{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VPTUSIWBQJNX75RCWW6X5UKWW3","short_pith_number":"pith:VPTUSIWB","schema_version":"1.0","canonical_sha256":"abe74922c1825b7ff622b5bd7ed156b6ee2d0199056da4c60a28c5f8be9aa80a","source":{"kind":"arxiv","id":"1211.0884","version":1},"attestation_state":"computed","paper":{"title":"Naturally reductive pseudo-Riemannian Lie groups in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Vittone, Gabriela P. Ovando, Viviana del Barco","submitted_at":"2012-11-05T15:09:28Z","abstract_excerpt":"This work concerns the non-flat metrics on the Heisenberg Lie group of dimension three $\\Heis_3(\\RR)$ and the bi-invariant metrics on the solvable Lie groups of dimension four. On $\\Heis_3(\\RR)$ we prove that the property of the metric being naturally reductive is equivalent to the property of the center being non-degenerate. These metrics are Lorentzian algebraic Ricci solitons. We start with the indecomposable Lie groups of dimension four admitting bi-invariant metrics and which act on $\\Heis_3(\\RR)$ by isometries and we finally study some geometrical features on these spaces."},"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":"1211.0884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T15:09:28Z","cross_cats_sorted":[],"title_canon_sha256":"c4fcc8a9a2224150c991e4e2a5412aa8ad7cec85c8a51634c3412db48b1e07d9","abstract_canon_sha256":"9bca7576d6af1b999bca68028e3d01bc21deb12bb3c3e74bc14bdbb1e1d3b27b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:06.288796Z","signature_b64":"+u2Tc2EthRlDk7i7l2Z/+vF5wtyNLL9gLxPa4lPAHah3TRr+LPMo0bFUywu121varav46yw+WuWd4NqtQI/2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe74922c1825b7ff622b5bd7ed156b6ee2d0199056da4c60a28c5f8be9aa80a","last_reissued_at":"2026-05-18T02:42:06.288065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:06.288065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Naturally reductive pseudo-Riemannian Lie groups in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Vittone, Gabriela P. Ovando, Viviana del Barco","submitted_at":"2012-11-05T15:09:28Z","abstract_excerpt":"This work concerns the non-flat metrics on the Heisenberg Lie group of dimension three $\\Heis_3(\\RR)$ and the bi-invariant metrics on the solvable Lie groups of dimension four. On $\\Heis_3(\\RR)$ we prove that the property of the metric being naturally reductive is equivalent to the property of the center being non-degenerate. These metrics are Lorentzian algebraic Ricci solitons. We start with the indecomposable Lie groups of dimension four admitting bi-invariant metrics and which act on $\\Heis_3(\\RR)$ by isometries and we finally study some geometrical features on these spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0884","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":"1211.0884","created_at":"2026-05-18T02:42:06.288150+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.0884v1","created_at":"2026-05-18T02:42:06.288150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0884","created_at":"2026-05-18T02:42:06.288150+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPTUSIWBQJNX","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPTUSIWBQJNX75RC","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPTUSIWB","created_at":"2026-05-18T12:27:25.539911+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/VPTUSIWBQJNX75RCWW6X5UKWW3","json":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3.json","graph_json":"https://pith.science/api/pith-number/VPTUSIWBQJNX75RCWW6X5UKWW3/graph.json","events_json":"https://pith.science/api/pith-number/VPTUSIWBQJNX75RCWW6X5UKWW3/events.json","paper":"https://pith.science/paper/VPTUSIWB"},"agent_actions":{"view_html":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3","download_json":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3.json","view_paper":"https://pith.science/paper/VPTUSIWB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.0884&json=true","fetch_graph":"https://pith.science/api/pith-number/VPTUSIWBQJNX75RCWW6X5UKWW3/graph.json","fetch_events":"https://pith.science/api/pith-number/VPTUSIWBQJNX75RCWW6X5UKWW3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3/action/storage_attestation","attest_author":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3/action/author_attestation","sign_citation":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3/action/citation_signature","submit_replication":"https://pith.science/pith/VPTUSIWBQJNX75RCWW6X5UKWW3/action/replication_record"}},"created_at":"2026-05-18T02:42:06.288150+00:00","updated_at":"2026-05-18T02:42:06.288150+00:00"}