{"id":"W2623620649","doi":"10.3934/dcds.2017197","title":"Notes on a theorem of Katznelson and Ornstein","year":2017,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Lebesgue measure; Type (biology); Absolute continuity; Combinatorics; Irrational number; Rotation number; Lebesgue integration; Conjugacy class; Rotation (mathematics); Measure (data warehouse); Discrete mathematics; Pure mathematics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004182962,0.0002025358,0.0006166746,0.00003626251,0.000183056,0.0002011286,0.0002106369,0.0001338989,0.000008543396],"category_scores_gemma":[0.0007326036,0.0001352765,0.00008126604,0.00002066807,0.0002648421,0.00007994976,0.0001250018,0.0001284625,0.00000215993],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009650517,"about_ca_system_score_gemma":0.000005888569,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001483187,"about_ca_topic_score_gemma":0.00002734636,"domain_scores_codex":[0.9988099,0.00006360176,0.0004104433,0.0002704485,0.0002171759,0.0002284503],"domain_scores_gemma":[0.9983063,0.0006396357,0.0003423239,0.0005363155,0.00005039888,0.0001249646],"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":[0.00004124283,0.00006713656,0.001877647,0.0004292392,0.00005496536,0.000008807084,0.000200046,5.245494e-7,0.0007010887,0.9921199,0.00001884915,0.004480523],"study_design_scores_gemma":[0.002578869,0.001025902,0.01168324,0.002581069,0.0002736402,0.00008661149,0.001166427,0.2570866,0.0002805036,0.7217126,0.0004641708,0.00106037],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9785315,0.0001397175,0.005418402,0.0002999304,0.0001017119,0.0004161824,0.00006093261,0.00003400331,0.01499762],"genre_scores_gemma":[0.9989544,0.00002580682,0.0003621193,0.00001431068,0.00004814311,0.00001856536,0.000003624707,0.00002422458,0.000548793],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2704073,"threshold_uncertainty_score":0.5516417,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02524048304689257,"score_gpt":0.2977343369526713,"score_spread":0.2724938539057787,"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."}}