Scope and fixed data

Let $M={\mathbb{R}}^{1+3}$, $M_{+}=\{t>0\}$, and $X=M_{+}^3$. We ask whether

exists strongly in ${\mathcal{D}}^{\prime }(X)$, with the counterterm class fixed to

The family ${T_{\epsilon }}^{\rho }$ is precisely the numerical VII-C family: both slots of each insertion are regularized with the same fixed mollifier $\rho$, while the single middle observable is unsmeared.

The formulas on the following convention sheet are from 085T_Landmark_VIIC_v1.tex VIIC. These displayed formulas define the family studied in this paper. The proof requires no companion methods manuscript and no unspecified normalization.

We reserve $\mu$ for the subtraction scale and write $\vartheta$ for the mollifier profile denoted by $\mu$ in VII-C. The symbol $g$ denotes the middle test; $s=y^0$ is a time coordinate.