Classical master

Foundation controls retained from the o61 calculation: the inverse-metric series satisfies $q{q^{-1}}_{\mathrm{series}}=1+O({\epsilon }^5)$, and a negative diagonal $h_{11}=B$ gives $q^{11}=-1-\epsilon B-{\epsilon }^2{B}^2-\cdots$. The quartic density is ${\ell }_4=-2[{\epsilon }^4](\sqrt{-q}R)$, and $S_{\mathrm{EH}}=-2{\kappa }^{-2}\int \sqrt{-q}R$. Sparse ${\ell }_4$ probes are not the proof. No $s_2$ is invented.

The authoritative scalar action is the single source XI-A, quoted and not re-proved:

At $m=0$ the free Hessian is $-\square$, not the bare $\square$. The cubic and quartic vertices $V_3=(\kappa /2)a_1\partial \varphi \partial \varphi$ and $V_4=({\kappa }^2/2)a_2\partial \varphi \partial \varphi$ are derived from the same ${\mathcal{L}}_q$. The old catalogue density $-\sqrt{-q}{q}^{\mu \nu }\partial \varphi \partial \varphi$ is withdrawn. The antifield split keeps ${V^{(0)}}_{\mathrm{af},h}=h^{\ast }{R}_0(c)$ distinct from ${V^{(1)}}_{\mathrm{af},h}=\kappa a{h}^{\ast }{\mathcal{L}}_{c}h$, with ghost normalization $a=\frac{1}{2}$ as in XVI-N. That $a$ is not the D11 coefficient pair $(\alpha ,\beta )$.