{"id":"W2026672820","doi":"10.1142/s1793042105000170","title":"LARGE SIEVE INEQUALITY WITH CHARACTERS FOR POWERFUL MODULI","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Harish-Chandra Research Institute","keywords":"Mathematics; Sieve (category theory); Moduli; Pure mathematics; Moduli space; Inequality; Combinatorics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003214312,0.0001781206,0.0003314593,0.0001457273,0.00004266656,0.00007177846,0.0007676962,0.00007508841,0.004253123],"category_scores_gemma":[0.00132957,0.0001320642,0.0002430589,0.0000907671,0.0001057725,0.0004562008,0.00008861325,0.0003373069,0.0001432355],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000240286,"about_ca_system_score_gemma":0.0001500595,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001314157,"about_ca_topic_score_gemma":0.000008807418,"domain_scores_codex":[0.9976902,0.0002310688,0.0006550357,0.0001681948,0.0009417522,0.0003137441],"domain_scores_gemma":[0.995769,0.001948013,0.0006059568,0.0002306327,0.001293598,0.0001527818],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00443631,0.001111288,0.003146856,0.00004545882,0.001793024,0.0001270608,0.002594646,0.00002343314,0.0002779113,0.9624758,0.01938957,0.004578692],"study_design_scores_gemma":[0.003959784,0.0001978385,0.0008407311,0.0002369569,0.000117359,0.0008896734,0.001389988,0.0002768913,0.001418451,0.9408117,0.04954275,0.0003178545],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8354939,0.00003634136,0.1476587,0.004486461,0.000570792,0.0003372343,0.0003230101,0.0000426382,0.01105102],"genre_scores_gemma":[0.98455,0.000008306389,0.008729568,0.0006311423,0.001169515,0.00000797638,0.00001652226,0.00004590878,0.004841047],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1490562,"threshold_uncertainty_score":0.9966571,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04377212977281009,"score_gpt":0.3873838728906629,"score_spread":0.3436117431178528,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}