Claims

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2004_11_03_lev: Lev's greedy construction gives a perfect difference set whose elements added at step n are O(n^3), so it has a_n << n^3 and a_n/n need not grow faster than n^2.

2026_04_23_price: An Overleaf note that Liam Price posted, written by GPT-5.4 Pro, claims a_n >> n^(3/2) for infinitely many n; unrefereed and unreviewed.

2026_05_02_mazur: Mazur, with GPT-5.5 Pro, Codex and a verification harness, claims that a_n > n^2/(2 log 2 (log n - log log n + B)) infinitely often for every B above an explicit constant, with a Lean proof not built here; unrefereed.

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