| ai.viXra.org > Mathematical Physics > 2603 |
|
 |
| ai.viXra.org > Mathematical Physics > 2603 |
|
|
[9] ai.viXra.org:2603.0084 [pdf] submitted on 2026-03-21 21:12:34
Authors: Xiangqian Zhang, Chao Greene, Mingming Zhao
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The Standard Model of modern physics contains dozens of free parameters that cannot be derivedfrom theory (such as the fine structure constant ), and faces severe theoretical gaps when bridgingmicroscopic quantum scales and macroscopic cosmic scales. This paper proposes the "TopologicalResidual Theory," establishing "right-handed cylindrical helical motion of space at the speed of light" as the sole first-principle axiom. Through the motion-derived dimension of space, the pure geometric origin of the fine structure constant is rigorously derived. Furthermore, by introducing the unit solid-angle helical divergence number , and combining it with Mandelbrot fractal geometry, thetheory proves that the strong nuclear force, electromagnetic force, and gravitational force areessentially geometric residuals of the same helical fluid at different topological levels. Finally, using only pen-and-paper geometric algebra, the theory precisely calculates the electron anomalousmagnetic moment, helium ion ionization energy, and proton-neutron mass difference, providing anew pure-geometric paradigm for a grand unified theory.
Category: Mathematical Physics
[8] ai.viXra.org:2603.0079 [pdf] submitted on 2026-03-18 14:58:48
Authors: Thomas Husmann
Comments: 8 pages, 5 tables, 1 supplementary code listing, 25 references. CC BY-NC-SA 4.0. Patent pending (Application No. 19/560,637). Source code: https://github.com/thusmann5327/Unified_Theory_Physics
Background: The Aubry—André—Harper (AAH) Hamiltonian, a one-dimensional quasiperiodic tight-binding model with irrational modulation frequency, exhibits a Cantor-set energy spectrum at its self-dual critical point. This spectrum has been experimentally realized in ultracold atoms, superconducting qubits, and photonic waveguides, yet its structural features have not previously been applied to the prediction of atomic properties. Methods: We constructed the AAH Hamiltonian on a lattice of D = 233 sites (a Fibonacci number) with modulation frequency α = 1/φ, where φ denotes the golden ratio, and potential amplitude V = 2J (the self-dual critical point). Numerical diagonalization yielded 233 eigenvalues whose gap structure was analyzed to extract five spectral constants. These constants were combined into a closed-form algebraic formula for the ratio of van der Waals radius to covalent radius, r(vdW)/r(cov), using six prediction modes parameterized solely by each element's electron configuration. No constants were fitted to experimental atomic data. Results: The formula was evaluated for 54 elements (Z = 3—56). Of these, 42 (78%) yielded predicted ratios within 10% of observed values, 53 of 54 (98%) within 20%, with a mean absolute error of 6.7%. Only one element (boron) exceeded a 20% error. The best-predicted element, cesium, showed agreement to 0.2%. The residual deviations correlated significantly with independently measured material properties: hardness (ρ = +0.66 for p-block elements), melting point (ρ = −0.61), and electrical conductivity (r = −0.74 for metals). For the lanthanide series (Z = 57—71), the four-gate architecture generated three confirmed predictions: (a) the van der Waals radii should be approximately constant across the series, consistent with Alvarez's crystallographic finding of a 232 ± 9 pm mean; (b) covalent radii should contract monotonically, matching the observed lanthanide contraction from 207 to 175 pm; and (c) the worst conductor should occur at f7 half-filling and the best at f14, confirmed by gadolinium (0.74 MS/m) and ytterbium (3.51 MS/m). Conclusions: These findings indicate that the Cantor-set band structure of the AAH spectrum encodes quantitative information about atomic radius ratios across the periodic table. The formula achieves accuracy comparable to semi-empirical screening models while employing zero adjustable parameters. Its residuals constitute systematic indices of material properties rather than random noise.
Category: Mathematical Physics
[7] ai.viXra.org:2603.0072 [pdf] submitted on 2026-03-16 13:35:11
Authors: Jason Merwin
Comments: This document contains 22 pages.
Relational Mathematical Realism (RMR) proposes that physical reality emerges from a discrete 137-node registry partitioned as 81 (spatial) + 40 (surface) + 16 (gravitational). We develop the thermodynamic screening mechanism introduced in the RMR synthesis paper [3] into a self-contained predictive framework. A universal screening unit δ0 = 5/137, derived from the registry’s electromagnetic surface fraction, generates mass corrections across leptons, hadrons, and the fine-structure constant with zero fitted parameters. Key results: (i) α−1 = 137.035 996 versus CODATA 137.035 999 (error 3 × 10−6); (ii) mΛ0 /me = 2183.328 versus PDG 2183.327 (error 4 × 10−7, sub-keV on a GeV-scale mass); (iii) a strangeness screening integer Bs = V (K3)2 = 9 derived from the K3 ⊗ K3 product graph, yielding correct corrections for Λ0 and K+; (iv) a {9, 13, 17} strangeness ladder for Λ0, Ξ−, Ξ0 with step size 4, arising from K5 interface topology; (v) a charge-dependentovershoot theorem: corrections exceeding the 42 = 16 gravitational threshold are clipped by 4for charged particles, with three-particle confirmation (τ −, Ξ−, Ξ0). Eleven independent mass predictions are tabulated. A screened-angle ladder extends these results to dimensionless mixing observables: the effective leptonic weak mixing angle, the three PMNS angles, and the reactor angle are all approximated by δ0-corrections of quarter/half base states using multipliers from established graph integers, with no new parameters. Open sectors (meson bases, Ω− decuplet, Σ0 isospin mixing, and radiative corrections to the mixing angles) are characterized precisely andreserved for future work.
Category: Mathematical Physics
[6] ai.viXra.org:2603.0058 [pdf] submitted on 2026-03-13 17:21:04
Authors: Tingfang Yi
Comments: 7 Pages.
Light’s propagation, phase, polarization, and frequency are projections of a minimal six-dimensional null entity unifying spacetime and photon internal degrees of freedom. Observed pairwise and triple couplings emerge naturally, explaining Spin Hall, Berry, Pancharatnam phases, optical activity, and relativistic shifts. Classical fields, quantum detections, and wave-particle duality arise as lower-dimensional projections, while photon discreteness reflects detector intersections. The framework agrees with relativity and QED and predicts testable interference deviations via controlled holonomy.
Category: Mathematical Physics
[5] ai.viXra.org:2603.0049 [pdf] submitted on 2026-03-12 02:40:35
Authors: J. W. McGreevy
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a unified relativistic field theory over the ring of adeles AQ, in whichthe nontrivial zeros of the Riemann zeta function emerge as quantized energy levelsof a self-adjoint Hilbert—P´olya operator ˆH. The theory begins with a Non-Hermitian"Adelic Carnot Pump" driven by local prime interactions (Cup and Cap products),Hermitianized globally through restriction to the cuspidal subspace of automorphicforms on GL2(Q)GL2(A).The Arithmetic Planck constant hA ∼ log 2 quantizes phase steps, while the weight-12 modular discriminant ∆ provides vacuum tension. Maxwell-like adelic field equa-tions govern the dynamics, culminating in a least-arithmetic-action principle whosegeodesics are confined to the critical line Re(s) = 1/2.A dimensionless Arithmetic Fine-Structure Constant αA ≈ 1/(log 2 · 2π) tunes thecoupling between local curvature and global flow. Invariance of αA under the fulladelic group action is enforced by an Arithmetic Noether Theorem, which acts as acentripetal force locking spectral ordinates to the critical line.Self-adjointness follows from cuspidal sealing and unitary Atkin—Lehner symmetry;spectral matching is achieved via a twisted trace formula that projects the GL2 cuspidalspectrum onto the GL1 zeta zeros through phase-cancellation of non-coherent modes.We conclude that the Riemann Hypothesis is the symmetry requirement for acausal, lossless arithmetic vacuum: all nontrivial zeros satisfy Re(ρ) = 1/2. Exten-sions to the Birch and Swinnerton-Dyer conjecture are suggested.Keywords: Riemann Hypothesis, Hilbert—P´olya conjecture, adelic geometry, au-tomorphic forms, Noether theorem, non-Hermitian dynamics, modular forms, criticalline1
Category: Mathematical Physics
[4] ai.viXra.org:2603.0046 [pdf] submitted on 2026-03-11 18:50:11
Authors: Thomas A. Husmann
Comments: 7 Pages. (Note by ai.viXra.org Admin: Please don't name title, equation/formula etc after the author's name)7 tables. Verification code at https://github.com/thusmann5327/Unified_Theory_Physics. Patent Application 19/560,637. CC BY-NC-SA 4.0.
We demonstrate that the [proposed] Decomposition, grounded in the single algebraic identity phi^2 = phi + 1, extends to atomic physics with sub-percent precision across three independent domains. Spectral: alpha_em^{-1} = N x W = 137.337 (0.22% vs. CODATA), where N = 294 and W = 0.467134 are derived from the topological invariants of a 233-site Aubry-Andre-Harper lattice at critical coupling. The bracket count N is independently derivable as N = F(13) + F(10) + F(5) + F(2) = 233 + 55 + 5 + 1, a spectral topology invariant generalizable to any Fibonacci lattice. This cascades through QED to predict the Bohr radius (0.22%), Rydberg energy (0.44%), and proton charge radius (0.14%). Spatial: Anchoring the hydrogen 1s peak at the Cantor shell center maps 42% of the probability into the sigma_2-sigma_4 wall zone; the H_2 bond length matches sigma_4 outer to 0.5%. Information-theoretic: The bipartite entanglement entropy at the Cantor sigma_4 outer wall reaches S = 0.6908 nats, 99.66% of the theoretical maximum ln 2, with zero free parameters. The Cantor outer wall lies 5.3% beyond the equal-partition point (p = 0.535), preserving 99.66% of the theoretical maximum entropy ln 2. Three additional exact identities are proved from phi^2 = phi + 1 alone: the unity partition 1/phi + 1/phi^3 + 1/phi^4 = 1, the boundary law 2/phi^4 + 3/phi^3 = 1, and the pi-phi bridge pi = 4*arctan(1/phi) + 4*arctan(1/phi^3). Systematic comparison with all metallic means and quadratic irrationals shows phi is unique: it alone produces a critical eigenstate with minimal fractal dimension D_2 ~ 0.538, a nested five-sector Cantor spectrum, stable baryon fraction Omega_b ~ 0.048, and dark-energy-dominated expansion. The fine-structure constant is the cumulative wall fraction of the Cantor vacuum: alpha_em = 1/(N x W). The hydrogen atom is the same self-consistent structure at bracket 117.
Category: Mathematical Physics
[3] ai.viXra.org:2603.0044 [pdf] submitted on 2026-03-10 00:06:15
Authors: Md Mubdiul Hasan
Comments: 8 Pages.
—This work presents the analysis and functionalcharacterization of a multi-tap AC voltage stabilizer implemented in LTspice, emphasizing its control, feedback, and protection mechanisms. The stabilizer employs an autotransformer with discrete tap selection, where relay-driven switching provides coarse regulation across varying mains conditions. A dedicated sensing network, consisting of a transformer secondary, rectifier, and precision divider, generates a DC feedback signalproportional to the output RMS voltage. This signal is processed by a window-comparator architecture built around the LM324,enabling the controller to determine whether the present tap is too high, too low, or within the acceptable regulation band. The design incorporates a soft-start and pre-regulation stage that ensures stable startup behavior by delaying relay activation until the reference, supply rail, and sensing nodes reach steady-state values. Comparator thresholds are derived analytically by mapping mains voltage through the transformer ratio, rectifier, and divider network to the LM324 input domain. This allows direct calculation of the window center and allowable mains range for each tap. A protection comparator monitors long-term deviationsoutside the window and, through a zener-coupled reference node, triggers a controlled shutdown or tap change when necessary. The resulting system combines discrete tap switching with analog decision logic to achieve robust voltage regulation across a wide input range, while maintaining predictable and mathematicallyverifiable operating boundaries.
Category: Mathematical Physics
[2] ai.viXra.org:2603.0031 [pdf] submitted on 2026-03-07 16:25:39
Authors: Tingfang Yi
Comments: 7 Pages.
We propose a unified minimal six-dimensional (6D) light null entity, where the fundamental properties of light are reinterpreted as intrinsic degrees of freedom within a singular closed manifold. This 6D structure integrates a two-dimensional null propagation geometry with four intrinsic 1D degrees of freedom: optical phase, polarization, frequency, and orientation relative to the null momentum generator. In this framework, conventional four-dimensional (4D) spacetime optical, electromagnetic, and quantum phenomena arise as lower- dimensional projection or section measurements of this structure, while preserving consistency with established theories at the level of current observations. Spacetime coordinates and photon internal degrees of freedom may be geometrically equivalent components of a higher-dimensional manifold.
Category: Mathematical Physics
[1] ai.viXra.org:2603.0012 [pdf] submitted on 2026-03-02 21:37:16
Authors: Rui Mateus Joaquim
Comments: 12 Pages.
Donald Hoffman’s Interface Theory of Perception (ITP) suggests that spacetime is not a fundamental reality but a functional interface hiding a complex network of conscious agents. However, the mathematical "engine" that drives the transition from informational dynamics to geometric perception remains largely undefined. This paper proposes the Ontodynamic Matrix Singularity (OMS) as the foundational mechanism for this transition. Through a series of computational simulations (N=15, 210 directional flows), we demonstrate that the application of an "Ambiguity Resolution Operator" (ϕΨ) over a symmetric adjacency matrix generates stable informational cores. Our results show that mass and spacetime curvature are not intrinsic properties of matter, but emergent regulatory structures arising from informational saturation. This model provides a formal bridge between Conscious Realism and physical observables
Category: Mathematical Physics