Rational superpolynomial Dyck-path formula

Let $Y_{m/n}$ be the set of $m/n$ Dyck paths, let $v(D)$ be the set of internal vertices of $D$, and let $\beta(P)$ be the stated vertex statistic. Let $\widetilde{\mathcal{P}}_{n,m}(u,q,t)$ denote the transformed refined invariant. Rational superpolynomial Dyck-path conjecture.

$$\sum_{D\in Y_{m/n}}q^{\delta_{m,n}-|D|}t^{h_{+}(D)}\prod_{P\in v(D)}(1-ut^{-\beta(P)})=\widetilde{\mathcal{P}}_{n,m}(u,q,t).$$

This extends the rational Catalan formula by the variable $u$ and is presented as an open conjecture in the source.