{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LRX3TO3UUYDHNNTOCMOUYBEJXI","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":"5277270f805fae637da0f123e1b1fd5e4e1d415570e5760a104eb3d40635a76a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-18T15:31:09Z","title_canon_sha256":"6fa872cb95dc9aa748bbc5ceb4d3ba9be544f3e5ff991bc967810affc681885a"},"schema_version":"1.0","source":{"id":"1108.3777","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3777","created_at":"2026-05-18T04:15:07Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3777v1","created_at":"2026-05-18T04:15:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3777","created_at":"2026-05-18T04:15:07Z"},{"alias_kind":"pith_short_12","alias_value":"LRX3TO3UUYDH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LRX3TO3UUYDHNNTO","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LRX3TO3U","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:3261254363209e42a5ac57341dabd8a2f5b7bcea6e97dbe69f0310ded0a686f1","target":"graph","created_at":"2026-05-18T04:15:07Z","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 N be a finite group of odd order and A a finite group that acts on N such that the orders of N and A are coprime. Isaacs constructed a natural correspondence between the set Irr_A(N) of irreducible complex characters invariant under the action of A, and the irreducible characters of the centralizer of A in N, Irr(C_N(A)). We show that this correspondence preserves Schur indices over the rational numbers. Moreover, suppose that the semidirect product AN is a normal subgroup of the finite group G and set U= N_G(A). Let \\chi \\in Irr_A(N) and \\chi* \\in Irr(C_N(A)) correspond. Then there is a c","authors_text":"Frieder Ladisch","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-18T15:31:09Z","title":"Character correspondences above fully ramified sections and Schur indices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3777","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:c9e3c35a241dd6aef07ffa633d0607bed5b28c1b11a36146ca02bb3907d37645","target":"record","created_at":"2026-05-18T04:15:07Z","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":"5277270f805fae637da0f123e1b1fd5e4e1d415570e5760a104eb3d40635a76a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-18T15:31:09Z","title_canon_sha256":"6fa872cb95dc9aa748bbc5ceb4d3ba9be544f3e5ff991bc967810affc681885a"},"schema_version":"1.0","source":{"id":"1108.3777","kind":"arxiv","version":1}},"canonical_sha256":"5c6fb9bb74a60676b66e131d4c0489ba39cc4db7447367d8586961858d0f8451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c6fb9bb74a60676b66e131d4c0489ba39cc4db7447367d8586961858d0f8451","first_computed_at":"2026-05-18T04:15:07.479560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:07.479560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4GFK8zNQCGrcZwB8RLxMqbHza0uiLtjh5nw79HGtSjKMAXF5TgujCfRQJHq0R1zkcjbKWa520qKbupwQ1YgqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:07.480254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3777","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9e3c35a241dd6aef07ffa633d0607bed5b28c1b11a36146ca02bb3907d37645","sha256:3261254363209e42a5ac57341dabd8a2f5b7bcea6e97dbe69f0310ded0a686f1"],"state_sha256":"b3e19fbb49974d6a47cdd719c3e3c6c55bf19856114ee21170efbb8d68e5566f"}