Kimura's large-genus boundary-volume asymptotic conjecture

Let $V_{g,n}(L_1,\ldots,L_n)$ denote the Weil–Petersson volume with boundary lengths $\mathbf{L}=(L_1,\ldots,L_n)$. For any given $n\geq 0$ and boundary lengths $\mathbf{L}$, consider the limit as $g\to\infty$.

Kimura's conjecture. For any given $n\geq 0$ and boundary lengths $\mathbf{L}=(L_1,\ldots,L_n)$, as $g\to\infty$,

$$V_{g,n}(L_1,\ldots,L_n)\sim\sqrt{\frac{2}{\pi}}(4\pi^2)^{2g-3+n}\Gamma\left(2g+n-\frac{5}{2}\right)\prod_{i=1}^{n}\frac{\operatorname{sinh}(L_i/2)}{L_i/2}.$$

This predicts the leading large-genus behavior of Weil–Petersson volumes with prescribed boundary lengths and extends the corresponding asymptotics for volumes without boundary lengths. The source does not state a resolution of the conjecture.