The site labels the problem OPEN (page last edited 31 December 2025; proof-claims tab accessed 2026-10-06). Two manuscripts claim the assertion in full, neither reviewed nor refereed: a note posted in the site's thread by Przemek Chojecki on 29 April 2026, produced with GPT-5.5 Pro as Chojecki wrote there and hosted at ulam.ai, which derives a finite obstruction from Beurling's interpolation-density theorem for the Bernstein space and plants it on short blocks of nodes (claim page (Chojecki, 2026)), and the manuscript of Jia-Qi Yang submitted to the site's proof-claims tab on 2026-09-13 (using GPT-6, as the tab writes it), which claims to prove the obstruction for sign data at any pointwise tolerance with $\epsilon$ of optimal exponential order in $C$, and the sharp coefficient $\pi/2$ on Chebyshev–Lobatto grids (claim page (Yang, 2026)). The site's commentary credits Erdős with a weaker statement, which he gives as Theorem 4 of [Er67, p. 72] and says he had stated without proof in an earlier paper: for every $C>0$ there is $\epsilon>0$ such that, for large $n$ and any $m=\lfloor(1+\epsilon)n\rfloor$ nodes in $[-1,1]$, some polynomial $P$ of degree $n$ has $\lvert P(x_i)\rvert\le1$ at every node and $\max\lvert P\rvert>C$; the assertion of the problem would imply it, and Erdős remarks in [Er67] that he could not prove the assertion even for $m=n$. This page records the claims without adopting them; the standing in the frontmatter follows from them.