{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X65HK2E2MMOYSNWGTH7QTXYZNJ","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":"ce89d6beb6b9c965f8ba94171823793b0d3e0894ecd0f74cf70e600bdad0b788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-23T02:00:24Z","title_canon_sha256":"9498a555ffc1d9a342cdc5e3e29212bd016060a9d705dbcecd9ade7b8b324794"},"schema_version":"1.0","source":{"id":"1409.6387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6387","created_at":"2026-05-18T02:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6387v1","created_at":"2026-05-18T02:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6387","created_at":"2026-05-18T02:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"X65HK2E2MMOY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X65HK2E2MMOYSNWG","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X65HK2E2","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:2d4a1f0e38cf51c2568d654b89b1b15502dfa49e66202dd9e25a0c8e7d445ec6","target":"graph","created_at":"2026-05-18T02:42:07Z","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 expression of the curvature tensor of a real hypersurface $M$ in complex hyperbolic two-plane Grassmannians $SU_{2,m}/S(U_2{\\cdot}U_m)$, $m{\\ge}2$ from the equation of Gauss. Next we derive a new formula for the Ricci tensor of $M$ in $SU_{2,m}/S(U_2{\\cdot}U_m)$. Finally we give a complete classification of Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians $SU_{2,m}/S(U_2{\\cdot}U_m)$ with commuting Ricci tensor. Each can be described as a tube over a totally geodesic $SU_{2,m-1}/S(U_2{\\cdot}U_{m-1})$ in $SU_{2,m}/S(U_2{\\cdot}U_m)$ or a h","authors_text":"Young Jin Suh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-23T02:00:24Z","title":"Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians with commuting Ricci tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6387","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:ecb693bd92dc7bdb81a56bfe74bf46900fe6b58bc7c3181b2ab77c0dab1f2ff0","target":"record","created_at":"2026-05-18T02:42:07Z","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":"ce89d6beb6b9c965f8ba94171823793b0d3e0894ecd0f74cf70e600bdad0b788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-23T02:00:24Z","title_canon_sha256":"9498a555ffc1d9a342cdc5e3e29212bd016060a9d705dbcecd9ade7b8b324794"},"schema_version":"1.0","source":{"id":"1409.6387","kind":"arxiv","version":1}},"canonical_sha256":"bfba75689a631d8936c699ff09df196a4bf2c2daa086a8f6e7812fe56072f0cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfba75689a631d8936c699ff09df196a4bf2c2daa086a8f6e7812fe56072f0cc","first_computed_at":"2026-05-18T02:42:07.253420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:07.253420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbT0vDCuixUFkc4xVDjhc57ZyvtRBxdDMwWuRx5grvJvBqufPGdd8M7FPo7IddHDlwwuzbSiBirrWyD/IuBpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:07.253870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecb693bd92dc7bdb81a56bfe74bf46900fe6b58bc7c3181b2ab77c0dab1f2ff0","sha256:2d4a1f0e38cf51c2568d654b89b1b15502dfa49e66202dd9e25a0c8e7d445ec6"],"state_sha256":"e014c37fec63ad669aab45baa1f724f47a88af433f7d738c3722167f45530f6c"}