{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PVSC5UODFI3364AIMAJA25PVXG","short_pith_number":"pith:PVSC5UOD","schema_version":"1.0","canonical_sha256":"7d642ed1c32a37bf700860120d75f5b9bc7a928851512f9ccb1fd8098bcd555f","source":{"kind":"arxiv","id":"1409.4679","version":2},"attestation_state":"computed","paper":{"title":"On a model of a population with variable motility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Olga Turanova","submitted_at":"2014-09-16T15:47:37Z","abstract_excerpt":"We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and long-range) behavior of the population. We perform a certain rescaling and prove that solutions of the rescaled problem converge locally uniformly to zero in a certain region and stay positive (in some sense) in another region. These regions are determined by two viscosity solutions of a related Hamilton-Jacobi equation."},"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":"1409.4679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-16T15:47:37Z","cross_cats_sorted":[],"title_canon_sha256":"4bad0922b4817dfcb028b9728c8c4ede27f3e3ba530e15af4f922cc160997993","abstract_canon_sha256":"60d6a9d339273f45c1815b4b4c7c1ea34e04b4165f1c36545b6039d744809ea9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:38.980646Z","signature_b64":"qv+BDRu0RSzLP8mxxBrMn0Ylbu5DRrynT3L4VR3QZ1i5vUwMS3ZyvyQ7TNXZCNmJncmV7t4BXftozpq1cviPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d642ed1c32a37bf700860120d75f5b9bc7a928851512f9ccb1fd8098bcd555f","last_reissued_at":"2026-05-18T01:19:38.980194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:38.980194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a model of a population with variable motility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Olga Turanova","submitted_at":"2014-09-16T15:47:37Z","abstract_excerpt":"We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and long-range) behavior of the population. We perform a certain rescaling and prove that solutions of the rescaled problem converge locally uniformly to zero in a certain region and stay positive (in some sense) in another region. These regions are determined by two viscosity solutions of a related Hamilton-Jacobi equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4679","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":"1409.4679","created_at":"2026-05-18T01:19:38.980258+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.4679v2","created_at":"2026-05-18T01:19:38.980258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4679","created_at":"2026-05-18T01:19:38.980258+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVSC5UODFI33","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVSC5UODFI3364AI","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVSC5UOD","created_at":"2026-05-18T12:28:43.426989+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/PVSC5UODFI3364AIMAJA25PVXG","json":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG.json","graph_json":"https://pith.science/api/pith-number/PVSC5UODFI3364AIMAJA25PVXG/graph.json","events_json":"https://pith.science/api/pith-number/PVSC5UODFI3364AIMAJA25PVXG/events.json","paper":"https://pith.science/paper/PVSC5UOD"},"agent_actions":{"view_html":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG","download_json":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG.json","view_paper":"https://pith.science/paper/PVSC5UOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.4679&json=true","fetch_graph":"https://pith.science/api/pith-number/PVSC5UODFI3364AIMAJA25PVXG/graph.json","fetch_events":"https://pith.science/api/pith-number/PVSC5UODFI3364AIMAJA25PVXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG/action/storage_attestation","attest_author":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG/action/author_attestation","sign_citation":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG/action/citation_signature","submit_replication":"https://pith.science/pith/PVSC5UODFI3364AIMAJA25PVXG/action/replication_record"}},"created_at":"2026-05-18T01:19:38.980258+00:00","updated_at":"2026-05-18T01:19:38.980258+00:00"}