{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AJVR5ZNUVAYHW5ZMBTAEAKDB6W","short_pith_number":"pith:AJVR5ZNU","schema_version":"1.0","canonical_sha256":"026b1ee5b4a8307b772c0cc0402861f585e5c3026790ad30882de4a24bcb84ed","source":{"kind":"arxiv","id":"1210.1255","version":1},"attestation_state":"computed","paper":{"title":"Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G. Uhlmann, M. Yamamoto, O. Imanuvilov","submitted_at":"2012-10-03T22:46:44Z","abstract_excerpt":"For the two dimensional Schr\\\"odinger equation in a bounded domain, we prove uniqueness of determination of potentials in $W^1_p(\\Omega),\\,\\, p>2$ in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set $\\widetilde\\Gamma$ of the boundary and observe the corresponding Dirichlet data on $\\widetilde{\\Gamma}$. An immediate consequence is that one can uniquely determine a conductivity in $W^3_p(\\Omega)$ with $p>2$ by measuring the voltage on an open subset of the boundary corresponding to current supported in the same set."},"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":"1210.1255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-03T22:46:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"75e673737383df238b0ea74efdea47e8e6318940f3d1eb0e48210a5608f9492d","abstract_canon_sha256":"642af2ac35ef7cdf989e9c293209c910213f1fe42cfceefa50be10cec7660ba6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:05.009992Z","signature_b64":"I+GHKGKTSUyvM9aBM9V08xBQ4tx6oqIYel8xO7SmlHm7jeQeZlKiUfACqCpyiawr0276x420Quz0EJZ+RTvTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"026b1ee5b4a8307b772c0cc0402861f585e5c3026790ad30882de4a24bcb84ed","last_reissued_at":"2026-05-18T03:44:05.009310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:05.009310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G. Uhlmann, M. Yamamoto, O. Imanuvilov","submitted_at":"2012-10-03T22:46:44Z","abstract_excerpt":"For the two dimensional Schr\\\"odinger equation in a bounded domain, we prove uniqueness of determination of potentials in $W^1_p(\\Omega),\\,\\, p>2$ in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set $\\widetilde\\Gamma$ of the boundary and observe the corresponding Dirichlet data on $\\widetilde{\\Gamma}$. An immediate consequence is that one can uniquely determine a conductivity in $W^3_p(\\Omega)$ with $p>2$ by measuring the voltage on an open subset of the boundary corresponding to current supported in the same set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1255","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":"1210.1255","created_at":"2026-05-18T03:44:05.009409+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1255v1","created_at":"2026-05-18T03:44:05.009409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1255","created_at":"2026-05-18T03:44:05.009409+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJVR5ZNUVAYH","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJVR5ZNUVAYHW5ZM","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJVR5ZNU","created_at":"2026-05-18T12:26:58.693483+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/AJVR5ZNUVAYHW5ZMBTAEAKDB6W","json":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W.json","graph_json":"https://pith.science/api/pith-number/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/graph.json","events_json":"https://pith.science/api/pith-number/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/events.json","paper":"https://pith.science/paper/AJVR5ZNU"},"agent_actions":{"view_html":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W","download_json":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W.json","view_paper":"https://pith.science/paper/AJVR5ZNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1255&json=true","fetch_graph":"https://pith.science/api/pith-number/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/graph.json","fetch_events":"https://pith.science/api/pith-number/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/action/storage_attestation","attest_author":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/action/author_attestation","sign_citation":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/action/citation_signature","submit_replication":"https://pith.science/pith/AJVR5ZNUVAYHW5ZMBTAEAKDB6W/action/replication_record"}},"created_at":"2026-05-18T03:44:05.009409+00:00","updated_at":"2026-05-18T03:44:05.009409+00:00"}