{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5MPRT4CZ7PKXHTYOMWHSCCXBCO","short_pith_number":"pith:5MPRT4CZ","canonical_record":{"source":{"id":"1702.01328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-04T19:25:19Z","cross_cats_sorted":[],"title_canon_sha256":"65c181b2fa472ee8d7f660c75b7f893b7bf82c87c46fdf1bbab646ba5a5d64aa","abstract_canon_sha256":"e897353283144264994a04e7723eb94f769d86700c31fbbe6bc19dd28d93d94a"},"schema_version":"1.0"},"canonical_sha256":"eb1f19f059fbd573cf0e658f210ae113b5120d82f60d543c8baa5f41af26c639","source":{"kind":"arxiv","id":"1702.01328","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01328","created_at":"2026-05-18T00:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01328v2","created_at":"2026-05-18T00:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01328","created_at":"2026-05-18T00:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"5MPRT4CZ7PKX","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5MPRT4CZ7PKXHTYO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5MPRT4CZ","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5MPRT4CZ7PKXHTYOMWHSCCXBCO","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-04T19:25:19Z","cross_cats_sorted":[],"title_canon_sha256":"65c181b2fa472ee8d7f660c75b7f893b7bf82c87c46fdf1bbab646ba5a5d64aa","abstract_canon_sha256":"e897353283144264994a04e7723eb94f769d86700c31fbbe6bc19dd28d93d94a"},"schema_version":"1.0"},"canonical_sha256":"eb1f19f059fbd573cf0e658f210ae113b5120d82f60d543c8baa5f41af26c639","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:54.880652Z","signature_b64":"3Z82oeMMmVcdsKFJo/N2PnZxVOrMUM4dqbhaGWnN2cLLER/RDoBSlvyw/bSqvN2uP48iMUcT/fnSS+amq+VZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb1f19f059fbd573cf0e658f210ae113b5120d82f60d543c8baa5f41af26c639","last_reissued_at":"2026-05-18T00:43:54.879971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:54.879971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01328","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPqrfcXJ0ppiPtizS5JFFckB3L6rfDJXlMeteEW+EaHKTNG4xF6e7m5EyxpYkPLffziwh6TUoQS+1fAIY3sZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:28:59.109073Z"},"content_sha256":"65cd6d04066122f19498c9de18970f3f8f78b6e7718af4b91ac80cfa3a494fd7","schema_version":"1.0","event_id":"sha256:65cd6d04066122f19498c9de18970f3f8f78b6e7718af4b91ac80cfa3a494fd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5MPRT4CZ7PKXHTYOMWHSCCXBCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal holonomy and rational properties of the shape operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Carlos Olmos, Richar Ria\\~no-Ria\\~no","submitted_at":"2017-02-04T19:25:19Z","abstract_excerpt":"Let $M$ be a most singular orbit of the isotropy representation of a simple symmetric space. Let $(\\nu _i, \\Phi _i)$ be an irreducible factor of the normal holonomy representation $(\\nu _pM, \\Phi (p))$. We prove that there exists a basis of a section $\\Sigma _i\\subset \\nu _i$ of $\\Phi _i$ such that the corresponding shape operators have rational eigenvalues (this is not in general true for other isotropy orbits). Conversely, this property, if referred to some non-transitive irreducible normal holonomy factor, characterizes the isotropy orbits. We also prove that the definition of a submanifold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01328","kind":"arxiv","version":2},"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":"2026-05-18T00:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SkT6Lbm+wwyQTHHTNE4VdYG7wzUoGHlMukpwV/+yq4sp/1Xfq7JNvY4FMhT0lL12Yn5M0XQB563bm3LN+jzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:28:59.109504Z"},"content_sha256":"c0756a1f92bd1e375e8cb1a0a08e193e675a64caa937b2293d27314246750504","schema_version":"1.0","event_id":"sha256:c0756a1f92bd1e375e8cb1a0a08e193e675a64caa937b2293d27314246750504"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO/bundle.json","state_url":"https://pith.science/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO/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":"2026-06-02T14:28:59Z","links":{"resolver":"https://pith.science/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO","bundle":"https://pith.science/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO/bundle.json","state":"https://pith.science/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5MPRT4CZ7PKXHTYOMWHSCCXBCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5MPRT4CZ7PKXHTYOMWHSCCXBCO","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":"e897353283144264994a04e7723eb94f769d86700c31fbbe6bc19dd28d93d94a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-04T19:25:19Z","title_canon_sha256":"65c181b2fa472ee8d7f660c75b7f893b7bf82c87c46fdf1bbab646ba5a5d64aa"},"schema_version":"1.0","source":{"id":"1702.01328","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01328","created_at":"2026-05-18T00:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01328v2","created_at":"2026-05-18T00:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01328","created_at":"2026-05-18T00:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"5MPRT4CZ7PKX","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5MPRT4CZ7PKXHTYO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5MPRT4CZ","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:c0756a1f92bd1e375e8cb1a0a08e193e675a64caa937b2293d27314246750504","target":"graph","created_at":"2026-05-18T00:43:54Z","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":"Let $M$ be a most singular orbit of the isotropy representation of a simple symmetric space. Let $(\\nu _i, \\Phi _i)$ be an irreducible factor of the normal holonomy representation $(\\nu _pM, \\Phi (p))$. We prove that there exists a basis of a section $\\Sigma _i\\subset \\nu _i$ of $\\Phi _i$ such that the corresponding shape operators have rational eigenvalues (this is not in general true for other isotropy orbits). Conversely, this property, if referred to some non-transitive irreducible normal holonomy factor, characterizes the isotropy orbits. We also prove that the definition of a submanifold","authors_text":"Carlos Olmos, Richar Ria\\~no-Ria\\~no","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-04T19:25:19Z","title":"Normal holonomy and rational properties of the shape operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01328","kind":"arxiv","version":2},"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":"sha256:65cd6d04066122f19498c9de18970f3f8f78b6e7718af4b91ac80cfa3a494fd7","target":"record","created_at":"2026-05-18T00:43:54Z","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":"e897353283144264994a04e7723eb94f769d86700c31fbbe6bc19dd28d93d94a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-04T19:25:19Z","title_canon_sha256":"65c181b2fa472ee8d7f660c75b7f893b7bf82c87c46fdf1bbab646ba5a5d64aa"},"schema_version":"1.0","source":{"id":"1702.01328","kind":"arxiv","version":2}},"canonical_sha256":"eb1f19f059fbd573cf0e658f210ae113b5120d82f60d543c8baa5f41af26c639","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb1f19f059fbd573cf0e658f210ae113b5120d82f60d543c8baa5f41af26c639","first_computed_at":"2026-05-18T00:43:54.879971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:54.879971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Z82oeMMmVcdsKFJo/N2PnZxVOrMUM4dqbhaGWnN2cLLER/RDoBSlvyw/bSqvN2uP48iMUcT/fnSS+amq+VZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:54.880652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01328","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65cd6d04066122f19498c9de18970f3f8f78b6e7718af4b91ac80cfa3a494fd7","sha256:c0756a1f92bd1e375e8cb1a0a08e193e675a64caa937b2293d27314246750504"],"state_sha256":"09413a12b7b08d033d99fd2e15c36d728c2979a6e4b765acabb44009ea6fba10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqdiEiDL9PyHybgkEOjCSsEqAs+eVzVyAMVH4IBTnXiT/efDXtom+11nRD+6/BG3EvNnQ83+e1yUSSEfkfcfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:28:59.111399Z","bundle_sha256":"2441c9c54016dc545716bdc4150ef8899051b0fce96e5a1142989d97b500c1e6"}}