Open. No proof, disproof, preprint or proof claim for the exact statement was found in the search whose scope the Current assessment records, beyond a forum-posted AI-assisted manuscript and a posted chat record of March 2026; a partial proof claim of 30 September 2026, with the authors' own Lean development, was listed on the site's tab on 5 October 2026. Chojecki's manuscript and that claim have claim pages below, and the March chat record is described in the Current assessment without one, since a thread post without a dated manuscript gets no claim page; all three report partial results on the two "in particular" questions, so the derived standing stays open. The only bounds verified here are the trivial $f(n)\ge(n+1)/2$ of the origin and its Theorem 2, which bounds the number of generators with distinct monochromatic unions by $(1+o(1))\log_2n$ and not $F(n)$ itself. This is a bounded negative finding, not a certificate of openness.