Not evaluated
Arithmetic rigidity of lattice von Neumann algebras (family 286)
The gist
OpenAI claims, in two manuscripts announced on October 6, 2026, results on the arithmeticity of twisted finite correspondences for lattices over local fields.
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-286-arithmetic-rigidity-lattice-von-neumann-r1
@misc{discoveria-oai-fam-286-arithmetic-rigidity-lattice-von-neumann-r1,
author = {{DiscoverIA}},
title = {Arithmetic rigidity of lattice von Neumann algebras (family 286)},
howpublished = {DiscoverIA registry, entry oai-fam-286-arithmetic-rigidity-lattice-von-neumann},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-286-arithmetic-rigidity-lattice-von-neumann#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 family title refers to the arithmetic rigidity of lattice von Neumann algebras. If the manuscripts hold, the second would concern an 'arithmetic category' and the stable recovery of 'lattice factors', without the sources read giving the precise statement.
What remains unclear
It is not known whether a third party has evaluated these manuscripts: no evaluation is recorded in the sources read. No Lean formalisation (Lean is a language in which a computer checks every step of a proof) is provided: there is no lean/docs/286.md.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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 · Arithmeticity-of-twisted…link only, reading not recorded
- Repositorygithub.com · The-arithmetic-category…link only, reading not recorded
Method
OpenAI's repository holds two manuscripts dated September 23, 2026. They are titled 'Arithmeticity of twisted finite correspondences for lattices over local fields' and 'The arithmetic category and stable recovery of lattice factors'. It files them under the section 'Operator algebras' (overview.tex). 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Operator algebras)
- In openai/math
- family 286, section “Operator algebras”, 2 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 280 of 372, by family number
- Not evaluated : Polynomial-time, constant-error unitary synthesis from a Boolean oracle (family 283)
- Not evaluated : The optimal randomized–quantum query exponent (family 284)
- Not evaluated : Counterexamples to Baum–Connes and Kadison–Kaplansky (family 285)
- Not evaluated : Arithmetic rigidity of lattice von Neumann algebras (family 286)
- Not evaluated : Isomorphism of free group factors (family 287)
- Not evaluated : Kadison's similarity conjecture (family 288)
- Not evaluated : The strong Kadison–Kastler conjecture (family 289)
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