What the regulator alters

For $t\le 0$, ${\mathfrak{A}}_{\epsilon }[q]={\eta }^{-1}$; for $t\ge \epsilon$, ${\mathfrak{A}}_{\epsilon }[q]={\mathfrak{A}}_q$. The sharp onset $\theta (t)$ of the zero-Cauchy coupling in the VII-B and IX-A prescriptions is replaced by the ramp ${\sigma }_{\epsilon }$. The Cauchy data remain on $\Sigma =\{t=0\}$; the initial surface is not moved. What changes is the singular structure of the linear coordinate kernel.