{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:77MKQ4QR4R3A3OUWA2JETCKVN6","short_pith_number":"pith:77MKQ4QR","schema_version":"1.0","canonical_sha256":"ffd8a87211e4760dba9606924989556faae306fb6d261893b32494f654b51b9a","source":{"kind":"arxiv","id":"1411.1831","version":1},"attestation_state":"computed","paper":{"title":"Optimal Venttsel Boundary Control of Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yousong Luo","submitted_at":"2014-11-07T05:22:08Z","abstract_excerpt":"In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is applied to the system via the Venttsel boundary condition. A first order necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained problem."},"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":"1411.1831","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-07T05:22:08Z","cross_cats_sorted":[],"title_canon_sha256":"d0981236df42b8b29b1425514deda668ff321388c9068cbeeaa3bccbde2a3ad6","abstract_canon_sha256":"87dfa41dc497d28144bafcc7355db8622e13c20373f5ba1b9f4dbe6e8d26d6ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:25.867091Z","signature_b64":"rG6nhK/6kKUPscZ3PGG59vsjUxqG4McTJ4QixmvYNAoLda+rs9LvKVtVKWb1TEdLAvobm4RtpU3pQSjkryOYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffd8a87211e4760dba9606924989556faae306fb6d261893b32494f654b51b9a","last_reissued_at":"2026-05-18T02:38:25.866487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:25.866487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Venttsel Boundary Control of Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yousong Luo","submitted_at":"2014-11-07T05:22:08Z","abstract_excerpt":"In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is applied to the system via the Venttsel boundary condition. A first order necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1831","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":"1411.1831","created_at":"2026-05-18T02:38:25.866581+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1831v1","created_at":"2026-05-18T02:38:25.866581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1831","created_at":"2026-05-18T02:38:25.866581+00:00"},{"alias_kind":"pith_short_12","alias_value":"77MKQ4QR4R3A","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"77MKQ4QR4R3A3OUW","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"77MKQ4QR","created_at":"2026-05-18T12:28:16.859392+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/77MKQ4QR4R3A3OUWA2JETCKVN6","json":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6.json","graph_json":"https://pith.science/api/pith-number/77MKQ4QR4R3A3OUWA2JETCKVN6/graph.json","events_json":"https://pith.science/api/pith-number/77MKQ4QR4R3A3OUWA2JETCKVN6/events.json","paper":"https://pith.science/paper/77MKQ4QR"},"agent_actions":{"view_html":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6","download_json":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6.json","view_paper":"https://pith.science/paper/77MKQ4QR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1831&json=true","fetch_graph":"https://pith.science/api/pith-number/77MKQ4QR4R3A3OUWA2JETCKVN6/graph.json","fetch_events":"https://pith.science/api/pith-number/77MKQ4QR4R3A3OUWA2JETCKVN6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6/action/storage_attestation","attest_author":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6/action/author_attestation","sign_citation":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6/action/citation_signature","submit_replication":"https://pith.science/pith/77MKQ4QR4R3A3OUWA2JETCKVN6/action/replication_record"}},"created_at":"2026-05-18T02:38:25.866581+00:00","updated_at":"2026-05-18T02:38:25.866581+00:00"}