Small-ray-class-field conjecture for SIC fiducials

Let $d=n^2+3=p$ be a prime in the specified sequence, let $K$ be the real quadratic base field, and let $\hat{\Psi}$ be the un-normalized SIC fiducial with components $x_j$. The two small ray class fields are the ray class fields of $K$ with finite moduli $\sqrt{d+1}+1$ and $\sqrt{d+1}-1$. Small-ray-class-field conjecture. The components of $\hat{\Psi}$ generate one of these two small ray class fields. This conjecture identifies the smaller abelian field expected to contain the fiducial components, whose intersection with the cyclotomic subfield is trivial.