Open on the site (label OPEN; page last edited 5 October 2025). The site's commentary records Erdős's theorem [Er64f] that the statement holds with $c_r=r^{-r}$ for every hypergraph with at least $\epsilon n^r$ edges, so the question is whether the constant can be raised above $r^{-r}$ under the stronger density hypothesis. One full claim is pending: Gu's disproof (5 September 2026), explicit $5$-uniform hypergraphs meant to show that no $c_5>5^{-5}$ works, lifted to every $r\ge5$; the forum entry described an earlier $16$-uniform version, whose Zenodo record was removed on 23 September 2026. It is not refereed and no outside reviewer has endorsed it, so the standing is claimed, not solved.