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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  \end{align*}  We also investigate the sensitivity of the stability energies to the LDA+U  correction (denoted $\Delta E_M$ in Eq. 6 of PRB 84, 045115 (2011)). \cite{Jain_2011}).  Varying $\Delta E_M$ from 0.75eV/atom to 0.65eV/atom shifts the stability energies by  less than ~20meV/atom, well within LDA’s error bars, and our conclusions remain  unchanged.