Claims

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1966_11_17_abbott_gardner: Abbott and Gardner's 1967 bound (Canadian Mathematical Bulletin) that some (1 - eps) N log log N / log N integers up to N have no three with equal pairwise least common multiples; refereed.

2026_05_03_saturnino: Brian Saturnino's note of May 2026 bounds the largest lcm-triangle-free set up to N by (43/48 + o(1))N through disjoint forbidden triples; posted to the site's thread, unreviewed.

2026_06_22_kitamura: Kenta Kitamura's Lean development of June 2026, prepared with Codex 5.5 and ChatGPT 5.5 Pro, proving that an lcm-triangle-free set in {1, ..., N} has at most N - floor(N/6) elements; unbuilt by the corpus.

2026_07_14_wang: Shouqiao Wang's AI-assisted manuscript of July 2026 claims f(N) = o(N) by a cap-set argument; posted to the site's proof-claims tab, relabeled partial by the curator since it does not estimate f(N), and unreviewed.

2026_08_17_logsdon: Sara Logsdon's Lean development of August 2026, prepared with ChatGPT and Codex, refining the 5/6 lattice bound for lcm-triangle-free sets to (813/1000 + o(1))N; unbuilt by the corpus.

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