{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P2LIZQ5RQBO7PIY7HHBZQ4A4H3","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":"0b8de99692755b8aa1151496ecceef090257a5f5bc826381d5dc5e7185b0eb90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-08-03T16:54:08Z","title_canon_sha256":"9c086a0f70ea4744bd404ecfd2ee39a9742ad50f5b16f25d380c7b9aae31dce9"},"schema_version":"1.0","source":{"id":"1508.00490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00490","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00490v1","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00490","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"P2LIZQ5RQBO7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P2LIZQ5RQBO7PIY7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P2LIZQ5R","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:2012098d46344ebfda93073ec46b7a7d1a8299072301873d3fd166857ae06e85","target":"graph","created_at":"2026-05-18T01:35:57Z","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":"Stochastic fluctuations are central to the understanding of extinction dynamics. In the context of population models they allow for the description of the transition from the vicinity of a non-trivial fixed point of the deterministic dynamics to a trivial fixed point, where the population has become extinct. To characterize analytically the fluctuations of a given stochastic population model, one can operate within the so-called linear-noise approximation. Here the fluctuations are taken to be Gaussian, and the phenomenon of extinction is so rare as to be negligible, for all practical purposes","authors_text":"Alan J. McKane, Claudia Cianci, Duccio Fanelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-08-03T16:54:08Z","title":"WKB versus generalized van Kampen system-size expansion: the stochastic logistic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00490","kind":"arxiv","version":1},"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":"sha256:0b72134064e1b6b7642a56c27752be6f3c98970784146bb7c659a805a6024737","target":"record","created_at":"2026-05-18T01:35:57Z","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":"0b8de99692755b8aa1151496ecceef090257a5f5bc826381d5dc5e7185b0eb90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-08-03T16:54:08Z","title_canon_sha256":"9c086a0f70ea4744bd404ecfd2ee39a9742ad50f5b16f25d380c7b9aae31dce9"},"schema_version":"1.0","source":{"id":"1508.00490","kind":"arxiv","version":1}},"canonical_sha256":"7e968cc3b1805df7a31f39c398701c3ed0921bdad00c331ec6c4ab0c11893cd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e968cc3b1805df7a31f39c398701c3ed0921bdad00c331ec6c4ab0c11893cd7","first_computed_at":"2026-05-18T01:35:57.956706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.956706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CtwmhZnCMUVC2l5B9SR42pEtPcwxh3R1hIuH1T3VXRvJ46i1u5WXihZhqOKkj0LdPCKYGpJ4VIHPdhwcAzKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.957369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b72134064e1b6b7642a56c27752be6f3c98970784146bb7c659a805a6024737","sha256:2012098d46344ebfda93073ec46b7a7d1a8299072301873d3fd166857ae06e85"],"state_sha256":"c661286f18f505c86cc28c7c7b74b15b7472cbebd2446f7f72bec4697df86871"}