Ray class field prediction for RM-value fields

Let $t=(d,r,Q)$ be an admissible tuple with associated real quadratic field $K$, let $d=d_{j,m}$, and let $f$ be the conductor of $Q$. Let $s=(d,r,Q,G,g)$ be a fiducial datum. Denote by $E_s^{(1)}$, $E_t^{(2)}$, and $E_t$ the fields defined in the source, and by $H^{O_f}_{db\bullet}$ the corresponding ray class fields. Ray class field prediction.

$$E_s^{(1)}=H^{\mathcal O_f}_{\mathfrak d\infty_1},\qquad E_t^{(2)}=H^{\mathcal O_f}_{\mathfrak d\infty_2},\qquad E_t=H^{\mathcal O_f}_{\mathfrak d\infty_1\infty_2}.$$

The paper presents this as a numerical prediction extending beyond what follows from the Stark--Tate conjecture, and notes that it implies a further ray-class-field conjecture.