{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NCCYCT6Y53WEIL7SXWV3G2NGFX","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":"e863603867339305360c90879d7820e44805b67a0f2bfc56a67a7580b9849bec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-29T08:08:20Z","title_canon_sha256":"00c96b5d6c710baa903d781b2d11d241cb44cbf9f10bdad2069de860d67d1e17"},"schema_version":"1.0","source":{"id":"1807.11021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11021","created_at":"2026-05-17T23:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11021v2","created_at":"2026-05-17T23:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11021","created_at":"2026-05-17T23:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"NCCYCT6Y53WE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NCCYCT6Y53WEIL7S","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NCCYCT6Y","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:44eff68c256436578ace7200f0df1e7a4961ceefd068bbc6e0d1adc541e3b8cf","target":"graph","created_at":"2026-05-17T23:55:42Z","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 real hypersurfaces in the complex quadric space $Q^m$ whose structure Jacobi operator commutes with their structure tensor field. We show that the Reeb curvature $\\alpha$ of such hypersurfaces is constant and if $\\alpha$ is non-zero then the hypersurface is a tube around a totally geodesic submanifold $\\mathbb{C} P^k \\subset Q^m$, where $m=2k$. We also consider Reeb flat hypersurfaces, namely, when the Reeb curvature is zero. We show that the tube around $\\mathbb{C} P^k \\subset Q^m$ ($m=2k$), with radius $\\frac{\\pi}{4}$ is the only Reeb flat Hopf hypersurface with commut","authors_text":"M.J. Vanaei, N. Heidari, S.M.B. Kashani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-29T08:08:20Z","title":"Real hypersurfaces in $Q^m$ with commuting structure Jacobi operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11021","kind":"arxiv","version":2},"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":"sha256:6146455526398df57bd6eb2cb0a4571868d72e512c92a37b864d2964c803194c","target":"record","created_at":"2026-05-17T23:55:42Z","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":"e863603867339305360c90879d7820e44805b67a0f2bfc56a67a7580b9849bec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-29T08:08:20Z","title_canon_sha256":"00c96b5d6c710baa903d781b2d11d241cb44cbf9f10bdad2069de860d67d1e17"},"schema_version":"1.0","source":{"id":"1807.11021","kind":"arxiv","version":2}},"canonical_sha256":"6885814fd8eeec442ff2bdabb369a62df3b6c298a24241f124e668bf362e6ced","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6885814fd8eeec442ff2bdabb369a62df3b6c298a24241f124e668bf362e6ced","first_computed_at":"2026-05-17T23:55:42.680183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:42.680183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dCcppkQQn76s1bhsE3/csYCIoq62cV6yga5Ip5ZSKe1NFQMLlz2LLXGy3NPbeGRXqeUA5YQO0fTV8Bz0WFzcCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:42.680831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6146455526398df57bd6eb2cb0a4571868d72e512c92a37b864d2964c803194c","sha256:44eff68c256436578ace7200f0df1e7a4961ceefd068bbc6e0d1adc541e3b8cf"],"state_sha256":"a4eee9ecaf6df4b869a3cb3524c3e1bfdef7602ece0318ab97df0eb71809c129"}