{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Y73RSROYJWJXEYQ4MWEOWH5STO","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":"45806d044ffa96e8b6dddab5194f43fcc6e70df8200995c0df155b3174b0af70","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-26T12:55:17Z","title_canon_sha256":"63af865bbbb548a4f0161002bfb2caca5dc8f41d3d1159d6e2f0b7de16e04481"},"schema_version":"1.0","source":{"id":"1909.12803","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.12803","created_at":"2026-07-05T00:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1909.12803v2","created_at":"2026-07-05T00:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.12803","created_at":"2026-07-05T00:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y73RSROYJWJX","created_at":"2026-07-05T00:55:59Z"},{"alias_kind":"pith_short_16","alias_value":"Y73RSROYJWJXEYQ4","created_at":"2026-07-05T00:55:59Z"},{"alias_kind":"pith_short_8","alias_value":"Y73RSROY","created_at":"2026-07-05T00:55:59Z"}],"graph_snapshots":[{"event_id":"sha256:d607474a370c55aa7c8ef0091fd2ffaeb9366a98199e66f6afb175d4f2d8d874","target":"graph","created_at":"2026-07-05T00:55:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.12803/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Genqian Liu","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-26T12:55:17Z","title":"Determining anisotropic real-analytic metric from boundary electromagnetic information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.12803","kind":"arxiv","version":2},"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:b8e01533b5d7b5281a5cd721517b173be3f03e870213898f2eb1c71c1c1d9376","target":"record","created_at":"2026-07-05T00:55:59Z","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":"45806d044ffa96e8b6dddab5194f43fcc6e70df8200995c0df155b3174b0af70","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-26T12:55:17Z","title_canon_sha256":"63af865bbbb548a4f0161002bfb2caca5dc8f41d3d1159d6e2f0b7de16e04481"},"schema_version":"1.0","source":{"id":"1909.12803","kind":"arxiv","version":2}},"canonical_sha256":"c7f71945d84d9372621c6588eb1fb29bba12c35fe9f766150450bec36c96908a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7f71945d84d9372621c6588eb1fb29bba12c35fe9f766150450bec36c96908a","first_computed_at":"2026-07-05T00:55:59.075154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:55:59.075154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YKA/6SEqhcuM2cc7NHzEswPFxpfEvxSd1eeco4s2iiH2rA7uI6RqtQvbCd/Q8asyOw7F6kSOS2k3FLhrI+aQDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:55:59.075507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.12803","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8e01533b5d7b5281a5cd721517b173be3f03e870213898f2eb1c71c1c1d9376","sha256:d607474a370c55aa7c8ef0091fd2ffaeb9366a98199e66f6afb175d4f2d8d874"],"state_sha256":"3a288a81c29cf15355abe455b4ffcfb92006874f83893a5e98b3d5e09847820b"}