{"id":"W2007467585","doi":"10.48550/arxiv.math/0608637","title":"Central Limit Theorems for Non-Invertible Measure Preserving Maps","year":2006,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Measure (data warehouse); Invertible matrix; Limit (mathematics); Mathematics; Calculus (dental); Pure mathematics; Computer science; Mathematical analysis; Data mining; Medicine","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":[0.003607281,0.000811153,0.0009807401,0.002437255,0.00122547,0.00218571,0.001650179,0.001187744,0.003731291],"category_scores_gemma":[0.01023107,0.000334262,0.00129768,0.0009742136,0.003675852,0.004333707,0.002440305,0.002158352,0.0004222637],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001637977,"about_ca_system_score_gemma":0.0008624283,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000626096,"about_ca_topic_score_gemma":0.0004859878,"domain_scores_codex":[0.9985433,0.0003543801,0.00007547806,0.0002851217,0.0005581911,0.0001836225],"domain_scores_gemma":[0.994419,0.002847015,0.0006356731,0.0004712917,0.001225654,0.0004013875],"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":[0.00001566667,0.00001625321,0.0001792843,0.00003879291,0.00001496438,0.0001069127,0.0001051201,0.003131815,0.002040508,0.9910675,0.0003273023,0.002955915],"study_design_scores_gemma":[0.00001685192,0.00003828293,0.0003036737,0.00001459769,0.00001291862,0.0002177327,0.00004357006,0.05774303,0.002317323,0.9376545,0.001616201,0.00002131262],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1846802,0.001272161,0.7803059,0.00130079,0.0003465432,0.00005263052,0.0001361387,0.0002278969,0.0316778],"genre_scores_gemma":[0.9353667,0.0007589953,0.04988664,0.0003716158,0.0003993977,0.0001964358,0.0001049305,0.0001604221,0.01275486],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003731291,"threshold_uncertainty_score":0.01907736,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08875162427047234,"score_gpt":0.3061957193595594,"score_spread":0.217444095089087,"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."}}