The r-Bouchard–Mariño conjecture for r-Hurwitz numbers

For each $g,n$, let $H_{g,r}(x_1,\dots,x_n)$ be the generating function formed from the invariants $h_{g,r;k_1,\dots,k_n}$, and let $D$ denote the differential operator

$$Df=\frac{\partial^n f}{\partial x_1\cdots\partial x_n}\,dx_1\cdots dx_n.$$

Let $\mathcal C$ be the plane curve

$$x=-y^r+\log y,$$

and let $\mathcal W_{g,n}$ be its $n$-point correlation forms. The $r$-Bouchard–Mariño conjecture.

$$DH_{g,r}(x_1,\ldots,x_n)=\mathcal W_{g,n}.$$

This conjecture connects the generating series of $r$-Hurwitz numbers with the topological-recursion correlation forms of the specified spectral curve. The source does not state a resolution status.