{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DPBIJLBLJUQKU7N3V2LFYYZ7TG","short_pith_number":"pith:DPBIJLBL","schema_version":"1.0","canonical_sha256":"1bc284ac2b4d20aa7dbbae965c633f99b2dfcdce08a4dc8319199c2a2d364ff3","source":{"kind":"arxiv","id":"1903.07412","version":2},"attestation_state":"computed","paper":{"title":"On the Non-Linear Integral Equation Approach for an Inverse Boundary Value Problem for the Heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Leonidas Mindrinos, Roman Chapko","submitted_at":"2019-03-18T13:07:02Z","abstract_excerpt":"We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time leads to a sequence of stationary inverse problems. Then, the application of the modified single-layer ansatz, reduces the problem to a sequence of systems of non-linear boundary integral equations. An iterative algorithm is developed for the numerical solution of the obtained integral equations. We find the Fr\\'echet derivative of the corresponding integral"},"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":"1903.07412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-18T13:07:02Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"101db1e78b109c2ff3de6ac4cc0f246f45996532b928e4e3d7f98dafb59c9422","abstract_canon_sha256":"bc4a8606cf3b8df9686472f8938b48388c8dd93408cf9c6a6e44aa73614f9100"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:14:14.987175Z","signature_b64":"EHs9O6mtZemHFiSfcE6wffbZisjtUOJdr1cLWj9eomB30Wjr6OhRsB/cdXL9cTo+t35a6b8GALuFA0A2fbMZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bc284ac2b4d20aa7dbbae965c633f99b2dfcdce08a4dc8319199c2a2d364ff3","last_reissued_at":"2026-06-04T20:14:14.986626Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:14:14.986626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Non-Linear Integral Equation Approach for an Inverse Boundary Value Problem for the Heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Leonidas Mindrinos, Roman Chapko","submitted_at":"2019-03-18T13:07:02Z","abstract_excerpt":"We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time leads to a sequence of stationary inverse problems. Then, the application of the modified single-layer ansatz, reduces the problem to a sequence of systems of non-linear boundary integral equations. An iterative algorithm is developed for the numerical solution of the obtained integral equations. We find the Fr\\'echet derivative of the corresponding integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07412","kind":"arxiv","version":2},"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/1903.07412/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":"1903.07412","created_at":"2026-06-04T20:14:14.986721+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.07412v2","created_at":"2026-06-04T20:14:14.986721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07412","created_at":"2026-06-04T20:14:14.986721+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPBIJLBLJUQK","created_at":"2026-06-04T20:14:14.986721+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPBIJLBLJUQKU7N3","created_at":"2026-06-04T20:14:14.986721+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPBIJLBL","created_at":"2026-06-04T20:14:14.986721+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/DPBIJLBLJUQKU7N3V2LFYYZ7TG","json":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG.json","graph_json":"https://pith.science/api/pith-number/DPBIJLBLJUQKU7N3V2LFYYZ7TG/graph.json","events_json":"https://pith.science/api/pith-number/DPBIJLBLJUQKU7N3V2LFYYZ7TG/events.json","paper":"https://pith.science/paper/DPBIJLBL"},"agent_actions":{"view_html":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG","download_json":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG.json","view_paper":"https://pith.science/paper/DPBIJLBL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.07412&json=true","fetch_graph":"https://pith.science/api/pith-number/DPBIJLBLJUQKU7N3V2LFYYZ7TG/graph.json","fetch_events":"https://pith.science/api/pith-number/DPBIJLBLJUQKU7N3V2LFYYZ7TG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG/action/storage_attestation","attest_author":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG/action/author_attestation","sign_citation":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG/action/citation_signature","submit_replication":"https://pith.science/pith/DPBIJLBLJUQKU7N3V2LFYYZ7TG/action/replication_record"}},"created_at":"2026-06-04T20:14:14.986721+00:00","updated_at":"2026-06-04T20:14:14.986721+00:00"}