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 δCKM = πR = 66. 89°, matching the observed 65. 5° ± 3. 4° (0. 4σ). Setting the unitarity triangle modulus Rb = 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 δPMNS = CA × πR = 3πR = 200. 7°, matching the observed 197° ± 25° (0. 15σ), where CA = 3 is the colour number. The factor of CA arises because leptons couple to all three torsion axes simultaneously, while quarks couple through a single colour channel. This gives a sharp prediction: δPMNS/δCKM = CA = 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, CA = 3, Δ = 17. Zero free parameters.