Mathematical Physics

2610 Submissions

[4] ai.viXra.org:2610.0069 [pdf] submitted on 2026-10-29 22:54:23

Three-Dimensional Lattice Yang—Mills Theory in a Forest Gauge: A Dobrushin Range and a Certified Curvature Bound

Authors: Tristan Romanov
Comments: 9 pages. Code and certificates: doi:10.5281/zenodo.23783317. License: CC BY 4.0

We study Wilson lattice Yang—Mills theory on ℤ3 in a gauge that fixes one link at every site along a period-3 forest, in which every free link shares a plaquette with exactly seven other free links. Two results follow.

(A) For SU(2), a single-link Dobrushin argument with the sharp one-quarter Kantorovich estimate of Bhattacharjee and Bhattacharya gives a unique infinite-volume state, invariance, reflection positivity, exponential decay of correlations and a transfer-matrix gap m ≥ −log(7βW/4) for βW < 4/7. The same estimate gives βW < 1/3 in three dimensions without gauge fixing and βW < 1/2 in the temporal gauge. As Bhattacharjee, Bhattacharya and Lockwood showed for 1/3 in four dimensions, we show that 4/7 is the ceiling of this argument for every gauge-fixing forest.

(B) For every compact group with a faithful unitary representation, the Hessian of Σp Re Tr Qp restricted to the free links is bounded in absolute value by h = 9.599991, uniformly in the field. The proof is a site-plus-plaquette certificate with rational data: its finite part is checked in exact rational arithmetic, and positivity of a two-parameter family of matrices of size at most 12 is proved with outward-rounded interval arithmetic. With the Bakry—Émery criterion this gives log-Sobolev inequalities, a unique state and an explicit gap for N|β| < κG/h; for SU(N) this is |β| < 1/(2h) ≈ 1/19.20, compared with 1/32 of Shen, Zhu and Zhu and 1/24 from the sharp un-gauge-fixed constant. An exact computation at the trivial field shows that no bound below 9.3479 is possible in this gauge. All statements are at strong coupling and fixed lattice spacing.
Category: Mathematical Physics

[3] ai.viXra.org:2610.0013 [pdf] submitted on 2026-10-04 21:59:09

Multi-Symplectic Topos Flows and Asymptotic Safety: The Riemann Hypothesis as the Ultimate Global Proper-Time Phase Lock

Authors: J. W. McGreevy
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

This monograph presents a coordinate-free, non-perturbative extension of the Thermodynamics of Arithmetic Action (TAA) framework by proving that the non-trivial zeros of the Riemann zeta function ζ(s) dictate the spectral frequencies of sub-quantum coordinate position tearing. Semiclassically, when energy-momentum compaction forces the ad´elic continuum toward its ultraviolet limits, the local integer rings Op lose unique principal ideal factorization, creating fractional ideal debts that manifest macroscopically as metric resistance and rest mass. We show that the global Wiles modularity isomorphism (R ∼= T ) forces a perfect cross-domain cancellation between continuous temporal deformations and discrete spinorial coordinates via the Kustaanheimo—Stiefel (KS) bilateral phase lock. By evaluating the global Leech lattice theta function ΘΛ24 against the 691 irregular prime firewall, we deliver an unyielding proof that the Riemann Hypothesis (R⌉(s) = 1/2) is the absolute, non-parametric requirement that confines spacetime coordinate tearing to a lossless, hyperbolically orthogonal quantum phase lock, securing first-principles Asymptotic Safety across the space-time continuum.
Category: Mathematical Physics

[2] ai.viXra.org:2610.0008 [pdf] replaced on 2026-10-09 03:58:41

Unified Physics Through Exceptional Symmetries: an E_n-Indexed Field and MGFT Framework

Authors: Robert L. Jackson
Comments: 34 Pages. Obtain zip files at https://zenodo.org/records/23197992. Contact information is rljacksonmd@gmail.com

This paper develops an En-indexed analytic and representation-valued field framework with thedefining opposite-lift sector E_5 = E_6^- and constituent content boldtf{16} circleplus boldtf{9} circleplus boldtf{1} of total dimension 26. The main text covers E_5 through E15. The finite exceptional levels E_6, E_7 and E_8 are distinguished from the affine E_9, hyperbolic E_10, very-extended E_11, and proposed E_12—E_15 framework extensions. The eight-sector mGFT ansatz uses hypergeometric, exponential and monomial generator factors; its (0, 1, 1) sector recovers the weighted hull Hn,n−1(2ξ) when Q = ξ and Z = 2ξ. This supplies a candidate profile family, while internal symmetry is carried by explicitly chosen Lie-algebra representations. Integral ft-{ht,lsr}-mGFT is formulated as a generated-core Green—Duhamel correction with stated boundary data, quadrature and convergence conditions. The primary reduction chain is E_15->...->E_5; reverse operations are constructive lifts. Physical equations are discussed as theoretical contexts for the framework. The quantitative results are confined to fully specified mathematical and effective-action benchmarks: local profile and sum identities, an exact canonical scalar wall and its generated-coordinate double lift, constituent threshold arithmetic, prescribed quadratic masses, conditional two-body kinematics, a manufactured nonlinear boundary-value problem, and the E_10 Cartan spectrum. The supplied atlases distinguish three opposing labels, anti-, mirror and negative matter, relative to ordinary matter. Charge conjugation, copy labels, signed energy and gravitational sign are treated separately; signed constituent sums do not establish physical negative masses or photon rest masses. The separate supplement supplies the inputs, derivations and reproducible numerical checks.
Category: Mathematical Physics

[1] ai.viXra.org:2610.0004 [pdf] submitted on 2026-10-01 21:07:04

The Canonical Architecture of Arithmetic Spacetime: R∼ = T Modularity, Proper Time Areal Invariants, and the Spectral Resolution of Mass

Authors: J. W. McGreevy
Comments: 17 Pages.

We present a rigorous, top-down axiomatic formulation of the Thermodynamics of ArithmeticAction (TAA) framework, anchoring the macroscopic space-time continuum within the algebraic and representation-theoretic structure of Andrew Wiles’ modularity lifting theorem (R ∼= T). We establish that the universal Galois deformation ring (R) parameterizes the continuous, smooth moduli of macroscopic metric charts (gµν), while the commutative Hecke algebra (T )natively captures the discrete, non-propagating algebraic constraints of the Einstein—Cartanspin-density torsion tensor (Σλ µν).By introducing a specialized representation-theoretic functor, the classical stress-energy ten sor (Tµν) is re-derived as a trace-free anisotropic Hecke shear matrix (∆p ≡ Tp − 12Tr[Tp]I2). At the isolated turning nodes of a four-quadrant orbital trajectory (Periapsis and Apoapsis), the systematic collapse of radial vanishing cycles forces a degenerate Frobenius lock on Pierre Deligne’s weight-11 shell boundary, causing the classical scalar mass-energy density placeholder (ρ) to vanish identically (ρ ≡ 0). Crucially, gravity does not fail; the off-diagonal elements survive as a non-vanishing vacuum expectation value, revealing that the vacuum is an activeadélic transmission medium filled with extreme, pure KMS states born from the spontaneoussymmetry breaking of the Bost—Connes C∗-dynamical system at critical inverse temperatureβ =1. We mathematically demonstrate that the continuous Weyl tensor field (Cµνρσ) emerges as thecontinuum limit of this trace-free arithmetic shear, driving the 2D transverse deformations of a photon null congruence (ds2 = 0) via the Sachs optical equations. To regularize high-frequencyphase overpressure at the 691 modular cusp anomaly threshold, the framework deploys thenon-linear Hopf—Lax infimum convolution, which acts as an automated wavefront minimizerthat eliminates phase dispersion and enforces a perfect, loss-free Heaviside Distortionless Match(RC =LG) along the Critical Line (R⌉(s) = 1/2).Finally, we evaluate the local-to-global convergence of the waveguide as the prime completion index scales upward (p → ∞). We demonstrate that as the local inverse Euler factorsasymptotically flatten to unity (limp→∞(1 − p−s) ≡ 1), they track in perfect analytical harmony with the sub-exponential saturation of the Deligne stabilizer ratio ( |τ(p)| 2p11/2 ≤ 1). This simultaneous flattening mirrors the geometric periapsis decay factor (1 − e) as the trajectory approaches the parabolic escape boundary (e → 1), smoothly shifting the system from a discrete algebraic regime into a continuous geometric manifold. This absolute, asymptotic equilibrium locks the global Tamagawa volume rigidly to unity (τ(G) ≡ 1) and secures first-principles, non-perturbative Asymptotic Safety across the spacetime continuum.
Category: Mathematical Physics