Common kernels, not point values

Because ${\mathcal{M}}_j$ is trilinear in $(\gamma ,h,\psi )$, let $K_j$ denote its compact distributional kernel:

All field and line derivatives are included in this kernel. Existence of these individual kernels follows from the inherited tree constructions, not from a two-cross-line composition.

The complete mixed kernel is

It lives on the common variables $(a,b,z)$ even when a branch was originally written with additional internal vertices. Those vertices have been integrated by its established tree kernel map.

This comparison does not pull a four-vertex distribution back to an arbitrarily imposed three-vertex diagonal. Such a pullback would require its own wavefront test FR (Appendix A).