{"id":"W2088170378","doi":"10.1063/1.4789541","title":"Characterization of compact and self-adjoint operators on free Banach spaces of countable type over the complex Levi-Civita field","year":2013,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"advanced mathematical theories","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Linear subspace; Combinatorics; Mathematics; Complement (music); Orthonormal basis; Banach space; Countable set; Type (biology); Product (mathematics); Field (mathematics); Subspace topology; Crystallography; Physics; Discrete mathematics; Mathematical analysis; Pure mathematics; Chemistry; Geometry; Quantum mechanics","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":[],"consensus_categories":[],"category_scores_codex":[0.0005579893,0.0002116022,0.0008033697,0.00004744387,0.00006146442,0.00004956382,0.000346167,0.00007449031,0.0003183346],"category_scores_gemma":[0.001313988,0.0001239048,0.0001327356,0.0001948542,0.0001788861,0.0003450158,0.00007879355,0.0002684767,0.00001157309],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003372577,"about_ca_system_score_gemma":0.00004212428,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002866046,"about_ca_topic_score_gemma":3.758325e-7,"domain_scores_codex":[0.9981512,0.0001026236,0.0008734626,0.0001078443,0.0005739205,0.0001909189],"domain_scores_gemma":[0.9956805,0.002426281,0.0009063484,0.0004566455,0.0004379113,0.00009238737],"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":[0.00006179551,0.001179211,0.0001000932,0.001240488,0.0002327861,0.00000166351,0.001822122,0.00001903183,0.04880279,0.9435954,0.002608473,0.0003361359],"study_design_scores_gemma":[0.0004701595,0.000519321,0.0005956551,0.0004787753,0.0001316776,0.00001818112,0.0003431063,0.001304048,0.0369541,0.958948,0.00009874741,0.0001382905],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9705389,0.00002420088,0.02595981,0.000648151,0.00007194107,0.0003992297,0.0000144168,0.00001778084,0.002325547],"genre_scores_gemma":[0.9817044,0.00003372972,0.01792399,0.0001280799,0.0001185665,0.000002700872,0.000001090535,0.0000341041,0.00005334294],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01535253,"threshold_uncertainty_score":0.5052693,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04198373085154793,"score_gpt":0.307558311259774,"score_spread":0.2655745804082261,"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."}}