What the next input must contain

The next substantive calculation requires an explicit package:

1. the complete frozen cross-line and vertex contraction, including all six retained operational blocks;

2. the actual reconstruction space and a complete method of handling its null relations;

3. the incidence equations and the actual coefficient distributions $v_{\alpha }$, $c_{D,\beta }$;

4. the exhaustive permitted construction and correction class;

5. the full graph microlocal target and the output definitions.

Once these are supplied, the supported-sector extension subtask can be attacked by proving (eq:jetbound) for (eq:degree3)–(eq:degree0), or by producing an actual failure sequence. A preliminary full lift can then be tested on (eq:actualnulltest) and on the remaining reconstruction relations.

Successful supported extension would still leave the characteristic compositions of $K_{47}$ and both $K_5$ placements to be joined into one coherent map. A construction of that full map would still leave the subsequent output and admission obligations.