{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:R5KJVJT3GWNHRB5HYNOMFR2TVM","short_pith_number":"pith:R5KJVJT3","schema_version":"1.0","canonical_sha256":"8f549aa67b359a7887a7c35cc2c753ab00e6d5502f590d9c1a2bd2f43ffae532","source":{"kind":"arxiv","id":"1506.01827","version":3},"attestation_state":"computed","paper":{"title":"On Jacobi fields and canonical connection 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":"2015-06-05T09:14:45Z","abstract_excerpt":"In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and we discuss some of its properties."},"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":"1506.01827","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-05T09:14:45Z","cross_cats_sorted":["math.MG","math.OC"],"title_canon_sha256":"6693f46de4a2be1b3c306f0e5eeecb51de97a3f3869772088d250db0eb22e686","abstract_canon_sha256":"8278c49ac4b359df60f1b11a920cb195b73e719eef63e48e696ce6c65f9d68be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:54.219892Z","signature_b64":"jH6MrTrDSDDaYe3oUBh95Dc5KO5jM9FIXoeCIj5tolX6d7dutIyo4qg73WfaG0d6NGgSl+txlt8gRmX/YIQHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f549aa67b359a7887a7c35cc2c753ab00e6d5502f590d9c1a2bd2f43ffae532","last_reissued_at":"2026-05-18T00:40:54.219447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:54.219447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Jacobi fields and canonical connection 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":"2015-06-05T09:14:45Z","abstract_excerpt":"In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and we discuss some of its properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01827","kind":"arxiv","version":3},"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":"1506.01827","created_at":"2026-05-18T00:40:54.219510+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01827v3","created_at":"2026-05-18T00:40:54.219510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01827","created_at":"2026-05-18T00:40:54.219510+00:00"},{"alias_kind":"pith_short_12","alias_value":"R5KJVJT3GWNH","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"R5KJVJT3GWNHRB5H","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"R5KJVJT3","created_at":"2026-05-18T12:29:39.896362+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/R5KJVJT3GWNHRB5HYNOMFR2TVM","json":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM.json","graph_json":"https://pith.science/api/pith-number/R5KJVJT3GWNHRB5HYNOMFR2TVM/graph.json","events_json":"https://pith.science/api/pith-number/R5KJVJT3GWNHRB5HYNOMFR2TVM/events.json","paper":"https://pith.science/paper/R5KJVJT3"},"agent_actions":{"view_html":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM","download_json":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM.json","view_paper":"https://pith.science/paper/R5KJVJT3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01827&json=true","fetch_graph":"https://pith.science/api/pith-number/R5KJVJT3GWNHRB5HYNOMFR2TVM/graph.json","fetch_events":"https://pith.science/api/pith-number/R5KJVJT3GWNHRB5HYNOMFR2TVM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM/action/storage_attestation","attest_author":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM/action/author_attestation","sign_citation":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM/action/citation_signature","submit_replication":"https://pith.science/pith/R5KJVJT3GWNHRB5HYNOMFR2TVM/action/replication_record"}},"created_at":"2026-05-18T00:40:54.219510+00:00","updated_at":"2026-05-18T00:40:54.219510+00:00"}