{"id":"W3043290813","doi":"10.1142/s1793042121500780","title":"Counting multiplicative groups with prescribed subgroups","year":2021,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; Kelowna General Hospital","funders":"","keywords":"Mathematics; Multiplicative function; Combinatorics; Prime factor; Coprime integers; Multiplicative group; Abelian group; Prime power; Group (periodic table); Prime (order theory); Additive group; Number theory; Prime number; Cyclic group; Discrete mathematics; Function (biology); Physics; 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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003164278,0.0004644991,0.000865803,0.0002828258,0.00007881391,0.0004181014,0.002199763,0.0003025616,0.005845987],"category_scores_gemma":[0.002826832,0.0003702284,0.0005355394,0.0001663702,0.0003487453,0.0003818122,0.001276248,0.002150067,0.00005864034],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005603808,"about_ca_system_score_gemma":0.0007105,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002411234,"about_ca_topic_score_gemma":0.0000270298,"domain_scores_codex":[0.9947823,0.0008351346,0.00122133,0.0004815797,0.002277472,0.0004022035],"domain_scores_gemma":[0.9891905,0.00361798,0.002035106,0.0006688411,0.004272385,0.0002151945],"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":[0.01094117,0.0052163,0.03022573,0.001347093,0.03798424,0.01175798,0.03577067,0.0007514661,0.001586719,0.8033065,0.04760001,0.01351217],"study_design_scores_gemma":[0.002374102,0.0001005154,0.001154583,0.003580996,0.0005454965,0.00282735,0.00555057,0.0005092973,0.00136224,0.9783925,0.002809349,0.000792964],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8156717,0.0005136573,0.1454384,0.00150405,0.002437468,0.0007561161,0.0004556669,0.0001230536,0.03309983],"genre_scores_gemma":[0.9695916,0.00008394155,0.02562535,0.0002357209,0.001464153,0.00003762484,0.00009500534,0.0001374636,0.002729177],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1750861,"threshold_uncertainty_score":0.9998749,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04816835291095123,"score_gpt":0.3634522436880479,"score_spread":0.3152838907770967,"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."}}