{"id":"W2126193701","doi":"10.1017/s0143385708080528","title":"Conjugacy, orbit equivalence and classification of measure-preserving group actions","year":2008,"lang":"en","type":"article","venue":"Ergodic Theory and Dynamical Systems","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Ergodic theory; Conjugacy class; Countable set; Abelian group; Measure (data warehouse); Standard probability space; Equivalence (formal languages); Almost everywhere; Second-countable space; Group (periodic table); Free group; Orbit (dynamics); Probability measure; Pure mathematics; Combinatorics; Discrete group; Discrete mathematics","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":[0.001053236,0.000136043,0.000309346,0.00005762539,0.0002629824,0.000008768843,0.0001238933,0.0001643908,0.00003913636],"category_scores_gemma":[0.0006926606,0.0001137868,0.00004183986,0.00008302975,0.000688408,0.0001552635,0.00007204813,0.0001972591,0.000004661394],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002369105,"about_ca_system_score_gemma":0.00001721775,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001058716,"about_ca_topic_score_gemma":0.000007834787,"domain_scores_codex":[0.9984838,0.0006057365,0.0003400086,0.0002441367,0.0001436458,0.0001827126],"domain_scores_gemma":[0.9976873,0.00172914,0.000161573,0.0002754165,0.00004988445,0.00009669734],"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":[0.0001847436,0.00006286886,0.001001354,0.0001564337,0.00003428756,0.000005903508,0.0005062298,0.000005806437,0.006794789,0.9909586,0.00004003557,0.000248967],"study_design_scores_gemma":[0.0007874063,0.0001457147,0.007875122,0.0002621464,0.00006359696,0.0004857286,0.001946393,0.006675767,0.00009094144,0.9810191,0.0003637255,0.0002843565],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8666785,0.001238819,0.1277424,0.00005143789,0.0002167787,0.000239097,0.00001485841,0.00007956093,0.003738595],"genre_scores_gemma":[0.9984607,0.0001670372,0.0005227091,0.00001422715,0.00005278659,0.00002383719,0.000004485884,0.00001408688,0.0007401579],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1317822,"threshold_uncertainty_score":0.4640091,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06854672102901917,"score_gpt":0.3160697053749051,"score_spread":0.2475229843458859,"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."}}