{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6PBDCRKJBSKLE6RV7JQ4IMPFNO","short_pith_number":"pith:6PBDCRKJ","schema_version":"1.0","canonical_sha256":"f3c23145490c94b27a35fa61c431e56b84d7e3b967ff5a16a3d8b4b44a1deb1e","source":{"kind":"arxiv","id":"1902.05182","version":1},"attestation_state":"computed","paper":{"title":"On reconstruction in the inverse conductivity problem with one measurement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaru Ikehata","submitted_at":"2019-02-14T01:48:55Z","abstract_excerpt":"We consider an inverse problem for electrically conductive material occupying a domain $\\Omega$ in $\\Bbb R^2$. Let $\\gamma$ be the conductivity of $\\Omega$, and $D$ a subdomain of $\\Omega$. We assume that $\\gamma$ is a positive constant $k$ on $D$, $k\\not=1$ and is $1$ on $\\Omega\\setminus D$; both $D$ and $k$ are unknown. The problem is to find a reconstruction formula of $D$ from the Cauchy data on $\\partial\\Omega$ of a non-constant solution $u$ of the equation $\\nabla\\cdot\\gamma\\nabla u=0$ in $\\Omega$. We prove that if $D$ is known to be a convex polygon such that $\\text{diam}\\,D<\\text{dist}"},"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":"1902.05182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-14T01:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"33aecfc7413ce00dcd6136e12374cfa13b922d478281bddac27cac800939ea52","abstract_canon_sha256":"a69faad122c09a83b98ea8ead37366160280d36274fa8426a2382ec84105457e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:01.683306Z","signature_b64":"v7Xl/kwc7sXOf5XVCcWylbubuFLwXilOd+6c4k2+ojLZ1d1PyKPKFPtNpkIhPvm4lWwYwA3w/bZLzgpy4HZvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3c23145490c94b27a35fa61c431e56b84d7e3b967ff5a16a3d8b4b44a1deb1e","last_reissued_at":"2026-05-17T23:54:01.682612Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:01.682612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On reconstruction in the inverse conductivity problem with one measurement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaru Ikehata","submitted_at":"2019-02-14T01:48:55Z","abstract_excerpt":"We consider an inverse problem for electrically conductive material occupying a domain $\\Omega$ in $\\Bbb R^2$. Let $\\gamma$ be the conductivity of $\\Omega$, and $D$ a subdomain of $\\Omega$. We assume that $\\gamma$ is a positive constant $k$ on $D$, $k\\not=1$ and is $1$ on $\\Omega\\setminus D$; both $D$ and $k$ are unknown. The problem is to find a reconstruction formula of $D$ from the Cauchy data on $\\partial\\Omega$ of a non-constant solution $u$ of the equation $\\nabla\\cdot\\gamma\\nabla u=0$ in $\\Omega$. We prove that if $D$ is known to be a convex polygon such that $\\text{diam}\\,D<\\text{dist}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05182","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":"1902.05182","created_at":"2026-05-17T23:54:01.682737+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.05182v1","created_at":"2026-05-17T23:54:01.682737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05182","created_at":"2026-05-17T23:54:01.682737+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PBDCRKJBSKL","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PBDCRKJBSKLE6RV","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PBDCRKJ","created_at":"2026-05-18T12:33:10.108867+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/6PBDCRKJBSKLE6RV7JQ4IMPFNO","json":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO.json","graph_json":"https://pith.science/api/pith-number/6PBDCRKJBSKLE6RV7JQ4IMPFNO/graph.json","events_json":"https://pith.science/api/pith-number/6PBDCRKJBSKLE6RV7JQ4IMPFNO/events.json","paper":"https://pith.science/paper/6PBDCRKJ"},"agent_actions":{"view_html":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO","download_json":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO.json","view_paper":"https://pith.science/paper/6PBDCRKJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.05182&json=true","fetch_graph":"https://pith.science/api/pith-number/6PBDCRKJBSKLE6RV7JQ4IMPFNO/graph.json","fetch_events":"https://pith.science/api/pith-number/6PBDCRKJBSKLE6RV7JQ4IMPFNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO/action/storage_attestation","attest_author":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO/action/author_attestation","sign_citation":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO/action/citation_signature","submit_replication":"https://pith.science/pith/6PBDCRKJBSKLE6RV7JQ4IMPFNO/action/replication_record"}},"created_at":"2026-05-17T23:54:01.682737+00:00","updated_at":"2026-05-17T23:54:01.682737+00:00"}