{"id":"W2963406834","doi":"10.1016/j.aim.2015.01.013","title":"Rational points near planar curves and Diophantine approximation","year":2015,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Diophantine approximation; Planar; Lebesgue integration; Divergence (linguistics); Diophantine equation; Degenerate energy levels; Lebesgue measure; Pure mathematics; Mathematical analysis","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":[0.0006318637,0.0009631834,0.001263352,0.002395707,0.001800896,0.002718077,0.001365779,0.001811134,0.005663363],"category_scores_gemma":[0.004027402,0.0005202157,0.0006654394,0.001704246,0.003427253,0.003841031,0.002622866,0.004201268,0.0009987667],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002046205,"about_ca_system_score_gemma":0.0005119941,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00160445,"about_ca_topic_score_gemma":0.0007290036,"domain_scores_codex":[0.9994593,0.0001239778,0.00002444874,0.00009875758,0.0001943133,0.00009915687],"domain_scores_gemma":[0.9992494,0.00035145,0.0001099089,0.00009588959,0.0001060153,0.00008732429],"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":[0.0000271543,0.000009048442,0.00008277279,0.00002215282,0.000004854227,0.00004527208,0.0001343086,0.001966723,0.0003753614,0.9946803,0.0004824382,0.002169584],"study_design_scores_gemma":[0.00001659098,0.000009491647,0.0001264812,0.000008632843,0.000005175694,0.00008650649,0.00007376535,0.005792162,0.0001832438,0.9915855,0.00210357,0.000008942618],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6077287,0.007184618,0.1567805,0.006525531,0.0008911525,0.00008677872,0.000508339,0.0003957649,0.2198987],"genre_scores_gemma":[0.9560012,0.001933889,0.01521053,0.0003319937,0.0004487184,0.00004490097,0.000239303,0.0000862989,0.02570322],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005663363,"threshold_uncertainty_score":0.01894587,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03807284483382647,"score_gpt":0.3262411703659628,"score_spread":0.2881683255321363,"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."}}