The classical kernel input

The superscript $A$ labels a source-tensor component, not an additional field species. The coefficients in (eq:t-test) include the complete preparation correction. They are not replaced by coefficients of ${\sigma }_{\epsilon }{J}_3$ alone.

The action on arbitrary smooth tests is meaningful because $B$, and hence $t_{\mathrm{D}}$, is compactly supported. Revised XVI-H supplies finite-order continuity on $C^{\infty }$, not only on compactly supported configurations XVIH.