{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ONVRUVYM64AGHC72F6QGDV2FS5","short_pith_number":"pith:ONVRUVYM","schema_version":"1.0","canonical_sha256":"736b1a570cf700638bfa2fa061d745974e1c06809fc9b88efeb4b2bec0315289","source":{"kind":"arxiv","id":"1404.5023","version":1},"attestation_state":"computed","paper":{"title":"The Betti numbers for a family of solvable Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Minh Thanh Duong","submitted_at":"2014-04-20T07:08:00Z","abstract_excerpt":"We give a characterization of symplectic quadratic Lie algebras that their Lie algebra of inner derivations has an invertible derivation. A family of symplectic quadratic Lie algebras is introduced to illustrate this situation. Finally, we calculate explicitly the Betti numbers of a family of solvable Lie algebras in two ways: using the cohomology of quadratic Lie algebras and applying a Pouseele's result on extensions of the one-dimensional Lie algebra by Heisenberg Lie algebras"},"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":"1404.5023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-20T07:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"ba0c5b54edc461121dc581f32cb2417f2f0c05043953002c7405da3ae52c5faf","abstract_canon_sha256":"f3daa03585d95da67298ef645cb47254f7bc05a30f0d95be5c925381e244df0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:52.183299Z","signature_b64":"vD//XNZY7X/etCdtmzlQ+UXzGL0RaH738pfaniazM/ixGkPmAlnMkID4vTQViEr5FqCrFazsiTejQKD3YPQSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"736b1a570cf700638bfa2fa061d745974e1c06809fc9b88efeb4b2bec0315289","last_reissued_at":"2026-05-18T02:53:52.182481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:52.182481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Betti numbers for a family of solvable Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Minh Thanh Duong","submitted_at":"2014-04-20T07:08:00Z","abstract_excerpt":"We give a characterization of symplectic quadratic Lie algebras that their Lie algebra of inner derivations has an invertible derivation. A family of symplectic quadratic Lie algebras is introduced to illustrate this situation. Finally, we calculate explicitly the Betti numbers of a family of solvable Lie algebras in two ways: using the cohomology of quadratic Lie algebras and applying a Pouseele's result on extensions of the one-dimensional Lie algebra by Heisenberg Lie algebras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5023","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":"1404.5023","created_at":"2026-05-18T02:53:52.182617+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5023v1","created_at":"2026-05-18T02:53:52.182617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5023","created_at":"2026-05-18T02:53:52.182617+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONVRUVYM64AG","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONVRUVYM64AGHC72","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONVRUVYM","created_at":"2026-05-18T12:28:41.024544+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/ONVRUVYM64AGHC72F6QGDV2FS5","json":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5.json","graph_json":"https://pith.science/api/pith-number/ONVRUVYM64AGHC72F6QGDV2FS5/graph.json","events_json":"https://pith.science/api/pith-number/ONVRUVYM64AGHC72F6QGDV2FS5/events.json","paper":"https://pith.science/paper/ONVRUVYM"},"agent_actions":{"view_html":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5","download_json":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5.json","view_paper":"https://pith.science/paper/ONVRUVYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5023&json=true","fetch_graph":"https://pith.science/api/pith-number/ONVRUVYM64AGHC72F6QGDV2FS5/graph.json","fetch_events":"https://pith.science/api/pith-number/ONVRUVYM64AGHC72F6QGDV2FS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5/action/storage_attestation","attest_author":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5/action/author_attestation","sign_citation":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5/action/citation_signature","submit_replication":"https://pith.science/pith/ONVRUVYM64AGHC72F6QGDV2FS5/action/replication_record"}},"created_at":"2026-05-18T02:53:52.182617+00:00","updated_at":"2026-05-18T02:53:52.182617+00:00"}