{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LIHABVJLGAK7TO3P4WVJINTD2E","short_pith_number":"pith:LIHABVJL","canonical_record":{"source":{"id":"1512.03671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-10T02:37:39Z","cross_cats_sorted":[],"title_canon_sha256":"41c52c531b9eac3fbcf2999b277e58519f59bd122ff95b7e22ee3d5c0cee953d","abstract_canon_sha256":"3a58e637fb295f286bc208d50b5b5a2dcbb12deee621f0761bd46c0f3270af22"},"schema_version":"1.0"},"canonical_sha256":"5a0e00d52b3015f9bb6fe5aa943663d12573c2ae3175820f16b607e5473f9bcd","source":{"kind":"arxiv","id":"1512.03671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03671","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03671v1","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03671","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"pith_short_12","alias_value":"LIHABVJLGAK7","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LIHABVJLGAK7TO3P","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LIHABVJL","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LIHABVJLGAK7TO3P4WVJINTD2E","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-10T02:37:39Z","cross_cats_sorted":[],"title_canon_sha256":"41c52c531b9eac3fbcf2999b277e58519f59bd122ff95b7e22ee3d5c0cee953d","abstract_canon_sha256":"3a58e637fb295f286bc208d50b5b5a2dcbb12deee621f0761bd46c0f3270af22"},"schema_version":"1.0"},"canonical_sha256":"5a0e00d52b3015f9bb6fe5aa943663d12573c2ae3175820f16b607e5473f9bcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:51.760646Z","signature_b64":"WDOwgZUhgHoDz6ouaXSGQNfhYlvteGTgLcayoTyMK21tGgrwVUPlvP6Y305rbXos9h4cdr0XLxNIWR1zq7lrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a0e00d52b3015f9bb6fe5aa943663d12573c2ae3175820f16b607e5473f9bcd","last_reissued_at":"2026-05-18T01:15:51.760254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:51.760254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03671","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":"2026-05-18T01:15:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gjSdCOYOlbGpuKmVetzkosr5ygmgHZnMHPQCdtUW+cUu1HShcEY5Eb5kYai3Ny+Ar9ZnsNnzEfvEth2swTcwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:36:30.663482Z"},"content_sha256":"1dbdb790e96a6a2d99fede33d13411d3492f6dcad0c329f382d56cb9eaca3652","schema_version":"1.0","event_id":"sha256:1dbdb790e96a6a2d99fede33d13411d3492f6dcad0c329f382d56cb9eaca3652"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LIHABVJLGAK7TO3P4WVJINTD2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real hypersurfaces in the complex quadric with commuting Ricci tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Doo Hyun Hwang, Young Jin Suh","submitted_at":"2015-12-10T02:37:39Z","abstract_excerpt":"We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ . It is shown that the commuting Ricci tensor gives that the unit normal vector field $N$ becomes $\\frak A$-principal or $\\frak A$-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^m = SO_{m+2}/SO_mSO_2$ with commuting Ricci tensor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03671","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":"2026-05-18T01:15:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIq8j6sLEgEiNjZQa2wA3sSpM6cz/l+Tw/GlxJcrgvNwDIfd51++YE+fmkUYcI9TN9OYisBlp/zbIwquBd4SBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:36:30.664155Z"},"content_sha256":"feb15753be0175ccdc1d0ead1c2d13daa67eb7efeb4f2c66e050197106f8b5bd","schema_version":"1.0","event_id":"sha256:feb15753be0175ccdc1d0ead1c2d13daa67eb7efeb4f2c66e050197106f8b5bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIHABVJLGAK7TO3P4WVJINTD2E/bundle.json","state_url":"https://pith.science/pith/LIHABVJLGAK7TO3P4WVJINTD2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIHABVJLGAK7TO3P4WVJINTD2E/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":"2026-06-11T06:36:30Z","links":{"resolver":"https://pith.science/pith/LIHABVJLGAK7TO3P4WVJINTD2E","bundle":"https://pith.science/pith/LIHABVJLGAK7TO3P4WVJINTD2E/bundle.json","state":"https://pith.science/pith/LIHABVJLGAK7TO3P4WVJINTD2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIHABVJLGAK7TO3P4WVJINTD2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LIHABVJLGAK7TO3P4WVJINTD2E","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":"3a58e637fb295f286bc208d50b5b5a2dcbb12deee621f0761bd46c0f3270af22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-10T02:37:39Z","title_canon_sha256":"41c52c531b9eac3fbcf2999b277e58519f59bd122ff95b7e22ee3d5c0cee953d"},"schema_version":"1.0","source":{"id":"1512.03671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03671","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03671v1","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03671","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"pith_short_12","alias_value":"LIHABVJLGAK7","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LIHABVJLGAK7TO3P","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LIHABVJL","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:feb15753be0175ccdc1d0ead1c2d13daa67eb7efeb4f2c66e050197106f8b5bd","target":"graph","created_at":"2026-05-18T01:15:51Z","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":"We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ . It is shown that the commuting Ricci tensor gives that the unit normal vector field $N$ becomes $\\frak A$-principal or $\\frak A$-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^m = SO_{m+2}/SO_mSO_2$ with commuting Ricci tensor.","authors_text":"Doo Hyun Hwang, Young Jin Suh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-10T02:37:39Z","title":"Real hypersurfaces in the complex quadric with commuting Ricci tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03671","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":"sha256:1dbdb790e96a6a2d99fede33d13411d3492f6dcad0c329f382d56cb9eaca3652","target":"record","created_at":"2026-05-18T01:15:51Z","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":"3a58e637fb295f286bc208d50b5b5a2dcbb12deee621f0761bd46c0f3270af22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-10T02:37:39Z","title_canon_sha256":"41c52c531b9eac3fbcf2999b277e58519f59bd122ff95b7e22ee3d5c0cee953d"},"schema_version":"1.0","source":{"id":"1512.03671","kind":"arxiv","version":1}},"canonical_sha256":"5a0e00d52b3015f9bb6fe5aa943663d12573c2ae3175820f16b607e5473f9bcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a0e00d52b3015f9bb6fe5aa943663d12573c2ae3175820f16b607e5473f9bcd","first_computed_at":"2026-05-18T01:15:51.760254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:51.760254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDOwgZUhgHoDz6ouaXSGQNfhYlvteGTgLcayoTyMK21tGgrwVUPlvP6Y305rbXos9h4cdr0XLxNIWR1zq7lrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:51.760646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dbdb790e96a6a2d99fede33d13411d3492f6dcad0c329f382d56cb9eaca3652","sha256:feb15753be0175ccdc1d0ead1c2d13daa67eb7efeb4f2c66e050197106f8b5bd"],"state_sha256":"2ee82d104d0f263c5ff4224920d8dee57801d91c7ad12743bd6971562bbd27ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKLbExIVCh/5LiNFnYzUjt2P+IEuBCSqP+ATy9I00aA1OSdwd8DmWA7cLcXh2lNvMpndwFB1ZztW4inv3b+TDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:36:30.667999Z","bundle_sha256":"62c327c7e1267a4d3753bd9c7e1ad785ba832b77137dbcedda802560ee23a516"}}