{"id":"W2751775677","doi":"10.1017/etds.2017.63","title":"Hausdorff dimension of invariant measure of circle diffeomorphisms with a break point","year":2017,"lang":"en","type":"article","venue":"Ergodic Theory and Dynamical Systems","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Hausdorff dimension; Diffeomorphism; Unicode; Irrational number; Invariant (physics); Pure mathematics; Dimension (graph theory); Combinatorics; Geometry; Mathematical physics","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":[0.001822036,0.0001986308,0.0007565853,0.0000521331,0.000175041,0.00005239833,0.0002810227,0.0001612765,0.00003611644],"category_scores_gemma":[0.0008406764,0.000135092,0.00009631649,0.00004245598,0.0005079165,0.0001086874,0.0001445861,0.0001611303,0.000003094983],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002008238,"about_ca_system_score_gemma":0.00002793719,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009248039,"about_ca_topic_score_gemma":0.00002001172,"domain_scores_codex":[0.9982805,0.0002684906,0.0005895616,0.000265139,0.0003736313,0.0002227073],"domain_scores_gemma":[0.9973334,0.0009517728,0.0006414147,0.0008109906,0.0001119387,0.0001505023],"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":[0.0003960358,0.0002947282,0.000377319,0.001014458,0.0001219167,0.00001960184,0.0004479992,0.000009988718,0.006659877,0.9901457,0.00001882387,0.0004935325],"study_design_scores_gemma":[0.002629374,0.0006466647,0.006564823,0.003001139,0.0002495072,0.0002498199,0.0007129782,0.04577357,0.0006625876,0.938972,0.0000219667,0.0005155844],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.901691,0.0001601108,0.09438123,0.00009157239,0.0001216915,0.0004979684,0.00005332401,0.00003073007,0.002972359],"genre_scores_gemma":[0.9989911,0.000009010433,0.0006286151,0.000008582497,0.0000290862,0.0000167965,0.000003947392,0.00002804789,0.0002848301],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09730007,"threshold_uncertainty_score":0.5508891,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01637108259600917,"score_gpt":0.2522633094285543,"score_spread":0.2358922268325452,"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."}}