Not evaluated
Frankl, Ota and Tokushige's conjecture: announced counterexample, found by ChatGPT 6.1 Sol (Patkós)
The gist
On October 20, 2026, Balázs Patkós posted on arXiv a counterexample, found by ChatGPT 6.1 Sol, to a conjecture of Frankl, Ota and Tokushige on intersecting families.
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-patkos-frankl-ota-tokushige-2026-10-20-r1
@misc{discoveria-patkos-frankl-ota-tokushige-2026-10-20-r1,
author = {{DiscoverIA}},
title = {Frankl, Ota and Tokushige's conjecture: announced counterexample, found by ChatGPT 6.1 Sol (Patkós)},
howpublished = {DiscoverIA registry, entry patkos-frankl-ota-tokushige-2026-10-20},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/patkos-frankl-ota-tokushige-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
An intersecting family is a collection of sets in which any two share an element. Frankl, Ota and Tokushige had conjectured the exact value of an extremal quantity b(t) attached to these families; if the counterexample held, b(t) would grow much more slowly than the conjectured value, like t to the power 3/2 up to a logarithmic factor.
What remains unclear
No third party has reviewed the counterexample or the new bound yet, and nothing is formalised.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.28029
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 sourcearxiv.org · abs/2610.28029page read word for word · consulted on Oct 24, 2026 ·
The counterexample was found by ChatGPT 6.1Sol, the lower bound proof is due to the human author.
- Paperarxiv.org · html/2610.28029page read word for word · consulted on Oct 24, 2026 ·
In this note, we present a counterexample to the conjecture
Method
ChatGPT 6.1 Sol found the counterexample, which gives b(t) ≤ 2√2 t^(3/2) √(log t) + O(t^(3/2)); the author gives a proof of the new lower bound (2/3^(3/4)) t^(3/2) − O(t). The model had also proposed a lower bound with a better leading coefficient, (1.09+o(1)) t^(3/2). 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: “The counterexample was found by ChatGPT 6.1Sol, the lower bound proof is due to the human author.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- Balázs Patkós, with ChatGPT 6.1 Sol (OpenAI)
announced on Oct 20, 2026 - Nature
- new result
- Field
- Mathematics (extremal combinatorics / intersecting families)
- 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
An observation is added; none is ever erased.
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.