Authorization, descent, and separate microlocal interfaces

Support-separated tests annihilate corrections supported in a disjoint closed set. This excludes the specified class, not every possible construction.

Let $P$ be Hausdorff locally convex, let $\mathsf{Rec}:P\to V_{\mathrm{int}}$ be continuous and linear with Hausdorff target, and give $K=\mathrm{im}\mathsf{Rec}$ the topology of $P/\ker \mathsf{Rec}$.