{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4IIIP5372YSKADNS5LXP4ITG2L","short_pith_number":"pith:4IIIP537","schema_version":"1.0","canonical_sha256":"e21087f77fd624a00db2eaeefe2266d2e309b1104e8163ce0ca3d55dd1f856c2","source":{"kind":"arxiv","id":"1905.12067","version":1},"attestation_state":"computed","paper":{"title":"On the identification of a nonlinear term in a reaction-diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Barbara Kaltenbacher, William Rundell","submitted_at":"2019-05-28T20:19:46Z","abstract_excerpt":"Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a driving force $f(u)$ that depends on the state variable $u$ and a diffusive mechanism that spreads this effect over a spatial domain. The canonical form is $u_t - \\triangle u = f(u)$. Application areas include chemical processes, heat flow models and population dynamics. The direct or forwards problem for such equations is now very well-developed and understood. However, our interest lies in the inverse problem of r"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.12067","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-28T20:19:46Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5178a6650747e9d4a532448e0bbb330df4194d460c5184afcd3e93ff4fb5157d","abstract_canon_sha256":"1cb21c3e12f5febe3f41fdfd698814535d70caf8ba9b77f95c124f11f28dab16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:14:33.652025Z","signature_b64":"Fo0mAn6Rn76bk/VB8o8uoKyr9sz6kPqeBbG1JR+im+knF9QXF/jPumMtQ2RjyeHXjpQOrmWyP63PYM19cOupDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e21087f77fd624a00db2eaeefe2266d2e309b1104e8163ce0ca3d55dd1f856c2","last_reissued_at":"2026-06-04T20:14:33.651530Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:14:33.651530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the identification of a nonlinear term in a reaction-diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Barbara Kaltenbacher, William Rundell","submitted_at":"2019-05-28T20:19:46Z","abstract_excerpt":"Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a driving force $f(u)$ that depends on the state variable $u$ and a diffusive mechanism that spreads this effect over a spatial domain. The canonical form is $u_t - \\triangle u = f(u)$. Application areas include chemical processes, heat flow models and population dynamics. The direct or forwards problem for such equations is now very well-developed and understood. However, our interest lies in the inverse problem of r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12067","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.12067/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.12067","created_at":"2026-06-04T20:14:33.651592+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12067v1","created_at":"2026-06-04T20:14:33.651592+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12067","created_at":"2026-06-04T20:14:33.651592+00:00"},{"alias_kind":"pith_short_12","alias_value":"4IIIP5372YSK","created_at":"2026-06-04T20:14:33.651592+00:00"},{"alias_kind":"pith_short_16","alias_value":"4IIIP5372YSKADNS","created_at":"2026-06-04T20:14:33.651592+00:00"},{"alias_kind":"pith_short_8","alias_value":"4IIIP537","created_at":"2026-06-04T20:14:33.651592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L","json":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L.json","graph_json":"https://pith.science/api/pith-number/4IIIP5372YSKADNS5LXP4ITG2L/graph.json","events_json":"https://pith.science/api/pith-number/4IIIP5372YSKADNS5LXP4ITG2L/events.json","paper":"https://pith.science/paper/4IIIP537"},"agent_actions":{"view_html":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L","download_json":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L.json","view_paper":"https://pith.science/paper/4IIIP537","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12067&json=true","fetch_graph":"https://pith.science/api/pith-number/4IIIP5372YSKADNS5LXP4ITG2L/graph.json","fetch_events":"https://pith.science/api/pith-number/4IIIP5372YSKADNS5LXP4ITG2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L/action/storage_attestation","attest_author":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L/action/author_attestation","sign_citation":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L/action/citation_signature","submit_replication":"https://pith.science/pith/4IIIP5372YSKADNS5LXP4ITG2L/action/replication_record"}},"created_at":"2026-06-04T20:14:33.651592+00:00","updated_at":"2026-06-04T20:14:33.651592+00:00"}