Open. The site labels the problem OPEN (page last edited 17 April 2026). Wanfang Chen claims a yes answer for every $k\ge3$, under the least-residue reading, in a manuscript posted with a Lean 4 development on 2026-07-28; the manuscript says the proof was generated by OpenAI's GPT-5.6-sol model. The work was pointed to on the site's discussion thread on 2026-09-05, the curator has not ruled on it, and it is recorded on Chen's claim page (2026). Przemek Chojecki's note of 16 April 2026, linked on the thread, proves a density-one weakening (a gap in its Theorem 7 was pointed out on the thread) and conditional implications between cases; it settles no case of the question, and its author asked that it be disregarded once the site corrected its remark, so it has no claim page.