{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2OVJK3CIYLIO3BAVEPSTKMNE32","short_pith_number":"pith:2OVJK3CI","schema_version":"1.0","canonical_sha256":"d3aa956c48c2d0ed841523e53531a4dea592e692205cddd97f478e1db4bf945b","source":{"kind":"arxiv","id":"1507.07517","version":2},"attestation_state":"computed","paper":{"title":"The Microscopic Dynamics of a Spatial Ecological Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yuri Kondratiev, Yuri Kozitsky","submitted_at":"2015-07-27T18:30:53Z","abstract_excerpt":"The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes a competition term. The system's states are probability measures on the space of configurations of entities, and their evolution is described by means of a hierarchical chain of equations for the corresponding correlation functions derived from the Fokker-Planck equation for measures. Under natural conditions imposed on the model parameters it is proved that"},"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":"1507.07517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-27T18:30:53Z","cross_cats_sorted":[],"title_canon_sha256":"839efda48b40115dbc8adb9e4abb060831a80c6a4cabd436c29eeb86d4937fa8","abstract_canon_sha256":"e2da456867fdac075825ce671b6b84884a0591b0e3b1bcfb81a86ea5fcceea5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:03.482231Z","signature_b64":"yioFMK5TyFhhQvRIPl6cwxuC8QCrlNykzuhmlS+QyAIaI/5osmb71OaAr1yfz9dkKjS4E8aGYDBZYGerVTpBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3aa956c48c2d0ed841523e53531a4dea592e692205cddd97f478e1db4bf945b","last_reissued_at":"2026-05-18T01:24:03.481548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:03.481548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Microscopic Dynamics of a Spatial Ecological Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yuri Kondratiev, Yuri Kozitsky","submitted_at":"2015-07-27T18:30:53Z","abstract_excerpt":"The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes a competition term. The system's states are probability measures on the space of configurations of entities, and their evolution is described by means of a hierarchical chain of equations for the corresponding correlation functions derived from the Fokker-Planck equation for measures. Under natural conditions imposed on the model parameters it is proved that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07517","kind":"arxiv","version":2},"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":"1507.07517","created_at":"2026-05-18T01:24:03.481656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07517v2","created_at":"2026-05-18T01:24:03.481656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07517","created_at":"2026-05-18T01:24:03.481656+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OVJK3CIYLIO","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OVJK3CIYLIO3BAV","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OVJK3CI","created_at":"2026-05-18T12:29:02.477457+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/2OVJK3CIYLIO3BAVEPSTKMNE32","json":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32.json","graph_json":"https://pith.science/api/pith-number/2OVJK3CIYLIO3BAVEPSTKMNE32/graph.json","events_json":"https://pith.science/api/pith-number/2OVJK3CIYLIO3BAVEPSTKMNE32/events.json","paper":"https://pith.science/paper/2OVJK3CI"},"agent_actions":{"view_html":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32","download_json":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32.json","view_paper":"https://pith.science/paper/2OVJK3CI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07517&json=true","fetch_graph":"https://pith.science/api/pith-number/2OVJK3CIYLIO3BAVEPSTKMNE32/graph.json","fetch_events":"https://pith.science/api/pith-number/2OVJK3CIYLIO3BAVEPSTKMNE32/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32/action/storage_attestation","attest_author":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32/action/author_attestation","sign_citation":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32/action/citation_signature","submit_replication":"https://pith.science/pith/2OVJK3CIYLIO3BAVEPSTKMNE32/action/replication_record"}},"created_at":"2026-05-18T01:24:03.481656+00:00","updated_at":"2026-05-18T01:24:03.481656+00:00"}