{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:73AANUWSA4HY6PT6BZJL235UA2","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":"1adf22689a2573aaf10eac32f62f5edfd239be0270634359cc1220a88fb6ca0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-24T20:18:21Z","title_canon_sha256":"5ca884710797bc3be2fe555e538e5c0123c3bbd49a29277b1c4ccfc3bc1e7c0c"},"schema_version":"1.0","source":{"id":"1602.07660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07660","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07660v1","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07660","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"73AANUWSA4HY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"73AANUWSA4HY6PT6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"73AANUWS","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:0ff2ebd317957da351aca45f14e0572424d684221b3cee8680c88cdb9a793f5c","target":"graph","created_at":"2026-05-18T01:20:02Z","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 study conjugate points along homogeneous geodesics in generalized flag manifolds. This is done by analyzing the second variation of the energy of such geodesics. We also give an example of how the homogeneous Ricci flow can evolve in such way to produce conjugate points in the complex projective space $\\mathbb{C} P^{2n+1} = Sp(n+1)/({U}(1)\\times{Sp}(n))$.","authors_text":"Lino Grama, Rafaela F. do Prado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-24T20:18:21Z","title":"Variational aspects of homogeneous geodesics on generalized flag manifolds and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07660","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":"sha256:17de27197496a40bff9fa978c2cce512233c2484794c2e7e2ddb8f3f93c6b074","target":"record","created_at":"2026-05-18T01:20:02Z","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":"1adf22689a2573aaf10eac32f62f5edfd239be0270634359cc1220a88fb6ca0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-24T20:18:21Z","title_canon_sha256":"5ca884710797bc3be2fe555e538e5c0123c3bbd49a29277b1c4ccfc3bc1e7c0c"},"schema_version":"1.0","source":{"id":"1602.07660","kind":"arxiv","version":1}},"canonical_sha256":"fec006d2d2070f8f3e7e0e52bd6fb4069378546ede3db12545fab651e43d88e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fec006d2d2070f8f3e7e0e52bd6fb4069378546ede3db12545fab651e43d88e2","first_computed_at":"2026-05-18T01:20:02.349067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:02.349067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HMt8aWs3vp+s/bAIkc69JMJVUOae+X9EDfbhAqjscHw5RSF/gS/Z865fMLVl2QCMn58gRgxzQKqSnX+48FspCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:02.349909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17de27197496a40bff9fa978c2cce512233c2484794c2e7e2ddb8f3f93c6b074","sha256:0ff2ebd317957da351aca45f14e0572424d684221b3cee8680c88cdb9a793f5c"],"state_sha256":"5505bcd85ef4a4ef64651a5ada6da2903371f0f422d3aa79cabe774b8d48c905"}