The channel causal-cut criterion

Consider a finite acyclic network of fixed channels, with every quantum, classical-control, record, and resource wire included. For an output interface $B$, let ${\mathrm{Sch}}^{-}(B)$ be the input wires reached by reverse traversal: whenever an output wire of a channel box is reached, include every input wire of that box.

If $\mathrm{Comp}$ is the network channel and $X$ its input interface, then

The reduced output channel on $B$ factors through the scheduled input ancestors. Inputs disjoint from that cut have zero signalling to $B$, including with an untouched reference.