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\emph{Reexamination} -- In the intervening years, the maturation of materials databases allowed us to revisit the question of global stability. Various databases have computed and tabulated the convex hulls of binary, ternary and some quaternary systems, and provided tools for researchers to apply their framework to novel chemical systems. In the following, we describe our new understanding of the global stability of La$_2$CuO$_2$S$_2$ and La$_2$CuO$_3$S$_S$ against all known competing phases in the La-Cu-S-O chemical system. Since the Cu site contains significant correlations, we must address the effect of $U$ on the energies provided by density functional theory.  Corrections to LDA/GGA energies for convex hull construction have been systematically investigated for transition metal oxides [PRB 73, 195107 (2006), PRB 84, 045115 (2011)]. \cite{Wang_2006,Jain_2011}.  The corrections arise from two sources: (a) the GGA overbinding of the anion (most commonly the $O_2$ molecule) and (b) correlations. The GGA overbinding differs based on the anion, and the corrections are tabulated in the Materials Project. The correlation corrections are further divided into two components: (1) a contribution due to the U for atomic-like orbitals, treated by LDA+U, and (2) a correction in the energies required when comparing correlated (modeled using LDA+U) and uncorrelated (modeled using LDA) compounds. This is often the case in construction phase diagrams containing transition metal ions as their behavior can be considered “correlated” or “uncorrelated” depending on their valence and chemical environment.  In earlier the above  work, we had proposed several chemical reaction pathways to synthesize La2CuS2O2 La$_2$CuS$_2$O$_2$  and La2CuSO3 [PRB 89, 094517 (2014)] 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 Hua He, unpublished] and concluded that the two compounds were unstable (at least at high temperatures).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 and La2CuSO3 are not among the stable compounds on the hull.