OpenAI reports a uniform quasipolynomial-time trace-reconstruction decoder

For every binary string of known length n and known rational deletion retention probability p, one randomized algorithm reconstructs the string with probability at least 2/3 using an explicit sample budget and bit time polynomial in that budget and the binary input length; for each fixed p, both are quasipolynomial in n.

Sources for this record

What was already known

Earlier work provided quasipolynomial sample bounds using nonlocal statistics but did not supply a uniform quasipolynomial-time decoder for an unknown string; pairwise distinguishability alone leaves an exponential search over candidates.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Notable

Turns worst-case quasipolynomial trace sample complexity into an efficient reconstruction algorithm with uniform parameter control.

Limitations

The guarantee assumes known length and rational retention probability. The linked Lean scope proves sample lower bounds, not the decoder or its running time.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and precise partial or mismatched Lean-scope review for non-notifying local inclusion.

Read this published revision