{"id":"W2049594083","doi":"10.1063/1.4772976","title":"${\\cal N}=2$ N = 2 gauge theories: Congruence subgroups, coset graphs, and modular surfaces","year":2013,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Black Holes and Theoretical Physics","field":"Physics and Astronomy","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"Science and Technology Facilities Council; National Science Foundation","keywords":"Congruence (geometry); Coset; Mathematics; Quiver; Pure mathematics; Torsion (gastropod); Gauge theory; Congruence subgroup; Modular group; Combinatorics; Algebra over a field; Mathematical physics; Geometry","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":[0.0002930858,0.0002429516,0.0005380439,0.00002592208,0.00009727591,0.0001541802,0.0002722845,0.00005318746,0.000462984],"category_scores_gemma":[0.00002813451,0.0001730089,0.0002182087,0.0001514715,0.0004600371,0.0004686326,0.0000890457,0.0003909441,0.0001007932],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001248381,"about_ca_system_score_gemma":0.00003632778,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001345346,"about_ca_topic_score_gemma":8.272076e-8,"domain_scores_codex":[0.9985128,0.00007417856,0.0005495308,0.0001650526,0.0003781327,0.00032028],"domain_scores_gemma":[0.9985095,0.0003880526,0.0003265639,0.0002378362,0.0002742317,0.000263807],"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":[0.0000117313,0.0003036118,0.0008624738,0.00005087061,0.0001087365,0.000002377345,0.0002280906,0.00002271393,0.0004361437,0.9948322,0.0005362867,0.002604736],"study_design_scores_gemma":[0.0004480178,0.0001226513,0.0005941346,0.00009061685,0.00007457409,0.000007990912,0.0004335594,0.001213571,0.001676165,0.995056,0.00008125413,0.0002014455],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9378068,0.00008371274,0.05542362,0.0002991235,0.00009922194,0.0001891002,0.00002483755,0.00001527495,0.006058349],"genre_scores_gemma":[0.9976575,0.00001143362,0.001897686,0.00007599657,0.0002605042,0.000005178025,0.00000421778,0.00002795219,0.00005947954],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05985079,"threshold_uncertainty_score":0.70551,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006458831504140125,"score_gpt":0.2247256416971102,"score_spread":0.2182668101929701,"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."}}