The weights σ and f

XIV-H calls ${\sigma }_{\epsilon }(a)$ and $f(b)$ “fixed smooth weights” Hkernel, so ${\sigma }_{\epsilon },f\in C^{\infty }({\mathbb{R}}^4)$ is copied. Their definitions precede eq:L in XIV-H and are not in the record HeqL. XII-D displays $f\in {C^{\infty }}_c({\mathring{M}}_T)$ with the observable ${\mathcal{A}}_1[f,g](r;\varphi )=\int f({\varphi }_1[r;\varphi ]-{X_1}^{\mu }[r]{\partial }_{\mu }\varphi )$ XIIDweight; whether XIV-H's $f$ is this $f$ is not stated in XIV-H. The ramp's cutoff $\chi$ lives on XII-B, a non-input, and can enter only through a quotation inside XIV-H.

Status. ${\sigma }_{\epsilon }$: open; missing sheet: XIV-H, the definition preceding eq:L, and, for the cutoff, the quotation of XII-B's ramp inside XIV-H. $f$: open; missing sheet: XIV-H, the same passage, or an input statement quoting XII-D's display. Per the plan this bullet stops here with the sheets named.