Maximal-denominator conjecture for queens

Let $F_q$ denote the $q$th Fibonacci number, and consider vertex configurations of the inside-out polytope for $q$ queens. Queen maximal-denominator conjecture. The largest denominator appearing in any vertex configuration for $q$ queens is $F_q$. The discrete Fibonacci spiral supplies a configuration with denominator $F_q$; the upper-bound assertion remains open.