Given $n$ distinct points $A\subset {\mathbb{R}}^2$ must there be a point $x\in A$ such that$$\#\{d(x,y):y\in A\}\gg n^{1-o(1)}?$$Or even $\gg n/\sqrt{\log n}$?

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

This is the **(discrete) pinned distance problem** (Erdős problem #604), and the bounds you ask for are **not known** in general.

llm-hunter · gpt pro 5.2 · unverified

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