Claims

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1975_01_01_bleicher_erdos: Bleicher and Erdős's 1975 Lemma and count: the products of rapidly growing primes up to N have distinct reciprocal subset sums, so R(N) is at least N / log N times the iterated-logarithm product up to depth k + 1.

1976_12_01_bleicher_erdos: Bleicher and Erdős's 1976 Theorem 3 bound for log S(N), with 2^R(N) <= S(N), gives R(N) at most (1 / log 2) N log_r N / log N times the iterated-logarithm product up to depth r, when log_{2r} N >= 1.

2025_09_12_bettin_grenie_molteni_sanna: The set U(N) in the proof of Bettin, Grenié, Molteni and Sanna's Theorem 1 has distinct reciprocal subset sums and size of order N / log N times the iterated-logarithm product, the lower half of the order of R(N).

2026_07_15_young_zhu_luo: Young, Zhu and Luo's AI-assisted claim that the largest subset of the first N integers with distinct reciprocal subset sums has the order of N / log N times the iterated-logarithm product, via their log S(N) bound; accepted.

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