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Erdős, Herzog and Piranian (1958) asked whether the regular n-gon maximizes the product of pairwise distances among n points of fixed diameter. After the recent discovery that it does not for even n, this paper proves the first exponential improvement over the n-gon's value, via a vector-field technique.
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The acknowledgments thank "Stijn Cambie, ChatGPT, and Quanyu Tang for discussion (in alphabetical order)" - a discussion credit, listed alongside the human colleagues, with no specific step attributed.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
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Correctness: unknown · statement fidelity: unaudited · peer review: none
An improved lower bound on the maximal product; the sharp maximizer for the 1958 question remains unknown.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.