Sagan–Swanson's monomial basis conjecture for superspace coinvariants

Let $n,r\geq 1$, let $SR_{n,r}$ be the superspace coinvariant ring for ${\mathbb{Z}}_r\wr{\mathfrak{S}}_n$, and let ${\mathcal{A}}_{n,r}$ be the set of superspace monomials constructed from the staircase bounds associated to subsets $J\subseteq[n]$:

$${\mathcal{A}}_{n,r}=\bigsqcup_{J\subseteq[n]}{\mathcal{A}}_{n,r}(J,r)\theta_J.$$

Sagan–Swanson's conjecture. The set of monomials ${\mathcal{A}}_{n,r}$ descends to a vector space basis of $SR_{n,r}$.

This conjecture would provide an explicit monomial basis for the wreath-product superspace coinvariant ring. The source states that it is proved there, including the first explicit basis for $r>2$ and the first monomial basis in the hyperoctahedral case $r=2$.