{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3DSHDLNDFHNH5FBZFDJIAHMHRB","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":"446f5281a53eea4a2480db275c243fe78c9c54b4e05af6ab008c1e2245aff036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-03-11T23:17:12Z","title_canon_sha256":"5f532711b8f41c35fa90959d4ce659ab17a6a93d6e1f5c1a91dc9c891337ddaa"},"schema_version":"1.0","source":{"id":"1603.03819","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03819","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03819v2","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03819","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"3DSHDLNDFHNH","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DSHDLNDFHNH5FBZ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DSHDLND","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:c59d6adb7c01c8f0d7e1bab81a565ee62e5e36c65a8bc8d9a81ee1eeae5437cd","target":"graph","created_at":"2026-05-18T00:38:32Z","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":"Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. I","authors_text":"Forrest W. Crawford, Jason Xu, Lam Si Tung Ho, Marc A. Suchard, Vladimir N. Minin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-03-11T23:17:12Z","title":"Birth/birth-death processes and their computable transition probabilities with biological applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03819","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:a2823452203fb3c91b84a17ae7458b2f99466d478b311e56b81c096c9a75fe2c","target":"record","created_at":"2026-05-18T00:38:32Z","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":"446f5281a53eea4a2480db275c243fe78c9c54b4e05af6ab008c1e2245aff036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-03-11T23:17:12Z","title_canon_sha256":"5f532711b8f41c35fa90959d4ce659ab17a6a93d6e1f5c1a91dc9c891337ddaa"},"schema_version":"1.0","source":{"id":"1603.03819","kind":"arxiv","version":2}},"canonical_sha256":"d8e471ada329da7e943928d2801d8788732d6a401d51c5d099587823b731a0c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8e471ada329da7e943928d2801d8788732d6a401d51c5d099587823b731a0c2","first_computed_at":"2026-05-18T00:38:32.187849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:32.187849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhB81HHjXmkSlVzrrOYhl/ZeQ/bAyN6lJYQfmGypm1ospSxu6EXkyUz67+8pGabt2ORkKj+Z1+6h9STY78oXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:32.188391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03819","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2823452203fb3c91b84a17ae7458b2f99466d478b311e56b81c096c9a75fe2c","sha256:c59d6adb7c01c8f0d7e1bab81a565ee62e5e36c65a8bc8d9a81ee1eeae5437cd"],"state_sha256":"7e3dbf710eaf93152ae10c7bec926289bca8b269346d240e8534d2d11b673bba"}