{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Y73RSROYJWJXEYQ4MWEOWH5STO","short_pith_number":"pith:Y73RSROY","schema_version":"1.0","canonical_sha256":"c7f71945d84d9372621c6588eb1fb29bba12c35fe9f766150450bec36c96908a","source":{"kind":"arxiv","id":"1909.12803","version":2},"attestation_state":"computed","paper":{"title":"Determining anisotropic real-analytic metric from boundary electromagnetic information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.AP","authors_text":"Genqian Liu","submitted_at":"2019-09-26T12:55:17Z","abstract_excerpt":"For a compact, connected, oriented Riemannian $3$-manifold $(M, g)$ with smooth boundary $\\partial M$, we explicitly give a local representation and a full symbol expression for the electromagnetic Dirichlet-to-Neumann map by factorizing Maxwell's equations and using an isometric transform. We prove that one can reconstruct a compact, connected, real-analytic Riemannian $3$-manifold $M$ with boundary from the set of tangential electric fields and tangential magnetic fields, given on a non-empty open subset $\\Gamma$ of the boundary, of all electric and magnetic fields with tangential electric d"},"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":"1909.12803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-26T12:55:17Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"63af865bbbb548a4f0161002bfb2caca5dc8f41d3d1159d6e2f0b7de16e04481","abstract_canon_sha256":"45806d044ffa96e8b6dddab5194f43fcc6e70df8200995c0df155b3174b0af70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:55:59.075507Z","signature_b64":"YKA/6SEqhcuM2cc7NHzEswPFxpfEvxSd1eeco4s2iiH2rA7uI6RqtQvbCd/Q8asyOw7F6kSOS2k3FLhrI+aQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7f71945d84d9372621c6588eb1fb29bba12c35fe9f766150450bec36c96908a","last_reissued_at":"2026-07-05T00:55:59.075154Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:55:59.075154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determining anisotropic real-analytic metric from boundary electromagnetic information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.AP","authors_text":"Genqian Liu","submitted_at":"2019-09-26T12:55:17Z","abstract_excerpt":"For a compact, connected, oriented Riemannian $3$-manifold $(M, g)$ with smooth boundary $\\partial M$, we explicitly give a local representation and a full symbol expression for the electromagnetic Dirichlet-to-Neumann map by factorizing Maxwell's equations and using an isometric transform. We prove that one can reconstruct a compact, connected, real-analytic Riemannian $3$-manifold $M$ with boundary from the set of tangential electric fields and tangential magnetic fields, given on a non-empty open subset $\\Gamma$ of the boundary, of all electric and magnetic fields with tangential electric d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.12803","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/1909.12803/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":"1909.12803","created_at":"2026-07-05T00:55:59.075206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.12803v2","created_at":"2026-07-05T00:55:59.075206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.12803","created_at":"2026-07-05T00:55:59.075206+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y73RSROYJWJX","created_at":"2026-07-05T00:55:59.075206+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y73RSROYJWJXEYQ4","created_at":"2026-07-05T00:55:59.075206+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y73RSROY","created_at":"2026-07-05T00:55:59.075206+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05096","citing_title":"Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifolds","ref_index":45,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO","json":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO.json","graph_json":"https://pith.science/api/pith-number/Y73RSROYJWJXEYQ4MWEOWH5STO/graph.json","events_json":"https://pith.science/api/pith-number/Y73RSROYJWJXEYQ4MWEOWH5STO/events.json","paper":"https://pith.science/paper/Y73RSROY"},"agent_actions":{"view_html":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO","download_json":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO.json","view_paper":"https://pith.science/paper/Y73RSROY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.12803&json=true","fetch_graph":"https://pith.science/api/pith-number/Y73RSROYJWJXEYQ4MWEOWH5STO/graph.json","fetch_events":"https://pith.science/api/pith-number/Y73RSROYJWJXEYQ4MWEOWH5STO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO/action/storage_attestation","attest_author":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO/action/author_attestation","sign_citation":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO/action/citation_signature","submit_replication":"https://pith.science/pith/Y73RSROYJWJXEYQ4MWEOWH5STO/action/replication_record"}},"created_at":"2026-07-05T00:55:59.075206+00:00","updated_at":"2026-07-05T00:55:59.075206+00:00"}