Plateau and the additional compact vertex

A nonzero profile satisfying (eq:a) exists in any nonempty $U$: choose a Euclidean ball whose closure lies in $U$, and a nonnegative smooth bump supported there.

For the optional finite-time response comparison in Section sec:response, we additionally require

for the specified output test support $K_{\mathrm{out}}$. This is a source-specific support certificate. It is not inferred from the existence of a finite reporting port.