{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DQWYW2OXXXHT4RDGWEV4STF7KE","short_pith_number":"pith:DQWYW2OX","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"},"canonical_sha256":"1c2d8b69d7bdcf3e4466b12bc94cbf512a3bcfa8d35a032041e8d06baafa7e16","source":{"kind":"arxiv","id":"1202.2452","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2452","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2452v1","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2452","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"DQWYW2OXXXHT","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DQWYW2OXXXHT4RDG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DQWYW2OX","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DQWYW2OXXXHT4RDGWEV4STF7KE","target":"record","payload":{"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"},"canonical_sha256":"1c2d8b69d7bdcf3e4466b12bc94cbf512a3bcfa8d35a032041e8d06baafa7e16","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"},"source_kind":"arxiv","source_id":"1202.2452","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3XhgrrnjmGJ1gOvPjGYBZ9FOrePFYruWyWj6u68CgRsHAYsOfS3P7Ye21zcL7fB8qDsU9XWZ80gCNFgvw/50Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:15:39.425979Z"},"content_sha256":"f820225a6d58cf854e95e8ea4c16b733a3ffa2557c94e310cafc1bacfa138114","schema_version":"1.0","event_id":"sha256:f820225a6d58cf854e95e8ea4c16b733a3ffa2557c94e310cafc1bacfa138114"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DQWYW2OXXXHT4RDGWEV4STF7KE","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pono9z6nDKcoTAaY0P2QEJCPOr9eaq1xMyUvWWH4QxbDnqBL8qdlrLH95O3p3hts3vTsaI6GOMDvIuVHGqwKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:15:39.426729Z"},"content_sha256":"bfdd6ea1d1e702c2bc179d69de1e7cec6111626f2ec633f736d0bcad723a1a71","schema_version":"1.0","event_id":"sha256:bfdd6ea1d1e702c2bc179d69de1e7cec6111626f2ec633f736d0bcad723a1a71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/bundle.json","state_url":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T04:15:39Z","links":{"resolver":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE","bundle":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/bundle.json","state":"https://pith.science/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQWYW2OXXXHT4RDGWEV4STF7KE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DQWYW2OXXXHT4RDGWEV4STF7KE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"596b32debc5a302f0bbff48d114b73f191c972f9fd34d4d91c8865741fcaf8db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-11T17:12:09Z","title_canon_sha256":"31547d46d5ae26d09acd52f995e9c2f96285c5c15d826ffd51e42280b1e9700f"},"schema_version":"1.0","source":{"id":"1202.2452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2452","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2452v1","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2452","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"DQWYW2OXXXHT","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DQWYW2OXXXHT4RDG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DQWYW2OX","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:bfdd6ea1d1e702c2bc179d69de1e7cec6111626f2ec633f736d0bcad723a1a71","target":"graph","created_at":"2026-05-18T02:32:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Aijun Zhang, Wenxian Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-11T17:12:09Z","title":"Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2452","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f820225a6d58cf854e95e8ea4c16b733a3ffa2557c94e310cafc1bacfa138114","target":"record","created_at":"2026-05-18T02:32:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"596b32debc5a302f0bbff48d114b73f191c972f9fd34d4d91c8865741fcaf8db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-11T17:12:09Z","title_canon_sha256":"31547d46d5ae26d09acd52f995e9c2f96285c5c15d826ffd51e42280b1e9700f"},"schema_version":"1.0","source":{"id":"1202.2452","kind":"arxiv","version":1}},"canonical_sha256":"1c2d8b69d7bdcf3e4466b12bc94cbf512a3bcfa8d35a032041e8d06baafa7e16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c2d8b69d7bdcf3e4466b12bc94cbf512a3bcfa8d35a032041e8d06baafa7e16","first_computed_at":"2026-05-18T02:32:00.537941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:00.537941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZDT1JU28MbaVqJnmcXuDPlOYRbbEg7EAIkCAlh3cpoJSBu+KH26D/OoVVud+URa5kNWoNQseiPHdPjoKHespCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:00.538442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f820225a6d58cf854e95e8ea4c16b733a3ffa2557c94e310cafc1bacfa138114","sha256:bfdd6ea1d1e702c2bc179d69de1e7cec6111626f2ec633f736d0bcad723a1a71"],"state_sha256":"067ba01cfaf63ed6ac883f0442e83d48894bc2e315627680253e9de3f797be8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D633nMiyQYWZ1jhn5j8seTb7LduRsIwaW/3q9WEvr4KT++KgDZpijkfPmYz6yzIhDetbMjrNAEWMhCfbOohLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:15:39.430193Z","bundle_sha256":"537a0f73ce752cffd131d73c19ac09b3e438428b894182f7fc302528398fc067"}}