Theorem: Exact J2 verdict

For the class fixed in Definition def:mapclass:

1. reconstruction descent is a necessary condition, made explicit by Proposition prop:descent;

2. the supported sector has the exact normal form (eq:normalform);

3. its grouped composition on $U\setminus N_U$ is Constructed by Theorem thm:reference;

4. a supported normal-order-preserving extension has the conditional coefficient interface of Theorem thm:conditionalextension;

5. no full joint characteristic map on tests meeting $N$ is constructed.

The ending for the required full map is Unresolved at J2, within the inherited I3/G2/F2/E1/D2/J2 analytic boundary.

No incompatibility excluding every map in the fixed class has been proved.

Proof. The cited propositions and theorems establish (i)–(iv). Their domains stop short of a characteristic composition for the full six-branch kernel.

The conditional interface produces no extension coefficients, and the reference theorem treats only $K_{\mathrm{supp}}$ away from $N_U$. Neither gives a value for the full reconstructed sum on a test crossing $N$. No generalized composition theorem for that operation has been supplied, proving (v) and the unresolved ending.

The missing construction is not a converse failure theorem for all possible constructions, so the obstructed ending is not warranted.