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OpenAI reports: Deterministic factorization over prime fields

OpenAI reports uniform deterministic complete factorization of a densely represented polynomial over a binary-specified prime field in bit complexity polynomial in (degree+1) log p, including irreducible factors and multiplicities.

Sources for this record

What was already known

A polynomial running time in p is not polynomial in the binary input length. Randomized polynomial-time factorization also differs from the uniform deterministic target.

What changed and why it matters

Attains the stated deterministic polynomial bit-complexity target for prime-field factorization.

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 proof invokes the companion’s uniform Hecke zero-free theorem. Its validity is a dependency of the claim; no unconditional audit of that input or result for every finite-field representation is recorded here. 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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