Abstract

XV-D continues the supplied XV-C manuscript at its source-completeness stop. Its task is to recover the frozen data for the six-branch joint characteristic target, define the preliminary full lift, compute its reconstruction-null defect, and test the inherited correction and analytic requirements; or, if the data cannot be recovered, to report precisely why the graph-level calculation cannot yet be performed.

The second alternative applies. A twenty-item provenance audit of the supplied record (the full XV-A, XV-B, and XV-C texts and the retrieved XIV-H, XIV-I, and XIV-J excerpts) shows that the presentation space, the full reconstruction map, the grouped cross-line operators, the canonical contraction, the frozen candidate and correction classes, the coefficient distributions $v_{\alpha }$ and $c_{D,\beta }$, and the output definitions $Q_H$, ${\mathcal{E}}_H$ are named but not defined in that record. No preliminary lift for the actual graph is therefore definable, and no graph-specific null defect, obstruction, or estimate is asserted. The graph-level outcome is Unresolved at D0.

The new mathematical content is the one null-defect calculation that the record does make source-complete. For the finite normal-jet module with reconstruction to a punctured base, we define the extension lifts ${F_0}^T={\mathsf{Rec}}_T$ associated with the distributional extensions $T$ of the punctured coefficient, compute their reconstruction-null defect exactly, prove that it is always supported on the puncture, that it depends on the extension, that it induces an injection of the quotient of the two reconstruction kernels, and that the inherited identity $\mathsf{Rec}((qi\theta +1)M_{\mathrm{R}})=0$ never contributes to it. An explicit nonzero defect is exhibited and cancelled by a change of extension. A conditional reduction of XV-C's coefficient estimates to extendability of the cross-line traces is proved under an explicit smoothness hypothesis on $v_{\alpha }$. None of these results is transferred to the inherited graph; they fix what must be computed once the missing definitions are supplied.