{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5M6TVAZNEHPLPTEIVC2UQV7L3U","short_pith_number":"pith:5M6TVAZN","schema_version":"1.0","canonical_sha256":"eb3d3a832d21deb7cc88a8b54857ebdd08443d6cf194097a7642f102f9f547cf","source":{"kind":"arxiv","id":"1111.5051","version":1},"attestation_state":"computed","paper":{"title":"Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guillaume Bal, Gunther Uhlmann","submitted_at":"2011-11-21T22:37:04Z","abstract_excerpt":"This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large number of solutions and for an open set of corresponding boundary conditions, all coefficients can be uniquely and stably reconstructed up to a well characterized gauge transformation. We also show that in some specific situations, a minimum number of such available solutions equal to $I_n=\\frac12n(n+3)$ is sufficient to uniquely and globally reconstruct the"},"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":"1111.5051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-21T22:37:04Z","cross_cats_sorted":[],"title_canon_sha256":"f64308bf8644d08ff2087a98edc44000a2dc4dbdf55e662e716c00a2793ee3d8","abstract_canon_sha256":"9b0c2739998f03de5f8dff35c01c90d1805b2a45fa4efeed555fe52591bb2c12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:53.554012Z","signature_b64":"CS9koePoFbygbcFy07VcqAWAqseHU1RQ4e0y/W7aWpiQyH+20bBwvDKFNLOhjwg2vtajYGLn73ITRW6bZCRpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb3d3a832d21deb7cc88a8b54857ebdd08443d6cf194097a7642f102f9f547cf","last_reissued_at":"2026-05-18T04:07:53.553403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:53.553403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guillaume Bal, Gunther Uhlmann","submitted_at":"2011-11-21T22:37:04Z","abstract_excerpt":"This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large number of solutions and for an open set of corresponding boundary conditions, all coefficients can be uniquely and stably reconstructed up to a well characterized gauge transformation. We also show that in some specific situations, a minimum number of such available solutions equal to $I_n=\\frac12n(n+3)$ is sufficient to uniquely and globally reconstruct the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5051","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":"1111.5051","created_at":"2026-05-18T04:07:53.553486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.5051v1","created_at":"2026-05-18T04:07:53.553486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5051","created_at":"2026-05-18T04:07:53.553486+00:00"},{"alias_kind":"pith_short_12","alias_value":"5M6TVAZNEHPL","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5M6TVAZNEHPLPTEI","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5M6TVAZN","created_at":"2026-05-18T12:26:20.644004+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/5M6TVAZNEHPLPTEIVC2UQV7L3U","json":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U.json","graph_json":"https://pith.science/api/pith-number/5M6TVAZNEHPLPTEIVC2UQV7L3U/graph.json","events_json":"https://pith.science/api/pith-number/5M6TVAZNEHPLPTEIVC2UQV7L3U/events.json","paper":"https://pith.science/paper/5M6TVAZN"},"agent_actions":{"view_html":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U","download_json":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U.json","view_paper":"https://pith.science/paper/5M6TVAZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.5051&json=true","fetch_graph":"https://pith.science/api/pith-number/5M6TVAZNEHPLPTEIVC2UQV7L3U/graph.json","fetch_events":"https://pith.science/api/pith-number/5M6TVAZNEHPLPTEIVC2UQV7L3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U/action/storage_attestation","attest_author":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U/action/author_attestation","sign_citation":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U/action/citation_signature","submit_replication":"https://pith.science/pith/5M6TVAZNEHPLPTEIVC2UQV7L3U/action/replication_record"}},"created_at":"2026-05-18T04:07:53.553486+00:00","updated_at":"2026-05-18T04:07:53.553486+00:00"}