A Reflection-Positive Constructive Program for 4D Yang–Mills

This record registers a constructive program addressing the four-dimensional SU(N) Yang–Mills existence and mass gap problem. The manuscript outlines a nonperturbative Euclidean framework that ensures reflection positivity, gauge invariance, and exponential clustering. Within a lattice formulation, two complementary strategies are introduced to establish a mass gap: one analytic, based on functional inequalities, and one geometric, based on loop-equation methods. Both approaches are designed to persist in the continuum limit, leading to a rigorous constructive setting for Yang–Mills theory. Full technical details are contained in the restricted preprint.