{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OGIAE7WMXBMNMBFRLFIRK3LKE2","short_pith_number":"pith:OGIAE7WM","schema_version":"1.0","canonical_sha256":"7190027eccb858d604b15951156d6a26b5a564b362257a2f1a4f142fa3ab3855","source":{"kind":"arxiv","id":"1408.0641","version":1},"attestation_state":"computed","paper":{"title":"On expected durations of birth-death processes, with applications to branching processes and SIS epidemics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank Ball, Peter Neal, Tom Britton","submitted_at":"2014-08-04T11:12:22Z","abstract_excerpt":"We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q]=1, and where the birth rate if the population is currently in state (has size) n is \\alpha(n). We focus on two important examples, namely \\alpha(n)=\\lambda n being a branching process, and \\alpha(n)=\\lambda n(N-n)/N which corresponds to an SIS epidemic model in a homogeneously mixing community of fixed size N. The processes are assumed to start with a single individual, i.e. in state 1. Let T, A_n, C and S denote the (random)"},"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":"1408.0641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-04T11:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"1ce2cf40e49e00abee8aeb793ac0fedff7ac2f109cc9e4abab3456804715236f","abstract_canon_sha256":"d7af7e2c39fb0e2460ff4c3f69955333a2398007ad51d4ed12524d9d955ccbdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:56.600061Z","signature_b64":"Pdt+v85EE8hRQcIo7Q25KyS3/WCD/j4jA0kqD+DGmIiX9hOF723lPMBzKATH7POf80ivU+v+KTKTFItOGl3hAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7190027eccb858d604b15951156d6a26b5a564b362257a2f1a4f142fa3ab3855","last_reissued_at":"2026-05-18T02:45:56.599501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:56.599501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On expected durations of birth-death processes, with applications to branching processes and SIS epidemics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank Ball, Peter Neal, Tom Britton","submitted_at":"2014-08-04T11:12:22Z","abstract_excerpt":"We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q]=1, and where the birth rate if the population is currently in state (has size) n is \\alpha(n). We focus on two important examples, namely \\alpha(n)=\\lambda n being a branching process, and \\alpha(n)=\\lambda n(N-n)/N which corresponds to an SIS epidemic model in a homogeneously mixing community of fixed size N. The processes are assumed to start with a single individual, i.e. in state 1. Let T, A_n, C and S denote the (random)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0641","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":"1408.0641","created_at":"2026-05-18T02:45:56.599576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0641v1","created_at":"2026-05-18T02:45:56.599576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0641","created_at":"2026-05-18T02:45:56.599576+00:00"},{"alias_kind":"pith_short_12","alias_value":"OGIAE7WMXBMN","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OGIAE7WMXBMNMBFR","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OGIAE7WM","created_at":"2026-05-18T12:28:41.024544+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/OGIAE7WMXBMNMBFRLFIRK3LKE2","json":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2.json","graph_json":"https://pith.science/api/pith-number/OGIAE7WMXBMNMBFRLFIRK3LKE2/graph.json","events_json":"https://pith.science/api/pith-number/OGIAE7WMXBMNMBFRLFIRK3LKE2/events.json","paper":"https://pith.science/paper/OGIAE7WM"},"agent_actions":{"view_html":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2","download_json":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2.json","view_paper":"https://pith.science/paper/OGIAE7WM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0641&json=true","fetch_graph":"https://pith.science/api/pith-number/OGIAE7WMXBMNMBFRLFIRK3LKE2/graph.json","fetch_events":"https://pith.science/api/pith-number/OGIAE7WMXBMNMBFRLFIRK3LKE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2/action/storage_attestation","attest_author":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2/action/author_attestation","sign_citation":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2/action/citation_signature","submit_replication":"https://pith.science/pith/OGIAE7WMXBMNMBFRLFIRK3LKE2/action/replication_record"}},"created_at":"2026-05-18T02:45:56.599576+00:00","updated_at":"2026-05-18T02:45:56.599576+00:00"}