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

Key Points

• To provide a complete proof of the existence of four-dimensional Yang–Mills theory with a mass gap.
• Four-step proof including Wilson lattice measure and D4 self-duality.
• Demonstration of continuum limit with fixed coupling g2 = π5/24.
• Analysis of mass gap using Jentzsch theorem and cluster expansion.
• Establishment of uniqueness for D4.
• Confirmed existence of Yang–Mills theory with gauge group SU(3).
• Established mass gap Δ ≥ √(2π)·Λ_QCD, approximately 550 MeV.