Equivariant formality conjecture for all diagonal affine Springer fibers

Let

$$\gamma=\operatorname{diag}(z_1t^{d_1},\ldots,z_nt^{d_n}),$$

where $z_i\in\mathbb{C}^*$ are pairwise distinct and $d_i\geq0$. Equivariant formality conjecture. The affine Springer fiber $\mathrm{Sp}_{\gamma}$ is equivariantly formal for all choices of $d_1,\ldots,d_n$ and all $n$. Equivariant formality is known for $n\leq4$ and for equal exponents, but the general case remains open.