Remark: Forcing sign versus action coefficient

Put $L=-\square \mathcal{P}$. Equation (eq:response) solves $L{u}_{\mathrm{D}}={\mathcal{J}}_{\mathrm{D}}$. The gravitational contribution to a perturbative coefficient of the action equation instead solves $Lr=-{\mathcal{J}}_{\mathrm{D}}$. That coefficient is $r=-u_{\mathrm{D}}$. This distinction changes a forcing sign, not the coefficient $-1$ in the inverse of $L$. It is essential in Section sec:plateau.