{"id":"W2951884879","doi":"10.48550/arxiv.math/0611805","title":"Ultimate Generalization to Monotonicity for Uniform Convergence of Trigonometric Series","year":2006,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"St. Francis Xavier University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; St. Francis Xavier University; National Science Foundation","keywords":"Monotonic function; Mathematics; Sequence (biology); Generalization; Trigonometric series; Series (stratigraphy); Uniform convergence; Convergence (economics); Bounded function; Space (punctuation); Limit of a sequence; Bounded variation; Combinatorics; Discrete mathematics; Pure mathematics; Mathematical analysis; Limit (mathematics); Computer science","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":[0.0005883265,0.0002778032,0.0005324424,0.0003033268,0.0001075614,0.00002789006,0.0003802752,0.0002517736,0.00008049399],"category_scores_gemma":[0.0006012716,0.0002643662,0.0001726287,0.0004380661,0.00008321738,0.0001839255,0.0002020333,0.0001522075,0.00001948157],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000107022,"about_ca_system_score_gemma":0.0001202152,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009086476,"about_ca_topic_score_gemma":0.00003755231,"domain_scores_codex":[0.9984328,0.00006295378,0.0006770555,0.0003898369,0.000183038,0.0002542742],"domain_scores_gemma":[0.9982336,0.000197876,0.00062841,0.0005349152,0.0003343076,0.00007093412],"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":[0.0008346654,0.0008404013,0.1465699,0.00948762,0.0005101555,0.00000542411,0.007658425,0.03528323,0.01110297,0.7816682,0.004288279,0.001750662],"study_design_scores_gemma":[0.000957742,0.0003004153,0.02058977,0.0003836044,0.0002896845,0.000004544698,0.0004826491,0.01549275,0.2661647,0.6923534,0.001749852,0.001230929],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7958479,0.00005048235,0.2017345,0.0001529566,0.0002639147,0.001142136,0.0001666073,0.00009012797,0.0005513281],"genre_scores_gemma":[0.9331226,0.00006073283,0.06429079,0.00005297068,0.0000972326,0.0003140183,0.0001873283,0.00004248837,0.001831819],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2550617,"threshold_uncertainty_score":0.9999809,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09065102137159263,"score_gpt":0.3340030529788796,"score_spread":0.2433520316072869,"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."}}