Theorem: XIV-J mathematical release

For the unchanged retained instance and the class fixed before the calculation:

1. a coefficient-level joint construction descends to reconstructed kernels exactly under (eq:descent);

2. the internal module has the explicit null presentation (eq:null), so presentation degree is not by itself an intrinsic joint-symbol filtration;

3. the supported response sector has the unique finite normal form (eq:normalform);

4. its complete grouped reference composition on $U\setminus N_U$ is (eq:reference), with the wavefront bound (eq:referenceWF);

5. supported realizations preserving that normal order have the conditional coefficient-extension interface of Theorem thm:conditionalextension;

6. no full joint characteristic map, joint section, or admitted ${R_1}^{(1)}$ is constructed.

The ending for the full required map is Unresolved at J2. The named partial reference construction is Constructed on its stated domain. XV-B remains closed.

No universal obstruction to the fixed joint-map class is asserted.

Proof. Proposition prop:descent proves (i). Lemma lem:null proves (ii). Proposition prop:normalform proves (iii). Lemma lem:traces and Theorem thm:reference prove (iv). Theorem thm:conditionalextension proves (v).

Theorem thm:J2 identifies the missing complete map. Sections sec:J3–sec:J5 record the unentered subsequent gates, and Corollary cor:noadmission gives (vi) and the exit consequence.