What was already known
Ryser’s inequality was proved in several low ranks. A separate published OpenAI result gives balanced counterexamples at every sufficiently large prime order using a later construction.
AI involvement
OpenAI credits its internal model with the original odd-extension construction. No named human proof check or explanation of it is documented.
The OpenAI-authored manuscript and release document central internal-model work, while the exact independence of this run is not established.
Importance
This earlier odd-extension family supplies a distinct, formally checked route to violating the covering inequality.
Limitations
The theorem uses existential large-prime and odd-degree thresholds; it does not assert balanced parts or a small-rank example. Its companion graph corollary addresses a separate covering conjecture.
Technical verification
The Lean eventual-odd theorem constructs finite intersecting r-partite hypergraphs with matching number one and cover number r for every sufficiently large eligible prime and odd extension degree. It does not assert balanced parts or explicit thresholds.
Formal checking
Lean proof of eventual odd-extension hypergraph counterexamples
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- Eventual odd-extension finite hypergraphs that violate Ryser's covering inequality
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the finite-plane modification, incidence argument or exceptional-edge construction is documented. Few is the evidence default.
Correction and publication history
This earlier odd-extension family supplies a distinct, formally checked route to violating the covering inequality.
Read this published revision