Theorem: Conditional fixed-order assembly

Under ass:retarded,ass:analytic, the finite assembled sum defines an admitted coefficient at the selected order and satisfies the selected Ward identity. A continuous state functional on its declared physical output domain gives a well-defined expectation.

This conclusion is an observable-level construction. It does not itself construct a measurement instrument or a quantum-return channel.

Proof. A2–A4 make every graph operation an actual distributional operation. A3 guarantees authorized presentation independence. A5 permits the projections and proves admission. A1 identifies the resulting finite sum with the formal inventory, and A6 supplies its claimed continuity.

A7 and thm:ward give the exact equation $a+Lc=0$, which is the selected identity. A continuous state functional can then be evaluated on a coefficient in its domain. No instrument or channel construction occurs in these steps.