Mathematical Physics

2512 Submissions

[4] ai.viXra.org:2512.0060 [pdf] submitted on 2025-12-17 02:23:22

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

Authors: Lluis Eriksson
Comments: 22 Pages.

We relate exponential clustering of vacuum correlations to approximate quantum state recovery via the Petz map in algebraic quantum field theory. In a regularized CCR (Gaussian/quasi-free) framework for a massive scalar field, we derive an explicit fidelity bound between a quasi-free state ω and the Petz-recovered state ω~ associated with the canonical split inclusion. The estimate controls 1 − F(ω, ω~) in terms of a Hilbert—Schmidt recovery error in the cross-correlation block, a vacuum correlation factor η_vac (decaying approximately as exp(−m r) with collar width r), and a perturbation parameter δ measuring deviations from vacuum cross-correlations. We also give a finite-rank corollary with an explicit 2n factor and discuss implications for quantitative locality and (conditionally) holographic reconstruction.
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