E3: the ledger, printed before addition

The two-jet row of the gravitational slot is therefore $+{\mathcal{A}}_1(s_{\xi };\varphi )$. It is the co-transformation. XI-E restored the co-transformation by hand because its slot was an external $k$; here the slot is $r_{\mathrm{D}}[\gamma ]$, and a separately added co-transformation row would count ${\mathcal{A}}_1(s_{\xi })$ twice.