Stark phase unit conjecture for SIC fiducials

Let $d=n^2+3=p$ be a prime in the specified sequence, let $K$ be the real quadratic field used in the construction, and let $e^{i\vartheta_j}$ be the phases in the almost-flat fiducial formula. Stark phase unit conjecture. The numbers $e^{i\vartheta_j}$ are Galois conjugates of Stark units for one of the two small ray class fields, and are therefore called Stark phase units. This hypothesis is the number-theoretic ingredient proposed to construct the fiducial vector from Stark units; the source treats it as conjectural.