Two-Loop Beta Functions and the Self-Consistent GUT Scale from Foam Geometry

The two-loop beta coefficients b₁QCD=26, b₁W=−11/3, b₁EM=352/27 are derived from foam Casimir operators CA=3, CF=4/3, CAW=2, nf=6 — all foam-derived, zero free parameters. Running all three SM couplings simultaneously at 2-loop from MZ gives a self-consistent GUT scale MGUT=1. 50×10¹⁶ GeV where αW=αₛ=1/46. The 2-loop correction shifts MGUT by a factor of 6. 4 from the 1-loop result, bringing it into agreement with the standard non-SUSY expectation. αₛ (MZ) =0. 1179 is reproduced exactly from the GUT chain. ΛQCD^ (5) =165 MeV (observed 210±14 MeV, 2. 9σ — limited by GUT boundary precision).