Algebraic backward recursion

Agreement of chosen complete kinematic block realizations is a sufficient certificate for condition (ii). Agreement only on $\mathfrak{A}(b)$ is not sufficient, by Proposition prop:extensiongap. A weaker sufficient condition is agreement of the layer restrictions on every algebra $\mathfrak{A}(N_{s+1}(Y))$ used in the backward proof.

The theorem is the gauge-net counterpart of the prescribed-support comparisons in En03-A, VII-E, VII-J, Psy04-B, and En06-A CheungEn03A,CheungVIIE,CheungVIIJ,CheungPsy04B,CheungEn06A. Their model-specific tensor wiring is not imported.