{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RIXV7SU2SPSB5RNUHIEPDJBG4C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6f185c6d4529c67b3500b7e0adc4dd87cdeb23e65e116ae845cf1710326f8736","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-14T19:33:40Z","title_canon_sha256":"04d2154f948def1c114c3084061480639182f29307534bdfc52a2f8c4c5bd69d"},"schema_version":"1.0","source":{"id":"1510.04247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04247","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04247v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04247","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"RIXV7SU2SPSB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RIXV7SU2SPSB5RNU","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RIXV7SU2","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:b3fd23e7bfe0742ef99409510740fc64de6b03202d7f01cfb9d66681ad0e84a3","target":"graph","created_at":"2026-05-18T01:30:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential or the magnetic field in a Schr\\\"odinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schr\\\"odinger equation. We prove that the knowledge of the Dirichlet-to-Neumann map for the Schr\\\"odinger equation uniquely determines the magnetic field and the electric potential and we establish H\\\"older-type stability.","authors_text":"Mourad Bellassoued","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-14T19:33:40Z","title":"Stable determination of coefficients in the dynamical Schr\\\"odinger equation in a magnetic field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04247","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b4972cdb06cb172105693f7842016ed2272a74a892072e1101dcbec727aed659","target":"record","created_at":"2026-05-18T01:30:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f185c6d4529c67b3500b7e0adc4dd87cdeb23e65e116ae845cf1710326f8736","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-14T19:33:40Z","title_canon_sha256":"04d2154f948def1c114c3084061480639182f29307534bdfc52a2f8c4c5bd69d"},"schema_version":"1.0","source":{"id":"1510.04247","kind":"arxiv","version":1}},"canonical_sha256":"8a2f5fca9a93e41ec5b43a08f1a426e099428d36f0ce61caaa5f6323c830a401","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a2f5fca9a93e41ec5b43a08f1a426e099428d36f0ce61caaa5f6323c830a401","first_computed_at":"2026-05-18T01:30:08.783017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:08.783017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWUZf49Vw9KL/0sIjfv1xtPjfg5uPmslQ9Sk2b5qom497dCr8yGMf40drOn8ceCI3oOcGxItngV0RZfIFIE0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:08.783786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4972cdb06cb172105693f7842016ed2272a74a892072e1101dcbec727aed659","sha256:b3fd23e7bfe0742ef99409510740fc64de6b03202d7f01cfb9d66681ad0e84a3"],"state_sha256":"60613a1f158c503a306bdbda3e4cb24caaf378db609787183b157a8e7a1fa03a"}