Large-genus asymptotics of mixed Weil–Petersson intersection numbers

Let $V_{g,n;d}$ denote the mixed intersection number associated with a fixed set $d=(d_1,\dots,d_n)$ of non-negative integers, and let $V_{g,n}$ denote the corresponding Weil–Petersson volume. For each $k\geq 1$, let $l_k$ be the number of indices $i$ such that $d_i=k$. Mixed-intersection asymptotics conjecture. For any fixed $n>0$ and fixed set $d=(d_1,\dots,d_n)$ of non-negative integers,

$$\lim_{g\rightarrow\infty}\frac{V_{g,n;d}}{V_{g,n}}=\prod_{k\geq 1}\left(\frac{\pi^{2k}}{2^k(2k+1)!!}\right)^{l_k}.$$

This predicts a universal limiting ratio for mixed intersection numbers as the genus tends to infinity with the marked-point data fixed. The source reports numerical computations for bounded genus and small values of the multiplicities, but gives no resolution of the conjecture.