{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FUJTKFUYWWXAHXUCP7VG6F534J","short_pith_number":"pith:FUJTKFUY","schema_version":"1.0","canonical_sha256":"2d13351698b5ae03de827fea6f17bbe271378a988eb63069a978de5686ed6ccc","source":{"kind":"arxiv","id":"1102.2286","version":1},"attestation_state":"computed","paper":{"title":"Global Dynamics of a Discrete Two-species Lottery-Ricker Competition Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hal Smith, Yun Kang","submitted_at":"2011-02-11T05:33:35Z","abstract_excerpt":"In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show that for a certain parameter range, there exists a compact interior attractor that attracts all interior points except a Lebesgue measure zero set. This result gives a weaker form of coexistence which is referred to as relative permanence. This new concept of coexistence combined with numerical simulations strongly suggests that th"},"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":"1102.2286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-11T05:33:35Z","cross_cats_sorted":[],"title_canon_sha256":"dc76e35434d37e5eb29f06b3af631d23496834901dff94e8746c8defbe910dbe","abstract_canon_sha256":"ce917b75d8ca712cab188c1e51dde599da90677e8813616a3c5c21be118664f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:56.347991Z","signature_b64":"EkIRjh1ex815UKlKnGMhKId2++52xQ+hz73XvlVOOcJLaxSYWNcTV66blw1W+ou5QDQ+F+SjBth9rOGWkdm/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d13351698b5ae03de827fea6f17bbe271378a988eb63069a978de5686ed6ccc","last_reissued_at":"2026-05-18T04:28:56.347499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:56.347499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Dynamics of a Discrete Two-species Lottery-Ricker Competition Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hal Smith, Yun Kang","submitted_at":"2011-02-11T05:33:35Z","abstract_excerpt":"In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show that for a certain parameter range, there exists a compact interior attractor that attracts all interior points except a Lebesgue measure zero set. This result gives a weaker form of coexistence which is referred to as relative permanence. This new concept of coexistence combined with numerical simulations strongly suggests that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2286","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":"1102.2286","created_at":"2026-05-18T04:28:56.347569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.2286v1","created_at":"2026-05-18T04:28:56.347569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2286","created_at":"2026-05-18T04:28:56.347569+00:00"},{"alias_kind":"pith_short_12","alias_value":"FUJTKFUYWWXA","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FUJTKFUYWWXAHXUC","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FUJTKFUY","created_at":"2026-05-18T12:26:28.662955+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/FUJTKFUYWWXAHXUCP7VG6F534J","json":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J.json","graph_json":"https://pith.science/api/pith-number/FUJTKFUYWWXAHXUCP7VG6F534J/graph.json","events_json":"https://pith.science/api/pith-number/FUJTKFUYWWXAHXUCP7VG6F534J/events.json","paper":"https://pith.science/paper/FUJTKFUY"},"agent_actions":{"view_html":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J","download_json":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J.json","view_paper":"https://pith.science/paper/FUJTKFUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.2286&json=true","fetch_graph":"https://pith.science/api/pith-number/FUJTKFUYWWXAHXUCP7VG6F534J/graph.json","fetch_events":"https://pith.science/api/pith-number/FUJTKFUYWWXAHXUCP7VG6F534J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J/action/storage_attestation","attest_author":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J/action/author_attestation","sign_citation":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J/action/citation_signature","submit_replication":"https://pith.science/pith/FUJTKFUYWWXAHXUCP7VG6F534J/action/replication_record"}},"created_at":"2026-05-18T04:28:56.347569+00:00","updated_at":"2026-05-18T04:28:56.347569+00:00"}