Abstract

We patch the source manifest supplied as XV-F-vav3.md, using only the full supplied texts of XIV-G.tex, XIII-C.tex, XIV-I.tex, and XIV-J.tex. The local amplitude generators, chart-function coefficient class, reconstruction rule, formal target, and five joint-map clauses are now reproduced rather than paraphrased. A polarized stress convention is fixed from the displayed metric–scalar vertex.

Two proposed completions require a narrower release. The metric residual tests in XIV-G do not identify an output bundle over the common graph space. Likewise, generic formulas for a graph differential operator, external weight, and spectator coefficient do not recover their frozen graphwise values. We therefore distinguish source definitions, definitions introduced by the patch, and parameterized formulas. The polynomial weight convention is not attributed to XIII-C, and the normal contact bound six is not used as a bound on the graph differential operator.

The displayed reconstruction is coefficientwise $C^{\infty }$-linear on the transcribed local module. Its chart-function relations are genuine local null presentations; they do not determine the complete six-entry reconstruction kernel. XIV-J's global descent criterion is transcribed, while canonical agreement verifies only its restricted version. The canonical-domain complement equality remains refused.

The four documentary patch ledgers are completed within these boundaries. The stronger assertion that every corresponding frozen-object gap passes XV-F's original F0 is not established. No preliminary lift, null-defect calculation, characteristic prescription, new analytic estimate, or admission of $Q_H{R}_1^{(1)}$ is supplied. Gates F1–F4 remain unentered.