Cocompact trace-set volume conjecture for large-genus hyperbolic surfaces

Let $V_g^\epsilon$ and $\overline{V_g^\epsilon}$ be the sets defined in Theorem~, and let $\mathcal{M}_g$ be the corresponding moduli space of genus-$g$ surfaces, with Weil--Petersson volume denoted by $\mathrm{Vol}_{\mathrm{WP}}$. Cocompact trace-set volume conjecture. There exists a number $0<\epsilon<1$ such that, for sufficiently large genus $g$,

$$\frac{\mathrm{Vol}_{\mathrm{WP}}(\overline{V_g^\epsilon})}{\mathrm{Vol}_{\mathrm{WP}}(\mathcal{M}_g)}=1.$$

The assertion predicts that, for some fixed positive exponent parameter, the relevant cocompact surfaces asymptotically occupy all Weil--Petersson volume in large genus. The source presents this as a conjecture and gives no further resolution evidence.