Proposition: No evaluable preliminary lift in the record

No linear map $F_0$ with domain ${\mathcal{P}}_{\mathrm{int}}$ and codomain ${\mathcal{D}}^{\prime }(W;E_{\mathrm{res}})$ is specified by the supplied record, and no such map can be specified from it without supplying at least the items D0.1, D0.2, D0.5, D0.10, D0.11, and D0.13.

Proof. A linear map is specified by its domain, codomain, and value on each element of the domain. The domain ${\mathcal{P}}_{\mathrm{int}}$ is not defined (D0.1), so “for each element of the domain” has no content. The codomain is not defined (D0.5). Even granting a domain and codomain, the value on a presentation of any of the six entries must be the composed distribution of the entry with the cross-line operators and vertex data (D0.10–D0.13), none of which is defined. Writing a formula with the undefined symbols would be a plausible-looking operator, not a definition.