Open: the site labels the problem OPEN (page last edited 8 February 2026), and the frontmatter standing is derived from the three claim pages under claims/, all partial, the two questions being its parts. The first question is settled: Gyárfás, Komlós and Szemerédi's refereed theorem gives $\sum1/a_i\gg\log k$ (claim page (Gyárfás, Komlós and Szemerédi, 1984), accepted, settling the part harmonic_bound), and Liu and Montgomery's refereed Corollary 1.2 gives the asymptotically sharp constant $1/2$ for large $k$ (claim page (Liu Montgomery, 2020), accepted). The second question is open: Milojević, Montgomery, Pokrovskiy and Sudakov's arXiv preprint of 22 September 2026 claims the complete bipartite minimizer for every sufficiently large $k$ (claim page (Milojević, Montgomery, Pokrovskiy and Sudakov, 2026), claimed), and nothing covers small $k$, so the standing is open. The site's commentary credits the first question to [GKS84] and the sharp constant to [LiMo20], and mentions the forthcoming work through Montgomery's survey.