{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZBIDISK47WCDJY6H56P4E4BFQH","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":"de17a62c572a90f4810c00ac6af52517e627b4fe2effc5b46dcecf9e88c67fd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-22T12:49:18Z","title_canon_sha256":"6ba2b75f05b655fd627faaac339d5e6cd2060dab7cf166b9aa04add61577d3b6"},"schema_version":"1.0","source":{"id":"1901.07285","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07285","created_at":"2026-05-17T23:43:50Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07285v3","created_at":"2026-05-17T23:43:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07285","created_at":"2026-05-17T23:43:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZBIDISK47WCD","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZBIDISK47WCDJY6H","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZBIDISK4","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:80143266eee07df1e0349a008d98726972ac28cbc722097d13e23e7c6d3a04d3","target":"graph","created_at":"2026-05-17T23:43:50Z","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":"The first main result of this paper is that a finite transitive nonabelian characteristically simple subgroup of a wreath product in product action must lie in the base group of the wreath product. This allows us to characterize nonabelian transitive characteristically simple subgroups $H$ of finite quasiprimitive permutation groups $G$. If the socle of $G$, denoted by $\\mbox{soc}(G)$, is nonabelian, then $H$ lies in $\\mbox{soc}(G)$. An explicit description is given for the possibilities of $H$ under the condition that $H$ does not contain a nontrivial normal subgroup of $\\mbox{soc}(G)$.","authors_text":"Csaba Schneider, Pedro H. P. Daldegan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-22T12:49:18Z","title":"Transitive characteristically simple subgroups of finite quasiprimitive permutation groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07285","kind":"arxiv","version":3},"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:d0b5e9acd32f3e37e591f2051621e706d70ae804ab0ec39c1d9677f24bcfdd8e","target":"record","created_at":"2026-05-17T23:43:50Z","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":"de17a62c572a90f4810c00ac6af52517e627b4fe2effc5b46dcecf9e88c67fd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-22T12:49:18Z","title_canon_sha256":"6ba2b75f05b655fd627faaac339d5e6cd2060dab7cf166b9aa04add61577d3b6"},"schema_version":"1.0","source":{"id":"1901.07285","kind":"arxiv","version":3}},"canonical_sha256":"c85034495cfd8434e3c7ef9fc2702581c1ea94199fa562f2822e25cc0a5349e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c85034495cfd8434e3c7ef9fc2702581c1ea94199fa562f2822e25cc0a5349e1","first_computed_at":"2026-05-17T23:43:50.074540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:50.074540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vt5jKAqgrRuimxOUF8VmsmvTTVrnQul0WV1vaQxvTTYYaFXHgY5Xc2jixbtU6STqNmwlnHrRPytYrvj/HlzUDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:50.075111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07285","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b5e9acd32f3e37e591f2051621e706d70ae804ab0ec39c1d9677f24bcfdd8e","sha256:80143266eee07df1e0349a008d98726972ac28cbc722097d13e23e7c6d3a04d3"],"state_sha256":"d6b0e3fb28a6cf125c74eb0fbd2253e04fa6991350321c41c95a9f95ac092164"}