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Energies relative to the convex hull for reactants and observe products in the La-Cu-S-O system. Negative energies indicate stable compounds, while unstable compounds have positive energies. It is clear that both La$_2$CuSO$_3$ and La$_2$CuS$_2$O$_2$ are highly unstable, lying nearly 500meV/atom above the hull. In contrast, LaCuSO lies well within the computational error bars. \label{fig:lcso-ehull}