Open, the site's label (OPEN, page last edited 1 April 2026). The site's commentary reports the second question, whether $O(n^{3/2})$ common differences always suffice, answered negatively, and the first, the order of magnitude, open: it records an observation from the discussion thread, credited to Koishi Chan, that the problem is equivalent to Bourgain's sums-differences question [Bo99], the largest exponent reachable here being the smallest exponent admissible there, so that the lower bound $1.77898\ldots$ of Lemm [Le15], slightly improved by AlphaEvolve [GGTW25], exceeds $3/2$. The resolution the curator credits is thus a thread observation applied to Lemm's refereed bound. Lemm's lower bound and Katz and Tao's upper bound $11/6$ [KaTa99], the refereed results the commentary credits, are accepted partial claims on Lemm's claim page (2014) and Katz and Tao's claim page (1999). Each reaches the problem through the embedding the Current assessment states. The thread's observation and its earlier direct constructions are thread posts and get no page. A self-contained Lean disproof of the $O(n^{3/2})$ bound, in Moritz Firsching's fork of formal-conjectures and pointed to by the catalog's entry described under Formalization, is recorded as claimed on its claim page (Firsching, 2026).