{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SHDUJOKE5S6N2XCB24JAP4XMR3","short_pith_number":"pith:SHDUJOKE","canonical_record":{"source":{"id":"1504.02525","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T00:53:45Z","cross_cats_sorted":[],"title_canon_sha256":"42cd820d028dde46955d1f320745ed521c67319e89c17fc1b111a8a95f6fe29a","abstract_canon_sha256":"05a5085c63da34ca92c22aac2f6800f46139f93b62b5cbf7d563f88e684f4f10"},"schema_version":"1.0"},"canonical_sha256":"91c744b944ecbcdd5c41d71207f2ec8ec6406faef1c97e927f203223fb2b8770","source":{"kind":"arxiv","id":"1504.02525","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02525","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02525v3","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02525","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"SHDUJOKE5S6N","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SHDUJOKE5S6N2XCB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SHDUJOKE","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SHDUJOKE5S6N2XCB24JAP4XMR3","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02525","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T00:53:45Z","cross_cats_sorted":[],"title_canon_sha256":"42cd820d028dde46955d1f320745ed521c67319e89c17fc1b111a8a95f6fe29a","abstract_canon_sha256":"05a5085c63da34ca92c22aac2f6800f46139f93b62b5cbf7d563f88e684f4f10"},"schema_version":"1.0"},"canonical_sha256":"91c744b944ecbcdd5c41d71207f2ec8ec6406faef1c97e927f203223fb2b8770","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:07.776950Z","signature_b64":"PaSU32H9blpgN3yEpHcQRGt7pKerg6Dn6N90ckYey0B3ZA7huB/bs3NiMV+geHqC6is43KorlhHNvKmrPJfRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91c744b944ecbcdd5c41d71207f2ec8ec6406faef1c97e927f203223fb2b8770","last_reissued_at":"2026-05-18T01:27:07.776227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:07.776227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02525","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+zTF5nRFX8sRpd64bdEz3gSd36Yp3yedYTbMaOQScsf8J7v6lanLtZhMxYKkzp+RhRbcGa1w/JSOnkP8vpCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:25.986646Z"},"content_sha256":"74d649b3b09c645ecf689189fd298f788d373da718eb3b28692e4b36f519b45f","schema_version":"1.0","event_id":"sha256:74d649b3b09c645ecf689189fd298f788d373da718eb3b28692e4b36f519b45f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SHDUJOKE5S6N2XCB24JAP4XMR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of transition fronts in nonlocal dispersal evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenxian Shen, Zhongwei Shen","submitted_at":"2015-04-10T00:53:45Z","abstract_excerpt":"It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, we establish some general criteria concerning space regularity of transition fronts in nonlocal dispersal evolution equations with a large class of nonlinearities, which allows the applicability of various techniques for reaction-diffusion equations to nonlocal equation, and hence serves as an initial and fundamental step for further studyin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02525","kind":"arxiv","version":3},"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":"2026-05-18T01:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTLkJHDFb1ymSURAeUvSVf7H/AA/6G3UxN35nIvw8x9wdMl2MdtJc3uiPSA4nOybPEHpVYv980PYL1Tn5n4XAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:25.986990Z"},"content_sha256":"b392b105f07ccc7b544a7037114cb47f3e7da43a8f70afb2dc4c26d5619a3d7a","schema_version":"1.0","event_id":"sha256:b392b105f07ccc7b544a7037114cb47f3e7da43a8f70afb2dc4c26d5619a3d7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHDUJOKE5S6N2XCB24JAP4XMR3/bundle.json","state_url":"https://pith.science/pith/SHDUJOKE5S6N2XCB24JAP4XMR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHDUJOKE5S6N2XCB24JAP4XMR3/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":"2026-06-01T19:40:25Z","links":{"resolver":"https://pith.science/pith/SHDUJOKE5S6N2XCB24JAP4XMR3","bundle":"https://pith.science/pith/SHDUJOKE5S6N2XCB24JAP4XMR3/bundle.json","state":"https://pith.science/pith/SHDUJOKE5S6N2XCB24JAP4XMR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHDUJOKE5S6N2XCB24JAP4XMR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SHDUJOKE5S6N2XCB24JAP4XMR3","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":"05a5085c63da34ca92c22aac2f6800f46139f93b62b5cbf7d563f88e684f4f10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T00:53:45Z","title_canon_sha256":"42cd820d028dde46955d1f320745ed521c67319e89c17fc1b111a8a95f6fe29a"},"schema_version":"1.0","source":{"id":"1504.02525","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02525","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02525v3","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02525","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"SHDUJOKE5S6N","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SHDUJOKE5S6N2XCB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SHDUJOKE","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:b392b105f07ccc7b544a7037114cb47f3e7da43a8f70afb2dc4c26d5619a3d7a","target":"graph","created_at":"2026-05-18T01:27:07Z","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":"It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, we establish some general criteria concerning space regularity of transition fronts in nonlocal dispersal evolution equations with a large class of nonlinearities, which allows the applicability of various techniques for reaction-diffusion equations to nonlocal equation, and hence serves as an initial and fundamental step for further studyin","authors_text":"Wenxian Shen, Zhongwei Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T00:53:45Z","title":"Regularity of transition fronts in nonlocal dispersal evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02525","kind":"arxiv","version":3},"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":"sha256:74d649b3b09c645ecf689189fd298f788d373da718eb3b28692e4b36f519b45f","target":"record","created_at":"2026-05-18T01:27:07Z","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":"05a5085c63da34ca92c22aac2f6800f46139f93b62b5cbf7d563f88e684f4f10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T00:53:45Z","title_canon_sha256":"42cd820d028dde46955d1f320745ed521c67319e89c17fc1b111a8a95f6fe29a"},"schema_version":"1.0","source":{"id":"1504.02525","kind":"arxiv","version":3}},"canonical_sha256":"91c744b944ecbcdd5c41d71207f2ec8ec6406faef1c97e927f203223fb2b8770","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91c744b944ecbcdd5c41d71207f2ec8ec6406faef1c97e927f203223fb2b8770","first_computed_at":"2026-05-18T01:27:07.776227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:07.776227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PaSU32H9blpgN3yEpHcQRGt7pKerg6Dn6N90ckYey0B3ZA7huB/bs3NiMV+geHqC6is43KorlhHNvKmrPJfRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:07.776950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02525","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74d649b3b09c645ecf689189fd298f788d373da718eb3b28692e4b36f519b45f","sha256:b392b105f07ccc7b544a7037114cb47f3e7da43a8f70afb2dc4c26d5619a3d7a"],"state_sha256":"e8d75a49b4b5529660f3460fe35ecfa8d9929b5b8564c065f6912d63d42db006"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BnujNeUc9QfUe2XJ8LyTWlkte0el3QuUaY5N2ieMtGzmXlX3JcM9NqQCxEOO7sVMDgnP8Q7+aCWd925YJODyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:40:25.988939Z","bundle_sha256":"02e5b7f0ddd6c07c6027d8b70c2a51b41c899bf445d418c160e22f9a6a4cc050"}}