{"id":"W2077592163","doi":"10.1017/s0143385707000314","title":"Non-standard smooth realizations of Liouville rotations","year":2007,"lang":"en","type":"article","venue":"Ergodic Theory and Dynamical Systems","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"Kingston Health Sciences Centre","funders":"","keywords":"Ergodic theory; Mathematics; Torus; Conjugacy class; A priori and a posteriori; Measure (data warehouse); Pure mathematics; Rotation (mathematics); Rotation number; Topological conjugacy; Variety (cybernetics); Mathematical analysis; Geometry; Statistics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002414468,0.0001570307,0.000412427,0.0001115032,0.0001365143,0.00003415688,0.000129463,0.0001555846,0.00007913825],"category_scores_gemma":[0.0007128663,0.0001241928,0.00008711443,0.0002179348,0.0001916178,0.0000669224,0.00005188721,0.0001378668,0.000006935738],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003622033,"about_ca_system_score_gemma":0.00002632091,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000236741,"about_ca_topic_score_gemma":0.00002924694,"domain_scores_codex":[0.9984858,0.0001230922,0.0006689408,0.0002027185,0.000264254,0.0002551732],"domain_scores_gemma":[0.9974049,0.001804164,0.0002079865,0.0002997272,0.0001079822,0.0001752232],"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":[0.00007411886,0.0001004041,0.0001902437,0.0002962479,0.00003510413,0.000004752862,0.0004314194,0.00003568471,0.0002593497,0.9979076,0.0001265148,0.0005385736],"study_design_scores_gemma":[0.0005622479,0.000137546,0.0006756907,0.0003103195,0.00007935463,0.00002674408,0.001146182,0.03044696,0.00005105487,0.9654427,0.000867906,0.0002533527],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2668488,0.0001214846,0.7117474,0.0000333117,0.0001700815,0.0003778976,0.00007138944,0.00005896545,0.02057069],"genre_scores_gemma":[0.9963877,0.00001888848,0.002229571,0.0000168729,0.00005674603,0.00001673479,0.0000166287,0.00002582093,0.001230996],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7295389,"threshold_uncertainty_score":0.5064435,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0129563222021673,"score_gpt":0.2936079402161419,"score_spread":0.2806516180139746,"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."}}