Theorem: Mathematical release

The results established in this manuscript are:

1. the complete-expansion raw decision, coefficient uniqueness, and intrinsic extraction;

2. the three sufficient verification routes, including the separately proved differentiated-origin estimate;

3. compact-local Taylor verification, finite assembly, and globalization under a common finite inventory;

4. the evaluated complete degenerate specialization (eq:appdecision), including its cancelled ${\delta }^{-2}$ coefficient, surviving ${\delta }^{-1}$ coefficient, fixed detecting test, and order-six remainder;

5. the additional inverse-scale $u$-jet cancellation, normal-order bounds, conormal coefficient wavefront bounds, zero off-attachment reference, and the stated finite-part profile comparison;

6. conditional authorization, normalization, and microlocal output results, each with its separate hypotheses.

Proof. Apply Theorem thm:decision, the results of Sections sec:routes and sec:protocol, Theorem thm:application, Corollary cor:appcancel, Propositions prop:appWF and prop:appconsequences, and Theorems thm:authorized and thm:microlocal.