{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:67C3IWUPKJZB36XJQRIP2ZZ3YR","short_pith_number":"pith:67C3IWUP","schema_version":"1.0","canonical_sha256":"f7c5b45a8f52721dfae98450fd673bc4633433ecab713654aceefd1c3ce7c381","source":{"kind":"arxiv","id":"1907.05985","version":1},"attestation_state":"computed","paper":{"title":"Geodesic orbit Finsler space with $K\\geq0$ and the (FP) condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ming Xu","submitted_at":"2019-07-13T00:40:43Z","abstract_excerpt":"In this paper, we study the interaction between the geodesic orbit (g.o.~in short) property and certain flag curvature conditions. A Finsler manifold is called g.o.~if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also concern the (FP) condition for the flag curvature, i.e., in any flag we can find a flag pole, such that the flag curvature is positive. The main theorem we will prove is the following. If a g.o.~Finsler space $(M,F)$ has non-negative flag curvature and satisfies the (FP) condition, then $M$ must be compact."},"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":"1907.05985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-13T00:40:43Z","cross_cats_sorted":[],"title_canon_sha256":"34b6168683600be82a23f371e66cf6f761b3ddbdd3bef297e049c88a59cffd1d","abstract_canon_sha256":"44c84dd2fef792fbc7b14254b67838f2738217ced52dc645238c3ca53355b77f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:42.773167Z","signature_b64":"tmd7aQ9Xfmr/GLPRXcL05I/x84pJ+lGgCF5acNhpBfCo3uFPSzwzCzKi8Jimb6tMuIHIaWfGhxErSGvA/dUPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7c5b45a8f52721dfae98450fd673bc4633433ecab713654aceefd1c3ce7c381","last_reissued_at":"2026-05-17T23:40:42.772580Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:42.772580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geodesic orbit Finsler space with $K\\geq0$ and the (FP) condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ming Xu","submitted_at":"2019-07-13T00:40:43Z","abstract_excerpt":"In this paper, we study the interaction between the geodesic orbit (g.o.~in short) property and certain flag curvature conditions. A Finsler manifold is called g.o.~if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also concern the (FP) condition for the flag curvature, i.e., in any flag we can find a flag pole, such that the flag curvature is positive. The main theorem we will prove is the following. If a g.o.~Finsler space $(M,F)$ has non-negative flag curvature and satisfies the (FP) condition, then $M$ must be compact."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05985","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":"1907.05985","created_at":"2026-05-17T23:40:42.772665+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05985v1","created_at":"2026-05-17T23:40:42.772665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05985","created_at":"2026-05-17T23:40:42.772665+00:00"},{"alias_kind":"pith_short_12","alias_value":"67C3IWUPKJZB","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"67C3IWUPKJZB36XJ","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"67C3IWUP","created_at":"2026-05-18T12:33:10.108867+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/67C3IWUPKJZB36XJQRIP2ZZ3YR","json":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR.json","graph_json":"https://pith.science/api/pith-number/67C3IWUPKJZB36XJQRIP2ZZ3YR/graph.json","events_json":"https://pith.science/api/pith-number/67C3IWUPKJZB36XJQRIP2ZZ3YR/events.json","paper":"https://pith.science/paper/67C3IWUP"},"agent_actions":{"view_html":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR","download_json":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR.json","view_paper":"https://pith.science/paper/67C3IWUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05985&json=true","fetch_graph":"https://pith.science/api/pith-number/67C3IWUPKJZB36XJQRIP2ZZ3YR/graph.json","fetch_events":"https://pith.science/api/pith-number/67C3IWUPKJZB36XJQRIP2ZZ3YR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR/action/storage_attestation","attest_author":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR/action/author_attestation","sign_citation":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR/action/citation_signature","submit_replication":"https://pith.science/pith/67C3IWUPKJZB36XJQRIP2ZZ3YR/action/replication_record"}},"created_at":"2026-05-17T23:40:42.772665+00:00","updated_at":"2026-05-17T23:40:42.772665+00:00"}