What was already known
Earlier exact uniform samplers covered two-row tables, while other methods required dense, balanced, sparse, or fixed-dimension conditions according to the manuscript’s review.
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 exact uniform sampling with no structural restriction on the margins or dimensions.
Limitations
The exact sampler has expected polynomial bit complexity, not a worst-case polynomial bound on every run; an exceptionally rare branch may perform exhaustive computation.
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 any nonnegative row and column margins with equal totals, an exact uniform sampler for integer contingency tables terminates almost surely and has expected bit complexity polynomial in both dimensions and the binary input length.
- 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