Extended order-to-multiplet conjecture for SIC fields

Fix $d\in\mathbb Z_{>0}$, $d\neq3$, write $\Delta=\Delta_d=(d+1)(d-3)=f^2\Delta_0$ with $\Delta_0$ a fundamental discriminant, and let $\mathcal M(f')$ be the multiplet indexed by a positive divisor $f'$ of $f$. Extended Order-to-Multiplet Conjecture. There is a bijection from the positive divisors of $f$ to Weyl–Heisenberg line-SIC multiplets such that the multiplet $\mathcal M(f')$ contains $|\operatorname{Cl}(\mathcal O_{(f')^2\Delta_0})|$ geometric equivalence classes; moreover, $f_1\mid f_2$ implies $\fieldtrip{S_1}\subseteq\fieldtrip{S_2}$ and $\fieldvec{S_1}=\fieldproj{S_1}\subseteq\fieldvec{S_2}=\fieldproj{S_2}$. This strengthens the basic order-to-multiplet conjecture by requiring field inclusions compatible with conductor divisibility; it remains open.