R1. An already invariant observable is not the convolution gap

On ${{\mathfrak{g}}_{\mathfrak{U}}}^{\mathrm{R}}$, the ramp coordinate response equals the gauge parameter: ${\mathrm{Co}}_1[K\xi ]=\xi$, both off shell and on the switched solution. Thus the first-order mismatch $\xi -{\mathrm{Co}}_1[K\xi ]$ vanishes on that algebra, supplying the classical cancellation in the ramp observable Ramp (Theorem (main)). The coordinate response itself is not an invariant numerical observable; it is the compensating response used in the cancellation.

There is no inherited convolution-type defect orbit $a(\lambda )=\lambda c_{\epsilon }$ for this invariant ramp coefficient. Lemma lem:orbit is therefore inapplicable to it. A function of an invariant number may vary across physically different invariant inputs while remaining constant along each gauge orbit. Invariance alone also does not prove that the ramp observable takes different physical values; that is a separate classical question.