{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:37H6TKSHJX7TEFEFQDHVDEFG6B","short_pith_number":"pith:37H6TKSH","schema_version":"1.0","canonical_sha256":"dfcfe9aa474dff32148580cf5190a6f06760d6c0d2b25458119f1698f09cbe6a","source":{"kind":"arxiv","id":"1403.5939","version":3},"attestation_state":"computed","paper":{"title":"Homogeneous geodesics in pseudo-Riemannian nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Viviana del Barco","submitted_at":"2014-03-24T12:58:44Z","abstract_excerpt":"We study the geodesic orbit property for nilpotent Lie groups $N$ when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When $N$ acts on itself by left-translations we show that it is a geodesic orbit space if and only if the metric is bi-invariant. Assuming $N$ is 2-step nilpotent and with non-degenerate center we give algebraic conditions on the Lie algebra $\\mathfrak n$ of $N$ in order to verify that every geodesic is the orbit of a one-parameter subgroup of $N\\rtimes\\operatorname{Auto}(N)$. In addition "},"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":"1403.5939","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-24T12:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"2fe35787cfbf60bda61e81e47863dd97481b9fd20819d7e09c0b67366d9de8a5","abstract_canon_sha256":"625249db2571d24245e96185b2ebd5daf8b4336f6859da9b8fbdde90e2000ccc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:05.946479Z","signature_b64":"4Bz2noOKHEeJVmy4QodpUI1bKx1gOUjHhsaMaWNsmHjRPHZQQCpInagEKiKALDLTF5cNmRa0I2Py7CMRkCxcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfcfe9aa474dff32148580cf5190a6f06760d6c0d2b25458119f1698f09cbe6a","last_reissued_at":"2026-05-18T02:42:05.946054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:05.946054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogeneous geodesics in pseudo-Riemannian nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Viviana del Barco","submitted_at":"2014-03-24T12:58:44Z","abstract_excerpt":"We study the geodesic orbit property for nilpotent Lie groups $N$ when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When $N$ acts on itself by left-translations we show that it is a geodesic orbit space if and only if the metric is bi-invariant. Assuming $N$ is 2-step nilpotent and with non-degenerate center we give algebraic conditions on the Lie algebra $\\mathfrak n$ of $N$ in order to verify that every geodesic is the orbit of a one-parameter subgroup of $N\\rtimes\\operatorname{Auto}(N)$. In addition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5939","kind":"arxiv","version":3},"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":"1403.5939","created_at":"2026-05-18T02:42:05.946114+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5939v3","created_at":"2026-05-18T02:42:05.946114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5939","created_at":"2026-05-18T02:42:05.946114+00:00"},{"alias_kind":"pith_short_12","alias_value":"37H6TKSHJX7T","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"37H6TKSHJX7TEFEF","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"37H6TKSH","created_at":"2026-05-18T12:28:11.866339+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/37H6TKSHJX7TEFEFQDHVDEFG6B","json":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B.json","graph_json":"https://pith.science/api/pith-number/37H6TKSHJX7TEFEFQDHVDEFG6B/graph.json","events_json":"https://pith.science/api/pith-number/37H6TKSHJX7TEFEFQDHVDEFG6B/events.json","paper":"https://pith.science/paper/37H6TKSH"},"agent_actions":{"view_html":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B","download_json":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B.json","view_paper":"https://pith.science/paper/37H6TKSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5939&json=true","fetch_graph":"https://pith.science/api/pith-number/37H6TKSHJX7TEFEFQDHVDEFG6B/graph.json","fetch_events":"https://pith.science/api/pith-number/37H6TKSHJX7TEFEFQDHVDEFG6B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B/action/storage_attestation","attest_author":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B/action/author_attestation","sign_citation":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B/action/citation_signature","submit_replication":"https://pith.science/pith/37H6TKSHJX7TEFEFQDHVDEFG6B/action/replication_record"}},"created_at":"2026-05-18T02:42:05.946114+00:00","updated_at":"2026-05-18T02:42:05.946114+00:00"}