{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:55ZGAOKX4XZDPJQUKTEHRKCLGD","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":"570ef0655de6f95e5046b631eeb85fd39f49e230873fcdfc2acdb710b90cf6e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-16T19:57:49Z","title_canon_sha256":"04a03a255fa38533cbcf9fa377f88ad070199a5ea0f0a4ef6daecf0c9aa84c17"},"schema_version":"1.0","source":{"id":"1809.05943","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05943","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05943v4","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05943","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"55ZGAOKX4XZD","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"55ZGAOKX4XZDPJQU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"55ZGAOKX","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:de63ba19a7e62114471fac4300ae08cc10b3f5f494c29598f69ee31082f1697b","target":"graph","created_at":"2026-05-17T23:42:43Z","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":"It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, th","authors_text":"Jos\\'e D. da Silva, Luiz C. B. da Silva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-16T19:57:49Z","title":"Characterization of manifolds of constant curvature by spherical curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05943","kind":"arxiv","version":4},"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:af177f0cd8d5738b83236635484083119332c22d6449c8b0fff94338aa266fcd","target":"record","created_at":"2026-05-17T23:42:43Z","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":"570ef0655de6f95e5046b631eeb85fd39f49e230873fcdfc2acdb710b90cf6e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-16T19:57:49Z","title_canon_sha256":"04a03a255fa38533cbcf9fa377f88ad070199a5ea0f0a4ef6daecf0c9aa84c17"},"schema_version":"1.0","source":{"id":"1809.05943","kind":"arxiv","version":4}},"canonical_sha256":"ef72603957e5f237a61454c878a84b30d320004b0ac7dcc3f5fb262a70875842","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef72603957e5f237a61454c878a84b30d320004b0ac7dcc3f5fb262a70875842","first_computed_at":"2026-05-17T23:42:43.017057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:43.017057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cA20D0cDIFOkrrU8Mm2Ag5YFHlW6xS5bqPEIDnHuAyw7Q9mIalkBrUfDfJ6y8LSBWfMW75Gua1cP5DCTxTzfCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:43.017537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05943","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af177f0cd8d5738b83236635484083119332c22d6449c8b0fff94338aa266fcd","sha256:de63ba19a7e62114471fac4300ae08cc10b3f5f494c29598f69ee31082f1697b"],"state_sha256":"5f0e41f4e3eabbf74ccb02d8fbec60fbf2445a5d88c44b1996c7468e23979909"}