{"id":"W2950148552","doi":"10.48550/arxiv.math/0309398","title":"Partially Isometric Dilations of Noncommuting $N$-tuples of Operators","year":2003,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Guelph","funders":"","keywords":"Isometric exercise; Tuple; Mathematics; Algebra over a field; Pure mathematics; Discrete mathematics; Medicine; Internal 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009190994,0.0003566956,0.0009020114,0.0005821119,0.0001265429,0.00002571573,0.0007814003,0.0003406892,0.0002974399],"category_scores_gemma":[0.00446723,0.0003420519,0.0002636061,0.00115426,0.0002165447,0.0001290547,0.001003092,0.0009106895,0.00002903233],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001274508,"about_ca_system_score_gemma":0.0004331297,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006167642,"about_ca_topic_score_gemma":0.00006094666,"domain_scores_codex":[0.9969551,0.0002982453,0.001180952,0.0004825953,0.0006366752,0.000446439],"domain_scores_gemma":[0.9960476,0.00110191,0.0006302285,0.001389089,0.0006966889,0.0001345301],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.000031322,0.0007882257,0.961975,0.001907647,0.0004380335,0.00001247681,0.001429289,0.00275097,0.01249412,0.01670365,0.0007255959,0.0007436998],"study_design_scores_gemma":[0.004345139,0.0008487442,0.2734349,0.003857025,0.0009678827,0.00002275961,0.002696976,0.003948706,0.6126388,0.09033517,0.003183629,0.003720241],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9897427,0.0005868927,0.006695736,0.00009667235,0.0002377511,0.0006636718,0.00007244165,0.0000628812,0.00184126],"genre_scores_gemma":[0.976637,0.0001487917,0.02265737,0.00003447232,0.00007733244,0.00006812884,0.00002180204,0.00009161493,0.00026346],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6885401,"threshold_uncertainty_score":0.9999031,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.171815135757984,"score_gpt":0.4013685232873858,"score_spread":0.2295533875294017,"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."}}