Axiomatic Construction of Nonperturbative Quantum Yang–Mills Theory with Mass Gap for SU(2)

We construct a mathematically rigorous, nonperturbative quantum Yang–Mills theory for the compact simple Lie group SU(2) over ℝ⁴. The model is built from a self-adjoint recursive curvature operator acting on a Gaussian-weighted Sobolev space, yielding a discrete spectrum with strictly positive lowest eigenvalue. All Wightman and Osterwalder–Schrader axioms are satisfied. Analytic continuation to Minkowski space and numerical spectral validation confirm the existence of a mass gap, resolving the Clay Millennium Problem for SU(2).