Definition: Instantiation data, itemized

A source-complete instantiation of the frozen joint target consists of the following items, each given by an actual definition.

1. the presentation space ${\mathcal{P}}_{\mathrm{int}}$;

2. the reconstruction map $\mathsf{Rec}:{\mathcal{P}}_{\mathrm{int}}\to {\mathcal{K}}_{\mathrm{int}}$ on all of ${\mathcal{P}}_{\mathrm{int}}$;

3. the carrier ${\mathcal{K}}_{\mathrm{int}}$ and the topology required of the joint map;

4. a complete description, or complete method of handling, of $\ker \mathsf{Rec}$;

5. the attachment domain $W$ and its coordinates;

6. the characteristic locus $N$ and its lift to $W$;

7. the response incidence $S_{\mathrm{resp}}$;

8. the canonical open domain $O=U_{\mathrm{can}}$;

9. the collision strata and observable diagonals;

10. the canonical contraction $m^{\circ }$ and its proved domain;

11. the grouped cross-line operators ${\mathcal{C}}_{\mathrm{cross}}$;

12. the mixed vertex Hessian and vertex weights;

13. the tensor maps ${\mathsf{A}}^{\alpha \beta ,I}$, ${\mathsf{D}}^{\alpha \mu ,I,J}$, the kernels $L^{\mu ,J}$, $R$, and the weights $f$, ${\sigma }_{\epsilon }$;

14. the explicit internal maps of $K_8$ and $K_9$;

15. the normalization of the pushed-forward coefficient;

16. the frozen candidate class of joint maps;

17. the frozen correction (ambiguity) class;

18. the coefficient distributions $v_{\alpha }$ and $c_{D,\beta }$;

19. the complete-graph target wavefront cone and uniform estimates, including the operator $\mathcal{L}(\cdot )$ of the XIV-J insertion wavefront lemma;

20. the output operations, $Q_H$, and ${\mathcal{E}}_H$.