Simplicial Lattice Field Theory (Vol VI): Coupling Constants from the Hodge Decomposition

The fine-structure constant α⁻¹ = 137.06 is derived from the Villain lattice action on the 24-cell face complex with instanton fugacity q = 1/3. The strong coupling αs = √2/12, the Higgs mass 125.25 GeV (via the Pell identity 17²−2×12²=1), the ρ-parameter 2702/2701, and the top Yukawa y²_t = 72/73 are all derived. The Spectral-Pell Unification Theorem proves that the prime 17 governing both the Higgs mass and fermion mixing is forced by z(z−8)=0.