{"id":"W2351657481","doi":"10.1016/j.jfa.2016.05.001","title":"Free entropy dimension and regularity of non-commutative polynomials","year":2016,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Commutative property; Tuple; Spectral measure; Dimension (graph theory); Polynomial; Entropy (arrow of time); Measure (data warehouse); Constant (computer programming); Pure mathematics; Combinatorics; Discrete mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005224942,0.00007589335,0.0004040811,0.0002635996,0.00006375884,0.00001023861,0.0001026615,0.00003906748,0.0002021571],"category_scores_gemma":[0.000281526,0.00004239942,0.000309093,0.0003617518,0.00006173838,0.0001205483,0.00004009442,0.0000629064,0.000001566811],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003389148,"about_ca_system_score_gemma":0.00003062115,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001691704,"about_ca_topic_score_gemma":0.000008120512,"domain_scores_codex":[0.9989752,0.00005522224,0.0005138072,0.000082531,0.0003005465,0.00007265418],"domain_scores_gemma":[0.9978557,0.000807588,0.0007406451,0.0001821509,0.0003498851,0.00006407671],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.003229645,0.002081292,0.09900113,0.0001961631,0.0244146,0.00002393494,0.001275781,0.0007824894,0.6566007,0.1337589,0.06397085,0.01466449],"study_design_scores_gemma":[0.009982091,0.0005442273,0.3241128,0.0001582188,0.01352816,0.0001175833,0.0005557543,0.001858937,0.03134466,0.6152084,0.002160053,0.0004290686],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8594934,0.0001373728,0.1378523,0.002204337,0.00004163503,0.0000552059,0.0000403947,0.000003506287,0.0001718204],"genre_scores_gemma":[0.9915465,0.00009029221,0.007828571,0.00002118327,0.0001116492,0.000001855944,0.000001354487,0.000004836469,0.0003937631],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.625256,"threshold_uncertainty_score":0.2213478,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02259599343383485,"score_gpt":0.2859925510438986,"score_spread":0.2633965576100638,"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."}}