Not evaluated
A group without fixed price (family 259)
The gist
In its release of October 6, 2026, OpenAI claims, using an unreleased internal model, to have obtained a group without fixed price.
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-259-group-without-fixed-price-r1
@misc{discoveria-oai-fam-259-group-without-fixed-price-r1,
author = {{DiscoverIA}},
title = {A group without fixed price (family 259)},
howpublished = {DiscoverIA registry, entry oai-fam-259-group-without-fixed-price},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-259-group-without-fixed-price#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 10 s reading time, estimated
What it changes
If the result held, it would show that such a group exists. The title states an existence: a single example of a group would suffice.
What remains unclear
No formalisation in Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party evaluation is recorded.
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 · A-group-without-fixed…link only, reading not recorded
Method
The openai/math repository contains the manuscript “A group without fixed price”, dated October 5, 2026. It is filed in the section “Group theory” of overview.tex. history.md reports no revision of this manuscript. 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 (Group theory)
- In openai/math
- family 259, section “Group theory”, 1 manuscript dated Oct 5, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 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 253 of 372, by family number
- Not evaluated : Howie's conjecture on equations over groups (family 256)
- Not evaluated : A hyperbolic group with no geometric CAT(0) action (family 257)
- 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)
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