Octonionic Flavor Structure: Discrete Rigidity, Conjugate Corrections, and a Rank-Deficient Neutrino Sector

We show that the algebra C⊗O, combined with Fano-plane combinatorics and a fixed vacuum, imposes a rigid set of discrete constraints on quark and lepton flavor mixing. The Quaternionic Kernel Theorem selects a unique Fano triplet pair; the Projection Principle determines the Cabibbo angle λ = 1/ (2√5) and the Wolfenstein parameter A² = 2/3; the associator phase selects a CP-odd branch. Second-order corrections are locked by the Fano involution σ₁ into conjugate channels: (3, 4, 7) for quarks and (2, 5, 7) for leptons. The three PMNS mixing angles are reproduced within 0. 5σ (χ² = 0. 27). The neutrino Yukawa matrix is structurally rank-deficient for all tν ∈ (0, 1). Five discrete interdictions reduce the viable parameter space to isolated regions. Companion scripts (Python 3 + NumPy) reproduce every numerical result in the paper. See READMEcompanionₛcripts. md for the mapping.