Not evaluated
Ordered Variable Word theorem: first-order part announced as determined (Patey, with Claude Opus 5.5)
The gist
On October 20, 2026, Ludovic Patey posted on arXiv an answer to an open question in mathematical logic about the Ordered Variable Word theorem, with a core lemma proved by Claude Opus 5.5.
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-patey-mots-variables-ordonnes-2026-10-20-r1
@misc{discoveria-patey-mots-variables-ordonnes-2026-10-20-r1,
author = {{DiscoverIA}},
title = {Ordered Variable Word theorem: first-order part announced as determined (Patey, with Claude Opus 5.5)},
howpublished = {DiscoverIA registry, entry patey-mots-variables-ordonnes-2026-10-20},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/patey-mots-variables-ordonnes-2026-10-20#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
In reverse mathematics, the strength of a theorem is measured by the axioms needed to prove it. If the proof held, the Ordered Variable Word theorem, a result in combinatorics, would prove no more arithmetic statements than RCA_0 + BΣ^0_2, the base system RCA_0 extended by the collection principle BΣ^0_2. The author derives the same property for Chubb, Hirst and McNicholl's tree theorem for singletons, which would answer a long-standing open question.
What remains unclear
No third party has reviewed the proof yet, and it is not formalised.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.27643
Step 1 of 4 on the scale: not evaluated. Next step: under review.
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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/2610.27643page read word for word · consulted on Oct 24, 2026 ·
Lemma 3.13 was found by Claude Opus 5.5 (Anthropic).
- Paperarxiv.org · html/2610.27643page read word for word · consulted on Oct 24, 2026 ·
The proof was completely rewritten by the author for clarity.
Method
The paper states that the theorem is Π^1_1-conservative over RCA_0 + BΣ^0_2. According to the paper, Claude Opus 5.5 proved the Π^0_1-extension lemma (Lemma 3.13), a core step, which Ludovic Patey rewrote completely; the original idea of the approach, proving Liu and Patey's weakly low basis theorem within a weak system with the techniques of Le Houérou, Patey and Yokoyama, was his. 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: “Lemma 3.13 was found by Claude Opus 5.5 (Anthropic).”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- Ludovic Patey, with Claude Opus 5.5 (Anthropic)
announced on Oct 20, 2026 - Nature
- new result
- Field
- Mathematics (mathematical logic / reverse mathematics)
- 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; no third-party evaluation found
Source: arxiv.orgread word for word
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