{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DQUF5YNG2LLIZ7ZMPD6HBNFDZH","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":"2e3dbb3dfe807b66eed83f8558931e589c4dcbcb8f7acc268bc5fec9dbcad96f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-04-28T06:20:31Z","title_canon_sha256":"c651834a3650cb193aae8d5e154e5171ba9e6c93e7a8f3808bbf1a018b5c5864"},"schema_version":"1.0","source":{"id":"2304.14646","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.14646","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"2304.14646v5","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.14646","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"DQUF5YNG2LLI","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"pith_short_16","alias_value":"DQUF5YNG2LLIZ7ZM","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"pith_short_8","alias_value":"DQUF5YNG","created_at":"2026-07-05T11:20:01Z"}],"graph_snapshots":[{"event_id":"sha256:a7be8d98ea7d87745014732441139d6940ad8f9e001256d907310a986b15c194","target":"graph","created_at":"2026-07-05T11:20:01Z","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/2304.14646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classification of the maximal subgroups of the Monster $\\mathbf{M}$ is a long-standing problem in finite group theory. According to the literature, the classification is complete apart from the question of whether $\\mathbf{M}$ contains maximal subgroups that are almost simple with socle $\\mathrm{PSL}_2(13)$. However, this conclusion relies on reported claims, with unpublished proofs, that $\\mathbf{M}$ has no maximal subgroups that are almost simple with socle $\\mathrm{PSL}_2(8)$, $\\mathrm{PSL}_2(16)$, or $\\mathrm{PSU}_3(4)$. The aim of this paper is to settle all of these questions, and th","authors_text":"Heiko Dietrich, Melissa Lee, Tomasz Popiel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-04-28T06:20:31Z","title":"The maximal subgroups of the Monster"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.14646","kind":"arxiv","version":5},"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:bbfeb2b309988b0e16e7bd297c5eb0cede59ec184d577585c5836d6a2afd4d19","target":"record","created_at":"2026-07-05T11:20:01Z","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":"2e3dbb3dfe807b66eed83f8558931e589c4dcbcb8f7acc268bc5fec9dbcad96f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-04-28T06:20:31Z","title_canon_sha256":"c651834a3650cb193aae8d5e154e5171ba9e6c93e7a8f3808bbf1a018b5c5864"},"schema_version":"1.0","source":{"id":"2304.14646","kind":"arxiv","version":5}},"canonical_sha256":"1c285ee1a6d2d68cff2c78fc70b4a3c9fd876abd845a6a02014303474cad9478","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c285ee1a6d2d68cff2c78fc70b4a3c9fd876abd845a6a02014303474cad9478","first_computed_at":"2026-07-05T11:20:01.202283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:01.202283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d32QbrFe2D/tyRxw78lESxFWjwzrQdj1SRdvuHzFKOg08sDexlYm7gUZzm3tqgjyUTndBxOuxd6+hXvHHkbiAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:01.202773Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.14646","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbfeb2b309988b0e16e7bd297c5eb0cede59ec184d577585c5836d6a2afd4d19","sha256:a7be8d98ea7d87745014732441139d6940ad8f9e001256d907310a986b15c194"],"state_sha256":"2cabc9bc350246724c4e953db101f97da3f251311283b1dccf5a1c0499e5036e"}