{"id":"W2501605261","doi":"10.1017/cbo9781316258231.011","title":"The commutant lifting theorem","year":2016,"lang":"en","type":"book-chapter","venue":"Cambridge University Press eBooks","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Centralizer and normalizer; Mathematics; Pure 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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002417901,0.0003872455,0.000396946,0.00009276377,0.0006730814,0.00004857367,0.0008404131,0.0002992686,0.000007417227],"category_scores_gemma":[0.00009982767,0.0002723617,0.0002676436,0.000007811163,0.0004600109,0.00006567308,0.0006300108,0.0005411596,0.00003632655],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001590695,"about_ca_system_score_gemma":0.00006363231,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001878398,"about_ca_topic_score_gemma":0.000001542851,"domain_scores_codex":[0.9986552,0.00005551134,0.0002428528,0.0003617219,0.0003005698,0.000384121],"domain_scores_gemma":[0.997019,0.001324022,0.000382048,0.0009851886,0.0001557036,0.00013405],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0000530797,0.000004322668,4.987921e-7,0.00004651745,0.0001435048,0.0001045523,0.00003416146,6.274554e-8,0.00001848776,0.9812574,0.01087185,0.007465601],"study_design_scores_gemma":[0.0003945632,0.00002855647,9.267076e-7,0.000322735,0.0001561551,0.00001951722,0.00006659826,0.000005067122,0.0002456256,0.03721041,0.961141,0.0004088293],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0001142938,0.0002197358,0.002724448,0.00005384621,0.0002549307,0.0003460854,0.0001660659,0.0002002948,0.9959203],"genre_scores_gemma":[0.001426551,0.000175314,0.0002016484,0.00004447421,0.0002188105,6.149494e-7,0.000004739652,0.00007716873,0.9978507],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.9502692,"threshold_uncertainty_score":0.9999729,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03135912404941354,"score_gpt":0.2353195148276445,"score_spread":0.203960390778231,"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."}}