{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CNHAGQRWDPJ4YCD3ARTNTWQEYN","short_pith_number":"pith:CNHAGQRW","schema_version":"1.0","canonical_sha256":"134e0342361bd3cc087b0466d9da04c376f138d32f5339d1f21fd1df80dba2ed","source":{"kind":"arxiv","id":"1307.2593","version":2},"attestation_state":"computed","paper":{"title":"Arithmetic quotients of the mapping class group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.GT","authors_text":"Alexander Lubotzky, Fritz Grunewald, Justin Malestein, Michael Larsen","submitted_at":"2013-07-09T20:44:32Z","abstract_excerpt":"To every $Q$-irreducible representation $r$ of a finite group $H$, there corresponds a simple factor $A$ of $Q[H]$ with an involution $\\tau$. To this pair $(A,\\tau)$, we associate an arithmetic group $\\Omega$ consisting of all $(2g-2)\\times (2g-2)$ matrices over a natural order of $A^{op}$ which preserve a natural skew-Hermitian sesquilinear form on $A^{2g-2}$. We show that if $H$ is generated by less than $g$ elements, then $\\Omega$ is a virtual quotient of the mapping class group $Mod(\\Sigma_g)$, i.e. a finite index subgroup of $\\Omega$ is a quotient of a finite index subgroup of $\\Mod(\\Sigm"},"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":"1307.2593","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-07-09T20:44:32Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"c0f6fc21ef980d82215cb5fe374128175445320ba7b82d7ba309e06c6c99db3d","abstract_canon_sha256":"ca271b05849cdf746d9baab6c9903013bb38f4796d264b55e1467ea4de1683d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:16.998275Z","signature_b64":"4VWarZpjgu+CIj0MJ7juKqbihc0M5GE2TLw4JmzZW/hpo0kz9/c1FDnsEyGxdLTatgBDPCOHWnlqKk/Q7PuuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"134e0342361bd3cc087b0466d9da04c376f138d32f5339d1f21fd1df80dba2ed","last_reissued_at":"2026-05-18T02:19:16.997626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:16.997626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic quotients of the mapping class group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.GT","authors_text":"Alexander Lubotzky, Fritz Grunewald, Justin Malestein, Michael Larsen","submitted_at":"2013-07-09T20:44:32Z","abstract_excerpt":"To every $Q$-irreducible representation $r$ of a finite group $H$, there corresponds a simple factor $A$ of $Q[H]$ with an involution $\\tau$. To this pair $(A,\\tau)$, we associate an arithmetic group $\\Omega$ consisting of all $(2g-2)\\times (2g-2)$ matrices over a natural order of $A^{op}$ which preserve a natural skew-Hermitian sesquilinear form on $A^{2g-2}$. We show that if $H$ is generated by less than $g$ elements, then $\\Omega$ is a virtual quotient of the mapping class group $Mod(\\Sigma_g)$, i.e. a finite index subgroup of $\\Omega$ is a quotient of a finite index subgroup of $\\Mod(\\Sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2593","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":"1307.2593","created_at":"2026-05-18T02:19:16.997741+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2593v2","created_at":"2026-05-18T02:19:16.997741+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2593","created_at":"2026-05-18T02:19:16.997741+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNHAGQRWDPJ4","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNHAGQRWDPJ4YCD3","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNHAGQRW","created_at":"2026-05-18T12:27:40.988391+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/CNHAGQRWDPJ4YCD3ARTNTWQEYN","json":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN.json","graph_json":"https://pith.science/api/pith-number/CNHAGQRWDPJ4YCD3ARTNTWQEYN/graph.json","events_json":"https://pith.science/api/pith-number/CNHAGQRWDPJ4YCD3ARTNTWQEYN/events.json","paper":"https://pith.science/paper/CNHAGQRW"},"agent_actions":{"view_html":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN","download_json":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN.json","view_paper":"https://pith.science/paper/CNHAGQRW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2593&json=true","fetch_graph":"https://pith.science/api/pith-number/CNHAGQRWDPJ4YCD3ARTNTWQEYN/graph.json","fetch_events":"https://pith.science/api/pith-number/CNHAGQRWDPJ4YCD3ARTNTWQEYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN/action/storage_attestation","attest_author":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN/action/author_attestation","sign_citation":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN/action/citation_signature","submit_replication":"https://pith.science/pith/CNHAGQRWDPJ4YCD3ARTNTWQEYN/action/replication_record"}},"created_at":"2026-05-18T02:19:16.997741+00:00","updated_at":"2026-05-18T02:19:16.997741+00:00"}