Claims

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1951_05_04_erdos: Erdős's 1951 theorem (Publicationes Mathematicae Debrecen) that the mean squared gap between consecutive squarefree numbers tends to a finite limit, the prime-squares case the site credits; refereed.

2026_04_20_chojecki: A note of 20 April 2026 by Przemyslaw Chojecki, produced with GPT-5.4 Pro: the normalized sum of squared gaps always has a limit in [0, +infinity], equal to 1 + 2 sum q_A(h), and the limit is finite for a structured class.

2026_07_15_snyder: Colin Snyder's July 2026 claim, produced with GPT 5.6 (custom harness), that for every divisor set of size o(sqrt x) the mean squared gap of the sieved integers converges, with a Lean 4 proof bundle; accepted by nobody.

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