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OpenAI reports: The three-dimensional Kakeya maximal conjecture

OpenAI reports the three-dimensional Kakeya maximal L³ estimate with tube-radius loss at most C_ε δ^(-ε) for every positive ε, uniformly over unit tubes of radius δ.

Sources for this record

What was already known

Full dimension of Kakeya sets and the quantitative maximal-operator estimate are different assertions. The maximal estimate must control all permitted functions and tube placements.

What changed and why it matters

Resolves the quantitative three-dimensional maximal target rather than only a set-dimension statement.

The AI contribution

OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.

Limitations

This entry concerns the three-dimensional maximal estimate. The family’s four-dimensional Hausdorff result is a separate statement, and no dimension-free maximal theorem is claimed. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.

Accessible artifact / proof

The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.

Correction and publication history

2026-10-11 · publication

Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.

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