Is it true that the number of incongruent sets of $n$ points in ${\mathbb{R}}^2$ which maximise the number of unit distances tends to infinity as $n\to \infty$? Is it always $>1$ for $n>3$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let $u(n)$ be the maximum possible number of unit distances determined by an $n$-point set in (\mathbb R^2), and let [ g(n)=|\\{\text{congruence classes of }n\text{-point sets achieving }u(n)\\}|. ]

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.