Theorem: Complete scheduled ancestry

Equal joint reductions on the ancestor region and an untouched reference give equal corresponding outputs. A local CPTP intervention outside the full backward region cannot change those outputs, with schedule and interfaces fixed. If each dependency edge has a certified regular future-causal host route, scheduled ancestry is contained in the prescribed metric causal relation.

Proof. An excluded block acts on an identity factor, preserved by its unital adjoint. A meeting block enlarges support only within itself. Backward induction proves support containment. Joint observables prove the reference and intervention claims. Concatenation proves metric containment.