{"id":"W2329143956","doi":"10.4153/cjm-2003-024-6","title":"Automorphic Orthogonal and Extremal Polynomials","year":2003,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Austrian Science Fund; Russian Foundation for Basic Research; Canadian Mathematical Society","keywords":"Mathematics; Chebyshev polynomials; Trigonometric polynomial; Orthogonal polynomials; Pure mathematics; Uniform norm; Trigonometry; Trigonometric functions; Discrete orthogonal polynomials; Orthogonality; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001685927,0.0002215126,0.0005956547,0.0003223354,0.0001867484,0.0001120194,0.0001924647,0.0001413246,0.0017268],"category_scores_gemma":[0.003464552,0.0001789071,0.0001620795,0.0001801118,0.0001597696,0.000142097,0.00001079196,0.0002700301,0.00003473221],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007724353,"about_ca_system_score_gemma":0.0009326822,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004157428,"about_ca_topic_score_gemma":0.00113396,"domain_scores_codex":[0.9981577,0.0001140805,0.0009547105,0.0001268481,0.000248819,0.0003978183],"domain_scores_gemma":[0.9971722,0.0009911726,0.000489604,0.0002846495,0.0002079631,0.0008543655],"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":[0.000004025846,0.0001007933,0.0009930531,0.0002973989,0.0001229601,0.000117865,0.001132061,0.000002535066,0.0002173088,0.9804661,0.01614369,0.0004022331],"study_design_scores_gemma":[0.0009902639,0.0002152152,0.0002426557,0.0004212443,0.0003063168,0.004646461,0.001287381,0.0001668879,0.001053093,0.9515769,0.03861276,0.0004807543],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9545554,0.0009968778,0.01288163,0.0005894041,0.000765646,0.000321827,0.00003617702,0.00002594154,0.02982709],"genre_scores_gemma":[0.8914678,0.00002773075,0.1058761,0.0001455931,0.0002335801,0.000005067649,7.349776e-7,0.000062366,0.002181019],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09299447,"threshold_uncertainty_score":0.9991857,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05776506347654913,"score_gpt":0.2742634691547893,"score_spread":0.2164984056782401,"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."}}