{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YTMG6KBMVXBZNVIPHGJWC2PNGE","short_pith_number":"pith:YTMG6KBM","schema_version":"1.0","canonical_sha256":"c4d86f282cadc396d50f39936169ed312a8ac84c6e16ce725a3fc568a43a5db7","source":{"kind":"arxiv","id":"1012.4657","version":2},"attestation_state":"computed","paper":{"title":"An inverse problem of Calderon type with partial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder, Jussi Behrndt","submitted_at":"2010-12-21T13:59:56Z","abstract_excerpt":"A generalized variant of the Calder\\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \\geq 2$. The following two results are shown: (i) The selfadjoint Dirichlet operator associated with an elliptic differential expression on a bounded Lipschitz domain is determined uniquely up to unitary equivalence by the knowledge of the Dirichlet-to-Neumann map on an open subset of the boundary, and (ii) the Dirichlet operator can be reconstructed from the residuals of the Dirichlet-to-Neumann map on "},"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":"1012.4657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-21T13:59:56Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bea563f2991f9f95cf2e97939c1949bf4945a78c22c207c205395ab1cff49bca","abstract_canon_sha256":"1b42aaa9961964655ef92947e95725db1411d12e156951fbc68d2390b93c820c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:21.784368Z","signature_b64":"Q57hfm6ngoBSyScxT6fEKDOHAedZAhYDr5W/xjOjT3DQvNg5ql3519v3Xp9VlXrfpe3eOiOfIfYY9S3iqnbdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4d86f282cadc396d50f39936169ed312a8ac84c6e16ce725a3fc568a43a5db7","last_reissued_at":"2026-05-18T03:55:21.783638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:21.783638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An inverse problem of Calderon type with partial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder, Jussi Behrndt","submitted_at":"2010-12-21T13:59:56Z","abstract_excerpt":"A generalized variant of the Calder\\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \\geq 2$. The following two results are shown: (i) The selfadjoint Dirichlet operator associated with an elliptic differential expression on a bounded Lipschitz domain is determined uniquely up to unitary equivalence by the knowledge of the Dirichlet-to-Neumann map on an open subset of the boundary, and (ii) the Dirichlet operator can be reconstructed from the residuals of the Dirichlet-to-Neumann map on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4657","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":"1012.4657","created_at":"2026-05-18T03:55:21.783729+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4657v2","created_at":"2026-05-18T03:55:21.783729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4657","created_at":"2026-05-18T03:55:21.783729+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTMG6KBMVXBZ","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTMG6KBMVXBZNVIP","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTMG6KBM","created_at":"2026-05-18T12:26:17.028572+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/YTMG6KBMVXBZNVIPHGJWC2PNGE","json":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE.json","graph_json":"https://pith.science/api/pith-number/YTMG6KBMVXBZNVIPHGJWC2PNGE/graph.json","events_json":"https://pith.science/api/pith-number/YTMG6KBMVXBZNVIPHGJWC2PNGE/events.json","paper":"https://pith.science/paper/YTMG6KBM"},"agent_actions":{"view_html":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE","download_json":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE.json","view_paper":"https://pith.science/paper/YTMG6KBM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4657&json=true","fetch_graph":"https://pith.science/api/pith-number/YTMG6KBMVXBZNVIPHGJWC2PNGE/graph.json","fetch_events":"https://pith.science/api/pith-number/YTMG6KBMVXBZNVIPHGJWC2PNGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE/action/storage_attestation","attest_author":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE/action/author_attestation","sign_citation":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE/action/citation_signature","submit_replication":"https://pith.science/pith/YTMG6KBMVXBZNVIPHGJWC2PNGE/action/replication_record"}},"created_at":"2026-05-18T03:55:21.783729+00:00","updated_at":"2026-05-18T03:55:21.783729+00:00"}