Paper 104: Toward a Yang–Mills Mass Gap Solution RG Stability and Universality of Coherence-Constrained Models

This paper completes the constructive framework for coherence-constrained lattice gauge models, building on Papers 102 and 103, by establishing renormalization group (RG) stability and analyzing universality. We prove that if the local weights are reflection-positive admissible, then cluster expansion convergence and additive gap stability yield a positive spectral gap uniformly in volume. Analytic expansion and numerical tests (Appendix B) show that the coherence penalty couples only to the standard Yang–Mills field strength operator, with a prefactor that vanishes in the continuum limit. For dimensionless weights the penalty is irrelevant for all positive scaling exponents, while for inverse-area weights it is irrelevant for exponents greater than two. In either case, the model flows to the pure Yang–Mills universality class. The mass gap construction is rigorous up to two remaining open problems: controlling the asymptotics of the additive correction term Delta(b), and verifying that the coherence penalty does not modify the Yang–Mills beta function. Resolution of these problems would complete a Clay-level proof of the Yang–Mills mass gap.