Degree and wavefront hypotheses

For a stated codimension-$q$ locus, use normal coordinates $(s,r)$ with $r\in {\mathbb{R}}^q$. A finite transverse degree must be proved uniformly over compact tangential sets with the necessary microlocal seminorm control.

When their hypotheses hold, submanifold extension theorems distinguish the degree-below-codimension uniqueness case from the case requiring normal-jet normalization BF (Section 6). Those hypotheses are not supplied by a superficial derivative count.

A prospective minimal wavefront estimate has the form

in the stated ambient space. Such an estimate requires the appropriate microlocal extension hypotheses, including control of how the off-$N$ wavefront approaches $N$ Dang (Sections 5–6).

The copied restriction warning remains in force: $\mathrm{WF}(t)\subset N^{\ast }N$ alone cannot retain a nonsmooth reference outside $N$.

In a common kernel already containing $\delta (a-z)$ or its derivatives, the inherited attachment singularities must also be accounted for. No estimate for adding those attachments after characteristic extension is asserted here.