Paper 102: Constructive Scaffold for Coherence-Constrained Gauge Models OS Axioms, Reflection Positivity, and Polymer Criteria

We establish the axiomatic and constructive framework underlying the coherence-constrained lattice gauge models of Paper 103. Our goal is not to solve the Clay Yang–Mills mass gap problem, but to state rigorously the conditions under which reflection positivity, cluster expansion convergence, and a uniform spectral gap can be obtained. We define the class of reflection-positive admissible central weights, prove a volume-uniform mass gap theorem, and state Open Problem 102.1 concerning the renormalization group stability of the gap in the continuum limit. This abstract scaffold prepares the ground for the explicit SU(3) implementation in Paper 103.