{"id":"W2039344137","doi":"10.1007/bf02985637","title":"A Very Mean Value Theorem","year":2003,"lang":"en","type":"article","venue":"The Mathematical Intelligencer","topic":"Numerical Methods and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Guelph","funders":"","keywords":"Mean value theorem (divided differences); Mathematics; Mean value; Mathematical economics; Statistics; Mathematical analysis; Picard–Lindelöf theorem; Fixed-point theorem","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001421068,0.0001549653,0.0002048433,0.00003129859,0.0001387854,0.0001501852,0.001098895,0.0000478288,0.0004718999],"category_scores_gemma":[0.0004836105,0.00008032198,0.0001250898,0.000416552,0.0001921589,0.0001337439,0.0001637119,0.0002079867,0.0009402086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002211909,"about_ca_system_score_gemma":0.00002974284,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003600454,"about_ca_topic_score_gemma":1.433402e-7,"domain_scores_codex":[0.9984285,0.0003449736,0.0002820178,0.0002716277,0.0003313362,0.0003415128],"domain_scores_gemma":[0.9979552,0.001046754,0.00005621732,0.0007794003,0.00004513465,0.0001173121],"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":[0.000001127422,0.00005552205,0.000001232006,0.000007363484,0.00001171974,0.000003516239,0.0008148871,0.00001467694,0.0001014533,0.9570071,0.0001193158,0.04186207],"study_design_scores_gemma":[0.00002726956,0.00004668802,0.000003223142,0.00001997707,0.000007565272,0.00003524301,0.0001175254,0.03738375,0.01383037,0.94473,0.003669071,0.0001293109],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0006856525,0.0001259285,0.9555073,0.0007879199,0.0002527452,0.0001463088,3.442734e-7,0.0001074034,0.0423864],"genre_scores_gemma":[0.195432,0.00002918077,0.8015976,0.00132343,0.00008872218,0.00003910947,1.097232e-7,0.00001993776,0.00146992],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.1947463,"threshold_uncertainty_score":0.9998377,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04306645498068984,"score_gpt":0.3171031996934598,"score_spread":0.27403674471277,"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."}}