What a successor construction must supply

The carrier and its admission criterion are already specified by IX-A. A successor must work relative to that carrier and fix:

1. allowed vertex valences and independently differentiated decorations;

2. bounded derivative stages or a precisely declared derivative module;

3. the regulator placement for each new decorated graph;

4. graph-specific extension conditions and restrictions on tangential weights, normal derivatives, and intersection terms;

5. quantum maps on partial outputs and proof of output admission;

6. compatibility with old products, the parent calibration, involution, presentation relations, and associativity.

A binary factorization reproducing ${u_{\mu }}^{\rho }+cr$ is a further construction, not a consequence of the calibration alone.