{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QYGTNF24NDO5VN4FP72WKP4MJN","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":"278768ae5f2f8c3a71a33387ba3482757d8a9de2469867746611e0e6c45068fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T09:48:29Z","title_canon_sha256":"fd0b55d32277396a0d2470c6e05451ec2e7e15bf657178ea880160a0f8b2366f"},"schema_version":"1.0","source":{"id":"1608.06438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06438","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06438v1","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06438","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"QYGTNF24NDO5","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QYGTNF24NDO5VN4F","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QYGTNF24","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:ec2e534eb240a13b8c3707a2635b3b9c7e7613b287f5c13e22d7e565059ea304","target":"graph","created_at":"2026-05-18T00:29:21Z","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":"A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for which one of the principal directions of the second fundamental form is the (para-)complex dual of the normal vector.\n  We consider particular Hopf hypersurfaces in the space of oriented geodesics of a non-flat space form of dimension greater than 2. For spherical and hyperbolic space forms, the oriented geodesic space admits a canonical Kaehler-Einstein and para-Kaehler-Einstein structure, respectively, so that a natural notion of a Hopf hypersurface exists.\n  The particular hypersurfaces considered are formed by the ","authors_text":"Brendan Guilfoyle, Nikos Georgiou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T09:48:29Z","title":"Hopf hypersurfaces in spaces of oriented geodesics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06438","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":"sha256:3b7765371335ef317e0ec259fa872522a28492ca7bff6b473f955de1d4204278","target":"record","created_at":"2026-05-18T00:29:21Z","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":"278768ae5f2f8c3a71a33387ba3482757d8a9de2469867746611e0e6c45068fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T09:48:29Z","title_canon_sha256":"fd0b55d32277396a0d2470c6e05451ec2e7e15bf657178ea880160a0f8b2366f"},"schema_version":"1.0","source":{"id":"1608.06438","kind":"arxiv","version":1}},"canonical_sha256":"860d36975c68dddab7857ff5653f8c4b62e5b688e840ce4d95d308a7618f55a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"860d36975c68dddab7857ff5653f8c4b62e5b688e840ce4d95d308a7618f55a2","first_computed_at":"2026-05-18T00:29:21.230292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:21.230292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nmo6ULg2Do23DdMQ5MsEA7jngjYuUcsMREo2rMXg4ZbJ8VYxxoRmIMblJyPm+7vJqonsA2woXGUPMkuc06QWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:21.230880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b7765371335ef317e0ec259fa872522a28492ca7bff6b473f955de1d4204278","sha256:ec2e534eb240a13b8c3707a2635b3b9c7e7613b287f5c13e22d7e565059ea304"],"state_sha256":"9f3948e0446657c8a0b1f4cc628f54c35303e5aa8c67fd43f1216cbc4e772765"}