Under review
Ten advances by the Astra model (non-sofic group, Connes, Erdős)
Ten advances by the Astra model (non-sofic group, Connes rigidity, Erdős 146/180/183…)
The gist
OpenAI announced on August 1, 2026 ten mathematical advances achieved by an internal version of Astra. An audit (arXiv 2608.14673) says no confirmed substantive error remains in a principal result. Status: under review.
DiscoverIA status on October 11, 2026: under review, meaning public review under way, no verdict yet.
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-astra-ten-advances-2026-08-01-r1
@misc{discoveria-oai-astra-ten-advances-2026-08-01-r1,
author = {{DiscoverIA}},
title = {Ten advances by the Astra model (non-sofic group, Connes rigidity, Erdős 146/180/183…)},
howpublished = {DiscoverIA registry, entry oai-astra-ten-advances-2026-08-01},
note = {Status “Under review”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-astra-ten-advances-2026-08-01#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 these results held, an AI model would have contributed to a range of research results: a non-sofic group, the refutation of Connes rigidity, Erdős problems. One of them, Connes rigidity, already has its own separate entry, also under review.
What remains unclear
The manuscripts were written by humans with the same model, and the Lean certificates were produced by the model and supplied by OpenAI. Only partial reviews by third parties exist. Chapter 8 of the audit expresses the strongest reservation: a specialist reviewer asks for a major revision.
In the glossary : Status: under review
Read the paper
A Human Audit of OpenAIs AI-Generated Mathematical Proofs
What it establishes : Sienicki and Sienicki review the human assessments of the ten chapters of OpenAI's collection and find no confirmed substantive error remaining in a principal result, while leaving room for gaps in the proofs.
Where to start : The abstract, then the conclusion (Section 8) and Table 1 (Section 2.1), which shows which assessments cover each chapter. Versions 1 and 2 covered Chapter 6 only.
Written by an AI · reviewed by a human
For experts
Sources, method, key facts, status history, report an error
Status
Under review
Recorded on · arxiv.org
Step 2 of 4 on the scale: under review. Next step: peer reviewed.
- Announced
- Recordedunder review
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
Public review under way, no verdict yet.
To move to “Peer reviewed”: a journal publication or a review by named experts. A sourced public objection would move it to “Contested”.
Sources
- Main sourceopenai.comlink only, reading not recorded
- Status sourceopenai.compage read word for word · consulted on Oct 11, 2026 ·
The results were achieved by an internal version of Astra
Method
DiscoverIA status: under review (a public review is under way, with no verdict yet). Set on October 11, 2026 from arxiv.org (page read, quotation checked word for word: “No confirmed substantive mathematical error in a principal result remains”).
Limits
The claimant supplies a Lean proof; DiscoverIA has found no independent verification of it.
Key facts
- Claimed by
- OpenAI
announced on Aug 1, 2026 - Nature
- new result
- Field
- Mathematics (mathematics / theoretical computer science)
- Checked by
- claimant; partial third-party reviews (audit)
- Sources
- 2 : 1 read word for word, 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
An observation is added; none is ever erased.
Parts of this announcement (1)
| Title | Status |
|---|---|
| Connes rigidity conjecture: OpenAI (Astra) says it is false | Under review |
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