{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JN5XNGB4OXT3TVUUMX6HEBN5CP","short_pith_number":"pith:JN5XNGB4","schema_version":"1.0","canonical_sha256":"4b7b76983c75e7b9d69465fc7205bd13def2fa874e69b140ace9eaa82f49eba6","source":{"kind":"arxiv","id":"1112.3941","version":2},"attestation_state":"computed","paper":{"title":"Growth of cross-characteristic representations of finite quasisimple groups of Lie type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Jokke H\\\"as\\\"a","submitted_at":"2011-12-16T20:24:27Z","abstract_excerpt":"In this paper we give a bound to the number of conjugacy classes of maximal subgroups of any almost simple group whose socle is a classical group of Lie type. The bound is $2n^{5.2}+n\\log_2\\log_2 q$, where $n$ is the dimension of the classical socle and $q$ is the size of the defining field. To obtain the bound, we first bound the number of projective cross-characteristic representations of simple groups of Lie type as a function of the representation degree. These bounds are computed for different families of groups separately. In the computation, we use information on class numbers, minimal "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.3941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-16T20:24:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"6905587e5675daed45105cea74a0b51153c8fc88497678c4068b70a049b36107","abstract_canon_sha256":"91e8506b234495a8779a990c5d23078d84f60377370e90b72341115c17555305"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:33.056595Z","signature_b64":"r68Ev7fESlsATzpxIqXanwNfzq8IpfzfUfwE+ZYB0n59bpYkc6CoI60LcC0MOnnj8iZlRN9Iyk/Mn8VGnn3fAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7b76983c75e7b9d69465fc7205bd13def2fa874e69b140ace9eaa82f49eba6","last_reissued_at":"2026-05-18T02:46:33.056156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:33.056156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth of cross-characteristic representations of finite quasisimple groups of Lie type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Jokke H\\\"as\\\"a","submitted_at":"2011-12-16T20:24:27Z","abstract_excerpt":"In this paper we give a bound to the number of conjugacy classes of maximal subgroups of any almost simple group whose socle is a classical group of Lie type. The bound is $2n^{5.2}+n\\log_2\\log_2 q$, where $n$ is the dimension of the classical socle and $q$ is the size of the defining field. To obtain the bound, we first bound the number of projective cross-characteristic representations of simple groups of Lie type as a function of the representation degree. These bounds are computed for different families of groups separately. In the computation, we use information on class numbers, minimal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3941","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.3941","created_at":"2026-05-18T02:46:33.056216+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3941v2","created_at":"2026-05-18T02:46:33.056216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3941","created_at":"2026-05-18T02:46:33.056216+00:00"},{"alias_kind":"pith_short_12","alias_value":"JN5XNGB4OXT3","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JN5XNGB4OXT3TVUU","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JN5XNGB4","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP","json":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP.json","graph_json":"https://pith.science/api/pith-number/JN5XNGB4OXT3TVUUMX6HEBN5CP/graph.json","events_json":"https://pith.science/api/pith-number/JN5XNGB4OXT3TVUUMX6HEBN5CP/events.json","paper":"https://pith.science/paper/JN5XNGB4"},"agent_actions":{"view_html":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP","download_json":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP.json","view_paper":"https://pith.science/paper/JN5XNGB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3941&json=true","fetch_graph":"https://pith.science/api/pith-number/JN5XNGB4OXT3TVUUMX6HEBN5CP/graph.json","fetch_events":"https://pith.science/api/pith-number/JN5XNGB4OXT3TVUUMX6HEBN5CP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP/action/storage_attestation","attest_author":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP/action/author_attestation","sign_citation":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP/action/citation_signature","submit_replication":"https://pith.science/pith/JN5XNGB4OXT3TVUUMX6HEBN5CP/action/replication_record"}},"created_at":"2026-05-18T02:46:33.056216+00:00","updated_at":"2026-05-18T02:46:33.056216+00:00"}