{"id":"W2115798635","doi":"10.1007/s00220-013-1706-1","title":"Renormalization Horseshoe and Rigidity for Circle Diffeomorphisms with Breaks","year":2013,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":39,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Horseshoe (symbol); Mathematics; Rotation number; Renormalization; Pure mathematics; Periodic point; Diophantine equation; Rigidity (electromagnetism); Mathematical analysis; Rotation (mathematics); Mathematical physics; Geometry; Physics; Quantum mechanics","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":[0.001468407,0.00109908,0.001318444,0.00410862,0.003826964,0.00296513,0.001508722,0.0032757,0.00738705],"category_scores_gemma":[0.004623175,0.000685299,0.001590743,0.001477196,0.004893189,0.006111449,0.003384637,0.003585791,0.0007647073],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001164539,"about_ca_system_score_gemma":0.0005575115,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008341908,"about_ca_topic_score_gemma":0.0007102364,"domain_scores_codex":[0.9991506,0.0002136627,0.00005147268,0.0001778481,0.000216594,0.0001898417],"domain_scores_gemma":[0.9976387,0.0006835297,0.0005294774,0.0004672817,0.0001736787,0.0005073684],"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":[0.00005650034,0.00001734402,0.0001457943,0.00002086796,0.000008330152,0.0001310405,0.000270302,0.0009452128,0.0008630828,0.9955035,0.0003796842,0.001658407],"study_design_scores_gemma":[0.00001693964,0.00002976554,0.0004380827,0.000007234081,0.00000777575,0.0001226364,0.00009470869,0.004465374,0.0002491532,0.9934081,0.001140589,0.00001968395],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8297302,0.002343877,0.08017198,0.003020766,0.0006709078,0.00009530337,0.0002672288,0.0005087589,0.08319094],"genre_scores_gemma":[0.9752702,0.0005837156,0.009779273,0.0002580656,0.0006004875,0.00005468677,0.0001802865,0.0001160655,0.0131573],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00738705,"threshold_uncertainty_score":0.02471215,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06553305525332938,"score_gpt":0.3297863508457696,"score_spread":0.2642532955924402,"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."}}