B3: the observable ledger, copied, and the separation lemma

The $\kappa$-corrections are printed and left unevaluated, as in XIV-A:

Since $\mathcal{O}$ is the ${\kappa }^2$ coefficient of the relational expansion, these terms enter at ${\kappa }^3$ there. A proposal that moves the lower coefficient $\kappa {\mathcal{A}}_1$ must display its own coupling power. $\mathcal{O}$, which already contains the classical scalar response and the slot $r_{\mathrm{D}}+r_g$, is not identified with a bare field observable of the BV complex; that is X-G's bare-versus-completed distinction and it is not made here.

B3 ends with the copied evaluation on ${{\mathcal{C}}_{\mathcal{W}}}^{\mathrm{bos}}$ and the nonzero pairing on ${{\mathcal{C}}_{\mathrm{sol}}}^{\mathrm{bos}}$.