{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DQWYW2OXXXHT4RDGWEV4STF7KE","short_pith_number":"pith:DQWYW2OX","schema_version":"1.0","canonical_sha256":"1c2d8b69d7bdcf3e4466b12bc94cbf512a3bcfa8d35a032041e8d06baafa7e16","source":{"kind":"arxiv","id":"1202.2452","version":1},"attestation_state":"computed","paper":{"title":"Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aijun Zhang, Wenxian Shen","submitted_at":"2012-02-11T17:12:09Z","abstract_excerpt":"This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal dispersal has a unique spatially periodic positive stationary solution and has a spreading speed in every direction. In this paper, we show that a spatially periodic nonlocal monostable equation with certain spatial homogeneity or small nonlocal dispersal distance has a unique stable periodic traveling wave solutions connecting its unique spatially periodic "},"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":"1202.2452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-11T17:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"31547d46d5ae26d09acd52f995e9c2f96285c5c15d826ffd51e42280b1e9700f","abstract_canon_sha256":"596b32debc5a302f0bbff48d114b73f191c972f9fd34d4d91c8865741fcaf8db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:00.538442Z","signature_b64":"ZDT1JU28MbaVqJnmcXuDPlOYRbbEg7EAIkCAlh3cpoJSBu+KH26D/OoVVud+URa5kNWoNQseiPHdPjoKHespCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c2d8b69d7bdcf3e4466b12bc94cbf512a3bcfa8d35a032041e8d06baafa7e16","last_reissued_at":"2026-05-18T02:32:00.537941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:00.537941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aijun Zhang, Wenxian Shen","submitted_at":"2012-02-11T17:12:09Z","abstract_excerpt":"This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal dispersal has a unique spatially periodic positive stationary solution and has a spreading speed in every direction. In this paper, we show that a spatially periodic nonlocal monostable equation with certain spatial homogeneity or small nonlocal dispersal distance has a unique stable periodic traveling wave solutions connecting its unique spatially periodic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2452","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":"1202.2452","created_at":"2026-05-18T02:32:00.538022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2452v1","created_at":"2026-05-18T02:32:00.538022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2452","created_at":"2026-05-18T02:32:00.538022+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQWYW2OXXXHT","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQWYW2OXXXHT4RDG","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQWYW2OX","created_at":"2026-05-18T12:27:04.183437+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/DQWYW2OXXXHT4RDGWEV4STF7KE","json":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE.json","graph_json":"https://pith.science/api/pith-number/DQWYW2OXXXHT4RDGWEV4STF7KE/graph.json","events_json":"https://pith.science/api/pith-number/DQWYW2OXXXHT4RDGWEV4STF7KE/events.json","paper":"https://pith.science/paper/DQWYW2OX"},"agent_actions":{"view_html":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE","download_json":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE.json","view_paper":"https://pith.science/paper/DQWYW2OX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2452&json=true","fetch_graph":"https://pith.science/api/pith-number/DQWYW2OXXXHT4RDGWEV4STF7KE/graph.json","fetch_events":"https://pith.science/api/pith-number/DQWYW2OXXXHT4RDGWEV4STF7KE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/action/storage_attestation","attest_author":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/action/author_attestation","sign_citation":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/action/citation_signature","submit_replication":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/action/replication_record"}},"created_at":"2026-05-18T02:32:00.538022+00:00","updated_at":"2026-05-18T02:32:00.538022+00:00"}