Not evaluated
Localization and delocalization in the Anderson model (family 261)
The gist
On October 6, 2026, OpenAI announced two manuscripts on the Anderson model: absolutely continuous spectrum at weak disorder (dimension three or more), pure-point in dimension two.
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-261-localization-delocalization-anderson-model-r1
@misc{discoveria-oai-fam-261-localization-delocalization-anderson-model-r1,
author = {{DiscoverIA}},
title = {Localization and delocalization in the Anderson model (family 261)},
howpublished = {DiscoverIA registry, entry oai-fam-261-localization-delocalization-anderson-model},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-261-localization-delocalization-anderson-model#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The Anderson model describes a quantum particle in a disordered medium; its spectrum is the set of possible energies. If these manuscripts held up, they would describe the nature of this spectrum in two regimes: weak disorder in dimension three or more, every positive disorder in dimension two. A pure-point spectrum means that the operator has a complete basis of eigenstates.
What remains unclear
OpenAI itself supplies the Lean (a language in which a computer checks every step of a proof), and its review is marked “unchecked”. No third-party check or evaluation has been read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 261.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 · Absolutely-Continuous…link only, reading not recorded
- Repositorygithub.com · Pure-Point-Spectrum-for…link only, reading not recorded
- Lean proofgithub.com · 261.mdpage read word for word
- Lean proofgithub.com · PlanarAndersonSpectrum.lea…link only, reading not recorded
Method
Two manuscripts dated September 23, 2026 are published: “Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three” and “Pure-Point Spectrum for the Two-Dimensional Anderson Model at Every Positive Disorder”. OpenAI supplies lean/docs/261.md and 1 Comparator statement, lean/ComparatorChallenges/PlanarAndersonSpectrum.lean. The file history.md reports no revision. 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 261, section “Mathematical physics”, 2 manuscripts dated Sep 23, 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
- 5 : 1 read word for word, 4 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 255 of 372, by family number
- Not evaluated : Gersten's conjecture for one-relator groups (family 258)
- Not evaluated : A group without fixed price (family 259)
- 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)
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