{"id":"openai-math/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation","pdf":"https://github.com/openai/math/blob/main/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026","tags":["density-functional-theory","quantum-chemistry","kohn-sham"],"score":0,"title":"A Coulomb ground-state density without Kohn-Sham ensemble representation","domain":"Mathematical physics","family":"278","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We construct a finite three-electron Coulomb molecule whose spin-summed ground-state density cannot be reproduced by any ground-state ensemble of noninteracting electrons in a single real, spin-independent local potential in $`L^{3/2}(\\mathbf R^3)+L^\\infty(\\mathbf R^3)`$. The molecule has two equal positive integer nuclear charges, specified by an exact finite nonnumerical formula.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Failure of Kohn–Sham ensemble representation"}