{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:APVG7VOYYBJIPCUTU43QKRLDM6","short_pith_number":"pith:APVG7VOY","schema_version":"1.0","canonical_sha256":"03ea6fd5d8c052878a93a737054563678bd023caf11268a0d5f2a72562520b10","source":{"kind":"arxiv","id":"1611.09955","version":1},"attestation_state":"computed","paper":{"title":"Inverse problems for parabolic equations 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.G.Ramm","submitted_at":"2016-11-30T00:41:15Z","abstract_excerpt":"Let $u_t-a(t)u_{xx}=f(x, t)$ in $0\\leq x \\leq \\pi,\\,\\,t\\geq 0.$ Assume that $u(0,t)=u_1(t)$, $u(\\pi,t)=u_2(t)$, $u(x,0)=h(x)$, and the extra data $u_x(0,t)=g(t)$ are known. The inverse problem is: {\\it\n  How does one determine the unknown $a(t)$?}\n  The function $a(t)>a_0>0$ is assumed continuous and bounded. This question is answered and a method for recovery of $a(t)$ is proposed. There are several papers in which sufficient conditions are given for the uniqueness and existence of $a(t)$, but apparently there was no method proposed for calculating of $a$. The method given in this paper for p"},"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":"1611.09955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-30T00:41:15Z","cross_cats_sorted":[],"title_canon_sha256":"ff2f30d5c12a3b08d18e8a97360691c7520746622b6b9c05f501a57f2858b5ec","abstract_canon_sha256":"bf8e5f9c15baba0bc1dc9158aaabfb36f05faa294efe450c8f5bafbb8388a4de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:11.544755Z","signature_b64":"pMtWFl8/kwMtbxCwiGg1Nsmhd7N9mg6PyIaWQgKPhlCHQW+3knCjwTW7nOtsJhMLchs0TXBFpnSgQcLePTkuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03ea6fd5d8c052878a93a737054563678bd023caf11268a0d5f2a72562520b10","last_reissued_at":"2026-05-18T00:56:11.544343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:11.544343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse problems for parabolic equations 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.G.Ramm","submitted_at":"2016-11-30T00:41:15Z","abstract_excerpt":"Let $u_t-a(t)u_{xx}=f(x, t)$ in $0\\leq x \\leq \\pi,\\,\\,t\\geq 0.$ Assume that $u(0,t)=u_1(t)$, $u(\\pi,t)=u_2(t)$, $u(x,0)=h(x)$, and the extra data $u_x(0,t)=g(t)$ are known. The inverse problem is: {\\it\n  How does one determine the unknown $a(t)$?}\n  The function $a(t)>a_0>0$ is assumed continuous and bounded. This question is answered and a method for recovery of $a(t)$ is proposed. There are several papers in which sufficient conditions are given for the uniqueness and existence of $a(t)$, but apparently there was no method proposed for calculating of $a$. The method given in this paper for p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09955","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":"1611.09955","created_at":"2026-05-18T00:56:11.544403+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.09955v1","created_at":"2026-05-18T00:56:11.544403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09955","created_at":"2026-05-18T00:56:11.544403+00:00"},{"alias_kind":"pith_short_12","alias_value":"APVG7VOYYBJI","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"APVG7VOYYBJIPCUT","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"APVG7VOY","created_at":"2026-05-18T12:30:07.202191+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/APVG7VOYYBJIPCUTU43QKRLDM6","json":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6.json","graph_json":"https://pith.science/api/pith-number/APVG7VOYYBJIPCUTU43QKRLDM6/graph.json","events_json":"https://pith.science/api/pith-number/APVG7VOYYBJIPCUTU43QKRLDM6/events.json","paper":"https://pith.science/paper/APVG7VOY"},"agent_actions":{"view_html":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6","download_json":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6.json","view_paper":"https://pith.science/paper/APVG7VOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.09955&json=true","fetch_graph":"https://pith.science/api/pith-number/APVG7VOYYBJIPCUTU43QKRLDM6/graph.json","fetch_events":"https://pith.science/api/pith-number/APVG7VOYYBJIPCUTU43QKRLDM6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6/action/storage_attestation","attest_author":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6/action/author_attestation","sign_citation":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6/action/citation_signature","submit_replication":"https://pith.science/pith/APVG7VOYYBJIPCUTU43QKRLDM6/action/replication_record"}},"created_at":"2026-05-18T00:56:11.544403+00:00","updated_at":"2026-05-18T00:56:11.544403+00:00"}