Manuscript XV-A@1 · XV-A.tex · section · f53f3515
Remaining obligations
The open gates and the exit contract › Remaining obligations · lines 1529–1592
The following table is a proposed order of research obligations, not a list of completed results and not a claim that the source's gate labels are identical to these six descriptive labels.
| Stage | Obligation | Completion test and retained limitation |
|---|---|---|
| 1 | Full joint characteristic map | Define (eq:map) for the full reconstructed sum on tests meeting , with reconstruction descent, prescribed grouped contractions, canonical agreement, and the required complete-graph microlocal control. Alternatively prove a precise obstruction in the frozen class. This alone is not admission. |
| 2 | Joint section and controlled remainder | Give a section for the same coefficient, together with its complete controlled remainder. A partial off-characteristic reference and the admitted tree datum are not substitutes. |
| 3 | Uniform transverse estimates | Prove the required estimates in the target's transverse variables and stated topology. Internal frequency homogeneity is not this theorem. Include lower-degree terms. |
| 4 | Contact compatibility | Check compatibility with the declared contact and ambiguity data. Do not import characteristic convergence, regulator independence, a selected finite part, or an unfinished XIII-E limit. |
| 5 | Output wavefront theorem | Prove the wavefront statement for the complete joint coefficient and its output operations, not only for individual internal branches. |
| 6 | Admission | Construct the normalized pushed-forward coefficient and prove under the inherited definitions. Only this stated admission opens the XV-B exit. |
The complete-graph control required at stage 1 concerns the joint operation; stage 5 concerns the final output after the remaining section, compatibility, and output operations. Neither is supplied by an internal-line wavefront estimate.
The meanings of and , and the normalization of the pushed-forward coefficient, are inherited interface data whose complete definitions were not supplied. XV-A consequently records the admission line without manufacturing a replacement output space or operator.