Debugging record

Title. The suggested title announced “the First Full Calculation.” Since that calculation is blocked at D0, the title names its boundary instead; no result is announced that the text does not prove.

Outcome selection. The unresolved alternative is taken at the gate named by the plan. No plausible-looking operator is written with undefined symbols.

Provenance discipline. A sentence in a predecessor proof (“multiplication by $v_{\alpha }$ adds no wavefront”) is recorded as a reading and converted into an explicit hypothesis (H1), not into a definition.

Branch counting. Six operational entries; $K_{47}$ groups two originals; both $K_5$ placements belong to $B_5$. The supported sector is not the full sum.

Model versus instance. The jet module is explicitly an instance of XV-B's interface with $m^{\circ }=\mathrm{id}$ and $O=U^{\circ }$. It is not declared equal to ${\mathcal{P}}_{\mathrm{int}}$; no result of Section sec:nulljet is transferred to the graph.

Two kernels. The null defect is defined relative to the punctured kernel $H$, which is the reconstruction actually available on the canonical domain; the full kernel $H_T$ depends on the extension. Conflating them would make every defect vanish trivially.

Tangential annihilators. The example uses $x_1\delta (x_1)=0$ versus $x_1{\partial }_{x_1}{\delta }_0=-{\delta }_0$; coefficient equations remain equations in ${\mathcal{D}}^{\prime }(X)$, as in XV-C.

Algebraic corrections. The cancelling correction in Proposition prop:unrestricted is algebraic and unrestricted; it is not offered as a graph prescription. The narrower class of extension changes is analysed separately.

Extendability versus admissibility. Proposition prop:reduction gives the unrestricted class only; membership in the frozen class is not inferred.

Dimensions. The numbers 16, 8, and the codimensions 5, 8, 3 are reported bookkeeping and are not used in any proof.

Prescription. Pole, propagators, carrier, normalization, and ambiguity class are unchanged. No regulator or finite part is introduced.

Obstruction language. “No separated witness in the jet module” is a theorem about that module, not a statement that the graph has no separated defect.

Compilation. All macros used are defined in the preamble; all || and || targets exist; tabularx column widths sum to less than ||; no non-ASCII characters occur in mathematics.