Minimal-Measurement Determination of the Fine-Structure Constant from a Self-Dual Anisotropic Lattice

1 Introduction article graphicx Alpha-Minimal-Measurement Determination of the Fine-Structure Constant from a Self-Dual Anisotropic Lattice Thomas Lyspiil October 2025 2 Introduction [11pt]article [a4paper,margin=1in]geometry amsmath,amssymb,amsthm hyper- ref enumitem booktabs microtype colorlinks=true,linkcolor=black,citecolor=black,urlcolor=black First-Principles Derivation of a Dimensionless Electro- magnetic Coupling from a Self-Dual Anisotropic Metric Comprehensive Version: Phases 1–4 (Referee-Ready) Independent Re- search Report October 11, 2025 plain Abstract We define an Epstein-type anisotropic spectral sum C(τ,η) = 1−cos(2πm1η) (m2 1 + τ2m2 2 + τ4m2 3)3/2 , m∈Z3 \{0} τ >0, 0 <η<1, prove absolute convergence and real-analyticity in τ, and establish a du- ality C(τ,η) = τ−3C(τ−1,η) via Poisson resummation. We show there is a unique stationary point τ with ∂τC(τ,η)=0. Regulator indepen- dence (heat-kernel = zeta) follows by dominated convergence. Using background-field/OPE locality, we verify that the one- and two-loop coef- ficients in the effective running coincide with the universal Abelian values. We provide a symbolic enclosure for the derived dimensionless coupling 1at τ by exact rational-interval arithmetic on a finite block plus a closed- form integral tail bound, yielding a fully analytic error < 2 ×10−12. A single low-energy observable fixes the length scale; no further adjustable