Theorem: Metric containment

Every directed scheduled dependency path in this execution model maps to a future-causal curve in $M$. In particular,

Operational influence under trace-preserving local interventions is contained in the scheduled dependency relation and hence in the prescribed metric causal relation.

Proof. Every elementary dependency connects two sites in one permitted block across duration $\delta$. Condition (eq:block-permission) and Lemma lem:local-causal supply a future-causal segment for that pair. Concatenation supplies a causal curve along a dependency path.

If an intervention acts outside the ancestors, its adjoint acts on an identity in the backward calculation, and therefore cannot change an unconditioned terminal expectation. This proves the influence inclusion.