What was already known
Ryser’s conjecture predicts covering number at most r−1 for intersecting r-partite hypergraphs; the manuscript reviews positive low-rank cases and restricted linear families.
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
Disproves Ryser’s covering conjecture even with equal-sized vertex parts.
Limitations
The counterexamples occur for sufficiently large prime q and rank r=q+1; the prime threshold is existential.
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 sufficiently large prime q, a finite intersecting (q+1)-partite (q+1)-uniform hypergraph has covering number q+1 and exactly q+1 nonisolated vertices in each part.
- 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