Problem detail · source-aware
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Let $g(r)$ be the fewest edges in an $r$-uniform intersecting hypergraph with cover number $r$. Erdos and Lovasz proved $g(r) \ge 8r/3 - 3$. An elementary argument gives $g(r) \ge 3r - 4$, and building on it with Kahn's small-codegree edge-colouring theorem pushes the bound further.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The acknowledgement states the proof was discovered with the help of ChatGPT 5.5 Pro, and that Theorem 1 was then formalized in Lean with Harmonic's Aristotle.
Provider: OpenAI / Harmonic · Prompt public: unknown · Independence: unknown
The Lean formalization is partial by the author's own account: part (i) of Theorem 1 is formalized in full and part (ii) only conditional on Kahn's theorem. We have not compiled it. arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
an improved lower bound; the true order of g(r) remains open
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.