OPEN, in the site's label. The site notes that for $A$ the set of prime squares, when $B$ is the squarefree numbers, Erdős proved the limit exists (Publ. Math. Debrecen 2 (1951), 103--109; claim page Erdős's squarefree case, accepted and partial). A full proof claim posted to the site's proof-claims tab on 15 July 2026 by Colin Snyder, produced with GPT 5.6 (custom harness), as the tab names the system, answers yes with a Lean 4 proof bundle; the site has not accepted it, nothing was built or audited here, and the claim page Snyder's Lean proof records it, together with the formal-conjectures collection's marking of the problem as solved on the strength of a hosted copy of that proof, which is not acceptance. A note of 20 April 2026 by Przemyslaw Chojecki, produced with GPT-5.4 Pro, as Chojecki's thread comment says, claims a proof that the limit always exists in $[0,+\infty]$ and is finite for a structured class of $A$; it is the partial claim page Chojecki's note. The frontmatter standing derives from the pending full claim, and it departs from the label for that reason: Snyder's claim answers the Statement yes and would settle it, so the derived standing is claimed with claim proved, while the site, which has not accepted the claim, labels the problem OPEN.