{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6MDF35MNI7XBTNEMJZGYANHK4Q","short_pith_number":"pith:6MDF35MN","canonical_record":{"source":{"id":"1806.05604","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-14T15:15:28Z","cross_cats_sorted":[],"title_canon_sha256":"c51bcafb8a4faf02e1edbc008feb4e14d7736ce2f8ce70c3e8c53980e84250eb","abstract_canon_sha256":"0b8d89e41f711ff38fb12f0fe799b4a42a9acc9ff0ec8672a4404690739c4245"},"schema_version":"1.0"},"canonical_sha256":"f3065df58d47ee19b48c4e4d8034eae4301a6864ab1dc5db0dfa4c0fbd850310","source":{"kind":"arxiv","id":"1806.05604","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05604","created_at":"2026-05-18T00:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05604v3","created_at":"2026-05-18T00:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05604","created_at":"2026-05-18T00:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"6MDF35MNI7XB","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6MDF35MNI7XBTNEM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6MDF35MN","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6MDF35MNI7XBTNEMJZGYANHK4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05604","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-14T15:15:28Z","cross_cats_sorted":[],"title_canon_sha256":"c51bcafb8a4faf02e1edbc008feb4e14d7736ce2f8ce70c3e8c53980e84250eb","abstract_canon_sha256":"0b8d89e41f711ff38fb12f0fe799b4a42a9acc9ff0ec8672a4404690739c4245"},"schema_version":"1.0"},"canonical_sha256":"f3065df58d47ee19b48c4e4d8034eae4301a6864ab1dc5db0dfa4c0fbd850310","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:27.452954Z","signature_b64":"EmjzAcJzOkLURagG6IxffBGgVCMLfZM8o6GU+ohipqUwjwPHkHZAm2TgxzyvDyCK4cuf6FbmoAh3htjfpbE5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3065df58d47ee19b48c4e4d8034eae4301a6864ab1dc5db0dfa4c0fbd850310","last_reissued_at":"2026-05-18T00:03:27.452476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:27.452476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05604","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phgUZ/LQtO7XU1Xs2DAu4Oh5oqs7Iz8zp2HP1qu4jIh5AMe5T3tElLEB94r97QxOrIMxGKMugJRSt1AIqgdnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:14:24.775827Z"},"content_sha256":"718f4d599b44b3e3d2b75ad99438496652826c7b2122b3921124a7c5cba97ef8","schema_version":"1.0","event_id":"sha256:718f4d599b44b3e3d2b75ad99438496652826c7b2122b3921124a7c5cba97ef8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6MDF35MNI7XBTNEMJZGYANHK4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank of Jacobi operator and existence of quadratic parallel differential form, with applications to geometry of almost para-contact metric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Piotr Dacko","submitted_at":"2018-06-14T15:15:28Z","abstract_excerpt":"It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows that manifold as pseudo-Riemannian manifold is locally non-reducible. In particular result can be applied directly to known classes of almost (para-) contact metric manifolds when considered Jacobi operator of characteristic vector field has maximal rank. There is effective algorithmic procedure which resolves the problem of existence of such vect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05604","kind":"arxiv","version":3},"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":"2026-05-18T00:03:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMoXoOH/KvpMAiwOVwvb44ENDRlQuoTYgybOLV6vc4NHVboDWKKOXSWG6LNouvk1F+VQEb+i6fvbVg5XOT5PAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:14:24.776179Z"},"content_sha256":"55b5dced420c49111663a5bbd34af76b3c055dd99e09cb50a04dda021898dc0c","schema_version":"1.0","event_id":"sha256:55b5dced420c49111663a5bbd34af76b3c055dd99e09cb50a04dda021898dc0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MDF35MNI7XBTNEMJZGYANHK4Q/bundle.json","state_url":"https://pith.science/pith/6MDF35MNI7XBTNEMJZGYANHK4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MDF35MNI7XBTNEMJZGYANHK4Q/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":"2026-06-22T18:14:24Z","links":{"resolver":"https://pith.science/pith/6MDF35MNI7XBTNEMJZGYANHK4Q","bundle":"https://pith.science/pith/6MDF35MNI7XBTNEMJZGYANHK4Q/bundle.json","state":"https://pith.science/pith/6MDF35MNI7XBTNEMJZGYANHK4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MDF35MNI7XBTNEMJZGYANHK4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6MDF35MNI7XBTNEMJZGYANHK4Q","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":"0b8d89e41f711ff38fb12f0fe799b4a42a9acc9ff0ec8672a4404690739c4245","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-14T15:15:28Z","title_canon_sha256":"c51bcafb8a4faf02e1edbc008feb4e14d7736ce2f8ce70c3e8c53980e84250eb"},"schema_version":"1.0","source":{"id":"1806.05604","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05604","created_at":"2026-05-18T00:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05604v3","created_at":"2026-05-18T00:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05604","created_at":"2026-05-18T00:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"6MDF35MNI7XB","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6MDF35MNI7XBTNEM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6MDF35MN","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:55b5dced420c49111663a5bbd34af76b3c055dd99e09cb50a04dda021898dc0c","target":"graph","created_at":"2026-05-18T00:03:27Z","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":"It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows that manifold as pseudo-Riemannian manifold is locally non-reducible. In particular result can be applied directly to known classes of almost (para-) contact metric manifolds when considered Jacobi operator of characteristic vector field has maximal rank. There is effective algorithmic procedure which resolves the problem of existence of such vect","authors_text":"Piotr Dacko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-14T15:15:28Z","title":"Rank of Jacobi operator and existence of quadratic parallel differential form, with applications to geometry of almost para-contact metric manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05604","kind":"arxiv","version":3},"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":"sha256:718f4d599b44b3e3d2b75ad99438496652826c7b2122b3921124a7c5cba97ef8","target":"record","created_at":"2026-05-18T00:03:27Z","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":"0b8d89e41f711ff38fb12f0fe799b4a42a9acc9ff0ec8672a4404690739c4245","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-14T15:15:28Z","title_canon_sha256":"c51bcafb8a4faf02e1edbc008feb4e14d7736ce2f8ce70c3e8c53980e84250eb"},"schema_version":"1.0","source":{"id":"1806.05604","kind":"arxiv","version":3}},"canonical_sha256":"f3065df58d47ee19b48c4e4d8034eae4301a6864ab1dc5db0dfa4c0fbd850310","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3065df58d47ee19b48c4e4d8034eae4301a6864ab1dc5db0dfa4c0fbd850310","first_computed_at":"2026-05-18T00:03:27.452476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:27.452476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EmjzAcJzOkLURagG6IxffBGgVCMLfZM8o6GU+ohipqUwjwPHkHZAm2TgxzyvDyCK4cuf6FbmoAh3htjfpbE5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:27.452954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05604","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:718f4d599b44b3e3d2b75ad99438496652826c7b2122b3921124a7c5cba97ef8","sha256:55b5dced420c49111663a5bbd34af76b3c055dd99e09cb50a04dda021898dc0c"],"state_sha256":"6134d22121634d6676c2a727f6cc844f21e03b39ce619f37dcda692f958ee6a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IP8InzptGiBZiUC4efV6Drytrv1tCblgDK6rXRdMPxIY+L+vO+Q5T8RVx4QwMVcHV6MsKbsR7AFs5aAfX0jADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:14:24.778132Z","bundle_sha256":"47178ed3ee2d8fdf5c7bf74984b61e907c8b22a789e247c7339b24c893e74a13"}}