What was already known
Bowler and Carmesin formulated the unrestricted packing/covering conjecture and its connection to infinite matroid intersection. Joó had positive results for two finitary matroids on countable ground sets.
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
Refutes the unrestricted packing/covering and intersection conjectures with only two matroids.
Limitations
The counterexample matroids are neither finitary nor cofinitary, so it does not contradict positive results under those restrictions.
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
- In ZFC, two self-dual partitional matroids on a countably infinite common ground set admit neither a packing/covering partition nor an intersection witness.
- 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