Proposition: D0 fails

The supplied record does not contain definitions for items D0.1, D0.2 (beyond two values), D0.4 (beyond one relation), D0.5–D0.12, D0.14–D0.18, and D0.20 of Definition def:package. In particular it does not define the domain, codomain, or value of a preliminary full lift $F_0:{\mathcal{P}}_{\mathrm{int}}\to {\mathcal{D}}^{\prime }(W;E_{\mathrm{res}})$, nor the correction space $\mathcal{A}$ against which a null defect would be tested.

Proof. Each row of the provenance table lists the literal content of the record for the item. For the items named, that content is a name, a locator, a defining relation in terms of a further undefined object ($\mathsf{D}$ via ${\dot{a}}_2$), or a sentence reporting a predecessor statement. The full texts of XV-A, XV-B, and XV-C themselves record that the source definitions of the cross-line factors, the frozen map class, $Q_H$, and ${\mathcal{E}}_H$ were not reproduced XVA,XVB,XVC; the present audit confirms that the retrieved excerpts do not add them.

A preliminary lift needs a domain (${\mathcal{P}}_{\mathrm{int}}$, D0.1), a codomain ($W$, $E_{\mathrm{res}}$, D0.5), and a defining operation on each presentation (the products of the internal kernels with ${\mathcal{C}}_{\mathrm{cross}}$ and the vertex data, D0.10–D0.13). The correction class needs D0.16–D0.17. Each is in status R or U. This is a statement about the record, not about the existence of the definitions elsewhere.