{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2CIQF26C6QE4NIVUASDC76RRU2","short_pith_number":"pith:2CIQF26C","schema_version":"1.0","canonical_sha256":"d09102ebc2f409c6a2b404862ffa31a695fd2c63ae0e3459694077f12601cb1e","source":{"kind":"arxiv","id":"1203.1893","version":1},"attestation_state":"computed","paper":{"title":"Lower central series of a free associative algebra over the integers and finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"David Jordan, Jason Li, Pavel Etingof, Surya Bhupatiraju, William Kuszmaul","submitted_at":"2012-03-08T19:25:14Z","abstract_excerpt":"Consider the free algebra A_n generated over Q by n generators x_1, ..., x_n. Interesting objects attached to A = A_n are members of its lower central series, L_i = L_i(A), defined inductively by L_1 = A, L_{i+1} = [A,L_{i}], and their associated graded components B_i = B_i(A) defined as B_i=L_i/L_{i+1}. These quotients B_i, for i at least 2, as well as the reduced quotient \\bar{B}_1=A/(L_2+A L_3), exhibit a rich geometric structure, as shown by Feigin and Shoikhet and later authors, (Dobrovolska-Kim-Ma,Dobrovolska-Etingof,Arbesfeld-Jordan,Bapat-Jordan).\n  We study the same problem over the in"},"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":"1203.1893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-08T19:25:14Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"97154178c11a35d0226ac67a101a4056613641a192f6f600f494c1e6ba096b19","abstract_canon_sha256":"a9a063a7b99a0e83db59524fee41caa2922cd87dceeaffe54cf8bc6fda79145d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:37.335274Z","signature_b64":"TWZZJUzVuNedi3TNXdp0Wzj6pEvJuYe50BOzTdqtAZk3CLFhHDqDp4DjsiOKKVUlrWtbJrcVEs7h/83U5asuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d09102ebc2f409c6a2b404862ffa31a695fd2c63ae0e3459694077f12601cb1e","last_reissued_at":"2026-05-18T01:03:37.334565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:37.334565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower central series of a free associative algebra over the integers and finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"David Jordan, Jason Li, Pavel Etingof, Surya Bhupatiraju, William Kuszmaul","submitted_at":"2012-03-08T19:25:14Z","abstract_excerpt":"Consider the free algebra A_n generated over Q by n generators x_1, ..., x_n. Interesting objects attached to A = A_n are members of its lower central series, L_i = L_i(A), defined inductively by L_1 = A, L_{i+1} = [A,L_{i}], and their associated graded components B_i = B_i(A) defined as B_i=L_i/L_{i+1}. These quotients B_i, for i at least 2, as well as the reduced quotient \\bar{B}_1=A/(L_2+A L_3), exhibit a rich geometric structure, as shown by Feigin and Shoikhet and later authors, (Dobrovolska-Kim-Ma,Dobrovolska-Etingof,Arbesfeld-Jordan,Bapat-Jordan).\n  We study the same problem over the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1893","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":"1203.1893","created_at":"2026-05-18T01:03:37.334678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1893v1","created_at":"2026-05-18T01:03:37.334678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1893","created_at":"2026-05-18T01:03:37.334678+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CIQF26C6QE4","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CIQF26C6QE4NIVU","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CIQF26C","created_at":"2026-05-18T12:26:50.516681+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/2CIQF26C6QE4NIVUASDC76RRU2","json":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2.json","graph_json":"https://pith.science/api/pith-number/2CIQF26C6QE4NIVUASDC76RRU2/graph.json","events_json":"https://pith.science/api/pith-number/2CIQF26C6QE4NIVUASDC76RRU2/events.json","paper":"https://pith.science/paper/2CIQF26C"},"agent_actions":{"view_html":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2","download_json":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2.json","view_paper":"https://pith.science/paper/2CIQF26C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1893&json=true","fetch_graph":"https://pith.science/api/pith-number/2CIQF26C6QE4NIVUASDC76RRU2/graph.json","fetch_events":"https://pith.science/api/pith-number/2CIQF26C6QE4NIVUASDC76RRU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2/action/storage_attestation","attest_author":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2/action/author_attestation","sign_citation":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2/action/citation_signature","submit_replication":"https://pith.science/pith/2CIQF26C6QE4NIVUASDC76RRU2/action/replication_record"}},"created_at":"2026-05-18T01:03:37.334678+00:00","updated_at":"2026-05-18T01:03:37.334678+00:00"}