What has advanced

The internal amplitude interface now has an explicit descent test. A construction on coefficient arrays must respect their exact reconstruction identities; it cannot declare an intrinsic leading section merely by retaining their highest polynomial degree.

For the local supported sector, the agreement problem is also more precise. Its reference is a finite array of normal-jet coefficients on $S_{\mathrm{resp}}\setminus N_U$, and the complete grouped reference distribution is constructed there. A supported normal-order-preserving realization would require actual extensions of that array, with their wavefront and compatibility data.

Neither advance supplies the complete characteristic composition. Both $K_5$ placements, the regrouped $K_{47}$ term, and all response coefficients remain in the required target.