{"id":"W770938370","doi":"10.1017/cbo9780511902659.004","title":"Metric theory of continued fractions","year":2014,"lang":"en","type":"book-chapter","venue":"Cambridge University Press eBooks","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Irrational number; Transcendental number; Rational number; Mathematics; Quotient; Metric (unit); Real number; Quadratic equation; Pure mathematics; Discrete mathematics; Algebra over a field; Mathematical analysis; Economics","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":[0.000420667,0.0005023566,0.000366076,0.001248509,0.0007338522,0.001944792,0.0003827423,0.0005305212,0.006180441],"category_scores_gemma":[0.001072899,0.0001401354,0.0002559483,0.0008265762,0.002280424,0.002555895,0.0009021453,0.0009906391,0.001616103],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001780801,"about_ca_system_score_gemma":0.0005726882,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001475093,"about_ca_topic_score_gemma":0.001191121,"domain_scores_codex":[0.999633,0.0001150445,0.00001448985,0.00005442964,0.0001538052,0.00002915824],"domain_scores_gemma":[0.9997187,0.00009062386,0.00002630397,0.00004103431,0.00008339859,0.00003980464],"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":[0.000001364569,7.108247e-7,0.00001639151,0.00001547491,0.000001010644,0.000008940062,0.00007888114,0.0001435726,0.0001105517,0.9955919,0.001184834,0.002846383],"study_design_scores_gemma":[0.000003264631,0.00001087639,0.0001414041,0.00002091262,0.0000019662,0.0000816645,0.00006516993,0.0009307528,0.0001790739,0.9052517,0.09330842,0.000004786333],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.04119414,0.02457945,0.07926288,0.005091696,0.0009430784,0.00003865716,0.0004386515,0.0003526069,0.8480988],"genre_scores_gemma":[0.7310706,0.01411925,0.02655307,0.0008618894,0.001327802,0.0001036247,0.0004173334,0.0002056665,0.2253406],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.006180441,"threshold_uncertainty_score":0.0206756,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0421239661322907,"score_gpt":0.2281702225790656,"score_spread":0.1860462564467749,"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."}}