Three operations

A preliminary lift $F_0:{\mathcal{P}}_{\mathrm{int}}\to {\mathcal{D}}^{\prime }(W;E_{\mathrm{res}})$ with $r_O{F}_0=m^{\circ }\mathsf{Rec}$ requires three distinct operations:

1. reconstruction of the internal distributions (defined in the named module, D0.1–D0.2);

2. canonical cross-line composition on $O=U_{\mathrm{can}}$ (D0.8, D0.10, D0.11);

3. the full operation on tests meeting $N$, including the products of the internal distributions with the singular cross-lines in the attachment variables.

The internal product calculations for the $K_5$ placements settle only (i). Operation (iii) is exactly the object left unresolved at I3 and J2 Ijoint,Jverdict.