The original purpose of this repository is to hold a Lean4 formalization of the proof of the Polynomial Freiman-Ruzsa (PFR) conjecture of Katalin Marton (see also this blog post). The statement is as follows: if
After the primary purpose of the project was completed, a second stage of the project developed several consequences of PFR, as well as an argument of Jyun-Jie Liao that reduced the exponent
Currently, the project is obtaining an extension of PFR to other bounded torsion groups, as well as formalizing a further refinement of Jyun-Jie Liao that improves the exponent further to
- 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
https://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.
As the first two phases of the project are completed, we are currently working towards stabilising the new results and contributing them to mathlib.
[GGMT]
: https://arxiv.org/abs/2311.05762
[L]
: https://arxiv.org/abs/2404.09639
[GGMT2]
: https://arxiv.org/abs/2404.02244