{"id":"W2149054972","doi":"10.1142/s1793042112501254","title":"ON MODULAR GALOIS REPRESENTATIONS MODULO PRIME POWERS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; Danmarks Frie Forskningsfond; Deutsche Forschungsgemeinschaft","keywords":"Mathematics; Modulo; Galois module; Prime (order theory); Modular form; Splitting of prime ideals in Galois extensions; Pure mathematics; Galois extension; Galois group; Primitive root modulo n; Algebra over a field; Arithmetic; Normal basis; Discrete mathematics; Combinatorics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001757039,0.0001747732,0.0002447379,0.000223857,0.00006665065,0.00004286429,0.0005997822,0.00009033357,0.009785687],"category_scores_gemma":[0.00227847,0.0001482112,0.0002852225,0.0001374717,0.00009754892,0.0005518685,0.00008401641,0.0003616491,0.0005052229],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001508767,"about_ca_system_score_gemma":0.00004610758,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002468704,"about_ca_topic_score_gemma":2.128093e-7,"domain_scores_codex":[0.9978731,0.0003132559,0.0005841813,0.0001282366,0.0008364301,0.0002648044],"domain_scores_gemma":[0.9966425,0.001905428,0.0005550017,0.0002805949,0.0004288762,0.0001875596],"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":[0.0005086612,0.000774246,0.002555227,0.000007864989,0.0007568186,0.00006018223,0.0017104,0.00004228779,0.0004824206,0.9693345,0.021082,0.002685409],"study_design_scores_gemma":[0.0007432204,0.00004918807,0.00241619,0.0001021975,0.00006755567,0.0007396111,0.0007021402,0.00001308337,0.002981393,0.9859696,0.006034738,0.0001810543],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9007685,0.0001047378,0.0269419,0.0006835198,0.003900265,0.0001249728,0.00006778657,0.00005011202,0.06735818],"genre_scores_gemma":[0.9913648,0.00001409403,0.003580804,0.0004559816,0.001032081,0.000004645228,0.00001016043,0.00003473572,0.003502718],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09059626,"threshold_uncertainty_score":0.9911195,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02633468474805074,"score_gpt":0.3415726499900421,"score_spread":0.3152379652419913,"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."}}