The purpose of this repository is to hold a Lean4 formalization of the proof of the Polynomial Freiman-Ruzsa (PFR) conjecture (see also this blog post). The statement is as follows: if $A$ is a non-empty subset of ${\bf F}_2^n$ such that $|A+A| \leq K|A|$, then $A$ can be covered by at most $2K^{12}$ cosets of a subspace $H$ of ${\bf F}_2^n$ of cardinality at most $|A|$. The proof relies on the theory of Shannon entropy, so in particular development of the Shannon entropy inequalities will be needed.

• Discussion of the project on Zulip
• Blueprint of the proof
• Documentation of the methods
• A quick "tour" of the project
• Some example Lean code to illustrate the results in the project

To build the Lean files of this project, you need to have a working version of Lean. See the installation instructions (under Regular install).

To build the project, run lake exe cache get and then lake build.

To build the web version of the blueprint, you need a working LaTeX installation. Furthermore, you need some packages:

sudo apt install graphviz libgraphviz-dev
pip uninstall -y leanblueprint
pip install -r blueprint/requirements.txt

To actually build the blueprint, run

lake exe cache get
lake build
inv all

To view the web-version of the blueprint locally, run inv serve and navigate to http://localhost:8000/ in your favorite browser.

Or you can just run inv dev instead of inv all and inv serve, after each edit to the LaTeX, it will automatically rebuild the blueprint, you just need to refresh the web page to see the rendered result.

Note: If you have something wrong in your LaTeX file, and the LaTeX compilation fails, LaTeX will stuck and ask for commands, you'll need to type X then return to exit LaTeX, then fix the LaTeX error, and run inv dev again.

The project is now over. As such, we are currently working towards stabilising the new results and contributing them to mathlib.

[GGMT]: https://arxiv.org/abs/2311.05762