{"id":"W4327918002","doi":"10.20944/preprints202303.0342.v1","title":"Norm of Hilbert Operator’s Commutants","year":2023,"lang":"en","type":"preprint","venue":"Preprints.org","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Transpose; Pure mathematics; Norm (philosophy); Operator norm; Hilbert space; Nuclear operator; Matrix norm; Algebra over a field; Approximation property; Eigenvalues and eigenvectors; Physics; Banach space","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":[0.001602261,0.000517397,0.0004562944,0.001050975,0.0008037236,0.001380003,0.0007402805,0.0006005412,0.00436761],"category_scores_gemma":[0.003438245,0.0002064825,0.0006556229,0.0004723746,0.00268179,0.002919258,0.001342701,0.001297977,0.0005628866],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007241167,"about_ca_system_score_gemma":0.0006668812,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006934845,"about_ca_topic_score_gemma":0.000359569,"domain_scores_codex":[0.9986059,0.0003099308,0.00007358097,0.0002734206,0.0005464287,0.0001907502],"domain_scores_gemma":[0.9982339,0.0006019453,0.0002358932,0.0001511605,0.000530415,0.0002467259],"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":[0.00003869176,0.00001995862,0.0004803146,0.00003382047,0.000009386161,0.00006998367,0.0002363704,0.001711385,0.00499518,0.9882298,0.0002932068,0.003882013],"study_design_scores_gemma":[0.00001718536,0.0001132189,0.0008747273,0.00001943206,0.00001214294,0.0003462444,0.0002461937,0.05386453,0.01220357,0.927634,0.004628318,0.00004042596],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5603052,0.0006838418,0.4087858,0.0004627347,0.0002299066,0.00004170622,0.0001354105,0.000161846,0.02919356],"genre_scores_gemma":[0.9531862,0.0003955262,0.03509891,0.0001573644,0.0001977462,0.0000660802,0.0002067328,0.0001044445,0.01058713],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00436761,"threshold_uncertainty_score":0.01461112,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3247042985401588,"score_gpt":0.4188289631477705,"score_spread":0.09412466460761165,"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."}}