{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4TIDX7KEEAOQUJCEJXAPY4SIW2","short_pith_number":"pith:4TIDX7KE","canonical_record":{"source":{"id":"1407.5226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-19T23:33:50Z","cross_cats_sorted":[],"title_canon_sha256":"7264ae0a31c2d228edc036518429d18e9a57a7dd0d0d5770c31d8c885457cb03","abstract_canon_sha256":"1773a02605e240288c07a999252837ca1d4431e82dd9dd16746ac5413aeff1a4"},"schema_version":"1.0"},"canonical_sha256":"e4d03bfd44201d0a24444dc0fc7248b699fafddfd0ce73580c964073023dc003","source":{"kind":"arxiv","id":"1407.5226","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5226","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5226v1","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5226","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"4TIDX7KEEAOQ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4TIDX7KEEAOQUJCE","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4TIDX7KE","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4TIDX7KEEAOQUJCEJXAPY4SIW2","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-19T23:33:50Z","cross_cats_sorted":[],"title_canon_sha256":"7264ae0a31c2d228edc036518429d18e9a57a7dd0d0d5770c31d8c885457cb03","abstract_canon_sha256":"1773a02605e240288c07a999252837ca1d4431e82dd9dd16746ac5413aeff1a4"},"schema_version":"1.0"},"canonical_sha256":"e4d03bfd44201d0a24444dc0fc7248b699fafddfd0ce73580c964073023dc003","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:14.637495Z","signature_b64":"Gi85I7K8zZP1bLwGfLgJood6qXt8Kbd3dBiOMHl2k0AWADN8xROj6rsakEAZXc9vAk9rThBsiwRnfDz95cyoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4d03bfd44201d0a24444dc0fc7248b699fafddfd0ce73580c964073023dc003","last_reissued_at":"2026-05-18T02:47:14.636912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:14.636912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5226","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ba6HT8+QpUrLTOInw9vaJUrNe6zVt4OkfhNlqO8RUZIG7BLHcNN+wXZaQ39ofzGuLRTWW8f/IcidFUOEfjrDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:22:41.993334Z"},"content_sha256":"800095cec0600303080c5bbb7d491a37f55bd5de4b2511f51aa09898d8e93243","schema_version":"1.0","event_id":"sha256:800095cec0600303080c5bbb7d491a37f55bd5de4b2511f51aa09898d8e93243"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4TIDX7KEEAOQUJCEJXAPY4SIW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness and Nonuniqueness in Inverse Hyperbolic Problems and The Black Hole Phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gregory Eskin","submitted_at":"2014-07-19T23:33:50Z","abstract_excerpt":"This paper consists of two parts. In the first part we describe the recent works on the inverse problems for the wave equation in $(n+1)$-dimensional space equipped with pseudo-Riemannian metric with Lorentz signature. We study the conditions of the existence of black (or white) holes for these wave equations. In the second part we prove energy type estimates on a finite time interval in the presence of black or white holes. We use these estimates to prove the nonuniqueness of the inverse problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5226","kind":"arxiv","version":1},"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":"2026-05-18T02:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AdQg02I8oDVHVIPrEMRkoiEEUko9wJA+hg1Xn+SIg+taj6Q3AMjJb6OuN7avMIY6x58R69hR5ONZ8VDaHQmmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:22:41.993671Z"},"content_sha256":"378df719d145ed8b76e7686e238029e5089cb4012d0a9a338939297136b36083","schema_version":"1.0","event_id":"sha256:378df719d145ed8b76e7686e238029e5089cb4012d0a9a338939297136b36083"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2/bundle.json","state_url":"https://pith.science/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2/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":"2026-06-20T21:22:41Z","links":{"resolver":"https://pith.science/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2","bundle":"https://pith.science/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2/bundle.json","state":"https://pith.science/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TIDX7KEEAOQUJCEJXAPY4SIW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4TIDX7KEEAOQUJCEJXAPY4SIW2","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":"1773a02605e240288c07a999252837ca1d4431e82dd9dd16746ac5413aeff1a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-19T23:33:50Z","title_canon_sha256":"7264ae0a31c2d228edc036518429d18e9a57a7dd0d0d5770c31d8c885457cb03"},"schema_version":"1.0","source":{"id":"1407.5226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5226","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5226v1","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5226","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"4TIDX7KEEAOQ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4TIDX7KEEAOQUJCE","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4TIDX7KE","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:378df719d145ed8b76e7686e238029e5089cb4012d0a9a338939297136b36083","target":"graph","created_at":"2026-05-18T02:47:14Z","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":"This paper consists of two parts. In the first part we describe the recent works on the inverse problems for the wave equation in $(n+1)$-dimensional space equipped with pseudo-Riemannian metric with Lorentz signature. We study the conditions of the existence of black (or white) holes for these wave equations. In the second part we prove energy type estimates on a finite time interval in the presence of black or white holes. We use these estimates to prove the nonuniqueness of the inverse problems.","authors_text":"Gregory Eskin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-19T23:33:50Z","title":"Uniqueness and Nonuniqueness in Inverse Hyperbolic Problems and The Black Hole Phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5226","kind":"arxiv","version":1},"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":"sha256:800095cec0600303080c5bbb7d491a37f55bd5de4b2511f51aa09898d8e93243","target":"record","created_at":"2026-05-18T02:47:14Z","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":"1773a02605e240288c07a999252837ca1d4431e82dd9dd16746ac5413aeff1a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-19T23:33:50Z","title_canon_sha256":"7264ae0a31c2d228edc036518429d18e9a57a7dd0d0d5770c31d8c885457cb03"},"schema_version":"1.0","source":{"id":"1407.5226","kind":"arxiv","version":1}},"canonical_sha256":"e4d03bfd44201d0a24444dc0fc7248b699fafddfd0ce73580c964073023dc003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4d03bfd44201d0a24444dc0fc7248b699fafddfd0ce73580c964073023dc003","first_computed_at":"2026-05-18T02:47:14.636912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:14.636912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gi85I7K8zZP1bLwGfLgJood6qXt8Kbd3dBiOMHl2k0AWADN8xROj6rsakEAZXc9vAk9rThBsiwRnfDz95cyoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:14.637495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:800095cec0600303080c5bbb7d491a37f55bd5de4b2511f51aa09898d8e93243","sha256:378df719d145ed8b76e7686e238029e5089cb4012d0a9a338939297136b36083"],"state_sha256":"80459ade339339a33289e245ade986ed2e470743da548d71b12fef9246262e8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dg3ddemdC1roXwaJXfDCRy8Dg27WRmk6yJzm4bL+feohrn5+XE9Cc9DirJuTQl19iS4zbi0Ue1TQJ5E3OZ/ACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:22:41.995643Z","bundle_sha256":"134246eb378203e854f345bf0c018b363846dad0184d44b7b0f8b13c656039bb"}}