Proposition: Conditional physical causal containment

Suppose an independently supplied physical embedding assigns events to the schedule and a transitive causal relation. Assume every allowed dependency through every local channel is certified to respect that relation. Then scheduled ancestors, and hence actual influences, lie in the physical causal past of the endpoint.

Proof. Every scheduled dependency path is a finite composition of certified causal steps. Transitivity gives containment. Theorem thm:support places actual influence inside the scheduled set.