{"id":"W2950262502","doi":"10.3842/sigma.2019.041","title":"Hecke Operators on Vector-Valued Modular Forms","year":2019,"lang":"en","type":"article","venue":"Symmetry Integrability and Geometry Methods and Applications","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Hecke operator; Mathematics; Modular form; Pure mathematics; Algebra over a field; Type (biology); Operator (biology)","routes":{"ca_aff":true,"ca_fund":true,"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"],"consensus_categories":[],"category_scores_codex":[0.001831076,0.0003653512,0.0006062505,0.0003438448,0.0002998889,0.0000839672,0.0002448786,0.0002447699,0.0002395104],"category_scores_gemma":[0.0009190796,0.0002801496,0.0001483395,0.001251239,0.000229321,0.0002052817,0.000150067,0.0005499031,0.00006050714],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005998417,"about_ca_system_score_gemma":0.00002877794,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001107532,"about_ca_topic_score_gemma":0.000003026408,"domain_scores_codex":[0.9977549,0.0002368368,0.0005162533,0.0008340492,0.0002520165,0.0004059351],"domain_scores_gemma":[0.996879,0.001634174,0.0001468646,0.0009517612,0.000133406,0.0002547268],"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":[0.00002662345,0.0002376528,0.004387401,0.000246727,0.00006076096,3.242321e-7,0.00008519783,0.000002835415,0.001478482,0.8843746,0.00003609248,0.1090634],"study_design_scores_gemma":[0.0005980583,0.000281476,0.006359961,0.00005674619,0.00006801845,0.00001560624,0.001019947,0.0004928843,0.007883985,0.9706388,0.012072,0.0005125455],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.778516,0.0004777608,0.2156227,0.0003046287,0.0001110809,0.001091726,0.00005834283,0.0001353123,0.003682433],"genre_scores_gemma":[0.812493,0.0001002197,0.1859545,0.0003256269,0.000099128,0.0002500272,0.00001926815,0.00004118233,0.0007170187],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1085508,"threshold_uncertainty_score":0.9999651,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02951963676357868,"score_gpt":0.3798976220147435,"score_spread":0.3503779852511649,"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."}}