Not evaluated
Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)
The gist
On October 6, 2026, OpenAI released two manuscripts from an unreleased internal model on Brennan's conjecture, with a Lean formalisation.
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-072-brennans-conjecture-counterexample-kraetzers-r1
@misc{discoveria-oai-fam-072-brennans-conjecture-counterexample-kraetzers-r1,
author = {{DiscoverIA}},
title = {Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)},
howpublished = {DiscoverIA registry, entry oai-fam-072-brennans-conjecture-counterexample-kraetzers},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-072-brennans-conjecture-counterexample-kraetzers#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Brennan's conjecture concerns univalent functions (injective holomorphic functions: they never send two distinct points to the same point). If the manuscripts held, they would, going by their titles, bring sharp (optimal) bounds on integral means of these functions and a strict bound; the sources read do not give their precise statement.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone and carries the label “unchecked”. The sources read do not describe the Kraetzer prediction that the family title says is contradicted, 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 · 072.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 · Brennans-conjecture-and…link only, reading not recorded
- Repositorygithub.com · A-strict-inverse-first…link only, reading not recorded
- Lean proofgithub.com · 072.mdpage read word for word
- Lean proofgithub.com · Brennan.leanlink only, reading not recorded
- Lean proofgithub.com · BrennanSharp.leanlink only, reading not recorded
- Lean proofgithub.com · StrictMeans.leanlink only, reading not recorded
Method
In the openai/math repository, family 072 comprises two manuscripts dated September 24, 2026: "Brennan's conjecture and sharp inverse-square integral means" and "A strict inverse-first-power bound for univalent functions". The file lean/docs/072.md describes the scope of the formalisation: three Comparator statements, in lean/ComparatorChallenges/Brennan.lean, lean/ComparatorChallenges/BrennanSharp.lean and lean/ComparatorChallenges/StrictMeans.lean. No revision is reported in history.md. 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 (Real and complex analysis)
- In openai/math
- family 072, section “Real and complex analysis”, 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
- 7 : 1 read word for word, 6 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 69 of 372, by family number
- Not evaluated : Anticanonical nonvanishing under smooth semipositivity (family 068)
- Not evaluated : Quantum geometric Langlands at irrational level (family 069)
- Not evaluated : Koebe's circle-domain conjecture and circle-domain rigidity (family 071)
- Not evaluated : Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)
- Not evaluated : The Falconer distance conjecture (family 073)
- Not evaluated : Kakeya in three and four dimensions (family 074)
- Not evaluated : The L log L Fourier-convergence conjecture (family 075)
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