The ionization and generalized ionization conjectures

For the full nonrelativistic Coulomb model with two electron spin states, proves that a molecule with M fixed nuclei of charges at least one and total charge Z strictly binds at most Z+CM 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 m electrons has Thomas–Fermi asymptotics as m\to\infty and Z/m\to\infty; neutral-atom outer radii have the corresponding iterated-limit asymptotics, taking Z\to\infty first. (Lean)

Manuscripts (3)

Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms

September 24, 2026 · source · cite as \cite{OAI:Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026}

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.

Generalized ionization energies for full Coulomb atoms

September 24, 2026 · source · Lean formalization available · cite as \cite{OAI:Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026}

We prove the energy part of the generalized ionization conjecture for full nonrelativistic Coulomb atoms with two electron spin states. The energy needed to remove m electrons is asymptotic to a_{\mathrm{TF}}m^{7/3} whenever m\to\infty and Z/m\to\infty, with the Thomas–Fermi constant in atomic units. We also obtain both conjectured iterated limits.

Generalized outer-electron radii of neutral Coulomb atoms

September 24, 2026 · source · cite as \cite{OAI:Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026}

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 (81\pi^2/2)^{1/3}m^{-1/3} as m tends to infinity.

Result 263 · Mathematical physics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.