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For any system of semisimple mod l Galois representations {\\phi_l:Gal_K->GL_N(F_l)} arising from \\'etale cohomology, there exists a finite normal extension L of K such that if we denote \\phi_l(Gal_K) and \\phi_l(Gal_L) by respectively \\Gamma_l and \\gamma_l for all l, and let S_l be the F_l-semisimple subgroup of GL_N associated to \\gamma_l (or \\Gamma_l) by Nori [No87] for all sufficiently large l, then the following statements hold for all sufficiently large l:\n  A(i) The formal character of S_l->GL_N is independent of l and is equal to the formal character of the tauto"},"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":"1305.2001","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-09T03:24:43Z","cross_cats_sorted":[],"title_canon_sha256":"0734037151985cebddf2d3e132c71f63f46fc8271de80ec9ba4125ab6cf01619","abstract_canon_sha256":"e88339497b60d164641254ea64ec6169782cfee5f4320e9bdaffede0540a30de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:15.866231Z","signature_b64":"QtKaQWZ0jPbCpAzgCY8Hn34Scjl80g4PBXNU9tQ6+Y2qf87qFZ1oV6dfSbSYx3oADU5wJhvi3Yt46Ip4/0YmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cb1a23abc572419a590f880bba190c1679df29b3db99add3f85933538dddc2f","last_reissued_at":"2026-05-18T01:36:15.865676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:15.865676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"l-independence for Compatible Systems of (mod l) Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chun Yin Hui","submitted_at":"2013-05-09T03:24:43Z","abstract_excerpt":"Let K be a number field. For any system of semisimple mod l Galois representations {\\phi_l:Gal_K->GL_N(F_l)} arising from \\'etale cohomology, there exists a finite normal extension L of K such that if we denote \\phi_l(Gal_K) and \\phi_l(Gal_L) by respectively \\Gamma_l and \\gamma_l for all l, and let S_l be the F_l-semisimple subgroup of GL_N associated to \\gamma_l (or \\Gamma_l) by Nori [No87] for all sufficiently large l, then the following statements hold for all sufficiently large l:\n  A(i) The formal character of S_l->GL_N is independent of l and is equal to the formal character of the tauto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2001","kind":"arxiv","version":5},"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":"1305.2001","created_at":"2026-05-18T01:36:15.865753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2001v5","created_at":"2026-05-18T01:36:15.865753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2001","created_at":"2026-05-18T01:36:15.865753+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSY2EOV4K4SB","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSY2EOV4K4SBTJMQ","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSY2EOV4","created_at":"2026-05-18T12:27:46.883200+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/HSY2EOV4K4SBTJMQ7CALXIMQYF","json":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF.json","graph_json":"https://pith.science/api/pith-number/HSY2EOV4K4SBTJMQ7CALXIMQYF/graph.json","events_json":"https://pith.science/api/pith-number/HSY2EOV4K4SBTJMQ7CALXIMQYF/events.json","paper":"https://pith.science/paper/HSY2EOV4"},"agent_actions":{"view_html":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF","download_json":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF.json","view_paper":"https://pith.science/paper/HSY2EOV4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2001&json=true","fetch_graph":"https://pith.science/api/pith-number/HSY2EOV4K4SBTJMQ7CALXIMQYF/graph.json","fetch_events":"https://pith.science/api/pith-number/HSY2EOV4K4SBTJMQ7CALXIMQYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF/action/storage_attestation","attest_author":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF/action/author_attestation","sign_citation":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF/action/citation_signature","submit_replication":"https://pith.science/pith/HSY2EOV4K4SBTJMQ7CALXIMQYF/action/replication_record"}},"created_at":"2026-05-18T01:36:15.865753+00:00","updated_at":"2026-05-18T01:36:15.865753+00:00"}