Open, the site's label as accessed on 2026-09-04 and unchanged, when the problem's proof-claim tab was empty. The site's commentary records $h(d)\ll d!$ from Cantor, Erdős, Schreiber and Straus, $h(d)\to\infty$ from van der Waerden's theorem, Beck's $h(d)\le d^{8+\epsilon}$ for every $\epsilon>0$ [Be17] and Roth's $h(d)\gg d^{1/2}$ [Ro64]. Erdős's 1966 report of the construction (printed p. 137) states its bound as $L(d)<c^dd!$, which is weaker than the site's $d!$ by the factor $c^d$. The bounds are recorded as partial claims: the construction on Cantor, Erdős, Schreiber and Straus 1966 (accepted on the journal publication alone), Beck's bound on Beck 2017 (claimed, an edited-volume chapter) and Roth's bound on Roth 1964 (accepted on the refereed publication alone). A claim of 19 September 2026, Korsky 2026, submitted on the site's proof-claim tab of Problem 178 and recorded here as a partial claim, would improve Beck's exponent to $5/2+2\sqrt2$; it is unreviewed. No full claim exists, and the standing derives from the claim pages.