{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:GGL554OBXL4UV5BMNU4WGLKICD","short_pith_number":"pith:GGL554OB","schema_version":"1.0","canonical_sha256":"3197def1c1baf94af42c6d39632d4810d45dbbd2291ef94d0a7c560e90e4e084","source":{"kind":"arxiv","id":"0805.0723","version":2},"attestation_state":"computed","paper":{"title":"Free subalgebras of Lie algebras close to nilpotent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Alexey Belov, Roman Mikhailov","submitted_at":"2008-05-06T13:49:43Z","abstract_excerpt":"We prove that for every automata algebra of exponential growth, the associated Lie algebra contains a free subalgebra. For n\\geq 1, let L_{n+2} be a Lie algebra with generator set x_1,..., x_{n+2} and the following relations: for k\\leq n, any commutator of length $k$ which consists of fewer than k different symbols from {x_1,...,x_{n+2}} is zero. As an application of this result about automata algebras, we prove that for every n\\geq 1, L_{n+2} contains a free subalgebra. We also prove the similar result about groups defined by commutator relations."},"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":"0805.0723","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-05-06T13:49:43Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"8312d61b156cf315bbddd47d9eaa5f8d102dabb49c074610c88f3ea992500636","abstract_canon_sha256":"7d8384358772119e5e5d14309823800d063c0a6d92fcc394db9ad34fa0594d53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:06.208380Z","signature_b64":"NdpJqbfsV2D43U0v0sek1npFvTFqvyJk3v3z3aOXY0KYBo8j7qZ3vkRqudseRRmvmmb1dXSEaNfK67MtLVw5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3197def1c1baf94af42c6d39632d4810d45dbbd2291ef94d0a7c560e90e4e084","last_reissued_at":"2026-05-18T00:29:06.207767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:06.207767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Free subalgebras of Lie algebras close to nilpotent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Alexey Belov, Roman Mikhailov","submitted_at":"2008-05-06T13:49:43Z","abstract_excerpt":"We prove that for every automata algebra of exponential growth, the associated Lie algebra contains a free subalgebra. For n\\geq 1, let L_{n+2} be a Lie algebra with generator set x_1,..., x_{n+2} and the following relations: for k\\leq n, any commutator of length $k$ which consists of fewer than k different symbols from {x_1,...,x_{n+2}} is zero. As an application of this result about automata algebras, we prove that for every n\\geq 1, L_{n+2} contains a free subalgebra. We also prove the similar result about groups defined by commutator relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.0723","kind":"arxiv","version":2},"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":"0805.0723","created_at":"2026-05-18T00:29:06.207840+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.0723v2","created_at":"2026-05-18T00:29:06.207840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.0723","created_at":"2026-05-18T00:29:06.207840+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGL554OBXL4U","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGL554OBXL4UV5BM","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGL554OB","created_at":"2026-05-18T12:25:57.157939+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/GGL554OBXL4UV5BMNU4WGLKICD","json":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD.json","graph_json":"https://pith.science/api/pith-number/GGL554OBXL4UV5BMNU4WGLKICD/graph.json","events_json":"https://pith.science/api/pith-number/GGL554OBXL4UV5BMNU4WGLKICD/events.json","paper":"https://pith.science/paper/GGL554OB"},"agent_actions":{"view_html":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD","download_json":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD.json","view_paper":"https://pith.science/paper/GGL554OB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.0723&json=true","fetch_graph":"https://pith.science/api/pith-number/GGL554OBXL4UV5BMNU4WGLKICD/graph.json","fetch_events":"https://pith.science/api/pith-number/GGL554OBXL4UV5BMNU4WGLKICD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD/action/storage_attestation","attest_author":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD/action/author_attestation","sign_citation":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD/action/citation_signature","submit_replication":"https://pith.science/pith/GGL554OBXL4UV5BMNU4WGLKICD/action/replication_record"}},"created_at":"2026-05-18T00:29:06.207840+00:00","updated_at":"2026-05-18T00:29:06.207840+00:00"}