Erdős Problem 654

### What is the conjecture

https://www.erdosproblems.com/654

Let $x_1,\ldots,x_n\in \mathbb{R}^2$ with no four points on a circle. Must there exist some $x_i$ with at least $(1-o(1))n$ distinct distances to other $x_i$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start with the linked Erdős Problems 654 statement and inspect existing formalized conjectures in the repository for the expected structure and conventions. No file or test is named in the issue; done means adding a complete Lean formalization of this conjecture that fits the repository's existing checks.

Written by the indexing model from the issue text.