Random stable commutator length conjecture for closed hyperbolic manifolds

Let $M$ be a closed hyperbolic $d$-manifold. Fix some $\delta>0$. Let $\gamma$ be a random geodesic of length in $[n-\delta,n+\delta]$ conditioned to be homologically trivial, and let $v$ be the corresponding conjugacy class in $\pi_1(M)$. Random stable commutator length conjecture. For any $\epsilon>0$ and $C>1$,

$$\left|\operatorname{scl}(v)\log(n)/n - (d-1)/6\right| \le \epsilon$$

with probability $1-O(n^{-C})$. This conjecture predicts the asymptotic stable commutator length of random homologically trivial closed geodesics; the source motivates it using the mixing properties of the geodesic flow on closed hyperbolic manifolds and gives no resolution.