{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WUIET7JOCK3LN7IA54FV6NTFZR","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":"5766f3b4e9e116c3e035526e9238b39d2f79c615f5879ba2a90049d6c3b7ee59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-14T19:18:53Z","title_canon_sha256":"e4182e263e8111e62ca61f763f6401545f84a38b62a1b4686331dad5a9819a2d"},"schema_version":"1.0","source":{"id":"1611.04530","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04530","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04530v3","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04530","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"WUIET7JOCK3L","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WUIET7JOCK3LN7IA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WUIET7JO","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:f0a0b3d5db0e3ee7643ca72b30022470270f092b34b74565125119374f44704b","target":"graph","created_at":"2026-05-17T23:54:36Z","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 present classifications of totally geodesic and totally umbilical Legendrian submanifolds of $(\\kappa,\\mu)$-spaces with Boeckx invariant $I \\leq -1$. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.","authors_text":"Alfonso Carriazo, Luc Vrancken, Ver\\'onica Mart\\'in-Molina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-14T19:18:53Z","title":"A classification of totally geodesic and totally umbilical Legendrian submanifolds of $(\\kappa,\\mu)$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04530","kind":"arxiv","version":3},"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:c498bca4e75e4d9662a7177bea49c6e020aa7ba3c285072d12cc8a9f1ede2078","target":"record","created_at":"2026-05-17T23:54:36Z","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":"5766f3b4e9e116c3e035526e9238b39d2f79c615f5879ba2a90049d6c3b7ee59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-14T19:18:53Z","title_canon_sha256":"e4182e263e8111e62ca61f763f6401545f84a38b62a1b4686331dad5a9819a2d"},"schema_version":"1.0","source":{"id":"1611.04530","kind":"arxiv","version":3}},"canonical_sha256":"b51049fd2e12b6b6fd00ef0b5f3665cc4a61e1080947707ff911af243ed7f840","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b51049fd2e12b6b6fd00ef0b5f3665cc4a61e1080947707ff911af243ed7f840","first_computed_at":"2026-05-17T23:54:36.971648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:36.971648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D0xxOb28bu7+bKam7AytmY1d96B8pEQX8hSvx5Y+/AO50z54cfpOiURUvhQ0hyPhKG5oZXVhsKM/tyXsMYudDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:36.972183Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04530","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c498bca4e75e4d9662a7177bea49c6e020aa7ba3c285072d12cc8a9f1ede2078","sha256:f0a0b3d5db0e3ee7643ca72b30022470270f092b34b74565125119374f44704b"],"state_sha256":"b2e9339164708adb6c7b5edeab119c845905f8b29865db324a37a291736ae162"}