{"id":"W2907282600","doi":"10.4153/s0008439519000110","title":"A Comment on Ergodic Theorem for Amenable Groups","year":2019,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Ergodic theory; Mixing (physics); Action (physics); Sequence (biology); Amenable group; Function (biology)","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001062651,0.0003509964,0.0006505708,0.0001726876,0.0001554056,0.0001179298,0.0004379507,0.0002077704,0.02880755],"category_scores_gemma":[0.001231936,0.0002853637,0.0002611127,0.0001296708,0.00009007385,0.00002862062,0.00004975464,0.0002662286,0.01778415],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002748233,"about_ca_system_score_gemma":0.0001067715,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000695642,"about_ca_topic_score_gemma":0.0001113793,"domain_scores_codex":[0.9976627,0.00007050291,0.0005972325,0.0004394064,0.0003574751,0.0008727435],"domain_scores_gemma":[0.9956231,0.002612223,0.0001358979,0.000803403,0.00009201099,0.000733409],"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":[0.00002160769,0.0001749156,0.00000613074,0.0005141787,0.00003978563,0.000007776416,0.0001454754,0.000002013973,0.00001742829,0.8998047,0.09904619,0.0002198302],"study_design_scores_gemma":[0.0005871536,0.0002011755,0.000003552125,0.000238262,0.00003495864,0.000009749603,0.0001505601,0.00404815,0.0000563998,0.8112222,0.1831288,0.0003190413],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2086496,0.00005888243,0.07197671,0.1272755,0.0006045056,0.008524404,0.000431731,0.0004290954,0.5820495],"genre_scores_gemma":[0.9310951,0.000005760414,0.0303289,0.02097482,0.0001887177,0.0005802945,0.00004669914,0.0002190463,0.01656071],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7224454,"threshold_uncertainty_score":0.9999598,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02220808467398361,"score_gpt":0.2581771393420852,"score_spread":0.2359690546681016,"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."}}