{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4G4CLGU7EUY6Z3YES2MPELAGDY","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":"79110e7ee55f91fca42fc15fb7c7bb9c1bf42e2cdbcdb14d758253b770817004","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-29T17:17:20Z","title_canon_sha256":"0004e0bd4ed85b9c4374d782197eda84bf4af961d47b52c30ca019ccf70a57ac"},"schema_version":"1.0","source":{"id":"1205.6425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6425","created_at":"2026-05-18T02:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6425v2","created_at":"2026-05-18T02:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6425","created_at":"2026-05-18T02:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"4G4CLGU7EUY6","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4G4CLGU7EUY6Z3YE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4G4CLGU7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:a2bb5a91049e1f24f7ac474619efbe80f26368c7dd2785268c317ca261b7436f","target":"graph","created_at":"2026-05-18T02:40:45Z","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":"Let (M,g) be a compact Riemmanian manifold with non-empty boundary. Consider the second order hyperbolic initial-boundary value problem (\\delta_t^2 + P(x,D))u = 0 in (0,T) x M, u(0,x) = \\delta_t u(0,x) = 0 for x in M, u(t,x) = f(t,x) on (0,T) x \\delta M; where P(x,D) is a first-order perturbation of the Laplace-Beltrami operator on (M,g). Let b and q be the covector field and the potential of P(x,D), respectively, in M. We prove H\\\"older type stability estimates near generic simple Riemannian metrics for the inverse problem of recovering g, b, and q from the hyperbolic Dirichlet-to-Neumann(DN)","authors_text":"Carlos Montalto","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-29T17:17:20Z","title":"Stable determination of a simple metric, a covector field and a potential from the hyperbolic Dirichlet-to-Neumann map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6425","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:e6c2e753b98d9658c4e225d10ed2e1035a88a0a152d7424c1e7a91fdaeba7333","target":"record","created_at":"2026-05-18T02:40:45Z","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":"79110e7ee55f91fca42fc15fb7c7bb9c1bf42e2cdbcdb14d758253b770817004","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-29T17:17:20Z","title_canon_sha256":"0004e0bd4ed85b9c4374d782197eda84bf4af961d47b52c30ca019ccf70a57ac"},"schema_version":"1.0","source":{"id":"1205.6425","kind":"arxiv","version":2}},"canonical_sha256":"e1b8259a9f2531ecef049698f22c061e3df7034fbbf6dec9eac2e52c050731b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1b8259a9f2531ecef049698f22c061e3df7034fbbf6dec9eac2e52c050731b8","first_computed_at":"2026-05-18T02:40:45.937785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:45.937785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PAguvFcQ5RfgNKm9Xg3IhYMXH/5QIyFYtp21gOSCyFwp0ghCsTAw/X6BoI7kjYUupHdm4ujMA1AmwQUDcrPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:45.938227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6c2e753b98d9658c4e225d10ed2e1035a88a0a152d7424c1e7a91fdaeba7333","sha256:a2bb5a91049e1f24f7ac474619efbe80f26368c7dd2785268c317ca261b7436f"],"state_sha256":"1c11b4385be3e2644c87899cec7f10687e94e19a10dded2e990882d4800558e8"}