{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VQP25DMQAKWUZB2A6JADRU7X4N","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":"6f1ab2478a46a5d02797bbc126fc26d4b493a6e277d01353c972f5d9f2995d87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-04T12:50:19Z","title_canon_sha256":"da24ce41c7fa91b392ca3bf70e66f580ee79f79c32a9a36e01e7b8f9176910d8"},"schema_version":"1.0","source":{"id":"1105.0808","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0808","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0808v2","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0808","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"VQP25DMQAKWU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VQP25DMQAKWUZB2A","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VQP25DMQ","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:722a69921c6ad9c5eedd7912f89a0a3008c74285852add7730b19f5c29c75a85","target":"graph","created_at":"2026-05-18T03:20:35Z","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 analyze the geometric structure of an Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings.","authors_text":"Marcos Dajczer, Ruy Tojeiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-04T12:50:19Z","title":"Submanifolds with nonparallel first normal bundle revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0808","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:c4f55e7ff62db5c91f240d65e119e92541ec45092f5f67dbe0cfee863133a26b","target":"record","created_at":"2026-05-18T03:20:35Z","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":"6f1ab2478a46a5d02797bbc126fc26d4b493a6e277d01353c972f5d9f2995d87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-04T12:50:19Z","title_canon_sha256":"da24ce41c7fa91b392ca3bf70e66f580ee79f79c32a9a36e01e7b8f9176910d8"},"schema_version":"1.0","source":{"id":"1105.0808","kind":"arxiv","version":2}},"canonical_sha256":"ac1fae8d9002ad4c8740f24038d3f7e34a0e340b660e7c9aef2e1f29a0d8ccce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac1fae8d9002ad4c8740f24038d3f7e34a0e340b660e7c9aef2e1f29a0d8ccce","first_computed_at":"2026-05-18T03:20:35.874474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:35.874474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EfZHRqDFsLnQydt3RUFjzcx8m4S4xyf/YAqOMGjoNwhcIo2ORBdXjjLof9OzErBUU5y2mrLmMOtyYgV68Gt5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:35.875426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0808","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4f55e7ff62db5c91f240d65e119e92541ec45092f5f67dbe0cfee863133a26b","sha256:722a69921c6ad9c5eedd7912f89a0a3008c74285852add7730b19f5c29c75a85"],"state_sha256":"3804c6931e4f62115210c8d5a3a8612937f43e806c9a6d9d6d5d923e80b53d4e"}