Not evaluated
Superexponential van der Waerden numbers
Family 160
The gist
In its release of October 6, 2026, OpenAI claims quantitative superexponential bounds for van der Waerden numbers.
DiscoverIA status on October 12, 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 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-160-superexponential-van-der-waerden-numbers-r1
@misc{discoveria-oai-fam-160-superexponential-van-der-waerden-numbers-r1,
author = {{DiscoverIA}},
title = {Superexponential van der Waerden numbers (family 160)},
howpublished = {DiscoverIA registry, entry oai-fam-160-superexponential-van-der-waerden-numbers},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-160-superexponential-van-der-waerden-numbers#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript held, there would be quantitative bounds on this length, with superexponential growth, meaning faster than any exponential. A van der Waerden number is this critical length, for a given number of colours and a given length of run.
What remains unclear
No independent assessment is recorded. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI and marked “review: status: unchecked” in formalization.yaml. The sources read do not say whether the bounds are lower or upper.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 160.md
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 sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Quantitative…link only, reading not recorded
- Lean proofgithub.com · 160.mdpage read word for word
- Lean proofgithub.com · QuantitativeVanDerWaerden.…link only, reading not recorded
Method
OpenAI publishes one manuscript, “Quantitative Superexponential Bounds for van der Waerden Numbers”, dated September 23, 2026. The repository also holds lean/docs/160.md, which describes the scope of the Lean formalisation (1 Comparator statement), and lean/ComparatorChallenges/QuantitativeVanDerWaerden.lean. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Combinatorics)
- In openai/math
- family 160, section “Combinatorics”, 1 manuscript dated Sep 23, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 155 of 372, by family number
- Not evaluated : Borsuk's conjecture fails in dimension nine (family 156)
- Not evaluated : The Euclidean plane cannot be colored with five colors (family 158)
- Not evaluated : Erdős's reciprocal-sum conjecture and quasipolynomial Szemerédi bounds (family 159)
- Not evaluated : Superexponential van der Waerden numbers (family 160)
- Not evaluated : Counterexamples to Sidorenko's conjecture and the forcing conjecture (family 161)
- Not evaluated : Counterexamples to Ryser's covering and Gyárfás's tree-cover conjectures (family 162)
- Not evaluated : Hindman's finite sums and products conjecture (family 164)
Related frontiers
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