The ramp changes the first harmonic response

This is a calculation for the displayed density ramp. It is not an identification with VI's separately reported compact-switch defect. The two defects retain their own prescriptions and domains.

If the external ramp is also pulled back under a diffeomorphism, one instead studies a construction depending covariantly on the enlarged data $(q,T,{\sigma }_{\epsilon })$. Treating a profile as an additional transforming background does not make it a dynamical matter clock.