Debugging record

• Displays, paraphrases, locators, refusals. Each pass is graded line by line; only T and S can pass F0; a refusal closes a search and does not supply a definition.

• Verification of displays. Every reproduced display that admits an internal check was checked (Proposition prop:checks); the checks that cannot be performed are listed, not suppressed.

• Corrections to the draft. (F1)–(F3) are recorded in sec:errata; the free-module statement is replaced by the two-case Lemma lem:recrule; the dependent instance is XIV-J's own null relation, which is the strongest internal evidence that the coefficient class contains chart functions.

• Existence is not regularity. Theorem thm:exist asserts existence as distributions for arbitrary completions; it asserts nothing about conormal regularity, compositions with ${\mathcal{C}}_{\mathrm{cross}}$ or the vertex data, or estimates.

• Module form is not membership. Proposition prop:K5chart shows that three internal expressions have the form of (eq:Recrule); whether they are values of $\mathsf{Rec}$ on elements of ${\mathcal{A}}^m(V)$ requires the generators.

• Candidates versus definitions. (eq:a1H) defines $\mathsf{A}$ through XIV-H's $a_1$ and does not define $a_1$; (eq:a1), (eq:a2), $f\in {C^{\infty }}_c$, (eq:T0) are XII-sheet displays; no XIV sentence identifies them. The reduction in Proposition prop:reduction is one-directional.

• Two normalizations. Lemma lem:polar shows that (eq:hess) is consistent with the reported vertex for exactly one of the two natural polarizations; the factor two is an open item, not an error attributed to any text.

• Advanced kernel. Lemma lem:advanced is self-contained (Paley–Wiener–Schwartz); its identification with XIV's ${E^{\mathrm{A}}}_m$ is conditional on a declaration not in the record.

• Four P's and four R's. $\mathcal{P}$ (XII-A), $\mathcal{P}$ (XII-B, explicit), $\mathfrak{P}$ (XII-D), $\mathsf{P}$ (XIV-I); $R$ (kernel), $R_1$ (output map), ${R_1}^{(1)}$ (admission), $\mathcal{R}$ (XII-B). None identified. Lemma lem:fiber relates XII-D's $a_1$ to XII-B's $\mathcal{P}$ only.

• Copied inputs. The $K_8$, $K_9$ formulas are XIV-I input statements copied from XIV-H; XIV-H's own eq:K9 is located and not reproduced.

• Values versus maps. XIII-C's class is a class of coefficient changes; XV-B's $\mathcal{A}$ is a class of maps on presentations. The passage from one to the other is hypothesis (H2).

• Variables. XIII-C's ${\Delta }_I$ live in XIII-C's graph variables (vertex table located); XIV-I's chart lives on $\{{d_{\pm }}^0>0\}\subset {\mathbb{R}}^{16}$; the lift of ${\Delta }_I$ to $W$ is not reproduced.

• {$q$-linearity.} Lemma lem:recrule(ii), (iv) are conditional on linearity of $\mathsf{Rec}$ over chart functions; the record displays the relation as null and does not display the module action.

• Cross-line blocks. (eq:cross) is T${}^{\ast }$; the blocks are C; Lemma lem:cross(iv) is conditional on the sm