The permutation formulation of the rational Shuffle Conjecture

Let $\widetilde{S}_n^m$ be the set of affine permutations used in the rational parking-function model, let $\operatorname{area}(\omega)$ and $\operatorname{dinv}(\omega)$ be their associated statistics, and let $Q_{\operatorname{des}(\omega^{-1})}(z)$ be the Gessel fundamental quasisymmetric function indexed by the descent set of $\omega^{-1}$.

Permutation formulation of the rational Shuffle Conjecture. The following equation holds:

$$P_{m,n}\cdot 1=\sum_{\omega\in \widetilde{S}_n^m}q^{\operatorname{area}(\omega)}t^{\operatorname{dinv}(\omega)}\cdot Q_{\operatorname{des}(\omega^{-1})}(z).$$

This reformulates the rational Shuffle Conjecture in terms of affine permutations rather than rational parking functions, using the correspondence between rational parking functions and the relevant affine-permutation data. Its resolution status is not specified in the supplied material.