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OpenAI reports: Brennan’s conformal-integrability conjecture

OpenAI reports area-integrability of the s-th power of the derivative of every conformal bijection from a simply connected planar domain to the unit disk whenever 4/3<s<4, together with the stated inverse-square integral-means exponent.

Sources for this record

What was already known

The target concerns the full conjectured exponent interval for arbitrary simply connected domains. Bounds for smoother domains or smaller exponent ranges do not establish it.

What changed and why it matters

Reaches the full open exponent interval in Brennan’s conjecture without imposing boundary regularity.

The AI contribution

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

Limitations

The endpoints are excluded. The claim concerns conformal bijections and the specified integral-means class; it should not be read as an endpoint integrability theorem. 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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