{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5EO5XMTHJVIBKN5XJ22YP6CXI7","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":"e2ed1f720afde922e624a71681e58659d770ac36f32bfd1e0611203c18b14234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-29T18:40:43Z","title_canon_sha256":"cd9722ece4060112ee9bbe3d1167f323b5711633da1addf35bdbd7520e88b102"},"schema_version":"1.0","source":{"id":"1412.8418","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8418","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8418v2","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8418","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"5EO5XMTHJVIB","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5EO5XMTHJVIBKN5X","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5EO5XMTH","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:3d0e5c989b25f411ae9a4bb139206019278ceb6ac273561ec32ed7795e8e78d8","target":"graph","created_at":"2026-05-18T02:28:31Z","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":"Using Frobenius normal forms of matrices over finite fields as well as the Burnside Basis Theorem, we give a direct proof of Horo\\v{s}evski\\u{i}'s result that every automorphism $\\alpha$ of a finite nilpotent group has a cycle whose length coincides with $\\mathrm{ord}(\\alpha)$. Also, we give two new sufficient conditions for an automorphism $\\alpha$ of an arbitrary finite group to satisfy this property, namely when $\\mathrm{ord}(\\alpha)$ is a product of at most two prime powers or when $\\alpha$ has a sufficiently large cycle. This will allow us to show that the least order of a group where thi","authors_text":"Alexander Bors","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-29T18:40:43Z","title":"On finite groups where the order of every automorphism is a cycle length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8418","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:e3840aa25577bc4f4586dc84b3a7939699369250c178e699449ea21a1d71fec5","target":"record","created_at":"2026-05-18T02:28:31Z","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":"e2ed1f720afde922e624a71681e58659d770ac36f32bfd1e0611203c18b14234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-29T18:40:43Z","title_canon_sha256":"cd9722ece4060112ee9bbe3d1167f323b5711633da1addf35bdbd7520e88b102"},"schema_version":"1.0","source":{"id":"1412.8418","kind":"arxiv","version":2}},"canonical_sha256":"e91ddbb2674d501537b74eb587f85747cac0422433a862ac9ae5b1dfb0688ab6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e91ddbb2674d501537b74eb587f85747cac0422433a862ac9ae5b1dfb0688ab6","first_computed_at":"2026-05-18T02:28:31.097400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:31.097400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xhJ2jK5cnNcHRyX/mjBncgbN5ltaPJ6LjhR0L7zJMhB4as66ghxghz1cCDBJbSiHiNhV0uvXevUR2ncZ/M/PAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:31.098056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8418","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3840aa25577bc4f4586dc84b3a7939699369250c178e699449ea21a1d71fec5","sha256:3d0e5c989b25f411ae9a4bb139206019278ceb6ac273561ec32ed7795e8e78d8"],"state_sha256":"64936333c217eae9a4ea9ecaabf4835667ea8241b41fcf028689f7c3703467cc"}