What X-D-ST does and does not transfer

X-D-ST does and does not transfer{ The ${\mathcal{D}}_C$ sheet and the closed scalar equation subspace apply directly to fixed-background scalar tests and to the smooth partial contractions above.

The whole cubic belongs to the polynomial on-shell carrier $\mathcal{W}/\mathcal{J}$, not to the degree-one space $Q_m$. Its kernel is distributional. Neither a fixed-support Fréchet theorem for smooth tests nor their quotient convergence is a theorem about arbitrary joint quantum metric kernels.}