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	+}