{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JVKJV5AIDZYNIBJKQKC2NN4U3W","short_pith_number":"pith:JVKJV5AI","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"},"canonical_sha256":"4d549af4081e70d4052a8285a6b794dd937d5db8566e81a00e6e9be8c6b9bb57","source":{"kind":"arxiv","id":"1009.4003","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4003","created_at":"2026-05-18T03:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4003v4","created_at":"2026-05-18T03:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4003","created_at":"2026-05-18T03:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"JVKJV5AIDZYN","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JVKJV5AIDZYNIBJK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JVKJV5AI","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JVKJV5AIDZYNIBJKQKC2NN4U3W","target":"record","payload":{"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"},"canonical_sha256":"4d549af4081e70d4052a8285a6b794dd937d5db8566e81a00e6e9be8c6b9bb57","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"},"source_kind":"arxiv","source_id":"1009.4003","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Psrstp4zohMC9P85XqwsaeB7S0ni82IF+E7DjM2eCTriyJIENUz3MN17drfqB7udA24tpl17ADRxeECvi/M/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:19:33.952516Z"},"content_sha256":"bb67100cc016d78649a42312c17564614266b2169d3afb6ddc374713739ddf20","schema_version":"1.0","event_id":"sha256:bb67100cc016d78649a42312c17564614266b2169d3afb6ddc374713739ddf20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JVKJV5AIDZYNIBJKQKC2NN4U3W","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tK9WeWqP7Q7kxz1wHksqwDCymXDyffUlg01LY/c5ae7l/vVnY7Br1vwdgSNRl3xzq58ROSW7wFXUssAHP4QGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:19:33.953240Z"},"content_sha256":"bd5f38590ff22e23c839dd11011ac95270ce0719a02cae77d5aafe0feba22356","schema_version":"1.0","event_id":"sha256:bd5f38590ff22e23c839dd11011ac95270ce0719a02cae77d5aafe0feba22356"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/bundle.json","state_url":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T04:19:33Z","links":{"resolver":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W","bundle":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/bundle.json","state":"https://pith.science/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVKJV5AIDZYNIBJKQKC2NN4U3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JVKJV5AIDZYNIBJKQKC2NN4U3W","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":"08a5529d3f8230665052c53f37e1a9cffe405dfb8a63729d4273701d5dac49c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-21T06:07:21Z","title_canon_sha256":"08517752edbc3474bebc63c4cf7b1cca271b312fc412333dd368ee46e89799f7"},"schema_version":"1.0","source":{"id":"1009.4003","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4003","created_at":"2026-05-18T03:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4003v4","created_at":"2026-05-18T03:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4003","created_at":"2026-05-18T03:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"JVKJV5AIDZYN","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JVKJV5AIDZYNIBJK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JVKJV5AI","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:bd5f38590ff22e23c839dd11011ac95270ce0719a02cae77d5aafe0feba22356","target":"graph","created_at":"2026-05-18T03:05:09Z","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":"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","authors_text":"Ricardo Salazar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-21T06:07:21Z","title":"Determination of time-dependent coefficients for a hyperbolic inverse problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4003","kind":"arxiv","version":4},"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:bb67100cc016d78649a42312c17564614266b2169d3afb6ddc374713739ddf20","target":"record","created_at":"2026-05-18T03:05:09Z","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":"08a5529d3f8230665052c53f37e1a9cffe405dfb8a63729d4273701d5dac49c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-21T06:07:21Z","title_canon_sha256":"08517752edbc3474bebc63c4cf7b1cca271b312fc412333dd368ee46e89799f7"},"schema_version":"1.0","source":{"id":"1009.4003","kind":"arxiv","version":4}},"canonical_sha256":"4d549af4081e70d4052a8285a6b794dd937d5db8566e81a00e6e9be8c6b9bb57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d549af4081e70d4052a8285a6b794dd937d5db8566e81a00e6e9be8c6b9bb57","first_computed_at":"2026-05-18T03:05:09.963401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:09.963401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KZPgPik7HSBFtU257QZcmMjswFnyLRWXEBtPKqn2cuHSxLP09qNz4BgqvoCtbDx0pTjELxwc2EE6TEtXDpElCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:09.963966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4003","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb67100cc016d78649a42312c17564614266b2169d3afb6ddc374713739ddf20","sha256:bd5f38590ff22e23c839dd11011ac95270ce0719a02cae77d5aafe0feba22356"],"state_sha256":"f47481504e6f8a5e9c04c0eb7255916a5d6f04213d55de312d846242ec396fce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+yC9aGd7UznUgPy59KFDuNqCFMr2QNZkRNY6h1VTo8dpI7jAybLzWZmVkrrvxz8dEf3eGCN1/v0wsLBf9A2AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:19:33.956536Z","bundle_sha256":"92d3f2803f2404dd3722fb14dfd1c0fe5c160ffed338579ecd4b915a360109b1"}}