{"id":"W3106242887","doi":"","title":"ON SIMULTANEOUS RATIONAL APPROXIMATIONS TO A REAL NUMBER, ITS SQUARE, AND ITS CUBE","year":2012,"lang":"en","type":"article","venue":"","topic":"semigroups and automata theory","field":"Computer Science","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Exponent; Transcendental number; Algebraic number; Rational number; Upper and lower bounds; Square (algebra); Combinatorics; Cube (algebra); Degree (music); Discrete mathematics; Real number; Mathematical analysis; Geometry","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":[0.001664379,0.0005104277,0.0007596738,0.0008388079,0.0006736815,0.001676503,0.0004319396,0.000457838,0.002956857],"category_scores_gemma":[0.01234555,0.0002961858,0.0005898448,0.0006163894,0.00227663,0.00318604,0.001721121,0.001120146,0.0005016355],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001005596,"about_ca_system_score_gemma":0.0002783259,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006703783,"about_ca_topic_score_gemma":0.0005175274,"domain_scores_codex":[0.9986085,0.0004759167,0.00008978167,0.0002495734,0.0003783347,0.0001978927],"domain_scores_gemma":[0.9917406,0.006164858,0.0005747799,0.0006598139,0.0005475978,0.0003122819],"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":[0.001008436,0.00004414534,0.003811105,0.0001542771,0.00004225897,0.0006891947,0.001036864,0.02630179,0.01890283,0.9259252,0.001337817,0.02074615],"study_design_scores_gemma":[0.0001168492,0.0003640508,0.002387895,0.0001095405,0.00007598633,0.001079522,0.0005107636,0.2606762,0.01468462,0.7116973,0.008221486,0.00007570892],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8609326,0.0009845297,0.117262,0.0005897218,0.000155122,0.0000297534,0.00008255931,0.0001864097,0.01977734],"genre_scores_gemma":[0.9866492,0.0002140881,0.01096333,0.00007548829,0.0000564489,0.00002267555,0.00004967238,0.00002492989,0.001944126],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002956857,"threshold_uncertainty_score":0.009891689,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01621041567378072,"score_gpt":0.2672075865085879,"score_spread":0.2509971708348072,"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."}}