Declarations

scope. The mathematical claims proved here are the reconstruction descent, normal-jet representation, supported-sector reference, wavefront bound, and conditional realization interface. The manuscript is not a claimed proof of the unresolved full joint coefficient.

scope. All new distributional constructions have explicitly stated domains. The supported-sector reference avoids the characteristic locus. No ordinary product theorem is invoked at the retained opposite covectors.

-product scope. The quantum line difference is kept as the difference of two defined tensor products and their submersion pullback. It is not expanded into undeclared mixed products.

debugging. The internal amplitude estimates of XIV-I concern presentations. The exact identity $q{\delta }^{\prime }+\delta =0$ shows why their polynomial degree alone cannot define an intrinsic joint symbol. A later coefficient-level construction must prove descent through the reconstruction kernel.

-coordinate scope. The response incidence has five normal coordinates. Its characteristic submanifold has three additional relative normal coordinates within that incidence. All distributions remain on the original common space, and the characteristic locus still has ambient codimension eight. No degree is inferred from the flag.

and branch scope. Every source coefficient and both scalar-root terms are retained in the finite normal-jet form. The supported sector is explicitly distinguished from the full six-branch sum. Neither $K_5$ placement is removed.

scope. No characteristic-supported distribution is added to ${\mathfrak{C}}_{\mathrm{part}}$. The displayed supported ambiguity is a conditional diagnostic, not a selected extension or a counterterm.

scope. XIV-I and the analytic predecessors supply the copied internal and graph data. XV-A is recorded only at the exit. XIV-A and XIV-B, the value $-8I$, XIII-E's family, and a resolved paired construction are not analytic inputs.

scope. No admitted ${R_1}^{(1)}$, interacting differential, Ward defect, quantum master-equation defect, anomaly, reduced algebra, state, numerical loop amplitude, new interaction vertex, or sharp-width limit is constructed.

. No successful pdflatex execution, proof-assistant verification, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. The claimed results are the displayed proofs.