Corollary: Readout dependence

A prescribed readout on $Y$ at tick $t$ depends only on the initial reduction to $N_{0,t}(Y)$. Replacing a prescribed block channel outside its backwards dependency region does not change its law, provided the supports and schedule remain fixed.

Proof. Apply thm:locality to the readout effects. A replacement outside the backwards region acts on an identity factor in the pulled-back effect, and every channel adjoint preserves that identity.