{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SF2EAUOSC4Q4Q6GAB4BG36ZE2Z","short_pith_number":"pith:SF2EAUOS","canonical_record":{"source":{"id":"1501.02029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-09T03:44:53Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"172f64627070af91829a98bb3fe2593a8a91d50d2e2d41d3ca363f67a7af1127","abstract_canon_sha256":"700a6593394efd1e6392278dabeae18347201e6480241c41e70add043bbd5850"},"schema_version":"1.0"},"canonical_sha256":"91744051d21721c878c00f026dfb24d64cdb4a9639a2931ed9591ddd173e4dc5","source":{"kind":"arxiv","id":"1501.02029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02029","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02029v1","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02029","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"SF2EAUOSC4Q4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SF2EAUOSC4Q4Q6GA","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SF2EAUOS","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SF2EAUOSC4Q4Q6GAB4BG36ZE2Z","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-09T03:44:53Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"172f64627070af91829a98bb3fe2593a8a91d50d2e2d41d3ca363f67a7af1127","abstract_canon_sha256":"700a6593394efd1e6392278dabeae18347201e6480241c41e70add043bbd5850"},"schema_version":"1.0"},"canonical_sha256":"91744051d21721c878c00f026dfb24d64cdb4a9639a2931ed9591ddd173e4dc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.012814Z","signature_b64":"IA2m+nooy4LVFyUHML5qL1wkzlv1dlxiiCXpcw1MSnCBEEXBpU6mykW6bGpC5IB9aUTepP+SBLh2BqiV8L9ZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91744051d21721c878c00f026dfb24d64cdb4a9639a2931ed9591ddd173e4dc5","last_reissued_at":"2026-05-18T02:29:45.012363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.012363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02029","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":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gF4owS9lnKed3O1wFJrYcR2YYN3kC2ivMTsCkPz4SBgxNjGDnSVvnn57EkYjz1HWDzzlUZST0v5SHxRCv1+0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:51:08.022373Z"},"content_sha256":"236b8b302542980f9c873d8a37375a14bd5b5424e4856c350cbad1bf6f5f4b29","schema_version":"1.0","event_id":"sha256:236b8b302542980f9c873d8a37375a14bd5b5424e4856c350cbad1bf6f5f4b29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SF2EAUOSC4Q4Q6GAB4BG36ZE2Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Wenxian Shen, Zhongwei Shen","submitted_at":"2015-01-09T03:44:53Z","abstract_excerpt":"The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a previous work. It is first shown that the transition front is continuously differentiable in space with uniformly bounded and uniformly Lipschitz continuous space partial derivative. This is the first time that regularity of transition fronts in nonlocal equations is ever studied. It is then shown that the transition front is uniformly steep. Finally, asymptotic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02029","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":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOWL+cl8/sw1pIEvTuXS0gPbUus9Va+/ewPl2Y6Hc9FRDnYhEX6IgbCtPuBbMRXiYBxFpyxXr2v6xFNqWqaWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:51:08.023085Z"},"content_sha256":"0a971e4ceee5eebbd7eb3cae8561799051831f7053691a82f6e782299d015540","schema_version":"1.0","event_id":"sha256:0a971e4ceee5eebbd7eb3cae8561799051831f7053691a82f6e782299d015540"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z/bundle.json","state_url":"https://pith.science/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z/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":"2026-05-31T17:51:08Z","links":{"resolver":"https://pith.science/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z","bundle":"https://pith.science/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z/bundle.json","state":"https://pith.science/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SF2EAUOSC4Q4Q6GAB4BG36ZE2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SF2EAUOSC4Q4Q6GAB4BG36ZE2Z","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":"700a6593394efd1e6392278dabeae18347201e6480241c41e70add043bbd5850","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-09T03:44:53Z","title_canon_sha256":"172f64627070af91829a98bb3fe2593a8a91d50d2e2d41d3ca363f67a7af1127"},"schema_version":"1.0","source":{"id":"1501.02029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02029","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02029v1","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02029","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"SF2EAUOSC4Q4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SF2EAUOSC4Q4Q6GA","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SF2EAUOS","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:0a971e4ceee5eebbd7eb3cae8561799051831f7053691a82f6e782299d015540","target":"graph","created_at":"2026-05-18T02:29:45Z","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":"The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a previous work. It is first shown that the transition front is continuously differentiable in space with uniformly bounded and uniformly Lipschitz continuous space partial derivative. This is the first time that regularity of transition fronts in nonlocal equations is ever studied. It is then shown that the transition front is uniformly steep. Finally, asymptotic s","authors_text":"Wenxian Shen, Zhongwei Shen","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-09T03:44:53Z","title":"Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02029","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":"sha256:236b8b302542980f9c873d8a37375a14bd5b5424e4856c350cbad1bf6f5f4b29","target":"record","created_at":"2026-05-18T02:29:45Z","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":"700a6593394efd1e6392278dabeae18347201e6480241c41e70add043bbd5850","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-09T03:44:53Z","title_canon_sha256":"172f64627070af91829a98bb3fe2593a8a91d50d2e2d41d3ca363f67a7af1127"},"schema_version":"1.0","source":{"id":"1501.02029","kind":"arxiv","version":1}},"canonical_sha256":"91744051d21721c878c00f026dfb24d64cdb4a9639a2931ed9591ddd173e4dc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91744051d21721c878c00f026dfb24d64cdb4a9639a2931ed9591ddd173e4dc5","first_computed_at":"2026-05-18T02:29:45.012363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:45.012363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IA2m+nooy4LVFyUHML5qL1wkzlv1dlxiiCXpcw1MSnCBEEXBpU6mykW6bGpC5IB9aUTepP+SBLh2BqiV8L9ZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:45.012814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:236b8b302542980f9c873d8a37375a14bd5b5424e4856c350cbad1bf6f5f4b29","sha256:0a971e4ceee5eebbd7eb3cae8561799051831f7053691a82f6e782299d015540"],"state_sha256":"fc6dfbec296e90e5346bffc57806fb4a3dc484cbbc3ed7a5459de173145b5626"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlgBd6ViQcWKclKSMxkNmTHte8KyzpLoSuYUy2H0tc6QThOw/76KQ6y/Ye/PsLW85FQhtehCMme6xgFWSu2sDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:51:08.026552Z","bundle_sha256":"d6bc0f197899092f9ddd22ee8b47fc41426221b9b06be2afa1831f253f95ca0a"}}