A response and a partial contraction are not a full kernel

The fields $R_{\lambda }$, $V_{\lambda }$, and $X_{\mathrm{cand}}$ are smooth fields on the slab. They are not compact distributions on a three-slot configuration product. In particular,

is the response tensor, not the coordinate field.

For completeness, the following elementary construction explains the witness boundary used in XVIII-A CheungXVIIIA (:witness,:smoothwitness).