Paper 105: Toward a Clay-Level Solution of the Yang–Mills Mass Gap Problem Asymptotics of ∆(b) and Preservation of the β-Function

This paper advances the constructive program for solving the Clay Millennium Yang-Mills mass gap problem, following Papers 102-104. Those works established a reflection-positive lattice measure, proved a volume-uniform mass gap at finite lattice spacing, and demonstrated renormalization group (RG) stability and universality up to two unresolved issues. Here we address these open problems: (i) the asymptotics of the additive correction Delta(b) in the RG gap stability theorem, and (ii) the perturbative effect of the coherence penalty on the Yang-Mills beta function. We show that Delta(b) decays with block size or is summable across scales, ensuring persistence of the mass gap in the continuum limit. We further compute the one-loop contribution of the coherence penalty to the gauge coupling renormalization and prove, via power counting and Weinberg's theorem, that all higher-loop corrections are irrelevant. Together these results demonstrate that the constructive mass gap established at finite lattice spacing persists in the continuum, and that the ultraviolet flow remains that of pure Yang-Mills theory. This closes the principal analytic gaps left by Paper 104 and brings the program within reach of a complete Clay-level proof.