Empires and percolation: regions merging at a constant rate

Decide whether planar regions merging with neighbours at a constant rate form an infinite region in finite time.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"probability"
5	],
6	"type": "proof",
7	"source": {
8	"key": "aldous",
9	"name": "David Aldous's open problems",
10	"url": "https://www.stat.berkeley.edu/~aldous/Research/OP/empires.html",
11	"id": "empires",
12	"curator": "David Aldous",
13	"poser": "David Aldous",
14	"status": "open",
15	"as_of": "2026-10-20",
16	"catalog": "0521c19bbd38"
17	},
18	"review": true,
19	"approval": "first-time"
20	}