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OpenAI reports: Strict hot spots on simply connected planar domains

OpenAI reports that every nonzero first-positive Neumann eigenfunction on a smooth bounded simply connected planar domain has nonvanishing interior gradient, placing all global extrema on the boundary even for a multiple eigenvalue.

Sources for this record

What was already known

The strict version concerns every eigenfunction, rather than existence of one favorable eigenfunction or results confined to convex or symmetric domains.

What changed and why it matters

Establishes the stated strict all-eigenfunction hot-spots target without convexity or symmetry restrictions.

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 domain is smooth, bounded, and simply connected. No assertion for domains with holes or arbitrary boundary regularity is recorded. 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.

Read this published revision