{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HB4IQCPHKE65E4EAJRH4YVPRRQ","short_pith_number":"pith:HB4IQCPH","schema_version":"1.0","canonical_sha256":"38788809e7513dd270804c4fcc55f18c3160f0b11fa20c223aa2850896103a64","source":{"kind":"arxiv","id":"1303.5832","version":1},"attestation_state":"computed","paper":{"title":"Metrizable isotropic second-order differential equations and Hilbert's fourth problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioan Bucataru, Zolt\\'an Muzsnay","submitted_at":"2013-03-23T11:27:49Z","abstract_excerpt":"It is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In Theorem 3.1 we show that the isotropy condition, together with three other conditions on the Jacobi endomorphism, characterize sprays that are metrizable by Finsler functions of scalar flag curvature. The proof of Theorem 3.1 provides an algorithm to construct the Finsler function of scalar flag curvature, in the case when a given spray is metrizable. One condition of Theorem 3.1, regarding the r"},"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":"1303.5832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-23T11:27:49Z","cross_cats_sorted":[],"title_canon_sha256":"36c70be5074f2f3464e02f3650b63a791b948ad403d45479f6147123cb82eca8","abstract_canon_sha256":"31575dc127848de5826c2956dfe7650938c9e542812683b40b6686b9b4069577"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:39.454718Z","signature_b64":"pPFom8TD7kebzuWjbJuBPOz4ihCh6OaRUEzfFegFr1F6PSTiK6/9vv6h5RPFVo3wWue7rD6owQRWAnL+P+iaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38788809e7513dd270804c4fcc55f18c3160f0b11fa20c223aa2850896103a64","last_reissued_at":"2026-05-18T02:46:39.454170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:39.454170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metrizable isotropic second-order differential equations and Hilbert's fourth problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioan Bucataru, Zolt\\'an Muzsnay","submitted_at":"2013-03-23T11:27:49Z","abstract_excerpt":"It is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In Theorem 3.1 we show that the isotropy condition, together with three other conditions on the Jacobi endomorphism, characterize sprays that are metrizable by Finsler functions of scalar flag curvature. The proof of Theorem 3.1 provides an algorithm to construct the Finsler function of scalar flag curvature, in the case when a given spray is metrizable. One condition of Theorem 3.1, regarding the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5832","kind":"arxiv","version":1},"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":"1303.5832","created_at":"2026-05-18T02:46:39.454253+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5832v1","created_at":"2026-05-18T02:46:39.454253+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5832","created_at":"2026-05-18T02:46:39.454253+00:00"},{"alias_kind":"pith_short_12","alias_value":"HB4IQCPHKE65","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HB4IQCPHKE65E4EA","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HB4IQCPH","created_at":"2026-05-18T12:27:46.883200+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/HB4IQCPHKE65E4EAJRH4YVPRRQ","json":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ.json","graph_json":"https://pith.science/api/pith-number/HB4IQCPHKE65E4EAJRH4YVPRRQ/graph.json","events_json":"https://pith.science/api/pith-number/HB4IQCPHKE65E4EAJRH4YVPRRQ/events.json","paper":"https://pith.science/paper/HB4IQCPH"},"agent_actions":{"view_html":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ","download_json":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ.json","view_paper":"https://pith.science/paper/HB4IQCPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5832&json=true","fetch_graph":"https://pith.science/api/pith-number/HB4IQCPHKE65E4EAJRH4YVPRRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/HB4IQCPHKE65E4EAJRH4YVPRRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ/action/storage_attestation","attest_author":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ/action/author_attestation","sign_citation":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ/action/citation_signature","submit_replication":"https://pith.science/pith/HB4IQCPHKE65E4EAJRH4YVPRRQ/action/replication_record"}},"created_at":"2026-05-18T02:46:39.454253+00:00","updated_at":"2026-05-18T02:46:39.454253+00:00"}