{"paper":{"title":"On the Stability of Inverse Conductivity Problem for Polyhedral Inclusions under a Single Measurement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Logarithmic stability estimate holds for the Hausdorff distance between convex polyhedral inclusions from a single boundary measurement error.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chun-Hsiang Tsou","submitted_at":"2026-05-17T14:52:17Z","abstract_excerpt":"In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are singularity decomposition for elliptic equations in non-smooth domains, propagation of smallness, and microlocal analysis. Combining these tools, we establish a logarithmic stability estimate for the Hausdorff distance between inclusions in terms of the measurement error."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Combining singularity decomposition for elliptic equations in non-smooth domains, propagation of smallness, and microlocal analysis, we establish a logarithmic stability estimate for the Hausdorff distance between inclusions in terms of the measurement error.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The unknown inclusion is a convex polyhedron and the background medium is homogeneous and isotropic; the analysis relies on the specific singularity structure that these assumptions produce near edges and vertices.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves logarithmic stability estimate for Hausdorff distance of convex polyhedral inclusions in the inverse conductivity problem from one boundary measurement using singularity decomposition, propagation of smallness, and microlocal analysis.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Logarithmic stability estimate holds for the Hausdorff distance between convex polyhedral inclusions from a single boundary measurement error.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b734398c3790d77896ca0e783bf25d4d361329684b359018b733ad4f02aadacd"},"source":{"id":"2605.17484","kind":"arxiv","version":1},"verdict":{"id":"05d10a8b-081c-4b59-b84f-5dc4dcf49375","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:23:38.064832Z","strongest_claim":"Combining singularity decomposition for elliptic equations in non-smooth domains, propagation of smallness, and microlocal analysis, we establish a logarithmic stability estimate for the Hausdorff distance between inclusions in terms of the measurement error.","one_line_summary":"Proves logarithmic stability estimate for Hausdorff distance of convex polyhedral inclusions in the inverse conductivity problem from one boundary measurement using singularity decomposition, propagation of smallness, and microlocal analysis.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The unknown inclusion is a convex polyhedron and the background medium is homogeneous and isotropic; the analysis relies on the specific singularity structure that these assumptions produce near edges and vertices.","pith_extraction_headline":"Logarithmic stability estimate holds for the Hausdorff distance between convex polyhedral inclusions from a single boundary measurement error."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17484/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.620118Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:31:09.266993Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.686666Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.646449Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"100588e76ab1ca673c2a32e38efd91346404c2ee27c75f414f6fa98d7bb0d30f"},"references":{"count":47,"sample":[{"doi":"","year":1988,"title":"Alessandrini","work_id":"f4efcb47-1c76-4e53-8f47-eb76387c21c4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"G. 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