{"id":"W185287106","doi":"","title":"A note on the spectral mapping theorem","year":2007,"lang":"en","type":"article","venue":"Kyungpook mathematical journal","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Separable space; Bounded function; Hilbert space; Bounded operator; Infimum and supremum; Contraction (grammar); Operator algebra; Unitary operator; Compact operator; Functional calculus; Operator (biology); Counterexample; C*-algebra; Combinatorics; Discrete mathematics; Pure mathematics; Algebra over a field; Mathematical analysis; Extension (predicate logic); Division algebra","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.00637768,0.0002889142,0.0003903791,0.0001272138,0.0004827606,0.0001681816,0.0005238445,0.0001451054,0.002971351],"category_scores_gemma":[0.001820406,0.0001558566,0.0002826685,0.0002112079,0.0002488343,0.0001019782,0.00007428532,0.001129202,0.0009609314],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001259001,"about_ca_system_score_gemma":0.00006522517,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.500205e-7,"about_ca_topic_score_gemma":0.000001180788,"domain_scores_codex":[0.9973882,0.0002224688,0.0007570991,0.0002070736,0.0007204539,0.0007047064],"domain_scores_gemma":[0.9954793,0.003411585,0.0002279706,0.0004858419,0.00009716809,0.0002981227],"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":[0.00003844225,0.000190657,0.00002118504,0.00003001428,0.00005650502,0.0002097132,0.002349932,8.523675e-7,0.001192902,0.9911162,0.00335545,0.001438183],"study_design_scores_gemma":[0.000392869,0.00009744351,0.0001284813,0.0002605559,0.00004016867,0.0009445139,0.001517802,0.0001502059,0.003207595,0.9916381,0.001392612,0.0002297005],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4681186,0.00005341476,0.2805841,0.003391456,0.0003630078,0.0004448664,0.000003173187,0.0001547661,0.2468866],"genre_scores_gemma":[0.9747289,0.000007723703,0.02112819,0.001441027,0.000768818,0.000003936101,3.56367e-7,0.00006653847,0.001854478],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5066103,"threshold_uncertainty_score":0.999817,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04951318885761637,"score_gpt":0.3114964111397627,"score_spread":0.2619832222821463,"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."}}