Let $k\ge 1$ and $H_k(n)$ be the maximal $r$ such that if $A\subset \mathbb{N}$ has $|A|=n$ and $\Vert 1_A\ast 1_A{\Vert }_{\infty }\le k$ then $A$ contains a Sidon set of size at least $r$.Is it true that $H_k(n)/n^{1/2}\to \infty$? Or even $H_k(n)>n^{1/2+c}$ for some constant $c>0$?

Vela Sidon frontier (A309370) · verified work

A B₂/Sidon problem — the same object family as Vela's verified Sidon records, where nine improved terms were accepted into OEIS A309370 (the campaign's first external adoption).

OEIS A309370 ↗ · verified-combinatorics (witnesses + verify.py) ↗ · the Erdős campaign