Erdős problem 90

Constructive form of the disproof. There is an absolute constant $c > 0$ such that infinitely many $n$ admit a configuration realising at least $n^{1+c}$ unit distances.

This is the qualitative content of Theorem 1.1 of Alon–Bloom–Gowers–Litt–Sawin–Shankar– Tsimerman–Wang–Matchett Wood, [*Remarks on the disproof of the unit distance conjecture*](https://arxiv.org/abs/2605.20695) (2026). An explicit bound $c \ge 0.014114$ is given by Sawin, [*An explicit lower bound for the unit distance problem*](https://arxiv.org/abs/2605.20579) (2026); see erdos_90.variants.sawin_explicit below.