{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:U3SWIERBA6TL7J4IEGHAVNZ2UG","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":"c7fa0b6679546af428617ccbf54688a8a4f2d21973b0bc93dc59801afa85bba9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.RA","submitted_at":"2014-03-28T19:13:44Z","title_canon_sha256":"f7cd6a4ae2a4ab631a6fcdf8a568f316ebc78debc2d50f9565c5f7aa6d83d042"},"schema_version":"1.0","source":{"id":"1403.7496","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7496","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7496v2","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7496","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"pith_short_12","alias_value":"U3SWIERBA6TL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U3SWIERBA6TL7J4I","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U3SWIERB","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:12a76db9888c4a3045bb6c00e4a86a950a275d6015d413bb85e5378ff0b57dc2","target":"graph","created_at":"2026-05-18T02:54:55Z","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 $D$ be a division ring with infinite center, $n$ be a positive integer and $w(x_1,x_2,\\cdots, x_m)=1$ be a generalized group identity over the general linear group $\\GL_n(D)$. The aim of this paper is to prove that every subnormal subgroup of $GL_n(D)$ which satisfies the generalized group identity $w(x_1,x_2,\\cdots, x_m)=1$ is central.","authors_text":"Mai Hoang Bien","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.RA","submitted_at":"2014-03-28T19:13:44Z","title":"Generalized group identities of subnormal subgroups of general linear groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7496","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":"sha256:9ab4c8dee54e59e137a34fbaafda0acd9aba74b6d2d37c288bfcf62ec8442dca","target":"record","created_at":"2026-05-18T02:54:55Z","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":"c7fa0b6679546af428617ccbf54688a8a4f2d21973b0bc93dc59801afa85bba9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.RA","submitted_at":"2014-03-28T19:13:44Z","title_canon_sha256":"f7cd6a4ae2a4ab631a6fcdf8a568f316ebc78debc2d50f9565c5f7aa6d83d042"},"schema_version":"1.0","source":{"id":"1403.7496","kind":"arxiv","version":2}},"canonical_sha256":"a6e564122107a6bfa788218e0ab73aa1ba3313c61405bb8cd6eea10607b38837","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6e564122107a6bfa788218e0ab73aa1ba3313c61405bb8cd6eea10607b38837","first_computed_at":"2026-05-18T02:54:55.732656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:55.732656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ov1taGDvVWh7PrZggm0WIveYnUmW/gMfQ0D2jUWpYhbA04NlXez2eGDoErAS4JEpE7MX4GBSnzuQxDglr1VyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:55.733131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7496","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ab4c8dee54e59e137a34fbaafda0acd9aba74b6d2d37c288bfcf62ec8442dca","sha256:12a76db9888c4a3045bb6c00e4a86a950a275d6015d413bb85e5378ff0b57dc2"],"state_sha256":"acf31e0733b248531dd6eb9bd4cfcf727a335e9afd64eeb5882e17c31f2fa6fd"}