Not evaluated
The ionization and generalized ionization conjectures (family 263)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, 3 manuscripts dated September 24, 2026 on ionization and the outer radius of Coulomb atoms.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-263-ionization-generalized-ionization-r1
@misc{discoveria-oai-fam-263-ionization-generalized-ionization-r1,
author = {{DiscoverIA}},
title = {The ionization and generalized ionization conjectures (family 263)},
howpublished = {DiscoverIA registry, entry oai-fam-263-ionization-generalized-ionization},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-263-ionization-generalized-ionization#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Ionization energy is the energy needed to remove an electron from an atom. If the manuscripts were correct, they would bring results on the generalized ionization energies of full Coulomb atoms, on the outer-electron radii of neutral atoms, and on the excess charge of Coulomb molecules.
What remains unclear
The sources read do not say what the ionization and generalized ionization conjectures state, nor how much of them the manuscripts address. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI only; formalization.yaml carries the note “review: status: unchecked”, and no third-party assessment is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 263.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Uniform-excess-charge-for…link only, reading not recorded
- Repositorygithub.com · Generalized-ionization…link only, reading not recorded
- Repositorygithub.com · Generalized-outer…link only, reading not recorded
- Lean proofgithub.com · 263.mdpage read word for word
- Lean proofgithub.com · CoulombIonization.leanlink only, reading not recorded
- Lean proofgithub.com · CoulombRadii.leanlink only, reading not recorded
Method
The openai/math repository contains 3 manuscripts: “Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms”, “Generalized ionization energies for full Coulomb atoms” and “Generalized outer-electron radii of neutral Coulomb atoms”. OpenAI supplies lean/docs/263.md and 2 Comparator files: lean/ComparatorChallenges/CoulombIonization.lean and lean/ComparatorChallenges/CoulombRadii.lean. According to history.md, no revision is reported. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Mathematical physics)
- In openai/math
- family 263, section “Mathematical physics”, 3 manuscripts dated Sep 24, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 7 : 1 read word for word, 6 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 257 of 372, by family number
- Not evaluated : Spacetime Penrose inequalities and rigidity (family 260)
- Not evaluated : Localization and delocalization in the Anderson model (family 261)
- Not evaluated : Sharp one-dimensional Lieb–Thirring inequalities (family 262)
- Not evaluated : The ionization and generalized ionization conjectures (family 263)
- Not evaluated : Strong cosmic censorship near two-ended Kerr data (family 264)
- Not evaluated : The two-dimensional gapped area law (family 265)
- Not evaluated : Exactly three mutually unbiased bases in dimension six (family 266)
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