Spectral Gap and Arithmetic Structure in a Unified 432-Lattice Framework: Finite Combinatorial Lattices and Discrete Gauge Transfer Operators

Abstract

Preprint (REVTeX 4.2 / APS two-column format): explicit finite-lattice results on index set Λ432 ≅ Z/16Z × Z/27Z ≅ Z/432Z. Includes exact Wilson transfer-matrix spectrum for Σ3 ⊂ SU(3) at L=1 (β=1/2), hybrid 432×432 contraction, twin-prime statistics mod 432 (p ≤ 106), Weil-form inertia on 144 Dirichlet characters, and a finite-dimensional spectral-decay lemma. All claims are scoped to finite lattices; no continuum Clay proofs. Bundled: PDF, LaTeX, Markdown source, and tabulated numerics JSON.