{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RHHZOONHSTREGFWWBCMVSBVSP3","short_pith_number":"pith:RHHZOONH","canonical_record":{"source":{"id":"1612.04437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T00:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"fa2f318c0e1507457c7e37570ce663cfa34add61f66974c741e2382323a68d7c","abstract_canon_sha256":"b0fdfb19b4eb9420eaf085d918d499fc249068db60d8ffffced06a6e71dda82d"},"schema_version":"1.0"},"canonical_sha256":"89cf9739a794e24316d608995906b27ed660603ac7bf208e9e7ef67a3975b22f","source":{"kind":"arxiv","id":"1612.04437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04437","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04437v1","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04437","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"RHHZOONHSTRE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHHZOONHSTREGFWW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHHZOONH","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RHHZOONHSTREGFWWBCMVSBVSP3","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T00:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"fa2f318c0e1507457c7e37570ce663cfa34add61f66974c741e2382323a68d7c","abstract_canon_sha256":"b0fdfb19b4eb9420eaf085d918d499fc249068db60d8ffffced06a6e71dda82d"},"schema_version":"1.0"},"canonical_sha256":"89cf9739a794e24316d608995906b27ed660603ac7bf208e9e7ef67a3975b22f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:59.565329Z","signature_b64":"ziimFwgqYDjH2Rz3mLm9K7EM8Fu3CVvwoct7fYVNO1FJLSt8GZLEz2UaKaXQ0Jn6XNithzKXu6ADUK3dXkfQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89cf9739a794e24316d608995906b27ed660603ac7bf208e9e7ef67a3975b22f","last_reissued_at":"2026-05-18T00:54:59.564853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:59.564853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04437","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":"2026-05-18T00:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZVO2JtRqoyfNkCAT9TBUgXqd5KBwdA6Bap3NyQRyMGfOxW0VZZyCaKI5IVvAud8KkaWjIoyPiRBaBHcNJbsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T12:32:10.001158Z"},"content_sha256":"f0aee762d9605ef3631a648d6fd8fa9953166ebefc8f9b1581500ed958e24a13","schema_version":"1.0","event_id":"sha256:f0aee762d9605ef3631a648d6fd8fa9953166ebefc8f9b1581500ed958e24a13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RHHZOONHSTREGFWWBCMVSBVSP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse problems for quadratic derivative nonlinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ting Zhou, Yiran Wang","submitted_at":"2016-12-14T00:07:26Z","abstract_excerpt":"For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from the source-to-solution map, one can determine the Lorentzian metric up to diffeomorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04437","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":"2026-05-18T00:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2XsG4Gsj9xtQfE6V4S1PPwSscCuVhzz+j0tTIbh7VG9QRx6LLOhqfByWWZEwJhUvpu4+rHX9QuqmIYPg/o96CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T12:32:10.001736Z"},"content_sha256":"c128904406820c172264883ad15c1a45a4be0500df26acc974a8b311ca600142","schema_version":"1.0","event_id":"sha256:c128904406820c172264883ad15c1a45a4be0500df26acc974a8b311ca600142"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHHZOONHSTREGFWWBCMVSBVSP3/bundle.json","state_url":"https://pith.science/pith/RHHZOONHSTREGFWWBCMVSBVSP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHHZOONHSTREGFWWBCMVSBVSP3/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":"2026-05-24T12:32:10Z","links":{"resolver":"https://pith.science/pith/RHHZOONHSTREGFWWBCMVSBVSP3","bundle":"https://pith.science/pith/RHHZOONHSTREGFWWBCMVSBVSP3/bundle.json","state":"https://pith.science/pith/RHHZOONHSTREGFWWBCMVSBVSP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHHZOONHSTREGFWWBCMVSBVSP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RHHZOONHSTREGFWWBCMVSBVSP3","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":"b0fdfb19b4eb9420eaf085d918d499fc249068db60d8ffffced06a6e71dda82d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T00:07:26Z","title_canon_sha256":"fa2f318c0e1507457c7e37570ce663cfa34add61f66974c741e2382323a68d7c"},"schema_version":"1.0","source":{"id":"1612.04437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04437","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04437v1","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04437","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"RHHZOONHSTRE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHHZOONHSTREGFWW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHHZOONH","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:c128904406820c172264883ad15c1a45a4be0500df26acc974a8b311ca600142","target":"graph","created_at":"2026-05-18T00:54:59Z","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"},"paper":{"abstract_excerpt":"For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from the source-to-solution map, one can determine the Lorentzian metric up to diffeomorphisms.","authors_text":"Ting Zhou, Yiran Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T00:07:26Z","title":"Inverse problems for quadratic derivative nonlinear wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04437","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:f0aee762d9605ef3631a648d6fd8fa9953166ebefc8f9b1581500ed958e24a13","target":"record","created_at":"2026-05-18T00:54:59Z","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":"b0fdfb19b4eb9420eaf085d918d499fc249068db60d8ffffced06a6e71dda82d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T00:07:26Z","title_canon_sha256":"fa2f318c0e1507457c7e37570ce663cfa34add61f66974c741e2382323a68d7c"},"schema_version":"1.0","source":{"id":"1612.04437","kind":"arxiv","version":1}},"canonical_sha256":"89cf9739a794e24316d608995906b27ed660603ac7bf208e9e7ef67a3975b22f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89cf9739a794e24316d608995906b27ed660603ac7bf208e9e7ef67a3975b22f","first_computed_at":"2026-05-18T00:54:59.564853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:59.564853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ziimFwgqYDjH2Rz3mLm9K7EM8Fu3CVvwoct7fYVNO1FJLSt8GZLEz2UaKaXQ0Jn6XNithzKXu6ADUK3dXkfQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:59.565329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0aee762d9605ef3631a648d6fd8fa9953166ebefc8f9b1581500ed958e24a13","sha256:c128904406820c172264883ad15c1a45a4be0500df26acc974a8b311ca600142"],"state_sha256":"839919acd09895fcb4a7d8de5e0c7cb349f3e40799011194437925fbcbcffbd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FulDtAl9k9/2TEzF0hynI3BFxM0tdBjjo2aiWztvFSeeI2yKVmb1HHPGPXawuoTe1SxWsE2lxCe1rc8pzSRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T12:32:10.005296Z","bundle_sha256":"14c1633d40e4fbb423d901909a6d07aa47e1f3883845f9e860b5532438a76c25"}}