Várilly-Alvarado and Vakil's Grothendieck-ring measure conjecture

Fix $d \geq 2$. Let $\mathcal{H}_{d,g}$ be the stack of smooth degree-$d$, genus-$g$ covers of $\mathbb{P}^1$, and let $\mathcal{H}_{\mathbf{e},g}$ be the locus with scrollar invariants $\mathbf{e}$. Define the Grothendieck-ring-valued quantity

$$\pi^{\textnormal{gr}}(B,g)=[\mathcal{H}_{d,g}]^{-1}\sum_{\mathbf{e}\in\mathbb{Z}^{d-1}:\,\mathbf{e}/(d+g-1)\in B}[\mathcal{H}_{\mathbf{e},g}].$$

Várilly-Alvarado and Vakil's Grothendieck-ring measure conjecture. For all $B$, the limit $\lim_{g\to\infty}\pi^{\textnormal{gr}}(B,g)$ converges to a measure $\pi^{\textnormal{gr}}$ valued in the Grothendieck ring of stacks. Understanding this limit requires controlling the singular loci in the parameter spaces of covers; the paper explicitly says that proving the conjecture for $d=5$ is outside its scope.