Open, the site's label (OPEN). Three claim pages are recorded, two pending partial claims and one withdrawn full claim. Liu's withdrawn proof, a note of 2026-05-16 posted to the site's discussion thread, derived the answer yes from a shifted-intersection bound that was retracted the same day, and the author withdrew it. Liu's divergence for asymptotically maximum Sidon sets, the corrected note dated 2026-05-20, entered in the author's repository on 2026-05-19 and posted to the thread on 2026-05-20, proves the answer yes for every family of Sidon sets whose diameter is $(1+o(1))n^2$ through Pikhurko's uniformity lemma. Kapoor's logarithmic lower bound, a write-up of 2026-08-14, entered on the site's proof-claims thread on 2026-08-21, bounds the mean squared gap below by a constant times $\min\{\log\frac1{\kappa-1},\log n\}$ with $\kappa$ the diameter over $n^2$, answering yes for sets of nearly minimal diameter and for dyadically non-concentrated families and reducing the general case without settling it. The proof-claims thread had no comment on it as of 2026-10-06.