What it means for a test to meet N

This collection is not generally a vector space. Two tests can cancel near $N$, and their sum can fail the meeting condition. Clause (iv) therefore does not define a linear map only on ${\mathcal{D}}_N(W)$. It requires a distributional value which is defined on all compact tests, including those whose supports meet the locus.

Support means the closed support of the test. A meeting test need not have a nonzero pointwise value at a point of $N$. The clause is not an instruction to evaluate a singular kernel at a point. It is also not a wavefront hypothesis on the test: smooth compact tests have no wavefront singularities. The difficulty lies in defining the coefficient which pairs with them.

The source abstract and scope statements say that no full map on these tests was constructed; the reported isolated line locators 203 and 480 point to that boundary. The labelled statements thm:J2 and thm:release give the same boundary unambiguously. This patch does not turn the support definition into a construction on that support class.