{"id":"W2946266372","doi":"10.48550/arxiv.1905.05805","title":"Elementary numerical methods for double integrals","year":2019,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of the Fraser Valley","keywords":"Bounded function; Trapezoidal rule; Midpoint method; Mathematics; Space (punctuation); Combinatorics; Midpoint; Discrete mathematics; Mathematical analysis; Numerical integration; Geometry; Computer science","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008847355,0.0003806681,0.0007863573,0.0001745422,0.0001152117,0.00005690287,0.0006083726,0.0003828245,0.001359487],"category_scores_gemma":[0.0002116552,0.0003659638,0.0005645521,0.0002049188,0.0000607566,0.000094503,0.0006545498,0.0004952736,0.0001630623],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001957177,"about_ca_system_score_gemma":0.0001333669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008376972,"about_ca_topic_score_gemma":0.000007127065,"domain_scores_codex":[0.9981827,0.0001895684,0.0004187171,0.0007488768,0.00006082807,0.0003993789],"domain_scores_gemma":[0.9965999,0.001713951,0.0003240957,0.001055319,0.0001450806,0.0001616416],"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":[0.0002925776,0.0002877938,0.000190541,0.001015114,0.0004318707,0.000007545037,0.0001331972,0.002109138,0.00004560177,0.9737062,0.02073479,0.001045626],"study_design_scores_gemma":[0.001211036,0.0001114231,0.000007531655,0.0001565916,0.0005957225,0.000002815282,0.0001976382,0.06835035,0.0007864719,0.9039973,0.02403293,0.0005501995],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02768818,0.00004715263,0.9587367,0.0001229394,0.000965636,0.001478967,0.00008776173,0.0001684265,0.0107043],"genre_scores_gemma":[0.4970549,0.00007673613,0.4597749,0.0002712589,0.00042731,0.00003587287,0.0001460648,0.0001399781,0.04207303],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.4989618,"threshold_uncertainty_score":0.9998792,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2514945059313076,"score_gpt":0.3270016073417069,"score_spread":0.07550710141039924,"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."}}