{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SI2XQF3BGQA5SPBII3FSSC3G4L","short_pith_number":"pith:SI2XQF3B","canonical_record":{"source":{"id":"1309.4753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-18T19:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"82b8f78fe4aae23ade4937ea3e1405cae0a951d67e81ffca4a7fe062989e377c","abstract_canon_sha256":"4454734ccbfc4a97416288eaf3cbf2ee77c5a79b0f427dc6505bd545a6d714cd"},"schema_version":"1.0"},"canonical_sha256":"92357817613401d93c2846cb290b66e2f8cacb86fe4fd285ff990f5cdd859ced","source":{"kind":"arxiv","id":"1309.4753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4753","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4753v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4753","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"SI2XQF3BGQA5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SI2XQF3BGQA5SPBI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SI2XQF3B","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SI2XQF3BGQA5SPBII3FSSC3G4L","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-18T19:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"82b8f78fe4aae23ade4937ea3e1405cae0a951d67e81ffca4a7fe062989e377c","abstract_canon_sha256":"4454734ccbfc4a97416288eaf3cbf2ee77c5a79b0f427dc6505bd545a6d714cd"},"schema_version":"1.0"},"canonical_sha256":"92357817613401d93c2846cb290b66e2f8cacb86fe4fd285ff990f5cdd859ced","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.422567Z","signature_b64":"B+VMK3VKJFsdFzacam5xd4Qa8xPP/O0M8kegt+i4q/xg3Mi9KDAtsa4ApngD0YOHpv15IEyv0WIgDW47K7SDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92357817613401d93c2846cb290b66e2f8cacb86fe4fd285ff990f5cdd859ced","last_reissued_at":"2026-05-18T03:12:58.421896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.421896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4753","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvgCwxpNB9jyYu2x9voVv6nwCivwSQxXAfCridtMhQVCCz8IWj0xnhd+ReBzKeWq9dfQOByBvG7k9nMWEFNeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:15:02.509962Z"},"content_sha256":"b4a94cc7d0b8cfc79ded9e5a04b49a8143b6d4a808b4513a4ef75c98fad2e105","schema_version":"1.0","event_id":"sha256:b4a94cc7d0b8cfc79ded9e5a04b49a8143b6d4a808b4513a4ef75c98fad2e105"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SI2XQF3BGQA5SPBII3FSSC3G4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wenxian Shen, Xiaoxia Xie","submitted_at":"2013-09-18T19:16:52Z","abstract_excerpt":"This paper is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the dispersal rate, and the dispersal distance on the existence of the principal eigenvalues, the magnitude of the principal spectrum points, and the asymptotic behavior of the principal spectrum points of nonlocal dispersal operators with Dirichlet type, Neumann type, and periodic boundary conditions in a unified way. We also discuss the applications of the princ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4753","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ybMqu+ZZjHorna5FIeE9TwM0ok119iC5vlqU2hKbRNpgjlZLB3vOLoQzuewevMZ0nb0BQ+1OMSh2a+WIFqYqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:15:02.510333Z"},"content_sha256":"e5f9321d383fa2ac5e8281f3120f822392bdea9572885c464dc89f0efb0c0c2e","schema_version":"1.0","event_id":"sha256:e5f9321d383fa2ac5e8281f3120f822392bdea9572885c464dc89f0efb0c0c2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SI2XQF3BGQA5SPBII3FSSC3G4L/bundle.json","state_url":"https://pith.science/pith/SI2XQF3BGQA5SPBII3FSSC3G4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SI2XQF3BGQA5SPBII3FSSC3G4L/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":"2026-06-01T04:15:02Z","links":{"resolver":"https://pith.science/pith/SI2XQF3BGQA5SPBII3FSSC3G4L","bundle":"https://pith.science/pith/SI2XQF3BGQA5SPBII3FSSC3G4L/bundle.json","state":"https://pith.science/pith/SI2XQF3BGQA5SPBII3FSSC3G4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SI2XQF3BGQA5SPBII3FSSC3G4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SI2XQF3BGQA5SPBII3FSSC3G4L","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":"4454734ccbfc4a97416288eaf3cbf2ee77c5a79b0f427dc6505bd545a6d714cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-18T19:16:52Z","title_canon_sha256":"82b8f78fe4aae23ade4937ea3e1405cae0a951d67e81ffca4a7fe062989e377c"},"schema_version":"1.0","source":{"id":"1309.4753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4753","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4753v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4753","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"SI2XQF3BGQA5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SI2XQF3BGQA5SPBI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SI2XQF3B","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:e5f9321d383fa2ac5e8281f3120f822392bdea9572885c464dc89f0efb0c0c2e","target":"graph","created_at":"2026-05-18T03:12:58Z","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 is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the dispersal rate, and the dispersal distance on the existence of the principal eigenvalues, the magnitude of the principal spectrum points, and the asymptotic behavior of the principal spectrum points of nonlocal dispersal operators with Dirichlet type, Neumann type, and periodic boundary conditions in a unified way. We also discuss the applications of the princ","authors_text":"Wenxian Shen, Xiaoxia Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-18T19:16:52Z","title":"On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4753","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:b4a94cc7d0b8cfc79ded9e5a04b49a8143b6d4a808b4513a4ef75c98fad2e105","target":"record","created_at":"2026-05-18T03:12:58Z","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":"4454734ccbfc4a97416288eaf3cbf2ee77c5a79b0f427dc6505bd545a6d714cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-18T19:16:52Z","title_canon_sha256":"82b8f78fe4aae23ade4937ea3e1405cae0a951d67e81ffca4a7fe062989e377c"},"schema_version":"1.0","source":{"id":"1309.4753","kind":"arxiv","version":1}},"canonical_sha256":"92357817613401d93c2846cb290b66e2f8cacb86fe4fd285ff990f5cdd859ced","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92357817613401d93c2846cb290b66e2f8cacb86fe4fd285ff990f5cdd859ced","first_computed_at":"2026-05-18T03:12:58.421896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.421896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+VMK3VKJFsdFzacam5xd4Qa8xPP/O0M8kegt+i4q/xg3Mi9KDAtsa4ApngD0YOHpv15IEyv0WIgDW47K7SDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.422567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4a94cc7d0b8cfc79ded9e5a04b49a8143b6d4a808b4513a4ef75c98fad2e105","sha256:e5f9321d383fa2ac5e8281f3120f822392bdea9572885c464dc89f0efb0c0c2e"],"state_sha256":"377d8d8558ce0fd05ae687e5e6762ff4e860a47f4451a078a14e3c69715c3983"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"11eRQPDkDIYle4WQVftuKeTehc7DtaewIYRsz9ptjJKecJbYNB1kP8MBRBJJymEGHXoYcSBlKJ2KQcIlRVo9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:15:02.512329Z","bundle_sha256":"f31d8741be63fa5cb21af7d03085cf508484e0dd94b6e78b854125a92c0ade9d"}}