Kahn–Marković asymptotic counting conjecture for surface subgroups

For a hyperbolic $3$-manifold $M$, let $S(M,g)$ denote the number of conjugacy classes of surface subgroups in $\pi_1(M)$ of genus $g$. Kahn–Marković's conjecture. There exists a constant $c(M)$ depending only on $M$ such that

$$\lim_{g\to\infty}\frac{1}{g}\left(S(M,g)\right)^{\frac{1}{2g}}=c(M).$$

This refines the known estimate $\lim_{g\to\infty}\frac{\log(S(M,g))}{2g\log(g)}=1$ and is conjectured also for counts of commensurability classes; the precise asymptotic remains unresolved.