The flavor-sector extension of the split-exceptional-Jordan-algebra program introduced in Paper 1. The same rank-2 vacuum Qvac = diag(φ², 1, 0) generates complementary mixing patterns through two canonical algebraic operations on J₃(𝕠ₛ) — the Jordan triple product (small CKM mixing) and the Freudenthal cross product (large PMNS mixing).
The CKM hierarchy |Vus| >> |Vcb| >> |Vub| is derived as a structural consequence of the degenerate vacuum eigenvalue λ₃ = 0. Both CP-violating phases emerge from one torsion coefficient βδ = 11/(6π) through a bilinear/linear vacuum weighting distinction: δCKM ≈ 70.2° (PDG 68.8° ± 3.4°, gap +0.4σ) and δPMNS ≈ −133.4° (PDG −141.8°, gap ~6%).
The vacuum admits a physical interpretation as a degenerate three-charge black hole in the E₆(₆) attractor framework: λ₃ = 0 corresponds to zero horizon area, the CKM hierarchy is horizon degeneracy, and CKM/PMNS CP sign duality is BH/WH time-reversal.
| CKM/PMNS Duality | Jordan triple product vs Freudenthal cross product | DERIVED |
| δCKM | ≈ 70.2° (PDG 68.8°, +0.4σ) | PROPOSED |
| δPMNS | ≈ −133.4° (PDG −141.8°, gap ~6%) | PROPOSED |
| Jarlskog J | 3.01 × 10⁻&sup5; (PDG 3.08, gap −2.2%) | PROPOSED |
| CKM Hierarchy | From λ₃ = 0 (degenerate vacuum) | DERIVED |
| P₃-Lift | Quantum correction to degenerate horizon | OPEN |