Assumption: Boundary-trace certificate (TC)

For every compact smooth covector source $a$ in $V$, the same actual adjoint $b={\mathsf{E}}_0^{\ast }a$ appearing in (eq:sharpadjoint) is smooth up to $\Sigma$, $C^{\ast }b$ is locally bounded there, and

with one fixed convention sign. All relevant initial points and cone segments are retained in the laboratory.