{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UK5OHPKUHPNZHJTUB7T7IQ3OAP","short_pith_number":"pith:UK5OHPKU","schema_version":"1.0","canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","source":{"kind":"arxiv","id":"1509.02022","version":1},"attestation_state":"computed","paper":{"title":"Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Helene Leman","submitted_at":"2015-09-07T13:07:40Z","abstract_excerpt":"We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process when the population size grows to $+\\infty$ and the mutation probability decreases to $0$. We prove a convergence towards a jump process that jumps in the infinite dimensional space of the stable spat"},"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":"1509.02022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T13:07:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c3af92841ab3933ac991569690dee848247cf299adf1b331459b57c119242c1e","abstract_canon_sha256":"6b20163ccc3124f8183094af4fadd1872309f07a42416b3465f47ba9573cb436"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:49.910656Z","signature_b64":"HPBGNQQQRkBZ5VmkW5AX4am68K881WFwZxLa37fRSA5yp9/7SMMoGs1KYGhU5psASVRSqn5juWuHFf6dbi71Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","last_reissued_at":"2026-05-18T01:33:49.910067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:49.910067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Helene Leman","submitted_at":"2015-09-07T13:07:40Z","abstract_excerpt":"We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process when the population size grows to $+\\infty$ and the mutation probability decreases to $0$. We prove a convergence towards a jump process that jumps in the infinite dimensional space of the stable spat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02022","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":"1509.02022","created_at":"2026-05-18T01:33:49.910165+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02022v1","created_at":"2026-05-18T01:33:49.910165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02022","created_at":"2026-05-18T01:33:49.910165+00:00"},{"alias_kind":"pith_short_12","alias_value":"UK5OHPKUHPNZ","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UK5OHPKUHPNZHJTU","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UK5OHPKU","created_at":"2026-05-18T12:29:44.643036+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/UK5OHPKUHPNZHJTUB7T7IQ3OAP","json":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP.json","graph_json":"https://pith.science/api/pith-number/UK5OHPKUHPNZHJTUB7T7IQ3OAP/graph.json","events_json":"https://pith.science/api/pith-number/UK5OHPKUHPNZHJTUB7T7IQ3OAP/events.json","paper":"https://pith.science/paper/UK5OHPKU"},"agent_actions":{"view_html":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP","download_json":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP.json","view_paper":"https://pith.science/paper/UK5OHPKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02022&json=true","fetch_graph":"https://pith.science/api/pith-number/UK5OHPKUHPNZHJTUB7T7IQ3OAP/graph.json","fetch_events":"https://pith.science/api/pith-number/UK5OHPKUHPNZHJTUB7T7IQ3OAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/action/storage_attestation","attest_author":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/action/author_attestation","sign_citation":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/action/citation_signature","submit_replication":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/action/replication_record"}},"created_at":"2026-05-18T01:33:49.910165+00:00","updated_at":"2026-05-18T01:33:49.910165+00:00"}