{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XUJYNHBOFJP7VDIQF4LPY4JTAK","short_pith_number":"pith:XUJYNHBO","schema_version":"1.0","canonical_sha256":"bd13869c2e2a5ffa8d102f16fc713302a36a3ec4a8460736fbb542e743d0845c","source":{"kind":"arxiv","id":"1501.07364","version":2},"attestation_state":"computed","paper":{"title":"A \"milder\" version of Calder\\'on's inverse problem for anisotropic conductivities and partial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz (IMB)","submitted_at":"2015-01-29T07:47:07Z","abstract_excerpt":"Given  a general symmetric elliptic operator $$ L\\_{a} := \\sum\\_{k,,j=1}^d \\p\\_k (a\\_{kj} \\p\\_j) + \\sum\\_{k=1}^d a\\_k \\p\\_k - \\p\\_k(\\overline{a\\_k} .) + a\\_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with  partial data, i.e.,  data supported in a part of the boundary. We prove positivity, $L^p$-estimates  and domination properties for the semigroup associated with this D-t-N operator. Given $L\\_a $ and $L\\_b$ of the previous type with bounded measurable coefficients $a = \\{a\\_{kj}, \\ a\\_k, a\\_0 \\}$ and $b = \\{b\\_{kj}, \\ b\\_k, b\\_0 \\}$, we prove that if  their  partial D-t"},"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":"1501.07364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-29T07:47:07Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"f74df2718038918df50cbbbdd57d845d9e16e66cea96f75f2b8e5c057fe53f05","abstract_canon_sha256":"a079a33fdc93b4b40e38d790e4167706ef40bde188692eca772ededb99b65ab1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:12.882266Z","signature_b64":"JTZYLJOCg03xwJOfjoELHs6ChaEmJo6GjcvpeBcHI7CHFl4Osk+S7DdLu4g3Gw1spPpRdsrvTHK9EyXW/SzzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd13869c2e2a5ffa8d102f16fc713302a36a3ec4a8460736fbb542e743d0845c","last_reissued_at":"2026-05-18T01:17:12.881558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:12.881558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A \"milder\" version of Calder\\'on's inverse problem for anisotropic conductivities and partial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz (IMB)","submitted_at":"2015-01-29T07:47:07Z","abstract_excerpt":"Given  a general symmetric elliptic operator $$ L\\_{a} := \\sum\\_{k,,j=1}^d \\p\\_k (a\\_{kj} \\p\\_j) + \\sum\\_{k=1}^d a\\_k \\p\\_k - \\p\\_k(\\overline{a\\_k} .) + a\\_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with  partial data, i.e.,  data supported in a part of the boundary. We prove positivity, $L^p$-estimates  and domination properties for the semigroup associated with this D-t-N operator. Given $L\\_a $ and $L\\_b$ of the previous type with bounded measurable coefficients $a = \\{a\\_{kj}, \\ a\\_k, a\\_0 \\}$ and $b = \\{b\\_{kj}, \\ b\\_k, b\\_0 \\}$, we prove that if  their  partial D-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07364","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":"1501.07364","created_at":"2026-05-18T01:17:12.881674+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07364v2","created_at":"2026-05-18T01:17:12.881674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07364","created_at":"2026-05-18T01:17:12.881674+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUJYNHBOFJP7","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUJYNHBOFJP7VDIQ","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUJYNHBO","created_at":"2026-05-18T12:29:50.041715+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/XUJYNHBOFJP7VDIQF4LPY4JTAK","json":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK.json","graph_json":"https://pith.science/api/pith-number/XUJYNHBOFJP7VDIQF4LPY4JTAK/graph.json","events_json":"https://pith.science/api/pith-number/XUJYNHBOFJP7VDIQF4LPY4JTAK/events.json","paper":"https://pith.science/paper/XUJYNHBO"},"agent_actions":{"view_html":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK","download_json":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK.json","view_paper":"https://pith.science/paper/XUJYNHBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07364&json=true","fetch_graph":"https://pith.science/api/pith-number/XUJYNHBOFJP7VDIQF4LPY4JTAK/graph.json","fetch_events":"https://pith.science/api/pith-number/XUJYNHBOFJP7VDIQF4LPY4JTAK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK/action/storage_attestation","attest_author":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK/action/author_attestation","sign_citation":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK/action/citation_signature","submit_replication":"https://pith.science/pith/XUJYNHBOFJP7VDIQF4LPY4JTAK/action/replication_record"}},"created_at":"2026-05-18T01:17:12.881674+00:00","updated_at":"2026-05-18T01:17:12.881674+00:00"}