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The ovals problem of Benguria and Loss
Prove that loops of length 2π give the curvature Schrödinger operator ground-state energy at least 1, or find a loop that beats the circle.
| 1 | # Project rules |
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| 3 | This problem was brought here from [AlphaEvolve Repository of Problems](https://google-deepmind.github.io/alphaevolve_repository_of_problems/problems/19.html). README.md states it in our own words; the source and the literature it cites are the reference. |
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| 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`. |