{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UEYOLVKULIFCHIXRDM5H6Y5GSY","short_pith_number":"pith:UEYOLVKU","schema_version":"1.0","canonical_sha256":"a130e5d5545a0a23a2f11b3a7f63a69600ce624216f8c60d67aa518a06a39af2","source":{"kind":"arxiv","id":"1812.05300","version":1},"attestation_state":"computed","paper":{"title":"Monotonicity based shape reconstruction in electrical impedance tomography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Bastian Harrach, Marcel Ullrich","submitted_at":"2018-12-13T07:39:03Z","abstract_excerpt":"Current-voltage measurements in electrical impedance tomography can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements.\n  We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (aka inclusion detection) problem in EIT. The outer shape of a region where the conductivity differs from a known background conductivity can be found "},"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":"1812.05300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-13T07:39:03Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"68dc42e72b0587c4f0e6fe11ec7dfb55ac15dbff5e1a50c634b32d7c5fb37820","abstract_canon_sha256":"db72c448dc378c113586a601e3e91f279dec9e5100c67266997836add73dcb08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:23.882761Z","signature_b64":"Qtm8As8AHI3evbO9kPO91ECMjsGX2Bo/Vzgtg1p7kui2fMN+2h26n4kCHRtnW+/E/kGyaAPXvUt4RQQ9M0lNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a130e5d5545a0a23a2f11b3a7f63a69600ce624216f8c60d67aa518a06a39af2","last_reissued_at":"2026-05-17T23:58:23.882238Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:23.882238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monotonicity based shape reconstruction in electrical impedance tomography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Bastian Harrach, Marcel Ullrich","submitted_at":"2018-12-13T07:39:03Z","abstract_excerpt":"Current-voltage measurements in electrical impedance tomography can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements.\n  We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (aka inclusion detection) problem in EIT. The outer shape of a region where the conductivity differs from a known background conductivity can be found "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05300","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":"1812.05300","created_at":"2026-05-17T23:58:23.882327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.05300v1","created_at":"2026-05-17T23:58:23.882327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05300","created_at":"2026-05-17T23:58:23.882327+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEYOLVKULIFC","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEYOLVKULIFCHIXR","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEYOLVKU","created_at":"2026-05-18T12:32:56.356000+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/UEYOLVKULIFCHIXRDM5H6Y5GSY","json":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY.json","graph_json":"https://pith.science/api/pith-number/UEYOLVKULIFCHIXRDM5H6Y5GSY/graph.json","events_json":"https://pith.science/api/pith-number/UEYOLVKULIFCHIXRDM5H6Y5GSY/events.json","paper":"https://pith.science/paper/UEYOLVKU"},"agent_actions":{"view_html":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY","download_json":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY.json","view_paper":"https://pith.science/paper/UEYOLVKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.05300&json=true","fetch_graph":"https://pith.science/api/pith-number/UEYOLVKULIFCHIXRDM5H6Y5GSY/graph.json","fetch_events":"https://pith.science/api/pith-number/UEYOLVKULIFCHIXRDM5H6Y5GSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY/action/storage_attestation","attest_author":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY/action/author_attestation","sign_citation":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY/action/citation_signature","submit_replication":"https://pith.science/pith/UEYOLVKULIFCHIXRDM5H6Y5GSY/action/replication_record"}},"created_at":"2026-05-17T23:58:23.882327+00:00","updated_at":"2026-05-17T23:58:23.882327+00:00"}