{"id":"W1980936214","doi":"10.1090/s0894-0347-08-00627-9","title":"Rotation numbers for quasiperiodically forced circle maps-mode-locking vs. strict monotonicity","year":2008,"lang":"en","type":"article","venue":"Journal of the American Mathematical Society","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":34,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Deutsche Forschungsgemeinschaft","keywords":"Monotonic function; Mathematics; Algorithm; Type (biology); Rotation (mathematics); Fibered knot; Rotation number; Pure mathematics; 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":[0.0005204434,0.000305755,0.0002427609,0.0005685773,0.0005681174,0.001183436,0.0006031828,0.0005494768,0.006321414],"category_scores_gemma":[0.002689659,0.0001771318,0.000359879,0.0002039416,0.001670057,0.001463834,0.0009036142,0.0005318986,0.0007363331],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006225203,"about_ca_system_score_gemma":0.0004210331,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007065632,"about_ca_topic_score_gemma":0.0006337448,"domain_scores_codex":[0.9996718,0.00006906307,0.00002554279,0.00007097013,0.00008683219,0.000075741],"domain_scores_gemma":[0.9990003,0.0003266586,0.0002419041,0.0002112424,0.0001155036,0.0001044295],"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":[0.00007726644,0.0000273249,0.0007028031,0.0000698497,0.000007306511,0.0002190048,0.0002786949,0.01346283,0.03233994,0.94063,0.0006578442,0.0115271],"study_design_scores_gemma":[0.00003485728,0.0001729855,0.001999182,0.00005592149,0.00001229156,0.0004807386,0.000286295,0.3117742,0.02717067,0.6512198,0.006713075,0.00007986783],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6613702,0.0006451428,0.276205,0.000768376,0.0001892418,0.00008821989,0.0001756319,0.0006396015,0.05991874],"genre_scores_gemma":[0.9741186,0.0002218495,0.02037482,0.00008688821,0.00003109244,0.0001014284,0.0000408968,0.0001186444,0.004905621],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006321414,"threshold_uncertainty_score":0.02114719,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02715978659896287,"score_gpt":0.3130588625716501,"score_spread":0.2858990759726872,"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."}}