A future map must identify its problem

No prescription is constructed in this section. Any future map must name:

1. its ambient graph or common-kernel space;

2. a distribution $t^{\circ }$ on a proved reference domain;

3. the exact closed characteristic locus $N$ across which it is extended;

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

5. a finite uniform transverse degree in specified normal coordinates;

6. a closed conic wavefront bound retaining the inherited off-characteristic singularities;

7. a normalization selecting a map, or a uniqueness theorem under the proved degree and wavefront hypotheses.

The numerical stratum ${\mathcal{N}}^{\circ }$, the full lift ${\overline{\mathcal{N}}}_{\mathrm{att}}$, and the attachment intersection ${\tilde{\mathcal{N}}}_{\mathrm{att}}$ are not interchangeable choices of $N$. The chosen stage must also account for other internal compositions present in the complete sum.