Input statement: Necessary prescription constraints

XIV-D established the following necessary distinctions:

1. an extension with wavefront set contained only in $N^{\ast }N$ on a whole neighborhood would require its off-$N$ reference distribution to be smooth;

2. in a codimension-four extension problem, degree at least four and allowance of the full conormal bundle permit tangential multiples of ${\delta }^{(4)}(r)$ unless an additional normalization or uniqueness result removes them;

3. on a collision-free neighborhood, such nonzero characteristic-supported differences are not members of ${\mathfrak{C}}_{\mathrm{part}}$.

These constraints do not assert the existence or the actual degree of the selected characteristic distribution XIVD.