What is being proved

The original plan has two different targets:

1. determine when a linear wave-shell representative can be compared with a compact conserved-current representative;

2. determine whether a prepared witness response supplies the missing joint-graph construction.

Neither target permits replacing an unidentified distribution by a similarly named object from another manuscript.

The first target admits a sharp conditional theorem in a common flat setting. The second admits rigorous non-implication and interface theorems, but not a construction of the actual graph from the supplied information.

The principal results are Theorem thm:compatibility, Proposition prop:counterexample, Theorem thm:descent, and Theorem thm:jetextension. Their proofs are given here. They do not depend on treating the registered manuscripts as a single theory.