The site labels the problem OPEN (the page shows no last-edited date). The bound in hand is Erdős's display (4.5) of 1973: $\sum_{a_i\le n}1/a_i<c_1r\log n/\log\log n$, from a double count of the products $pa_i\le n^2$ and Mertens's estimate for $\sum_{p\le n}1/p$. No published improvement, and no published lower construction of the same order, was found in the search whose scope the Current assessment records. A full proof claim of 15 July 2026 on the site's tab, by Colin Snyder with the AI system GPT 5.6, asserts that the order $\log N/\log\log N$ is sharp for every fixed $r$, with a matching construction and a Lean development; the formal-conjectures file records the same matching-order statement as a solved variant pointing at that development, and its docstring says that this fixes the order but not the best possible upper bound the site asks for. The claim is recorded on its claim page (Snyder, 2026), pending and not accepted by the site. The derived standing, claimed, answered, departs from the site's OPEN only by counting that pending full claim, following the claimant's own scope label on the tab; it is not a judgment on the argument, which no outside review has accepted, and it becomes solved only if the claim is accepted. The search is a bounded negative finding, not a certificate of openness.