Theorem: XIV-H mathematical release

For the unchanged retained instance:

1. the local source incidence is defined before residual testing and retains its complete coefficients;

2. the two gravitational-response legs have the exact kernel maps (eq:K8reduced) and (eq:K9);

3. on the retained separated-endpoint patch these legs have regular conormal representations of upper order $\frac{3}{2}$;

4. the two $K_5$ placements have the exact tensor-product pullback formula (eq:K5);

5. their regular separated-cone and noncharacteristic-diagonal orders are those proved above;

6. their internal diagonal and limiting flow-out pieces intersect cleanly but cannot be identified as one smooth ordinary Lagrangian relation;

7. the uniform internal amplitude construction at that transition, and hence the common characteristic representation, is not supplied.

The ending is Unresolved at H2, within G2/F2/E1/D2/J2.

No universal representation obstruction, joint-section conclusion, characteristic prescription, or admitted ${R_1}^{(1)}$ is asserted.

Proof. Proposition prop:sourceincidence proves (i). Proposition prop:K8exact and Proposition prop:K9 prove (ii). Corollary cor:K8order and Proposition prop:K9 prove (iii).

Proposition prop:K5exact proves (iv). Propositions prop:K5flow and prop:K5diag prove (v). Proposition prop:branching proves (vi). Theorem thm:H2 identifies the missing amplitude theorem and the correct first stop. Proposition prop:nocancellation separates these results from a cancellation verdict.