Claims

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2016_05_24_khopkar: A 2016 preprint whose Theorem 4 asserts that a unit distance graph on n points in convex position has O(n) edges; never published, found incomplete in the discussion, and contradicted by Kruer and Kohlmeyer's disproof.

2026_09_10_kruer_kohlmeyer: Kruer and Kohlmeyer construct, for every d at least 2, a set of 2 d^d 2^(d^(d+1)) points in strictly convex position with at least d/4 times as many unit-distance pairs as points, so the count is not O(n); Lean, certified by Conjectures.io.

2026_09_13_kruer_kohlmeyer_price: A manuscript with a Lean file constructing, for every large n, n points in strictly convex position with at least (1/4 - o(1)) n log log n unit-distance pairs, so the count is not O(n); posted as a proof claim under Problem 97.

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