CP-Violating Phases of the CKM and PMNS Matrices from the T₁u Eigenvalue Ratio

The CP-violating phases of both the CKM and PMNS mixing matrices are derived from a single algebraic quantity: the eigenvalue ratio R = r₁/r₂ = (9−√17)/(9+√17) of the T₁u sector of the truncated octahedron face Laplacian. The CKM phase is δ_CKM = πR = 66.89°, matching the observed 65.5° ± 3.4° (0.4σ). Setting the unitarity triangle modulus R_b = R gives ρ̄ = R cos(πR) = 0.146 (1.3σ) and η̄ = R sin(πR) = 0.342 (0.6σ), closing the CKM matrix to 4/4 Wolfenstein parameters. The derived sin(2β) = 0.690 matches the B-factory measurement 0.699 ± 0.017 (0.5σ). The PMNS phase is δ_PMNS = C_A × πR = 3πR = 200.7°, matching the observed 197° ± 25° (0.15σ), where C_A = 3 is the colour number. The factor of C_A arises because leptons couple to all three torsion axes simultaneously, while quarks couple through a single colour channel. This gives a sharp prediction: δ_PMNS/δ_CKM = C_A = 3 exactly, testable by DUNE and Hyper-Kamiokande within the decade. Combined with previous results, the complete quark and lepton mixing sector — 9 parameters — is determined by three cell integers: F = 14, C_A = 3, Δ = 17. Zero free parameters.