What a future output must prove

For a proposed compact polynomial graph output $G$, membership in the present carrier requires:

for every fixed smooth configuration and every finite direction list.

Proving only that $G$ has compact support is insufficient. Proving only that a fully contracted scalar coefficient has a finite part is also insufficient.

An output that fails this criterion is not automatically discarded: it identifies a precise further domain problem. A new enlargement would have to specify additional intrinsic coordinates and re-establish the compatibility boundary.