Wegner's Piercing Conjecture for Rectangles
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Statement
Wegner conjectured in 1965 that every finite family of axis-parallel rectangles satisfies , where is the minimum number of piercing points and the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.
Context
A sixty-year-old named conjecture on piercing axis-parallel rectangles, one of the reference points for the Hadwiger-Debrunner style (p,q) programme.
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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.
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0 human reviews · 1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: correctscope Reproduction by the VibeMathed site
The refutation is an explicit finite family of rectangles, so it reduces to a finite piercing computation. arXiv preprint, not peer-reviewed.
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