Corollary: Plateau contraction, not a response law

For $\xi \in {\mathfrak{g}}_U$, the new action correction and scalar-switch breaking vanish in the contracted variational identity. Thus

Proof. On a neighborhood of $\mathrm{supp}\xi$, one has $g={\sigma }_{\epsilon }=1$ and all their derivatives vanish. Hence ${\mathcal{B}}_g$, $w$, ${{\mathcal{D}}_{\sigma }}_{\epsilon }$, ${Z_{\sigma }}_{\epsilon }$, and ${{\mathfrak{R}}_{\sigma }}_{\epsilon }$ vanish there.