{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:IHRRP5GU7IOIE24DD25ERUXRZS","short_pith_number":"pith:IHRRP5GU","schema_version":"1.0","canonical_sha256":"41e317f4d4fa1c826b831eba48d2f1ccbaa57a96242696a8e0203012e674c0cb","source":{"kind":"arxiv","id":"0903.3519","version":5},"attestation_state":"computed","paper":{"title":"Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Antonio Masiello, Erasmo Caponio, Miguel Angel Javaloyes","submitted_at":"2009-03-20T13:36:05Z","abstract_excerpt":"We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standard timelike Killing vector field by using Morse theory on the associated Finsler manifold. To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike"},"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":"0903.3519","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-03-20T13:36:05Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"5ac5f59b4af243796536b71d675d158fc7f155b40b00954d1a21c77234db966a","abstract_canon_sha256":"7911c502c1a4a7d18fa8a034b0e97c4f7d84d60e749704364e7efc72fe66d044"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:51.750850Z","signature_b64":"3KzJLYAtNBUxgHkuHzlGRauWK38CQg0IkCTA5IU5UsflAH5Bv5vDI3wDo2CC//4J013WmqTuFULTzDXDyHD1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41e317f4d4fa1c826b831eba48d2f1ccbaa57a96242696a8e0203012e674c0cb","last_reissued_at":"2026-05-18T03:40:51.750328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:51.750328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Antonio Masiello, Erasmo Caponio, Miguel Angel Javaloyes","submitted_at":"2009-03-20T13:36:05Z","abstract_excerpt":"We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standard timelike Killing vector field by using Morse theory on the associated Finsler manifold. To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3519","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":"0903.3519","created_at":"2026-05-18T03:40:51.750408+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.3519v5","created_at":"2026-05-18T03:40:51.750408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3519","created_at":"2026-05-18T03:40:51.750408+00:00"},{"alias_kind":"pith_short_12","alias_value":"IHRRP5GU7IOI","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"IHRRP5GU7IOIE24D","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"IHRRP5GU","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2503.21203","citing_title":"Massive particle surfaces and black hole shadows from intrinsic curvature","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS","json":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS.json","graph_json":"https://pith.science/api/pith-number/IHRRP5GU7IOIE24DD25ERUXRZS/graph.json","events_json":"https://pith.science/api/pith-number/IHRRP5GU7IOIE24DD25ERUXRZS/events.json","paper":"https://pith.science/paper/IHRRP5GU"},"agent_actions":{"view_html":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS","download_json":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS.json","view_paper":"https://pith.science/paper/IHRRP5GU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.3519&json=true","fetch_graph":"https://pith.science/api/pith-number/IHRRP5GU7IOIE24DD25ERUXRZS/graph.json","fetch_events":"https://pith.science/api/pith-number/IHRRP5GU7IOIE24DD25ERUXRZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS/action/storage_attestation","attest_author":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS/action/author_attestation","sign_citation":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS/action/citation_signature","submit_replication":"https://pith.science/pith/IHRRP5GU7IOIE24DD25ERUXRZS/action/replication_record"}},"created_at":"2026-05-18T03:40:51.750408+00:00","updated_at":"2026-05-18T03:40:51.750408+00:00"}