{"paper":{"title":"A Proof Of The Block Model Threshold Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"math.PR","authors_text":"Allan Sly, Elchanan Mossel, Joe Neeman","submitted_at":"2013-11-17T05:16:47Z","abstract_excerpt":"We study a random graph model named the \"block model\" in statistics and the \"planted partition model\" in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge probability of $q$ and a within-class edge probability of $p$.\n  A striking conjecture of Decelle, Krzkala, Moore and Zdeborov\\'a based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if $p = a/n$ and $q = b/n$, $s=(a-b)/2$ and $p=(a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4115","kind":"arxiv","version":4},"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"}