Frankl's union-closed sets conjecture

Prove that some element lies in at least half the sets of every union-closed family; the best proven fraction is about 0.38.

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

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "combinatorics"
	5	+ ],
	6	+ "type": "proof",
	7	+ "also": [
	8	+ "construction"
	9	+ ],
	10	+ "source": {
	11	+ "key": "optimization-constants",
	12	+ "name": "Optimization Constants in Mathematics",
	13	+ "url": "https://teorth.github.io/optimizationproblems/constants/6a.html",
	14	+ "id": "6",
	15	+ "curator": "Terence Tao and contributors",
	16	+ "poser": "Péter Frankl",
	17	+ "status": "open",
	18	+ "as_of": "2026-10-20",
	19	+ "catalog": "0521c19bbd38"
	20	+ }
	21	+}