Theorem: Source-locked IX-B calibration package

Retain the exact off-shell insertion, fixed covariance, prescribed regulator placement, the IX-A carrier, and Assumption ass:VIID. Then:

1. the eight unlabelled connected skeletons through three edges are exactly those in Theorem thm:skeletons;

2. the selected fully contracted word has the unique triangle coefficient (eq:T);

3. its numerical finite part and complete conversion transfer to every fixed observation differential operator and smooth spectator multiplier, with order loss $64\to 64+d$;

4. the inherited diagonal limitation is detected by the exact coefficient $⟨r,f\otimes g\otimes f^{\prime }⟩=\mathcal{C}(f,g,f^{\prime })>0$;

5. the residue derivatives $r_n$ are linearly independent, while compatible conversions can retain the single parent parameter;

6. the admitted two-factor output in ${\mathcal{P}}_{\Sigma }$ is exactly (eq:Qpartial);

7. both regularized associations have the same coefficient ${\mathcal{G}}_{\epsilon }$ and the same subtracted numerical limit.

These results neither remove the VII-C obstruction nor construct either sharp second multiplication.

Proof. The assertions follow respectively from Theorem thm:skeletons, Proposition prop:unique, Theorem thm:descendants and Corollary cor:conversion, Theorem thm:diagonal, Theorem thm:independence and the inherited parent conversion, Proposition prop:partial, and Theorem thm:regularassociation. Proposition prop:missing and Section sec:continuity establish the stated logical boundaries.