OPEN

Let $A\subseteq \mathbb{R}^d$ be a set of $n$ points such that all pairwise distances differ by at least $1$. Is the diameter of $A$ ast least $(1+o(1))n^2$?

The lower bound of $\binom{n}{2}$ for the diameter is trivial. Erdős

[Er97f] proved the claim when $d=1$.