The polynomial Bogolyubov conjecture

Show that if A has density α in F_2^n, then 10A contains a coset of a subspace of codimension O(log(1/α)).

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "combinatorics"
	5	+ ],
	6	+ "type": "proof",
	7	+ "source": {
	8	+ "key": "green-100",
	9	+ "name": "Ben Green's 100 open problems",
	10	+ "url": "https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.50",
	11	+ "id": "50",
	12	+ "curator": "Ben Green",
	13	+ "status": "open",
	14	+ "as_of": "2026-10-20",
	15	+ "catalog": "0521c19bbd38"
	16	+ }
	17	+}