Delecroix–Goujard–Zograf–Zorich frequency-ratio conjecture for simple closed geodesics

Let $X$ be a hyperbolic surface of genus $g$ with $n$ cusps. A simple closed geodesic is a closed geodesic without self-intersections; it is separating if it splits $X$ into two parts and nonseparating otherwise. Write $c_{g,n,sep}$ and $c_{g,n,nonsep}$ for the corresponding frequencies.

Delecroix–Goujard–Zograf–Zorich conjecture. The ratio of frequencies of separating over nonseparating simple closed geodesics admits the uniform asymptotics

$$\frac{c_{g,n,sep}}{c_{g,n,nonsep}}=\sqrt{\frac{2}{3\pi g}}\cdot\frac{1}{4^g}\cdot f\left(\frac{n}{g}\right)\cdot\left(1+\varepsilon(g,n)\right),$$

where $f:[0,\infty)\mapsto\mathbb{R}$ is continuous and increases monotonically from $f(0)=1$ to $f(\infty)=\sqrt{2}$, and the error term $\varepsilon(g,n)$ tends to $0$ as $g\to\infty$ uniformly in $n$.

This conjecture predicts the large-genus asymptotic ratio of separating to nonseparating simple closed geodesic frequencies and expresses its dependence on the cusp-to-genus ratio through the function $f$. The source presents it as a conjecture from Delecroix, Goujard, Zograf and Zorich; no resolution is supplied here.