The operation that can be constructed independently

The contact support $\mathbf{y}=\mathbf{z}$ is therefore not retained as compact output support after Newton composition. Conversely, the distributional formula does not authorize an additional diagonal evaluation at $\mathbf{x}=\mathbf{z}$.

For comparison, a contact source acted on by ${\mathsf{G}}_{\mathrm{sp}}$ without the divergence has a $1/r$ Newton image. One must not assign every Newton-contact image the dipole rate regardless of its source structure.