Theorem: Exact characteristic-gate verdict

For the retained instance of the pair frozen in J0:

1. the separate-line product criterion fails on the noncoincident characteristic configuration and its smooth null-collinear stratum;

2. that failure is not removed by collision exclusion, line differentiation in the retained temporal component, or collision-supported contact changes;

3. neither a uniform cancellation theorem for the complete pair nor a prescription through the characteristic set with the required ambiguity and wavefront control has been constructed;

4. no contradiction excluding every possible successful construction in the frozen class has been proved.

The first unresolved gate is therefore J2, and its ending is Unresolved.

Proof. The copied wavefront selections and the new Proposition prop:geometry and Corollary cor:positive give (i). Proposition prop:component and Proposition prop:rigidity give the precise statements in (ii).

The calculations prove a failure of the sufficient criterion for the retained separate-line incidence and a restriction on permissible contact differences. They do not construct the complete branch sum across this domain, prove its cancellation, or define a characteristic finite part. Those missing constructions are exactly (iii). None of the proved statements is a converse to the distribution product criterion or a universal incompatibility of all prescriptions, giving (iv).