Spectral Syzygies, Arithmetic Selection, and Galois Rigidity in an Octonionic Yukawa Sector

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 physical reading, including comparison with entanglement-minimization and vacuum-phase approaches to CP violation, is discussed in Section 10. v2: substantially revised introduction, expanded bibliography (43 references), explicit Casimir matrices, Fano-plane figure added. Prepared for journal submission.