{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MFFM7UODPWJMT5L7YM2F2SD32Q","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":"70c1892d2248d1681ce734b6123289fa32f4517c88c7815208a4bd942e4a86a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-05-31T10:30:13Z","title_canon_sha256":"b9c48029fb595367ba3d29b3b51de13dd2e8774599e1d667f30617c8f169e82d"},"schema_version":"1.0","source":{"id":"1805.12411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12411","created_at":"2026-05-18T00:14:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12411v1","created_at":"2026-05-18T00:14:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12411","created_at":"2026-05-18T00:14:30Z"},{"alias_kind":"pith_short_12","alias_value":"MFFM7UODPWJM","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MFFM7UODPWJMT5L7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MFFM7UOD","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:8ac066dd4461c44ffcdb4d11ac497e6cacf7caad524daaddef95c4030a853081","target":"graph","created_at":"2026-05-18T00:14:30Z","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":"We give an affrmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G with an identity, we prove that the set of right Engel elements of G is contained in the Hirsch-Plotkin radical of G. Given an arbitrary word w, we also show that the class of all groups G in which the w-values are right n-Engel and w(G) is locally nilpotent is a variety.","authors_text":"Antonio Tortora, Maria Tota, Pavel Shumyatsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-05-31T10:30:13Z","title":"Engel groups with an identity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12411","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":"sha256:1d3d466286ef7b65ae568b125d9c7a182c1f01235bc3c6b4ea29d6cab8eb4565","target":"record","created_at":"2026-05-18T00:14:30Z","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":"70c1892d2248d1681ce734b6123289fa32f4517c88c7815208a4bd942e4a86a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-05-31T10:30:13Z","title_canon_sha256":"b9c48029fb595367ba3d29b3b51de13dd2e8774599e1d667f30617c8f169e82d"},"schema_version":"1.0","source":{"id":"1805.12411","kind":"arxiv","version":1}},"canonical_sha256":"614acfd1c37d92c9f57fc3345d487bd40115273f45504e1e51cf2c0d9ed1c1ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"614acfd1c37d92c9f57fc3345d487bd40115273f45504e1e51cf2c0d9ed1c1ec","first_computed_at":"2026-05-18T00:14:30.269383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:30.269383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EBTUivAWM7WwvubAWYsuQTeO82zO8TNT6XuDJofgn6dEIG8O0z6cASVN3DY2Re1WYzZiCeZEMrOGWYd3+KrFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:30.270078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.12411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d3d466286ef7b65ae568b125d9c7a182c1f01235bc3c6b4ea29d6cab8eb4565","sha256:8ac066dd4461c44ffcdb4d11ac497e6cacf7caad524daaddef95c4030a853081"],"state_sha256":"ee4ab93f828ecb94cab0f971f09680b86051613e3e1fd03ea8015a417f72bbc1"}