Gauge-fixed and Einstein-shell conditions are not identified

The supplied XI-F excerpt contains a cubic transformation law with both a gauge-fixing companion and an Einstein-equation contribution. The supplied XI-G coverage also states that its witness lies on the gauge-fixed shell and off the Einstein shell XIF,XIG.

Accordingly:

• the gauge companion is retained;

• the Einstein-shell contribution is retained;

• a gauge-fixed free-shell condition is not used as a substitute for an Einstein-shell hypothesis;

• a transformation law for the unramped response is not asserted for the prepared response without proof.

The relevant prepared terms have not been supplied as explicit kernels. Retaining them is a requirement on a future derivation, not a claim that they have already been constructed.