Theorem: Encoded physical containment

Suppose the full encoded–computed–decoded network is complete, and every dependency edge has the stated causal certificate. For a joint output $B$, let ${\mathrm{Phys}}^{-}(B)$ contain input factors whose assigned events can reach at least one output event of $B$. Then

Every intervention supported outside ${\mathrm{Phys}}^{-}(B)$ has zero signalling to $B$, with arbitrary untouched references.

Proof. Theorem thm:schedule gives the first inclusion. Concatenate the supplied causal routes along a scheduled path. Transitivity gives the second inclusion. Apply Theorem thm:nosignal to the complement of the physical past.