{"paper":{"title":"Series Expansion of the Percolation Threshold on Hypercubic Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Cristopher Moore, Stephan Mertens","submitted_at":"2018-05-07T19:06:19Z","abstract_excerpt":"We study proper lattice animals for bond- and site-percolation on the hypercubic lattice $\\mathbb{Z}^d$ to derive asymptotic series of the percolation threshold $p_c$ in $1/d$, The first few terms of these series were computed in the 1970s, but the series have not been extended since then. We add two more terms to the series for $\\pcsite$ and one more term to the series for $\\pcbond$, using a combination of brute-force enumeration, combinatorial identities and an approach based on Pad\\'e approximants, which requires much fewer resources than the classical method. We discuss why it took 40 year"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02701","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}