Paper O28 established that the per-pair covariance Cc in End (H₄₅₅) has rank r₄₅₅ = 3 with invariant eigenvalue structure 1: 12: 12. The present paper provides the complete analytical explanation of this result and carries out the sector identification required for O26. We prove that the BornInfeld parity involution c q-c of O18, which implies ₐ-₂ (v) = c (v) in the canonical basis of H₄₅₅ (up to a slowly varying phase factor, as discussed in Section 6), forces every outer product Mⱼ = c (vⱼ) ₐ-₂ (vⱼ) ^* to lie in the complex symmetric subspace Sym (V_, C), where V_ = span₂\c (vⱼ) \ H₄₅₅ is the trajectory subspace. This is an algebraic identity that holds independently of the specific values of c (vⱼ) (the symmetry structure requires no genericity assumption; the rank formula of Theorem 3. 3 additionally requires the trajectory to span V_, which is verified numerically) equation*r₄₅₅ = d (₃_+1) 2, equation*where d_ = ₂ V_ is the complex dimension of the trajectory subspace. The observed value r₄₅₅ = 3 has the unique positive integer solution d_ = 2, confirming the spin-12 sector candidate without ambiguity. This result holds in both End (H₄₅₅) (proxy computation of O28) and End (V_) (correct O26 test space): restricting to End (V_) does not change the rank, since the symmetric constraint is intrinsic to the pair structure. We show that the O26 Criterion~5. 4 target of r₄₅₅ = d_² = 4 is structurally inaccessible from conjugate-pair data and must be reformulated as r₄₅₅ = d_ (d_+1) /2 for the present measurement setting. The reformulated criterion is satisfied uniquely by d_ = 2, and the numerical computation from Q5a-O5 checkpoints at q \61, 101, 151, 211\ confirms r₄₅₅ = 3 for 98\% of conjugate pairs at each prime, with zero inter-pair variance at q \61, 151\.
Jérôme Beau (Sun,) studied this question.