  Let $\Omega$ be the {\em superspace ring} of polynomial-valued differential
forms on affine $n$-space. The natural action of the symmetric group
$\mathfrak{S}_n$ on $n$-space induces an action of $\mathfrak{S}_n$ on
$\Omega$. The {\em superspace coinvariant ring} is the quotient $SR$ of
$\Omega$ by the ideal generated by $\mathfrak{S}_n$-invariants with vanishing
constant term. We give the first explicit basis of $SR$, proving a conjecture
of Sagan and Swanson. Our techniques use the theory of hyperplane arrangements.
We relate $SR$ to instances of the Solomon-Terao algebras of
Abe-Maeno-Murai-Numata and use exact sequences relating the derivation modules
of certain `southwest closed' arrangements to obtain the desired basis of $SR$.
