The rational Shuffle Conjecture

Let $m,n$ be the parameters for rational parking functions, let $P_{m,n}$ be the degree-$n$ operator acting on symmetric functions, and let $\operatorname{\mathcal{PF}}_{m/n}$ be the set of rational parking functions. For $f\in\operatorname{\mathcal{PF}}_{m/n}$, let $\operatorname{area}(f)$ and $\operatorname{dinv}(f)$ be the corresponding rational statistics, and let $Q_{\operatorname{ides}(f)}(z)$ be the Gessel fundamental quasisymmetric function indexed by the inverse diagonal-word descents.

The rational Shuffle Conjecture. The following equation holds:

$$P_{m,n}\cdot 1=\sum_{f\in \operatorname{\mathcal{PF}}_{m/n}}q^{\operatorname{area}(f)}t^{\operatorname{dinv}(f)}\cdot Q_{\operatorname{ides}(f)}(z).$$

This is the rational analogue of the Shuffle Conjecture, extending the parking-function formula for diagonal coinvariants to rational parking functions. The statement is presented as a conjecture in the source, while its resolution status is not specified in the supplied material.