{"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"}