between energy, geometry, and information in the PG field. It bridges electromagnetism, gravitation, and quantum-like discreteness into a single tensional ontology and points toward a matter transceiver as a long-term technological possibility: a device that encodes, transmits, and reconstructs matter as coherent patterns of vacuum tension.
Category: Mathematical Physics
[3] ai.viXra.org:2511.0037 [pdf] submitted on 2025-11-12 21:42:12
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 7 Pages.
Part I (Mathematics). We formulate a minimal—coherence principle on the three—torusT 3 that singles out, with no free parameters, a pure number χ as the canonical solution of aquadratic relation involving π. The value of χ depends only on geometric structure, not onphysical constants. Part II (Physics). We map χ to the vacuum unifying constant αU = keAP by defining the numerical part of αU as χ × 1060−1 in SI units. This furnishes a parameter—free prediction for G (or, dually, for ke) through αU ≡ keℓ2 P . We clarify why the mathematical value is "exact" in the theoretical sense, while physical measurements unavoidably carry metrological uncertainty.
Category: Mathematical Physics
[2] ai.viXra.org:2511.0031 [pdf] submitted on 2025-11-10 21:25:44
Authors: J. W. McGreevy
Comments: 4 Pages.
We present GRQFT (General Relativistic Quantum Field Theory) as a theory of everything (TOE)grounded in arithmetic geometry over Spec(Z), where physical reality emerges as an entropic computation maximizing information under cohomological constraints. The framework integrates U(1) gauge theory (Maxwell’s equations) via μ4 i-cycle bundles, sources gravity from Monster moonshine polarization, andderives entropy volumes from failures of surjectivity (Hn cohomology). Key refinements include p-adic causality for discrete time arrows and arithmetic backreaction in field equations. Supporting evidence includes predictive alignments with QCD σ, CMB Cℓ, Higgs λhhh, and novel EM quantization. Testablesimulations (e.g., p-adic Faraday induction) are provided.
Category: Mathematical Physics
[1] ai.viXra.org:2511.0021 [pdf] submitted on 2025-11-08 17:59:51
Authors: Paul Emmett Zaffuto
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
This paper presents a novel 18-digit period that serves as the foundational structure for a precision mapping system rooted entirely in integer arithmetic. The period, derived from a minimal deviation from 10¹u2078, creates an exact wavelength via the speed of light and a potentially infinite decimal counter in its frequency domain. The system is mathematically reversible, scale-invariant, and self-documenting across dimensional magnitudes. While the counter is potentially infinite, its manifestation depends on the presence of an observer or measuring system—making it a construct of potential, not actuality. The implications for time-based harmonic structures, integer-driven physics, and digital precision frameworks are explored.
Category: Mathematical Physics