{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UEMBMMVJ6672ISWYRCFNGD5MHW","short_pith_number":"pith:UEMBMMVJ","schema_version":"1.0","canonical_sha256":"a1181632a9f7bfa44ad8888ad30fac3db1ddeb95c96f5796f284337662d7e6a5","source":{"kind":"arxiv","id":"1611.03010","version":1},"attestation_state":"computed","paper":{"title":"Population processes with unbounded extinction rate conditioned to non-extinction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Villemonais, Nicolas Champagnat","submitted_at":"2016-11-09T16:47:35Z","abstract_excerpt":"This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling biological populations in interaction. To handle this situation, we develop original non-linear Lyapunov criteria. We obtain the exponential convergence in total variation of the conditional distributions to a unique quasi-stationary distribution, uniformly with respect to the initial distribution. Our results cover all one-dimensional birth and death processes "},"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":"1611.03010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-09T16:47:35Z","cross_cats_sorted":[],"title_canon_sha256":"2fd0dc69440da29933a7a358ffbacf431187d34b8f5ad17161fa36550cd0b1d9","abstract_canon_sha256":"e39024da67f4f6dbf4e0b4eb9ff361d9be43b2c925fae8e66594792aa9900450"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:42.873891Z","signature_b64":"cYyinX7GwPq1ZeLXnVC0VhAgIMdK8Acpvnspo3t72RmCIIQ1ADKWNF9hLkLCwMFHDvygbhGnfrVOx8WyVSqRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1181632a9f7bfa44ad8888ad30fac3db1ddeb95c96f5796f284337662d7e6a5","last_reissued_at":"2026-05-18T00:59:42.873263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:42.873263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Population processes with unbounded extinction rate conditioned to non-extinction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Villemonais, Nicolas Champagnat","submitted_at":"2016-11-09T16:47:35Z","abstract_excerpt":"This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling biological populations in interaction. To handle this situation, we develop original non-linear Lyapunov criteria. We obtain the exponential convergence in total variation of the conditional distributions to a unique quasi-stationary distribution, uniformly with respect to the initial distribution. Our results cover all one-dimensional birth and death processes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03010","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":"1611.03010","created_at":"2026-05-18T00:59:42.873359+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.03010v1","created_at":"2026-05-18T00:59:42.873359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03010","created_at":"2026-05-18T00:59:42.873359+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEMBMMVJ6672","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEMBMMVJ6672ISWY","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEMBMMVJ","created_at":"2026-05-18T12:30:46.583412+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/UEMBMMVJ6672ISWYRCFNGD5MHW","json":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW.json","graph_json":"https://pith.science/api/pith-number/UEMBMMVJ6672ISWYRCFNGD5MHW/graph.json","events_json":"https://pith.science/api/pith-number/UEMBMMVJ6672ISWYRCFNGD5MHW/events.json","paper":"https://pith.science/paper/UEMBMMVJ"},"agent_actions":{"view_html":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW","download_json":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW.json","view_paper":"https://pith.science/paper/UEMBMMVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.03010&json=true","fetch_graph":"https://pith.science/api/pith-number/UEMBMMVJ6672ISWYRCFNGD5MHW/graph.json","fetch_events":"https://pith.science/api/pith-number/UEMBMMVJ6672ISWYRCFNGD5MHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW/action/storage_attestation","attest_author":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW/action/author_attestation","sign_citation":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW/action/citation_signature","submit_replication":"https://pith.science/pith/UEMBMMVJ6672ISWYRCFNGD5MHW/action/replication_record"}},"created_at":"2026-05-18T00:59:42.873359+00:00","updated_at":"2026-05-18T00:59:42.873359+00:00"}