O'Rourke–Wei central limit conjecture for von Neumann entropy

Let $m$ and $n$ be the dimensions of the two subsystems, let $c=m/n$, and let $X$ be the standardized von Neumann entropy. Consider the fixed-trace ensemble of reduced density matrices. O'Rourke–Wei conjecture. In the limit

$$m\to\infty,\qquad n\to\infty,\qquad \frac{m}{n}=c\in(0,1],$$

the standardized von Neumann entropy $X$ converges in distribution to a Gaussian random variable with zero mean and unit variance. This is a central limit conjecture motivated by numerical evidence and by central limit behavior for linear spectral statistics over random matrix ensembles; the supplied text does not state a resolution.