Claims

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2001_04_01_schoen: Schoen's 2001 theorem: a pairwise coprime set with property P has fewer than 2N^{2/3} elements up to N for infinitely many N, which answers the second question yes for pairwise coprime sets; refereed in J. Combin. Theory Ser. A.

2004_10_08_baier: Baier's 2004 theorem: a pairwise coprime set with property P has fewer than (3+epsilon)N^{2/3}/log N elements up to N for infinitely many N, sharpening Schoen's bound for the second question; refereed in Integers.

2026_04_03_deepmind: DeepMind's construction (first posted 3 April 2026) of an infinite set with property P and counting function at least N to the 1 - epsilon for every epsilon, answering the first question yes and the second no; site-credited.

2026_04_07_sothanaphan: Sothanaphan's note, produced with GPT-5.4 Thinking, builds sets with property P from narrow tagged blocks, answering the first question yes and the second no by its own construction; posted in the thread, not refereed.

2026_07_30_ndikum_ndikum: A partial proof claim of 30 July 2026 by Philip Ndikum and Serge Ndikum, made with Libertas Superintelligence: every good set has a convergent reciprocal sum; its Lean development rests on a declared axiom that is false.

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