{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7FO6ATGBSUN77ZGKSUVMSQYRRV","short_pith_number":"pith:7FO6ATGB","canonical_record":{"source":{"id":"1705.06842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-19T01:17:24Z","cross_cats_sorted":[],"title_canon_sha256":"9bec82bb33b9d613ef4e6e78d0ee993d9062d932299cc4fa1043f4c6f705dee4","abstract_canon_sha256":"d98d065e7289c1a8645c8ef80adb58b98d9c79f65e1aafc3d252b5fb7c9b44c6"},"schema_version":"1.0"},"canonical_sha256":"f95de04cc1951bffe4ca952ac943118d7c30ba7204b30e08f5f746970f67129a","source":{"kind":"arxiv","id":"1705.06842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06842","created_at":"2026-05-18T00:44:11Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06842v1","created_at":"2026-05-18T00:44:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06842","created_at":"2026-05-18T00:44:11Z"},{"alias_kind":"pith_short_12","alias_value":"7FO6ATGBSUN7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7FO6ATGBSUN77ZGK","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7FO6ATGB","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7FO6ATGBSUN77ZGKSUVMSQYRRV","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-19T01:17:24Z","cross_cats_sorted":[],"title_canon_sha256":"9bec82bb33b9d613ef4e6e78d0ee993d9062d932299cc4fa1043f4c6f705dee4","abstract_canon_sha256":"d98d065e7289c1a8645c8ef80adb58b98d9c79f65e1aafc3d252b5fb7c9b44c6"},"schema_version":"1.0"},"canonical_sha256":"f95de04cc1951bffe4ca952ac943118d7c30ba7204b30e08f5f746970f67129a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:11.175309Z","signature_b64":"vtV7XdCJTuCwcEuLyEcPJGZzpFDT1WihGfyDbx2jOT7ccnTqMp3xv5oD2C1OI/YbzanItRKtZBH8+bJxLTGHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f95de04cc1951bffe4ca952ac943118d7c30ba7204b30e08f5f746970f67129a","last_reissued_at":"2026-05-18T00:44:11.174830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:11.174830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06842","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":"2026-05-18T00:44:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LclAMen/dIwIeW13J0myuYvSr4q0B2a+DNAnSldgmTbdPGmDPKV7c7C2Q8UEtgAR75UOecvIxI6RkMckWVLyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:23:13.417160Z"},"content_sha256":"3ade23142fd55c5c93401819026237297b9e1fd82dd834fa4a65299bf57561fe","schema_version":"1.0","event_id":"sha256:3ade23142fd55c5c93401819026237297b9e1fd82dd834fa4a65299bf57561fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7FO6ATGBSUN77ZGKSUVMSQYRRV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On groups where the twisted conjugacy class of the unit element is a subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daciberg Gon\\c{c}alves, Timur Nasybullov","submitted_at":"2017-05-19T01:17:24Z","abstract_excerpt":"We study groups $G$ where the $\\varphi$-conjugacy class $[e]_{\\varphi}=\\{g^{-1}\\varphi(g)~|~g\\in G\\}$ of the unit element is a subgroup of $G$ for every automorphism $\\varphi$ of $G$. If $G$ has $n$ generators, then we prove that the $k$-th member of the lower central series has a finite verbal width bounded in terms of $n,k$. Moreover, we prove that if such group $G$ satisfies the descending chain condition for normal subgroups, then $G$ is nilpotent. Finally, if $G$ is a finite abelian-by-cyclic group, we construct a good upper bound of the nilpotency class of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06842","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":"2026-05-18T00:44:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TST8Ov8p3HmBGDK+Di6fkbFwRZQOEN/Z/QIZkojBW0WSBpGHYGM0aLbiYLax4Cvz5VFZEEtxt55dHukOo3U9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:23:13.417728Z"},"content_sha256":"8edecf55af589e98ac5d5562cd4076caf96c0d3ce3adf322eed3a8611f446508","schema_version":"1.0","event_id":"sha256:8edecf55af589e98ac5d5562cd4076caf96c0d3ce3adf322eed3a8611f446508"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV/bundle.json","state_url":"https://pith.science/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV/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":"2026-06-05T01:23:13Z","links":{"resolver":"https://pith.science/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV","bundle":"https://pith.science/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV/bundle.json","state":"https://pith.science/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FO6ATGBSUN77ZGKSUVMSQYRRV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7FO6ATGBSUN77ZGKSUVMSQYRRV","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":"d98d065e7289c1a8645c8ef80adb58b98d9c79f65e1aafc3d252b5fb7c9b44c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-19T01:17:24Z","title_canon_sha256":"9bec82bb33b9d613ef4e6e78d0ee993d9062d932299cc4fa1043f4c6f705dee4"},"schema_version":"1.0","source":{"id":"1705.06842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06842","created_at":"2026-05-18T00:44:11Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06842v1","created_at":"2026-05-18T00:44:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06842","created_at":"2026-05-18T00:44:11Z"},{"alias_kind":"pith_short_12","alias_value":"7FO6ATGBSUN7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7FO6ATGBSUN77ZGK","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7FO6ATGB","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:8edecf55af589e98ac5d5562cd4076caf96c0d3ce3adf322eed3a8611f446508","target":"graph","created_at":"2026-05-18T00:44:11Z","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 study groups $G$ where the $\\varphi$-conjugacy class $[e]_{\\varphi}=\\{g^{-1}\\varphi(g)~|~g\\in G\\}$ of the unit element is a subgroup of $G$ for every automorphism $\\varphi$ of $G$. If $G$ has $n$ generators, then we prove that the $k$-th member of the lower central series has a finite verbal width bounded in terms of $n,k$. Moreover, we prove that if such group $G$ satisfies the descending chain condition for normal subgroups, then $G$ is nilpotent. Finally, if $G$ is a finite abelian-by-cyclic group, we construct a good upper bound of the nilpotency class of $G$.","authors_text":"Daciberg Gon\\c{c}alves, Timur Nasybullov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-19T01:17:24Z","title":"On groups where the twisted conjugacy class of the unit element is a subgroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06842","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":"sha256:3ade23142fd55c5c93401819026237297b9e1fd82dd834fa4a65299bf57561fe","target":"record","created_at":"2026-05-18T00:44:11Z","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":"d98d065e7289c1a8645c8ef80adb58b98d9c79f65e1aafc3d252b5fb7c9b44c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-19T01:17:24Z","title_canon_sha256":"9bec82bb33b9d613ef4e6e78d0ee993d9062d932299cc4fa1043f4c6f705dee4"},"schema_version":"1.0","source":{"id":"1705.06842","kind":"arxiv","version":1}},"canonical_sha256":"f95de04cc1951bffe4ca952ac943118d7c30ba7204b30e08f5f746970f67129a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f95de04cc1951bffe4ca952ac943118d7c30ba7204b30e08f5f746970f67129a","first_computed_at":"2026-05-18T00:44:11.174830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:11.174830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vtV7XdCJTuCwcEuLyEcPJGZzpFDT1WihGfyDbx2jOT7ccnTqMp3xv5oD2C1OI/YbzanItRKtZBH8+bJxLTGHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:11.175309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ade23142fd55c5c93401819026237297b9e1fd82dd834fa4a65299bf57561fe","sha256:8edecf55af589e98ac5d5562cd4076caf96c0d3ce3adf322eed3a8611f446508"],"state_sha256":"ddf2a671d58b9a3dfb5a16d20403196f93198c7d82bae0959b6e85035f55083b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDZThfRzQvpLkxF59By6OihbrXYLKnB9i1xPDSk8vrYFQ5yEP+8GBWP+rAHNoF8g5uYDdQ4Mh56E/lhxoGAxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:23:13.420548Z","bundle_sha256":"9eec9ad2c126305bcb5cfd68675976431946f79f1e4a57141cf533aa92f2f69d"}}