Problem detail · source-aware
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Wegner conjectured in 1965 that every finite family $\mathcal{R}$ of axis-parallel rectangles satisfies $\tau(\mathcal{R}) \le 2\nu(\mathcal{R}) - 1$, where $\tau$ is the minimum number of piercing points and $\nu$ the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.
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The authors say the construction of the initial counterexamples relied heavily on trial and error, and that GPT-5.5 Pro was used extensively to search for suitable constructions. Codex drew the figures and drafted portions of the text. They note the correctness of the proofs does not rest on the auxiliary machine verifications.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The refutation is an explicit finite family of rectangles, so it reduces to a finite piercing computation. arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.