Yang–Mills existence and mass gap

Construct four-dimensional quantum Yang–Mills theory for every compact simple gauge group and prove that it has a positive mass gap.

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

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	1	+{
	2	+ "domain": "physics-astronomy",
	3	+ "topics": [
	4	+ "mathematical-physics"
	5	+ ],
	6	+ "type": "proof",
	7	+ "source": {
	8	+ "key": "clay",
	9	+ "name": "Clay Millennium Prize Problems",
	10	+ "url": "https://www.claymath.org/millennium/yang-mills-the-maths-gap/",
	11	+ "curator": "Clay Mathematics Institute",
	12	+ "poser": "Clay Mathematics Institute, with the problem description by Arthur Jaffe and Edward Witten",
	13	+ "status": "unsolved",
	14	+ "as_of": "2026-10-20",
	15	+ "prize": "$1,000,000",
	16	+ "catalog": "0521c19bbd38"
	17	+ }
	18	+}