The complete joint map remains missing

The supported-sector reference is not the required value of $\mathsf{M}$ on

It does not include:

1. a characteristic composition for $K_{47}$;

2. a characteristic composition for either $K_5$ placement;

3. coefficient extensions of the supported-sector reference;

4. a complete-graph wavefront theorem after summing all tensor and branch contributions;

5. a proof that a coefficient-level construction descends through every internal reconstruction identity.

The inherited internal pole estimates do not give any of these by themselves. They control a different operation before the new cross-line composition.

No attempt is made to multiply the complete sum by ${\mathcal{C}}_{\mathrm{cross}}$ at the retained opposite covectors using the ordinary product theorem.