PROVED, the site's label. Almost surely the union has size $O((\log n)^2)$; the cited estimates give the more precise upper limit

The constant is a consequence of those estimates, not a claim of a sharp asymptotic for the union. The derived standing is claimed and proved, not solved: the pending claim is the favorite-count bound of Hao, Li, Okada and Zheng with the Erdős–Taylor estimate, two refereed theorems; the site's page states their combination itself and credits the eventual bound through Problem 1165 to Tóth, a misattribution (Hao–Li–Okada–Zheng Theorem 1.1 supplies it), so no review credits the deduction, and the claim stays claimed although both of its inputs are refereed. An independent Lean proof of the deduction is a second pending claim, on its own claim page (Alexeev, 2026).