{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KNYZJSWEDXJE4FJVM7QRA2URTB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0e77a2d2305f825131e87b957fa6b36885a71af341fbe85dc0072551ce7874d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-19T20:55:29Z","title_canon_sha256":"2c603439534d1e03d5e7f244ea60b214a4648f4a62a12677cf9634aed9a0a876"},"schema_version":"1.0","source":{"id":"1308.4172","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4172","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4172v2","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4172","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"KNYZJSWEDXJE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KNYZJSWEDXJE4FJV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KNYZJSWE","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:cc384c255c07cefd8b5ec4b1c576e9c76df3cb6b1d35b4dea244452e94213c1e","target":"graph","created_at":"2026-05-18T01:31:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\mathbb Z \\langle X \\rangle$ be the free unital associative ring freely generated by an infinite countable set $X = \\{ x_1,x_2, \\dots \\}$. Define a left-normed commutator $[x_1,x_2, \\dots, x_n]$ by $[a,b] = ab - ba$, $[a,b,c] = [[a,b],c]$. For $n \\ge 2$, let $T^{(n)}$ be the two-sided ideal in $\\mathbb Z \\langle X \\rangle$ generated by all commutators $[a_1,a_2, \\dots, a_n]$ $( a_i \\in \\mathbb Z \\langle X \\rangle )$. Let $T^{(3,2)}$ be the two-sided ideal of the ring $\\mathbb Z \\langle X \\rangle$ generated by all elements $[a_1, a_2, a_3, a_4]$ and $[a_1, a_2] [a_3, a_4, a_5]$ $(a_i \\in \\","authors_text":"Alexei Krasilnikov, Galina Deryabina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-19T20:55:29Z","title":"The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4172","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7794729a032c0849dafab8df7a0ad282174cf3b3a2128eba5b4bfb5ef1db946c","target":"record","created_at":"2026-05-18T01:31:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0e77a2d2305f825131e87b957fa6b36885a71af341fbe85dc0072551ce7874d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-19T20:55:29Z","title_canon_sha256":"2c603439534d1e03d5e7f244ea60b214a4648f4a62a12677cf9634aed9a0a876"},"schema_version":"1.0","source":{"id":"1308.4172","kind":"arxiv","version":2}},"canonical_sha256":"537194cac41dd24e153567e1106a91987d2974d361d76aab81712f9553d3e78a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"537194cac41dd24e153567e1106a91987d2974d361d76aab81712f9553d3e78a","first_computed_at":"2026-05-18T01:31:46.824879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:46.824879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lAuqXwXlmiTLchq3cxcEUQMzPrhVHFz0Qk5aDherPPgNMbkCLD4vJ4paenzyPt/t4fk8AiY0osJ8u8vdLYyvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:46.825469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4172","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7794729a032c0849dafab8df7a0ad282174cf3b3a2128eba5b4bfb5ef1db946c","sha256:cc384c255c07cefd8b5ec4b1c576e9c76df3cb6b1d35b4dea244452e94213c1e"],"state_sha256":"a3d9ea4be68ed4dd0e6959f8c5b94a22e1cf4894711a902c4c4930c278547762"}