Claims

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1970_01_01_erdos: Erdős proves in 1970 that a set up to x with reciprocal sum above c log x has k members with pairwise equal least common multiples; the argument gives f_k(N) << log N / log log N.

2025_12_23_tang_zhang: Tang and Zhang's 2025 preprint bounds f_k(N) between powers of log N, the exponents given by an explicit constant and by the sunflower-free capacity, and proves f_k(N) = (log N)^{1-o(1)} exactly when that capacity is 2.

2026_04_15_chojecki: A 2026 note in the site's discussion thread, written with GPT-5.4 Pro, claims f_k(N) = (log N)^{gamma_k + o(1)} with gamma_k given by a weighted sunflower partition function; the exponent's value is left open, so the claim is partial.

2026_07_18_rayyoung_zhu_luo: A 2026 manuscript on the site's proof-claim tab, written with GPT 5.6 Sol Pro, claims f_k(N) = (log N)^{gamma_k + o(1)} with gamma_k a supremum over uniform families with no k sets of equal pairwise union; the exponent's value is open.

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