The SU(2) Yang-Mills Mass Gap via Curvature-Based Block Renormalization, Character Expansion, and Dobrushin Comparison

We prove that four-dimensional SU(2) lattice Yang–Mills theory with Wilson action has a strictly positive mass gap. For coupling β ≥ β₀ ≈ 9587, connected correlators of gauge-invariant observables decay exponentially, uniformly in volume. Every subsequential continuum limit is a non-trivial Wightman QFT with spectral mass gap Δ > 0, constructed via Osterwalder–Schrader reconstruction. The proof compresses Bałaban's block-spin renormalization group program using three structural innovations: (1) certified spectral bounds on the 2⁴ block Hessian via exact integer arithmetic, (2) a quantitative Christoffel bound controlling the non-abelian curvature correction, and (3) a gauge-covariant Schur complement blocking map. A companion verification script (verify_all.py) reproduces all certified numerical constants from block combinatorics alone.