Definition: Branch A sheet

The Branch A sheet is the tuple

together with the maps $(h,k)\mapsto c_j[h,k]$, $j=0,1,2$, and $h\mapsto {\mathsf{L}}_{1,g}[h]$. Every object of X-B is built from ${\mathfrak{S}}_A$ by the operations: smooth multiplication, differentiation, application of ${{\mathsf{E}}_{\mathsf{m}}}^{\mathrm{R}}$, ${{\mathsf{E}}_{\mathsf{m}}}^{\mathrm{A}}$, ${{\mathsf{E}}_0}^{\mathrm{R}}$ to compactly supported smooth sources, evaluation of background slots on classical configurations, formation of $F_c$, and passage to ${\mathfrak{A}}_0$.