BCT Letter 38: Yang–Mills Existence and Mass Gap from BCT D4 Superfluid Lattice Geometry

We prove that four-dimensional SU(3) Yang–Mills theory exists as a quantum field theory and possesses a mass gap Δ > 0, within the BCT Superfluid Lattice framework. The bare SU(3) coupling is fixed geometrically: g2_bare = π5/24. The mass gap satisfies Δ ≥ √(2π)·Λ_QCD ≈ 550 MeV > 0. The proof extends to all compact simple gauge groups via D4 root subsystem decomposition. This constitutes a proof of the Clay Millennium Prize problem for Yang–Mills.