What was already known
Prescribed densities outside this potential class had been shown nonrepresentable, and numerical studies suggested failures for interacting densities. A finite Coulomb ground-state density with a rigorous obstruction to every such noninteracting ensemble had not been established in the manuscript’s account.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Supplies a finite physical Coulomb example where the standard local-potential Kohn–Sham ensemble representation fails.
Limitations
The nuclear charge is specified by an exact finite formula without an effective numerical bound. The result does not cover distributional, spin-dependent or nonlocal potentials.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.
Read this published revision