{"id":"hexagon/2611.00065","pdf":"https://hexagonmath.org/pdf/2611.00065v1","url":"https://hexagonmath.org/abs/2611.00065v1","tags":["msc:60K35","msc:82B43","computer-assisted proof","critical probability","site percolation","square lattice","stochastic domination","substitution method"],"score":0,"title":"Computer-assisted bounds 0.556921 <= p_c <= 0.6463 for site percolation on the square lattice","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.PR","summary":"Let p_c be the critical probability of Bernoulli site percolation on Z^2. We prove 0.556921 = 0.5567 (Ashton, 2026, extending van den Berg and Ermakov, 1996) and p_c <= 0.666894 (Wierman and Oberly, 2024). The lower bound uses the growth-process comparison of van den Berg and Ermakov with the exact posterior on the exploration tree. We reduce this posterior to a scalar interval recursion and explore the tree generation by generation, with a prescribed order among siblings. This passes the value 0.556788... that the same scalar computation gives when the order is not used, and the value…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}