{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:REQD3R3VT66WEWP5GUZY7WZW2C","short_pith_number":"pith:REQD3R3V","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"},"canonical_sha256":"89203dc7759fbd6259fd35338fdb36d0a827c5681d86378a83c64019c6354006","source":{"kind":"arxiv","id":"1202.3869","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3869","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3869v2","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3869","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"REQD3R3VT66W","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"REQD3R3VT66WEWP5","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"REQD3R3V","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:REQD3R3VT66WEWP5GUZY7WZW2C","target":"record","payload":{"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"},"canonical_sha256":"89203dc7759fbd6259fd35338fdb36d0a827c5681d86378a83c64019c6354006","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"},"source_kind":"arxiv","source_id":"1202.3869","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLQfqpBf04fhVsHnl1DCFAXyWKUFaroY0/Zp0WBNsGcPo7A1AN80oX3joIlDmHEXputbzee6cw7Bt4m7PLwBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:55:05.922345Z"},"content_sha256":"805156752466187a37b77656b2b52535963c7d4a00e5ca90608b4788dadbeb90","schema_version":"1.0","event_id":"sha256:805156752466187a37b77656b2b52535963c7d4a00e5ca90608b4788dadbeb90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:REQD3R3VT66WEWP5GUZY7WZW2C","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"niNtzrMYPjpe23R3mU9pjKjuYCiws2CThGuIAXspc7LfbaIE9H1y7yk0oE8QxgmVCLMXgdRTfinNEkg8GtzHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:55:05.922805Z"},"content_sha256":"8cd62d8508bac67645f2fd784c71575329489a6c7548e94a52b951c9cee5796f","schema_version":"1.0","event_id":"sha256:8cd62d8508bac67645f2fd784c71575329489a6c7548e94a52b951c9cee5796f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/bundle.json","state_url":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REQD3R3VT66WEWP5GUZY7WZW2C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T18:55:05Z","links":{"resolver":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C","bundle":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/bundle.json","state":"https://pith.science/pith/REQD3R3VT66WEWP5GUZY7WZW2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REQD3R3VT66WEWP5GUZY7WZW2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:REQD3R3VT66WEWP5GUZY7WZW2C","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":"16ab8ea03860bb1cd7fcc530d932b9b2bfb8d3608c516773be27433b68479ab0","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-17T10:41:59Z","title_canon_sha256":"9d215bf21bf303399626cd802e3e687a3f6c0bc63011cb5fa35d8b45043b3053"},"schema_version":"1.0","source":{"id":"1202.3869","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3869","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3869v2","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3869","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"REQD3R3VT66W","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"REQD3R3VT66WEWP5","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"REQD3R3V","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:8cd62d8508bac67645f2fd784c71575329489a6c7548e94a52b951c9cee5796f","target":"graph","created_at":"2026-05-18T01:58:24Z","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":"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.","authors_text":"Henrique Vit\\'orio, Paolo Piccione, Ricardo Gallego Torrom\\'e","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-17T10:41:59Z","title":"On Fermat's principle for causal curves in time oriented Finsler spacetimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3869","kind":"arxiv","version":2},"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":"sha256:805156752466187a37b77656b2b52535963c7d4a00e5ca90608b4788dadbeb90","target":"record","created_at":"2026-05-18T01:58:24Z","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":"16ab8ea03860bb1cd7fcc530d932b9b2bfb8d3608c516773be27433b68479ab0","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-17T10:41:59Z","title_canon_sha256":"9d215bf21bf303399626cd802e3e687a3f6c0bc63011cb5fa35d8b45043b3053"},"schema_version":"1.0","source":{"id":"1202.3869","kind":"arxiv","version":2}},"canonical_sha256":"89203dc7759fbd6259fd35338fdb36d0a827c5681d86378a83c64019c6354006","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89203dc7759fbd6259fd35338fdb36d0a827c5681d86378a83c64019c6354006","first_computed_at":"2026-05-18T01:58:24.150283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:24.150283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6eelyx9vjMwrvsKcuScTyLKcbYn/saauEua08kGImeGhAmZQPkEj9UMU5Q5egK2i1AaL9tfZsXNk7FqOWAICA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:24.150763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3869","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:805156752466187a37b77656b2b52535963c7d4a00e5ca90608b4788dadbeb90","sha256:8cd62d8508bac67645f2fd784c71575329489a6c7548e94a52b951c9cee5796f"],"state_sha256":"dfdd6c517aebbf93c3d98b2c390c804ae6d93148c2f1c100b5dd47edfd23e530"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7mwlPaEr1EDvEPnjUDZmiO1NxweutlHOSKj55PcGdqInmQW3PTrNFYLbd/2Y15g5+CpOgz9fj/7puyC2mwEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:55:05.925992Z","bundle_sha256":"e3330ebf2709766fc14b683c0309bfc70ef73e191a6e5cf63b6da031864ead25"}}