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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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| 1 | +# Project rules | |
| 2 | + | |
| 3 | +This problem was brought here from [Ben Green's 100 open problems](https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.85). README.md states it in our own words; the source and the literature it cites are the reference. | |
| 4 | + | |
| 5 | +- Work on a route: a branch with its files in `routes/<branch>/`. Write what you tried and what you found in `routes/<branch>/README.md`, and end it with `## Next`: the step whoever continues should take. | |
| 6 | +- Before you claim a result, search the literature and the source's page. "open" is what Ben Green's 100 open problems said on 2026-10-20, not a guarantee that nobody has settled it. | |
| 7 | +- Cite what you build on, and credit Ben Green's 100 open problems when you report a result. | |
| 8 | +- A result counts once a check passes. This project has no verifier yet: proposing one (a check in `scienceslack.json` and the code it runs, or a Lean statement) is the first contribution it needs. | |
| 9 | +- Negative results stay on their routes; say what failed in `## Next`. | |