Constructs a three-electron Coulomb molecule with two equal positive-integer-charge nuclei whose absolute ground-state density has no noninteracting ground-state ensemble representation by a single real spin-independent local potential in L^{3/2}(\mathbb R^3)+L^\infty(\mathbb R^3). This disproves Kohn–Sham ensemble representability for that potential class; the required nuclear charge is specified nonnumerically.
Manuscript
A Coulomb ground-state density without Kohn-Sham ensemble representation
September 25, 2026 · source · cite as \cite{OAI:A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026}
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.
Result 278 · Mathematical physics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md