Corollary: Readout laws and prescribed interventions

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

Proof. Readout effects are output observables. On an excluded block the pulled-back observable is the identity, which every replacement channel adjoint preserves.