{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3KJBPIKK7FWPYR5RG6T6666JXH","short_pith_number":"pith:3KJBPIKK","schema_version":"1.0","canonical_sha256":"da9217a14af96cfc47b137a7ef7bc9b9e616e7c6e484bb777c01715c61c1af92","source":{"kind":"arxiv","id":"1401.8149","version":3},"attestation_state":"computed","paper":{"title":"Geodesics and Jacobi fields of pseudo-Finsler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bruno Learth Soares, Miguel Angel Javaloyes","submitted_at":"2014-01-31T12:16:32Z","abstract_excerpt":"In this paper, we derive the first and the second variation of the energy functional for a pseudo-Finsler metric using the family of affine connections associated to the Chern connection. This opens the possibility to accomplish computations with coordinate-free methods. Using the second variation formula, we introduce the index form and present some properties of Jacobi fields."},"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":"1401.8149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-31T12:16:32Z","cross_cats_sorted":[],"title_canon_sha256":"2513f8277679e888a1d89d3fc8dfb801890b4699dd4789daa2c9f90ae4303e0d","abstract_canon_sha256":"59cf4cec58d2abc3feb93c79b612ffc7aad0d196c23e9c4d9d2b8892fb4a52d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.026735Z","signature_b64":"SMvagAdnzJ0jQ9t7IfLKg2hAFxGmpomBlRGUK9XV9Bfg2DUao7/890DGoISQCkiHA7ozJ8oqqe1t6X2bkwE8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da9217a14af96cfc47b137a7ef7bc9b9e616e7c6e484bb777c01715c61c1af92","last_reissued_at":"2026-05-18T02:25:19.026388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.026388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geodesics and Jacobi fields of pseudo-Finsler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bruno Learth Soares, Miguel Angel Javaloyes","submitted_at":"2014-01-31T12:16:32Z","abstract_excerpt":"In this paper, we derive the first and the second variation of the energy functional for a pseudo-Finsler metric using the family of affine connections associated to the Chern connection. This opens the possibility to accomplish computations with coordinate-free methods. Using the second variation formula, we introduce the index form and present some properties of Jacobi fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8149","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":"1401.8149","created_at":"2026-05-18T02:25:19.026445+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.8149v3","created_at":"2026-05-18T02:25:19.026445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8149","created_at":"2026-05-18T02:25:19.026445+00:00"},{"alias_kind":"pith_short_12","alias_value":"3KJBPIKK7FWP","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3KJBPIKK7FWPYR5R","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3KJBPIKK","created_at":"2026-05-18T12:28:11.866339+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/3KJBPIKK7FWPYR5RG6T6666JXH","json":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH.json","graph_json":"https://pith.science/api/pith-number/3KJBPIKK7FWPYR5RG6T6666JXH/graph.json","events_json":"https://pith.science/api/pith-number/3KJBPIKK7FWPYR5RG6T6666JXH/events.json","paper":"https://pith.science/paper/3KJBPIKK"},"agent_actions":{"view_html":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH","download_json":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH.json","view_paper":"https://pith.science/paper/3KJBPIKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.8149&json=true","fetch_graph":"https://pith.science/api/pith-number/3KJBPIKK7FWPYR5RG6T6666JXH/graph.json","fetch_events":"https://pith.science/api/pith-number/3KJBPIKK7FWPYR5RG6T6666JXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH/action/storage_attestation","attest_author":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH/action/author_attestation","sign_citation":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH/action/citation_signature","submit_replication":"https://pith.science/pith/3KJBPIKK7FWPYR5RG6T6666JXH/action/replication_record"}},"created_at":"2026-05-18T02:25:19.026445+00:00","updated_at":"2026-05-18T02:25:19.026445+00:00"}