{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:43EX3DG3TX5TEAK34CYBPR2TO4","short_pith_number":"pith:43EX3DG3","schema_version":"1.0","canonical_sha256":"e6c97d8cdb9dfb32015be0b017c753772296e4d05251d3266369bb142f05cdb6","source":{"kind":"arxiv","id":"2305.04227","version":2},"attestation_state":"computed","paper":{"title":"A Reduction of the Fractional Calder\\'on Problem to the Local Calder\\'on Problem by Means of the Caffarelli-Silvestre Extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angkana R\\\"uland, Giovanni Covi, Gunther Uhlmann, Tuhin Ghosh","submitted_at":"2023-05-07T09:23:01Z","abstract_excerpt":"We relate the (anisotropic) variable coefficient local and nonlocal Calder\\'on problems by means of the Caffarelli-Silvestre extension. In particular, we prove that (partial) Dirichlet-to-Neumann data for the fractional Calder\\'on problem in three and higher dimensions determine the (full) Dirichlet-to-Neumann data for the local Calder\\'on problem. As a consequence, any (variable coefficient) uniqueness result for the local problem also implies a uniqueness result for the nonlocal problem. Moreover, our approach is constructive and associated Tikhonov regularization schemes can be used to reco"},"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":"2305.04227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-05-07T09:23:01Z","cross_cats_sorted":[],"title_canon_sha256":"1049a434f68cd9ee3bde204efe14fb4cd5a81d721f6bccab75521b41273d4b31","abstract_canon_sha256":"7dbeb47f30e2ac9d0e5ee8a110df4c1b235e4e22fd837b667330a5291a230330"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:22:04.389841Z","signature_b64":"WXD0H1rpEKCe1QyXhEk8aTcUtnXNxm3VOCuZRTAx9BUGYCHrnYWPv6zwtD+Uf5b71LIpdOmiwZzqTDOj7QMmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6c97d8cdb9dfb32015be0b017c753772296e4d05251d3266369bb142f05cdb6","last_reissued_at":"2026-07-05T06:22:04.389366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:22:04.389366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Reduction of the Fractional Calder\\'on Problem to the Local Calder\\'on Problem by Means of the Caffarelli-Silvestre Extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angkana R\\\"uland, Giovanni Covi, Gunther Uhlmann, Tuhin Ghosh","submitted_at":"2023-05-07T09:23:01Z","abstract_excerpt":"We relate the (anisotropic) variable coefficient local and nonlocal Calder\\'on problems by means of the Caffarelli-Silvestre extension. In particular, we prove that (partial) Dirichlet-to-Neumann data for the fractional Calder\\'on problem in three and higher dimensions determine the (full) Dirichlet-to-Neumann data for the local Calder\\'on problem. As a consequence, any (variable coefficient) uniqueness result for the local problem also implies a uniqueness result for the nonlocal problem. Moreover, our approach is constructive and associated Tikhonov regularization schemes can be used to reco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.04227","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.04227/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.04227","created_at":"2026-07-05T06:22:04.389425+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.04227v2","created_at":"2026-07-05T06:22:04.389425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.04227","created_at":"2026-07-05T06:22:04.389425+00:00"},{"alias_kind":"pith_short_12","alias_value":"43EX3DG3TX5T","created_at":"2026-07-05T06:22:04.389425+00:00"},{"alias_kind":"pith_short_16","alias_value":"43EX3DG3TX5TEAK3","created_at":"2026-07-05T06:22:04.389425+00:00"},{"alias_kind":"pith_short_8","alias_value":"43EX3DG3","created_at":"2026-07-05T06:22:04.389425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.12535","citing_title":"Anisotropic Calder\\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4","json":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4.json","graph_json":"https://pith.science/api/pith-number/43EX3DG3TX5TEAK34CYBPR2TO4/graph.json","events_json":"https://pith.science/api/pith-number/43EX3DG3TX5TEAK34CYBPR2TO4/events.json","paper":"https://pith.science/paper/43EX3DG3"},"agent_actions":{"view_html":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4","download_json":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4.json","view_paper":"https://pith.science/paper/43EX3DG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.04227&json=true","fetch_graph":"https://pith.science/api/pith-number/43EX3DG3TX5TEAK34CYBPR2TO4/graph.json","fetch_events":"https://pith.science/api/pith-number/43EX3DG3TX5TEAK34CYBPR2TO4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4/action/storage_attestation","attest_author":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4/action/author_attestation","sign_citation":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4/action/citation_signature","submit_replication":"https://pith.science/pith/43EX3DG3TX5TEAK34CYBPR2TO4/action/replication_record"}},"created_at":"2026-07-05T06:22:04.389425+00:00","updated_at":"2026-07-05T06:22:04.389425+00:00"}