V.R04 — The cross-couplings bind the halves

The crossed tensor product tau^3 = tau^1 x_f T^2 is not a direct product: the six cross-couplings kappa(A,B), kappa(A,C), kappa(B,D), kappa(C,D) etc. are nonzero rational functions of iota_tau encoding real physical interactions (gravitational lensing, weak hadron decays, electroweak channel), and the Hermetic Principle ensures these are the complete base-fiber interface.