{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SVWQH43XPVLZSDYRJP7H7VDTXY","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":"cd220a131b391879a006b59109ea059101a802fabe374a20e731db5b0e31daff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-10T11:04:45Z","title_canon_sha256":"9d388e9b2748779103ce3833f3e59298edbd7a04ee36ee610603f69270be5ad4"},"schema_version":"1.0","source":{"id":"1411.2379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2379","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2379v1","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2379","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"SVWQH43XPVLZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SVWQH43XPVLZSDYR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SVWQH43X","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:a2997b23c5e0293e2ae5aaa4bd3b4bfe4a1d962d51923c9001d876ee60b276b7","target":"graph","created_at":"2026-05-18T02:38:07Z","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 introduce new notions of semi-parallel shape operators and structure Jacobi operators in complex two-plane Grassmannians $G_2({\\mathbb C}^{m+2})$. By using such a semi-parallel condition, we give a complete classification of Hopf hypersurfaces in $G_2({\\mathbb C}^{m+2})$.","authors_text":"Changhwa Woo, Doo Hyun Hwang, Hyunjin Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-10T11:04:45Z","title":"Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2379","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":"sha256:7a0e5572fa63b2a0cbdd7721cd1909f90292a0a9e4458c445f629b9f41809ce1","target":"record","created_at":"2026-05-18T02:38:07Z","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":"cd220a131b391879a006b59109ea059101a802fabe374a20e731db5b0e31daff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-10T11:04:45Z","title_canon_sha256":"9d388e9b2748779103ce3833f3e59298edbd7a04ee36ee610603f69270be5ad4"},"schema_version":"1.0","source":{"id":"1411.2379","kind":"arxiv","version":1}},"canonical_sha256":"956d03f3777d57990f114bfe7fd473be1e6e823db836cb845b0f4394e248b1b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"956d03f3777d57990f114bfe7fd473be1e6e823db836cb845b0f4394e248b1b0","first_computed_at":"2026-05-18T02:38:07.640085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:07.640085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZaN8nJv4qUMOYpgINPRvBfqEaSJ3najCs9zcEY0q9o+6hXJCZZ1Mjm1bs/kndkNZrrFexBDVGmOwbTtt1/VaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:07.640513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a0e5572fa63b2a0cbdd7721cd1909f90292a0a9e4458c445f629b9f41809ce1","sha256:a2997b23c5e0293e2ae5aaa4bd3b4bfe4a1d962d51923c9001d876ee60b276b7"],"state_sha256":"71fe828709afb6206abf50ae7650497fea706fcf0a9dd114d2726c087ddd977e"}