Claims

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2026_07_14_itabe: Rio Itabe's claimed bound h(N) ≤ N^{1/3+o(1)}, lowering the recorded upper exponent log 3 / log 22, with a write-up and a Lean development credited to GPT-5.6 on the site's proof-claims tab; unreviewed, unbuilt here, claimed.

2026_07_22_shi_dong: Ruizhe Shi and Yiqi Dong's arXiv preprint of July 2026 colors Z/p^4 with O(p) colors and no symmetrically colored four-term progression, and with Behrend-style product colorings claims h(N) ≤ N^{1/4+o(1)}.

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