Lemma: One-step domain of dependence

There is a complete affine channel $K_s$, determined only by the schedule and the inner block channels at tick $s$, such that

Proof. The blocks meeting $I_{s+1}$ are contained in $I_s$ by Lemma lem:geometry. Restrict the input snapshot to their union, apply their product channel, and restrict its output to $I_{s+1}$. This is a complete channel $K_s$.

All other block adjoints act on identity factors when testing an observable supported in $I_{s+1}$; they are therefore invisible by Lemma lem:onelayer. Lemma lem:comparison gives (eq:onesnapshot). External outcomes are summed, not postselected.