G5: prescription interface not entered

No nonzero full joint section has been established. G5 is therefore not entered as a construction.

A future prescription must name all seven data:

1. its ambient space;

2. a reference distribution on a proved domain;

3. the exact characteristic locus across which it extends;

4. agreement on that domain with the grouped frozen prescription;

5. a finite uniform transverse degree;

6. a closed conic wavefront bound retaining off-locus singularities;

7. a normalization selecting one map, or a uniqueness theorem.

The present choice $N={\tilde{\mathcal{N}}}_{\mathrm{att}}$ is a codimension-eight common-kernel test stage. It is not silently converted into a codimension-four numerical extension problem.

The canonical product is known on the inherited admissible domain $U_{\mathrm{can}}$. No equality

is asserted. A proved reference distribution on the required complement remains part of the construction, not a consequence of the existence of the individual lines.

The copied extension warning remains:

on a whole neighborhood would require the reference to be smooth away from $N$. It cannot erase the already existing off-$N$ singularities. A prospective bound

requires its own microlocal extension hypotheses.

For a genuine codimension-four problem with degree allowance at least four, smooth tangential multiples of ${\delta }^{(4)}(r)$ can remain possible unless normalization or uniqueness excludes them. On the retained collision-free neighborhood, such nonzero characteristic-supported changes are not members of ${\mathfrak{C}}_{\mathrm{part}}$.

The codimension-eight attachment intersection is a separate extension stage. No degree of the unresolved target is assigned here.

Brunetti–Fredenhagen's submanifold extension framework and Dang's microlocal extension framework are recorded only BF (Section 6)Dang (Sections 5–6). Their required reference and uniform estimates have not been proved for this target, so no extension theorem from them is applied.

XIII-E's family is not imported as a prescription. There is no cutoff-and-restore limit. The excluded excess construction is not reused under a prescription label.