BCT Appendix JH4: Yang–Mills Existence and Mass Gap — Complete Proof from BCT D4 Superfluid Lattice Geometry

Complete proof that four-dimensional Yang–Mills theory with gauge group SU(3) exists as a quantum field theory and possesses a mass gap Δ > 0. Proof in four steps: (I) existence via Wilson lattice measure and D4 self-duality; (II) continuum limit with geometrically fixed coupling g2 = π5/24; (III) mass gap via Jentzsch theorem and cluster expansion; (IV) uniqueness of D4. Lower bound Δ ≥ √(2π)·Λ_QCD ≈ 550 MeV. Companion technical appendix to Letter 38.