{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:A6FFGF2EVH5CJOQMP7UPBE5ZAL","short_pith_number":"pith:A6FFGF2E","schema_version":"1.0","canonical_sha256":"078a531744a9fa24ba0c7fe8f093b902f37c9a3009e63a560617226443d4e67f","source":{"kind":"arxiv","id":"1308.3782","version":2},"attestation_state":"computed","paper":{"title":"Inverse boundary problems for polyharmonic operators with unbounded potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gunther Uhlmann, Katsiaryna Krupchyk","submitted_at":"2013-08-17T13:27:35Z","abstract_excerpt":"We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in $R^n$ for the perturbed polyharmonic operator $(-\\Delta)^m +q$ with $q\\in L^{n/2m}$, $n>2m$, determines the potential $q$ in the set uniquely. In the course of the proof, we construct a special Green function for the polyharmonic operator and establish its mapping properties in suitable weighted $L^2$ and $L^p$ spaces. The $L^p$ estimates for the special Green function are derived from $L^p$ Carleman estimates with linear weights for the polyharmonic operator."},"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":"1308.3782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-17T13:27:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4c75bd3e756084dce996aa72442d2a08ab13e54355fd3b7f6dbb00bfe49c57f3","abstract_canon_sha256":"69cadff90ebe5a0bad3d36a08b92d625e47956fa34077c2cde8fa4baef31033e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:02.210965Z","signature_b64":"aKmDRtYjaTCzVNVetgioux3doAZS6jUyf9g9hhJuHaslgQY4kNw89EmL7MVZRHgo60mWH5BnarybuZSR5V/zBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"078a531744a9fa24ba0c7fe8f093b902f37c9a3009e63a560617226443d4e67f","last_reissued_at":"2026-05-18T01:36:02.210281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:02.210281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse boundary problems for polyharmonic operators with unbounded potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gunther Uhlmann, Katsiaryna Krupchyk","submitted_at":"2013-08-17T13:27:35Z","abstract_excerpt":"We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in $R^n$ for the perturbed polyharmonic operator $(-\\Delta)^m +q$ with $q\\in L^{n/2m}$, $n>2m$, determines the potential $q$ in the set uniquely. In the course of the proof, we construct a special Green function for the polyharmonic operator and establish its mapping properties in suitable weighted $L^2$ and $L^p$ spaces. The $L^p$ estimates for the special Green function are derived from $L^p$ Carleman estimates with linear weights for the polyharmonic operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3782","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":""},"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":"1308.3782","created_at":"2026-05-18T01:36:02.210414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3782v2","created_at":"2026-05-18T01:36:02.210414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3782","created_at":"2026-05-18T01:36:02.210414+00:00"},{"alias_kind":"pith_short_12","alias_value":"A6FFGF2EVH5C","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"A6FFGF2EVH5CJOQM","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"A6FFGF2E","created_at":"2026-05-18T12:27:38.830355+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/A6FFGF2EVH5CJOQMP7UPBE5ZAL","json":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL.json","graph_json":"https://pith.science/api/pith-number/A6FFGF2EVH5CJOQMP7UPBE5ZAL/graph.json","events_json":"https://pith.science/api/pith-number/A6FFGF2EVH5CJOQMP7UPBE5ZAL/events.json","paper":"https://pith.science/paper/A6FFGF2E"},"agent_actions":{"view_html":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL","download_json":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL.json","view_paper":"https://pith.science/paper/A6FFGF2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3782&json=true","fetch_graph":"https://pith.science/api/pith-number/A6FFGF2EVH5CJOQMP7UPBE5ZAL/graph.json","fetch_events":"https://pith.science/api/pith-number/A6FFGF2EVH5CJOQMP7UPBE5ZAL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL/action/storage_attestation","attest_author":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL/action/author_attestation","sign_citation":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL/action/citation_signature","submit_replication":"https://pith.science/pith/A6FFGF2EVH5CJOQMP7UPBE5ZAL/action/replication_record"}},"created_at":"2026-05-18T01:36:02.210414+00:00","updated_at":"2026-05-18T01:36:02.210414+00:00"}