{"id":"W3008403333","doi":"10.1142/s1793042120500736","title":"The smallest invariant factor of the multiplicative group","year":2020,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; University of Toronto","funders":"","keywords":"Mathematics; Multiplicative function; Asymptotic formula; Multiplicative group; Invariant (physics); Prime factor; Coprime integers; Combinatorics; Moduli; Pure mathematics; Discrete mathematics; Prime (order theory); 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":[0.001293002,0.0001292841,0.0002294231,0.00003194048,0.00009926822,0.00005571011,0.002008184,0.00005299528,0.001968249],"category_scores_gemma":[0.005040908,0.00006596436,0.0003141119,0.0001453217,0.0003640548,0.0001056908,0.0003608874,0.0004790463,0.00005397993],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008689998,"about_ca_system_score_gemma":0.0001298322,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005249711,"about_ca_topic_score_gemma":0.00000851402,"domain_scores_codex":[0.9975255,0.0005333512,0.0006697953,0.000117081,0.0009882472,0.0001660378],"domain_scores_gemma":[0.9933599,0.004640193,0.0008380163,0.0002666504,0.0007832783,0.000111956],"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":[0.0009123346,0.0001785068,0.004830569,0.0000172925,0.001181796,0.00003879402,0.003671965,0.00000592672,0.002294269,0.9735788,0.01009235,0.003197399],"study_design_scores_gemma":[0.001234935,0.00008729946,0.004681813,0.000170082,0.00007327098,0.0002514,0.002637812,0.0002643239,0.003381086,0.9741364,0.01292292,0.000158644],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8363826,0.0003461567,0.0550829,0.04988039,0.002562791,0.001131931,0.0006573204,0.00005974724,0.05389615],"genre_scores_gemma":[0.9973193,0.0000276494,0.00101753,0.0004145673,0.0004129254,0.000004419457,0.000001107656,0.00002253377,0.0007800006],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1609367,"threshold_uncertainty_score":0.9989441,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07310333011707912,"score_gpt":0.3580763166669346,"score_spread":0.2849729865498555,"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."}}