Open. The site labels the problem OPEN and its commentary points to the OEIS entry A375077 for the least $n$ of each $k$; the entry's sixteen terms settle the instances $1\le k\le16$ with the answer yes and are pending partial claims on the pages of their contributors, Stephan 2024 ($k\le4$), Wu 2024 ($k=5$), Alekseyev 2025 ($k=6,7$), Kesarwani 2026 ($k=8$ to $11$ and $15$), Dehorty 2026 ($k=12,13,16$) and Dehorty and Kesarwani 2026 ($k=14$). The standing in the frontmatter derives from the claim pages.