Theorem: Geometric, source, and analytic release

For the explicitly specified setting:

1. the propagated source convention is (eq:source-conversion), and its finite coefficient rule is (eq:jet-Hessian);

2. the internal response reduction and local order bound are (eq:response-reduction) and (eq:internal-order);

3. the plateau equalities (eq:plateau-identity) hold on the retained patch;

4. the characteristic coordinates, density, rank relation, and quadratic defect are those of Theorem thm:coordinates and Corollary cor:rank;

5. the complete regularized contraction has the exact translation and scale-profile representations (eq:origin-evaluation)–(eq:increment-vertex), with reconstruction descent;

6. an integrable complete-sum scale bound gives the quantitative fixed-kernel limit of Theorem thm:Dini;

7. the scalar order-zero and derivative families have the explicit asymptotics and fixed-test conclusions of Theorems thm:scalar-limit and thm:scalar-derivative;

8. cutoff locality is exact, and microlocal agreement has the explicit hypotheses stated in Section sec:ledger.

Proof. Use Proposition prop:source-rule, Lemma lem:internal-order, Proposition prop:plateau, Theorem thm:coordinates, Corollary cor:rank, Theorem thm:translation, Proposition prop:scale, Theorem thm:Dini, the scalar theorems, and Proposition prop:cutoff. The stated microlocal agreement is the fixed-factor application specified in Section sec:ledger.