Green's Open Problems #69

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.69

Fix a number $k$. Let $A \subset \mathbb{R}^2$ be a set of $n$ points, with no more than $k$ on any line. Suppose that, for at least $\delta n^2$ pairs of points $(x, y) \in A \times A$, the line $xy$ contains a third point of $A$. Is there some cubic curve containing at least $cn$ points of $A$, for some $c = c(k, \delta) > 0$?

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-05
* ams-14
* ams-52

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

Start with Green's Open Problems PDF, specifically problem 69, and inspect existing formalized conjectures in the formal-conjectures repository for the expected structure. Done means the stated conjecture has been added in Lean with an appropriate formal statement.

Written by the indexing model from the issue text.