Theorem: Typed scheduled support

A terminal observable on $Y$ pulls back to an observable supported on $N_{0,n}(Y)$, and

Input states agreeing on that backward region, jointly with any retained reference, have equal corresponding output reductions.

Proof. The adjoint of a trace-preserving block map fixes its identity. Blocks disjoint from the current backward support therefore cannot enlarge it. A block meeting it enlarges it only inside that block. Backward induction proves support containment. Each layer adds at most one block diameter, proving the metric bound. Pairing all terminal observables proves the reduction statement, also with reference observables included.