{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UPNETH5AYD4TN2XX73YZIE7RZQ","short_pith_number":"pith:UPNETH5A","schema_version":"1.0","canonical_sha256":"a3da499fa0c0f936eaf7fef19413f1cc2d716914ca837af848c0c228620e32cb","source":{"kind":"arxiv","id":"1401.3193","version":5},"attestation_state":"computed","paper":{"title":"Comparison theorems for conjugate points in sub-Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.OC"],"primary_cat":"math.DG","authors_text":"Davide Barilari, Luca Rizzi","submitted_at":"2014-01-14T14:22:02Z","abstract_excerpt":"We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting, we identify a class of models, namely linear quadratic optimal control systems, that play the role of the constant curvature spaces. As an application, we prove a version of sub-Riemannian Bonnet-Myers theorem and we obtain some new results on conjugate points for three dimensional left-invariant sub-Riemannian structures."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.3193","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-14T14:22:02Z","cross_cats_sorted":["math.MG","math.OC"],"title_canon_sha256":"37404d393ebb3e91d4fcffe76f43492c89e6cd76570d9f187e3de26852aa32a8","abstract_canon_sha256":"2030df3aafd4feb8038c803df5d9c8c380cc399c4f4fb3f3ab4c26f8a964c96d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:59.082049Z","signature_b64":"/vyO62XIQAoZxeAkOyDTqDgJSo8CeNocFvRsr8Jrm+/TcDfCv6KlOGgQNzrbEEJW2TSvg2nkDndKT82GE/3lAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3da499fa0c0f936eaf7fef19413f1cc2d716914ca837af848c0c228620e32cb","last_reissued_at":"2026-05-18T01:14:59.081571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:59.081571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison theorems for conjugate points in sub-Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.OC"],"primary_cat":"math.DG","authors_text":"Davide Barilari, Luca Rizzi","submitted_at":"2014-01-14T14:22:02Z","abstract_excerpt":"We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting, we identify a class of models, namely linear quadratic optimal control systems, that play the role of the constant curvature spaces. As an application, we prove a version of sub-Riemannian Bonnet-Myers theorem and we obtain some new results on conjugate points for three dimensional left-invariant sub-Riemannian structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3193","kind":"arxiv","version":5},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.3193","created_at":"2026-05-18T01:14:59.081648+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3193v5","created_at":"2026-05-18T01:14:59.081648+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3193","created_at":"2026-05-18T01:14:59.081648+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPNETH5AYD4T","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPNETH5AYD4TN2XX","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPNETH5A","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ","json":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ.json","graph_json":"https://pith.science/api/pith-number/UPNETH5AYD4TN2XX73YZIE7RZQ/graph.json","events_json":"https://pith.science/api/pith-number/UPNETH5AYD4TN2XX73YZIE7RZQ/events.json","paper":"https://pith.science/paper/UPNETH5A"},"agent_actions":{"view_html":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ","download_json":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ.json","view_paper":"https://pith.science/paper/UPNETH5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3193&json=true","fetch_graph":"https://pith.science/api/pith-number/UPNETH5AYD4TN2XX73YZIE7RZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/UPNETH5AYD4TN2XX73YZIE7RZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ/action/storage_attestation","attest_author":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ/action/author_attestation","sign_citation":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ/action/citation_signature","submit_replication":"https://pith.science/pith/UPNETH5AYD4TN2XX73YZIE7RZQ/action/replication_record"}},"created_at":"2026-05-18T01:14:59.081648+00:00","updated_at":"2026-05-18T01:14:59.081648+00:00"}