OpenAI reports a uniform excess-charge bound for Coulomb molecules

For any fixed nuclei at distinct positions with real charges at least one, total nuclear charge Z and M nuclei, the full two-spin nonrelativistic Coulomb Hamiltonian can strictly bind no more than Z+CM electrons, where C is universal and independent of the nuclear positions and charges.

Sources for this record

What was already known

Lieb established bounds linear in total charge, and later fermionic atomic estimates proved asymptotic neutrality and quantitative sublinear excess bounds. A universal additive bound per nucleus for the full correlated Coulomb model remained open.

AI involvement AI-led

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 Major

Resolves the strict-binding excess-charge form of the molecular ionization conjecture.

Limitations

The result bounds strictly binding sectors and does not exclude threshold ground states. The linked Lean note instead checks companion large-ionization and outer-electron-radius asymptotics.

Technical verification Reported

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

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

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision