{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WBZFEAV3V3XQJOGB56IDACS7L4","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":"5ff74b7e91698c5501476d374175ac211b4db14422464fce5a9c160dd3e19e5e","cross_cats_sorted":["math.FA","math.MP","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-03-25T14:32:00Z","title_canon_sha256":"b0087c4e8b5ae8ebdffc71d15112f63efc8f6f73723bd06a4b9ab6193e0ee341"},"schema_version":"1.0","source":{"id":"0803.3565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3565","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3565v1","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3565","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"WBZFEAV3V3XQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WBZFEAV3V3XQJOGB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WBZFEAV3","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:50c080b5fb18342eb12261fe281846c82fac98a507d1ff525fd962f71bf35e0e","target":"graph","created_at":"2026-05-18T02:28:48Z","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":"We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in course of the stochastic evolution.","authors_text":"Dmitri Finkelshtein, Oleksandr Kutoviy, Yuri Kondratiev","cross_cats":["math.FA","math.MP","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-03-25T14:32:00Z","title":"Individual based model with competition in spatial ecology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3565","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":"sha256:0bbbd8bbd9937a3a700594674aa733e4b91955d6c0a23e911bd35c3b60229ce4","target":"record","created_at":"2026-05-18T02:28:48Z","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":"5ff74b7e91698c5501476d374175ac211b4db14422464fce5a9c160dd3e19e5e","cross_cats_sorted":["math.FA","math.MP","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-03-25T14:32:00Z","title_canon_sha256":"b0087c4e8b5ae8ebdffc71d15112f63efc8f6f73723bd06a4b9ab6193e0ee341"},"schema_version":"1.0","source":{"id":"0803.3565","kind":"arxiv","version":1}},"canonical_sha256":"b0725202bbaeef04b8c1ef90300a5f5f358613fa792293529e66ecae5e6d9c50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0725202bbaeef04b8c1ef90300a5f5f358613fa792293529e66ecae5e6d9c50","first_computed_at":"2026-05-18T02:28:48.662999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:48.662999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KaSlbANeCAbQ7c69wD0DTrCDfoN/SMJc7QVvsHJihJ69G1pOnRXjAGxvH0sNbzkNud3VNHbem7qnJ6RZutVQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:48.663361Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.3565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bbbd8bbd9937a3a700594674aa733e4b91955d6c0a23e911bd35c3b60229ce4","sha256:50c080b5fb18342eb12261fe281846c82fac98a507d1ff525fd962f71bf35e0e"],"state_sha256":"fbdb005ddae8058d0a40d0f4dda0e8ba2e3f5747b2ba19d3d38820de447a53c4"}