What was already known
One-sample guarantees for general matroids were known, but the manuscript says they lost a factor depending on rank or used weaker arrival models. Known-distribution guarantees also did not give the adversary unseen values and the full random seed.
AI involvement
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
Gives a constant independent of matroid rank under an unusually strong adversarial arrival model.
Limitations
Values must be nonnegative and independent across elements; each sample is paired with an identically distributed online value. The rule is not claimed to run in polynomial time.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every finite matroid, one independent sample per element supports an online rule with expected reward at least 2^-310 times the expected offline optimum, even when the arrival-order adversary sees all samples, online values, and the rule’s seed.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
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
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision