Claims

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1975_01_01_choi_erdos_szemeredi: Theorems 1--6 of the 1975 Acta Arithmetica paper: g_4 is bounded, g_6 is of order N^{1/2}, and g_k lies between N^{1-ε} for large k and 2^{k-1} N^{1-2^{1-k}}; refereed, settling the order of g_k for k = 4 and 6.

2026_04_28_van_doorn: Theorems 1, 3, 5 and 8 of van Doorn's 2026 arXiv preprint: g_3(N) = 1 (N ≥ 3), g_4(N) = 3 (N ≥ 2), 4 ≤ g_5(N) < 1.2·10^8 (N ≥ 3); made with ChatGPT and Aristotle; unrefereed, with the author's own Lean file.

2026_07_08_erlbacher: An AI-produced release of 8 July 2026 (Draft v5 and a Lean development) claims g_5(N) <= 3,519,219 for all N, with h_4(n) = 4 for n >= 331,777 for the positive variant; unrefereed, its Lean not built here; pending.

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