Not evaluated
Lie groups: announced proof that every Lie group can be realised by permutations of a countable set (Monod and Thom, with GPT 6 Astra)
The gist
On October 13, 2026, Nicolas Monod and Andreas Thom posted on arXiv a proof that every Lie group can be realised by permutations of a countable set, a question of Ulam, building on a construction found by GPT 6 Astra.
DiscoverIA status on October 24, 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 24, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 24, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-monod-thom-groupes-de-lie-2026-10-13-r1
@misc{discoveria-monod-thom-groupes-de-lie-2026-10-13-r1,
author = {{DiscoverIA}},
title = {Lie groups: announced proof that every Lie group can be realised by permutations of a countable set (Monod and Thom, with GPT 6 Astra)},
howpublished = {DiscoverIA registry, entry monod-thom-groupes-de-lie-2026-10-13},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/monod-thom-groupes-de-lie-2026-10-13#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A group can be realised by permutations of a countable set when it can be viewed as a group of bijections of a countably infinite set. If the proof held, every Lie group, the groups that describe continuous symmetries, would have this property, answering a question of Ulam.
What remains unclear
No third party has reviewed the proof yet, and it is not formalised. The authors point out that a substantial part of the argument already appeared in earlier work, notably the Parusiński–Rond construction; they regard the Puiseux embedding of Lemma 2.4 and its combination with the gluing argument as new.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.18464
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What this status means
Source reading : Source read word for word (level 3 of 3)
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To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcearxiv.org · abs/2610.18464page read word for word · consulted on Oct 24, 2026 ·
We prove that every Lie group can be realized by permutations of a countable set, answering a classical question of Ulam.
- Paperarxiv.org · html/2610.18464page read word for word · consulted on Oct 24, 2026 ·
The key countable-index deformation was first constructed by OpenAI's GPT 6 Astra during extended mathematical discussions.
Method
After three weeks of discussions, GPT 6 Astra produced the countable-index deformation underlying Theorem C; the authors suggested extending it to SL_n(R) and the other simple Lie groups, which, with an earlier reduction, gave the general theorem. Nicolas Monod and Andreas Thom then developed, checked and substantially rewrote the argument. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 24, 2026 from arxiv.org (page read, quotation checked word for word: “We prove that every Lie group can be realized by permutations of a countable set”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- Nicolas Monod et Andreas Thom, with GPT 6 Astra (OpenAI)
announced on Oct 13, 2026 - Nature
- new result
- Field
- Mathematics (group theory / Lie groups)
- Checked by
- no verifier identified
- Sources
- 2 : 2 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
arXiv preprint, not peer-reviewed or formalised; proof checked and rewritten by the authors; no third-party evaluation found
Source: arxiv.orgread word for word
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