Remark: Scope of the point result

The correction is simultaneous for the entire smooth annihilator ideal, not a separate choice for each null relation. It uses the finite-dimensional jet algebra of one point.

The result assumes extendability of $T^{\circ }$; it does not create an extension for a nonextendable coefficient. It does not prove preservation of a specified scaling degree, a frozen normalization, or a restricted physical contact class. The order $M$ depends on the chosen local extension; it is not bounded by the response-normal order $r$ alone.

The presentation maps in this local construction are continuous for the usual smooth coefficient topology, since they multiply fixed finite-order distributions by smooth coefficients. No identification with the physical carrier topology follows.