The site's wording, accessed 2026-09-04 (last edited on the site on 30 December 2025), fails in three places. With "largest $k$", every $k>n$ qualifies vacuously, since $K_n$ has no induced subgraph on more than $n$ vertices, so no largest $k$ exists. If $k\le n$ is imposed, a nearly balanced coloring makes $k=n$ qualify for each fixed $\alpha<1/2$ and all large $n$, so $F(n,\alpha)=n$ and $F(n,\alpha)\sim c_\alpha\log n$ fails. At $\alpha=1/2$ no induced subgraph has more than half of its edges in each color, and the opening "Let $\alpha>0$" conflicts with the range $0\le\alpha\le1/2$ of the display. The change replaces "largest" by "smallest", "$\alpha\leq 1/2$" by "$\alpha<1/2$", and "Let $\alpha>0$" by "Let $0\leq\alpha<1/2$"; nothing else changes. The evidence is Erdős's source [Er90b, printed p. 21], which defines the threshold as "the smallest integer for which it is possible" to give every class more than the $\alpha$ share on every large set, and prints the range with its endpoint, $0\le\alpha\le\frac1k$, which its next sentence, "$c_k'(\alpha)\to\infty$ as $\alpha\to1/k$", excludes. Conlon, Fox and Sudakov [CFS10, Section 6.2] print "largest", as the site does, with the range $0\le\alpha<1/2$. So corrected, with two classes, the question is that of Problem 563, which is open; the only known result is the two-sided bound $c_1(\alpha)\log n<F(n,\alpha)<c_2(\alpha)\log n$, asserted without proof by Erdős (display (29)) and by Conlon, Fox and Sudakov (Section 6.2). A comment in the site's thread raised the three failures on 28 April 2026; it is a thread post, so it has no claim page. The page's standing judges the corrected Statement.