It should be noted that many of the "above-hull" structures are in fact predicted to decompose into phases are that are themselves found by the search, as shown in Table . If only the ternary and binary compounds in the Li-Fe-S-O chemical spaces are considered, many of them would be regarded as stable. This highlights the importance of performing a sufficient and unbiased sampling of the target chemical space for reliably predicting the thermodynamic stabilities.