We establish exact spectral laws (syzygies) for the two physical Yukawa channels of the octonionic flavor framework. In the protected channel Tᵤ = (2, 4, 6), the product of eigenvalues is affine in their sum. In the charged channel Td = (3, 5, 6), a factorized characteristic polynomial selects the unique rational interior point t = 6/7 with spectrum in Q (√3). A three-entry Gram lemma classifies the seven Fano lines into five affine and two radical. The Casimir commutator satisfies the cubic law C₂³ = −ω²C₂ with ω² ∈ Q (√6). The four-field arithmetic constellation Q (√2), Q (√3), Q (√5), Q (√6) forms a Galois sub-complex stable under order-2 corrections. The principal branch predicts δPMNS ≈ +45° (sin δ > 0), experimentally distinguishable from entanglement minimization (~180°) and vacuum-phase 2HDM models (~293°).
M. Bakhtaoui (Tue,) studied this question.