Definition

Gate 0 freezes the following conventions. The metric is $q_{\mu \nu }={\eta }_{\mu \nu }+\kappa h_{\mu \nu }$, with $\eta =\mathrm{diag}(+---)$. XI-A writes $\gamma$; the map is $h\leftrightarrow \gamma$. The massless scalar action is

and $B^{\mu \nu }=\sqrt{-q}{q}^{\mu \nu }=\eta +\kappa a_1+{\kappa }^2{a}_2$ with the XI-A coefficients $a_1,a_2$. The path integral is $e^{iS/\hslash }$, with Fourier convention ${\partial }_{\mu }\to i{k}_{\mu }$ and $\square \to -k^2$. The Green function and the Feynman propagator are separate. $G_F$ is a Hessian inverse. XIV-A uses $G^R=-P{E}^R$ with coefficient $-1$. XI-B is not a Hadamard statement of this kernel. After stripping $\hslash$, the Wick propagator is $D_F(k)=i/(k^2+i0)$, and $(-\square )D_F=i\delta$. The conversion ${\Delta }_F=-D_F$ is written once. The effective action is $\Gamma =S+\hslash {\Gamma }_1+\cdots$, with ${\Gamma }_{1,\mathrm{matter}}=-i\log Z$. The factor of $i$ inside $D_F$ is not counted again in $-i\log Z$. The scope is the massless scalar matter loop on a background metric. It is not complete bulk BV, not $F_t$, and not an insertion completion. En01 and Em01 are not premises. Track II stays frozen. O.1 stays NOT_CLOSED. Bulk symmetry_restored stays false. Every later factor follows this sheet. No convention is changed midway.