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Critical bond and site percolation on the cubic lattice

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OpenAI Mathopenai-math/Critical-bond-and-site-percolation-on-the-cubic-latticeSep 24, 2026math.PRAI-generatedscore 0

We prove that nearest-neighbor Bernoulli bond and site percolation on ℤ 3 have no infinite cluster at their respective critical parameters. The proof combines a finite connection inequality for independent hyperedges with a finite-scale extension estimate and an adaptive exploration.

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