Failure of Kohn–Sham ensemble representation

What OpenAI claims

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(ℝ³)+L^∞(ℝ³). This disproves Kohn–Sham ensemble representability for that potential class; the required nuclear charge is specified nonnumerically.

Paper

1. A Coulomb ground-state density without Kohn-Sham ensemble representation

   25 September 2026 · Preprint, not peer reviewed · PDF

   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(R³)+L^∞(R³). The molecule has two equal positive integer nuclear charges, specified by an exact finite nonnumerical formula.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.