{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A7Q4MNNWBYJEDZCM6OSFUNZWSN","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":"f8cc950379dee2bdcfc6f4f1e2823e3cf206b6a833ee8891381b9bba3c8fd55b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-29T20:11:50Z","title_canon_sha256":"f2c9f0188baba657403e9cb3b2d019b3f2222d140b177022aad9c822e421daf0"},"schema_version":"1.0","source":{"id":"1403.7666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7666","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7666v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7666","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"A7Q4MNNWBYJE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A7Q4MNNWBYJEDZCM","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A7Q4MNNW","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f6083387b76a4a38e52fbec79b17d64ac419f92ed1b1187ac123331a027cbcb5","target":"graph","created_at":"2026-05-18T02:55:12Z","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 $G$ be a finite primitive permutation group and let $\\kappa(G)$ be the number of conjugacy classes of derangements in $G$. By a classical theorem of Jordan, $\\kappa(G) \\geqslant 1$. In this paper we classify the groups $G$ with $\\kappa(G)=1$, and we use this to obtain new results on the structure of finite groups with an irreducible complex character that vanishes on a unique conjugacy class. We also obtain detailed structural information on the groups with $\\kappa(G)=2$, including a complete classification for almost simple groups.","authors_text":"Hung P. Tong-Viet, Timothy C. Burness","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-29T20:11:50Z","title":"Derangements in primitive permutation groups, with an application to character theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7666","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":"sha256:0b7c992f164b09085b0ee70b2588ce0a4250af59e187c51d30450d4efb0443d5","target":"record","created_at":"2026-05-18T02:55:12Z","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":"f8cc950379dee2bdcfc6f4f1e2823e3cf206b6a833ee8891381b9bba3c8fd55b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-29T20:11:50Z","title_canon_sha256":"f2c9f0188baba657403e9cb3b2d019b3f2222d140b177022aad9c822e421daf0"},"schema_version":"1.0","source":{"id":"1403.7666","kind":"arxiv","version":1}},"canonical_sha256":"07e1c635b60e1241e44cf3a45a3736937aba2020871ebf23028426c03115d969","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07e1c635b60e1241e44cf3a45a3736937aba2020871ebf23028426c03115d969","first_computed_at":"2026-05-18T02:55:12.730325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:12.730325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r/a7fy9wehT7pETrm7E9YMREQNJt35xwEeAOoghbrjIkWqPV5ldNAPIJBlM61v+E6Njllj0LEOw9ZkJl0XFRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:12.730838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b7c992f164b09085b0ee70b2588ce0a4250af59e187c51d30450d4efb0443d5","sha256:f6083387b76a4a38e52fbec79b17d64ac419f92ed1b1187ac123331a027cbcb5"],"state_sha256":"894ece3f0dfcfc4ae80f0df33cf372de617b7355fe669fa386ee1a406bcd4e0f"}