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.

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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	+ "mathematical-physics"
	6	+ ],
	7	+ "type": "proof",
	8	+ "also": [
	9	+ "construction"
	10	+ ],
	11	+ "source": {
	12	+ "key": "alphaevolve",
	13	+ "name": "AlphaEvolve Repository of Problems",
	14	+ "url": "https://google-deepmind.github.io/alphaevolve_repository_of_problems/problems/19.html",
	15	+ "id": "19",
	16	+ "curator": "Google DeepMind",
	17	+ "poser": "Rafael D. Benguria and Michael Loss",
	18	+ "status": "open",
	19	+ "as_of": "2026-10-20",
	20	+ "catalog": "0521c19bbd38"
	21	+ }
	22	+}