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OpenAI reports: Worst-case Subset Sum algorithms

The manuscript reports a randomized classical Subset Sum algorithm in O(2^(0.49n)) time for polynomial-bit inputs.

Sources for this record

What was already known

The familiar meet-in-the-middle scale is 2^(n/2). Compare the same input-bit restrictions and computation model.

What changed and why it matters

Improves the exponential running-time bound from the meet-in-the-middle scale. It remains exponential and does not resolve P versus NP.

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

This remains exponential time and does not resolve P versus NP. The result has bounded error and uses the stated word-RAM model. 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.

Read this published revision