OpenAI · 263-03 · 2026-09-24 · Mathematical physics
Generalized outer-electron radii of neutral Coulomb atoms
preprints/Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026
Family 263. The ionization and generalized ionization conjectures.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For the full nonrelativistic Coulomb model with two electron spin states, proves that a molecule with fixed nuclei of charges at least one and total charge strictly binds at most electrons. Neutral-atom first ionization energies and radii containing all but an expected half-electron have universal positive upper and lower bounds. The energy cost of removing electrons has Thomas–Fermi asymptotics as and ; neutral-atom outer radii have the corresponding iterated-limit asymptotics, taking first.
We prove the radius part of the generalized ionization conjecture for neutral nonrelativistic Coulomb atoms with two spin states. For every choice of ground states, the upper and lower large-nuclear-charge limits of the radius defined by an expected exterior electron mass m are both asymptotic to as m tends to infinity.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 263: The ionization and generalized ionization conjectures. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.