{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JVKJV5AIDZYNIBJKQKC2NN4U3W","short_pith_number":"pith:JVKJV5AI","schema_version":"1.0","canonical_sha256":"4d549af4081e70d4052a8285a6b794dd937d5db8566e81a00e6e9be8c6b9bb57","source":{"kind":"arxiv","id":"1009.4003","version":4},"attestation_state":"computed","paper":{"title":"Determination of time-dependent coefficients for a hyperbolic inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ricardo Salazar","submitted_at":"2010-09-21T06:07:21Z","abstract_excerpt":"We consider an inverse boundary value problem for the hyperbolic partial differential equation $ (-i\\partial_{t} + A_{0}(t,x))^2 u(t,x) - \\sum_{j=1}^n (-i\\partial_{x_j} + A_{j}(t,x))^2 u(t,x) + V(t,x)u(t,x) = 0 $ with time dependent vector and scalar potentials ($\\mathcal{A}= (A_{0},...,A_{m})$ and $V(t,x)$ respectively) on a bounded, smooth cylindric domain $(-\\infty,\\infty)\\times\\Omega$. Using a geometric optics construction we show that the boundary data allows us to recover integrals of the potentials along `light rays' and we then establish the uniqueness of these potentials modulo a gaug"},"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":"1009.4003","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-21T06:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"08517752edbc3474bebc63c4cf7b1cca271b312fc412333dd368ee46e89799f7","abstract_canon_sha256":"08a5529d3f8230665052c53f37e1a9cffe405dfb8a63729d4273701d5dac49c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:09.963966Z","signature_b64":"KZPgPik7HSBFtU257QZcmMjswFnyLRWXEBtPKqn2cuHSxLP09qNz4BgqvoCtbDx0pTjELxwc2EE6TEtXDpElCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d549af4081e70d4052a8285a6b794dd937d5db8566e81a00e6e9be8c6b9bb57","last_reissued_at":"2026-05-18T03:05:09.963401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:09.963401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determination of time-dependent coefficients for a hyperbolic inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ricardo Salazar","submitted_at":"2010-09-21T06:07:21Z","abstract_excerpt":"We consider an inverse boundary value problem for the hyperbolic partial differential equation $ (-i\\partial_{t} + A_{0}(t,x))^2 u(t,x) - \\sum_{j=1}^n (-i\\partial_{x_j} + A_{j}(t,x))^2 u(t,x) + V(t,x)u(t,x) = 0 $ with time dependent vector and scalar potentials ($\\mathcal{A}= (A_{0},...,A_{m})$ and $V(t,x)$ respectively) on a bounded, smooth cylindric domain $(-\\infty,\\infty)\\times\\Omega$. Using a geometric optics construction we show that the boundary data allows us to recover integrals of the potentials along `light rays' and we then establish the uniqueness of these potentials modulo a gaug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4003","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1009.4003","created_at":"2026-05-18T03:05:09.963489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4003v4","created_at":"2026-05-18T03:05:09.963489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4003","created_at":"2026-05-18T03:05:09.963489+00:00"},{"alias_kind":"pith_short_12","alias_value":"JVKJV5AIDZYN","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JVKJV5AIDZYNIBJK","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JVKJV5AI","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W","json":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W.json","graph_json":"https://pith.science/api/pith-number/JVKJV5AIDZYNIBJKQKC2NN4U3W/graph.json","events_json":"https://pith.science/api/pith-number/JVKJV5AIDZYNIBJKQKC2NN4U3W/events.json","paper":"https://pith.science/paper/JVKJV5AI"},"agent_actions":{"view_html":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W","download_json":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W.json","view_paper":"https://pith.science/paper/JVKJV5AI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4003&json=true","fetch_graph":"https://pith.science/api/pith-number/JVKJV5AIDZYNIBJKQKC2NN4U3W/graph.json","fetch_events":"https://pith.science/api/pith-number/JVKJV5AIDZYNIBJKQKC2NN4U3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/action/storage_attestation","attest_author":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/action/author_attestation","sign_citation":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/action/citation_signature","submit_replication":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/action/replication_record"}},"created_at":"2026-05-18T03:05:09.963489+00:00","updated_at":"2026-05-18T03:05:09.963489+00:00"}