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We will study the uniqueness of an unknown potential for the Schr\\\"{o}dinger operator $ -\\triangle_g + q $ from the associated local Dirichlet to Neumann map, $C_q^{\\Gamma,\\Gamma}$. Indeed, we will prove that if the potential $q$ is a priori explicitly known in $U^c$, then one can uniquely recon"},"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":"1802.05361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-14T23:43:22Z","cross_cats_sorted":[],"title_canon_sha256":"16d1de92326279e8b5545a96dda1253aeb311bff888b0b699e0a7148adc09a50","abstract_canon_sha256":"98d85d7da5091683e2d22451ce36eb73cd3547c5cebf7a21a315c455e9481e19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:15.857411Z","signature_b64":"COLx6igs4E6Uc4Ly8T8GZ1PN27tpv2SuVXjZkWnUzxxWdBcNYjsJvdCCI1hpBmhFB+rMAG6twlCCuQcKam6GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df98724bbd2b613ac1f9fcc709fec48366bdec56fd91f984d786d5cc32d5e893","last_reissued_at":"2026-05-18T00:23:15.856841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:15.856841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of a Potential from Local Boundary Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Feizmohammadi","submitted_at":"2018-02-14T23:43:22Z","abstract_excerpt":"Let $(\\Omega^3,g)$ be a compact smooth Riemannian manifold with smooth boundary and suppose that $U$ is an open set in $\\Omega$ such that $g|_U$ is the Euclidean metric. 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