Claims

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2026_06_14_lee: Sungchul Lee's manuscript of 14 June 2026 claims $F_2(n)\ll n^{1/2-\varepsilon}$ for an absolute $\varepsilon>0$, a fixed power below the square-grid bound $n^{1/2}/(\log n)^{1/4}$.

2026_07_06_lee_pohoata_zhu: An arXiv preprint by Lee, Pohoata and Zhu claims a set of $n$ points in the plane in which every subset of at least $n^{1/2-\delta}$ points repeats a distance, so that $F_2(n)\lesssim n^{1/2-\delta}$ for an absolute $\delta>0$.

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