Fermion Mass Ratios and CKM Mixing from the Spectral Architecture of the Binary Icosahedral Group

We derive intergenerational fermion mass ratios and CKM mixing matrix elements from a single geometric object: the 600-cell, the Cayley graph of the binary icosahedral group 2I. The Laplacian eigenvalue ratio in the generation-carrying irreducible representations is exactly 1/φ², where φ = (1+√5)/2 is the golden ratio. This yields the mass formula m(heavy)/m(light) = φ2Q with Q determined by the McKay correspondence. The CKM mixing angles follow from θ ∝ φ−Q with Q values inherited from the mass formula. We compute 8 independent predictions—four mass ratios, three CKM angles, and the CP-violating phase—with zero continuous free parameters, obtaining 4.2% average deviation from experiment. The CP phase is exactly δ = arccos(1/φ²) = 67.5°, consistent with the measured 67° ± 4° at 0.14σ.