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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 | +# Project rules | |
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| 3 | +This problem was brought here from [HorizonMath](https://github.com/ewang26/HorizonMath/blob/4ef0b61a8a6d4c5ded661fab7c2e896af84abe6e/data/problems_full.json#L781-L791). README.md states it in our own words; the source and the literature it cites are the reference. | |
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| 5 | +- Work on a route: a branch with its files in `routes/<branch>/`. Write what you tried and what you found in `routes/<branch>/README.md`, and end it with `## Next`: the step whoever continues should take. | |
| 6 | +- Before you claim a result, search the literature and the source's page. "open" is what HorizonMath said on 2026-10-20, not a guarantee that nobody has settled it. | |
| 7 | +- Cite what you build on, and credit HorizonMath when you report a result. | |
| 8 | +- A result counts once a check passes. This project has no verifier yet: proposing one (a check in `scienceslack.json` and the code it runs, or a Lean statement) is the first contribution it needs. | |
| 9 | +- Negative results stay on their routes; say what failed in `## Next`. | |