{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:44TGSBGJF6FV6FSWFQED5H3RRB","short_pith_number":"pith:44TGSBGJ","canonical_record":{"source":{"id":"1806.03442","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-09T08:43:36Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"63ea8020f911a99863ed43ae99ed6c9e7ce725f14fe0b995a437d3194d35694f","abstract_canon_sha256":"688ed3ce75e005f9828dd3cf16baba0ef7f3b4da36a856d8abf002b0aa199ff7"},"schema_version":"1.0"},"canonical_sha256":"e7266904c92f8b5f16562c083e9f71884cfc472791d595636f0524bf7f7c8dd5","source":{"kind":"arxiv","id":"1806.03442","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03442","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03442v1","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03442","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"44TGSBGJF6FV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"44TGSBGJF6FV6FSW","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"44TGSBGJ","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:44TGSBGJF6FV6FSWFQED5H3RRB","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03442","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-09T08:43:36Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"63ea8020f911a99863ed43ae99ed6c9e7ce725f14fe0b995a437d3194d35694f","abstract_canon_sha256":"688ed3ce75e005f9828dd3cf16baba0ef7f3b4da36a856d8abf002b0aa199ff7"},"schema_version":"1.0"},"canonical_sha256":"e7266904c92f8b5f16562c083e9f71884cfc472791d595636f0524bf7f7c8dd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:43.379451Z","signature_b64":"+SpIvYPOUwIxwD/sdG1eQoTRvLXAadp/SaIb0wWGMzCsD0ciKzK10HRxIqbk3RnU8z87TxYbPk8Ncj9tWgEZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7266904c92f8b5f16562c083e9f71884cfc472791d595636f0524bf7f7c8dd5","last_reissued_at":"2026-05-18T00:13:43.378969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:43.378969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03442","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":"2026-05-18T00:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f6iqRVW6vNyoL64WNV2Z8cNyZows2RHOrO76bWvczG3e1ZTtqJIpHGKH4jHouI6YwH+j74stUIya2RZAnssJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:48.224468Z"},"content_sha256":"ad8e61573ce564debe6913ce0cb42e367d4f5df18f61e0e0b9b2e07b2f0913ca","schema_version":"1.0","event_id":"sha256:ad8e61573ce564debe6913ce0cb42e367d4f5df18f61e0e0b9b2e07b2f0913ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:44TGSBGJF6FV6FSWFQED5H3RRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness result for an age-dependent reaction-diffusion problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Daniel Lesnic, Tran The Hung, Vo Anh Khoa","submitted_at":"2018-06-09T08:43:36Z","abstract_excerpt":"This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two population densities obey the same evolution equation and possess the same terminal data of time and age, then their distributions must coincide therein."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03442","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":"2026-05-18T00:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3u9OnxTxn8VLEyDmG2xtSS4zUwK4n+YU76UYDm/6k9D6+Xtrmwc1QoT1PVOgdQfq795BGFqLG0tJy+5yJNoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:48.224860Z"},"content_sha256":"557281c19986bbdb8add58a371c60cd4c1c1243f16ed853bf04ccadb1de8f6ea","schema_version":"1.0","event_id":"sha256:557281c19986bbdb8add58a371c60cd4c1c1243f16ed853bf04ccadb1de8f6ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/44TGSBGJF6FV6FSWFQED5H3RRB/bundle.json","state_url":"https://pith.science/pith/44TGSBGJF6FV6FSWFQED5H3RRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/44TGSBGJF6FV6FSWFQED5H3RRB/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":"2026-05-31T08:38:48Z","links":{"resolver":"https://pith.science/pith/44TGSBGJF6FV6FSWFQED5H3RRB","bundle":"https://pith.science/pith/44TGSBGJF6FV6FSWFQED5H3RRB/bundle.json","state":"https://pith.science/pith/44TGSBGJF6FV6FSWFQED5H3RRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/44TGSBGJF6FV6FSWFQED5H3RRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:44TGSBGJF6FV6FSWFQED5H3RRB","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":"688ed3ce75e005f9828dd3cf16baba0ef7f3b4da36a856d8abf002b0aa199ff7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-09T08:43:36Z","title_canon_sha256":"63ea8020f911a99863ed43ae99ed6c9e7ce725f14fe0b995a437d3194d35694f"},"schema_version":"1.0","source":{"id":"1806.03442","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03442","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03442v1","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03442","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"44TGSBGJF6FV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"44TGSBGJF6FV6FSW","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"44TGSBGJ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:557281c19986bbdb8add58a371c60cd4c1c1243f16ed853bf04ccadb1de8f6ea","target":"graph","created_at":"2026-05-18T00:13:43Z","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 concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two population densities obey the same evolution equation and possess the same terminal data of time and age, then their distributions must coincide therein.","authors_text":"Daniel Lesnic, Tran The Hung, Vo Anh Khoa","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-09T08:43:36Z","title":"Uniqueness result for an age-dependent reaction-diffusion problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03442","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:ad8e61573ce564debe6913ce0cb42e367d4f5df18f61e0e0b9b2e07b2f0913ca","target":"record","created_at":"2026-05-18T00:13:43Z","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":"688ed3ce75e005f9828dd3cf16baba0ef7f3b4da36a856d8abf002b0aa199ff7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-09T08:43:36Z","title_canon_sha256":"63ea8020f911a99863ed43ae99ed6c9e7ce725f14fe0b995a437d3194d35694f"},"schema_version":"1.0","source":{"id":"1806.03442","kind":"arxiv","version":1}},"canonical_sha256":"e7266904c92f8b5f16562c083e9f71884cfc472791d595636f0524bf7f7c8dd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7266904c92f8b5f16562c083e9f71884cfc472791d595636f0524bf7f7c8dd5","first_computed_at":"2026-05-18T00:13:43.378969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:43.378969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+SpIvYPOUwIxwD/sdG1eQoTRvLXAadp/SaIb0wWGMzCsD0ciKzK10HRxIqbk3RnU8z87TxYbPk8Ncj9tWgEZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:43.379451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03442","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad8e61573ce564debe6913ce0cb42e367d4f5df18f61e0e0b9b2e07b2f0913ca","sha256:557281c19986bbdb8add58a371c60cd4c1c1243f16ed853bf04ccadb1de8f6ea"],"state_sha256":"54cca8cb04116f5e2f1329b372179029ca51e2bc93cdef0a1cb92bf9dcf589d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4BXeDXjlMB4SggMeHN/XRtkp2H4PbjR+RhAGnfldq/1uCYvEdA2GfiaL/V0iIq/hDxPNa1U6RmewFKkhXikcDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:48.227666Z","bundle_sha256":"09e3c9bb92d36d29ed5a963d84ac5fc7c2afb606940ee2c55bf3dd8973ee1512"}}