{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PTOVSQUMQJD7VADRCTH6WRXW3D","short_pith_number":"pith:PTOVSQUM","canonical_record":{"source":{"id":"1907.04661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-09T00:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"b3fb185495e3076d5ab9470240f10664b3e66fbc62072ba8df084de2e08f4760","abstract_canon_sha256":"2fcb9f3e81128ad5212abefd8cac24580ab66f05ff9e013f8445098931b7333d"},"schema_version":"1.0"},"canonical_sha256":"7cdd59428c8247fa807114cfeb46f6d8d0fc20cd62c89abb3285753a7c34ea01","source":{"kind":"arxiv","id":"1907.04661","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04661","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04661v1","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04661","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"PTOVSQUMQJD7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PTOVSQUMQJD7VADR","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PTOVSQUM","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PTOVSQUMQJD7VADRCTH6WRXW3D","target":"record","payload":{"canonical_record":{"source":{"id":"1907.04661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-09T00:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"b3fb185495e3076d5ab9470240f10664b3e66fbc62072ba8df084de2e08f4760","abstract_canon_sha256":"2fcb9f3e81128ad5212abefd8cac24580ab66f05ff9e013f8445098931b7333d"},"schema_version":"1.0"},"canonical_sha256":"7cdd59428c8247fa807114cfeb46f6d8d0fc20cd62c89abb3285753a7c34ea01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:57.184527Z","signature_b64":"1PuU3BV/YEBWWfeGosl9fzs0z07Q2dfJyk7XS6Hw/1f4OteLEPDyB3cfX6pLOQRFQDhnMME9Jv1b4r06MUwEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cdd59428c8247fa807114cfeb46f6d8d0fc20cd62c89abb3285753a7c34ea01","last_reissued_at":"2026-05-17T23:40:57.183969Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:57.183969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.04661","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":"2026-05-17T23:40:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gg71BmZFOziWmA9pcxCdMbTv217SpwbU92hMSGv1j4vLO8oTVy/rG21kktvaGaI9HB+3lE0bEGQxMMbYuCIzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:55:08.083092Z"},"content_sha256":"244bdc615888aa066eedfaa0facb1e765041c1c8aa0e7ced11876a72380886dd","schema_version":"1.0","event_id":"sha256:244bdc615888aa066eedfaa0facb1e765041c1c8aa0e7ced11876a72380886dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PTOVSQUMQJD7VADRCTH6WRXW3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hyunjin Lee, Young Jin Suh","submitted_at":"2019-07-09T00:46:28Z","abstract_excerpt":"In this paper, we first introduce the full express of the Riemannian curvature tensor of a real hypersurface $M$ in complex quadric $Q^{m}$ from the equation of Gauss. Next we derive a formula for the structure Jacobi operator $R_{\\xi}$ and its derivative under the Levi-Civita connection of $M$. We give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, $\\nabla_{\\xi}R_{\\xi} =0$, in the complex quadric $Q^{m}$, $m \\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04661","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":"2026-05-17T23:40:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g6Y7bRwDDp25ThycT/vmo1O1Crsv1lSx43uKl0tCrmbMHs27RTJWsC9y5RhLlgjizhDGjFVna/BYH1bVSNzEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:55:08.083730Z"},"content_sha256":"496cfc074cddc1a221d0510e7d93e0ac4e26ea73de4ffcb4ca210f72a24a0f8d","schema_version":"1.0","event_id":"sha256:496cfc074cddc1a221d0510e7d93e0ac4e26ea73de4ffcb4ca210f72a24a0f8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTOVSQUMQJD7VADRCTH6WRXW3D/bundle.json","state_url":"https://pith.science/pith/PTOVSQUMQJD7VADRCTH6WRXW3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTOVSQUMQJD7VADRCTH6WRXW3D/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":"2026-05-25T19:55:08Z","links":{"resolver":"https://pith.science/pith/PTOVSQUMQJD7VADRCTH6WRXW3D","bundle":"https://pith.science/pith/PTOVSQUMQJD7VADRCTH6WRXW3D/bundle.json","state":"https://pith.science/pith/PTOVSQUMQJD7VADRCTH6WRXW3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTOVSQUMQJD7VADRCTH6WRXW3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PTOVSQUMQJD7VADRCTH6WRXW3D","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":"2fcb9f3e81128ad5212abefd8cac24580ab66f05ff9e013f8445098931b7333d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-09T00:46:28Z","title_canon_sha256":"b3fb185495e3076d5ab9470240f10664b3e66fbc62072ba8df084de2e08f4760"},"schema_version":"1.0","source":{"id":"1907.04661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04661","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04661v1","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04661","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"PTOVSQUMQJD7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PTOVSQUMQJD7VADR","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PTOVSQUM","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:496cfc074cddc1a221d0510e7d93e0ac4e26ea73de4ffcb4ca210f72a24a0f8d","target":"graph","created_at":"2026-05-17T23:40:57Z","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":"In this paper, we first introduce the full express of the Riemannian curvature tensor of a real hypersurface $M$ in complex quadric $Q^{m}$ from the equation of Gauss. Next we derive a formula for the structure Jacobi operator $R_{\\xi}$ and its derivative under the Levi-Civita connection of $M$. We give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, $\\nabla_{\\xi}R_{\\xi} =0$, in the complex quadric $Q^{m}$, $m \\geq 3$.","authors_text":"Hyunjin Lee, Young Jin Suh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-09T00:46:28Z","title":"Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04661","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":"sha256:244bdc615888aa066eedfaa0facb1e765041c1c8aa0e7ced11876a72380886dd","target":"record","created_at":"2026-05-17T23:40:57Z","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":"2fcb9f3e81128ad5212abefd8cac24580ab66f05ff9e013f8445098931b7333d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-09T00:46:28Z","title_canon_sha256":"b3fb185495e3076d5ab9470240f10664b3e66fbc62072ba8df084de2e08f4760"},"schema_version":"1.0","source":{"id":"1907.04661","kind":"arxiv","version":1}},"canonical_sha256":"7cdd59428c8247fa807114cfeb46f6d8d0fc20cd62c89abb3285753a7c34ea01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cdd59428c8247fa807114cfeb46f6d8d0fc20cd62c89abb3285753a7c34ea01","first_computed_at":"2026-05-17T23:40:57.183969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:57.183969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1PuU3BV/YEBWWfeGosl9fzs0z07Q2dfJyk7XS6Hw/1f4OteLEPDyB3cfX6pLOQRFQDhnMME9Jv1b4r06MUwEDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:57.184527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:244bdc615888aa066eedfaa0facb1e765041c1c8aa0e7ced11876a72380886dd","sha256:496cfc074cddc1a221d0510e7d93e0ac4e26ea73de4ffcb4ca210f72a24a0f8d"],"state_sha256":"dd671da5310ec2f6344953a8a0c221b3f24860a0d8e74417815f1308de3964e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8uuhAUR7/LbP8KkGKqQx/xijtiF9c2oH4FZKk03npmyp5QzjXEfbEVNbEmkP6RfPNBipfatZ9MoaomIIHrmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:55:08.087363Z","bundle_sha256":"c2a04f47f856a8ef850f6a80367fbbd788e174ab9229614c816892850ee6e134"}}