{"id":"W1612834753","doi":"10.48550/arxiv.1401.7086","title":"N derivatives are necessary for order N+1 convergence in quadrature: a converse result","year":2014,"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":"Natural Sciences and Engineering Research Council of Canada","keywords":"Converse; Mathematics; Quadrature (astronomy); Degree (music); Applied mathematics; Convergence (economics); Order (exchange); Physics; Geometry","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"],"consensus_categories":[],"category_scores_codex":[0.0005479032,0.0004135963,0.0007714215,0.0002457755,0.0001222108,0.00004975976,0.0005700461,0.0005461532,0.0003383702],"category_scores_gemma":[0.001336307,0.000425213,0.0002486803,0.0004423138,0.000164404,0.0001312457,0.0004179279,0.0005817904,0.00005741778],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001314066,"about_ca_system_score_gemma":0.0001632437,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007105549,"about_ca_topic_score_gemma":0.0001816892,"domain_scores_codex":[0.9980096,0.0002059801,0.0004620661,0.0008325075,0.00008736188,0.0004024442],"domain_scores_gemma":[0.996648,0.001478051,0.0005226327,0.0009122434,0.0002863896,0.0001527224],"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":[0.0005962498,0.0005698284,0.003437665,0.003649144,0.0003096862,0.0001050105,0.001070841,0.009501327,0.00009039065,0.9494359,0.03117455,0.00005941889],"study_design_scores_gemma":[0.002186316,0.00009651717,0.0004848996,0.000917262,0.0002807867,0.000003464264,0.001277902,0.09849962,0.0003495847,0.8887797,0.006105932,0.001018036],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6172857,0.00007965844,0.3737018,0.0004339828,0.00113756,0.001869956,0.0002714433,0.0002347521,0.004985154],"genre_scores_gemma":[0.9891465,0.00009306016,0.00479072,0.0001517609,0.0001435501,0.00001654214,0.00004189624,0.00005118143,0.005564785],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3718607,"threshold_uncertainty_score":0.99982,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1443252765758518,"score_gpt":0.251812053651916,"score_spread":0.1074867770760642,"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."}}