Remark: Scope of the criterion

Because $\varphi +g$ coincides with $g$ near $Z$, $p_k(\varphi +g)\ge {\sup }_Z{\max }_{|\alpha |\le k}|{\partial }^{\alpha }g|$, so (eq:relest) asks that $T^{\circ }$ be controlled by the $k$-jet of the annihilator $g$ along $Z$, tangential derivatives included. Theorem thm:point shows that for a point puncture (eq:relest) follows from the existence of any extension. For a puncture $Z$ that is not finite, the jet space along $Z$ is infinite-dimensional, and whether (eq:relest) can fail for an extendable $T^{\circ }$ is not decided in this release. No example in either direction is asserted for such $Z$.