{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UDZVNBZPU5FKXPUJ4TEFZO3AHO","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":"f01c843e200453265f39c760cb532e3733ea8e539185e8805cd07930d60832af","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-26T15:29:09Z","title_canon_sha256":"416a8c5a867c44e7c7808c84f88c92584bbbc587e80d179a0b521f6febca98c4"},"schema_version":"1.0","source":{"id":"1405.6616","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6616","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6616v2","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6616","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"UDZVNBZPU5FK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UDZVNBZPU5FKXPUJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UDZVNBZP","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:46c15ec4204550db279eb2a3c2a5f50c8218e77dae3ff5167207867f62c1455e","target":"graph","created_at":"2026-05-18T01:21:45Z","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 investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.","authors_text":"Alex Bartel, Tim Dokchitser","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-26T15:29:09Z","title":"Rational representations and permutation representations of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6616","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":"sha256:1066a7087c5202b602fb962f1b6ee81667bae90cb504864ff78e8f9a5255e1d8","target":"record","created_at":"2026-05-18T01:21:45Z","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":"f01c843e200453265f39c760cb532e3733ea8e539185e8805cd07930d60832af","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-26T15:29:09Z","title_canon_sha256":"416a8c5a867c44e7c7808c84f88c92584bbbc587e80d179a0b521f6febca98c4"},"schema_version":"1.0","source":{"id":"1405.6616","kind":"arxiv","version":2}},"canonical_sha256":"a0f356872fa74aabbe89e4c85cbb603bad0f263b5192584379c9f79524143378","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0f356872fa74aabbe89e4c85cbb603bad0f263b5192584379c9f79524143378","first_computed_at":"2026-05-18T01:21:45.272655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:45.272655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VQUI1n5iog3LAm++PvTpdeP6/9Ofi6AFnzIQy5XjSjxwiN7lc9aIfQghR02aZ8uFQgI+wRXVW6KbymFmLyZ4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:45.273180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6616","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1066a7087c5202b602fb962f1b6ee81667bae90cb504864ff78e8f9a5255e1d8","sha256:46c15ec4204550db279eb2a3c2a5f50c8218e77dae3ff5167207867f62c1455e"],"state_sha256":"635953e5ccdfc4184187b60ad2e726e177ad23048fa9def053aa7204060ee2f0"}