{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OJPDGFZNSAEYK575KTPNL3AOO5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d981a0ec046d33fe2ed81e43b5ff56d360e53740d7ae7f6dfc747887571b7dec","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.TO","submitted_at":"2012-05-22T22:21:44Z","title_canon_sha256":"8c31ed27640af45df774e9720622151d7c490d9e83a002cfba00c07fec533fad"},"schema_version":"1.0","source":{"id":"1205.5066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5066","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5066v2","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5066","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"pith_short_12","alias_value":"OJPDGFZNSAEY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJPDGFZNSAEYK575","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJPDGFZN","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:707347192b1ec7c7fa563bf10e2b8f08f60e30f840f39cbc68eb884f5664133e","target":"graph","created_at":"2026-05-18T03:46:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Jacob N. Oppenheim, Marcelo O. Magnasco","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.TO","submitted_at":"2012-05-22T22:21:44Z","title":"A Topological Phase Transition in the Scheidegger Model of River Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5066","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:637f6603337d16f63dc1c4588c67588f54ffd16def0f0c821b5a23d4e1da8ee7","target":"record","created_at":"2026-05-18T03:46:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d981a0ec046d33fe2ed81e43b5ff56d360e53740d7ae7f6dfc747887571b7dec","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.TO","submitted_at":"2012-05-22T22:21:44Z","title_canon_sha256":"8c31ed27640af45df774e9720622151d7c490d9e83a002cfba00c07fec533fad"},"schema_version":"1.0","source":{"id":"1205.5066","kind":"arxiv","version":2}},"canonical_sha256":"725e33172d90098577fd54ded5ec0e7776939d72a953180d273413ac245f0f4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"725e33172d90098577fd54ded5ec0e7776939d72a953180d273413ac245f0f4b","first_computed_at":"2026-05-18T03:46:47.151155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:47.151155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OepceapDroPCyf8muenaWlDmOek6byEI4pGUX6YSs5IS8eB7NYe/fBICnuKFHdv2hs7xuwxBYv4emG6Jd4mrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:47.151914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:637f6603337d16f63dc1c4588c67588f54ffd16def0f0c821b5a23d4e1da8ee7","sha256:707347192b1ec7c7fa563bf10e2b8f08f60e30f840f39cbc68eb884f5664133e"],"state_sha256":"5128af167e158f9afb4a9dec4e33858a0fbcabce65b3397190f0786c37704cc2"}