Mathematical Physics

2512 Submissions

[4] ai.viXra.org:2512.0060 [pdf] replaced on 2026-07-04 16:52:36

Clustering, Recovery, and Locality in Algebraic Quantum Field Theory: Quantitative Bounds via Split Inclusions and Modular Theory

Authors: Lluis Eriksson
Comments: 29 Pages. v2 replaces v1; itemized changelog in Appendix F. Exact numerical verification suite distributed in a companion repository.

We prove that exponential clustering of vacuum correlations enables approximate reconstruction of global quasi-free states from local data in algebraic quantum field theory. The reconstruction is an explicit Gaussian procedure — conditional reattachment through the vacuum's regression structure — which coincides with the output of the Petz recovery map when the reference state factorizes across the split, but not in general: for a pure reference the Petz map returns the reference itself for every input, and version 1 of this paper incorrectly identified the two. For quasi-free states of a massive scalar field satisfying natural constraints, including a symplectic-gap (mixedness) condition on the reference state and an admissibility (no-steering) condition on the split geometry, we prove 1 - F <= C(d,kappa) / [eps^2 (1 - (eta_vac + delta)^2/eps)^2] * ||Delta12||_HS^2, where Delta12 is the reconstruction error, eta_vac <~ e^(-mr) is the vacuum correlation factor, delta controls cross-correlation perturbations, and C(d,kappa) = C_k(6+C_k)/(16 min(c1,c2)^2) with C_k = (1+kappa)^2/(kappa(kappa+2)) determined by the symplectic gap kappa > 0. A finite-rank corollary with explicit factor 2n recovers physical intuition. All counterexamples and bounds are verified by an exact truncated-Fock numerical suite distributed with the paper. Applications to holographic reconstruction are discussed.Version 2 makes three corrections to v1: (i) the reconstruction map of v1's Proposition 2.14 is not the Petz map — its "marginal preservation" step fails for correlated references — and the main theorem is restated for the reconstruction procedure the proof actually controls; (ii) the simplified constant is corrected (3/8 to 7/16 in the strongly mixed limit); (iii) a symplectic-gap hypothesis is added to the Gaussian fidelity lemma, shown necessary by an explicit counterexample.
Category: Mathematical Physics

[3] ai.viXra.org:2512.0010 [pdf] submitted on 2025-12-03 21:19:45

Spacetime, the Standard Model, and All of Physics from Archimedean Exhaustion of the Arithmetic Circle [?]

Authors: J. W. McGreevy
Comments: 3 Pages.

We prove that the entirety of known physics — Einstein—Cartan gravity, the Standard Model with three generations, QCD confinement, electroweak unification, the Kerr—Newman black hole, the CMB power spectrum, and the resolution of five Clay Millennium Problems — emerges from a single mathematical process: the Archimedean exhaustion of the circle at the infinite prime applied to the global arithmetic orbifold O = h Spec(Z).Gbm ⋊ Gal(Q/Q) i ⊔ h SL(2, Z)H i followed by sequential double-negation closure. All observables are fixed without parameters.
Category: Mathematical Physics

[2] ai.viXra.org:2512.0004 [pdf] submitted on 2025-12-01 16:56:15

Emergence of Classical Spacetime and the Complete Standard Model from Archimedean Exhaustion of the Arithmetic Circle Within Moonshine: Generalized Relativistic Quantum Field Theory

Authors: J. W. McGreevy
Comments: 3 Pages.

We prove that the Einstein—Cartan spacetime of our universe, together with the complete Standard Model (including three generations, the Higgs mechanism, and all observed charges), is the crepant resolution of a single global arithmetic orbifoldO = h Spec(Z). Gbm ⋊ Gal(Q/Q) i⊔h SL(2, Z)Hivia sequential double-negation closure driven by Archimedes’ exhaustion of the circle at the infinite prime. The Runge—Lenz vector, the Rydberg formula, proper time, torsion, and the equivalence principle arise as direct mathematical consequences. The Riemann Hypothesis is proven as a consistency condition.
Category: Mathematical Physics

[1] ai.viXra.org:2512.0003 [pdf] replaced on 2025-12-05 21:28:04

Geometric Reconstruction from Correlation Structure

Authors: N. J. Kettlewell
Comments: 6 Pages.

We begin with a complex two-point correlation kernel W(x,y) defined on an abstract smooth label space Xwith no assumed metric, signature, causal structure, or geometric fields. From four operational constraints—finite propagation, passivity, regularity, and local homogeneity—we show that Lorentzian cones, Hadamard singularities, and a metric emerge as statistical summaries of propagation behaviour. Mixed derivatives of the correlation phase reconstruct the metric, and stability of a least-change functional selects Lorentzian signature and statistically favours three spatial dimensions. Allowing coefficients of the correlation generator to vary introduces curvature, and ensemble-averaging the correlation stress yields the statistical consistency conditionGAB + ΛgAB = κ⟨EAB ⟩,linking curvature to averaged correlation tension. Thus spacetime geometry arises not as a background structure but as the collective behaviour of correlations satisfying operational postulates.
Category: Mathematical Physics