{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OQ2RTPIS4FIC7TWYKSVTOON22C","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":"4952e02ce8475c4213d18905e20920bf06381a0a87d9bf993b96cd3fe7ac5dc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T04:39:58Z","title_canon_sha256":"dc6b56083c9322bc8540fd71a7cacc680b52cf4d0bcdf727a289e6324bc61e12"},"schema_version":"1.0","source":{"id":"1506.02774","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02774","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02774v2","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02774","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"OQ2RTPIS4FIC","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQ2RTPIS4FIC7TWY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQ2RTPIS","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:900e94a8fbe7a8dd71a25e7c08acd0b187137355507f97b9b7c8b5ce15f40a22","target":"graph","created_at":"2026-05-18T01:17:55Z","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":"This work derives sufficient conditions for the permanence and ergodicity of a stochastic predator-prey model with Beddington-DeAngelis functional response. The conditions obtained in fact are very close to the necessary conditions. Both non-degenerate and degenerate diffusions are considered. One of the distinctive features of our results is that our results enables characterization of the support of a unique invariant probability measure. It proves the convergence in total variation norm of the transition probability to the invariant measure. Comparisons to existing literature and related ma","authors_text":"George Yin, Hai Dang Nguyen, Nguyen Huu Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T04:39:58Z","title":"Conditions for Permanence and Ergodicity of Certain Stochastic Predator-Prey Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02774","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":"sha256:7d1dae91df8b3b11660afcfffac2df5666f448685774fbc189272eb93697facd","target":"record","created_at":"2026-05-18T01:17:55Z","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":"4952e02ce8475c4213d18905e20920bf06381a0a87d9bf993b96cd3fe7ac5dc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T04:39:58Z","title_canon_sha256":"dc6b56083c9322bc8540fd71a7cacc680b52cf4d0bcdf727a289e6324bc61e12"},"schema_version":"1.0","source":{"id":"1506.02774","kind":"arxiv","version":2}},"canonical_sha256":"743519bd12e1502fced854ab3739bad0b18be14241db876ae3569b3eb5d3a9a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"743519bd12e1502fced854ab3739bad0b18be14241db876ae3569b3eb5d3a9a0","first_computed_at":"2026-05-18T01:17:55.513252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:55.513252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMEYQamz6Ugz5DtSIaASPQjcv3qwaPfiuDvqs8trWVaxQAUYH47qot0T8rC9iZFgPWKa7YLJiB8FAqRaJHxLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:55.513986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02774","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d1dae91df8b3b11660afcfffac2df5666f448685774fbc189272eb93697facd","sha256:900e94a8fbe7a8dd71a25e7c08acd0b187137355507f97b9b7c8b5ce15f40a22"],"state_sha256":"7e57fb659b56c502f6fe4f87161f13a0f35a857197dfe1cf8096a24b40e1adcd"}