{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FGYNXGZKFC32JZ2VN3HSIH33EU","short_pith_number":"pith:FGYNXGZK","canonical_record":{"source":{"id":"1109.5439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T04:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"9337ac2a4ef33bd06194e333faf6b0ddb3f724f9ed733bc44d8b3767f5a9a00b","abstract_canon_sha256":"5eb0ed9aba4e56ca3136771878041fd01e3a05a396431a4feb0417b72cc5c405"},"schema_version":"1.0"},"canonical_sha256":"29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb","source":{"kind":"arxiv","id":"1109.5439","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5439","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5439v1","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5439","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"FGYNXGZKFC32","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FGYNXGZKFC32JZ2V","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FGYNXGZK","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FGYNXGZKFC32JZ2VN3HSIH33EU","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T04:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"9337ac2a4ef33bd06194e333faf6b0ddb3f724f9ed733bc44d8b3767f5a9a00b","abstract_canon_sha256":"5eb0ed9aba4e56ca3136771878041fd01e3a05a396431a4feb0417b72cc5c405"},"schema_version":"1.0"},"canonical_sha256":"29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:19.796447Z","signature_b64":"s8VqDaLQ5oJfezuDXFPUASXw+xxSegUxE7LULYCNrsPOVD0M8KSCNFz9KNdueYGGIlRqcTLls5WIPgIf3Ce7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb","last_reissued_at":"2026-05-18T04:12:19.795871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:19.795871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5439","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0EDQvwhMngO6rV12u7TPPSAtDAY7zZbHSivXz8TXJstdu+fnB5LV7Fv7M5b7G5xaKnERjB4yXFOxhyRmUYqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:11:46.746129Z"},"content_sha256":"50bf13a3be237ee6a1670b110c9f87a7934d399b03bc2061f734fe60e3e4143c","schema_version":"1.0","event_id":"sha256:50bf13a3be237ee6a1670b110c9f87a7934d399b03bc2061f734fe60e3e4143c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FGYNXGZKFC32JZ2VN3HSIH33EU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groups generated by a finite Engel set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Abdollahi, Antonio Tortora, Rolf Brandl","submitted_at":"2011-09-26T04:01:21Z","abstract_excerpt":"A subset $S$ of a group $G$ is called an Engel set if, for all $x,y\\in S$, there is a non-negative integer $n=n(x,y)$ such that $[x,\\,_n y]=1$. In this paper we are interested in finding conditions for a group generated by a finite Engel set to be nilpotent. In particular, we focus our investigation on groups generated by an Engel set of size two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5439","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kjbrocWnNeDXy9vBzUsPa80RyFERjU8iSeeeXTQuWX6aRwscZRHvUyQyVtjO1OxKVc6fcXKom5wcoOxTuvRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:11:46.746489Z"},"content_sha256":"18610707480745b0b5a3a1803cfbd1d7b52e53bfbf9c15e903cbe45a9a0b3c38","schema_version":"1.0","event_id":"sha256:18610707480745b0b5a3a1803cfbd1d7b52e53bfbf9c15e903cbe45a9a0b3c38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGYNXGZKFC32JZ2VN3HSIH33EU/bundle.json","state_url":"https://pith.science/pith/FGYNXGZKFC32JZ2VN3HSIH33EU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGYNXGZKFC32JZ2VN3HSIH33EU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T11:11:46Z","links":{"resolver":"https://pith.science/pith/FGYNXGZKFC32JZ2VN3HSIH33EU","bundle":"https://pith.science/pith/FGYNXGZKFC32JZ2VN3HSIH33EU/bundle.json","state":"https://pith.science/pith/FGYNXGZKFC32JZ2VN3HSIH33EU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGYNXGZKFC32JZ2VN3HSIH33EU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FGYNXGZKFC32JZ2VN3HSIH33EU","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":"5eb0ed9aba4e56ca3136771878041fd01e3a05a396431a4feb0417b72cc5c405","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T04:01:21Z","title_canon_sha256":"9337ac2a4ef33bd06194e333faf6b0ddb3f724f9ed733bc44d8b3767f5a9a00b"},"schema_version":"1.0","source":{"id":"1109.5439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5439","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5439v1","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5439","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"FGYNXGZKFC32","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FGYNXGZKFC32JZ2V","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FGYNXGZK","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:18610707480745b0b5a3a1803cfbd1d7b52e53bfbf9c15e903cbe45a9a0b3c38","target":"graph","created_at":"2026-05-18T04:12:19Z","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":"A subset $S$ of a group $G$ is called an Engel set if, for all $x,y\\in S$, there is a non-negative integer $n=n(x,y)$ such that $[x,\\,_n y]=1$. In this paper we are interested in finding conditions for a group generated by a finite Engel set to be nilpotent. In particular, we focus our investigation on groups generated by an Engel set of size two.","authors_text":"Alireza Abdollahi, Antonio Tortora, Rolf Brandl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T04:01:21Z","title":"Groups generated by a finite Engel set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5439","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":"sha256:50bf13a3be237ee6a1670b110c9f87a7934d399b03bc2061f734fe60e3e4143c","target":"record","created_at":"2026-05-18T04:12:19Z","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":"5eb0ed9aba4e56ca3136771878041fd01e3a05a396431a4feb0417b72cc5c405","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T04:01:21Z","title_canon_sha256":"9337ac2a4ef33bd06194e333faf6b0ddb3f724f9ed733bc44d8b3767f5a9a00b"},"schema_version":"1.0","source":{"id":"1109.5439","kind":"arxiv","version":1}},"canonical_sha256":"29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb","first_computed_at":"2026-05-18T04:12:19.795871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:19.795871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s8VqDaLQ5oJfezuDXFPUASXw+xxSegUxE7LULYCNrsPOVD0M8KSCNFz9KNdueYGGIlRqcTLls5WIPgIf3Ce7CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:19.796447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50bf13a3be237ee6a1670b110c9f87a7934d399b03bc2061f734fe60e3e4143c","sha256:18610707480745b0b5a3a1803cfbd1d7b52e53bfbf9c15e903cbe45a9a0b3c38"],"state_sha256":"627d3f2da6a3af808a393fd6c4f55fac612066bc6508dd59fc26956917557b1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aO7pxCjzy8HuU37VRyVWPVvhSHkeIIh8OsQmjgZW78/nUzQrjwKAzb+c/8yzChVfJoNyDTteqaetFEvAZ5GJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:11:46.748442Z","bundle_sha256":"3990983b299551da0b45ba6e9e2bb196d13ae197df10f247678d3998d9a172e3"}}