R3. The excluded edge supports the same negative lemma

Suppose, as a new comparison, that the ramp gauge algebra is enlarged to include the tested edge vector while its coordinate prescription is kept fixed. Real multiples of that vector remain in the enlarged algebra. For the tested first-order discrepancy, linearity and (eq:copied-edge) then give the coefficient orbit

Its image is $\mathbb{R}$: for any $x$, take $\lambda =(x-e_0)/d_{\mathrm{edge}}$. The proof of Lemma lem:orbit therefore applies unchanged in substance. No readout of this gap alone can be both invariant on that enlarged orbit and informative about the gap.

This is a comparison outside the frozen ramp algebra. The ramp manuscript did not admit the edge vector and then remove it after readout; its support restriction is part of its stated prescription. The edge integral is neither $c_{\epsilon }$ nor an independently charged reference coefficient $r$.