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In the above work, we had proposed several chemical reaction pathways to synthesize La$_2$CuS$_2$O$_2$ and La$_2$CuSO$_3$ which were subsequently tested by experiment [ref. Hua He, unpublished] and concluded that the two compounds were unstable (at least at high temperatures). Additionally, the phase with composition LaCuSO seemed to be quite stable at high temperatures, as it was the preferred quaternary composition in almost all the experimentally analyzed reactions.  With modern materials databases, we are able to reanalyze the entire La-Cu-S-O system to construct the convex hull (plotted in Fig. 1) and globally investigate stability. Notice that La2CuS2O2 La$_2$CuS$_2$O$_2$  and La2CuSO3 La$_2$CuSO$_3$  are not among the stable compounds on the hull.