Not evaluated
Kakeya in three and four dimensions (family 074)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, two manuscripts on the Kakeya conjecture, one in three dimensions, the other in four.
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-074-kakeya-three-four-dimensions-r1
@misc{discoveria-oai-fam-074-kakeya-three-four-dimensions-r1,
author = {{DiscoverIA}},
title = {Kakeya in three and four dimensions (family 074)},
howpublished = {DiscoverIA registry, entry oai-fam-074-kakeya-three-four-dimensions},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-074-kakeya-three-four-dimensions#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 establish the Kakeya maximal conjecture in three dimensions and the fact that every four-dimensional Kakeya set has full Hausdorff dimension. Hausdorff dimension is a way of measuring the size of a set, even a very irregular one; “full” means equal to that of the whole space.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The sources read do not say where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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-Kakeya-maximal…link only, reading not recorded
- Repositorygithub.com · Every-four-dimensional…link only, reading not recorded
Method
In the openai/math repository, family 074 comprises two manuscripts: “The Kakeya maximal conjecture in three dimensions” (September 23, 2026) and “Every four-dimensional Kakeya set has full Hausdorff dimension” (September 24, 2026), filed under the section “Real and complex analysis”. There is no file lean/docs/074.md, and history.md reports no revision of these 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
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 074, section “Real and complex analysis”, 2 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 71 of 372, by family number
- 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)
- Not evaluated : Ultraflat real Littlewood polynomials (family 076)
- Not evaluated : Fourier restriction for positively curved surfaces (family 077)
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