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There exists a constant such that, for all large , if has size at least then there are distinct such that .
Source: erdosproblems.com/865
An accepted solution exists. The statement is true.
PROVED (LEAN). The status-defining source is Theorem 1.1 of a seven-page arXiv preprint, R. Cipollini, A sharp 5/8 bound for an Erdős--Sós pairwise-sums problem, arXiv:2606.29361v1 (28 June 2026): there is a constant such that for all , not only large , every with contains a pairwise-sum triple, with the explicit form for every triple-free . The manuscript's first page declares that it was written by an AI model, GPT-5.5 Pro, from a proof developed by the author together with that model, and that the Lean formalization was carried out with the prover Aristotle; the site's commentary credits the solution to Cipollini and GPT Pro, and the site accepted it on 2 July 2026 with the label PROVED (LEAN); Stijn Cambie, a contributor the paper's acknowledgments thank for feedback and improvements, reported in the site's thread on 27 June 2026 that he had read a version of the paper in detail and confirmed it. This is a source-supported solution accepted by the site, distinct from a claim of journal refereeing: no refereed publication, no later arXiv version, no citing paper and no written expert review beyond the thread were found. Two external Lean developments prove the theorem for their own definitions; the corpus holds no build of either, so they give no formalized evidence. The refereed content behind the label is the density bound of Choi, Erdős and Szemerédi (1975), and the folklore fact the site states. The standing is derived from the claim page (Cipollini, 2026), accepted on the site's documented review with these qualifications.