Debugging record

Candidates are not definitions. The XII-A and XII-D formulas are recorded under a separate status code C. They are not substituted into (eq:K5a)–(eq:K6), and no calculation uses them.

Scope of the recovery pass. The pass is over the supplied record only. No external search is reported as a source, and no statement about documents outside the record is made.

Erratum direction. The plan's proposed erratum said that clause (a) of XV-D's item (iii) needs invertibility of $v_{\gamma }$. Under (H1) it does not (Proposition prop:erratum(a)); invertibility-type hypotheses are needed for the converse (Proposition prop:erratum(b)). The genuine overstatement in XV-D is the witness-transfer clause, corrected in (d).

Two annihilators. $\mathrm{Ann}(T^{\circ })$ is defined by annihilation on $X^{\circ }$ and $\mathrm{Ann}(T)$ on $X$; conflating them would make every defect vanish trivially. The isomorphism (eq:iso) depends on the surjectivity of $\beta$ (Lemma lem:surj).

Nearest points. Lemma lem:taylor uses a nearest point of $Z$, which exists because $Z$ is relatively closed and the relevant closed ball lies in $X$; the hypothesis $\mathrm{dist}(x,Z)<\varrho$ is essential and is enforced in Lemma lem:flat by $3\epsilon <\varrho$.

Finite versus infinite punctures. The descent theorem uses the finite dimension of the jet space at a point. For non-finite $Z$ the question is left open (Remark rem:open); no guess is recorded as a result.

Class of the correction. The correction $s$ in Theorem thm:point is a change of extension, supported in $Z$; it is a statement about the jet module and is not offered as a graph prescription.

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.

Prescription. Pole, propagators, carrier, normalization, and ambiguity class are unchanged.

Compilation. The preambles of XV-A through XV-D use || without loading a package that defines it; mathrsfs is loaded here. All macros used are defined; all || and || targets exist; tabularx column widths sum to less than ||; no non-ASCII characters occur in mathematics.