{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X65HK2E2MMOYSNWGTH7QTXYZNJ","short_pith_number":"pith:X65HK2E2","canonical_record":{"source":{"id":"1409.6387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-23T02:00:24Z","cross_cats_sorted":[],"title_canon_sha256":"9498a555ffc1d9a342cdc5e3e29212bd016060a9d705dbcecd9ade7b8b324794","abstract_canon_sha256":"ce89d6beb6b9c965f8ba94171823793b0d3e0894ecd0f74cf70e600bdad0b788"},"schema_version":"1.0"},"canonical_sha256":"bfba75689a631d8936c699ff09df196a4bf2c2daa086a8f6e7812fe56072f0cc","source":{"kind":"arxiv","id":"1409.6387","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X65HK2E2MMOYSNWGTH7QTXYZNJ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-23T02:00:24Z","cross_cats_sorted":[],"title_canon_sha256":"9498a555ffc1d9a342cdc5e3e29212bd016060a9d705dbcecd9ade7b8b324794","abstract_canon_sha256":"ce89d6beb6b9c965f8ba94171823793b0d3e0894ecd0f74cf70e600bdad0b788"},"schema_version":"1.0"},"canonical_sha256":"bfba75689a631d8936c699ff09df196a4bf2c2daa086a8f6e7812fe56072f0cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:07.253870Z","signature_b64":"vbT0vDCuixUFkc4xVDjhc57ZyvtRBxdDMwWuRx5grvJvBqufPGdd8M7FPo7IddHDlwwuzbSiBirrWyD/IuBpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfba75689a631d8936c699ff09df196a4bf2c2daa086a8f6e7812fe56072f0cc","last_reissued_at":"2026-05-18T02:42:07.253420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:07.253420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6387","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":"2026-05-18T02:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k65M1cYTBW2d00v0hyBiUzSGymPhixHkIvcR4WM0FwKLntXokvztvC9+8jEq5c+wqR50gHydUAkWqOzjcM1oDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:04:31.230662Z"},"content_sha256":"ecb693bd92dc7bdb81a56bfe74bf46900fe6b58bc7c3181b2ab77c0dab1f2ff0","schema_version":"1.0","event_id":"sha256:ecb693bd92dc7bdb81a56bfe74bf46900fe6b58bc7c3181b2ab77c0dab1f2ff0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X65HK2E2MMOYSNWGTH7QTXYZNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians with commuting Ricci tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Young Jin Suh","submitted_at":"2014-09-23T02:00:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6387","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":"2026-05-18T02:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PA8EbIYxOyiWD726doz/RKIiMZ35cP7QNUrp7XMXGgmZ58hNIp4EZw7w6RMVU3G34E5es7xkpV24CKft9u2DCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:04:31.231011Z"},"content_sha256":"2d4a1f0e38cf51c2568d654b89b1b15502dfa49e66202dd9e25a0c8e7d445ec6","schema_version":"1.0","event_id":"sha256:2d4a1f0e38cf51c2568d654b89b1b15502dfa49e66202dd9e25a0c8e7d445ec6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ/bundle.json","state_url":"https://pith.science/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ/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":"2026-06-11T12:04:31Z","links":{"resolver":"https://pith.science/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ","bundle":"https://pith.science/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ/bundle.json","state":"https://pith.science/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X65HK2E2MMOYSNWGTH7QTXYZNJ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ydiob79fpcczZLnwc7htyO475yyT0dyswoYnI0mY1dBe82jpKTPHFn/VFKZEa+ERSJIXf9/+8+cBd/P8H7VCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:04:31.233040Z","bundle_sha256":"cf267960bfa39e3bcc9d5a006bc8d619dc55ce263bb8216e7bc5a20fd36e947b"}}