{"id":"W2972034997","doi":"10.1112/jlms.12388","title":"Rational approximation to real points on quadratic hypersurfaces","year":2020,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Uncountable set; Hypersurface; Mathematics; Quadratic equation; Combinatorics; Exponent; Inverse; Upper and lower bounds; Countable set; Discrete mathematics; Pure mathematics; Mathematical analysis; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00078269,0.0006064473,0.0007123078,0.001869953,0.0008389417,0.001610713,0.0006338369,0.0004283601,0.002917309],"category_scores_gemma":[0.003891435,0.0003000262,0.0005181417,0.0007710324,0.002753737,0.002143177,0.001760911,0.001199396,0.000374547],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001524181,"about_ca_system_score_gemma":0.0002038104,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001019394,"about_ca_topic_score_gemma":0.0005146764,"domain_scores_codex":[0.9993365,0.0001359857,0.00003390564,0.000105034,0.0002355765,0.0001529569],"domain_scores_gemma":[0.9989717,0.0003939154,0.0001959999,0.0001222685,0.000144085,0.0001719752],"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":[0.0001528941,0.0000276618,0.001832715,0.00007247665,0.00001662884,0.0002931382,0.0004364043,0.008442289,0.006518785,0.9736278,0.0004296848,0.008149453],"study_design_scores_gemma":[0.00006116221,0.0001400679,0.00454029,0.00005491384,0.00001949474,0.0004394035,0.0003711631,0.1372734,0.005535319,0.8472444,0.004275909,0.00004431652],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9369817,0.0004316108,0.0413934,0.0002991977,0.00003883212,0.00002329873,0.00008684244,0.0001101094,0.02063499],"genre_scores_gemma":[0.9929965,0.0001585029,0.003754415,0.00002119901,0.00004321719,0.000012608,0.00007742045,0.00001843105,0.002917766],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002917309,"threshold_uncertainty_score":0.01105875,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05241633159311376,"score_gpt":0.3054787064004992,"score_spread":0.2530623748073854,"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."}}