Definition: Instantiation data

A source-complete instantiation requires:

1. the actual presentation space ${\mathcal{P}}_{\mathrm{int}}$, reconstruction map $\mathsf{Rec}$, carrier ${\mathcal{K}}_{\mathrm{int}}=\mathrm{im}\mathsf{Rec}$, and the topology required of the map;

2. the attachment domain $W$, characteristic loci, canonical open domain $O=U_{\mathrm{can}}$, and the relevant incidence equations;

3. the canonical contraction $m^{\circ }$, the grouped cross-line operators, mixed vertex Hessian, tensor coefficients, weights, and normalization;

4. the permitted candidate and correction classes, with their contact, partial-diagonal, continuity, tensor, and microlocal restrictions;

5. the complete-graph target bounds and the definitions of the output operations, $Q_H$, and ${\mathcal{E}}_H$.