The site percolation threshold of the square lattice

Find a closed form for the site percolation threshold of the square lattice, p_c ≈ 0.5927460508; bond percolation has p_c = 1/2.

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	1	+{
	2	+ "domain": "physics-astronomy",
	3	+ "topics": [
	4	+ "statistical-mechanics",
	5	+ "probability"
	6	+ ],
	7	+ "type": "construction",
	8	+ "source": {
	9	+ "key": "horizonmath",
	10	+ "name": "HorizonMath",
	11	+ "url": "https://github.com/ewang26/HorizonMath/blob/4ef0b61a8a6d4c5ded661fab7c2e896af84abe6e/data/problems_full.json#L781-L791",
	12	+ "id": "site_percolation_square",
	13	+ "curator": "Erik Y. Wang, Sumeet R. Motwani et al.",
	14	+ "status": "open",
	15	+ "as_of": "2026-10-20",
	16	+ "catalog": "0521c19bbd38"
	17	+ }
	18	+}