{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:M5JXAWC2M6G7ZGW3VDIGQDTVK5","short_pith_number":"pith:M5JXAWC2","schema_version":"1.0","canonical_sha256":"675370585a678dfc9adba8d0680e75576eda5fb45fe19435ae2e37c68174fa22","source":{"kind":"arxiv","id":"1008.3125","version":1},"attestation_state":"computed","paper":{"title":"On Nonlocal Parabolic Steady-State Equations of Cooperative or Competing Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Walker","submitted_at":"2010-08-18T16:21:02Z","abstract_excerpt":"Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation techniques are employed to derive a detailed description of the structure of positive coexistence solutions."},"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":"1008.3125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-18T16:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"2eb11f5e88568b5397bef97c43df40c6be056cd45f6b431fd6824620f25affb4","abstract_canon_sha256":"1d5b84e63a0fcebb8732aad76f5408e6d78855eb6d9978231c2ecd09bed10d1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.567428Z","signature_b64":"uKO7vV5H7r+O1YOQ5gE2QvbiyGNkPwnddKbFcFJeeipMNjoTr9tgwcZjvHJu+gVCWE+b6Fmuy75wzKU6O8ehBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"675370585a678dfc9adba8d0680e75576eda5fb45fe19435ae2e37c68174fa22","last_reissued_at":"2026-05-18T04:42:03.567011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.567011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Nonlocal Parabolic Steady-State Equations of Cooperative or Competing Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Walker","submitted_at":"2010-08-18T16:21:02Z","abstract_excerpt":"Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation techniques are employed to derive a detailed description of the structure of positive coexistence solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3125","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":"1008.3125","created_at":"2026-05-18T04:42:03.567082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3125v1","created_at":"2026-05-18T04:42:03.567082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3125","created_at":"2026-05-18T04:42:03.567082+00:00"},{"alias_kind":"pith_short_12","alias_value":"M5JXAWC2M6G7","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"M5JXAWC2M6G7ZGW3","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"M5JXAWC2","created_at":"2026-05-18T12:26:10.704358+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/M5JXAWC2M6G7ZGW3VDIGQDTVK5","json":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5.json","graph_json":"https://pith.science/api/pith-number/M5JXAWC2M6G7ZGW3VDIGQDTVK5/graph.json","events_json":"https://pith.science/api/pith-number/M5JXAWC2M6G7ZGW3VDIGQDTVK5/events.json","paper":"https://pith.science/paper/M5JXAWC2"},"agent_actions":{"view_html":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5","download_json":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5.json","view_paper":"https://pith.science/paper/M5JXAWC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3125&json=true","fetch_graph":"https://pith.science/api/pith-number/M5JXAWC2M6G7ZGW3VDIGQDTVK5/graph.json","fetch_events":"https://pith.science/api/pith-number/M5JXAWC2M6G7ZGW3VDIGQDTVK5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5/action/storage_attestation","attest_author":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5/action/author_attestation","sign_citation":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5/action/citation_signature","submit_replication":"https://pith.science/pith/M5JXAWC2M6G7ZGW3VDIGQDTVK5/action/replication_record"}},"created_at":"2026-05-18T04:42:03.567082+00:00","updated_at":"2026-05-18T04:42:03.567082+00:00"}