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The purpose of this repository is to hold a Lean4 formalization of the proof of the Polynomial Freiman-Ruzsa (PFR) conjecture, recently proven in https://arxiv.org/abs/2311.05762 . 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 will be held on this Zulip stream: https://leanprover.zulipchat.com/#narrow/stream/412902-Polynomial-Freiman-Ruzsa-conjecture

Additional discussion of the project may be found at https://terrytao.wordpress.com/2023/11/13/on-a-conjecture-of-marton/

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