Theorem: Separate physical-containment certificate

Suppose every port is assigned a regular host event and every dependency edge is realized by a future-causal curve in the supported laboratory. Then actual intervention influence is contained in scheduled ancestry, which is contained in the prescribed physical causal past of the joint output.

Proof. The first inclusion follows from Theorem thm:locality or its port-network version. Concatenation of the installed future-causal curves proves the second. Proposition prop:nosignal gives exact deterministic no-signalling outside that region.