{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BNFRECHQSCIJSMYM67MKIZNOA4","short_pith_number":"pith:BNFRECHQ","schema_version":"1.0","canonical_sha256":"0b4b1208f0909099330cf7d8a465ae0700413a560782e51614e06455ea77dc57","source":{"kind":"arxiv","id":"1408.0871","version":1},"attestation_state":"computed","paper":{"title":"Generic properties of 2-step nilpotent Lie algebras and torsion-free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.RA","authors_text":"Maria V. Milentyeva","submitted_at":"2014-08-05T05:53:56Z","abstract_excerpt":"To define the notion of a generic property of finite dimensional 2-step nilpotent Lie algebras we use standard correspondence between such Lie algebras and points of an appropriate algebraic variety, where a negligible set is one contained in a proper Zariski-closed subset. We compute the maximal dimension of an abelian subalgebra of a generic Lie algebra and give a sufficient condition for a generic Lie algebra to admit no surjective homomorphism onto a non-abelian Lie algebra of a given dimension. Also we consider analogous questions for finitely generated torsion free nilpotent groups of cl"},"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":"1408.0871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-05T05:53:56Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"62eb2b025b020f8f79244b99ba609a03528991a3f6868ef55d58514f68e76fcd","abstract_canon_sha256":"3f7489e50d79fd89156e059690c4165e9756c37e5703eb7629e8613ff244af35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:50.231619Z","signature_b64":"TS0xFnQEqYkriGe+KbKdxyli6ZhwXvMRkyitwSND1BwY6fJDN9sizVMcEO8rClfHWyfyMaFgjJnQQCSUxXqGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b4b1208f0909099330cf7d8a465ae0700413a560782e51614e06455ea77dc57","last_reissued_at":"2026-05-18T02:45:50.231062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:50.231062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic properties of 2-step nilpotent Lie algebras and torsion-free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.RA","authors_text":"Maria V. Milentyeva","submitted_at":"2014-08-05T05:53:56Z","abstract_excerpt":"To define the notion of a generic property of finite dimensional 2-step nilpotent Lie algebras we use standard correspondence between such Lie algebras and points of an appropriate algebraic variety, where a negligible set is one contained in a proper Zariski-closed subset. We compute the maximal dimension of an abelian subalgebra of a generic Lie algebra and give a sufficient condition for a generic Lie algebra to admit no surjective homomorphism onto a non-abelian Lie algebra of a given dimension. Also we consider analogous questions for finitely generated torsion free nilpotent groups of cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0871","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":"1408.0871","created_at":"2026-05-18T02:45:50.231144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0871v1","created_at":"2026-05-18T02:45:50.231144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0871","created_at":"2026-05-18T02:45:50.231144+00:00"},{"alias_kind":"pith_short_12","alias_value":"BNFRECHQSCIJ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BNFRECHQSCIJSMYM","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BNFRECHQ","created_at":"2026-05-18T12:28:22.404517+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/BNFRECHQSCIJSMYM67MKIZNOA4","json":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4.json","graph_json":"https://pith.science/api/pith-number/BNFRECHQSCIJSMYM67MKIZNOA4/graph.json","events_json":"https://pith.science/api/pith-number/BNFRECHQSCIJSMYM67MKIZNOA4/events.json","paper":"https://pith.science/paper/BNFRECHQ"},"agent_actions":{"view_html":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4","download_json":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4.json","view_paper":"https://pith.science/paper/BNFRECHQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0871&json=true","fetch_graph":"https://pith.science/api/pith-number/BNFRECHQSCIJSMYM67MKIZNOA4/graph.json","fetch_events":"https://pith.science/api/pith-number/BNFRECHQSCIJSMYM67MKIZNOA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4/action/storage_attestation","attest_author":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4/action/author_attestation","sign_citation":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4/action/citation_signature","submit_replication":"https://pith.science/pith/BNFRECHQSCIJSMYM67MKIZNOA4/action/replication_record"}},"created_at":"2026-05-18T02:45:50.231144+00:00","updated_at":"2026-05-18T02:45:50.231144+00:00"}