Open on the site, which explains the label by the ambiguity of the original source: the OPEN describes the question Erdős intended, which the site cannot identify, not the question the site prints. The Statement asks for a constant $C(r)$ with $R(n;3,r)<C^{\sqrt n}$ and fails for every $r$, and the site says so: its commentary credits Girão with the observation that a random coloring gives $R(n;3,2)\ge C^n$ for some $C>1$. Take a uniformly random red-blue coloring of $K_N$ and a fixed set $S$ of $n$ vertices: $S$ contains $t\gg n^2$ edge-disjoint triangles, each monochromatic red with probability $1/8$ independently, so the probability that $S$ has no red triangle is at most $(7/8)^t$, and the same for blue; summing over the $\binom Nn\le(eN/n)^n$ sets $S$ and the two colors, the expected number of $n$-sets missing a triangle in some color is at most $2(eN/n)^n(7/8)^t<1$ once $N\le C^n$ for a suitable absolute $C>1$, so some coloring has every $n$-set containing both a red and a blue triangle, and $R(n;3,2)>N$. The thread's Steiner-triple-system version extends the argument to an exponential lower bound for every $r\ge3$, and no $C^{\sqrt n}$ exceeds an exponential in $n$ for large $n$. The failure holds for every $r$ and every large $n$, not only at boundary values, and the bound is Erdős's own print in [Er97b], so the Statement is judged as printed. The claim page Girão's observation records the disproof and its postings as a pending claim: the curator wrote its only posting and keeps the problem OPEN, so there is no independent review. The frontmatter standing is claimed, through that full claim.