{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:57IJF3LFI26SQYPDDTL7ARTE2K","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":"9766f86b499991481bb0a7c567b279a69c64c545e9eb8bf68af559b1139b414a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-16T12:01:26Z","title_canon_sha256":"6fdc2677cca4456252b225284d7272ef7996d897473c0ed51537f23975991db7"},"schema_version":"1.0","source":{"id":"1710.05639","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05639","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05639v3","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05639","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"57IJF3LFI26S","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"57IJF3LFI26SQYPD","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"57IJF3LF","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:7ba938b099f56ecf160885fc4661bb7a963bad0058272cdc73173e62a3d618eb","target":"graph","created_at":"2026-05-17T23:59:53Z","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":"In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods widely used in studying such physical systems, for instance, Wentzel-Kramers-Brillouin (WKB) and Fokker-Planck methods, can be applied to solve similar biological problems. In this article, we comparatively analyse applications of WKB and Fokker-Planck methods to some typical stochastic population dynamical models, including the logistic growth, endemic SIR, pred","authors_text":"Xiang-Yi Li, Xiaoquan Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-16T12:01:26Z","title":"Applications of WKB and Fokker-Planck methods in analyzing population extinction driven by weak demographic fluctuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05639","kind":"arxiv","version":3},"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":"sha256:7872c730353492abd4c317bf803e9878862b8388c29616f0fdcebb298b21da36","target":"record","created_at":"2026-05-17T23:59:53Z","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":"9766f86b499991481bb0a7c567b279a69c64c545e9eb8bf68af559b1139b414a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-16T12:01:26Z","title_canon_sha256":"6fdc2677cca4456252b225284d7272ef7996d897473c0ed51537f23975991db7"},"schema_version":"1.0","source":{"id":"1710.05639","kind":"arxiv","version":3}},"canonical_sha256":"efd092ed6546bd2861e31cd7f04664d2ac8c8d39037a8ecb20061248d681af37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efd092ed6546bd2861e31cd7f04664d2ac8c8d39037a8ecb20061248d681af37","first_computed_at":"2026-05-17T23:59:53.595205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:53.595205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3b3nMCEVo5bq8Sqd5ClK8STBHJkoX7MzFsibHg/B+y4Rb/K3fZziOBeQ29Y6en7ev7aStdQWz6awIeal83nAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:53.595910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05639","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7872c730353492abd4c317bf803e9878862b8388c29616f0fdcebb298b21da36","sha256:7ba938b099f56ecf160885fc4661bb7a963bad0058272cdc73173e62a3d618eb"],"state_sha256":"d42c602b5968edd9adf94fb7ef44529aa4380fe6055ee365cecc61b3e75477c2"}