Weyl–Heisenberg algebraicity conjecture

Let $d\geq1$, $d\neq3$, and let a Weyl–Heisenberg line-SIC consist of projective-algebraic lines in $\C^d$ when its vectors can be represented by algebraic coordinates. Weyl–Heisenberg Algebraicity Conjecture. Every Weyl–Heisenberg SIC in dimension $d$ is projective-algebraic. This is equivalent in the source to finiteness of the real projective algebraic variety of Weyl–Heisenberg SICs for all $d\neq3$; it remains open in general.