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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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2026_04_22_openai: Theorem 1 of a three-page manuscript hosted by OpenAI, dated 22 April 2026 in its metadata: for every fixed k at least 2 the ratio R(k,l+1)/R(k,l) tends to 1, by dependent random choice; accepted by the site's curator.