{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SJ35CFEBSWTM7BHRGPIB3JKNRD","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":"4e34e7d45723f3787b8fa37b3f0f704e32fc5fd0274c910a669530e378119777","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-08T21:17:10Z","title_canon_sha256":"36808f597c65383e01dbcb6cd6b45d99ab66b4a1950128883d660a070a1ca694"},"schema_version":"1.0","source":{"id":"1410.2284","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2284","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2284v6","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2284","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"SJ35CFEBSWTM","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SJ35CFEBSWTM7BHR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SJ35CFEB","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:02109a3f0cfea527f2c08515f882bc596acc8265f6983de01fd05c34a5482055","target":"graph","created_at":"2026-05-18T02:19:52Z","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":"Let $\\psi$ be a permutation of a finite set $X$. We define $\\lambda(\\psi)$ to be the largest fraction of elements of $X$ lying on a single cycle of $\\psi$. For a finite group $G$, we define $\\lambda(G)$ to be the maximum among the values $\\lambda(\\alpha)$, where $\\alpha$ runs through the automorphisms of $G$. In this paper, we develop tools to deal with questions related to $\\lambda$-values of finite groups and of their automorphisms. As a consequence, we will be able to give a classification, up to a natural notion of isomorphism, of those pairs $(G,\\alpha)$ where $G$ is a finite group, $\\alp","authors_text":"Alexander Bors","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-08T21:17:10Z","title":"Classification of finite group automorphisms with a large cycle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2284","kind":"arxiv","version":6},"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:efefc1da680c9f7d6caad8346f7a5ffef10433638dbeb013cd99f6daefa20615","target":"record","created_at":"2026-05-18T02:19:52Z","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":"4e34e7d45723f3787b8fa37b3f0f704e32fc5fd0274c910a669530e378119777","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-08T21:17:10Z","title_canon_sha256":"36808f597c65383e01dbcb6cd6b45d99ab66b4a1950128883d660a070a1ca694"},"schema_version":"1.0","source":{"id":"1410.2284","kind":"arxiv","version":6}},"canonical_sha256":"9277d1148195a6cf84f133d01da54d88cc5faf9ad516afb4f1ff743e807cd295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9277d1148195a6cf84f133d01da54d88cc5faf9ad516afb4f1ff743e807cd295","first_computed_at":"2026-05-18T02:19:52.940702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:52.940702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IIF6tkQYXX4oho5Utyufg2K1MdqMOw1CLhNA5DBGhg+2mUBAZe60zu4GUhAhPdLe7xT2zVkXYVjOhpDBinwfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:52.941289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2284","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efefc1da680c9f7d6caad8346f7a5ffef10433638dbeb013cd99f6daefa20615","sha256:02109a3f0cfea527f2c08515f882bc596acc8265f6983de01fd05c34a5482055"],"state_sha256":"6f9c89086c01cc11dfa7840a7f72318cf17b1ef8273ab824467319823e3bf157"}