Definition: Core and downstream

The core items of XVD, Definition D0.1–D0.20, are those required to state a preliminary lift and its correction class: D0.1 (${\mathcal{P}}_{\mathrm{int}}$), D0.2 ($\mathsf{Rec}$ on ${\mathcal{P}}_{\mathrm{int}}$), D0.3 (${\mathcal{K}}_{\mathrm{int}}$, topology), D0.4 ($\ker \mathsf{Rec}$), D0.5 ($W$, $E_{\mathrm{res}}$), D0.8 ($O=U_{\mathrm{can}}$), D0.10 ($m^{\circ }$), D0.11 (${\mathcal{C}}_{\mathrm{cross}}$), D0.12 (vertex Hessian, weights), D0.13 (tensor maps, $L$, $R$, $f$, ${\sigma }_{\epsilon }$), D0.14 ($K_8$, $K_9$), D0.16 (candidate class), D0.17 (correction class). The downstream items are D0.6, D0.7, D0.9 (loci and strata), D0.15 (normalization), D0.18 ($v_{\alpha }$, $c_{D,\beta }$), D0.19 (target cone, estimates), D0.20 ($Q_H$, ${\mathcal{E}}_H$, output operations).