Conjecture on the asymptotic proportion of simple abelian-variety isogeny classes

Let $m_q(g)$ be the number of isogeny classes of abelian varieties over $\mathbb{F}_q$ of dimension $g$, and let $s_q(g)$ be the number of isogeny classes of simple abelian varieties over $\mathbb{F}_q$ of dimension $g$. The preceding theorem shows that

$$\limsup_{g \rightarrow \infty}\frac{s_q(g)}{m_q(g)}=1.$$

Asymptotic simplicity conjecture. The proportion of isogeny classes that are simple should converge to one:

$$\lim_{g \rightarrow \infty}\frac{s_q(g)}{m_q(g)}=1.$$

The conjecture strengthens the proved limsup statement by asserting convergence rather than merely the existence of subsequences along which the proportion tends to one. It concerns the distribution of simple isogeny classes among all isogeny classes of $g$-dimensional abelian varieties over $\mathbb{F}_q$.