Proposition: Influence bound and conditional physical containment

One has

and the inclusion can be strict.

If a location map places every dependency edge in a transitive physical causal relation, then operational influence is contained in the corresponding physical past of the located outputs. This statement requires location and causal certification for encoders, controllers, communication, and decoders as well.

Proof. Proposition prop:schedule and its port-network proof exclude influence outside scheduled ancestry. For strict inclusion, let a channel with a scheduled input return a fixed output state. Its output is unaffected by interventions at that input.

For the physical assertion, every scheduled path maps to a chain of physical causal relations. Transitivity puts its initial event in the physical past of its final event. Combine this with the influence inclusion.