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Claim. Corollary 4 of Damek Davis, Forbidden subgraphs in divisor graphs and an Erdős divisibility problem, arXiv:2604.17613 (19 April 2026), gives $f(n)=c_2n+o(n)$ for an effectively computable constant $c_2$, with an explicit error term, and the growth rate $q(n)=\beta_2^{n+o(n)}$ of the number of fork-free subsets of $\{1,\ldots,n\}$, through McNew's theorem on local statistics of divisor graphs. The sentence after the corollary leaves the irrationality of $c_2$ open. The library card records the paper; no file of it is held.

Covers. The first question, how large $f(n)$ can be, in asymptotic form: $f(n)=c_2n+o(n)$ for an effectively computable constant $c_2$, so that $\lim f(n)/n$ exists; the claim value is answered because the result determines that size. It does not cover the irrationality question, and the paper gives no closed form for $f(n)$; its numerical estimate (Section 5.1, p. 7) is the bound $c_2\ge0.6729$, which with Lebensold's $c_2\le0.6736$ leaves a gap of about $7\times10^{-4}$.

Standing. The thread post of 19 April 2026 by the author announces the paper as a partial solution, links the write-up on GitHub (the pinned preprint link above, at its first commit of that day) and credits the initial solution to GPT 5.4 pro; on 20 April 2026 Nat Sothanaphan reported that a standard check found no issues, and on 4 May 2026 the site's curator wrote that, if correct, it is not a full solution, since the irrationality question remains. The site's label stayed OPEN, there is no refereed version, and no body has accepted the paper so the claim stays claimed. The later Conjectures.io proof (claim page) reproves the existence of the limit on its way to irrationality.