Not evaluated
Torsion-free group algebras that are not directly finite (family 197)
The gist
On October 6, 2026, OpenAI announced torsion-free group algebras that would not be directly finite, in characteristic two and in odd characteristic.
DiscoverIA status on October 11, 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 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-197-kaplansky-direct-finiteness-r1
@misc{discoveria-oai-fam-197-kaplansky-direct-finiteness-r1,
author = {{DiscoverIA}},
title = {Torsion-free group algebras that are not directly finite (family 197)},
howpublished = {DiscoverIA registry, entry oai-fam-197-kaplansky-direct-finiteness},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-197-kaplansky-direct-finiteness#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the result held, it would supply counterexamples to what the source calls Kaplansky's direct-finiteness conjecture. A torsion-free group algebra would then contain elements a and b such that ab equals the identity element while ba differs from it.
What remains unclear
No third-party evaluation appears in the sources read. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and no third-party check of it appears.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · raw.githubusercontent.com
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.comlink only, reading not recorded
Method
The sources read cite manuscripts (preprints), a reasoning summary for family 197 and Lean supplied by OpenAI (formalization.yaml:47 and :52, configuration OddKaplansky). The source cites “Kaplansky's direct-finiteness conjecture in characteristic two”. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from github.com (page read, quotation checked word for word).
Limits
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
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (group theory / algebra)
- Checked by
- claimant
- Sources
- 1 : 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
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 191 of 372, by family number
- Not evaluated : Lech's multiplicity conjecture (family 194)
- Not evaluated : A counterexample to the small Cohen–Macaulay module conjecture (family 195)
- Not evaluated : Counterexample to Kaplansky's zero-divisor conjecture (family 196)
- Not evaluated : Torsion-free group algebras that are not directly finite (family 197)
- Not evaluated : A counterexample to the little finitistic-dimension conjecture (family 198)
- Not evaluated : Counterexamples to conjectures of Auslander–Reiten, Tachikawa, and Nakayama (family 199)
- Not evaluated : Eisenbud–Green–Harris and lex-plus-powers in characteristic zero (family 200)
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