{"id":"W1985216266","doi":"10.4153/cmb-2002-034-9","title":"Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant","year":2002,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Canadian Mathematical Society","keywords":"Mathematics; Subalgebra; Centralizer and normalizer; Toeplitz matrix; Compact space; Separable space; Pure mathematics; Discrete mathematics; Algebra over a field; Combinatorics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001474079,0.0002769681,0.0004732525,0.0001734665,0.000458996,0.0001406031,0.0003030983,0.000172412,0.002891077],"category_scores_gemma":[0.0008500625,0.0002115998,0.00005548613,0.0002483478,0.0008224432,0.00007505476,0.0001946148,0.0006106296,0.0003516138],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002354603,"about_ca_system_score_gemma":0.0000588381,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001270464,"about_ca_topic_score_gemma":0.01524761,"domain_scores_codex":[0.9974984,0.0004344236,0.0005343471,0.0003677206,0.0004774996,0.0006876198],"domain_scores_gemma":[0.9975102,0.001233889,0.0000720672,0.0006010545,0.00007089228,0.0005119154],"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":[0.00002666435,0.0003673548,0.0002477157,0.0005644225,0.00005312721,0.0003782323,0.008922734,0.00002028628,0.0001730635,0.9626212,0.01431753,0.01230765],"study_design_scores_gemma":[0.001918729,0.0003377314,0.001125483,0.0004302175,0.00007142358,0.0007055956,0.006147509,0.03849177,0.0004188064,0.9371452,0.01229014,0.0009173533],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9427727,0.0003967364,0.02661652,0.02199298,0.00003518344,0.001221833,0.00004116037,0.00006023706,0.006862624],"genre_scores_gemma":[0.9963773,0.00003147372,0.002466285,0.0007746883,0.00004813889,0.00004966988,0.000003851198,0.00004000145,0.0002085631],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0536046,"threshold_uncertainty_score":0.9980204,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04323362460091206,"score_gpt":0.28337164746884,"score_spread":0.2401380228679279,"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."}}