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If points in form a convex polygon then there are many pairs which are distance apart.
Source: erdosproblems.com/96
An accepted solution exists. The statement is false.
Open on the site: its export of 2026-09-04 records the label "OPEN", and its page, last edited 23 January 2026, carries no proof claim and no proof exposition. The standing in the frontmatter derives from the claim pages: the disproof of Kruer and Kohlmeyer, a Lean proof that the bounty site Conjectures.io verified on 10 September 2026 and certified, is accepted on that certification alone, with no refereed publication and no acceptance by erdosproblems.com, on its claim page (Kruer and Kohlmeyer, 2026); the stronger disproof of Kruer, Kohlmeyer and Price, a manuscript with a Lean file of 13 September 2026 giving unit distances and posted as a proof claim under Problem 97, is pending on its claim page (Kruer Kohlmeyer Price, 2026); Khopkar's 2016 preprint claiming the linear bound is rejected on its claim page (Khopkar, 2016). The disproof answers the Statement: the maximum number of unit-distance pairs among points in strictly convex position is not . The site's remarks record that a positive answer here would follow from a positive answer to Problem 97; in the other direction, Kruer and Kohlmeyer's construction yields a counterexample to Problem 97 by deleting points of low unit degree, as their claim page records.