Zvonkine's $qr$-ELSV formula

Let $g\geq 0$, let $q,r\geq 1$, and let $\mu=(\mu_1,\ldots,\mu_n)$ be a partition with $n=\ell(\mu)$ and $|\mu|=\sum_{i=1}^n\mu_i$ divisible by $q$. Assume that $b=((2g-2+n)q+|\mu|)/(qr)$ is an integer, and let $h_{g;\mu}^{\circ,q,r}$ denote the connected $q$-orbifold $r$-spin Hurwitz number. Write $\lfloor a\rfloor$ for the integral part of $a\in\mathbb{Q}$, let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of stable curves, let $\psi_i$ be the cotangent-line classes, and let $\mathrm{C}_{g,\mu}^{q,r}$ be the associated Chiodo classes. Zvonkine's $qr$-ELSV formula.

$$h_{g;\mu}^{\circ,q,r}=\prod_{j=1}^n\frac{\left(\frac{\mu_j}{qr}\right)^{\left\lfloor\frac{\mu_j}{qr}\right\rfloor}}{\left\lfloor\frac{\mu_j}{qr}\right\rfloor!}\times\frac{(qr)^{2g-2+n+\frac{(2g-2+n)q+|\mu|}{qr}}}{q^{2g-2+n}}\times\int_{\overline{\mathcal{M}}_{g,n}}\frac{\mathrm{C}_{g,\mu}^{q,r}}{\prod_{j=1}^n\left(1-\frac{\mu_i}{qr}\psi_i\right)}.$$

This formula generalizes the ELSV formula for simple Hurwitz numbers and the Johnson–Pandharipande–Tseng formula for orbifold Hurwitz numbers. It was conjectural in the cited work and is presented here as a recalled conjecture; the paper proves only special cases of the broader orbifold formula.