We prove that four-dimensional SU(2) lattice Yang–Mills theory with Wilson action has a strictly positive mass gap. Specifically: (A) for coupling β ≥ β₀ ≈ 9587, connected correlators of gauge-invariant observables decay exponentially, uniformly in volume (correlation-length mass gap); (B) every subsequential continuum limit is a non-trivial Wightman QFT with spectral mass gap Δ > 0, via Osterwalder–Schrader reconstruction. The proof follows Bałaban's block-spin renormalization group architecture, taking a different analytical route through three structural inputs: (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. Parity cancellation of the cubic vertex reduces the polymer activity from O(g) to O(g²); the surviving O(g²) term has Wilson form (by the Peter–Weyl theorem for SU(2)) and is absorbed into the effective coupling, leaving an O(g⁴) remainder controlled by a convergent Kotecký–Preiss cluster expansion. A verification script (verify_all.py) reproduces all certified numerical constants from block combinatorics alone.