The Häggström–Pemantle conjecture on competing growth

Prove that two competing growth processes on the lattice cannot both grow forever when their speeds differ.

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "probability",
	5	+ "statistical-mechanics"
	6	+ ],
	7	+ "type": "proof",
	8	+ "source": {
	9	+ "key": "aimpl",
	10	+ "name": "AIM Problem Lists",
	11	+ "url": "http://aimpl.org/firstpercolation/5/",
	12	+ "id": "firstpercolation 5.2",
	13	+ "curator": "American Institute of Mathematics",
	14	+ "poser": "Olle Häggström and Robin Pemantle; posed by Christopher Hoffman",
	15	+ "status": "open",
	16	+ "as_of": "2026-10-20",
	17	+ "catalog": "0521c19bbd38"
	18	+ }
	19	+}