{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NDTKTXRVWL2S2YYCUXUHWUW7TX","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":"32af0eea1e55ff8fcb5b00ad1d1b69da7fe98bb246c47b12c99f7216169b4e92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2022-08-16T14:51:32Z","title_canon_sha256":"c4a96a22a689f4f2c0d15382a9390a158a5dea6311edd3f30e83264cb5091423"},"schema_version":"1.0","source":{"id":"2208.07782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07782","created_at":"2026-07-05T04:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07782v1","created_at":"2026-07-05T04:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07782","created_at":"2026-07-05T04:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"NDTKTXRVWL2S","created_at":"2026-07-05T04:49:08Z"},{"alias_kind":"pith_short_16","alias_value":"NDTKTXRVWL2S2YYC","created_at":"2026-07-05T04:49:08Z"},{"alias_kind":"pith_short_8","alias_value":"NDTKTXRV","created_at":"2026-07-05T04:49:08Z"}],"graph_snapshots":[{"event_id":"sha256:95f11cc70399a8ea4e1b16051b757423ae45ba4c84b3878c6036cff494933e8f","target":"graph","created_at":"2026-07-05T04:49:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.07782/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.","authors_text":"Dongfang Yang, Yu Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2022-08-16T14:51:32Z","title":"A characterization of finite groups by certain Galois conjugacy class of irreducible characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07782","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":"sha256:56a3da8d9e6a7f5713173bcf5af362e886a0580f499239edfa1b32a11010d9b5","target":"record","created_at":"2026-07-05T04:49:08Z","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":"32af0eea1e55ff8fcb5b00ad1d1b69da7fe98bb246c47b12c99f7216169b4e92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2022-08-16T14:51:32Z","title_canon_sha256":"c4a96a22a689f4f2c0d15382a9390a158a5dea6311edd3f30e83264cb5091423"},"schema_version":"1.0","source":{"id":"2208.07782","kind":"arxiv","version":1}},"canonical_sha256":"68e6a9de35b2f52d6302a5e87b52df9dd719dde2e7f128b2e5b643149a557906","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68e6a9de35b2f52d6302a5e87b52df9dd719dde2e7f128b2e5b643149a557906","first_computed_at":"2026-07-05T04:49:08.894764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:49:08.894764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LqSfI18Nn/xD5zFPsKImg/9m0VJyDcQXwhh/efkoCptq51DkRbdzGYjyBPHrV+Ft5YIs6qmV8H3rlDGS8K7sBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:49:08.895177Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.07782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56a3da8d9e6a7f5713173bcf5af362e886a0580f499239edfa1b32a11010d9b5","sha256:95f11cc70399a8ea4e1b16051b757423ae45ba4c84b3878c6036cff494933e8f"],"state_sha256":"09bb26f588519790f78b203aff94e8bd850e278d0659dbdbf89e772ff9cc673f"}