Remaining items

The next step requires the following, each with file, label, and line numbers, recorded as defines rather than cites:

1. XIV-I, def:amodule: the generators of ${\mathcal{A}}^m(V)$, the coefficient class (in particular its dependence on $q_{\pm }$, $r_{\pm }$), and the module action (linearity over chart functions); with these, $\ker \mathsf{Rec}$ follows from Lemma lem:recrule.

2. XIV-G/XIV-H: $E_{\mathrm{res}}$ as an object (D0.5).

3. XIV-I: the inherited list of “specified products already proved” that constitutes $U_{\mathrm{can}}$ (D0.8); the equality with $W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is refused and is not to be searched again.

4. XIV-J, eq:target: the display of $m^{\circ }$ (D0.10).

5. XIV-J, def:mapclass and def:class: the displays, including the meaning of “meet $N$” (D0.16).

6. XIV-J, lines 1112–1145: XIV-J's own symbol and definition for the replaced blocks in (eq:cross); the normalization of $T^{\mu \nu }(\varphi ,\psi )$ in (eq:hess) ($T^{\mathrm{pol}}$ or $T^{\mathrm{sym}}$) and the display of the vertex (D0.11, D0.12).

7. XIV-H, preceding eq:L: the definitions of $a_1$, ${\sigma }_{\epsilon }(a)$, $f$, $a_2$ and the construction of $\mathsf{D}$ from ${\dot{a}}_2$ (D0.13); XIV-H, lines 653–665 and eq:K9 (line 1055): the expansion of ${q^{L,I,J}}_{\alpha \beta }$ from XII-C's density-weighted cubic, $\mathsf{P}$, $\mathfrak{b}$, $g$, the declaration of ${E^{\mathrm{A}}}_m$, and the meaning of “separated chronological patch” and “regular conormal representation” (D0.14, Remark rem:conormal).

8. XIII-C: the formulas for $D_{\Gamma }$, the admissible $w_{\Gamma }$, $S_{\Gamma /I}$, and the statement of which presentation-level maps the frozen class permits (D0.17); the lift of ${\Delta }_I$ to $W$ and its position relative to $U_{\mathrm{can}}$.

9. XII-A or XI-B: the support sentence for ${E_0}^{\mathrm{R}}$; with it candidate (a) is decided by Lemma lem:R(iii)–(iv). Candidates (b)–(g) are decided by items (6)–(7).