The rational Catalan length-skew-length conjecture for core partitions

Let $m$ and $n$ be coprime positive integers. An $(m,n)$-core is a partition that is simultaneously an $m$-core and an $n$-core; denote the set of such cores by $\mathcal P_{m,n}$. Let $\ell(\lambda)$ and $s\ell(\lambda)$ be the length and skew-length statistics of an $(m,n)$-core $\lambda$. Define $[a]_q=1+q+\cdots+q^{a-1}$ and $\left[m+n \atop m,n \right]_q$ as the relevant $q$-multinomial coefficient. The rational Catalan length-skew-length conjecture.

$$\sum_{\lambda\in\mathcal P_{m,n}}q^{\ell(\lambda)+s\ell(\lambda)}=\operatorname{Cat}_{m,n}(q)=\frac{1}{[m+n]_q}\left[m+n \atop m,n \right]_q.$$

This is the core-partition formulation of a combinatorial interpretation for the rational Catalan polynomial. The source attributes it to Armstrong and collaborators and gives no evidence that it has been resolved.