Claims

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1967_04_01_danzer_pommerenke: Danzer and Pommerenke determine the maximum for n = 2, 3, 4 and prove that the regular polygon is beaten for every even n at least 4.

2025_10_03_hu_tang: A note of Hu and Tang gives four- and six-point sets of diameter 2 whose distance product exceeds that of the regular polygon.

2026_03_07_cambie_decadt_dong_hu_tang: An arXiv preprint of Cambie, Decadt, Dong, Hu and Tang determines the maximum for every n at most 5, with the kite the unique maximizer at n = 4 and the regular pentagon at n = 5.

2026_09_11_coleski: A repository by coleski, developed using Codex, claims a Lean-checked proof that the six-point maximum of the ordered product is 64(2 sqrt 3 - 2)^18.

2026_09_22_hu: Boyang Hu's manuscript, drafted with GPT-6 Pro and accompanied by a Lean development, claims the unique maximizer of the distance product for every odd n at least 2^(10^8) and every even n at least 2^(10^120); pending.

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