The supported-sector reference

The supplied XIV-J theorem gives, for every vertex component $D$, a reference on $U\setminus N_U$:

It is supported on $S_{\mathrm{resp}}$ on that domain, retains every normal derivative and both scalar-root terms, and agrees with the canonical grouped composition on their common proved domain CheungXIVJ.

Collecting insertion orders gives

This is an exact finite reindexing, not an extension of the coefficients to the missing locus.

In a specified normal chart with relatively closed $N_U$, Theorem thm:jetextension applies with

It gives the precise supported coefficient interface, and Corollary cor:jetestimate gives the uniform local estimates that would establish unrestricted distributional extendability of the coefficients. Neither statement supplies those estimates for the actual ${b_{D,\gamma }}^{\circ }$.

The inherited reference wavefront theorem is a predecessor input, not a complete-graph output theorem. Extending the reference alone would still omit the characteristic contractions of $K_{47}$ and both $K_5$ placements.