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The {\em superspace ring} of rank $n$ is the bigraded algebra of differential forms on affine $n$-space. This algebra carries a natural action of the symmetric group $\mathfrak{S}_n$, and the {\em superspace coinvariant ring} $SR_n$ is the quotient of superspace by the ideal generated by $\mathfrak{S}_n$-invariants with vanishing constant term. Sagan and Swanson conjectured a monomial basis for $SR_n$ which extends E. Artin's staircase monomial basis of the classical $\mathfrak{S}_n$-coinvariant ring. We describe how this conjecture can be proven using Solomon-Terao algebras of a new family of {\em southwest subarrangements} of the braid arrangement. There are curious parallels to a basis of the diagonal coinvariant ring $DR_n$ due to Carlsson and Oblomkov. Joint work with Robert Angarone, Patricia Commins, Trevor Karn, Satoshi Murai, and Andy Wilson.