{"id":"W2950321107","doi":"10.48550/arxiv.math/0406372","title":"Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integral","year":2004,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of the Fraser Valley","funders":"","keywords":"Remainder; Chinese remainder theorem; Mathematics; Taylor series; Taylor's theorem; Pure mathematics; Mathematical economics; Arithmetic; Mathematical analysis; Discrete mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004768069,0.001562239,0.001089394,0.002036351,0.00066729,0.001457044,0.001318125,0.0007545836,0.00242935],"category_scores_gemma":[0.01329273,0.0003400098,0.001006468,0.0008229649,0.002380907,0.003845641,0.002324009,0.002603067,0.001257082],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001187638,"about_ca_system_score_gemma":0.0007479627,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001391874,"about_ca_topic_score_gemma":0.001228557,"domain_scores_codex":[0.9990649,0.000357031,0.00004682808,0.0001173712,0.0003181559,0.00009581503],"domain_scores_gemma":[0.9954445,0.002639638,0.0003670684,0.0004292432,0.0007669088,0.0003526472],"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":[0.0003746201,0.00006759454,0.001879325,0.0003821024,0.00009519286,0.0003706092,0.0004477943,0.07405911,0.0170235,0.8590164,0.004149204,0.04213456],"study_design_scores_gemma":[0.00002078265,0.0001469913,0.001319095,0.0001029319,0.00005347628,0.0002793054,0.0001344601,0.6141995,0.01116858,0.3642169,0.008269186,0.0000887213],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06053539,0.001936721,0.9250785,0.0006905313,0.0002458721,0.00003089212,0.0001632497,0.0002910698,0.01102786],"genre_scores_gemma":[0.6420268,0.005164904,0.3192193,0.00036178,0.0008930471,0.0002031081,0.0006260633,0.000976656,0.03052843],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004768069,"threshold_uncertainty_score":0.02521628,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04029678136090467,"score_gpt":0.2786280257936846,"score_spread":0.2383312444327799,"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."}}