# Atomic binding and asymptotic plausibility checks

Family 263: The ionization and generalized ionization conjectures. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Electronic-structure researchers can compare modeled electron counts, ionization costs and outer radii with rigorous qualitative or asymptotic constraints.

## Applicability and commercial boundary

The full nonrelativistic Coulomb model, fixed nuclei and two spin states differ from many approximations. Universal constants and ordered limits need effective numerical control before a finite-atom prediction.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Identify effective constants and a finite benchmark where the new bound is tighter than existing model diagnostics.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026/paper.pdf).