{"paper":{"title":"A Topological Phase Transition in the Scheidegger Model of River Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.TO","authors_text":"Jacob N. Oppenheim, Marcelo O. Magnasco","submitted_at":"2012-05-22T22:21:44Z","abstract_excerpt":"We investigate the canonical Scheidegger Model of river network morphology for the case of convergent and divergent underlying topography, by embedding it on a cone. We find two distinct phases corresponding to few, long basins and many, short basins, respectively, separated by a singularity in number of basins, indicating a phase transition. Quantifying basin shape through Hack's Law $l\\sim a^h$ gives distinct values for the exponent $h$, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular differing number and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5066","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"}