{"id":"W2165037137","doi":"10.1016/j.jat.2006.04.001","title":"An extrapolation theorem for nonlinear approximation and its applications","year":2006,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Extrapolation; Mathematics; Nonlinear system; Term (time); Linear approximation; Applied mathematics; Point (geometry); Mathematical analysis; Approximation theory; 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":[0.002834217,0.0002162131,0.0003630781,0.0002876212,0.0002009456,0.0001334758,0.0002053348,0.000158504,0.00008575151],"category_scores_gemma":[0.0006478439,0.0001719754,0.0001450473,0.0002273051,0.00006837079,0.001040816,0.00001344106,0.0001791805,0.000006598832],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006589523,"about_ca_system_score_gemma":0.00005512854,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":5.155218e-7,"about_ca_topic_score_gemma":0.000001410716,"domain_scores_codex":[0.9978185,0.0002159507,0.00117044,0.0002081025,0.0003959248,0.0001910787],"domain_scores_gemma":[0.9967384,0.0009453241,0.001148738,0.0002345158,0.0008296695,0.0001032926],"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":[0.0001197615,0.0004102752,0.000005667491,0.0002930482,0.00002266906,1.737486e-7,0.000426478,0.00002545822,0.00665623,0.9825987,0.0002541976,0.009187334],"study_design_scores_gemma":[0.0007658754,0.0001762101,0.00003444618,0.0000566282,0.00008802141,0.00004096789,0.0004606591,0.1068071,0.01395309,0.876283,0.001164578,0.000169399],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.06183933,0.0001377093,0.9341256,0.0002919802,0.00006768623,0.001228869,0.00002566255,0.00007535717,0.002207809],"genre_scores_gemma":[0.439876,0.00002189226,0.5585161,0.0000977583,0.0007469272,0.0002263835,0.0001171848,0.00006024591,0.0003374394],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3780367,"threshold_uncertainty_score":0.7012954,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02908618351939337,"score_gpt":0.316654922392937,"score_spread":0.2875687388735437,"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."}}