The asymptotic proportion conjecture for hyperelliptic Jacobians in dimension three

Let $q$ range over powers of $2$, and consider isogeny classes of $3$-dimensional abelian varieties over the finite field of characteristic $2$ with $q$ elements. The classes under consideration are those containing the Jacobian of a hyperelliptic curve. Asymptotic proportion conjecture. The proportion of such isogeny classes approaches

$$\frac{1}{2}$$

as $q\to\infty$. This predicts a positive limiting proportion, contrasting with the vanishing proportion in dimensions tending to infinity for a fixed field; the supplied text does not indicate whether the conjecture has been resolved.