Explicit Strong-Coupling Bounds and Vacuum-Adapted Coercivity for SU(N) Lattice Gauge Hamiltonians

This standalone preprint proves quantitative finite-lattice spectral estimates for SU(N) gauge Hamiltonians under explicitly stated normalizations. A sector-valued Kirkwood–Thomas argument gives a gap of at least 3g²/16 for g² ≥ 59.9 in three spatial dimensions, uniformly in lattice size and N ≥ 2. A separate Feynman–Kac argument bounds fixed-block discarded fluctuations in the actual interacting vacuum, uniformly in exterior volume. An exact metric-normalized Schur comparison gives conditional additive inverse-gap costs. Counterexamples clarify a counting correction in the original BDL preprint and failures of unweighted Schur transfer and automatic oscillator closure. Scope: This paper does not prove continuum Yang–Mills existence, a continuum mass gap, or confinement. Whole-layer nonlinear coercivity, control of generated coarse operators, a physical terminal gap, and continuum spectral transfer remain open in this work. No global novelty or priority claim is made. This is an AI-assisted preprint, not independently human peer reviewed. The deposit contains the 20-page PDF, complete LaTeX source and selected historical evidence, exact standard-library Python checks, two limited Lean certificates, source hashes, and AI-assisted review records. Software and formal sources retain AGPL-3.0-or-later; manuscript and scientific prose are CC BY 4.0.