{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:U3NF3LI4UKWXITUFGFDB4HT6EN","short_pith_number":"pith:U3NF3LI4","schema_version":"1.0","canonical_sha256":"a6da5dad1ca2ad744e8531461e1e7e234fac162e12f7892816963a6207a3e6c3","source":{"kind":"arxiv","id":"1304.1612","version":2},"attestation_state":"computed","paper":{"title":"On projectively flat Kropina metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaoling Zhang, Yibing Shen","submitted_at":"2013-04-05T05:08:57Z","abstract_excerpt":"In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=\\alpha^2/\\beta$ with constant curvature $K$ and $\\|\\beta\\|_{\\alpha}=1$ is projectively flat if and only if $F$ is locally Minkowskian."},"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":"1304.1612","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-05T05:08:57Z","cross_cats_sorted":[],"title_canon_sha256":"cdb5f6ca0095de9e9b6a00bf964fc437ce51982f940d233732a8c3b975b98522","abstract_canon_sha256":"92c0f5df2ca6beabf3ddd0753493f362b3175c1cb4040a85f9bbfd1cb21124e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:32.690659Z","signature_b64":"talo9LaBm08pj/uWNWbKgiioLahWOxK9EEhJW3zh9ncXVHlype4vqHXftdFr3sZi9BcBoWnBmFTF13cCHdEeDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6da5dad1ca2ad744e8531461e1e7e234fac162e12f7892816963a6207a3e6c3","last_reissued_at":"2026-05-18T03:28:32.690024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:32.690024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On projectively flat Kropina metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaoling Zhang, Yibing Shen","submitted_at":"2013-04-05T05:08:57Z","abstract_excerpt":"In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=\\alpha^2/\\beta$ with constant curvature $K$ and $\\|\\beta\\|_{\\alpha}=1$ is projectively flat if and only if $F$ is locally Minkowskian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1612","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":"1304.1612","created_at":"2026-05-18T03:28:32.690115+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.1612v2","created_at":"2026-05-18T03:28:32.690115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1612","created_at":"2026-05-18T03:28:32.690115+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3NF3LI4UKWX","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3NF3LI4UKWXITUF","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3NF3LI4","created_at":"2026-05-18T12:28:02.375192+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/U3NF3LI4UKWXITUFGFDB4HT6EN","json":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN.json","graph_json":"https://pith.science/api/pith-number/U3NF3LI4UKWXITUFGFDB4HT6EN/graph.json","events_json":"https://pith.science/api/pith-number/U3NF3LI4UKWXITUFGFDB4HT6EN/events.json","paper":"https://pith.science/paper/U3NF3LI4"},"agent_actions":{"view_html":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN","download_json":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN.json","view_paper":"https://pith.science/paper/U3NF3LI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.1612&json=true","fetch_graph":"https://pith.science/api/pith-number/U3NF3LI4UKWXITUFGFDB4HT6EN/graph.json","fetch_events":"https://pith.science/api/pith-number/U3NF3LI4UKWXITUFGFDB4HT6EN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN/action/storage_attestation","attest_author":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN/action/author_attestation","sign_citation":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN/action/citation_signature","submit_replication":"https://pith.science/pith/U3NF3LI4UKWXITUFGFDB4HT6EN/action/replication_record"}},"created_at":"2026-05-18T03:28:32.690115+00:00","updated_at":"2026-05-18T03:28:32.690115+00:00"}