Weyl–Heisenberg boundedness conjecture

For each $d\geq1$, except $d=3$, let $\WHSIC{d}$ denote the set of Weyl–Heisenberg SICs and identify scalar-equivalent SICs when they share a fiducial vector up to a nonzero scalar. Weyl–Heisenberg Boundedness Conjecture. There are finitely many scalar-equivalence classes of Weyl–Heisenberg SICs. The conjecture is known in a few small dimensions, including $d\in\{1,2,4,5\}$, but remains open in general.