Not evaluated
Dimension of posets excluding a standard example: new bounds found by ChatGPT-6 Astra (Hodor, Micek, Trotter)
The gist
On October 17, 2026, Jędrzej Hodor, Piotr Micek and William T. Trotter posted on arXiv new bounds on the dimension of posets excluding a standard example, with proofs found by ChatGPT-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-hodor-micek-trotter-dimension-2026-10-17-r1
@misc{discoveria-hodor-micek-trotter-dimension-2026-10-17-r1,
author = {{DiscoverIA}},
title = {Dimension of posets excluding a standard example: new bounds found by ChatGPT-6 Astra (Hodor, Micek, Trotter)},
howpublished = {DiscoverIA registry, entry hodor-micek-trotter-dimension-2026-10-17},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/hodor-micek-trotter-dimension-2026-10-17#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The dimension of a poset is the smallest number of total orders whose intersection it is. For every order d ≥ 3 of the excluded standard example, the paper would show that the maximum dimension of an n-element poset grows at most like a power of n strictly below 1, where it was only known to grow more slowly than n. For d = 3, it would grow at least like n to the power 1/3 and at most like n to the power 2/3, up to logarithmic factors.
What remains unclear
No third party has reviewed the proofs yet, and they are not formalised. The exact growth exponent for S_3, denoted γ_3, remains open: it is only known to lie between 1/3 and 2/3.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.24774
Step 1 of 4 on the scale: not evaluated. Next step: under review.
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- Recordednot evaluated
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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/2610.24774page read word for word · consulted on Oct 24, 2026 ·
The proofs were found by OpenAI's ChatGPT-6 Astra.
- Paperarxiv.org · html/2610.24774page read word for word · consulted on Oct 24, 2026 ·
For d=3, we obtain an upper bound O(n^{2/3} log n)
Method
The paper gives, for every d ≥ 3, a bound O_d(n^α) with α < 1 (Biró, Hamburger and Pór had shown o(n)); for d = 3, an upper bound O(n^(2/3) log n) and posets without S_3 of dimension Ω(n^(1/3)/log n). ChatGPT-6 Astra found the proofs; Jędrzej Hodor, Piotr Micek and William T. Trotter worked through the generated output to present it in a readable, optimised form, and take responsibility for its correctness. 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 proofs were found by OpenAI's ChatGPT-6 Astra.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- Jędrzej Hodor, Piotr Micek et William T. Trotter, with ChatGPT-6 Astra (OpenAI)
announced on Oct 17, 2026 - Nature
- new result
- Field
- Mathematics (combinatorics / posets)
- 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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