Carbery's rectangle problem

Show that an open subset of the unit square with area α contains the corners of an axis-parallel rectangle of area at least cα².

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "analysis",
	5	+ "combinatorics"
	6	+ ],
	7	+ "type": "proof",
	8	+ "source": {
	9	+ "key": "green-100",
	10	+ "name": "Ben Green's 100 open problems",
	11	+ "url": "https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.85",
	12	+ "id": "85",
	13	+ "curator": "Ben Green",
	14	+ "poser": "Anthony Carbery, Michael Christ and James Wright",
	15	+ "status": "open",
	16	+ "as_of": "2026-10-20",
	17	+ "catalog": "0521c19bbd38"
	18	+ }
	19	+}