{"id":"W2963178601","doi":"10.1307/mmj/1441116662","title":"Congruences with intervals and subgroups modulo a prime","year":2015,"lang":"en","type":"article","venue":"CINECA IRIS Institutial Research Information System (University of Genoa)","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Modulo; Congruence relation; Prime (order theory); Mathematics; Arithmetic; Combinatorics","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":[],"consensus_categories":[],"category_scores_codex":[0.004349108,0.0001401085,0.0003703919,0.0006133561,0.0003604848,0.00009667615,0.0005637807,0.0001168013,0.00004775118],"category_scores_gemma":[0.0007744655,0.0001159496,0.00004927212,0.000696682,0.0009915435,0.001701281,0.0004044544,0.0003176752,0.0001748559],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003608017,"about_ca_system_score_gemma":0.0007113784,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001082522,"about_ca_topic_score_gemma":0.0001956719,"domain_scores_codex":[0.9972807,0.0003510119,0.0003153347,0.0001932786,0.001462115,0.0003975777],"domain_scores_gemma":[0.9968567,0.0002788505,0.0002173898,0.0004445554,0.001815875,0.0003866151],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"qualitative","study_design_scores_codex":[0.005416074,0.0002509906,0.01431363,0.005303879,0.0008990967,0.000283915,0.09048053,0.0002302023,0.0004354538,0.8367181,0.02503265,0.02063549],"study_design_scores_gemma":[0.01971487,0.004016915,0.005844205,0.003232063,0.0002861239,0.0008392284,0.7707492,0.05606904,0.001747681,0.01891378,0.1169179,0.001669024],"study_design_candidate":"qualitative","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8078451,0.00004934378,0.1095257,0.0006424985,0.00009079748,0.001190556,0.00004872508,0.0001274759,0.08047984],"genre_scores_gemma":[0.9953305,0.00001141695,0.003729129,0.000007194938,0.00003324002,0.000002136374,0.00001020641,0.000007670174,0.0008684802],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8178043,"threshold_uncertainty_score":0.4728285,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1517750784332834,"score_gpt":0.3440063960443953,"score_spread":0.1922313176111118,"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."}}