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OpenAI reports: Integer-multiplication complexity

The manuscript reports deterministic multiplication in O(n (log n)^(1−κ)) time with κ = 2^−182 on a fixed finite-tape Turing machine.

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Sources for this record

What was already known

The manuscript addresses the conjectured n log n optimality barrier in its stated tape model.

What changed and why it matters

Addresses a substantive research target in the specified setting; this is a reported advance whose correctness and novelty remain subject to mathematical assessment.

The AI contribution

OpenAI attributes the manuscript to an internal frontier model. This entry does not infer the exact human contribution to this individual result from the release-wide description.

Limitations

The exponent improvement is extremely small; an asymptotic theorem does not imply a usable speedup at ordinary input sizes. Preprint. AIProofWatch reviewed the source statement and scope, not the full proof, and has not independently run a formal checker.

Verification evidence

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

Author claim

Reported theorem in the pinned manuscript. This records the claim, not an independent proof check.

Accessible artifact / proof

Manuscript proof is accessible. Formalization availability alone is not labelled as successful formal verification.

Correction and publication history

2026-10-11 · amendment

Editorial importance reassessment: rate the scoped impact if correct independently from verification. The claim, limitations, sources, and verification evidence are unchanged.

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