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	}