{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WMGIKMMIUGQDTOZBVOEHBFXCLH","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":"0df8fd6a92d94fa9ca59bf1876dfc1f4c177583ec4a514f9f500a8c6d2e18317","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-26T16:10:29Z","title_canon_sha256":"26fd8cbc5e14577a75e1cdae14a0c6d43799211d6633eb126a7981297b1890a0"},"schema_version":"1.0","source":{"id":"1905.10827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10827","created_at":"2026-05-17T23:45:03Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10827v1","created_at":"2026-05-17T23:45:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10827","created_at":"2026-05-17T23:45:03Z"},{"alias_kind":"pith_short_12","alias_value":"WMGIKMMIUGQD","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WMGIKMMIUGQDTOZB","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WMGIKMMI","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:31756e45f3af367096e38ce5e6c091b8c65d1abc5d241c93694264646d0c9d40","target":"graph","created_at":"2026-05-17T23:45:03Z","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 prove that there exists an integer-valued function f on positive integers such that if a finite group G has at most k real-valued irreducible characters, then |G/Sol(G)| is at most f(k), where Sol(G) denotes the largest solvable normal subgroup of G. In the case k = 5, we further classify G/Sol(G). This partly answers a question of Iwasaki [15] on the relationship between the structure of a finite group and its number of real-valued irreducible characters.","authors_text":"A. A. Schaeffer Fry, C. Ryan Vinroot, Hung P. Tong-Viet, Nguyen Ngoc Hung","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-26T16:10:29Z","title":"On the number of irreducible real-valued characters of a finite group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10827","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":"sha256:4277c6642f2a1ce5132c920560e4cbedde59af209d3d895d00fb3cdf8c8a5c2d","target":"record","created_at":"2026-05-17T23:45:03Z","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":"0df8fd6a92d94fa9ca59bf1876dfc1f4c177583ec4a514f9f500a8c6d2e18317","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-26T16:10:29Z","title_canon_sha256":"26fd8cbc5e14577a75e1cdae14a0c6d43799211d6633eb126a7981297b1890a0"},"schema_version":"1.0","source":{"id":"1905.10827","kind":"arxiv","version":1}},"canonical_sha256":"b30c853188a1a039bb21ab887096e259eb8562f8486bc885804319c4e05d90b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b30c853188a1a039bb21ab887096e259eb8562f8486bc885804319c4e05d90b3","first_computed_at":"2026-05-17T23:45:03.659706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:03.659706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hy+GavzcNQwFvoJjdIVnSIBhMyE2PGEbcqZrArN7IM8zCcOQ6l+UtMLF7mv7HR1QjF4tdA+rUL9Vdv6QUD7gCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:03.660193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4277c6642f2a1ce5132c920560e4cbedde59af209d3d895d00fb3cdf8c8a5c2d","sha256:31756e45f3af367096e38ce5e6c091b8c65d1abc5d241c93694264646d0c9d40"],"state_sha256":"9da840cfcaf13424c85c9628b2508b7e614456e17757138163123c817ad62575"}