Proposition: Scheduled support is an upper bound

In a finite circuit of prescribed local CPTP operations, include every quantum wire, classical control, random-kick selector, and record wire in the operation's input interface. The Heisenberg pullback of a terminal record observable is supported within its backwards scheduled ancestor set. A replacement of an operation outside that set leaves the terminal law unchanged.

Neither a minimal influence region nor a spacetime causal embedding follows from this support statement.

Proof. At a backwards step, a channel on wires disjoint from the current observable support acts on an identity factor. Its adjoint is unital, so it preserves that factor. A channel meeting the support can enlarge it only into its declared input wires. Backwards induction gives the scheduled ancestor bound. A disjoint replacement still acts on an identity and changes no expectation.

The construction contains no location map into spacetime, metric, or causal-curve certificate. Those additional data are therefore not conclusions of this support proof.