Registry · Theorem
IV.T163
conjectural
formalized
IV.T163 — QLC-Exact: sin(theta_12) = (sqrt(1-lambda_C^2) - lambda_C)/sqrt(2)
QLC complementarity (conjectural): if theta_12(PMNS) + theta_C(CKM) = pi/4 exactly, then sin(theta_12) = (sqrt(1-lambda_C^2) - lambda_C)/sqrt(2) where lambda_C = iota_tau*(1-iota_tau). Numerical: sin(theta_12) = 0.5290 -> theta_12 = 31.93 degrees, PDG 33.41 degrees, -41965 ppm. Gap: 1.48 degrees. The QLC formula predicts theta_12 within 1.5 degrees without free parameters. Structural motivation: in the tau^3 fibration, the A-sector and CKM mixing are complementary projections of the same holonomy on L = S^1 v S^1. Scope: conjectural (>10000 ppm but structurally motivated).
Book IV
Part 5
Ch. 36