{"id":"W2045199562","doi":"10.1017/etds.2014.103","title":"Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable","year":2014,"lang":"en","type":"article","venue":"Ergodic Theory and Dynamical Systems","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Algebraic number; Space (punctuation); Algebraically closed field; Polynomial; Pure mathematics; Periodic orbits; Degree (music); Variable (mathematics); Independence (probability theory); Field (mathematics); Algebraic surface; Algebra over a field; Mathematical analysis; Physics; Computer science","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":[0.004099992,0.0001600011,0.0008138593,0.0001028009,0.00002995267,0.000009687096,0.00032928,0.0002044162,0.00003346154],"category_scores_gemma":[0.001535332,0.0001098563,0.00009542195,0.0002121435,0.0004495133,0.0000521418,0.00008728764,0.000212637,9.589559e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001534968,"about_ca_system_score_gemma":0.00004055983,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001405145,"about_ca_topic_score_gemma":0.00001258167,"domain_scores_codex":[0.9975734,0.0006744193,0.0009353631,0.0001919306,0.0004229034,0.0002019688],"domain_scores_gemma":[0.9954552,0.003425653,0.000569342,0.0004066515,0.00008101085,0.00006214247],"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":[0.000190464,0.0003698551,0.0005631619,0.002167275,0.00004667942,8.253645e-7,0.001727547,0.00009125985,0.007305984,0.9873879,0.00001258259,0.0001364585],"study_design_scores_gemma":[0.002074003,0.0006265332,0.001695028,0.002041974,0.0001747078,0.00003916164,0.003471816,0.08694969,0.001275383,0.9012605,0.00004253234,0.0003486591],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9482582,0.0001666924,0.04825694,0.00002640285,0.0001050476,0.000448222,0.00007947489,0.000008791319,0.00265024],"genre_scores_gemma":[0.9981467,0.000009565105,0.00167664,0.000005648074,0.0000228309,0.00001263795,0.00000458787,0.000014588,0.0001068781],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08685843,"threshold_uncertainty_score":0.4479808,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01263415869958254,"score_gpt":0.2445896871266875,"score_spread":0.231955528427105,"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."}}