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Using the convex hull, we can assess the stability of the reactants and products reported in experiment. In Fig.~\ref{fig:lcso-ehull}, we plot the energies relative to the convex hull for all reported compounds. Negative values are stability energies against decomposition. We find that La2CuS2O2 La$_2$CuS$_2$O$_2$  and La2CuSO3 La$_2$CuSO$_3$  are highly unstable at nearly 500meV/atom above the hull. Additionally, LaCuSO is marginally unstable at 23meV/atom above the hull, but this is indistinguishable from zero given the error bars of the current method. In hindsight, we could have predicted that the proposed compounds would not have formed and instead have decomposed into: \begin{align*}  \text{La}_2\text{CuS}_2\text{O}_2 &\rightarrow \text{La}_2\text{SO}_2 + \text{CuS} \\  4 \text{La}_2\text{CuS}\text{O}_3 &\rightarrow 3 \text{La}_2\text{SO}_2 + 4\text{Cu} + \text{La}_2\text{SO}_6