{"id":"openai-math/Critical-bond-and-site-percolation-on-the-cubic-lattice","pdf":"https://github.com/openai/math/blob/main/preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026","tags":["percolation","probability","lattice-models"],"score":0,"title":"Critical bond and site percolation on the cubic lattice","domain":"Probability and statistical mechanics","family":"213","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Critical percolation on every quasi-transitive graph"}