{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HHSJ26CWBRAQE4VR3QDFIJS2ZD","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":"8f8fe8ee8ba8befd23a163d1178f8cf3a8354d0cb4ffaf7b003c9e37e447753c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-17T22:38:34Z","title_canon_sha256":"d235793ab4c79fb1e865fa5ab82e2a72f4c63d9243934c27619d900752b15a93"},"schema_version":"1.0","source":{"id":"1502.05080","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05080","created_at":"2026-05-18T01:35:20Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05080v2","created_at":"2026-05-18T01:35:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05080","created_at":"2026-05-18T01:35:20Z"},{"alias_kind":"pith_short_12","alias_value":"HHSJ26CWBRAQ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HHSJ26CWBRAQE4VR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HHSJ26CW","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:126ff32276968e584bd04d4bd470dd001de8b8afea971128a4a313f49eb0b049","target":"graph","created_at":"2026-05-18T01:35:20Z","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":"Given a finite group $G$, let $P_G(s)$ be the probability that $s$ randomly chosen elements generate $G$, and let $H$ be a finite group with $P_G(s)=P_H(s)$. We show that if the nonabelian composition factors of $G$ and $H$ are $\\mathrm{PSL}(2,p)$ for some non-Mersense prime $p\\geq 5$, then $G$ and $H$ have the same non-Frattini chief factors.","authors_text":"Duong Hoang Dung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-17T22:38:34Z","title":"Recognizing $\\mathrm{PSL}(2,p)$ in the non-Frattini chief factors of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05080","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":"sha256:4d1ed652ad683d06317c9e9867778835a34a8970e30d3f21729ea6048c1daa58","target":"record","created_at":"2026-05-18T01:35:20Z","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":"8f8fe8ee8ba8befd23a163d1178f8cf3a8354d0cb4ffaf7b003c9e37e447753c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-17T22:38:34Z","title_canon_sha256":"d235793ab4c79fb1e865fa5ab82e2a72f4c63d9243934c27619d900752b15a93"},"schema_version":"1.0","source":{"id":"1502.05080","kind":"arxiv","version":2}},"canonical_sha256":"39e49d78560c410272b1dc0654265ac8ff85a8a5dfa0e454511175f686e29850","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39e49d78560c410272b1dc0654265ac8ff85a8a5dfa0e454511175f686e29850","first_computed_at":"2026-05-18T01:35:20.426165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:20.426165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"peo+g23BiZUPsr+S8nEAeMcraJyg51Yzv+vDDEQssZDW0vxuV/xSHHg9PwTw4KSi5JUg3Ysc1EAusrnBvYZcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:20.426864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05080","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1ed652ad683d06317c9e9867778835a34a8970e30d3f21729ea6048c1daa58","sha256:126ff32276968e584bd04d4bd470dd001de8b8afea971128a4a313f49eb0b049"],"state_sha256":"09762d25e01c81ae6e500ee449807557501138a5e0d1544ce77789a9f41f778f"}