Hypothesis: Boundary-trace certificate (TC)

For every compact smooth covector source $a$ in $M_{+}^{\circ }$, the inherited $b={\mathsf{E}}_0^{\ast }a$ is smooth up to $\Sigma$, $C^{\ast }b$ is locally bounded there, and its componentwise trace is

A fixed overall nonzero sign in this formula would give the same support conclusions.