Tight sample complexity of instance-optimal identity testing

Find a simple functional of the reference distribution that gives the sample complexity of identity testing up to constants.

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1	{
2	"domain": "computer-science",
3	"topics": [
4	"learning-theory",
5	"algorithms-complexity"
6	],
7	"type": "proof",
8	"source": {
9	"key": "colt",
10	"name": "COLT open problems",
11	"url": "https://proceedings.mlr.press/v247/canonne24a.html",
12	"id": "v247/canonne24a",
13	"curator": "Conference on Learning Theory (COLT)",
14	"poser": "Clément Canonne",
15	"status": "open",
16	"as_of": "2026-10-20",
17	"prize": "$200 (AUD)",
18	"catalog": "0521c19bbd38"
19	},
20	"review": true,
21	"approval": "first-time"
22	}