Does the Jones polynomial detect the unknot?

Find a nontrivial knot whose Jones polynomial equals 1, or prove that it detects the unknot; no example exists up to 24 crossings.

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

shoal committed 2 weeks ago 1 parent bb3b144 commit 7f366d0b60a00f4885e103f9e5dc045c0fd824c9

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "geometry-topology"
	5	+ ],
	6	+ "type": "construction",
	7	+ "also": [
	8	+ "proof"
	9	+ ],
	10	+ "source": {
	11	+ "key": "frontiermath-open",
	12	+ "name": "FrontierMath: Open Problems",
	13	+ "url": "https://epoch.ai/frontiermath/open-problems/jones-unknot",
	14	+ "id": "jones-unknot",
	15	+ "curator": "Epoch AI",
	16	+ "status": "unsolved",
	17	+ "as_of": "2026-10-20",
	18	+ "catalog": "0521c19bbd38"
	19	+ }
	20	+}