{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DFV52UVFNIVNKBVSKOYQHXECFF","short_pith_number":"pith:DFV52UVF","schema_version":"1.0","canonical_sha256":"196bdd52a56a2ad506b253b103dc8229688aa9cae5c21eccc558daa1e8ef3118","source":{"kind":"arxiv","id":"1709.05728","version":1},"attestation_state":"computed","paper":{"title":"On Lie nilpotent associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Claud W. G. Dias Jr","submitted_at":"2017-09-17T23:47:11Z","abstract_excerpt":"Let $G$ be a group generated by a set $X$. It is well known and easy to check that \\[ [g_1, g_2, \\dots ,g_n] = 1 \\mbox{ for all } g_i \\in G \\qquad \\iff \\qquad [x_1, x_2, \\dots , x_n] =1 \\mbox{ for all } x_i \\in X. \\] Let $L$ be a Lie algebra generated by a set $X$. Then it is also well known and easy to check that \\[ [h_1, h_2, \\dots , h_n] = 0 \\mbox{ for all } h_i \\in L \\qquad \\iff \\qquad [x_1, x_2, \\dots ,x_n] = 0 \\mbox{ for all } x_i \\in X. \\]\n  Now let $A$ be a unital associative algebra generated by a set $X$. Then the assertion similar to the above does not hold: for $n > 2$, it is easy "},"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":"1709.05728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-17T23:47:11Z","cross_cats_sorted":[],"title_canon_sha256":"d11e108c55cd2600c3c94a02c3eb48c9dc7c5bbc249abe4b356084aea2df8bc7","abstract_canon_sha256":"96c2f9527ede3c2f9bab5cb009cddbe5e286a473bf8e3aefde3e819d1b392ed3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:59.639785Z","signature_b64":"x2T+7OgVHsKDHFDetcd9lQwha+RU15NZWJQp+z25AglL4hMV5mc+niPPstLfhNJODAnY4DVWyRVmGFZ4ch/fAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"196bdd52a56a2ad506b253b103dc8229688aa9cae5c21eccc558daa1e8ef3118","last_reissued_at":"2026-05-18T00:34:59.639126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:59.639126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Lie nilpotent associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Claud W. G. Dias Jr","submitted_at":"2017-09-17T23:47:11Z","abstract_excerpt":"Let $G$ be a group generated by a set $X$. It is well known and easy to check that \\[ [g_1, g_2, \\dots ,g_n] = 1 \\mbox{ for all } g_i \\in G \\qquad \\iff \\qquad [x_1, x_2, \\dots , x_n] =1 \\mbox{ for all } x_i \\in X. \\] Let $L$ be a Lie algebra generated by a set $X$. Then it is also well known and easy to check that \\[ [h_1, h_2, \\dots , h_n] = 0 \\mbox{ for all } h_i \\in L \\qquad \\iff \\qquad [x_1, x_2, \\dots ,x_n] = 0 \\mbox{ for all } x_i \\in X. \\]\n  Now let $A$ be a unital associative algebra generated by a set $X$. Then the assertion similar to the above does not hold: for $n > 2$, it is easy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05728","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":"1709.05728","created_at":"2026-05-18T00:34:59.639249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.05728v1","created_at":"2026-05-18T00:34:59.639249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05728","created_at":"2026-05-18T00:34:59.639249+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFV52UVFNIVN","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFV52UVFNIVNKBVS","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFV52UVF","created_at":"2026-05-18T12:31:10.602751+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/DFV52UVFNIVNKBVSKOYQHXECFF","json":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF.json","graph_json":"https://pith.science/api/pith-number/DFV52UVFNIVNKBVSKOYQHXECFF/graph.json","events_json":"https://pith.science/api/pith-number/DFV52UVFNIVNKBVSKOYQHXECFF/events.json","paper":"https://pith.science/paper/DFV52UVF"},"agent_actions":{"view_html":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF","download_json":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF.json","view_paper":"https://pith.science/paper/DFV52UVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.05728&json=true","fetch_graph":"https://pith.science/api/pith-number/DFV52UVFNIVNKBVSKOYQHXECFF/graph.json","fetch_events":"https://pith.science/api/pith-number/DFV52UVFNIVNKBVSKOYQHXECFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF/action/storage_attestation","attest_author":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF/action/author_attestation","sign_citation":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF/action/citation_signature","submit_replication":"https://pith.science/pith/DFV52UVFNIVNKBVSKOYQHXECFF/action/replication_record"}},"created_at":"2026-05-18T00:34:59.639249+00:00","updated_at":"2026-05-18T00:34:59.639249+00:00"}