Open on the site, with pending full claims. No refereed proof or disproof was found in the searches whose scope the Current assessment records, and the site keeps the label OPEN: its maintainer wrote in the thread on 2 June 2026 that two full-solution claims had been posted, both built on the sketch developed in the thread mainly by Sawhney and Tao, and that he would wait for a refereed publication or a careful reading by an expert before changing the label. Three claim pages record the pending claims, all answering yes for all large $n$ and all declaring AI assistance: Zribi's notes of 25 April to 2 June 2026 (claim page (Zribi, 2026)); Chojecki's working manuscript dated 27 April 2026, posted 30 April (claim page (Chojecki, 2026)), whose page also carries, as a formalization link, Xu's Lean development registered on the Palomar registry on 20 September 2026, which declares itself a formalization of that manuscript's Theorem 1.1; and their joint submission to the proof-claim tab of 21 July 2026, with a shorter version of 5 September (claim page (Zribi and Chojecki, 2026)). None is refereed, accepted by the site or reviewed independently, so each is claimed, and the frontmatter standing claimed/proved derives from them. The results in hand are Erdős's questions, the thread's sketch of a construction for $r=2$ and its obstruction remarks for $r\ge3$, and the trivial bound that the multiplicity cannot exceed $(1+o(1))\log\log n$.