Definition: Exact source-preserving variational upgrade

An exact source-preserving upgrade of X-F consists of:

1. its frozen free metric operator and causal relations;

2. an even interaction functional with symmetric bosonic second variation, after elimination of the algebraic auxiliary field;

3. a classical retarded metric field map agreeing with X-F's mixed response on every smooth free metric solution and every allowed smooth classical background;

4. quantum corrections containing only nonnegative powers of $\hslash$.

Agreement in (c) is equality of the field map, equivalently equality after every compact smooth linear metric smearing. It is stronger than agreement of one selected relational observable.