VII-C's hypotheses, copied

In VII-C's signature ${\eta }_{\mathrm{VII}}=-\eta$, ${\square }_{\mathrm{VII}}=-\square$, ${\mathsf{E}}_{0,\mathrm{VII}}=-{{\mathsf{E}}_0}^{\mathrm{R}}$. Its insertion is $B_f[h,\varphi ]=-\int f{w}^{\mu }[h]{\partial }_{\mu }\varphi$, $w={\mathsf{E}}_{0,\mathrm{VII}}{C}_{\mathrm{VII}}h$, sharp and zero-Cauchy. Its Wick matrix has $H_{hh}=P{\Delta }_0^{+}$, $P_{\alpha \beta \rho \sigma }={\eta }_{\mathrm{VII}\alpha (\rho }{\eta }_{\mathrm{VII}\sigma )\beta }-\frac{1}{2}{\eta }_{\mathrm{VII}\alpha \beta }{\eta }_{\mathrm{VII}\rho \sigma }$, $H_{\varphi \varphi }={\Delta }_m^{+}$, zero cross blocks.