The candidate basis conjecture for the super-diagonal coinvariant ring

Let $n\geq1$. For each ordered set partition $\Pi$ of $[n]$, let $\mathcal{B}_\Pi$ be the set of monomials constructed from the associated permutation, Grassmann monomial, and schedule-number factors, and define $\mathcal{B}_n$ to be the union of the sets $\mathcal{B}_\Pi$. Candidate basis conjecture. For $n\geq1$, $\mathcal{B}_n$ forms a basis for $\operatorname{SDR}_n$. The construction is designed to match area, diagonal-inversion, and marking degrees of marked parking functions. The text presents this as a candidate basis and gives evidence, while noting that even the specialization with all $y_i=0$ is not known to be a basis.