The response fiber map, b , g , and the advanced operator

Status. $\mathsf{P}$, $\mathfrak{b}$: open (XIV-H's source-incidence proposition and eq:K9 at line 1055 HK9). $g$: role identified as the switch, formula open. ${E^{\mathrm{A}}}_m$: open; the one sentence to locate is a declaration in XIV-H that ${E^{\mathrm{A}}}_m$ is the advanced inverse of $\square +m^2$, after which Lemma lem:advanced fixes it and Corollary cor:compact applies.