Claims

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1962_01_01_erdos: Theorem IV of Erdős (Mat. Lapok 1962): an admissible sequence has A(x) less than C x^{5/6}, which gives h(n) < C n^{5/6}, the first upper bound for Problem 789; refereed; the paper holds no (n log n)^{1/3} lower bound.

1966_01_01_straus: Straus's 1966 theorem (J. Math. Sci.) that an admissible subset of {1,...,N} has at most a constant times N^{1/2} elements, which gives h(n) << n^{1/2}; refereed, known here through the 1991 reproof and the 1999 account.

1974_04_01_choi: Choi's estimate (1) (J. Number Theory 1974): any n nonzero integers contain an admissible subset of size >> (n log n)^{1/3}, the best refereed lower bound for h(n), refining Erdős's n^{1/3}; refereed.

2026_09_12_korsky: AI-assisted full claim that every set of n integers has an admissible subset of size at least c (n log log n / log n)^{1/2}, fixing h(n) up to logarithms with Straus's bound; a file-sharing write-up with a third-party Lean proof.

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