Claims

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2025_10_19_sawhney: Sawhney's note proves that for all large N no set in {1,...,N} with no squarefree ab+1 has more members than the class 7 mod 25, with a stability statement; the site's curator credits it and leaves a finite check.

2026_03_23_sothanaphan: Sothanaphan's note of 23 March 2026, produced with GPT-5.2 Thinking and GPT-5.4 Thinking, claims that for every N at least 2.64e17 the class 7 mod 25 attains the maximum, making Sawhney's threshold explicit; nothing accepted.

2026_07_28_pitchford: A candidate computer-assisted proof published on Zenodo on 28 July 2026 by Ian Pitchford, with OpenAI Codex as its reported author: the maximum is floor((N+18)/25) for every N, by certificates and envelopes up to 2.64e17.

2026_07_30_li: Li's full proof claim, released 30 July 2026 and submitted to the site on 16 August 2026, produced with OpenAI ChatGPT 5.5 and 5.6: the largest set in {1,...,N} with no squarefree ab+1 has exactly floor((N+18)/25) members.

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