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Erdős problem 90

Conjectured upper bound on how many pairs among nn points in the plane can be exactly one unit apart.

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9 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

90.lean

Retained formal statement4 of 8

Sawin's explicit exponent. The constructive disproof can be realised with c0.014114c \ge 0.014114 (absorbing the implicit constant CC of Sawin's Theorem 1 into a slightly smaller exponent for all large enough nn). Reference: Theorem 1 of Sawin, [arXiv:2605.20579](https://arxiv.org/abs/2605.20579) (2026).

FormalConjectures/ErdosProblems/90.leanErdos90.erdos_90.variants.sawin_explicit1 lineExact file
{n | ↑n ^ 1.014114 ≤ ↑(Erdos90.maxUnitDistances n)}.Infinite
SolvedStatement only, no proof

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