{"id":"W2151818595","doi":"10.4153/cmb-2002-033-1","title":"Modular Subgroups, Forms, Curves and Surfaces","year":2002,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Congruence (geometry); PSL; Modular form; Modular design; Modular group; Modular curve; Elliptic curve; Class (philosophy); Pure mathematics; Congruence subgroup; Modular elliptic curve; Algebra over a field; Combinatorics; Geometry; Computer science; Quarter period","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":["insufficient_payload"],"category_scores_codex":[0.0009731385,0.0002564392,0.0004161428,0.0001799509,0.0001964844,0.00009962758,0.000355293,0.00015238,0.03724199],"category_scores_gemma":[0.002232024,0.0002238926,0.00007888632,0.0002022611,0.0002825141,0.0000647581,0.00008084122,0.0003207344,0.007341149],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001101951,"about_ca_system_score_gemma":0.00003751166,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002942121,"about_ca_topic_score_gemma":0.0008516072,"domain_scores_codex":[0.9979303,0.0001331373,0.0003943584,0.0003513049,0.0003958258,0.0007950739],"domain_scores_gemma":[0.9973548,0.001056445,0.00005915408,0.0005537171,0.00007989766,0.0008959743],"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":[0.000006350044,0.0001286689,0.0001665321,0.001951605,0.00006282819,0.0001625863,0.0005658829,6.305391e-7,0.0001052613,0.8211873,0.174496,0.001166363],"study_design_scores_gemma":[0.0005045686,0.0001075776,0.0001978713,0.0006568362,0.00005357017,0.0001715719,0.0002556186,0.002901918,0.0001108226,0.8914968,0.1029486,0.0005941734],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7768924,0.004823019,0.0007436051,0.03081631,0.00007461374,0.001466265,0.0001179426,0.0002853922,0.1847805],"genre_scores_gemma":[0.9743492,0.0004348307,0.006074158,0.00153722,0.00007078445,0.00008018281,0.00001001542,0.0001131388,0.0173305],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1974568,"threshold_uncertainty_score":0.9934317,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05983022143244113,"score_gpt":0.2729258683935941,"score_spread":0.2130956469611529,"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."}}