{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:REQD3R3VT66WEWP5GUZY7WZW2C","short_pith_number":"pith:REQD3R3V","schema_version":"1.0","canonical_sha256":"89203dc7759fbd6259fd35338fdb36d0a827c5681d86378a83c64019c6354006","source":{"kind":"arxiv","id":"1202.3869","version":2},"attestation_state":"computed","paper":{"title":"On Fermat's principle for causal curves in time oriented Finsler spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Henrique Vit\\'orio, Paolo Piccione, Ricardo Gallego Torrom\\'e","submitted_at":"2012-02-17T10:41:59Z","abstract_excerpt":"In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented."},"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":"1202.3869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-17T10:41:59Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"9d215bf21bf303399626cd802e3e687a3f6c0bc63011cb5fa35d8b45043b3053","abstract_canon_sha256":"16ab8ea03860bb1cd7fcc530d932b9b2bfb8d3608c516773be27433b68479ab0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:24.150763Z","signature_b64":"t6eelyx9vjMwrvsKcuScTyLKcbYn/saauEua08kGImeGhAmZQPkEj9UMU5Q5egK2i1AaL9tfZsXNk7FqOWAICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89203dc7759fbd6259fd35338fdb36d0a827c5681d86378a83c64019c6354006","last_reissued_at":"2026-05-18T01:58:24.150283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:24.150283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Fermat's principle for causal curves in time oriented Finsler spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Henrique Vit\\'orio, Paolo Piccione, Ricardo Gallego Torrom\\'e","submitted_at":"2012-02-17T10:41:59Z","abstract_excerpt":"In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3869","kind":"arxiv","version":2},"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":"1202.3869","created_at":"2026-05-18T01:58:24.150359+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.3869v2","created_at":"2026-05-18T01:58:24.150359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3869","created_at":"2026-05-18T01:58:24.150359+00:00"},{"alias_kind":"pith_short_12","alias_value":"REQD3R3VT66W","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"REQD3R3VT66WEWP5","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"REQD3R3V","created_at":"2026-05-18T12:27:20.899486+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/REQD3R3VT66WEWP5GUZY7WZW2C","json":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C.json","graph_json":"https://pith.science/api/pith-number/REQD3R3VT66WEWP5GUZY7WZW2C/graph.json","events_json":"https://pith.science/api/pith-number/REQD3R3VT66WEWP5GUZY7WZW2C/events.json","paper":"https://pith.science/paper/REQD3R3V"},"agent_actions":{"view_html":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C","download_json":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C.json","view_paper":"https://pith.science/paper/REQD3R3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.3869&json=true","fetch_graph":"https://pith.science/api/pith-number/REQD3R3VT66WEWP5GUZY7WZW2C/graph.json","fetch_events":"https://pith.science/api/pith-number/REQD3R3VT66WEWP5GUZY7WZW2C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/action/storage_attestation","attest_author":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/action/author_attestation","sign_citation":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/action/citation_signature","submit_replication":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/action/replication_record"}},"created_at":"2026-05-18T01:58:24.150359+00:00","updated_at":"2026-05-18T01:58:24.150359+00:00"}