{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IC7W7HKXTX2XYNPQFCLNEKVBTJ","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":"b37baca5bb4e9a92238c72fdbb38e7078322ce6b3124df7cc20360a5a00c4b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-05T06:41:41Z","title_canon_sha256":"708374e53c5906e4e5e073f5e85cc01e36ab404457f8c3815ffb554e8f58b8b0"},"schema_version":"1.0","source":{"id":"1303.0941","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0941","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0941v2","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0941","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"IC7W7HKXTX2X","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IC7W7HKXTX2XYNPQ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IC7W7HKX","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:395169c3a1e84927c3aa006471501a3315ce5bfee143dfbfce16cdf8b85acdc4","target":"graph","created_at":"2026-05-18T03:31:44Z","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 twisted conjugacy classes of the unit element in different groups. Fel'shtyn and Troitsky showed that the twisted conjugacy class of the unit element of an abelian group is a subgroup for every automorphism. The structure is investigated of a group whose twisted conjugacy class of the unit element is a subgroup for every automorphism (inner automorphism).","authors_text":"M. V. Neshchadim, T. R. Nasybullov, V. G. Bardakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-05T06:41:41Z","title":"Twisted conjugacy classes of the unit element"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0941","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":"sha256:69c47822aa418f665afaaa8fd7d5f31b41fdf8f293b8ec4caf551a350ded05ad","target":"record","created_at":"2026-05-18T03:31:44Z","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":"b37baca5bb4e9a92238c72fdbb38e7078322ce6b3124df7cc20360a5a00c4b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-05T06:41:41Z","title_canon_sha256":"708374e53c5906e4e5e073f5e85cc01e36ab404457f8c3815ffb554e8f58b8b0"},"schema_version":"1.0","source":{"id":"1303.0941","kind":"arxiv","version":2}},"canonical_sha256":"40bf6f9d579df57c35f02896d22aa19a77d9fad7edccb05e7429e5790629fcc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40bf6f9d579df57c35f02896d22aa19a77d9fad7edccb05e7429e5790629fcc9","first_computed_at":"2026-05-18T03:31:44.224899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:44.224899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LF7zS/s1hWw7cyZ6GubYSyA8HMjUKxENrMkedPiZB1SYxZN48ZCUSez3WZpoJvHXr7d2aCo3YygAcQlL/ahBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:44.225743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0941","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69c47822aa418f665afaaa8fd7d5f31b41fdf8f293b8ec4caf551a350ded05ad","sha256:395169c3a1e84927c3aa006471501a3315ce5bfee143dfbfce16cdf8b85acdc4"],"state_sha256":"6c9e3cae3a5b8ff77c0704aa133bad4b5796ac618db0820644d6d4644af5fede"}