{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2H5QNRR2BEF7T6K4TXQTSMQQLH","short_pith_number":"pith:2H5QNRR2","schema_version":"1.0","canonical_sha256":"d1fb06c63a090bf9f95c9de139321059cf2d89dc6fafc466961f7523b3c82628","source":{"kind":"arxiv","id":"1905.12232","version":1},"attestation_state":"computed","paper":{"title":"Recovery of multiple coefficients in a reaction-diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Barbara Kaltenbacher, William Rundell","submitted_at":"2019-05-29T06:09:54Z","abstract_excerpt":"This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a later time $T$. We show both uniqueness results and the convergence of an iteration scheme designed to recover these coefficients. We also allow a more general setting, in particular when the usual time derivative is replaced by one of fractional order and when the potential term is coupled with a known nonlinearity $f$ of the form $q(x)f(u)$."},"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":"1905.12232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-29T06:09:54Z","cross_cats_sorted":[],"title_canon_sha256":"6d19694c837a56ef2a52ea324d67fe341c131eec12ff1d6daa361823dca49c7d","abstract_canon_sha256":"3be5b40a6a058a7f0c6ea1e61124217bf2f19ad0d8692ed9f5ac379fcdd33f87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:44.939819Z","signature_b64":"JZuXv/uM/4daTkuflSkNsei9RXnSQMEq461LF+K1Y7NTHqJQATZ/ZAoFJ/rC5b+6Lqsy/FkouUyz7sZAEjnlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1fb06c63a090bf9f95c9de139321059cf2d89dc6fafc466961f7523b3c82628","last_reissued_at":"2026-05-17T23:44:44.939347Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:44.939347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recovery of multiple coefficients in a reaction-diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Barbara Kaltenbacher, William Rundell","submitted_at":"2019-05-29T06:09:54Z","abstract_excerpt":"This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a later time $T$. We show both uniqueness results and the convergence of an iteration scheme designed to recover these coefficients. We also allow a more general setting, in particular when the usual time derivative is replaced by one of fractional order and when the potential term is coupled with a known nonlinearity $f$ of the form $q(x)f(u)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12232","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.12232","created_at":"2026-05-17T23:44:44.939418+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12232v1","created_at":"2026-05-17T23:44:44.939418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12232","created_at":"2026-05-17T23:44:44.939418+00:00"},{"alias_kind":"pith_short_12","alias_value":"2H5QNRR2BEF7","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"2H5QNRR2BEF7T6K4","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"2H5QNRR2","created_at":"2026-05-18T12:33:07.085635+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/2H5QNRR2BEF7T6K4TXQTSMQQLH","json":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH.json","graph_json":"https://pith.science/api/pith-number/2H5QNRR2BEF7T6K4TXQTSMQQLH/graph.json","events_json":"https://pith.science/api/pith-number/2H5QNRR2BEF7T6K4TXQTSMQQLH/events.json","paper":"https://pith.science/paper/2H5QNRR2"},"agent_actions":{"view_html":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH","download_json":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH.json","view_paper":"https://pith.science/paper/2H5QNRR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12232&json=true","fetch_graph":"https://pith.science/api/pith-number/2H5QNRR2BEF7T6K4TXQTSMQQLH/graph.json","fetch_events":"https://pith.science/api/pith-number/2H5QNRR2BEF7T6K4TXQTSMQQLH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH/action/storage_attestation","attest_author":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH/action/author_attestation","sign_citation":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH/action/citation_signature","submit_replication":"https://pith.science/pith/2H5QNRR2BEF7T6K4TXQTSMQQLH/action/replication_record"}},"created_at":"2026-05-17T23:44:44.939418+00:00","updated_at":"2026-05-17T23:44:44.939418+00:00"}