Uniform Spectral Gap and Renormalization Stability in Lattice Yang–Mills Theory

This record presents the technical preprint Uniform Spectral Gap and Renormalization Stability in Lattice Yang–Mills Theory. The manuscript develops a strict supplied-data architecture and proof map for studying spectral-gap persistence in lattice Yang–Mills theory and its controlled passage toward a physical continuum formulation. The work is organized around a finite gate structure: Euclidean finite certificates, the physical Osterwalder–Schrader bridge, full non-vacuum sector control, COSL continuum passage, QFT object identity, theorem-scope restriction, and final no-overclaim audit. The manuscript includes the Wilson lattice setup, auxiliary heat-bath and blocked contraction estimates, local coercivity and finite-certificate ledgers, same-sector Osterwalder–Schrader comparison, sector-total and no-escape alternatives, renormalization-stability gates, and a unified supplied-data closure ledger. A central purpose of the document is to separate proof architecture, reduced certificates, and unconditional theorem release. The manuscript does not identify auxiliary heat-bath dynamics with the physical Osterwalder–Schrader transfer operator, and it does not assert an unconditional solution of the Yang–Mills mass gap problem unless the complete actual-source chain is explicitly supplied and verified. The present record should therefore be read as a rigorous proof-map and supplied-data framework for the Yang–Mills mass gap problem, with the remaining theorem-release requirements localized into named auditable packets.