{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TVBXJZAY47OEAAVPYZMI2Q2B2H","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":"c3142fea68389424be8d57ad7b57f32bab3f3c07aa1810b1c1ce0040f5194e3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-03T21:26:06Z","title_canon_sha256":"38149a8312dde1a94c80c477f5dc1f4e1d00316308a73b27bf3b52d404a2c776"},"schema_version":"1.0","source":{"id":"1901.01859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01859","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01859v1","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01859","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"TVBXJZAY47OE","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TVBXJZAY47OEAAVP","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TVBXJZAY","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:fed1512567ca3cd9e609429e2a0f07bfb533e55e32062b4f43eb357bc6f29e35","target":"graph","created_at":"2026-05-17T23:56:49Z","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 $m,n$ be positive integers and $w$ a multilinear commutator word. Assume that $G$ is a finite group having subgroups $G_1,\\ldots,G_m$ whose union contains all $w$-values in $G$. Assume further that all elements of the subgroups $G_1,\\ldots,G_m$ are $n$-Engel in $G$. It is shown that the verbal subgroup $w(G)$ is $s$-Engel for some $\\{m,n,w\\}$-bounded number $s$.","authors_text":"Danilo Silveira, Pavel Shumyatsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-03T21:26:06Z","title":"On finite groups in which commutators are covered by Engel subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01859","kind":"arxiv","version":1},"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":"sha256:316bc6f552a94c307a19651ceae774694e397f4cc48bef1e546c5ce32232742d","target":"record","created_at":"2026-05-17T23:56:49Z","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":"c3142fea68389424be8d57ad7b57f32bab3f3c07aa1810b1c1ce0040f5194e3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-03T21:26:06Z","title_canon_sha256":"38149a8312dde1a94c80c477f5dc1f4e1d00316308a73b27bf3b52d404a2c776"},"schema_version":"1.0","source":{"id":"1901.01859","kind":"arxiv","version":1}},"canonical_sha256":"9d4374e418e7dc4002afc6588d4341d1dd0975c54c8cebdf37615198581cf20c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d4374e418e7dc4002afc6588d4341d1dd0975c54c8cebdf37615198581cf20c","first_computed_at":"2026-05-17T23:56:49.465274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:49.465274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t4DMNznTzdgkGTnIF+/HWy4RkoKdJV5Ezf0FvWQHTlL6nciD0GAMWc1CkjGsNCaLShGRuC/o3vbM2QNN/HTuCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:49.465666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:316bc6f552a94c307a19651ceae774694e397f4cc48bef1e546c5ce32232742d","sha256:fed1512567ca3cd9e609429e2a0f07bfb533e55e32062b4f43eb357bc6f29e35"],"state_sha256":"967eb8170e2307abb2df03f0acafaf6e8f5b3ff0e3f13c89aa02cd1675390ecc"}