Green's Open Problems #55

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.55

Let $p$ be an odd prime and suppose that $f : \mathbb{F}\_p^n \times \mathbb{F}\_p^n \to \mathbb{C}$ is a function bounded pointwise by 1. Suppose that $\mathbb{E}\_h \lVert \Delta\_{(h,h)} f \rVert\_{\square}^4 \geq \delta$. Does $f$ correlate with a function of the form $a(x)b(y)c(x+y)(-1)^{q(x,y)}$?

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

* ams-05
* ams-11

### 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 by reading Green's linked open-problems PDF at problem 55 and inspect the repository's existing formalized conjectures to understand the expected statement structure. The work is complete when this conjecture is added to the repository in the appropriate Lean form, with its AMS categories preserved.

Written by the indexing model from the issue text.