The actual changed identity

This is not XI-A's identity with a relabeled source. The additional term $-w{Q}_{\nu }(A\gamma )$ is important: weighting only the cubic coefficient, while leaving the quadratic coefficient unchanged, produces breaking even where the weight is a constant different from one. Thus the new breaking is not exclusively a ramp-derivative term. Omitting this bulk coefficient mismatch would falsely treat a cubic-only modification as weighting the complete natural gravitational density.

For the gauge-fixed action, add the separate contribution ${\mathcal{N}}_{\nu }(e_{\mathrm{gf}})$ to the right, where

Gauge fixing is not made invariant by the ramp.