{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:V6DH7CCQZO53IR3J3UTFISCD6H","short_pith_number":"pith:V6DH7CCQ","schema_version":"1.0","canonical_sha256":"af867f8850cbbbb44769dd26544843f1e21e7d91232c5a46d9705bf72b90dd64","source":{"kind":"arxiv","id":"1409.6122","version":1},"attestation_state":"computed","paper":{"title":"Convergence of generalized urn models to non-equilibrium attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mathieu Faure, Sebastian Schreiber","submitted_at":"2014-09-22T09:16:20Z","abstract_excerpt":"Generalized Polya urn models have been used to model the establishment dynamics of a small founding population consisting of k different genotypes or strategies. As population sizes get large, these population processes are well-approximated by a mean limit ordinary differential equation whose state space is the k simplex. We prove that if this mean limit ODE has an attractor at which the temporal averages of the population growth rate is positive, then there is a positive probability of the population not going extinct (i.e. growing without bound) and its distribution converging to the attrac"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.6122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-22T09:16:20Z","cross_cats_sorted":[],"title_canon_sha256":"3d5d0adcc35033a1f9cac2fea370b7db62993afeeecf9e7bbcb8d342668e4e5f","abstract_canon_sha256":"32fbd61568b7680d644eca7661ccc0b85415ac255265b8382343048633fdad8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:20.341297Z","signature_b64":"uT5/Bk2QrNec7Q3yNHAJw0vWrHlplmm7INtLyzn8Jwwxl2ztHSGaFfSmPTf5om3hZEvfv44PqLNeu/9sK6U+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af867f8850cbbbb44769dd26544843f1e21e7d91232c5a46d9705bf72b90dd64","last_reissued_at":"2026-05-18T01:00:20.340750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:20.340750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of generalized urn models to non-equilibrium attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mathieu Faure, Sebastian Schreiber","submitted_at":"2014-09-22T09:16:20Z","abstract_excerpt":"Generalized Polya urn models have been used to model the establishment dynamics of a small founding population consisting of k different genotypes or strategies. As population sizes get large, these population processes are well-approximated by a mean limit ordinary differential equation whose state space is the k simplex. We prove that if this mean limit ODE has an attractor at which the temporal averages of the population growth rate is positive, then there is a positive probability of the population not going extinct (i.e. growing without bound) and its distribution converging to the attrac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6122","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.6122","created_at":"2026-05-18T01:00:20.340841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.6122v1","created_at":"2026-05-18T01:00:20.340841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6122","created_at":"2026-05-18T01:00:20.340841+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6DH7CCQZO53","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6DH7CCQZO53IR3J","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6DH7CCQ","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H","json":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H.json","graph_json":"https://pith.science/api/pith-number/V6DH7CCQZO53IR3J3UTFISCD6H/graph.json","events_json":"https://pith.science/api/pith-number/V6DH7CCQZO53IR3J3UTFISCD6H/events.json","paper":"https://pith.science/paper/V6DH7CCQ"},"agent_actions":{"view_html":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H","download_json":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H.json","view_paper":"https://pith.science/paper/V6DH7CCQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.6122&json=true","fetch_graph":"https://pith.science/api/pith-number/V6DH7CCQZO53IR3J3UTFISCD6H/graph.json","fetch_events":"https://pith.science/api/pith-number/V6DH7CCQZO53IR3J3UTFISCD6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H/action/storage_attestation","attest_author":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H/action/author_attestation","sign_citation":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H/action/citation_signature","submit_replication":"https://pith.science/pith/V6DH7CCQZO53IR3J3UTFISCD6H/action/replication_record"}},"created_at":"2026-05-18T01:00:20.340841+00:00","updated_at":"2026-05-18T01:00:20.340841+00:00"}