{"id":"W4234196338","doi":"10.4169/amermathmont.117.10.0918","title":"A Concise, Elementary Proof of Arzelà’s Bounded Convergence Theorem","year":2010,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"Iterative Methods for Nonlinear Equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"University of Toronto","keywords":"Elementary proof; Bounded function; Mathematics; Convergence (economics); Calculus (dental); Pure mathematics; Mathematical analysis; Economics; Medicine","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0009694746,0.0002802384,0.0007025826,0.0001140662,0.00009882342,0.00003110471,0.0004261104,0.00006528618,0.001354273],"category_scores_gemma":[0.002494928,0.0002275929,0.000198399,0.0004279558,0.001219718,0.0001185536,0.0001091053,0.0003875274,0.00006324729],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003126807,"about_ca_system_score_gemma":0.0001010783,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004360352,"about_ca_topic_score_gemma":0.00007636106,"domain_scores_codex":[0.9977123,0.0002186083,0.0008395654,0.0003334069,0.0005065668,0.0003895756],"domain_scores_gemma":[0.9962763,0.002029253,0.000527823,0.0007743199,0.0002215486,0.0001707391],"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":[0.00003964591,0.0006255938,0.0003734444,0.0001568328,0.0001071781,0.000005664797,0.001683924,0.000001238925,0.01169229,0.9822398,0.0005849493,0.002489365],"study_design_scores_gemma":[0.0003402705,0.0002491682,0.0001547977,0.00004952941,0.0000933294,0.000008533372,0.0007170436,0.004359349,0.02958485,0.9633653,0.0008148588,0.0002629959],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.721158,0.00001986735,0.1983745,0.0007627784,0.0002760643,0.001470068,0.0001738439,0.0002035556,0.0775613],"genre_scores_gemma":[0.5276225,4.584205e-7,0.4717653,0.0001519189,0.00006186013,0.0000721455,0.000009654764,0.00004011408,0.0002759794],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2733908,"threshold_uncertainty_score":0.9995586,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03772077284912799,"score_gpt":0.3590863442866766,"score_spread":0.3213655714375486,"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."}}