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anions less electronegative than Cu, as these anions would capture dopants  intended for the superconducting plane, producing additional Fermi surfaces.  \emph{Global stability} -- In order We construct the convex hull by computing the energies of all known compounds in the Hg-Ca-Cu-S-O system, which would produce a 4-dimensional tetrahedron. Realistic synthesis is performed in an oxygen environment parameterized by the chemical potential $\mu(\text{O}_2)$. We find that for all values of $\mu(\text{O}_2)$, HCSCO is unstable, so we pick the value for which the compound is closest  to perform the convex hull and plot the results in Fig.~\ref{fig:hcsco-hull}.  Outcome : proposed compound with more confidence.  Jury is out.  Discuss the notion of confidence.  Accuracy of LDA. Metastable structures do exist. One cuprates are above the hull.