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OpenAI reports: Almost-linear approximation of edit distance

The manuscript reports a randomized (1+ε)-approximation in N^(1+o(1)) worst-case expected time for each fixed rational ε in (0,1).

Sources for this record

What was already known

The target is a uniform approximation scheme under explicit input and alphabet conditions. It is not exact edit distance.

What changed and why it matters

Gives an almost-linear approximation scheme for arbitrary permitted strings, a broad advance in edit-distance algorithms.

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 success probability is at least 2/3, epsilon is fixed, and the runtime is expected in the stated 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