Extended ray class fields of orders conjecture for SICs

Fix $d\geq4$, write $\Delta=(d+1)(d-3)=f^2\Delta_0$ with $\Delta_0$ a fundamental discriminant, and let $f'\mid f$. Let $\mathcal M$ satisfy the extended order-to-multiplet conjecture, and let $E_{d,f'}$ and $\widetilde E_{d,f'}$ be the ray class fields associated with the order $\mathcal O_{(f')^2\Delta_0}$, with levels $d\mathcal O'$ and $d'\mathcal O'$ respectively, where $d'=d$ for odd $d$ and $d'=2d$ for even $d$. Extended Ray Class Fields of Orders Conjecture. If $[S]\in\mathcal M(f')$, then $\fieldtrip{S}=E_{d,f'}$ and $\fieldvec{S}=\fieldproj{S}=\widetilde E_{d,f'}$. This extends the original ray class prediction from the maximal order to every order indexing a SIC multiplet; it remains open.