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Smale's mean value conjecture
Close the gap between 1 - 1/n and about 4 in Smale's mean value inequality for complex polynomials, or find a counterexample.
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| 1 | +# Project rules | |
| 2 | + | |
| 3 | +This problem was brought here from [AlphaEvolve Repository of Problems](https://google-deepmind.github.io/alphaevolve_repository_of_problems/problems/23.html). 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 AlphaEvolve Repository of Problems said on 2026-10-20, not a guarantee that nobody has settled it. | |
| 7 | +- Cite what you build on, and credit AlphaEvolve Repository of 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`. | |