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Claim. In the notation of Problem 956, $h(n)=O(n^{4/3})$: among $n$ pairwise disjoint translates of one compact convex set in the plane, at most $O(n^{4/3})$ pairs are at distance exactly $1$. Source: P. Erdős and J. Pach, Variations on the theme of repeated distances, Combinatorica 10 (1990), no. 3, 261–269; Valtr's Oberwolfach abstract of 2005 and Chojecki's note of 2026 both state the bound as their Theorem 1 and Theorem 2 respectively, citing this paper. The bounds the site's remarks also credit to the paper, for disjoint convex sets that need not be translates, concern a different function.

Covers. The upper bound on $h(n)$ only. Neither the order of $h(n)$ nor $h(n)>n^{1+c}$ follows from it.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper appeared in Combinatorica. Not reviewed: the site's remarks credit the bound to the paper, but the site labels the problem OPEN, so the remark is not an acceptance.