Density of ones in the Kolakoski sequence

Prove that the self-describing Kolakoski sequence of 1s and 2s has a density of 1s, equal to 1/2.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"combinatorics"
5	],
6	"type": "proof",
7	"cover": {
8	"motif": "blocks"
9	},
10	"source": {
11	"key": "formal-conjectures",
12	"name": "Formal Conjectures",
13	"url": "https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/OEIS/2.lean",
14	"id": "OEIS/2",
15	"curator": "Google DeepMind and contributors",
16	"status": "open",
17	"as_of": "2026-10-20",
18	"catalog": "0521c19bbd38"
19	},
20	"review": true,
21	"approval": "first-time"
22	}