Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 263-01. Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms
Manuscript map · lines 7685–7694
OpenAI@2026-10-07#rem:oai-p-263-01
Authors: OpenAI. Family 263.
Title: Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms.
Abstract: We prove that a molecule with M fixed nuclei of real charges at least one and total nuclear charge Z strictly binds at most $Z+CM$ electrons, where C is universal. The result holds for the full nonrelativistic Coulomb Hamiltonian with two spin states and arbitrary distinct nuclear positions. For neutral atoms with integer nuclear charge Z ≥ 1, the first ionization energy and, for every ground state, the radius outside which one half of an electron remains are each bounded above and below by positive universal constants.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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