Claims

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2026_02_11_chojecki: A write-up of 2026-02-11 produced with GPT-5.2 Pro claims a set with f(n) at least c log n for all large n; issues were raised the next day and Tao's manuscript records that it fell short of a complete proof.

2026_02_18_sothanaphan: A write-up of 2026-02-18 produced with GPT-5.2 Thinking claims a set with f(n) at least c log n for all large n; Tao found a gap in its Lemma 17 that day, and the author reported on 2026-02-20 that the system could not fix it.

2026_02_23_tao: A probabilistic construction of a set of positive integers in which every large n is a sum of consecutive elements in at least a constant times log n ways, answering both questions yes; the site records it as proved (Lean).

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