Printed κ -corrections and the bare/completed caveat

The bracket in (eq:sextO) is printed and not evaluated. With XIII-D's expansion of the scalar derivative,

with $Y=\frac{\kappa }{2}{c}^{\mu }{\partial }_{\mu }\varphi$. Since $\mathcal{O}$ is the coefficient of ${\kappa }^2$ in the relational expansion, these terms enter at ${\kappa }^3$ there; a proposal acting on the lower coefficient $\kappa {\mathcal{A}}_1$ must print that coupling power separately. Moreover $\mathcal{O}$ already contains the classical scalar response $p_1,p_2$ and the slot $r_{\mathrm{D}}+r_g$; its identification with a bare field observable of the BV complex, on which $s_{\mathrm{ext}}$ acts through the single off-shell scalar, is X-G's bare-versus-completed distinction and is not made here. Proposition prop:relO does not depend on that identification: it concerns $⟨{{\mathcal{O}}^{\prime }}_{\gamma },\mathcal{R}c⟩$ alone.