{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JQCVMXKRMODAO5WJRMEUOZQXQO","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":"0fe25764ff00f1eb6286e677c219900d53fee77d472e8992face21dcff7d6d41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-10T14:22:30Z","title_canon_sha256":"29ebb2ea0da2bac7d33f921ddd33453637b97e41b57027c879656cf207122408"},"schema_version":"1.0","source":{"id":"1208.2185","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2185","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2185v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2185","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"JQCVMXKRMODA","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JQCVMXKRMODAO5WJ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JQCVMXKR","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:dbe8129c5c6e02db2b9cb56f09e2117743818d098a0255f775094d14e9a46302","target":"graph","created_at":"2026-05-18T03:07:42Z","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":"Verbally prime algebras are important in PI theory. They were described by Kemer over a field $K$ of characteristic zero: 0 and $K<T>$ (the trivial ones), $M_n(K)$, $M_n(E)$, $M_{ab}(E)$. Here $K<T>$ is the free associative algebra of infinite rank, with free generators $T$, $E$ denotes the infinite dimensional Grassmann algebra over $K$, $M_n(K)$ and $M_n(E)$ are the $n\\times n$ matrices over $K$ and over $E$, respectively. The algebras $M_{ab}(E)$ are subalgebras of $M_{a+b}(E)$, see their definition below. The generic (also called relatively free) algebras of these algebras have been studie","authors_text":"Plamen Koshlukov, Thiago Castilho de Mello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-10T14:22:30Z","title":"On the polynomial identities of the algebra $M_{11}(E)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2185","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:dd1d50afdf09a9d04cdd56de8aba68432d5a824f0a8f0a2e1a826d7138bbb266","target":"record","created_at":"2026-05-18T03:07:42Z","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":"0fe25764ff00f1eb6286e677c219900d53fee77d472e8992face21dcff7d6d41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-10T14:22:30Z","title_canon_sha256":"29ebb2ea0da2bac7d33f921ddd33453637b97e41b57027c879656cf207122408"},"schema_version":"1.0","source":{"id":"1208.2185","kind":"arxiv","version":2}},"canonical_sha256":"4c05565d5163860776c98b09476617839ab783e78073d70eec389a0bb6c513e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c05565d5163860776c98b09476617839ab783e78073d70eec389a0bb6c513e5","first_computed_at":"2026-05-18T03:07:42.498041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:42.498041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cf7Vipvq26jQNUTpgiKvlFX+n5rG5VOXVhO7bE0JzcnN8PsmUWnSSmLyS5nhFb7lLDPLNiOh2vWVvBqGNJ9zDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:42.498600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2185","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd1d50afdf09a9d04cdd56de8aba68432d5a824f0a8f0a2e1a826d7138bbb266","sha256:dbe8129c5c6e02db2b9cb56f09e2117743818d098a0255f775094d14e9a46302"],"state_sha256":"a93e49d41f9a6adadf5d7885f117a186cfbc8c1cba0467b3144299722351a31e"}