{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VYBVT4H7C34GLS3E6TVC7PWVPA","short_pith_number":"pith:VYBVT4H7","schema_version":"1.0","canonical_sha256":"ae0359f0ff16f865cb64f4ea2fbed5780770dc60bd75b7d24a72c38770acf763","source":{"kind":"arxiv","id":"1508.03909","version":2},"attestation_state":"computed","paper":{"title":"Stationary and time periodic patterns of two-predator and one-prey systems with prey-taxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Yu, Ke Wang, Qi Wang","submitted_at":"2015-08-17T02:04:31Z","abstract_excerpt":"This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population density gradient of the preys which can defend themselves as a group. We prove the global existence and uniform boundedness of positive classical solutions for the fully parabolic system over a bounded domain with space dimension $N=1,2$ and for the parabolic- -parabolic-elliptic system over higher space dimensions. Linearized stability analysis shows that pre"},"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":"1508.03909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-17T02:04:31Z","cross_cats_sorted":[],"title_canon_sha256":"9bd5f3b4220d4e590ea6097544a843df022c546abcd4674578ffb40811eccd76","abstract_canon_sha256":"b279669115ed3561da276abaa029e3d130707f481c82631c01f8e79ea651cea2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:29.128042Z","signature_b64":"DN3rM68hbS6SbvA9rvnreFl3VIkStHqhpYKxBE1u+BHDzM/svmyaJXCwxN7iSJ7p9rJ9n30dPOCyUpOJBmW7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae0359f0ff16f865cb64f4ea2fbed5780770dc60bd75b7d24a72c38770acf763","last_reissued_at":"2026-05-18T01:01:29.127605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:29.127605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary and time periodic patterns of two-predator and one-prey systems with prey-taxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Yu, Ke Wang, Qi Wang","submitted_at":"2015-08-17T02:04:31Z","abstract_excerpt":"This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population density gradient of the preys which can defend themselves as a group. We prove the global existence and uniform boundedness of positive classical solutions for the fully parabolic system over a bounded domain with space dimension $N=1,2$ and for the parabolic- -parabolic-elliptic system over higher space dimensions. Linearized stability analysis shows that pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03909","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":"1508.03909","created_at":"2026-05-18T01:01:29.127671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03909v2","created_at":"2026-05-18T01:01:29.127671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03909","created_at":"2026-05-18T01:01:29.127671+00:00"},{"alias_kind":"pith_short_12","alias_value":"VYBVT4H7C34G","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VYBVT4H7C34GLS3E","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VYBVT4H7","created_at":"2026-05-18T12:29:47.479230+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/VYBVT4H7C34GLS3E6TVC7PWVPA","json":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA.json","graph_json":"https://pith.science/api/pith-number/VYBVT4H7C34GLS3E6TVC7PWVPA/graph.json","events_json":"https://pith.science/api/pith-number/VYBVT4H7C34GLS3E6TVC7PWVPA/events.json","paper":"https://pith.science/paper/VYBVT4H7"},"agent_actions":{"view_html":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA","download_json":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA.json","view_paper":"https://pith.science/paper/VYBVT4H7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03909&json=true","fetch_graph":"https://pith.science/api/pith-number/VYBVT4H7C34GLS3E6TVC7PWVPA/graph.json","fetch_events":"https://pith.science/api/pith-number/VYBVT4H7C34GLS3E6TVC7PWVPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA/action/storage_attestation","attest_author":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA/action/author_attestation","sign_citation":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA/action/citation_signature","submit_replication":"https://pith.science/pith/VYBVT4H7C34GLS3E6TVC7PWVPA/action/replication_record"}},"created_at":"2026-05-18T01:01:29.127671+00:00","updated_at":"2026-05-18T01:01:29.127671+00:00"}