Remark: Mechanism and genericity

Formula (eq:Lambda) is a particular case of ${\Lambda }_f=-\int fY$, where $Y:={{\mathsf{E}}_0}^{\mathrm{R}}{\partial }_t[t({\sigma }_{\epsilon }-g)]$ for $m=0$; on $\{t>\epsilon \}$ outside $\mathrm{supp}g$ one has $\square Y=1$, so $Y\not\equiv 0$ and nonnegative bumps $f$ with ${\Lambda }_f\ne 0$ exist above the ramp as well. The special choice $\mathrm{supp}f\subset \{t<t_g\}$ only makes the sign of ${\Lambda }_f$ manifest for every $m$. The boundary coefficient $\beta {|}_{\Sigma }$ is nonzero whenever ${\mathcal{D}}_f$ meets $\Sigma$ with nonvanishing data; the theorem exhibits one admissible instance, which suffices to defeat a construction that admits ${\mathcal{C}}_3(f,g)$ for all admissible $f$.