{"id":"W2059779061","doi":"10.1016/j.jat.2012.06.002","title":"Pointwise estimates for 3-monotone approximation","year":2012,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"Natural Sciences and Engineering Research Council of Canada; University of Manitoba","keywords":"Mathematics; Pointwise; Monotone polygon; Partition (number theory); Spline (mechanical); Combinatorics; Quadratic equation; Strongly monotone; Polynomial; Discrete mathematics; Mathematical analysis; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.006682226,0.0002605058,0.0005090942,0.000320231,0.0002035265,0.00007519904,0.0003105033,0.0001607117,0.0001801406],"category_scores_gemma":[0.003247637,0.0002076246,0.0002944675,0.0002366626,0.0001415254,0.001794777,0.00003349536,0.0002353405,0.0000296044],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001195988,"about_ca_system_score_gemma":0.00007138653,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.999398e-7,"about_ca_topic_score_gemma":1.859388e-7,"domain_scores_codex":[0.9976454,0.0002836075,0.001080878,0.0001441807,0.0004400002,0.0004059191],"domain_scores_gemma":[0.9955341,0.001873146,0.001583555,0.0002869055,0.0005246316,0.0001976487],"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":[0.0004178043,0.0003648817,0.0001261121,0.0003028701,0.0001199749,6.965499e-7,0.004060148,0.00004132729,0.004521658,0.9851145,0.001233437,0.003696635],"study_design_scores_gemma":[0.0009720989,0.0001626442,0.0001095251,0.0001073981,0.0001911222,0.0001329635,0.002319118,0.002028676,0.04169089,0.9513621,0.0006831965,0.0002403169],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1299382,0.0004776621,0.8656049,0.0004008776,0.0004845682,0.0007311318,0.00001128239,0.00008383306,0.002267631],"genre_scores_gemma":[0.7032857,0.00001484023,0.2955488,0.0001235158,0.0005838363,0.00006921155,0.00001378345,0.00005022188,0.0003100478],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5733476,"threshold_uncertainty_score":0.8466687,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04896152160824357,"score_gpt":0.3321691672273006,"score_spread":0.283207645619057,"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."}}