Not evaluated
Sharp logarithmic exponents for off-diagonal Ramsey numbers (family 170)
The gist
In its release of October 6, 2026, OpenAI presents two manuscripts on the logarithmic exponent of off-diagonal Ramsey numbers, including r(5,t).
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-170-sharp-logarithmic-exponents-off-diagonal-r1
@misc{discoveria-oai-fam-170-sharp-logarithmic-exponents-off-diagonal-r1,
author = {{DiscoverIA}},
title = {Sharp logarithmic exponents for off-diagonal Ramsey numbers (family 170)},
howpublished = {DiscoverIA registry, entry oai-fam-170-sharp-logarithmic-exponents-off-diagonal},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-170-sharp-logarithmic-exponents-off-diagonal#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 manuscripts were correct, they would concern the exponent of the logarithm in the size of r(5,t), the smallest number of points such that, in any network of that size, 5 points are all linked to one another or t points have no link among them. The titles announce a “sharp” (optimal) exponent and also cover other off-diagonal Ramsey numbers.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: its review field reads “unchecked”, and no third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 170.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 · The-Sharp-Logarithmic…link only, reading not recorded
- Repositorygithub.com · Sharp-Logarithmic…link only, reading not recorded
- Lean proofgithub.com · 170.mdpage read word for word
- Lean proofgithub.com · RamseyFive.leanlink only, reading not recorded
- Lean proofgithub.com · SharpLogRamsey.leanlink only, reading not recorded
Method
The manuscripts “The sharp logarithmic exponent of r(5,t)” and “Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers”, dated September 24, 2026, are attributed to an unreleased internal OpenAI model. The file lean/docs/170.md describes the scope of the Lean formalisation, which has 2 Comparator statements (lean/ComparatorChallenges/RamseyFive.lean and lean/ComparatorChallenges/SharpLogRamsey.lean); the family is absent from the sources of formalization.yaml, and history.md reports no revision of the manuscripts. 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 170, section “Combinatorics”, 2 manuscripts dated Sep 24, 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
- 6 : 1 read word for word, 5 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 164 of 372, by family number
- Not evaluated : Pinned distances and a power saving for planar unit distances (family 167)
- Not evaluated : Combinatorial invariance of Kazhdan–Lusztig polynomials (family 168)
- Not evaluated : The Shareshian–Wachs e-positivity conjecture (family 169)
- Not evaluated : Sharp logarithmic exponents for off-diagonal Ramsey numbers (family 170)
- Not evaluated : The hypercube Ramsey conjecture (family 171)
- Not evaluated : Classification of finite Euclidean Ramsey configurations (family 172)
- Not evaluated : Seymour's second-neighborhood conjecture (family 173)
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