Claims

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2026_03_18_chojecki: Chojecki, 18 March 2026, with GPT-5.4 Pro: some 2-coloring of the subsets of an n-set has no monochromatic union-closed family of more than n^{log_2 n + O(log log n)} sets, so F(n) is subexponential; unreviewed.

2026_09_30_bhattacharjee_mandal_bhattacharya: Bhattacharjee, Mandal and Bhattacharya (Zenodo 30 September 2026, arXiv 2 October): F(n) ≥ n^{ω(n)} with ω(n) → ∞ and F(n) < (1 + o(1))^n for any number of colors, with a Lean 4 development of their own; unreviewed here.

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