{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YQP27Z6BFX23Z6IYPUEPS3WZZH","short_pith_number":"pith:YQP27Z6B","canonical_record":{"source":{"id":"1510.05916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T12:47:59Z","cross_cats_sorted":[],"title_canon_sha256":"15a1e7e75a060515c86a36beb28516e632b289122777d2d77d5c3dbbc26a866f","abstract_canon_sha256":"1a074a8eff69a0709da5d13e1705ca437e4d0080afa9069c0cf7550aa03ccd64"},"schema_version":"1.0"},"canonical_sha256":"c41fafe7c12df5bcf9187d08f96ed9c9c7fc04483b03eb410e3697986156892b","source":{"kind":"arxiv","id":"1510.05916","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05916","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05916v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05916","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"YQP27Z6BFX23","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YQP27Z6BFX23Z6IY","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YQP27Z6B","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YQP27Z6BFX23Z6IYPUEPS3WZZH","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T12:47:59Z","cross_cats_sorted":[],"title_canon_sha256":"15a1e7e75a060515c86a36beb28516e632b289122777d2d77d5c3dbbc26a866f","abstract_canon_sha256":"1a074a8eff69a0709da5d13e1705ca437e4d0080afa9069c0cf7550aa03ccd64"},"schema_version":"1.0"},"canonical_sha256":"c41fafe7c12df5bcf9187d08f96ed9c9c7fc04483b03eb410e3697986156892b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:39.341690Z","signature_b64":"aY/Bt1sgf8cFCxMRHSfqYVQXpZ/CjOE+J+0dlszX4TtzZMxbWXm1PUOX/1LRRixlh4iB5RhAfJLpBhKv4weCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c41fafe7c12df5bcf9187d08f96ed9c9c7fc04483b03eb410e3697986156892b","last_reissued_at":"2026-05-18T01:29:39.340966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:39.340966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05916","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":"2026-05-18T01:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4MmgObzi5VrkGRjjnzrxgxwl5aBHuq8lIX6yXDsY/I50wdab3UoFXjW6cSsqZW/dK48afnmUrLI+BLc7McABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:40:47.466360Z"},"content_sha256":"9d46bab062162af517482b5357b81ec0cdbf58bf9e1b7b610d5a51fdf9ae3470","schema_version":"1.0","event_id":"sha256:9d46bab062162af517482b5357b81ec0cdbf58bf9e1b7b610d5a51fdf9ae3470"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YQP27Z6BFX23Z6IYPUEPS3WZZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature Properties of Normal Complex Contact metric Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aysel Turgut Vanli, Inan Unal","submitted_at":"2015-10-13T12:47:59Z","abstract_excerpt":"In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold. Also, we give some new equailities for Ricci curvature of normal complex contact metric manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05916","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":"2026-05-18T01:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4u9bGPOJs4EYoRVeWxCqORX7pRVZ5+jH2TX4eTUmcSd2k/3KIJMEEpdVBk9PejZcwgSU5m+UXJ+Z2OeasMpCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:40:47.466707Z"},"content_sha256":"076bf55204bf961c4cf595d905bab637e84fd5c2611a8ffa5efa49c54aa0a970","schema_version":"1.0","event_id":"sha256:076bf55204bf961c4cf595d905bab637e84fd5c2611a8ffa5efa49c54aa0a970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH/bundle.json","state_url":"https://pith.science/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH/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":"2026-07-04T10:40:47Z","links":{"resolver":"https://pith.science/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH","bundle":"https://pith.science/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH/bundle.json","state":"https://pith.science/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQP27Z6BFX23Z6IYPUEPS3WZZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YQP27Z6BFX23Z6IYPUEPS3WZZH","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":"1a074a8eff69a0709da5d13e1705ca437e4d0080afa9069c0cf7550aa03ccd64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T12:47:59Z","title_canon_sha256":"15a1e7e75a060515c86a36beb28516e632b289122777d2d77d5c3dbbc26a866f"},"schema_version":"1.0","source":{"id":"1510.05916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05916","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05916v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05916","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"YQP27Z6BFX23","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YQP27Z6BFX23Z6IY","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YQP27Z6B","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:076bf55204bf961c4cf595d905bab637e84fd5c2611a8ffa5efa49c54aa0a970","target":"graph","created_at":"2026-05-18T01:29:39Z","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 study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold. Also, we give some new equailities for Ricci curvature of normal complex contact metric manifolds.","authors_text":"Aysel Turgut Vanli, Inan Unal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T12:47:59Z","title":"Curvature Properties of Normal Complex Contact metric Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05916","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":"sha256:9d46bab062162af517482b5357b81ec0cdbf58bf9e1b7b610d5a51fdf9ae3470","target":"record","created_at":"2026-05-18T01:29:39Z","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":"1a074a8eff69a0709da5d13e1705ca437e4d0080afa9069c0cf7550aa03ccd64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T12:47:59Z","title_canon_sha256":"15a1e7e75a060515c86a36beb28516e632b289122777d2d77d5c3dbbc26a866f"},"schema_version":"1.0","source":{"id":"1510.05916","kind":"arxiv","version":1}},"canonical_sha256":"c41fafe7c12df5bcf9187d08f96ed9c9c7fc04483b03eb410e3697986156892b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c41fafe7c12df5bcf9187d08f96ed9c9c7fc04483b03eb410e3697986156892b","first_computed_at":"2026-05-18T01:29:39.340966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:39.340966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aY/Bt1sgf8cFCxMRHSfqYVQXpZ/CjOE+J+0dlszX4TtzZMxbWXm1PUOX/1LRRixlh4iB5RhAfJLpBhKv4weCCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:39.341690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d46bab062162af517482b5357b81ec0cdbf58bf9e1b7b610d5a51fdf9ae3470","sha256:076bf55204bf961c4cf595d905bab637e84fd5c2611a8ffa5efa49c54aa0a970"],"state_sha256":"f98775d171545038c8904d1cd61f27b6e2927f77049e99d52c3be409474eda1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olAoeuY1NX0pHovpEcsfAGnDZc7Bt3gwyuSitdaOM7JgVo+DmyO66tU1F05aooaco834a4Ps5uFKMju9rje4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T10:40:47.468713Z","bundle_sha256":"7c4b1a07dc7ccd1057b25bdad0baa6bf58b81be065ccb90faafdb826794047fe"}}