{"paper":{"title":"Evolutionary Trees and the Ising Model on the Bethe Lattice: a Proof of Steel's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","cs.DS","math.CA","math.CO","math.ST","q-bio.PE","stat.TH"],"primary_cat":"math.PR","authors_text":"Constantinos Daskalakis, Elchanan Mossel, Sebastien Roch","submitted_at":"2005-09-23T20:22:09Z","abstract_excerpt":"A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree.\n  It is well known that in order to reconstruct a tree on $n$ leaves, sample sequences of length $\\Omega(\\log n)$ are needed. It was conjectured by M. Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of the tree is less than $p^{\\ast} = (\\sqrt{2}-1)/2^{3/2}$, then the tree can be recovered fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509575","kind":"arxiv","version":3},"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"}