Definition: Fixed-order and ultraviolet targets

The fixed-order target is one named renormalized interacting relational correlator or response in a frozen Einstein–scalar specification, at stated orders in the gravitational coupling and $\hslash$, with:

1. an admitted coefficient in a declared output space;

2. a complete contribution inventory at that order;

3. a compatible and completely parameterized counterterm prescription;

4. a proved gauge, background, or BRST/BV identity on its stated domain;

5. a specified physical state or representation whenever an expectation is claimed.

If a classical record is claimed, a separately declared measurement instrument and its comparison to that correlator or response are additionally required.

The ultraviolet target is a continuum theory with a controlled high-scale construction, a physically acceptable state space and evolution, finitely many independent essential physical inputs, and a connecting theorem recovering the same prepared low-energy observable with a stated remainder.