The Shuffle Conjecture for bivariate diagonal higher harmonics

Let $\mathscr{H}_n^{(r)}(\mathbf{w};q,t)$ denote the graded Frobenius characteristic of the bivariate diagonal higher-harmonic space. Let $\delta_n^{(r)}$ be the relevant $r$-staircase shape, let $\lambda\subseteq\delta_n^{(r)}$, and let $\tau$ be a semistandard filling of the skew shape $(\lambda+1^n)/\lambda$ by nonnegative integers. Write $\operatorname{area}(\lambda)$ for the number of cells of $\delta_n^{(r)}/\lambda$, $\operatorname{dinv}_r(\tau)$ for the $r$-refined diagonal-inversion statistic, and $\mathbf{w}_\tau$ for the monomial associated with $\tau$. The Shuffle Conjecture.

$$\mathscr{H}_{n}^{(r)}(\mathbf{w};q,t)=\sum_{\lambda\subseteq\delta_n^{(r)}}\sum_{\substack{\tau:(\lambda+1^n)/\lambda\longrightarrow {\mathbb N}\tau\ \text{semistandard}}}q^{\operatorname{area}(\lambda)}t^{\operatorname{dinv}_r(\tau)}\mathbf{w}_\tau.$$

This is presented as an explicit combinatorial formula for the Frobenius characteristic of bivariate higher harmonics; the supplied source describes it as still conjectural.