Loehr–Warrington rational $q,t$-Catalan symmetry conjecture

For $a,b\in\mathbb{N}$, let $\mathcal{D}(N^aE^b)$ be the set of rational Dyck paths and define

$$\mathsf{Cat}_{a,b}(q,t)=\sum_{D\in\mathcal{D}(N^aE^b)}q^{\mathsf{area}(D)}t^{\mathsf{area}(\mathsf{sweep}(D))}.$$

Rational $q,t$-Catalan symmetry conjecture.

$$\mathsf{Cat}_{a,b}(q,t)=\mathsf{Cat}_{a,b}(t,q).$$

The weaker specialization symmetry would follow from bijectivity of the sweep map, which the source says is known only for certain parameters; the general joint symmetry is presented as conjectural.