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OpenAI reports: Ordinary two-point Chowla correlations

OpenAI reports cancellation with a power-of-logarithm saving for ordinary two-point Liouville averages along fixed nonproportional affine forms, and a binary corrected Elliott result under uniform nonpretentiousness.

Sources for this record

What was already known

Logarithmically weighted averages and ordinary averages have different targets. The ordinary result must control the final scale rather than aggregate many scales.

What changed and why it matters

Resolves the ordinary two-point target, rather than only its logarithmically averaged counterpart.

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 forms are fixed. The result does not assert uniformity for growing coefficients or resolve every higher-order Chowla correlation; the Elliott statement has a nonpretentiousness hypothesis. 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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