Yang–Mills Mass Gap on the Poincaré Homology Sphere

We compute the SU(2) Yang–Mills mass gap on the Poincaré homology sphere S³/2I, where 2I is the binary icosahedral group of order 120. Three independent arguments establish the result: a Weitzenböck curvature floor (λ ≥ 2/R²), topological vacuum isolation (three isolated flat connections with vanishing H¹), and explicit spectral computation via the McKay correspondence for the extended E₈ diagram. The Galois conjugate vacuum exhibits a ninefold enhancement (Δ² = 36/R²) over the baseline gap (Δ² = 4/R²), arising from icosahedral filtering of the first four coexact levels. The existence of the gap is topological; its numerical value is metric-dependent.